Properties

Label 210.2.u.a.187.4
Level $210$
Weight $2$
Character 210.187
Analytic conductor $1.677$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [210,2,Mod(73,210)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(210, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 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("210.73");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 210.u (of order \(12\), 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: \(1.67685844245\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 187.4
Root \(-0.709944 + 0.925217i\) of defining polynomial
Character \(\chi\) \(=\) 210.187
Dual form 210.2.u.a.73.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.55103 - 1.61069i) q^{5} -1.00000i q^{6} +(-1.38658 + 2.25331i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\) \(q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.55103 - 1.61069i) q^{5} -1.00000i q^{6} +(-1.38658 + 2.25331i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.08130 - 1.95724i) q^{10} +(0.582897 + 1.00961i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-1.92501 - 1.92501i) q^{13} +(-0.756134 + 2.53540i) q^{14} +(-1.15437 - 1.91505i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.0209315 - 0.00560858i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(-0.989363 + 1.71363i) q^{19} +(0.537883 - 2.17041i) q^{20} +(1.81766 + 1.92253i) q^{21} +(0.824341 + 0.824341i) q^{22} +(1.85829 + 6.93525i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.188640 - 4.99644i) q^{25} +(-2.35765 - 1.36119i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.0741591 + 2.64471i) q^{28} +5.60604i q^{29} +(-1.61069 - 1.55103i) q^{30} +(6.86850 - 3.96553i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.12607 - 0.301730i) q^{33} -0.0216699 q^{34} +(1.47876 + 5.72829i) q^{35} -1.00000 q^{36} +(-10.2592 + 2.74894i) q^{37} +(-0.512132 + 1.91130i) q^{38} +(-2.35765 + 1.36119i) q^{39} +(-0.0421887 - 2.23567i) q^{40} -2.48977i q^{41} +(2.25331 + 1.38658i) q^{42} +(-7.87756 + 7.87756i) q^{43} +(1.00961 + 0.582897i) q^{44} +(-2.14857 + 0.619385i) q^{45} +(3.58995 + 6.21797i) q^{46} +(-1.05773 - 3.94750i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(-3.15479 - 6.24878i) q^{49} +(-1.47539 - 4.77737i) q^{50} +(-0.0108349 + 0.0187667i) q^{51} +(-2.62962 - 0.704604i) q^{52} +(2.82745 + 0.757613i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(2.53025 + 0.627061i) q^{55} +(0.612870 + 2.57379i) q^{56} +(1.39917 + 1.39917i) q^{57} +(1.45095 + 5.41502i) q^{58} +(5.34623 + 9.25995i) q^{59} +(-1.95724 - 1.08130i) q^{60} +(-3.15795 - 1.82324i) q^{61} +(5.60811 - 5.60811i) q^{62} +(2.32747 - 1.25813i) q^{63} -1.00000i q^{64} +(-6.08634 + 0.114854i) q^{65} +(1.00961 - 0.582897i) q^{66} +(3.76794 - 14.0621i) q^{67} +(-0.0209315 + 0.00560858i) q^{68} +7.17989 q^{69} +(2.91096 + 5.15037i) q^{70} +7.51848 q^{71} +(-0.965926 + 0.258819i) q^{72} +(0.969376 - 3.61776i) q^{73} +(-9.19815 + 5.31055i) q^{74} +(-4.87501 - 1.11096i) q^{75} +1.97873i q^{76} +(-3.08319 - 0.0864543i) q^{77} +(-1.92501 + 1.92501i) q^{78} +(-1.39464 - 0.805197i) q^{79} +(-0.619385 - 2.14857i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.644400 - 2.40493i) q^{82} +(-9.74815 - 9.74815i) q^{83} +(2.53540 + 0.756134i) q^{84} +(-0.0414990 + 0.0250151i) q^{85} +(-5.57028 + 9.64800i) q^{86} +(5.41502 + 1.45095i) q^{87} +(1.12607 + 0.301730i) q^{88} +(1.80255 - 3.12211i) q^{89} +(-1.91505 + 1.15437i) q^{90} +(7.00683 - 1.66846i) q^{91} +(5.07695 + 5.07695i) q^{92} +(-2.05271 - 7.66082i) q^{93} +(-2.04338 - 3.53923i) q^{94} +(1.22559 + 4.25144i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(-0.265501 + 0.265501i) q^{97} +(-4.66460 - 5.21934i) q^{98} -1.16579i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 12 q^{5} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 12 q^{5} - 8 q^{7} + 8 q^{10} + 4 q^{11} - 16 q^{13} + 16 q^{14} + 4 q^{15} + 8 q^{16} - 12 q^{17} - 8 q^{19} - 8 q^{20} + 8 q^{21} + 4 q^{22} + 32 q^{23} - 8 q^{24} - 32 q^{25} - 12 q^{26} - 8 q^{28} - 4 q^{30} - 24 q^{31} + 8 q^{33} + 16 q^{34} + 4 q^{35} - 16 q^{36} - 8 q^{37} - 28 q^{38} - 12 q^{39} - 4 q^{42} - 24 q^{43} + 4 q^{45} - 4 q^{46} - 24 q^{47} + 52 q^{49} + 8 q^{51} - 8 q^{52} + 44 q^{53} - 8 q^{54} - 56 q^{55} + 8 q^{56} - 8 q^{57} + 48 q^{58} + 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 16 q^{65} + 36 q^{67} - 12 q^{68} - 8 q^{69} + 32 q^{70} - 32 q^{71} - 40 q^{73} - 24 q^{74} - 24 q^{75} - 44 q^{77} - 16 q^{78} + 12 q^{79} + 12 q^{80} + 8 q^{81} + 12 q^{82} - 16 q^{83} + 4 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{87} + 8 q^{88} - 16 q^{89} + 8 q^{91} + 8 q^{92} + 40 q^{93} + 8 q^{94} - 48 q^{95} + 44 q^{97} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) 0.258819 0.965926i 0.149429 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 1.55103 1.61069i 0.693640 0.720322i
\(6\) 1.00000i 0.408248i
\(7\) −1.38658 + 2.25331i −0.524078 + 0.851670i
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −0.866025 0.500000i −0.288675 0.166667i
\(10\) 1.08130 1.95724i 0.341937 0.618934i
\(11\) 0.582897 + 1.00961i 0.175750 + 0.304408i 0.940421 0.340013i \(-0.110432\pi\)
−0.764670 + 0.644422i \(0.777098\pi\)
\(12\) −0.258819 0.965926i −0.0747146 0.278839i
\(13\) −1.92501 1.92501i −0.533903 0.533903i 0.387829 0.921731i \(-0.373225\pi\)
−0.921731 + 0.387829i \(0.873225\pi\)
\(14\) −0.756134 + 2.53540i −0.202085 + 0.677615i
\(15\) −1.15437 1.91505i −0.298057 0.494464i
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −0.0209315 0.00560858i −0.00507664 0.00136028i 0.256280 0.966603i \(-0.417503\pi\)
−0.261356 + 0.965242i \(0.584170\pi\)
\(18\) −0.965926 0.258819i −0.227671 0.0610042i
\(19\) −0.989363 + 1.71363i −0.226976 + 0.393133i −0.956910 0.290384i \(-0.906217\pi\)
0.729935 + 0.683517i \(0.239550\pi\)
\(20\) 0.537883 2.17041i 0.120274 0.485319i
\(21\) 1.81766 + 1.92253i 0.396645 + 0.419531i
\(22\) 0.824341 + 0.824341i 0.175750 + 0.175750i
\(23\) 1.85829 + 6.93525i 0.387481 + 1.44610i 0.834219 + 0.551434i \(0.185919\pi\)
−0.446738 + 0.894665i \(0.647414\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −0.188640 4.99644i −0.0377280 0.999288i
\(26\) −2.35765 1.36119i −0.462373 0.266951i
\(27\) −0.707107 + 0.707107i −0.136083 + 0.136083i
\(28\) −0.0741591 + 2.64471i −0.0140148 + 0.499804i
\(29\) 5.60604i 1.04102i 0.853857 + 0.520508i \(0.174257\pi\)
−0.853857 + 0.520508i \(0.825743\pi\)
\(30\) −1.61069 1.55103i −0.294070 0.283177i
\(31\) 6.86850 3.96553i 1.23362 0.712231i 0.265837 0.964018i \(-0.414352\pi\)
0.967783 + 0.251787i \(0.0810183\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) 1.12607 0.301730i 0.196024 0.0525244i
\(34\) −0.0216699 −0.00371636
\(35\) 1.47876 + 5.72829i 0.249956 + 0.968257i
\(36\) −1.00000 −0.166667
\(37\) −10.2592 + 2.74894i −1.68660 + 0.451924i −0.969509 0.245054i \(-0.921194\pi\)
−0.717093 + 0.696978i \(0.754528\pi\)
\(38\) −0.512132 + 1.91130i −0.0830788 + 0.310054i
\(39\) −2.35765 + 1.36119i −0.377526 + 0.217965i
\(40\) −0.0421887 2.23567i −0.00667062 0.353490i
\(41\) 2.48977i 0.388837i −0.980919 0.194418i \(-0.937718\pi\)
0.980919 0.194418i \(-0.0622819\pi\)
\(42\) 2.25331 + 1.38658i 0.347693 + 0.213954i
\(43\) −7.87756 + 7.87756i −1.20132 + 1.20132i −0.227550 + 0.973766i \(0.573072\pi\)
−0.973766 + 0.227550i \(0.926928\pi\)
\(44\) 1.00961 + 0.582897i 0.152204 + 0.0878751i
\(45\) −2.14857 + 0.619385i −0.320290 + 0.0923325i
\(46\) 3.58995 + 6.21797i 0.529309 + 0.916790i
\(47\) −1.05773 3.94750i −0.154286 0.575802i −0.999165 0.0408457i \(-0.986995\pi\)
0.844880 0.534956i \(-0.179672\pi\)
\(48\) −0.707107 0.707107i −0.102062 0.102062i
\(49\) −3.15479 6.24878i −0.450685 0.892683i
\(50\) −1.47539 4.77737i −0.208651 0.675622i
\(51\) −0.0108349 + 0.0187667i −0.00151720 + 0.00262786i
\(52\) −2.62962 0.704604i −0.364662 0.0977110i
\(53\) 2.82745 + 0.757613i 0.388380 + 0.104066i 0.447725 0.894171i \(-0.352234\pi\)
