Properties

Label 690.2.j.a.367.12
Level $690$
Weight $2$
Character 690.367
Analytic conductor $5.510$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [690,2,Mod(367,690)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(690, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("690.367");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.j (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 367.12
Character \(\chi\) \(=\) 690.367
Dual form 690.2.j.a.643.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(2.22154 + 0.254460i) q^{5} -1.00000 q^{6} +(-2.54671 + 2.54671i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(2.22154 + 0.254460i) q^{5} -1.00000 q^{6} +(-2.54671 + 2.54671i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(1.39094 + 1.75080i) q^{10} +3.50160i q^{11} +(-0.707107 - 0.707107i) q^{12} +(2.40571 - 2.40571i) q^{13} -3.60159 q^{14} +(-1.75080 + 1.39094i) q^{15} -1.00000 q^{16} +(-1.37206 + 1.37206i) q^{17} +(0.707107 - 0.707107i) q^{18} -2.31155 q^{19} +(-0.254460 + 2.22154i) q^{20} -3.60159i q^{21} +(-2.47600 + 2.47600i) q^{22} +(-4.21961 + 2.27923i) q^{23} -1.00000i q^{24} +(4.87050 + 1.13059i) q^{25} +3.40219 q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.54671 - 2.54671i) q^{28} -0.113162i q^{29} +(-2.22154 - 0.254460i) q^{30} +1.27272 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.47600 - 2.47600i) q^{33} -1.94038 q^{34} +(-6.30566 + 5.00959i) q^{35} +1.00000 q^{36} +(-3.74806 + 3.74806i) q^{37} +(-1.63451 - 1.63451i) q^{38} +3.40219i q^{39} +(-1.75080 + 1.39094i) q^{40} +5.08960 q^{41} +(2.54671 - 2.54671i) q^{42} +(2.71117 + 2.71117i) q^{43} -3.50160 q^{44} +(0.254460 - 2.22154i) q^{45} +(-4.59537 - 1.37206i) q^{46} +(-0.775445 - 0.775445i) q^{47} +(0.707107 - 0.707107i) q^{48} -5.97146i q^{49} +(2.64452 + 4.24341i) q^{50} -1.94038i q^{51} +(2.40571 + 2.40571i) q^{52} +(2.61742 + 2.61742i) q^{53} +1.00000i q^{54} +(-0.891017 + 7.77894i) q^{55} -3.60159i q^{56} +(1.63451 - 1.63451i) q^{57} +(0.0800174 - 0.0800174i) q^{58} -13.2983i q^{59} +(-1.39094 - 1.75080i) q^{60} -0.841493i q^{61} +(0.899946 + 0.899946i) q^{62} +(2.54671 + 2.54671i) q^{63} -1.00000i q^{64} +(5.95656 - 4.73224i) q^{65} -3.50160i q^{66} +(-5.33351 + 5.33351i) q^{67} +(-1.37206 - 1.37206i) q^{68} +(1.37206 - 4.59537i) q^{69} +(-8.00109 - 0.916462i) q^{70} +14.2568 q^{71} +(0.707107 + 0.707107i) q^{72} +(-7.88793 + 7.88793i) q^{73} -5.30056 q^{74} +(-4.24341 + 2.64452i) q^{75} -2.31155i q^{76} +(-8.91755 - 8.91755i) q^{77} +(-2.40571 + 2.40571i) q^{78} -2.37992 q^{79} +(-2.22154 - 0.254460i) q^{80} -1.00000 q^{81} +(3.59889 + 3.59889i) q^{82} +(-1.02759 - 1.02759i) q^{83} +3.60159 q^{84} +(-3.39722 + 2.69895i) q^{85} +3.83417i q^{86} +(0.0800174 + 0.0800174i) q^{87} +(-2.47600 - 2.47600i) q^{88} +14.7757 q^{89} +(1.75080 - 1.39094i) q^{90} +12.2533i q^{91} +(-2.27923 - 4.21961i) q^{92} +(-0.899946 + 0.899946i) q^{93} -1.09665i q^{94} +(-5.13520 - 0.588197i) q^{95} +1.00000 q^{96} +(4.66285 - 4.66285i) q^{97} +(4.22246 - 4.22246i) q^{98} +3.50160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 24 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 24 q^{6} - 24 q^{16} - 8 q^{23} - 16 q^{25} - 16 q^{26} + 16 q^{31} - 16 q^{35} + 24 q^{36} - 8 q^{46} - 8 q^{47} + 24 q^{50} + 24 q^{55} + 16 q^{58} - 56 q^{62} - 32 q^{70} - 16 q^{71} - 48 q^{73} - 24 q^{81} + 24 q^{82} + 16 q^{87} - 8 q^{92} + 56 q^{93} + 24 q^{95} + 24 q^{96} - 32 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 2.22154 + 0.254460i 0.993504 + 0.113798i
\(6\) −1.00000 −0.408248
\(7\) −2.54671 + 2.54671i −0.962566 + 0.962566i −0.999324 0.0367582i \(-0.988297\pi\)
0.0367582 + 0.999324i \(0.488297\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 1.39094 + 1.75080i 0.439853 + 0.553651i
\(11\) 3.50160i 1.05577i 0.849316 + 0.527886i \(0.177015\pi\)
−0.849316 + 0.527886i \(0.822985\pi\)
\(12\) −0.707107 0.707107i −0.204124 0.204124i
\(13\) 2.40571 2.40571i 0.667225 0.667225i −0.289848 0.957073i \(-0.593605\pi\)
0.957073 + 0.289848i \(0.0936046\pi\)
\(14\) −3.60159 −0.962566
\(15\) −1.75080 + 1.39094i −0.452054 + 0.359138i
\(16\) −1.00000 −0.250000
\(17\) −1.37206 + 1.37206i −0.332773 + 0.332773i −0.853639 0.520866i \(-0.825609\pi\)
0.520866 + 0.853639i \(0.325609\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) −2.31155 −0.530305 −0.265153 0.964206i \(-0.585422\pi\)
−0.265153 + 0.964206i \(0.585422\pi\)
\(20\) −0.254460 + 2.22154i −0.0568991 + 0.496752i
\(21\) 3.60159i 0.785932i
\(22\) −2.47600 + 2.47600i −0.527886 + 0.527886i
\(23\) −4.21961 + 2.27923i −0.879850 + 0.475252i
\(24\) 1.00000i 0.204124i
\(25\) 4.87050 + 1.13059i 0.974100 + 0.226118i
\(26\) 3.40219 0.667225
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −2.54671 2.54671i −0.481283 0.481283i
\(29\) 0.113162i 0.0210136i −0.999945 0.0105068i \(-0.996656\pi\)
0.999945 0.0105068i \(-0.00334448\pi\)
\(30\) −2.22154 0.254460i −0.405596 0.0464579i
\(31\) 1.27272 0.228586 0.114293 0.993447i \(-0.463540\pi\)
0.114293 + 0.993447i \(0.463540\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −2.47600 2.47600i −0.431017 0.431017i
\(34\) −1.94038 −0.332773
\(35\) −6.30566 + 5.00959i −1.06585 + 0.846775i
\(36\) 1.00000 0.166667
\(37\) −3.74806 + 3.74806i −0.616178 + 0.616178i −0.944549 0.328371i \(-0.893500\pi\)
0.328371 + 0.944549i \(0.393500\pi\)
\(38\) −1.63451 1.63451i −0.265153 0.265153i
\(39\) 3.40219i 0.544787i
\(40\) −1.75080 + 1.39094i −0.276826 + 0.219926i
\(41\) 5.08960 0.794863 0.397431 0.917632i \(-0.369902\pi\)
0.397431 + 0.917632i \(0.369902\pi\)
\(42\) 2.54671 2.54671i 0.392966 0.392966i
\(43\) 2.71117 + 2.71117i 0.413449 + 0.413449i 0.882938 0.469489i \(-0.155562\pi\)
−0.469489 + 0.882938i \(0.655562\pi\)
\(44\) −3.50160 −0.527886
\(45\) 0.254460 2.22154i 0.0379327 0.331168i
\(46\) −4.59537 1.37206i −0.677551 0.202299i
\(47\) −0.775445 0.775445i −0.113110 0.113110i 0.648286 0.761397i \(-0.275486\pi\)
−0.761397 + 0.648286i \(0.775486\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 5.97146i 0.853066i
\(50\) 2.64452 + 4.24341i 0.373991 + 0.600109i
\(51\) 1.94038i 0.271708i
\(52\) 2.40571 + 2.40571i 0.333613 + 0.333613i
\(53\) 2.61742 + 2.61742i 0.359530 + 0.359530i 0.863640 0.504110i \(-0.168179\pi\)
−0.504110 + 0.863640i \(0.668179\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −0.891017 + 7.77894i −0.120145 + 1.04891i
\(56\) 3.60159i 0.481283i
\(57\) 1.63451 1.63451i 0.216496 0.216496i
\(58\) 0.0800174 0.0800174i 0.0105068 0.0105068i
\(59\) 13.2983i 1.73128i −0.500663 0.865642i \(-0.666910\pi\)
0.500663 0.865642i \(-0.333090\pi\)
\(60\) −1.39094 1.75080i −0.179569 0.226027i
\(61\) 0.841493i 0.107742i −0.998548 0.0538710i \(-0.982844\pi\)
0.998548 0.0538710i \(-0.0171560\pi\)
\(62\) 0.899946 + 0.899946i 0.114293 + 0.114293i
\(63\) 2.54671 + 2.54671i 0.320855 + 0.320855i
\(64\) 1.00000i 0.125000i
\(65\) 5.95656 4.73224i 0.738820 0.586962i
\(66\) 3.50160i 0.431017i
