Properties

Label 95.2.r.a.48.6
Level $95$
Weight $2$
Character 95.48
Analytic conductor $0.759$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,2,Mod(2,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.r (of order \(36\), degree \(12\), 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: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(8\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 48.6
Character \(\chi\) \(=\) 95.48
Dual form 95.2.r.a.2.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.259809 - 0.371046i) q^{2} +(0.264820 - 3.02691i) q^{3} +(0.613866 + 1.68658i) q^{4} +(-1.63140 - 1.52922i) q^{5} +(-1.05432 - 0.884679i) q^{6} +(0.508516 + 1.89781i) q^{7} +(1.66034 + 0.444888i) q^{8} +(-6.13763 - 1.08223i) q^{9} +O(q^{10})\) \(q+(0.259809 - 0.371046i) q^{2} +(0.264820 - 3.02691i) q^{3} +(0.613866 + 1.68658i) q^{4} +(-1.63140 - 1.52922i) q^{5} +(-1.05432 - 0.884679i) q^{6} +(0.508516 + 1.89781i) q^{7} +(1.66034 + 0.444888i) q^{8} +(-6.13763 - 1.08223i) q^{9} +(-0.991264 + 0.208020i) q^{10} +(0.238127 + 0.412449i) q^{11} +(5.26770 - 1.41148i) q^{12} +(4.16333 - 0.364244i) q^{13} +(0.836290 + 0.304385i) q^{14} +(-5.06085 + 4.53315i) q^{15} +(-2.15338 + 1.80690i) q^{16} +(0.661787 + 0.463388i) q^{17} +(-1.99617 + 1.99617i) q^{18} +(2.59888 + 3.49940i) q^{19} +(1.57770 - 3.69024i) q^{20} +(5.87916 - 1.03665i) q^{21} +(0.214905 + 0.0188017i) q^{22} +(-4.23599 - 1.97527i) q^{23} +(1.78633 - 4.90790i) q^{24} +(0.322962 + 4.98956i) q^{25} +(0.946520 - 1.63942i) q^{26} +(-2.54194 + 9.48666i) q^{27} +(-2.88865 + 2.02265i) q^{28} +(-0.693994 + 3.93584i) q^{29} +(0.367151 + 3.05556i) q^{30} +(-8.78658 - 5.07294i) q^{31} +(0.410602 + 4.69320i) q^{32} +(1.31151 - 0.611565i) q^{33} +(0.343876 - 0.125161i) q^{34} +(2.07257 - 3.87373i) q^{35} +(-1.94241 - 11.0160i) q^{36} +(-4.48456 - 4.48456i) q^{37} +(1.97365 - 0.0551271i) q^{38} -12.6985i q^{39} +(-2.02836 - 3.26483i) q^{40} +(4.84667 + 5.77603i) q^{41} +(1.14281 - 2.45077i) q^{42} +(0.462984 + 0.992873i) q^{43} +(-0.549451 + 0.654810i) q^{44} +(8.35800 + 11.1514i) q^{45} +(-1.83346 + 1.05855i) q^{46} +(-5.33230 - 7.61531i) q^{47} +(4.89908 + 6.99661i) q^{48} +(2.71909 - 1.56987i) q^{49} +(1.93526 + 1.17650i) q^{50} +(1.57789 - 1.88046i) q^{51} +(3.17006 + 6.79821i) q^{52} +(3.03662 - 6.51205i) q^{53} +(2.85956 + 3.40789i) q^{54} +(0.242243 - 1.03702i) q^{55} +3.37725i q^{56} +(11.2806 - 6.93987i) q^{57} +(1.28007 + 1.28007i) q^{58} +(-0.304047 - 1.72434i) q^{59} +(-10.7522 - 5.75279i) q^{60} +(-3.30814 + 1.20406i) q^{61} +(-4.16512 + 1.94223i) q^{62} +(-1.06722 - 12.1984i) q^{63} +(-3.02080 - 1.74406i) q^{64} +(-7.34909 - 5.77243i) q^{65} +(0.113822 - 0.645519i) q^{66} +(-2.48924 + 1.74299i) q^{67} +(-0.375294 + 1.40062i) q^{68} +(-7.10075 + 12.2989i) q^{69} +(-0.898856 - 1.77545i) q^{70} +(-0.907322 + 2.49285i) q^{71} +(-9.70912 - 4.52744i) q^{72} +(0.394051 + 0.0344750i) q^{73} +(-2.82911 + 0.498848i) q^{74} +(15.1885 + 0.343758i) q^{75} +(-4.30667 + 6.53139i) q^{76} +(-0.661657 + 0.661657i) q^{77} +(-4.71172 - 3.29918i) q^{78} +(-3.51787 + 2.95185i) q^{79} +(6.27620 + 0.345210i) q^{80} +(10.4727 + 3.81176i) q^{81} +(3.40238 - 0.297669i) q^{82} +(-7.60197 + 2.03694i) q^{83} +(5.35742 + 9.27933i) q^{84} +(-0.371019 - 1.76799i) q^{85} +(0.488688 + 0.0861690i) q^{86} +(11.7296 + 3.14295i) q^{87} +(0.211880 + 0.790747i) q^{88} +(0.225503 + 0.189219i) q^{89} +(6.30915 - 0.203975i) q^{90} +(2.80839 + 7.71598i) q^{91} +(0.731134 - 8.35690i) q^{92} +(-17.6822 + 25.2528i) q^{93} -4.21101 q^{94} +(1.11154 - 9.68321i) q^{95} +14.3146 q^{96} +(2.37298 - 3.38897i) q^{97} +(0.123952 - 1.41677i) q^{98} +(-1.01517 - 2.78917i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8} - 12 q^{10} - 12 q^{11} - 18 q^{12} - 12 q^{13} + 6 q^{15} + 12 q^{16} - 30 q^{17} - 84 q^{20} + 24 q^{21} - 24 q^{22} + 12 q^{25} - 48 q^{26} - 18 q^{27} - 6 q^{30} - 36 q^{31} + 18 q^{32} + 90 q^{33} - 30 q^{35} + 24 q^{36} + 54 q^{38} + 54 q^{40} + 12 q^{41} + 24 q^{42} + 48 q^{43} + 12 q^{45} - 36 q^{46} - 24 q^{47} + 60 q^{48} + 126 q^{50} - 96 q^{51} - 30 q^{53} + 18 q^{55} - 66 q^{57} + 120 q^{58} + 84 q^{60} - 48 q^{61} + 60 q^{62} - 126 q^{63} + 72 q^{65} + 72 q^{66} + 108 q^{67} + 18 q^{68} + 36 q^{70} - 24 q^{71} + 48 q^{72} + 6 q^{73} + 60 q^{76} + 168 q^{77} - 138 q^{78} - 60 q^{80} - 120 q^{81} + 60 q^{82} - 36 q^{85} - 180 q^{86} - 6 q^{87} - 198 q^{88} - 270 q^{90} - 24 q^{91} - 72 q^{92} - 90 q^{93} - 24 q^{95} - 192 q^{96} - 72 q^{97} - 90 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.259809 0.371046i 0.183713 0.262369i −0.716723 0.697358i \(-0.754359\pi\)
0.900436 + 0.434989i \(0.143248\pi\)
\(3\) 0.264820 3.02691i 0.152894 1.74759i −0.401976 0.915650i \(-0.631676\pi\)
0.554870 0.831937i \(-0.312768\pi\)
\(4\) 0.613866 + 1.68658i 0.306933 + 0.843292i
\(5\) −1.63140 1.52922i −0.729586 0.683889i
\(6\) −1.05432 0.884679i −0.430424 0.361169i
\(7\) 0.508516 + 1.89781i 0.192201 + 0.717304i 0.992974 + 0.118336i \(0.0377558\pi\)
−0.800773 + 0.598968i \(0.795577\pi\)
\(8\) 1.66034 + 0.444888i 0.587020 + 0.157292i
\(9\) −6.13763 1.08223i −2.04588 0.360744i
\(10\) −0.991264 + 0.208020i −0.313465 + 0.0657817i
\(11\) 0.238127 + 0.412449i 0.0717981 + 0.124358i 0.899689 0.436531i \(-0.143793\pi\)
−0.827891 + 0.560889i \(0.810460\pi\)
\(12\) 5.26770 1.41148i 1.52065 0.407458i
\(13\) 4.16333 0.364244i 1.15470 0.101023i 0.506324 0.862343i \(-0.331004\pi\)
0.648377 + 0.761320i \(0.275448\pi\)
\(14\) 0.836290 + 0.304385i 0.223508 + 0.0813503i
\(15\) −5.06085 + 4.53315i −1.30670 + 1.17045i
\(16\) −2.15338 + 1.80690i −0.538346 + 0.451726i
\(17\) 0.661787 + 0.463388i 0.160507 + 0.112388i 0.651071 0.759017i \(-0.274320\pi\)
−0.490564 + 0.871405i \(0.663209\pi\)
\(18\) −1.99617 + 1.99617i −0.470502 + 0.470502i
\(19\) 2.59888 + 3.49940i 0.596224 + 0.802818i
\(20\) 1.57770 3.69024i 0.352783 0.825162i
\(21\) 5.87916 1.03665i 1.28294 0.226217i
\(22\) 0.214905 + 0.0188017i 0.0458179 + 0.00400854i
\(23\) −4.23599 1.97527i −0.883265 0.411873i −0.0725845 0.997362i \(-0.523125\pi\)
−0.810680 + 0.585489i \(0.800902\pi\)
\(24\) 1.78633 4.90790i 0.364633 1.00182i
\(25\) 0.322962 + 4.98956i 0.0645925 + 0.997912i
\(26\) 0.946520 1.63942i 0.185628 0.321517i
\(27\) −2.54194 + 9.48666i −0.489197 + 1.82571i
\(28\) −2.88865 + 2.02265i −0.545904 + 0.382246i
\(29\) −0.693994 + 3.93584i −0.128871 + 0.730866i 0.850061 + 0.526684i \(0.176565\pi\)
−0.978933 + 0.204183i \(0.934546\pi\)
\(30\) 0.367151 + 3.05556i 0.0670323 + 0.557866i
\(31\) −8.78658 5.07294i −1.57812 0.911126i −0.995122 0.0986501i \(-0.968548\pi\)
−0.582995 0.812476i \(-0.698119\pi\)
\(32\) 0.410602 + 4.69320i 0.0725849 + 0.829649i
\(33\) 1.31151 0.611565i 0.228304 0.106460i
\(34\) 0.343876 0.125161i 0.0589743 0.0214649i
\(35\) 2.07257 3.87373i 0.350329 0.654779i
\(36\) −1.94241 11.0160i −0.323736 1.83600i
\(37\) −4.48456 4.48456i −0.737257 0.737257i 0.234789 0.972046i \(-0.424560\pi\)
−0.972046 + 0.234789i \(0.924560\pi\)
\(38\) 1.97365 0.0551271i 0.320168 0.00894280i
\(39\) 12.6985i 2.03339i
\(40\) −2.02836 3.26483i −0.320712 0.516215i
\(41\) 4.84667 + 5.77603i 0.756922 + 0.902064i 0.997649 0.0685283i \(-0.0218304\pi\)
−0.240727 + 0.970593i \(0.577386\pi\)
\(42\) 1.14281 2.45077i 0.176340 0.378162i
\(43\) 0.462984 + 0.992873i 0.0706044 + 0.151412i 0.938443 0.345435i \(-0.112269\pi\)
−0.867838 + 0.496847i \(0.834491\pi\)
\(44\) −0.549451 + 0.654810i −0.0828328 + 0.0987163i
\(45\) 8.35800 + 11.1514i 1.24594 + 1.66235i
\(46\) −1.83346 + 1.05855i −0.270330 + 0.156075i
\(47\) −5.33230 7.61531i −0.777796 1.11081i −0.991008 0.133802i \(-0.957282\pi\)
0.213212 0.977006i \(-0.431607\pi\)
\(48\) 4.89908 + 6.99661i 0.707121 + 1.00987i
\(49\) 2.71909 1.56987i 0.388442 0.224267i
\(50\) 1.93526 + 1.17650i 0.273687 + 0.166382i
\(51\) 1.57789 1.88046i 0.220949 0.263317i
\(52\) 3.17006 + 6.79821i 0.439608 + 0.942742i
\(53\) 3.03662 6.51205i 0.417112 0.894499i −0.579709 0.814824i \(-0.696834\pi\)
0.996821 0.0796756i \(-0.0253884\pi\)
\(54\) 2.85956 + 3.40789i 0.389137 + 0.463756i
\(55\) 0.242243 1.03702i 0.0326641 0.139832i