−0.0593446 + 0.998238i \(0.518901\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) 2.53025 + 0.627061i 0.341179 + 0.0845529i
\(56\) 0.612870 + 2.57379i 0.0818981 + 0.343937i
\(57\) 1.39917 + 1.39917i 0.185325 + 0.185325i
\(58\) 1.45095 + 5.41502i 0.190519 + 0.711027i
\(59\) 5.34623 + 9.25995i 0.696020 + 1.20554i 0.969835 + 0.243760i \(0.0783810\pi\)
−0.273815 + 0.961782i \(0.588286\pi\)
\(60\) −1.95724 1.08130i −0.252679 0.139595i
\(61\) −3.15795 1.82324i −0.404334 0.233442i 0.284018 0.958819i \(-0.408332\pi\)
−0.688352 + 0.725376i \(0.741666\pi\)
\(62\) 5.60811 5.60811i 0.712231 0.712231i
\(63\) 2.32747 1.25813i 0.293233 0.158510i
\(64\) 1.00000i 0.125000i
\(65\) −6.08634 + 0.114854i −0.754918 + 0.0142459i
\(66\) 1.00961 0.582897i 0.124274 0.0717497i
\(67\) 3.76794 14.0621i 0.460327 1.71796i −0.211608 0.977355i \(-0.567870\pi\)
0.671935 0.740610i \(-0.265463\pi\)
\(68\) −0.0209315 + 0.00560858i −0.00253832 + 0.000680140i
\(69\) 7.17989 0.864358
\(70\) 2.91096 + 5.15037i 0.347926 + 0.615587i
\(71\) 7.51848 0.892280 0.446140 0.894963i \(-0.352798\pi\)
0.446140 + 0.894963i \(0.352798\pi\)
\(72\) −0.965926 + 0.258819i −0.113835 + 0.0305021i
\(73\) 0.969376 3.61776i 0.113457 0.423427i −0.885710 0.464239i \(-0.846328\pi\)
0.999167 + 0.0408122i \(0.0129945\pi\)
\(74\) −9.19815 + 5.31055i −1.06926 + 0.617339i
\(75\) −4.87501 1.11096i −0.562918 0.128283i
\(76\) 1.97873i 0.226976i
\(77\) −3.08319 0.0864543i −0.351362 0.00985238i
\(78\) −1.92501 + 1.92501i −0.217965 + 0.217965i
\(79\) −1.39464 0.805197i −0.156910 0.0905918i 0.419489 0.907760i \(-0.362209\pi\)
−0.576399 + 0.817169i \(0.695543\pi\)
\(80\) −0.619385 2.14857i −0.0692494 0.240218i
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) −0.644400 2.40493i −0.0711620 0.265580i
\(83\) −9.74815 9.74815i −1.07000 1.07000i −0.997358 0.0726405i \(-0.976857\pi\)
−0.0726405 0.997358i \(-0.523143\pi\)
\(84\) 2.53540 + 0.756134i 0.276635 + 0.0825010i
\(85\) −0.0414990 + 0.0250151i −0.00450120 + 0.00271327i
\(86\) −5.57028 + 9.64800i −0.600658 + 1.04037i
\(87\) 5.41502 + 1.45095i 0.580551 + 0.155558i
\(88\) 1.12607 + 0.301730i 0.120040 + 0.0321645i
\(89\) 1.80255 3.12211i 0.191070 0.330943i −0.754535 0.656260i \(-0.772138\pi\)
0.945605 + 0.325317i \(0.105471\pi\)
\(90\) −1.91505 + 1.15437i −0.201864 + 0.121681i
\(91\) 7.00683 1.66846i 0.734516 0.174903i
\(92\) 5.07695 + 5.07695i 0.529309 + 0.529309i
\(93\) −2.05271 7.66082i −0.212856 0.794390i
\(94\) −2.04338 3.53923i −0.210758 0.365044i
\(95\) 1.22559 + 4.25144i 0.125743 + 0.436188i
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) −0.265501 + 0.265501i −0.0269575 + 0.0269575i −0.720457 0.693500i \(-0.756068\pi\)
0.693500 + 0.720457i \(0.256068\pi\)
\(98\) −4.66460 5.21934i −0.471196 0.527233i
\(99\) 1.16579i 0.117167i
\(100\) −2.66159 4.23272i −0.266159 0.423272i
\(101\) 12.0515 6.95796i 1.19917 0.692343i 0.238802 0.971068i \(-0.423245\pi\)
0.960371 + 0.278725i \(0.0899119\pi\)
\(102\) −0.00560858 + 0.0209315i −0.000555332 + 0.00207253i
\(103\) −11.5757 + 3.10171i −1.14059 + 0.305621i −0.779189 0.626789i \(-0.784369\pi\)
−0.361403 + 0.932410i \(0.617702\pi\)
\(104\) −2.72238 −0.266951
\(105\) 5.91583 + 0.0542182i 0.577326 + 0.00529116i
\(106\) 2.92719 0.284314
\(107\) −6.67031 + 1.78730i −0.644843 + 0.172785i −0.566396 0.824133i \(-0.691663\pi\)
−0.0784469 + 0.996918i \(0.524996\pi\)
\(108\) −0.258819 + 0.965926i −0.0249049 + 0.0929463i
\(109\) −0.499969 + 0.288657i −0.0478883 + 0.0276483i −0.523753 0.851870i \(-0.675469\pi\)
0.475865 + 0.879519i \(0.342135\pi\)
\(110\) 2.60633 0.0491834i 0.248504 0.00468945i
\(111\) 10.6211i 1.00811i
\(112\) 1.25813 + 2.32747i 0.118882 + 0.219925i
\(113\) 13.2689 13.2689i 1.24823 1.24823i 0.291728 0.956501i \(-0.405770\pi\)
0.956501 0.291728i \(-0.0942301\pi\)
\(114\) 1.71363 + 0.989363i 0.160496 + 0.0926624i
\(115\) 14.0528 + 7.76361i 1.31043 + 0.723960i
\(116\) 2.80302 + 4.85498i 0.260254 + 0.450773i
\(117\) 0.704604 + 2.62962i 0.0651406 + 0.243108i
\(118\) 7.56072 + 7.56072i 0.696020 + 0.696020i
\(119\) 0.0416611 0.0393884i 0.00381906 0.00361073i
\(120\) −2.17041 0.537883i −0.198130 0.0491018i
\(121\) 4.82046 8.34928i 0.438224 0.759026i
\(122\) −3.52224 0.943781i −0.318888 0.0854459i
\(123\) −2.40493 0.644400i −0.216845 0.0581036i
\(124\) 3.96553 6.86850i 0.356115 0.616810i
\(125\) −8.34030 7.44577i −0.745979 0.665969i
\(126\) 1.92253 1.81766i 0.171273 0.161930i
\(127\) 1.36110 + 1.36110i 0.120778 + 0.120778i 0.764912 0.644134i \(-0.222782\pi\)
−0.644134 + 0.764912i \(0.722782\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) 5.57028 + 9.64800i 0.490435 + 0.849459i
\(130\) −5.84923 + 1.68620i −0.513011 + 0.147890i
\(131\) −14.8522 8.57489i −1.29764 0.749192i −0.317643 0.948210i \(-0.602891\pi\)
−0.979996 + 0.199019i \(0.936225\pi\)
\(132\) 0.824341 0.824341i 0.0717497 0.0717497i
\(133\) −2.48950 4.60542i −0.215867 0.399341i
\(134\) 14.5582i 1.25764i
\(135\) 0.0421887 + 2.23567i 0.00363103 + 0.192416i
\(136\) −0.0187667 + 0.0108349i −0.00160923 + 0.000929089i
\(137\) 2.64921 9.88699i 0.226337 0.844702i −0.755527 0.655117i \(-0.772619\pi\)
0.981864 0.189585i \(-0.0607142\pi\)
\(138\) 6.93525 1.85829i 0.590367 0.158188i
\(139\) 5.65119 0.479327 0.239664 0.970856i \(-0.422963\pi\)
0.239664 + 0.970856i \(0.422963\pi\)
\(140\) 4.14479 + 4.22146i 0.350298 + 0.356779i
\(141\) −4.08675 −0.344166
\(142\) 7.26230 1.94593i 0.609439 0.163299i
\(143\) 0.821423 3.06559i 0.0686909 0.256358i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 9.02960 + 8.69512i 0.749867 + 0.722090i
\(146\) 3.74538i 0.309970i
\(147\) −6.85238 + 1.42999i −0.565175 + 0.117944i
\(148\) −7.51026 + 7.51026i −0.617339 + 0.617339i
\(149\) 0.191221 + 0.110402i 0.0156655 + 0.00904446i 0.507812 0.861468i \(-0.330454\pi\)
−0.492147 + 0.870512i \(0.663788\pi\)
\(150\) −4.99644 + 0.188640i −0.407958 + 0.0154024i
\(151\) 3.18442 + 5.51559i 0.259145 + 0.448852i 0.966013 0.258493i \(-0.0832260\pi\)
−0.706868 + 0.707345i \(0.749893\pi\)
\(152\) 0.512132 + 1.91130i 0.0415394 + 0.155027i
\(153\) 0.0153229 + 0.0153229i 0.00123879 + 0.00123879i
\(154\) −3.00051 + 0.714480i −0.241788 + 0.0575745i
\(155\) 4.26598 17.2137i 0.342652 1.38264i
\(156\) −1.36119 + 2.35765i −0.108982 + 0.188763i
\(157\) −13.9830 3.74673i −1.11596 0.299022i −0.346715 0.937970i \(-0.612703\pi\)
−0.769249 + 0.638949i \(0.779370\pi\)
\(158\) −1.55552 0.416801i −0.123751 0.0331589i
\(159\) 1.46360 2.53502i 0.116071 0.201040i
\(160\) −1.15437 1.91505i −0.0912611 0.151398i
\(161\) −18.2039 5.42896i −1.43467 0.427862i
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) 5.66960 + 21.1592i 0.444078 + 1.65732i 0.718360 + 0.695671i \(0.244893\pi\)
−0.274283 + 0.961649i \(0.588440\pi\)
\(164\) −1.24488 2.15620i −0.0972091 0.168371i
\(165\) 1.26057 2.28174i 0.0981354 0.177633i
\(166\) −11.9390 6.89298i −0.926646 0.534999i
\(167\) −11.3917 + 11.3917i −0.881515 + 0.881515i −0.993689 0.112174i \(-0.964219\pi\)
0.112174 + 0.993689i \(0.464219\pi\)
\(168\) 2.64471 + 0.0741591i 0.204044 + 0.00572150i
\(169\) 5.58865i 0.429896i
\(170\) −0.0336106 + 0.0349035i −0.00257781 + 0.00267697i
\(171\) 1.71363 0.989363i 0.131044 0.0756585i
\(172\) −2.88339 + 10.7609i −0.219856 + 0.820515i
\(173\) 10.0874 2.70291i 0.766932 0.205499i 0.145916 0.989297i \(-0.453387\pi\)
0.621016 + 0.783798i \(0.286720\pi\)
\(174\) 5.60604 0.424993
\(175\) 11.5201 + 6.50290i 0.870836 + 0.491573i
\(176\) 1.16579 0.0878751
\(177\) 10.3281 2.76741i 0.776310 0.208012i
\(178\) 0.933068 3.48226i 0.0699364 0.261006i
\(179\) 1.30513 0.753516i 0.0975498 0.0563204i −0.450431 0.892811i \(-0.648730\pi\)
0.547981 + 0.836491i \(0.315397\pi\)
\(180\) −1.55103 + 1.61069i −0.115607 + 0.120054i
\(181\) 21.3457i 1.58662i 0.608821 + 0.793308i \(0.291643\pi\)
−0.608821 + 0.793308i \(0.708357\pi\)
\(182\) 6.33625 3.42511i 0.469674 0.253886i
\(183\) −2.57846 + 2.57846i −0.190605 + 0.190605i
\(184\) 6.21797 + 3.58995i 0.458395 + 0.264654i
\(185\) −11.4846 + 20.7881i −0.844364 + 1.52837i
\(186\) −3.96553 6.86850i −0.290767 0.503623i
