Properties

Label 63.2.i.b.5.3
Level $63$
Weight $2$
Character 63.5
Analytic conductor $0.503$
Analytic rank $0$
Dimension $10$
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] = [63,2,Mod(5,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 63.i (of order \(6\), 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: \(0.503057532734\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: 10.0.288778218147.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 5.3
Root \(-0.539982 + 0.935277i\) of defining polynomial
Character \(\chi\) \(=\) 63.5
Dual form 63.2.i.b.38.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.293869i q^{2} +(-1.65249 + 0.518912i) q^{3} +1.91364 q^{4} +(1.53014 + 2.65027i) q^{5} +(-0.152492 - 0.485617i) q^{6} +(-1.41763 - 2.23391i) q^{7} +1.15010i q^{8} +(2.46146 - 1.71499i) q^{9} +O(q^{10})\) \(q+0.293869i q^{2} +(-1.65249 + 0.518912i) q^{3} +1.91364 q^{4} +(1.53014 + 2.65027i) q^{5} +(-0.152492 - 0.485617i) q^{6} +(-1.41763 - 2.23391i) q^{7} +1.15010i q^{8} +(2.46146 - 1.71499i) q^{9} +(-0.778834 + 0.449660i) q^{10} +(-3.37445 - 1.94824i) q^{11} +(-3.16228 + 0.993010i) q^{12} +(-2.02935 - 1.17164i) q^{13} +(0.656477 - 0.416597i) q^{14} +(-3.90379 - 3.58555i) q^{15} +3.48930 q^{16} +(-1.68263 - 2.91440i) q^{17} +(0.503985 + 0.723348i) q^{18} +(2.20696 + 1.27419i) q^{19} +(2.92813 + 5.07167i) q^{20} +(3.50182 + 2.95589i) q^{21} +(0.572527 - 0.991647i) q^{22} +(2.58141 - 1.49038i) q^{23} +(-0.596800 - 1.90053i) q^{24} +(-2.18263 + 3.78042i) q^{25} +(0.344311 - 0.596363i) q^{26} +(-3.17762 + 4.11130i) q^{27} +(-2.71283 - 4.27489i) q^{28} +(-3.67241 + 2.12027i) q^{29} +(1.05368 - 1.14721i) q^{30} +0.472735i q^{31} +3.32560i q^{32} +(6.58721 + 1.46841i) q^{33} +(0.856452 - 0.494473i) q^{34} +(3.75130 - 7.17527i) q^{35} +(4.71035 - 3.28188i) q^{36} +(-3.89395 + 6.74451i) q^{37} +(-0.374446 + 0.648559i) q^{38} +(3.96146 + 0.883081i) q^{39} +(-3.04808 + 1.75981i) q^{40} +(3.12737 - 5.41676i) q^{41} +(-0.868646 + 1.02908i) q^{42} +(2.06191 + 3.57133i) q^{43} +(-6.45748 - 3.72823i) q^{44} +(8.31157 + 3.89937i) q^{45} +(0.437976 + 0.758597i) q^{46} -4.05388 q^{47} +(-5.76605 + 1.81064i) q^{48} +(-2.98068 + 6.33369i) q^{49} +(-1.11095 - 0.641408i) q^{50} +(4.29284 + 3.94288i) q^{51} +(-3.88344 - 2.24211i) q^{52} +(4.99439 - 2.88351i) q^{53} +(-1.20818 - 0.933804i) q^{54} -11.9243i q^{55} +(2.56921 - 1.63041i) q^{56} +(-4.30818 - 0.960372i) q^{57} +(-0.623082 - 1.07921i) q^{58} -4.68705 q^{59} +(-7.47046 - 6.86145i) q^{60} -1.60018i q^{61} -0.138922 q^{62} +(-7.32057 - 3.06745i) q^{63} +6.00131 q^{64} -7.17110i q^{65} +(-0.431520 + 1.93578i) q^{66} +1.57566 q^{67} +(-3.21994 - 5.57711i) q^{68} +(-3.49238 + 3.80236i) q^{69} +(2.10859 + 1.10239i) q^{70} +13.6132i q^{71} +(1.97241 + 2.83093i) q^{72} +(-0.856452 + 0.494473i) q^{73} +(-1.98201 - 1.14431i) q^{74} +(1.64507 - 7.37971i) q^{75} +(4.22333 + 2.43834i) q^{76} +(0.431520 + 10.3001i) q^{77} +(-0.259511 + 1.16415i) q^{78} -9.27815 q^{79} +(5.33910 + 9.24760i) q^{80} +(3.11759 - 8.44279i) q^{81} +(1.59182 + 0.919038i) q^{82} +(5.49361 + 9.51520i) q^{83} +(6.70122 + 5.65651i) q^{84} +(5.14930 - 8.91884i) q^{85} +(-1.04950 + 0.605932i) q^{86} +(4.96840 - 5.40938i) q^{87} +(2.24067 - 3.88095i) q^{88} +(-2.15849 + 3.73861i) q^{89} +(-1.14591 + 2.44252i) q^{90} +(0.259511 + 6.19433i) q^{91} +(4.93989 - 2.85205i) q^{92} +(-0.245308 - 0.781191i) q^{93} -1.19131i q^{94} +7.79874i q^{95} +(-1.72569 - 5.49553i) q^{96} +(4.98797 - 2.87980i) q^{97} +(-1.86128 - 0.875930i) q^{98} +(-11.6473 + 0.991647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 3 q^{3} - 8 q^{4} + 12 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 3 q^{3} - 8 q^{4} + 12 q^{6} - 6 q^{7} + 3 q^{9} - 15 q^{10} - 12 q^{11} - 12 q^{12} - 6 q^{13} + 12 q^{14} - 3 q^{15} + 12 q^{16} + 12 q^{17} + 24 q^{18} + 3 q^{19} + 3 q^{20} - 9 q^{21} + 5 q^{22} - 15 q^{23} + 7 q^{25} - 3 q^{26} - 27 q^{27} + 2 q^{28} - 15 q^{29} + 6 q^{30} - 3 q^{34} + 15 q^{35} - 18 