Properties

Label 731.2.f.c.259.15
Level $731$
Weight $2$
Character 731.259
Analytic conductor $5.837$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [731,2,Mod(259,731)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(731, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("731.259");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.f (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: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 259.15
Character \(\chi\) \(=\) 731.259
Dual form 731.2.f.c.302.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.395202i q^{2} +(-2.06164 + 2.06164i) q^{3} +1.84382 q^{4} +(-2.29638 + 2.29638i) q^{5} +(0.814765 + 0.814765i) q^{6} +(2.83331 + 2.83331i) q^{7} -1.51908i q^{8} -5.50076i q^{9} +O(q^{10})\) \(q-0.395202i q^{2} +(-2.06164 + 2.06164i) q^{3} +1.84382 q^{4} +(-2.29638 + 2.29638i) q^{5} +(0.814765 + 0.814765i) q^{6} +(2.83331 + 2.83331i) q^{7} -1.51908i q^{8} -5.50076i q^{9} +(0.907534 + 0.907534i) q^{10} +(4.59477 + 4.59477i) q^{11} +(-3.80129 + 3.80129i) q^{12} +3.25648 q^{13} +(1.11973 - 1.11973i) q^{14} -9.46864i q^{15} +3.08729 q^{16} +(0.188473 - 4.11880i) q^{17} -2.17391 q^{18} +5.98861i q^{19} +(-4.23410 + 4.23410i) q^{20} -11.6825 q^{21} +(1.81586 - 1.81586i) q^{22} +(-0.638007 - 0.638007i) q^{23} +(3.13181 + 3.13181i) q^{24} -5.54673i q^{25} -1.28697i q^{26} +(5.15567 + 5.15567i) q^{27} +(5.22410 + 5.22410i) q^{28} +(1.30010 - 1.30010i) q^{29} -3.74202 q^{30} +(-2.41856 + 2.41856i) q^{31} -4.25827i q^{32} -18.9456 q^{33} +(-1.62775 - 0.0744847i) q^{34} -13.0127 q^{35} -10.1424i q^{36} +(1.08960 - 1.08960i) q^{37} +2.36671 q^{38} +(-6.71371 + 6.71371i) q^{39} +(3.48839 + 3.48839i) q^{40} +(-5.14794 - 5.14794i) q^{41} +4.61696i q^{42} +1.00000i q^{43} +(8.47190 + 8.47190i) q^{44} +(12.6318 + 12.6318i) q^{45} +(-0.252141 + 0.252141i) q^{46} -2.76213 q^{47} +(-6.36489 + 6.36489i) q^{48} +9.05525i q^{49} -2.19208 q^{50} +(8.10293 + 8.88006i) q^{51} +6.00435 q^{52} -12.4587i q^{53} +(2.03753 - 2.03753i) q^{54} -21.1027 q^{55} +(4.30403 - 4.30403i) q^{56} +(-12.3464 - 12.3464i) q^{57} +(-0.513801 - 0.513801i) q^{58} +2.60962i q^{59} -17.4584i q^{60} +(-3.44132 - 3.44132i) q^{61} +(0.955817 + 0.955817i) q^{62} +(15.5853 - 15.5853i) q^{63} +4.49170 q^{64} +(-7.47812 + 7.47812i) q^{65} +7.48731i q^{66} -1.40688 q^{67} +(0.347509 - 7.59430i) q^{68} +2.63069 q^{69} +5.14264i q^{70} +(-3.96268 + 3.96268i) q^{71} -8.35610 q^{72} +(9.21476 - 9.21476i) q^{73} +(-0.430613 - 0.430613i) q^{74} +(11.4354 + 11.4354i) q^{75} +11.0419i q^{76} +26.0368i q^{77} +(2.65327 + 2.65327i) q^{78} +(-0.825486 - 0.825486i) q^{79} +(-7.08959 + 7.08959i) q^{80} -4.75605 q^{81} +(-2.03447 + 2.03447i) q^{82} -0.937343i q^{83} -21.5405 q^{84} +(9.02552 + 9.89113i) q^{85} +0.395202 q^{86} +5.36068i q^{87} +(6.97983 - 6.97983i) q^{88} +12.8547 q^{89} +(4.99212 - 4.99212i) q^{90} +(9.22661 + 9.22661i) q^{91} +(-1.17637 - 1.17637i) q^{92} -9.97240i q^{93} +1.09160i q^{94} +(-13.7521 - 13.7521i) q^{95} +(8.77903 + 8.77903i) q^{96} +(-2.38498 + 2.38498i) q^{97} +3.57865 q^{98} +(25.2747 - 25.2747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 4 q^{3} - 60 q^{4} - 2 q^{5} + 8 q^{6} + 4 q^{7} + 4 q^{10} - 6 q^{11} - 14 q^{12} + 16 q^{13} + 6 q^{14} + 44 q^{16} + 8 q^{17} - 16 q^{18} + 12 q^{20} + 28 q^{21} + 14 q^{22} + 6 q^{23} + 62 q^{24} - 4 q^{27} + 34 q^{28} - 12 q^{29} - 96 q^{30} + 14 q^{31} - 44 q^{33} + 6 q^{34} - 32 q^{35} + 8 q^{37} + 72 q^{38} - 32 q^{39} - 84 q^{40} + 24 q^{41} + 4 q^{44} + 48 q^{45} - 4 q^{46} - 8 q^{47} + 38 q^{48} - 64 q^{50} + 28 q^{51} - 48 q^{52} + 34 q^{54} + 56 q^{55} - 26 q^{56} - 102 q^{57} + 76 q^{58} - 40 q^{61} + 34 q^{62} + 4 q^{63} - 204 q^{64} + 18 q^{65} - 20 q^{67} + 30 q^{68} - 16 q^{69} - 26 q^{71} + 144 q^{72} + 8 q^{73} - 80 q^{74} + 142 q^{75} - 32 q^{78} - 22 q^{79} - 32 q^{80} - 32 q^{81} + 100 q^{82} - 20 q^{84} - 2 q^{85} + 12 q^{86} + 34 q^{88} + 68 q^{89} - 10 q^{90} - 28 q^{91} + 68 q^{92} - 62 q^{95} + 62 q^{96} - 2 q^{97} - 32 q^{98} + 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.395202i 0.279450i −0.990190 0.139725i \(-0.955378\pi\)
0.990190 0.139725i \(-0.0446218\pi\)
\(3\) −2.06164 + 2.06164i −1.19029 + 1.19029i −0.213305 + 0.976986i \(0.568423\pi\)
−0.976986 + 0.213305i \(0.931577\pi\)
\(4\) 1.84382 0.921908
\(5\) −2.29638 + 2.29638i −1.02697 + 1.02697i −0.0273470 + 0.999626i \(0.508706\pi\)
−0.999626 + 0.0273470i \(0.991294\pi\)
\(6\) 0.814765 + 0.814765i 0.332626 + 0.332626i
\(7\) 2.83331 + 2.83331i 1.07089 + 1.07089i 0.997288 + 0.0736015i \(0.0234493\pi\)
0.0736015 + 0.997288i \(0.476551\pi\)
\(8\) 1.51908i 0.537077i
\(9\) 5.50076i 1.83359i
\(10\) 0.907534 + 0.907534i 0.286987 + 0.286987i
\(11\) 4.59477 + 4.59477i 1.38537 + 1.38537i 0.834759 + 0.550616i \(0.185607\pi\)
0.550616 + 0.834759i \(0.314393\pi\)
\(12\) −3.80129 + 3.80129i −1.09734 + 1.09734i
\(13\) 3.25648 0.903185 0.451593 0.892224i \(-0.350856\pi\)
0.451593 + 0.892224i \(0.350856\pi\)
\(14\) 1.11973 1.11973i 0.299260 0.299260i
\(15\) 9.46864i 2.44479i
\(16\) 3.08729 0.771822
\(17\) 0.188473 4.11880i 0.0457113 0.998955i
\(18\) −2.17391 −0.512395
\(19\) 5.98861i 1.37388i 0.726714 + 0.686941i \(0.241047\pi\)
−0.726714 + 0.686941i \(0.758953\pi\)
\(20\) −4.23410 + 4.23410i −0.946774 + 0.946774i
\(21\) −11.6825 −2.54934
\(22\) 1.81586 1.81586i 0.387143 0.387143i
\(23\) −0.638007 0.638007i −0.133034 0.133034i 0.637454 0.770488i \(-0.279987\pi\)
−0.770488 + 0.637454i \(0.779987\pi\)
\(24\) 3.13181 + 3.13181i 0.639277 + 0.639277i
\(25\) 5.54673i 1.10935i
\(26\) 1.28697i 0.252395i
\(27\) 5.15567 + 5.15567i 0.992209 + 0.992209i
\(28\) 5.22410 + 5.22410i 0.987261 + 0.987261i
\(29\) 1.30010 1.30010i 0.241422 0.241422i −0.576016 0.817438i \(-0.695393\pi\)
0.817438 + 0.576016i \(0.195393\pi\)
\(30\) −3.74202 −0.683197
\(31\) −2.41856 + 2.41856i −0.434385 + 0.434385i −0.890117 0.455732i \(-0.849378\pi\)
0.455732 + 0.890117i \(0.349378\pi\)
\(32\) 4.25827i 0.752762i
\(33\) −18.9456 −3.29800
\(34\) −1.62775 0.0744847i −0.279158 0.0127740i
\(35\) −13.0127 −2.19955
\(36\) 10.1424i 1.69040i
\(37\) 1.08960 1.08960i 0.179130 0.179130i −0.611847 0.790976i \(-0.709573\pi\)
0.790976 + 0.611847i \(0.209573\pi\)
\(38\) 2.36671 0.383931
\(39\) −6.71371 + 6.71371i −1.07505 + 1.07505i
\(40\) 3.48839 + 3.48839i 0.551563 + 0.551563i
\(41\) −5.14794 5.14794i −0.803973 0.803973i 0.179741 0.983714i \(-0.442474\pi\)
−0.983714 + 0.179741i \(0.942474\pi\)
\(42\) 4.61696i 0.712412i
\(43\) 1.00000i 0.152499i
\(44\) 8.47190 + 8.47190i 1.27719 + 1.27719i
\(45\) 12.6318 + 12.6318i 1.88304 + 1.88304i
\(46\) −0.252141 + 0.252141i −0.0371762 + 0.0371762i
\(47\) −2.76213 −0.402898 −0.201449 0.979499i \(-0.564565\pi\)
−0.201449 + 0.979499i \(0.564565\pi\)