\(187\) −0.00653845 0.0244018i −0.000478139 0.00178444i
\(188\) −2.88977 2.88977i −0.210758 0.210758i
\(189\) −0.612870 2.57379i −0.0445797 0.187216i
\(190\) 2.28419 + 3.78937i 0.165712 + 0.274909i
\(191\) −3.22543 + 5.58661i −0.233384 + 0.404233i −0.958802 0.284076i \(-0.908313\pi\)
0.725418 + 0.688309i \(0.241647\pi\)
\(192\) −0.965926 0.258819i −0.0697097 0.0186787i
\(193\) 4.96349 + 1.32996i 0.357280 + 0.0957328i 0.432994 0.901397i \(-0.357457\pi\)
−0.0757145 + 0.997130i \(0.524124\pi\)
\(194\) −0.187737 + 0.325171i −0.0134788 + 0.0233459i
\(195\) −1.46432 + 5.90868i −0.104862 + 0.423129i
\(196\) −5.85652 3.83421i −0.418323 0.273872i
\(197\) 17.8347 + 17.8347i 1.27067 + 1.27067i 0.945738 + 0.324931i \(0.105341\pi\)
0.324931 + 0.945738i \(0.394659\pi\)
\(198\) −0.301730 1.12607i −0.0214430 0.0800264i
\(199\) −2.47098 4.27987i −0.175163 0.303392i 0.765054 0.643966i \(-0.222712\pi\)
−0.940218 + 0.340574i \(0.889379\pi\)
\(200\) −3.66641 3.39963i −0.259254 0.240390i
\(201\) −12.6078 7.27910i −0.889284 0.513428i
\(202\) 9.84004 9.84004i 0.692343 0.692343i
\(203\) −12.6321 7.77323i −0.886603 0.545574i
\(204\) 0.0216699i 0.00151720i
\(205\) −4.01024 3.86169i −0.280088 0.269712i
\(206\) −10.3785 + 5.99204i −0.723106 + 0.417485i
\(207\) 1.85829 6.93525i 0.129160 0.482033i
\(208\) −2.62962 + 0.704604i −0.182331 + 0.0488555i
\(209\) −2.30679 −0.159564
\(210\) 5.72829 1.47876i 0.395289 0.102044i
\(211\) −19.0455 −1.31115 −0.655574 0.755131i \(-0.727573\pi\)
−0.655574 + 0.755131i \(0.727573\pi\)
\(212\) 2.82745 0.757613i 0.194190 0.0520331i
\(213\) 1.94593 7.26230i 0.133333 0.497604i
\(214\) −5.98043 + 3.45281i −0.408814 + 0.236029i
\(215\) 0.470006 + 24.9066i 0.0320541 + 1.69862i
\(216\) 1.00000i 0.0680414i
\(217\) −0.588161 + 20.9754i −0.0399270 + 1.42390i
\(218\) −0.408223 + 0.408223i −0.0276483 + 0.0276483i
\(219\) −3.24360 1.87269i −0.219182 0.126545i
\(220\) 2.50479 0.722076i 0.168873 0.0486824i
\(221\) 0.0294968 + 0.0510900i 0.00198417 + 0.00343669i
\(222\) 2.74894 + 10.2592i 0.184497 + 0.688553i
\(223\) 2.94490 + 2.94490i 0.197205 + 0.197205i 0.798801 0.601596i \(-0.205468\pi\)
−0.601596 + 0.798801i \(0.705468\pi\)
\(224\) 1.81766 + 1.92253i 0.121447 + 0.128455i
\(225\) −2.33485 + 4.42136i −0.155657 + 0.294758i
\(226\) 9.38250 16.2510i 0.624115 1.08100i
\(227\) −17.8106 4.77234i −1.18213 0.316751i −0.386360 0.922348i \(-0.626268\pi\)
−0.795772 + 0.605597i \(0.792935\pi\)
\(228\) 1.91130 + 0.512132i 0.126579 + 0.0339168i
\(229\) −2.95505 + 5.11830i −0.195276 + 0.338227i −0.946991 0.321261i \(-0.895893\pi\)
0.751715 + 0.659488i \(0.229227\pi\)
\(230\) 15.5833 + 3.86194i 1.02753 + 0.254649i
\(231\) −0.881497 + 2.95576i −0.0579983 + 0.194475i
\(232\) 3.96407 + 3.96407i 0.260254 + 0.260254i
\(233\) 1.87264 + 6.98879i 0.122681 + 0.457851i 0.999746 0.0225196i \(-0.00716882\pi\)
−0.877066 + 0.480371i \(0.840502\pi\)
\(234\) 1.36119 + 2.35765i 0.0889838 + 0.154124i
\(235\) −7.99876 4.41900i −0.521781 0.288264i
\(236\) 9.25995 + 5.34623i 0.602771 + 0.348010i
\(237\) −1.13872 + 1.13872i −0.0739679 + 0.0739679i
\(238\) 0.0300470 0.0488289i 0.00194766 0.00316511i
\(239\) 4.20172i 0.271787i −0.990723 0.135893i \(-0.956610\pi\)
0.990723 0.135893i \(-0.0433904\pi\)
\(240\) −2.23567 + 0.0421887i −0.144312 + 0.00272327i
\(241\) −18.9970 + 10.9679i −1.22371 + 0.706507i −0.965706 0.259638i \(-0.916397\pi\)
−0.258000 + 0.966145i \(0.583064\pi\)
\(242\) 2.49525 9.31242i 0.160401 0.598625i
\(243\) 0.965926 0.258819i 0.0619642 0.0166032i
\(244\) −3.64649 −0.233442
\(245\) −14.9580 4.61063i −0.955632 0.294562i
\(246\) −2.48977 −0.158742
\(247\) 5.20329 1.39422i 0.331078 0.0887120i
\(248\) 2.05271 7.66082i 0.130347 0.486463i
\(249\) −11.9390 + 6.89298i −0.756603 + 0.436825i
\(250\) −9.98322 5.03343i −0.631394 0.318342i
\(251\) 15.1293i 0.954952i −0.878645 0.477476i \(-0.841552\pi\)
0.878645 0.477476i \(-0.158448\pi\)
\(252\) 1.38658 2.25331i 0.0873463 0.141945i
\(253\) −5.91868 + 5.91868i −0.372105 + 0.372105i
\(254\) 1.66700 + 0.962442i 0.104597 + 0.0603890i
\(255\) 0.0134220 + 0.0465593i 0.000840519 + 0.00291566i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 5.95653 + 22.2301i 0.371558 + 1.38667i 0.858309 + 0.513133i \(0.171515\pi\)
−0.486751 + 0.873541i \(0.661818\pi\)
\(258\) 7.87756 + 7.87756i 0.490435 + 0.490435i
\(259\) 8.03098 26.9288i 0.499021 1.67327i
\(260\) −5.21350 + 3.14264i −0.323328 + 0.194898i
\(261\) 2.80302 4.85498i 0.173503 0.300516i
\(262\) −16.5654 4.43869i −1.02342 0.274223i
\(263\) 19.4349 + 5.20756i 1.19841 + 0.321112i 0.802203 0.597051i \(-0.203661\pi\)
0.396203 + 0.918163i \(0.370328\pi\)
\(264\) 0.582897 1.00961i 0.0358749 0.0621371i
\(265\) 5.60573 3.37907i 0.344357 0.207574i
\(266\) −3.59664 3.80417i −0.220524 0.233248i
\(267\) −2.54919 2.54919i −0.156008 0.156008i
\(268\) −3.76794 14.0621i −0.230164 0.858982i
\(269\) 4.63479 + 8.02770i 0.282588 + 0.489457i 0.972021 0.234892i \(-0.0754736\pi\)
−0.689433 + 0.724349i \(0.742140\pi\)
\(270\) 0.619385 + 2.14857i 0.0376946 + 0.130758i
\(271\) 22.7157 + 13.1149i 1.37988 + 0.796673i 0.992144 0.125098i \(-0.0399244\pi\)
0.387734 + 0.921771i \(0.373258\pi\)
\(272\) −0.0153229 + 0.0153229i −0.000929089 + 0.000929089i
\(273\) 0.201889 7.19991i 0.0122189 0.435758i
\(274\) 10.2358i 0.618365i
\(275\) 4.93449 3.10286i 0.297561 0.187110i
\(276\) 6.21797 3.58995i 0.374278 0.216089i
\(277\) 3.44216 12.8463i 0.206819 0.771860i −0.782068 0.623193i \(-0.785835\pi\)
0.988887 0.148667i \(-0.0474982\pi\)
\(278\) 5.45863 1.46263i 0.327387 0.0877230i
\(279\) −7.93107 −0.474821
\(280\) 5.09615 + 3.00487i 0.304553 + 0.179575i
\(281\) −13.5101 −0.805944 −0.402972 0.915212i \(-0.632023\pi\)
−0.402972 + 0.915212i \(0.632023\pi\)
\(282\) −3.94750 + 1.05773i −0.235070 + 0.0629868i
\(283\) 5.14819 19.2133i 0.306028 1.14211i −0.626028 0.779800i \(-0.715321\pi\)
0.932057 0.362313i \(-0.118013\pi\)
\(284\) 6.51120 3.75924i 0.386369 0.223070i
\(285\) 4.42378 0.0834800i 0.262042 0.00494493i
\(286\) 3.17374i 0.187667i
\(287\) 5.61022 + 3.45226i 0.331161 + 0.203781i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) −14.7220 8.49977i −0.866001 0.499986i
\(290\) 10.9724 + 6.06181i 0.644320 + 0.355962i
\(291\) 0.187737 + 0.325171i 0.0110054 + 0.0190618i
\(292\) −0.969376 3.61776i −0.0567284 0.211713i
\(293\) 17.4044 + 17.4044i 1.01677 + 1.01677i 0.999857 + 0.0169176i \(0.00538531\pi\)
0.0169176 + 0.999857i \(0.494615\pi\)
\(294\) −6.24878 + 3.15479i −0.364436 + 0.183991i
\(295\) 23.2070 + 5.75129i 1.35117 + 0.334853i
\(296\) −5.31055 + 9.19815i −0.308670 + 0.534632i
\(297\) −1.12607 0.301730i −0.0653413 0.0175081i
\(298\) 0.213280 + 0.0571481i 0.0123550 + 0.00331050i
\(299\) 9.77320 16.9277i 0.565199 0.978953i
\(300\) −4.77737 + 1.47539i −0.275821 + 0.0851815i
\(301\) −6.82771 28.6734i −0.393542 1.65271i
\(302\) 4.50346 + 4.50346i 0.259145 + 0.259145i
\(303\) −3.60170 13.4417i −0.206913 0.772208i
\(304\) 0.989363 + 1.71363i 0.0567439 + 0.0982833i
\(305\) −7.83474 + 2.25858i −0.448616 + 0.129326i
\(306\) 0.0187667 + 0.0108349i 0.00107282 + 0.000619393i
\(307\) −0.566349 + 0.566349i −0.0323232 + 0.0323232i −0.723084 0.690760i \(-0.757276\pi\)
0.690760 + 0.723084i \(0.257276\pi\)
\(308\) −2.71335 + 1.46672i −0.154607 + 0.0835744i
\(309\) 11.9841i 0.681751i
\(310\) −0.334602 17.7312i −0.0190041 1.00707i
\(311\) 11.6023 6.69862i 0.657909 0.379844i −0.133571 0.991039i \(-0.542644\pi\)
0.791480 + 0.611196i \(0.209311\pi\)
\(312\) −0.704604 + 2.62962i −0.0398903 + 0.148873i
\(313\) 27.7781 7.44312i 1.57011 0.420710i 0.634263 0.773117i \(-0.281303\pi\)
0.935847 + 0.352407i \(0.114637\pi\)
\(314\) −14.4763 −0.816943
\(315\) 1.58350 5.70022i 0.0892202 0.321171i
\(316\) −1.61039 −0.0905918
\(317\) 32.5854 8.73124i 1.83018 0.490395i 0.832232 0.554427i \(-0.187062\pi\)
0.997948 + 0.0640314i \(0.0203958\pi\)
\(318\) 0.757613 2.82745i 0.0424848 0.158556i
\(319\) −5.65991 + 3.26775i −0.316894 + 0.182959i
\(320\) −1.61069 1.55103i −0.0900403 0.0867050i
\(321\) 6.90561i 0.385434i
\(322\) −18.9888 0.532455i −1.05820 0.0296725i