q^{36} + 6 q^{37} + 18 q^{38} + 18 q^{39} + 15 q^{40} + 9 q^{41} - 12 q^{42} + 3 q^{43} - 24 q^{44} + 30 q^{45} - 13 q^{46} + 30 q^{47} + 15 q^{48} + 4 q^{49} + 3 q^{50} + 21 q^{51} - 12 q^{52} + 9 q^{53} + 9 q^{54} - 30 q^{56} - 36 q^{57} + 8 q^{58} - 36 q^{59} - 48 q^{60} - 12 q^{62} - 15 q^{63} + 6 q^{64} - 39 q^{66} + 20 q^{67} - 27 q^{68} + 3 q^{69} + 6 q^{70} - 30 q^{72} + 3 q^{73} - 30 q^{74} + 6 q^{75} - 9 q^{76} + 39 q^{77} + 24 q^{78} - 40 q^{79} + 30 q^{80} + 15 q^{81} + 9 q^{82} + 15 q^{83} + 93 q^{84} + 18 q^{85} + 54 q^{86} + 6 q^{87} - 8 q^{88} - 24 q^{89} - 24 q^{90} - 24 q^{91} + 39 q^{92} + 36 q^{93} + 33 q^{96} - 6 q^{97} - 45 q^{98} + 21 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.293869i 0.207797i 0.994588 + 0.103899i \(0.0331317\pi\)
−0.994588 + 0.103899i \(0.966868\pi\)
\(3\) −1.65249 + 0.518912i −0.954067 + 0.299594i
\(4\) 1.91364 0.956820
\(5\) 1.53014 + 2.65027i 0.684297 + 1.18524i 0.973657 + 0.228017i \(0.0732243\pi\)
−0.289360 + 0.957220i \(0.593442\pi\)
\(6\) −0.152492 0.485617i −0.0622547 0.198252i
\(7\) −1.41763 2.23391i −0.535812 0.844337i
\(8\) 1.15010i 0.406622i
\(9\) 2.46146 1.71499i 0.820487 0.571665i
\(10\) −0.778834 + 0.449660i −0.246289 + 0.142195i
\(11\) −3.37445 1.94824i −1.01743 0.587416i −0.104074 0.994570i \(-0.533188\pi\)
−0.913360 + 0.407154i \(0.866521\pi\)
\(12\) −3.16228 + 0.993010i −0.912871 + 0.286657i
\(13\) −2.02935 1.17164i −0.562840 0.324956i 0.191445 0.981503i \(-0.438683\pi\)
−0.754285 + 0.656548i \(0.772016\pi\)
\(14\) 0.656477 0.416597i 0.175451 0.111340i
\(15\) −3.90379 3.58555i −1.00796 0.925785i
\(16\) 3.48930 0.872326
\(17\) −1.68263 2.91440i −0.408097 0.706845i 0.586579 0.809892i \(-0.300474\pi\)
−0.994677 + 0.103047i \(0.967141\pi\)
\(18\) 0.503985 + 0.723348i 0.118790 + 0.170495i
\(19\) 2.20696 + 1.27419i 0.506312 + 0.292319i 0.731316 0.682038i \(-0.238906\pi\)
−0.225004 + 0.974358i \(0.572240\pi\)
\(20\) 2.92813 + 5.07167i 0.654750 + 1.13406i
\(21\) 3.50182 + 2.95589i 0.764159 + 0.645028i
\(22\) 0.572527 0.991647i 0.122063 0.211420i
\(23\) 2.58141 1.49038i 0.538261 0.310765i −0.206113 0.978528i \(-0.566081\pi\)
0.744374 + 0.667763i \(0.232748\pi\)
\(24\) −0.596800 1.90053i −0.121821 0.387944i
\(25\) −2.18263 + 3.78042i −0.436525 + 0.756084i
\(26\) 0.344311 0.596363i 0.0675249 0.116956i
\(27\) −3.17762 + 4.11130i −0.611532 + 0.791219i
\(28\) −2.71283 4.27489i −0.512676 0.807879i
\(29\) −3.67241 + 2.12027i −0.681949 + 0.393724i −0.800589 0.599214i \(-0.795480\pi\)
0.118640 + 0.992937i \(0.462147\pi\)
\(30\) 1.05368 1.14721i 0.192375 0.209450i
\(31\) 0.472735i 0.0849057i 0.999098 + 0.0424528i \(0.0135172\pi\)
−0.999098 + 0.0424528i \(0.986483\pi\)
\(32\) 3.32560i 0.587888i
\(33\) 6.58721 + 1.46841i 1.14669 + 0.255617i
\(34\) 0.856452 0.494473i 0.146880 0.0848014i
\(35\) 3.75130 7.17527i 0.634086 1.21284i
\(36\) 4.71035 3.28188i 0.785059 0.546981i
\(37\) −3.89395 + 6.74451i −0.640161 + 1.10879i 0.345236 + 0.938516i \(0.387799\pi\)
−0.985397 + 0.170275i \(0.945534\pi\)
\(38\) −0.374446 + 0.648559i −0.0607431 + 0.105210i
\(39\) 3.96146 + 0.883081i 0.634342 + 0.141406i
\(40\) −3.04808 + 1.75981i −0.481943 + 0.278250i
\(41\) 3.12737 5.41676i 0.488413 0.845956i −0.511498 0.859284i \(-0.670909\pi\)
0.999911 + 0.0133282i \(0.00424262\pi\)
\(42\) −0.868646 + 1.02908i −0.134035 + 0.158790i
\(43\) 2.06191 + 3.57133i 0.314438 + 0.544623i 0.979318 0.202328i \(-0.0648506\pi\)
−0.664880 + 0.746950i \(0.731517\pi\)
\(44\) −6.45748 3.72823i −0.973501 0.562051i
\(45\) 8.31157 + 3.89937i 1.23902 + 0.581283i
\(46\) 0.437976 + 0.758597i 0.0645761 + 0.111849i
\(47\) −4.05388 −0.591319 −0.295659 0.955293i \(-0.595539\pi\)
−0.295659 + 0.955293i \(0.595539\pi\)
\(48\) −5.76605 + 1.81064i −0.832257 + 0.261343i
\(49\) −2.98068 + 6.33369i −0.425811 + 0.904812i
\(50\) −1.11095 0.641408i −0.157112 0.0907087i
\(51\) 4.29284 + 3.94288i 0.601118 + 0.552114i
\(52\) −3.88344 2.24211i −0.538537 0.310924i
\(53\) 4.99439 2.88351i 0.686033 0.396081i −0.116091 0.993239i \(-0.537037\pi\)
