Properties

Label 429.2.n.b.196.4
Level $429$
Weight $2$
Character 429.196
Analytic conductor $3.426$
Analytic rank $0$
Dimension $20$
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] = [429,2,Mod(157,429)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(429, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("429.157");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 429 = 3 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 429.n (of order \(5\), degree \(4\), 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: \(3.42558224671\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(5\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + 4 x^{18} + 4 x^{17} + 37 x^{16} - 74 x^{15} + 398 x^{14} - 224 x^{13} + 978 x^{12} + 115 x^{11} + 1963 x^{10} + 323 x^{9} + 3007 x^{8} + 1828 x^{7} + 6736 x^{6} + \cdots + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 196.4
Root \(0.566002 + 1.74197i\) of defining polynomial
Character \(\chi\) \(=\) 429.196
Dual form 429.2.n.b.313.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.566002 - 1.74197i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-1.09608 - 0.796352i) q^{4} +(0.725100 + 2.23163i) q^{5} +(-0.566002 - 1.74197i) q^{6} +(-1.01039 - 0.734092i) q^{7} +(0.956015 - 0.694585i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.566002 - 1.74197i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-1.09608 - 0.796352i) q^{4} +(0.725100 + 2.23163i) q^{5} +(-0.566002 - 1.74197i) q^{6} +(-1.01039 - 0.734092i) q^{7} +(0.956015 - 0.694585i) q^{8} +(0.309017 - 0.951057i) q^{9} +4.29785 q^{10} +(1.67300 - 2.86375i) q^{11} -1.35483 q^{12} +(-0.309017 + 0.951057i) q^{13} +(-1.85065 + 1.34458i) q^{14} +(1.89834 + 1.37922i) q^{15} +(-1.50618 - 4.63554i) q^{16} +(-0.204024 - 0.627921i) q^{17} +(-1.48181 - 1.07660i) q^{18} +(4.72903 - 3.43584i) q^{19} +(0.982390 - 3.02349i) q^{20} -1.24891 q^{21} +(-4.04166 - 4.53522i) q^{22} -6.58972 q^{23} +(0.365165 - 1.12386i) q^{24} +(-0.409307 + 0.297379i) q^{25} +(1.48181 + 1.07660i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.522878 + 1.60925i) q^{28} +(8.07280 + 5.86523i) q^{29} +(3.47703 - 2.52621i) q^{30} +(-2.24966 + 6.92373i) q^{31} -6.56409 q^{32} +(-0.329783 - 3.30019i) q^{33} -1.20930 q^{34} +(0.905586 - 2.78711i) q^{35} +(-1.09608 + 0.796352i) q^{36} +(5.94939 + 4.32248i) q^{37} +(-3.30851 - 10.1825i) q^{38} +(0.309017 + 0.951057i) q^{39} +(2.24326 + 1.62982i) q^{40} +(-9.00644 + 6.54356i) q^{41} +(-0.706887 + 2.17557i) q^{42} -3.18815 q^{43} +(-4.11430 + 1.80661i) q^{44} +2.34647 q^{45} +(-3.72980 + 11.4791i) q^{46} +(-10.6940 + 7.76963i) q^{47} +(-3.94322 - 2.86492i) q^{48} +(-1.68112 - 5.17396i) q^{49} +(0.286358 + 0.881319i) q^{50} +(-0.534141 - 0.388076i) q^{51} +(1.09608 - 0.796352i) q^{52} +(-3.01253 + 9.27163i) q^{53} -1.83162 q^{54} +(7.60392 + 1.65701i) q^{55} -1.47584 q^{56} +(1.80633 - 5.55930i) q^{57} +(14.7863 - 10.7429i) q^{58} +(-7.02390 - 5.10316i) q^{59} +(-0.982390 - 3.02349i) q^{60} +(3.00154 + 9.23780i) q^{61} +(10.7877 + 7.83769i) q^{62} +(-1.01039 + 0.734092i) q^{63} +(-0.702933 + 2.16340i) q^{64} -2.34647 q^{65} +(-5.93550 - 1.29344i) q^{66} +8.16010 q^{67} +(-0.276418 + 0.850729i) q^{68} +(-5.33120 + 3.87334i) q^{69} +(-4.34251 - 3.15501i) q^{70} +(-3.52354 - 10.8443i) q^{71} +(-0.365165 - 1.12386i) q^{72} +(2.85886 + 2.07709i) q^{73} +(10.8970 - 7.91715i) q^{74} +(-0.156341 + 0.481169i) q^{75} -7.91954 q^{76} +(-3.79264 + 1.66537i) q^{77} +1.83162 q^{78} +(2.78885 - 8.58321i) q^{79} +(9.25266 - 6.72245i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(6.30106 + 19.3927i) q^{82} +(2.87005 + 8.83309i) q^{83} +(1.36891 + 0.994573i) q^{84} +(1.25335 - 0.910610i) q^{85} +(-1.80450 + 5.55367i) q^{86} +9.97852 q^{87} +(-0.389704 - 3.89983i) q^{88} -13.6611 q^{89} +(1.32811 - 4.08749i) q^{90} +(1.01039 - 0.734092i) q^{91} +(7.22289 + 5.24773i) q^{92} +(2.24966 + 6.92373i) q^{93} +(7.48169 + 23.0263i) q^{94} +(11.0965 + 8.06210i) q^{95} +(-5.31046 + 3.85828i) q^{96} +(-0.821393 + 2.52799i) q^{97} -9.96442 q^{98} +(-2.20660 - 2.47607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\) \(287\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.566002 1.74197i 0.400224 1.23176i −0.524594 0.851352i \(-0.675783\pi\)
0.924818 0.380410i \(-0.124217\pi\)
\(3\) 0.809017 0.587785i 0.467086 0.339358i
\(4\) −1.09608 0.796352i −0.548042 0.398176i
\(5\) 0.725100 + 2.23163i 0.324274 + 0.998014i 0.971767 + 0.235942i \(0.0758177\pi\)
−0.647493 + 0.762072i \(0.724182\pi\)
\(6\) −0.566002 1.74197i −0.231069 0.711158i
\(7\) −1.01039 0.734092i −0.381892 0.277461i 0.380233 0.924891i \(-0.375844\pi\)
−0.762125 + 0.647430i \(0.775844\pi\)
\(8\) 0.956015 0.694585i 0.338002 0.245573i
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) 4.29785 1.35910
\(11\) 1.67300 2.86375i 0.504429 0.863453i
\(12\) −1.35483 −0.391107
\(13\) −0.309017 + 0.951057i −0.0857059 + 0.263776i
\(14\) −1.85065 + 1.34458i −0.494608 + 0.359354i
\(15\) 1.89834 + 1.37922i 0.490148 + 0.356113i
\(16\) −1.50618 4.63554i −0.376544 1.15888i
\(17\) −0.204024 0.627921i −0.0494830 0.152293i 0.923262 0.384172i \(-0.125513\pi\)
−0.972745 + 0.231878i \(0.925513\pi\)
\(18\) −1.48181 1.07660i −0.349266 0.253757i
\(19\) 4.72903 3.43584i 1.08491 0.788235i 0.106380 0.994326i \(-0.466074\pi\)
0.978533 + 0.206090i \(0.0660740\pi\)
\(20\) 0.982390 3.02349i 0.219669 0.676072i
\(21\) −1.24891 −0.272535
\(22\) −4.04166 4.53522i −0.861684 0.966911i
\(23\) −6.58972 −1.37405 −0.687026 0.726633i \(-0.741084\pi\)
−0.687026 + 0.726633i \(0.741084\pi\)
\(24\) 0.365165 1.12386i 0.0745390 0.229408i
\(25\) −0.409307 + 0.297379i −0.0818613 + 0.0594757i
\(26\) 1.48181 + 1.07660i 0.290607 + 0.211139i
\(27\) −0.309017 0.951057i −0.0594703 0.183031i
\(28\) 0.522878 + 1.60925i 0.0988146 + 0.304120i
\(29\) 8.07280 + 5.86523i 1.49908 + 1.08915i 0.970746 + 0.240110i \(0.0771834\pi\)
0.528335 + 0.849036i \(0.322817\pi\)
\(30\) 3.47703 2.52621i 0.634816 0.461221i
\(31\) −2.24966 + 6.92373i −0.404050 + 1.24354i 0.517635 + 0.855601i \(0.326812\pi\)
−0.921686 + 0.387938i \(0.873188\pi\)
\(32\) −6.56409 −1.16038
\(33\) −0.329783 3.30019i −0.0574079 0.574489i
\(34\) −1.20930 −0.207393
\(35\) 0.905586 2.78711i 0.153072 0.471107i
\(36\) −1.09608 + 0.796352i −0.182681 + 0.132725i
\(37\) 5.94939 + 4.32248i 0.978073 + 0.710612i 0.957277 0.289172i \(-0.0933799\pi\)
0.0207961 + 0.999784i \(0.493380\pi\)
\(38\) −3.30851 10.1825i −0.536711 1.65183i
\(39\) 0.309017 + 0.951057i 0.0494823 + 0.152291i
\(40\) 2.24326 + 1.62982i 0.354691 + 0.257698i
\(41\) −9.00644 + 6.54356i −1.40657 + 1.02193i −0.412760 + 0.910840i \(0.635435\pi\)
−0.993810 + 0.111093i \(0.964565\pi\)
\(42\) −0.706887 + 2.17557i −0.109075 + 0.335698i
\(43\) −3.18815 −0.486188 −0.243094 0.970003i \(-0.578162\pi\)
−0.243094 + 0.970003i \(0.578162\pi\)
\(44\) −4.11430 + 1.80661i −0.620254 + 0.272357i
\(45\) 2.34647 0.349791
\(46\) −3.72980 + 11.4791i −0.549928 + 1.69251i
\(47\) −10.6940 + 7.76963i −1.55988 + 1.13332i −0.623766 + 0.781611i \(0.714398\pi\)
−0.936111 + 0.351706i \(0.885602\pi\)
\(48\) −3.94322 2.86492i −0.569155 0.413516i
\(49\) −1.68112 5.17396i −0.240160 0.739137i
\(50\) 0.286358 + 0.881319i 0.0404971 + 0.124637i
\(51\) −0.534141 0.388076i −0.0747947 0.0543416i
\(52\) 1.09608 0.796352i 0.151999 0.110434i
\(53\) −3.01253 + 9.27163i −0.413803 + 1.27356i 0.499513 + 0.866306i \(0.333512\pi\)
−0.913317 + 0.407250i \(0.866488\pi\)
\(54\) −1.83162 −0.249252
\(55\) 7.60392 + 1.65701i 1.02531 + 0.223432i
\(56\) −1.47584 −0.197217
\(57\) 1.80633 5.55930i 0.239254 0.736348i