\(56\) 3.37725i 0.451304i
\(57\) 11.2806 6.93987i 1.49415 0.919208i
\(58\) 1.28007 + 1.28007i 0.168081 + 0.168081i
\(59\) −0.304047 1.72434i −0.0395836 0.224490i 0.958598 0.284761i \(-0.0919144\pi\)
−0.998182 + 0.0602717i \(0.980803\pi\)
\(60\) −10.7522 5.75279i −1.38810 0.742682i
\(61\) −3.30814 + 1.20406i −0.423564 + 0.154165i −0.545003 0.838434i \(-0.683471\pi\)
0.121439 + 0.992599i \(0.461249\pi\)
\(62\) −4.16512 + 1.94223i −0.528971 + 0.246663i
\(63\) −1.06722 12.1984i −0.134457 1.53685i
\(64\) −3.02080 1.74406i −0.377600 0.218008i
\(65\) −7.34909 5.77243i −0.911543 0.715982i
\(66\) 0.113822 0.645519i 0.0140106 0.0794579i
\(67\) −2.48924 + 1.74299i −0.304110 + 0.212940i −0.715663 0.698446i \(-0.753875\pi\)
0.411553 + 0.911386i \(0.364986\pi\)
\(68\) −0.375294 + 1.40062i −0.0455111 + 0.169850i
\(69\) −7.10075 + 12.2989i −0.854830 + 1.48061i
\(70\) −0.898856 1.77545i −0.107434 0.212207i
\(71\) −0.907322 + 2.49285i −0.107679 + 0.295847i −0.981816 0.189833i \(-0.939205\pi\)
0.874137 + 0.485679i \(0.161428\pi\)
\(72\) −9.70912 4.52744i −1.14423 0.533563i
\(73\) 0.394051 + 0.0344750i 0.0461202 + 0.00403499i 0.110192 0.993910i \(-0.464853\pi\)
−0.0640723 + 0.997945i \(0.520409\pi\)
\(74\) −2.82911 + 0.498848i −0.328877 + 0.0579899i
\(75\) 15.1885 + 0.343758i 1.75381 + 0.0396938i
\(76\) −4.30667 + 6.53139i −0.494009 + 0.749202i
\(77\) −0.661657 + 0.661657i −0.0754028 + 0.0754028i
\(78\) −4.71172 3.29918i −0.533497 0.373559i
\(79\) −3.51787 + 2.95185i −0.395792 + 0.332109i −0.818864 0.573987i \(-0.805396\pi\)
0.423073 + 0.906096i \(0.360952\pi\)
\(80\) 6.27620 + 0.345210i 0.701700 + 0.0385957i
\(81\) 10.4727 + 3.81176i 1.16364 + 0.423529i
\(82\) 3.40238 0.297669i 0.375730 0.0328721i
\(83\) −7.60197 + 2.03694i −0.834425 + 0.223583i −0.650643 0.759384i \(-0.725501\pi\)
−0.183782 + 0.982967i \(0.558834\pi\)
\(84\) 5.35742 + 9.27933i 0.584543 + 1.01246i
\(85\) −0.371019 1.76799i −0.0402427 0.191766i
\(86\) 0.488688 + 0.0861690i 0.0526966 + 0.00929184i
\(87\) 11.7296 + 3.14295i 1.25755 + 0.336959i
\(88\) 0.211880 + 0.790747i 0.0225865 + 0.0842939i
\(89\) 0.225503 + 0.189219i 0.0239032 + 0.0200572i 0.654661 0.755923i \(-0.272811\pi\)
−0.630758 + 0.775980i \(0.717256\pi\)
\(90\) 6.30915 0.203975i 0.665042 0.0215008i
\(91\) 2.80839 + 7.71598i 0.294399 + 0.808855i
\(92\) 0.731134 8.35690i 0.0762260 0.871267i
\(93\) −17.6822 + 25.2528i −1.83356 + 2.61859i
\(94\) −4.21101 −0.434332
\(95\) 1.11154 9.68321i 0.114041 0.993476i
\(96\) 14.3146 1.46098
\(97\) 2.37298 3.38897i 0.240940 0.344097i −0.680411 0.732831i \(-0.738199\pi\)
0.921350 + 0.388734i \(0.127087\pi\)
\(98\) 0.123952 1.41677i 0.0125210 0.143116i
\(99\) −1.01517 2.78917i −0.102029 0.280322i
\(100\) −8.21705 + 3.60762i −0.821705 + 0.360762i
\(101\) 7.59390 + 6.37204i 0.755622 + 0.634042i 0.936983 0.349375i \(-0.113606\pi\)
−0.181361 + 0.983417i \(0.558050\pi\)
\(102\) −0.287785 1.07403i −0.0284950 0.106345i
\(103\) 16.5649 + 4.43855i 1.63219 + 0.437344i 0.954550 0.298051i \(-0.0963367\pi\)
0.677639 + 0.735395i \(0.263003\pi\)
\(104\) 7.07462 + 1.24745i 0.693723 + 0.122322i
\(105\) −11.1766 7.29934i −1.09072 0.712342i
\(106\) −1.62733 2.81861i −0.158060 0.273768i
\(107\) −1.01491 + 0.271946i −0.0981155 + 0.0262900i −0.307543 0.951534i \(-0.599507\pi\)
0.209427 + 0.977824i \(0.432840\pi\)
\(108\) −17.5605 + 1.53634i −1.68976 + 0.147834i
\(109\) 7.91145 + 2.87953i 0.757780 + 0.275809i 0.691876 0.722017i \(-0.256785\pi\)
0.0659041 + 0.997826i \(0.479007\pi\)
\(110\) −0.321845 0.359310i −0.0306867 0.0342589i
\(111\) −14.7620 + 12.3868i −1.40114 + 1.17570i
\(112\) −4.52419 3.16787i −0.427496 0.299336i
\(113\) 7.71845 7.71845i 0.726091 0.726091i −0.243748 0.969839i \(-0.578377\pi\)
0.969839 + 0.243748i \(0.0783769\pi\)
\(114\) 0.355798 5.98866i 0.0333235 0.560890i
\(115\) 3.88998 + 9.70024i 0.362743 + 0.904552i
\(116\) −7.06413 + 1.24560i −0.655888 + 0.115651i
\(117\) −25.9472 2.27009i −2.39882 0.209870i
\(118\) −0.718802 0.335183i −0.0661711 0.0308561i
\(119\) −0.542893 + 1.49159i −0.0497669 + 0.136733i
\(120\) −10.4195 + 5.27508i −0.951165 + 0.481546i
\(121\) 5.38659 9.32985i 0.489690 0.848168i
\(122\) −0.412721 + 1.54030i −0.0373660 + 0.139452i
\(123\) 18.7670 13.1408i 1.69217 1.18487i
\(124\) 3.16214 17.9334i 0.283969 1.61047i
\(125\) 7.10326 8.63387i 0.635335 0.772237i
\(126\) −4.80343 2.77326i −0.427924 0.247062i
\(127\) −0.875911 10.0117i −0.0777245 0.888395i −0.930542 0.366186i \(-0.880663\pi\)
0.852817 0.522210i \(-0.174892\pi\)
\(128\) −9.97142 + 4.64975i −0.881358 + 0.410984i
\(129\) 3.12794 1.13848i 0.275400 0.100237i
\(130\) −4.05119 + 1.22712i −0.355313 + 0.107626i
\(131\) −2.04515 11.5986i −0.178686 1.01338i −0.933803 0.357787i \(-0.883531\pi\)
0.755118 0.655589i \(-0.227580\pi\)
\(132\) 1.83655 + 1.83655i 0.159851 + 0.159851i
\(133\) −5.31962 + 6.71168i −0.461270 + 0.581976i
\(134\) 1.37647i 0.118909i
\(135\) 18.6541 11.5894i 1.60549 0.997455i
\(136\) 0.892639 + 1.06381i 0.0765432 + 0.0912206i
\(137\) −7.93960 + 17.0265i −0.678325 + 1.45467i 0.201554 + 0.979477i \(0.435401\pi\)
−0.879880 + 0.475196i \(0.842377\pi\)
\(138\) 2.71860 + 5.83006i 0.231423 + 0.496288i
\(139\) 6.70183 7.98693i 0.568441 0.677442i −0.402869 0.915258i \(-0.631987\pi\)
0.971310 + 0.237816i \(0.0764314\pi\)
\(140\) 7.80564 + 1.11762i 0.659697 + 0.0944560i
\(141\) −24.4630 + 14.1237i −2.06015 + 1.18943i
\(142\) 0.689230 + 0.984322i 0.0578389 + 0.0826025i
\(143\) 1.14164 + 1.63042i 0.0954684 + 0.136343i
\(144\) 15.1722 8.75966i 1.26435 0.729972i
\(145\) 7.15095 5.35967i 0.593854 0.445096i
\(146\) 0.115170 0.137254i 0.00953151 0.0113592i
\(147\) −4.03178 8.64618i −0.332536 0.713125i
\(148\) 4.81067 10.3165i 0.395434 0.848012i
\(149\) 14.5924 + 17.3906i 1.19546 + 1.42469i 0.879487 + 0.475922i \(0.157886\pi\)
0.315970 + 0.948769i \(0.397670\pi\)
\(150\) 4.07365 5.54631i 0.332612 0.452854i
\(151\) 3.39398i 0.276198i 0.990418 + 0.138099i \(0.0440992\pi\)
−0.990418 + 0.138099i \(0.955901\pi\)
\(152\) 2.75820 + 6.96643i 0.223719 + 0.565052i
\(153\) −3.56032 3.56032i −0.287834 0.287834i
\(154\) 0.0736005 + 0.417409i 0.00593090 + 0.0336358i
\(155\) 6.57683 + 21.7126i 0.528264 + 1.74400i
\(156\) 21.4171 7.79518i 1.71474 0.624114i
\(157\) 11.1996 5.22244i 0.893823 0.416796i 0.0792479 0.996855i \(-0.474748\pi\)
0.814575 + 0.580059i \(0.196970\pi\)
\(158\) 0.181295 + 2.07221i 0.0144230 + 0.164856i
\(159\) −18.9072 10.9161i −1.49944 0.865703i
\(160\) 6.50709 8.28441i 0.514431 0.654940i
\(161\) 1.59462 9.04355i 0.125674 0.712732i
\(162\) 4.13524 2.89553i 0.324895 0.227494i
\(163\) −0.206494 + 0.770648i −0.0161739 + 0.0603618i −0.973541 0.228512i \(-0.926614\pi\)
0.957367 + 0.288874i \(0.0932807\pi\)
\(164\) −6.76655 + 11.7200i −0.528379 + 0.915179i
\(165\) −3.07482 1.00787i −0.239374 0.0784628i
\(166\) −1.21926 + 3.34989i −0.0946331 + 0.260002i
\(167\) −11.8591 5.53000i −0.917687 0.427924i −0.0943898 0.995535i \(-0.530090\pi\)
−0.823297 + 0.567611i \(0.807868\pi\)
\(168\) 10.2226 + 0.894364i 0.788693 + 0.0690017i
\(169\) 4.39817 0.775516i 0.338321 0.0596551i
\(170\) −0.752400 0.321675i −0.0577065 0.0246714i
\(171\) −12.1638 24.2906i −0.930191 1.85755i
\(172\) −1.39035 + 1.39035i −0.106013 + 0.106013i
\(173\) −8.58372 6.01038i −0.652608 0.456961i 0.199801 0.979836i \(-0.435970\pi\)
−0.852409 + 0.522875i \(0.824859\pi\)
\(174\) 4.21364 3.53567i 0.319435 0.268038i
\(175\) −9.30499 + 3.15019i −0.703391 + 0.238132i
\(176\) −1.25803 0.457887i −0.0948279 0.0345145i
\(177\) −5.29994 + 0.463684i −0.398368 + 0.0348526i
\(178\) 0.128796 0.0345109i 0.00965370 0.00258670i
\(179\) 2.06040 + 3.56872i 0.154002 + 0.266739i 0.932695 0.360666i \(-0.117451\pi\)
−0.778693 + 0.627405i \(0.784117\pi\)
\(180\) −13.6770 + 20.9419i −1.01942 + 1.56092i
\(181\) 1.86465 + 0.328788i 0.138598 + 0.0244386i 0.242517 0.970147i \(-0.422027\pi\)
−0.103919 + 0.994586i \(0.533138\pi\)
\(182\) 3.59263 + 0.962641i 0.266303 + 0.0713557i
\(183\) 2.76853 + 10.3323i 0.204656 + 0.763785i
\(184\) −6.15443 5.16418i −0.453710 0.380708i
\(185\) 0.458246 + 14.1740i 0.0336909 + 1.04209i
\(186\) 4.77594 + 13.1218i 0.350189 + 0.962137i
