Properties

Label 80.2.l.a.61.8
Level $80$
Weight $2$
Character 80.61
Analytic conductor $0.639$
Analytic rank $0$
Dimension $16$
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] = [80,2,Mod(21,80)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(80, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("80.21");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 80.l (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.638803216170\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} - 112 x^{6} - 64 x^{5} + 112 x^{4} + 256 x^{2} - 512 x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 61.8
Root \(1.38652 + 0.278517i\) of defining polynomial
Character \(\chi\) \(=\) 80.61
Dual form 80.2.l.a.21.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.40727 + 0.139945i) q^{2} +(-2.32624 - 2.32624i) q^{3} +(1.96083 + 0.393883i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-2.94811 - 3.59920i) q^{6} +0.982011i q^{7} +(2.70430 + 0.828709i) q^{8} +7.82281i q^{9} +O(q^{10})\) \(q+(1.40727 + 0.139945i) q^{2} +(-2.32624 - 2.32624i) q^{3} +(1.96083 + 0.393883i) q^{4} +(0.707107 - 0.707107i) q^{5} +(-2.94811 - 3.59920i) q^{6} +0.982011i q^{7} +(2.70430 + 0.828709i) q^{8} +7.82281i q^{9} +(1.09405 - 0.896135i) q^{10} +(-1.62645 + 1.62645i) q^{11} +(-3.64510 - 5.47764i) q^{12} +(-0.690562 - 0.690562i) q^{13} +(-0.137428 + 1.38196i) q^{14} -3.28980 q^{15} +(3.68971 + 1.54467i) q^{16} -2.19577 q^{17} +(-1.09477 + 11.0088i) q^{18} +(1.92659 + 1.92659i) q^{19} +(1.66503 - 1.10800i) q^{20} +(2.28440 - 2.28440i) q^{21} +(-2.51647 + 2.06124i) q^{22} -2.01442i q^{23} +(-4.36308 - 8.21864i) q^{24} -1.00000i q^{25} +(-0.875168 - 1.06845i) q^{26} +(11.2190 - 11.2190i) q^{27} +(-0.386797 + 1.92556i) q^{28} +(-5.27182 - 5.27182i) q^{29} +(-4.62965 - 0.460393i) q^{30} +0.435286 q^{31} +(4.97626 + 2.69014i) q^{32} +7.56703 q^{33} +(-3.09004 - 0.307288i) q^{34} +(0.694387 + 0.694387i) q^{35} +(-3.08127 + 15.3392i) q^{36} +(-5.79805 + 5.79805i) q^{37} +(2.44162 + 2.98086i) q^{38} +3.21283i q^{39} +(2.49822 - 1.32624i) q^{40} -3.93139i q^{41} +(3.53446 - 2.89508i) q^{42} +(-0.507592 + 0.507592i) q^{43} +(-3.82982 + 2.54856i) q^{44} +(5.53157 + 5.53157i) q^{45} +(0.281909 - 2.83484i) q^{46} -9.21960 q^{47} +(-4.98988 - 12.1765i) q^{48} +6.03565 q^{49} +(0.139945 - 1.40727i) q^{50} +(5.10789 + 5.10789i) q^{51} +(-1.08208 - 1.62608i) q^{52} +(6.29357 - 6.29357i) q^{53} +(17.3583 - 14.2182i) q^{54} +2.30015i q^{55} +(-0.813802 + 2.65565i) q^{56} -8.96345i q^{57} +(-6.68111 - 8.15665i) q^{58} +(-5.67778 + 5.67778i) q^{59} +(-6.45075 - 1.29580i) q^{60} +(-3.60301 - 3.60301i) q^{61} +(0.612566 + 0.0609163i) q^{62} -7.68209 q^{63} +(6.62648 + 4.48216i) q^{64} -0.976603 q^{65} +(10.6489 + 1.05897i) q^{66} +(4.53563 + 4.53563i) q^{67} +(-4.30553 - 0.864875i) q^{68} +(-4.68603 + 4.68603i) q^{69} +(0.880015 + 1.07437i) q^{70} -10.3984i q^{71} +(-6.48284 + 21.1552i) q^{72} +9.24439i q^{73} +(-8.97085 + 7.34803i) q^{74} +(-2.32624 + 2.32624i) q^{75} +(3.01887 + 4.53658i) q^{76} +(-1.59719 - 1.59719i) q^{77} +(-0.449621 + 4.52133i) q^{78} +15.4493 q^{79} +(3.70127 - 1.51677i) q^{80} -28.7280 q^{81} +(0.550180 - 5.53253i) q^{82} +(-0.683244 - 0.683244i) q^{83} +(5.37910 - 3.57953i) q^{84} +(-1.55264 + 1.55264i) q^{85} +(-0.785356 + 0.643285i) q^{86} +24.5271i q^{87} +(-5.74626 + 3.05055i) q^{88} -5.44401i q^{89} +(7.01030 + 8.55854i) q^{90} +(0.678140 - 0.678140i) q^{91} +(0.793445 - 3.94994i) q^{92} +(-1.01258 - 1.01258i) q^{93} +(-12.9745 - 1.29024i) q^{94} +2.72461 q^{95} +(-5.31808 - 17.8339i) q^{96} +5.54540 q^{97} +(8.49381 + 0.844662i) q^{98} +(-12.7234 - 12.7234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} - 16 q^{37} + 20 q^{38} + 60 q^{42} + 8 q^{43} + 40 q^{44} - 4 q^{46} - 40 q^{47} - 40 q^{48} - 16 q^{49} - 4 q^{50} - 32 q^{51} + 56 q^{52} + 16 q^{53} + 32 q^{54} + 16 q^{56} - 12 q^{58} - 8 q^{59} - 28 q^{60} + 16 q^{61} - 8 q^{62} + 40 q^{63} - 16 q^{64} + 40 q^{67} - 48 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{72} - 72 q^{74} + 16 q^{77} - 16 q^{78} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 76 q^{82} + 40 q^{83} - 64 q^{84} - 16 q^{85} + 28 q^{86} + 36 q^{90} + 32 q^{91} - 52 q^{92} - 48 q^{93} - 36 q^{94} + 32 q^{95} + 8 q^{96} + 60 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40727 + 0.139945i 0.995092 + 0.0989564i
\(3\) −2.32624 2.32624i −1.34306 1.34306i −0.893000 0.450058i \(-0.851403\pi\)
−0.450058 0.893000i \(-0.648597\pi\)
\(4\) 1.96083 + 0.393883i 0.980415 + 0.196941i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) −2.94811 3.59920i −1.20356 1.46937i
\(7\) 0.982011i 0.371165i 0.982629 + 0.185583i \(0.0594172\pi\)
−0.982629 + 0.185583i \(0.940583\pi\)
\(8\) 2.70430 + 0.828709i 0.956115 + 0.292993i
\(9\) 7.82281i 2.60760i
\(10\) 1.09405 0.896135i 0.345968 0.283383i
\(11\) −1.62645 + 1.62645i −0.490393 + 0.490393i −0.908430 0.418037i \(-0.862718\pi\)
0.418037 + 0.908430i \(0.362718\pi\)
\(12\) −3.64510 5.47764i −1.05225 1.58126i
\(13\) −0.690562 0.690562i −0.191528 0.191528i 0.604828 0.796356i \(-0.293242\pi\)
−0.796356 + 0.604828i \(0.793242\pi\)
\(14\) −0.137428 + 1.38196i −0.0367292 + 0.369344i
\(15\) −3.28980 −0.849424
\(16\) 3.68971 + 1.54467i 0.922428 + 0.386169i
\(17\) −2.19577 −0.532552 −0.266276 0.963897i \(-0.585793\pi\)
−0.266276 + 0.963897i \(0.585793\pi\)
\(18\) −1.09477 + 11.0088i −0.258039 + 2.59481i
\(19\) 1.92659 + 1.92659i 0.441991 + 0.441991i 0.892681 0.450690i \(-0.148822\pi\)
−0.450690 + 0.892681i \(0.648822\pi\)
\(20\) 1.66503 1.10800i 0.372313 0.247756i
\(21\) 2.28440 2.28440i 0.498496 0.498496i
\(22\) −2.51647 + 2.06124i −0.536513 + 0.439458i
\(23\) 2.01442i 0.420035i −0.977698 0.210018i \(-0.932648\pi\)
0.977698 0.210018i \(-0.0673522\pi\)
\(24\) −4.36308 8.21864i −0.890610 1.67762i
\(25\) 1.00000i 0.200000i
\(26\) −0.875168 1.06845i −0.171635 0.209540i
\(27\) 11.2190 11.2190i 2.15911 2.15911i
\(28\) −0.386797 + 1.92556i −0.0730978 + 0.363896i
\(29\) −5.27182 5.27182i −0.978952 0.978952i 0.0208314 0.999783i \(-0.493369\pi\)
−0.999783 + 0.0208314i \(0.993369\pi\)
\(30\) −4.62965 0.460393i −0.845255 0.0840559i
\(31\) 0.435286 0.0781797 0.0390898 0.999236i \(-0.487554\pi\)
0.0390898 + 0.999236i \(0.487554\pi\)
\(32\) 4.97626 + 2.69014i 0.879687 + 0.475553i
\(33\) 7.56703 1.31725
\(34\) −3.09004 0.307288i −0.529938 0.0526994i
\(35\) 0.694387 + 0.694387i 0.117373 + 0.117373i
\(36\) −3.08127 + 15.3392i −0.513545 + 2.55654i
\(37\) −5.79805 + 5.79805i −0.953194 + 0.953194i −0.998953 0.0457583i \(-0.985430\pi\)
0.0457583 + 0.998953i \(0.485430\pi\)
\(38\) 2.44162 + 2.98086i 0.396084 + 0.483559i
\(39\) 3.21283i 0.514465i
\(40\) 2.49822 1.32624i 0.395003 0.209697i
\(41\) 3.93139i 0.613980i −0.951713 0.306990i \(-0.900678\pi\)
0.951713 0.306990i \(-0.0993218\pi\)
\(42\) 3.53446 2.89508i 0.545379 0.446720i
\(43\) −0.507592 + 0.507592i −0.0774071 + 0.0774071i −0.744750 0.667343i \(-0.767431\pi\)
0.667343 + 0.744750i \(0.267431\pi\)
\(44\) −3.82982 + 2.54856i −0.577367 + 0.384210i
\(45\) 5.53157 + 5.53157i 0.824597 + 0.824597i
\(46\) 0.281909 2.83484i 0.0415652 0.417974i
\(47\) −9.21960 −1.34482 −0.672409 0.740180i \(-0.734740\pi\)
−0.672409 + 0.740180i \(0.734740\pi\)
\(48\) −4.98988 12.1765i −0.720227 1.75752i
\(49\) 6.03565 0.862236
\(50\) 0.139945 1.40727i 0.0197913 0.199018i
\(51\) 5.10789 + 5.10789i 0.715248 + 0.715248i
\(52\) −1.08208 1.62608i −0.150057 0.225496i
\(53\) 6.29357 6.29357i 0.864488 0.864488i −0.127367 0.991856i \(-0.540653\pi\)
0.991856 + 0.127367i \(0.0406527\pi\)
\(54\) 17.3583 14.2182i 2.36216 1.93485i
\(55\) 2.30015i 0.310152i