0.802124 + 0.597157i \(0.203703\pi\)
\(54\) −1.20818 0.933804i −0.164413 0.127075i
\(55\) 11.9243i 1.60787i
\(56\) 2.56921 1.63041i 0.343326 0.217873i
\(57\) −4.30818 0.960372i −0.570633 0.127204i
\(58\) −0.623082 1.07921i −0.0818146 0.141707i
\(59\) −4.68705 −0.610201 −0.305101 0.952320i \(-0.598690\pi\)
−0.305101 + 0.952320i \(0.598690\pi\)
\(60\) −7.47046 6.86145i −0.964432 0.885810i
\(61\) 1.60018i 0.204883i −0.994739 0.102441i \(-0.967335\pi\)
0.994739 0.102441i \(-0.0326654\pi\)
\(62\) −0.138922 −0.0176432
\(63\) −7.32057 3.06745i −0.922305 0.386463i
\(64\) 6.00131 0.750164
\(65\) 7.17110i 0.889465i
\(66\) −0.431520 + 1.93578i −0.0531165 + 0.238278i
\(67\) 1.57566 0.192498 0.0962489 0.995357i \(-0.469316\pi\)
0.0962489 + 0.995357i \(0.469316\pi\)
\(68\) −3.21994 5.57711i −0.390476 0.676324i
\(69\) −3.49238 + 3.80236i −0.420434 + 0.457750i
\(70\) 2.10859 + 1.10239i 0.252025 + 0.131761i
\(71\) 13.6132i 1.61559i 0.589462 + 0.807796i \(0.299340\pi\)
−0.589462 + 0.807796i \(0.700660\pi\)
\(72\) 1.97241 + 2.83093i 0.232451 + 0.333628i
\(73\) −0.856452 + 0.494473i −0.100240 + 0.0578737i −0.549282 0.835637i \(-0.685099\pi\)
0.449042 + 0.893511i \(0.351765\pi\)
\(74\) −1.98201 1.14431i −0.230404 0.133024i
\(75\) 1.64507 7.37971i 0.189956 0.852135i
\(76\) 4.22333 + 2.43834i 0.484450 + 0.279697i
\(77\) 0.431520 + 10.3001i 0.0491763 + 1.17380i
\(78\) −0.259511 + 1.16415i −0.0293838 + 0.131814i
\(79\) −9.27815 −1.04387 −0.521937 0.852984i \(-0.674790\pi\)
−0.521937 + 0.852984i \(0.674790\pi\)
\(80\) 5.33910 + 9.24760i 0.596930 + 1.03391i
\(81\) 3.11759 8.44279i 0.346398 0.938088i
\(82\) 1.59182 + 0.919038i 0.175787 + 0.101491i
\(83\) 5.49361 + 9.51520i 0.603002 + 1.04443i 0.992364 + 0.123345i \(0.0393621\pi\)
−0.389362 + 0.921085i \(0.627305\pi\)
\(84\) 6.70122 + 5.65651i 0.731163 + 0.617176i
\(85\) 5.14930 8.91884i 0.558519 0.967384i
\(86\) −1.04950 + 0.605932i −0.113171 + 0.0653393i
\(87\) 4.96840 5.40938i 0.532668 0.579946i
\(88\) 2.24067 3.88095i 0.238856 0.413710i
\(89\) −2.15849 + 3.73861i −0.228799 + 0.396292i −0.957452 0.288591i \(-0.906813\pi\)
0.728653 + 0.684883i \(0.240147\pi\)
\(90\) −1.14591 + 2.44252i −0.120789 + 0.257464i
\(91\) 0.259511 + 6.19433i 0.0272041 + 0.649342i
\(92\) 4.93989 2.85205i 0.515019 0.297346i
\(93\) −0.245308 0.781191i −0.0254372 0.0810057i
\(94\) 1.19131i 0.122874i
\(95\) 7.79874i 0.800133i
\(96\) −1.72569 5.49553i −0.176128 0.560885i
\(97\) 4.98797 2.87980i 0.506451 0.292400i −0.224923 0.974377i \(-0.572213\pi\)
0.731374 + 0.681977i \(0.238880\pi\)
\(98\) −1.86128 0.875930i −0.188017 0.0884823i
\(99\) −11.6473 + 0.991647i −1.17060 + 0.0996642i
\(100\) −4.17676 + 7.23437i −0.417676 + 0.723437i
\(101\) 8.57900 14.8593i 0.853642 1.47855i −0.0242566 0.999706i \(-0.507722\pi\)
0.877899 0.478846i \(-0.158945\pi\)
\(102\) −1.15869 + 1.26154i −0.114728 + 0.124911i
\(103\) 8.50422 4.90992i 0.837946 0.483788i −0.0186195 0.999827i \(-0.505927\pi\)
0.856566 + 0.516038i \(0.172594\pi\)
\(104\) 1.34751 2.33395i 0.132134 0.228863i
\(105\) −2.47566 + 13.8037i −0.241600 + 1.34710i
\(106\) 0.847377 + 1.46770i 0.0823045 + 0.142556i
\(107\) −3.00501 1.73494i −0.290505 0.167723i 0.347664 0.937619i \(-0.386975\pi\)
−0.638170 + 0.769896i \(0.720308\pi\)
\(108\) −6.08081 + 7.86755i −0.585127 + 0.757055i
\(109\) 0.611066 + 1.05840i 0.0585295 + 0.101376i 0.893806 0.448455i \(-0.148025\pi\)
−0.835276 + 0.549831i \(0.814692\pi\)
\(110\) 3.50418 0.334110
\(111\) 2.93491 13.1659i 0.278569 1.24965i
\(112\) −4.94652 7.79478i −0.467403 0.736537i
\(113\) −1.87681 1.08358i −0.176555 0.101934i 0.409118 0.912482i \(-0.365836\pi\)
−0.585673 + 0.810547i \(0.699170\pi\)
\(114\) 0.282224 1.26604i 0.0264327 0.118576i
\(115\) 7.89981 + 4.56096i 0.736661 + 0.425311i
\(116\) −7.02767 + 4.05743i −0.652503 + 0.376723i
\(117\) −7.00453 + 0.596363i −0.647569 + 0.0551338i
\(118\) 1.37738i 0.126798i
\(119\) −4.12515 + 7.89035i −0.378152 + 0.723308i
\(120\) 4.12374 4.48975i 0.376444 0.409856i
