Properties

Label 930.2.i.n.811.3
Level $930$
Weight $2$
Character 930.811
Analytic conductor $7.426$
Analytic rank $0$
Dimension $6$
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] = [930,2,Mod(211,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.211");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.i (of order \(3\), 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: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.3636603.4
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 4x^{3} + 12x^{2} - 16x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 811.3
Root \(1.34370 + 1.48137i\) of defining polynomial
Character \(\chi\) \(=\) 930.811
Dual form 930.2.i.n.211.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.954758 - 1.65369i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.954758 - 1.65369i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(3.18740 + 5.52074i) q^{11} +(0.500000 - 0.866025i) q^{12} +(2.90952 + 5.03943i) q^{13} +(-0.954758 + 1.65369i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(-3.45476 + 5.98382i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.22212 + 2.11677i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.954758 - 1.65369i) q^{21} +(-3.18740 - 5.52074i) q^{22} -0.909516 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.90952 - 5.03943i) q^{26} -1.00000 q^{27} +(0.954758 - 1.65369i) q^{28} +5.46528 q^{29} +1.00000 q^{30} +(4.42004 - 3.38574i) q^{31} -1.00000 q^{32} +6.37480 q^{33} +(3.45476 - 5.98382i) q^{34} -1.90952 q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.45476 - 7.71587i) q^{37} +(1.22212 - 2.11677i) q^{38} +5.81903 q^{39} +(0.500000 + 0.866025i) q^{40} +(3.59692 + 6.23004i) q^{41} +(0.954758 + 1.65369i) q^{42} +(0.232642 - 0.402947i) q^{43} +(3.18740 + 5.52074i) q^{44} +(-0.500000 + 0.866025i) q^{45} +0.909516 q^{46} -8.72855 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.67687 + 2.90443i) q^{49} +(0.500000 - 0.866025i) q^{50} +(3.45476 + 5.98382i) q^{51} +(2.90952 + 5.03943i) q^{52} +(-3.64216 - 6.30840i) q^{53} +1.00000 q^{54} +(3.18740 - 5.52074i) q^{55} +(-0.954758 + 1.65369i) q^{56} +(1.22212 + 2.11677i) q^{57} -5.46528 q^{58} +(2.86427 - 4.96107i) q^{59} -1.00000 q^{60} -4.44423 q^{61} +(-4.42004 + 3.38574i) q^{62} -1.90952 q^{63} +1.00000 q^{64} +(2.90952 - 5.03943i) q^{65} -6.37480 q^{66} +(-4.45476 - 7.71587i) q^{67} +(-3.45476 + 5.98382i) q^{68} +(-0.454758 + 0.787664i) q^{69} +1.90952 q^{70} +(4.90952 + 8.50353i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 + 1.73205i) q^{73} +(-4.45476 + 7.71587i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-1.22212 + 2.11677i) q^{76} +12.1728 q^{77} -5.81903 q^{78} +(0.232642 - 0.402947i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.59692 - 6.23004i) q^{82} +(6.32956 + 10.9631i) q^{83} +(-0.954758 - 1.65369i) q^{84} +6.90952 q^{85} +(-0.232642 + 0.402947i) q^{86} +(2.73264 - 4.73307i) q^{87} +(-3.18740 - 5.52074i) q^{88} -15.8190 q^{89} +(0.500000 - 0.866025i) q^{90} +11.1115 q^{91} -0.909516 q^{92} +(-0.722116 - 5.52074i) q^{93} +8.72855 q^{94} +2.44423 q^{95} +(-0.500000 + 0.866025i) q^{96} +18.1728 q^{97} +(-1.67687 - 2.90443i) q^{98} +(3.18740 - 5.52074i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{4} - 3 q^{5} - 3 q^{6} - 4 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 5 q^{11} + 3 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} + 6 q^{16} - 11 q^{17} + 3 q^{18} - 2 q^{19} - 3 q^{20} + 4 q^{21} - 5 q^{22} + 14 q^{23} - 3 q^{24} - 3 q^{25} + 2 q^{26} - 6 q^{27} - 4 q^{28} + 24 q^{29} + 6 q^{30} + 8 q^{31} - 6 q^{32} + 10 q^{33} + 11 q^{34} + 8 q^{35} - 3 q^{36} + 17 q^{37} + 2 q^{38} - 4 q^{39} + 3 q^{40} - 12 q^{41} - 4 q^{42} - 3 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} + 6 q^{47} + 3 q^{48} - 5 q^{49} + 3 q^{50} + 11 q^{51} - 2 q^{52} + 2 q^{53} + 6 q^{54} + 5 q^{55} + 4 q^{56} + 2 q^{57} - 24 q^{58} - 12 q^{59} - 6 q^{60} - 16 q^{61} - 8 q^{62} + 8 q^{63} + 6 q^{64} - 2 q^{65} - 10 q^{66} - 17 q^{67} - 11 q^{68} + 7 q^{69} - 8 q^{70} + 10 q^{71} + 3 q^{72} + 6 q^{73} - 17 q^{74} + 3 q^{75} - 2 q^{76} + 4 q^{77} + 4 q^{78} - 3 q^{79} - 3 q^{80} - 3 q^{81} + 12 q^{82} + 4 q^{84} + 22 q^{85} + 3 q^{86} + 12 q^{87} - 5 q^{88} - 56 q^{89} + 3 q^{90} + 88 q^{91} + 14 q^{92} + q^{93} - 6 q^{94} + 4 q^{95} - 3 q^{96} + 40 q^{97} + 5 q^{98} + 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 1.00000 0.500000
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 0.954758 1.65369i 0.360865 0.625036i −0.627239 0.778827i \(-0.715815\pi\)
0.988103 + 0.153791i \(0.0491483\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 3.18740 + 5.52074i 0.961037 + 1.66457i 0.719905 + 0.694073i \(0.244185\pi\)
0.241132 + 0.970492i \(0.422481\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 2.90952 + 5.03943i 0.806955 + 1.39769i 0.914964 + 0.403536i \(0.132219\pi\)
−0.108009 + 0.994150i \(0.534448\pi\)
\(14\) −0.954758 + 1.65369i −0.255170 + 0.441967i
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −3.45476 + 5.98382i −0.837902 + 1.45129i 0.0537438 + 0.998555i \(0.482885\pi\)
−0.891646 + 0.452734i \(0.850449\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −1.22212 + 2.11677i −0.280373 + 0.485620i −0.971477 0.237136i \(-0.923791\pi\)
0.691104 + 0.722756i \(0.257125\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) −0.954758 1.65369i −0.208345 0.360865i
\(22\) −3.18740 5.52074i −0.679556 1.17703i
\(23\) −0.909516 −0.189647 −0.0948236 0.995494i \(-0.530229\pi\)
−0.0948236 + 0.995494i \(0.530229\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −2.90952 5.03943i −0.570603 0.988313i
\(27\) −1.00000 −0.192450
\(28\) 0.954758 1.65369i 0.180432 0.312518i
\(29\) 5.46528 1.01488 0.507439 0.861688i \(-0.330592\pi\)
0.507439 + 0.861688i \(0.330592\pi\)
\(30\) 1.00000 0.182574
\(31\) 4.42004 3.38574i 0.793863 0.608097i
\(32\) −1.00000 −0.176777
\(33\) 6.37480 1.10971
\(34\) 3.45476 5.98382i 0.592486 1.02622i
\(35\) −1.90952 −0.322767
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 4.45476 7.71587i 0.732358 1.26848i −0.223515 0.974700i \(-0.571753\pi\)
0.955873 0.293780i \(-0.0949134\pi\)
\(38\) 1.22212 2.11677i 0.198253 0.343385i
\(39\) 5.81903 0.931791
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 3.59692 + 6.23004i 0.561744 + 0.972969i 0.997344 + 0.0728288i \(0.0232027\pi\)
−0.435601 + 0.900140i \(0.643464\pi\)
\(42\) 0.954758 + 1.65369i 0.147322 + 0.255170i
\(43\) 0.232642 0.402947i 0.0354775 0.0614488i −0.847741 0.530410i \(-0.822038\pi\)
0.883219 + 0.468961i \(0.155371\pi\)
\(44\) 3.18740 + 5.52074i 0.480519 + 0.832283i
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) 0.909516 0.134101
\(47\) −8.72855 −1.27319 −0.636595 0.771198i \(-0.719658\pi\)
−0.636595 + 0.771198i \(0.719658\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 1.67687 + 2.90443i 0.239553 + 0.414919i
\(50\) 0.500000 0.866025i 0.0707107 0.122474i
\(51\) 3.45476 + 5.98382i 0.483763 + 0.837902i
\(52\) 2.90952 + 5.03943i 0.403477 + 0.698843i
\(53\) −3.64216 6.30840i −0.500289 0.866526i −1.00000 0.000333526i \(-0.999894\pi\)
0.499711 0.866192i \(-0.333439\pi\)