\(67\) −5.33351 + 5.33351i −0.651592 + 0.651592i −0.953376 0.301784i \(-0.902418\pi\)
0.301784 + 0.953376i \(0.402418\pi\)
\(68\) −1.37206 1.37206i −0.166386 0.166386i
\(69\) 1.37206 4.59537i 0.165176 0.553218i
\(70\) −8.00109 0.916462i −0.956313 0.109538i
\(71\) 14.2568 1.69198 0.845988 0.533203i \(-0.179012\pi\)
0.845988 + 0.533203i \(0.179012\pi\)
\(72\) 0.707107 + 0.707107i 0.0833333 + 0.0833333i
\(73\) −7.88793 + 7.88793i −0.923212 + 0.923212i −0.997255 0.0740430i \(-0.976410\pi\)
0.0740430 + 0.997255i \(0.476410\pi\)
\(74\) −5.30056 −0.616178
\(75\) −4.24341 + 2.64452i −0.489987 + 0.305362i
\(76\) 2.31155i 0.265153i
\(77\) −8.91755 8.91755i −1.01625 1.01625i
\(78\) −2.40571 + 2.40571i −0.272394 + 0.272394i
\(79\) −2.37992 −0.267761 −0.133881 0.990997i \(-0.542744\pi\)
−0.133881 + 0.990997i \(0.542744\pi\)
\(80\) −2.22154 0.254460i −0.248376 0.0284495i
\(81\) −1.00000 −0.111111
\(82\) 3.59889 + 3.59889i 0.397431 + 0.397431i
\(83\) −1.02759 1.02759i −0.112793 0.112793i 0.648458 0.761251i \(-0.275414\pi\)
−0.761251 + 0.648458i \(0.775414\pi\)
\(84\) 3.60159 0.392966
\(85\) −3.39722 + 2.69895i −0.368480 + 0.292742i
\(86\) 3.83417i 0.413449i
\(87\) 0.0800174 + 0.0800174i 0.00857877 + 0.00857877i
\(88\) −2.47600 2.47600i −0.263943 0.263943i
\(89\) 14.7757 1.56622 0.783109 0.621885i \(-0.213633\pi\)
0.783109 + 0.621885i \(0.213633\pi\)
\(90\) 1.75080 1.39094i 0.184550 0.146618i
\(91\) 12.2533i 1.28450i
\(92\) −2.27923 4.21961i −0.237626 0.439925i
\(93\) −0.899946 + 0.899946i −0.0933200 + 0.0933200i
\(94\) 1.09665i 0.113110i
\(95\) −5.13520 0.588197i −0.526860 0.0603477i
\(96\) 1.00000 0.102062
\(97\) 4.66285 4.66285i 0.473441 0.473441i −0.429585 0.903026i \(-0.641340\pi\)
0.903026 + 0.429585i \(0.141340\pi\)
\(98\) 4.22246 4.22246i 0.426533 0.426533i
\(99\) 3.50160 0.351924
\(100\) −1.13059 + 4.87050i −0.113059 + 0.487050i
\(101\) 0.433231 0.0431081 0.0215541 0.999768i \(-0.493139\pi\)
0.0215541 + 0.999768i \(0.493139\pi\)
\(102\) 1.37206 1.37206i 0.135854 0.135854i
\(103\) 8.99956 + 8.99956i 0.886753 + 0.886753i 0.994210 0.107457i \(-0.0342706\pi\)
−0.107457 + 0.994210i \(0.534271\pi\)
\(104\) 3.40219i 0.333613i
\(105\) 0.916462 8.00109i 0.0894376 0.780826i
\(106\) 3.70159i 0.359530i
\(107\) 13.7709 13.7709i 1.33128 1.33128i 0.427056 0.904225i \(-0.359551\pi\)
0.904225 0.427056i \(-0.140449\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) −3.09267 −0.296224 −0.148112 0.988971i \(-0.547320\pi\)
−0.148112 + 0.988971i \(0.547320\pi\)
\(110\) −6.13059 + 4.87050i −0.584529 + 0.464384i
\(111\) 5.30056i 0.503107i
\(112\) 2.54671 2.54671i 0.240641 0.240641i
\(113\) −2.36212 2.36212i −0.222209 0.222209i 0.587219 0.809428i \(-0.300223\pi\)
−0.809428 + 0.587219i \(0.800223\pi\)
\(114\) 2.31155 0.216496
\(115\) −9.95402 + 3.98968i −0.928217 + 0.372040i
\(116\) 0.113162 0.0105068
\(117\) −2.40571 2.40571i −0.222408 0.222408i
\(118\) 9.40328 9.40328i 0.865642 0.865642i
\(119\) 6.98846i 0.640631i
\(120\) 0.254460 2.22154i 0.0232289 0.202798i
\(121\) −1.26118 −0.114653
\(122\) 0.595025 0.595025i 0.0538710 0.0538710i
\(123\) −3.59889 + 3.59889i −0.324501 + 0.324501i
\(124\) 1.27272i 0.114293i
\(125\) 10.5323 + 3.75100i 0.942040 + 0.335500i
\(126\) 3.60159i 0.320855i
\(127\) 8.49034 + 8.49034i 0.753396 + 0.753396i 0.975111 0.221715i \(-0.0711656\pi\)
−0.221715 + 0.975111i \(0.571166\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −3.83417 −0.337580
\(130\) 7.55812 + 0.865724i 0.662891 + 0.0759290i
\(131\) 18.8562 1.64747 0.823736 0.566973i \(-0.191886\pi\)
0.823736 + 0.566973i \(0.191886\pi\)
\(132\) 2.47600 2.47600i 0.215508 0.215508i
\(133\) 5.88684 5.88684i 0.510454 0.510454i
\(134\) −7.54272 −0.651592
\(135\) 1.39094 + 1.75080i 0.119713 + 0.150685i
\(136\) 1.94038i 0.166386i
\(137\) 3.49960 3.49960i 0.298991 0.298991i −0.541628 0.840618i \(-0.682192\pi\)
0.840618 + 0.541628i \(0.182192\pi\)
\(138\) 4.21961 2.27923i 0.359197 0.194021i
\(139\) 14.4705i 1.22737i −0.789552 0.613684i \(-0.789687\pi\)
0.789552 0.613684i \(-0.210313\pi\)
\(140\) −5.00959 6.30566i −0.423387 0.532926i
\(141\) 1.09665 0.0923542
\(142\) 10.0811 + 10.0811i 0.845988 + 0.845988i
\(143\) 8.42384 + 8.42384i 0.704437 + 0.704437i
\(144\) 1.00000i 0.0833333i
\(145\) 0.0287952 0.251394i 0.00239131 0.0208771i
\(146\) −11.1552 −0.923212
\(147\) 4.22246 + 4.22246i 0.348263 + 0.348263i
\(148\) −3.74806 3.74806i −0.308089 0.308089i
\(149\) 2.64129 0.216383 0.108192 0.994130i \(-0.465494\pi\)
0.108192 + 0.994130i \(0.465494\pi\)
\(150\) −4.87050 1.13059i −0.397675 0.0923122i
\(151\) 21.1977 1.72505 0.862524 0.506016i \(-0.168882\pi\)
0.862524 + 0.506016i \(0.168882\pi\)
\(152\) 1.63451 1.63451i 0.132576 0.132576i
\(153\) 1.37206 + 1.37206i 0.110924 + 0.110924i
\(154\) 12.6113i 1.01625i
\(155\) 2.82739 + 0.323856i 0.227102 + 0.0260127i
\(156\) −3.40219 −0.272394
\(157\) 17.0584 17.0584i 1.36141 1.36141i 0.489278 0.872128i \(-0.337260\pi\)
0.872128 0.489278i \(-0.162740\pi\)
\(158\) −1.68285 1.68285i −0.133881 0.133881i
\(159\) −3.70159 −0.293555
\(160\) −1.39094 1.75080i −0.109963 0.138413i
\(161\) 4.94159 16.5507i 0.389452 1.30437i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) 2.81143 2.81143i 0.220208 0.220208i −0.588378 0.808586i \(-0.700233\pi\)
0.808586 + 0.588378i \(0.200233\pi\)
\(164\) 5.08960i 0.397431i
\(165\) −4.87050 6.13059i −0.379168 0.477266i
\(166\) 1.45324i 0.112793i
\(167\) −8.40826 8.40826i −0.650651 0.650651i 0.302499 0.953150i \(-0.402179\pi\)
−0.953150 + 0.302499i \(0.902179\pi\)
\(168\) 2.54671 + 2.54671i 0.196483 + 0.196483i
\(169\) 1.42507i 0.109621i
\(170\) −4.31064 0.493750i −0.330611 0.0378689i
\(171\) 2.31155i 0.176768i
\(172\) −2.71117 + 2.71117i −0.206724 + 0.206724i
\(173\) −8.59500 + 8.59500i −0.653466 + 0.653466i −0.953826 0.300360i \(-0.902893\pi\)
0.300360 + 0.953826i \(0.402893\pi\)
\(174\) 0.113162i 0.00857877i
\(175\) −15.2830 + 9.52447i −1.15529 + 0.719982i
\(176\) 3.50160i 0.263943i
\(177\) 9.40328 + 9.40328i 0.706794 + 0.706794i
\(178\) 10.4480 + 10.4480i 0.783109 + 0.783109i
\(179\) 22.1597i 1.65629i 0.560511 + 0.828147i \(0.310605\pi\)
−0.560511 + 0.828147i \(0.689395\pi\)
\(180\) 2.22154 + 0.254460i 0.165584 + 0.0189664i
\(181\) 7.71976i 0.573805i 0.957960 + 0.286903i \(0.0926256\pi\)
−0.957960 + 0.286903i \(0.907374\pi\)
\(182\) −8.66440 + 8.66440i −0.642248 + 0.642248i
\(183\) 0.595025 + 0.595025i 0.0439855 + 0.0439855i
\(184\) 1.37206 4.59537i 0.101149 0.338775i
\(185\) −9.28022 + 7.37275i −0.682295 + 0.542055i
\(186\) −1.27272 −0.0933200
\(187\) −4.80439 4.80439i −0.351332 0.351332i
\(188\) 0.775445 0.775445i 0.0565552 0.0565552i
\(189\) −3.60159 −0.261977
\(190\) −3.21522 4.04705i −0.233256 0.293604i
\(191\) 22.6783i 1.64094i −0.571689 0.820471i \(-0.693711\pi\)
0.571689 0.820471i \(-0.306289\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) −13.9176 + 13.9176i −1.00181 + 1.00181i −0.00180888 + 0.999998i \(0.500576\pi\)
−0.999998 + 0.00180888i \(0.999424\pi\)
\(194\) 6.59427 0.473441