\(121\) 2.09126 + 3.62216i 0.190114 + 0.329287i
\(122\) 0.470245 0.0425740
\(123\) −2.35713 + 10.5740i −0.212535 + 0.953424i
\(124\) 0.904645i 0.0812395i
\(125\) 1.94249 0.173742
\(126\) 0.901431 2.15129i 0.0803059 0.191652i
\(127\) 2.74889 0.243925 0.121962 0.992535i \(-0.461081\pi\)
0.121962 + 0.992535i \(0.461081\pi\)
\(128\) 8.41480i 0.743770i
\(129\) −5.26049 4.83165i −0.463160 0.425403i
\(130\) 2.10737 0.184828
\(131\) −3.73911 6.47632i −0.326687 0.565839i 0.655165 0.755486i \(-0.272599\pi\)
−0.981852 + 0.189647i \(0.939266\pi\)
\(132\) 12.6056 + 2.81000i 1.09717 + 0.244580i
\(133\) −0.282224 6.73647i −0.0244719 0.584126i
\(134\) 0.463039i 0.0400005i
\(135\) −15.7582 2.13070i −1.35625 0.183382i
\(136\) 3.35185 1.93519i 0.287418 0.165941i
\(137\) −10.5731 6.10439i −0.903321 0.521533i −0.0250451 0.999686i \(-0.507973\pi\)
−0.878276 + 0.478153i \(0.841306\pi\)
\(138\) −1.11740 1.02631i −0.0951192 0.0873649i
\(139\) −11.5501 6.66842i −0.979663 0.565608i −0.0774943 0.996993i \(-0.524692\pi\)
−0.902168 + 0.431384i \(0.858025\pi\)
\(140\) 7.17864 13.7309i 0.606706 1.16047i
\(141\) 6.69900 2.10360i 0.564157 0.177155i
\(142\) −4.00051 −0.335715
\(143\) 4.56528 + 7.90730i 0.381768 + 0.661242i
\(144\) 8.58878 5.98414i 0.715732 0.498678i
\(145\) −11.2386 6.48859i −0.933312 0.538848i
\(146\) −0.145310 0.251685i −0.0120260 0.0208296i
\(147\) 1.63892 12.0131i 0.135176 0.990822i
\(148\) −7.45161 + 12.9066i −0.612519 + 1.06091i
\(149\) −7.33827 + 4.23675i −0.601174 + 0.347088i −0.769503 0.638643i \(-0.779496\pi\)
0.168329 + 0.985731i \(0.446163\pi\)
\(150\) 2.16867 + 0.483436i 0.177071 + 0.0394724i
\(151\) 1.67827 2.90685i 0.136576 0.236556i −0.789623 0.613593i \(-0.789724\pi\)
0.926198 + 0.377037i \(0.123057\pi\)
\(152\) −1.46545 + 2.53823i −0.118863 + 0.205877i
\(153\) −9.13990 4.28798i −0.738917 0.346662i
\(154\) −3.02688 + 0.126811i −0.243913 + 0.0102187i
\(155\) −1.25288 + 0.723348i −0.100633 + 0.0581007i
\(156\) 7.58081 + 1.68990i 0.606951 + 0.135300i
\(157\) 16.7085i 1.33349i 0.745288 + 0.666743i \(0.232312\pi\)
−0.745288 + 0.666743i \(0.767688\pi\)
\(158\) 2.72657i 0.216914i
\(159\) −6.75691 + 7.35663i −0.535858 + 0.583419i
\(160\) −8.81374 + 5.08862i −0.696787 + 0.402290i
\(161\) −6.98883 3.65383i −0.550797 0.287962i
\(162\) 2.48108 + 0.916163i 0.194932 + 0.0719806i
\(163\) 12.6662 21.9385i 0.992094 1.71836i 0.387363 0.921927i \(-0.373386\pi\)
0.604731 0.796430i \(-0.293281\pi\)
\(164\) 5.98466 10.3657i 0.467324 0.809428i
\(165\) 6.18764 + 19.7048i 0.481707 + 1.53401i
\(166\) −2.79623 + 1.61440i −0.217029 + 0.125302i
\(167\) 0.875828 1.51698i 0.0677736 0.117387i −0.830147 0.557544i \(-0.811744\pi\)
0.897921 + 0.440157i \(0.145077\pi\)
\(168\) −3.39957 + 4.02744i −0.262282 + 0.310723i
\(169\) −3.75450 6.50298i −0.288808 0.500229i
\(170\) 2.62097 + 1.51322i 0.201020 + 0.116059i
\(171\) 7.61759 0.648559i 0.582531 0.0495965i
\(172\) 3.94575 + 6.83424i 0.300861 + 0.521106i
\(173\) 23.9266 1.81910 0.909551 0.415592i \(-0.136426\pi\)
0.909551 + 0.415592i \(0.136426\pi\)
\(174\) 1.58965 + 1.46006i 0.120511 + 0.110687i
\(175\) 11.5393 0.483436i 0.872286 0.0365443i
\(176\) −11.7745 6.79799i −0.887533 0.512418i
\(177\) 7.74531 2.43216i 0.582173 0.182813i
\(178\) −1.09866 0.634313i −0.0823482 0.0475438i
\(179\) 21.9857 12.6935i 1.64329 0.948755i 0.663639 0.748053i \(-0.269011\pi\)
0.979652 0.200702i \(-0.0643223\pi\)
\(180\) 15.9054 + 7.46199i 1.18552 + 0.556184i
\(181\) 22.4032i 1.66522i 0.553859 + 0.832610i \(0.313155\pi\)
−0.553859 + 0.832610i \(0.686845\pi\)
\(182\) −1.82032 + 0.0762622i −0.134931 + 0.00565293i
\(183\) 0.830354 + 2.64429i 0.0613815 + 0.195472i
\(184\) 1.71408 + 2.96888i 0.126364 + 0.218869i
\(185\) −23.8331 −1.75224
\(186\) 0.229568 0.0720884i 0.0168328 0.00528578i
\(187\) 13.1126i 0.958890i
\(188\) −7.75766 −0.565786
\(189\) 13.6889 + 1.27022i 0.995722 + 0.0923947i
\(190\) −2.29181 −0.166265
\(191\) 4.28895i 0.310337i 0.987888 + 0.155169i \(0.0495921\pi\)