\(48\) −6.36489 + 6.36489i −0.918693 + 0.918693i
\(49\) 9.05525i 1.29361i
\(50\) −2.19208 −0.310007
\(51\) 8.10293 + 8.88006i 1.13464 + 1.24346i
\(52\) 6.00435 0.832654
\(53\) 12.4587i 1.71134i −0.517522 0.855670i \(-0.673145\pi\)
0.517522 0.855670i \(-0.326855\pi\)
\(54\) 2.03753 2.03753i 0.277273 0.277273i
\(55\) −21.1027 −2.84548
\(56\) 4.30403 4.30403i 0.575150 0.575150i
\(57\) −12.3464 12.3464i −1.63532 1.63532i
\(58\) −0.513801 0.513801i −0.0674654 0.0674654i
\(59\) 2.60962i 0.339743i 0.985466 + 0.169872i \(0.0543353\pi\)
−0.985466 + 0.169872i \(0.945665\pi\)
\(60\) 17.4584i 2.25387i
\(61\) −3.44132 3.44132i −0.440616 0.440616i 0.451603 0.892219i \(-0.350852\pi\)
−0.892219 + 0.451603i \(0.850852\pi\)
\(62\) 0.955817 + 0.955817i 0.121389 + 0.121389i
\(63\) 15.5853 15.5853i 1.96357 1.96357i
\(64\) 4.49170 0.561463
\(65\) −7.47812 + 7.47812i −0.927547 + 0.927547i
\(66\) 7.48731i 0.921625i
\(67\) −1.40688 −0.171878 −0.0859390 0.996300i \(-0.527389\pi\)
−0.0859390 + 0.996300i \(0.527389\pi\)
\(68\) 0.347509 7.59430i 0.0421416 0.920944i
\(69\) 2.63069 0.316698
\(70\) 5.14264i 0.614663i
\(71\) −3.96268 + 3.96268i −0.470283 + 0.470283i −0.902006 0.431723i \(-0.857906\pi\)
0.431723 + 0.902006i \(0.357906\pi\)
\(72\) −8.35610 −0.984776
\(73\) 9.21476 9.21476i 1.07851 1.07851i 0.0818619 0.996644i \(-0.473913\pi\)
0.996644 0.0818619i \(-0.0260866\pi\)
\(74\) −0.430613 0.430613i −0.0500577 0.0500577i
\(75\) 11.4354 + 11.4354i 1.32045 + 1.32045i
\(76\) 11.0419i 1.26659i
\(77\) 26.0368i 2.96717i
\(78\) 2.65327 + 2.65327i 0.300423 + 0.300423i
\(79\) −0.825486 0.825486i −0.0928745 0.0928745i 0.659143 0.752018i \(-0.270919\pi\)
−0.752018 + 0.659143i \(0.770919\pi\)
\(80\) −7.08959 + 7.08959i −0.792640 + 0.792640i
\(81\) −4.75605 −0.528450
\(82\) −2.03447 + 2.03447i −0.224670 + 0.224670i
\(83\) 0.937343i 0.102887i −0.998676 0.0514434i \(-0.983618\pi\)
0.998676 0.0514434i \(-0.0163822\pi\)
\(84\) −21.5405 −2.35026
\(85\) 9.02552 + 9.89113i 0.978955 + 1.07284i
\(86\) 0.395202 0.0426157
\(87\) 5.36068i 0.574726i
\(88\) 6.97983 6.97983i 0.744052 0.744052i
\(89\) 12.8547 1.36259 0.681297 0.732007i \(-0.261416\pi\)
0.681297 + 0.732007i \(0.261416\pi\)
\(90\) 4.99212 4.99212i 0.526216 0.526216i
\(91\) 9.22661 + 9.22661i 0.967211 + 0.967211i
\(92\) −1.17637 1.17637i −0.122645 0.122645i
\(93\) 9.97240i 1.03409i
\(94\) 1.09160i 0.112590i
\(95\) −13.7521 13.7521i −1.41094 1.41094i
\(96\) 8.77903 + 8.77903i 0.896006 + 0.896006i
\(97\) −2.38498 + 2.38498i −0.242158 + 0.242158i −0.817742 0.575584i \(-0.804775\pi\)
0.575584 + 0.817742i \(0.304775\pi\)
\(98\) 3.57865 0.361498
\(99\) 25.2747 25.2747i 2.54020 2.54020i
\(100\) 10.2272i 1.02272i
\(101\) −15.1399 −1.50648 −0.753238 0.657748i \(-0.771509\pi\)
−0.753238 + 0.657748i \(0.771509\pi\)
\(102\) 3.50941 3.20229i 0.347484 0.317074i
\(103\) 11.4286 1.12610 0.563048 0.826424i \(-0.309629\pi\)
0.563048 + 0.826424i \(0.309629\pi\)
\(104\) 4.94686i 0.485080i
\(105\) 26.8276 26.8276i 2.61810 2.61810i
\(106\) −4.92371 −0.478233
\(107\) 0.251416 0.251416i 0.0243053 0.0243053i −0.694850 0.719155i \(-0.744529\pi\)
0.719155 + 0.694850i \(0.244529\pi\)
\(108\) 9.50611 + 9.50611i 0.914726 + 0.914726i
\(109\) 3.23558 + 3.23558i 0.309912 + 0.309912i 0.844875 0.534963i \(-0.179674\pi\)
−0.534963 + 0.844875i \(0.679674\pi\)
\(110\) 8.33981i 0.795170i
\(111\) 4.49275i 0.426433i
\(112\) 8.74723 + 8.74723i 0.826536 + 0.826536i
\(113\) −10.1991 10.1991i −0.959447 0.959447i 0.0397626 0.999209i \(-0.487340\pi\)
−0.999209 + 0.0397626i \(0.987340\pi\)
\(114\) −4.87931 + 4.87931i −0.456989 + 0.456989i
\(115\) 2.93022 0.273244
\(116\) 2.39714 2.39714i 0.222569 0.222569i
\(117\) 17.9131i 1.65607i
\(118\) 1.03132 0.0949411
\(119\) 12.2038 11.1358i 1.11872 1.02082i
\(120\) −14.3836 −1.31304
\(121\) 31.2238i 2.83852i
\(122\) −1.36001 + 1.36001i −0.123130 + 0.123130i
\(123\) 21.2264 1.91392
\(124\) −4.45937 + 4.45937i −0.400463 + 0.400463i
\(125\) 1.25551 + 1.25551i 0.112296 + 0.112296i
\(126\) −6.15935 6.15935i −0.548718 0.548718i
\(127\) 20.0587i 1.77992i −0.456039 0.889960i \(-0.650732\pi\)
0.456039 0.889960i \(-0.349268\pi\)
\(128\) 10.2917i 0.909663i
\(129\) −2.06164 2.06164i −0.181518 0.181518i
\(130\) 2.95537 + 2.95537i 0.259203 + 0.259203i
\(131\) −2.21750 + 2.21750i −0.193744 + 0.193744i −0.797312 0.603568i \(-0.793745\pi\)
0.603568 + 0.797312i \(0.293745\pi\)
\(132\) −34.9321 −3.04045
\(133\) −16.9676 + 16.9676i −1.47127 + 1.47127i
\(134\) 0.556002i 0.0480313i
\(135\) −23.6788 −2.03794
\(136\) −6.25679 0.286305i −0.536515 0.0245505i
\(137\) 0.434569 0.0371278 0.0185639 0.999828i \(-0.494091\pi\)
0.0185639 + 0.999828i \(0.494091\pi\)
\(138\) 1.03965i 0.0885011i
\(139\) 9.73694 9.73694i 0.825876 0.825876i −0.161067 0.986943i \(-0.551494\pi\)
0.986943 + 0.161067i \(0.0514936\pi\)
\(140\) −23.9930 −2.02778
\(141\) 5.69454 5.69454i 0.479566 0.479566i
\(142\) 1.56606 + 1.56606i 0.131421 + 0.131421i
\(143\) 14.9628 + 14.9628i 1.25125 + 1.25125i
\(144\) 16.9824i 1.41520i
\(145\) 5.97105i 0.495868i
\(146\) −3.64169 3.64169i −0.301388 0.301388i
\(147\) −18.6687 18.6687i −1.53977 1.53977i
\(148\) 2.00903 2.00903i 0.165141 0.165141i
\(149\) 15.1662 1.24246 0.621230 0.783628i \(-0.286633\pi\)
0.621230 + 0.783628i \(0.286633\pi\)
\(150\) 4.51929 4.51929i 0.368998 0.368998i
\(151\) 21.7696i 1.77158i −0.464085 0.885791i \(-0.653617\pi\)
0.464085 0.885791i \(-0.346383\pi\)
\(152\) 9.09719 0.737879
\(153\) −22.6565 1.03674i −1.83167 0.0838156i
\(154\) 10.2898 0.829174
\(155\) 11.1078i 0.892204i
\(156\) −12.3788 + 12.3788i −0.991100 + 0.991100i
\(157\) −7.12853 −0.568918 −0.284459 0.958688i \(-0.591814\pi\)
−0.284459 + 0.958688i \(0.591814\pi\)
\(158\) −0.326234 + 0.326234i −0.0259537 + 0.0259537i
\(159\) 25.6855 + 25.6855i 2.03699 + 2.03699i
\(160\) 9.77860 + 9.77860i 0.773066 + 0.773066i
\(161\) 3.61534i 0.284929i
\(162\) 1.87960i 0.147675i
\(163\) −11.2828 11.2828i −0.883735 0.883735i 0.110177 0.993912i \(-0.464858\pi\)
−0.993912 + 0.110177i \(0.964858\pi\)
\(164\) −9.49185 9.49185i −0.741189 0.741189i
\(165\) 43.5062 43.5062i 3.38695 3.38695i
\(166\) −0.370439 −0.0287517
\(167\) −12.3901 + 12.3901i −0.958771 + 0.958771i −0.999183 0.0404116i \(-0.987133\pi\)
0.0404116 + 0.999183i \(0.487133\pi\)
\(168\) 17.7467i 1.36919i
\(169\) −2.39533 −0.184256
\(170\) 3.90899 3.56690i 0.299806 0.273569i
\(171\) 32.9419 2.51913
\(172\) 1.84382i 0.140590i
\(173\) 7.18265 7.18265i 0.546087 0.546087i −0.379220 0.925307i \(-0.623808\pi\)
0.925307 + 0.379220i \(0.123808\pi\)
\(174\) 2.11855 0.160607
\(175\) 15.7156 15.7156i 1.18799 1.18799i
\(176\) 14.1854 + 14.1854i 1.06926 + 1.06926i
\(177\) −5.38010 5.38010i −0.404393 0.404393i
\(178\) 5.08019i 0.380777i
\(179\) 11.4517i 0.855941i 0.903793 + 0.427970i \(0.140771\pi\)