\(58\) 14.7863 10.7429i 1.94154 1.41061i
\(59\) −7.02390 5.10316i −0.914433 0.664375i 0.0276989 0.999616i \(-0.491182\pi\)
−0.942132 + 0.335242i \(0.891182\pi\)
\(60\) −0.982390 3.02349i −0.126826 0.390330i
\(61\) 3.00154 + 9.23780i 0.384308 + 1.18278i 0.936981 + 0.349380i \(0.113608\pi\)
−0.552673 + 0.833398i \(0.686392\pi\)
\(62\) 10.7877 + 7.83769i 1.37003 + 0.995388i
\(63\) −1.01039 + 0.734092i −0.127297 + 0.0924869i
\(64\) −0.702933 + 2.16340i −0.0878666 + 0.270426i
\(65\) −2.34647 −0.291044
\(66\) −5.93550 1.29344i −0.730610 0.159211i
\(67\) 8.16010 0.996914 0.498457 0.866914i \(-0.333900\pi\)
0.498457 + 0.866914i \(0.333900\pi\)
\(68\) −0.276418 + 0.850729i −0.0335207 + 0.103166i
\(69\) −5.33120 + 3.87334i −0.641801 + 0.466295i
\(70\) −4.34251 3.15501i −0.519029 0.377096i
\(71\) −3.52354 10.8443i −0.418167 1.28698i −0.909388 0.415950i \(-0.863449\pi\)
0.491221 0.871035i \(-0.336551\pi\)
\(72\) −0.365165 1.12386i −0.0430351 0.132448i
\(73\) 2.85886 + 2.07709i 0.334605 + 0.243104i 0.742382 0.669977i \(-0.233696\pi\)
−0.407777 + 0.913081i \(0.633696\pi\)
\(74\) 10.8970 7.91715i 1.26675 0.920350i
\(75\) −0.156341 + 0.481169i −0.0180527 + 0.0555606i
\(76\) −7.91954 −0.908434
\(77\) −3.79264 + 1.66537i −0.432212 + 0.189787i
\(78\) 1.83162 0.207390
\(79\) 2.78885 8.58321i 0.313770 0.965686i −0.662487 0.749073i \(-0.730499\pi\)
0.976258 0.216613i \(-0.0695009\pi\)
\(80\) 9.25266 6.72245i 1.03448 0.751593i
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) 6.30106 + 19.3927i 0.695835 + 2.14156i
\(83\) 2.87005 + 8.83309i 0.315028 + 0.969558i 0.975743 + 0.218920i \(0.0702535\pi\)
−0.660714 + 0.750637i \(0.729747\pi\)
\(84\) 1.36891 + 0.994573i 0.149361 + 0.108517i
\(85\) 1.25335 0.910610i 0.135945 0.0987696i
\(86\) −1.80450 + 5.55367i −0.194584 + 0.598868i
\(87\) 9.97852 1.06981
\(88\) −0.389704 3.89983i −0.0415426 0.415723i
\(89\) −13.6611 −1.44807 −0.724036 0.689762i \(-0.757715\pi\)
−0.724036 + 0.689762i \(0.757715\pi\)
\(90\) 1.32811 4.08749i 0.139995 0.430860i
\(91\) 1.01039 0.734092i 0.105918 0.0769538i
\(92\) 7.22289 + 5.24773i 0.753038 + 0.547114i
\(93\) 2.24966 + 6.92373i 0.233279 + 0.717958i
\(94\) 7.48169 + 23.0263i 0.771677 + 2.37498i
\(95\) 11.0965 + 8.06210i 1.13848 + 0.827154i
\(96\) −5.31046 + 3.85828i −0.541997 + 0.393784i
\(97\) −0.821393 + 2.52799i −0.0833998 + 0.256678i −0.984057 0.177851i \(-0.943085\pi\)
0.900658 + 0.434530i \(0.143085\pi\)
\(98\) −9.96442 −1.00656
\(99\) −2.20660 2.47607i −0.221772 0.248854i
\(100\) 0.685452 0.0685452
\(101\) 4.25727 13.1025i 0.423615 1.30375i −0.480700 0.876885i \(-0.659617\pi\)
0.904315 0.426867i \(-0.140383\pi\)
\(102\) −0.978344 + 0.710809i −0.0968705 + 0.0703806i
\(103\) −5.23467 3.80321i −0.515787 0.374742i 0.299227 0.954182i \(-0.403271\pi\)
−0.815015 + 0.579440i \(0.803271\pi\)
\(104\) 0.365165 + 1.12386i 0.0358074 + 0.110204i
\(105\) −0.905586 2.78711i −0.0883761 0.271994i
\(106\) 14.4458 + 10.4955i 1.40310 + 1.01941i
\(107\) 4.07286 2.95911i 0.393738 0.286068i −0.373247 0.927732i \(-0.621756\pi\)
0.766986 + 0.641664i \(0.221756\pi\)
\(108\) −0.418667 + 1.28852i −0.0402862 + 0.123988i
\(109\) −4.51232 −0.432202 −0.216101 0.976371i \(-0.569334\pi\)
−0.216101 + 0.976371i \(0.569334\pi\)
\(110\) 7.19031 12.3080i 0.685569 1.17352i
\(111\) 7.35385 0.697996
\(112\) −1.88108 + 5.78938i −0.177746 + 0.547045i
\(113\) 3.46703 2.51894i 0.326151 0.236962i −0.412645 0.910892i \(-0.635395\pi\)
0.738795 + 0.673930i \(0.235395\pi\)
\(114\) −8.66178 6.29315i −0.811250 0.589408i
\(115\) −4.77821 14.7058i −0.445570 1.37132i
\(116\) −4.17768 12.8576i −0.387888 1.19380i
\(117\) 0.809017 + 0.587785i 0.0747936 + 0.0543408i
\(118\) −12.8651 + 9.34705i −1.18433 + 0.860466i
\(119\) −0.254808 + 0.784218i −0.0233582 + 0.0718891i
\(120\) 2.77282 0.253123
\(121\) −5.40213 9.58212i −0.491103 0.871102i
\(122\) 17.7909 1.61071
\(123\) −3.44015 + 10.5877i −0.310188 + 0.954661i
\(124\) 7.97954 5.79747i 0.716584 0.520629i
\(125\) 8.53125 + 6.19832i 0.763058 + 0.554394i
\(126\) 0.706887 + 2.17557i 0.0629745 + 0.193815i
\(127\) −1.83647 5.65208i −0.162961 0.501541i 0.835920 0.548852i \(-0.184935\pi\)
−0.998880 + 0.0473109i \(0.984935\pi\)
\(128\) −7.25019 5.26757i −0.640832 0.465592i
\(129\) −2.57927 + 1.87395i −0.227092 + 0.164992i
\(130\) −1.32811 + 4.08749i −0.116483 + 0.358497i
\(131\) 12.1877 1.06485 0.532424 0.846478i \(-0.321281\pi\)
0.532424 + 0.846478i \(0.321281\pi\)
\(132\) −2.26664 + 3.87991i −0.197286 + 0.337703i
\(133\) −7.30039 −0.633024
\(134\) 4.61863 14.2147i 0.398989 1.22796i
\(135\) 1.89834 1.37922i 0.163383 0.118704i
\(136\) −0.631194 0.458590i −0.0541245 0.0393237i
\(137\) 4.64698 + 14.3019i 0.397019 + 1.22190i 0.927378 + 0.374125i \(0.122057\pi\)
−0.530360 + 0.847773i \(0.677943\pi\)
\(138\) 3.72980 + 11.4791i 0.317501 + 0.977168i
\(139\) 1.03867 + 0.754639i 0.0880989 + 0.0640076i 0.630963 0.775813i \(-0.282660\pi\)
−0.542864 + 0.839821i \(0.682660\pi\)
\(140\) −3.21211 + 2.33374i −0.271473 + 0.197237i
\(141\) −4.08474 + 12.5715i −0.343997 + 1.05871i
\(142\) −20.8849 −1.75262
\(143\) 2.20660 + 2.47607i 0.184525 + 0.207059i
\(144\) −4.87409 −0.406174
\(145\) −7.23543 + 22.2684i −0.600869 + 1.84929i
\(146\) 5.23635 3.80443i 0.433364 0.314857i
\(147\) −4.40123 3.19768i −0.363007 0.263740i
\(148\) −3.07881 9.47561i −0.253077 0.778890i
\(149\) −3.94032 12.1271i −0.322804 0.993487i −0.972422 0.233227i \(-0.925071\pi\)
0.649619 0.760260i \(-0.274929\pi\)
\(150\) 0.749694 + 0.544685i 0.0612123 + 0.0444733i
\(151\) 6.58135 4.78163i 0.535582 0.389123i −0.286859 0.957973i \(-0.592611\pi\)
0.822442 + 0.568849i \(0.192611\pi\)
\(152\) 2.13453 6.56942i 0.173134 0.532851i
\(153\) −0.660235 −0.0533768
\(154\) 0.754390 + 7.54929i 0.0607905 + 0.608339i
\(155\) −17.0824 −1.37209
\(156\) 0.418667 1.28852i 0.0335202 0.103164i
\(157\) 2.58343 1.87697i 0.206180 0.149799i −0.479904 0.877321i \(-0.659328\pi\)
0.686084 + 0.727523i \(0.259328\pi\)
\(158\) −13.3732 9.71622i −1.06392 0.772981i
\(159\) 3.01253 + 9.27163i 0.238909 + 0.735288i
\(160\) −4.75962 14.6486i −0.376281 1.15807i
\(161\) 6.65820 + 4.83746i 0.524739 + 0.381245i
\(162\) −1.48181 + 1.07660i −0.116422 + 0.0845857i
\(163\) −1.62343 + 4.99641i −0.127157 + 0.391349i −0.994288 0.106731i \(-0.965962\pi\)
0.867131 + 0.498080i \(0.165962\pi\)
\(164\) 15.0828 1.17777
\(165\) 7.12567 3.12892i 0.554732 0.243586i
\(166\) 17.0115 1.32035
\(167\) −4.03467 + 12.4175i −0.312213 + 0.960891i 0.664674 + 0.747133i \(0.268570\pi\)
−0.976887 + 0.213758i \(0.931430\pi\)
\(168\) −1.19398 + 0.867476i −0.0921174 + 0.0669272i
\(169\) −0.809017 0.587785i −0.0622321 0.0452143i
\(170\) −0.876863 2.69871i −0.0672523 0.206981i
\(171\) −1.80633 5.55930i −0.138133 0.425131i
\(172\) 3.49448 + 2.53889i 0.266451 + 0.193588i
\(173\) −1.98841 + 1.44467i −0.151176 + 0.109836i −0.660802 0.750560i \(-0.729784\pi\)
0.509626 + 0.860396i \(0.329784\pi\)
\(174\) 5.64786 17.3823i 0.428163 1.31775i
\(175\) 0.631863 0.0477643
\(176\) −15.7949 3.44195i −1.19058 0.259447i
\(177\) −8.68201 −0.652580
\(178\) −7.73220 + 23.7973i −0.579553 + 1.78368i
\(179\) −2.77090 + 2.01317i −0.207107 + 0.150472i −0.686504 0.727126i \(-0.740855\pi\)
0.479397 + 0.877598i \(0.340855\pi\)
\(180\) −2.57193 1.86862i −0.191700 0.139278i
\(181\) −0.888085 2.73324i −0.0660108 0.203160i 0.912611 0.408830i \(-0.134063\pi\)
−0.978622 + 0.205669i \(0.934063\pi\)
\(182\) −0.706887 2.17557i −0.0523979 0.161264i
\(183\) 7.85814 + 5.70927i 0.580890 + 0.422041i
\(184\) −6.29987 + 4.57712i −0.464433 + 0.337430i
\(185\) −5.33227 + 16.4110i −0.392036 + 1.20656i
\(186\) 13.3343 0.977717