\(187\) −0.0335343 + 0.383299i −0.00245227 + 0.0280296i
\(188\) 9.57054 13.6681i 0.698003 0.996852i
\(189\) −19.2965 −1.40361
\(190\) −3.30412 2.92821i −0.239706 0.212435i
\(191\) −10.2817 −0.743955 −0.371977 0.928242i \(-0.621320\pi\)
−0.371977 + 0.928242i \(0.621320\pi\)
\(192\) −6.07908 + 8.68183i −0.438720 + 0.626557i
\(193\) −0.160524 + 1.83479i −0.0115547 + 0.132071i −0.999781 0.0209284i \(-0.993338\pi\)
0.988226 + 0.153000i \(0.0488934\pi\)
\(194\) −0.640940 1.76097i −0.0460168 0.126430i
\(195\) −19.4188 + 20.7164i −1.39061 + 1.48353i
\(196\) 4.31687 + 3.62229i 0.308348 + 0.258735i
\(197\) −1.75700 6.55723i −0.125181 0.467183i 0.874665 0.484728i \(-0.161082\pi\)
−0.999846 + 0.0175452i \(0.994415\pi\)
\(198\) −1.29866 0.347975i −0.0922917 0.0247295i
\(199\) −13.7215 2.41947i −0.972691 0.171512i −0.335350 0.942094i \(-0.608855\pi\)
−0.637341 + 0.770582i \(0.719966\pi\)
\(200\) −1.68357 + 8.42807i −0.119046 + 0.595954i
\(201\) 4.61667 + 7.99630i 0.325634 + 0.564015i
\(202\) 4.33728 1.16217i 0.305170 0.0817701i
\(203\) −7.82237 + 0.684368i −0.549023 + 0.0480332i
\(204\) 4.14016 + 1.50689i 0.289869 + 0.105504i
\(205\) 0.925959 16.8347i 0.0646718 1.17578i
\(206\) 5.95062 4.99316i 0.414599 0.347890i
\(207\) 23.8613 + 16.7078i 1.65847 + 1.16127i
\(208\) −8.30710 + 8.30710i −0.575994 + 0.575994i
\(209\) −0.824459 + 1.90521i −0.0570290 + 0.131786i
\(210\) −5.61216 + 2.25058i −0.387276 + 0.155305i
\(211\) 10.8661 1.91599i 0.748053 0.131902i 0.213390 0.976967i \(-0.431550\pi\)
0.534663 + 0.845065i \(0.320438\pi\)
\(212\) 12.8472 + 1.12398i 0.882349 + 0.0771955i
\(213\) 7.30535 + 3.40654i 0.500554 + 0.233412i
\(214\) −0.162780 + 0.447234i −0.0111274 + 0.0305723i
\(215\) 0.763008 2.32778i 0.0520367 0.158753i
\(216\) −8.44100 + 14.6202i −0.574337 + 0.994781i
\(217\) 5.15934 19.2549i 0.350239 1.30711i
\(218\) 3.12390 2.18738i 0.211578 0.148148i
\(219\) 0.208705 1.18363i 0.0141030 0.0799821i
\(220\) 1.89773 0.228028i 0.127945 0.0153736i
\(221\) 2.92403 + 1.68819i 0.196691 + 0.113560i
\(222\) 0.760763 + 8.69556i 0.0510590 + 0.583608i
\(223\) −0.189557 + 0.0883919i −0.0126937 + 0.00591916i −0.428955 0.903326i \(-0.641118\pi\)
0.416261 + 0.909245i \(0.363340\pi\)
\(224\) −8.69800 + 3.16581i −0.581159 + 0.211525i
\(225\) 3.41763 30.9736i 0.227842 2.06491i
\(226\) −0.858575 4.86922i −0.0571116 0.323896i
\(227\) 13.3368 + 13.3368i 0.885192 + 0.885192i 0.994057 0.108864i \(-0.0347214\pi\)
−0.108864 + 0.994057i \(0.534721\pi\)
\(228\) 18.6295 + 14.7655i 1.23377 + 0.977872i
\(229\) 1.82322i 0.120482i −0.998184 0.0602408i \(-0.980813\pi\)
0.998184 0.0602408i \(-0.0191869\pi\)
\(230\) 4.60988 + 1.07685i 0.303967 + 0.0710053i
\(231\) 1.82756 + 2.17800i 0.120244 + 0.143302i
\(232\) −2.90328 + 6.22609i −0.190609 + 0.408763i
\(233\) −7.65042 16.4064i −0.501195 1.07482i −0.980383 0.197104i \(-0.936846\pi\)
0.479187 0.877713i \(-0.340932\pi\)
\(234\) −7.58362 + 9.03781i −0.495757 + 0.590820i
\(235\) −2.94636 + 20.5779i −0.192199 + 1.34236i
\(236\) 2.72160 1.57131i 0.177161 0.102284i
\(237\) 8.00337 + 11.4300i 0.519875 + 0.742458i
\(238\) 0.412398 + 0.588965i 0.0267318 + 0.0381769i
\(239\) −26.1511 + 15.0983i −1.69157 + 0.976630i −0.738323 + 0.674448i \(0.764382\pi\)
−0.953250 + 0.302183i \(0.902285\pi\)
\(240\) 2.70699 18.9061i 0.174735 1.22038i
\(241\) 14.7560 17.5855i 0.950516 1.13278i −0.0405195 0.999179i \(-0.512901\pi\)
0.991035 0.133602i \(-0.0426543\pi\)
\(242\) −2.06232 4.42265i −0.132571 0.284299i
\(243\) 1.85924 3.98716i 0.119270 0.255776i
\(244\) −4.06151 4.84032i −0.260011 0.309869i
\(245\) −6.83662 1.59700i −0.436775 0.102029i
\(246\) 10.3775i 0.661647i
\(247\) 12.0946 + 13.6226i 0.769564 + 0.866782i
\(248\) −12.3319 12.3319i −0.783074 0.783074i
\(249\) 4.15249 + 23.5499i 0.263153 + 1.49242i
\(250\) −1.35807 4.87879i −0.0858919 0.308562i
\(251\) 3.28776 1.19665i 0.207522 0.0755317i −0.236168 0.971712i \(-0.575892\pi\)
0.443689 + 0.896181i \(0.353669\pi\)
\(252\) 19.9185 9.28813i 1.25475 0.585097i
\(253\) −0.194006 2.21749i −0.0121970 0.139413i
\(254\) −3.94237 2.27613i −0.247366 0.142817i
\(255\) −5.44981 + 0.654841i −0.341280 + 0.0410078i
\(256\) 0.346016 1.96236i 0.0216260 0.122647i
\(257\) −3.46264 + 2.42456i −0.215993 + 0.151240i −0.676566 0.736382i \(-0.736533\pi\)
0.460573 + 0.887622i \(0.347644\pi\)
\(258\) 0.390240 1.45640i 0.0242953 0.0906713i
\(259\) 6.23036 10.7913i 0.387136 0.670539i
\(260\) 5.22432 15.9384i 0.323999 0.988455i
\(261\) 8.51896 23.4057i 0.527311 1.44877i
\(262\) −4.83497 2.25458i −0.298705 0.139289i
\(263\) −17.5477 1.53523i −1.08204 0.0946662i −0.467837 0.883815i \(-0.654967\pi\)
−0.614202 + 0.789148i \(0.710522\pi\)
\(264\) 2.44963 0.431936i 0.150764 0.0265838i
\(265\) −14.9123 + 5.98013i −0.916057 + 0.367356i
\(266\) 1.10825 + 3.71758i 0.0679514 + 0.227939i
\(267\) 0.632467 0.632467i 0.0387063 0.0387063i
\(268\) −4.46776 3.12836i −0.272912 0.191095i
\(269\) 10.0078 8.39751i 0.610184 0.512006i −0.284517 0.958671i \(-0.591833\pi\)
0.894701 + 0.446666i \(0.147389\pi\)
\(270\) 0.546322 9.93256i 0.0332481 0.604476i
\(271\) −13.0902 4.76443i −0.795171 0.289419i −0.0876870 0.996148i \(-0.527948\pi\)
−0.707484 + 0.706730i \(0.750170\pi\)
\(272\) −2.26238 + 0.197933i −0.137177 + 0.0120014i
\(273\) 24.0993 6.45739i 1.45856 0.390819i
\(274\) 4.25484 + 7.36959i 0.257044 + 0.445213i
\(275\) −1.98103 + 1.32136i −0.119461 + 0.0796807i
\(276\) −25.1020 4.42616i −1.51096 0.266423i
\(277\) −15.7870 4.23013i −0.948552 0.254164i −0.248804 0.968554i \(-0.580038\pi\)
−0.699748 + 0.714390i \(0.746704\pi\)
\(278\) −1.22232 4.56176i −0.0733098 0.273596i
\(279\) 48.4387 + 40.6449i 2.89995 + 2.43335i
\(280\) 5.16456 5.50966i 0.308642 0.329265i
\(281\) 9.89365 + 27.1826i 0.590206 + 1.62158i 0.770123 + 0.637895i \(0.220195\pi\)
−0.179918 + 0.983682i \(0.557583\pi\)
\(282\) −1.11516 + 12.7463i −0.0664068 + 0.759034i
\(283\) −11.0054 + 15.7173i −0.654202 + 0.934297i −0.999992 0.00401516i \(-0.998722\pi\)
0.345790 + 0.938312i \(0.387611\pi\)
\(284\) −4.76137 −0.282535
\(285\) −29.0158 5.92883i −1.71875 0.351194i
\(286\) 0.901569 0.0533109
\(287\) −8.49719 + 12.1352i −0.501573 + 0.716321i
\(288\) 2.55900 29.2495i 0.150791 1.72354i
\(289\) −5.59111 15.3614i −0.328889 0.903614i
\(290\) −0.130801 4.04582i −0.00768092 0.237579i
\(291\) −9.62968 8.08026i −0.564502 0.473673i
\(292\) 0.183750 + 0.685763i 0.0107531 + 0.0401312i
\(293\) −2.71171 0.726601i −0.158420 0.0424485i 0.178737 0.983897i \(-0.442799\pi\)
−0.337157 + 0.941448i \(0.609465\pi\)
\(294\) −4.25562 0.750381i −0.248193 0.0437631i
\(295\) −2.14087 + 3.27805i −0.124646 + 0.190855i
\(296\) −5.45079 9.44105i −0.316821 0.548750i
\(297\) −4.51806 + 1.21061i −0.262165 + 0.0702468i
\(298\) 10.2439 0.896228i 0.593415 0.0519171i
\(299\) −18.3553 6.68079i −1.06152 0.386360i
\(300\) 8.74391 + 25.8277i 0.504830 + 1.49116i
\(301\) −1.64885 + 1.38355i −0.0950379 + 0.0797463i
\(302\) 1.25932 + 0.881786i 0.0724658 + 0.0507411i
\(303\) 21.2986 21.2986i 1.22357 1.22357i
\(304\) −11.9195 2.83963i −0.683629 0.162864i
\(305\) 7.23819 + 3.09456i 0.414458 + 0.177194i
\(306\) −2.24604 + 0.396038i −0.128398 + 0.0226400i
\(307\) 9.48532 + 0.829858i 0.541356 + 0.0473625i 0.354555 0.935035i \(-0.384632\pi\)
0.186801 + 0.982398i \(0.440188\pi\)
\(308\) −1.52211 0.709770i −0.0867301 0.0404429i
\(309\) 17.8218 48.9651i 1.01385 2.78553i
\(310\) 9.76510 + 3.20084i 0.554620 + 0.181795i
\(311\) 11.9740 20.7396i 0.678982 1.17603i −0.296305 0.955093i \(-0.595755\pi\)
0.975288 0.220939i \(-0.0709121\pi\)
\(312\) 5.64941 21.0839i 0.319835 1.19364i
\(313\) −6.87983 + 4.81731i −0.388871 + 0.272290i −0.751620 0.659597i \(-0.770727\pi\)
0.362749 + 0.931887i \(0.381838\pi\)
\(314\) 0.971983 5.51239i 0.0548521 0.311082i
\(315\) −16.9130 + 21.5325i −0.952938 + 1.21322i
\(316\) −7.13804 4.12115i −0.401546 0.231833i
\(317\) 0.300916 + 3.43949i 0.0169011 + 0.193181i 0.999952 + 0.00984528i \(0.00313390\pi\)
−0.983050 + 0.183335i \(0.941311\pi\)
\(318\) −8.96264 + 4.17935i −0.502600 + 0.234366i
\(319\) −1.78859 + 0.650993i −0.100142 + 0.0364486i
\(320\) 2.26109 + 7.46474i 0.126399 + 0.417292i