\(54\) 1.00000 0.136083
\(55\) 3.18740 5.52074i 0.429789 0.744416i
\(56\) −0.954758 + 1.65369i −0.127585 + 0.220984i
\(57\) 1.22212 + 2.11677i 0.161873 + 0.280373i
\(58\) −5.46528 −0.717627
\(59\) 2.86427 4.96107i 0.372897 0.645876i −0.617113 0.786874i \(-0.711698\pi\)
0.990010 + 0.140998i \(0.0450312\pi\)
\(60\) −1.00000 −0.129099
\(61\) −4.44423 −0.569026 −0.284513 0.958672i \(-0.591832\pi\)
−0.284513 + 0.958672i \(0.591832\pi\)
\(62\) −4.42004 + 3.38574i −0.561346 + 0.429989i
\(63\) −1.90952 −0.240576
\(64\) 1.00000 0.125000
\(65\) 2.90952 5.03943i 0.360881 0.625064i
\(66\) −6.37480 −0.784684
\(67\) −4.45476 7.71587i −0.544235 0.942643i −0.998655 0.0518553i \(-0.983487\pi\)
0.454419 0.890788i \(-0.349847\pi\)
\(68\) −3.45476 + 5.98382i −0.418951 + 0.725644i
\(69\) −0.454758 + 0.787664i −0.0547464 + 0.0948236i
\(70\) 1.90952 0.228231
\(71\) 4.90952 + 8.50353i 0.582652 + 1.00918i 0.995164 + 0.0982310i \(0.0313184\pi\)
−0.412511 + 0.910952i \(0.635348\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) −4.45476 + 7.71587i −0.517855 + 0.896951i
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) −1.22212 + 2.11677i −0.140186 + 0.242810i
\(77\) 12.1728 1.38722
\(78\) −5.81903 −0.658876
\(79\) 0.232642 0.402947i 0.0261742 0.0453351i −0.852642 0.522496i \(-0.825001\pi\)
0.878816 + 0.477161i \(0.158334\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −3.59692 6.23004i −0.397213 0.687993i
\(83\) 6.32956 + 10.9631i 0.694759 + 1.20336i 0.970262 + 0.242058i \(0.0778224\pi\)
−0.275503 + 0.961300i \(0.588844\pi\)
\(84\) −0.954758 1.65369i −0.104173 0.180432i
\(85\) 6.90952 0.749442
\(86\) −0.232642 + 0.402947i −0.0250864 + 0.0434509i
\(87\) 2.73264 4.73307i 0.292970 0.507439i
\(88\) −3.18740 5.52074i −0.339778 0.588513i
\(89\) −15.8190 −1.67681 −0.838407 0.545045i \(-0.816513\pi\)
−0.838407 + 0.545045i \(0.816513\pi\)
\(90\) 0.500000 0.866025i 0.0527046 0.0912871i
\(91\) 11.1115 1.16481
\(92\) −0.909516 −0.0948236
\(93\) −0.722116 5.52074i −0.0748800 0.572474i
\(94\) 8.72855 0.900281
\(95\) 2.44423 0.250773
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 18.1728 1.84517 0.922583 0.385798i \(-0.126074\pi\)
0.922583 + 0.385798i \(0.126074\pi\)
\(98\) −1.67687 2.90443i −0.169390 0.293392i
\(99\) 3.18740 5.52074i 0.320346 0.554855i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 1.93057 0.192099 0.0960493 0.995377i \(-0.469379\pi\)
0.0960493 + 0.995377i \(0.469379\pi\)
\(102\) −3.45476 5.98382i −0.342072 0.592486i
\(103\) 1.86427 + 3.22902i 0.183692 + 0.318165i 0.943135 0.332410i \(-0.107862\pi\)
−0.759443 + 0.650574i \(0.774528\pi\)
\(104\) −2.90952 5.03943i −0.285302 0.494157i
\(105\) −0.954758 + 1.65369i −0.0931748 + 0.161384i
\(106\) 3.64216 + 6.30840i 0.353758 + 0.612726i
\(107\) 0.954758 1.65369i 0.0922999 0.159868i −0.816179 0.577800i \(-0.803911\pi\)
0.908479 + 0.417932i \(0.137245\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −2.44423 −0.234115 −0.117058 0.993125i \(-0.537346\pi\)
−0.117058 + 0.993125i \(0.537346\pi\)
\(110\) −3.18740 + 5.52074i −0.303907 + 0.526382i
\(111\) −4.45476 7.71587i −0.422827 0.732358i
\(112\) 0.954758 1.65369i 0.0902161 0.156259i
\(113\) −4.67687 8.10058i −0.439963 0.762039i 0.557723 0.830027i \(-0.311675\pi\)
−0.997686 + 0.0679884i \(0.978342\pi\)
\(114\) −1.22212 2.11677i −0.114462 0.198253i
\(115\) 0.454758 + 0.787664i 0.0424064 + 0.0734500i
\(116\) 5.46528 0.507439
\(117\) 2.90952 5.03943i 0.268985 0.465895i
\(118\) −2.86427 + 4.96107i −0.263678 + 0.456703i
\(119\) 6.59692 + 11.4262i 0.604738 + 1.04744i
\(120\) 1.00000 0.0912871
\(121\) −14.8190 + 25.6673i −1.34718 + 2.33339i
\(122\) 4.44423 0.402362
\(123\) 7.19383 0.648646
\(124\) 4.42004 3.38574i 0.396931 0.304048i
\(125\) 1.00000 0.0894427
\(126\) 1.90952 0.170113
\(127\) 7.32956 12.6952i 0.650393 1.12651i −0.332635 0.943056i \(-0.607938\pi\)
0.983028 0.183458i \(-0.0587291\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.232642 0.402947i −0.0204829 0.0354775i
\(130\) −2.90952 + 5.03943i −0.255181 + 0.441987i
\(131\) −1.14216 + 1.97827i −0.0997908 + 0.172843i −0.911598 0.411083i \(-0.865151\pi\)
0.811807 + 0.583926i \(0.198484\pi\)
\(132\) 6.37480 0.554855
\(133\) 2.33365 + 4.04200i 0.202353 + 0.350486i
\(134\) 4.45476 + 7.71587i 0.384832 + 0.666549i
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) 3.45476 5.98382i 0.296243 0.513108i
\(137\) −9.73907 16.8686i −0.832065 1.44118i −0.896398 0.443251i \(-0.853825\pi\)
0.0643326 0.997929i \(-0.479508\pi\)
\(138\) 0.454758 0.787664i 0.0387116 0.0670504i
\(139\) 11.3748 0.964798 0.482399 0.875952i \(-0.339766\pi\)
0.482399 + 0.875952i \(0.339766\pi\)
\(140\) −1.90952 −0.161384
\(141\) −4.36427 + 7.55914i −0.367538 + 0.636595i
\(142\) −4.90952 8.50353i −0.411997 0.713600i
\(143\) −18.5476 + 32.1254i −1.55103 + 2.68646i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −2.73264 4.73307i −0.226934 0.393060i
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) 3.35375 0.276613
\(148\) 4.45476 7.71587i 0.366179 0.634240i
\(149\) 3.35784 5.81595i 0.275085 0.476461i −0.695071 0.718941i \(-0.744627\pi\)
0.970157 + 0.242479i \(0.0779606\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) −4.55577 −0.370743 −0.185372 0.982669i \(-0.559349\pi\)
−0.185372 + 0.982669i \(0.559349\pi\)
\(152\) 1.22212 2.11677i 0.0991267 0.171693i
\(153\) 6.90952 0.558601
\(154\) −12.1728 −0.980911
\(155\) −5.14216 2.13500i −0.413028 0.171487i
\(156\) 5.81903 0.465895
\(157\) −17.9434 −1.43204 −0.716021 0.698079i \(-0.754038\pi\)
−0.716021 + 0.698079i \(0.754038\pi\)
\(158\) −0.232642 + 0.402947i −0.0185080 + 0.0320567i
\(159\) −7.28432 −0.577684
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) −0.868368 + 1.50406i −0.0684370 + 0.118536i
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) 5.79798 0.454133 0.227066 0.973879i \(-0.427087\pi\)
0.227066 + 0.973879i \(0.427087\pi\)
\(164\) 3.59692 + 6.23004i 0.280872 + 0.486484i
\(165\) −3.18740 5.52074i −0.248139 0.429789i
\(166\) −6.32956 10.9631i −0.491269 0.850903i
\(167\) 8.06220 13.9641i 0.623872 1.08058i −0.364886 0.931052i \(-0.618892\pi\)
0.988758 0.149525i \(-0.0477745\pi\)
\(168\) 0.954758 + 1.65369i 0.0736612 + 0.127585i
\(169\) −10.4306 + 18.0663i −0.802351 + 1.38971i
\(170\) −6.90952 −0.529936
\(171\) 2.44423 0.186915
\(172\) 0.232642 0.402947i 0.0177388 0.0307244i
\(173\) 0.732642 + 1.26897i 0.0557017 + 0.0964782i 0.892532 0.450985i \(-0.148927\pi\)
−0.836830 + 0.547463i \(0.815594\pi\)
\(174\) −2.73264 + 4.73307i −0.207161 + 0.358813i
\(175\) 0.954758 + 1.65369i 0.0721729 + 0.125007i
\(176\) 3.18740 + 5.52074i 0.240259 + 0.416141i
\(177\) −2.86427 4.96107i −0.215292 0.372897i
\(178\) 15.8190 1.18569
\(179\) 8.00643 13.8675i 0.598429 1.03651i −0.394624 0.918843i \(-0.629125\pi\)
0.993053 0.117667i \(-0.0375414\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) 1.46528 + 2.53794i 0.108914 + 0.188644i 0.915330 0.402704i \(-0.131929\pi\)
−0.806417 + 0.591348i \(0.798596\pi\)
\(182\) −11.1115 −0.823642
\(183\) −2.22212 + 3.84882i −0.164264 + 0.284513i
\(184\) 0.909516 0.0670504
\(185\) −8.90952 −0.655041
\(186\) 0.722116 + 5.52074i 0.0529481 + 0.404800i
\(187\) −44.0468 −3.22102