\(56\) −0.813802 + 2.65565i −0.108749 + 0.354877i
\(57\) 8.96345i 1.18724i
\(58\) −6.68111 8.15665i −0.877273 1.07102i
\(59\) −5.67778 + 5.67778i −0.739183 + 0.739183i −0.972420 0.233237i \(-0.925068\pi\)
0.233237 + 0.972420i \(0.425068\pi\)
\(60\) −6.45075 1.29580i −0.832788 0.167287i
\(61\) −3.60301 3.60301i −0.461318 0.461318i 0.437770 0.899087i \(-0.355769\pi\)
−0.899087 + 0.437770i \(0.855769\pi\)
\(62\) 0.612566 + 0.0609163i 0.0777959 + 0.00773637i
\(63\) −7.68209 −0.967852
\(64\) 6.62648 + 4.48216i 0.828310 + 0.560270i
\(65\) −0.976603 −0.121133
\(66\) 10.6489 + 1.05897i 1.31079 + 0.130350i
\(67\) 4.53563 + 4.53563i 0.554116 + 0.554116i 0.927626 0.373510i \(-0.121846\pi\)
−0.373510 + 0.927626i \(0.621846\pi\)
\(68\) −4.30553 0.864875i −0.522122 0.104882i
\(69\) −4.68603 + 4.68603i −0.564132 + 0.564132i
\(70\) 0.880015 + 1.07437i 0.105182 + 0.128411i
\(71\) 10.3984i 1.23407i −0.786937 0.617033i \(-0.788335\pi\)
0.786937 0.617033i \(-0.211665\pi\)
\(72\) −6.48284 + 21.1552i −0.764010 + 2.49317i
\(73\) 9.24439i 1.08197i 0.841031 + 0.540987i \(0.181949\pi\)
−0.841031 + 0.540987i \(0.818051\pi\)
\(74\) −8.97085 + 7.34803i −1.04284 + 0.854191i
\(75\) −2.32624 + 2.32624i −0.268611 + 0.268611i
\(76\) 3.01887 + 4.53658i 0.346288 + 0.520381i
\(77\) −1.59719 1.59719i −0.182017 0.182017i
\(78\) −0.449621 + 4.52133i −0.0509096 + 0.511940i
\(79\) 15.4493 1.73818 0.869091 0.494653i \(-0.164705\pi\)
0.869091 + 0.494653i \(0.164705\pi\)
\(80\) 3.70127 1.51677i 0.413815 0.169580i
\(81\) −28.7280 −3.19200
\(82\) 0.550180 5.53253i 0.0607572 0.610966i
\(83\) −0.683244 0.683244i −0.0749957 0.0749957i 0.668614 0.743610i \(-0.266888\pi\)
−0.743610 + 0.668614i \(0.766888\pi\)
\(84\) 5.37910 3.57953i 0.586908 0.390559i
\(85\) −1.55264 + 1.55264i −0.168408 + 0.168408i
\(86\) −0.785356 + 0.643285i −0.0846871 + 0.0693672i
\(87\) 24.5271i 2.62958i
\(88\) −5.74626 + 3.05055i −0.612553 + 0.325190i
\(89\) 5.44401i 0.577064i −0.957470 0.288532i \(-0.906833\pi\)
0.957470 0.288532i \(-0.0931672\pi\)
\(90\) 7.01030 + 8.55854i 0.738951 + 0.902149i
\(91\) 0.678140 0.678140i 0.0710884 0.0710884i
\(92\) 0.793445 3.94994i 0.0827223 0.411809i
\(93\) −1.01258 1.01258i −0.105000 0.105000i
\(94\) −12.9745 1.29024i −1.33822 0.133078i
\(95\) 2.72461 0.279540
\(96\) −5.31808 17.8339i −0.542775 1.82016i
\(97\) 5.54540 0.563050 0.281525 0.959554i \(-0.409160\pi\)
0.281525 + 0.959554i \(0.409160\pi\)
\(98\) 8.49381 + 0.844662i 0.858004 + 0.0853238i
\(99\) −12.7234 12.7234i −1.27875 1.27875i
\(100\) 0.393883 1.96083i 0.0393883 0.196083i
\(101\) −0.291294 + 0.291294i −0.0289848 + 0.0289848i −0.721451 0.692466i \(-0.756524\pi\)
0.692466 + 0.721451i \(0.256524\pi\)
\(102\) 6.47337 + 7.90302i 0.640959 + 0.782516i
\(103\) 4.50219i 0.443614i −0.975091 0.221807i \(-0.928805\pi\)
0.975091 0.221807i \(-0.0711955\pi\)
\(104\) −1.29521 2.43976i −0.127006 0.239239i
\(105\) 3.23062i 0.315277i
\(106\) 9.73752 7.97601i 0.945792 0.774698i
\(107\) −6.49890 + 6.49890i −0.628272 + 0.628272i −0.947633 0.319361i \(-0.896532\pi\)
0.319361 + 0.947633i \(0.396532\pi\)
\(108\) 26.4176 17.5796i 2.54204 1.69160i
\(109\) −2.51950 2.51950i −0.241324 0.241324i 0.576074 0.817398i \(-0.304584\pi\)
−0.817398 + 0.576074i \(0.804584\pi\)
\(110\) −0.321895 + 3.23693i −0.0306915 + 0.308629i
\(111\) 26.9754 2.56039
\(112\) −1.51689 + 3.62334i −0.143332 + 0.342373i
\(113\) 5.38101 0.506203 0.253102 0.967440i \(-0.418549\pi\)
0.253102 + 0.967440i \(0.418549\pi\)
\(114\) 1.25439 12.6140i 0.117485 1.18141i
\(115\) −1.42441 1.42441i −0.132827 0.132827i
\(116\) −8.26066 12.4136i −0.766983 1.15258i
\(117\) 5.40214 5.40214i 0.499428 0.499428i
\(118\) −8.78476 + 7.19560i −0.808702 + 0.662408i
\(119\) 2.15627i 0.197665i
\(120\) −8.89662 2.72629i −0.812147 0.248875i
\(121\) 5.70933i 0.519030i
\(122\) −4.56619 5.57464i −0.413403 0.504704i
\(123\) −9.14536 + 9.14536i −0.824610 + 0.824610i
\(124\) 0.853522 + 0.171452i 0.0766485 + 0.0153968i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) −10.8108 1.07507i −0.963102 0.0957751i
\(127\) 4.86578 0.431768 0.215884 0.976419i \(-0.430737\pi\)
0.215884 + 0.976419i \(0.430737\pi\)
\(128\) 8.69801 + 7.23496i 0.768802 + 0.639486i
\(129\) 2.36157 0.207924
\(130\) −1.37435 0.136671i −0.120538 0.0119868i
\(131\) 8.00581 + 8.00581i 0.699471 + 0.699471i 0.964296 0.264825i \(-0.0853143\pi\)
−0.264825 + 0.964296i \(0.585314\pi\)
\(132\) 14.8377 + 2.98052i 1.29145 + 0.259421i
\(133\) −1.89194 + 1.89194i −0.164052 + 0.164052i
\(134\) 5.74813 + 7.01761i 0.496563 + 0.606229i
\(135\) 15.8661i 1.36554i
\(136\) −5.93802 1.81965i −0.509181 0.156034i
\(137\) 13.5567i 1.15822i 0.815248 + 0.579112i \(0.196601\pi\)
−0.815248 + 0.579112i \(0.803399\pi\)
\(138\) −7.25031 + 5.93873i −0.617187 + 0.505538i
\(139\) 8.22645 8.22645i 0.697758 0.697758i −0.266168 0.963927i \(-0.585758\pi\)
0.963927 + 0.266168i \(0.0857577\pi\)
\(140\) 1.08807 + 1.63508i 0.0919585 + 0.138190i
\(141\) 21.4470 + 21.4470i 1.80617 + 1.80617i
\(142\) 1.45521 14.6334i 0.122119 1.22801i
\(143\) 2.24633 0.187847
\(144\) −12.0837 + 28.8639i −1.00697 + 2.40533i
\(145\) −7.45547 −0.619143
\(146\) −1.29371 + 13.0094i −0.107068 + 1.07666i
\(147\) −14.0404 14.0404i −1.15803 1.15803i
\(148\) −13.6528 + 9.08525i −1.12225 + 0.746803i
\(149\) 12.6363 12.6363i 1.03521 1.03521i 0.0358519 0.999357i \(-0.488586\pi\)
0.999357 0.0358519i \(-0.0114144\pi\)
\(150\) −3.59920 + 2.94811i −0.293874 + 0.240712i
\(151\) 15.1562i 1.23339i −0.787201 0.616696i \(-0.788471\pi\)
0.787201 0.616696i \(-0.211529\pi\)
\(152\) 3.61350 + 6.80667i 0.293094 + 0.552094i
\(153\) 17.1771i 1.38869i
\(154\) −2.02416 2.47120i −0.163112 0.199135i
\(155\) 0.307794 0.307794i 0.0247226 0.0247226i
\(156\) −1.26548 + 6.29982i −0.101319 + 0.504389i
\(157\) −1.75816 1.75816i −0.140316 0.140316i 0.633460 0.773776i \(-0.281634\pi\)
−0.773776 + 0.633460i \(0.781634\pi\)
\(158\) 21.7414 + 2.16206i 1.72965 + 0.172004i
\(159\) −29.2807 −2.32211
\(160\) 5.42096 1.61653i 0.428565 0.127798i
\(161\) 1.97818 0.155903
\(162\) −40.4281 4.02035i −3.17633 0.315868i
\(163\) −13.9102 13.9102i −1.08953 1.08953i −0.995576 0.0939562i \(-0.970049\pi\)
−0.0939562 0.995576i \(-0.529951\pi\)
\(164\) 1.54851 7.70879i 0.120918 0.601955i
\(165\) 5.35070 5.35070i 0.416551 0.416551i
\(166\) −0.865893 1.05713i −0.0672063 0.0820490i
\(167\) 18.8620i 1.45958i −0.683669 0.729792i \(-0.739617\pi\)
0.683669 0.729792i \(-0.260383\pi\)
\(168\) 8.07079 4.28459i 0.622675 0.330564i
\(169\) 12.0462i 0.926634i
\(170\) −2.40228 + 1.96771i −0.184246 + 0.150916i
\(171\) −15.0714 + 15.0714i −1.15254 + 1.15254i
\(172\) −1.19523 + 0.795370i −0.0911357 + 0.0606464i
\(173\) 16.0724 + 16.0724i 1.22196 + 1.22196i 0.966933 + 0.255031i \(0.0820856\pi\)
0.255031 + 0.966933i \(0.417914\pi\)
\(174\) −3.43245 + 34.5162i −0.260213 + 2.61667i
\(175\) 0.982011 0.0742331
\(176\) −8.51346 + 3.48879i −0.641726 + 0.262978i
\(177\) 26.4158 1.98553
\(178\) 0.761865 7.66121i 0.0571042 0.574232i
\(179\) 16.4341 + 16.4341i 1.22834 + 1.22834i 0.964591 + 0.263749i \(0.0849591\pi\)
0.263749 + 0.964591i \(0.415041\pi\)
\(180\) 8.66767 + 13.0252i 0.646050 + 0.970845i
\(181\) −15.4539 + 15.4539i −1.14868 + 1.14868i −0.161870 + 0.986812i \(0.551753\pi\)
−0.986812 + 0.161870i \(0.948247\pi\)
\(182\) 1.04923 0.859425i 0.0777741 0.0637048i
\(183\) 16.7629i 1.23915i
\(184\) 1.66937 5.44760i 0.123067 0.401602i
\(185\) 8.19969i 0.602853i
\(186\) −1.28327 1.56668i −0.0940940 0.114875i
\(187\) 3.57130 3.57130i 0.261160 0.261160i
\(188\) −18.0781 3.63144i −1.31848 0.264850i
\(189\) 11.0172 + 11.0172i 0.801385 + 0.801385i
