Properties

Label 770.2.n.j.141.1
Level $770$
Weight $2$
Character 770.141
Analytic conductor $6.148$
Analytic rank $0$
Dimension $12$
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] = [770,2,Mod(71,770)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(770, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("770.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.n (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.14848095564\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} - 350 x^{3} + 510 x^{2} - 175 x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 141.1
Root \(-0.674672 + 2.07643i\) of defining polynomial
Character \(\chi\) \(=\) 770.141
Dual form 770.2.n.j.71.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(-1.76631 + 1.28330i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.674672 - 2.07643i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.545950 - 1.68026i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(-1.76631 + 1.28330i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.674672 - 2.07643i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.545950 - 1.68026i) q^{9} -1.00000 q^{10} +(2.35838 - 2.33197i) q^{11} +2.18328 q^{12} +(0.782625 - 2.40867i) q^{13} +(0.809017 - 0.587785i) q^{14} +(-1.76631 - 1.28330i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-1.77318 - 5.45728i) q^{17} +(1.42932 + 1.03846i) q^{18} +(1.81268 - 1.31699i) q^{19} +(0.309017 - 0.951057i) q^{20} +2.18328 q^{21} +(1.48905 + 2.96357i) q^{22} -2.51489 q^{23} +(-0.674672 + 2.07643i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(2.04894 + 1.48864i) q^{26} +(-0.832051 - 2.56079i) q^{27} +(0.309017 + 0.951057i) q^{28} +(6.97373 + 5.06671i) q^{29} +(1.76631 - 1.28330i) q^{30} +(0.568867 - 1.75079i) q^{31} -1.00000 q^{32} +(-1.17301 + 7.14549i) q^{33} +5.73813 q^{34} +(0.309017 - 0.951057i) q^{35} +(-1.42932 + 1.03846i) q^{36} +(3.74676 + 2.72218i) q^{37} +(0.692383 + 2.13094i) q^{38} +(1.70869 + 5.25882i) q^{39} +(0.809017 + 0.587785i) q^{40} +(8.53702 - 6.20251i) q^{41} +(-0.674672 + 2.07643i) q^{42} -2.18804 q^{43} +(-3.27866 + 0.500382i) q^{44} +1.76673 q^{45} +(0.777143 - 2.39180i) q^{46} +(-2.60894 + 1.89550i) q^{47} +(-1.76631 - 1.28330i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(10.1353 + 7.36375i) q^{51} +(-2.04894 + 1.48864i) q^{52} +(-1.24146 + 3.82083i) q^{53} +2.69257 q^{54} +(2.94661 + 1.52233i) q^{55} -1.00000 q^{56} +(-1.51167 + 4.65244i) q^{57} +(-6.97373 + 5.06671i) q^{58} +(-1.62940 - 1.18383i) q^{59} +(0.674672 + 2.07643i) q^{60} +(-0.0828892 - 0.255107i) q^{61} +(1.48931 + 1.08205i) q^{62} +(-1.42932 + 1.03846i) q^{63} +(0.309017 - 0.951057i) q^{64} +2.53263 q^{65} +(-6.43329 - 3.32368i) q^{66} +3.86233 q^{67} +(-1.77318 + 5.45728i) q^{68} +(4.44208 - 3.22736i) q^{69} +(0.809017 + 0.587785i) q^{70} +(-2.95270 - 9.08747i) q^{71} +(-0.545950 - 1.68026i) q^{72} +(9.24371 + 6.71595i) q^{73} +(-3.74676 + 2.72218i) q^{74} +(0.674672 - 2.07643i) q^{75} -2.24060 q^{76} +(-3.27866 + 0.500382i) q^{77} -5.52945 q^{78} +(-3.63201 + 11.1782i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(9.04388 + 6.57077i) q^{81} +(3.26085 + 10.0359i) q^{82} +(-2.27081 - 6.98885i) q^{83} +(-1.76631 - 1.28330i) q^{84} +(4.64224 - 3.37279i) q^{85} +(0.676140 - 2.08095i) q^{86} -18.8199 q^{87} +(0.537270 - 3.27282i) q^{88} -2.65397 q^{89} +(-0.545950 + 1.68026i) q^{90} +(-2.04894 + 1.48864i) q^{91} +(2.03459 + 1.47821i) q^{92} +(1.24200 + 3.82248i) q^{93} +(-0.996525 - 3.06699i) q^{94} +(1.81268 + 1.31699i) q^{95} +(1.76631 - 1.28330i) q^{96} +(5.10018 - 15.6967i) q^{97} -1.00000 q^{98} +(-2.63076 - 5.23583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 6 q^{9} - 12 q^{10} - q^{11} - 2 q^{12} + 2 q^{13} + 3 q^{14} + 3 q^{15} - 3 q^{16} + 7 q^{17} + 9 q^{18} + 6 q^{19} - 3 q^{20} - 2 q^{21} + q^{22} + 8 q^{23} + 2 q^{24} - 3 q^{25} - 7 q^{26} - 3 q^{27} - 3 q^{28} + 20 q^{29} - 3 q^{30} + 6 q^{31} - 12 q^{32} - 12 q^{33} + 18 q^{34} - 3 q^{35} - 9 q^{36} + 22 q^{37} - 6 q^{38} + 23 q^{39} + 3 q^{40} + 2 q^{41} + 2 q^{42} - 60 q^{43} - 11 q^{44} + 6 q^{45} + 2 q^{46} - 4 q^{47} + 3 q^{48} - 3 q^{49} + 3 q^{50} + 13 q^{51} + 7 q^{52} + 18 q^{53} + 8 q^{54} + 14 q^{55} - 12 q^{56} + 8 q^{57} - 20 q^{58} - 32 q^{59} - 2 q^{60} + 8 q^{61} + 14 q^{62} - 9 q^{63} - 3 q^{64} - 18 q^{65} - 8 q^{66} + 36 q^{67} + 7 q^{68} + 50 q^{69} + 3 q^{70} - 34 q^{71} - 6 q^{72} + 14 q^{73} - 22 q^{74} - 2 q^{75} - 24 q^{76} - 11 q^{77} - 38 q^{78} - 12 q^{79} - 3 q^{80} + 4 q^{81} - 2 q^{82} + 30 q^{83} + 3 q^{84} + 2 q^{85} - 28 q^{87} + q^{88} - 36 q^{89} - 6 q^{90} + 7 q^{91} - 2 q^{92} + 12 q^{93} - 11 q^{94} + 6 q^{95} - 3 q^{96} + 39 q^{97} - 12 q^{98} - 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(617\) \(661\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i
\(3\) −1.76631 + 1.28330i −1.01978 + 0.740915i −0.966238 0.257650i \(-0.917052\pi\)
−0.0535440 + 0.998565i \(0.517052\pi\)
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0.309017 + 0.951057i 0.138197 + 0.425325i
\(6\) −0.674672 2.07643i −0.275434 0.847698i
\(7\) −0.809017 0.587785i −0.305780 0.222162i
\(8\) 0.809017 0.587785i 0.286031 0.207813i
\(9\) 0.545950 1.68026i 0.181983 0.560088i
\(10\) −1.00000 −0.316228
\(11\) 2.35838 2.33197i 0.711077 0.703114i
\(12\) 2.18328 0.630260
\(13\) 0.782625 2.40867i 0.217061 0.668046i −0.781940 0.623354i \(-0.785769\pi\)
0.999001 0.0446916i \(-0.0142305\pi\)
\(14\) 0.809017 0.587785i 0.216219 0.157092i
\(15\) −1.76631 1.28330i −0.456060 0.331347i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −1.77318 5.45728i −0.430059 1.32359i −0.898066 0.439861i \(-0.855028\pi\)
0.468007 0.883725i \(-0.344972\pi\)
\(18\) 1.42932 + 1.03846i 0.336893 + 0.244767i
\(19\) 1.81268 1.31699i 0.415858 0.302139i −0.360111 0.932909i \(-0.617261\pi\)
0.775969 + 0.630771i \(0.217261\pi\)
\(20\) 0.309017 0.951057i 0.0690983 0.212663i
\(21\) 2.18328 0.476432
\(22\) 1.48905 + 2.96357i 0.317467 + 0.631834i
\(23\) −2.51489 −0.524390 −0.262195 0.965015i \(-0.584446\pi\)
−0.262195 + 0.965015i \(0.584446\pi\)
\(24\) −0.674672 + 2.07643i −0.137717 + 0.423849i
\(25\) −0.809017 + 0.587785i −0.161803 + 0.117557i
\(26\) 2.04894 + 1.48864i 0.401830 + 0.291947i
\(27\) −0.832051 2.56079i −0.160128 0.492824i
\(28\) 0.309017 + 0.951057i 0.0583987 + 0.179733i
\(29\) 6.97373 + 5.06671i 1.29499 + 0.940864i 0.999893 0.0146039i \(-0.00464873\pi\)
0.295095 + 0.955468i \(0.404649\pi\)
\(30\) 1.76631 1.28330i 0.322483 0.234298i
\(31\) 0.568867 1.75079i 0.102171 0.314451i −0.886885 0.461991i \(-0.847135\pi\)
0.989056 + 0.147539i \(0.0471353\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.17301 + 7.14549i −0.204195 + 1.24387i
\(34\) 5.73813 0.984080
\(35\) 0.309017 0.951057i 0.0522334 0.160758i
\(36\) −1.42932 + 1.03846i −0.238219 + 0.173077i
\(37\) 3.74676 + 2.72218i 0.615963 + 0.447523i 0.851509 0.524340i \(-0.175688\pi\)
−0.235546 + 0.971863i \(0.575688\pi\)
\(38\) 0.692383 + 2.13094i 0.112319 + 0.345684i
\(39\) 1.70869 + 5.25882i 0.273610 + 0.842085i
\(40\) 0.809017 + 0.587785i 0.127917 + 0.0929370i
\(41\) 8.53702 6.20251i 1.33326 0.968669i 0.333595 0.942716i \(-0.391738\pi\)
0.999663 0.0259525i \(-0.00826185\pi\)
\(42\) −0.674672 + 2.07643i −0.104104 + 0.320400i
\(43\) −2.18804 −0.333672 −0.166836 0.985985i \(-0.553355\pi\)
−0.166836 + 0.985985i \(0.553355\pi\)
\(44\) −3.27866 + 0.500382i −0.494277 + 0.0754355i
\(45\) 1.76673 0.263369
\(46\) 0.777143 2.39180i 0.114583 0.352652i
\(47\) −2.60894 + 1.89550i −0.380552 + 0.276487i −0.761573 0.648079i \(-0.775573\pi\)
0.381021 + 0.924566i \(0.375573\pi\)
\(48\) −1.76631 1.28330i −0.254946 0.185229i
\(49\) 0.309017 + 0.951057i 0.0441453 + 0.135865i