\(321\) 0.554385 + 3.14407i 0.0309427 + 0.175485i
\(322\) −2.94127 2.94127i −0.163911 0.163911i
\(323\) 0.0983233 + 3.52015i 0.00547086 + 0.195866i
\(324\) 20.0030i 1.11128i
\(325\) 3.16202 + 20.6556i 0.175397 + 1.14576i
\(326\) 0.232296 + 0.276840i 0.0128657 + 0.0153328i
\(327\) 10.8112 23.1847i 0.597861 1.28212i
\(328\) 5.47745 + 11.7464i 0.302441 + 0.648588i
\(329\) 11.7408 13.9922i 0.647293 0.771414i
\(330\) −1.17283 + 0.879043i −0.0645623 + 0.0483897i
\(331\) 13.8683 8.00688i 0.762272 0.440098i −0.0678392 0.997696i \(-0.521610\pi\)
0.830111 + 0.557599i \(0.188277\pi\)
\(332\) −8.10207 11.5710i −0.444659 0.635038i
\(333\) 22.6713 + 32.3779i 1.24238 + 1.77430i
\(334\) −5.13299 + 2.96353i −0.280865 + 0.162157i
\(335\) 6.72638 + 0.963088i 0.367501 + 0.0526191i
\(336\) −10.7870 + 12.8554i −0.588477 + 0.701319i
\(337\) 7.78587 + 16.6969i 0.424123 + 0.909536i 0.996013 + 0.0892052i \(0.0284327\pi\)
−0.571890 + 0.820330i \(0.693790\pi\)
\(338\) 0.854932 1.83341i 0.0465022 0.0997242i
\(339\) −21.3191 25.4071i −1.15789 1.37992i
\(340\) 2.75411 1.71107i 0.149363 0.0927956i
\(341\) 4.83202i 0.261668i
\(342\) −12.1732 1.79759i −0.658252 0.0972028i
\(343\) 14.0871 + 14.0871i 0.760629 + 0.760629i
\(344\) 0.326996 + 1.85449i 0.0176304 + 0.0999872i
\(345\) 30.3919 9.20580i 1.63624 0.495624i
\(346\) −4.46025 + 1.62340i −0.239785 + 0.0872745i
\(347\) −12.0762 + 5.63123i −0.648285 + 0.302300i −0.718807 0.695210i \(-0.755311\pi\)
0.0705217 + 0.997510i \(0.477534\pi\)
\(348\) 1.89959 + 21.7124i 0.101828 + 1.16390i
\(349\) 14.8650 + 8.58233i 0.795707 + 0.459401i 0.841968 0.539528i \(-0.181397\pi\)
−0.0462610 + 0.998929i \(0.514731\pi\)
\(350\) −1.24866 + 4.27102i −0.0667434 + 0.228296i
\(351\) −7.12749 + 40.4220i −0.380437 + 2.15757i
\(352\) −1.83793 + 1.28693i −0.0979620 + 0.0685937i
\(353\) −3.01262 + 11.2432i −0.160345 + 0.598417i 0.838243 + 0.545297i \(0.183583\pi\)
−0.998588 + 0.0531199i \(0.983083\pi\)
\(354\) −1.20492 + 2.08699i −0.0640409 + 0.110922i
\(355\) 5.29233 2.67935i 0.280888 0.142205i
\(356\) −0.180705 + 0.496484i −0.00957737 + 0.0263136i
\(357\) 4.37113 + 2.03829i 0.231345 + 0.107878i
\(358\) 1.85947 + 0.162683i 0.0982761 + 0.00859804i
\(359\) 20.8766 3.68111i 1.10183 0.194282i 0.406978 0.913438i \(-0.366583\pi\)
0.694848 + 0.719156i \(0.255472\pi\)
\(360\) 8.91605 + 22.2335i 0.469917 + 1.17181i
\(361\) −5.49164 + 18.1891i −0.289034 + 0.957319i
\(362\) 0.606448 0.606448i 0.0318742 0.0318742i
\(363\) −26.8141 18.7755i −1.40738 0.985456i
\(364\) −11.2897 + 9.47316i −0.591740 + 0.496529i
\(365\) −0.590137 0.658834i −0.0308892 0.0344849i
\(366\) 4.55304 + 1.65717i 0.237991 + 0.0866218i
\(367\) −0.325699 + 0.0284950i −0.0170014 + 0.00148743i −0.0956532 0.995415i \(-0.530494\pi\)
0.0786519 + 0.996902i \(0.474938\pi\)
\(368\) 12.6908 3.40050i 0.661556 0.177263i
\(369\) −23.4961 40.6964i −1.22316 2.11857i
\(370\) 5.37827 + 3.51251i 0.279603 + 0.182607i
\(371\) 13.9028 + 2.45144i 0.721797 + 0.127272i
\(372\) −53.4454 14.3207i −2.77102 0.742491i
\(373\) −3.71828 13.8768i −0.192525 0.718515i −0.992894 0.119006i \(-0.962029\pi\)
0.800368 0.599509i \(-0.204637\pi\)
\(374\) 0.133509 + 0.112027i 0.00690358 + 0.00579279i
\(375\) −24.2529 23.7874i −1.25241 1.22837i
\(376\) −5.46549 15.0163i −0.281861 0.774407i
\(377\) −1.45572 + 16.6390i −0.0749735 + 0.856951i
\(378\) −5.01340 + 7.15987i −0.257861 + 0.368264i
\(379\) 9.33155 0.479330 0.239665 0.970856i \(-0.422962\pi\)
0.239665 + 0.970856i \(0.422962\pi\)
\(380\) 17.0139 4.06949i 0.872793 0.208761i
\(381\) −30.5365 −1.56443
\(382\) −2.67127 + 3.81496i −0.136674 + 0.195191i
\(383\) 0.679954 7.77191i 0.0347440 0.397126i −0.958833 0.283970i \(-0.908348\pi\)
0.993577 0.113156i \(-0.0360960\pi\)
\(384\) 11.4337 + 31.4140i 0.583476 + 1.60309i
\(385\) 2.09125 0.0676101i 0.106580 0.00344573i
\(386\) 0.639086 + 0.536257i 0.0325286 + 0.0272948i
\(387\) −1.76711 6.59495i −0.0898273 0.335240i
\(388\) 7.17247 + 1.92186i 0.364127 + 0.0975675i
\(389\) 5.11375 + 0.901692i 0.259277 + 0.0457176i 0.301776 0.953379i \(-0.402421\pi\)
−0.0424983 + 0.999097i \(0.513532\pi\)
\(390\) 2.64154 + 12.5876i 0.133760 + 0.637396i
\(391\) −1.88800 3.27012i −0.0954805 0.165377i
\(392\) 5.21305 1.39683i 0.263299 0.0705506i
\(393\) −35.6496 + 3.11894i −1.79828 + 0.157330i
\(394\) −2.88952 1.05170i −0.145572 0.0529838i
\(395\) 10.2531 + 0.563952i 0.515890 + 0.0283755i
\(396\) 4.08098 3.42435i 0.205077 0.172080i
\(397\) −6.74142 4.72039i −0.338342 0.236910i 0.392040 0.919948i \(-0.371769\pi\)
−0.730383 + 0.683038i \(0.760658\pi\)
\(398\) −4.46270 + 4.46270i −0.223695 + 0.223695i
\(399\) 18.9069 + 17.8794i 0.946529 + 0.895090i
\(400\) −9.71112 10.1609i −0.485556 0.508044i
\(401\) 1.97650 0.348511i 0.0987019 0.0174038i −0.124079 0.992272i \(-0.539598\pi\)
0.222781 + 0.974869i \(0.428487\pi\)
\(402\) 4.16644 + 0.364517i 0.207803 + 0.0181804i
\(403\) −38.4293 17.9199i −1.91430 0.892652i
\(404\) −6.08534 + 16.7193i −0.302757 + 0.831818i
\(405\) −11.2562 22.2336i −0.559326 1.10480i
\(406\) −1.77839 + 3.08026i −0.0882600 + 0.152871i
\(407\) 0.781755 2.91755i 0.0387501 0.144617i
\(408\) 3.45643 2.42022i 0.171119 0.119819i
\(409\) −2.66460 + 15.1117i −0.131756 + 0.747224i 0.845308 + 0.534279i \(0.179417\pi\)
−0.977064 + 0.212945i \(0.931694\pi\)
\(410\) −6.00586 4.71737i −0.296608 0.232974i
\(411\) 49.4352 + 28.5414i 2.43846 + 1.40784i
\(412\) 2.68264 + 30.6628i 0.132164 + 1.51065i
\(413\) 3.11785 1.45388i 0.153419 0.0715406i
\(414\) 12.3987 4.51277i 0.609364 0.221791i
\(415\) 15.5168 + 8.30202i 0.761691 + 0.407530i
\(416\) 3.41895 + 19.3898i 0.167628 + 0.950663i
\(417\) −22.4009 22.4009i −1.09698 1.09698i
\(418\) 0.492717 + 0.800902i 0.0240996 + 0.0391734i
\(419\) 5.33874i 0.260814i −0.991461 0.130407i \(-0.958372\pi\)
0.991461 0.130407i \(-0.0416284\pi\)
\(420\) 5.45002 23.3310i 0.265934 1.13844i
\(421\) 6.17855 + 7.36331i 0.301124 + 0.358866i 0.895295 0.445473i \(-0.146964\pi\)
−0.594171 + 0.804338i \(0.702520\pi\)
\(422\) 2.11219 4.52961i 0.102820 0.220498i
\(423\) 24.4862 + 52.5108i 1.19056 + 2.55316i
\(424\) 7.93897 9.46129i 0.385550 0.459481i
\(425\) −2.09837 + 3.45168i −0.101786 + 0.167431i
\(426\) 3.16198 1.82557i 0.153198 0.0884491i
\(427\) −3.96732 5.66592i −0.191992 0.274193i
\(428\) −1.08168 1.54480i −0.0522850 0.0746707i
\(429\) 5.23748 3.02386i 0.252868 0.145993i
\(430\) −0.665477 0.887889i −0.0320922 0.0428178i
\(431\) 1.69479 2.01978i 0.0816354 0.0972892i −0.723681 0.690135i \(-0.757551\pi\)
0.805316 + 0.592846i \(0.201996\pi\)
\(432\) −11.6677 25.0215i −0.561363 1.20385i
\(433\) 8.66419 18.5804i 0.416375 0.892918i −0.580526 0.814242i \(-0.697153\pi\)
0.996900 0.0786761i \(-0.0250693\pi\)
\(434\) −5.80401 6.91695i −0.278601 0.332024i
\(435\) −14.3295 23.0646i −0.687048 1.10586i
\(436\) 15.1110i 0.723684i
\(437\) −4.09655 19.9569i −0.195965 0.954670i
\(438\) −0.384956 0.384956i −0.0183939 0.0183939i
\(439\) 6.25393 + 35.4678i 0.298484 + 1.69279i 0.652696 + 0.757620i \(0.273638\pi\)
−0.354212 + 0.935165i \(0.615251\pi\)
\(440\) 0.863565 1.61404i 0.0411689 0.0769463i
\(441\) −18.3878 + 6.69259i −0.875607 + 0.318695i
\(442\) 1.38608 0.646341i 0.0659293 0.0307433i
\(443\) 1.89203 + 21.6260i 0.0898931 + 1.02748i 0.898453 + 0.439069i \(0.144692\pi\)
−0.808560 + 0.588414i \(0.799753\pi\)
\(444\) −29.9532 17.2935i −1.42152 0.820712i
\(445\) −0.0785280 0.653536i −0.00372258 0.0309806i
\(446\) −0.0164512 + 0.0932993i −0.000778986 + 0.00441785i
\(447\) 56.5041 39.5646i 2.67255 1.87134i
\(448\) 1.77377 6.61978i 0.0838025 0.312755i
\(449\) 4.13533 7.16260i 0.195158 0.338024i −0.751794 0.659398i \(-0.770811\pi\)
0.946952 + 0.321374i \(0.104145\pi\)
\(450\) −10.6047 9.31532i −0.499910 0.439128i
\(451\) −1.22819 + 3.37443i −0.0578333 + 0.158896i
\(452\) 17.7559 + 8.27972i 0.835168 + 0.389445i
\(453\) 10.2733 + 0.898795i 0.482680 + 0.0422291i
\(454\) 8.41356 1.48354i 0.394868 0.0696259i
\(455\) 7.21783 16.8825i 0.338377 0.791466i
\(456\) 21.8172 6.50396i 1.02168 0.304576i
\(457\) −11.1032 + 11.1032i −0.519384 + 0.519384i −0.917385 0.398001i \(-0.869704\pi\)
0.398001 + 0.917385i \(0.369704\pi\)