−0.987888 + 0.155169i \(0.950408\pi\)
\(192\) −9.91712 + 3.11415i −0.715707 + 0.224744i
\(193\) −23.3449 −1.68041 −0.840203 0.542272i \(-0.817564\pi\)
−0.840203 + 0.542272i \(0.817564\pi\)
\(194\) 0.846286 + 1.46581i 0.0607598 + 0.105239i
\(195\) 3.72117 + 11.8502i 0.266478 + 0.848609i
\(196\) −5.70394 + 12.1204i −0.407425 + 0.865743i
\(197\) 18.7811i 1.33809i −0.743220 0.669047i \(-0.766702\pi\)
0.743220 0.669047i \(-0.233298\pi\)
\(198\) −0.291415 3.42278i −0.0207099 0.243246i
\(199\) −3.92927 + 2.26856i −0.278539 + 0.160814i −0.632762 0.774347i \(-0.718079\pi\)
0.354223 + 0.935161i \(0.384745\pi\)
\(200\) −4.34786 2.51024i −0.307440 0.177501i
\(201\) −2.60377 + 0.817629i −0.183656 + 0.0576711i
\(202\) 4.36668 + 2.52111i 0.307239 + 0.177384i
\(203\) 9.94258 + 5.19808i 0.697832 + 0.364833i
\(204\) 8.21496 + 7.54526i 0.575162 + 0.528274i
\(205\) 19.1412 1.33688
\(206\) 1.44287 + 2.49913i 0.100530 + 0.174123i
\(207\) 3.79805 8.09561i 0.263983 0.562684i
\(208\) −7.08101 4.08822i −0.490980 0.283467i
\(209\) −4.96485 8.59937i −0.343426 0.594831i
\(210\) −4.05648 0.727522i −0.279924 0.0502038i
\(211\) −3.44148 + 5.96082i −0.236921 + 0.410360i −0.959829 0.280584i \(-0.909472\pi\)
0.722908 + 0.690944i \(0.242805\pi\)
\(212\) 9.55747 5.51801i 0.656410 0.378978i
\(213\) −7.06406 22.4958i −0.484021 1.54138i
\(214\) 0.509847 0.883081i 0.0348524 0.0603662i
\(215\) −6.31000 + 10.9292i −0.430338 + 0.745368i
\(216\) −4.72840 3.65457i −0.321727 0.248662i
\(217\) 1.05605 0.670161i 0.0716890 0.0454935i
\(218\) −0.311031 + 0.179574i −0.0210657 + 0.0121623i
\(219\) 1.15869 1.26154i 0.0782972 0.0852467i
\(220\) 22.8188i 1.53844i
\(221\) 7.88576i 0.530454i
\(222\) 3.86905 + 0.862480i 0.259673 + 0.0578859i
\(223\) 5.57176 3.21686i 0.373113 0.215417i −0.301705 0.953401i \(-0.597556\pi\)
0.674818 + 0.737985i \(0.264222\pi\)
\(224\) 7.42908 4.71445i 0.496376 0.314998i
\(225\) 1.11095 + 13.0486i 0.0740634 + 0.869904i
\(226\) 0.318430 0.551537i 0.0211816 0.0366877i
\(227\) −9.86983 + 17.0951i −0.655084 + 1.13464i 0.326789 + 0.945097i \(0.394033\pi\)
−0.981873 + 0.189541i \(0.939300\pi\)
\(228\) −8.24431 1.83781i −0.545993 0.121712i
\(229\) 9.44564 5.45344i 0.624185 0.360373i −0.154311 0.988022i \(-0.549316\pi\)
0.778497 + 0.627649i \(0.215983\pi\)
\(230\) −1.34033 + 2.32151i −0.0883785 + 0.153076i
\(231\) −6.05791 16.7969i −0.398581 1.10515i
\(232\) −2.43852 4.22364i −0.160097 0.277295i
\(233\) 17.9944 + 10.3891i 1.17885 + 0.680611i 0.955749 0.294184i \(-0.0950478\pi\)
0.223104 + 0.974795i \(0.428381\pi\)
\(234\) −0.175253 2.05842i −0.0114566 0.134563i
\(235\) −6.20298 10.7439i −0.404638 0.700853i
\(236\) −8.96932 −0.583853
\(237\) 15.3321 4.81454i 0.995925 0.312738i
\(238\) −2.31873 1.21226i −0.150301 0.0785789i
\(239\) 23.6739 + 13.6681i 1.53134 + 0.884119i 0.999300 + 0.0373991i \(0.0119073\pi\)
0.532039 + 0.846720i \(0.321426\pi\)
\(240\) −13.6215 12.5111i −0.879265 0.807586i
\(241\) −18.4688 10.6630i −1.18968 0.686861i −0.231445 0.972848i \(-0.574345\pi\)
−0.958234 + 0.285987i \(0.907679\pi\)
\(242\) −1.06444 + 0.614556i −0.0684250 + 0.0395052i
\(243\) −0.770725 + 15.5694i −0.0494420 + 0.998777i
\(244\) 3.06218i 0.196036i
\(245\) −21.3468 + 1.79179i −1.36380 + 0.114473i
\(246\) −3.10737 0.692689i −0.198119 0.0441643i
\(247\) −2.98580 5.17155i −0.189982 0.329058i
\(248\) −0.543692 −0.0345245
\(249\) −14.0157 12.8731i −0.888208 0.815800i
\(250\) 0.570839i 0.0361030i
\(251\) −26.7381 −1.68769 −0.843847 0.536584i \(-0.819714\pi\)
−0.843847 + 0.536584i \(0.819714\pi\)
\(252\) −14.0089 5.87001i −0.882480 0.369776i
\(253\) −11.6144 −0.730193
\(254\) 0.807815i 0.0506868i
\(255\) −3.88108 + 17.4103i −0.243043 + 1.09028i
\(256\) 9.52977 0.595611
\(257\) −1.52640 2.64380i −0.0952140 0.164916i 0.814484 0.580186i \(-0.197020\pi\)
−0.909698 + 0.415271i \(0.863687\pi\)
\(258\) 1.41987 1.54590i 0.0883975 0.0962434i
\(259\) 20.5868 0.862480i 1.27920 0.0535919i
\(260\) 13.7229i 0.851058i
\(261\) −5.40325 + 11.5171i −0.334453 + 0.712892i