\(50\) −0.309017 0.951057i −0.0437016 0.134500i
\(51\) 10.1353 + 7.36375i 1.41923 + 1.03113i
\(52\) −2.04894 + 1.48864i −0.284137 + 0.206438i
\(53\) −1.24146 + 3.82083i −0.170528 + 0.524832i −0.999401 0.0346052i \(-0.988983\pi\)
0.828873 + 0.559437i \(0.188983\pi\)
\(54\) 2.69257 0.366413
\(55\) 2.94661 + 1.52233i 0.397321 + 0.205271i
\(56\) −1.00000 −0.133631
\(57\) −1.51167 + 4.65244i −0.200226 + 0.616231i
\(58\) −6.97373 + 5.06671i −0.915695 + 0.665291i
\(59\) −1.62940 1.18383i −0.212130 0.154121i 0.476647 0.879095i \(-0.341852\pi\)
−0.688777 + 0.724974i \(0.741852\pi\)
\(60\) 0.674672 + 2.07643i 0.0870998 + 0.268066i
\(61\) −0.0828892 0.255107i −0.0106129 0.0326631i 0.945610 0.325303i \(-0.105466\pi\)
−0.956223 + 0.292640i \(0.905466\pi\)
\(62\) 1.48931 + 1.08205i 0.189143 + 0.137420i
\(63\) −1.42932 + 1.03846i −0.180077 + 0.130834i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) 2.53263 0.314134
\(66\) −6.43329 3.32368i −0.791883 0.409117i
\(67\) 3.86233 0.471859 0.235929 0.971770i \(-0.424187\pi\)
0.235929 + 0.971770i \(0.424187\pi\)
\(68\) −1.77318 + 5.45728i −0.215029 + 0.661793i
\(69\) 4.44208 3.22736i 0.534764 0.388529i
\(70\) 0.809017 + 0.587785i 0.0966960 + 0.0702538i
\(71\) −2.95270 9.08747i −0.350421 1.07848i −0.958617 0.284698i \(-0.908107\pi\)
0.608196 0.793787i \(-0.291893\pi\)
\(72\) −0.545950 1.68026i −0.0643409 0.198021i
\(73\) 9.24371 + 6.71595i 1.08189 + 0.786042i 0.978012 0.208548i \(-0.0668737\pi\)
0.103882 + 0.994590i \(0.466874\pi\)
\(74\) −3.74676 + 2.72218i −0.435552 + 0.316447i
\(75\) 0.674672 2.07643i 0.0779044 0.239765i
\(76\) −2.24060 −0.257014
\(77\) −3.27866 + 0.500382i −0.373638 + 0.0570239i
\(78\) −5.52945 −0.626087
\(79\) −3.63201 + 11.1782i −0.408633 + 1.25764i 0.509190 + 0.860654i \(0.329945\pi\)
−0.917823 + 0.396990i \(0.870055\pi\)
\(80\) −0.809017 + 0.587785i −0.0904508 + 0.0657164i
\(81\) 9.04388 + 6.57077i 1.00488 + 0.730085i
\(82\) 3.26085 + 10.0359i 0.360101 + 1.10828i
\(83\) −2.27081 6.98885i −0.249254 0.767126i −0.994908 0.100792i \(-0.967862\pi\)
0.745653 0.666334i \(-0.232138\pi\)
\(84\) −1.76631 1.28330i −0.192721 0.140020i
\(85\) 4.64224 3.37279i 0.503522 0.365830i
\(86\) 0.676140 2.08095i 0.0729101 0.224394i
\(87\) −18.8199 −2.01771
\(88\) 0.537270 3.27282i 0.0572732 0.348884i
\(89\) −2.65397 −0.281321 −0.140660 0.990058i \(-0.544923\pi\)
−0.140660 + 0.990058i \(0.544923\pi\)
\(90\) −0.545950 + 1.68026i −0.0575482 + 0.177115i
\(91\) −2.04894 + 1.48864i −0.214787 + 0.156052i
\(92\) 2.03459 + 1.47821i 0.212120 + 0.154114i
\(93\) 1.24200 + 3.82248i 0.128789 + 0.396372i
\(94\) −0.996525 3.06699i −0.102784 0.316336i
\(95\) 1.81268 + 1.31699i 0.185977 + 0.135120i
\(96\) 1.76631 1.28330i 0.180274 0.130977i
\(97\) 5.10018 15.6967i 0.517845 1.59376i −0.260200 0.965555i \(-0.583789\pi\)
0.778045 0.628208i \(-0.216211\pi\)
\(98\) −1.00000 −0.101015
\(99\) −2.63076 5.23583i −0.264401 0.526220i
\(100\) 1.00000 0.100000
\(101\) 4.95905 15.2624i 0.493444 1.51866i −0.325925 0.945396i \(-0.605676\pi\)
0.819368 0.573267i \(-0.194324\pi\)
\(102\) −10.1353 + 7.36375i −1.00355 + 0.729120i
\(103\) 10.4387 + 7.58413i 1.02855 + 0.747287i 0.968018 0.250879i \(-0.0807197\pi\)
0.0605337 + 0.998166i \(0.480720\pi\)
\(104\) −0.782625 2.40867i −0.0767427 0.236190i
\(105\) 0.674672 + 2.07643i 0.0658413 + 0.202639i
\(106\) −3.25019 2.36140i −0.315687 0.229360i
\(107\) 5.45736 3.96501i 0.527583 0.383312i −0.291870 0.956458i \(-0.594277\pi\)
0.819453 + 0.573146i \(0.194277\pi\)
\(108\) −0.832051 + 2.56079i −0.0800642 + 0.246412i
\(109\) 18.6864 1.78983 0.894916 0.446235i \(-0.147235\pi\)
0.894916 + 0.446235i \(0.147235\pi\)
\(110\) −2.35838 + 2.33197i −0.224862 + 0.222344i
\(111\) −10.1113 −0.959725
\(112\) 0.309017 0.951057i 0.0291994 0.0898664i
\(113\) −6.11968 + 4.44620i −0.575691 + 0.418264i −0.837168 0.546946i \(-0.815790\pi\)
0.261477 + 0.965210i \(0.415790\pi\)
\(114\) −3.95760 2.87537i −0.370664 0.269303i
\(115\) −0.777143 2.39180i −0.0724689 0.223036i
\(116\) −2.66373 8.19811i −0.247321 0.761175i
\(117\) −3.61993 2.63003i −0.334663 0.243147i
\(118\) 1.62940 1.18383i 0.149998 0.108980i
\(119\) −1.77318 + 5.45728i −0.162547 + 0.500268i
\(120\) −2.18328 −0.199306
\(121\) 0.123865 10.9993i 0.0112605 0.999937i
\(122\) 0.268235 0.0242849
\(123\) −7.11937 + 21.9112i −0.641932 + 1.97566i
\(124\) −1.48931 + 1.08205i −0.133744 + 0.0971708i
\(125\) −0.809017 0.587785i −0.0723607 0.0525731i
\(126\) −0.545950 1.68026i −0.0486371 0.149690i
\(127\) −3.31964 10.2168i −0.294570 0.906594i −0.983365 0.181638i \(-0.941860\pi\)
0.688795 0.724956i \(-0.258140\pi\)
\(128\) 0.809017 + 0.587785i 0.0715077 + 0.0519534i
\(129\) 3.86476 2.80791i 0.340273 0.247223i
\(130\) −0.782625 + 2.40867i −0.0686408 + 0.211255i
\(131\) −17.0221 −1.48723 −0.743613 0.668610i \(-0.766890\pi\)
−0.743613 + 0.668610i \(0.766890\pi\)
\(132\) 5.14900 5.09135i 0.448163 0.443145i
\(133\) −2.24060 −0.194285
\(134\) −1.19353 + 3.67329i −0.103105 + 0.317324i
\(135\) 2.17834 1.58266i 0.187481 0.136213i
\(136\) −4.64224 3.37279i −0.398069 0.289214i
\(137\) −3.85581 11.8670i −0.329424 1.01386i −0.969404 0.245471i \(-0.921057\pi\)
0.639980 0.768392i \(-0.278943\pi\)
\(138\) 1.69672 + 5.22198i 0.144435 + 0.444524i
\(139\) −14.0617 10.2164i −1.19270 0.866547i −0.199153 0.979968i \(-0.563819\pi\)
−0.993547 + 0.113421i \(0.963819\pi\)
\(140\) −0.809017 + 0.587785i −0.0683744 + 0.0496769i
\(141\) 2.17570 6.69611i 0.183227 0.563914i
\(142\) 9.55514 0.801849
\(143\) −3.77122 7.50561i −0.315365 0.627651i
\(144\) 1.76673 0.147228
\(145\) −2.66373 + 8.19811i −0.221210 + 0.680816i
\(146\) −9.24371 + 6.71595i −0.765015 + 0.555816i
\(147\) −1.76631 1.28330i −0.145683 0.105845i
\(148\) −1.43113 4.40458i −0.117638 0.362054i
\(149\) −0.461073 1.41904i −0.0377726 0.116252i 0.930392 0.366565i \(-0.119466\pi\)
−0.968165 + 0.250313i \(0.919466\pi\)
\(150\) 1.76631 + 1.28330i 0.144219 + 0.104781i
\(151\) 6.46853 4.69966i 0.526402 0.382453i −0.292608 0.956232i \(-0.594523\pi\)
0.819010 + 0.573779i \(0.194523\pi\)
\(152\) 0.692383 2.13094i 0.0561597 0.172842i
\(153\) −10.1377 −0.819587
\(154\) 0.537270 3.27282i 0.0432945 0.263731i
\(155\) 1.84089 0.147864
\(156\) 1.70869 5.25882i 0.136805 0.421043i
\(157\) −1.65988 + 1.20598i −0.132473 + 0.0962473i −0.652048 0.758177i \(-0.726090\pi\)
0.519575 + 0.854425i \(0.326090\pi\)
\(158\) −9.50873 6.90850i −0.756474 0.549610i
\(159\) −2.71047 8.34197i −0.214954 0.661561i
\(160\) −0.309017 0.951057i −0.0244299 0.0751876i
\(161\) 2.03459 + 1.47821i 0.160348 + 0.116500i
\(162\) −9.04388 + 6.57077i −0.710555 + 0.516248i
\(163\) 6.39590 19.6846i 0.500966 1.54181i −0.306483 0.951876i \(-0.599152\pi\)
0.807449 0.589938i \(-0.200848\pi\)
\(164\) −10.5523 −0.823999
\(165\) −7.15825 + 1.09248i −0.557269 + 0.0850492i
\(166\) 7.34851 0.570355
\(167\) 0.408057 1.25587i 0.0315764 0.0971823i −0.934026 0.357205i \(-0.883730\pi\)
0.965603 + 0.260022i \(0.0837299\pi\)
\(168\) 1.76631 1.28330i 0.136274 0.0990089i
\(169\) 5.32802 + 3.87103i 0.409847 + 0.297772i
\(170\) 1.77318 + 5.45728i 0.135997 + 0.418554i
\(171\) −1.22326 3.76480i −0.0935447 0.287901i
\(172\) 1.77016 + 1.28609i 0.134973 + 0.0980638i
\(173\) −12.7039 + 9.22991i −0.965858 + 0.701737i −0.954504 0.298199i \(-0.903614\pi\)
−0.0113541 + 0.999936i \(0.503614\pi\)
\(174\) 5.81567 17.8988i 0.440885 1.35690i
\(175\) 1.00000 0.0755929
\(176\) 2.94661 + 1.52233i 0.222109 + 0.114750i
\(177\) 4.39724 0.330517
\(178\) 0.820123 2.52408i 0.0614708 0.189188i
\(179\) −3.76595 + 2.73612i −0.281480 + 0.204507i −0.719563 0.694427i \(-0.755658\pi\)
0.438083 + 0.898935i \(0.355658\pi\)
\(180\) −1.42932 1.03846i −0.106535 0.0774022i