\(458\) −0.676497 0.473688i −0.0316106 0.0221340i
\(459\) −6.07823 + 5.10024i −0.283708 + 0.238059i
\(460\) −13.9723 + 12.5154i −0.651463 + 0.583535i
\(461\) −20.8249 7.57966i −0.969914 0.353020i −0.192003 0.981394i \(-0.561498\pi\)
−0.777911 + 0.628374i \(0.783721\pi\)
\(462\) 1.28295 0.112244i 0.0596883 0.00522205i
\(463\) 6.40852 1.71716i 0.297829 0.0798031i −0.106810 0.994279i \(-0.534064\pi\)
0.404639 + 0.914476i \(0.367397\pi\)
\(464\) −5.61724 9.72935i −0.260774 0.451674i
\(465\) 67.4639 14.1575i 3.12856 0.656539i
\(466\) −8.07516 1.42387i −0.374074 0.0659594i
\(467\) 36.5016 + 9.78057i 1.68909 + 0.452591i 0.970155 0.242485i \(-0.0779626\pi\)
0.718936 + 0.695076i \(0.244629\pi\)
\(468\) −12.0994 45.1557i −0.559296 2.08732i
\(469\) −4.57368 3.83777i −0.211193 0.177212i
\(470\) 6.86986 + 6.43956i 0.316883 + 0.297035i
\(471\) −12.8420 35.2831i −0.591728 1.62576i
\(472\) 0.262314 2.99826i 0.0120740 0.138006i
\(473\) −0.299260 + 0.427387i −0.0137600 + 0.0196513i
\(474\) 6.32040 0.290306
\(475\) −16.6211 + 14.0974i −0.762630 + 0.646835i
\(476\) −2.84895 −0.130581
\(477\) −25.6852 + 36.6823i −1.17604 + 1.67957i
\(478\) −1.19211 + 13.6259i −0.0545260 + 0.623235i
\(479\) 4.30184 + 11.8192i 0.196556 + 0.540033i 0.998341 0.0575797i \(-0.0183383\pi\)
−0.801785 + 0.597613i \(0.796116\pi\)
\(480\) −23.3530 21.8903i −1.06591 0.999149i
\(481\) −20.3042 17.0372i −0.925792 0.776832i
\(482\) −2.69128 10.0440i −0.122585 0.457492i
\(483\) −26.9517 7.22170i −1.22635 0.328599i
\(484\) 19.0422 + 3.35766i 0.865555 + 0.152621i
\(485\) −9.05377 + 1.89996i −0.411111 + 0.0862729i
\(486\) −0.996369 1.72576i −0.0451962 0.0782822i
\(487\) −24.7641 + 6.63552i −1.12217 + 0.300684i −0.771761 0.635913i \(-0.780624\pi\)
−0.350408 + 0.936597i \(0.613957\pi\)
\(488\) −6.02832 + 0.527410i −0.272889 + 0.0238747i
\(489\) 2.27800 + 0.829124i 0.103015 + 0.0374943i
\(490\) −2.36877 + 2.12178i −0.107010 + 0.0958523i
\(491\) 26.2335 22.0125i 1.18390 0.993410i 0.183955 0.982935i \(-0.441110\pi\)
0.999945 0.0104757i \(-0.00333458\pi\)
\(492\) 33.6835 + 23.5855i 1.51857 + 1.06331i
\(493\) −2.28310 + 2.28310i −0.102826 + 0.102826i
\(494\) 8.19688 0.948404i 0.368795 0.0426707i
\(495\) −2.60910 + 6.10269i −0.117270 + 0.274295i
\(496\) 28.0872 4.95253i 1.26115 0.222375i
\(497\) −5.19233 0.454270i −0.232908 0.0203768i
\(498\) 9.81695 + 4.57772i 0.439908 + 0.205132i
\(499\) −9.81630 + 26.9701i −0.439438 + 1.20735i 0.500421 + 0.865782i \(0.333179\pi\)
−0.939859 + 0.341563i \(0.889044\pi\)
\(500\) 18.9222 + 6.68020i 0.846226 + 0.298747i
\(501\) −19.8794 + 34.4321i −0.888144 + 1.53831i
\(502\) 0.410179 1.53081i 0.0183072 0.0683233i
\(503\) 8.81131 6.16974i 0.392877 0.275095i −0.360401 0.932797i \(-0.617360\pi\)
0.753278 + 0.657702i \(0.228471\pi\)
\(504\) 3.65496 20.7283i 0.162805 0.923312i
\(505\) −2.64447 22.0081i −0.117677 0.979349i
\(506\) −0.873196 0.504140i −0.0388183 0.0224118i
\(507\) −1.18269 13.5182i −0.0525252 0.600366i
\(508\) 16.3479 7.62315i 0.725320 0.338222i
\(509\) −25.8598 + 9.41220i −1.14622 + 0.417188i −0.844154 0.536100i \(-0.819897\pi\)
−0.302061 + 0.953288i \(0.597675\pi\)
\(510\) −1.17293 + 2.19226i −0.0519384 + 0.0970750i
\(511\) 0.134954 + 0.765364i 0.00597003 + 0.0338577i
\(512\) −16.1978 16.1978i −0.715846 0.715846i
\(513\) −39.8038 + 15.7594i −1.75738 + 0.695795i
\(514\) 1.91472i 0.0844547i
\(515\) −20.2365 32.5725i −0.891728 1.43532i
\(516\) 3.84028 + 4.57667i 0.169059 + 0.201476i
\(517\) 1.87116 4.01271i 0.0822935 0.176479i
\(518\) −2.38536 5.11543i −0.104807 0.224759i
\(519\) −20.4660 + 24.3905i −0.898360 + 1.07062i
\(520\) −9.63394 12.8537i −0.422476 0.563674i
\(521\) 29.9147 17.2713i 1.31059 0.756669i 0.328395 0.944540i \(-0.393492\pi\)
0.982194 + 0.187871i \(0.0601588\pi\)
\(522\) −6.47127 9.24192i −0.283240 0.404508i
\(523\) −18.9785 27.1041i −0.829870 1.18518i −0.980487 0.196585i \(-0.937015\pi\)
0.150616 0.988592i \(-0.451874\pi\)
\(524\) 18.3066 10.5693i 0.799728 0.461723i
\(525\) 7.07120 + 28.9996i 0.308612 + 1.26565i
\(526\) −5.12870 + 6.11214i −0.223622 + 0.266502i
\(527\) −3.46411 7.42880i −0.150899 0.323604i
\(528\) −1.71914 + 3.68670i −0.0748158 + 0.160443i
\(529\) −0.742222 0.884546i −0.0322705 0.0384585i
\(530\) −1.65546 + 7.08684i −0.0719084 + 0.307833i
\(531\) 10.9124i 0.473558i
\(532\) −14.5853 4.85191i −0.632355 0.210357i
\(533\) 22.2822 + 22.2822i 0.965148 + 0.965148i
\(534\) −0.0703535 0.398995i −0.00304449 0.0172662i
\(535\) 2.07160 + 1.10838i 0.0895631 + 0.0479193i
\(536\) −4.90844 + 1.78653i −0.212012 + 0.0771661i
\(537\) 11.3478 5.29159i 0.489696 0.228349i
\(538\) −0.515753 5.89509i −0.0222357 0.254155i
\(539\) 1.29498 + 0.747657i 0.0557787 + 0.0322039i
\(540\) 30.9976 + 24.3474i 1.33392 + 1.04775i
\(541\) −5.47144 + 31.0301i −0.235235 + 1.33409i 0.606882 + 0.794792i \(0.292420\pi\)
−0.842117 + 0.539294i \(0.818691\pi\)
\(542\) −5.16876 + 3.61921i −0.222017 + 0.155458i
\(543\) 1.48901 5.55706i 0.0638995 0.238476i
\(544\) −1.90304 + 3.29617i −0.0815924 + 0.141322i
\(545\) −8.50334 16.7960i −0.364243 0.719464i
\(546\) 3.86523 10.6196i 0.165417 0.454478i
\(547\) 31.4152 + 14.6492i 1.34322 + 0.626352i 0.955381 0.295376i \(-0.0954449\pi\)
0.387836 + 0.921728i \(0.373223\pi\)
\(548\) −33.5905 2.93879i −1.43491 0.125539i
\(549\) 21.6072 3.80994i 0.922173 0.162604i
\(550\) −0.0244062 + 1.07835i −0.00104068 + 0.0459811i
\(551\) −15.5767 + 7.80020i −0.663589 + 0.332300i
\(552\) −17.2613 + 17.2613i −0.734690 + 0.734690i
\(553\) −7.39093 5.17519i −0.314294 0.220071i
\(554\) −5.67119 + 4.75869i −0.240946 + 0.202177i
\(555\) 43.0249 + 2.36650i 1.82630 + 0.100452i
\(556\) 17.5846 + 6.40029i 0.745755 + 0.271433i
\(557\) −17.5353 + 1.53414i −0.742996 + 0.0650037i −0.452367 0.891832i \(-0.649420\pi\)
−0.290629 + 0.956836i \(0.593865\pi\)
\(558\) 27.6659 7.41307i 1.17119 0.313820i
\(559\) 2.28921 + 3.96502i 0.0968231 + 0.167703i
\(560\) 2.53641 + 12.0866i 0.107183 + 0.510751i
\(561\) 1.15133 + 0.203011i 0.0486092 + 0.00857111i
\(562\) 12.6564 + 3.39128i 0.533879 + 0.143053i
\(563\) 8.16017 + 30.4542i 0.343910 + 1.28349i 0.893880 + 0.448306i \(0.147973\pi\)
−0.549970 + 0.835184i \(0.685361\pi\)
\(564\) −38.8378 32.5888i −1.63537 1.37223i
\(565\) −24.3951 + 0.788695i −1.02631 + 0.0331806i
\(566\) 2.97254 + 8.16699i 0.124945 + 0.343284i
\(567\) −1.90844 + 21.8135i −0.0801469 + 0.916083i
\(568\) −2.61551 + 3.73533i −0.109744 + 0.156731i
\(569\) −1.63769 −0.0686556 −0.0343278 0.999411i \(-0.510929\pi\)
−0.0343278 + 0.999411i \(0.510929\pi\)
\(570\) −9.73844 + 9.22584i −0.407898 + 0.386428i
\(571\) 24.8017 1.03792 0.518959 0.854799i \(-0.326320\pi\)
0.518959 + 0.854799i \(0.326320\pi\)
\(572\) −2.04904 + 2.92633i −0.0856745 + 0.122356i
\(573\) −2.72279 + 31.1217i −0.113746 + 1.30013i
\(574\) 2.29508 + 6.30569i 0.0957949 + 0.263194i
\(575\) 8.48768 21.7737i 0.353961 0.908024i
\(576\) 16.6531 + 13.9736i 0.693879 + 0.582234i
\(577\) −11.1898 41.7607i −0.465835 1.73852i −0.654104 0.756404i \(-0.726954\pi\)
0.188269 0.982118i \(-0.439712\pi\)
\(578\) −7.15242 1.91648i −0.297501 0.0797152i
\(579\) 5.51125 + 0.971781i 0.229040 + 0.0403858i
\(580\) 13.4293 + 8.77055i 0.557620 + 0.364177i
\(581\) −7.73145 13.3913i −0.320755 0.555563i
\(582\) −5.50002 + 1.47373i −0.227983 + 0.0610880i
\(583\) 3.40899 0.298248i 0.141186 0.0123522i
\(584\) 0.638923 + 0.232549i 0.0264388 + 0.00962294i
\(585\) 38.8589 + 43.3825i 1.60662 + 1.79364i
\(586\) −0.974129 + 0.817392i −0.0402409 + 0.0337661i
\(587\) −22.9473 16.0679i −0.947138 0.663193i −0.00555837 0.999985i \(-0.501769\pi\)
−0.941579 + 0.336792i \(0.890658\pi\)
\(588\) 12.1075 12.1075i 0.499306 0.499306i
\(589\) −5.08303 43.9317i −0.209443 1.81018i
\(590\) 0.660088 + 1.64603i 0.0271754 + 0.0677659i
\(591\) −20.3134 + 3.58181i −0.835583 + 0.147336i
\(592\) 17.7602 + 1.55381i 0.729938 + 0.0638613i
\(593\) 37.6638 + 17.5629i 1.54667 + 0.721223i 0.993710 0.111985i \(-0.0357209\pi\)
0.552959 + 0.833209i \(0.313499\pi\)
\(594\) −0.724641 + 1.99094i −0.0297324 + 0.0816891i
\(595\) 3.16664 1.60318i 0.129820 0.0657238i
\(596\) −20.3729 + 35.2868i −0.834505 + 1.44540i