\(187\) −2.13954 0.466239i −0.156459 0.0340948i
\(188\) 17.9089 1.30614
\(189\) −0.385935 + 1.18779i −0.0280726 + 0.0863987i
\(190\) 20.3246 14.7667i 1.47450 1.07129i
\(191\) 0.770354 + 0.559695i 0.0557409 + 0.0404981i 0.615307 0.788288i \(-0.289032\pi\)
−0.559566 + 0.828786i \(0.689032\pi\)
\(192\) 0.702933 + 2.16340i 0.0507298 + 0.156130i
\(193\) −3.03999 9.35613i −0.218823 0.673469i −0.998860 0.0477351i \(-0.984800\pi\)
0.780037 0.625734i \(-0.215200\pi\)
\(194\) 3.93878 + 2.86169i 0.282788 + 0.205457i
\(195\) −1.89834 + 1.37922i −0.135943 + 0.0987681i
\(196\) −2.27764 + 7.00985i −0.162688 + 0.500704i
\(197\) 6.22868 0.443775 0.221888 0.975072i \(-0.428778\pi\)
0.221888 + 0.975072i \(0.428778\pi\)
\(198\) −5.56219 + 2.44239i −0.395287 + 0.173573i
\(199\) 19.6648 1.39400 0.697001 0.717070i \(-0.254517\pi\)
0.697001 + 0.717070i \(0.254517\pi\)
\(200\) −0.184748 + 0.568597i −0.0130637 + 0.0402059i
\(201\) 6.60166 4.79638i 0.465645 0.338311i
\(202\) −20.4147 14.8321i −1.43637 1.04358i
\(203\) −3.85106 11.8524i −0.270292 0.831872i
\(204\) 0.276418 + 0.850729i 0.0193532 + 0.0595629i
\(205\) −21.1334 15.3543i −1.47602 1.07239i
\(206\) −9.58793 + 6.96604i −0.668023 + 0.485347i
\(207\) −2.03634 + 6.26720i −0.141535 + 0.435600i
\(208\) 4.87409 0.337958
\(209\) −1.92771 19.2909i −0.133343 1.33438i
\(210\) −5.36763 −0.370402
\(211\) 0.991032 3.05008i 0.0682254 0.209976i −0.911131 0.412117i \(-0.864790\pi\)
0.979357 + 0.202140i \(0.0647897\pi\)
\(212\) 10.6855 7.76344i 0.733881 0.533196i
\(213\) −9.22474 6.70216i −0.632068 0.459225i
\(214\) −2.84944 8.76968i −0.194784 0.599483i
\(215\) −2.31173 7.11476i −0.157658 0.485222i
\(216\) −0.956015 0.694585i −0.0650486 0.0472605i
\(217\) 7.35569 5.34422i 0.499337 0.362789i
\(218\) −2.55398 + 7.86035i −0.172977 + 0.532370i
\(219\) 3.53375 0.238789
\(220\) −7.01497 7.87162i −0.472949 0.530704i
\(221\) 0.660235 0.0444122
\(222\) 4.16229 12.8102i 0.279355 0.859765i
\(223\) −14.1619 + 10.2892i −0.948351 + 0.689017i −0.950416 0.310980i \(-0.899343\pi\)
0.00206512 + 0.999998i \(0.499343\pi\)
\(224\) 6.63230 + 4.81865i 0.443139 + 0.321959i
\(225\) 0.156341 + 0.481169i 0.0104227 + 0.0320779i
\(226\) −2.42559 7.46520i −0.161348 0.496578i
\(227\) −1.07516 0.781147i −0.0713606 0.0518465i 0.551533 0.834153i \(-0.314043\pi\)
−0.622894 + 0.782307i \(0.714043\pi\)
\(228\) −6.40705 + 4.65499i −0.424317 + 0.308284i
\(229\) −1.24789 + 3.84062i −0.0824632 + 0.253795i −0.983784 0.179356i \(-0.942599\pi\)
0.901321 + 0.433152i \(0.142599\pi\)
\(230\) −28.3216 −1.86747
\(231\) −2.08943 + 3.57657i −0.137475 + 0.235321i
\(232\) 11.7916 0.774157
\(233\) 4.50383 13.8614i 0.295056 0.908088i −0.688147 0.725571i \(-0.741576\pi\)
0.983203 0.182517i \(-0.0584244\pi\)
\(234\) 1.48181 1.07660i 0.0968691 0.0703795i
\(235\) −25.0931 18.2312i −1.63689 1.18927i
\(236\) 3.63487 + 11.1870i 0.236610 + 0.728210i
\(237\) −2.78885 8.58321i −0.181155 0.557539i
\(238\) 1.22187 + 0.887738i 0.0792018 + 0.0575435i
\(239\) −2.08395 + 1.51408i −0.134799 + 0.0979375i −0.653142 0.757236i \(-0.726549\pi\)
0.518342 + 0.855173i \(0.326549\pi\)
\(240\) 3.53420 10.8772i 0.228132 0.702118i
\(241\) −14.1580 −0.911994 −0.455997 0.889981i \(-0.650717\pi\)
−0.455997 + 0.889981i \(0.650717\pi\)
\(242\) −19.7494 + 3.98688i −1.26954 + 0.256286i
\(243\) −1.00000 −0.0641500
\(244\) 4.06659 12.5157i 0.260337 0.801234i
\(245\) 10.3274 7.50327i 0.659791 0.479366i
\(246\) 16.4964 + 11.9853i 1.05177 + 0.764156i
\(247\) 1.80633 + 5.55930i 0.114934 + 0.353730i
\(248\) 2.65842 + 8.18177i 0.168810 + 0.519543i
\(249\) 7.51388 + 5.45915i 0.476173 + 0.345960i
\(250\) 15.6260 11.3530i 0.988276 0.718025i
\(251\) −2.32634 + 7.15973i −0.146837 + 0.451918i −0.997243 0.0742097i \(-0.976357\pi\)
0.850406 + 0.526128i \(0.176357\pi\)
\(252\) 1.69207 0.106590
\(253\) −11.0246 + 18.8713i −0.693112 + 1.18643i
\(254\) −10.8852 −0.683000
\(255\) 0.478736 1.47340i 0.0299796 0.0922678i
\(256\) −16.9602 + 12.3223i −1.06001 + 0.770144i
\(257\) 9.40071 + 6.83001i 0.586400 + 0.426045i 0.841026 0.540995i \(-0.181952\pi\)
−0.254626 + 0.967040i \(0.581952\pi\)
\(258\) 1.80450 + 5.55367i 0.112343 + 0.345757i
\(259\) −2.83811 8.73480i −0.176351 0.542754i
\(260\) 2.57193 + 1.86862i 0.159504 + 0.115887i
\(261\) 8.07280 5.86523i 0.499694 0.363049i
\(262\) 6.89829 21.2307i 0.426178 1.31164i
\(263\) −12.1716 −0.750536 −0.375268 0.926916i \(-0.622449\pi\)
−0.375268 + 0.926916i \(0.622449\pi\)
\(264\) −2.60754 2.92597i −0.160483 0.180081i
\(265\) −22.8752 −1.40521
\(266\) −4.13203 + 12.7171i −0.253351 + 0.779735i
\(267\) −11.0521 + 8.02979i −0.676375 + 0.491415i
\(268\) −8.94415 6.49830i −0.546351 0.396947i
\(269\) −9.68752 29.8151i −0.590659 1.81786i −0.575247 0.817980i \(-0.695094\pi\)
−0.0154115 0.999881i \(-0.504906\pi\)
\(270\) −1.32811 4.08749i −0.0808261 0.248757i
\(271\) −5.25083 3.81495i −0.318965 0.231742i 0.416769 0.909013i \(-0.363163\pi\)
−0.735734 + 0.677271i \(0.763163\pi\)
\(272\) −2.60345 + 1.89152i −0.157858 + 0.114690i
\(273\) 0.385935 1.18779i 0.0233579 0.0718881i
\(274\) 27.5438 1.66398
\(275\) 0.166847 + 1.66967i 0.0100613 + 0.100685i
\(276\) 8.92798 0.537401
\(277\) −1.71510 + 5.27852i −0.103050 + 0.317156i −0.989268 0.146113i \(-0.953324\pi\)
0.886218 + 0.463269i \(0.153324\pi\)
\(278\) 1.90245 1.38221i 0.114101 0.0828996i
\(279\) 5.88968 + 4.27910i 0.352606 + 0.256183i
\(280\) −1.07013 3.29352i −0.0639525 0.196826i
\(281\) 4.08252 + 12.5647i 0.243543 + 0.749547i 0.995873 + 0.0907610i \(0.0289299\pi\)
−0.752330 + 0.658786i \(0.771070\pi\)
\(282\) 19.5873 + 14.2310i 1.16641 + 0.847444i
\(283\) 18.7307 13.6087i 1.11343 0.808951i 0.130226 0.991484i \(-0.458430\pi\)
0.983200 + 0.182533i \(0.0584296\pi\)
\(284\) −4.77381 + 14.6923i −0.283273 + 0.871826i
\(285\) 13.7161 0.812469
\(286\) 5.56219 2.44239i 0.328899 0.144421i
\(287\) 13.9036 0.820704
\(288\) −2.02842 + 6.24282i −0.119526 + 0.367862i
\(289\) 13.4006 9.73613i 0.788272 0.572713i
\(290\) 34.6956 + 25.2079i 2.03740 + 1.48026i
\(291\) 0.821393 + 2.52799i 0.0481509 + 0.148193i
\(292\) −1.47946 4.55332i −0.0865790 0.266463i
\(293\) −7.59960 5.52143i −0.443973 0.322565i 0.343238 0.939248i \(-0.388476\pi\)
−0.787212 + 0.616683i \(0.788476\pi\)
\(294\) −8.06138 + 5.85694i −0.470149 + 0.341584i
\(295\) 6.29532 19.3750i 0.366528 1.12806i
\(296\) 8.69004 0.505098
\(297\) −3.24057 0.706172i −0.188037 0.0409762i
\(298\) −23.3553 −1.35293
\(299\) 2.03634 6.26720i 0.117764 0.362441i
\(300\) 0.554542 0.402899i 0.0320165 0.0232614i
\(301\) 3.22128 + 2.34039i 0.185671 + 0.134898i
\(302\) −4.60442 14.1709i −0.264955 0.815446i
\(303\) −4.25727 13.1025i −0.244574 0.752721i
\(304\) −23.0497 16.7466i −1.32199 0.960483i
\(305\) −18.4389 + 13.3966i −1.05581 + 0.767090i
\(306\) −0.373694 + 1.15011i −0.0213627 + 0.0657476i
\(307\) 25.1837 1.43731 0.718656 0.695366i \(-0.244758\pi\)
0.718656 + 0.695366i \(0.244758\pi\)
\(308\) 5.48327 + 1.19489i 0.312439 + 0.0680852i
\(309\) −6.47041 −0.368089
\(310\) −9.66868 + 29.7571i −0.549144 + 1.69009i
\(311\) −2.92371 + 2.12420i −0.165788 + 0.120452i −0.667586 0.744533i \(-0.732672\pi\)
0.501797 + 0.864985i \(0.332672\pi\)
\(312\) 0.956015 + 0.694585i 0.0541237 + 0.0393231i
\(313\) −7.19236 22.1358i −0.406536 1.25119i −0.919606 0.392843i \(-0.871492\pi\)
0.513070 0.858347i \(-0.328508\pi\)
\(314\) −1.80741 5.56264i −0.101998 0.313918i
\(315\) −2.37085 1.72253i −0.133583 0.0970534i
\(316\) −9.89206 + 7.18701i −0.556472 + 0.404301i
\(317\) −5.50231 + 16.9344i −0.309041 + 0.951129i 0.669098 + 0.743174i \(0.266681\pi\)
−0.978138 + 0.207955i \(0.933319\pi\)