\(262\) 1.90319 1.09881i 0.117580 0.0678847i
\(263\) 14.0447 + 8.10868i 0.866030 + 0.500003i 0.866027 0.499997i \(-0.166666\pi\)
3.24009e−6 1.00000i \(0.499999\pi\)
\(264\) −1.68881 + 7.57595i −0.103939 + 0.466267i
\(265\) 15.2842 + 8.82433i 0.938901 + 0.542074i
\(266\) 1.97964 0.0829370i 0.121380 0.00508519i
\(267\) 1.62687 7.29808i 0.0995631 0.446635i
\(268\) 3.01525 0.184186
\(269\) 0.303255 + 0.525254i 0.0184898 + 0.0320253i 0.875122 0.483902i \(-0.160781\pi\)
−0.856632 + 0.515927i \(0.827448\pi\)
\(270\) 0.626149 4.63086i 0.0381062 0.281825i
\(271\) 19.8948 + 11.4863i 1.20852 + 0.697742i 0.962437 0.271505i \(-0.0875215\pi\)
0.246088 + 0.969248i \(0.420855\pi\)
\(272\) −5.87120 10.1692i −0.355994 0.616599i
\(273\) −3.64315 10.1014i −0.220493 0.611365i
\(274\) 1.79389 3.10711i 0.108373 0.187708i
\(275\) 14.7303 8.50455i 0.888271 0.512844i
\(276\) −6.68317 + 7.27635i −0.402279 + 0.437985i
\(277\) −6.64173 + 11.5038i −0.399063 + 0.691197i −0.993611 0.112863i \(-0.963998\pi\)
0.594548 + 0.804060i \(0.297331\pi\)
\(278\) 1.95965 3.39421i 0.117532 0.203571i
\(279\) 0.810738 + 1.16362i 0.0485376 + 0.0696640i
\(280\) 8.25228 + 4.31437i 0.493168 + 0.257833i
\(281\) 5.68377 3.28153i 0.339065 0.195759i −0.320793 0.947149i \(-0.603950\pi\)
0.659859 + 0.751390i \(0.270616\pi\)
\(282\) 0.618185 + 1.96863i 0.0368124 + 0.117230i
\(283\) 2.97234i 0.176687i −0.996090 0.0883437i \(-0.971843\pi\)
0.996090 0.0883437i \(-0.0281574\pi\)
\(284\) 26.0508i 1.54583i
\(285\) −4.04685 12.8874i −0.239715 0.763381i
\(286\) −2.32371 + 1.34160i −0.137404 + 0.0793303i
\(287\) −16.5340 + 0.692689i −0.975970 + 0.0408882i
\(288\) 5.70338 + 8.18583i 0.336075 + 0.482355i
\(289\) 2.83753 4.91475i 0.166914 0.289103i
\(290\) 1.90680 3.30267i 0.111971 0.193940i
\(291\) −6.74821 + 7.34717i −0.395587 + 0.430698i
\(292\) −1.63894 + 0.946243i −0.0959118 + 0.0553747i
\(293\) 3.03087 5.24962i 0.177065 0.306686i −0.763809 0.645443i \(-0.776673\pi\)
0.940874 + 0.338756i \(0.110006\pi\)
\(294\) 3.53028 + 0.481629i 0.205890 + 0.0280892i
\(295\) −7.17181 12.4219i −0.417559 0.723234i
\(296\) −7.75686 4.47843i −0.450858 0.260303i
\(297\) 18.7325 7.68260i 1.08697 0.445790i
\(298\) −1.24505 2.15649i −0.0721239 0.124922i
\(299\) −6.98477 −0.403940
\(300\) 3.14807 14.1221i 0.181754 0.815340i
\(301\) 5.05500 9.66892i 0.291366 0.557307i
\(302\) 0.854235 + 0.493193i 0.0491557 + 0.0283801i
\(303\) −6.46609 + 29.0066i −0.371467 + 1.66638i
\(304\) 7.70076 + 4.44604i 0.441669 + 0.254998i
\(305\) 4.24092 2.44850i 0.242834 0.140201i
\(306\) 1.26011 2.68594i 0.0720354 0.153545i
\(307\) 21.6030i 1.23295i 0.787375 + 0.616474i \(0.211439\pi\)
−0.787375 + 0.616474i \(0.788561\pi\)
\(308\) 0.825775 + 19.7106i 0.0470529 + 1.12312i
\(309\) −11.5054 + 12.5265i −0.654517 + 0.712610i
\(310\) −0.212570 0.368182i −0.0120732 0.0209113i
\(311\) 11.0234 0.625081 0.312540 0.949905i \(-0.398820\pi\)
0.312540 + 0.949905i \(0.398820\pi\)
\(312\) −1.01563 + 4.55607i −0.0574988 + 0.257937i
\(313\) 13.5542i 0.766129i −0.923722 0.383064i \(-0.874869\pi\)
0.923722 0.383064i \(-0.125131\pi\)
\(314\) −4.91012 −0.277094
\(315\) −3.07187 24.0951i −0.173080 1.35761i
\(316\) −17.7551 −0.998800
\(317\) 11.1541i 0.626479i 0.949674 + 0.313240i \(0.101414\pi\)
−0.949674 + 0.313240i \(0.898586\pi\)
\(318\) −2.16189 1.98565i −0.121233 0.111350i
\(319\) 16.5231 0.925118
\(320\) 9.18282 + 15.9051i 0.513335 + 0.889123i
\(321\) 5.86604 + 1.30765i 0.327411 + 0.0729857i
\(322\) 1.07375 2.05380i 0.0598377 0.114454i
\(323\) 8.57595i 0.477179i
\(324\) 5.96594 16.1565i 0.331441 0.897581i
\(325\) 8.85862 5.11453i 0.491388 0.283703i
\(326\) 6.44706 + 3.72221i 0.357070 + 0.206154i
\(327\) −1.55900 1.43190i −0.0862127 0.0791845i
\(328\) 6.22982 + 3.59679i 0.343984 + 0.198599i
\(329\) 5.74688 + 9.05598i 0.316836 + 0.499272i
\(330\) −5.79063 + 1.81836i −0.318763 + 0.100097i
\(331\) −19.0202 −1.04544 −0.522722 0.852503i \(-0.675083\pi\)
−0.522722 + 0.852503i \(0.675083\pi\)
\(332\) 10.5128 + 18.2087i 0.576964 + 0.999331i