\(323\) 0.0303199 0.0303199i 0.00168704 0.00168704i
\(324\) 0.866025 + 0.500000i 0.0481125 + 0.0277778i
\(325\) −9.25508 + 9.98135i −0.513379 + 0.553666i
\(326\) 10.9528 + 18.9709i 0.606621 + 1.05070i
\(327\) 0.149420 + 0.557643i 0.00826294 + 0.0308377i
\(328\) −1.76053 1.76053i −0.0972091 0.0972091i
\(329\) 10.3616 + 3.09013i 0.571251 + 0.170364i
\(330\) 0.627061 2.53025i 0.0345186 0.139286i
\(331\) 5.46781 9.47053i 0.300538 0.520547i −0.675720 0.737159i \(-0.736167\pi\)
0.976258 + 0.216611i \(0.0695004\pi\)
\(332\) −13.3162 3.56807i −0.730823 0.195823i
\(333\) 10.2592 + 2.74894i 0.562201 + 0.150641i
\(334\) −8.05513 + 13.9519i −0.440757 + 0.763414i
\(335\) −16.8056 27.8797i −0.918187 1.52323i
\(336\) 2.57379 0.612870i 0.140412 0.0334348i
\(337\) −10.2916 10.2916i −0.560617 0.560617i 0.368866 0.929483i \(-0.379746\pi\)
−0.929483 + 0.368866i \(0.879746\pi\)
\(338\) −1.44645 5.39822i −0.0786764 0.293624i
\(339\) −9.38250 16.2510i −0.509587 0.882631i
\(340\) −0.0234316 + 0.0424132i −0.00127076 + 0.00230018i
\(341\) 8.00727 + 4.62300i 0.433618 + 0.250349i
\(342\) 1.39917 1.39917i 0.0756585 0.0756585i
\(343\) 18.4548 + 1.55571i 0.996466 + 0.0840004i
\(344\) 11.1406i 0.600658i
\(345\) 11.1362 11.5646i 0.599553 0.622616i
\(346\) 9.04413 5.22163i 0.486215 0.280717i
\(347\) −0.661173 + 2.46753i −0.0354936 + 0.132464i −0.981399 0.191978i \(-0.938510\pi\)
0.945906 + 0.324442i \(0.105176\pi\)
\(348\) 5.41502 1.45095i 0.290276 0.0777791i
\(349\) −18.6079 −0.996058 −0.498029 0.867160i \(-0.665943\pi\)
−0.498029 + 0.867160i \(0.665943\pi\)
\(350\) 12.8106 + 3.29970i 0.684756 + 0.176376i
\(351\) 2.72238 0.145310
\(352\) 1.12607 0.301730i 0.0600198 0.0160823i
\(353\) −4.09742 + 15.2918i −0.218084 + 0.813900i 0.766974 + 0.641678i \(0.221761\pi\)
−0.985058 + 0.172222i \(0.944905\pi\)
\(354\) 9.25995 5.34623i 0.492161 0.284149i
\(355\) 11.6614 12.1099i 0.618921 0.642729i
\(356\) 3.60510i 0.191070i
\(357\) −0.0272636 0.0504360i −0.00144294 0.00266935i
\(358\) 1.06563 1.06563i 0.0563204 0.0563204i
\(359\) 6.50055 + 3.75309i 0.343086 + 0.198081i 0.661636 0.749825i \(-0.269863\pi\)
−0.318550 + 0.947906i \(0.603196\pi\)
\(360\) −1.08130 + 1.95724i −0.0569894 + 0.103156i
\(361\) 7.54232 + 13.0637i 0.396964 + 0.687562i
\(362\) 5.52468 + 20.6184i 0.290371 + 1.08368i
\(363\) −6.81716 6.81716i −0.357808 0.357808i
\(364\) 5.23386 4.94835i 0.274329 0.259364i
\(365\) −4.32356 7.17260i −0.226306 0.375431i
\(366\) −1.82324 + 3.15795i −0.0953025 + 0.165069i
\(367\) 3.81343 + 1.02181i 0.199060 + 0.0533379i 0.356971 0.934115i \(-0.383809\pi\)
−0.157912 + 0.987453i \(0.550476\pi\)
\(368\) 6.93525 + 1.85829i 0.361525 + 0.0968702i
\(369\) −1.24488 + 2.15620i −0.0648061 + 0.112247i
\(370\) −5.71291 + 23.0522i −0.297000 + 1.19842i
\(371\) −5.62762 + 5.32063i −0.292172 + 0.276233i
\(372\) −5.60811 5.60811i −0.290767 0.290767i
\(373\) 1.39610 + 5.21031i 0.0722872 + 0.269780i 0.992605 0.121393i \(-0.0387362\pi\)
−0.920317 + 0.391173i \(0.872069\pi\)
\(374\) −0.0126313 0.0218781i −0.000653150 0.00113129i
\(375\) −9.35068 + 6.12900i −0.482867 + 0.316500i
\(376\) −3.53923 2.04338i −0.182522 0.105379i
\(377\) 10.7917 10.7917i 0.555801 0.555801i
\(378\) −1.25813 2.32747i −0.0647113 0.119712i
\(379\) 2.47403i 0.127082i −0.997979 0.0635411i \(-0.979761\pi\)
0.997979 0.0635411i \(-0.0202394\pi\)
\(380\) 3.18711 + 3.06906i 0.163495 + 0.157439i
\(381\) 1.66700 0.962442i 0.0854029 0.0493074i
\(382\) −1.66960 + 6.23105i −0.0854244 + 0.318808i
\(383\) −23.2872 + 6.23980i −1.18992 + 0.318839i −0.798855 0.601524i \(-0.794561\pi\)
−0.391067 + 0.920362i \(0.627894\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −4.92136 + 4.83197i −0.250816 + 0.246260i
\(386\) 5.13858 0.261547
\(387\) 10.7609 2.88339i 0.547010 0.146571i
\(388\) −0.0971800 + 0.362681i −0.00493357 + 0.0184123i
\(389\) 5.58638 3.22530i 0.283241 0.163529i −0.351649 0.936132i \(-0.614379\pi\)
0.634890 + 0.772603i \(0.281046\pi\)
\(390\) 0.114854 + 6.08634i 0.00581585 + 0.308194i
\(391\) 0.155588i 0.00786840i
\(392\) −6.64933 2.18778i −0.335842 0.110500i
\(393\) −12.1267 + 12.1267i −0.611713 + 0.611713i
\(394\) 21.8429 + 12.6110i 1.10043 + 0.635334i
\(395\) −3.46005 + 0.997455i −0.174094 + 0.0501874i
\(396\) −0.582897 1.00961i −0.0292917 0.0507347i
\(397\) 4.84423 + 18.0789i 0.243125 + 0.907354i 0.974317 + 0.225182i \(0.0722978\pi\)
−0.731192 + 0.682172i \(0.761036\pi\)
\(398\) −3.49450 3.49450i −0.175163 0.175163i
\(399\) −5.09283 + 1.21270i −0.254960 + 0.0607110i
\(400\) −4.42136 2.33485i −0.221068 0.116743i
\(401\) 9.36968 16.2288i 0.467900 0.810426i −0.531428 0.847104i \(-0.678344\pi\)
0.999327 + 0.0366779i \(0.0116776\pi\)
\(402\) −14.0621 3.76794i −0.701356 0.187928i
\(403\) −20.8557 5.58826i −1.03889 0.278371i
\(404\) 6.95796 12.0515i 0.346171 0.599587i
\(405\) 2.17041 + 0.537883i 0.107849 + 0.0267276i
\(406\) −14.2136 4.23892i −0.705408 0.210374i
\(407\) −8.75542 8.75542i −0.433990 0.433990i
\(408\) 0.00560858 + 0.0209315i 0.000277666 + 0.00103626i
\(409\) 11.6768 + 20.2248i 0.577381 + 1.00005i 0.995778 + 0.0917890i \(0.0292585\pi\)
−0.418398 + 0.908264i \(0.637408\pi\)
\(410\) −4.87308 2.69218i −0.240664 0.132957i
\(411\) −8.86443 5.11788i −0.437250 0.252446i
\(412\) −8.47403 + 8.47403i −0.417485 + 0.417485i
\(413\) −28.2785 0.792944i −1.39149 0.0390182i
\(414\) 7.17989i 0.352873i
\(415\) −30.8209 + 0.581613i −1.51294 + 0.0285502i
\(416\) −2.35765 + 1.36119i −0.115593 + 0.0667378i
\(417\) 1.46263 5.45863i 0.0716255 0.267310i
\(418\) −2.22819 + 0.597041i −0.108984 + 0.0292022i
\(419\) 8.27092 0.404061 0.202030 0.979379i \(-0.435246\pi\)
0.202030 + 0.979379i \(0.435246\pi\)
\(420\) 5.15037 2.91096i 0.251312 0.142040i
\(421\) −33.3728 −1.62649 −0.813246 0.581920i \(-0.802302\pi\)
−0.813246 + 0.581920i \(0.802302\pi\)
\(422\) −18.3966 + 4.92934i −0.895530 + 0.239957i
\(423\) −1.05773 + 3.94750i −0.0514285 + 0.191934i
\(424\) 2.53502 1.46360i 0.123112 0.0710785i
\(425\) −0.0240744 + 0.105641i −0.00116778 + 0.00512434i
\(426\) 7.51848i 0.364272i
\(427\) 8.48708 4.58776i 0.410719 0.222017i
\(428\) −4.88300 + 4.88300i −0.236029 + 0.236029i
\(429\) −2.74854 1.58687i −0.132701 0.0766147i
\(430\) 6.90029 + 23.9363i 0.332762 + 1.15431i
\(431\) 12.1733 + 21.0848i 0.586369 + 1.01562i 0.994703 + 0.102788i \(0.0327764\pi\)
−0.408334 + 0.912832i \(0.633890\pi\)
\(432\) 0.258819 + 0.965926i 0.0124524 + 0.0464731i
\(433\) −18.0803 18.0803i −0.868885 0.868885i 0.123464 0.992349i \(-0.460600\pi\)
−0.992349 + 0.123464i \(0.960600\pi\)
\(434\) 4.86071 + 20.4129i 0.233322 + 0.979850i
\(435\) 10.7359 6.47146i 0.514746 0.310283i
\(436\) −0.288657 + 0.499969i −0.0138242 + 0.0239442i
\(437\) −13.7230 3.67705i −0.656458 0.175897i
\(438\) −3.61776 0.969376i −0.172863 0.0463186i
\(439\) −8.11012 + 14.0471i −0.387075 + 0.670433i −0.992055 0.125808i \(-0.959848\pi\)
0.604980 + 0.796241i \(0.293181\pi\)
\(440\) 2.23256 1.34576i 0.106433 0.0641566i
\(441\) −0.392259 + 6.98900i −0.0186790 + 0.332810i
\(442\) 0.0417148 + 0.0417148i 0.00198417 + 0.00198417i
\(443\) 5.63860 + 21.0436i 0.267898 + 0.999810i 0.960452 + 0.278444i \(0.0898186\pi\)
−0.692554 + 0.721366i \(0.743515\pi\)
\(444\) 5.31055 + 9.19815i 0.252028 + 0.436525i
\(445\) −2.23294 7.74582i −0.105852 0.367187i
\(446\) 3.60676 + 2.08236i 0.170785 + 0.0986027i
\(447\) 0.156132 0.156132i 0.00738477 0.00738477i
\(448\) 2.25331 + 1.38658i 0.106459 + 0.0655097i
\(449\) 10.1648i 0.479708i 0.970809 + 0.239854i \(0.0770996\pi\)
−0.970809 + 0.239854i \(0.922900\pi\)
\(450\) −1.11096 + 4.87501i −0.0523712 + 0.229810i
\(451\) 2.51369 1.45128i 0.118365 0.0683381i
\(452\) 4.85674 18.1256i 0.228442 0.852556i
\(453\) 6.15184 1.64838i 0.289038 0.0774476i
\(454\) −18.4389 −0.865381
\(455\) 8.18040 13.8737i 0.383503 0.650407i
\(456\) 1.97873 0.0926624
\(457\) 27.5526 7.38270i 1.28886 0.345348i 0.451631 0.892205i \(-0.350842\pi\)
0.837226 + 0.546856i \(0.184176\pi\)
\(458\) −1.52965 + 5.70873i −0.0714758 + 0.266751i
\(459\) 0.0187667 0.0108349i 0.000875953 0.000505732i