\(190\) 3.83427 + 0.381297i 0.278168 + 0.0276622i
\(191\) −14.7872 −1.06997 −0.534983 0.844863i \(-0.679682\pi\)
−0.534983 + 0.844863i \(0.679682\pi\)
\(192\) −4.98822 25.8414i −0.359994 1.86494i
\(193\) −11.2912 −0.812758 −0.406379 0.913705i \(-0.633209\pi\)
−0.406379 + 0.913705i \(0.633209\pi\)
\(194\) 7.80388 + 0.776053i 0.560286 + 0.0557173i
\(195\) 2.27182 + 2.27182i 0.162688 + 0.162688i
\(196\) 11.8349 + 2.37734i 0.845350 + 0.169810i
\(197\) −10.6152 + 10.6152i −0.756302 + 0.756302i −0.975647 0.219345i \(-0.929608\pi\)
0.219345 + 0.975647i \(0.429608\pi\)
\(198\) −16.1247 19.6859i −1.14593 1.39901i
\(199\) 4.68789i 0.332316i 0.986099 + 0.166158i \(0.0531361\pi\)
−0.986099 + 0.166158i \(0.946864\pi\)
\(200\) 0.828709 2.70430i 0.0585986 0.191223i
\(201\) 21.1020i 1.48842i
\(202\) −0.450695 + 0.369165i −0.0317108 + 0.0259743i
\(203\) 5.17698 5.17698i 0.363353 0.363353i
\(204\) 8.00380 + 12.0276i 0.560378 + 0.842102i
\(205\) −2.77991 2.77991i −0.194157 0.194157i
\(206\) 0.630061 6.33581i 0.0438984 0.441437i
\(207\) 15.7584 1.09529
\(208\) −1.48128 3.61467i −0.102709 0.250632i
\(209\) −6.26701 −0.433498
\(210\) 0.452111 4.54637i 0.0311986 0.313729i
\(211\) −2.63215 2.63215i −0.181205 0.181205i 0.610676 0.791881i \(-0.290898\pi\)
−0.791881 + 0.610676i \(0.790898\pi\)
\(212\) 14.8195 9.86169i 1.01781 0.677304i
\(213\) −24.1893 + 24.1893i −1.65742 + 1.65742i
\(214\) −10.0552 + 8.23623i −0.687360 + 0.563017i
\(215\) 0.717844i 0.0489565i
\(216\) 39.6370 21.0423i 2.69695 1.43175i
\(217\) 0.427456i 0.0290176i
\(218\) −3.19303 3.89821i −0.216259 0.264020i
\(219\) 21.5047 21.5047i 1.45315 1.45315i
\(220\) −0.905987 + 4.51020i −0.0610816 + 0.304077i
\(221\) 1.51632 + 1.51632i 0.101998 + 0.101998i
\(222\) 37.9617 + 3.77508i 2.54782 + 0.253367i
\(223\) 3.45644 0.231461 0.115730 0.993281i \(-0.463079\pi\)
0.115730 + 0.993281i \(0.463079\pi\)
\(224\) −2.64174 + 4.88674i −0.176509 + 0.326509i
\(225\) 7.82281 0.521521
\(226\) 7.57255 + 0.753048i 0.503719 + 0.0500920i
\(227\) −4.74550 4.74550i −0.314970 0.314970i 0.531862 0.846831i \(-0.321493\pi\)
−0.846831 + 0.531862i \(0.821493\pi\)
\(228\) 3.53055 17.5758i 0.233816 1.16399i
\(229\) −13.3576 + 13.3576i −0.882697 + 0.882697i −0.993808 0.111111i \(-0.964559\pi\)
0.111111 + 0.993808i \(0.464559\pi\)
\(230\) −1.80519 2.20387i −0.119031 0.145319i
\(231\) 7.43091i 0.488918i
\(232\) −9.88777 18.6254i −0.649164 1.22282i
\(233\) 4.82691i 0.316222i 0.987421 + 0.158111i \(0.0505403\pi\)
−0.987421 + 0.158111i \(0.949460\pi\)
\(234\) 8.35829 6.84628i 0.546399 0.447555i
\(235\) −6.51924 + 6.51924i −0.425269 + 0.425269i
\(236\) −13.3695 + 8.89678i −0.870282 + 0.579131i
\(237\) −35.9388 35.9388i −2.33448 2.33448i
\(238\) 0.301760 3.03446i 0.0195602 0.196695i
\(239\) −8.82497 −0.570840 −0.285420 0.958403i \(-0.592133\pi\)
−0.285420 + 0.958403i \(0.592133\pi\)
\(240\) −12.1384 5.08168i −0.783533 0.328021i
\(241\) −3.74147 −0.241009 −0.120504 0.992713i \(-0.538451\pi\)
−0.120504 + 0.992713i \(0.538451\pi\)
\(242\) −0.798995 + 8.03458i −0.0513613 + 0.516483i
\(243\) 33.1712 + 33.1712i 2.12793 + 2.12793i
\(244\) −5.64572 8.48405i −0.361430 0.543135i
\(245\) 4.26785 4.26785i 0.272663 0.272663i
\(246\) −14.1499 + 11.5902i −0.902163 + 0.738962i
\(247\) 2.66087i 0.169307i
\(248\) 1.17714 + 0.360725i 0.0747487 + 0.0229061i
\(249\) 3.17878i 0.201447i
\(250\) −0.896135 1.09405i −0.0566766 0.0691937i
\(251\) −5.99322 + 5.99322i −0.378289 + 0.378289i −0.870484 0.492196i \(-0.836194\pi\)
0.492196 + 0.870484i \(0.336194\pi\)
\(252\) −15.0633 3.02584i −0.948897 0.190610i
\(253\) 3.27635 + 3.27635i 0.205982 + 0.205982i
\(254\) 6.84748 + 0.680944i 0.429649 + 0.0427262i
\(255\) 7.22365 0.452362
\(256\) 11.2280 + 11.3988i 0.701748 + 0.712426i
\(257\) −14.7662 −0.921091 −0.460545 0.887636i \(-0.652346\pi\)
−0.460545 + 0.887636i \(0.652346\pi\)
\(258\) 3.32337 + 0.330490i 0.206904 + 0.0205754i
\(259\) −5.69375 5.69375i −0.353793 0.353793i
\(260\) −1.91495 0.384667i −0.118760 0.0238560i
\(261\) 41.2404 41.2404i 2.55272 2.55272i
\(262\) 10.1460 + 12.3867i 0.626821 + 0.765255i
\(263\) 6.79486i 0.418989i 0.977810 + 0.209494i \(0.0671818\pi\)
−0.977810 + 0.209494i \(0.932818\pi\)
\(264\) 20.4635 + 6.27087i 1.25944 + 0.385945i
\(265\) 8.90045i 0.546750i
\(266\) −2.92724 + 2.39770i −0.179480 + 0.147013i
\(267\) −12.6641 + 12.6641i −0.775030 + 0.775030i
\(268\) 7.10710 + 10.6801i 0.434135 + 0.652392i
\(269\) −6.03990 6.03990i −0.368259 0.368259i 0.498583 0.866842i \(-0.333854\pi\)
−0.866842 + 0.498583i \(0.833854\pi\)
\(270\) 2.22039 22.3279i 0.135129 1.35884i
\(271\) −24.6221 −1.49568 −0.747842 0.663877i \(-0.768910\pi\)
−0.747842 + 0.663877i \(0.768910\pi\)
\(272\) −8.10175 3.39175i −0.491241 0.205655i
\(273\) −3.15504 −0.190952
\(274\) −1.89719 + 19.0779i −0.114614 + 1.15254i
\(275\) 1.62645 + 1.62645i 0.0980785 + 0.0980785i
\(276\) −11.0343 + 7.34276i −0.664184 + 0.441982i
\(277\) 9.98018 9.98018i 0.599651 0.599651i −0.340569 0.940220i \(-0.610620\pi\)
0.940220 + 0.340569i \(0.110620\pi\)
\(278\) 12.7281 10.4256i 0.763381 0.625286i
\(279\) 3.40516i 0.203862i
\(280\) 1.30239 + 2.45327i 0.0778324 + 0.146611i
\(281\) 14.4611i 0.862675i 0.902191 + 0.431337i \(0.141958\pi\)
−0.902191 + 0.431337i \(0.858042\pi\)
\(282\) 27.1804 + 33.1832i 1.61857 + 1.97603i
\(283\) 20.0783 20.0783i 1.19353 1.19353i 0.217462 0.976069i \(-0.430222\pi\)
0.976069 0.217462i \(-0.0697777\pi\)
\(284\) 4.09576 20.3895i 0.243039 1.20990i
\(285\) −6.33812 6.33812i −0.375438 0.375438i
\(286\) 3.16120 + 0.314363i 0.186925 + 0.0185887i
\(287\) 3.86067 0.227888
\(288\) −21.0444 + 38.9284i −1.24006 + 2.29388i
\(289\) −12.1786 −0.716388
\(290\) −10.4919 1.04336i −0.616104 0.0612682i
\(291\) −12.8999 12.8999i −0.756208 0.756208i
\(292\) −3.64121 + 18.1267i −0.213085 + 1.06078i
\(293\) 15.4038 15.4038i 0.899899 0.899899i −0.0955279 0.995427i \(-0.530454\pi\)
0.995427 + 0.0955279i \(0.0304539\pi\)
\(294\) −17.7938 21.7236i −1.03775 1.26694i
\(295\) 8.02959i 0.467501i
\(296\) −20.4846 + 10.8748i −1.19064 + 0.632084i
\(297\) 36.4944i 2.11762i
\(298\) 19.5512 16.0144i 1.13257 0.927687i
\(299\) −1.39108 + 1.39108i −0.0804484 + 0.0804484i
\(300\) −5.47764 + 3.64510i −0.316251 + 0.210450i
\(301\) −0.498461 0.498461i −0.0287308 0.0287308i
\(302\) 2.12104 21.3289i 0.122052 1.22734i
\(303\) 1.35524 0.0778566
\(304\) 4.13262 + 10.0845i 0.237022 + 0.578388i
\(305\) −5.09542 −0.291763
\(306\) 2.40385 24.1728i 0.137419 1.38187i
\(307\) 9.12398 + 9.12398i 0.520733 + 0.520733i 0.917793 0.397060i \(-0.129969\pi\)
−0.397060 + 0.917793i \(0.629969\pi\)
\(308\) −2.50271 3.76092i −0.142605 0.214299i
\(309\) −10.4732 + 10.4732i −0.595799 + 0.595799i
\(310\) 0.476224 0.390075i 0.0270477 0.0221548i
\(311\) 0.642911i 0.0364561i 0.999834 + 0.0182281i \(0.00580249\pi\)
−0.999834 + 0.0182281i \(0.994198\pi\)
\(312\) −2.66250 + 8.68846i −0.150735 + 0.491887i
\(313\) 21.3775i 1.20833i 0.796860 + 0.604164i \(0.206493\pi\)
−0.796860 + 0.604164i \(0.793507\pi\)
\(314\) −2.22816 2.72025i −0.125742 0.153513i
\(315\) −5.43206 + 5.43206i −0.306062 + 0.306062i
\(316\) 30.2935 + 6.08521i 1.70414 + 0.342320i
\(317\) 8.66200 + 8.66200i 0.486507 + 0.486507i 0.907202 0.420695i \(-0.138214\pi\)
−0.420695 + 0.907202i \(0.638214\pi\)
\(318\) −41.2060 4.09771i −2.31072 0.229788i
\(319\) 17.1487 0.960141
\(320\) 7.85499 1.51627i 0.439108 0.0847618i
\(321\) 30.2360 1.68761
\(322\) 2.78384 + 0.276838i 0.155137 + 0.0154276i
\(323\) −4.23035 4.23035i −0.235383 0.235383i
\(324\) −56.3307 11.3155i −3.12948 0.628636i
\(325\) −0.690562 + 0.690562i −0.0383055 + 0.0383055i
\(326\) −17.6288 21.5221i −0.976369 1.19200i