\(333\) 1.98201 + 23.2795i 0.108613 + 1.27571i
\(334\) 0.445794 + 0.257379i 0.0243927 + 0.0140832i
\(335\) 2.41098 + 4.17593i 0.131726 + 0.228156i
\(336\) 12.2189 + 10.3140i 0.666595 + 0.562675i
\(337\) 3.32635 5.76140i 0.181198 0.313843i −0.761091 0.648645i \(-0.775336\pi\)
0.942289 + 0.334802i \(0.108669\pi\)
\(338\) 1.91103 1.10333i 0.103946 0.0600134i
\(339\) 3.66369 + 0.816703i 0.198984 + 0.0443572i
\(340\) 9.85390 17.0675i 0.534403 0.925613i
\(341\) 0.921000 1.59522i 0.0498749 0.0863859i
\(342\) 0.190592 + 2.23858i 0.0103060 + 0.121048i
\(343\) 18.3743 2.32024i 0.992121 0.125281i
\(344\) −4.10738 + 2.37140i −0.221455 + 0.127857i
\(345\) −15.4211 3.43764i −0.830244 0.185076i
\(346\) 7.03128i 0.378004i
\(347\) 26.6501i 1.43065i −0.698792 0.715325i \(-0.746279\pi\)
0.698792 0.715325i \(-0.253721\pi\)
\(348\) 9.50773 10.3516i 0.509668 0.554904i
\(349\) −20.5135 + 11.8435i −1.09806 + 0.633966i −0.935711 0.352768i \(-0.885241\pi\)
−0.162350 + 0.986733i \(0.551907\pi\)
\(350\) 0.142067 + 3.39104i 0.00759380 + 0.181258i
\(351\) 11.2655 4.62022i 0.601306 0.246609i
\(352\) 6.47905 11.2221i 0.345335 0.598137i
\(353\) 2.29422 3.97371i 0.122109 0.211499i −0.798490 0.602008i \(-0.794368\pi\)
0.920599 + 0.390509i \(0.127701\pi\)
\(354\) 0.714738 + 2.27611i 0.0379879 + 0.120974i
\(355\) −36.0788 + 20.8301i −1.91486 + 1.10555i
\(356\) −4.13057 + 7.15435i −0.218920 + 0.379180i
\(357\) 2.72239 15.1793i 0.144084 0.803376i
\(358\) 3.73022 + 6.46094i 0.197148 + 0.341471i
\(359\) −5.30942 3.06540i −0.280221 0.161785i 0.353303 0.935509i \(-0.385059\pi\)
−0.633523 + 0.773724i \(0.718392\pi\)
\(360\) −4.48466 + 9.55913i −0.236362 + 0.503811i
\(361\) −6.25288 10.8303i −0.329099 0.570016i
\(362\) −6.58363 −0.346028
\(363\) −5.33537 4.90042i −0.280034 0.257205i
\(364\) 0.496610 + 11.8537i 0.0260294 + 0.621303i
\(365\) −2.62097 1.51322i −0.137188 0.0792056i
\(366\) −0.777076 + 0.244016i −0.0406184 + 0.0127549i
\(367\) 22.8860 + 13.2132i 1.19464 + 0.689725i 0.959355 0.282202i \(-0.0910650\pi\)
0.235283 + 0.971927i \(0.424398\pi\)
\(368\) 9.00732 5.20038i 0.469539 0.271088i
\(369\) −1.59182 18.6966i −0.0828669 0.973305i
\(370\) 7.00381i 0.364111i
\(371\) −13.5217 7.06926i −0.702011 0.367018i
\(372\) −0.469431 1.49492i −0.0243388 0.0775079i
\(373\) −10.0581 17.4211i −0.520789 0.902033i −0.999708 0.0241735i \(-0.992305\pi\)
0.478919 0.877859i \(-0.341029\pi\)
\(374\) −3.85340 −0.199255
\(375\) −3.20995 + 1.00798i −0.165761 + 0.0520519i
\(376\) 4.66236i 0.240443i
\(377\) 9.93679 0.511771
\(378\) −0.373278 + 4.02276i −0.0191993 + 0.206908i
\(379\) −17.4561 −0.896660 −0.448330 0.893868i \(-0.647981\pi\)
−0.448330 + 0.893868i \(0.647981\pi\)
\(380\) 14.9240i 0.765584i
\(381\) −4.54252 + 1.42643i −0.232720 + 0.0730783i
\(382\) −1.26039 −0.0644872
\(383\) −14.0317 24.3036i −0.716985 1.24185i −0.962189 0.272383i \(-0.912188\pi\)
0.245204 0.969471i \(-0.421145\pi\)
\(384\) −4.36654 13.9054i −0.222829 0.709607i
\(385\) −26.6377 + 16.9041i −1.35758 + 0.861515i
\(386\) 6.86037i 0.349183i
\(387\) 11.2001 + 5.25453i 0.569334 + 0.267103i
\(388\) 9.54517 5.51091i 0.484583 0.279774i
\(389\) −29.6520 17.1196i −1.50342 0.867999i −0.999992 0.00396103i \(-0.998739\pi\)
−0.503426 0.864038i \(-0.667928\pi\)
\(390\) −3.48241 + 1.09354i −0.176339 + 0.0553734i
\(391\) −8.68710 5.01550i −0.439325 0.253645i
\(392\) −7.28437 3.42807i −0.367916 0.173144i
\(393\) 9.53949 + 8.76181i 0.481203 + 0.441975i
\(394\) 5.51918 0.278052
\(395\) −14.1968 24.5896i −0.714320 1.23724i
\(396\) −22.2887 + 1.89766i −1.12005 + 0.0953608i
\(397\) −11.2926 6.51981i −0.566762 0.327220i 0.189093 0.981959i \(-0.439445\pi\)
−0.755855 + 0.654739i \(0.772778\pi\)
\(398\) −0.666662 1.15469i −0.0334167 0.0578795i
\(399\) 3.96201 + 10.9855i 0.198348 + 0.549964i
\(400\) −7.61585 + 13.1910i −0.380792 + 0.659552i
\(401\) −15.8943 + 9.17659i −0.793725 + 0.458257i −0.841272 0.540612i \(-0.818193\pi\)
0.0475475 + 0.998869i \(0.484859\pi\)
\(402\) −0.240276 0.765168i −0.0119839 0.0381631i