\(195\) −0.865724 + 7.55812i −0.0619958 + 0.541248i
\(196\) 5.97146 0.426533
\(197\) −3.68741 3.68741i −0.262717 0.262717i 0.563440 0.826157i \(-0.309478\pi\)
−0.826157 + 0.563440i \(0.809478\pi\)
\(198\) 2.47600 + 2.47600i 0.175962 + 0.175962i
\(199\) −11.8404 −0.839343 −0.419672 0.907676i \(-0.637855\pi\)
−0.419672 + 0.907676i \(0.637855\pi\)
\(200\) −4.24341 + 2.64452i −0.300054 + 0.186996i
\(201\) 7.54272i 0.532023i
\(202\) 0.306341 + 0.306341i 0.0215541 + 0.0215541i
\(203\) 0.288190 + 0.288190i 0.0202270 + 0.0202270i
\(204\) 1.94038 0.135854
\(205\) 11.3068 + 1.29510i 0.789699 + 0.0904539i
\(206\) 12.7273i 0.886753i
\(207\) 2.27923 + 4.21961i 0.158417 + 0.293283i
\(208\) −2.40571 + 2.40571i −0.166806 + 0.166806i
\(209\) 8.09410i 0.559881i
\(210\) 6.30566 5.00959i 0.435132 0.345694i
\(211\) −24.3012 −1.67296 −0.836482 0.547994i \(-0.815392\pi\)
−0.836482 + 0.547994i \(0.815392\pi\)
\(212\) −2.61742 + 2.61742i −0.179765 + 0.179765i
\(213\) −10.0811 + 10.0811i −0.690746 + 0.690746i
\(214\) 19.4750 1.33128
\(215\) 5.33309 + 6.71285i 0.363713 + 0.457813i
\(216\) −1.00000 −0.0680414
\(217\) −3.24124 + 3.24124i −0.220030 + 0.220030i
\(218\) −2.18685 2.18685i −0.148112 0.148112i
\(219\) 11.1552i 0.753799i
\(220\) −7.77894 0.891017i −0.524456 0.0600724i
\(221\) 6.60156i 0.444069i
\(222\) 3.74806 3.74806i 0.251554 0.251554i
\(223\) −1.60241 + 1.60241i −0.107306 + 0.107306i −0.758721 0.651416i \(-0.774175\pi\)
0.651416 + 0.758721i \(0.274175\pi\)
\(224\) 3.60159 0.240641
\(225\) 1.13059 4.87050i 0.0753726 0.324700i
\(226\) 3.34054i 0.222209i
\(227\) −15.4161 + 15.4161i −1.02320 + 1.02320i −0.0234786 + 0.999724i \(0.507474\pi\)
−0.999724 + 0.0234786i \(0.992526\pi\)
\(228\) 1.63451 + 1.63451i 0.108248 + 0.108248i
\(229\) −12.8440 −0.848754 −0.424377 0.905486i \(-0.639507\pi\)
−0.424377 + 0.905486i \(0.639507\pi\)
\(230\) −9.85968 4.21742i −0.650128 0.278089i
\(231\) 12.6113 0.829764
\(232\) 0.0800174 + 0.0800174i 0.00525340 + 0.00525340i
\(233\) −12.2901 + 12.2901i −0.805153 + 0.805153i −0.983896 0.178743i \(-0.942797\pi\)
0.178743 + 0.983896i \(0.442797\pi\)
\(234\) 3.40219i 0.222408i
\(235\) −1.52536 1.92000i −0.0995038 0.125247i
\(236\) 13.2983 0.865642
\(237\) 1.68285 1.68285i 0.109313 0.109313i
\(238\) 4.94159 4.94159i 0.320316 0.320316i
\(239\) 18.1727i 1.17549i −0.809045 0.587747i \(-0.800015\pi\)
0.809045 0.587747i \(-0.199985\pi\)
\(240\) 1.75080 1.39094i 0.113014 0.0897846i
\(241\) 11.7886i 0.759373i 0.925115 + 0.379687i \(0.123968\pi\)
−0.925115 + 0.379687i \(0.876032\pi\)
\(242\) −0.891787 0.891787i −0.0573263 0.0573263i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 0.841493 0.0538710
\(245\) 1.51950 13.2659i 0.0970774 0.847525i
\(246\) −5.08960 −0.324501
\(247\) −5.56092 + 5.56092i −0.353833 + 0.353833i
\(248\) −0.899946 + 0.899946i −0.0571466 + 0.0571466i
\(249\) 1.45324 0.0920950
\(250\) 4.79513 + 10.0998i 0.303270 + 0.638770i
\(251\) 12.8428i 0.810631i −0.914177 0.405315i \(-0.867162\pi\)
0.914177 0.405315i \(-0.132838\pi\)
\(252\) −2.54671 + 2.54671i −0.160428 + 0.160428i
\(253\) −7.98094 14.7754i −0.501757 0.928920i
\(254\) 12.0072i 0.753396i
\(255\) 0.493750 4.31064i 0.0309198 0.269943i
\(256\) 1.00000 0.0625000
\(257\) 1.42623 + 1.42623i 0.0889659 + 0.0889659i 0.750189 0.661223i \(-0.229962\pi\)
−0.661223 + 0.750189i \(0.729962\pi\)
\(258\) −2.71117 2.71117i −0.168790 0.168790i
\(259\) 19.0905i 1.18622i
\(260\) 4.73224 + 5.95656i 0.293481 + 0.369410i
\(261\) −0.113162 −0.00700453
\(262\) 13.3333 + 13.3333i 0.823736 + 0.823736i
\(263\) −18.6079 18.6079i −1.14741 1.14741i −0.987060 0.160349i \(-0.948738\pi\)
−0.160349 0.987060i \(-0.551262\pi\)
\(264\) 3.50160 0.215508
\(265\) 5.14867 + 6.48073i 0.316281 + 0.398108i
\(266\) 8.32525 0.510454
\(267\) −10.4480 + 10.4480i −0.639406 + 0.639406i
\(268\) −5.33351 5.33351i −0.325796 0.325796i
\(269\) 13.7120i 0.836034i −0.908439 0.418017i \(-0.862725\pi\)
0.908439 0.418017i \(-0.137275\pi\)
\(270\) −0.254460 + 2.22154i −0.0154860 + 0.135199i
\(271\) −11.6831 −0.709696 −0.354848 0.934924i \(-0.615467\pi\)
−0.354848 + 0.934924i \(0.615467\pi\)
\(272\) 1.37206 1.37206i 0.0831932 0.0831932i
\(273\) −8.66440 8.66440i −0.524394 0.524394i
\(274\) 4.94918 0.298991
\(275\) −3.95887 + 17.0545i −0.238729 + 1.02843i
\(276\) 4.59537 + 1.37206i 0.276609 + 0.0825881i
\(277\) 10.3117 + 10.3117i 0.619572 + 0.619572i 0.945422 0.325850i \(-0.105650\pi\)
−0.325850 + 0.945422i \(0.605650\pi\)
\(278\) 10.2322 10.2322i 0.613684 0.613684i
\(279\) 1.27272i 0.0761955i
\(280\) 0.916462 8.00109i 0.0547691 0.478157i
\(281\) 29.4216i 1.75514i −0.479445 0.877572i \(-0.659162\pi\)
0.479445 0.877572i \(-0.340838\pi\)
\(282\) 0.775445 + 0.775445i 0.0461771 + 0.0461771i
\(283\) 18.0041 + 18.0041i 1.07023 + 1.07023i 0.997340 + 0.0728932i \(0.0232232\pi\)
0.0728932 + 0.997340i \(0.476777\pi\)
\(284\) 14.2568i 0.845988i
\(285\) 4.04705 3.21522i 0.239727 0.190453i
\(286\) 11.9131i 0.704437i
\(287\) −12.9617 + 12.9617i −0.765108 + 0.765108i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 13.2349i 0.778525i
\(290\) 0.198123 0.157401i 0.0116342 0.00924289i
\(291\) 6.59427i 0.386563i
\(292\) −7.88793 7.88793i −0.461606 0.461606i
\(293\) 11.1818 + 11.1818i 0.653249 + 0.653249i 0.953774 0.300525i \(-0.0971618\pi\)
−0.300525 + 0.953774i \(0.597162\pi\)
\(294\) 5.97146i 0.348263i
\(295\) 3.38388 29.5426i 0.197017 1.72004i
\(296\) 5.30056i 0.308089i
\(297\) −2.47600 + 2.47600i −0.143672 + 0.143672i
\(298\) 1.86768 + 1.86768i 0.108192 + 0.108192i
\(299\) −4.66800 + 15.6344i −0.269958 + 0.904158i
\(300\) −2.64452 4.24341i −0.152681 0.244993i
\(301\) −13.8091 −0.795944
\(302\) 14.9891 + 14.9891i 0.862524 + 0.862524i
\(303\) −0.306341 + 0.306341i −0.0175988 + 0.0175988i
\(304\) 2.31155 0.132576
\(305\) 0.214126 1.86941i 0.0122608 0.107042i
\(306\) 1.94038i 0.110924i
\(307\) 9.99514 + 9.99514i 0.570453 + 0.570453i 0.932255 0.361802i \(-0.117838\pi\)
−0.361802 + 0.932255i \(0.617838\pi\)
\(308\) 8.91755 8.91755i 0.508125 0.508125i
\(309\) −12.7273 −0.724031
\(310\) 1.77027 + 2.22827i 0.100544 + 0.126557i
\(311\) 3.18731 0.180736 0.0903678 0.995908i \(-0.471196\pi\)
0.0903678 + 0.995908i \(0.471196\pi\)
\(312\) −2.40571 2.40571i −0.136197 0.136197i
\(313\) −19.6532 19.6532i −1.11086 1.11086i −0.993034 0.117830i \(-0.962406\pi\)
−0.117830 0.993034i \(-0.537594\pi\)
\(314\) 24.1242 1.36141
\(315\) 5.00959 + 6.30566i 0.282258 + 0.355284i
\(316\) 2.37992i 0.133881i
\(317\) 3.39018 + 3.39018i 0.190411 + 0.190411i 0.795874 0.605463i \(-0.207012\pi\)
−0.605463 + 0.795874i \(0.707012\pi\)
\(318\) −2.61742 2.61742i −0.146777 0.146777i
\(319\) 0.396247 0.0221856
\(320\) 0.254460 2.22154i 0.0142248 0.124188i
\(321\) 19.4750i 1.08699i
\(322\) 15.1973 8.20885i 0.846913 0.457462i
\(323\) 3.17157 3.17157i 0.176471 0.176471i
\(324\) 1.00000i 0.0555556i
\(325\) 14.4369 8.99716i 0.800816 0.499073i
\(326\) 3.97596 0.220208
\(327\) 2.18685 2.18685i 0.120933 0.120933i
\(328\) −3.59889 + 3.59889i −0.198716 + 0.198716i