\(460\) 16.0519 0.302911i 0.748423 0.0141233i
\(461\) 20.0972i 0.936022i 0.883723 + 0.468011i \(0.155029\pi\)
−0.883723 + 0.468011i \(0.844971\pi\)
\(462\) −0.0864543 + 3.08319i −0.00402222 + 0.143443i
\(463\) −7.34462 + 7.34462i −0.341334 + 0.341334i −0.856869 0.515535i \(-0.827593\pi\)
0.515535 + 0.856869i \(0.327593\pi\)
\(464\) 4.85498 + 2.80302i 0.225387 + 0.130127i
\(465\) −15.5230 8.57585i −0.719862 0.397695i
\(466\) 3.61767 + 6.26598i 0.167585 + 0.290266i
\(467\) −6.10926 22.8001i −0.282703 1.05506i −0.950502 0.310720i \(-0.899430\pi\)
0.667799 0.744342i \(-0.267237\pi\)
\(468\) 1.92501 + 1.92501i 0.0889838 + 0.0889838i
\(469\) 26.4618 + 27.9886i 1.22189 + 1.29239i
\(470\) −8.86993 2.19819i −0.409139 0.101395i
\(471\) −7.23813 + 12.5368i −0.333515 + 0.577666i
\(472\) 10.3281 + 2.76741i 0.475391 + 0.127381i
\(473\) −12.5451 3.36144i −0.576822 0.154559i
\(474\) −0.805197 + 1.39464i −0.0369839 + 0.0640581i
\(475\) 8.74867 + 4.62004i 0.401417 + 0.211982i
\(476\) 0.0163853 0.0549419i 0.000751021 0.00251826i
\(477\) −2.06984 2.06984i −0.0947714 0.0947714i
\(478\) −1.08748 4.05855i −0.0497404 0.185634i
\(479\) −12.3892 21.4588i −0.566079 0.980478i −0.996948 0.0780633i \(-0.975126\pi\)
0.430869 0.902414i \(-0.358207\pi\)
\(480\) −2.14857 + 0.619385i −0.0980685 + 0.0282709i
\(481\) 25.0409 + 14.4573i 1.14176 + 0.659198i
\(482\) −15.5110 + 15.5110i −0.706507 + 0.706507i
\(483\) −9.95550 + 16.1785i −0.452991 + 0.736148i
\(484\) 9.64092i 0.438224i
\(485\) 0.0158408 + 0.839438i 0.000719294 + 0.0381169i
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) 6.15129 22.9569i 0.278741 1.04028i −0.674551 0.738228i \(-0.735663\pi\)
0.953292 0.302049i \(-0.0976706\pi\)
\(488\) −3.52224 + 0.943781i −0.159444 + 0.0427229i
\(489\) 21.9057 0.990608
\(490\) −15.6416 0.582104i −0.706618 0.0262968i
\(491\) −0.386093 −0.0174242 −0.00871208 0.999962i \(-0.502773\pi\)
−0.00871208 + 0.999962i \(0.502773\pi\)
\(492\) −2.40493 + 0.644400i −0.108423 + 0.0290518i
\(493\) 0.0314419 0.117343i 0.00141607 0.00528486i
\(494\) 4.66514 2.69342i 0.209895 0.121183i
\(495\) −1.87773 1.80818i −0.0843978 0.0812715i
\(496\) 7.93107i 0.356115i
\(497\) −10.4250 + 16.9415i −0.467624 + 0.759928i
\(498\) −9.74815 + 9.74815i −0.436825 + 0.436825i
\(499\) −6.94992 4.01254i −0.311121 0.179626i 0.336307 0.941752i \(-0.390822\pi\)
−0.647428 + 0.762127i \(0.724155\pi\)
\(500\) −10.9458 2.27807i −0.489511 0.101878i
\(501\) 8.05513 + 13.9519i 0.359877 + 0.623325i
\(502\) −3.91575 14.6138i −0.174768 0.652244i
\(503\) 11.5901 + 11.5901i 0.516775 + 0.516775i 0.916594 0.399819i \(-0.130927\pi\)
−0.399819 + 0.916594i \(0.630927\pi\)
\(504\) 0.756134 2.53540i 0.0336809 0.112936i
\(505\) 7.48513 30.2033i 0.333084 1.34403i
\(506\) −4.18514 + 7.24888i −0.186052 + 0.322252i
\(507\) −5.39822 1.44645i −0.239743 0.0642390i
\(508\) 1.85929 + 0.498197i 0.0824929 + 0.0221039i
\(509\) 7.77422 13.4654i 0.344586 0.596841i −0.640692 0.767798i \(-0.721352\pi\)
0.985279 + 0.170957i \(0.0546858\pi\)
\(510\) 0.0250151 + 0.0414990i 0.00110769 + 0.00183761i
\(511\) 6.80781 + 7.20062i 0.301160 + 0.318536i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −0.512132 1.91130i −0.0226112 0.0843861i
\(514\) 11.5071 + 19.9309i 0.507558 + 0.879116i
\(515\) −12.9584 + 23.4557i −0.571014 + 1.03358i
\(516\) 9.64800 + 5.57028i 0.424730 + 0.245218i
\(517\) 3.36888 3.36888i 0.148163 0.148163i
\(518\) 0.787652 28.0898i 0.0346074 1.23419i
\(519\) 10.4433i 0.458408i
\(520\) −4.22248 + 4.38491i −0.185168 + 0.192291i
\(521\) 22.8573 13.1967i 1.00140 0.578156i 0.0927347 0.995691i \(-0.470439\pi\)
0.908661 + 0.417535i \(0.137106\pi\)
\(522\) 1.45095 5.41502i 0.0635064 0.237009i
\(523\) −38.1134 + 10.2125i −1.66658 + 0.446559i −0.964186 0.265227i \(-0.914553\pi\)
−0.702396 + 0.711786i \(0.747886\pi\)
\(524\) −17.1498 −0.749192
\(525\) 9.26293 9.44447i 0.404268 0.412191i
\(526\) 20.1205 0.877294
\(527\) −0.166009 + 0.0444820i −0.00723147 + 0.00193767i
\(528\) 0.301730 1.12607i 0.0131311 0.0490060i
\(529\) −24.7258 + 14.2754i −1.07503 + 0.620671i
\(530\) 4.54015 4.71480i 0.197212 0.204798i
\(531\) 10.6925i 0.464014i
\(532\) −4.45868 2.74366i −0.193308 0.118953i
\(533\) −4.79284 + 4.79284i −0.207601 + 0.207601i
\(534\) −3.12211 1.80255i −0.135107 0.0780040i
\(535\) −7.46703 + 13.5159i −0.322828 + 0.584345i
\(536\) −7.27910 12.6078i −0.314409 0.544573i
\(537\) −0.390048 1.45568i −0.0168318 0.0628172i
\(538\) 6.55459 + 6.55459i 0.282588 + 0.282588i
\(539\) 4.46990 6.82750i 0.192532 0.294081i
\(540\) 1.15437 + 1.91505i 0.0496762 + 0.0824107i
\(541\) −4.06849 + 7.04683i −0.174918 + 0.302967i −0.940133 0.340808i \(-0.889299\pi\)
0.765215 + 0.643775i \(0.222633\pi\)
\(542\) 25.3360 + 6.78877i 1.08828 + 0.291603i
\(543\) 20.6184 + 5.52468i 0.884820 + 0.237087i
\(544\) −0.0108349 + 0.0187667i −0.000464544 + 0.000804615i
\(545\) −0.310527 + 1.25301i −0.0133015 + 0.0536730i
\(546\) −1.66846 7.00683i −0.0714037 0.299865i
\(547\) 12.5204 + 12.5204i 0.535335 + 0.535335i 0.922155 0.386820i \(-0.126427\pi\)
−0.386820 + 0.922155i \(0.626427\pi\)
\(548\) −2.64921 9.88699i −0.113169 0.422351i
\(549\) 1.82324 + 3.15795i 0.0778142 + 0.134778i
\(550\) 3.96327 4.27428i 0.168994 0.182256i
\(551\) −9.60667 5.54641i −0.409258 0.236285i
\(552\) 5.07695 5.07695i 0.216089 0.216089i
\(553\) 3.74814 2.02609i 0.159387 0.0861581i
\(554\) 13.2995i 0.565040i
\(555\) 17.1073 + 16.4736i 0.726165 + 0.699266i
\(556\) 4.89407 2.82559i 0.207555 0.119832i
\(557\) −4.19123 + 15.6419i −0.177588 + 0.662768i 0.818508 + 0.574495i \(0.194802\pi\)
−0.996096 + 0.0882732i \(0.971865\pi\)
\(558\) −7.66082 + 2.05271i −0.324308 + 0.0868982i
\(559\) 30.3288 1.28277
\(560\) 5.70022 + 1.58350i 0.240878 + 0.0669151i
\(561\) −0.0252626 −0.00106659
\(562\) −13.0497 + 3.49667i −0.550470 + 0.147498i
\(563\) 2.26573 8.45582i 0.0954892 0.356370i −0.901604 0.432562i \(-0.857610\pi\)
0.997093 + 0.0761920i \(0.0242762\pi\)
\(564\) −3.53923 + 2.04338i −0.149028 + 0.0860416i
\(565\) −0.791671 41.9523i −0.0333059 1.76495i
\(566\) 19.8911i 0.836085i
\(567\) −2.64471 0.0741591i −0.111067 0.00311439i
\(568\) 5.31637 5.31637i 0.223070 0.223070i
\(569\) −35.9794 20.7727i −1.50833 0.870838i −0.999953 0.00970591i \(-0.996910\pi\)
−0.508382 0.861132i \(-0.669756\pi\)
\(570\) 4.25144 1.22559i 0.178073 0.0513345i
\(571\) −6.59259 11.4187i −0.275891 0.477858i 0.694468 0.719523i \(-0.255640\pi\)
−0.970360 + 0.241666i \(0.922306\pi\)
\(572\) −0.821423 3.06559i −0.0343454 0.128179i
\(573\) 4.56144 + 4.56144i 0.190557 + 0.190557i
\(574\) 6.31256 + 1.88260i 0.263481 + 0.0785782i
\(575\) 34.3010 10.5931i 1.43045 0.441764i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 17.3319 + 4.64406i 0.721535 + 0.193335i 0.600857 0.799357i \(-0.294826\pi\)
0.120679 + 0.992692i \(0.461493\pi\)
\(578\) −16.4203 4.39980i −0.682994 0.183008i
\(579\) 2.56929 4.45014i 0.106776 0.184942i
\(580\) 12.1674 + 3.01539i 0.505225 + 0.125207i
\(581\) 35.4822 8.44900i 1.47205 0.350524i
\(582\) 0.265501 + 0.265501i 0.0110054 + 0.0110054i
\(583\) 0.883222 + 3.29623i 0.0365793 + 0.136516i
\(584\) −1.87269 3.24360i −0.0774925 0.134221i
\(585\) 5.32835 + 2.94371i 0.220300 + 0.121707i
\(586\) 21.3159 + 12.3068i 0.880553 + 0.508387i
\(587\) 7.68342 7.68342i 0.317129 0.317129i −0.530535 0.847663i \(-0.678009\pi\)
0.847663 + 0.530535i \(0.178009\pi\)
\(588\) −5.21934 + 4.66460i −0.215242 + 0.192365i
\(589\) 15.6934i 0.646636i
\(590\) 23.9048 0.451102i 0.984146 0.0185716i
\(591\) 21.8429 12.6110i 0.898499 0.518748i
\(592\) −2.74894 + 10.2592i −0.112981 + 0.421651i
\(593\) −7.58832 + 2.03328i −0.311615 + 0.0834970i −0.411237 0.911528i \(-0.634903\pi\)
0.0996223 + 0.995025i \(0.468237\pi\)
\(594\) −1.16579 −0.0478331
\(595\) 0.00117490 0.128195i 4.81663e−5 0.00525550i
\(596\) 0.220803 0.00904446
\(597\) −4.77357 + 1.27908i −0.195369 + 0.0523491i
\(598\) 5.05898 18.8804i 0.206877 0.772076i
\(599\) −20.5520 + 11.8657i −0.839731 + 0.484819i −0.857173 0.515029i \(-0.827781\pi\)
0.0174418 + 0.999848i \(0.494448\pi\)