\(181\) −1.82459 5.61552i −0.135621 0.417398i 0.860065 0.510184i \(-0.170423\pi\)
−0.995686 + 0.0927860i \(0.970423\pi\)
\(182\) −0.782625 2.40867i −0.0580121 0.178543i
\(183\) 0.473787 + 0.344227i 0.0350234 + 0.0254460i
\(184\) −2.03459 + 1.47821i −0.149992 + 0.108975i
\(185\) −1.43113 + 4.40458i −0.105219 + 0.323831i
\(186\) −4.01919 −0.294701
\(187\) −16.9080 8.73532i −1.23644 0.638790i
\(188\) 3.22482 0.235194
\(189\) −0.832051 + 2.56079i −0.0605228 + 0.186270i
\(190\) −1.81268 + 1.31699i −0.131506 + 0.0955446i
\(191\) 4.80071 + 3.48792i 0.347367 + 0.252377i 0.747764 0.663965i \(-0.231128\pi\)
−0.400397 + 0.916342i \(0.631128\pi\)
\(192\) 0.674672 + 2.07643i 0.0486903 + 0.149853i
\(193\) 3.34902 + 10.3072i 0.241068 + 0.741931i 0.996258 + 0.0864256i \(0.0275445\pi\)
−0.755190 + 0.655506i \(0.772456\pi\)
\(194\) 13.3525 + 9.70112i 0.958650 + 0.696500i
\(195\) −4.47342 + 3.25013i −0.320348 + 0.232747i
\(196\) 0.309017 0.951057i 0.0220726 0.0679326i
\(197\) 12.0176 0.856216 0.428108 0.903728i \(-0.359180\pi\)
0.428108 + 0.903728i \(0.359180\pi\)
\(198\) 5.79252 0.884042i 0.411656 0.0628261i
\(199\) 18.4014 1.30444 0.652220 0.758030i \(-0.273838\pi\)
0.652220 + 0.758030i \(0.273838\pi\)
\(200\) −0.309017 + 0.951057i −0.0218508 + 0.0672499i
\(201\) −6.82209 + 4.95654i −0.481193 + 0.349607i
\(202\) 12.9830 + 9.43267i 0.913477 + 0.663680i
\(203\) −2.66373 8.19811i −0.186957 0.575394i
\(204\) −3.87135 11.9148i −0.271049 0.834203i
\(205\) 8.53702 + 6.20251i 0.596251 + 0.433202i
\(206\) −10.4387 + 7.58413i −0.727296 + 0.528412i
\(207\) −1.37300 + 4.22567i −0.0954303 + 0.293704i
\(208\) 2.53263 0.175606
\(209\) 1.20381 7.33308i 0.0832691 0.507239i
\(210\) −2.18328 −0.150661
\(211\) 6.19337 19.0612i 0.426369 1.31223i −0.475308 0.879820i \(-0.657663\pi\)
0.901677 0.432410i \(-0.142337\pi\)
\(212\) 3.25019 2.36140i 0.223224 0.162182i
\(213\) 16.8774 + 12.2621i 1.15642 + 0.840187i
\(214\) 2.08453 + 6.41552i 0.142495 + 0.438556i
\(215\) −0.676140 2.08095i −0.0461124 0.141919i
\(216\) −2.17834 1.58266i −0.148217 0.107686i
\(217\) −1.48931 + 1.08205i −0.101101 + 0.0734543i
\(218\) −5.77441 + 17.7718i −0.391093 + 1.20366i
\(219\) −24.9459 −1.68569
\(220\) −1.48905 2.96357i −0.100392 0.199804i
\(221\) −14.5325 −0.977565
\(222\) 3.12457 9.61644i 0.209708 0.645413i
\(223\) −9.54638 + 6.93585i −0.639273 + 0.464459i −0.859600 0.510967i \(-0.829287\pi\)
0.220328 + 0.975426i \(0.429287\pi\)
\(224\) 0.809017 + 0.587785i 0.0540547 + 0.0392731i
\(225\) 0.545950 + 1.68026i 0.0363967 + 0.112018i
\(226\) −2.33751 7.19411i −0.155489 0.478545i
\(227\) −0.801025 0.581979i −0.0531659 0.0386273i 0.560885 0.827894i \(-0.310461\pi\)
−0.614051 + 0.789267i \(0.710461\pi\)
\(228\) 3.95760 2.87537i 0.262099 0.190426i
\(229\) 5.67228 17.4575i 0.374835 1.15362i −0.568755 0.822507i \(-0.692575\pi\)
0.943590 0.331116i \(-0.107425\pi\)
\(230\) 2.51489 0.165827
\(231\) 5.14900 5.09135i 0.338780 0.334986i
\(232\) 8.62000 0.565931
\(233\) −5.36608 + 16.5151i −0.351543 + 1.08194i 0.606443 + 0.795127i \(0.292596\pi\)
−0.957987 + 0.286813i \(0.907404\pi\)
\(234\) 3.61993 2.63003i 0.236642 0.171931i
\(235\) −2.60894 1.89550i −0.170188 0.123649i
\(236\) 0.622375 + 1.91547i 0.0405131 + 0.124687i
\(237\) −7.92972 24.4052i −0.515090 1.58529i
\(238\) −4.64224 3.37279i −0.300912 0.218625i
\(239\) −7.21735 + 5.24371i −0.466851 + 0.339187i −0.796213 0.605017i \(-0.793166\pi\)
0.329362 + 0.944204i \(0.393166\pi\)
\(240\) 0.674672 2.07643i 0.0435499 0.134033i
\(241\) −0.896696 −0.0577613 −0.0288806 0.999583i \(-0.509194\pi\)
−0.0288806 + 0.999583i \(0.509194\pi\)
\(242\) 10.4227 + 3.51677i 0.669995 + 0.226067i
\(243\) −16.3289 −1.04750
\(244\) −0.0828892 + 0.255107i −0.00530644 + 0.0163315i
\(245\) −0.809017 + 0.587785i −0.0516862 + 0.0375522i
\(246\) −18.6387 13.5418i −1.18836 0.863396i
\(247\) −1.75355 5.39687i −0.111576 0.343395i
\(248\) −0.568867 1.75079i −0.0361231 0.111175i
\(249\) 12.9798 + 9.43036i 0.822560 + 0.597625i
\(250\) 0.809017 0.587785i 0.0511667 0.0371748i
\(251\) −6.95222 + 21.3967i −0.438820 + 1.35055i 0.450301 + 0.892877i \(0.351317\pi\)
−0.889121 + 0.457672i \(0.848683\pi\)
\(252\) 1.76673 0.111294
\(253\) −5.93105 + 5.86463i −0.372882 + 0.368706i
\(254\) 10.7426 0.674049
\(255\) −3.87135 + 11.9148i −0.242434 + 0.746134i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 20.1808 + 14.6622i 1.25884 + 0.914604i 0.998700 0.0509660i \(-0.0162300\pi\)
0.260144 + 0.965570i \(0.416230\pi\)
\(258\) 1.47621 + 4.54330i 0.0919046 + 0.282853i
\(259\) −1.43113 4.40458i −0.0889263 0.273687i
\(260\) −2.04894 1.48864i −0.127070 0.0923217i
\(261\) 12.3207 8.95152i 0.762633 0.554085i
\(262\) 5.26012 16.1890i 0.324971 1.00016i
\(263\) 6.25594 0.385758 0.192879 0.981223i \(-0.438218\pi\)
0.192879 + 0.981223i \(0.438218\pi\)
\(264\) 3.25103 + 6.47031i 0.200087 + 0.398220i
\(265\) −4.01746 −0.246791
\(266\) 0.692383 2.13094i 0.0424527 0.130656i
\(267\) 4.68775 3.40585i 0.286886 0.208435i
\(268\) −3.12469 2.27022i −0.190871 0.138676i
\(269\) −4.03802 12.4277i −0.246202 0.757733i −0.995436 0.0954274i \(-0.969578\pi\)
0.749234 0.662305i \(-0.230422\pi\)
\(270\) 0.832051 + 2.56079i 0.0506370 + 0.155845i
\(271\) 19.6718 + 14.2924i 1.19498 + 0.868200i 0.993781 0.111351i \(-0.0355178\pi\)
0.201194 + 0.979551i \(0.435518\pi\)
\(272\) 4.64224 3.37279i 0.281477 0.204505i
\(273\) 1.70869 5.25882i 0.103415 0.318278i
\(274\) 12.4777 0.753803
\(275\) −0.537270 + 3.27282i −0.0323986 + 0.197358i
\(276\) −5.49071 −0.330502
\(277\) −4.14375 + 12.7531i −0.248974 + 0.766262i 0.745984 + 0.665964i \(0.231980\pi\)
−0.994957 + 0.100298i \(0.968020\pi\)
\(278\) 14.0617 10.2164i 0.843366 0.612741i
\(279\) −2.63122 1.91169i −0.157527 0.114450i
\(280\) −0.309017 0.951057i −0.0184673 0.0568365i
\(281\) 3.93682 + 12.1163i 0.234851 + 0.722797i 0.997141 + 0.0755613i \(0.0240749\pi\)
−0.762290 + 0.647235i \(0.775925\pi\)
\(282\) 5.69605 + 4.13842i 0.339195 + 0.246439i
\(283\) 11.1236 8.08177i 0.661230 0.480412i −0.205848 0.978584i \(-0.565995\pi\)
0.867078 + 0.498172i \(0.165995\pi\)
\(284\) −2.95270 + 9.08747i −0.175210 + 0.539242i
\(285\) −4.89187 −0.289769
\(286\) 8.30363 1.26728i 0.491004 0.0749360i
\(287\) −10.5523 −0.622885
\(288\) −0.545950 + 1.68026i −0.0321704 + 0.0990104i
\(289\) −12.8845 + 9.36112i −0.757910 + 0.550654i
\(290\) −6.97373 5.06671i −0.409511 0.297527i
\(291\) 11.1352 + 34.2705i 0.652754 + 2.00897i
\(292\) −3.53078 10.8666i −0.206623 0.635921i
\(293\) −13.4601 9.77936i −0.786350 0.571316i 0.120528 0.992710i \(-0.461541\pi\)
−0.906878 + 0.421393i \(0.861541\pi\)
\(294\) 1.76631 1.28330i 0.103014 0.0748437i
\(295\) 0.622375 1.91547i 0.0362361 0.111523i
\(296\) 4.63124 0.269186
\(297\) −7.93396 4.09899i −0.460375 0.237847i
\(298\) 1.49206 0.0864329
\(299\) −1.96821 + 6.05754i −0.113825 + 0.350317i
\(300\) −1.76631 + 1.28330i −0.101978 + 0.0740915i
\(301\) 1.77016 + 1.28609i 0.102030 + 0.0741293i
\(302\) 2.47076 + 7.60422i 0.142176 + 0.437574i
\(303\) 10.8270 + 33.3221i 0.621996 + 1.91431i
\(304\) 1.81268 + 1.31699i 0.103965 + 0.0755346i
\(305\) 0.217007 0.157665i 0.0124258 0.00902785i
\(306\) 3.13273 9.64156i 0.179086 0.551171i
\(307\) 5.56226 0.317455 0.158728 0.987322i \(-0.449261\pi\)
0.158728 + 0.987322i \(0.449261\pi\)
\(308\) 2.94661 + 1.52233i 0.167899 + 0.0867428i
\(309\) −28.1707 −1.60258
\(310\) −0.568867 + 1.75079i −0.0323095 + 0.0994383i
\(311\) −14.4959 + 10.5319i −0.821985 + 0.597207i −0.917280 0.398242i \(-0.869620\pi\)
0.0952956 + 0.995449i \(0.469620\pi\)
\(312\) 4.47342 + 3.25013i 0.253258 + 0.184002i
\(313\) 1.59291 + 4.90249i 0.0900368 + 0.277105i 0.985928 0.167168i \(-0.0534622\pi\)
−0.895892 + 0.444273i \(0.853462\pi\)