\(329\) 3.94967 0.217752
\(330\) 0.891017 7.77894i 0.0490489 0.428217i
\(331\) −2.32929 −0.128029 −0.0640146 0.997949i \(-0.520390\pi\)
−0.0640146 + 0.997949i \(0.520390\pi\)
\(332\) 1.02759 1.02759i 0.0563965 0.0563965i
\(333\) 3.74806 + 3.74806i 0.205393 + 0.205393i
\(334\) 11.8911i 0.650651i
\(335\) −13.2058 + 10.4915i −0.721509 + 0.573209i
\(336\) 3.60159i 0.196483i
\(337\) 19.2106 19.2106i 1.04647 1.04647i 0.0476036 0.998866i \(-0.484842\pi\)
0.998866 0.0476036i \(-0.0151584\pi\)
\(338\) −1.00768 + 1.00768i −0.0548104 + 0.0548104i
\(339\) 3.34054 0.181433
\(340\) −2.69895 3.39722i −0.146371 0.184240i
\(341\) 4.45654i 0.241335i
\(342\) −1.63451 + 1.63451i −0.0883842 + 0.0883842i
\(343\) −2.61938 2.61938i −0.141433 0.141433i
\(344\) −3.83417 −0.206724
\(345\) 4.21742 9.85968i 0.227058 0.530827i
\(346\) −12.1552 −0.653466
\(347\) −6.50382 6.50382i −0.349143 0.349143i 0.510647 0.859790i \(-0.329406\pi\)
−0.859790 + 0.510647i \(0.829406\pi\)
\(348\) −0.0800174 + 0.0800174i −0.00428938 + 0.00428938i
\(349\) 4.27903i 0.229051i 0.993420 + 0.114526i \(0.0365348\pi\)
−0.993420 + 0.114526i \(0.963465\pi\)
\(350\) −17.5416 4.07192i −0.937635 0.217653i
\(351\) 3.40219 0.181596
\(352\) 2.47600 2.47600i 0.131971 0.131971i
\(353\) 16.8716 16.8716i 0.897983 0.897983i −0.0972747 0.995258i \(-0.531013\pi\)
0.995258 + 0.0972747i \(0.0310125\pi\)
\(354\) 13.2983i 0.706794i
\(355\) 31.6722 + 3.62780i 1.68098 + 0.192544i
\(356\) 14.7757i 0.783109i
\(357\) 4.94159 + 4.94159i 0.261537 + 0.261537i
\(358\) −15.6693 + 15.6693i −0.828147 + 0.828147i
\(359\) −24.2841 −1.28166 −0.640832 0.767681i \(-0.721410\pi\)
−0.640832 + 0.767681i \(0.721410\pi\)
\(360\) 1.39094 + 1.75080i 0.0733088 + 0.0922752i
\(361\) −13.6568 −0.718777
\(362\) −5.45870 + 5.45870i −0.286903 + 0.286903i
\(363\) 0.891787 0.891787i 0.0468067 0.0468067i
\(364\) −12.2533 −0.642248
\(365\) −19.5305 + 15.5162i −1.02227 + 0.812155i
\(366\) 0.841493i 0.0439855i
\(367\) −16.5877 + 16.5877i −0.865871 + 0.865871i −0.992012 0.126141i \(-0.959741\pi\)
0.126141 + 0.992012i \(0.459741\pi\)
\(368\) 4.21961 2.27923i 0.219962 0.118813i
\(369\) 5.08960i 0.264954i
\(370\) −11.7754 1.34878i −0.612175 0.0701199i
\(371\) −13.3316 −0.692143
\(372\) −0.899946 0.899946i −0.0466600 0.0466600i
\(373\) −0.545949 0.545949i −0.0282682 0.0282682i 0.692831 0.721100i \(-0.256363\pi\)
−0.721100 + 0.692831i \(0.756363\pi\)
\(374\) 6.79443i 0.351332i
\(375\) −10.0998 + 4.79513i −0.521554 + 0.247619i
\(376\) 1.09665 0.0565552
\(377\) −0.272235 0.272235i −0.0140208 0.0140208i
\(378\) −2.54671 2.54671i −0.130989 0.130989i
\(379\) −11.6412 −0.597971 −0.298985 0.954258i \(-0.596648\pi\)
−0.298985 + 0.954258i \(0.596648\pi\)
\(380\) 0.588197 5.13520i 0.0301739 0.263430i
\(381\) −12.0072 −0.615145
\(382\) 16.0360 16.0360i 0.820471 0.820471i
\(383\) −15.6586 15.6586i −0.800116 0.800116i 0.182997 0.983113i \(-0.441420\pi\)
−0.983113 + 0.182997i \(0.941420\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −17.5416 22.0799i −0.894000 1.12529i
\(386\) −19.6824 −1.00181
\(387\) 2.71117 2.71117i 0.137816 0.137816i
\(388\) 4.66285 + 4.66285i 0.236720 + 0.236720i
\(389\) −34.3765 −1.74296 −0.871478 0.490435i \(-0.836838\pi\)
−0.871478 + 0.490435i \(0.836838\pi\)
\(390\) −5.95656 + 4.73224i −0.301622 + 0.239626i
\(391\) 2.66231 8.91678i 0.134639 0.450941i
\(392\) 4.22246 + 4.22246i 0.213267 + 0.213267i
\(393\) −13.3333 + 13.3333i −0.672578 + 0.672578i
\(394\) 5.21479i 0.262717i
\(395\) −5.28708 0.605594i −0.266022 0.0304707i
\(396\) 3.50160i 0.175962i
\(397\) 3.67637 + 3.67637i 0.184512 + 0.184512i 0.793318 0.608807i \(-0.208352\pi\)
−0.608807 + 0.793318i \(0.708352\pi\)
\(398\) −8.37242 8.37242i −0.419672 0.419672i
\(399\) 8.32525i 0.416784i
\(400\) −4.87050 1.13059i −0.243525 0.0565294i
\(401\) 8.61364i 0.430145i 0.976598 + 0.215072i \(0.0689988\pi\)
−0.976598 + 0.215072i \(0.931001\pi\)
\(402\) 5.33351 5.33351i 0.266011 0.266011i
\(403\) 3.06179 3.06179i 0.152519 0.152519i
\(404\) 0.433231i 0.0215541i
\(405\) −2.22154 0.254460i −0.110389 0.0126442i
\(406\) 0.407562i 0.0202270i
\(407\) −13.1242 13.1242i −0.650543 0.650543i
\(408\) 1.37206 + 1.37206i 0.0679269 + 0.0679269i
\(409\) 10.5576i 0.522038i −0.965334 0.261019i \(-0.915941\pi\)
0.965334 0.261019i \(-0.0840585\pi\)
\(410\) 7.07932 + 8.91087i 0.349623 + 0.440077i
\(411\) 4.94918i 0.244125i
\(412\) −8.99956 + 8.99956i −0.443377 + 0.443377i
\(413\) 33.8668 + 33.8668i 1.66648 + 1.66648i
\(414\) −1.37206 + 4.59537i −0.0674329 + 0.225850i
\(415\) −2.02136 2.54432i −0.0992246 0.124896i
\(416\) −3.40219 −0.166806
\(417\) 10.2322 + 10.2322i 0.501071 + 0.501071i
\(418\) 5.72339 5.72339i 0.279940 0.279940i
\(419\) 31.5043 1.53909 0.769543 0.638594i \(-0.220484\pi\)
0.769543 + 0.638594i \(0.220484\pi\)
\(420\) 8.00109 + 0.916462i 0.390413 + 0.0447188i
\(421\) 29.1199i 1.41922i −0.704595 0.709609i \(-0.748871\pi\)
0.704595 0.709609i \(-0.251129\pi\)
\(422\) −17.1835 17.1835i −0.836482 0.836482i
\(423\) −0.775445 + 0.775445i −0.0377034 + 0.0377034i
\(424\) −3.70159 −0.179765
\(425\) −8.23383 + 5.13137i −0.399400 + 0.248908i
\(426\) −14.2568 −0.690746
\(427\) 2.14304 + 2.14304i 0.103709 + 0.103709i
\(428\) 13.7709 + 13.7709i 0.665641 + 0.665641i
\(429\) −11.9131 −0.575170
\(430\) −0.975644 + 8.51777i −0.0470497 + 0.410763i
\(431\) 29.7497i 1.43299i 0.697592 + 0.716495i \(0.254255\pi\)
−0.697592 + 0.716495i \(0.745745\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) −15.2332 15.2332i −0.732060 0.732060i 0.238967 0.971028i \(-0.423191\pi\)
−0.971028 + 0.238967i \(0.923191\pi\)
\(434\) −4.58380 −0.220030
\(435\) 0.157401 + 0.198123i 0.00754679 + 0.00949929i
\(436\) 3.09267i 0.148112i
\(437\) 9.75383 5.26854i 0.466589 0.252029i
\(438\) 7.88793 7.88793i 0.376900 0.376900i
\(439\) 32.1103i 1.53254i 0.642518 + 0.766271i \(0.277890\pi\)
−0.642518 + 0.766271i \(0.722110\pi\)
\(440\) −4.87050 6.13059i −0.232192 0.292264i
\(441\) −5.97146 −0.284355
\(442\) −4.66800 + 4.66800i −0.222034 + 0.222034i
\(443\) 5.81843 5.81843i 0.276442 0.276442i −0.555245 0.831687i \(-0.687375\pi\)
0.831687 + 0.555245i \(0.187375\pi\)
\(444\) 5.30056 0.251554
\(445\) 32.8248 + 3.75982i 1.55604 + 0.178233i
\(446\) −2.26616 −0.107306
\(447\) −1.86768 + 1.86768i −0.0883380 + 0.0883380i
\(448\) 2.54671 + 2.54671i 0.120321 + 0.120321i
\(449\) 9.11228i 0.430035i −0.976610 0.215018i \(-0.931019\pi\)
0.976610 0.215018i \(-0.0689809\pi\)
\(450\) 4.24341 2.64452i 0.200036 0.124664i
\(451\) 17.8217i 0.839193i
\(452\) 2.36212 2.36212i 0.111105 0.111105i
\(453\) −14.9891 + 14.9891i −0.704248 + 0.704248i
\(454\) −21.8017 −1.02320
\(455\) −3.11798 + 27.2213i −0.146173 + 1.27615i
\(456\) 2.31155i 0.108248i
\(457\) 1.84839 1.84839i 0.0864641 0.0864641i −0.662552 0.749016i \(-0.730527\pi\)
0.749016 + 0.662552i \(0.230527\pi\)
\(458\) −9.08206 9.08206i −0.424377 0.424377i
\(459\) −1.94038 −0.0905692
\(460\) −3.98968 9.95402i −0.186020 0.464108i
\(461\) 24.8093 1.15549 0.577743 0.816219i \(-0.303934\pi\)