\(600\) −4.23272 + 2.66159i −0.172800 + 0.108659i
\(601\) 14.4348i 0.588806i 0.955681 + 0.294403i \(0.0951208\pi\)
−0.955681 + 0.294403i \(0.904879\pi\)
\(602\) −14.0163 25.9293i −0.571261 1.05680i
\(603\) −10.2942 + 10.2942i −0.419213 + 0.419213i
\(604\) 5.51559 + 3.18442i 0.224426 + 0.129572i
\(605\) −5.97144 20.7142i −0.242774 0.842153i
\(606\) −6.95796 12.0515i −0.282648 0.489560i
\(607\) 0.172772 + 0.644795i 0.00701261 + 0.0261714i 0.969343 0.245710i \(-0.0790210\pi\)
−0.962331 + 0.271881i \(0.912354\pi\)
\(608\) 1.39917 + 1.39917i 0.0567439 + 0.0567439i
\(609\) −10.7778 + 10.1899i −0.436738 + 0.412914i
\(610\) −6.98322 + 4.20940i −0.282742 + 0.170434i
\(611\) −5.56284 + 9.63513i −0.225049 + 0.389796i
\(612\) 0.0209315 + 0.00560858i 0.000846106 + 0.000226713i
\(613\) 14.2571 + 3.82018i 0.575839 + 0.154296i 0.534973 0.844869i \(-0.320322\pi\)
0.0408659 + 0.999165i \(0.486988\pi\)
\(614\) −0.400469 + 0.693633i −0.0161616 + 0.0279927i
\(615\) −4.76804 + 2.87412i −0.192266 + 0.115896i
\(616\) −2.24128 + 2.11901i −0.0903037 + 0.0853775i
\(617\) −4.88322 4.88322i −0.196591 0.196591i 0.601946 0.798537i \(-0.294392\pi\)
−0.798537 + 0.601946i \(0.794392\pi\)
\(618\) 3.10171 + 11.5757i 0.124769 + 0.465644i
\(619\) −13.8975 24.0712i −0.558589 0.967504i −0.997615 0.0690295i \(-0.978010\pi\)
0.439026 0.898474i \(-0.355324\pi\)
\(620\) −4.91238 17.0405i −0.197286 0.684362i
\(621\) −6.21797 3.58995i −0.249519 0.144060i
\(622\) 9.47327 9.47327i 0.379844 0.379844i
\(623\) 4.53569 + 8.39075i 0.181719 + 0.336168i
\(624\) 2.72238i 0.108982i
\(625\) −24.9288 + 1.88506i −0.997153 + 0.0754023i
\(626\) 24.9051 14.3790i 0.995410 0.574700i
\(627\) −0.597041 + 2.22819i −0.0238435 + 0.0889852i
\(628\) −13.9830 + 3.74673i −0.557982 + 0.149511i
\(629\) 0.230158 0.00917701
\(630\) 0.0542182 5.91583i 0.00216011 0.235692i
\(631\) 6.30112 0.250844 0.125422 0.992104i \(-0.459972\pi\)
0.125422 + 0.992104i \(0.459972\pi\)
\(632\) −1.55552 + 0.416801i −0.0618753 + 0.0165794i
\(633\) −4.92934 + 18.3966i −0.195924 + 0.731197i
\(634\) 29.2153 16.8675i 1.16029 0.669893i
\(635\) 4.30340 0.0812084i 0.170775 0.00322266i
\(636\) 2.92719i 0.116071i
\(637\) −5.95597 + 18.1020i −0.235984 + 0.717228i
\(638\) −4.62129 + 4.62129i −0.182959 + 0.182959i
\(639\) −6.51120 3.75924i −0.257579 0.148713i
\(640\) −1.95724 1.08130i −0.0773668 0.0427421i
\(641\) −2.63684 4.56715i −0.104149 0.180391i 0.809241 0.587477i \(-0.199879\pi\)
−0.913390 + 0.407085i \(0.866545\pi\)
\(642\) 1.78730 + 6.67031i 0.0705393 + 0.263256i
\(643\) −5.34948 5.34948i −0.210963 0.210963i 0.593714 0.804677i \(-0.297661\pi\)
−0.804677 + 0.593714i \(0.797661\pi\)
\(644\) −18.4795 + 4.40034i −0.728196 + 0.173398i
\(645\) 24.1796 + 5.99231i 0.952070 + 0.235947i
\(646\) 0.0214394 0.0371341i 0.000843522 0.00146102i
\(647\) −21.4035 5.73506i −0.841460 0.225469i −0.187753 0.982216i \(-0.560120\pi\)
−0.653707 + 0.756748i \(0.726787\pi\)
\(648\) 0.965926 + 0.258819i 0.0379452 + 0.0101674i
\(649\) −6.23261 + 10.7952i −0.244651 + 0.423749i
\(650\) −6.35636 + 12.0366i −0.249317 + 0.472116i
\(651\) 20.1084 + 5.99695i 0.788112 + 0.235039i
\(652\) 15.4896 + 15.4896i 0.606621 + 0.606621i
\(653\) −11.4754 42.8267i −0.449066 1.67594i −0.704972 0.709235i \(-0.749041\pi\)
0.255907 0.966702i \(-0.417626\pi\)
\(654\) 0.288657 + 0.499969i 0.0112874 + 0.0195503i
\(655\) −36.8476 + 10.6223i −1.43975 + 0.415049i
\(656\) −2.15620 1.24488i −0.0841856 0.0486046i
\(657\) −2.64838 + 2.64838i −0.103323 + 0.103323i
\(658\) 10.8083 + 0.303070i 0.421351 + 0.0118149i
\(659\) 38.6387i 1.50515i 0.658507 + 0.752575i \(0.271188\pi\)
−0.658507 + 0.752575i \(0.728812\pi\)
\(660\) −0.0491834 2.60633i −0.00191446 0.101451i
\(661\) −24.7737 + 14.3031i −0.963587 + 0.556327i −0.897275 0.441472i \(-0.854457\pi\)
−0.0663118 + 0.997799i \(0.521123\pi\)
\(662\) 2.83035 10.5630i 0.110005 0.410543i
\(663\) 0.0569835 0.0152687i 0.00221306 0.000592987i
\(664\) −13.7860 −0.534999
\(665\) −11.2792 3.13331i −0.437388 0.121505i
\(666\) 10.6211 0.411560
\(667\) −38.8793 + 10.4177i −1.50541 + 0.403374i
\(668\) −4.16964 + 15.5613i −0.161328 + 0.602086i
\(669\) 3.60676 2.08236i 0.139445 0.0805088i
\(670\) −23.4487 22.5801i −0.905904 0.872347i
\(671\) 4.25106i 0.164110i
\(672\) 2.32747 1.25813i 0.0897840 0.0485335i
\(673\) 36.6126 36.6126i 1.41131 1.41131i 0.660379 0.750932i \(-0.270396\pi\)
0.750932 0.660379i \(-0.229604\pi\)
\(674\) −12.6045 7.27723i −0.485509 0.280309i
\(675\) 3.66641 + 3.39963i 0.141120 + 0.130852i
\(676\) −2.79432 4.83991i −0.107474 0.186150i
\(677\) −6.94951 25.9359i −0.267091 0.996798i −0.960958 0.276695i \(-0.910761\pi\)
0.693867 0.720104i \(-0.255906\pi\)
\(678\) −13.2689 13.2689i −0.509587 0.509587i
\(679\) −0.230117 0.966393i −0.00883108 0.0370868i
\(680\) −0.0116559 + 0.0470326i −0.000446982 + 0.00180362i
\(681\) −9.21945 + 15.9686i −0.353290 + 0.611917i
\(682\) 8.93095 + 2.39304i 0.341984 + 0.0916342i
\(683\) 1.91999 + 0.514460i 0.0734664 + 0.0196853i 0.295365 0.955384i \(-0.404559\pi\)
−0.221899 + 0.975070i \(0.571225\pi\)
\(684\) 0.989363 1.71363i 0.0378293 0.0655222i
\(685\) −11.8159 19.6020i −0.451461 0.748955i
\(686\) 18.2286 3.27375i 0.695972 0.124993i
\(687\) 4.17908 + 4.17908i 0.159442 + 0.159442i
\(688\) 2.88339 + 10.7609i 0.109928 + 0.410257i
\(689\) −3.98446 6.90130i −0.151796 0.262918i
\(690\) 7.76361 14.0528i 0.295556 0.534980i
\(691\) −8.33571 4.81262i −0.317105 0.183081i 0.332996 0.942928i \(-0.391940\pi\)
−0.650102 + 0.759847i \(0.725274\pi\)
\(692\) 7.38450 7.38450i 0.280717 0.280717i
\(693\) 2.62690 + 1.61647i 0.0997875 + 0.0614045i
\(694\) 2.55458i 0.0969703i
\(695\) 8.76513 9.10231i 0.332480 0.345270i
\(696\) 4.85498 2.80302i 0.184027 0.106248i
\(697\) −0.0139641 + 0.0521146i −0.000528927 + 0.00197398i
\(698\) −17.9739 + 4.81608i −0.680320 + 0.182291i
\(699\) 7.23533 0.273665
\(700\) 13.2281 0.128367i 0.499976 0.00485183i
\(701\) −12.4958 −0.471959 −0.235980 0.971758i \(-0.575830\pi\)
−0.235980 + 0.971758i \(0.575830\pi\)
\(702\) 2.62962 0.704604i 0.0992485 0.0265936i
\(703\) 5.43941 20.3002i 0.205151 0.765635i
\(704\) 1.00961 0.582897i 0.0380510 0.0219688i
\(705\) −6.33865 + 6.58249i −0.238728 + 0.247911i
\(706\) 15.8312i 0.595816i
\(707\) −1.03199 + 36.8036i −0.0388121 + 1.38414i
\(708\) 7.56072 7.56072i 0.284149 0.284149i
\(709\) 39.6174 + 22.8731i 1.48786 + 0.859018i 0.999904 0.0138494i \(-0.00440856\pi\)
0.487958 + 0.872867i \(0.337742\pi\)
\(710\) 8.12973 14.7155i 0.305103 0.552262i
\(711\) 0.805197 + 1.39464i 0.0301973 + 0.0523032i
\(712\) −0.933068 3.48226i −0.0349682 0.130503i
\(713\) 40.2656 + 40.2656i 1.50796 + 1.50796i
\(714\) −0.0393884 0.0416611i −0.00147407 0.00155913i
\(715\) −3.66367 6.07787i −0.137014 0.227300i
\(716\) 0.753516 1.30513i 0.0281602 0.0487749i
\(717\) −4.05855 1.08748i −0.151569 0.0406129i
\(718\) 7.25042 + 1.94274i 0.270583 + 0.0725025i
\(719\) −8.05439 + 13.9506i −0.300378 + 0.520270i −0.976222 0.216775i \(-0.930446\pi\)
0.675844 + 0.737045i \(0.263779\pi\)
\(720\) −0.537883 + 2.17041i −0.0200457 + 0.0808864i
\(721\) 9.06157 30.3845i 0.337471 1.13158i
\(722\) 10.6665 + 10.6665i 0.396964 + 0.396964i
\(723\) 5.67742 + 21.1884i 0.211146 + 0.788006i
\(724\) 10.6729 + 18.4859i 0.396654 + 0.687025i
\(725\) 28.0103 1.05753i 1.04028 0.0392755i
\(726\) −8.34928 4.82046i −0.309871 0.178904i
\(727\) 26.7345 26.7345i 0.991528 0.991528i −0.00843633 0.999964i \(-0.502685\pi\)
0.999964 + 0.00843633i \(0.00268540\pi\)
\(728\) 3.77480 6.13436i 0.139903 0.227355i
\(729\) 1.00000i 0.0370370i
\(730\) −6.03265 5.80918i −0.223278 0.215007i
\(731\) 0.209071 0.120707i 0.00773278 0.00446452i
\(732\) −0.943781 + 3.52224i −0.0348831 + 0.130186i
\(733\) −9.81640 + 2.63030i −0.362577 + 0.0971523i −0.435508 0.900185i \(-0.643431\pi\)
0.0729311 + 0.997337i \(0.476765\pi\)
\(734\) 3.94796 0.145722
\(735\) −8.32494 + 13.2550i −0.307070 + 0.488918i
\(736\) 7.17989 0.264654
\(737\) 16.3936 4.39265i 0.603865 0.161805i
\(738\) −0.644400 + 2.40493i −0.0237207 + 0.0885268i