−0.903793 + 0.427970i \(0.859229\pi\)
\(180\) 23.2908 + 23.2908i 1.73599 + 1.73599i
\(181\) 7.04766 + 7.04766i 0.523849 + 0.523849i 0.918731 0.394883i \(-0.129215\pi\)
−0.394883 + 0.918731i \(0.629215\pi\)
\(182\) 3.64637 3.64637i 0.270287 0.270287i
\(183\) 14.1896 1.04892
\(184\) −0.969185 + 0.969185i −0.0714493 + 0.0714493i
\(185\) 5.00429i 0.367923i
\(186\) −3.94111 −0.288976
\(187\) 19.7909 18.0589i 1.44725 1.32060i
\(188\) −5.09286 −0.371435
\(189\) 29.2152i 2.12509i
\(190\) −5.43486 + 5.43486i −0.394286 + 0.394286i
\(191\) 4.33508 0.313675 0.156838 0.987624i \(-0.449870\pi\)
0.156838 + 0.987624i \(0.449870\pi\)
\(192\) −9.26029 + 9.26029i −0.668304 + 0.668304i
\(193\) −5.68265 5.68265i −0.409046 0.409046i 0.472360 0.881406i \(-0.343402\pi\)
−0.881406 + 0.472360i \(0.843402\pi\)
\(194\) 0.942549 + 0.942549i 0.0676710 + 0.0676710i
\(195\) 30.8345i 2.20810i
\(196\) 16.6962i 1.19259i
\(197\) 10.7322 + 10.7322i 0.764636 + 0.764636i 0.977157 0.212521i \(-0.0681673\pi\)
−0.212521 + 0.977157i \(0.568167\pi\)
\(198\) −9.98860 9.98860i −0.709859 0.709859i
\(199\) −14.9004 + 14.9004i −1.05626 + 1.05626i −0.0579402 + 0.998320i \(0.518453\pi\)
−0.998320 + 0.0579402i \(0.981547\pi\)
\(200\) −8.42595 −0.595804
\(201\) 2.90049 2.90049i 0.204585 0.204585i
\(202\) 5.98331i 0.420984i
\(203\) 7.36716 0.517073
\(204\) 14.9403 + 16.3732i 1.04603 + 1.14635i
\(205\) 23.6433 1.65132
\(206\) 4.51661i 0.314687i
\(207\) −3.50952 + 3.50952i −0.243929 + 0.243929i
\(208\) 10.0537 0.697098
\(209\) −27.5163 + 27.5163i −1.90334 + 1.90334i
\(210\) −10.6023 10.6023i −0.731628 0.731628i
\(211\) 3.38854 + 3.38854i 0.233277 + 0.233277i 0.814059 0.580782i \(-0.197253\pi\)
−0.580782 + 0.814059i \(0.697253\pi\)
\(212\) 22.9716i 1.57770i
\(213\) 16.3393i 1.11955i
\(214\) −0.0993601 0.0993601i −0.00679211 0.00679211i
\(215\) −2.29638 2.29638i −0.156612 0.156612i
\(216\) 7.83189 7.83189i 0.532892 0.532892i
\(217\) −13.7050 −0.930357
\(218\) 1.27871 1.27871i 0.0866049 0.0866049i
\(219\) 37.9951i 2.56747i
\(220\) −38.9094 −2.62327
\(221\) 0.613757 13.4128i 0.0412858 0.902241i
\(222\) 1.77554 0.119167
\(223\) 19.5394i 1.30845i −0.756299 0.654226i \(-0.772994\pi\)
0.756299 0.654226i \(-0.227006\pi\)
\(224\) 12.0650 12.0650i 0.806125 0.806125i
\(225\) −30.5112 −2.03408
\(226\) −4.03068 + 4.03068i −0.268117 + 0.268117i
\(227\) 3.55396 + 3.55396i 0.235885 + 0.235885i 0.815144 0.579259i \(-0.196658\pi\)
−0.579259 + 0.815144i \(0.696658\pi\)
\(228\) −22.7645 22.7645i −1.50761 1.50761i
\(229\) 1.92855i 0.127442i 0.997968 + 0.0637212i \(0.0202968\pi\)
−0.997968 + 0.0637212i \(0.979703\pi\)
\(230\) 1.15803i 0.0763580i
\(231\) −53.6786 53.6786i −3.53179 3.53179i
\(232\) −1.97496 1.97496i −0.129662 0.129662i
\(233\) −20.6011 + 20.6011i −1.34962 + 1.34962i −0.463548 + 0.886072i \(0.653424\pi\)
−0.886072 + 0.463548i \(0.846576\pi\)
\(234\) −7.07929 −0.462788
\(235\) 6.34291 6.34291i 0.413766 0.413766i
\(236\) 4.81165i 0.313212i
\(237\) 3.40372 0.221095
\(238\) −4.40089 4.82297i −0.285267 0.312626i
\(239\) 23.8145 1.54043 0.770215 0.637785i \(-0.220149\pi\)
0.770215 + 0.637785i \(0.220149\pi\)
\(240\) 29.2324i 1.88695i
\(241\) 8.38719 8.38719i 0.540266 0.540266i −0.383341 0.923607i \(-0.625226\pi\)
0.923607 + 0.383341i \(0.125226\pi\)
\(242\) 12.3397 0.793225
\(243\) −5.66172 + 5.66172i −0.363200 + 0.363200i
\(244\) −6.34516 6.34516i −0.406207 0.406207i
\(245\) −20.7943 20.7943i −1.32850 1.32850i
\(246\) 8.38872i 0.534846i
\(247\) 19.5018i 1.24087i
\(248\) 3.67398 + 3.67398i 0.233298 + 0.233298i
\(249\) 1.93247 + 1.93247i 0.122465 + 0.122465i
\(250\) 0.496180 0.496180i 0.0313812 0.0313812i
\(251\) −10.5472 −0.665731 −0.332866 0.942974i \(-0.608016\pi\)
−0.332866 + 0.942974i \(0.608016\pi\)
\(252\) 28.7365 28.7365i 1.81023 1.81023i
\(253\) 5.86299i 0.368603i
\(254\) −7.92722 −0.497398
\(255\) −38.9994 1.78458i −2.44224 0.111755i
\(256\) 4.91613 0.307258
\(257\) 10.0789i 0.628706i 0.949306 + 0.314353i \(0.101788\pi\)
−0.949306 + 0.314353i \(0.898212\pi\)
\(258\) −0.814765 + 0.814765i −0.0507251 + 0.0507251i
\(259\) 6.17436 0.383656
\(260\) −13.7883 + 13.7883i −0.855113 + 0.855113i
\(261\) −7.15153 7.15153i −0.442668 0.442668i
\(262\) 0.876360 + 0.876360i 0.0541417 + 0.0541417i
\(263\) 23.0328i 1.42026i 0.704069 + 0.710132i \(0.251365\pi\)
−0.704069 + 0.710132i \(0.748635\pi\)
\(264\) 28.7799i 1.77128i
\(265\) 28.6100 + 28.6100i 1.75750 + 1.75750i
\(266\) 6.70561 + 6.70561i 0.411147 + 0.411147i
\(267\) −26.5018 + 26.5018i −1.62188 + 1.62188i
\(268\) −2.59403 −0.158456
\(269\) 7.75002 7.75002i 0.472527 0.472527i −0.430204 0.902732i \(-0.641558\pi\)
0.902732 + 0.430204i \(0.141558\pi\)
\(270\) 9.35789i 0.569503i
\(271\) −21.5552 −1.30939 −0.654693 0.755895i \(-0.727202\pi\)
−0.654693 + 0.755895i \(0.727202\pi\)
\(272\) 0.581869 12.7159i 0.0352810 0.771015i
\(273\) −38.0440 −2.30253
\(274\) 0.171742i 0.0103753i
\(275\) 25.4860 25.4860i 1.53686 1.53686i
\(276\) 4.85050 0.291966
\(277\) 5.16679 5.16679i 0.310442 0.310442i −0.534639 0.845081i \(-0.679552\pi\)
0.845081 + 0.534639i \(0.179552\pi\)
\(278\) −3.84805 3.84805i −0.230791 0.230791i
\(279\) 13.3039 + 13.3039i 0.796483 + 0.796483i
\(280\) 19.7674i 1.18133i
\(281\) 6.71403i 0.400525i 0.979742 + 0.200263i \(0.0641795\pi\)
−0.979742 + 0.200263i \(0.935820\pi\)
\(282\) −2.25049 2.25049i −0.134015 0.134015i
\(283\) 5.20126 + 5.20126i 0.309183 + 0.309183i 0.844592 0.535410i \(-0.179843\pi\)
−0.535410 + 0.844592i \(0.679843\pi\)
\(284\) −7.30645 + 7.30645i −0.433558 + 0.433558i
\(285\) 56.7040 3.35886
\(286\) 5.91331 5.91331i 0.349661 0.349661i
\(287\) 29.1714i 1.72193i
\(288\) −23.4237 −1.38025
\(289\) −16.9290 1.55256i −0.995821 0.0913271i
\(290\) 2.35977 0.138570
\(291\) 9.83397i 0.576478i
\(292\) 16.9903 16.9903i 0.994283 0.994283i
\(293\) 22.9344 1.33984 0.669922 0.742431i \(-0.266327\pi\)
0.669922 + 0.742431i \(0.266327\pi\)
\(294\) −7.37791 + 7.37791i −0.430288 + 0.430288i
\(295\) −5.99267 5.99267i −0.348907 0.348907i
\(296\) −1.65520 1.65520i −0.0962064 0.0962064i
\(297\) 47.3782i 2.74916i
\(298\) 5.99369i 0.347205i
\(299\) −2.07766 2.07766i −0.120154 0.120154i
\(300\) 21.0848 + 21.0848i 1.21733 + 1.21733i
\(301\) −2.83331 + 2.83331i −0.163309 + 0.163309i
\(302\) −8.60336 −0.495068
\(303\) 31.2131 31.2131i 1.79314 1.79314i
\(304\) 18.4886i 1.06039i
\(305\) 15.8052 0.905001
\(306\) −0.409722 + 8.95388i −0.0234222 + 0.511859i
\(307\) −8.33848 −0.475902 −0.237951 0.971277i \(-0.576476\pi\)
−0.237951 + 0.971277i \(0.576476\pi\)
\(308\) 48.0070i 2.73545i
\(309\) −23.5618 + 23.5618i −1.34038 + 1.34038i
\(310\) −4.38984 −0.249326
\(311\) −8.53171 + 8.53171i −0.483789 + 0.483789i −0.906339 0.422551i \(-0.861135\pi\)
0.422551 + 0.906339i \(0.361135\pi\)
\(312\) 10.1987 + 10.1987i 0.577386 + 0.577386i