\(318\) 17.8560 1.00132
\(319\) 30.3024 13.3059i 1.69661 0.744989i
\(320\) −5.33761 −0.298381
\(321\) 1.55570 4.78794i 0.0868304 0.267237i
\(322\) 12.1953 8.86040i 0.679617 0.493771i
\(323\) −3.12227 2.26846i −0.173728 0.126221i
\(324\) 0.418667 + 1.28852i 0.0232593 + 0.0715847i
\(325\) −0.156341 0.481169i −0.00867225 0.0266904i
\(326\) 7.78476 + 5.65596i 0.431158 + 0.313255i
\(327\) −3.65054 + 2.65227i −0.201876 + 0.146671i
\(328\) −4.06523 + 12.5115i −0.224465 + 0.690831i
\(329\) 16.5087 0.910155
\(330\) −1.41736 14.1837i −0.0780230 0.780787i
\(331\) 24.0291 1.32076 0.660378 0.750933i \(-0.270396\pi\)
0.660378 + 0.750933i \(0.270396\pi\)
\(332\) 3.88844 11.9674i 0.213406 0.656795i
\(333\) 5.94939 4.32248i 0.326024 0.236871i
\(334\) 19.3473 + 14.0566i 1.05863 + 0.769143i
\(335\) 5.91688 + 18.2103i 0.323274 + 0.994935i
\(336\) 1.88108 + 5.78938i 0.102621 + 0.315836i
\(337\) 7.32066 + 5.31877i 0.398782 + 0.289732i 0.769045 0.639195i \(-0.220732\pi\)
−0.370263 + 0.928927i \(0.620732\pi\)
\(338\) −1.48181 + 1.07660i −0.0806000 + 0.0585593i
\(339\) 1.32429 4.07574i 0.0719254 0.221364i
\(340\) −2.09894 −0.113831
\(341\) 16.0642 + 18.0259i 0.869923 + 0.976156i
\(342\) −10.7065 −0.578944
\(343\) −4.80112 + 14.7763i −0.259236 + 0.797846i
\(344\) −3.04792 + 2.21444i −0.164333 + 0.119395i
\(345\) −12.5095 9.08869i −0.673489 0.489318i
\(346\) 1.39113 + 4.28145i 0.0747875 + 0.230172i
\(347\) 9.35859 + 28.8028i 0.502396 + 1.54621i 0.805105 + 0.593132i \(0.202109\pi\)
−0.302710 + 0.953083i \(0.597891\pi\)
\(348\) −10.9373 7.94641i −0.586301 0.425972i
\(349\) −14.5595 + 10.5781i −0.779351 + 0.566232i −0.904784 0.425870i \(-0.859968\pi\)
0.125433 + 0.992102i \(0.459968\pi\)
\(350\) 0.357636 1.10069i 0.0191164 0.0588343i
\(351\) 1.00000 0.0533761
\(352\) −10.9817 + 18.7979i −0.585328 + 1.00193i
\(353\) 0.659345 0.0350934 0.0175467 0.999846i \(-0.494414\pi\)
0.0175467 + 0.999846i \(0.494414\pi\)
\(354\) −4.91404 + 15.1238i −0.261178 + 0.803823i
\(355\) 21.6456 15.7264i 1.14883 0.834673i
\(356\) 14.9737 + 10.8790i 0.793605 + 0.576588i
\(357\) 0.254808 + 0.784218i 0.0134859 + 0.0415052i
\(358\) 1.93857 + 5.96629i 0.102456 + 0.315328i
\(359\) 7.89566 + 5.73653i 0.416717 + 0.302763i 0.776315 0.630345i \(-0.217086\pi\)
−0.359599 + 0.933107i \(0.617086\pi\)
\(360\) 2.24326 1.62982i 0.118230 0.0858993i
\(361\) 4.68738 14.4263i 0.246704 0.759277i
\(362\) −5.26390 −0.276664
\(363\) −10.0026 4.57680i −0.525003 0.240220i
\(364\) −1.69207 −0.0886885
\(365\) −2.56232 + 7.88601i −0.134118 + 0.412773i
\(366\) 14.3931 10.4572i 0.752341 0.546608i
\(367\) −7.05518 5.12589i −0.368277 0.267569i 0.388219 0.921567i \(-0.373090\pi\)
−0.756496 + 0.653998i \(0.773090\pi\)
\(368\) 9.92529 + 30.5469i 0.517392 + 1.59237i
\(369\) 3.44015 + 10.5877i 0.179087 + 0.551174i
\(370\) 25.5696 + 18.5774i 1.32930 + 0.965791i
\(371\) 9.85006 7.15649i 0.511390 0.371546i
\(372\) 3.04791 9.38051i 0.158027 0.486357i
\(373\) 10.9749 0.568261 0.284130 0.958786i \(-0.408295\pi\)
0.284130 + 0.958786i \(0.408295\pi\)
\(374\) −2.02316 + 3.46313i −0.104615 + 0.179074i
\(375\) 10.5452 0.544552
\(376\) −4.82693 + 14.8558i −0.248930 + 0.766127i
\(377\) −8.07280 + 5.86523i −0.415770 + 0.302075i
\(378\) 1.85065 + 1.34458i 0.0951873 + 0.0691576i
\(379\) −8.99087 27.6710i −0.461830 1.42137i −0.862926 0.505330i \(-0.831371\pi\)
0.401096 0.916036i \(-0.368629\pi\)
\(380\) −5.74246 17.6735i −0.294582 0.906630i
\(381\) −4.80795 3.49318i −0.246319 0.178961i
\(382\) 1.41100 1.02515i 0.0721929 0.0524512i
\(383\) −1.20672 + 3.71392i −0.0616607 + 0.189772i −0.977142 0.212589i \(-0.931810\pi\)
0.915481 + 0.402361i \(0.131810\pi\)
\(384\) −8.96172 −0.457326
\(385\) −6.46653 7.25621i −0.329565 0.369810i
\(386\) −18.0188 −0.917132
\(387\) −0.985192 + 3.03211i −0.0500801 + 0.154131i
\(388\) 2.91348 2.11677i 0.147910 0.107463i
\(389\) −17.7746 12.9140i −0.901208 0.654766i 0.0375677 0.999294i \(-0.488039\pi\)
−0.938776 + 0.344528i \(0.888039\pi\)
\(390\) 1.32811 + 4.08749i 0.0672513 + 0.206978i
\(391\) 1.34446 + 4.13782i 0.0679923 + 0.209259i
\(392\) −5.20093 3.77870i −0.262687 0.190853i
\(393\) 9.86009 7.16378i 0.497376 0.361365i
\(394\) 3.52545 10.8502i 0.177609 0.546626i
\(395\) 21.1767 1.06552
\(396\) 0.446801 + 4.47121i 0.0224526 + 0.224687i
\(397\) 6.96474 0.349550 0.174775 0.984608i \(-0.444080\pi\)
0.174775 + 0.984608i \(0.444080\pi\)
\(398\) 11.1303 34.2556i 0.557913 1.71708i
\(399\) −5.90614 + 4.29106i −0.295677 + 0.214822i
\(400\) 1.99500 + 1.44945i 0.0997499 + 0.0724725i
\(401\) −10.8370 33.3530i −0.541176 1.66557i −0.729912 0.683542i \(-0.760439\pi\)
0.188735 0.982028i \(-0.439561\pi\)
\(402\) −4.61863 14.2147i −0.230356 0.708964i
\(403\) −5.88968 4.27910i −0.293386 0.213157i
\(404\) −15.1006 + 10.9712i −0.751281 + 0.545838i
\(405\) 0.725100 2.23163i 0.0360305 0.110890i
\(406\) −22.8262 −1.13285
\(407\) 22.3318 9.80604i 1.10695 0.486067i
\(408\) −0.780199 −0.0386256
\(409\) −9.22887 + 28.4036i −0.456338 + 1.40447i 0.413218 + 0.910632i \(0.364405\pi\)
−0.869557 + 0.493833i \(0.835595\pi\)
\(410\) −38.7083 + 28.1232i −1.91167 + 1.38891i
\(411\) 12.1660 + 8.83909i 0.600103 + 0.436000i
\(412\) 2.70895 + 8.33728i 0.133460 + 0.410748i
\(413\) 3.35069 + 10.3124i 0.164877 + 0.507439i
\(414\) 9.76473 + 7.09449i 0.479910 + 0.348675i
\(415\) −17.6311 + 12.8097i −0.865477 + 0.628806i
\(416\) 2.02842 6.24282i 0.0994513 0.306079i
\(417\) 1.28387 0.0628713
\(418\) −34.6954 7.56066i −1.69701 0.369804i
\(419\) −4.38709 −0.214324 −0.107162 0.994242i \(-0.534176\pi\)
−0.107162 + 0.994242i \(0.534176\pi\)
\(420\) −1.22692 + 3.77607i −0.0598675 + 0.184253i
\(421\) −18.1662 + 13.1985i −0.885366 + 0.643256i −0.934666 0.355528i \(-0.884301\pi\)
0.0492998 + 0.998784i \(0.484301\pi\)
\(422\) −4.75224 3.45271i −0.231335 0.168075i
\(423\) 4.08474 + 12.5715i 0.198607 + 0.611248i
\(424\) 3.55991 + 10.9563i 0.172884 + 0.532084i
\(425\) 0.270239 + 0.196340i 0.0131085 + 0.00952388i
\(426\) −16.8962 + 12.2758i −0.818624 + 0.594765i
\(427\) 3.74866 11.5372i 0.181410 0.558324i
\(428\) −6.82069 −0.329690
\(429\) 3.24057 + 0.706172i 0.156456 + 0.0340943i
\(430\) −13.7022 −0.660777
\(431\) 9.23981 28.4372i 0.445066 1.36977i −0.437345 0.899294i \(-0.644081\pi\)
0.882411 0.470479i \(-0.155919\pi\)
\(432\) −3.94322 + 2.86492i −0.189718 + 0.137839i
\(433\) −2.85047 2.07098i −0.136985 0.0995252i 0.517183 0.855875i \(-0.326981\pi\)
−0.654167 + 0.756350i \(0.726981\pi\)
\(434\) −5.14617 15.8383i −0.247024 0.760261i
\(435\) 7.23543 + 22.2684i 0.346912 + 1.06769i
\(436\) 4.94588 + 3.59339i 0.236865 + 0.172092i
\(437\) −31.1630 + 22.6412i −1.49073 + 1.08308i
\(438\) 2.00011 6.15570i 0.0955689 0.294131i
\(439\) 19.7905 0.944550 0.472275 0.881451i \(-0.343433\pi\)
0.472275 + 0.881451i \(0.343433\pi\)
\(440\) 8.42039 3.69744i 0.401426 0.176269i
\(441\) −5.44022 −0.259058
\(442\) 0.373694 1.15011i 0.0177748 0.0547053i
\(443\) 21.2362 15.4290i 1.00896 0.733056i 0.0449728 0.998988i \(-0.485680\pi\)
0.963992 + 0.265933i \(0.0856799\pi\)
\(444\) −8.06043 5.85625i −0.382531 0.277925i
\(445\) −9.90565 30.4865i −0.469573 1.44520i
\(446\) 9.90791 + 30.4934i 0.469153 + 1.44390i
\(447\) −10.3159 7.49493i −0.487925 0.354498i
\(448\) 2.29838 1.66987i 0.108588 0.0788938i
\(449\) −9.62804 + 29.6321i −0.454375 + 1.39842i 0.417491 + 0.908681i \(0.362909\pi\)
−0.871867 + 0.489743i \(0.837091\pi\)
\(450\) 0.926673 0.0436838
\(451\) 3.67134 + 36.7396i 0.172876 + 1.73000i
\(452\) −5.80612 −0.273097
\(453\) 2.51385 7.73684i 0.118111 0.363508i
\(454\) −1.96928 + 1.43076i −0.0924228 + 0.0671491i
\(455\) 2.37085 + 1.72253i 0.111147 + 0.0807533i