\(327\) 11.7219i 0.648224i
\(328\) 3.25798 10.6317i 0.179892 0.587035i
\(329\) 9.05375i 0.499150i
\(330\) 8.27869 6.78108i 0.455727 0.373286i
\(331\) −8.43941 + 8.43941i −0.463872 + 0.463872i −0.899922 0.436050i \(-0.856377\pi\)
0.436050 + 0.899922i \(0.356377\pi\)
\(332\) −1.07061 1.60884i −0.0587572 0.0882967i
\(333\) −45.3571 45.3571i −2.48555 2.48555i
\(334\) 2.63965 26.5440i 0.144435 1.45242i
\(335\) 6.41435 0.350454
\(336\) 11.9574 4.90012i 0.652330 0.267323i
\(337\) 30.7047 1.67259 0.836295 0.548280i \(-0.184717\pi\)
0.836295 + 0.548280i \(0.184717\pi\)
\(338\) 1.68582 16.9523i 0.0916964 0.922086i
\(339\) −12.5175 12.5175i −0.679860 0.679860i
\(340\) −3.65603 + 2.43291i −0.198276 + 0.131943i
\(341\) −0.707970 + 0.707970i −0.0383387 + 0.0383387i
\(342\) −23.3187 + 19.1004i −1.26093 + 1.03283i
\(343\) 12.8012i 0.691197i
\(344\) −1.79333 + 0.952035i −0.0966898 + 0.0513303i
\(345\) 6.62705i 0.356788i
\(346\) 20.3690 + 24.8675i 1.09504 + 1.33689i
\(347\) 13.6418 13.6418i 0.732329 0.732329i −0.238752 0.971081i \(-0.576738\pi\)
0.971081 + 0.238752i \(0.0767383\pi\)
\(348\) −9.66078 + 48.0934i −0.517872 + 2.57808i
\(349\) 9.97321 + 9.97321i 0.533854 + 0.533854i 0.921717 0.387863i \(-0.126787\pi\)
−0.387863 + 0.921717i \(0.626787\pi\)
\(350\) 1.38196 + 0.137428i 0.0738687 + 0.00734583i
\(351\) −15.4949 −0.827056
\(352\) −12.4690 + 3.71826i −0.664600 + 0.198184i
\(353\) −26.7843 −1.42559 −0.712793 0.701374i \(-0.752570\pi\)
−0.712793 + 0.701374i \(0.752570\pi\)
\(354\) 37.1742 + 3.69677i 1.97579 + 0.196481i
\(355\) −7.35280 7.35280i −0.390246 0.390246i
\(356\) 2.14430 10.6748i 0.113648 0.565763i
\(357\) −5.01601 + 5.01601i −0.265475 + 0.265475i
\(358\) 20.8273 + 25.4271i 1.10076 + 1.34386i
\(359\) 19.1190i 1.00906i 0.863393 + 0.504532i \(0.168335\pi\)
−0.863393 + 0.504532i \(0.831665\pi\)
\(360\) 10.3750 + 19.5431i 0.546808 + 1.03001i
\(361\) 11.5765i 0.609288i
\(362\) −23.9106 + 19.5852i −1.25671 + 1.02937i
\(363\) 13.2813 13.2813i 0.697087 0.697087i
\(364\) 1.59683 1.06261i 0.0836964 0.0556959i
\(365\) 6.53677 + 6.53677i 0.342150 + 0.342150i
\(366\) −2.34590 + 23.5900i −0.122622 + 1.23307i
\(367\) 4.24385 0.221527 0.110764 0.993847i \(-0.464670\pi\)
0.110764 + 0.993847i \(0.464670\pi\)
\(368\) 3.11162 7.43263i 0.162204 0.387453i
\(369\) 30.7545 1.60102
\(370\) −1.14751 + 11.5392i −0.0596561 + 0.599894i
\(371\) 6.18035 + 6.18035i 0.320868 + 0.320868i
\(372\) −1.58666 2.38434i −0.0822646 0.123622i
\(373\) 23.9514 23.9514i 1.24016 1.24016i 0.280221 0.959935i \(-0.409592\pi\)
0.959935 0.280221i \(-0.0904078\pi\)
\(374\) 5.52558 4.52601i 0.285721 0.234034i
\(375\) 3.28980i 0.169885i
\(376\) −24.9326 7.64037i −1.28580 0.394022i
\(377\) 7.28104i 0.374992i
\(378\) 13.9624 + 17.0460i 0.718149 + 0.876754i
\(379\) −7.45685 + 7.45685i −0.383033 + 0.383033i −0.872194 0.489161i \(-0.837303\pi\)
0.489161 + 0.872194i \(0.337303\pi\)
\(380\) 5.34251 + 1.07318i 0.274065 + 0.0550529i
\(381\) −11.3190 11.3190i −0.579890 0.579890i
\(382\) −20.8097 2.06941i −1.06472 0.105880i
\(383\) 5.19667 0.265538 0.132769 0.991147i \(-0.457613\pi\)
0.132769 + 0.991147i \(0.457613\pi\)
\(384\) −3.40340 37.0640i −0.173679 1.89141i
\(385\) −2.25877 −0.115117
\(386\) −15.8898 1.58015i −0.808768 0.0804275i
\(387\) −3.97080 3.97080i −0.201847 0.201847i
\(388\) 10.8736 + 2.18424i 0.552022 + 0.110888i
\(389\) 10.3846 10.3846i 0.526522 0.526522i −0.393011 0.919534i \(-0.628567\pi\)
0.919534 + 0.393011i \(0.128567\pi\)
\(390\) 2.87913 + 3.51499i 0.145791 + 0.177989i
\(391\) 4.42320i 0.223691i
\(392\) 16.3222 + 5.00180i 0.824397 + 0.252629i
\(393\) 37.2469i 1.87886i
\(394\) −16.4240 + 13.4529i −0.827431 + 0.677749i
\(395\) 10.9243 10.9243i 0.549661 0.549661i
\(396\) −19.9369 29.9600i −1.00187 1.50554i
\(397\) 9.93104 + 9.93104i 0.498425 + 0.498425i 0.910947 0.412523i \(-0.135352\pi\)
−0.412523 + 0.910947i \(0.635352\pi\)
\(398\) −0.656048 + 6.59714i −0.0328847 + 0.330684i
\(399\) 8.80221 0.440662
\(400\) 1.54467 3.68971i 0.0772337 0.184486i
\(401\) 9.51392 0.475102 0.237551 0.971375i \(-0.423655\pi\)
0.237551 + 0.971375i \(0.423655\pi\)
\(402\) 2.95312 29.6962i 0.147288 1.48111i
\(403\) −0.300592 0.300592i −0.0149736 0.0149736i
\(404\) −0.685914 + 0.456442i −0.0341255 + 0.0227089i
\(405\) −20.3138 + 20.3138i −1.00940 + 1.00940i
\(406\) 8.00992 6.56093i 0.397525 0.325613i
\(407\) 18.8605i 0.934879i
\(408\) 9.58031 + 18.0462i 0.474296 + 0.893421i
\(409\) 4.81799i 0.238234i −0.992880 0.119117i \(-0.961994\pi\)
0.992880 0.119117i \(-0.0380064\pi\)
\(410\) −3.52306 4.30113i −0.173991 0.212418i
\(411\) 31.5361 31.5361i 1.55556 1.55556i
\(412\) 1.77333 8.82803i 0.0873659 0.434926i
\(413\) −5.57564 5.57564i −0.274359 0.274359i
\(414\) 22.1764 + 2.20532i 1.08991 + 0.108386i
\(415\) −0.966253 −0.0474315
\(416\) −1.57871 5.29413i −0.0774027 0.259566i
\(417\) −38.2734 −1.87426
\(418\) −8.81939 0.877039i −0.431370 0.0428974i
\(419\) 21.4380 + 21.4380i 1.04731 + 1.04731i 0.998824 + 0.0484914i \(0.0154413\pi\)
0.0484914 + 0.998824i \(0.484559\pi\)
\(420\) 1.27249 6.33471i 0.0620910 0.309102i
\(421\) −4.80145 + 4.80145i −0.234008 + 0.234008i −0.814363 0.580355i \(-0.802914\pi\)
0.580355 + 0.814363i \(0.302914\pi\)
\(422\) −3.33579 4.07251i −0.162384 0.198246i
\(423\) 72.1232i 3.50675i
\(424\) 22.2352 11.8042i 1.07984 0.573261i
\(425\) 2.19577i 0.106510i
\(426\) −37.4261 + 30.6557i −1.81330 + 1.48527i
\(427\) 3.53819 3.53819i 0.171225 0.171225i
\(428\) −15.3030 + 10.1834i −0.739700 + 0.492235i
\(429\) −5.22551 5.22551i −0.252290 0.252290i
\(430\) −0.100459 + 1.01020i −0.00484456 + 0.0487162i
\(431\) 13.2369 0.637597 0.318799 0.947822i \(-0.396721\pi\)
0.318799 + 0.947822i \(0.396721\pi\)
\(432\) 58.7248 24.0653i 2.82540 1.15784i
\(433\) −1.50709 −0.0724259 −0.0362129 0.999344i \(-0.511529\pi\)
−0.0362129 + 0.999344i \(0.511529\pi\)
\(434\) −0.0598204 + 0.601546i −0.00287147 + 0.0288751i
\(435\) 17.3432 + 17.3432i 0.831545 + 0.831545i
\(436\) −3.94792 5.93270i −0.189071 0.284125i
\(437\) 3.88097 3.88097i 0.185652 0.185652i
\(438\) 33.2725 27.2535i 1.58982 1.30222i
\(439\) 10.3092i 0.492033i 0.969266 + 0.246016i \(0.0791217\pi\)
−0.969266 + 0.246016i \(0.920878\pi\)
\(440\) −1.90615 + 6.22028i −0.0908722 + 0.296540i
\(441\) 47.2158i 2.24837i
\(442\) 1.92167 + 2.34607i 0.0914044 + 0.111591i
\(443\) −14.2651 + 14.2651i −0.677755 + 0.677755i −0.959492 0.281736i \(-0.909090\pi\)
0.281736 + 0.959492i \(0.409090\pi\)
\(444\) 52.8941 + 10.6251i 2.51024 + 0.504246i
\(445\) −3.84950 3.84950i −0.182484 0.182484i
\(446\) 4.86416 + 0.483713i 0.230324 + 0.0229045i
\(447\) −58.7904 −2.78069
\(448\) −4.40153 + 6.50728i −0.207953 + 0.307440i
\(449\) −19.5711 −0.923618 −0.461809 0.886979i \(-0.652799\pi\)
−0.461809 + 0.886979i \(0.652799\pi\)
\(450\) 11.0088 + 1.09477i 0.518961 + 0.0516078i
\(451\) 6.39420 + 6.39420i 0.301091 + 0.301091i
\(452\) 10.5513 + 2.11949i 0.496289 + 0.0996923i
\(453\) −35.2569 + 35.2569i −1.65652 + 1.65652i
\(454\) −6.01410 7.34232i −0.282256 0.344592i
\(455\) 0.959035i 0.0449602i
\(456\) 7.42810 24.2399i 0.347852 1.13514i
\(457\) 39.0185i 1.82521i −0.408845 0.912604i \(-0.634068\pi\)
0.408845 0.912604i \(-0.365932\pi\)
\(458\) −20.6672 + 16.9285i −0.965713 + 0.791016i
\(459\) −24.6344 + 24.6344i −1.14984 + 1.14984i
\(460\) −2.23198 3.35408i −0.104066 0.156385i
\(461\) 19.6941 + 19.6941i 0.917245 + 0.917245i 0.996828 0.0795833i \(-0.0253590\pi\)
−0.0795833 + 0.996828i \(0.525359\pi\)
\(462\) −1.03992 + 10.4573i −0.0483815 + 0.486518i
\(463\) −14.9979 −0.697009 −0.348505 0.937307i \(-0.613310\pi\)
−0.348505 + 0.937307i \(0.613310\pi\)