\(188\) −8.72855 −0.636595
\(189\) −0.954758 + 1.65369i −0.0694484 + 0.120288i
\(190\) −2.44423 −0.177323
\(191\) 0.222116 + 0.384717i 0.0160718 + 0.0278371i 0.873949 0.486017i \(-0.161551\pi\)
−0.857878 + 0.513854i \(0.828217\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −8.73264 + 15.1254i −0.628589 + 1.08875i 0.359246 + 0.933243i \(0.383034\pi\)
−0.987835 + 0.155506i \(0.950299\pi\)
\(194\) −18.1728 −1.30473
\(195\) −2.90952 5.03943i −0.208355 0.360881i
\(196\) 1.67687 + 2.90443i 0.119777 + 0.207459i
\(197\) 5.28432 + 9.15270i 0.376492 + 0.652103i 0.990549 0.137158i \(-0.0437969\pi\)
−0.614057 + 0.789261i \(0.710464\pi\)
\(198\) −3.18740 + 5.52074i −0.226519 + 0.392342i
\(199\) 4.32956 + 7.49901i 0.306914 + 0.531591i 0.977686 0.210073i \(-0.0673702\pi\)
−0.670772 + 0.741664i \(0.734037\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) −8.90952 −0.628429
\(202\) −1.93057 −0.135834
\(203\) 5.21802 9.03788i 0.366233 0.634335i
\(204\) 3.45476 + 5.98382i 0.241881 + 0.418951i
\(205\) 3.59692 6.23004i 0.251219 0.435125i
\(206\) −1.86427 3.22902i −0.129890 0.224976i
\(207\) 0.454758 + 0.787664i 0.0316079 + 0.0547464i
\(208\) 2.90952 + 5.03943i 0.201739 + 0.349422i
\(209\) −15.5815 −1.07779
\(210\) 0.954758 1.65369i 0.0658846 0.114115i
\(211\) 5.22212 9.04497i 0.359505 0.622681i −0.628373 0.777912i \(-0.716279\pi\)
0.987878 + 0.155231i \(0.0496121\pi\)
\(212\) −3.64216 6.30840i −0.250144 0.433263i
\(213\) 9.81903 0.672789
\(214\) −0.954758 + 1.65369i −0.0652659 + 0.113044i
\(215\) −0.465283 −0.0317320
\(216\) 1.00000 0.0680414
\(217\) −1.37889 10.5419i −0.0936053 0.715633i
\(218\) 2.44423 0.165544
\(219\) 2.00000 0.135147
\(220\) 3.18740 5.52074i 0.214894 0.372208i
\(221\) −40.2067 −2.70459
\(222\) 4.45476 + 7.71587i 0.298984 + 0.517855i
\(223\) 7.42004 12.8519i 0.496883 0.860626i −0.503111 0.864222i \(-0.667811\pi\)
0.999994 + 0.00359581i \(0.00114458\pi\)
\(224\) −0.954758 + 1.65369i −0.0637925 + 0.110492i
\(225\) 1.00000 0.0666667
\(226\) 4.67687 + 8.10058i 0.311101 + 0.538843i
\(227\) −1.48947 2.57985i −0.0988599 0.171230i 0.812353 0.583166i \(-0.198186\pi\)
−0.911213 + 0.411935i \(0.864853\pi\)
\(228\) 1.22212 + 2.11677i 0.0809366 + 0.140186i
\(229\) 3.75683 6.50703i 0.248259 0.429996i −0.714784 0.699345i \(-0.753475\pi\)
0.963043 + 0.269349i \(0.0868084\pi\)
\(230\) −0.454758 0.787664i −0.0299859 0.0519370i
\(231\) 6.08639 10.5419i 0.400455 0.693609i
\(232\) −5.46528 −0.358813
\(233\) 12.9095 0.845731 0.422865 0.906193i \(-0.361024\pi\)
0.422865 + 0.906193i \(0.361024\pi\)
\(234\) −2.90952 + 5.03943i −0.190201 + 0.329438i
\(235\) 4.36427 + 7.55914i 0.284694 + 0.493104i
\(236\) 2.86427 4.96107i 0.186448 0.322938i
\(237\) −0.232642 0.402947i −0.0151117 0.0261742i
\(238\) −6.59692 11.4262i −0.427615 0.740650i
\(239\) 6.46528 + 11.1982i 0.418204 + 0.724351i 0.995759 0.0920008i \(-0.0293262\pi\)
−0.577555 + 0.816352i \(0.695993\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 5.35784 9.28006i 0.345129 0.597781i −0.640248 0.768168i \(-0.721169\pi\)
0.985377 + 0.170387i \(0.0545018\pi\)
\(242\) 14.8190 25.6673i 0.952603 1.64996i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −4.44423 −0.284513
\(245\) 1.67687 2.90443i 0.107132 0.185557i
\(246\) −7.19383 −0.458662
\(247\) −14.2231 −0.904992
\(248\) −4.42004 + 3.38574i −0.280673 + 0.214995i
\(249\) 12.6591 0.802239
\(250\) −1.00000 −0.0632456
\(251\) −1.76736 + 3.06115i −0.111555 + 0.193218i −0.916397 0.400270i \(-0.868916\pi\)
0.804843 + 0.593488i \(0.202250\pi\)
\(252\) −1.90952 −0.120288
\(253\) −2.89899 5.02120i −0.182258 0.315680i
\(254\) −7.32956 + 12.6952i −0.459897 + 0.796566i
\(255\) 3.45476 5.98382i 0.216345 0.374721i
\(256\) 1.00000 0.0625000
\(257\) −12.2948 21.2953i −0.766931 1.32836i −0.939220 0.343317i \(-0.888449\pi\)
0.172289 0.985047i \(-0.444884\pi\)
\(258\) 0.232642 + 0.402947i 0.0144836 + 0.0250864i
\(259\) −8.50643 14.7336i −0.528564 0.915500i
\(260\) 2.90952 5.03943i 0.180441 0.312532i
\(261\) −2.73264 4.73307i −0.169146 0.292970i
\(262\) 1.14216 1.97827i 0.0705627 0.122218i
\(263\) −1.53472 −0.0946347 −0.0473173 0.998880i \(-0.515067\pi\)
−0.0473173 + 0.998880i \(0.515067\pi\)
\(264\) −6.37480 −0.392342
\(265\) −3.64216 + 6.30840i −0.223736 + 0.387522i
\(266\) −2.33365 4.04200i −0.143085 0.247831i
\(267\) −7.90952 + 13.6997i −0.484055 + 0.838407i
\(268\) −4.45476 7.71587i −0.272118 0.471322i
\(269\) 7.96119 + 13.7892i 0.485402 + 0.840741i 0.999859 0.0167747i \(-0.00533982\pi\)
−0.514457 + 0.857516i \(0.672006\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) 16.4781 1.00098 0.500488 0.865743i \(-0.333154\pi\)
0.500488 + 0.865743i \(0.333154\pi\)
\(272\) −3.45476 + 5.98382i −0.209475 + 0.362822i
\(273\) 5.55577 9.62287i 0.336250 0.582403i
\(274\) 9.73907 + 16.8686i 0.588359 + 1.01907i
\(275\) −6.37480 −0.384415
\(276\) −0.454758 + 0.787664i −0.0273732 + 0.0474118i
\(277\) −25.6591 −1.54171 −0.770853 0.637013i \(-0.780170\pi\)
−0.770853 + 0.637013i \(0.780170\pi\)
\(278\) −11.3748 −0.682215
\(279\) −5.14216 2.13500i −0.307853 0.127819i
\(280\) 1.90952 0.114115
\(281\) −31.1373 −1.85749 −0.928747 0.370715i \(-0.879113\pi\)
−0.928747 + 0.370715i \(0.879113\pi\)
\(282\) 4.36427 7.55914i 0.259889 0.450140i
\(283\) −16.9918 −1.01006 −0.505029 0.863102i \(-0.668518\pi\)
−0.505029 + 0.863102i \(0.668518\pi\)
\(284\) 4.90952 + 8.50353i 0.291326 + 0.504592i
\(285\) 1.22212 2.11677i 0.0723919 0.125386i
\(286\) 18.5476 32.1254i 1.09674 1.89961i
\(287\) 13.7367 0.810854
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) −15.3707 26.6228i −0.904159 1.56605i
\(290\) 2.73264 + 4.73307i 0.160466 + 0.277936i
\(291\) 9.08639 15.7381i 0.532654 0.922583i
\(292\) 1.00000 + 1.73205i 0.0585206 + 0.101361i
\(293\) −13.4612 + 23.3155i −0.786411 + 1.36210i 0.141741 + 0.989904i \(0.454730\pi\)
−0.928152 + 0.372200i \(0.878603\pi\)
\(294\) −3.35375 −0.195595
\(295\) −5.72855 −0.333529
\(296\) −4.45476 + 7.71587i −0.258928 + 0.448476i
\(297\) −3.18740 5.52074i −0.184952 0.320346i
\(298\) −3.35784 + 5.81595i −0.194515 + 0.336909i
\(299\) −2.64625 4.58344i −0.153037 0.265067i
\(300\) 0.500000 + 0.866025i 0.0288675 + 0.0500000i
\(301\) −0.444233 0.769434i −0.0256052 0.0443494i
\(302\) 4.55577 0.262155
\(303\) 0.965283 1.67192i 0.0554541 0.0960493i
\(304\) −1.22212 + 2.11677i −0.0700932 + 0.121405i
\(305\) 2.22212 + 3.84882i 0.127238 + 0.220383i
\(306\) −6.90952 −0.394991
\(307\) −9.97171 + 17.2715i −0.569116 + 0.985738i 0.427538 + 0.903997i \(0.359381\pi\)
−0.996654 + 0.0817401i \(0.973952\pi\)
\(308\) 12.1728 0.693609
\(309\) 3.72855 0.212110
\(310\) 5.14216 + 2.13500i 0.292055 + 0.121260i
\(311\) 24.5686 1.39316 0.696580 0.717480i \(-0.254704\pi\)
0.696580 + 0.717480i \(0.254704\pi\)
\(312\) −5.81903 −0.329438
\(313\) −11.9265 + 20.6573i −0.674124 + 1.16762i 0.302600 + 0.953118i \(0.402145\pi\)
−0.976724 + 0.214500i \(0.931188\pi\)
\(314\) 17.9434 1.01261
\(315\) 0.954758 + 1.65369i 0.0537945 + 0.0931748i
\(316\) 0.232642 0.402947i 0.0130871 0.0226675i
\(317\) 7.55167 13.0799i 0.424144 0.734639i −0.572196 0.820117i \(-0.693908\pi\)
0.996340 + 0.0854776i \(0.0272416\pi\)
\(318\) 7.28432 0.408484