\(456\) −2.13453 6.56942i −0.0999588 0.307641i
\(457\) −2.21580 6.81953i −0.103651 0.319004i 0.885761 0.464142i \(-0.153637\pi\)
−0.989411 + 0.145138i \(0.953637\pi\)
\(458\) 5.98396 + 4.34760i 0.279612 + 0.203150i
\(459\) −0.534141 + 0.388076i −0.0249316 + 0.0181139i
\(460\) −6.47368 + 19.9239i −0.301837 + 0.928958i
\(461\) 35.4005 1.64876 0.824382 0.566034i \(-0.191523\pi\)
0.824382 + 0.566034i \(0.191523\pi\)
\(462\) 5.04768 + 5.66408i 0.234839 + 0.263517i
\(463\) −17.3932 −0.808332 −0.404166 0.914686i \(-0.632438\pi\)
−0.404166 + 0.914686i \(0.632438\pi\)
\(464\) 15.0294 46.2558i 0.697724 2.14737i
\(465\) −13.8200 + 10.0408i −0.640886 + 0.465631i
\(466\) −21.5970 15.6911i −1.00046 0.726877i
\(467\) 6.53856 + 20.1236i 0.302568 + 0.931210i 0.980573 + 0.196152i \(0.0628447\pi\)
−0.678005 + 0.735057i \(0.737155\pi\)
\(468\) −0.418667 1.28852i −0.0193529 0.0595620i
\(469\) −8.24489 5.99026i −0.380714 0.276605i
\(470\) −45.9611 + 33.3927i −2.12003 + 1.54029i
\(471\) 0.986782 3.03700i 0.0454685 0.139938i
\(472\) −10.2595 −0.472233
\(473\) −5.33378 + 9.13006i −0.245247 + 0.419801i
\(474\) −16.5302 −0.759258
\(475\) −0.913876 + 2.81262i −0.0419315 + 0.129052i
\(476\) 0.903804 0.656652i 0.0414258 0.0300976i
\(477\) 7.88692 + 5.73018i 0.361117 + 0.262367i
\(478\) 1.45797 + 4.48716i 0.0666858 + 0.205238i
\(479\) −8.80709 27.1054i −0.402406 1.23848i −0.923042 0.384700i \(-0.874305\pi\)
0.520635 0.853779i \(-0.325695\pi\)
\(480\) −12.4608 9.05334i −0.568757 0.413226i
\(481\) −5.94939 + 4.32248i −0.271269 + 0.197088i
\(482\) −8.01343 + 24.6628i −0.365002 + 1.12336i
\(483\) 8.22998 0.374477
\(484\) −1.70955 + 14.8048i −0.0777067 + 0.672945i
\(485\) −6.23712 −0.283213
\(486\) −0.566002 + 1.74197i −0.0256744 + 0.0790176i
\(487\) 2.99794 2.17813i 0.135850 0.0987005i −0.517785 0.855511i \(-0.673243\pi\)
0.653635 + 0.756810i \(0.273243\pi\)
\(488\) 9.28595 + 6.74664i 0.420355 + 0.305406i
\(489\) 1.62343 + 4.99641i 0.0734142 + 0.225946i
\(490\) −7.22520 22.2369i −0.326401 1.00456i
\(491\) −29.1694 21.1928i −1.31640 0.956417i −0.999970 0.00779960i \(-0.997517\pi\)
−0.316425 0.948617i \(-0.602483\pi\)
\(492\) 12.2022 8.86544i 0.550119 0.399685i
\(493\) 2.03586 6.26572i 0.0916904 0.282194i
\(494\) 10.7065 0.481710
\(495\) 3.92565 6.71971i 0.176445 0.302028i
\(496\) 35.4836 1.59326
\(497\) −4.40059 + 13.5436i −0.197393 + 0.607514i
\(498\) 13.7626 9.99909i 0.616715 0.448070i
\(499\) 21.4965 + 15.6182i 0.962317 + 0.699165i 0.953688 0.300798i \(-0.0972531\pi\)
0.00862966 + 0.999963i \(0.497253\pi\)
\(500\) −4.41493 13.5878i −0.197442 0.607663i
\(501\) 4.03467 + 12.4175i 0.180256 + 0.554771i
\(502\) 11.1554 + 8.10484i 0.497888 + 0.361737i
\(503\) 6.19728 4.50259i 0.276323 0.200761i −0.440989 0.897513i \(-0.645372\pi\)
0.717312 + 0.696752i \(0.245372\pi\)
\(504\) −0.456059 + 1.40361i −0.0203145 + 0.0625216i
\(505\) 32.3269 1.43853
\(506\) 26.6334 + 29.8858i 1.18400 + 1.32859i
\(507\) −1.00000 −0.0444116
\(508\) −2.48811 + 7.65763i −0.110392 + 0.339752i
\(509\) 27.4173 19.9198i 1.21525 0.882930i 0.219553 0.975601i \(-0.429540\pi\)
0.995697 + 0.0926703i \(0.0295403\pi\)
\(510\) −2.29566 1.66789i −0.101653 0.0738555i
\(511\) −1.36380 4.19734i −0.0603308 0.185679i
\(512\) 6.32699 + 19.4725i 0.279616 + 0.860570i
\(513\) −4.72903 3.43584i −0.208792 0.151696i
\(514\) 17.2185 12.5100i 0.759477 0.551792i
\(515\) 4.69169 14.4395i 0.206741 0.636282i
\(516\) 4.31941 0.190151
\(517\) 4.35923 + 43.6235i 0.191719 + 1.91856i
\(518\) −16.8222 −0.739124
\(519\) −0.759506 + 2.33752i −0.0333386 + 0.102606i
\(520\) −2.24326 + 1.62982i −0.0983735 + 0.0714726i
\(521\) 19.0034 + 13.8067i 0.832552 + 0.604884i 0.920280 0.391260i \(-0.127961\pi\)
−0.0877282 + 0.996144i \(0.527961\pi\)
\(522\) −5.64786 17.3823i −0.247200 0.760804i
\(523\) −7.66110 23.5784i −0.334996 1.03101i −0.966724 0.255822i \(-0.917654\pi\)
0.631728 0.775191i \(-0.282346\pi\)
\(524\) −13.3588 9.70573i −0.583581 0.423997i
\(525\) 0.511188 0.371400i 0.0223101 0.0162092i
\(526\) −6.88918 + 21.2027i −0.300382 + 0.924482i
\(527\) 4.80654 0.209376
\(528\) −14.8014 + 6.49939i −0.644150 + 0.282850i
\(529\) 20.4244 0.888019
\(530\) −12.9474 + 39.8480i −0.562400 + 1.73089i
\(531\) −7.02390 + 5.10316i −0.304811 + 0.221458i
\(532\) 8.00184 + 5.81367i 0.346924 + 0.252055i
\(533\) −3.44015 10.5877i −0.149010 0.458604i
\(534\) 7.73220 + 23.7973i 0.334605 + 1.02981i
\(535\) 9.55686 + 6.94346i 0.413179 + 0.300192i
\(536\) 7.80117 5.66788i 0.336959 0.244815i
\(537\) −1.05839 + 3.25738i −0.0456728 + 0.140567i
\(538\) −57.4204 −2.47557
\(539\) −17.6294 3.84173i −0.759353 0.165475i
\(540\) −3.17908 −0.136806
\(541\) 4.99251 15.3654i 0.214645 0.660608i −0.784534 0.620086i \(-0.787098\pi\)
0.999179 0.0405224i \(-0.0129022\pi\)
\(542\) −9.61753 + 6.98754i −0.413108 + 0.300141i
\(543\) −2.32504 1.68924i −0.0997769 0.0724921i
\(544\) 1.33923 + 4.12173i 0.0574191 + 0.176718i
\(545\) −3.27188 10.0698i −0.140152 0.431344i
\(546\) −1.85065 1.34458i −0.0792006 0.0575426i
\(547\) −17.8444 + 12.9647i −0.762971 + 0.554331i −0.899820 0.436261i \(-0.856302\pi\)
0.136849 + 0.990592i \(0.456302\pi\)
\(548\) 6.29589 19.3768i 0.268947 0.827734i
\(549\) 9.71319 0.414549
\(550\) 3.00295 + 0.654391i 0.128046 + 0.0279033i
\(551\) 58.3284 2.48488
\(552\) −2.40634 + 7.40594i −0.102420 + 0.315218i
\(553\) −9.11869 + 6.62512i −0.387766 + 0.281729i
\(554\) 8.22430 + 5.97531i 0.349417 + 0.253866i
\(555\) 5.33227 + 16.4110i 0.226342 + 0.696610i
\(556\) −0.537513 1.65429i −0.0227956 0.0701577i
\(557\) −27.8190 20.2117i −1.17873 0.856398i −0.186702 0.982417i \(-0.559780\pi\)
−0.992028 + 0.126019i \(0.959780\pi\)
\(558\) 10.7877 7.83769i 0.456678 0.331796i
\(559\) 0.985192 3.03211i 0.0416692 0.128245i
\(560\) −14.2837 −0.603597
\(561\) −2.00497 + 0.880395i −0.0846500 + 0.0371703i
\(562\) 24.1981 1.02074
\(563\) 3.28457 10.1089i 0.138428 0.426038i −0.857679 0.514185i \(-0.828094\pi\)
0.996107 + 0.0881468i \(0.0280945\pi\)
\(564\) 14.4886 10.5266i 0.610079 0.443248i
\(565\) 8.13529 + 5.91063i 0.342254 + 0.248662i
\(566\) −13.1043 40.3310i −0.550816 1.69524i
\(567\) 0.385935 + 1.18779i 0.0162077 + 0.0498823i
\(568\) −10.9009 7.91994i −0.457390 0.332313i
\(569\) 11.1839 8.12556i 0.468852 0.340641i −0.328141 0.944629i \(-0.606422\pi\)
0.796994 + 0.603987i \(0.206422\pi\)
\(570\) 7.76332 23.8930i 0.325170 1.00077i
\(571\) −17.1095 −0.716010 −0.358005 0.933720i \(-0.616543\pi\)
−0.358005 + 0.933720i \(0.616543\pi\)
\(572\) −0.446801 4.47121i −0.0186817 0.186951i
\(573\) 0.952210 0.0397791
\(574\) 7.86947 24.2197i 0.328465 1.01091i
\(575\) 2.69722 1.95964i 0.112482 0.0817227i
\(576\) 1.84030 + 1.33706i 0.0766792 + 0.0557107i
\(577\) −10.1830 31.3402i −0.423925 1.30471i −0.904020 0.427491i \(-0.859398\pi\)
0.480094 0.877217i \(-0.340602\pi\)
\(578\) −9.37531 28.8542i −0.389961 1.20018i
\(579\) −7.95880 5.78241i −0.330756 0.240309i
\(580\) 25.6641 18.6460i 1.06564 0.774235i
\(581\) 3.58443 11.0318i 0.148707 0.457674i
\(582\) 4.86860 0.201810
\(583\) 21.5116 + 24.1386i 0.890921 + 0.999718i
\(584\) 4.17583 0.172797
\(585\) −0.725100 + 2.23163i −0.0299792 + 0.0922664i
\(586\) −13.9196 + 10.1132i −0.575012 + 0.417771i
\(587\) 22.9206 + 16.6528i 0.946035 + 0.687334i 0.949866 0.312658i \(-0.101219\pi\)
−0.00383099 + 0.999993i \(0.501219\pi\)
\(588\) 2.27764 + 7.00985i 0.0939282 + 0.289081i
\(589\) 13.1501 + 40.4720i 0.541842 + 1.66762i
\(590\) −30.1876 21.9326i −1.24280 0.902951i
\(591\) 5.03911 3.66113i 0.207281 0.150599i
\(592\) 11.0762 34.0890i 0.455229 1.40105i
\(593\) −30.5267 −1.25358 −0.626790 0.779188i \(-0.715632\pi\)