\(464\) −11.3082 27.5947i −0.524972 1.28105i
\(465\) −1.43201 −0.0664077
\(466\) −0.675505 + 6.79278i −0.0312921 + 0.314670i
\(467\) 4.88870 + 4.88870i 0.226222 + 0.226222i 0.811112 0.584890i \(-0.198862\pi\)
−0.584890 + 0.811112i \(0.698862\pi\)
\(468\) 12.7205 8.46488i 0.588005 0.391289i
\(469\) −4.45404 + 4.45404i −0.205669 + 0.205669i
\(470\) −10.0867 + 8.26201i −0.465264 + 0.381098i
\(471\) 8.17980i 0.376905i
\(472\) −20.0596 + 10.6492i −0.923320 + 0.490168i
\(473\) 1.65114i 0.0759197i
\(474\) −45.5462 55.6052i −2.09201 2.55403i
\(475\) 1.92659 1.92659i 0.0883982 0.0883982i
\(476\) 0.849317 4.22808i 0.0389284 0.193794i
\(477\) 49.2334 + 49.2334i 2.25424 + 2.25424i
\(478\) −12.4191 1.23501i −0.568038 0.0564883i
\(479\) −27.3381 −1.24911 −0.624555 0.780981i \(-0.714720\pi\)
−0.624555 + 0.780981i \(0.714720\pi\)
\(480\) −16.3709 8.85002i −0.747227 0.403946i
\(481\) 8.00784 0.365126
\(482\) −5.26526 0.523601i −0.239826 0.0238494i
\(483\) −4.60173 4.60173i −0.209386 0.209386i
\(484\) −2.24881 + 11.1950i −0.102218 + 0.508865i
\(485\) 3.92119 3.92119i 0.178052 0.178052i
\(486\) 42.0387 + 51.3230i 1.90691 + 2.32806i
\(487\) 35.4769i 1.60761i 0.594892 + 0.803806i \(0.297195\pi\)
−0.594892 + 0.803806i \(0.702805\pi\)
\(488\) −6.75777 12.7295i −0.305910 0.576235i
\(489\) 64.7171i 2.92661i
\(490\) 6.60330 5.40876i 0.298307 0.244343i
\(491\) 3.55614 3.55614i 0.160486 0.160486i −0.622296 0.782782i \(-0.713800\pi\)
0.782782 + 0.622296i \(0.213800\pi\)
\(492\) −21.5347 + 14.3303i −0.970860 + 0.646060i
\(493\) 11.5757 + 11.5757i 0.521343 + 0.521343i
\(494\) 0.372376 3.74456i 0.0167540 0.168476i
\(495\) −17.9936 −0.808753
\(496\) 1.60608 + 0.672375i 0.0721151 + 0.0301905i
\(497\) 10.2114 0.458042
\(498\) −0.444856 + 4.47341i −0.0199345 + 0.200458i
\(499\) −17.6521 17.6521i −0.790218 0.790218i 0.191312 0.981529i \(-0.438726\pi\)
−0.981529 + 0.191312i \(0.938726\pi\)
\(500\) −1.10800 1.66503i −0.0495512 0.0744626i
\(501\) −43.8776 + 43.8776i −1.96031 + 1.96031i
\(502\) −9.27281 + 7.59537i −0.413866 + 0.338998i
\(503\) 31.8567i 1.42042i 0.703990 + 0.710210i \(0.251400\pi\)
−0.703990 + 0.710210i \(0.748600\pi\)
\(504\) −20.7747 6.36622i −0.925378 0.283574i
\(505\) 0.411952i 0.0183316i
\(506\) 4.15220 + 5.06923i 0.184588 + 0.225355i
\(507\) −28.0225 + 28.0225i −1.24452 + 1.24452i
\(508\) 9.54097 + 1.91655i 0.423312 + 0.0850330i
\(509\) −5.61054 5.61054i −0.248683 0.248683i 0.571747 0.820430i \(-0.306266\pi\)
−0.820430 + 0.571747i \(0.806266\pi\)
\(510\) 10.1656 + 1.01092i 0.450142 + 0.0447641i
\(511\) −9.07810 −0.401591
\(512\) 14.2056 + 17.6125i 0.627804 + 0.778371i
\(513\) 43.2291 1.90861
\(514\) −20.7801 2.06646i −0.916570 0.0911478i
\(515\) −3.18353 3.18353i −0.140283 0.140283i
\(516\) 4.63063 + 0.930180i 0.203852 + 0.0409489i
\(517\) 14.9952 14.9952i 0.659489 0.659489i
\(518\) −7.21585 8.80948i −0.317046 0.387066i
\(519\) 74.7767i 3.28233i
\(520\) −2.64103 0.809320i −0.115817 0.0354910i
\(521\) 33.1977i 1.45442i −0.686417 0.727208i \(-0.740818\pi\)
0.686417 0.727208i \(-0.259182\pi\)
\(522\) 63.8079 52.2651i 2.79280 2.28758i
\(523\) −2.60707 + 2.60707i −0.113999 + 0.113999i −0.761805 0.647806i \(-0.775687\pi\)
0.647806 + 0.761805i \(0.275687\pi\)
\(524\) 12.5447 + 18.8514i 0.548017 + 0.823527i
\(525\) −2.28440 2.28440i −0.0996992 0.0996992i
\(526\) −0.950909 + 9.56221i −0.0414616 + 0.416932i
\(527\) −0.955787 −0.0416347
\(528\) 27.9202 + 11.6886i 1.21507 + 0.508681i
\(529\) 18.9421 0.823570
\(530\) 1.24558 12.5254i 0.0541044 0.544067i
\(531\) −44.4162 44.4162i −1.92750 1.92750i
\(532\) −4.45497 + 2.96457i −0.193147 + 0.128530i
\(533\) −2.71487 + 2.71487i −0.117594 + 0.117594i
\(534\) −19.5941 + 16.0496i −0.847921 + 0.694532i
\(535\) 9.19083i 0.397354i
\(536\) 8.50699 + 16.0244i 0.367446 + 0.692150i
\(537\) 76.4593i 3.29946i
\(538\) −7.65452 9.34504i −0.330010 0.402893i
\(539\) −9.81668 + 9.81668i −0.422834 + 0.422834i
\(540\) 6.24939 31.1108i 0.268931 1.33879i
\(541\) −22.6839 22.6839i −0.975257 0.975257i 0.0244439 0.999701i \(-0.492218\pi\)
−0.999701 + 0.0244439i \(0.992218\pi\)
\(542\) −34.6499 3.44574i −1.48834 0.148007i
\(543\) 71.8992 3.08549
\(544\) −10.9267 5.90691i −0.468479 0.253257i
\(545\) −3.56311 −0.152627
\(546\) −4.44000 0.441533i −0.190014 0.0188959i
\(547\) −3.02284 3.02284i −0.129248 0.129248i 0.639524 0.768771i \(-0.279132\pi\)
−0.768771 + 0.639524i \(0.779132\pi\)
\(548\) −5.33974 + 26.5823i −0.228102 + 1.13554i
\(549\) 28.1857 28.1857i 1.20293 1.20293i
\(550\) 2.06124 + 2.51647i 0.0878916 + 0.107303i
\(551\) 20.3133i 0.865375i
\(552\) −16.5558 + 8.78907i −0.704661 + 0.374088i
\(553\) 15.1714i 0.645153i
\(554\) 15.4415 12.6481i 0.656047 0.537368i
\(555\) 19.0745 19.0745i 0.809666 0.809666i
\(556\) 19.3709 12.8904i 0.821510 0.546675i
\(557\) 9.27495 + 9.27495i 0.392992 + 0.392992i 0.875753 0.482760i \(-0.160366\pi\)
−0.482760 + 0.875753i \(0.660366\pi\)
\(558\) −0.476537 + 4.79199i −0.0201734 + 0.202861i
\(559\) 0.701048 0.0296512
\(560\) 1.48949 + 3.63469i 0.0629423 + 0.153594i
\(561\) −16.6154 −0.701504
\(562\) −2.02376 + 20.3507i −0.0853672 + 0.858441i
\(563\) −20.3025 20.3025i −0.855649 0.855649i 0.135173 0.990822i \(-0.456841\pi\)
−0.990822 + 0.135173i \(0.956841\pi\)
\(564\) 33.6064 + 50.5016i 1.41508 + 2.12650i
\(565\) 3.80495 3.80495i 0.160076 0.160076i
\(566\) 31.0655 25.4458i 1.30578 1.06956i
\(567\) 28.2112i 1.18476i
\(568\) 8.61727 28.1205i 0.361573 1.17991i
\(569\) 14.3362i 0.601005i 0.953781 + 0.300503i \(0.0971544\pi\)
−0.953781 + 0.300503i \(0.902846\pi\)
\(570\) −8.03247 9.80645i −0.336443 0.410747i
\(571\) 8.54368 8.54368i 0.357542 0.357542i −0.505364 0.862906i \(-0.668642\pi\)
0.862906 + 0.505364i \(0.168642\pi\)
\(572\) 4.40467 + 0.884790i 0.184168 + 0.0369949i
\(573\) 34.3987 + 34.3987i 1.43703 + 1.43703i
\(574\) 5.43301 + 0.540283i 0.226769 + 0.0225510i
\(575\) −2.01442 −0.0840071
\(576\) −35.0631 + 51.8377i −1.46096 + 2.15991i
\(577\) −8.68179 −0.361428 −0.180714 0.983536i \(-0.557841\pi\)
−0.180714 + 0.983536i \(0.557841\pi\)
\(578\) −17.1386 1.70434i −0.712872 0.0708912i
\(579\) 26.2661 + 26.2661i 1.09158 + 1.09158i
\(580\) −14.6189 2.93658i −0.607018 0.121935i
\(581\) 0.670953 0.670953i 0.0278358 0.0278358i
\(582\) −16.3484 19.9590i −0.677665 0.827328i
\(583\) 20.4723i 0.847877i
\(584\) −7.66092 + 24.9996i −0.317011 + 1.03449i
\(585\) 7.63978i 0.315866i
\(586\) 23.8330 19.5216i 0.984533 0.806431i
\(587\) 21.9042 21.9042i 0.904082 0.904082i −0.0917043 0.995786i \(-0.529231\pi\)
0.995786 + 0.0917043i \(0.0292315\pi\)
\(588\) −22.0006 33.0611i −0.907288 1.36342i
\(589\) 0.838619 + 0.838619i 0.0345547 + 0.0345547i
\(590\) −1.12370 + 11.2998i −0.0462622 + 0.465206i
\(591\) 49.3871 2.03151
\(592\) −30.3493 + 12.4371i −1.24735 + 0.511160i
\(593\) −17.5142 −0.719222 −0.359611 0.933102i \(-0.617091\pi\)
−0.359611 + 0.933102i \(0.617091\pi\)
\(594\) −5.10722 + 51.3575i −0.209552 + 2.10722i
\(595\) −1.52471 1.52471i −0.0625071 0.0625071i
\(596\) 29.7549 19.8005i 1.21881 0.811059i
\(597\) 10.9052 10.9052i 0.446319 0.446319i
\(598\) −2.15231 + 1.76296i −0.0880144 + 0.0720926i
\(599\) 19.0276i 0.777447i 0.921354 + 0.388724i \(0.127084\pi\)
−0.921354 + 0.388724i \(0.872916\pi\)
\(600\) −8.21864 + 4.36308i −0.335525 + 0.178122i
\(601\) 5.52545i 0.225388i −0.993630 0.112694i \(-0.964052\pi\)
0.993630 0.112694i \(-0.0359479\pi\)
\(602\) −0.631713 0.771228i −0.0257467 0.0314329i
\(603\) −35.4814 + 35.4814i −1.44491 + 1.44491i
\(604\) 5.96975 29.7187i 0.242906 1.20924i
\(605\) 4.03711 + 4.03711i 0.164132 + 0.164132i
\(606\) 1.90719 + 0.189660i 0.0774744 + 0.00770440i
\(607\) −12.1064 −0.491384 −0.245692 0.969348i \(-0.579015\pi\)