\(597\) −10.9573 + 40.8930i −0.448451 + 1.67364i
\(598\) −7.24775 + 5.07493i −0.296383 + 0.207529i
\(599\) 6.78798 38.4965i 0.277349 1.57293i −0.454050 0.890976i \(-0.650021\pi\)
0.731399 0.681949i \(-0.238868\pi\)
\(600\) 25.0652 + 7.32793i 1.02328 + 0.299161i
\(601\) −10.8442 6.26090i −0.442344 0.255388i 0.262247 0.965001i \(-0.415536\pi\)
−0.704592 + 0.709613i \(0.748870\pi\)
\(602\) 0.0849738 + 0.971255i 0.00346327 + 0.0395854i
\(603\) 17.1644 8.00389i 0.698988 0.325943i
\(604\) −5.72423 + 2.08345i −0.232916 + 0.0847743i
\(605\) −23.0551 + 6.98347i −0.937324 + 0.283918i
\(606\) −2.36919 13.4363i −0.0962417 0.545814i
\(607\) 4.99686 + 4.99686i 0.202816 + 0.202816i 0.801206 0.598389i \(-0.204192\pi\)
−0.598389 + 0.801206i \(0.704192\pi\)
\(608\) −15.3563 + 13.6339i −0.622780 + 0.552929i
\(609\) 23.8588i 0.966809i
\(610\) 3.02877 1.88170i 0.122631 0.0761880i
\(611\) −24.9740 29.7628i −1.01034 1.20407i
\(612\) 3.81921 8.19033i 0.154382 0.331074i
\(613\) 19.1572 + 41.0827i 0.773750 + 1.65931i 0.751655 + 0.659557i \(0.229256\pi\)
0.0220954 + 0.999756i \(0.492966\pi\)
\(614\) 2.77229 3.30388i 0.111880 0.133334i
\(615\) −50.7118 7.26096i −2.04490 0.292790i
\(616\) −1.39294 + 0.804215i −0.0561232 + 0.0324027i
\(617\) 0.516710 + 0.737938i 0.0208019 + 0.0297083i 0.829418 0.558628i \(-0.188672\pi\)
−0.808616 + 0.588336i \(0.799783\pi\)
\(618\) −13.5380 19.3343i −0.544578 0.777738i
\(619\) −14.0597 + 8.11739i −0.565108 + 0.326266i −0.755193 0.655502i \(-0.772457\pi\)
0.190085 + 0.981768i \(0.439124\pi\)
\(620\) −32.5829 + 24.4210i −1.30856 + 0.980772i
\(621\) 29.5064 35.1643i 1.18405 1.41110i
\(622\) −4.58437 9.83122i −0.183817 0.394196i
\(623\) −0.244430 + 0.524181i −0.00979287 + 0.0210009i
\(624\) 22.9450 + 27.3447i 0.918534 + 1.09467i
\(625\) −24.7914 + 3.22288i −0.991656 + 0.128915i
\(626\) 3.80431i 0.152051i
\(627\) 5.54856 + 3.00010i 0.221588 + 0.119813i
\(628\) 15.6831 + 15.6831i 0.625825 + 0.625825i
\(629\) −0.889732 5.04592i −0.0354759 0.201194i
\(630\) 3.59541 + 11.8698i 0.143244 + 0.472905i
\(631\) −28.4762 + 10.3645i −1.13362 + 0.412603i −0.839604 0.543198i \(-0.817213\pi\)
−0.294013 + 0.955801i \(0.594991\pi\)
\(632\) −7.15412 + 3.33602i −0.284576 + 0.132700i
\(633\) −2.92196 33.3981i −0.116137 1.32746i
\(634\) 1.35439 + 0.781955i 0.0537896 + 0.0310554i
\(635\) −13.8812 + 17.6726i −0.550857 + 0.701316i
\(636\) 6.80440 38.5897i 0.269812 1.53018i
\(637\) 10.7487 7.52630i 0.425878 0.298203i
\(638\) −0.223143 + 0.832782i −0.00883433 + 0.0329702i
\(639\) 8.26665 14.3183i 0.327024 0.566422i
\(640\) 23.3779 + 7.66289i 0.924094 + 0.302902i
\(641\) −10.4710 + 28.7688i −0.413580 + 1.13630i 0.541694 + 0.840576i \(0.317783\pi\)
−0.955273 + 0.295725i \(0.904439\pi\)
\(642\) 1.31063 + 0.611156i 0.0517264 + 0.0241204i
\(643\) −1.33347 0.116664i −0.0525870 0.00460077i 0.0608319 0.998148i \(-0.480625\pi\)
−0.113419 + 0.993547i \(0.536180\pi\)
\(644\) 16.2316 2.86207i 0.639614 0.112781i
\(645\) −6.84393 2.92600i −0.269479 0.115211i
\(646\) 1.33168 + 0.878084i 0.0523943 + 0.0345478i
\(647\) −3.23855 + 3.23855i −0.127320 + 0.127320i −0.767896 0.640575i \(-0.778696\pi\)
0.640575 + 0.767896i \(0.278696\pi\)
\(648\) 15.6925 + 10.9880i 0.616460 + 0.431650i
\(649\) 0.638799 0.536016i 0.0250751 0.0210405i
\(650\) 8.48568 + 4.19325i 0.332836 + 0.164473i
\(651\) −56.9166 20.7160i −2.23074 0.811922i
\(652\) −1.42652 + 0.124804i −0.0558669 + 0.00488772i
\(653\) −0.697739 + 0.186959i −0.0273047 + 0.00731626i −0.272446 0.962171i \(-0.587832\pi\)
0.245141 + 0.969487i \(0.421166\pi\)
\(654\) −5.79373 10.0350i −0.226553 0.392401i
\(655\) −14.4004 + 22.0495i −0.562670 + 0.861547i
\(656\) −20.8735 3.68056i −0.814972 0.143702i
\(657\) −2.38123 0.638049i −0.0929006 0.0248927i
\(658\) −2.14136 7.99168i −0.0834791 0.311548i
\(659\) −1.32005 1.10766i −0.0514220 0.0431482i 0.616714 0.787187i \(-0.288463\pi\)
−0.668136 + 0.744039i \(0.732908\pi\)
\(660\) −0.187664 5.80463i −0.00730480 0.225945i
\(661\) −12.2612 33.6874i −0.476905 1.31029i −0.912106 0.409954i \(-0.865545\pi\)
0.435201 0.900333i \(-0.356677\pi\)
\(662\) 0.632196 7.22603i 0.0245710 0.280848i
\(663\) 5.88434 8.40370i 0.228529 0.326373i
\(664\) −13.5281 −0.524992
\(665\) 18.9421 2.81458i 0.734543 0.109145i
\(666\) 17.9039 0.693762
\(667\) 10.7141 15.3013i 0.414852 0.592470i
\(668\) 2.04689 23.3961i 0.0791966 0.905222i
\(669\) 0.217356 + 0.597180i 0.00840346 + 0.0230883i
\(670\) 2.10492 2.24557i 0.0813203 0.0867541i
\(671\) −1.28437 1.07772i −0.0495826 0.0416048i
\(672\) 7.27922 + 27.1664i 0.280802 + 1.04797i
\(673\) −12.6585 3.39184i −0.487950 0.130746i 0.00645186 0.999979i \(-0.497946\pi\)
−0.494402 + 0.869233i \(0.664613\pi\)
\(674\) 8.21813 + 1.44908i 0.316551 + 0.0558164i
\(675\) −48.1552 9.61934i −1.85349 0.370248i
\(676\) 4.00786 + 6.94182i 0.154148 + 0.266993i
\(677\) 7.08859 1.89938i 0.272437 0.0729992i −0.120014 0.992772i \(-0.538294\pi\)
0.392451 + 0.919773i \(0.371627\pi\)
\(678\) −14.9661 + 1.30936i −0.574768 + 0.0502857i
\(679\) 7.63830 + 2.78012i 0.293131 + 0.106691i
\(680\) 0.170539 3.10054i 0.00653988 0.118900i
\(681\) 43.9011 36.8374i 1.68229 1.41161i
\(682\) −1.79290 1.25540i −0.0686537 0.0480718i
\(683\) 29.0355 29.0355i 1.11101 1.11101i 0.117997 0.993014i \(-0.462353\pi\)
0.993014 0.117997i \(-0.0376472\pi\)
\(684\) 33.5012 35.4265i 1.28095 1.35457i
\(685\) 38.9900 15.6357i 1.48973 0.597411i
\(686\) 8.88688 1.56700i 0.339303 0.0598282i
\(687\) −5.51872 0.482825i −0.210552 0.0184209i
\(688\) −2.79101 1.30147i −0.106406 0.0496180i
\(689\) 10.2705 28.2179i 0.391274 1.07502i
\(690\) 4.48031 13.6685i 0.170563 0.520352i
\(691\) 7.26116 12.5767i 0.276228 0.478440i −0.694217 0.719766i \(-0.744249\pi\)
0.970444 + 0.241326i \(0.0775823\pi\)
\(692\) 4.86776 18.1667i 0.185044 0.690595i
\(693\) 4.77707 3.34494i 0.181466 0.127064i
\(694\) −1.04806 + 5.94387i −0.0397840 + 0.225626i
\(695\) −23.1472 + 2.78133i −0.878022 + 0.105502i
\(696\) 18.0770 + 10.4368i 0.685206 + 0.395604i
\(697\) 0.530916 + 6.06839i 0.0201099 + 0.229857i
\(698\) 7.04650 3.28584i 0.266714 0.124371i
\(699\) −51.6866 + 18.8124i −1.95497 + 0.711550i
\(700\) −11.0251 13.7598i −0.416709 0.520073i
\(701\) 6.45153 + 36.5885i 0.243671 + 1.38193i 0.823559 + 0.567231i \(0.191985\pi\)
−0.579888 + 0.814696i \(0.696904\pi\)
\(702\) 13.1466 + 13.1466i 0.496187 + 0.496187i
\(703\) 4.03845 27.3481i 0.152313 1.03145i
\(704\) 1.66123i 0.0626101i
\(705\) 61.5073 + 14.3678i 2.31650 + 0.541124i
\(706\) 3.38905 + 4.03891i 0.127549 + 0.152006i
\(707\) −8.23129 + 17.6521i −0.309569 + 0.663874i
\(708\) −4.03549 8.65414i −0.151663 0.325243i
\(709\) −14.2659 + 17.0015i −0.535768 + 0.638503i −0.964233 0.265055i \(-0.914610\pi\)
0.428466 + 0.903558i \(0.359054\pi\)
\(710\) 0.380834 2.65981i 0.0142924 0.0998210i
\(711\) 24.7860 14.3102i 0.929548 0.536675i
\(712\) 0.290231 + 0.414492i 0.0108769 + 0.0155338i
\(713\) 27.1994 + 38.8448i 1.01863 + 1.45475i
\(714\) 1.89196 1.09232i 0.0708047 0.0408791i
\(715\) 0.630811 4.40570i 0.0235910 0.164764i
\(716\) −4.75414 + 5.66576i −0.177670 + 0.211739i
\(717\) 38.7760 + 83.1553i 1.44812 + 3.10549i
\(718\) 4.05807 8.70256i 0.151446 0.324777i
\(719\) 16.1088 + 19.1978i 0.600758 + 0.715956i 0.977635 0.210308i \(-0.0674466\pi\)
−0.376877 + 0.926263i \(0.623002\pi\)
\(720\) −38.1474 8.91107i −1.42167 0.332096i
\(721\) 33.6941i 1.25483i
\(722\) 5.32219 + 6.76333i 0.198072 + 0.251705i
\(723\) −49.3220 49.3220i −1.83430 1.83430i
\(724\) 0.590117 + 3.34672i 0.0219315 + 0.124380i
\(725\) −19.8622 2.19160i −0.737664 0.0813939i
\(726\) −13.9331 + 5.07124i −0.517106 + 0.188211i
\(727\) 17.2023 8.02156i 0.637998 0.297503i −0.0765756 0.997064i \(-0.524399\pi\)
0.714573 + 0.699561i \(0.246621\pi\)
\(728\) 1.23014 + 14.0606i 0.0455922 + 0.521121i
\(729\) 17.3787 + 10.0336i 0.643656 + 0.371615i
\(730\) −0.397780 + 0.0477967i −0.0147225 + 0.00176903i
\(731\) −0.153689 + 0.871612i −0.00568438 + 0.0322377i
\(732\) −15.7268 + 11.0120i −0.581278 + 0.407015i
\(733\) 9.56681 35.7038i 0.353358 1.31875i −0.529180 0.848510i \(-0.677500\pi\)
0.882538 0.470241i \(-0.155833\pi\)
\(734\) −0.0740466 + 0.128252i −0.00273311 + 0.00473388i