−0.626790 + 0.779188i \(0.715632\pi\)
\(594\) −3.06430 + 5.24530i −0.125730 + 0.215217i
\(595\) −1.93484 −0.0793208
\(596\) −5.33848 + 16.4302i −0.218673 + 0.673005i
\(597\) 15.9092 11.5587i 0.651119 0.473066i
\(598\) −9.76473 7.09449i −0.399310 0.290115i
\(599\) 1.44269 + 4.44016i 0.0589469 + 0.181420i 0.976194 0.216898i \(-0.0695940\pi\)
−0.917247 + 0.398318i \(0.869594\pi\)
\(600\) 0.184748 + 0.568597i 0.00754232 + 0.0232129i
\(601\) 0.307025 + 0.223067i 0.0125238 + 0.00909909i 0.594030 0.804443i \(-0.297536\pi\)
−0.581506 + 0.813542i \(0.697536\pi\)
\(602\) 5.90016 4.28671i 0.240472 0.174713i
\(603\) 2.52161 7.76071i 0.102688 0.316041i
\(604\) −11.0216 −0.448461
\(605\) 17.4666 19.0035i 0.710120 0.772603i
\(606\) −25.2339 −1.02506
\(607\) 8.48174 26.1041i 0.344263 1.05953i −0.617714 0.786403i \(-0.711941\pi\)
0.961977 0.273130i \(-0.0880589\pi\)
\(608\) −31.0418 + 22.5532i −1.25891 + 0.914651i
\(609\) −10.0822 7.32516i −0.408552 0.296830i
\(610\) 12.9002 + 39.7026i 0.522312 + 1.60751i
\(611\) −4.08474 12.5715i −0.165251 0.508589i
\(612\) 0.723673 + 0.525779i 0.0292527 + 0.0212534i
\(613\) 24.9296 18.1124i 1.00690 0.731555i 0.0433422 0.999060i \(-0.486199\pi\)
0.963556 + 0.267506i \(0.0861994\pi\)
\(614\) 14.2540 43.8694i 0.575246 1.77043i
\(615\) −26.1223 −1.05335
\(616\) −2.46908 + 4.22643i −0.0994821 + 0.170288i
\(617\) 2.05318 0.0826581 0.0413290 0.999146i \(-0.486841\pi\)
0.0413290 + 0.999146i \(0.486841\pi\)
\(618\) −3.66226 + 11.2713i −0.147318 + 0.453398i
\(619\) −9.22767 + 6.70430i −0.370891 + 0.269468i −0.757581 0.652742i \(-0.773619\pi\)
0.386689 + 0.922210i \(0.373619\pi\)
\(620\) 18.7238 + 13.6036i 0.751964 + 0.546334i
\(621\) 2.03634 + 6.26720i 0.0817153 + 0.251494i
\(622\) 2.04548 + 6.29533i 0.0820162 + 0.252420i
\(623\) 13.8030 + 10.0285i 0.553007 + 0.401783i
\(624\) 3.94322 2.86492i 0.157855 0.114689i
\(625\) −8.42803 + 25.9388i −0.337121 + 1.03755i
\(626\) −42.6309 −1.70387
\(627\) −12.8985 14.4736i −0.515115 0.578020i
\(628\) −4.32638 −0.172641
\(629\) 1.50036 4.61763i 0.0598233 0.184117i
\(630\) −4.34251 + 3.15501i −0.173010 + 0.125699i
\(631\) 8.80933 + 6.40035i 0.350694 + 0.254794i 0.749160 0.662389i \(-0.230457\pi\)
−0.398466 + 0.917183i \(0.630457\pi\)
\(632\) −3.29558 10.1428i −0.131091 0.403458i
\(633\) −0.991032 3.05008i −0.0393900 0.121230i
\(634\) 26.3849 + 19.1698i 1.04788 + 0.761329i
\(635\) 11.2817 8.19664i 0.447701 0.325274i
\(636\) 4.08148 12.5615i 0.161841 0.498097i
\(637\) 5.44022 0.215549
\(638\) −6.02740 60.3171i −0.238627 2.38798i
\(639\) −11.4024 −0.451072
\(640\) 6.49814 19.9992i 0.256862 0.790539i
\(641\) −13.6541 + 9.92026i −0.539303 + 0.391827i −0.823826 0.566842i \(-0.808165\pi\)
0.284523 + 0.958669i \(0.408165\pi\)
\(642\) −7.45994 5.41996i −0.294420 0.213909i
\(643\) −6.51399 20.0480i −0.256887 0.790616i −0.993452 0.114250i \(-0.963554\pi\)
0.736565 0.676366i \(-0.236446\pi\)
\(644\) −3.44562 10.6045i −0.135776 0.417877i
\(645\) −6.05217 4.39716i −0.238304 0.173138i
\(646\) −5.71881 + 4.15496i −0.225004 + 0.163475i
\(647\) −1.22818 + 3.77995i −0.0482848 + 0.148605i −0.972292 0.233770i \(-0.924894\pi\)
0.924007 + 0.382375i \(0.124894\pi\)
\(648\) −1.18170 −0.0464215
\(649\) −26.3652 + 11.5771i −1.03492 + 0.454440i
\(650\) −0.926673 −0.0363471
\(651\) 2.80962 8.64713i 0.110118 0.338908i
\(652\) 5.75832 4.18366i 0.225513 0.163845i
\(653\) −17.9600 13.0487i −0.702830 0.510636i 0.178023 0.984026i \(-0.443030\pi\)
−0.880853 + 0.473391i \(0.843030\pi\)
\(654\) 2.55398 + 7.86035i 0.0998686 + 0.307364i
\(655\) 8.83733 + 27.1985i 0.345303 + 1.06273i
\(656\) 43.8982 + 31.8939i 1.71394 + 1.24525i
\(657\) 2.85886 2.07709i 0.111535 0.0810348i
\(658\) 9.34397 28.7578i 0.364266 1.12109i
\(659\) −14.4189 −0.561682 −0.280841 0.959754i \(-0.590613\pi\)
−0.280841 + 0.959754i \(0.590613\pi\)
\(660\) −10.3020 2.24498i −0.401007 0.0873856i
\(661\) −10.6304 −0.413474 −0.206737 0.978397i \(-0.566284\pi\)
−0.206737 + 0.978397i \(0.566284\pi\)
\(662\) 13.6005 41.8580i 0.528598 1.62686i
\(663\) 0.534141 0.388076i 0.0207443 0.0150716i
\(664\) 8.87914 + 6.45107i 0.344577 + 0.250350i
\(665\) −5.29351 16.2917i −0.205273 0.631767i
\(666\) −4.16229 12.8102i −0.161286 0.496386i
\(667\) −53.1975 38.6502i −2.05981 1.49654i
\(668\) 14.3110 10.3975i 0.553709 0.402293i
\(669\) −5.40937 + 16.6483i −0.209138 + 0.643661i
\(670\) 35.0708 1.35490
\(671\) 31.4763 + 6.85918i 1.21513 + 0.264796i
\(672\) 8.19797 0.316244
\(673\) −5.02735 + 15.4726i −0.193790 + 0.596424i 0.806199 + 0.591645i \(0.201521\pi\)
−0.999989 + 0.00477910i \(0.998479\pi\)
\(674\) 13.4087 9.74197i 0.516483 0.375247i
\(675\) 0.409307 + 0.297379i 0.0157542 + 0.0114461i
\(676\) 0.418667 + 1.28852i 0.0161026 + 0.0495586i
\(677\) −14.6867 45.2010i −0.564455 1.73721i −0.669565 0.742753i \(-0.733519\pi\)
0.105110 0.994461i \(-0.466481\pi\)
\(678\) −6.35028 4.61375i −0.243881 0.177190i
\(679\) 2.68570 1.95128i 0.103068 0.0748832i
\(680\) 0.565722 1.74111i 0.0216945 0.0667687i
\(681\) −1.32897 −0.0509261
\(682\) 40.4930 17.7807i 1.55056 0.680858i
\(683\) −33.3076 −1.27448 −0.637239 0.770666i \(-0.719924\pi\)
−0.637239 + 0.770666i \(0.719924\pi\)
\(684\) −2.44727 + 7.53193i −0.0935738 + 0.287991i
\(685\) −28.5471 + 20.7407i −1.09073 + 0.792460i
\(686\) 23.0225 + 16.7268i 0.879004 + 0.638634i
\(687\) 1.24789 + 3.84062i 0.0476101 + 0.146529i
\(688\) 4.80192 + 14.7788i 0.183071 + 0.563436i
\(689\) −7.88692 5.73018i −0.300468 0.218302i
\(690\) −22.9127 + 16.6470i −0.872270 + 0.633741i
\(691\) −1.52007 + 4.67830i −0.0578263 + 0.177971i −0.975798 0.218676i \(-0.929826\pi\)
0.917971 + 0.396647i \(0.129826\pi\)
\(692\) 3.32993 0.126585
\(693\) 0.411870 + 4.12164i 0.0156457 + 0.156568i
\(694\) 55.4707 2.10564
\(695\) −0.930933 + 2.86512i −0.0353123 + 0.108680i
\(696\) 9.53962 6.93094i 0.361598 0.262716i
\(697\) 5.94637 + 4.32029i 0.225235 + 0.163643i
\(698\) 10.1861 + 31.3495i 0.385548 + 1.18659i
\(699\) −4.50383 13.8614i −0.170350 0.524285i
\(700\) −0.692575 0.503185i −0.0261769 0.0190186i
\(701\) −3.74878 + 2.72365i −0.141590 + 0.102871i −0.656325 0.754478i \(-0.727890\pi\)
0.514736 + 0.857349i \(0.327890\pi\)
\(702\) 0.566002 1.74197i 0.0213624 0.0657466i
\(703\) 42.9862 1.62125
\(704\) 5.01944 + 5.63240i 0.189177 + 0.212279i
\(705\) −31.0168 −1.16816
\(706\) 0.373191 1.14856i 0.0140452 0.0432267i
\(707\) −13.9200 + 10.1135i −0.523515 + 0.380356i
\(708\) 9.51621 + 6.91393i 0.357641 + 0.259842i
\(709\) 14.4720 + 44.5402i 0.543507 + 1.67274i 0.724514 + 0.689260i \(0.242064\pi\)
−0.181008 + 0.983482i \(0.557936\pi\)
\(710\) −15.1436 46.6073i −0.568330 1.74914i
\(711\) −7.30131 5.30471i −0.273821 0.198942i
\(712\) −13.0602 + 9.48879i −0.489452 + 0.355608i
\(713\) 14.8246 45.6255i 0.555186 1.70869i
\(714\) 1.51031 0.0565219
\(715\) −3.92565 + 6.71971i −0.146811 + 0.251303i
\(716\) 4.64033 0.173417
\(717\) −0.795998 + 2.44983i −0.0297271 + 0.0914905i
\(718\) 14.4619 10.5071i 0.539711 0.392123i
\(719\) −9.14050 6.64096i −0.340883 0.247666i 0.404151 0.914692i \(-0.367567\pi\)
−0.745034 + 0.667026i \(0.767567\pi\)
\(720\) −3.53420 10.8772i −0.131712 0.405368i
\(721\) 2.49716 + 7.68546i 0.0929990 + 0.286222i
\(722\) −22.4771 16.3306i −0.836512 0.607761i
\(723\) −11.4540 + 8.32184i −0.425980 + 0.309493i
\(724\) −1.20321 + 3.70309i −0.0447169 + 0.137624i
\(725\) −5.04844 −0.187494
\(726\) −13.6342 + 14.8339i −0.506012 + 0.550537i
\(727\) −15.0362 −0.557660 −0.278830 0.960340i \(-0.589947\pi\)
−0.278830 + 0.960340i \(0.589947\pi\)
\(728\) 0.456059 1.40361i 0.0169027 0.0520211i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) 12.2870 + 8.92699i 0.454760 + 0.330403i