−0.245692 + 0.969348i \(0.579015\pi\)
\(608\) 4.40443 + 14.7700i 0.178623 + 0.599004i
\(609\) −24.0858 −0.976007
\(610\) −7.17064 0.713081i −0.290331 0.0288718i
\(611\) 6.36671 + 6.36671i 0.257570 + 0.257570i
\(612\) 6.76576 33.6814i 0.273490 1.36149i
\(613\) 17.8073 17.8073i 0.719230 0.719230i −0.249218 0.968448i \(-0.580173\pi\)
0.968448 + 0.249218i \(0.0801734\pi\)
\(614\) 11.5631 + 14.1168i 0.466647 + 0.569707i
\(615\) 12.9335i 0.521529i
\(616\) −2.99568 5.64289i −0.120699 0.227358i
\(617\) 1.10944i 0.0446642i 0.999751 + 0.0223321i \(0.00710912\pi\)
−0.999751 + 0.0223321i \(0.992891\pi\)
\(618\) −16.2043 + 13.2730i −0.651833 + 0.533917i
\(619\) −31.8702 + 31.8702i −1.28097 + 1.28097i −0.340859 + 0.940115i \(0.610718\pi\)
−0.940115 + 0.340859i \(0.889282\pi\)
\(620\) 0.724766 0.482297i 0.0291073 0.0193695i
\(621\) −22.5998 22.5998i −0.906901 0.906901i
\(622\) −0.0899724 + 0.904750i −0.00360756 + 0.0362772i
\(623\) 5.34608 0.214186
\(624\) −4.96278 + 11.8544i −0.198670 + 0.474557i
\(625\) −1.00000 −0.0400000
\(626\) −2.99168 + 30.0840i −0.119572 + 1.20240i
\(627\) 14.5786 + 14.5786i 0.582213 + 0.582213i
\(628\) −2.75494 4.13996i −0.109934 0.165202i
\(629\) 12.7312 12.7312i 0.507626 0.507626i
\(630\) −8.40458 + 6.88419i −0.334846 + 0.274273i
\(631\) 6.80064i 0.270729i −0.990796 0.135365i \(-0.956779\pi\)
0.990796 0.135365i \(-0.0432206\pi\)
\(632\) 41.7795 + 12.8030i 1.66190 + 0.509275i
\(633\) 12.2460i 0.486736i
\(634\) 10.9776 + 13.4020i 0.435976 + 0.532262i
\(635\) 3.44063 3.44063i 0.136537 0.136537i
\(636\) −57.4146 11.5332i −2.27664 0.457320i
\(637\) −4.16800 4.16800i −0.165142 0.165142i
\(638\) 24.1328 + 2.39988i 0.955429 + 0.0950121i
\(639\) 81.3449 3.21796
\(640\) 11.2663 1.03453i 0.445340 0.0408933i
\(641\) 14.2566 0.563100 0.281550 0.959547i \(-0.409151\pi\)
0.281550 + 0.959547i \(0.409151\pi\)
\(642\) 42.5503 + 4.23139i 1.67933 + 0.167000i
\(643\) 14.4137 + 14.4137i 0.568422 + 0.568422i 0.931686 0.363264i \(-0.118338\pi\)
−0.363264 + 0.931686i \(0.618338\pi\)
\(644\) 3.87888 + 0.779172i 0.152849 + 0.0307037i
\(645\) 1.66988 1.66988i 0.0657514 0.0657514i
\(646\) −5.36124 6.54528i −0.210935 0.257520i
\(647\) 20.5723i 0.808782i −0.914586 0.404391i \(-0.867483\pi\)
0.914586 0.404391i \(-0.132517\pi\)
\(648\) −77.6891 23.8071i −3.05192 0.935233i
\(649\) 18.4692i 0.724980i
\(650\) −1.06845 + 0.875168i −0.0419081 + 0.0343269i
\(651\) 0.994365 0.994365i 0.0389723 0.0389723i
\(652\) −21.7966 32.7546i −0.853620 1.28277i
\(653\) −9.79946 9.79946i −0.383482 0.383482i 0.488873 0.872355i \(-0.337408\pi\)
−0.872355 + 0.488873i \(0.837408\pi\)
\(654\) −1.64043 + 16.4960i −0.0641459 + 0.645043i
\(655\) 11.3219 0.442384
\(656\) 6.07271 14.5057i 0.237100 0.566352i
\(657\) −72.3172 −2.82136
\(658\) 1.26703 12.7411i 0.0493940 0.496700i
\(659\) −8.70669 8.70669i −0.339165 0.339165i 0.516888 0.856053i \(-0.327090\pi\)
−0.856053 + 0.516888i \(0.827090\pi\)
\(660\) 12.5994 8.38426i 0.490429 0.326357i
\(661\) 19.7899 19.7899i 0.769737 0.769737i −0.208323 0.978060i \(-0.566801\pi\)
0.978060 + 0.208323i \(0.0668006\pi\)
\(662\) −13.0576 + 10.6955i −0.507498 + 0.415692i
\(663\) 7.05464i 0.273979i
\(664\) −1.28149 2.41391i −0.0497313 0.0936778i
\(665\) 2.67560i 0.103755i
\(666\) −57.4823 70.1773i −2.22739 2.71932i
\(667\) −10.6196 + 10.6196i −0.411194 + 0.411194i
\(668\) 7.42941 36.9852i 0.287453 1.43100i
\(669\) −8.04053 8.04053i −0.310865 0.310865i
\(670\) 9.02674 + 0.897659i 0.348733 + 0.0346796i
\(671\) 11.7202 0.452454
\(672\) 17.5131 5.22242i 0.675582 0.201459i
\(673\) −14.0829 −0.542857 −0.271429 0.962459i \(-0.587496\pi\)
−0.271429 + 0.962459i \(0.587496\pi\)
\(674\) 43.2098 + 4.29698i 1.66438 + 0.165513i
\(675\) −11.2190 11.2190i −0.431821 0.431821i
\(676\) 4.74481 23.6206i 0.182493 0.908487i
\(677\) −29.8166 + 29.8166i −1.14594 + 1.14594i −0.158601 + 0.987343i \(0.550698\pi\)
−0.987343 + 0.158601i \(0.949302\pi\)
\(678\) −15.8638 19.3674i −0.609247 0.743799i
\(679\) 5.44564i 0.208984i
\(680\) −5.48550 + 2.91212i −0.210359 + 0.111675i
\(681\) 22.0784i 0.846045i
\(682\) −1.09538 + 0.897229i −0.0419444 + 0.0343567i
\(683\) −12.0646 + 12.0646i −0.461641 + 0.461641i −0.899193 0.437552i \(-0.855845\pi\)
0.437552 + 0.899193i \(0.355845\pi\)
\(684\) −35.4888 + 23.6161i −1.35695 + 0.902983i
\(685\) 9.58601 + 9.58601i 0.366263 + 0.366263i
\(686\) −1.79146 + 18.0147i −0.0683984 + 0.687805i
\(687\) 62.1462 2.37102
\(688\) −2.65693 + 1.08880i −0.101295 + 0.0415103i
\(689\) −8.69221 −0.331147
\(690\) −0.927425 + 9.32606i −0.0353065 + 0.355037i
\(691\) 2.58867 + 2.58867i 0.0984776 + 0.0984776i 0.754629 0.656152i \(-0.227817\pi\)
−0.656152 + 0.754629i \(0.727817\pi\)
\(692\) 25.1847 + 37.8459i 0.957377 + 1.43869i
\(693\) 12.4945 12.4945i 0.474628 0.474628i
\(694\) 21.1068 17.2886i 0.801203 0.656266i
\(695\) 11.6340i 0.441301i
\(696\) −20.3258 + 66.3285i −0.770447 + 2.51418i
\(697\) 8.63242i 0.326976i
\(698\) 12.6393 + 15.4307i 0.478405 + 0.584062i
\(699\) 11.2286 11.2286i 0.424704 0.424704i
\(700\) 1.92556 + 0.386797i 0.0727792 + 0.0146196i
\(701\) −26.9943 26.9943i −1.01956 1.01956i −0.999805 0.0197572i \(-0.993711\pi\)
−0.0197572 0.999805i \(-0.506289\pi\)
\(702\) −21.8055 2.16844i −0.822997 0.0818425i
\(703\) −22.3410 −0.842606
\(704\) −18.0676 + 3.48763i −0.680949 + 0.131445i
\(705\) 30.3307 1.14232
\(706\) −37.6929 3.74835i −1.41859 0.141071i
\(707\) −0.286054 0.286054i −0.0107582 0.0107582i
\(708\) 51.7969 + 10.4047i 1.94665 + 0.391033i
\(709\) −35.0639 + 35.0639i −1.31685 + 1.31685i −0.400598 + 0.916254i \(0.631198\pi\)
−0.916254 + 0.400598i \(0.868802\pi\)
\(710\) −9.31840 11.3764i −0.349713 0.426948i
\(711\) 120.857i 4.53249i
\(712\) 4.51151 14.7223i 0.169076 0.551740i
\(713\) 0.876848i 0.0328382i
\(714\) −7.76085 + 6.35692i −0.290443 + 0.237902i
\(715\) 1.58839 1.58839i 0.0594026 0.0594026i
\(716\) 25.7513 + 38.6975i 0.962373 + 1.44619i
\(717\) 20.5290 + 20.5290i 0.766671 + 0.766671i
\(718\) −2.67562 + 26.9057i −0.0998534 + 1.00411i
\(719\) −0.436840 −0.0162914 −0.00814568 0.999967i \(-0.502593\pi\)
−0.00814568 + 0.999967i \(0.502593\pi\)
\(720\) 11.8654 + 28.9544i 0.442198 + 1.07907i
\(721\) 4.42120 0.164654
\(722\) 1.62007 16.2913i 0.0602929 0.606298i
\(723\) 8.70356 + 8.70356i 0.323689 + 0.323689i
\(724\) −36.3896 + 24.2155i −1.35241 + 0.899963i
\(725\) −5.27182 + 5.27182i −0.195790 + 0.195790i
\(726\) 20.5491 16.8317i 0.762647 0.624684i
\(727\) 38.8072i 1.43928i −0.694348 0.719640i \(-0.744307\pi\)
0.694348 0.719640i \(-0.255693\pi\)
\(728\) 2.39588 1.27191i 0.0887970 0.0471402i
\(729\) 68.1444i 2.52387i
\(730\) 8.28423 + 10.1138i 0.306613 + 0.374329i
\(731\) 1.11455 1.11455i 0.0412233 0.0412233i
\(732\) −6.60263 + 32.8693i −0.244040 + 1.21488i
\(733\) −24.3059 24.3059i −0.897758 0.897758i 0.0974793 0.995238i \(-0.468922\pi\)
−0.995238 + 0.0974793i \(0.968922\pi\)
\(734\) 5.97226 + 0.593908i 0.220440 + 0.0219215i
\(735\) −19.8561 −0.732404
\(736\) 5.41906 10.0243i 0.199749 0.369500i
\(737\) −14.7539 −0.543469
\(738\) 43.2800 + 4.30395i 1.59316 + 0.158431i
\(739\) −27.0262 27.0262i −0.994174 0.994174i 0.00580951 0.999983i \(-0.498151\pi\)
−0.999983 + 0.00580951i \(0.998151\pi\)
\(740\) −3.22971 + 16.0782i −0.118727 + 0.591046i
\(741\) −6.18982 + 6.18982i −0.227389 + 0.227389i
\(742\) 7.83253 + 9.56235i 0.287541 + 0.351045i
\(743\) 12.1663i 0.446337i −0.974780 0.223169i \(-0.928360\pi\)
0.974780 0.223169i \(-0.0716401\pi\)
\(744\) −1.89919 3.57746i −0.0696276 0.131156i
\(745\) 17.8705i 0.654724i
\(746\) 37.0580 30.3543i 1.35679 1.11135i
\(747\) 5.34489 5.34489i 0.195559 0.195559i