\(735\) −6.64446 + 20.2709i −0.245085 + 0.747704i
\(736\) 7.53105 20.6914i 0.277598 0.762695i
\(737\) −1.31165 0.611632i −0.0483153 0.0225298i
\(738\) −21.2047 1.85517i −0.780556 0.0682898i
\(739\) 22.2479 3.92291i 0.818404 0.144307i 0.251254 0.967921i \(-0.419157\pi\)
0.567150 + 0.823615i \(0.308046\pi\)
\(740\) −23.6244 + 9.47382i −0.868449 + 0.348265i
\(741\) 44.4372 33.0019i 1.63244 1.21235i
\(742\) 4.52166 4.52166i 0.165996 0.165996i
\(743\) 11.5972 + 8.12048i 0.425462 + 0.297912i 0.766628 0.642091i \(-0.221933\pi\)
−0.341166 + 0.940003i \(0.610822\pi\)
\(744\) −40.5932 + 34.0617i −1.48822 + 1.24876i
\(745\) 2.78789 50.6861i 0.102140 1.85700i
\(746\) −6.11498 2.22567i −0.223885 0.0814876i
\(747\) 48.8626 4.27492i 1.78779 0.156411i
\(748\) −0.667051 + 0.178736i −0.0243898 + 0.00653523i
\(749\) −1.03220 1.78782i −0.0377158 0.0653257i
\(750\) −15.1273 + 2.81875i −0.552371 + 0.102926i
\(751\) −3.03316 0.534827i −0.110681 0.0195161i 0.118033 0.993010i \(-0.462341\pi\)
−0.228715 + 0.973494i \(0.573452\pi\)
\(752\) 25.2426 + 6.76374i 0.920504 + 0.246648i
\(753\) −2.75148 10.2687i −0.100269 0.374210i
\(754\) 5.79561 + 4.86309i 0.211064 + 0.177103i
\(755\) 5.19015 5.53695i 0.188889 0.201510i
\(756\) −11.8455 32.5451i −0.430815 1.18365i
\(757\) 1.05854 12.0991i 0.0384731 0.439750i −0.952390 0.304881i \(-0.901383\pi\)
0.990864 0.134869i \(-0.0430612\pi\)
\(758\) 2.42442 3.46243i 0.0880589 0.125761i
\(759\) −6.76353 −0.245501
\(760\) 6.15348 15.5830i 0.223210 0.565253i
\(761\) −42.4931 −1.54037 −0.770187 0.637819i \(-0.779837\pi\)
−0.770187 + 0.637819i \(0.779837\pi\)
\(762\) −7.93366 + 11.3304i −0.287406 + 0.410458i
\(763\) −1.44170 + 16.4787i −0.0521930 + 0.596569i
\(764\) −6.31156 17.3409i −0.228344 0.627371i
\(765\) 0.363804 + 11.2528i 0.0131534 + 0.406847i
\(766\) −2.70708 2.27151i −0.0978106 0.0820728i
\(767\) −1.89393 7.06825i −0.0683859 0.255220i
\(768\) −5.84824 1.56703i −0.211030 0.0565454i
\(769\) −35.2926 6.22304i −1.27268 0.224408i −0.503813 0.863813i \(-0.668070\pi\)
−0.768871 + 0.639404i \(0.779181\pi\)
\(770\) 0.518239 0.793515i 0.0186760 0.0285963i
\(771\) 6.42196 + 11.1232i 0.231281 + 0.400591i
\(772\) −3.19307 + 0.855581i −0.114921 + 0.0307930i
\(773\) 9.69376 0.848094i 0.348660 0.0305038i 0.0885194 0.996074i \(-0.471786\pi\)
0.260141 + 0.965571i \(0.416231\pi\)
\(774\) −2.90614 1.05775i −0.104459 0.0380199i
\(775\) 22.4740 45.4795i 0.807289 1.63367i
\(776\) 5.44767 4.57114i 0.195560 0.164094i
\(777\) −31.0144 21.7165i −1.11264 0.779076i
\(778\) 1.66317 1.66317i 0.0596274 0.0596274i
\(779\) −7.61675 + 31.9716i −0.272899 + 1.14550i
\(780\) −46.8605 20.0344i −1.67787 0.717345i
\(781\) −1.24423 + 0.219391i −0.0445220 + 0.00785044i
\(782\) −1.70388 0.149071i −0.0609308 0.00533075i
\(783\) −35.5738 16.5884i −1.27131 0.592819i
\(784\) −3.01865 + 8.29367i −0.107809 + 0.296202i
\(785\) −26.2573 8.60670i −0.937163 0.307186i
\(786\) −8.10482 + 14.0380i −0.289089 + 0.500717i
\(787\) −8.00629 + 29.8799i −0.285393 + 1.06510i 0.663158 + 0.748479i \(0.269216\pi\)
−0.948551 + 0.316623i \(0.897451\pi\)
\(788\) 9.98075 6.98859i 0.355549 0.248958i
\(789\) −9.29400 + 52.7089i −0.330875 + 1.87649i
\(790\) 2.87310 3.65785i 0.102220 0.130140i
\(791\) 18.5731 + 10.7232i 0.660383 + 0.381272i
\(792\) −0.444672 5.08262i −0.0158007 0.180603i
\(793\) −13.3343 + 6.21789i −0.473515 + 0.220804i
\(794\) −3.50296 + 1.27497i −0.124316 + 0.0452471i
\(795\) 14.1522 + 46.7219i 0.501928 + 1.65706i
\(796\) −4.34252 24.6277i −0.153917 0.872905i
\(797\) 18.1021 + 18.1021i 0.641208 + 0.641208i 0.950852 0.309644i \(-0.100210\pi\)
−0.309644 + 0.950852i \(0.600210\pi\)
\(798\) 11.5463 2.37009i 0.408733 0.0839005i
\(799\) 7.51064i 0.265707i
\(800\) −23.2844 + 3.56445i −0.823228 + 0.126022i
\(801\) −1.17927 1.40540i −0.0416676 0.0496575i
\(802\) 0.384200 0.823919i 0.0135666 0.0290936i
\(803\) 0.0796151 + 0.170735i 0.00280956 + 0.00602511i
\(804\) −10.6524 + 12.6950i −0.375682 + 0.447720i
\(805\) −16.4311 + 12.3152i −0.579119 + 0.434052i
\(806\) −16.6333 + 9.60327i −0.585885 + 0.338261i
\(807\) −22.7683 32.5165i −0.801481 1.14463i
\(808\) 9.77365 + 13.9582i 0.343836 + 0.491049i
\(809\) −23.1968 + 13.3927i −0.815557 + 0.470862i −0.848882 0.528582i \(-0.822724\pi\)
0.0333247 + 0.999445i \(0.489390\pi\)
\(810\) −11.1742 1.59992i −0.392620 0.0562156i
\(811\) −19.0809 + 22.7397i −0.670020 + 0.798499i −0.988787 0.149334i \(-0.952287\pi\)
0.318767 + 0.947833i \(0.396731\pi\)
\(812\) −5.95613 12.7730i −0.209019 0.448243i
\(813\) −17.8880 + 38.3610i −0.627361 + 1.34538i
\(814\) −0.879437 1.04807i −0.0308242 0.0367349i
\(815\) 1.51537 0.941463i 0.0530810 0.0329780i
\(816\) 6.90044i 0.241564i
\(817\) −2.27122 + 4.20053i −0.0794600 + 0.146958i
\(818\) 4.91483 + 4.91483i 0.171843 + 0.171843i
\(819\) −8.88639 50.3972i −0.310516 1.76102i
\(820\) 28.9615 8.77253i 1.01138 0.306350i
\(821\) 36.7112 13.3618i 1.28123 0.466329i 0.390390 0.920649i \(-0.372340\pi\)
0.890838 + 0.454320i \(0.150118\pi\)
\(822\) 23.4339 10.9274i 0.817350 0.381137i
\(823\) −0.200621 2.29311i −0.00699320 0.0799326i 0.991896 0.127052i \(-0.0405515\pi\)
−0.998889 + 0.0471193i \(0.984996\pi\)
\(824\) 25.5288 + 14.7391i 0.889338 + 0.513459i
\(825\) 3.47501 + 6.34632i 0.120984 + 0.220951i
\(826\) 0.270590 1.53459i 0.00941505 0.0533954i
\(827\) −3.28088 + 2.29730i −0.114087 + 0.0798848i −0.629228 0.777221i \(-0.716629\pi\)
0.515140 + 0.857106i \(0.327740\pi\)
\(828\) −13.5315 + 50.5004i −0.470253 + 1.75501i
\(829\) 14.2569 24.6936i 0.495161 0.857645i −0.504823 0.863223i \(-0.668442\pi\)
0.999984 + 0.00557813i \(0.00177558\pi\)
\(830\) 7.11184 3.60051i 0.246856 0.124976i
\(831\) −16.9849 + 46.6658i −0.589201 + 1.61882i
\(832\) −13.2119 6.16079i −0.458039 0.213587i
\(833\) 2.52692 + 0.221077i 0.0875526 + 0.00765986i
\(834\) −14.1317 + 2.49180i −0.489342 + 0.0862842i
\(835\) 10.8904 + 27.1569i 0.376879 + 0.939803i
\(836\) −3.71940 0.220977i −0.128638 0.00764264i
\(837\) 70.4602 70.4602i 2.43546 2.43546i
\(838\) −1.98091 1.38705i −0.0684295 0.0479149i
\(839\) 5.48743 4.60450i 0.189447 0.158965i −0.543131 0.839648i \(-0.682761\pi\)
0.732578 + 0.680683i \(0.238317\pi\)
\(840\) −15.3096 17.0917i −0.528230 0.589721i
\(841\) 12.2419 + 4.45569i 0.422135 + 0.153645i
\(842\) 4.33736 0.379470i 0.149475 0.0130774i
\(843\) 84.8993 22.7487i 2.92409 0.783507i
\(844\) 9.90180 + 17.1504i 0.340834 + 0.590342i
\(845\) −8.36113 5.46060i −0.287632 0.187850i
\(846\) 25.8456 + 4.55728i 0.888591 + 0.156683i
\(847\) 20.4454 + 5.47834i 0.702513 + 0.188238i
\(848\) 5.22764 + 19.5098i 0.179518 + 0.669970i
\(849\) 44.6604 + 37.4745i 1.53274 + 1.28612i
\(850\) 0.735556 + 1.67537i 0.0252294 + 0.0574647i
\(851\) 10.1383 + 27.8548i 0.347537 + 0.954850i
\(852\) −1.26091 + 14.4122i −0.0431980 + 0.493755i
\(853\) 9.87932 14.1091i 0.338261 0.483087i −0.613600 0.789617i \(-0.710279\pi\)
0.951861 + 0.306530i \(0.0991679\pi\)
\(854\) −3.13306 −0.107211
\(855\) −17.3017 + 58.2290i −0.591705 + 1.99139i
\(856\) −1.80609 −0.0617310
\(857\) 28.3078 40.4277i 0.966975 1.38098i 0.0427711 0.999085i \(-0.486381\pi\)
0.924204 0.381899i \(-0.124730\pi\)
\(858\) 0.238754 2.72897i 0.00815092 0.0931655i
\(859\) −9.95294 27.3455i −0.339590 0.933016i −0.985511 0.169611i \(-0.945749\pi\)
0.645921 0.763404i \(-0.276473\pi\)
\(860\) 4.39438 0.142070i 0.149847 0.00484456i
\(861\) 34.4821 + 28.9339i 1.17515 + 0.986064i
\(862\) −0.309107 1.15360i −0.0105282 0.0392918i
\(863\) −13.4123 3.59381i −0.456560 0.122335i 0.0232074 0.999731i \(-0.492612\pi\)
−0.479767 + 0.877396i \(0.659279\pi\)
\(864\) −45.5665 8.03461i −1.55020 0.273343i
\(865\) 4.81231 + 22.9318i 0.163623 + 0.779704i
\(866\) −4.64315 8.04217i −0.157781 0.273284i
\(867\) −47.9784 + 12.8558i −1.62943 + 0.436605i
\(868\) 35.6422 3.11828i 1.20977 0.105841i
\(869\) −2.05519 0.748027i −0.0697174 0.0253751i
\(870\) −12.2810 0.675491i −0.416364 0.0229013i
\(871\) −9.72868 + 8.16333i −0.329644 + 0.276604i
\(872\) 11.8547 + 8.30073i 0.401450 + 0.281098i
\(873\) −18.2321 + 18.2321i −0.617064 + 0.617064i
\(874\) −8.46925 3.66498i −0.286477 0.123970i
\(875\) 19.9975 + 9.09016i 0.676041 + 0.307303i