\(731\) 0.650458 + 2.00190i 0.0240581 + 0.0740431i
\(732\) −4.06659 12.5157i −0.150306 0.462593i
\(733\) −10.1338 7.36265i −0.374301 0.271946i 0.384691 0.923045i \(-0.374308\pi\)
−0.758992 + 0.651100i \(0.774308\pi\)
\(734\) −12.9224 + 9.38868i −0.476975 + 0.346542i
\(735\) 3.94470 12.1405i 0.145502 0.447811i
\(736\) 43.2555 1.59442
\(737\) 13.6519 23.3685i 0.502873 0.860789i
\(738\) 20.3907 0.750590
\(739\) 14.2955 43.9970i 0.525868 1.61846i −0.236725 0.971577i \(-0.576074\pi\)
0.762593 0.646878i \(-0.223926\pi\)
\(740\) 18.9136 13.7415i 0.695277 0.505148i
\(741\) 4.72903 + 3.43584i 0.173725 + 0.126219i
\(742\) −6.89127 21.2092i −0.252987 0.778612i
\(743\) −6.07429 18.6947i −0.222844 0.685844i −0.998503 0.0546917i \(-0.982582\pi\)
0.775659 0.631152i \(-0.217418\pi\)
\(744\) 6.95983 + 5.05661i 0.255160 + 0.185384i
\(745\) 24.2059 17.5867i 0.886837 0.644325i
\(746\) 6.21183 19.1181i 0.227431 0.699962i
\(747\) 9.28766 0.339818
\(748\) 1.97383 + 2.21486i 0.0721702 + 0.0809834i
\(749\) −6.28744 −0.229738
\(750\) 5.96861 18.3695i 0.217943 0.670759i
\(751\) 18.1738 13.2040i 0.663171 0.481822i −0.204561 0.978854i \(-0.565577\pi\)
0.867732 + 0.497032i \(0.165577\pi\)
\(752\) 52.1234 + 37.8699i 1.90075 + 1.38097i
\(753\) 2.32634 + 7.15973i 0.0847764 + 0.260915i
\(754\) 5.64786 + 17.3823i 0.205683 + 0.633027i
\(755\) 15.4429 + 11.2200i 0.562026 + 0.408336i
\(756\) 1.36891 0.994573i 0.0497869 0.0361723i
\(757\) −5.34460 + 16.4490i −0.194253 + 0.597848i 0.805732 + 0.592281i \(0.201772\pi\)
−0.999985 + 0.00556772i \(0.998228\pi\)
\(758\) −53.2911 −1.93562
\(759\) 2.17318 + 21.7473i 0.0788814 + 0.789378i
\(760\) 16.2083 0.587935
\(761\) 5.86939 18.0641i 0.212765 0.654824i −0.786540 0.617540i \(-0.788129\pi\)
0.999305 0.0372839i \(-0.0118706\pi\)
\(762\) −8.80633 + 6.39817i −0.319020 + 0.231781i
\(763\) 4.55921 + 3.31246i 0.165054 + 0.119919i
\(764\) −0.398659 1.22695i −0.0144230 0.0443893i
\(765\) −0.478736 1.47340i −0.0173087 0.0532708i
\(766\) 5.78654 + 4.20417i 0.209076 + 0.151903i
\(767\) 7.02390 5.10316i 0.253618 0.184264i
\(768\) −6.47822 + 19.9379i −0.233763 + 0.719447i
\(769\) −6.72145 −0.242382 −0.121191 0.992629i \(-0.538671\pi\)
−0.121191 + 0.992629i \(0.538671\pi\)
\(770\) −16.3002 + 7.15750i −0.587418 + 0.257939i
\(771\) 11.6199 0.418481
\(772\) −4.11868 + 12.6760i −0.148235 + 0.456219i
\(773\) −0.529226 + 0.384505i −0.0190349 + 0.0138297i −0.597262 0.802046i \(-0.703745\pi\)
0.578227 + 0.815876i \(0.303745\pi\)
\(774\) 4.72424 + 3.43236i 0.169809 + 0.123374i
\(775\) −1.13817 3.50293i −0.0408843 0.125829i
\(776\) 0.970639 + 2.98732i 0.0348439 + 0.107239i
\(777\) −7.43026 5.39840i −0.266559 0.193667i
\(778\) −32.5563 + 23.6536i −1.16720 + 0.848021i
\(779\) −20.1091 + 61.8893i −0.720482 + 2.21742i
\(780\) 3.17908 0.113829
\(781\) −36.9503 8.05205i −1.32219 0.288125i
\(782\) 7.96895 0.284969
\(783\) 3.08353 9.49014i 0.110197 0.339150i
\(784\) −21.4520 + 15.5858i −0.766143 + 0.556635i
\(785\) 6.06194 + 4.40426i 0.216360 + 0.157195i
\(786\) −6.89829 21.2307i −0.246054 0.757275i
\(787\) −3.15914 9.72284i −0.112611 0.346582i 0.878830 0.477135i \(-0.158325\pi\)
−0.991441 + 0.130553i \(0.958325\pi\)
\(788\) −6.82716 4.96022i −0.243207 0.176701i
\(789\) −9.84707 + 7.15432i −0.350565 + 0.254700i
\(790\) 11.9861 36.8893i 0.426445 1.31246i
\(791\) −5.35219 −0.190302
\(792\) −3.82938 0.834483i −0.136071 0.0296521i
\(793\) −9.71319 −0.344926
\(794\) 3.94206 12.1324i 0.139898 0.430563i
\(795\) −18.5064 + 13.4457i −0.656355 + 0.476870i
\(796\) −21.5543 15.6601i −0.763972 0.555058i
\(797\) 15.4278 + 47.4819i 0.546481 + 1.68189i 0.717443 + 0.696617i \(0.245312\pi\)
−0.170962 + 0.985278i \(0.554688\pi\)
\(798\) 4.13203 + 12.7171i 0.146272 + 0.450180i
\(799\) 7.06054 + 5.12978i 0.249784 + 0.181479i
\(800\) 2.68673 1.95202i 0.0949901 0.0690143i
\(801\) −4.22151 + 12.9925i −0.149160 + 0.459066i
\(802\) −64.2339 −2.26818
\(803\) 10.7311 4.71210i 0.378694 0.166286i
\(804\) −11.0556 −0.389900
\(805\) −5.96756 + 18.3663i −0.210329 + 0.647325i
\(806\) −10.7877 + 7.83769i −0.379979 + 0.276071i
\(807\) −25.3623 18.4268i −0.892794 0.648653i
\(808\) −5.03082 15.4833i −0.176984 0.544699i
\(809\) 3.64815 + 11.2279i 0.128262 + 0.394751i 0.994481 0.104914i \(-0.0334567\pi\)
−0.866219 + 0.499664i \(0.833457\pi\)
\(810\) −3.47703 2.52621i −0.122170 0.0887620i
\(811\) −8.82279 + 6.41014i −0.309810 + 0.225090i −0.731815 0.681503i \(-0.761327\pi\)
0.422005 + 0.906594i \(0.361327\pi\)
\(812\) −5.21755 + 16.0580i −0.183100 + 0.563524i
\(813\) −6.49038 −0.227628
\(814\) −4.44200 44.4518i −0.155692 1.55803i
\(815\) −12.3273 −0.431806
\(816\) −0.994431 + 3.06054i −0.0348121 + 0.107140i
\(817\) −15.0768 + 10.9540i −0.527472 + 0.383231i
\(818\) 44.2547 + 32.1529i 1.54733 + 1.12420i
\(819\) −0.385935 1.18779i −0.0134857 0.0415046i
\(820\) 10.9365 + 33.6592i 0.381920 + 1.17543i
\(821\) 34.9585 + 25.3988i 1.22006 + 0.886425i 0.996105 0.0881751i \(-0.0281035\pi\)
0.223954 + 0.974600i \(0.428104\pi\)
\(822\) 22.2834 16.1899i 0.777224 0.564686i
\(823\) −1.89544 + 5.83357i −0.0660709 + 0.203345i −0.978642 0.205573i \(-0.934094\pi\)
0.912571 + 0.408919i \(0.134094\pi\)
\(824\) −7.64608 −0.266364
\(825\) 1.11639 + 1.25272i 0.0388676 + 0.0436141i
\(826\) 19.8604 0.691031
\(827\) −15.0660 + 46.3683i −0.523896 + 1.61238i 0.242594 + 0.970128i \(0.422002\pi\)
−0.766489 + 0.642257i \(0.777998\pi\)
\(828\) 7.22289 5.24773i 0.251013 0.182371i
\(829\) 2.86395 + 2.08078i 0.0994689 + 0.0722684i 0.636408 0.771353i \(-0.280419\pi\)
−0.536939 + 0.843621i \(0.680419\pi\)
\(830\) 12.3350 + 37.9633i 0.428155 + 1.31772i
\(831\) 1.71510 + 5.27852i 0.0594960 + 0.183110i
\(832\) −1.84030 1.33706i −0.0638010 0.0463541i
\(833\) −2.90585 + 2.11122i −0.100682 + 0.0731495i
\(834\) 0.726672 2.23647i 0.0251626 0.0774425i
\(835\) −30.6367 −1.06023
\(836\) −13.2494 + 22.6796i −0.458240 + 0.784390i
\(837\) 7.28004 0.251635
\(838\) −2.48310 + 7.64221i −0.0857774 + 0.263996i
\(839\) −21.4859 + 15.6104i −0.741776 + 0.538931i −0.893267 0.449527i \(-0.851592\pi\)
0.151491 + 0.988459i \(0.451592\pi\)
\(840\) −2.80164 2.03551i −0.0966656 0.0702317i
\(841\) 21.8076 + 67.1170i 0.751987 + 2.31438i
\(842\) 12.7094 + 39.1154i 0.437994 + 1.34801i
\(843\) 10.6882 + 7.76542i 0.368120 + 0.267455i
\(844\) −3.51519 + 2.55394i −0.120998 + 0.0879101i
\(845\) 0.725100 2.23163i 0.0249442 0.0767703i
\(846\) 24.2112 0.832400
\(847\) −1.57589 + 13.6473i −0.0541484 + 0.468928i
\(848\) 47.5164 1.63172
\(849\) 7.15450 22.0193i 0.245542 0.755700i
\(850\) 0.494974 0.359620i 0.0169775 0.0123349i
\(851\) −39.2048 28.4840i −1.34392 0.976418i
\(852\) 4.77381 + 14.6923i 0.163548 + 0.503349i
\(853\) 9.80387 + 30.1732i 0.335678 + 1.03311i 0.966387 + 0.257091i \(0.0827641\pi\)
−0.630709 + 0.776019i \(0.717236\pi\)
\(854\) −17.9757 13.0601i −0.615117 0.446909i
\(855\) 11.0965 8.06210i 0.379493 0.275718i
\(856\) 1.83836 5.65790i 0.0628340 0.193383i
\(857\) 13.2476 0.452528 0.226264 0.974066i \(-0.427349\pi\)
0.226264 + 0.974066i \(0.427349\pi\)
\(858\) 3.06430 5.24530i 0.104614 0.179072i
\(859\) −29.2959 −0.999562 −0.499781 0.866152i \(-0.666586\pi\)
−0.499781 + 0.866152i \(0.666586\pi\)
\(860\) −3.13200 + 9.63932i −0.106800 + 0.328698i
\(861\) 11.2483 8.17233i 0.383339 0.278512i
\(862\) −44.3072 32.1910i −1.50911 1.09643i
\(863\) −6.71103 20.6544i −0.228446 0.703085i −0.997923 0.0644108i \(-0.979483\pi\)
0.769477 0.638674i \(-0.220517\pi\)
\(864\) 2.02842 + 6.24282i 0.0690081 + 0.212385i
\(865\) −4.66575 3.38987i −0.158640 0.115259i