\(748\) 8.40940 5.59605i 0.307478 0.204612i
\(749\) −6.38199 6.38199i −0.233193 0.233193i
\(750\) −0.460393 + 4.62965i −0.0168112 + 0.169051i
\(751\) −40.8606 −1.49102 −0.745512 0.666492i \(-0.767795\pi\)
−0.745512 + 0.666492i \(0.767795\pi\)
\(752\) −34.0177 14.2413i −1.24050 0.519326i
\(753\) 27.8834 1.01613
\(754\) −1.01895 + 10.2464i −0.0371079 + 0.373152i
\(755\) −10.7170 10.7170i −0.390033 0.390033i
\(756\) 17.2634 + 25.9424i 0.627864 + 0.943516i
\(757\) −0.00399171 + 0.00399171i −0.000145081 + 0.000145081i −0.707179 0.707034i \(-0.750033\pi\)
0.707034 + 0.707179i \(0.250033\pi\)
\(758\) −11.5374 + 9.45026i −0.419056 + 0.343249i
\(759\) 15.2432i 0.553292i
\(760\) 7.36818 + 2.25791i 0.267272 + 0.0819031i
\(761\) 0.751325i 0.0272355i −0.999907 0.0136178i \(-0.995665\pi\)
0.999907 0.0136178i \(-0.00433480\pi\)
\(762\) −14.3449 17.5129i −0.519660 0.634427i
\(763\) 2.47418 2.47418i 0.0895712 0.0895712i
\(764\) −28.9953 5.82443i −1.04901 0.210721i
\(765\) −12.1460 12.1460i −0.439141 0.439141i
\(766\) 7.31313 + 0.727250i 0.264234 + 0.0262766i
\(767\) 7.84172 0.283148
\(768\) 0.397428 52.6354i 0.0143410 1.89932i
\(769\) 35.4522 1.27844 0.639219 0.769025i \(-0.279258\pi\)
0.639219 + 0.769025i \(0.279258\pi\)
\(770\) −3.17870 0.316104i −0.114552 0.0113916i
\(771\) 34.3498 + 34.3498i 1.23708 + 1.23708i
\(772\) −22.1401 4.44740i −0.796840 0.160066i
\(773\) −5.50186 + 5.50186i −0.197888 + 0.197888i −0.799094 0.601206i \(-0.794687\pi\)
0.601206 + 0.799094i \(0.294687\pi\)
\(774\) −5.03230 6.14369i −0.180882 0.220830i
\(775\) 0.435286i 0.0156359i
\(776\) 14.9964 + 4.59552i 0.538340 + 0.164970i
\(777\) 26.4901i 0.950327i
\(778\) 16.0673 13.1607i 0.576041 0.471835i
\(779\) 7.57419 7.57419i 0.271373 0.271373i
\(780\) 3.55982 + 5.34947i 0.127462 + 0.191542i
\(781\) 16.9125 + 16.9125i 0.605177 + 0.605177i
\(782\) −0.619006 + 6.22464i −0.0221356 + 0.222593i
\(783\) −118.289 −4.22732
\(784\) 22.2698 + 9.32312i 0.795351 + 0.332969i
\(785\) −2.48641 −0.0887438
\(786\) 5.21254 52.4166i 0.185925 1.86964i
\(787\) 28.6944 + 28.6944i 1.02284 + 1.02284i 0.999733 + 0.0231107i \(0.00735700\pi\)
0.0231107 + 0.999733i \(0.492643\pi\)
\(788\) −24.9958 + 16.6335i −0.890437 + 0.592543i
\(789\) 15.8065 15.8065i 0.562726 0.562726i
\(790\) 16.9023 13.8447i 0.601356 0.492571i
\(791\) 5.28422i 0.187885i
\(792\) −23.8639 44.9519i −0.847967 1.59730i
\(793\) 4.97620i 0.176710i
\(794\) 12.5859 + 15.3655i 0.446656 + 0.545300i
\(795\) −20.7046 + 20.7046i −0.734317 + 0.734317i
\(796\) −1.84648 + 9.19215i −0.0654467 + 0.325807i
\(797\) −6.29277 6.29277i −0.222901 0.222901i 0.586818 0.809719i \(-0.300381\pi\)
−0.809719 + 0.586818i \(0.800381\pi\)
\(798\) 12.3871 + 1.23183i 0.438499 + 0.0436063i
\(799\) 20.2441 0.716185
\(800\) 2.69014 4.97626i 0.0951107 0.175937i
\(801\) 42.5875 1.50476
\(802\) 13.3887 + 1.33143i 0.472771 + 0.0470144i
\(803\) −15.0355 15.0355i −0.530592 0.530592i
\(804\) 8.31170 41.3774i 0.293131 1.45927i
\(805\) 1.39879 1.39879i 0.0493007 0.0493007i
\(806\) −0.380948 0.465081i −0.0134183 0.0163818i
\(807\) 28.1005i 0.989186i
\(808\) −1.02914 + 0.546348i −0.0362052 + 0.0192205i
\(809\) 27.0850i 0.952257i −0.879376 0.476128i \(-0.842040\pi\)
0.879376 0.476128i \(-0.157960\pi\)
\(810\) −31.4298 + 25.7442i −1.10433 + 0.904558i
\(811\) −14.6690 + 14.6690i −0.515098 + 0.515098i −0.916084 0.400986i \(-0.868668\pi\)
0.400986 + 0.916084i \(0.368668\pi\)
\(812\) 12.1903 8.11206i 0.427796 0.284677i
\(813\) 57.2769 + 57.2769i 2.00879 + 2.00879i
\(814\) 2.63944 26.5418i 0.0925122 0.930290i
\(815\) −19.6720 −0.689081
\(816\) 10.9566 + 26.7367i 0.383559 + 0.935971i
\(817\) −1.95585 −0.0684264
\(818\) 0.674256 6.78022i 0.0235748 0.237065i
\(819\) 5.30496 + 5.30496i 0.185370 + 0.185370i
\(820\) −4.35598 6.54589i −0.152117 0.228592i
\(821\) −15.4717 + 15.4717i −0.539965 + 0.539965i −0.923519 0.383553i \(-0.874700\pi\)
0.383553 + 0.923519i \(0.374700\pi\)
\(822\) 48.7932 39.9666i 1.70186 1.39399i
\(823\) 7.64319i 0.266425i −0.991088 0.133212i \(-0.957471\pi\)
0.991088 0.133212i \(-0.0425292\pi\)
\(824\) 3.73101 12.1753i 0.129976 0.424146i
\(825\) 7.56703i 0.263450i
\(826\) −7.06616 8.62673i −0.245863 0.300162i
\(827\) −0.781185 + 0.781185i −0.0271645 + 0.0271645i −0.720559 0.693394i \(-0.756115\pi\)
0.693394 + 0.720559i \(0.256115\pi\)
\(828\) 30.8996 + 6.20697i 1.07384 + 0.215707i
\(829\) 28.9122 + 28.9122i 1.00416 + 1.00416i 0.999991 + 0.00417165i \(0.00132788\pi\)
0.00417165 + 0.999991i \(0.498672\pi\)
\(830\) −1.35978 0.135223i −0.0471987 0.00469365i
\(831\) −46.4326 −1.61073
\(832\) −1.48079 7.67121i −0.0513371 0.265951i
\(833\) −13.2529 −0.459186
\(834\) −53.8612 5.35619i −1.86506 0.185470i
\(835\) −13.3374 13.3374i −0.461561 0.461561i
\(836\) −12.2885 2.46847i −0.425008 0.0853737i
\(837\) 4.88349 4.88349i 0.168798 0.168798i
\(838\) 27.1690 + 33.1693i 0.938536 + 1.14581i
\(839\) 35.9665i 1.24170i −0.783928 0.620851i \(-0.786787\pi\)
0.783928 0.620851i \(-0.213213\pi\)
\(840\) 2.67725 8.73658i 0.0923739 0.301441i
\(841\) 26.5841i 0.916692i
\(842\) −7.42888 + 6.08500i −0.256016 + 0.209703i
\(843\) 33.6400 33.6400i 1.15862 1.15862i
\(844\) −4.12444 6.19795i −0.141969 0.213342i
\(845\) −8.51798 8.51798i −0.293028 0.293028i
\(846\) 10.0933 101.497i 0.347015 3.48954i
\(847\) −5.60663 −0.192646
\(848\) 32.9430 13.4999i 1.13127 0.463590i
\(849\) −93.4140 −3.20596
\(850\) −0.307288 + 3.09004i −0.0105399 + 0.105988i
\(851\) 11.6797 + 11.6797i 0.400375 + 0.400375i
\(852\) −56.9588 + 37.9033i −1.95138 + 1.29855i
\(853\) 8.53167 8.53167i 0.292119 0.292119i −0.545798 0.837917i \(-0.683773\pi\)
0.837917 + 0.545798i \(0.183773\pi\)
\(854\) 5.47435 4.48405i 0.187329 0.153441i
\(855\) 21.3142i 0.728929i
\(856\) −22.9607 + 12.1893i −0.784779 + 0.416621i
\(857\) 20.6681i 0.706010i 0.935621 + 0.353005i \(0.114840\pi\)
−0.935621 + 0.353005i \(0.885160\pi\)
\(858\) −6.62242 8.08500i −0.226086 0.276017i
\(859\) 26.6003 26.6003i 0.907590 0.907590i −0.0884877 0.996077i \(-0.528203\pi\)
0.996077 + 0.0884877i \(0.0282034\pi\)
\(860\) −0.282746 + 1.40757i −0.00964156 + 0.0479977i
\(861\) −8.98085 8.98085i −0.306066 0.306066i
\(862\) 18.6279 + 1.85244i 0.634468 + 0.0630943i
\(863\) 24.2911 0.826880 0.413440 0.910531i \(-0.364327\pi\)
0.413440 + 0.910531i \(0.364327\pi\)
\(864\) 86.0096 25.6481i 2.92611 0.872567i
\(865\) 22.7298 0.772838
\(866\) −2.12088 0.210910i −0.0720704 0.00716700i
\(867\) 28.3304 + 28.3304i 0.962150 + 0.962150i
\(868\) −0.168367 + 0.838168i −0.00571476 + 0.0284493i
\(869\) −25.1275 + 25.1275i −0.852391 + 0.852391i
\(870\) 21.9796 + 26.8338i 0.745177 + 0.909750i
\(871\) 6.26428i 0.212257i
\(872\) −4.72555 8.90141i −0.160027 0.301440i
\(873\) 43.3806i 1.46821i
\(874\) 6.00470 4.91845i 0.203112 0.166369i
\(875\) 0.694387 0.694387i 0.0234746 0.0234746i
\(876\) 50.6374 33.6968i 1.71088 1.13851i
\(877\) −17.5305 17.5305i −0.591963 0.591963i 0.346198 0.938161i \(-0.387472\pi\)
−0.938161 + 0.346198i \(0.887472\pi\)
\(878\) −1.44273 + 14.5079i −0.0486898 + 0.489618i
\(879\) −71.6659 −2.41723
\(880\) −3.55298 + 8.48688i −0.119771 + 0.286093i
\(881\) 35.1334 1.18367 0.591837 0.806058i \(-0.298403\pi\)
0.591837 + 0.806058i \(0.298403\pi\)
\(882\) −6.60764 + 66.4455i −0.222491 + 2.23734i
\(883\) 18.0965 + 18.0965i 0.608997 + 0.608997i 0.942684 0.333687i \(-0.108293\pi\)
−0.333687 + 0.942684i \(0.608293\pi\)
\(884\) 2.37599 + 3.57049i 0.0799131 + 0.120088i
\(885\) 18.6788 18.6788i 0.627880 0.627880i
\(886\) −22.0712 + 18.0785i −0.741497 + 0.607361i
\(887\) 14.6666i 0.492455i −0.969212 0.246228i \(-0.920809\pi\)
0.969212 0.246228i \(-0.0791911\pi\)