\(314\) −0.634019 1.95131i −0.0357798 0.110119i
\(315\) −1.42932 1.03846i −0.0805329 0.0585106i
\(316\) 9.50873 6.90850i 0.534908 0.388633i
\(317\) 8.79505 27.0684i 0.493979 1.52031i −0.324563 0.945864i \(-0.605217\pi\)
0.818542 0.574447i \(-0.194783\pi\)
\(318\) 8.77126 0.491868
\(319\) 28.2621 4.31330i 1.58237 0.241498i
\(320\) 1.00000 0.0559017
\(321\) −4.55112 + 14.0069i −0.254019 + 0.781789i
\(322\) −2.03459 + 1.47821i −0.113383 + 0.0823776i
\(323\) −10.4014 7.55706i −0.578750 0.420486i
\(324\) −3.45446 10.6317i −0.191914 0.590651i
\(325\) 0.782625 + 2.40867i 0.0434122 + 0.133609i
\(326\) 16.7447 + 12.1657i 0.927402 + 0.673797i
\(327\) −33.0060 + 23.9803i −1.82524 + 1.32611i
\(328\) 3.26085 10.0359i 0.180050 0.554138i
\(329\) 3.22482 0.177790
\(330\) 1.17301 7.14549i 0.0645723 0.393347i
\(331\) −24.8572 −1.36627 −0.683136 0.730291i \(-0.739385\pi\)
−0.683136 + 0.730291i \(0.739385\pi\)
\(332\) −2.27081 + 6.98885i −0.124627 + 0.383563i
\(333\) 6.61952 4.80936i 0.362747 0.263551i
\(334\) 1.06831 + 0.776171i 0.0584552 + 0.0424702i
\(335\) 1.19353 + 3.67329i 0.0652092 + 0.200693i
\(336\) 0.674672 + 2.07643i 0.0368064 + 0.113278i
\(337\) 12.6590 + 9.19732i 0.689581 + 0.501010i 0.876522 0.481361i \(-0.159858\pi\)
−0.186942 + 0.982371i \(0.559858\pi\)
\(338\) −5.32802 + 3.87103i −0.289806 + 0.210556i
\(339\) 5.10345 15.7068i 0.277181 0.853076i
\(340\) −5.73813 −0.311194
\(341\) −2.74119 5.45560i −0.148444 0.295437i
\(342\) 3.95854 0.214053
\(343\) 0.309017 0.951057i 0.0166853 0.0513522i
\(344\) −1.77016 + 1.28609i −0.0954405 + 0.0693416i
\(345\) 4.44208 + 3.22736i 0.239154 + 0.173755i
\(346\) −4.85245 14.9343i −0.260869 0.802873i
\(347\) 4.53162 + 13.9469i 0.243270 + 0.748709i 0.995916 + 0.0902833i \(0.0287773\pi\)
−0.752646 + 0.658426i \(0.771223\pi\)
\(348\) 15.2256 + 11.0621i 0.816179 + 0.592989i
\(349\) −21.8243 + 15.8563i −1.16823 + 0.848767i −0.990796 0.135367i \(-0.956779\pi\)
−0.177431 + 0.984133i \(0.556779\pi\)
\(350\) −0.309017 + 0.951057i −0.0165177 + 0.0508361i
\(351\) −6.81929 −0.363987
\(352\) −2.35838 + 2.33197i −0.125702 + 0.124294i
\(353\) 4.77463 0.254128 0.127064 0.991895i \(-0.459445\pi\)
0.127064 + 0.991895i \(0.459445\pi\)
\(354\) −1.35882 + 4.18202i −0.0722205 + 0.222272i
\(355\) 7.73027 5.61637i 0.410280 0.298086i
\(356\) 2.14711 + 1.55997i 0.113797 + 0.0826780i
\(357\) −3.87135 11.9148i −0.204894 0.630598i
\(358\) −1.43846 4.42714i −0.0760252 0.233982i
\(359\) −27.5860 20.0424i −1.45593 1.05780i −0.984399 0.175950i \(-0.943700\pi\)
−0.471534 0.881848i \(-0.656300\pi\)
\(360\) 1.42932 1.03846i 0.0753316 0.0547316i
\(361\) −4.31997 + 13.2955i −0.227367 + 0.699763i
\(362\) 5.90450 0.310334
\(363\) 13.8966 + 19.5872i 0.729385 + 1.02806i
\(364\) 2.53263 0.132746
\(365\) −3.53078 + 10.8666i −0.184810 + 0.568785i
\(366\) −0.473787 + 0.344227i −0.0247653 + 0.0179930i
\(367\) 8.08180 + 5.87177i 0.421866 + 0.306504i 0.778388 0.627783i \(-0.216038\pi\)
−0.356522 + 0.934287i \(0.616038\pi\)
\(368\) −0.777143 2.39180i −0.0405114 0.124681i
\(369\) −5.76105 17.7307i −0.299908 0.923023i
\(370\) −3.74676 2.72218i −0.194785 0.141519i
\(371\) 3.25019 2.36140i 0.168742 0.122598i
\(372\) 1.24200 3.82248i 0.0643946 0.198186i
\(373\) −0.510916 −0.0264542 −0.0132271 0.999913i \(-0.504210\pi\)
−0.0132271 + 0.999913i \(0.504210\pi\)
\(374\) 13.5327 13.3811i 0.699757 0.691921i
\(375\) 2.18328 0.112744
\(376\) −0.996525 + 3.06699i −0.0513918 + 0.158168i
\(377\) 17.6619 12.8321i 0.909632 0.660886i
\(378\) −2.17834 1.58266i −0.112042 0.0814030i
\(379\) 1.64204 + 5.05369i 0.0843460 + 0.259590i 0.984331 0.176330i \(-0.0564227\pi\)
−0.899985 + 0.435921i \(0.856423\pi\)
\(380\) −0.692383 2.13094i −0.0355185 0.109315i
\(381\) 18.9748 + 13.7860i 0.972106 + 0.706277i
\(382\) −4.80071 + 3.48792i −0.245626 + 0.178458i
\(383\) 7.26815 22.3691i 0.371385 1.14301i −0.574500 0.818505i \(-0.694803\pi\)
0.945885 0.324502i \(-0.105197\pi\)
\(384\) −2.18328 −0.111415
\(385\) −1.48905 2.96357i −0.0758892 0.151037i
\(386\) −10.8377 −0.551623
\(387\) −1.19456 + 3.67647i −0.0607228 + 0.186886i
\(388\) −13.3525 + 9.70112i −0.677868 + 0.492500i
\(389\) −7.42999 5.39820i −0.376715 0.273700i 0.383275 0.923634i \(-0.374796\pi\)
−0.759990 + 0.649935i \(0.774796\pi\)
\(390\) −1.70869 5.25882i −0.0865231 0.266291i
\(391\) 4.45934 + 13.7244i 0.225519 + 0.694075i
\(392\) 0.809017 + 0.587785i 0.0408615 + 0.0296876i
\(393\) 30.0664 21.8445i 1.51665 1.10191i
\(394\) −3.71363 + 11.4294i −0.187090 + 0.575804i
\(395\) −11.7534 −0.591380
\(396\) −0.949212 + 5.78220i −0.0476997 + 0.290566i
\(397\) −31.5709 −1.58450 −0.792248 0.610199i \(-0.791089\pi\)
−0.792248 + 0.610199i \(0.791089\pi\)
\(398\) −5.68634 + 17.5008i −0.285031 + 0.877234i
\(399\) 3.95760 2.87537i 0.198128 0.143948i
\(400\) −0.809017 0.587785i −0.0404508 0.0293893i
\(401\) −3.30043 10.1577i −0.164816 0.507250i 0.834207 0.551451i \(-0.185926\pi\)
−0.999023 + 0.0442012i \(0.985926\pi\)
\(402\) −2.60581 8.01984i −0.129966 0.399993i
\(403\) −3.77188 2.74043i −0.187891 0.136510i
\(404\) −12.9830 + 9.43267i −0.645926 + 0.469293i
\(405\) −3.45446 + 10.6317i −0.171653 + 0.528294i
\(406\) 8.62000 0.427803
\(407\) 15.1843 2.31739i 0.752657 0.114869i
\(408\) 12.5280 0.620227
\(409\) −7.28568 + 22.4230i −0.360254 + 1.10875i 0.592647 + 0.805463i \(0.298083\pi\)
−0.952900 + 0.303284i \(0.901917\pi\)
\(410\) −8.53702 + 6.20251i −0.421613 + 0.306320i
\(411\) 22.0395 + 16.0126i 1.08713 + 0.789844i
\(412\) −3.98721 12.2714i −0.196436 0.604568i
\(413\) 0.622375 + 1.91547i 0.0306251 + 0.0942542i
\(414\) −3.59457 2.61161i −0.176663 0.128354i
\(415\) 5.94507 4.31934i 0.291832 0.212028i
\(416\) −0.782625 + 2.40867i −0.0383714 + 0.118095i
\(417\) 37.9482 1.85833
\(418\) 6.60217 + 3.41093i 0.322923 + 0.166834i
\(419\) −15.9235 −0.777915 −0.388958 0.921256i \(-0.627165\pi\)
−0.388958 + 0.921256i \(0.627165\pi\)
\(420\) 0.674672 2.07643i 0.0329206 0.101319i
\(421\) 32.2476 23.4292i 1.57165 1.14187i 0.646096 0.763256i \(-0.276401\pi\)
0.925554 0.378615i \(-0.123599\pi\)
\(422\) 16.2145 + 11.7805i 0.789307 + 0.573465i
\(423\) 1.76059 + 5.41855i 0.0856029 + 0.263459i
\(424\) 1.24146 + 3.82083i 0.0602908 + 0.185556i
\(425\) 4.64224 + 3.37279i 0.225182 + 0.163604i
\(426\) −16.8774 + 12.2621i −0.817712 + 0.594102i
\(427\) −0.0828892 + 0.255107i −0.00401129 + 0.0123455i
\(428\) −6.74567 −0.326064
\(429\) 16.2931 + 8.41765i 0.786640 + 0.406408i
\(430\) 2.18804 0.105516
\(431\) −5.43589 + 16.7300i −0.261838 + 0.805854i 0.730567 + 0.682841i \(0.239256\pi\)
−0.992405 + 0.123013i \(0.960744\pi\)
\(432\) 2.17834 1.58266i 0.104805 0.0761455i
\(433\) −16.6207 12.0756i −0.798739 0.580318i 0.111805 0.993730i \(-0.464337\pi\)
−0.910544 + 0.413412i \(0.864337\pi\)
\(434\) −0.568867 1.75079i −0.0273065 0.0840407i
\(435\) −5.81567 17.8988i −0.278840 0.858182i
\(436\) −15.1176 10.9836i −0.724002 0.526018i
\(437\) −4.55869 + 3.31208i −0.218072 + 0.158438i
\(438\) 7.70870 23.7249i 0.368336 1.13362i
\(439\) 22.4200 1.07005 0.535023 0.844837i \(-0.320303\pi\)
0.535023 + 0.844837i \(0.320303\pi\)
\(440\) 3.27866 0.500382i 0.156304 0.0238548i
\(441\) 1.76673 0.0841301
\(442\) 4.49080 13.8213i 0.213606 0.657411i
\(443\) −6.17697 + 4.48783i −0.293477 + 0.213223i −0.724774 0.688986i \(-0.758056\pi\)
0.431297 + 0.902210i \(0.358056\pi\)
\(444\) 8.18023 + 5.94329i 0.388217 + 0.282056i
\(445\) −0.820123 2.52408i −0.0388775 0.119653i
\(446\) −3.64639 11.2224i −0.172662 0.531398i
\(447\) 2.63545 + 1.91477i 0.124653 + 0.0905655i
\(448\) −0.809017 + 0.587785i −0.0382225 + 0.0277702i
\(449\) −0.201624 + 0.620536i −0.00951524 + 0.0292849i −0.955701 0.294338i \(-0.904901\pi\)
0.946186 + 0.323623i \(0.104901\pi\)