\(319\) 17.4200 + 30.1724i 0.975335 + 1.68933i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) −0.954758 1.65369i −0.0532894 0.0922999i
\(322\) 0.868368 1.50406i 0.0483922 0.0838178i
\(323\) −8.44423 14.6258i −0.469850 0.813804i
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −5.81903 −0.322782
\(326\) −5.79798 −0.321121
\(327\) −1.22212 + 2.11677i −0.0675832 + 0.117058i
\(328\) −3.59692 6.23004i −0.198606 0.343996i
\(329\) −8.33365 + 14.4343i −0.459449 + 0.795789i
\(330\) 3.18740 + 5.52074i 0.175461 + 0.303907i
\(331\) −0.0621987 0.107731i −0.00341875 0.00592145i 0.864311 0.502958i \(-0.167755\pi\)
−0.867730 + 0.497036i \(0.834422\pi\)
\(332\) 6.32956 + 10.9631i 0.347380 + 0.601679i
\(333\) −8.90952 −0.488238
\(334\) −8.06220 + 13.9641i −0.441144 + 0.764084i
\(335\) −4.45476 + 7.71587i −0.243389 + 0.421563i
\(336\) −0.954758 1.65369i −0.0520863 0.0902161i
\(337\) −11.4653 −0.624554 −0.312277 0.949991i \(-0.601092\pi\)
−0.312277 + 0.949991i \(0.601092\pi\)
\(338\) 10.4306 18.0663i 0.567348 0.982676i
\(339\) −9.35375 −0.508026
\(340\) 6.90952 0.374721
\(341\) 32.7802 + 13.6102i 1.77515 + 0.737033i
\(342\) −2.44423 −0.132169
\(343\) 19.7706 1.06751
\(344\) −0.232642 + 0.402947i −0.0125432 + 0.0217254i
\(345\) 0.909516 0.0489667
\(346\) −0.732642 1.26897i −0.0393871 0.0682204i
\(347\) −2.48947 + 4.31190i −0.133642 + 0.231475i −0.925078 0.379777i \(-0.876001\pi\)
0.791436 + 0.611252i \(0.209334\pi\)
\(348\) 2.73264 4.73307i 0.146485 0.253719i
\(349\) −26.1244 −1.39841 −0.699203 0.714923i \(-0.746462\pi\)
−0.699203 + 0.714923i \(0.746462\pi\)
\(350\) −0.954758 1.65369i −0.0510340 0.0883934i
\(351\) −2.90952 5.03943i −0.155298 0.268985i
\(352\) −3.18740 5.52074i −0.169889 0.294256i
\(353\) 14.4054 24.9509i 0.766723 1.32800i −0.172607 0.984991i \(-0.555219\pi\)
0.939331 0.343013i \(-0.111447\pi\)
\(354\) 2.86427 + 4.96107i 0.152234 + 0.263678i
\(355\) 4.90952 8.50353i 0.260570 0.451321i
\(356\) −15.8190 −0.838407
\(357\) 13.1938 0.698292
\(358\) −8.00643 + 13.8675i −0.423153 + 0.732923i
\(359\) −3.31260 5.73759i −0.174832 0.302819i 0.765271 0.643708i \(-0.222605\pi\)
−0.940103 + 0.340890i \(0.889272\pi\)
\(360\) 0.500000 0.866025i 0.0263523 0.0456435i
\(361\) 6.51286 + 11.2806i 0.342782 + 0.593716i
\(362\) −1.46528 2.53794i −0.0770136 0.133391i
\(363\) 14.8190 + 25.6673i 0.777797 + 1.34718i
\(364\) 11.1115 0.582403
\(365\) 1.00000 1.73205i 0.0523424 0.0906597i
\(366\) 2.22212 3.84882i 0.116152 0.201181i
\(367\) 12.0000 + 20.7846i 0.626395 + 1.08495i 0.988269 + 0.152721i \(0.0488036\pi\)
−0.361874 + 0.932227i \(0.617863\pi\)
\(368\) −0.909516 −0.0474118
\(369\) 3.59692 6.23004i 0.187248 0.324323i
\(370\) 8.90952 0.463184
\(371\) −13.9095 −0.722146
\(372\) −0.722116 5.52074i −0.0374400 0.286237i
\(373\) −27.4360 −1.42058 −0.710292 0.703907i \(-0.751437\pi\)
−0.710292 + 0.703907i \(0.751437\pi\)
\(374\) 44.0468 2.27760
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) 8.72855 0.450140
\(377\) 15.9013 + 27.5419i 0.818960 + 1.41848i
\(378\) 0.954758 1.65369i 0.0491075 0.0850566i
\(379\) −9.26326 + 16.0444i −0.475822 + 0.824148i −0.999616 0.0276969i \(-0.991183\pi\)
0.523794 + 0.851845i \(0.324516\pi\)
\(380\) 2.44423 0.125386
\(381\) −7.32956 12.6952i −0.375505 0.650393i
\(382\) −0.222116 0.384717i −0.0113645 0.0196838i
\(383\) −1.36427 2.36299i −0.0697111 0.120743i 0.829063 0.559155i \(-0.188874\pi\)
−0.898774 + 0.438412i \(0.855541\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) −6.08639 10.5419i −0.310191 0.537267i
\(386\) 8.73264 15.1254i 0.444480 0.769862i
\(387\) −0.465283 −0.0236517
\(388\) 18.1728 0.922583
\(389\) 8.87071 15.3645i 0.449763 0.779012i −0.548608 0.836080i \(-0.684842\pi\)
0.998370 + 0.0570682i \(0.0181753\pi\)
\(390\) 2.90952 + 5.03943i 0.147329 + 0.255181i
\(391\) 3.14216 5.44238i 0.158906 0.275233i
\(392\) −1.67687 2.90443i −0.0846949 0.146696i
\(393\) 1.14216 + 1.97827i 0.0576142 + 0.0997908i
\(394\) −5.28432 9.15270i −0.266220 0.461106i
\(395\) −0.465283 −0.0234109
\(396\) 3.18740 5.52074i 0.160173 0.277428i
\(397\) 5.85784 10.1461i 0.293997 0.509217i −0.680754 0.732512i \(-0.738348\pi\)
0.974751 + 0.223295i \(0.0716812\pi\)
\(398\) −4.32956 7.49901i −0.217021 0.375892i
\(399\) 4.66730 0.233657
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 14.7075 0.734457 0.367229 0.930131i \(-0.380307\pi\)
0.367229 + 0.930131i \(0.380307\pi\)
\(402\) 8.90952 0.444366
\(403\) 29.9224 + 12.4236i 1.49054 + 0.618865i
\(404\) 1.93057 0.0960493
\(405\) 1.00000 0.0496904
\(406\) −5.21802 + 9.03788i −0.258966 + 0.448542i
\(407\) 56.7964 2.81529
\(408\) −3.45476 5.98382i −0.171036 0.296243i
\(409\) 11.6938 20.2543i 0.578223 1.00151i −0.417461 0.908695i \(-0.637080\pi\)
0.995683 0.0928161i \(-0.0295869\pi\)
\(410\) −3.59692 + 6.23004i −0.177639 + 0.307680i
\(411\) −19.4781 −0.960786
\(412\) 1.86427 + 3.22902i 0.0918462 + 0.159082i
\(413\) −5.46938 9.47324i −0.269130 0.466148i
\(414\) −0.454758 0.787664i −0.0223501 0.0387116i
\(415\) 6.32956 10.9631i 0.310706 0.538158i
\(416\) −2.90952 5.03943i −0.142651 0.247078i
\(417\) 5.68740 9.85087i 0.278513 0.482399i
\(418\) 15.5815 0.762116
\(419\) −14.3748 −0.702255 −0.351127 0.936328i \(-0.614202\pi\)
−0.351127 + 0.936328i \(0.614202\pi\)
\(420\) −0.954758 + 1.65369i −0.0465874 + 0.0806918i
\(421\) 7.15268 + 12.3888i 0.348600 + 0.603794i 0.986001 0.166739i \(-0.0533237\pi\)
−0.637401 + 0.770533i \(0.719990\pi\)
\(422\) −5.22212 + 9.04497i −0.254209 + 0.440302i
\(423\) 4.36427 + 7.55914i 0.212198 + 0.367538i
\(424\) 3.64216 + 6.30840i 0.176879 + 0.306363i
\(425\) −3.45476 5.98382i −0.167580 0.290258i
\(426\) −9.81903 −0.475734
\(427\) −4.24317 + 7.34938i −0.205341 + 0.355661i
\(428\) 0.954758 1.65369i 0.0461500 0.0799341i
\(429\) 18.5476 + 32.1254i 0.895486 + 1.55103i
\(430\) 0.465283 0.0224379
\(431\) 11.3255 19.6163i 0.545528 0.944883i −0.453045 0.891488i \(-0.649662\pi\)
0.998573 0.0533953i \(-0.0170043\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 26.5686 1.27681 0.638403 0.769702i \(-0.279595\pi\)
0.638403 + 0.769702i \(0.279595\pi\)
\(434\) 1.37889 + 10.5419i 0.0661890 + 0.506029i
\(435\) −5.46528 −0.262040
\(436\) −2.44423 −0.117058
\(437\) 1.11153 1.92523i 0.0531719 0.0920964i
\(438\) −2.00000 −0.0955637
\(439\) 3.91595 + 6.78262i 0.186898 + 0.323717i 0.944214 0.329331i \(-0.106823\pi\)
−0.757316 + 0.653048i \(0.773490\pi\)
\(440\) −3.18740 + 5.52074i −0.151953 + 0.263191i
\(441\) 1.67687 2.90443i 0.0798512 0.138306i
\(442\) 40.2067 1.91244
\(443\) 9.35375 + 16.2012i 0.444410 + 0.769741i 0.998011 0.0630414i \(-0.0200800\pi\)
−0.553601 + 0.832782i \(0.686747\pi\)
\(444\) −4.45476 7.71587i −0.211413 0.366179i
\(445\) 7.90952 + 13.6997i 0.374947 + 0.649427i
\(446\) −7.42004 + 12.8519i −0.351349 + 0.608555i
\(447\) −3.35784 5.81595i −0.158820 0.275085i
\(448\) 0.954758 1.65369i 0.0451081 0.0781295i
\(449\) −14.8885 −0.702630 −0.351315 0.936257i \(-0.614265\pi\)
−0.351315 + 0.936257i \(0.614265\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −22.9296 + 39.7153i −1.07971 + 1.87012i
\(452\) −4.67687 8.10058i −0.219982 0.381019i
\(453\) −2.27788 + 3.94541i −0.107024 + 0.185372i