\(313\) −11.1722 11.1722i −0.631489 0.631489i 0.316952 0.948441i \(-0.397340\pi\)
−0.948441 + 0.316952i \(0.897340\pi\)
\(314\) 2.81720i 0.158984i
\(315\) 71.5797i 4.03306i
\(316\) −1.52204 1.52204i −0.0856217 0.0856217i
\(317\) 8.64878 + 8.64878i 0.485764 + 0.485764i 0.906967 0.421202i \(-0.138392\pi\)
−0.421202 + 0.906967i \(0.638392\pi\)
\(318\) 10.1509 10.1509i 0.569237 0.569237i
\(319\) 11.9473 0.668921
\(320\) −10.3147 + 10.3147i −0.576607 + 0.576607i
\(321\) 1.03666i 0.0578608i
\(322\) −1.42879 −0.0796232
\(323\) 24.6659 + 1.12869i 1.37245 + 0.0628019i
\(324\) −8.76929 −0.487183
\(325\) 18.0628i 1.00195i
\(326\) −4.45897 + 4.45897i −0.246960 + 0.246960i
\(327\) −13.3412 −0.737772
\(328\) −7.82014 + 7.82014i −0.431795 + 0.431795i
\(329\) −7.82597 7.82597i −0.431460 0.431460i
\(330\) −17.1937 17.1937i −0.946483 0.946483i
\(331\) 8.06878i 0.443500i −0.975104 0.221750i \(-0.928823\pi\)
0.975104 0.221750i \(-0.0711769\pi\)
\(332\) 1.72829i 0.0948521i
\(333\) −5.99364 5.99364i −0.328450 0.328450i
\(334\) 4.89657 + 4.89657i 0.267928 + 0.267928i
\(335\) 3.23074 3.23074i 0.176514 0.176514i
\(336\) −36.0674 −1.96764
\(337\) 16.3929 16.3929i 0.892978 0.892978i −0.101825 0.994802i \(-0.532468\pi\)
0.994802 + 0.101825i \(0.0324681\pi\)
\(338\) 0.946640i 0.0514904i
\(339\) 42.0537 2.28404
\(340\) 16.6414 + 18.2374i 0.902506 + 0.989063i
\(341\) −22.2254 −1.20357
\(342\) 13.0187i 0.703970i
\(343\) −5.82316 + 5.82316i −0.314421 + 0.314421i
\(344\) 1.51908 0.0819034
\(345\) −6.04106 + 6.04106i −0.325240 + 0.325240i
\(346\) −2.83859 2.83859i −0.152604 0.152604i
\(347\) 4.41512 + 4.41512i 0.237016 + 0.237016i 0.815613 0.578597i \(-0.196400\pi\)
−0.578597 + 0.815613i \(0.696400\pi\)
\(348\) 9.88411i 0.529844i
\(349\) 17.9709i 0.961958i 0.876732 + 0.480979i \(0.159719\pi\)
−0.876732 + 0.480979i \(0.840281\pi\)
\(350\) −6.21083 6.21083i −0.331983 0.331983i
\(351\) 16.7893 + 16.7893i 0.896149 + 0.896149i
\(352\) 19.5657 19.5657i 1.04286 1.04286i
\(353\) 13.3305 0.709512 0.354756 0.934959i \(-0.384564\pi\)
0.354756 + 0.934959i \(0.384564\pi\)
\(354\) −2.12622 + 2.12622i −0.113008 + 0.113008i
\(355\) 18.1996i 0.965936i
\(356\) 23.7017 1.25619
\(357\) −2.20184 + 48.1180i −0.116534 + 2.54667i
\(358\) 4.52573 0.239192
\(359\) 10.2334i 0.540096i 0.962847 + 0.270048i \(0.0870396\pi\)
−0.962847 + 0.270048i \(0.912960\pi\)
\(360\) 19.1888 19.1888i 1.01134 1.01134i
\(361\) −16.8634 −0.887550
\(362\) 2.78525 2.78525i 0.146389 0.146389i
\(363\) −64.3723 64.3723i −3.37867 3.37867i
\(364\) 17.0122 + 17.0122i 0.891680 + 0.891680i
\(365\) 42.3212i 2.21519i
\(366\) 5.60773i 0.293121i
\(367\) 10.0427 + 10.0427i 0.524227 + 0.524227i 0.918845 0.394618i \(-0.129123\pi\)
−0.394618 + 0.918845i \(0.629123\pi\)
\(368\) −1.96971 1.96971i −0.102678 0.102678i
\(369\) −28.3176 + 28.3176i −1.47415 + 1.47415i
\(370\) 1.97770 0.102816
\(371\) 35.2994 35.2994i 1.83266 1.83266i
\(372\) 18.3873i 0.953336i
\(373\) −25.6931 −1.33034 −0.665168 0.746693i \(-0.731640\pi\)
−0.665168 + 0.746693i \(0.731640\pi\)
\(374\) −7.13691 7.82139i −0.369041 0.404435i
\(375\) −5.17684 −0.267331
\(376\) 4.19591i 0.216387i
\(377\) 4.23375 4.23375i 0.218049 0.218049i
\(378\) 11.5459 0.593857
\(379\) −4.29359 + 4.29359i −0.220547 + 0.220547i −0.808729 0.588182i \(-0.799844\pi\)
0.588182 + 0.808729i \(0.299844\pi\)
\(380\) −25.3564 25.3564i −1.30076 1.30076i
\(381\) 41.3538 + 41.3538i 2.11862 + 2.11862i
\(382\) 1.71323i 0.0876564i
\(383\) 23.1778i 1.18433i 0.805816 + 0.592166i \(0.201727\pi\)
−0.805816 + 0.592166i \(0.798273\pi\)
\(384\) 21.2177 + 21.2177i 1.08276 + 1.08276i
\(385\) −59.7904 59.7904i −3.04720 3.04720i
\(386\) −2.24579 + 2.24579i −0.114308 + 0.114308i
\(387\) 5.50076 0.279619
\(388\) −4.39747 + 4.39747i −0.223248 + 0.223248i
\(389\) 16.0941i 0.816005i 0.912981 + 0.408002i \(0.133774\pi\)
−0.912981 + 0.408002i \(0.866226\pi\)
\(390\) −12.1858 −0.617053
\(391\) −2.74807 + 2.50757i −0.138976 + 0.126813i
\(392\) 13.7557 0.694766
\(393\) 9.14340i 0.461224i
\(394\) 4.24137 4.24137i 0.213677 0.213677i
\(395\) 3.79126 0.190759
\(396\) 46.6019 46.6019i 2.34183 2.34183i
\(397\) 2.44867 + 2.44867i 0.122895 + 0.122895i 0.765879 0.642984i \(-0.222304\pi\)
−0.642984 + 0.765879i \(0.722304\pi\)
\(398\) 5.88866 + 5.88866i 0.295172 + 0.295172i
\(399\) 69.9622i 3.50249i
\(400\) 17.1244i 0.856218i
\(401\) 11.0274 + 11.0274i 0.550681 + 0.550681i 0.926637 0.375957i \(-0.122686\pi\)
−0.375957 + 0.926637i \(0.622686\pi\)
\(402\) −1.14628 1.14628i −0.0571712 0.0571712i
\(403\) −7.87598 + 7.87598i −0.392330 + 0.392330i
\(404\) −27.9152 −1.38883
\(405\) 10.9217 10.9217i 0.542704 0.542704i
\(406\) 2.91151i 0.144496i
\(407\) 10.0129 0.496323
\(408\) 13.4895 12.3090i 0.667831 0.609387i
\(409\) 19.3698 0.957773 0.478887 0.877877i \(-0.341041\pi\)
0.478887 + 0.877877i \(0.341041\pi\)
\(410\) 9.34386i 0.461460i
\(411\) −0.895927 + 0.895927i −0.0441928 + 0.0441928i
\(412\) 21.0723 1.03816
\(413\) −7.39384 + 7.39384i −0.363827 + 0.363827i
\(414\) 1.38697 + 1.38697i 0.0681658 + 0.0681658i
\(415\) 2.15250 + 2.15250i 0.105662 + 0.105662i
\(416\) 13.8670i 0.679884i
\(417\) 40.1482i 1.96607i
\(418\) 10.8745 + 10.8745i 0.531888 + 0.531888i
\(419\) −16.8811 16.8811i −0.824696 0.824696i 0.162081 0.986777i \(-0.448179\pi\)
−0.986777 + 0.162081i \(0.948179\pi\)
\(420\) 49.4651 49.4651i 2.41365 2.41365i
\(421\) 10.6382 0.518473 0.259237 0.965814i \(-0.416529\pi\)
0.259237 + 0.965814i \(0.416529\pi\)
\(422\) 1.33916 1.33916i 0.0651892 0.0651892i
\(423\) 15.1938i 0.738749i
\(424\) −18.9258 −0.919121
\(425\) −22.8459 1.04541i −1.10819 0.0507097i
\(426\) −6.45730 −0.312857
\(427\) 19.5006i 0.943701i
\(428\) 0.463565 0.463565i 0.0224073 0.0224073i
\(429\) −61.6958 −2.97870
\(430\) −0.907534 + 0.907534i −0.0437652 + 0.0437652i
\(431\) −12.2207 12.2207i −0.588651 0.588651i 0.348615 0.937266i \(-0.386652\pi\)
−0.937266 + 0.348615i \(0.886652\pi\)
\(432\) 15.9170 + 15.9170i 0.765809 + 0.765809i
\(433\) 33.4188i 1.60601i 0.595975 + 0.803003i \(0.296766\pi\)
−0.595975 + 0.803003i \(0.703234\pi\)
\(434\) 5.41624i 0.259988i
\(435\) −12.3102 12.3102i −0.590228 0.590228i
\(436\) 5.96581 + 5.96581i 0.285711 + 0.285711i
\(437\) 3.82078 3.82078i 0.182772 0.182772i
\(438\) 15.0157 0.717479
\(439\) 12.2275 12.2275i 0.583587 0.583587i −0.352300 0.935887i \(-0.614600\pi\)
0.935887 + 0.352300i \(0.114600\pi\)
\(440\) 32.0567i 1.52824i
\(441\) 49.8107 2.37194
\(442\) −5.30075 0.242558i −0.252131 0.0115373i
\(443\) −10.3059 −0.489647 −0.244823 0.969568i \(-0.578730\pi\)
−0.244823 + 0.969568i \(0.578730\pi\)
\(444\) 8.28380i 0.393132i
\(445\) −29.5193 + 29.5193i −1.39935 + 1.39935i
\(446\) −7.72199 −0.365647
\(447\) −31.2672 + 31.2672i −1.47889 + 1.47889i
\(448\) 12.7264 + 12.7264i 0.601264 + 0.601264i