\(450\) −1.76673 −0.0832846
\(451\) 5.66945 34.5359i 0.266964 1.62623i
\(452\) 7.56433 0.355796
\(453\) −5.39437 + 16.6022i −0.253450 + 0.780038i
\(454\) 0.801025 0.581979i 0.0375940 0.0273136i
\(455\) −2.04894 1.48864i −0.0960558 0.0697886i
\(456\) 1.51167 + 4.65244i 0.0707904 + 0.217871i
\(457\) 9.44637 + 29.0729i 0.441882 + 1.35997i 0.885867 + 0.463940i \(0.153565\pi\)
−0.443984 + 0.896035i \(0.646435\pi\)
\(458\) 14.8502 + 10.7893i 0.693905 + 0.504152i
\(459\) −12.4996 + 9.08147i −0.583430 + 0.423887i
\(460\) −0.777143 + 2.39180i −0.0362345 + 0.111518i
\(461\) −3.55735 −0.165682 −0.0828412 0.996563i \(-0.526399\pi\)
−0.0828412 + 0.996563i \(0.526399\pi\)
\(462\) 3.25103 + 6.47031i 0.151252 + 0.301026i
\(463\) 6.57677 0.305648 0.152824 0.988253i \(-0.451163\pi\)
0.152824 + 0.988253i \(0.451163\pi\)
\(464\) −2.66373 + 8.19811i −0.123660 + 0.380588i
\(465\) −3.25159 + 2.36242i −0.150789 + 0.109555i
\(466\) −14.0486 10.2069i −0.650787 0.472825i
\(467\) −5.68391 17.4933i −0.263020 0.809492i −0.992143 0.125109i \(-0.960072\pi\)
0.729123 0.684383i \(-0.239928\pi\)
\(468\) 1.38269 + 4.25548i 0.0639149 + 0.196710i
\(469\) −3.12469 2.27022i −0.144285 0.104829i
\(470\) 2.60894 1.89550i 0.120341 0.0874330i
\(471\) 1.38424 4.26026i 0.0637826 0.196303i
\(472\) −2.01405 −0.0927040
\(473\) −5.16021 + 5.10242i −0.237267 + 0.234610i
\(474\) 25.6611 1.17865
\(475\) −0.692383 + 2.13094i −0.0317687 + 0.0977741i
\(476\) 4.64224 3.37279i 0.212777 0.154591i
\(477\) 5.74222 + 4.17197i 0.262918 + 0.191021i
\(478\) −2.75678 8.48450i −0.126092 0.388072i
\(479\) 10.2288 + 31.4810i 0.467366 + 1.43840i 0.855983 + 0.517004i \(0.172953\pi\)
−0.388617 + 0.921399i \(0.627047\pi\)
\(480\) 1.76631 + 1.28330i 0.0806209 + 0.0585745i
\(481\) 9.48914 6.89427i 0.432668 0.314351i
\(482\) 0.277094 0.852808i 0.0126213 0.0388444i
\(483\) −5.49071 −0.249836
\(484\) −6.56544 + 8.82582i −0.298429 + 0.401173i
\(485\) 16.5045 0.749432
\(486\) 5.04591 15.5297i 0.228887 0.704442i
\(487\) 12.6192 9.16836i 0.571829 0.415458i −0.263940 0.964539i \(-0.585022\pi\)
0.835769 + 0.549081i \(0.185022\pi\)
\(488\) −0.217007 0.157665i −0.00982343 0.00713714i
\(489\) 13.9641 + 42.9770i 0.631477 + 1.94349i
\(490\) −0.309017 0.951057i −0.0139600 0.0429644i
\(491\) 33.7066 + 24.4893i 1.52116 + 1.10519i 0.960910 + 0.276860i \(0.0892938\pi\)
0.560247 + 0.828326i \(0.310706\pi\)
\(492\) 18.6387 13.5418i 0.840299 0.610513i
\(493\) 15.2848 47.0418i 0.688393 2.11865i
\(494\) 5.67461 0.255313
\(495\) 4.16662 4.11996i 0.187276 0.185178i
\(496\) 1.84089 0.0826585
\(497\) −2.95270 + 9.08747i −0.132447 + 0.407629i
\(498\) −12.9798 + 9.43036i −0.581638 + 0.422585i
\(499\) 1.98298 + 1.44072i 0.0887703 + 0.0644954i 0.631285 0.775551i \(-0.282528\pi\)
−0.542515 + 0.840046i \(0.682528\pi\)
\(500\) 0.309017 + 0.951057i 0.0138197 + 0.0425325i
\(501\) 0.890905 + 2.74193i 0.0398027 + 0.122500i
\(502\) −18.2011 13.2239i −0.812357 0.590212i
\(503\) 5.41115 3.93143i 0.241271 0.175294i −0.460578 0.887619i \(-0.652358\pi\)
0.701849 + 0.712325i \(0.252358\pi\)
\(504\) −0.545950 + 1.68026i −0.0243186 + 0.0748448i
\(505\) 16.0478 0.714118
\(506\) −3.74480 7.45303i −0.166477 0.331328i
\(507\) −14.3787 −0.638579
\(508\) −3.31964 + 10.2168i −0.147285 + 0.453297i
\(509\) 11.3879 8.27379i 0.504760 0.366729i −0.306072 0.952008i \(-0.599015\pi\)
0.810832 + 0.585279i \(0.199015\pi\)
\(510\) −10.1353 7.36375i −0.448800 0.326072i
\(511\) −3.53078 10.8666i −0.156193 0.480711i
\(512\) −0.309017 0.951057i −0.0136568 0.0420312i
\(513\) −4.88078 3.54610i −0.215492 0.156564i
\(514\) −20.1808 + 14.6622i −0.890137 + 0.646723i
\(515\) −3.98721 + 12.2714i −0.175698 + 0.540742i
\(516\) −4.77710 −0.210300
\(517\) −1.73260 + 10.5543i −0.0761997 + 0.464176i
\(518\) 4.63124 0.203485
\(519\) 10.5943 32.6058i 0.465037 1.43124i
\(520\) 2.04894 1.48864i 0.0898520 0.0652813i
\(521\) −33.7351 24.5100i −1.47796 1.07380i −0.978206 0.207638i \(-0.933423\pi\)
−0.499757 0.866166i \(-0.666577\pi\)
\(522\) 4.70609 + 14.4839i 0.205980 + 0.633941i
\(523\) 3.30524 + 10.1725i 0.144528 + 0.444812i 0.996950 0.0780428i \(-0.0248671\pi\)
−0.852422 + 0.522855i \(0.824867\pi\)
\(524\) 13.7712 + 10.0053i 0.601596 + 0.437085i
\(525\) −1.76631 + 1.28330i −0.0770883 + 0.0560079i
\(526\) −1.93319 + 5.94975i −0.0842911 + 0.259421i
\(527\) −10.5633 −0.460143
\(528\) −7.15825 + 1.09248i −0.311523 + 0.0475440i
\(529\) −16.6753 −0.725015
\(530\) 1.24146 3.82083i 0.0539257 0.165966i
\(531\) −2.87871 + 2.09151i −0.124925 + 0.0907636i
\(532\) 1.81268 + 1.31699i 0.0785898 + 0.0570988i
\(533\) −8.25853 25.4171i −0.357716 1.10094i
\(534\) 1.79056 + 5.51078i 0.0774852 + 0.238475i
\(535\) 5.45736 + 3.96501i 0.235942 + 0.171422i
\(536\) 3.12469 2.27022i 0.134966 0.0980586i
\(537\) 3.14058 9.66570i 0.135526 0.417106i
\(538\) 13.0673 0.563371
\(539\) 2.94661 + 1.52233i 0.126919 + 0.0655714i
\(540\) −2.69257 −0.115870
\(541\) 2.98174 9.17684i 0.128195 0.394543i −0.866275 0.499568i \(-0.833492\pi\)
0.994470 + 0.105025i \(0.0334921\pi\)
\(542\) −19.6718 + 14.2924i −0.844975 + 0.613910i
\(543\) 10.4292 + 7.57727i 0.447560 + 0.325172i
\(544\) 1.77318 + 5.45728i 0.0760244 + 0.233979i
\(545\) 5.77441 + 17.7718i 0.247349 + 0.761261i
\(546\) 4.47342 + 3.25013i 0.191445 + 0.139093i
\(547\) −12.0176 + 8.73126i −0.513834 + 0.373322i −0.814276 0.580478i \(-0.802866\pi\)
0.300442 + 0.953800i \(0.402866\pi\)
\(548\) −3.85581 + 11.8670i −0.164712 + 0.506931i
\(549\) −0.473900 −0.0202255
\(550\) −2.94661 1.52233i −0.125644 0.0649124i
\(551\) 19.3140 0.822803
\(552\) 1.69672 5.22198i 0.0722174 0.222262i
\(553\) 9.50873 6.90850i 0.404352 0.293779i
\(554\) −10.8485 7.88188i −0.460907 0.334869i
\(555\) −3.12457 9.61644i −0.132631 0.408195i
\(556\) 5.37110 + 16.5305i 0.227785 + 0.701051i
\(557\) −32.3080 23.4732i −1.36893 0.994589i −0.997819 0.0660025i \(-0.978975\pi\)
−0.371115 0.928587i \(-0.621025\pi\)
\(558\) 2.63122 1.91169i 0.111388 0.0809283i
\(559\) −1.71241 + 5.27026i −0.0724273 + 0.222908i
\(560\) 1.00000 0.0422577
\(561\) 41.0749 6.26877i 1.73419 0.264668i
\(562\) −12.7398 −0.537396
\(563\) 1.25587 3.86518i 0.0529287 0.162898i −0.921098 0.389331i \(-0.872706\pi\)
0.974027 + 0.226433i \(0.0727064\pi\)
\(564\) −5.69605 + 4.13842i −0.239847 + 0.174259i
\(565\) −6.11968 4.44620i −0.257457 0.187053i
\(566\) 4.24884 + 13.0766i 0.178592 + 0.549650i
\(567\) −3.45446 10.6317i −0.145074 0.446490i
\(568\) −7.73027 5.61637i −0.324355 0.235658i
\(569\) −25.8072 + 18.7500i −1.08189 + 0.786041i −0.978012 0.208548i \(-0.933126\pi\)
−0.103881 + 0.994590i \(0.533126\pi\)
\(570\) 1.51167 4.65244i 0.0633169 0.194869i
\(571\) 20.3883 0.853222 0.426611 0.904435i \(-0.359707\pi\)
0.426611 + 0.904435i \(0.359707\pi\)
\(572\) −1.36071 + 8.28884i −0.0568940 + 0.346574i
\(573\) −12.9556 −0.541229
\(574\) 3.26085 10.0359i 0.136105 0.418889i
\(575\) 2.03459 1.47821i 0.0848481 0.0616458i
\(576\) −1.42932 1.03846i −0.0595549 0.0432691i
\(577\) −8.04835 24.7703i −0.335057 1.03120i −0.966694 0.255936i \(-0.917617\pi\)
0.631637 0.775265i \(-0.282383\pi\)
\(578\) −4.92143 15.1466i −0.204705 0.630016i
\(579\) −19.1427 13.9080i −0.795545 0.577997i
\(580\) 6.97373 5.06671i 0.289568 0.210384i
\(581\) −2.27081 + 6.98885i −0.0942092 + 0.289946i
\(582\) −36.0341 −1.49366
\(583\) 5.98222 + 11.9060i 0.247758 + 0.493096i
\(584\) 11.4258 0.472805
\(585\) 1.38269 4.25548i 0.0571672 0.175943i
\(586\) 13.4601 9.77936i 0.556033 0.403982i
\(587\) 31.5393 + 22.9146i 1.30177 + 0.945788i 0.999971 0.00758441i \(-0.00241422\pi\)
0.301795 + 0.953373i \(0.402414\pi\)
\(588\) 0.674672 + 2.07643i 0.0278230 + 0.0856304i
\(589\) −1.27460 3.92282i −0.0525191 0.161637i
\(590\) 1.62940 + 1.18383i 0.0670813 + 0.0487374i