\(888\) 72.9495 + 22.3547i 2.44802 + 0.750176i
\(889\) 4.77825i 0.160257i
\(890\) −4.87857 5.95601i −0.163530 0.199646i
\(891\) 46.7246 46.7246i 1.56533 1.56533i
\(892\) 6.77750 + 1.36143i 0.226927 + 0.0455841i
\(893\) −17.7624 17.7624i −0.594397 0.594397i
\(894\) −82.7341 8.22744i −2.76704 0.275167i
\(895\) 23.2413 0.776871
\(896\) −7.10481 + 8.54154i −0.237355 + 0.285353i
\(897\) 6.47199 0.216094
\(898\) −27.5419 2.73889i −0.919085 0.0913979i
\(899\) −2.29475 2.29475i −0.0765341 0.0765341i
\(900\) 15.3392 + 3.08127i 0.511307 + 0.102709i
\(901\) −13.8192 + 13.8192i −0.460385 + 0.460385i
\(902\) 8.10354 + 9.89322i 0.269818 + 0.329408i
\(903\) 2.31908i 0.0771743i
\(904\) 14.5519 + 4.45930i 0.483988 + 0.148314i
\(905\) 21.8552i 0.726490i
\(906\) −54.5502 + 44.6821i −1.81231 + 1.48446i
\(907\) −25.4429 + 25.4429i −0.844817 + 0.844817i −0.989481 0.144664i \(-0.953790\pi\)
0.144664 + 0.989481i \(0.453790\pi\)
\(908\) −7.43595 11.1743i −0.246771 0.370832i
\(909\) −2.27874 2.27874i −0.0755810 0.0755810i
\(910\) 0.134213 1.34962i 0.00444910 0.0447396i
\(911\) 14.6852 0.486542 0.243271 0.969958i \(-0.421780\pi\)
0.243271 + 0.969958i \(0.421780\pi\)
\(912\) 13.8456 33.0726i 0.458474 1.09514i
\(913\) 2.22252 0.0735547
\(914\) 5.46046 54.9096i 0.180616 1.81625i
\(915\) 11.8532 + 11.8532i 0.391854 + 0.391854i
\(916\) −31.4534 + 20.9307i −1.03925 + 0.691570i
\(917\) −7.86179 + 7.86179i −0.259619 + 0.259619i
\(918\) −38.1148 + 31.2199i −1.25798 + 1.03041i
\(919\) 46.2157i 1.52451i −0.647274 0.762257i \(-0.724091\pi\)
0.647274 0.762257i \(-0.275909\pi\)
\(920\) −2.67161 5.03245i −0.0880804 0.165915i
\(921\) 42.4492i 1.39875i
\(922\) 24.9588 + 30.4710i 0.821976 + 1.00351i
\(923\) −7.18076 + 7.18076i −0.236358 + 0.236358i
\(924\) −2.92690 + 14.5707i −0.0962881 + 0.479342i
\(925\) 5.79805 + 5.79805i 0.190639 + 0.190639i
\(926\) −21.1061 2.09888i −0.693588 0.0689735i
\(927\) 35.2198 1.15677
\(928\) −12.0520 40.4158i −0.395627 1.32671i
\(929\) 52.0543 1.70785 0.853923 0.520400i \(-0.174217\pi\)
0.853923 + 0.520400i \(0.174217\pi\)
\(930\) −2.01522 0.200403i −0.0660817 0.00657146i
\(931\) 11.6283 + 11.6283i 0.381101 + 0.381101i
\(932\) −1.90124 + 9.46476i −0.0622771 + 0.310029i
\(933\) 1.49557 1.49557i 0.0489627 0.0489627i
\(934\) 6.19558 + 7.56389i 0.202726 + 0.247498i
\(935\) 5.05059i 0.165172i
\(936\) 19.0858 10.1322i 0.623840 0.331182i
\(937\) 33.7454i 1.10241i 0.834368 + 0.551207i \(0.185833\pi\)
−0.834368 + 0.551207i \(0.814167\pi\)
\(938\) −6.89137 + 5.64473i −0.225011 + 0.184307i
\(939\) 49.7293 49.7293i 1.62285 1.62285i
\(940\) −15.3510 + 10.2153i −0.500693 + 0.333187i
\(941\) −14.5814 14.5814i −0.475341 0.475341i 0.428297 0.903638i \(-0.359114\pi\)
−0.903638 + 0.428297i \(0.859114\pi\)
\(942\) −1.14473 + 11.5112i −0.0372972 + 0.375056i
\(943\) −7.91946 −0.257893
\(944\) −29.7197 + 12.1790i −0.967293 + 0.396394i
\(945\) 15.5807 0.506840
\(946\) 0.231070 2.32361i 0.00751274 0.0755471i
\(947\) −37.7582 37.7582i −1.22698 1.22698i −0.965102 0.261876i \(-0.915659\pi\)
−0.261876 0.965102i \(-0.584341\pi\)
\(948\) −56.3143 84.6256i −1.82900 2.74851i
\(949\) 6.38383 6.38383i 0.207228 0.207228i
\(950\) 2.98086 2.44162i 0.0967119 0.0792167i
\(951\) 40.2998i 1.30681i
\(952\) 1.78692 5.83120i 0.0579144 0.188990i
\(953\) 48.6441i 1.57574i −0.615844 0.787868i \(-0.711185\pi\)
0.615844 0.787868i \(-0.288815\pi\)
\(954\) 62.3948 + 76.1748i 2.02011 + 2.46625i
\(955\) −10.4562 + 10.4562i −0.338353 + 0.338353i
\(956\) −17.3043 3.47600i −0.559660 0.112422i
\(957\) −39.8920 39.8920i −1.28952 1.28952i
\(958\) −38.4721 3.82584i −1.24298 0.123607i
\(959\) −13.3128 −0.429893
\(960\) −21.7998 14.7454i −0.703586 0.475907i
\(961\) −30.8105 −0.993888
\(962\) 11.2692 + 1.12066i 0.363334 + 0.0361315i
\(963\) −50.8397 50.8397i −1.63829 1.63829i
\(964\) −7.33638 1.47370i −0.236289 0.0474646i
\(965\) −7.98408 + 7.98408i −0.257017 + 0.257017i
\(966\) −5.83190 7.11988i −0.187638 0.229078i
\(967\) 12.4521i 0.400433i 0.979752 + 0.200216i \(0.0641645\pi\)
−0.979752 + 0.200216i \(0.935835\pi\)
\(968\) −4.73138 + 15.4397i −0.152072 + 0.496252i
\(969\) 19.6817i 0.632266i
\(970\) 6.06693 4.96943i 0.194797 0.159559i
\(971\) 14.1931 14.1931i 0.455478 0.455478i −0.441690 0.897168i \(-0.645621\pi\)
0.897168 + 0.441690i \(0.145621\pi\)
\(972\) 51.9775 + 78.1086i 1.66718 + 2.50533i
\(973\) 8.07846 + 8.07846i 0.258984 + 0.258984i
\(974\) −4.96483 + 49.9256i −0.159083 + 1.59972i
\(975\) 3.21283 0.102893
\(976\) −7.72859 18.8595i −0.247386 0.603679i
\(977\) 18.3144 0.585929 0.292965 0.956123i \(-0.405358\pi\)
0.292965 + 0.956123i \(0.405358\pi\)
\(978\) −9.05686 + 91.0746i −0.289607 + 2.91224i
\(979\) 8.85441 + 8.85441i 0.282988 + 0.282988i
\(980\) 10.0496 6.68750i 0.321022 0.213624i
\(981\) 19.7096 19.7096i 0.629278 0.629278i
\(982\) 5.50212 4.50679i 0.175580 0.143817i
\(983\) 27.0583i 0.863027i 0.902107 + 0.431513i \(0.142020\pi\)
−0.902107 + 0.431513i \(0.857980\pi\)
\(984\) −32.3107 + 17.1530i −1.03003 + 0.546816i
\(985\) 15.0122i 0.478328i
\(986\) 14.6702 + 17.9101i 0.467194 + 0.570374i
\(987\) −21.0612 + 21.0612i −0.670386 + 0.670386i
\(988\) 1.04807 5.21751i 0.0333435 0.165991i
\(989\) 1.02250 + 1.02250i 0.0325137 + 0.0325137i
\(990\) −25.3219 2.51812i −0.804783 0.0800312i
\(991\) 25.7759 0.818799 0.409400 0.912355i \(-0.365738\pi\)
0.409400 + 0.912355i \(0.365738\pi\)
\(992\) 2.16610 + 1.17098i 0.0687736 + 0.0371786i
\(993\) 39.2642 1.24601
\(994\) 14.3702 + 1.42903i 0.455794 + 0.0453262i
\(995\) 3.31484 + 3.31484i 0.105087 + 0.105087i
\(996\) −1.25207 + 6.23305i −0.0396733 + 0.197502i
\(997\) 11.1158 11.1158i 0.352041 0.352041i −0.508828 0.860868i \(-0.669921\pi\)
0.860868 + 0.508828i \(0.169921\pi\)
\(998\) −22.3710 27.3117i −0.708142 0.864536i
\(999\) 130.097i 4.11609i
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 80.2.l.a.61.8 yes 16
3.2 odd 2 720.2.t.c.541.1 16
4.3 odd 2 320.2.l.a.81.8 16
5.2 odd 4 400.2.q.h.349.3 16
5.3 odd 4 400.2.q.g.349.6 16
5.4 even 2 400.2.l.h.301.1 16
8.3 odd 2 640.2.l.a.161.1 16
8.5 even 2 640.2.l.b.161.8 16
12.11 even 2 2880.2.t.c.721.2 16
16.3 odd 4 640.2.l.a.481.1 16
16.5 even 4 inner 80.2.l.a.21.8 16
16.11 odd 4 320.2.l.a.241.8 16
16.13 even 4 640.2.l.b.481.8 16
20.3 even 4 1600.2.q.h.849.1 16
20.7 even 4 1600.2.q.g.849.8 16
20.19 odd 2 1600.2.l.i.401.1 16
32.5 even 8 5120.2.a.v.1.8 8
32.11 odd 8 5120.2.a.u.1.8 8
32.21 even 8 5120.2.a.s.1.1 8
32.27 odd 8 5120.2.a.t.1.1 8
48.5 odd 4 720.2.t.c.181.1 16
48.11 even 4 2880.2.t.c.2161.3 16
80.27 even 4 1600.2.q.h.49.1 16
80.37 odd 4 400.2.q.g.149.6 16
80.43 even 4 1600.2.q.g.49.8 16
80.53 odd 4 400.2.q.h.149.3 16
80.59 odd 4 1600.2.l.i.1201.1 16
80.69 even 4 400.2.l.h.101.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
80.2.l.a.21.8 16 16.5 even 4 inner
80.2.l.a.61.8 yes 16 1.1 even 1 trivial
320.2.l.a.81.8 16 4.3 odd 2
320.2.l.a.241.8 16 16.11 odd 4
400.2.l.h.101.1 16 80.69 even 4
400.2.l.h.301.1 16 5.4 even 2
400.2.q.g.149.6 16 80.37 odd 4
400.2.q.g.349.6 16 5.3 odd 4
400.2.q.h.149.3 16 80.53 odd 4
400.2.q.h.349.3 16 5.2 odd 4
640.2.l.a.161.1 16 8.3 odd 2
640.2.l.a.481.1 16 16.3 odd 4
640.2.l.b.161.8 16 8.5 even 2
640.2.l.b.481.8 16 16.13 even 4
720.2.t.c.181.1 16 48.5 odd 4
720.2.t.c.541.1 16 3.2 odd 2
1600.2.l.i.401.1 16 20.19 odd 2
1600.2.l.i.1201.1 16 80.59 odd 4
1600.2.q.g.49.8 16 80.43 even 4
1600.2.q.g.849.8 16 20.7 even 4
1600.2.q.h.49.1 16 80.27 even 4
1600.2.q.h.849.1 16 20.3 even 4
2880.2.t.c.721.2 16 12.11 even 2
2880.2.t.c.2161.3 16 48.11 even 4
5120.2.a.s.1.1 8 32.21 even 8
5120.2.a.t.1.1 8 32.27 odd 8
5120.2.a.u.1.8 8 32.11 odd 8
5120.2.a.v.1.8 8 32.5 even 8