0.577743 + 0.816219i \(0.303934\pi\)
\(462\) 8.91755 + 8.91755i 0.414882 + 0.414882i
\(463\) −11.8812 + 11.8812i −0.552166 + 0.552166i −0.927065 0.374899i \(-0.877677\pi\)
0.374899 + 0.927065i \(0.377677\pi\)
\(464\) 0.113162i 0.00525340i
\(465\) −2.22827 + 1.77027i −0.103333 + 0.0820942i
\(466\) −17.3809 −0.805153
\(467\) 19.0071 19.0071i 0.879542 0.879542i −0.113945 0.993487i \(-0.536349\pi\)
0.993487 + 0.113945i \(0.0363487\pi\)
\(468\) 2.40571 2.40571i 0.111204 0.111204i
\(469\) 27.1658i 1.25440i
\(470\) 0.279053 2.43624i 0.0128717 0.112376i
\(471\) 24.1242i 1.11158i
\(472\) 9.40328 + 9.40328i 0.432821 + 0.432821i
\(473\) −9.49341 + 9.49341i −0.436507 + 0.436507i
\(474\) 2.37992 0.109313
\(475\) −11.2584 2.61341i −0.516570 0.119911i
\(476\) 6.98846 0.320316
\(477\) 2.61742 2.61742i 0.119843 0.119843i
\(478\) 12.8500 12.8500i 0.587747 0.587747i
\(479\) −4.09469 −0.187091 −0.0935455 0.995615i \(-0.529820\pi\)
−0.0935455 + 0.995615i \(0.529820\pi\)
\(480\) 2.22154 + 0.254460i 0.101399 + 0.0116145i
\(481\) 18.0335i 0.822259i
\(482\) −8.33583 + 8.33583i −0.379687 + 0.379687i
\(483\) 8.20885 + 15.1973i 0.373516 + 0.691502i
\(484\) 1.26118i 0.0573263i
\(485\) 11.5452 9.17221i 0.524242 0.416489i
\(486\) 1.00000 0.0453609
\(487\) 21.9539 + 21.9539i 0.994826 + 0.994826i 0.999987 0.00516029i \(-0.00164258\pi\)
−0.00516029 + 0.999987i \(0.501643\pi\)
\(488\) 0.595025 + 0.595025i 0.0269355 + 0.0269355i
\(489\) 3.97596i 0.179799i
\(490\) 10.4548 8.30593i 0.472301 0.375224i
\(491\) 27.8777 1.25810 0.629051 0.777364i \(-0.283444\pi\)
0.629051 + 0.777364i \(0.283444\pi\)
\(492\) −3.59889 3.59889i −0.162251 0.162251i
\(493\) 0.155264 + 0.155264i 0.00699275 + 0.00699275i
\(494\) −7.86433 −0.353833
\(495\) 7.77894 + 0.891017i 0.349638 + 0.0400483i
\(496\) −1.27272 −0.0571466
\(497\) −36.3080 + 36.3080i −1.62864 + 1.62864i
\(498\) 1.02759 + 1.02759i 0.0460475 + 0.0460475i
\(499\) 3.43975i 0.153984i 0.997032 + 0.0769921i \(0.0245316\pi\)
−0.997032 + 0.0769921i \(0.975468\pi\)
\(500\) −3.75100 + 10.5323i −0.167750 + 0.471020i
\(501\) 11.8911 0.531254
\(502\) 9.08123 9.08123i 0.405315 0.405315i
\(503\) 10.5623 + 10.5623i 0.470951 + 0.470951i 0.902222 0.431271i \(-0.141935\pi\)
−0.431271 + 0.902222i \(0.641935\pi\)
\(504\) −3.60159 −0.160428
\(505\) 0.962442 + 0.110240i 0.0428281 + 0.00490562i
\(506\) 4.80439 16.0911i 0.213581 0.715339i
\(507\) −1.00768 1.00768i −0.0447525 0.0447525i
\(508\) −8.49034 + 8.49034i −0.376698 + 0.376698i
\(509\) 26.4803i 1.17372i 0.809690 + 0.586858i \(0.199636\pi\)
−0.809690 + 0.586858i \(0.800364\pi\)
\(510\) 3.39722 2.69895i 0.150431 0.119511i
\(511\) 40.1765i 1.77730i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −1.63451 1.63451i −0.0721654 0.0721654i
\(514\) 2.01700i 0.0889659i
\(515\) 17.7029 + 22.2829i 0.780082 + 0.981904i
\(516\) 3.83417i 0.168790i
\(517\) 2.71530 2.71530i 0.119419 0.119419i
\(518\) 13.4990 13.4990i 0.593112 0.593112i
\(519\) 12.1552i 0.533553i
\(520\) −0.865724 + 7.55812i −0.0379645 + 0.331445i
\(521\) 36.7888i 1.61175i 0.592089 + 0.805873i \(0.298304\pi\)
−0.592089 + 0.805873i \(0.701696\pi\)
\(522\) −0.0800174 0.0800174i −0.00350227 0.00350227i
\(523\) −0.561001 0.561001i −0.0245309 0.0245309i 0.694735 0.719266i \(-0.255522\pi\)
−0.719266 + 0.694735i \(0.755522\pi\)
\(524\) 18.8562i 0.823736i
\(525\) 4.07192 17.5416i 0.177713 0.765576i
\(526\) 26.3155i 1.14741i
\(527\) −1.74624 + 1.74624i −0.0760673 + 0.0760673i
\(528\) 2.47600 + 2.47600i 0.107754 + 0.107754i
\(529\) 12.6102 19.2349i 0.548271 0.836301i
\(530\) −0.941907 + 8.22323i −0.0409138 + 0.357194i
\(531\) −13.2983 −0.577095
\(532\) 5.88684 + 5.88684i 0.255227 + 0.255227i
\(533\) 12.2441 12.2441i 0.530352 0.530352i
\(534\) −14.7757 −0.639406
\(535\) 34.0967 27.0885i 1.47413 1.17114i
\(536\) 7.54272i 0.325796i
\(537\) −15.6693 15.6693i −0.676179 0.676179i
\(538\) 9.69584 9.69584i 0.418017 0.418017i
\(539\) 20.9097 0.900643
\(540\) −1.75080 + 1.39094i −0.0753424 + 0.0598564i
\(541\) −34.6074 −1.48789 −0.743945 0.668241i \(-0.767047\pi\)
−0.743945 + 0.668241i \(0.767047\pi\)
\(542\) −8.26118 8.26118i −0.354848 0.354848i
\(543\) −5.45870 5.45870i −0.234255 0.234255i
\(544\) 1.94038 0.0831932
\(545\) −6.87050 0.786962i −0.294300 0.0337098i
\(546\) 12.2533i 0.524394i
\(547\) −32.8328 32.8328i −1.40383 1.40383i −0.787451 0.616378i \(-0.788599\pi\)
−0.616378 0.787451i \(-0.711401\pi\)
\(548\) 3.49960 + 3.49960i 0.149495 + 0.149495i
\(549\) −0.841493 −0.0359140
\(550\) −14.8587 + 9.26003i −0.633578 + 0.394849i
\(551\) 0.261579i 0.0111436i
\(552\) 2.27923 + 4.21961i 0.0970104 + 0.179599i
\(553\) 6.06095 6.06095i 0.257738 0.257738i
\(554\) 14.5830i 0.619572i
\(555\) 1.34878 11.7754i 0.0572527 0.499839i
\(556\) 14.4705 0.613684
\(557\) −1.66595 + 1.66595i −0.0705886 + 0.0705886i −0.741520 0.670931i \(-0.765895\pi\)
0.670931 + 0.741520i \(0.265895\pi\)
\(558\) 0.899946 0.899946i 0.0380977 0.0380977i
\(559\) 13.0446 0.551727
\(560\) 6.30566 5.00959i 0.266463 0.211694i
\(561\) 6.79443 0.286861
\(562\) 20.8042 20.8042i 0.877572 0.877572i
\(563\) −4.02393 4.02393i −0.169588 0.169588i 0.617210 0.786798i \(-0.288263\pi\)
−0.786798 + 0.617210i \(0.788263\pi\)
\(564\) 1.09665i 0.0461771i
\(565\) −4.64648 5.84861i −0.195479 0.246053i
\(566\) 25.4617i 1.07023i
\(567\) 2.54671 2.54671i 0.106952 0.106952i
\(568\) −10.0811 + 10.0811i −0.422994 + 0.422994i
\(569\) 21.4834 0.900630 0.450315 0.892870i \(-0.351312\pi\)
0.450315 + 0.892870i \(0.351312\pi\)
\(570\) 5.13520 + 0.588197i 0.215090 + 0.0246369i
\(571\) 5.17146i 0.216419i 0.994128 + 0.108209i \(0.0345117\pi\)
−0.994128 + 0.108209i \(0.965488\pi\)
\(572\) −8.42384 + 8.42384i −0.352219 + 0.352219i
\(573\) 16.0360 + 16.0360i 0.669911 + 0.669911i
\(574\) −18.3307 −0.765108
\(575\) −23.1285 + 6.33034i −0.964524 + 0.263993i
\(576\) −1.00000 −0.0416667
\(577\) −16.9864 16.9864i −0.707152 0.707152i 0.258784 0.965935i \(-0.416678\pi\)
−0.965935 + 0.258784i \(0.916678\pi\)
\(578\) −9.35850 + 9.35850i −0.389262 + 0.389262i
\(579\) 19.6824i 0.817972i
\(580\) 0.251394 + 0.0287952i 0.0104385 + 0.00119565i
\(581\) 5.23396 0.217141
\(582\) −4.66285 + 4.66285i −0.193281 + 0.193281i
\(583\) −9.16514 + 9.16514i −0.379581 + 0.379581i
\(584\) 11.1552i 0.461606i
\(585\) −4.73224 5.95656i −0.195654 0.246273i
\(586\) 15.8135i 0.653249i
\(587\) 1.63768 + 1.63768i 0.0675943 + 0.0675943i 0.740096 0.672501i \(-0.234780\pi\)
−0.672501 + 0.740096i \(0.734780\pi\)
\(588\) −4.22246 + 4.22246i −0.174131 + 0.174131i
\(589\) −2.94194 −0.121221
\(590\) 23.2826 18.4970i 0.958528 0.761511i
\(591\) 5.21479 0.214508
\(592\) 3.74806 3.74806i 0.154044 0.154044i
\(593\) 32.8241 32.8241i 1.34792 1.34792i 0.460010 0.887914i \(-0.347846\pi\)
0.887914 0.460010i \(-0.152154\pi\)
\(594\) −3.50160 −0.143672
\(595\) 1.77829 15.5252i 0.0729026 0.636470i
\(596\) 2.64129i 0.108192i
\(597\) 8.37242 8.37242i 0.342660 0.342660i
\(598\) −14.3559 + 7.75438i −0.587058 + 0.317100i