\(449\) −5.46474 5.46474i −0.257897 0.257897i 0.566301 0.824198i \(-0.308374\pi\)
−0.824198 + 0.566301i \(0.808374\pi\)
\(450\) 12.0581i 0.568424i
\(451\) 47.3072i 2.22761i
\(452\) −18.8052 18.8052i −0.884521 0.884521i
\(453\) 44.8811 + 44.8811i 2.10870 + 2.10870i
\(454\) 1.40453 1.40453i 0.0659179 0.0659179i
\(455\) −42.3756 −1.98660
\(456\) −18.7552 + 18.7552i −0.878291 + 0.878291i
\(457\) 28.1596i 1.31725i 0.752470 + 0.658626i \(0.228862\pi\)
−0.752470 + 0.658626i \(0.771138\pi\)
\(458\) 0.762167 0.0356137
\(459\) 22.2069 20.2635i 1.03653 0.945817i
\(460\) 5.40278 0.251906
\(461\) 32.2892i 1.50386i −0.659245 0.751929i \(-0.729124\pi\)
0.659245 0.751929i \(-0.270876\pi\)
\(462\) −21.2139 + 21.2139i −0.986958 + 0.986958i
\(463\) −34.1422 −1.58672 −0.793361 0.608751i \(-0.791671\pi\)
−0.793361 + 0.608751i \(0.791671\pi\)
\(464\) 4.01378 4.01378i 0.186335 0.186335i
\(465\) 22.9004 + 22.9004i 1.06198 + 1.06198i
\(466\) 8.14157 + 8.14157i 0.377151 + 0.377151i
\(467\) 24.5040i 1.13391i −0.823749 0.566954i \(-0.808122\pi\)
0.823749 0.566954i \(-0.191878\pi\)
\(468\) 33.0285i 1.52674i
\(469\) −3.98613 3.98613i −0.184062 0.184062i
\(470\) −2.50673 2.50673i −0.115627 0.115627i
\(471\) 14.6965 14.6965i 0.677178 0.677178i
\(472\) 3.96422 0.182468
\(473\) −4.59477 + 4.59477i −0.211268 + 0.211268i
\(474\) 1.34516i 0.0617850i
\(475\) 33.2172 1.52411
\(476\) 22.5016 20.5324i 1.03136 0.941100i
\(477\) −68.5325 −3.13789
\(478\) 9.41151i 0.430473i
\(479\) 30.3065 30.3065i 1.38474 1.38474i 0.548756 0.835983i \(-0.315102\pi\)
0.835983 0.548756i \(-0.184898\pi\)
\(480\) −40.3200 −1.84035
\(481\) 3.54827 3.54827i 0.161787 0.161787i
\(482\) −3.31463 3.31463i −0.150977 0.150977i
\(483\) 7.45355 + 7.45355i 0.339148 + 0.339148i
\(484\) 57.5709i 2.61686i
\(485\) 10.9537i 0.497380i
\(486\) 2.23752 + 2.23752i 0.101496 + 0.101496i
\(487\) −7.99832 7.99832i −0.362438 0.362438i 0.502272 0.864710i \(-0.332498\pi\)
−0.864710 + 0.502272i \(0.832498\pi\)
\(488\) −5.22765 + 5.22765i −0.236644 + 0.236644i
\(489\) 46.5222 2.10380
\(490\) −8.21795 + 8.21795i −0.371249 + 0.371249i
\(491\) 4.23781i 0.191250i −0.995417 0.0956248i \(-0.969515\pi\)
0.995417 0.0956248i \(-0.0304849\pi\)
\(492\) 39.1377 1.76446
\(493\) −5.10981 5.59987i −0.230134 0.252206i
\(494\) 7.70714 0.346761
\(495\) 116.081i 5.21744i
\(496\) −7.46678 + 7.46678i −0.335268 + 0.335268i
\(497\) −22.4550 −1.00724
\(498\) 0.763714 0.763714i 0.0342229 0.0342229i
\(499\) 14.2904 + 14.2904i 0.639727 + 0.639727i 0.950488 0.310761i \(-0.100584\pi\)
−0.310761 + 0.950488i \(0.600584\pi\)
\(500\) 2.31493 + 2.31493i 0.103527 + 0.103527i
\(501\) 51.0878i 2.28243i
\(502\) 4.16826i 0.186038i
\(503\) 18.3954 + 18.3954i 0.820211 + 0.820211i 0.986138 0.165927i \(-0.0530616\pi\)
−0.165927 + 0.986138i \(0.553062\pi\)
\(504\) −23.6754 23.6754i −1.05459 1.05459i
\(505\) 34.7670 34.7670i 1.54711 1.54711i
\(506\) −2.31706 −0.103006
\(507\) 4.93833 4.93833i 0.219319 0.219319i
\(508\) 36.9845i 1.64092i
\(509\) −10.1205 −0.448585 −0.224292 0.974522i \(-0.572007\pi\)
−0.224292 + 0.974522i \(0.572007\pi\)
\(510\) −0.705269 + 15.4126i −0.0312298 + 0.682483i
\(511\) 52.2165 2.30992
\(512\) 22.5262i 0.995526i
\(513\) −30.8753 + 30.8753i −1.36318 + 1.36318i
\(514\) 3.98320 0.175692
\(515\) −26.2445 + 26.2445i −1.15647 + 1.15647i
\(516\) −3.80129 3.80129i −0.167343 0.167343i
\(517\) −12.6914 12.6914i −0.558165 0.558165i
\(518\) 2.44012i 0.107213i
\(519\) 29.6161i 1.30000i
\(520\) 11.3599 + 11.3599i 0.498164 + 0.498164i
\(521\) −19.6572 19.6572i −0.861196 0.861196i 0.130281 0.991477i \(-0.458412\pi\)
−0.991477 + 0.130281i \(0.958412\pi\)
\(522\) −2.82629 + 2.82629i −0.123704 + 0.123704i
\(523\) −17.1365 −0.749326 −0.374663 0.927161i \(-0.622242\pi\)
−0.374663 + 0.927161i \(0.622242\pi\)
\(524\) −4.08867 + 4.08867i −0.178614 + 0.178614i
\(525\) 64.8000i 2.82810i
\(526\) 9.10260 0.396892
\(527\) 9.50570 + 10.4174i 0.414075 + 0.453788i
\(528\) −58.4904 −2.54547
\(529\) 22.1859i 0.964604i
\(530\) 11.3067 11.3067i 0.491133 0.491133i
\(531\) 14.3549 0.622948
\(532\) −31.2851 + 31.2851i −1.35638 + 1.35638i
\(533\) −16.7642 16.7642i −0.726137 0.726137i
\(534\) 10.4736 + 10.4736i 0.453235 + 0.453235i
\(535\) 1.15469i 0.0499218i
\(536\) 2.13717i 0.0923117i
\(537\) −23.6094 23.6094i −1.01882 1.01882i
\(538\) −3.06282 3.06282i −0.132048 0.132048i
\(539\) −41.6068 + 41.6068i −1.79213 + 1.79213i
\(540\) −43.6593 −1.87880
\(541\) −10.3717 + 10.3717i −0.445915 + 0.445915i −0.893994 0.448079i \(-0.852108\pi\)
0.448079 + 0.893994i \(0.352108\pi\)
\(542\) 8.51866i 0.365908i
\(543\) −29.0596 −1.24706
\(544\) −17.5389 0.802566i −0.751975 0.0344097i
\(545\) −14.8603 −0.636543
\(546\) 15.0350i 0.643440i
\(547\) −1.84488 + 1.84488i −0.0788812 + 0.0788812i −0.745447 0.666565i \(-0.767764\pi\)
0.666565 + 0.745447i \(0.267764\pi\)
\(548\) 0.801266 0.0342284
\(549\) −18.9299 + 18.9299i −0.807907 + 0.807907i
\(550\) −10.0721 10.0721i −0.429475 0.429475i
\(551\) 7.78578 + 7.78578i 0.331686 + 0.331686i
\(552\) 3.99623i 0.170091i
\(553\) 4.67771i 0.198917i
\(554\) −2.04192 2.04192i −0.0867529 0.0867529i
\(555\) −10.3171 10.3171i −0.437935 0.437935i
\(556\) 17.9531 17.9531i 0.761382 0.761382i
\(557\) −4.40379 −0.186595 −0.0932973 0.995638i \(-0.529741\pi\)
−0.0932973 + 0.995638i \(0.529741\pi\)
\(558\) 5.25772 5.25772i 0.222577 0.222577i
\(559\) 3.25648i 0.137734i
\(560\) −40.1740 −1.69766
\(561\) −3.57072 + 78.0329i −0.150756 + 3.29455i
\(562\) 2.65339 0.111927
\(563\) 27.8666i 1.17444i 0.809428 + 0.587220i \(0.199777\pi\)
−0.809428 + 0.587220i \(0.800223\pi\)
\(564\) 10.4997 10.4997i 0.442116 0.442116i
\(565\) 46.8418 1.97065
\(566\) 2.05554 2.05554i 0.0864010 0.0864010i
\(567\) −13.4754 13.4754i −0.565912 0.565912i
\(568\) 6.01963 + 6.01963i 0.252578 + 0.252578i
\(569\) 11.9329i 0.500255i 0.968213 + 0.250128i \(0.0804726\pi\)
−0.968213 + 0.250128i \(0.919527\pi\)
\(570\) 22.4095i 0.938631i
\(571\) −9.98575 9.98575i −0.417891 0.417891i 0.466585 0.884476i \(-0.345484\pi\)
−0.884476 + 0.466585i \(0.845484\pi\)
\(572\) 27.5886 + 27.5886i 1.15354 + 1.15354i
\(573\) −8.93739 + 8.93739i −0.373365 + 0.373365i
\(574\) −11.5286 −0.481194
\(575\) −3.53886 + 3.53886i −0.147581 + 0.147581i
\(576\) 24.7078i 1.02949i
\(577\) 3.02120 0.125774 0.0628871 0.998021i \(-0.479969\pi\)
0.0628871 + 0.998021i \(0.479969\pi\)
\(578\) −0.613574 + 6.69035i −0.0255213 + 0.278282i
\(579\) 23.4312 0.973768
\(580\) 11.0095i 0.457145i
\(581\) 2.65578 2.65578i 0.110180 0.110180i
\(582\) −3.88640 −0.161096
\(583\) 57.2450 57.2450i 2.37085 2.37085i
\(584\) −13.9980 13.9980i −0.579240 0.579240i
\(585\) 41.1353 + 41.1353i 1.70074 + 1.70074i
\(586\) 9.06373i 0.374419i
\(587\) 34.4373i 1.42138i −0.703505 0.710691i \(-0.748383\pi\)
0.703505 0.710691i \(-0.251617\pi\)