\(454\) 1.48947 + 2.57985i 0.0699045 + 0.121078i
\(455\) −5.55577 9.62287i −0.260458 0.451127i
\(456\) −1.22212 2.11677i −0.0572308 0.0991267i
\(457\) −14.2067 −0.664561 −0.332281 0.943181i \(-0.607818\pi\)
−0.332281 + 0.943181i \(0.607818\pi\)
\(458\) −3.75683 + 6.50703i −0.175545 + 0.304053i
\(459\) 3.45476 5.98382i 0.161254 0.279301i
\(460\) 0.454758 + 0.787664i 0.0212032 + 0.0367250i
\(461\) 22.6802 1.05632 0.528160 0.849145i \(-0.322882\pi\)
0.528160 + 0.849145i \(0.322882\pi\)
\(462\) −6.08639 + 10.5419i −0.283165 + 0.490455i
\(463\) −22.6170 −1.05110 −0.525551 0.850762i \(-0.676141\pi\)
−0.525551 + 0.850762i \(0.676141\pi\)
\(464\) 5.46528 0.253719
\(465\) −4.42004 + 3.38574i −0.204974 + 0.157010i
\(466\) −12.9095 −0.598022
\(467\) 35.5897 1.64689 0.823447 0.567393i \(-0.192048\pi\)
0.823447 + 0.567393i \(0.192048\pi\)
\(468\) 2.90952 5.03943i 0.134492 0.232948i
\(469\) −17.0129 −0.785581
\(470\) −4.36427 7.55914i −0.201309 0.348677i
\(471\) −8.97171 + 15.5395i −0.413395 + 0.716021i
\(472\) −2.86427 + 4.96107i −0.131839 + 0.228352i
\(473\) 2.96609 0.136381
\(474\) 0.232642 + 0.402947i 0.0106856 + 0.0185080i
\(475\) −1.22212 2.11677i −0.0560745 0.0971240i
\(476\) 6.59692 + 11.4262i 0.302369 + 0.523719i
\(477\) −3.64216 + 6.30840i −0.166763 + 0.288842i
\(478\) −6.46528 11.1982i −0.295715 0.512194i
\(479\) 1.24317 2.15323i 0.0568017 0.0983835i −0.836226 0.548384i \(-0.815243\pi\)
0.893028 + 0.450001i \(0.148576\pi\)
\(480\) 1.00000 0.0456435
\(481\) 51.8448 2.36392
\(482\) −5.35784 + 9.28006i −0.244043 + 0.422695i
\(483\) 0.868368 + 1.50406i 0.0395121 + 0.0684370i
\(484\) −14.8190 + 25.6673i −0.673592 + 1.16670i
\(485\) −9.08639 15.7381i −0.412592 0.714630i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 4.51053 + 7.81246i 0.204391 + 0.354016i 0.949939 0.312436i \(-0.101145\pi\)
−0.745547 + 0.666453i \(0.767812\pi\)
\(488\) 4.44423 0.201181
\(489\) 2.89899 5.02120i 0.131097 0.227066i
\(490\) −1.67687 + 2.90443i −0.0757535 + 0.131209i
\(491\) −9.07587 15.7199i −0.409588 0.709427i 0.585255 0.810849i \(-0.300994\pi\)
−0.994844 + 0.101422i \(0.967661\pi\)
\(492\) 7.19383 0.324323
\(493\) −18.8812 + 32.7033i −0.850368 + 1.47288i
\(494\) 14.2231 0.639926
\(495\) −6.37480 −0.286526
\(496\) 4.42004 3.38574i 0.198466 0.152024i
\(497\) 18.7496 0.841034
\(498\) −12.6591 −0.567268
\(499\) 15.5759 26.9782i 0.697271 1.20771i −0.272137 0.962258i \(-0.587731\pi\)
0.969409 0.245451i \(-0.0789361\pi\)
\(500\) 1.00000 0.0447214
\(501\) −8.06220 13.9641i −0.360192 0.623872i
\(502\) 1.76736 3.06115i 0.0788811 0.136626i
\(503\) 13.4370 23.2736i 0.599126 1.03772i −0.393824 0.919186i \(-0.628848\pi\)
0.992950 0.118531i \(-0.0378185\pi\)
\(504\) 1.90952 0.0850566
\(505\) −0.965283 1.67192i −0.0429545 0.0743994i
\(506\) 2.89899 + 5.02120i 0.128876 + 0.223220i
\(507\) 10.4306 + 18.0663i 0.463238 + 0.802351i
\(508\) 7.32956 12.6952i 0.325197 0.563257i
\(509\) −18.8877 32.7144i −0.837181 1.45004i −0.892242 0.451557i \(-0.850869\pi\)
0.0550614 0.998483i \(-0.482465\pi\)
\(510\) −3.45476 + 5.98382i −0.152979 + 0.264968i
\(511\) 3.81903 0.168944
\(512\) −1.00000 −0.0441942
\(513\) 1.22212 2.11677i 0.0539578 0.0934576i
\(514\) 12.2948 + 21.2953i 0.542302 + 0.939295i
\(515\) 1.86427 3.22902i 0.0821497 0.142287i
\(516\) −0.232642 0.402947i −0.0102415 0.0177388i
\(517\) −27.8214 48.1880i −1.22358 2.11931i
\(518\) 8.50643 + 14.7336i 0.373751 + 0.647356i
\(519\) 1.46528 0.0643188
\(520\) −2.90952 + 5.03943i −0.127591 + 0.220994i
\(521\) 19.1938 33.2447i 0.840897 1.45648i −0.0482403 0.998836i \(-0.515361\pi\)
0.889137 0.457641i \(-0.151305\pi\)
\(522\) 2.73264 + 4.73307i 0.119604 + 0.207161i
\(523\) 17.0339 0.744841 0.372421 0.928064i \(-0.378528\pi\)
0.372421 + 0.928064i \(0.378528\pi\)
\(524\) −1.14216 + 1.97827i −0.0498954 + 0.0864213i
\(525\) 1.90952 0.0833381
\(526\) 1.53472 0.0669168
\(527\) 4.98947 + 38.1456i 0.217345 + 1.66165i
\(528\) 6.37480 0.277428
\(529\) −22.1728 −0.964034
\(530\) 3.64216 6.30840i 0.158205 0.274019i
\(531\) −5.72855 −0.248598
\(532\) 2.33365 + 4.04200i 0.101177 + 0.175243i
\(533\) −20.9306 + 36.2528i −0.906603 + 1.57028i
\(534\) 7.90952 13.6997i 0.342278 0.592843i
\(535\) −1.90952 −0.0825556
\(536\) 4.45476 + 7.71587i 0.192416 + 0.333275i
\(537\) −8.00643 13.8675i −0.345503 0.598429i
\(538\) −7.96119 13.7892i −0.343231 0.594494i
\(539\) −10.6897 + 18.5152i −0.460440 + 0.797505i
\(540\) 0.500000 + 0.866025i 0.0215166 + 0.0372678i
\(541\) 2.97171 5.14716i 0.127764 0.221294i −0.795046 0.606549i \(-0.792553\pi\)
0.922810 + 0.385255i \(0.125887\pi\)
\(542\) −16.4781 −0.707797
\(543\) 2.93057 0.125763
\(544\) 3.45476 5.98382i 0.148122 0.256554i
\(545\) 1.22212 + 2.11677i 0.0523497 + 0.0906724i
\(546\) −5.55577 + 9.62287i −0.237765 + 0.411821i
\(547\) 4.42647 + 7.66688i 0.189262 + 0.327812i 0.945005 0.327057i \(-0.106057\pi\)
−0.755742 + 0.654869i \(0.772724\pi\)
\(548\) −9.73907 16.8686i −0.416033 0.720590i
\(549\) 2.22212 + 3.84882i 0.0948376 + 0.164264i
\(550\) 6.37480 0.271822
\(551\) −6.67921 + 11.5687i −0.284544 + 0.492845i
\(552\) 0.454758 0.787664i 0.0193558 0.0335252i
\(553\) −0.444233 0.769434i −0.0188907 0.0327197i
\(554\) 25.6591 1.09015
\(555\) −4.45476 + 7.71587i −0.189094 + 0.327520i
\(556\) 11.3748 0.482399
\(557\) −9.42318 −0.399273 −0.199637 0.979870i \(-0.563976\pi\)
−0.199637 + 0.979870i \(0.563976\pi\)
\(558\) 5.14216 + 2.13500i 0.217685 + 0.0903817i
\(559\) 2.70750 0.114515
\(560\) −1.90952 −0.0806918
\(561\) −22.0234 + 38.1456i −0.929828 + 1.61051i
\(562\) 31.1373 1.31345
\(563\) −19.5023 33.7790i −0.821926 1.42362i −0.904246 0.427011i \(-0.859567\pi\)
0.0823209 0.996606i \(-0.473767\pi\)
\(564\) −4.36427 + 7.55914i −0.183769 + 0.318297i
\(565\) −4.67687 + 8.10058i −0.196758 + 0.340794i
\(566\) 16.9918 0.714219
\(567\) 0.954758 + 1.65369i 0.0400961 + 0.0694484i
\(568\) −4.90952 8.50353i −0.205999 0.356800i
\(569\) −22.5897 39.1265i −0.947009 1.64027i −0.751679 0.659530i \(-0.770756\pi\)
−0.195330 0.980738i \(-0.562578\pi\)
\(570\) −1.22212 + 2.11677i −0.0511888 + 0.0886616i
\(571\) −5.46528 9.46615i −0.228715 0.396146i 0.728713 0.684820i \(-0.240119\pi\)
−0.957428 + 0.288674i \(0.906786\pi\)
\(572\) −18.5476 + 32.1254i −0.775513 + 1.34323i
\(573\) 0.444233 0.0185581
\(574\) −13.7367 −0.573360
\(575\) 0.454758 0.787664i 0.0189647 0.0328479i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −2.71568 + 4.70370i −0.113055 + 0.195818i −0.917001 0.398885i \(-0.869397\pi\)
0.803945 + 0.594703i \(0.202730\pi\)
\(578\) 15.3707 + 26.6228i 0.639337 + 1.10736i
\(579\) 8.73264 + 15.1254i 0.362916 + 0.628589i
\(580\) −2.73264 4.73307i −0.113467 0.196530i
\(581\) 24.1728 1.00286
\(582\) −9.08639 + 15.7381i −0.376643 + 0.652365i
\(583\) 23.2180 40.2148i 0.961592 1.66553i
\(584\) −1.00000 1.73205i −0.0413803 0.0716728i
\(585\) −5.81903 −0.240587
\(586\) 13.4612 23.3155i 0.556077 0.963153i
\(587\) −39.9095 −1.64724 −0.823621 0.567141i \(-0.808050\pi\)
−0.823621 + 0.567141i \(0.808050\pi\)
\(588\) 3.35375 0.138306
\(589\) 1.76502 + 13.4940i 0.0727264 + 0.556009i
\(590\) 5.72855 0.235841
\(591\) 10.5686 0.434735
\(592\) 4.45476 7.71587i 0.183089 0.317120i
\(593\) 43.5394 1.78795 0.893974 0.448118i \(-0.147906\pi\)