\(591\) −21.2268 + 15.4222i −0.873153 + 0.634383i
\(592\) −1.43113 + 4.40458i −0.0588192 + 0.181027i
\(593\) −0.526179 −0.0216076 −0.0108038 0.999942i \(-0.503439\pi\)
−0.0108038 + 0.999942i \(0.503439\pi\)
\(594\) 6.35010 6.27899i 0.260548 0.257630i
\(595\) −5.73813 −0.235240
\(596\) −0.461073 + 1.41904i −0.0188863 + 0.0581260i
\(597\) −32.5026 + 23.6146i −1.33024 + 0.966479i
\(598\) −5.15285 3.74377i −0.210716 0.153094i
\(599\) −3.82883 11.7839i −0.156442 0.481478i 0.841862 0.539692i \(-0.181459\pi\)
−0.998304 + 0.0582143i \(0.981459\pi\)
\(600\) −0.674672 2.07643i −0.0275434 0.0847698i
\(601\) −21.7409 15.7957i −0.886830 0.644320i 0.0482193 0.998837i \(-0.484645\pi\)
−0.935050 + 0.354517i \(0.884645\pi\)
\(602\) −1.77016 + 1.28609i −0.0721462 + 0.0524173i
\(603\) 2.10864 6.48973i 0.0858705 0.264282i
\(604\) −7.99555 −0.325334
\(605\) 10.4992 3.28117i 0.426855 0.133398i
\(606\) −35.0369 −1.42328
\(607\) −11.1655 + 34.3640i −0.453196 + 1.39479i 0.420045 + 0.907503i \(0.362014\pi\)
−0.873241 + 0.487289i \(0.837986\pi\)
\(608\) −1.81268 + 1.31699i −0.0735140 + 0.0534110i
\(609\) 15.2256 + 11.0621i 0.616974 + 0.448258i
\(610\) 0.0828892 + 0.255107i 0.00335608 + 0.0103290i
\(611\) 2.52383 + 7.76754i 0.102103 + 0.314241i
\(612\) 8.20160 + 5.95881i 0.331530 + 0.240871i
\(613\) 26.9071 19.5492i 1.08677 0.789583i 0.107917 0.994160i \(-0.465582\pi\)
0.978850 + 0.204577i \(0.0655819\pi\)
\(614\) −1.71883 + 5.29003i −0.0693665 + 0.213488i
\(615\) −23.0388 −0.929012
\(616\) −2.35838 + 2.33197i −0.0950216 + 0.0939576i
\(617\) −27.1415 −1.09267 −0.546337 0.837565i \(-0.683978\pi\)
−0.546337 + 0.837565i \(0.683978\pi\)
\(618\) 8.70523 26.7919i 0.350176 1.07773i
\(619\) −2.37231 + 1.72359i −0.0953513 + 0.0692768i −0.634439 0.772973i \(-0.718769\pi\)
0.539088 + 0.842249i \(0.318769\pi\)
\(620\) −1.48931 1.08205i −0.0598122 0.0434561i
\(621\) 2.09251 + 6.44010i 0.0839697 + 0.258432i
\(622\) −5.53692 17.0409i −0.222010 0.683278i
\(623\) 2.14711 + 1.55997i 0.0860221 + 0.0624987i
\(624\) −4.47342 + 3.25013i −0.179080 + 0.130109i
\(625\) 0.309017 0.951057i 0.0123607 0.0380423i
\(626\) −5.15478 −0.206026
\(627\) 7.28425 + 14.4974i 0.290905 + 0.578969i
\(628\) 2.05173 0.0818729
\(629\) 8.21202 25.2740i 0.327435 1.00774i
\(630\) 1.42932 1.03846i 0.0569453 0.0413732i
\(631\) 5.74575 + 4.17453i 0.228735 + 0.166185i 0.696250 0.717800i \(-0.254851\pi\)
−0.467515 + 0.883985i \(0.654851\pi\)
\(632\) 3.63201 + 11.1782i 0.144474 + 0.444644i
\(633\) 13.5219 + 41.6161i 0.537447 + 1.65409i
\(634\) 23.0257 + 16.7292i 0.914469 + 0.664400i
\(635\) 8.69092 6.31432i 0.344889 0.250576i
\(636\) −2.71047 + 8.34197i −0.107477 + 0.330780i
\(637\) 2.53263 0.100346
\(638\) −4.63127 + 28.2117i −0.183354 + 1.11691i
\(639\) −16.8814 −0.667817
\(640\) −0.309017 + 0.951057i −0.0122150 + 0.0375938i
\(641\) −1.30237 + 0.946231i −0.0514407 + 0.0373739i −0.613208 0.789921i \(-0.710121\pi\)
0.561768 + 0.827295i \(0.310121\pi\)
\(642\) −11.9150 8.65674i −0.470247 0.341654i
\(643\) −5.53544 17.0363i −0.218297 0.671848i −0.998903 0.0468249i \(-0.985090\pi\)
0.780607 0.625023i \(-0.214910\pi\)
\(644\) −0.777143 2.39180i −0.0306237 0.0942501i
\(645\) 3.86476 + 2.80791i 0.152175 + 0.110561i
\(646\) 10.4014 7.55706i 0.409238 0.297329i
\(647\) −1.66471 + 5.12345i −0.0654464 + 0.201423i −0.978432 0.206568i \(-0.933771\pi\)
0.912986 + 0.407991i \(0.133771\pi\)
\(648\) 11.1789 0.439147
\(649\) −6.60338 + 1.00779i −0.259205 + 0.0395594i
\(650\) −2.53263 −0.0993379
\(651\) 1.24200 3.82248i 0.0486777 0.149815i
\(652\) −16.7447 + 12.1657i −0.655773 + 0.476447i
\(653\) −39.3609 28.5973i −1.54031 1.11910i −0.950141 0.311820i \(-0.899062\pi\)
−0.590168 0.807281i \(-0.700938\pi\)
\(654\) −12.6072 38.8009i −0.492980 1.51724i
\(655\) −5.26012 16.1890i −0.205530 0.632555i
\(656\) 8.53702 + 6.20251i 0.333315 + 0.242167i
\(657\) 16.3312 11.8653i 0.637139 0.462909i
\(658\) −0.996525 + 3.06699i −0.0388486 + 0.119564i
\(659\) −29.0793 −1.13277 −0.566385 0.824141i \(-0.691658\pi\)
−0.566385 + 0.824141i \(0.691658\pi\)
\(660\) 6.43329 + 3.32368i 0.250415 + 0.129374i
\(661\) −13.9160 −0.541270 −0.270635 0.962682i \(-0.587234\pi\)
−0.270635 + 0.962682i \(0.587234\pi\)
\(662\) 7.68128 23.6406i 0.298542 0.918816i
\(663\) 25.6690 18.6497i 0.996903 0.724292i
\(664\) −5.94507 4.31934i −0.230713 0.167623i
\(665\) −0.692383 2.13094i −0.0268495 0.0826342i
\(666\) 2.52843 + 7.78171i 0.0979747 + 0.301535i
\(667\) −17.5381 12.7422i −0.679079 0.493380i
\(668\) −1.06831 + 0.776171i −0.0413341 + 0.0300310i
\(669\) 7.96111 24.5018i 0.307794 0.947294i
\(670\) −3.86233 −0.149215
\(671\) −0.790384 0.408342i −0.0305124 0.0157639i
\(672\) −2.18328 −0.0842220
\(673\) −10.0802 + 31.0236i −0.388562 + 1.19587i 0.545301 + 0.838240i \(0.316415\pi\)
−0.933863 + 0.357631i \(0.883585\pi\)
\(674\) −12.6590 + 9.19732i −0.487607 + 0.354267i
\(675\) 2.17834 + 1.58266i 0.0838443 + 0.0609164i
\(676\) −2.03512 6.26346i −0.0782739 0.240902i
\(677\) 11.6155 + 35.7489i 0.446421 + 1.37394i 0.880918 + 0.473270i \(0.156926\pi\)
−0.434496 + 0.900674i \(0.643074\pi\)
\(678\) 13.3610 + 9.70733i 0.513126 + 0.372808i
\(679\) −13.3525 + 9.70112i −0.512420 + 0.372295i
\(680\) 1.77318 5.45728i 0.0679983 0.209277i
\(681\) 2.16172 0.0828372
\(682\) 6.03566 0.921150i 0.231117 0.0352726i
\(683\) −17.5199 −0.670380 −0.335190 0.942151i \(-0.608800\pi\)
−0.335190 + 0.942151i \(0.608800\pi\)
\(684\) −1.22326 + 3.76480i −0.0467724 + 0.143951i
\(685\) 10.0946 7.33418i 0.385696 0.280225i
\(686\) 0.809017 + 0.587785i 0.0308884 + 0.0224417i
\(687\) 12.3842 + 38.1146i 0.472487 + 1.45416i
\(688\) −0.676140 2.08095i −0.0257776 0.0793353i
\(689\) 8.23154 + 5.98056i 0.313597 + 0.227841i
\(690\) −4.44208 + 3.22736i −0.169107 + 0.122864i
\(691\) 2.20747 6.79389i 0.0839760 0.258452i −0.900248 0.435377i \(-0.856615\pi\)
0.984224 + 0.176925i \(0.0566151\pi\)
\(692\) 15.7029 0.596933
\(693\) −0.949212 + 5.78220i −0.0360576 + 0.219647i
\(694\) −14.6646 −0.556662
\(695\) 5.37110 16.5305i 0.203737 0.627039i
\(696\) −15.2256 + 11.0621i −0.577126 + 0.419307i
\(697\) −48.9865 35.5908i −1.85550 1.34810i
\(698\) −8.33613 25.6560i −0.315527 0.971093i
\(699\) −11.7157 36.0571i −0.443127 1.36381i
\(700\) −0.809017 0.587785i −0.0305780 0.0222162i
\(701\) 31.3683 22.7904i 1.18476 0.860781i 0.192063 0.981383i \(-0.438482\pi\)
0.992701 + 0.120601i \(0.0384823\pi\)
\(702\) 2.10728 6.48553i 0.0795340 0.244781i
\(703\) 10.3768 0.391367
\(704\) −1.48905 2.96357i −0.0561208 0.111694i
\(705\) 7.04070 0.265168
\(706\) −1.47544 + 4.54094i −0.0555290 + 0.170901i
\(707\) −12.9830 + 9.43267i −0.488274 + 0.354752i
\(708\) −3.55744 2.58463i −0.133697 0.0971364i
\(709\) 9.37902 + 28.8656i 0.352236 + 1.08407i 0.957595 + 0.288119i \(0.0930298\pi\)
−0.605358 + 0.795953i \(0.706970\pi\)
\(710\) 2.95270 + 9.08747i 0.110813 + 0.341047i
\(711\) 16.7994 + 12.2055i 0.630026 + 0.457741i
\(712\) −2.14711 + 1.55997i −0.0804663 + 0.0584622i
\(713\) −1.43064 + 4.40304i −0.0535777 + 0.164895i
\(714\) 12.5280 0.468847
\(715\) 5.97289 5.90601i 0.223373 0.220872i
\(716\) 4.65497 0.173964
\(717\) 6.01884 18.5241i 0.224778 0.691794i
\(718\) 27.5860 20.0424i 1.02950 0.747976i
\(719\) −29.1535 21.1813i −1.08724 0.789928i −0.108311 0.994117i \(-0.534544\pi\)
−0.978931 + 0.204189i \(0.934544\pi\)
\(720\) 0.545950 + 1.68026i 0.0203464 + 0.0626197i
\(721\) −3.98721 12.2714i −0.148492 0.457010i
\(722\) −11.3098 8.21707i −0.420908 0.305808i
\(723\) 1.58385 1.15073i 0.0589039 0.0427962i
\(724\) −1.82459 + 5.61552i −0.0678104 + 0.208699i
\(725\) −8.62000 −0.320139
\(726\) −22.9228 + 7.16373i −0.850746 + 0.265871i
\(727\) 31.1833 1.15653 0.578263 0.815850i \(-0.303731\pi\)