\(588\) −34.4217 34.4217i −1.41953 1.41953i
\(589\) −14.4838 14.4838i −0.596794 0.596794i
\(590\) −2.36831 + 2.36831i −0.0975020 + 0.0975020i
\(591\) −44.2519 −1.82028
\(592\) 3.36392 3.36392i 0.138256 0.138256i
\(593\) 43.7413i 1.79624i −0.439751 0.898120i \(-0.644933\pi\)
0.439751 0.898120i \(-0.355067\pi\)
\(594\) 18.7239 0.768253
\(595\) −2.45254 + 53.5967i −0.100544 + 2.19725i
\(596\) 27.9636 1.14543
\(597\) 61.4386i 2.51451i
\(598\) −0.821094 + 0.821094i −0.0335770 + 0.0335770i
\(599\) 8.65224 0.353521 0.176760 0.984254i \(-0.443438\pi\)
0.176760 + 0.984254i \(0.443438\pi\)
\(600\) 17.3713 17.3713i 0.709181 0.709181i
\(601\) −18.0238 18.0238i −0.735206 0.735206i 0.236440 0.971646i \(-0.424019\pi\)
−0.971646 + 0.236440i \(0.924019\pi\)
\(602\) 1.11973 + 1.11973i 0.0456367 + 0.0456367i
\(603\) 7.73892i 0.315153i
\(604\) 40.1390i 1.63323i
\(605\) −71.7017 71.7017i −2.91509 2.91509i
\(606\) −12.3355 12.3355i −0.501094 0.501094i
\(607\) 15.2491 15.2491i 0.618941 0.618941i −0.326319 0.945260i \(-0.605808\pi\)
0.945260 + 0.326319i \(0.105808\pi\)
\(608\) 25.5011 1.03421
\(609\) −15.1885 + 15.1885i −0.615467 + 0.615467i
\(610\) 6.24622i 0.252902i
\(611\) −8.99483 −0.363892
\(612\) −41.7744 1.91156i −1.68863 0.0772703i
\(613\) 5.19888 0.209981 0.104990 0.994473i \(-0.466519\pi\)
0.104990 + 0.994473i \(0.466519\pi\)
\(614\) 3.29538i 0.132991i
\(615\) −48.7440 + 48.7440i −1.96555 + 1.96555i
\(616\) 39.5520 1.59360
\(617\) 10.2893 10.2893i 0.414230 0.414230i −0.468979 0.883209i \(-0.655378\pi\)
0.883209 + 0.468979i \(0.155378\pi\)
\(618\) 9.31165 + 9.31165i 0.374570 + 0.374570i
\(619\) −8.77436 8.77436i −0.352671 0.352671i 0.508431 0.861103i \(-0.330226\pi\)
−0.861103 + 0.508431i \(0.830226\pi\)
\(620\) 20.4808i 0.822530i
\(621\) 6.57871i 0.263995i
\(622\) 3.37174 + 3.37174i 0.135195 + 0.135195i
\(623\) 36.4213 + 36.4213i 1.45919 + 1.45919i
\(624\) −20.7271 + 20.7271i −0.829750 + 0.829750i
\(625\) 21.9674 0.878696
\(626\) −4.41526 + 4.41526i −0.176469 + 0.176469i
\(627\) 113.458i 4.53106i
\(628\) −13.1437 −0.524490
\(629\) −4.28249 4.69321i −0.170754 0.187131i
\(630\) 28.2884 1.12704
\(631\) 17.8274i 0.709696i −0.934924 0.354848i \(-0.884533\pi\)
0.934924 0.354848i \(-0.115467\pi\)
\(632\) −1.25398 + 1.25398i −0.0498807 + 0.0498807i
\(633\) −13.9719 −0.555335
\(634\) 3.41801 3.41801i 0.135747 0.135747i
\(635\) 46.0624 + 46.0624i 1.82793 + 1.82793i
\(636\) 47.3593 + 47.3593i 1.87792 + 1.87792i
\(637\) 29.4883i 1.16837i
\(638\) 4.72159i 0.186930i
\(639\) 21.7977 + 21.7977i 0.862305 + 0.862305i
\(640\) 23.6336 + 23.6336i 0.934199 + 0.934199i
\(641\) 3.60093 3.60093i 0.142228 0.142228i −0.632408 0.774636i \(-0.717933\pi\)
0.774636 + 0.632408i \(0.217933\pi\)
\(642\) 0.409690 0.0161692
\(643\) −17.3740 + 17.3740i −0.685162 + 0.685162i −0.961159 0.275997i \(-0.910992\pi\)
0.275997 + 0.961159i \(0.410992\pi\)
\(644\) 6.66602i 0.262678i
\(645\) 9.46864 0.372828
\(646\) 0.446060 9.74799i 0.0175500 0.383529i
\(647\) −30.4910 −1.19873 −0.599363 0.800477i \(-0.704579\pi\)
−0.599363 + 0.800477i \(0.704579\pi\)
\(648\) 7.22484i 0.283818i
\(649\) −11.9906 + 11.9906i −0.470671 + 0.470671i
\(650\) −7.13846 −0.279993
\(651\) 28.2549 28.2549i 1.10740 1.10740i
\(652\) −20.8034 20.8034i −0.814723 0.814723i
\(653\) −1.41809 1.41809i −0.0554940 0.0554940i 0.678815 0.734309i \(-0.262494\pi\)
−0.734309 + 0.678815i \(0.762494\pi\)
\(654\) 5.27248i 0.206170i
\(655\) 10.1845i 0.397940i
\(656\) −15.8932 15.8932i −0.620524 0.620524i
\(657\) −50.6881 50.6881i −1.97753 1.97753i
\(658\) −3.09284 + 3.09284i −0.120571 + 0.120571i
\(659\) 17.6191 0.686341 0.343171 0.939273i \(-0.388499\pi\)
0.343171 + 0.939273i \(0.388499\pi\)
\(660\) 80.2174 80.2174i 3.12246 3.12246i
\(661\) 4.93702i 0.192028i −0.995380 0.0960140i \(-0.969391\pi\)
0.995380 0.0960140i \(-0.0306094\pi\)
\(662\) −3.18879 −0.123936
\(663\) 26.3870 + 28.9177i 1.02479 + 1.12307i
\(664\) −1.42390 −0.0552581
\(665\) 77.9280i 3.02192i
\(666\) −2.36870 + 2.36870i −0.0917851 + 0.0917851i
\(667\) −1.65894 −0.0642346
\(668\) −22.8450 + 22.8450i −0.883899 + 0.883899i
\(669\) 40.2832 + 40.2832i 1.55744 + 1.55744i
\(670\) −1.27679 1.27679i −0.0493268 0.0493268i
\(671\) 31.6241i 1.22084i
\(672\) 49.7474i 1.91905i
\(673\) −0.0359806 0.0359806i −0.00138695 0.00138695i 0.706413 0.707800i \(-0.250312\pi\)
−0.707800 + 0.706413i \(0.750312\pi\)
\(674\) −6.47850 6.47850i −0.249542 0.249542i
\(675\) 28.5971 28.5971i 1.10070 1.10070i
\(676\) −4.41655 −0.169867
\(677\) 21.0357 21.0357i 0.808468 0.808468i −0.175934 0.984402i \(-0.556294\pi\)
0.984402 + 0.175934i \(0.0562944\pi\)
\(678\) 16.6197i 0.638275i
\(679\) −13.5148 −0.518649
\(680\) 15.0254 13.7105i 0.576199 0.525774i
\(681\) −14.6540 −0.561543
\(682\) 8.78351i 0.336338i
\(683\) −24.7129 + 24.7129i −0.945612 + 0.945612i −0.998595 0.0529832i \(-0.983127\pi\)
0.0529832 + 0.998595i \(0.483127\pi\)
\(684\) 60.7388 2.32240
\(685\) −0.997937 + 0.997937i −0.0381292 + 0.0381292i
\(686\) 2.30132 + 2.30132i 0.0878649 + 0.0878649i
\(687\) −3.97599 3.97599i −0.151693 0.151693i
\(688\) 3.08729i 0.117702i
\(689\) 40.5716i 1.54566i
\(690\) 2.38744 + 2.38744i 0.0908882 + 0.0908882i
\(691\) 26.6121 + 26.6121i 1.01237 + 1.01237i 0.999923 + 0.0124487i \(0.00396265\pi\)
0.0124487 + 0.999923i \(0.496037\pi\)
\(692\) 13.2435 13.2435i 0.503441 0.503441i
\(693\) 143.222 5.44055
\(694\) 1.74486 1.74486i 0.0662340 0.0662340i
\(695\) 44.7194i 1.69630i
\(696\) 8.14332 0.308672
\(697\) −22.1736 + 20.2331i −0.839883 + 0.766382i
\(698\) 7.10211 0.268819
\(699\) 84.9441i 3.21288i
\(700\) 28.9767 28.9767i 1.09522 1.09522i
\(701\) 8.84988 0.334255 0.167128 0.985935i \(-0.446551\pi\)
0.167128 + 0.985935i \(0.446551\pi\)
\(702\) 6.63518 6.63518i 0.250429 0.250429i
\(703\) 6.52521 + 6.52521i 0.246103 + 0.246103i
\(704\) 20.6383 + 20.6383i 0.777836 + 0.777836i
\(705\) 26.1537i 0.985004i
\(706\) 5.26824i 0.198273i
\(707\) −42.8960 42.8960i −1.61327 1.61327i
\(708\) −9.91992 9.91992i −0.372813 0.372813i
\(709\) 1.65271 1.65271i 0.0620689 0.0620689i −0.675391 0.737460i \(-0.736025\pi\)
0.737460 + 0.675391i \(0.236025\pi\)
\(710\) −7.19252 −0.269931
\(711\) −4.54080 + 4.54080i −0.170293 + 0.170293i
\(712\) 19.5273i 0.731818i
\(713\) 3.08611 0.115576
\(714\) 19.0163 + 0.870170i 0.711668 + 0.0325653i
\(715\) −68.7205 −2.57000
\(716\) 21.1148i 0.789099i
\(717\) −49.0970 + 49.0970i −1.83356 + 1.83356i
\(718\) 4.04424 0.150930
\(719\) −16.0655 + 16.0655i −0.599142 + 0.599142i −0.940084 0.340942i \(-0.889254\pi\)
0.340942 + 0.940084i \(0.389254\pi\)
\(720\) 38.9981 + 38.9981i 1.45337 + 1.45337i
\(721\) 32.3808 + 32.3808i 1.20592 + 1.20592i
\(722\) 6.66446i 0.248025i
\(723\) 34.5828i 1.28615i
\(724\) 12.9946 + 12.9946i 0.482940 + 0.482940i
\(725\) −7.21130 7.21130i −0.267821 0.267821i