\(876\) 2.12440 0.374590i 0.0717769 0.0126562i
\(877\) −24.0873 2.10737i −0.813372 0.0711608i −0.327124 0.944982i \(-0.606079\pi\)
−0.486248 + 0.873821i \(0.661635\pi\)
\(878\) 14.7850 + 6.89436i 0.498969 + 0.232673i
\(879\) −2.91747 + 8.01569i −0.0984039 + 0.270363i
\(880\) 1.35215 + 2.67081i 0.0455811 + 0.0900331i
\(881\) −11.2657 + 19.5128i −0.379552 + 0.657403i −0.990997 0.133884i \(-0.957255\pi\)
0.611445 + 0.791287i \(0.290588\pi\)
\(882\) −2.29404 + 8.56149i −0.0772445 + 0.288280i
\(883\) −15.3698 + 10.7621i −0.517236 + 0.362172i −0.802858 0.596170i \(-0.796689\pi\)
0.285623 + 0.958342i \(0.407800\pi\)
\(884\) −1.05231 + 5.96794i −0.0353930 + 0.200723i
\(885\) 9.35542 + 7.34832i 0.314479 + 0.247011i
\(886\) 8.51580 + 4.91660i 0.286094 + 0.165176i
\(887\) 3.65695 + 41.7992i 0.122788 + 1.40348i 0.768477 + 0.639877i \(0.221015\pi\)
−0.645689 + 0.763601i \(0.723430\pi\)
\(888\) −30.0207 + 13.9989i −1.00743 + 0.469771i
\(889\) 18.5549 6.75343i 0.622311 0.226503i
\(890\) −0.262894 0.140657i −0.00881223 0.00471484i
\(891\) 0.921686 + 5.22714i 0.0308776 + 0.175116i
\(892\) −0.265443 0.265443i −0.00888768 0.00888768i
\(893\) 12.7910 38.4511i 0.428036 1.28672i
\(894\) 31.2448i 1.04498i
\(895\) 2.09602 8.97284i 0.0700621 0.299929i
\(896\) −13.8950 16.5594i −0.464198 0.553210i
\(897\) −25.0830 + 53.7907i −0.837497 + 1.79602i
\(898\) −1.58326 3.39530i −0.0528339 0.113303i
\(899\) 26.0641 31.0620i 0.869286 1.03597i
\(900\) 54.3375 13.2495i 1.81125 0.441651i
\(901\) 5.02721 2.90246i 0.167481 0.0966949i
\(902\) 0.932973 + 1.33242i 0.0310646 + 0.0443648i
\(903\) 3.75122 + 5.35730i 0.124833 + 0.178280i
\(904\) 16.2491 9.38144i 0.540438 0.312022i
\(905\) −2.53921 3.38785i −0.0844061 0.112616i
\(906\) 3.00258 3.57834i 0.0997541 0.118882i
\(907\) −17.7677 38.1030i −0.589967 1.26519i −0.943997 0.329954i \(-0.892967\pi\)
0.354030 0.935234i \(-0.384811\pi\)
\(908\) −14.3066 + 30.6806i −0.474781 + 1.01817i
\(909\) −39.7126 47.3276i −1.31718 1.56976i
\(910\) −4.38893 7.06438i −0.145492 0.234182i
\(911\) 43.1012i 1.42801i −0.700142 0.714003i \(-0.746880\pi\)
0.700142 0.714003i \(-0.253120\pi\)
\(912\) −11.7518 + 35.3272i −0.389142 + 1.16980i
\(913\) −2.65037 2.65037i −0.0877145 0.0877145i
\(914\) 1.23508 + 7.00448i 0.0408528 + 0.231688i
\(915\) 11.2838 21.0899i 0.373030 0.697209i
\(916\) 3.07501 1.11921i 0.101601 0.0369798i
\(917\) 20.9720 9.77939i 0.692555 0.322944i
\(918\) 0.313244 + 3.58039i 0.0103386 + 0.118170i
\(919\) 5.67097 + 3.27413i 0.187068 + 0.108004i 0.590609 0.806958i \(-0.298887\pi\)
−0.403541 + 0.914961i \(0.632221\pi\)
\(920\) 2.14319 + 17.8363i 0.0706588 + 0.588047i
\(921\) 5.02381 28.4914i 0.165540 0.938825i
\(922\) −8.22291 + 5.75774i −0.270807 + 0.189621i
\(923\) −2.86948 + 10.7090i −0.0944501 + 0.352492i
\(924\) −2.55150 + 4.41932i −0.0839381 + 0.145385i
\(925\) 20.9276 23.8243i 0.688097 0.783339i
\(926\) 1.02785 2.82399i 0.0337771 0.0928019i
\(927\) −96.8658 45.1693i −3.18149 1.48355i
\(928\) −18.7566 1.64099i −0.615717 0.0538682i
\(929\) −28.0269 + 4.94190i −0.919533 + 0.162138i −0.613329 0.789827i \(-0.710170\pi\)
−0.306204 + 0.951966i \(0.599059\pi\)
\(930\) 12.2746 28.7104i 0.402501 0.941452i
\(931\) 12.5602 + 5.43530i 0.411644 + 0.178135i
\(932\) 22.9744 22.9744i 0.752551 0.752551i
\(933\) −59.6058 41.7364i −1.95141 1.36639i
\(934\) 13.1125 11.0027i 0.429053 0.360018i
\(935\) 0.640857 0.574034i 0.0209583 0.0187729i
\(936\) −42.0714 15.3127i −1.37515 0.500512i
\(937\) −31.4504 + 2.75156i −1.02744 + 0.0898895i −0.588394 0.808574i \(-0.700240\pi\)
−0.439047 + 0.898464i \(0.644684\pi\)
\(938\) −2.61227 + 0.699956i −0.0852936 + 0.0228544i
\(939\) 12.7596 + 22.1003i 0.416395 + 0.721217i
\(940\) −36.5151 + 7.66280i −1.19099 + 0.249933i
\(941\) −39.5313 6.97043i −1.28868 0.227229i −0.513020 0.858377i \(-0.671473\pi\)
−0.775663 + 0.631147i \(0.782584\pi\)
\(942\) −16.4281 4.40190i −0.535256 0.143422i
\(943\) −9.12118 34.0407i −0.297026 1.10852i
\(944\) 3.77044 + 3.16378i 0.122718 + 0.102972i
\(945\) 31.4804 + 29.5086i 1.02406 + 0.959914i
\(946\) 0.0808298 + 0.222078i 0.00262800 + 0.00722038i
\(947\) −0.604220 + 6.90626i −0.0196345 + 0.224423i 0.980037 + 0.198813i \(0.0637086\pi\)
−0.999672 + 0.0256106i \(0.991847\pi\)
\(948\) −14.3646 + 20.5148i −0.466542 + 0.666291i
\(949\) 1.65312 0.0536626
\(950\) 0.912475 + 9.82984i 0.0296046 + 0.318922i
\(951\) 10.4907 0.340184
\(952\) −1.56498 + 2.23502i −0.0507212 + 0.0724374i
\(953\) 1.06076 12.1246i 0.0343615 0.392754i −0.959467 0.281822i \(-0.909061\pi\)
0.993828 0.110931i \(-0.0353833\pi\)
\(954\) 6.93755 + 19.0608i 0.224612 + 0.617115i
\(955\) 16.7735 + 15.7229i 0.542779 + 0.508782i
\(956\) −41.5179 34.8376i −1.34278 1.12673i
\(957\) 1.49684 + 5.58630i 0.0483861 + 0.180579i
\(958\) 5.50312 + 1.47456i 0.177798 + 0.0476407i
\(959\) −36.3505 6.40957i −1.17382 0.206976i
\(960\) 23.1939 4.86731i 0.748580 0.157092i
\(961\) 35.9694 + 62.3007i 1.16030 + 2.00970i
\(962\) −11.5968 + 3.10736i −0.373896 + 0.100185i
\(963\) 6.52348 0.570731i 0.210216 0.0183915i
\(964\) 38.7176 + 14.0920i 1.24701 + 0.453874i
\(965\) 3.06768 2.74781i 0.0987523 0.0884553i
\(966\) −9.68188 + 8.12406i −0.311509 + 0.261387i
\(967\) 8.72367 + 6.10838i 0.280534 + 0.196432i 0.705372 0.708837i \(-0.250780\pi\)
−0.424838 + 0.905269i \(0.639669\pi\)
\(968\) 13.0943 13.0943i 0.420868 0.420868i
\(969\) 10.6812 + 0.634592i 0.343130 + 0.0203860i
\(970\) −1.64728 + 3.85299i −0.0528909 + 0.123712i
\(971\) 2.17846 0.384122i 0.0699102 0.0123270i −0.138584 0.990351i \(-0.544255\pi\)
0.208494 + 0.978024i \(0.433144\pi\)
\(972\) 7.86600 + 0.688186i 0.252302 + 0.0220736i
\(973\) 18.5656 + 8.65730i 0.595187 + 0.277540i
\(974\) −3.97185 + 10.9126i −0.127266 + 0.349662i
\(975\) 63.3599 4.10114i 2.02914 0.131342i
\(976\) 4.94806 8.57030i 0.158384 0.274329i
\(977\) −5.98245 + 22.3268i −0.191396 + 0.714298i 0.801775 + 0.597626i \(0.203889\pi\)
−0.993171 + 0.116672i \(0.962777\pi\)
\(978\) 0.899487 0.629828i 0.0287624 0.0201397i
\(979\) −0.0243448 + 0.138066i −0.000778064 + 0.00441262i
\(980\) −1.50329 12.5109i −0.0480208 0.399645i
\(981\) −45.4413 26.2355i −1.45083 0.837636i
\(982\) −1.35195 15.4529i −0.0431425 0.493121i
\(983\) 12.4704 5.81504i 0.397744 0.185471i −0.213446 0.976955i \(-0.568469\pi\)
0.611190 + 0.791484i \(0.290691\pi\)
\(984\) 37.0059 13.4691i 1.17971 0.429378i
\(985\) −7.16107 + 13.3843i −0.228171 + 0.426461i
\(986\) 0.253964 + 1.44030i 0.00808787 + 0.0458686i
\(987\) −39.2439 39.2439i −1.24915 1.24915i
\(988\) −15.5511 + 28.7610i −0.494746 + 0.915011i
\(989\) 5.12032i 0.162817i
\(990\) 1.58651 + 2.55363i 0.0504226 + 0.0811596i
\(991\) −23.8389 28.4101i −0.757267 0.902476i 0.240405 0.970673i \(-0.422720\pi\)
−0.997672 + 0.0681968i \(0.978275\pi\)
\(992\) 20.2005 43.3202i 0.641367 1.37542i
\(993\) −20.5635 44.0985i −0.652562 1.39942i
\(994\) −1.51757 + 1.80857i −0.0481344 + 0.0573643i
\(995\) 18.6854 + 24.9303i 0.592367 + 0.790345i
\(996\) −37.1698 + 21.4600i −1.17777 + 0.679986i
\(997\) 8.80465 + 12.5743i 0.278846 + 0.398234i 0.934006 0.357256i \(-0.116288\pi\)
−0.655160 + 0.755490i \(0.727399\pi\)
\(998\) 7.45676 + 10.6494i 0.236040 + 0.337099i
\(999\) 53.9430 31.1440i 1.70668 0.985353i
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 95.2.r.a.48.6 yes 96
3.2 odd 2 855.2.dl.a.523.3 96
5.2 odd 4 inner 95.2.r.a.67.6 yes 96
5.3 odd 4 475.2.bb.b.257.3 96
5.4 even 2 475.2.bb.b.143.3 96
15.2 even 4 855.2.dl.a.352.3 96
19.2 odd 18 inner 95.2.r.a.78.6 yes 96
57.2 even 18 855.2.dl.a.838.3 96
95.2 even 36 inner 95.2.r.a.2.6 96
95.59 odd 18 475.2.bb.b.268.3 96
95.78 even 36 475.2.bb.b.382.3 96
285.2 odd 36 855.2.dl.a.667.3 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.r.a.2.6 96 95.2 even 36 inner
95.2.r.a.48.6 yes 96 1.1 even 1 trivial
95.2.r.a.67.6 yes 96 5.2 odd 4 inner
95.2.r.a.78.6 yes 96 19.2 odd 18 inner
475.2.bb.b.143.3 96 5.4 even 2
475.2.bb.b.257.3 96 5.3 odd 4
475.2.bb.b.268.3 96 95.59 odd 18
475.2.bb.b.382.3 96 95.78 even 36
855.2.dl.a.352.3 96 15.2 even 4
855.2.dl.a.523.3 96 3.2 odd 2
855.2.dl.a.667.3 96 285.2 odd 36
855.2.dl.a.838.3 96 57.2 even 18