0.893974 + 0.448118i \(0.147906\pi\)
\(594\) 3.18740 + 5.52074i 0.130781 + 0.226519i
\(595\) 6.59692 11.4262i 0.270447 0.468428i
\(596\) 3.35784 5.81595i 0.137543 0.238231i
\(597\) 8.65911 0.354394
\(598\) 2.64625 + 4.58344i 0.108213 + 0.187431i
\(599\) −6.28432 10.8848i −0.256770 0.444739i 0.708605 0.705606i \(-0.249325\pi\)
−0.965375 + 0.260867i \(0.915992\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) 1.41361 2.44844i 0.0576623 0.0998741i −0.835753 0.549105i \(-0.814969\pi\)
0.893416 + 0.449231i \(0.148302\pi\)
\(602\) 0.444233 + 0.769434i 0.0181056 + 0.0313598i
\(603\) −4.45476 + 7.71587i −0.181412 + 0.314214i
\(604\) −4.55577 −0.185372
\(605\) 29.6381 1.20496
\(606\) −0.965283 + 1.67192i −0.0392119 + 0.0679171i
\(607\) 4.93057 + 8.53999i 0.200126 + 0.346628i 0.948569 0.316571i \(-0.102532\pi\)
−0.748443 + 0.663199i \(0.769198\pi\)
\(608\) 1.22212 2.11677i 0.0495634 0.0858463i
\(609\) −5.21802 9.03788i −0.211445 0.366233i
\(610\) −2.22212 3.84882i −0.0899709 0.155834i
\(611\) −25.3958 43.9869i −1.02741 1.77952i
\(612\) 6.90952 0.279301
\(613\) −19.4781 + 33.7371i −0.786715 + 1.36263i 0.141254 + 0.989973i \(0.454886\pi\)
−0.927969 + 0.372657i \(0.878447\pi\)
\(614\) 9.97171 17.2715i 0.402426 0.697022i
\(615\) −3.59692 6.23004i −0.145042 0.251219i
\(616\) −12.1728 −0.490455
\(617\) −18.2738 + 31.6511i −0.735675 + 1.27423i 0.218751 + 0.975781i \(0.429802\pi\)
−0.954427 + 0.298446i \(0.903532\pi\)
\(618\) −3.72855 −0.149984
\(619\) −45.6802 −1.83604 −0.918020 0.396533i \(-0.870213\pi\)
−0.918020 + 0.396533i \(0.870213\pi\)
\(620\) −5.14216 2.13500i −0.206514 0.0857436i
\(621\) 0.909516 0.0364976
\(622\) −24.5686 −0.985112
\(623\) −15.1033 + 26.1598i −0.605103 + 1.04807i
\(624\) 5.81903 0.232948
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 11.9265 20.6573i 0.476678 0.825630i
\(627\) −7.79075 + 13.4940i −0.311132 + 0.538897i
\(628\) −17.9434 −0.716021
\(629\) 30.7802 + 53.3129i 1.22729 + 2.12572i
\(630\) −0.954758 1.65369i −0.0380385 0.0658846i
\(631\) 9.16635 + 15.8766i 0.364907 + 0.632037i 0.988761 0.149504i \(-0.0477676\pi\)
−0.623855 + 0.781540i \(0.714434\pi\)
\(632\) −0.232642 + 0.402947i −0.00925399 + 0.0160284i
\(633\) −5.22212 9.04497i −0.207560 0.359505i
\(634\) −7.55167 + 13.0799i −0.299915 + 0.519468i
\(635\) −14.6591 −0.581729
\(636\) −7.28432 −0.288842
\(637\) −9.75779 + 16.9010i −0.386618 + 0.669641i
\(638\) −17.4200 30.1724i −0.689666 1.19454i
\(639\) 4.90952 8.50353i 0.194217 0.336394i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −6.86837 11.8964i −0.271284 0.469878i 0.697907 0.716189i \(-0.254115\pi\)
−0.969191 + 0.246311i \(0.920782\pi\)
\(642\) 0.954758 + 1.65369i 0.0376813 + 0.0652659i
\(643\) 40.6509 1.60312 0.801558 0.597917i \(-0.204005\pi\)
0.801558 + 0.597917i \(0.204005\pi\)
\(644\) −0.868368 + 1.50406i −0.0342185 + 0.0592681i
\(645\) −0.232642 + 0.402947i −0.00916025 + 0.0158660i
\(646\) 8.44423 + 14.6258i 0.332234 + 0.575446i
\(647\) 30.6930 1.20667 0.603334 0.797489i \(-0.293839\pi\)
0.603334 + 0.797489i \(0.293839\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 36.5183 1.43347
\(650\) 5.81903 0.228241
\(651\) −9.81903 4.07681i −0.384838 0.159783i
\(652\) 5.79798 0.227066
\(653\) −15.6463 −0.612285 −0.306143 0.951986i \(-0.599038\pi\)
−0.306143 + 0.951986i \(0.599038\pi\)
\(654\) 1.22212 2.11677i 0.0477885 0.0827722i
\(655\) 2.28432 0.0892556
\(656\) 3.59692 + 6.23004i 0.140436 + 0.243242i
\(657\) 1.00000 1.73205i 0.0390137 0.0675737i
\(658\) 8.33365 14.4343i 0.324880 0.562708i
\(659\) 27.8319 1.08418 0.542088 0.840321i \(-0.317634\pi\)
0.542088 + 0.840321i \(0.317634\pi\)
\(660\) −3.18740 5.52074i −0.124069 0.214894i
\(661\) 0.0411483 + 0.0712710i 0.00160048 + 0.00277212i 0.866825 0.498613i \(-0.166157\pi\)
−0.865224 + 0.501385i \(0.832824\pi\)
\(662\) 0.0621987 + 0.107731i 0.00241742 + 0.00418710i
\(663\) −20.1033 + 34.8200i −0.780749 + 1.35230i
\(664\) −6.32956 10.9631i −0.245634 0.425451i
\(665\) 2.33365 4.04200i 0.0904951 0.156742i
\(666\) 8.90952 0.345237
\(667\) −4.97076 −0.192469
\(668\) 8.06220 13.9641i 0.311936 0.540289i
\(669\) −7.42004 12.8519i −0.286875 0.496883i
\(670\) 4.45476 7.71587i 0.172102 0.298090i
\(671\) −14.1655 24.5354i −0.546855 0.947180i
\(672\) 0.954758 + 1.65369i 0.0368306 + 0.0637925i
\(673\) −4.73264 8.19718i −0.182430 0.315978i 0.760278 0.649598i \(-0.225063\pi\)
−0.942707 + 0.333620i \(0.891730\pi\)
\(674\) 11.4653 0.441626
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) −10.4306 + 18.0663i −0.401176 + 0.694857i
\(677\) −7.39176 12.8029i −0.284088 0.492055i 0.688299 0.725427i \(-0.258358\pi\)
−0.972388 + 0.233371i \(0.925024\pi\)
\(678\) 9.35375 0.359229
\(679\) 17.3506 30.0521i 0.665855 1.15330i
\(680\) −6.90952 −0.264968
\(681\) −2.97895 −0.114154
\(682\) −32.7802 13.6102i −1.25522 0.521161i
\(683\) 11.5219 0.440871 0.220436 0.975401i \(-0.429252\pi\)
0.220436 + 0.975401i \(0.429252\pi\)
\(684\) 2.44423 0.0934576
\(685\) −9.73907 + 16.8686i −0.372111 + 0.644515i
\(686\) −19.7706 −0.754847
\(687\) −3.75683 6.50703i −0.143332 0.248259i
\(688\) 0.232642 0.402947i 0.00886938 0.0153622i
\(689\) 21.1938 36.7088i 0.807421 1.39849i
\(690\) −0.909516 −0.0346247
\(691\) 5.86837 + 10.1643i 0.223243 + 0.386669i 0.955791 0.294047i \(-0.0950023\pi\)
−0.732548 + 0.680716i \(0.761669\pi\)
\(692\) 0.732642 + 1.26897i 0.0278509 + 0.0482391i
\(693\) −6.08639 10.5419i −0.231203 0.400455i
\(694\) 2.48947 4.31190i 0.0944992 0.163677i
\(695\) −5.68740 9.85087i −0.215735 0.373665i
\(696\) −2.73264 + 4.73307i −0.103581 + 0.179407i
\(697\) −49.7059 −1.88274
\(698\) 26.1244 0.988823
\(699\) 6.45476 11.1800i 0.244141 0.422865i
\(700\) 0.954758 + 1.65369i 0.0360865 + 0.0625036i
\(701\) −6.68097 + 11.5718i −0.252337 + 0.437060i −0.964169 0.265290i \(-0.914532\pi\)
0.711832 + 0.702350i \(0.247866\pi\)
\(702\) 2.90952 + 5.03943i 0.109813 + 0.190201i
\(703\) 10.8885 + 18.8594i 0.410666 + 0.711295i
\(704\) 3.18740 + 5.52074i 0.120130 + 0.208071i
\(705\) 8.72855 0.328736
\(706\) −14.4054 + 24.9509i −0.542155 + 0.939040i
\(707\) 1.84322 3.19256i 0.0693216 0.120068i
\(708\) −2.86427 4.96107i −0.107646 0.186448i
\(709\) −24.1665 −0.907592 −0.453796 0.891106i \(-0.649930\pi\)
−0.453796 + 0.891106i \(0.649930\pi\)
\(710\) −4.90952 + 8.50353i −0.184251 + 0.319132i
\(711\) −0.465283 −0.0174495
\(712\) 15.8190 0.592843
\(713\) −4.02010 + 3.07938i −0.150554 + 0.115324i
\(714\) −13.1938 −0.493767
\(715\) 37.0952 1.38728
\(716\) 8.00643 13.8675i 0.299214 0.518255i
\(717\) 12.9306 0.482901
\(718\) 3.31260 + 5.73759i 0.123625 + 0.214125i
\(719\) −5.84732 + 10.1279i −0.218068 + 0.377705i −0.954217 0.299114i \(-0.903309\pi\)
0.736149 + 0.676819i \(0.236642\pi\)
\(720\) −0.500000 + 0.866025i −0.0186339 + 0.0322749i
\(721\) 7.11972 0.265152
\(722\) −6.51286 11.2806i −0.242384 0.419821i
\(723\) −5.35784 9.28006i −0.199260 0.345129i
\(724\) 1.46528 + 2.53794i 0.0544568 + 0.0943220i
\(725\) −2.73264 + 4.73307i −0.101488 + 0.175782i
\(726\) −14.8190 25.6673i −0.549986 0.952603i
\(727\) 11.8771 20.5718i 0.440499 0.762966i −0.557228 0.830360i \(-0.688135\pi\)
0.997726 + 0.0673936i \(0.0214683\pi\)