\(599\) 7.24916i 0.296193i −0.988973 0.148096i \(-0.952685\pi\)
0.988973 0.148096i \(-0.0473146\pi\)
\(600\) 1.13059 4.87050i 0.0461561 0.198837i
\(601\) −36.4196 −1.48559 −0.742793 0.669522i \(-0.766499\pi\)
−0.742793 + 0.669522i \(0.766499\pi\)
\(602\) −9.76452 9.76452i −0.397972 0.397972i
\(603\) 5.33351 + 5.33351i 0.217197 + 0.217197i
\(604\) 21.1977i 0.862524i
\(605\) −2.80176 0.320920i −0.113908 0.0130472i
\(606\) −0.433231 −0.0175988
\(607\) −27.1733 27.1733i −1.10293 1.10293i −0.994055 0.108877i \(-0.965275\pi\)
−0.108877 0.994055i \(-0.534725\pi\)
\(608\) 1.63451 + 1.63451i 0.0662881 + 0.0662881i
\(609\) −0.407562 −0.0165153
\(610\) 1.47328 1.17046i 0.0596515 0.0473907i
\(611\) −3.73100 −0.150940
\(612\) −1.37206 + 1.37206i −0.0554621 + 0.0554621i
\(613\) −16.1170 16.1170i −0.650961 0.650961i 0.302264 0.953224i \(-0.402258\pi\)
−0.953224 + 0.302264i \(0.902258\pi\)
\(614\) 14.1353i 0.570453i
\(615\) −8.91087 + 7.07932i −0.359321 + 0.285466i
\(616\) 12.6113 0.508125
\(617\) 23.2043 23.2043i 0.934171 0.934171i −0.0637926 0.997963i \(-0.520320\pi\)
0.997963 + 0.0637926i \(0.0203196\pi\)
\(618\) −8.99956 8.99956i −0.362016 0.362016i
\(619\) 46.2965 1.86081 0.930407 0.366527i \(-0.119453\pi\)
0.930407 + 0.366527i \(0.119453\pi\)
\(620\) −0.323856 + 2.82739i −0.0130064 + 0.113551i
\(621\) −4.59537 1.37206i −0.184406 0.0550587i
\(622\) 2.25377 + 2.25377i 0.0903678 + 0.0903678i
\(623\) −37.6293 + 37.6293i −1.50759 + 1.50759i
\(624\) 3.40219i 0.136197i
\(625\) 22.4435 + 11.0131i 0.897742 + 0.440523i
\(626\) 27.7938i 1.11086i
\(627\) 5.72339 + 5.72339i 0.228570 + 0.228570i
\(628\) 17.0584 + 17.0584i 0.680703 + 0.680703i
\(629\) 10.2851i 0.410094i
\(630\) −0.916462 + 8.00109i −0.0365127 + 0.318771i
\(631\) 5.61950i 0.223709i −0.993725 0.111854i \(-0.964321\pi\)
0.993725 0.111854i \(-0.0356790\pi\)
\(632\) 1.68285 1.68285i 0.0669403 0.0669403i
\(633\) 17.1835 17.1835i 0.682985 0.682985i
\(634\) 4.79443i 0.190411i
\(635\) 16.7012 + 21.0221i 0.662767 + 0.834237i
\(636\) 3.70159i 0.146777i
\(637\) −14.3656 14.3656i −0.569187 0.569187i
\(638\) 0.280189 + 0.280189i 0.0110928 + 0.0110928i
\(639\) 14.2568i 0.563992i
\(640\) 1.75080 1.39094i 0.0692064 0.0549816i
\(641\) 34.0178i 1.34362i 0.740723 + 0.671810i \(0.234483\pi\)
−0.740723 + 0.671810i \(0.765517\pi\)
\(642\) −13.7709 + 13.7709i −0.543493 + 0.543493i
\(643\) 20.2441 + 20.2441i 0.798350 + 0.798350i 0.982835 0.184486i \(-0.0590619\pi\)
−0.184486 + 0.982835i \(0.559062\pi\)
\(644\) 16.5507 + 4.94159i 0.652187 + 0.194726i
\(645\) −8.51777 0.975644i −0.335387 0.0384159i
\(646\) 4.48528 0.176471
\(647\) −14.0759 14.0759i −0.553381 0.553381i 0.374034 0.927415i \(-0.377974\pi\)
−0.927415 + 0.374034i \(0.877974\pi\)
\(648\) 0.707107 0.707107i 0.0277778 0.0277778i
\(649\) 46.5651 1.82784
\(650\) 16.5704 + 3.84648i 0.649944 + 0.150871i
\(651\) 4.58380i 0.179653i
\(652\) 2.81143 + 2.81143i 0.110104 + 0.110104i
\(653\) −1.54803 + 1.54803i −0.0605792 + 0.0605792i −0.736747 0.676168i \(-0.763639\pi\)
0.676168 + 0.736747i \(0.263639\pi\)
\(654\) 3.09267 0.120933
\(655\) 41.8898 + 4.79815i 1.63677 + 0.187479i
\(656\) −5.08960 −0.198716
\(657\) 7.88793 + 7.88793i 0.307737 + 0.307737i
\(658\) 2.79284 + 2.79284i 0.108876 + 0.108876i
\(659\) −27.5842 −1.07453 −0.537264 0.843414i \(-0.680542\pi\)
−0.537264 + 0.843414i \(0.680542\pi\)
\(660\) 6.13059 4.87050i 0.238633 0.189584i
\(661\) 41.5932i 1.61779i −0.587954 0.808894i \(-0.700066\pi\)
0.587954 0.808894i \(-0.299934\pi\)
\(662\) −1.64705 1.64705i −0.0640146 0.0640146i
\(663\) −4.66800 4.66800i −0.181290 0.181290i
\(664\) 1.45324 0.0563965
\(665\) 14.5758 11.5799i 0.565226 0.449049i
\(666\) 5.30056i 0.205393i
\(667\) 0.257921 + 0.477498i 0.00998676 + 0.0184888i
\(668\) 8.40826 8.40826i 0.325325 0.325325i
\(669\) 2.26616i 0.0876147i
\(670\) −16.7565 1.91932i −0.647359 0.0741499i
\(671\) 2.94657 0.113751
\(672\) −2.54671 + 2.54671i −0.0982415 + 0.0982415i
\(673\) −27.7520 + 27.7520i −1.06976 + 1.06976i −0.0723860 + 0.997377i \(0.523061\pi\)
−0.997377 + 0.0723860i \(0.976939\pi\)
\(674\) 27.1679 1.04647
\(675\) 2.64452 + 4.24341i 0.101787 + 0.163329i
\(676\) −1.42507 −0.0548104
\(677\) 0.758084 0.758084i 0.0291355 0.0291355i −0.692389 0.721524i \(-0.743442\pi\)
0.721524 + 0.692389i \(0.243442\pi\)
\(678\) 2.36212 + 2.36212i 0.0907165 + 0.0907165i
\(679\) 23.7499i 0.911436i
\(680\) 0.493750 4.31064i 0.0189345 0.165305i
\(681\) 21.8017i 0.835442i
\(682\) −3.15125 + 3.15125i −0.120667 + 0.120667i
\(683\) 29.8443 29.8443i 1.14196 1.14196i 0.153870 0.988091i \(-0.450826\pi\)
0.988091 0.153870i \(-0.0491737\pi\)
\(684\) −2.31155 −0.0883842
\(685\) 8.66501 6.88400i 0.331073 0.263024i
\(686\) 3.70436i 0.141433i
\(687\) 9.08206 9.08206i 0.346502 0.346502i
\(688\) −2.71117 2.71117i −0.103362 0.103362i
\(689\) 12.5935 0.479775
\(690\) 9.95402 3.98968i 0.378943 0.151885i
\(691\) 29.2340 1.11211 0.556056 0.831145i \(-0.312314\pi\)
0.556056 + 0.831145i \(0.312314\pi\)
\(692\) −8.59500 8.59500i −0.326733 0.326733i
\(693\) −8.91755 + 8.91755i −0.338750 + 0.338750i
\(694\) 9.19779i 0.349143i
\(695\) 3.68216 32.1467i 0.139672 1.21940i
\(696\) −0.113162 −0.00428938
\(697\) −6.98323 + 6.98323i −0.264509 + 0.264509i
\(698\) −3.02573 + 3.02573i −0.114526 + 0.114526i
\(699\) 17.3809i 0.657404i
\(700\) −9.52447 15.2830i −0.359991 0.577644i
\(701\) 14.5948i 0.551239i −0.961267 0.275619i \(-0.911117\pi\)
0.961267 0.275619i \(-0.0888830\pi\)
\(702\) 2.40571 + 2.40571i 0.0907979 + 0.0907979i
\(703\) 8.66382 8.66382i 0.326762 0.326762i
\(704\) 3.50160 0.131971
\(705\) 2.43624 + 0.279053i 0.0917542 + 0.0105097i
\(706\) 23.8600 0.897983
\(707\) −1.10331 + 1.10331i −0.0414944 + 0.0414944i
\(708\) −9.40328 + 9.40328i −0.353397 + 0.353397i
\(709\) 40.4789 1.52022 0.760109 0.649796i \(-0.225146\pi\)
0.760109 + 0.649796i \(0.225146\pi\)
\(710\) 19.8304 + 24.9608i 0.744220 + 0.936764i
\(711\) 2.37992i 0.0892538i
\(712\) −10.4480 + 10.4480i −0.391554 + 0.391554i
\(713\) −5.37036 + 2.90081i −0.201122 + 0.108636i
\(714\) 6.98846i 0.261537i
\(715\) 16.5704 + 20.8575i 0.619697 + 0.780025i
\(716\) −22.1597 −0.828147
\(717\) 12.8500 + 12.8500i 0.479893 + 0.479893i
\(718\) −17.1714 17.1714i −0.640832 0.640832i
\(719\) 34.5861i 1.28984i 0.764249 + 0.644922i \(0.223110\pi\)
−0.764249 + 0.644922i \(0.776890\pi\)
\(720\) −0.254460 + 2.22154i −0.00948318 + 0.0827920i
\(721\) −45.8386 −1.70712
\(722\) −9.65678 9.65678i −0.359388 0.359388i
\(723\) −8.33583 8.33583i −0.310013 0.310013i
\(724\) −7.71976 −0.286903
\(725\) 0.127939 0.551154i 0.00475155 0.0204693i
\(726\) 1.26118 0.0468067
\(727\) −28.3874 + 28.3874i −1.05283 + 1.05283i −0.0543047 + 0.998524i \(0.517294\pi\)
−0.998524 + 0.0543047i \(0.982706\pi\)
\(728\) −8.66440 8.66440i −0.321124 0.321124i
\(729\) 1.00000i 0.0370370i
\(730\) −24.7818 2.83856i −0.917215 0.105060i
\(731\) −7.43975 −0.275169
\(732\) −0.595025 + 0.595025i −0.0219928 + 0.0219928i
\(733\) 19.5867 + 19.5867i 0.723452 + 0.723452i 0.969307 0.245855i \(-0.0790686\pi\)