\(726\) −25.4400 + 25.4400i −0.944169 + 0.944169i
\(727\) 38.1913 1.41644 0.708218 0.705994i \(-0.249499\pi\)
0.708218 + 0.705994i \(0.249499\pi\)
\(728\) 14.0160 14.0160i 0.519467 0.519467i
\(729\) 37.6131i 1.39308i
\(730\) 16.7254 0.619035
\(731\) 4.11880 + 0.188473i 0.152339 + 0.00697091i
\(732\) 26.1629 0.967009
\(733\) 4.37235i 0.161496i −0.996735 0.0807482i \(-0.974269\pi\)
0.996735 0.0807482i \(-0.0257310\pi\)
\(734\) 3.96891 3.96891i 0.146495 0.146495i
\(735\) 85.7410 3.16260
\(736\) −2.71680 + 2.71680i −0.100143 + 0.100143i
\(737\) −6.46430 6.46430i −0.238115 0.238115i
\(738\) 11.1911 + 11.1911i 0.411952 + 0.411952i
\(739\) 30.7137i 1.12982i 0.825153 + 0.564910i \(0.191089\pi\)
−0.825153 + 0.564910i \(0.808911\pi\)
\(740\) 9.22699i 0.339191i
\(741\) −40.2058 40.2058i −1.47700 1.47700i
\(742\) −13.9504 13.9504i −0.512135 0.512135i
\(743\) 15.1621 15.1621i 0.556245 0.556245i −0.371991 0.928236i \(-0.621325\pi\)
0.928236 + 0.371991i \(0.121325\pi\)
\(744\) −15.1489 −0.555386
\(745\) −34.8273 + 34.8273i −1.27597 + 1.27597i
\(746\) 10.1539i 0.371762i
\(747\) −5.15610 −0.188652
\(748\) 36.4908 33.2973i 1.33423 1.21747i
\(749\) 1.42468 0.0520566
\(750\) 2.04589i 0.0747055i
\(751\) 16.8945 16.8945i 0.616488 0.616488i −0.328141 0.944629i \(-0.606422\pi\)
0.944629 + 0.328141i \(0.106422\pi\)
\(752\) −8.52750 −0.310966
\(753\) 21.7445 21.7445i 0.792414 0.792414i
\(754\) −1.67318 1.67318i −0.0609337 0.0609337i
\(755\) 49.9912 + 49.9912i 1.81937 + 1.81937i
\(756\) 53.8674i 1.95914i
\(757\) 2.81540i 0.102327i 0.998690 + 0.0511637i \(0.0162930\pi\)
−0.998690 + 0.0511637i \(0.983707\pi\)
\(758\) 1.69683 + 1.69683i 0.0616318 + 0.0616318i
\(759\) 12.0874 + 12.0874i 0.438745 + 0.438745i
\(760\) −20.8906 + 20.8906i −0.757782 + 0.757782i
\(761\) 22.7702 0.825421 0.412710 0.910862i \(-0.364582\pi\)
0.412710 + 0.910862i \(0.364582\pi\)
\(762\) 16.3431 16.3431i 0.592048 0.592048i
\(763\) 18.3348i 0.663764i
\(764\) 7.99308 0.289180
\(765\) 54.4087 49.6472i 1.96715 1.79500i
\(766\) 9.15992 0.330961
\(767\) 8.49817i 0.306851i
\(768\) −10.1353 + 10.1353i −0.365726 + 0.365726i
\(769\) −25.9882 −0.937160 −0.468580 0.883421i \(-0.655234\pi\)
−0.468580 + 0.883421i \(0.655234\pi\)
\(770\) −23.6292 + 23.6292i −0.851539 + 0.851539i
\(771\) −20.7791 20.7791i −0.748343 0.748343i
\(772\) −10.4778 10.4778i −0.377103 0.377103i
\(773\) 22.0854i 0.794355i −0.917742 0.397177i \(-0.869990\pi\)
0.917742 0.397177i \(-0.130010\pi\)
\(774\) 2.17391i 0.0781395i
\(775\) 13.4151 + 13.4151i 0.481884 + 0.481884i
\(776\) 3.62298 + 3.62298i 0.130058 + 0.130058i
\(777\) −12.7293 + 12.7293i −0.456662 + 0.456662i
\(778\) 6.36043 0.228032
\(779\) 30.8290 30.8290i 1.10456 1.10456i
\(780\) 56.8531i 2.03567i
\(781\) −36.4152 −1.30304
\(782\) 0.990997 + 1.08604i 0.0354380 + 0.0388367i
\(783\) 13.4058 0.479083
\(784\) 27.9562i 0.998435i
\(785\) 16.3698 16.3698i 0.584264 0.584264i
\(786\) −3.61349 −0.128889
\(787\) 19.5539 19.5539i 0.697020 0.697020i −0.266747 0.963767i \(-0.585949\pi\)
0.963767 + 0.266747i \(0.0859488\pi\)
\(788\) 19.7882 + 19.7882i 0.704924 + 0.704924i
\(789\) −47.4855 47.4855i −1.69053 1.69053i
\(790\) 1.49831i 0.0533076i
\(791\) 57.7941i 2.05492i
\(792\) −38.3943 38.3943i −1.36428 1.36428i
\(793\) −11.2066 11.2066i −0.397958 0.397958i
\(794\) 0.967718 0.967718i 0.0343430 0.0343430i
\(795\) −117.967 −4.18387
\(796\) −27.4736 + 27.4736i −0.973775 + 0.973775i
\(797\) 29.5654i 1.04726i −0.851946 0.523630i \(-0.824577\pi\)
0.851946 0.523630i \(-0.175423\pi\)
\(798\) −27.6492 −0.978770
\(799\) −0.520586 + 11.3767i −0.0184170 + 0.402477i
\(800\) −23.6195 −0.835074
\(801\) 70.7105i 2.49843i
\(802\) 4.35803 4.35803i 0.153888 0.153888i
\(803\) 84.6793 2.98827
\(804\) 5.34797 5.34797i 0.188608 0.188608i
\(805\) 8.30220 + 8.30220i 0.292614 + 0.292614i
\(806\) 3.11260 + 3.11260i 0.109637 + 0.109637i
\(807\) 31.9556i 1.12489i
\(808\) 22.9987i 0.809093i
\(809\) 32.4208 + 32.4208i 1.13985 + 1.13985i 0.988476 + 0.151378i \(0.0483711\pi\)
0.151378 + 0.988476i \(0.451629\pi\)
\(810\) −4.31628 4.31628i −0.151659 0.151659i
\(811\) −25.3883 + 25.3883i −0.891505 + 0.891505i −0.994665 0.103160i \(-0.967105\pi\)
0.103160 + 0.994665i \(0.467105\pi\)
\(812\) 13.5837 0.476694
\(813\) 44.4392 44.4392i 1.55855 1.55855i
\(814\) 3.95713i 0.138697i
\(815\) 51.8191 1.81514
\(816\) 25.0161 + 27.4153i 0.875738 + 0.959727i
\(817\) −5.98861 −0.209515
\(818\) 7.65496i 0.267649i
\(819\) 50.7533 50.7533i 1.77346 1.77346i
\(820\) 43.5938 1.52236
\(821\) −0.652865 + 0.652865i −0.0227851 + 0.0227851i −0.718408 0.695622i \(-0.755129\pi\)
0.695622 + 0.718408i \(0.255129\pi\)
\(822\) 0.354072 + 0.354072i 0.0123497 + 0.0123497i
\(823\) −13.2358 13.2358i −0.461371 0.461371i 0.437734 0.899105i \(-0.355781\pi\)
−0.899105 + 0.437734i \(0.855781\pi\)
\(824\) 17.3610i 0.604800i
\(825\) 105.086i 3.65862i
\(826\) 2.92206 + 2.92206i 0.101671 + 0.101671i
\(827\) −0.361808 0.361808i −0.0125813 0.0125813i 0.700788 0.713369i \(-0.252832\pi\)
−0.713369 + 0.700788i \(0.752832\pi\)
\(828\) −6.47091 + 6.47091i −0.224880 + 0.224880i
\(829\) 7.59855 0.263908 0.131954 0.991256i \(-0.457875\pi\)
0.131954 + 0.991256i \(0.457875\pi\)
\(830\) 0.850670 0.850670i 0.0295272 0.0295272i
\(831\) 21.3042i 0.739033i
\(832\) 14.6271 0.507105
\(833\) 37.2967 + 1.70667i 1.29226 + 0.0591325i
\(834\) 15.8666 0.549417
\(835\) 56.9046i 1.96926i
\(836\) −50.7349 + 50.7349i −1.75470 + 1.75470i
\(837\) −24.9386 −0.862002
\(838\) −6.67144 + 6.67144i −0.230461 + 0.230461i
\(839\) −21.4529 21.4529i −0.740636 0.740636i 0.232064 0.972700i \(-0.425452\pi\)
−0.972700 + 0.232064i \(0.925452\pi\)
\(840\) −40.7533 40.7533i −1.40612 1.40612i
\(841\) 25.6195i 0.883431i
\(842\) 4.20423i 0.144887i
\(843\) −13.8419 13.8419i −0.476742 0.476742i
\(844\) 6.24785 + 6.24785i 0.215060 + 0.215060i
\(845\) 5.50060 5.50060i 0.189226 0.189226i
\(846\) 6.00462 0.206443
\(847\) −88.4665 + 88.4665i −3.03975 + 3.03975i
\(848\) 38.4637i 1.32085i
\(849\) −21.4463 −0.736035
\(850\) −0.413147 + 9.02872i −0.0141708 + 0.309683i
\(851\) −1.39035 −0.0476606
\(852\) 30.1266i 1.03212i
\(853\) −26.7850 + 26.7850i −0.917102 + 0.917102i −0.996818 0.0797153i \(-0.974599\pi\)
0.0797153 + 0.996818i \(0.474599\pi\)
\(854\) −7.70668 −0.263717
\(855\) −75.6471 + 75.6471i −2.58708 + 2.58708i
\(856\) −0.381922 0.381922i −0.0130538 0.0130538i
\(857\) −23.6022 23.6022i −0.806235 0.806235i 0.177827 0.984062i \(-0.443093\pi\)
−0.984062 + 0.177827i \(0.943093\pi\)
\(858\) 24.3823i 0.832398i
\(859\) 15.3675i 0.524333i 0.965023 + 0.262167i \(0.0844370\pi\)
−0.965023 + 0.262167i \(0.915563\pi\)
\(860\) −4.23410 4.23410i −0.144382 0.144382i
\(861\) 60.1410 + 60.1410i 2.04960 + 2.04960i
\(862\) −4.82964 + 4.82964i −0.164498 + 0.164498i