\(728\) −11.1115 −0.411821
\(729\) 1.00000 0.0370370
\(730\) −1.00000 + 1.73205i −0.0370117 + 0.0641061i
\(731\) 1.60744 + 2.78417i 0.0594533 + 0.102976i
\(732\) −2.22212 + 3.84882i −0.0821318 + 0.142256i
\(733\) −24.0645 41.6810i −0.888844 1.53952i −0.841244 0.540656i \(-0.818176\pi\)
−0.0476004 0.998866i \(-0.515157\pi\)
\(734\) −12.0000 20.7846i −0.442928 0.767174i
\(735\) −1.67687 2.90443i −0.0618524 0.107132i
\(736\) 0.909516 0.0335252
\(737\) 28.3982 49.1871i 1.04606 1.81183i
\(738\) −3.59692 + 6.23004i −0.132404 + 0.229331i
\(739\) 2.49357 + 4.31899i 0.0917274 + 0.158877i 0.908238 0.418454i \(-0.137428\pi\)
−0.816511 + 0.577330i \(0.804094\pi\)
\(740\) −8.90952 −0.327520
\(741\) −7.11153 + 12.3175i −0.261249 + 0.452496i
\(742\) 13.9095 0.510634
\(743\) −28.2843 −1.03765 −0.518825 0.854880i \(-0.673631\pi\)
−0.518825 + 0.854880i \(0.673631\pi\)
\(744\) 0.722116 + 5.52074i 0.0264741 + 0.202400i
\(745\) −6.71568 −0.246044
\(746\) 27.4360 1.00450
\(747\) 6.32956 10.9631i 0.231586 0.401119i
\(748\) −44.0468 −1.61051
\(749\) −1.82313 3.15775i −0.0666156 0.115382i
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) 2.74317 4.75130i 0.100100 0.173378i −0.811626 0.584177i \(-0.801417\pi\)
0.911726 + 0.410800i \(0.134751\pi\)
\(752\) −8.72855 −0.318297
\(753\) 1.76736 + 3.06115i 0.0644061 + 0.111555i
\(754\) −15.9013 27.5419i −0.579092 1.00302i
\(755\) 2.27788 + 3.94541i 0.0829007 + 0.143588i
\(756\) −0.954758 + 1.65369i −0.0347242 + 0.0601441i
\(757\) 1.12111 + 1.94181i 0.0407473 + 0.0705765i 0.885680 0.464297i \(-0.153693\pi\)
−0.844932 + 0.534873i \(0.820359\pi\)
\(758\) 9.26326 16.0444i 0.336457 0.582760i
\(759\) −5.79798 −0.210453
\(760\) −2.44423 −0.0886616
\(761\) −11.9717 + 20.7356i −0.433974 + 0.751666i −0.997211 0.0746298i \(-0.976222\pi\)
0.563237 + 0.826295i \(0.309556\pi\)
\(762\) 7.32956 + 12.6952i 0.265522 + 0.459897i
\(763\) −2.33365 + 4.04200i −0.0844838 + 0.146330i
\(764\) 0.222116 + 0.384717i 0.00803589 + 0.0139186i
\(765\) −3.45476 5.98382i −0.124907 0.216345i
\(766\) 1.36427 + 2.36299i 0.0492932 + 0.0853784i
\(767\) 33.3346 1.20364
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −6.73264 + 11.6613i −0.242785 + 0.420516i −0.961507 0.274782i \(-0.911394\pi\)
0.718721 + 0.695298i \(0.244728\pi\)
\(770\) 6.08639 + 10.5419i 0.219338 + 0.379905i
\(771\) −24.5897 −0.885576
\(772\) −8.73264 + 15.1254i −0.314295 + 0.544374i
\(773\) −2.36194 −0.0849529 −0.0424765 0.999097i \(-0.513525\pi\)
−0.0424765 + 0.999097i \(0.513525\pi\)
\(774\) 0.465283 0.0167243
\(775\) 0.722116 + 5.52074i 0.0259392 + 0.198311i
\(776\) −18.1728 −0.652365
\(777\) −17.0129 −0.610333
\(778\) −8.87071 + 15.3645i −0.318030 + 0.550844i
\(779\) −17.5834 −0.629991
\(780\) −2.90952 5.03943i −0.104177 0.180441i
\(781\) −31.2972 + 54.2083i −1.11990 + 1.93973i
\(782\) −3.14216 + 5.44238i −0.112363 + 0.194619i
\(783\) −5.46528 −0.195313
\(784\) 1.67687 + 2.90443i 0.0598884 + 0.103730i
\(785\) 8.97171 + 15.5395i 0.320214 + 0.554627i
\(786\) −1.14216 1.97827i −0.0407394 0.0705627i
\(787\) 4.19149 7.25988i 0.149411 0.258787i −0.781599 0.623781i \(-0.785596\pi\)
0.931010 + 0.364994i \(0.118929\pi\)
\(788\) 5.28432 + 9.15270i 0.188246 + 0.326052i
\(789\) −0.767358 + 1.32910i −0.0273187 + 0.0473173i
\(790\) 0.465283 0.0165540
\(791\) −17.8611 −0.635069
\(792\) −3.18740 + 5.52074i −0.113259 + 0.196171i
\(793\) −12.9306 22.3964i −0.459178 0.795319i
\(794\) −5.85784 + 10.1461i −0.207887 + 0.360071i
\(795\) 3.64216 + 6.30840i 0.129174 + 0.223736i
\(796\) 4.32956 + 7.49901i 0.153457 + 0.265795i
\(797\) 4.08639 + 7.07784i 0.144747 + 0.250710i 0.929279 0.369379i \(-0.120430\pi\)
−0.784531 + 0.620089i \(0.787096\pi\)
\(798\) −4.66730 −0.165221
\(799\) 30.1550 52.2300i 1.06681 1.84777i
\(800\) 0.500000 0.866025i 0.0176777 0.0306186i
\(801\) 7.90952 + 13.6997i 0.279469 + 0.484055i
\(802\) −14.7075 −0.519340
\(803\) −6.37480 + 11.0415i −0.224962 + 0.389645i
\(804\) −8.90952 −0.314214
\(805\) 1.73674 0.0612119
\(806\) −29.9224 12.4236i −1.05397 0.437603i
\(807\) 15.9224 0.560494
\(808\) −1.93057 −0.0679171
\(809\) 8.11058 14.0479i 0.285153 0.493899i −0.687493 0.726191i \(-0.741289\pi\)
0.972646 + 0.232291i \(0.0746223\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −19.2843 33.4014i −0.677164 1.17288i −0.975831 0.218525i \(-0.929875\pi\)
0.298667 0.954357i \(-0.403458\pi\)
\(812\) 5.21802 9.03788i 0.183117 0.317167i
\(813\) 8.23907 14.2705i 0.288957 0.500488i
\(814\) −56.7964 −1.99071
\(815\) −2.89899 5.02120i −0.101547 0.175885i
\(816\) 3.45476 + 5.98382i 0.120941 + 0.209475i
\(817\) 0.568630 + 0.984896i 0.0198939 + 0.0344572i
\(818\) −11.6938 + 20.2543i −0.408865 + 0.708175i
\(819\) −5.55577 9.62287i −0.194134 0.336250i
\(820\) 3.59692 6.23004i 0.125610 0.217562i
\(821\) −29.3877 −1.02564 −0.512818 0.858497i \(-0.671399\pi\)
−0.512818 + 0.858497i \(0.671399\pi\)
\(822\) 19.4781 0.679378
\(823\) 19.5928 33.9358i 0.682963 1.18293i −0.291110 0.956690i \(-0.594024\pi\)
0.974072 0.226237i \(-0.0726423\pi\)
\(824\) −1.86427 3.22902i −0.0649451 0.112488i
\(825\) −3.18740 + 5.52074i −0.110971 + 0.192207i
\(826\) 5.46938 + 9.47324i 0.190304 + 0.329616i
\(827\) 0.180968 + 0.313446i 0.00629288 + 0.0108996i 0.869155 0.494540i \(-0.164664\pi\)
−0.862862 + 0.505440i \(0.831330\pi\)
\(828\) 0.454758 + 0.787664i 0.0158039 + 0.0273732i
\(829\) 37.4005 1.29897 0.649487 0.760373i \(-0.274984\pi\)
0.649487 + 0.760373i \(0.274984\pi\)
\(830\) −6.32956 + 10.9631i −0.219702 + 0.380535i
\(831\) −12.8296 + 22.2214i −0.445052 + 0.770853i
\(832\) 2.90952 + 5.03943i 0.100869 + 0.174711i
\(833\) −23.1728 −0.802889
\(834\) −5.68740 + 9.85087i −0.196939 + 0.341108i
\(835\) −16.1244 −0.558008
\(836\) −15.5815 −0.538897
\(837\) −4.42004 + 3.38574i −0.152779 + 0.117028i
\(838\) 14.3748 0.496569
\(839\) 49.4005 1.70550 0.852748 0.522323i \(-0.174934\pi\)
0.852748 + 0.522323i \(0.174934\pi\)
\(840\) 0.954758 1.65369i 0.0329423 0.0570577i
\(841\) 0.869320 0.0299766
\(842\) −7.15268 12.3888i −0.246498 0.426947i
\(843\) −15.5686 + 26.9657i −0.536212 + 0.928747i
\(844\) 5.22212 9.04497i 0.179753 0.311341i
\(845\) 20.8611 0.717645
\(846\) −4.36427 7.55914i −0.150047 0.259889i
\(847\) 28.2972 + 49.0122i 0.972303 + 1.68408i
\(848\) −3.64216 6.30840i −0.125072 0.216631i
\(849\) −8.49591 + 14.7153i −0.291579 + 0.505029i
\(850\) 3.45476 + 5.98382i 0.118497 + 0.205243i
\(851\) −4.05167 + 7.01770i −0.138890 + 0.240564i
\(852\) 9.81903 0.336394
\(853\) 11.5960 0.397038 0.198519 0.980097i \(-0.436387\pi\)
0.198519 + 0.980097i \(0.436387\pi\)
\(854\) 4.24317 7.34938i 0.145198 0.251491i
\(855\) −1.22212 2.11677i −0.0417955 0.0723919i
\(856\) −0.954758 + 1.65369i −0.0326330 + 0.0565219i
\(857\) 23.5298 + 40.7548i 0.803763 + 1.39216i 0.917123 + 0.398605i \(0.130506\pi\)
−0.113359 + 0.993554i \(0.536161\pi\)
\(858\) −18.5476 32.1254i −0.633204 1.09674i
\(859\) 1.31260 + 2.27349i 0.0447853 + 0.0775705i 0.887549 0.460713i \(-0.152406\pi\)
−0.842764 + 0.538284i \(0.819073\pi\)
\(860\) −0.465283 −0.0158660
\(861\) 6.86837 11.8964i 0.234073 0.405427i
\(862\) −11.3255 + 19.6163i −0.385747 + 0.668133i
\(863\) −15.8497 27.4524i −0.539529 0.934491i −0.998929 0.0462618i \(-0.985269\pi\)