−0.245855 + 0.969307i \(0.579069\pi\)
\(734\) −23.4586 −0.865871
\(735\) 8.30593 + 10.4548i 0.306369 + 0.385632i
\(736\) 4.59537 + 1.37206i 0.169388 + 0.0505747i
\(737\) −18.6758 18.6758i −0.687932 0.687932i
\(738\) 3.59889 3.59889i 0.132477 0.132477i
\(739\) 7.22496i 0.265775i 0.991131 + 0.132887i \(0.0424248\pi\)
−0.991131 + 0.132887i \(0.957575\pi\)
\(740\) −7.37275 9.28022i −0.271028 0.341148i
\(741\) 7.86433i 0.288903i
\(742\) −9.42687 9.42687i −0.346071 0.346071i
\(743\) −38.0467 38.0467i −1.39580 1.39580i −0.811641 0.584157i \(-0.801425\pi\)
−0.584157 0.811641i \(-0.698575\pi\)
\(744\) 1.27272i 0.0466600i
\(745\) 5.86774 + 0.672104i 0.214977 + 0.0246240i
\(746\) 0.772089i 0.0282682i
\(747\) −1.02759 + 1.02759i −0.0375976 + 0.0375976i
\(748\) 4.80439 4.80439i 0.175666 0.175666i
\(749\) 70.1409i 2.56289i
\(750\) −10.5323 3.75100i −0.384586 0.136967i
\(751\) 14.7440i 0.538017i −0.963138 0.269009i \(-0.913304\pi\)
0.963138 0.269009i \(-0.0866960\pi\)
\(752\) 0.775445 + 0.775445i 0.0282776 + 0.0282776i
\(753\) 9.08123 + 9.08123i 0.330939 + 0.330939i
\(754\) 0.384998i 0.0140208i
\(755\) 47.0917 + 5.39399i 1.71384 + 0.196307i
\(756\) 3.60159i 0.130989i
\(757\) 5.21529 5.21529i 0.189553 0.189553i −0.605950 0.795503i \(-0.707207\pi\)
0.795503 + 0.605950i \(0.207207\pi\)
\(758\) −8.23160 8.23160i −0.298985 0.298985i
\(759\) 16.0911 + 4.80439i 0.584072 + 0.174388i
\(760\) 4.04705 3.21522i 0.146802 0.116628i
\(761\) 9.25446 0.335474 0.167737 0.985832i \(-0.446354\pi\)
0.167737 + 0.985832i \(0.446354\pi\)
\(762\) −8.49034 8.49034i −0.307573 0.307573i
\(763\) 7.87614 7.87614i 0.285135 0.285135i
\(764\) 22.6783 0.820471
\(765\) 2.69895 + 3.39722i 0.0975807 + 0.122827i
\(766\) 22.1446i 0.800116i
\(767\) −31.9918 31.9918i −1.15516 1.15516i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 13.1928 0.475744 0.237872 0.971296i \(-0.423550\pi\)
0.237872 + 0.971296i \(0.423550\pi\)
\(770\) 3.20908 28.0166i 0.115647 1.00965i
\(771\) −2.01700 −0.0726404
\(772\) −13.9176 13.9176i −0.500904 0.500904i
\(773\) 15.6399 + 15.6399i 0.562527 + 0.562527i 0.930025 0.367497i \(-0.119785\pi\)
−0.367497 + 0.930025i \(0.619785\pi\)
\(774\) 3.83417 0.137816
\(775\) 6.19876 + 1.43892i 0.222666 + 0.0516875i
\(776\) 6.59427i 0.236720i
\(777\) 13.4990 + 13.4990i 0.484274 + 0.484274i
\(778\) −24.3078 24.3078i −0.871478 0.871478i
\(779\) −11.7649 −0.421520
\(780\) −7.55812 0.865724i −0.270624 0.0309979i
\(781\) 49.9217i 1.78634i
\(782\) 8.18765 4.42257i 0.292790 0.158151i
\(783\) 0.0800174 0.0800174i 0.00285959 0.00285959i
\(784\) 5.97146i 0.213267i
\(785\) 42.2366 33.5552i 1.50749 1.19764i
\(786\) −18.8562 −0.672578
\(787\) 21.0340 21.0340i 0.749782 0.749782i −0.224656 0.974438i \(-0.572126\pi\)
0.974438 + 0.224656i \(0.0721258\pi\)
\(788\) 3.68741 3.68741i 0.131359 0.131359i
\(789\) 26.3155 0.936856
\(790\) −3.31031 4.16675i −0.117776 0.148246i
\(791\) 12.0312 0.427782
\(792\) −2.47600 + 2.47600i −0.0879809 + 0.0879809i
\(793\) −2.02439 2.02439i −0.0718882 0.0718882i
\(794\) 5.19917i 0.184512i
\(795\) −8.22323 0.941907i −0.291648 0.0334060i
\(796\) 11.8404i 0.419672i
\(797\) −20.3632 + 20.3632i −0.721300 + 0.721300i −0.968870 0.247570i \(-0.920368\pi\)
0.247570 + 0.968870i \(0.420368\pi\)
\(798\) −5.88684 + 5.88684i −0.208392 + 0.208392i
\(799\) 2.12791 0.0752800
\(800\) −2.64452 4.24341i −0.0934978 0.150027i
\(801\) 14.7757i 0.522072i
\(802\) −6.09077 + 6.09077i −0.215072 + 0.215072i
\(803\) −27.6203 27.6203i −0.974701 0.974701i
\(804\) 7.54272 0.266011
\(805\) 15.1894 35.5106i 0.535357 1.25158i
\(806\) 4.33003 0.152519
\(807\) 9.69584 + 9.69584i 0.341310 + 0.341310i
\(808\) −0.306341 + 0.306341i −0.0107770 + 0.0107770i
\(809\) 21.8823i 0.769340i −0.923054 0.384670i \(-0.874315\pi\)
0.923054 0.384670i \(-0.125685\pi\)
\(810\) −1.39094 1.75080i −0.0488725 0.0615168i
\(811\) 8.99460 0.315843 0.157922 0.987452i \(-0.449521\pi\)
0.157922 + 0.987452i \(0.449521\pi\)
\(812\) −0.288190 + 0.288190i −0.0101135 + 0.0101135i
\(813\) 8.26118 8.26118i 0.289732 0.289732i
\(814\) 18.5604i 0.650543i
\(815\) 6.96111 5.53031i 0.243837 0.193718i
\(816\) 1.94038i 0.0679269i
\(817\) −6.26699 6.26699i −0.219254 0.219254i
\(818\) 7.46533 7.46533i 0.261019 0.261019i
\(819\) 12.2533 0.428166
\(820\) −1.29510 + 11.3068i −0.0452269 + 0.394850i
\(821\) −29.3828 −1.02547 −0.512734 0.858548i \(-0.671367\pi\)
−0.512734 + 0.858548i \(0.671367\pi\)
\(822\) −3.49960 + 3.49960i −0.122062 + 0.122062i
\(823\) 21.1671 21.1671i 0.737838 0.737838i −0.234321 0.972159i \(-0.575287\pi\)
0.972159 + 0.234321i \(0.0752868\pi\)
\(824\) −12.7273 −0.443377
\(825\) −9.26003 14.8587i −0.322393 0.517314i
\(826\) 47.8949i 1.66648i
\(827\) 17.5954 17.5954i 0.611853 0.611853i −0.331576 0.943429i \(-0.607580\pi\)
0.943429 + 0.331576i \(0.107580\pi\)
\(828\) −4.21961 + 2.27923i −0.146642 + 0.0792087i
\(829\) 52.8512i 1.83560i 0.397045 + 0.917799i \(0.370036\pi\)
−0.397045 + 0.917799i \(0.629964\pi\)
\(830\) 0.369791 3.22842i 0.0128356 0.112060i
\(831\) −14.5830 −0.505878
\(832\) −2.40571 2.40571i −0.0834032 0.0834032i
\(833\) 8.19319 + 8.19319i 0.283877 + 0.283877i
\(834\) 14.4705i 0.501071i
\(835\) −16.5397 20.8189i −0.572381 0.720467i
\(836\) 8.09410 0.279940
\(837\) 0.899946 + 0.899946i 0.0311067 + 0.0311067i
\(838\) 22.2769 + 22.2769i 0.769543 + 0.769543i
\(839\) −14.3452 −0.495250 −0.247625 0.968856i \(-0.579650\pi\)
−0.247625 + 0.968856i \(0.579650\pi\)
\(840\) 5.00959 + 6.30566i 0.172847 + 0.217566i
\(841\) 28.9872 0.999558
\(842\) 20.5909 20.5909i 0.709609 0.709609i
\(843\) 20.8042 + 20.8042i 0.716535 + 0.716535i
\(844\) 24.3012i 0.836482i
\(845\) −0.362624 + 3.16586i −0.0124747 + 0.108909i
\(846\) −1.09665 −0.0377034
\(847\) 3.21185 3.21185i 0.110361 0.110361i
\(848\) −2.61742 2.61742i −0.0898825 0.0898825i
\(849\) −25.4617 −0.873842
\(850\) −9.45063 2.19377i −0.324154 0.0752458i
\(851\) 7.27267 24.3581i 0.249304 0.834984i
\(852\) −10.0811 10.0811i −0.345373 0.345373i
\(853\) 15.6696 15.6696i 0.536515 0.536515i −0.385988 0.922504i \(-0.626140\pi\)
0.922504 + 0.385988i \(0.126140\pi\)
\(854\) 3.03071i 0.103709i
\(855\) −0.588197 + 5.13520i −0.0201159 + 0.175620i
\(856\) 19.4750i 0.665641i
\(857\) 18.8824 + 18.8824i 0.645011 + 0.645011i 0.951783 0.306772i \(-0.0992488\pi\)
−0.306772 + 0.951783i \(0.599249\pi\)
\(858\) −8.42384 8.42384i −0.287585 0.287585i
\(859\) 27.2280i 0.929009i 0.885571 + 0.464504i \(0.153768\pi\)
−0.885571 + 0.464504i \(0.846232\pi\)
\(860\) −6.71285 + 5.33309i −0.228906 + 0.181857i
\(861\) 18.3307i 0.624708i
\(862\) −21.0362 + 21.0362i −0.716495 + 0.716495i
\(863\) 23.0409 23.0409i 0.784321 0.784321i −0.196236 0.980557i \(-0.562872\pi\)
0.980557 + 0.196236i \(0.0628718\pi\)
\(864\) 1.00000i 0.0340207i
\(865\) −21.2813 + 16.9071i −0.723584 + 0.574858i
\(866\) 21.5430i 0.732060i
\(867\) −9.35850 9.35850i −0.317831 0.317831i
\(868\) −3.24124 3.24124i −0.110015 0.110015i
\(869\) 8.33350i 0.282695i
\(870\) −0.0287952 + 0.251394i −0.000976248 + 0.00852304i