0.578263 + 0.815850i \(0.303731\pi\)
\(728\) −0.782625 + 2.40867i −0.0290060 + 0.0892714i
\(729\) 1.71032 1.24262i 0.0633454 0.0460231i
\(730\) −9.24371 6.71595i −0.342125 0.248568i
\(731\) 3.87978 + 11.9407i 0.143499 + 0.441644i
\(732\) −0.180971 0.556970i −0.00668887 0.0205862i
\(733\) 21.0611 + 15.3018i 0.777909 + 0.565184i 0.904351 0.426790i \(-0.140356\pi\)
−0.126442 + 0.991974i \(0.540356\pi\)
\(734\) −8.08180 + 5.87177i −0.298305 + 0.216731i
\(735\) 0.674672 2.07643i 0.0248857 0.0765902i
\(736\) 2.51489 0.0927000
\(737\) 9.10882 9.00682i 0.335528 0.331771i
\(738\) 18.6432 0.686264
\(739\) 6.92632 21.3170i 0.254789 0.784159i −0.739083 0.673615i \(-0.764741\pi\)
0.993871 0.110544i \(-0.0352593\pi\)
\(740\) 3.74676 2.72218i 0.137733 0.100069i
\(741\) 10.0231 + 7.28224i 0.368209 + 0.267520i
\(742\) 1.24146 + 3.82083i 0.0455756 + 0.140267i
\(743\) −13.6919 42.1394i −0.502308 1.54595i −0.805249 0.592936i \(-0.797969\pi\)
0.302941 0.953009i \(-0.402031\pi\)
\(744\) 3.25159 + 2.36242i 0.119209 + 0.0866105i
\(745\) 1.20710 0.877013i 0.0442249 0.0321313i
\(746\) 0.157882 0.485910i 0.00578046 0.0177904i
\(747\) −12.9828 −0.475018
\(748\) 8.54438 + 17.0053i 0.312413 + 0.621776i
\(749\) −6.74567 −0.246482
\(750\) −0.674672 + 2.07643i −0.0246355 + 0.0758204i
\(751\) −31.8495 + 23.1400i −1.16221 + 0.844392i −0.990055 0.140678i \(-0.955072\pi\)
−0.172151 + 0.985071i \(0.555072\pi\)
\(752\) −2.60894 1.89550i −0.0951381 0.0691219i
\(753\) −15.1787 46.7151i −0.553142 1.70239i
\(754\) 6.74623 + 20.7628i 0.245683 + 0.756135i
\(755\) 6.46853 + 4.69966i 0.235414 + 0.171038i
\(756\) 2.17834 1.58266i 0.0792254 0.0575606i
\(757\) −10.3242 + 31.7746i −0.375239 + 1.15487i 0.568079 + 0.822974i \(0.307687\pi\)
−0.943317 + 0.331892i \(0.892313\pi\)
\(758\) −5.31376 −0.193004
\(759\) 2.95000 17.9701i 0.107078 0.652274i
\(760\) 2.24060 0.0812751
\(761\) 12.0356 37.0418i 0.436290 1.34276i −0.455469 0.890252i \(-0.650528\pi\)
0.891759 0.452511i \(-0.149472\pi\)
\(762\) −18.9748 + 13.7860i −0.687383 + 0.499413i
\(763\) −15.1176 10.9836i −0.547294 0.397632i
\(764\) −1.83371 5.64357i −0.0663412 0.204177i
\(765\) −3.13273 9.64156i −0.113264 0.348591i
\(766\) 19.0283 + 13.8249i 0.687520 + 0.499512i
\(767\) −4.12666 + 2.99819i −0.149005 + 0.108259i
\(768\) 0.674672 2.07643i 0.0243451 0.0749266i
\(769\) −0.875099 −0.0315569 −0.0157784 0.999876i \(-0.505023\pi\)
−0.0157784 + 0.999876i \(0.505023\pi\)
\(770\) 3.27866 0.500382i 0.118155 0.0180325i
\(771\) −54.4617 −1.96139
\(772\) 3.34902 10.3072i 0.120534 0.370966i
\(773\) 18.5371 13.4680i 0.666731 0.484409i −0.202198 0.979345i \(-0.564808\pi\)
0.868929 + 0.494936i \(0.164808\pi\)
\(774\) −3.12740 2.27219i −0.112412 0.0816720i
\(775\) 0.568867 + 1.75079i 0.0204343 + 0.0628903i
\(776\) −5.10018 15.6967i −0.183086 0.563480i
\(777\) 8.18023 + 5.94329i 0.293464 + 0.213214i
\(778\) 7.42999 5.39820i 0.266378 0.193535i
\(779\) 7.30626 22.4864i 0.261774 0.805657i
\(780\) 5.52945 0.197986
\(781\) −28.1553 14.5461i −1.00747 0.520500i
\(782\) −14.4307 −0.516042
\(783\) 7.17228 22.0740i 0.256316 0.788861i
\(784\) −0.809017 + 0.587785i −0.0288935 + 0.0209923i
\(785\) −1.65988 1.20598i −0.0592438 0.0430431i
\(786\) 11.4843 + 35.3451i 0.409632 + 1.26072i
\(787\) −10.3240 31.7741i −0.368012 1.13262i −0.948074 0.318051i \(-0.896972\pi\)
0.580062 0.814572i \(-0.303028\pi\)
\(788\) −9.72241 7.06374i −0.346347 0.251635i
\(789\) −11.0500 + 8.02826i −0.393389 + 0.285814i
\(790\) 3.63201 11.1782i 0.129221 0.397702i
\(791\) 7.56433 0.268957
\(792\) −5.20587 2.68955i −0.184983 0.0955690i
\(793\) −0.679340 −0.0241241
\(794\) 9.75593 30.0257i 0.346225 1.06557i
\(795\) 7.09610 5.15562i 0.251673 0.182851i
\(796\) −14.8870 10.8161i −0.527657 0.383365i
\(797\) −1.06246 3.26992i −0.0376343 0.115827i 0.930474 0.366357i \(-0.119395\pi\)
−0.968109 + 0.250530i \(0.919395\pi\)
\(798\) 1.51167 + 4.65244i 0.0535125 + 0.164695i
\(799\) 14.9704 + 10.8766i 0.529615 + 0.384788i
\(800\) 0.809017 0.587785i 0.0286031 0.0207813i
\(801\) −1.44894 + 4.45937i −0.0511957 + 0.157564i
\(802\) 10.6804 0.377138
\(803\) 37.4615 5.71729i 1.32199 0.201759i
\(804\) 8.43256 0.297394
\(805\) −0.777143 + 2.39180i −0.0273907 + 0.0842999i
\(806\) 3.77188 2.74043i 0.132859 0.0965275i
\(807\) 23.0810 + 16.7693i 0.812488 + 0.590307i
\(808\) −4.95905 15.2624i −0.174459 0.536929i
\(809\) −10.9180 33.6022i −0.383857 1.18139i −0.937306 0.348506i \(-0.886689\pi\)
0.553450 0.832883i \(-0.313311\pi\)
\(810\) −9.04388 6.57077i −0.317770 0.230873i
\(811\) −39.3826 + 28.6132i −1.38291 + 1.00474i −0.386310 + 0.922369i \(0.626251\pi\)
−0.996601 + 0.0823753i \(0.973749\pi\)
\(812\) −2.66373 + 8.19811i −0.0934785 + 0.287697i
\(813\) −53.0880 −1.86188
\(814\) −2.48823 + 15.1572i −0.0872124 + 0.531260i
\(815\) 20.6976 0.725004
\(816\) −3.87135 + 11.9148i −0.135524 + 0.417101i
\(817\) −3.96621 + 2.88162i −0.138760 + 0.100815i
\(818\) −19.0742 13.8582i −0.666912 0.484540i
\(819\) 1.38269 + 4.25548i 0.0483151 + 0.148699i
\(820\) −3.26085 10.0359i −0.113874 0.350468i
\(821\) −13.9084 10.1050i −0.485406 0.352668i 0.318009 0.948088i \(-0.396986\pi\)
−0.803415 + 0.595420i \(0.796986\pi\)
\(822\) −22.0395 + 16.0126i −0.768715 + 0.558504i
\(823\) −14.1777 + 43.6343i −0.494202 + 1.52100i 0.323995 + 0.946059i \(0.394974\pi\)
−0.818197 + 0.574939i \(0.805026\pi\)
\(824\) 12.9029 0.449494
\(825\) −3.25103 6.47031i −0.113186 0.225267i
\(826\) −2.01405 −0.0700777
\(827\) −8.64150 + 26.5958i −0.300494 + 0.924827i 0.680826 + 0.732445i \(0.261621\pi\)
−0.981320 + 0.192381i \(0.938379\pi\)
\(828\) 3.59457 2.61161i 0.124920 0.0907596i
\(829\) 15.2755 + 11.0983i 0.530539 + 0.385459i 0.820559 0.571561i \(-0.193662\pi\)
−0.290020 + 0.957021i \(0.593662\pi\)
\(830\) 2.27081 + 6.98885i 0.0788211 + 0.242586i
\(831\) −9.04698 27.8437i −0.313836 0.965889i
\(832\) −2.04894 1.48864i −0.0710342 0.0516094i
\(833\) 4.64224 3.37279i 0.160844 0.116860i
\(834\) −11.7266 + 36.0909i −0.406060 + 1.24973i
\(835\) 1.32050 0.0456978
\(836\) −5.28417 + 5.22500i −0.182757 + 0.180710i
\(837\) −4.95674 −0.171330
\(838\) 4.92064 15.1442i 0.169981 0.523147i
\(839\) 15.9470 11.5862i 0.550553 0.400000i −0.277436 0.960744i \(-0.589485\pi\)
0.827989 + 0.560744i \(0.189485\pi\)
\(840\) 1.76631 + 1.28330i 0.0609436 + 0.0442781i
\(841\) 13.9998 + 43.0870i 0.482752 + 1.48576i
\(842\) 12.3175 + 37.9093i 0.424488 + 1.30644i
\(843\) −22.5025 16.3490i −0.775028 0.563091i
\(844\) −16.2145 + 11.7805i −0.558125 + 0.405501i
\(845\) −2.03512 + 6.26346i −0.0700103 + 0.215470i
\(846\) −5.69740 −0.195881
\(847\) −6.56544 + 8.82582i −0.225591 + 0.303259i
\(848\) −4.01746 −0.137960
\(849\) −9.27643 + 28.5499i −0.318366 + 0.979830i
\(850\) −4.64224 + 3.37279i −0.159228 + 0.115686i
\(851\) −9.42267 6.84597i −0.323005 0.234677i
\(852\) −6.44658 19.8405i −0.220856 0.679726i
\(853\) −9.54664 29.3815i −0.326871 1.00600i −0.970589 0.240742i \(-0.922609\pi\)
0.643718 0.765262i \(-0.277391\pi\)
\(854\) −0.217007 0.157665i −0.00742582 0.00539517i
\(855\) 3.20253 2.32677i 0.109524 0.0795739i
\(856\) 2.08453 6.41552i 0.0712477 0.219278i
\(857\) 24.2847 0.829550 0.414775 0.909924i \(-0.363860\pi\)
0.414775 + 0.909924i \(0.363860\pi\)
\(858\) −13.0405 + 12.8945i −0.445196 + 0.440211i
\(859\) 22.0877 0.753621 0.376811 0.926290i \(-0.377021\pi\)
0.376811 + 0.926290i \(0.377021\pi\)
\(860\) −0.676140 + 2.08095i −0.0230562 + 0.0709596i
\(861\) 18.6387 13.5418i 0.635207 0.461505i
\(862\) −14.2314 10.3397i −0.484722 0.352171i
\(863\) −4.35874 13.4148i −0.148373 0.456646i 0.849056 0.528303i \(-0.177171\pi\)
−0.997429 + 0.0716566i \(0.977171\pi\)
\(864\) 0.832051 + 2.56079i 0.0283070 + 0.0871198i
\(865\) −12.7039 9.22991i −0.431945 0.313826i