\(739\) 1.51357 0.873858i 0.0556775 0.0321454i −0.471903 0.881651i \(-0.656433\pi\)
0.527580 + 0.849505i \(0.323099\pi\)
\(740\) 0.448091 + 23.7453i 0.0164722 + 0.872894i
\(741\) 5.38685i 0.197891i
\(742\) −4.05879 + 6.59587i −0.149003 + 0.242142i
\(743\) 4.26452 4.26452i 0.156450 0.156450i −0.624542 0.780992i \(-0.714714\pi\)
0.780992 + 0.624542i \(0.214714\pi\)
\(744\) −6.86850 3.96553i −0.251812 0.145383i
\(745\) 0.474412 0.136762i 0.0173811 0.00501059i
\(746\) 2.69706 + 4.67144i 0.0987462 + 0.171033i
\(747\) 3.56807 + 13.3162i 0.130549 + 0.487215i
\(748\) −0.0178634 0.0178634i −0.000653150 0.000653150i
\(749\) 5.22157 17.5085i 0.190792 0.639747i
\(750\) −7.44577 + 8.34030i −0.271881 + 0.304545i
\(751\) −7.54354 + 13.0658i −0.275268 + 0.476778i −0.970203 0.242295i \(-0.922100\pi\)
0.694935 + 0.719073i \(0.255433\pi\)
\(752\) −3.94750 1.05773i −0.143950 0.0385714i
\(753\) −14.6138 3.91575i −0.532555 0.142698i
\(754\) 7.63089 13.2171i 0.277901 0.481338i
\(755\) 13.8230 + 3.42569i 0.503071 + 0.124674i
\(756\) −1.81766 1.92253i −0.0661075 0.0699218i
\(757\) −7.26095 7.26095i −0.263904 0.263904i 0.562734 0.826638i \(-0.309749\pi\)
−0.826638 + 0.562734i \(0.809749\pi\)
\(758\) −0.640325 2.38973i −0.0232576 0.0867987i
\(759\) 4.18514 + 7.24888i 0.151911 + 0.263118i
\(760\) 3.87285 + 2.13959i 0.140483 + 0.0776112i
\(761\) −10.7048 6.18041i −0.388048 0.224040i 0.293266 0.956031i \(-0.405258\pi\)
−0.681314 + 0.731991i \(0.738591\pi\)
\(762\) 1.36110 1.36110i 0.0493074 0.0493074i
\(763\) 0.0428131 1.52683i 0.00154994 0.0552750i
\(764\) 6.45086i 0.233384i
\(765\) 0.0484467 0.000914225i 0.00175159 3.30539e-5i
\(766\) −20.8788 + 12.0544i −0.754380 + 0.435542i
\(767\) 7.53395 28.1171i 0.272035 1.01525i
\(768\) −0.965926 + 0.258819i −0.0348548 + 0.00933933i
\(769\) 17.1708 0.619196 0.309598 0.950867i \(-0.399805\pi\)
0.309598 + 0.950867i \(0.399805\pi\)
\(770\) −3.50306 + 5.94107i −0.126242 + 0.214101i
\(771\) 23.0143 0.828839
\(772\) 4.96349 1.32996i 0.178640 0.0478664i
\(773\) −0.327680 + 1.22292i −0.0117858 + 0.0439853i −0.971568 0.236759i \(-0.923915\pi\)
0.959783 + 0.280745i \(0.0905814\pi\)
\(774\) 9.64800 5.57028i 0.346790 0.200219i
\(775\) −21.1092 33.5700i −0.758266 1.20587i
\(776\) 0.375475i 0.0134788i
\(777\) −23.9326 14.7270i −0.858578 0.528329i
\(778\) 4.56126 4.56126i 0.163529 0.163529i
\(779\) 4.26654 + 2.46329i 0.152865 + 0.0882564i
\(780\) 1.68620 + 5.84923i 0.0603757 + 0.209436i
\(781\) 4.38251 + 7.59072i 0.156818 + 0.271617i
\(782\) −0.0402690 0.150286i −0.00144002 0.00537422i
\(783\) −3.96407 3.96407i −0.141664 0.141664i
\(784\) −6.98900 0.392259i −0.249607 0.0140092i
\(785\) −27.7228 + 16.7110i −0.989469 + 0.596441i
\(786\) −8.57489 + 14.8522i −0.305856 + 0.529759i
\(787\) 14.8015 + 3.96605i 0.527617 + 0.141375i 0.512788 0.858515i \(-0.328613\pi\)
0.0148294 + 0.999890i \(0.495279\pi\)
\(788\) 24.3626 + 6.52795i 0.867883 + 0.232549i
\(789\) 10.0602 17.4248i 0.358154 0.620341i
\(790\) −3.08399 + 1.85899i −0.109723 + 0.0661400i
\(791\) 11.5005 + 48.2971i 0.408911 + 1.71725i
\(792\) −0.824341 0.824341i −0.0292917 0.0292917i
\(793\) 2.56933 + 9.58887i 0.0912396 + 0.340511i
\(794\) 9.35833 + 16.2091i 0.332115 + 0.575240i
\(795\) −1.81306 6.28928i −0.0643026 0.223058i
\(796\) −4.27987 2.47098i −0.151696 0.0875817i
\(797\) −36.4737 + 36.4737i −1.29197 + 1.29197i −0.358396 + 0.933570i \(0.616676\pi\)
−0.933570 + 0.358396i \(0.883324\pi\)
\(798\) −4.60542 + 2.48950i −0.163030 + 0.0881273i
\(799\) 0.0885594i 0.00313301i
\(800\) −4.87501 1.11096i −0.172358 0.0392784i
\(801\) −3.12211 + 1.80255i −0.110314 + 0.0636900i
\(802\) 4.85010 18.1008i 0.171263 0.639163i
\(803\) 4.21757 1.13009i 0.148835 0.0398801i
\(804\) −14.5582 −0.513428
\(805\) −36.9791 + 20.9004i −1.30334 + 0.736642i
\(806\) −21.5914 −0.760524
\(807\) 8.95373 2.39915i 0.315186 0.0844539i
\(808\) 3.60170 13.4417i 0.126708 0.472879i
\(809\) −12.0158 + 6.93731i −0.422452 + 0.243903i −0.696126 0.717920i \(-0.745094\pi\)
0.273674 + 0.961823i \(0.411761\pi\)
\(810\) 2.23567 0.0421887i 0.0785534 0.00148236i
\(811\) 18.4047i 0.646275i −0.946352 0.323137i \(-0.895262\pi\)
0.946352 0.323137i \(-0.104738\pi\)
\(812\) −14.8264 0.415739i −0.520304 0.0145896i
\(813\) 18.5473 18.5473i 0.650481 0.650481i
\(814\) −10.7232 6.19102i −0.375846 0.216995i
\(815\) 42.8747 + 23.6866i 1.50183 + 0.829704i
\(816\) 0.0108349 + 0.0187667i 0.000379299 + 0.000656965i
\(817\) −5.70544 21.2930i −0.199608 0.744947i
\(818\) 16.5135 + 16.5135i 0.577381 + 0.577381i
\(819\) −6.90233 2.05848i −0.241187 0.0719292i
\(820\) −5.40382 1.33920i −0.188710 0.0467670i
\(821\) −16.4402 + 28.4753i −0.573768 + 0.993796i 0.422406 + 0.906407i \(0.361186\pi\)
−0.996174 + 0.0873891i \(0.972148\pi\)
\(822\) −9.88699 2.64921i −0.344848 0.0924018i
\(823\) 23.5835 + 6.31918i 0.822069 + 0.220273i 0.645251 0.763971i \(-0.276753\pi\)
0.176818 + 0.984244i \(0.443420\pi\)
\(824\) −5.99204 + 10.3785i −0.208743 + 0.361553i
\(825\) −1.72000 5.56943i −0.0598826 0.193903i
\(826\) −27.5202 + 6.55309i −0.957549 + 0.228011i
\(827\) 1.94367 + 1.94367i 0.0675881 + 0.0675881i 0.740093 0.672505i \(-0.234782\pi\)
−0.672505 + 0.740093i \(0.734782\pi\)
\(828\) −1.85829 6.93525i −0.0645802 0.241016i
\(829\) −8.99161 15.5739i −0.312291 0.540905i 0.666567 0.745446i \(-0.267763\pi\)
−0.978858 + 0.204541i \(0.934430\pi\)
\(830\) −29.6201 + 8.53882i −1.02813 + 0.296387i
\(831\) −11.5177 6.64974i −0.399544 0.230677i
\(832\) −1.92501 + 1.92501i −0.0667378 + 0.0667378i
\(833\) 0.0309878 + 0.148490i 0.00107366 + 0.00514489i
\(834\) 5.65119i 0.195685i
\(835\) 0.679672 + 36.0172i 0.0235210 + 1.24643i
\(836\) −1.99774 + 1.15339i −0.0690932 + 0.0398910i
\(837\) −2.05271 + 7.66082i −0.0709521 + 0.264797i
\(838\) 7.98909 2.14067i 0.275979 0.0739483i
\(839\) −4.25819 −0.147009 −0.0735045 0.997295i \(-0.523418\pi\)
−0.0735045 + 0.997295i \(0.523418\pi\)
\(840\) 4.22146 4.14479i 0.145654 0.143009i
\(841\) −2.42773 −0.0837148
\(842\) −32.2357 + 8.63752i −1.11091 + 0.297669i
\(843\) −3.49667 + 13.0497i −0.120432 + 0.449457i
\(844\) −16.4939 + 9.52276i −0.567743 + 0.327787i
\(845\) −9.00158 8.66814i −0.309664 0.298193i
\(846\) 4.08675i 0.140505i
\(847\) 12.1296 + 22.4389i 0.416776 + 0.771011i
\(848\) 2.06984 2.06984i 0.0710785 0.0710785i
\(849\) −17.2262 9.94554i −0.591201 0.341330i
\(850\) 0.00408781 + 0.108272i 0.000140211 + 0.00371371i
\(851\) −38.1292 66.0417i −1.30705 2.26388i
\(852\) −1.94593 7.26230i −0.0666664 0.248802i
\(853\) −36.5310 36.5310i −1.25080 1.25080i −0.955362 0.295436i \(-0.904535\pi\)
−0.295436 0.955362i \(-0.595465\pi\)
\(854\) 7.01049 6.62806i 0.239894 0.226807i
\(855\) 1.06432 4.29465i 0.0363991 0.146874i
\(856\) −3.45281 + 5.98043i −0.118014 + 0.204407i
\(857\) −3.06389 0.820966i −0.104660 0.0280437i 0.206109 0.978529i \(-0.433920\pi\)
−0.310769 + 0.950485i \(0.600587\pi\)
\(858\) −3.06559 0.821423i −0.104658 0.0280429i
\(859\) −14.9376 + 25.8726i −0.509663 + 0.882763i 0.490274 + 0.871568i \(0.336897\pi\)
−0.999937 + 0.0111943i \(0.996437\pi\)
\(860\) 12.8603 + 21.3347i 0.438534 + 0.727509i
\(861\) 4.78666 4.52554i 0.163129 0.154230i
\(862\) 17.2157 + 17.2157i 0.586369 + 0.586369i
\(863\) 8.36277 + 31.2103i 0.284672 + 1.06241i 0.949079 + 0.315039i \(0.102018\pi\)
−0.664407 + 0.747371i \(0.731316\pi\)
\(864\) 0.500000 + 0.866025i 0.0170103 + 0.0294628i
\(865\) 11.2923 20.4400i 0.383949 0.694980i
\(866\) −22.1438 12.7847i −0.752477 0.434443i
\(867\) −12.0205 + 12.0205i −0.408237 + 0.408237i
\(868\) 9.97833 + 18.4593i 0.338687 + 0.626549i
\(869\) 1.87739i 0.0636861i
\(870\) 8.69512 9.02960i 0.294792 0.306132i
\(871\) −34.3232 + 19.8165i −1.16300 + 0.671456i
\(872\) −0.149420 + 0.557643i −0.00506000 + 0.0188842i
\(873\) 0.362681 0.0971800i 0.0122749 0.00328905i
\(874\) −14.2070 −0.480561
\(875\) 28.3421 8.46912i 0.958138 0.286308i
\(876\) −3.74538 −0.126545
\(877\) −3.93603 + 1.05466i −0.132910 + 0.0356132i −0.324661 0.945830i \(-0.605250\pi\)
0.191751 + 0.981444i \(0.438584\pi\)
\(878\) −4.19811 + 15.6675i −0.141679 + 0.528754i