\(871\) 25.6618i 0.869517i
\(872\) 2.18685 2.18685i 0.0740560 0.0740560i
\(873\) −4.66285 4.66285i −0.157814 0.157814i
\(874\) 10.6224 + 3.17157i 0.359309 + 0.107280i
\(875\) −36.3755 + 17.2701i −1.22972 + 0.583835i
\(876\) 11.1552 0.376900
\(877\) 28.0528 + 28.0528i 0.947275 + 0.947275i 0.998678 0.0514032i \(-0.0163694\pi\)
−0.0514032 + 0.998678i \(0.516369\pi\)
\(878\) −22.7054 + 22.7054i −0.766271 + 0.766271i
\(879\) −15.8135 −0.533376
\(880\) 0.891017 7.77894i 0.0300362 0.262228i
\(881\) 2.20846i 0.0744050i 0.999308 + 0.0372025i \(0.0118447\pi\)
−0.999308 + 0.0372025i \(0.988155\pi\)
\(882\) −4.22246 4.22246i −0.142178 0.142178i
\(883\) 10.1952 10.1952i 0.343097 0.343097i −0.514433 0.857530i \(-0.671998\pi\)
0.857530 + 0.514433i \(0.171998\pi\)
\(884\) −6.60156 −0.222034
\(885\) 18.4970 + 23.2826i 0.621771 + 0.782634i
\(886\) 8.22850 0.276442
\(887\) −31.6815 31.6815i −1.06376 1.06376i −0.997824 0.0659369i \(-0.978996\pi\)
−0.0659369 0.997824i \(-0.521004\pi\)
\(888\) 3.74806 + 3.74806i 0.125777 + 0.125777i
\(889\) −43.2449 −1.45039
\(890\) 20.5520 + 25.8692i 0.688905 + 0.867138i
\(891\) 3.50160i 0.117308i
\(892\) −1.60241 1.60241i −0.0536528 0.0536528i
\(893\) 1.79248 + 1.79248i 0.0599830 + 0.0599830i
\(894\) −2.64129 −0.0883380
\(895\) −5.63877 + 49.2287i −0.188483 + 1.64554i
\(896\) 3.60159i 0.120321i
\(897\) −7.75438 14.3559i −0.258911 0.479331i
\(898\) 6.44336 6.44336i 0.215018 0.215018i
\(899\) 0.144023i 0.00480343i
\(900\) 4.87050 + 1.13059i 0.162350 + 0.0376863i
\(901\) −7.18249 −0.239283
\(902\) −12.6019 + 12.6019i −0.419597 + 0.419597i
\(903\) 9.76452 9.76452i 0.324943 0.324943i
\(904\) 3.34054 0.111105
\(905\) −1.96437 + 17.1498i −0.0652980 + 0.570078i
\(906\) −21.1977 −0.704248
\(907\) 8.04728 8.04728i 0.267205 0.267205i −0.560768 0.827973i \(-0.689494\pi\)
0.827973 + 0.560768i \(0.189494\pi\)
\(908\) −15.4161 15.4161i −0.511601 0.511601i
\(909\) 0.433231i 0.0143694i
\(910\) −21.4531 + 17.0436i −0.711163 + 0.564990i
\(911\) 1.59474i 0.0528363i 0.999651 + 0.0264181i \(0.00841013\pi\)
−0.999651 + 0.0264181i \(0.991590\pi\)
\(912\) −1.63451 + 1.63451i −0.0541240 + 0.0541240i
\(913\) 3.59821 3.59821i 0.119084 0.119084i
\(914\) 2.61402 0.0864641
\(915\) 1.17046 + 1.47328i 0.0386943 + 0.0487053i
\(916\) 12.8440i 0.424377i
\(917\) −48.0212 + 48.0212i −1.58580 + 1.58580i
\(918\) −1.37206 1.37206i −0.0452846 0.0452846i
\(919\) −37.8146 −1.24739 −0.623695 0.781668i \(-0.714369\pi\)
−0.623695 + 0.781668i \(0.714369\pi\)
\(920\) 4.21742 9.85968i 0.139044 0.325064i
\(921\) −14.1353 −0.465773
\(922\) 17.5428 + 17.5428i 0.577743 + 0.577743i
\(923\) 34.2979 34.2979i 1.12893 1.12893i
\(924\) 12.6113i 0.414882i
\(925\) −22.4925 + 14.0174i −0.739548 + 0.460890i
\(926\) −16.8025 −0.552166
\(927\) 8.99956 8.99956i 0.295584 0.295584i
\(928\) −0.0800174 + 0.0800174i −0.00262670 + 0.00262670i
\(929\) 11.2022i 0.367532i 0.982970 + 0.183766i \(0.0588288\pi\)
−0.982970 + 0.183766i \(0.941171\pi\)
\(930\) −2.82739 0.323856i −0.0927138 0.0106196i
\(931\) 13.8033i 0.452385i
\(932\) −12.2901 12.2901i −0.402576 0.402576i
\(933\) −2.25377 + 2.25377i −0.0737850 + 0.0737850i
\(934\) 26.8801 0.879542
\(935\) −9.45063 11.8957i −0.309069 0.389030i
\(936\) 3.40219 0.111204
\(937\) 0.0232922 0.0232922i 0.000760923 0.000760923i −0.706726 0.707487i \(-0.749829\pi\)
0.707487 + 0.706726i \(0.249829\pi\)
\(938\) 19.2091 19.2091i 0.627200 0.627200i
\(939\) 27.7938 0.907016
\(940\) 1.92000 1.52536i 0.0626236 0.0497519i
\(941\) 10.8405i 0.353389i 0.984266 + 0.176694i \(0.0565404\pi\)
−0.984266 + 0.176694i \(0.943460\pi\)
\(942\) −17.0584 + 17.0584i −0.555792 + 0.555792i
\(943\) −21.4762 + 11.6004i −0.699360 + 0.377760i
\(944\) 13.2983i 0.432821i
\(945\) −8.00109 0.916462i −0.260275 0.0298125i
\(946\) −13.4257 −0.436507
\(947\) 3.30449 + 3.30449i 0.107382 + 0.107382i 0.758756 0.651375i \(-0.225807\pi\)
−0.651375 + 0.758756i \(0.725807\pi\)
\(948\) 1.68285 + 1.68285i 0.0546566 + 0.0546566i
\(949\) 37.9522i 1.23198i
\(950\) −6.11292 9.80884i −0.198329 0.318241i
\(951\) −4.79443 −0.155470
\(952\) 4.94159 + 4.94159i 0.160158 + 0.160158i
\(953\) −7.79694 7.79694i −0.252568 0.252568i 0.569455 0.822023i \(-0.307154\pi\)
−0.822023 + 0.569455i \(0.807154\pi\)
\(954\) 3.70159 0.119843
\(955\) 5.77072 50.3807i 0.186736 1.63028i
\(956\) 18.1727 0.587747
\(957\) −0.280189 + 0.280189i −0.00905721 + 0.00905721i
\(958\) −2.89538 2.89538i −0.0935455 0.0935455i
\(959\) 17.8249i 0.575597i
\(960\) 1.39094 + 1.75080i 0.0448923 + 0.0565068i
\(961\) −29.3802 −0.947748
\(962\) −12.7516 + 12.7516i −0.411129 + 0.411129i
\(963\) −13.7709 13.7709i −0.443760 0.443760i
\(964\) −11.7886 −0.379687
\(965\) −34.4599 + 27.3770i −1.10930 + 0.881296i
\(966\) −4.94159 + 16.5507i −0.158993 + 0.532509i
\(967\) −27.5837 27.5837i −0.887033 0.887033i 0.107204 0.994237i \(-0.465810\pi\)
−0.994237 + 0.107204i \(0.965810\pi\)
\(968\) 0.891787 0.891787i 0.0286631 0.0286631i
\(969\) 4.48528i 0.144088i
\(970\) 14.6494 + 1.67798i 0.470365 + 0.0538767i
\(971\) 40.8842i 1.31204i −0.754745 0.656019i \(-0.772239\pi\)
0.754745 0.656019i \(-0.227761\pi\)
\(972\) 0.707107 + 0.707107i 0.0226805 + 0.0226805i
\(973\) 36.8521 + 36.8521i 1.18142 + 1.18142i
\(974\) 31.0475i 0.994826i
\(975\) −3.84648 + 16.5704i −0.123186 + 0.530677i
\(976\) 0.841493i 0.0269355i
\(977\) −0.566178 + 0.566178i −0.0181136 + 0.0181136i −0.716106 0.697992i \(-0.754077\pi\)
0.697992 + 0.716106i \(0.254077\pi\)
\(978\) −2.81143 + 2.81143i −0.0898996 + 0.0898996i
\(979\) 51.7384i 1.65357i
\(980\) 13.2659 + 1.51950i 0.423762 + 0.0485387i
\(981\) 3.09267i 0.0987414i
\(982\) 19.7125 + 19.7125i 0.629051 + 0.629051i
\(983\) −12.9460 12.9460i −0.412913 0.412913i 0.469839 0.882752i \(-0.344312\pi\)
−0.882752 + 0.469839i \(0.844312\pi\)
\(984\) 5.08960i 0.162251i
\(985\) −7.25344 9.13004i −0.231114 0.290907i
\(986\) 0.219577i 0.00699275i
\(987\) −2.79284 + 2.79284i −0.0888970 + 0.0888970i
\(988\) −5.56092 5.56092i −0.176916 0.176916i
\(989\) −17.6194 5.26070i −0.560265 0.167280i
\(990\) 4.87050 + 6.13059i 0.154795 + 0.194843i
\(991\) 57.4401 1.82464 0.912322 0.409473i \(-0.134287\pi\)
0.912322 + 0.409473i \(0.134287\pi\)
\(992\) −0.899946 0.899946i −0.0285733 0.0285733i
\(993\) 1.64705 1.64705i 0.0522677 0.0522677i
\(994\) −51.3473 −1.62864
\(995\) −26.3039 3.01291i −0.833891 0.0955157i
\(996\) 1.45324i 0.0460475i
\(997\) −7.80361 7.80361i −0.247143 0.247143i 0.572654 0.819797i \(-0.305914\pi\)
−0.819797 + 0.572654i \(0.805914\pi\)
\(998\) −2.43227 + 2.43227i −0.0769921 + 0.0769921i
\(999\) −5.30056 −0.167702
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 690.2.j.a.367.12 yes 24
5.3 odd 4 inner 690.2.j.a.643.7 yes 24
23.22 odd 2 inner 690.2.j.a.367.7 24
115.68 even 4 inner 690.2.j.a.643.12 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
690.2.j.a.367.7 24 23.22 odd 2 inner
690.2.j.a.367.12 yes 24 1.1 even 1 trivial
690.2.j.a.643.7 yes 24 5.3 odd 4 inner
690.2.j.a.643.12 yes 24 115.68 even 4 inner