\(863\) −34.4359 −1.17221 −0.586106 0.810234i \(-0.699340\pi\)
−0.586106 + 0.810234i \(0.699340\pi\)
\(864\) 21.9542 21.9542i 0.746898 0.746898i
\(865\) 32.9882i 1.12163i
\(866\) 13.2072 0.448798
\(867\) 38.1023 31.7007i 1.29402 1.07661i
\(868\) −25.2695 −0.857704
\(869\) 7.58584i 0.257332i
\(870\) −4.86500 + 4.86500i −0.164939 + 0.164939i
\(871\) −4.58149 −0.155238
\(872\) 4.91511 4.91511i 0.166447 0.166447i
\(873\) 13.1192 + 13.1192i 0.444018 + 0.444018i
\(874\) −1.50998 1.50998i −0.0510757 0.0510757i
\(875\) 7.11450i 0.240514i
\(876\) 70.0560i 2.36697i
\(877\) 33.0294 + 33.0294i 1.11532 + 1.11532i 0.992418 + 0.122906i \(0.0392215\pi\)
0.122906 + 0.992418i \(0.460778\pi\)
\(878\) −4.83233 4.83233i −0.163083 0.163083i
\(879\) −47.2827 + 47.2827i −1.59480 + 1.59480i
\(880\) −65.1500 −2.19621
\(881\) 2.52417 2.52417i 0.0850415 0.0850415i −0.663306 0.748348i \(-0.730847\pi\)
0.748348 + 0.663306i \(0.230847\pi\)
\(882\) 19.6853i 0.662838i
\(883\) −9.16688 −0.308490 −0.154245 0.988033i \(-0.549295\pi\)
−0.154245 + 0.988033i \(0.549295\pi\)
\(884\) 1.13166 24.7307i 0.0380617 0.831783i
\(885\) 24.7095 0.830602
\(886\) 4.07290i 0.136832i
\(887\) −1.22744 + 1.22744i −0.0412133 + 0.0412133i −0.727413 0.686200i \(-0.759278\pi\)
0.686200 + 0.727413i \(0.259278\pi\)
\(888\) 6.82485 0.229027
\(889\) 56.8324 56.8324i 1.90610 1.90610i
\(890\) 11.6661 + 11.6661i 0.391047 + 0.391047i
\(891\) −21.8530 21.8530i −0.732102 0.732102i
\(892\) 36.0270i 1.20627i
\(893\) 16.5413i 0.553535i
\(894\) 12.3569 + 12.3569i 0.413275 + 0.413275i
\(895\) −26.2975 26.2975i −0.879028 0.879028i
\(896\) 29.1594 29.1594i 0.974148 0.974148i
\(897\) 8.56678 0.286037
\(898\) −2.15968 + 2.15968i −0.0720693 + 0.0720693i
\(899\) 6.28872i 0.209741i
\(900\) −56.2571 −1.87524
\(901\) −51.3150 2.34813i −1.70955 0.0782276i
\(902\) −18.6959 −0.622504
\(903\) 11.6825i 0.388771i
\(904\) −15.4932 + 15.4932i −0.515296 + 0.515296i
\(905\) −32.3682 −1.07596
\(906\) 17.7371 17.7371i 0.589275 0.589275i
\(907\) −14.5712 14.5712i −0.483827 0.483827i 0.422524 0.906352i \(-0.361144\pi\)
−0.906352 + 0.422524i \(0.861144\pi\)
\(908\) 6.55285 + 6.55285i 0.217464 + 0.217464i
\(909\) 83.2809i 2.76225i
\(910\) 16.7469i 0.555155i
\(911\) −3.90158 3.90158i −0.129265 0.129265i 0.639514 0.768779i \(-0.279136\pi\)
−0.768779 + 0.639514i \(0.779136\pi\)
\(912\) −38.1168 38.1168i −1.26217 1.26217i
\(913\) 4.30687 4.30687i 0.142537 0.142537i
\(914\) 11.1287 0.368106
\(915\) −32.5846 + 32.5846i −1.07721 + 1.07721i
\(916\) 3.55590i 0.117490i
\(917\) −12.5657 −0.414957
\(918\) −8.00815 8.77619i −0.264308 0.289657i
\(919\) 21.8990 0.722380 0.361190 0.932492i \(-0.382371\pi\)
0.361190 + 0.932492i \(0.382371\pi\)
\(920\) 4.45124i 0.146753i
\(921\) 17.1910 17.1910i 0.566462 0.566462i
\(922\) −12.7607 −0.420252
\(923\) −12.9044 + 12.9044i −0.424753 + 0.424753i
\(924\) −98.9734 98.9734i −3.25599 3.25599i
\(925\) −6.04374 6.04374i −0.198717 0.198717i
\(926\) 13.4931i 0.443409i
\(927\) 62.8661i 2.06479i
\(928\) −5.53617 5.53617i −0.181734 0.181734i
\(929\) 13.8275 + 13.8275i 0.453665 + 0.453665i 0.896569 0.442904i \(-0.146052\pi\)
−0.442904 + 0.896569i \(0.646052\pi\)
\(930\) 9.05029 9.05029i 0.296771 0.296771i
\(931\) −54.2284 −1.77726
\(932\) −37.9845 + 37.9845i −1.24423 + 1.24423i
\(933\) 35.1787i 1.15170i
\(934\) −9.68400 −0.316870
\(935\) −3.97728 + 86.9176i −0.130071 + 2.84251i
\(936\) −27.2115 −0.889435
\(937\) 36.6330i 1.19675i 0.801217 + 0.598374i \(0.204186\pi\)
−0.801217 + 0.598374i \(0.795814\pi\)
\(938\) −1.57532 + 1.57532i −0.0514362 + 0.0514362i
\(939\) 46.0661 1.50331
\(940\) 11.6952 11.6952i 0.381454 0.381454i
\(941\) −9.41006 9.41006i −0.306759 0.306759i 0.536892 0.843651i \(-0.319598\pi\)
−0.843651 + 0.536892i \(0.819598\pi\)
\(942\) −5.80807 5.80807i −0.189237 0.189237i
\(943\) 6.56884i 0.213911i
\(944\) 8.05664i 0.262221i
\(945\) −67.0892 67.0892i −2.18241 2.18241i
\(946\) 1.81586 + 1.81586i 0.0590387 + 0.0590387i
\(947\) −37.3481 + 37.3481i −1.21365 + 1.21365i −0.243834 + 0.969817i \(0.578405\pi\)
−0.969817 + 0.243834i \(0.921595\pi\)
\(948\) 6.27583 0.203830
\(949\) 30.0077 30.0077i 0.974090 0.974090i
\(950\) 13.1275i 0.425912i
\(951\) −35.6614 −1.15640
\(952\) −16.9162 18.5386i −0.548258 0.600839i
\(953\) 37.1414 1.20313 0.601563 0.798825i \(-0.294545\pi\)
0.601563 + 0.798825i \(0.294545\pi\)
\(954\) 27.0842i 0.876882i
\(955\) −9.95499 + 9.95499i −0.322136 + 0.322136i
\(956\) 43.9095 1.42013
\(957\) −24.6311 + 24.6311i −0.796210 + 0.796210i
\(958\) −11.9772 11.9772i −0.386965 0.386965i
\(959\) 1.23127 + 1.23127i 0.0397597 + 0.0397597i
\(960\) 42.5303i 1.37266i
\(961\) 19.3012i 0.622619i
\(962\) −1.40228 1.40228i −0.0452114 0.0452114i
\(963\) −1.38298 1.38298i −0.0445659 0.0445659i
\(964\) 15.4644 15.4644i 0.498076 0.498076i
\(965\) 26.0991 0.840159
\(966\) 2.94565 2.94565i 0.0947748 0.0947748i
\(967\) 38.6224i 1.24201i 0.783806 + 0.621006i \(0.213276\pi\)
−0.783806 + 0.621006i \(0.786724\pi\)
\(968\) 47.4315 1.52451
\(969\) −53.1792 + 48.5253i −1.70836 + 1.55886i
\(970\) −4.32890 −0.138993
\(971\) 42.1948i 1.35409i 0.735940 + 0.677047i \(0.236741\pi\)
−0.735940 + 0.677047i \(0.763259\pi\)
\(972\) −10.4392 + 10.4392i −0.334837 + 0.334837i
\(973\) 55.1755 1.76884
\(974\) −3.16095 + 3.16095i −0.101283 + 0.101283i
\(975\) 37.2391 + 37.2391i 1.19261 + 1.19261i
\(976\) −10.6243 10.6243i −0.340077 0.340077i
\(977\) 46.5826i 1.49031i 0.666892 + 0.745154i \(0.267624\pi\)
−0.666892 + 0.745154i \(0.732376\pi\)
\(978\) 18.3856i 0.587908i
\(979\) 59.0643 + 59.0643i 1.88770 + 1.88770i
\(980\) −38.3409 38.3409i −1.22475 1.22475i
\(981\) 17.7981 17.7981i 0.568251 0.568251i
\(982\) −1.67479 −0.0534447
\(983\) −39.6812 + 39.6812i −1.26563 + 1.26563i −0.317314 + 0.948320i \(0.602781\pi\)
−0.948320 + 0.317314i \(0.897219\pi\)
\(984\) 32.2447i 1.02792i
\(985\) −49.2903 −1.57052
\(986\) −2.21308 + 2.01940i −0.0704788 + 0.0643109i
\(987\) 32.2687 1.02713
\(988\) 35.9577i 1.14397i
\(989\) 0.638007 0.638007i 0.0202874 0.0202874i
\(990\) 45.8753 1.45801
\(991\) −26.0834 + 26.0834i −0.828567 + 0.828567i −0.987319 0.158751i \(-0.949253\pi\)
0.158751 + 0.987319i \(0.449253\pi\)
\(992\) 10.2988 + 10.2988i 0.326989 + 0.326989i
\(993\) 16.6350 + 16.6350i 0.527894 + 0.527894i
\(994\) 8.87423i 0.281474i
\(995\) 68.4339i 2.16950i
\(996\) 3.56312 + 3.56312i 0.112902 + 0.112902i
\(997\) 21.0916 + 21.0916i 0.667978 + 0.667978i 0.957248 0.289270i \(-0.0934125\pi\)
−0.289270 + 0.957248i \(0.593413\pi\)
\(998\) 5.64759 5.64759i 0.178771 0.178771i
\(999\) 11.2353 0.355468
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 731.2.f.c.259.15 56
17.13 even 4 inner 731.2.f.c.302.14 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
731.2.f.c.259.15 56 1.1 even 1 trivial
731.2.f.c.302.14 yes 56 17.13 even 4 inner