\(866\) −5.22097 + 3.79326i −0.177416 + 0.128900i
\(867\) 5.11859 15.7534i 0.173836 0.535013i
\(868\) −12.3183 −0.418112
\(869\) −19.9144 22.3463i −0.675550 0.758046i
\(870\) 42.8862 1.45398
\(871\) −2.52161 + 7.76071i −0.0854414 + 0.262962i
\(872\) −4.31384 + 3.13419i −0.146085 + 0.106137i
\(873\) 2.15043 + 1.56238i 0.0727812 + 0.0528786i
\(874\) 21.8021 + 67.1001i 0.737468 + 2.26969i
\(875\) −4.06977 12.5254i −0.137583 0.423437i
\(876\) −3.87328 2.81411i −0.130866 0.0950798i
\(877\) −36.0322 + 26.1790i −1.21672 + 0.884001i −0.995824 0.0912961i \(-0.970899\pi\)
−0.220899 + 0.975297i \(0.570899\pi\)
\(878\) 11.2015 34.4746i 0.378031 1.16346i
\(879\) −9.39362 −0.316839
\(880\) −3.77170 37.7440i −0.127144 1.27235i
\(881\) 12.1937 0.410817 0.205409 0.978676i \(-0.434148\pi\)
0.205409 + 0.978676i \(0.434148\pi\)
\(882\) −3.07917 + 9.47672i −0.103681 + 0.319098i
\(883\) −5.10126 + 3.70628i −0.171671 + 0.124726i −0.670303 0.742087i \(-0.733836\pi\)
0.498632 + 0.866814i \(0.333836\pi\)
\(884\) −0.723673 0.525779i −0.0243398 0.0176839i
\(885\) −6.29532 19.3750i −0.211615 0.651284i
\(886\) −14.8572 45.7259i −0.499138 1.53619i
\(887\) −18.9371 13.7586i −0.635846 0.461969i 0.222574 0.974916i \(-0.428554\pi\)
−0.858421 + 0.512946i \(0.828554\pi\)
\(888\) 7.03039 5.10787i 0.235924 0.171409i
\(889\) −2.29359 + 7.05895i −0.0769246 + 0.236750i
\(890\) −58.7133 −1.96807
\(891\) −3.03676 + 1.33346i −0.101735 + 0.0446725i
\(892\) 23.7165 0.794086
\(893\) −23.8769 + 73.4855i −0.799010 + 2.45910i
\(894\) −18.8948 + 13.7279i −0.631937 + 0.459129i
\(895\) −6.50183 4.72386i −0.217332 0.157901i
\(896\) 3.45864 + 10.6446i 0.115545 + 0.355611i
\(897\) −2.03634 6.26720i −0.0679913 0.209256i
\(898\) 46.1688 + 33.5436i 1.54067 + 1.11937i
\(899\) −58.7703 + 42.6991i −1.96010 + 1.42410i
\(900\) 0.211816 0.651904i 0.00706055 0.0217301i
\(901\) 6.43648 0.214430
\(902\) 66.0774 + 14.3993i 2.20014 + 0.479444i
\(903\) 3.98172 0.132503
\(904\) 1.56491 4.81629i 0.0520481 0.160188i
\(905\) 5.45563 3.96375i 0.181351 0.131760i
\(906\) −12.0545 8.75813i −0.400485 0.290969i
\(907\) 10.7831 + 33.1868i 0.358045 + 1.10195i 0.954223 + 0.299098i \(0.0966856\pi\)
−0.596177 + 0.802853i \(0.703314\pi\)
\(908\) 0.556394 + 1.71240i 0.0184646 + 0.0568281i
\(909\) −11.1457 8.09782i −0.369679 0.268588i
\(910\) 4.34251 3.15501i 0.143953 0.104588i
\(911\) −16.3189 + 50.2245i −0.540670 + 1.66401i 0.190397 + 0.981707i \(0.439022\pi\)
−0.731068 + 0.682305i \(0.760978\pi\)
\(912\) −28.4910 −0.943432
\(913\) 30.0974 + 6.55869i 0.996077 + 0.217061i
\(914\) −13.1336 −0.434420
\(915\) −7.04303 + 21.6762i −0.232835 + 0.716594i
\(916\) 4.42628 3.21588i 0.146248 0.106256i
\(917\) −12.3144 8.94693i −0.406657 0.295454i
\(918\) 0.373694 + 1.15011i 0.0123337 + 0.0379594i
\(919\) −13.8045 42.4857i −0.455367 1.40148i −0.870704 0.491808i \(-0.836336\pi\)
0.415337 0.909668i \(-0.363664\pi\)
\(920\) −14.7825 10.7401i −0.487364 0.354090i
\(921\) 20.3741 14.8026i 0.671348 0.487763i
\(922\) 20.0367 61.6667i 0.659875 2.03088i
\(923\) 11.4024 0.375315
\(924\) 5.13840 2.25630i 0.169041 0.0742268i
\(925\) −3.72054 −0.122331
\(926\) −9.84461 + 30.2986i −0.323514 + 0.995673i
\(927\) −5.23467 + 3.80321i −0.171929 + 0.124914i
\(928\) −52.9906 38.4999i −1.73950 1.26382i
\(929\) −2.71131 8.34457i −0.0889553 0.273776i 0.896676 0.442688i \(-0.145975\pi\)
−0.985631 + 0.168911i \(0.945975\pi\)
\(930\) 9.66868 + 29.7571i 0.317049 + 0.975775i
\(931\) −25.7269 18.6917i −0.843166 0.612596i
\(932\) −15.9751 + 11.6066i −0.523282 + 0.380186i
\(933\) −1.11676 + 3.43703i −0.0365610 + 0.112523i
\(934\) 38.7557 1.26812
\(935\) −0.510908 5.11273i −0.0167085 0.167204i
\(936\) 1.18170 0.0386250
\(937\) −1.96982 + 6.06250i −0.0643514 + 0.198053i −0.978063 0.208311i \(-0.933203\pi\)
0.913711 + 0.406364i \(0.133203\pi\)
\(938\) −15.1015 + 10.9719i −0.493082 + 0.358245i
\(939\) −18.8298 13.6807i −0.614489 0.446452i
\(940\) 12.9857 + 39.9659i 0.423547 + 1.30354i
\(941\) −10.4244 32.0831i −0.339826 1.04588i −0.964296 0.264829i \(-0.914685\pi\)
0.624469 0.781049i \(-0.285315\pi\)
\(942\) −4.73186 3.43790i −0.154172 0.112013i
\(943\) 59.3499 43.1203i 1.93270 1.40419i
\(944\) −13.0767 + 40.2458i −0.425609 + 1.30989i
\(945\) −2.93054 −0.0953304
\(946\) 12.8854 + 14.4589i 0.418941 + 0.470101i
\(947\) −3.21082 −0.104338 −0.0521688 0.998638i \(-0.516613\pi\)
−0.0521688 + 0.998638i \(0.516613\pi\)
\(948\) −3.77843 + 11.6288i −0.122718 + 0.377686i
\(949\) −2.85886 + 2.07709i −0.0928026 + 0.0674250i
\(950\) 4.38226 + 3.18390i 0.142179 + 0.103299i
\(951\) 5.50231 + 16.9344i 0.178425 + 0.549135i
\(952\) 0.301106 + 0.926710i 0.00975891 + 0.0300348i
\(953\) 1.57601 + 1.14504i 0.0510518 + 0.0370913i 0.613019 0.790069i \(-0.289955\pi\)
−0.561967 + 0.827160i \(0.689955\pi\)
\(954\) 14.4458 10.4955i 0.467701 0.339805i
\(955\) −0.690447 + 2.12498i −0.0223423 + 0.0687627i
\(956\) 3.48992 0.112872
\(957\) 16.6941 28.5760i 0.539643 0.923731i
\(958\) −52.2018 −1.68656
\(959\) 5.80367 17.8619i 0.187410 0.576790i
\(960\) −4.31822 + 3.13737i −0.139370 + 0.101258i
\(961\) −17.7976 12.9307i −0.574116 0.417120i
\(962\) 4.16229 + 12.8102i 0.134198 + 0.413018i
\(963\) −1.55570 4.78794i −0.0501316 0.154289i
\(964\) 15.5183 + 11.2747i 0.499811 + 0.363134i
\(965\) 18.6751 13.5683i 0.601173 0.436777i
\(966\) 4.65819 14.3364i 0.149875 0.461267i
\(967\) 33.4224 1.07479 0.537396 0.843330i \(-0.319408\pi\)
0.537396 + 0.843330i \(0.319408\pi\)
\(968\) −11.8201 5.40841i −0.379913 0.173833i
\(969\) −3.85934 −0.123980
\(970\) −3.53022 + 10.8649i −0.113349 + 0.348851i
\(971\) −2.61592 + 1.90058i −0.0839488 + 0.0609924i −0.628968 0.777431i \(-0.716522\pi\)
0.545019 + 0.838424i \(0.316522\pi\)
\(972\) 1.09608 + 0.796352i 0.0351569 + 0.0255430i
\(973\) −0.495490 1.52496i −0.0158847 0.0488880i
\(974\) −2.09741 6.45516i −0.0672053 0.206837i
\(975\) −0.409307 0.297379i −0.0131083 0.00952374i
\(976\) 38.3013 27.8275i 1.22599 0.890737i
\(977\) −10.8607 + 33.4258i −0.347464 + 1.06939i 0.612787 + 0.790248i \(0.290048\pi\)
−0.960251 + 0.279137i \(0.909952\pi\)
\(978\) 9.62249 0.307693
\(979\) −22.8550 + 39.1220i −0.730450 + 1.25034i
\(980\) −17.2949 −0.552465
\(981\) −1.39438 + 4.29147i −0.0445192 + 0.137016i
\(982\) −53.4272 + 38.8171i −1.70493 + 1.23870i
\(983\) −31.1949 22.6644i −0.994963 0.722883i −0.0339608 0.999423i \(-0.510812\pi\)
−0.961002 + 0.276540i \(0.910812\pi\)
\(984\) 4.06523 + 12.5115i 0.129595 + 0.398852i
\(985\) 4.51642 + 13.9001i 0.143905 + 0.442894i
\(986\) −9.76243 7.09282i −0.310899 0.225881i
\(987\) 13.3558 9.70358i 0.425121 0.308868i
\(988\) 2.44727 7.53193i 0.0778581 0.239623i
\(989\) 21.0090 0.668048
\(990\) −9.48364 10.6418i −0.301410 0.338217i
\(991\) −23.7277 −0.753737 −0.376868 0.926267i \(-0.622999\pi\)
−0.376868 + 0.926267i \(0.622999\pi\)
\(992\) 14.7670 45.4480i 0.468851 1.44298i
\(993\) 19.4399 14.1239i 0.616907 0.448209i
\(994\) 21.1019 + 15.3314i 0.669311 + 0.486283i
\(995\) 14.2590 + 43.8845i 0.452039 + 1.39123i
\(996\) −3.88844 11.9674i −0.123210 0.379201i
\(997\) 12.0832 + 8.77898i 0.382680 + 0.278033i 0.762449 0.647048i \(-0.223997\pi\)
−0.379770 + 0.925081i \(0.623997\pi\)
\(998\) 39.3735 28.6065i 1.24635 0.905524i
\(999\) 2.27246 6.99392i 0.0718976 0.221278i
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 429.2.n.b.196.4 20
11.4 even 5 4719.2.a.bn.1.8 10
11.5 even 5 inner 429.2.n.b.313.4 yes 20
11.7 odd 10 4719.2.a.bi.1.3 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
429.2.n.b.196.4 20 1.1 even 1 trivial
429.2.n.b.313.4 yes 20 11.5 even 5 inner
4719.2.a.bi.1.3 10 11.7 odd 10
4719.2.a.bn.1.8 10 11.4 even 5