\(866\) 16.6207 12.0756i 0.564794 0.410347i
\(867\) 10.7449 33.0694i 0.364915 1.12309i
\(868\) 1.84089 0.0624839
\(869\) 17.5015 + 34.8321i 0.593698 + 1.18160i
\(870\) 18.8199 0.638055
\(871\) 3.02276 9.30309i 0.102422 0.315223i
\(872\) 15.1176 10.9836i 0.511947 0.371951i
\(873\) −23.5902 17.1393i −0.798408 0.580077i
\(874\) −1.74127 5.35906i −0.0588992 0.181273i
\(875\) 0.309017 + 0.951057i 0.0104467 + 0.0321516i
\(876\) 20.1816 + 14.6628i 0.681875 + 0.495411i
\(877\) −45.2424 + 32.8706i −1.52773 + 1.10996i −0.570244 + 0.821475i \(0.693151\pi\)
−0.957485 + 0.288484i \(0.906849\pi\)
\(878\) −6.92815 + 21.3226i −0.233814 + 0.719604i
\(879\) 36.3247 1.22520
\(880\) −0.537270 + 3.27282i −0.0181114 + 0.110327i
\(881\) −46.2057 −1.55671 −0.778354 0.627826i \(-0.783945\pi\)
−0.778354 + 0.627826i \(0.783945\pi\)
\(882\) −0.545950 + 1.68026i −0.0183831 + 0.0565774i
\(883\) 11.4320 8.30582i 0.384717 0.279513i −0.378570 0.925572i \(-0.623584\pi\)
0.763287 + 0.646060i \(0.223584\pi\)
\(884\) 11.7571 + 8.54201i 0.395433 + 0.287299i
\(885\) 1.35882 + 4.18202i 0.0456763 + 0.140577i
\(886\) −2.35939 7.26147i −0.0792654 0.243954i
\(887\) 30.4359 + 22.1129i 1.02194 + 0.742480i 0.966679 0.255992i \(-0.0824022\pi\)
0.0552571 + 0.998472i \(0.482402\pi\)
\(888\) −8.18023 + 5.94329i −0.274511 + 0.199444i
\(889\) −3.31964 + 10.2168i −0.111337 + 0.342660i
\(890\) 2.65397 0.0889614
\(891\) 36.6517 5.59370i 1.22788 0.187396i
\(892\) 11.8000 0.395092
\(893\) −2.23281 + 6.87189i −0.0747182 + 0.229959i
\(894\) −2.63545 + 1.91477i −0.0881428 + 0.0640395i
\(895\) −3.76595 2.73612i −0.125882 0.0914585i
\(896\) −0.309017 0.951057i −0.0103235 0.0317726i
\(897\) −4.29717 13.2253i −0.143478 0.441581i
\(898\) −0.527860 0.383512i −0.0176149 0.0127980i
\(899\) 12.8379 9.32726i 0.428167 0.311081i
\(900\) 0.545950 1.68026i 0.0181983 0.0560088i
\(901\) 23.0527 0.767997
\(902\) 31.0936 + 16.0641i 1.03530 + 0.534877i
\(903\) −4.77710 −0.158972
\(904\) −2.33751 + 7.19411i −0.0777444 + 0.239273i
\(905\) 4.77684 3.47058i 0.158788 0.115366i
\(906\) −14.1227 10.2607i −0.469194 0.340889i
\(907\) −0.919382 2.82957i −0.0305276 0.0939542i 0.934632 0.355617i \(-0.115729\pi\)
−0.965159 + 0.261663i \(0.915729\pi\)
\(908\) 0.305964 + 0.941661i 0.0101538 + 0.0312501i
\(909\) −22.9374 16.6650i −0.760786 0.552743i
\(910\) 2.04894 1.48864i 0.0679217 0.0493480i
\(911\) −16.6469 + 51.2340i −0.551538 + 1.69746i 0.153377 + 0.988168i \(0.450985\pi\)
−0.704915 + 0.709292i \(0.749015\pi\)
\(912\) −4.89187 −0.161986
\(913\) −21.6532 11.1869i −0.716616 0.370231i
\(914\) −30.5691 −1.01114
\(915\) −0.180971 + 0.556970i −0.00598271 + 0.0184129i
\(916\) −14.8502 + 10.7893i −0.490665 + 0.356489i
\(917\) 13.7712 + 10.0053i 0.454764 + 0.330405i
\(918\) −4.77441 14.6941i −0.157579 0.484979i
\(919\) −5.24298 16.1362i −0.172950 0.532286i 0.826584 0.562814i \(-0.190281\pi\)
−0.999534 + 0.0305280i \(0.990281\pi\)
\(920\) −2.03459 1.47821i −0.0670783 0.0487353i
\(921\) −9.82471 + 7.13807i −0.323735 + 0.235207i
\(922\) 1.09928 3.38324i 0.0362029 0.111421i
\(923\) −24.1996 −0.796540
\(924\) −7.15825 + 1.09248i −0.235489 + 0.0359399i
\(925\) −4.63124 −0.152274
\(926\) −2.03233 + 6.25488i −0.0667866 + 0.205548i
\(927\) 18.4423 13.3991i 0.605725 0.440085i
\(928\) −6.97373 5.06671i −0.228924 0.166323i
\(929\) 10.0083 + 30.8024i 0.328362 + 1.01060i 0.969900 + 0.243504i \(0.0782968\pi\)
−0.641538 + 0.767092i \(0.721703\pi\)
\(930\) −1.24200 3.82248i −0.0407267 0.125344i
\(931\) 1.81268 + 1.31699i 0.0594083 + 0.0431626i
\(932\) 14.0486 10.2069i 0.460176 0.334338i
\(933\) 12.0887 37.2051i 0.395766 1.21804i
\(934\) 18.3935 0.601854
\(935\) 3.08292 18.7798i 0.100822 0.614167i
\(936\) −4.47448 −0.146253
\(937\) −7.46123 + 22.9633i −0.243748 + 0.750178i 0.752092 + 0.659058i \(0.229045\pi\)
−0.995840 + 0.0911204i \(0.970955\pi\)
\(938\) 3.12469 2.27022i 0.102025 0.0741253i
\(939\) −9.10496 6.61514i −0.297129 0.215877i
\(940\) 0.996525 + 3.06699i 0.0325031 + 0.100034i
\(941\) 12.5475 + 38.6173i 0.409037 + 1.25889i 0.917477 + 0.397790i \(0.130223\pi\)
−0.508439 + 0.861098i \(0.669777\pi\)
\(942\) 3.62400 + 2.63299i 0.118076 + 0.0857874i
\(943\) −21.4696 + 15.5986i −0.699148 + 0.507960i
\(944\) 0.622375 1.91547i 0.0202566 0.0623433i
\(945\) −2.69257 −0.0875894
\(946\) −3.25810 6.48439i −0.105930 0.210826i
\(947\) 0.111103 0.00361036 0.00180518 0.999998i \(-0.499425\pi\)
0.00180518 + 0.999998i \(0.499425\pi\)
\(948\) −7.92972 + 24.4052i −0.257545 + 0.792643i
\(949\) 23.4109 17.0090i 0.759949 0.552135i
\(950\) −1.81268 1.31699i −0.0588112 0.0427288i
\(951\) 19.2021 + 59.0980i 0.622671 + 1.91638i
\(952\) 1.77318 + 5.45728i 0.0574690 + 0.176872i
\(953\) 6.23263 + 4.52827i 0.201895 + 0.146685i 0.684139 0.729352i \(-0.260178\pi\)
−0.482244 + 0.876037i \(0.660178\pi\)
\(954\) −5.74222 + 4.17197i −0.185911 + 0.135073i
\(955\) −1.83371 + 5.64357i −0.0593374 + 0.182622i
\(956\) 8.92113 0.288530
\(957\) −44.3844 + 43.8874i −1.43474 + 1.41868i
\(958\) −33.1011 −1.06945
\(959\) −3.85581 + 11.8670i −0.124511 + 0.383204i
\(960\) −1.76631 + 1.28330i −0.0570076 + 0.0414184i
\(961\) 22.3379 + 16.2294i 0.720576 + 0.523529i
\(962\) 3.62453 + 11.1552i 0.116860 + 0.359657i
\(963\) −3.68280 11.3345i −0.118677 0.365249i
\(964\) 0.725442 + 0.527065i 0.0233649 + 0.0169756i
\(965\) −8.76786 + 6.37022i −0.282247 + 0.205065i
\(966\) 1.69672 5.22198i 0.0545912 0.168014i
\(967\) 41.8250 1.34500 0.672501 0.740096i \(-0.265220\pi\)
0.672501 + 0.740096i \(0.265220\pi\)
\(968\) −6.36502 8.97143i −0.204579 0.288353i
\(969\) 28.0701 0.901743
\(970\) −5.10018 + 15.6967i −0.163757 + 0.503992i
\(971\) −30.1680 + 21.9184i −0.968138 + 0.703394i −0.955026 0.296520i \(-0.904174\pi\)
−0.0131117 + 0.999914i \(0.504174\pi\)
\(972\) 13.2104 + 9.59789i 0.423722 + 0.307852i
\(973\) 5.37110 + 16.5305i 0.172190 + 0.529945i
\(974\) 4.82009 + 14.8347i 0.154446 + 0.475335i
\(975\) −4.47342 3.25013i −0.143264 0.104087i
\(976\) 0.217007 0.157665i 0.00694621 0.00504672i
\(977\) 0.745160 2.29337i 0.0238398 0.0733713i −0.938429 0.345473i \(-0.887719\pi\)
0.962269 + 0.272101i \(0.0877186\pi\)
\(978\) −45.1887 −1.44498
\(979\) −6.25906 + 6.18898i −0.200041 + 0.197801i
\(980\) 1.00000 0.0319438
\(981\) 10.2018 31.3980i 0.325720 1.00246i
\(982\) −33.7066 + 24.4893i −1.07562 + 0.781484i
\(983\) 32.7154 + 23.7691i 1.04346 + 0.758118i 0.970958 0.239250i \(-0.0769016\pi\)
0.0725021 + 0.997368i \(0.476902\pi\)
\(984\) 7.11937 + 21.9112i 0.226957 + 0.698502i
\(985\) 3.71363 + 11.4294i 0.118326 + 0.364170i
\(986\) 40.0161 + 29.0734i 1.27437 + 0.925886i
\(987\) −5.69605 + 4.13842i −0.181307 + 0.131727i
\(988\) −1.75355 + 5.39687i −0.0557879 + 0.171697i
\(989\) 5.50266 0.174974
\(990\) 2.63076 + 5.23583i 0.0836110 + 0.166406i
\(991\) 26.7075 0.848392 0.424196 0.905570i \(-0.360557\pi\)
0.424196 + 0.905570i \(0.360557\pi\)
\(992\) −0.568867 + 1.75079i −0.0180615 + 0.0555877i
\(993\) 43.9055 31.8992i 1.39330 1.01229i
\(994\) −7.73027 5.61637i −0.245189 0.178140i
\(995\) 5.68634 + 17.5008i 0.180269 + 0.554811i
\(996\) −4.95783 15.2586i −0.157095 0.483489i
\(997\) 22.1125 + 16.0657i 0.700310 + 0.508805i 0.880033 0.474912i \(-0.157520\pi\)
−0.179723 + 0.983717i \(0.557520\pi\)
\(998\) −1.98298 + 1.44072i −0.0627701 + 0.0456051i
\(999\) 3.85343 11.8596i 0.121917 0.375223i
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 770.2.n.j.141.1 yes 12
11.4 even 5 8470.2.a.cw.1.6 6
11.5 even 5 inner 770.2.n.j.71.1 12
11.7 odd 10 8470.2.a.dc.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
770.2.n.j.71.1 12 11.5 even 5 inner
770.2.n.j.141.1 yes 12 1.1 even 1 trivial
8470.2.a.cw.1.6 6 11.4 even 5
8470.2.a.dc.1.6 6 11.7 odd 10