\(879\) 21.3159 12.3068i 0.718968 0.415096i
\(880\) 1.80818 1.87773i 0.0609537 0.0632984i
\(881\) 19.0783i 0.642764i −0.946950 0.321382i \(-0.895853\pi\)
0.946950 0.321382i \(-0.104147\pi\)
\(882\) 1.42999 + 6.85238i 0.0481504 + 0.230732i
\(883\) 6.02976 6.02976i 0.202918 0.202918i −0.598331 0.801249i \(-0.704169\pi\)
0.801249 + 0.598331i \(0.204169\pi\)
\(884\) 0.0510900 + 0.0294968i 0.00171834 + 0.000992086i
\(885\) 11.5618 20.9277i 0.388644 0.703478i
\(886\) 10.8929 + 18.8671i 0.365956 + 0.633854i
\(887\) −11.2725 42.0695i −0.378494 1.41256i −0.848173 0.529720i \(-0.822297\pi\)
0.469679 0.882837i \(-0.344370\pi\)
\(888\) 7.51026 + 7.51026i 0.252028 + 0.252028i
\(889\) −4.95424 + 1.17970i −0.166160 + 0.0395660i
\(890\) −4.16162 6.90395i −0.139498 0.231421i
\(891\) −0.582897 + 1.00961i −0.0195278 + 0.0338231i
\(892\) 4.02281 + 1.07791i 0.134694 + 0.0360911i
\(893\) 7.81102 + 2.09296i 0.261386 + 0.0700381i
\(894\) 0.110402 0.191221i 0.00369239 0.00639540i
\(895\) 0.810606 3.27088i 0.0270956 0.109333i
\(896\) 2.53540 + 0.756134i 0.0847018 + 0.0252607i
\(897\) −13.8214 13.8214i −0.461483 0.461483i
\(898\) 2.63085 + 9.81847i 0.0877926 + 0.327647i
\(899\) 22.2310 + 38.5051i 0.741444 + 1.28422i
\(900\) 0.188640 + 4.99644i 0.00628801 + 0.166548i
\(901\) −0.0549337 0.0317160i −0.00183011 0.00105661i
\(902\) 2.05242 2.05242i 0.0683381 0.0683381i
\(903\) −29.4636 0.826173i −0.980486 0.0274933i
\(904\) 18.7650i 0.624115i
\(905\) 34.3813 + 33.1078i 1.14287 + 1.10054i
\(906\) 5.51559 3.18442i 0.183243 0.105795i
\(907\) −14.7658 + 55.1066i −0.490290 + 1.82979i 0.0646668 + 0.997907i \(0.479402\pi\)
−0.554957 + 0.831879i \(0.687265\pi\)
\(908\) −17.8106 + 4.77234i −0.591066 + 0.158376i
\(909\) −13.9159 −0.461562
\(910\) 4.31089 15.5182i 0.142905 0.514422i
\(911\) −32.4993 −1.07675 −0.538375 0.842705i \(-0.680962\pi\)
−0.538375 + 0.842705i \(0.680962\pi\)
\(912\) 1.91130 0.512132i 0.0632896 0.0169584i
\(913\) 4.15964 15.5240i 0.137664 0.513769i
\(914\) 24.7030 14.2623i 0.817103 0.471755i
\(915\) 0.153841 + 8.15234i 0.00508582 + 0.269508i
\(916\) 5.91011i 0.195276i
\(917\) 39.9156 21.5767i 1.31813 0.712525i
\(918\) 0.0153229 0.0153229i 0.000505732 0.000505732i
\(919\) −1.92544 1.11165i −0.0635143 0.0366700i 0.467907 0.883778i \(-0.345008\pi\)
−0.531421 + 0.847108i \(0.678342\pi\)
\(920\) 15.4265 4.44712i 0.508597 0.146617i
\(921\) 0.400469 + 0.693633i 0.0131959 + 0.0228560i
\(922\) 5.20155 + 19.4125i 0.171304 + 0.639315i
\(923\) −14.4732 14.4732i −0.476391 0.476391i
\(924\) 0.714480 + 3.00051i 0.0235047 + 0.0987095i
\(925\) 15.6702 + 50.7409i 0.515234 + 1.66835i
\(926\) −5.19343 + 8.99529i −0.170667 + 0.295604i
\(927\) 11.5757 + 3.10171i 0.380197 + 0.101874i
\(928\) 5.41502 + 1.45095i 0.177757 + 0.0476298i
\(929\) −0.358305 + 0.620603i −0.0117556 + 0.0203613i −0.871843 0.489785i \(-0.837075\pi\)
0.860088 + 0.510146i \(0.170409\pi\)
\(930\) −17.2137 4.26598i −0.564458 0.139887i
\(931\) 13.8293 + 0.776173i 0.453238 + 0.0254380i
\(932\) 5.11615 + 5.11615i 0.167585 + 0.167585i
\(933\) −3.46746 12.9407i −0.113520 0.423661i
\(934\) −11.8022 20.4420i −0.386179 0.668882i
\(935\) −0.0494451 0.0273165i −0.00161703 0.000893344i
\(936\) 2.35765 + 1.36119i 0.0770622 + 0.0444919i
\(937\) 11.6639 11.6639i 0.381042 0.381042i −0.490435 0.871478i \(-0.663162\pi\)
0.871478 + 0.490435i \(0.163162\pi\)
\(938\) 32.8041 + 20.1861i 1.07109 + 0.659100i
\(939\) 28.7580i 0.938481i
\(940\) −9.13663 + 0.172415i −0.298004 + 0.00562355i
\(941\) 26.7812 15.4621i 0.873041 0.504051i 0.00468360 0.999989i \(-0.498509\pi\)
0.868358 + 0.495938i \(0.165176\pi\)
\(942\) −3.74673 + 13.9830i −0.122075 + 0.455591i
\(943\) 17.2672 4.62672i 0.562296 0.150667i
\(944\) 10.6925 0.348010
\(945\) −5.09615 3.00487i −0.165778 0.0977484i
\(946\) −12.9876 −0.422263
\(947\) 15.7786 4.22786i 0.512735 0.137387i 0.00683099 0.999977i \(-0.497826\pi\)
0.505904 + 0.862590i \(0.331159\pi\)
\(948\) −0.416801 + 1.55552i −0.0135371 + 0.0505210i
\(949\) −8.83030 + 5.09817i −0.286644 + 0.165494i
\(950\) 9.64632 + 2.19829i 0.312968 + 0.0713219i
\(951\) 33.7349i 1.09393i
\(952\) 0.00160702 0.0573106i 5.20838e−5 0.00185745i
\(953\) −8.22927 + 8.22927i −0.266572 + 0.266572i −0.827717 0.561145i \(-0.810361\pi\)
0.561145 + 0.827717i \(0.310361\pi\)
\(954\) −2.53502 1.46360i −0.0820744 0.0473857i
\(955\) 3.99556 + 13.8601i 0.129293 + 0.448503i
\(956\) −2.10086 3.63880i −0.0679467 0.117687i
\(957\) 1.69151 + 6.31281i 0.0546788 + 0.204064i
\(958\) −17.5210 17.5210i −0.566079 0.566079i
\(959\) 18.6051 + 19.6786i 0.600789 + 0.635454i
\(960\) −1.91505 + 1.15437i −0.0618081 + 0.0372572i
\(961\) 15.9509 27.6278i 0.514545 0.891219i
\(962\) 27.9294 + 7.48367i 0.900481 + 0.241283i
\(963\) 6.67031 + 1.78730i 0.214948 + 0.0575951i
\(964\) −10.9679 + 18.9970i −0.353254 + 0.611853i
\(965\) 9.84065 5.93183i 0.316782 0.190952i
\(966\) −5.42896 + 18.2039i −0.174674 + 0.585701i
\(967\) 1.15164 + 1.15164i 0.0370342 + 0.0370342i 0.725381 0.688347i \(-0.241663\pi\)
−0.688347 + 0.725381i \(0.741663\pi\)
\(968\) −2.49525 9.31242i −0.0802005 0.299312i
\(969\) −0.0214394 0.0371341i −0.000688733 0.00119292i
\(970\) 0.232564 + 0.806735i 0.00746717 + 0.0259027i
\(971\) 12.4747 + 7.20230i 0.400334 + 0.231133i 0.686628 0.727009i \(-0.259090\pi\)
−0.286294 + 0.958142i \(0.592424\pi\)
\(972\) 0.707107 0.707107i 0.0226805 0.0226805i
\(973\) −7.83582 + 12.7339i −0.251205 + 0.408229i
\(974\) 23.7668i 0.761536i
\(975\) 7.24585 + 11.5231i 0.232053 + 0.369034i
\(976\) −3.15795 + 1.82324i −0.101084 + 0.0583606i
\(977\) −9.63078 + 35.9426i −0.308116 + 1.14990i 0.622114 + 0.782927i \(0.286274\pi\)
−0.930230 + 0.366977i \(0.880393\pi\)
\(978\) 21.1592 5.66960i 0.676598 0.181294i
\(979\) 4.20281 0.134322
\(980\) −15.2593 + 3.48609i −0.487441 + 0.111359i
\(981\) 0.577314 0.0184322
\(982\) −0.372938 + 0.0999283i −0.0119009 + 0.00318884i
\(983\) 7.32286 27.3293i 0.233563 0.871669i −0.745228 0.666809i \(-0.767659\pi\)
0.978791 0.204860i \(-0.0656739\pi\)
\(984\) −2.15620 + 1.24488i −0.0687372 + 0.0396855i
\(985\) 56.3882 1.06409i 1.79668 0.0339046i
\(986\) 0.121482i 0.00386879i
\(987\) 5.66660 9.20871i 0.180370 0.293116i
\(988\) 3.80907 3.80907i 0.121183 0.121183i
\(989\) −69.2716 39.9940i −2.20271 1.27174i
\(990\) −2.28174 1.26057i −0.0725185 0.0400636i
\(991\) −18.6725 32.3417i −0.593151 1.02737i −0.993805 0.111139i \(-0.964550\pi\)
0.400654 0.916230i \(-0.368783\pi\)
\(992\) −2.05271 7.66082i −0.0651736 0.243231i
\(993\) −7.73266 7.73266i −0.245388 0.245388i
\(994\) −5.68498 + 19.0624i −0.180317 + 0.604622i
\(995\) −10.7261 2.65820i −0.340040 0.0842706i
\(996\) −6.89298 + 11.9390i −0.218413 + 0.378302i
\(997\) 35.7963 + 9.59160i 1.13368 + 0.303769i 0.776408 0.630231i \(-0.217040\pi\)
0.357274 + 0.934000i \(0.383706\pi\)
\(998\) −7.75163 2.07704i −0.245373 0.0657476i
\(999\) 5.31055 9.19815i 0.168018 0.291017i
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 210.2.u.a.187.4 yes 16
3.2 odd 2 630.2.bv.a.397.1 16
5.2 odd 4 1050.2.bc.g.943.3 16
5.3 odd 4 210.2.u.b.103.1 yes 16
5.4 even 2 1050.2.bc.h.607.2 16
7.2 even 3 1470.2.m.d.97.1 16
7.3 odd 6 210.2.u.b.157.1 yes 16
7.5 odd 6 1470.2.m.e.97.4 16
15.8 even 4 630.2.bv.b.523.4 16
21.17 even 6 630.2.bv.b.577.4 16
35.3 even 12 inner 210.2.u.a.73.4 16
35.17 even 12 1050.2.bc.h.493.2 16
35.23 odd 12 1470.2.m.e.1273.4 16
35.24 odd 6 1050.2.bc.g.157.3 16
35.33 even 12 1470.2.m.d.1273.1 16
105.38 odd 12 630.2.bv.a.73.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.u.a.73.4 16 35.3 even 12 inner
210.2.u.a.187.4 yes 16 1.1 even 1 trivial
210.2.u.b.103.1 yes 16 5.3 odd 4
210.2.u.b.157.1 yes 16 7.3 odd 6
630.2.bv.a.73.1 16 105.38 odd 12
630.2.bv.a.397.1 16 3.2 odd 2
630.2.bv.b.523.4 16 15.8 even 4
630.2.bv.b.577.4 16 21.17 even 6
1050.2.bc.g.157.3 16 35.24 odd 6
1050.2.bc.g.943.3 16 5.2 odd 4
1050.2.bc.h.493.2 16 35.17 even 12
1050.2.bc.h.607.2 16 5.4 even 2
1470.2.m.d.97.1 16 7.2 even 3
1470.2.m.d.1273.1 16 35.33 even 12
1470.2.m.e.97.4 16 7.5 odd 6
1470.2.m.e.1273.4 16 35.23 odd 12