0.459401 0.888229i \(-0.348064\pi\)
\(864\) 1.00000 0.0340207
\(865\) 0.732642 1.26897i 0.0249106 0.0431464i
\(866\) −26.5686 −0.902839
\(867\) −30.7414 −1.04403
\(868\) −1.37889 10.5419i −0.0468027 0.357817i
\(869\) 2.96609 0.100618
\(870\) 5.46528 0.185290
\(871\) 25.9224 44.8989i 0.878346 1.52134i
\(872\) 2.44423 0.0827722
\(873\) −9.08639 15.7381i −0.307528 0.532654i
\(874\) −1.11153 + 1.92523i −0.0375982 + 0.0651220i
\(875\) 0.954758 1.65369i 0.0322767 0.0559049i
\(876\) 2.00000 0.0675737
\(877\) 15.8085 + 27.3811i 0.533815 + 0.924595i 0.999220 + 0.0394971i \(0.0125756\pi\)
−0.465404 + 0.885098i \(0.654091\pi\)
\(878\) −3.91595 6.78262i −0.132157 0.228902i
\(879\) 13.4612 + 23.3155i 0.454035 + 0.786411i
\(880\) 3.18740 5.52074i 0.107447 0.186104i
\(881\) −26.9507 46.6799i −0.907991 1.57269i −0.816851 0.576848i \(-0.804282\pi\)
−0.0911397 0.995838i \(-0.529051\pi\)
\(882\) −1.67687 + 2.90443i −0.0564633 + 0.0977973i
\(883\) −44.5055 −1.49773 −0.748864 0.662723i \(-0.769401\pi\)
−0.748864 + 0.662723i \(0.769401\pi\)
\(884\) −40.2067 −1.35230
\(885\) −2.86427 + 4.96107i −0.0962815 + 0.166764i
\(886\) −9.35375 16.2012i −0.314245 0.544289i
\(887\) −16.0645 + 27.8246i −0.539394 + 0.934258i 0.459542 + 0.888156i \(0.348013\pi\)
−0.998937 + 0.0461026i \(0.985320\pi\)
\(888\) 4.45476 + 7.71587i 0.149492 + 0.258928i
\(889\) −13.9959 24.2416i −0.469408 0.813038i
\(890\) −7.90952 13.6997i −0.265128 0.459214i
\(891\) −6.37480 −0.213564
\(892\) 7.42004 12.8519i 0.248441 0.430313i
\(893\) 10.6673 18.4763i 0.356968 0.618286i
\(894\) 3.35784 + 5.81595i 0.112303 + 0.194515i
\(895\) −16.0129 −0.535251
\(896\) −0.954758 + 1.65369i −0.0318962 + 0.0552459i
\(897\) −5.29250 −0.176712
\(898\) 14.8885 0.496835
\(899\) 24.1568 18.5040i 0.805674 0.617144i
\(900\) 1.00000 0.0333333
\(901\) 50.3311 1.67677
\(902\) 22.9296 39.7153i 0.763473 1.32237i
\(903\) −0.888466 −0.0295663
\(904\) 4.67687 + 8.10058i 0.155551 + 0.269421i
\(905\) 1.46528 2.53794i 0.0487077 0.0843641i
\(906\) 2.27788 3.94541i 0.0756776 0.131077i
\(907\) 24.3619 0.808925 0.404462 0.914555i \(-0.367459\pi\)
0.404462 + 0.914555i \(0.367459\pi\)
\(908\) −1.48947 2.57985i −0.0494300 0.0856152i
\(909\) −0.965283 1.67192i −0.0320164 0.0554541i
\(910\) 5.55577 + 9.62287i 0.184172 + 0.318995i
\(911\) −11.7084 + 20.2796i −0.387918 + 0.671894i −0.992169 0.124900i \(-0.960139\pi\)
0.604251 + 0.796794i \(0.293472\pi\)
\(912\) 1.22212 + 2.11677i 0.0404683 + 0.0700932i
\(913\) −40.3497 + 69.8877i −1.33538 + 2.31294i
\(914\) 14.2067 0.469916
\(915\) 4.44423 0.146922
\(916\) 3.75683 6.50703i 0.124129 0.214998i
\(917\) 2.18097 + 3.77755i 0.0720219 + 0.124746i
\(918\) −3.45476 + 5.98382i −0.114024 + 0.197495i
\(919\) −4.11797 7.13253i −0.135839 0.235280i 0.790079 0.613006i \(-0.210040\pi\)
−0.925918 + 0.377725i \(0.876706\pi\)
\(920\) −0.454758 0.787664i −0.0149929 0.0259685i
\(921\) 9.97171 + 17.2715i 0.328579 + 0.569116i
\(922\) −22.6802 −0.746931
\(923\) −28.5686 + 49.4823i −0.940348 + 1.62873i
\(924\) 6.08639 10.5419i 0.200228 0.346804i
\(925\) 4.45476 + 7.71587i 0.146472 + 0.253696i
\(926\) 22.6170 0.743241
\(927\) 1.86427 3.22902i 0.0612308 0.106055i
\(928\) −5.46528 −0.179407
\(929\) −34.8062 −1.14195 −0.570977 0.820966i \(-0.693435\pi\)
−0.570977 + 0.820966i \(0.693435\pi\)
\(930\) 4.42004 3.38574i 0.144939 0.111023i
\(931\) −8.19734 −0.268657
\(932\) 12.9095 0.422865
\(933\) 12.2843 21.2771i 0.402170 0.696580i
\(934\) −35.5897 −1.16453
\(935\) 22.0234 + 38.1456i 0.720242 + 1.24750i
\(936\) −2.90952 + 5.03943i −0.0951005 + 0.164719i
\(937\) 11.8885 20.5914i 0.388379 0.672693i −0.603852 0.797096i \(-0.706368\pi\)
0.992232 + 0.124404i \(0.0397017\pi\)
\(938\) 17.0129 0.555490
\(939\) 11.9265 + 20.6573i 0.389206 + 0.674124i
\(940\) 4.36427 + 7.55914i 0.142347 + 0.246552i
\(941\) −6.59048 11.4151i −0.214844 0.372120i 0.738381 0.674384i \(-0.235591\pi\)
−0.953224 + 0.302264i \(0.902258\pi\)
\(942\) 8.97171 15.5395i 0.292314 0.506303i
\(943\) −3.27145 5.66632i −0.106533 0.184521i
\(944\) 2.86427 4.96107i 0.0932242 0.161469i
\(945\) 1.90952 0.0621166
\(946\) −2.96609 −0.0964358
\(947\) −24.7285 + 42.8311i −0.803570 + 1.39182i 0.113682 + 0.993517i \(0.463735\pi\)
−0.917252 + 0.398307i \(0.869598\pi\)
\(948\) −0.232642 0.402947i −0.00755585 0.0130871i
\(949\) −5.81903 + 10.0789i −0.188894 + 0.327174i
\(950\) 1.22212 + 2.11677i 0.0396507 + 0.0686770i
\(951\) −7.55167 13.0799i −0.244880 0.424144i
\(952\) −6.59692 11.4262i −0.213807 0.370325i
\(953\) 36.4442 1.18054 0.590272 0.807204i \(-0.299020\pi\)
0.590272 + 0.807204i \(0.299020\pi\)
\(954\) 3.64216 6.30840i 0.117919 0.204242i
\(955\) 0.222116 0.384717i 0.00718752 0.0124491i
\(956\) 6.46528 + 11.1982i 0.209102 + 0.362176i
\(957\) 34.8401 1.12622
\(958\) −1.24317 + 2.15323i −0.0401649 + 0.0695676i
\(959\) −37.1938 −1.20105
\(960\) −1.00000 −0.0322749
\(961\) 8.07353 29.9302i 0.260436 0.965491i
\(962\) −51.8448 −1.67154
\(963\) −1.90952 −0.0615333
\(964\) 5.35784 9.28006i 0.172564 0.298890i
\(965\) 17.4653 0.562227
\(966\) −0.868368 1.50406i −0.0279393 0.0483922i
\(967\) −29.2761 + 50.7077i −0.941457 + 1.63065i −0.178762 + 0.983892i \(0.557209\pi\)
−0.762695 + 0.646759i \(0.776124\pi\)
\(968\) 14.8190 25.6673i 0.476302 0.824979i
\(969\) −16.8885 −0.542536
\(970\) 9.08639 + 15.7381i 0.291746 + 0.505320i
\(971\) 17.0969 + 29.6127i 0.548666 + 0.950318i 0.998366 + 0.0571380i \(0.0181975\pi\)
−0.449700 + 0.893180i \(0.648469\pi\)
\(972\) 0.500000 + 0.866025i 0.0160375 + 0.0277778i
\(973\) 10.8602 18.8104i 0.348161 0.603033i
\(974\) −4.51053 7.81246i −0.144527 0.250327i
\(975\) −2.90952 + 5.03943i −0.0931791 + 0.161391i
\(976\) −4.44423 −0.142256
\(977\) −22.1810 −0.709632 −0.354816 0.934936i \(-0.615456\pi\)
−0.354816 + 0.934936i \(0.615456\pi\)
\(978\) −2.89899 + 5.02120i −0.0926995 + 0.160560i
\(979\) −50.4216 87.3327i −1.61148 2.79117i
\(980\) 1.67687 2.90443i 0.0535658 0.0927787i
\(981\) 1.22212 + 2.11677i 0.0390192 + 0.0675832i
\(982\) 9.07587 + 15.7199i 0.289622 + 0.501641i
\(983\) 4.53472 + 7.85436i 0.144635 + 0.250515i 0.929237 0.369485i \(-0.120466\pi\)
−0.784602 + 0.620000i \(0.787133\pi\)
\(984\) −7.19383 −0.229331
\(985\) 5.28432 9.15270i 0.168372 0.291629i
\(986\) 18.8812 32.7033i 0.601301 1.04148i
\(987\) 8.33365 + 14.4343i 0.265263 + 0.459449i
\(988\) −14.2231 −0.452496
\(989\) −0.211591 + 0.366487i −0.00672821 + 0.0116536i
\(990\) 6.37480 0.202604
\(991\) 34.3877 1.09236 0.546180 0.837668i \(-0.316081\pi\)
0.546180 + 0.837668i \(0.316081\pi\)
\(992\) −4.42004 + 3.38574i −0.140336 + 0.107497i
\(993\) −0.124397 −0.00394763
\(994\) −18.7496 −0.594701
\(995\) 4.32956 7.49901i 0.137256 0.237735i
\(996\) 12.6591 0.401119
\(997\) −16.9296 29.3230i −0.536166 0.928667i −0.999106 0.0422774i \(-0.986539\pi\)
0.462940 0.886390i \(-0.346795\pi\)
\(998\) −15.5759 + 26.9782i −0.493045 + 0.853980i
\(999\) −4.45476 + 7.71587i −0.140942 + 0.244119i
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 930.2.i.n.811.3 yes 6
31.25 even 3 inner 930.2.i.n.211.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.i.n.211.3 6 31.25 even 3 inner
930.2.i.n.811.3 yes 6 1.1 even 1 trivial