\(403\) 0.553877 0.959344i 0.0275906 0.0477883i
\(404\) 16.4171 28.4353i 0.816782 1.41471i
\(405\) 27.1460 4.65616i 1.34890 0.231366i
\(406\) −1.52756 + 2.92182i −0.0758113 + 0.145007i
\(407\) 26.2798 15.1727i 1.30264 0.752081i
\(408\) −4.53471 + 4.93720i −0.224501 + 0.244428i
\(409\) 6.46786i 0.319815i 0.987132 + 0.159907i \(0.0511196\pi\)
−0.987132 + 0.159907i \(0.948880\pi\)
\(410\) 5.62501i 0.277800i
\(411\) 20.6396 + 4.60094i 1.01808 + 0.226948i
\(412\) 16.2740 9.39581i 0.801764 0.462899i
\(413\) 6.64448 + 10.4704i 0.326953 + 0.515216i
\(414\) 2.37905 + 1.11613i 0.116924 + 0.0548548i
\(415\) −16.8119 + 29.1191i −0.825265 + 1.42940i
\(416\) 3.89642 6.74880i 0.191038 0.330887i
\(417\) 22.5467 + 5.02607i 1.10412 + 0.246127i
\(418\) 2.52709 1.45902i 0.123604 0.0713629i
\(419\) 7.11542 12.3243i 0.347611 0.602080i −0.638214 0.769859i \(-0.720326\pi\)
0.985825 + 0.167779i \(0.0536596\pi\)
\(420\) −4.73753 + 26.4153i −0.231168 + 1.28893i
\(421\) 15.1718 + 26.2784i 0.739429 + 1.28073i 0.952753 + 0.303747i \(0.0982378\pi\)
−0.213324 + 0.976982i \(0.568429\pi\)
\(422\) −1.75170 1.01135i −0.0852716 0.0492316i
\(423\) −9.97846 + 6.95238i −0.485169 + 0.338036i
\(424\) 3.31633 + 5.74405i 0.161055 + 0.278956i
\(425\) 14.6902 0.712579
\(426\) 6.61081 2.07591i 0.320295 0.100578i
\(427\) −3.57466 + 2.26846i −0.172990 + 0.109779i
\(428\) −5.75051 3.32006i −0.277962 0.160481i
\(429\) −11.6473 10.6978i −0.562336 0.516494i
\(430\) −3.21177 1.85432i −0.154885 0.0894230i
\(431\) −2.12663 + 1.22781i −0.102436 + 0.0591415i −0.550343 0.834939i \(-0.685503\pi\)
0.447907 + 0.894080i \(0.352170\pi\)
\(432\) −11.0877 + 14.3456i −0.533455 + 0.690201i
\(433\) 12.4545i 0.598525i −0.954171 0.299262i \(-0.903259\pi\)
0.954171 0.299262i \(-0.0967406\pi\)
\(434\) 0.196940 + 0.310340i 0.00945342 + 0.0148968i
\(435\) 21.9386 + 4.89052i 1.05188 + 0.234483i
\(436\) 1.16936 + 2.02539i 0.0560022 + 0.0969987i
\(437\) 7.59610 0.363371
\(438\) 0.370727 + 0.340504i 0.0177140 + 0.0162699i
\(439\) 17.5300i 0.836663i −0.908294 0.418331i \(-0.862615\pi\)
0.908294 0.418331i \(-0.137385\pi\)
\(440\) 13.7141 0.653794
\(441\) 3.52542 + 20.7020i 0.167877 + 0.985808i
\(442\) −2.31739 −0.110227
\(443\) 9.00464i 0.427824i −0.976853 0.213912i \(-0.931379\pi\)
0.976853 0.213912i \(-0.0686205\pi\)
\(444\) 5.61636 25.1947i 0.266541 1.19569i
\(445\) −13.2111 −0.626266
\(446\) 0.945337 + 1.63737i 0.0447630 + 0.0775318i
\(447\) 9.92793 10.8091i 0.469575 0.511254i
\(448\) −8.50761 13.4064i −0.401947 0.633392i
\(449\) 30.8120i 1.45411i 0.686581 + 0.727054i \(0.259111\pi\)
−0.686581 + 0.727054i \(0.740889\pi\)
\(450\) −3.83457 + 0.326474i −0.180763 + 0.0153902i
\(451\) −21.1063 + 12.1857i −0.993856 + 0.573803i
\(452\) −3.59154 2.07357i −0.168932 0.0975327i
\(453\) −1.26493 + 5.67443i −0.0594317 + 0.266608i
\(454\) −5.02371 2.90044i −0.235775 0.136125i
\(455\) −16.0196 + 10.1659i −0.751009 + 0.476586i
\(456\) 1.10452 4.95484i 0.0517240 0.232032i
\(457\) 13.8286 0.646874 0.323437 0.946250i \(-0.395162\pi\)
0.323437 + 0.946250i \(0.395162\pi\)
\(458\) 1.60260 + 2.77578i 0.0748846 + 0.129704i
\(459\) 17.3287 + 2.34305i 0.808834 + 0.109364i
\(460\) 15.1174 + 8.72803i 0.704852 + 0.406947i
\(461\) 6.16989 + 10.6866i 0.287360 + 0.497723i 0.973179 0.230050i \(-0.0738889\pi\)
−0.685818 + 0.727773i \(0.740556\pi\)
\(462\) 4.93608 1.78023i 0.229647 0.0828240i
\(463\) 6.37802 11.0471i 0.296412 0.513401i −0.678900 0.734230i \(-0.737543\pi\)
0.975312 + 0.220830i \(0.0708765\pi\)
\(464\) −12.8141 + 7.39825i −0.594882 + 0.343455i
\(465\) 1.69501 1.84546i 0.0786044 0.0855811i
\(466\) −3.05303 + 5.28801i −0.141429 + 0.244962i
\(467\) −5.48999 + 9.50894i −0.254046 + 0.440021i −0.964636 0.263585i \(-0.915095\pi\)
0.710590 + 0.703607i \(0.248428\pi\)
\(468\) −13.4041 + 1.14123i −0.619607 + 0.0527532i
\(469\) −2.23370 3.51988i −0.103143 0.162533i
\(470\) 3.15730 1.82287i 0.145635 0.0840825i
\(471\) −8.67025 27.6107i −0.399504 1.27223i
\(472\) 5.39057i 0.248121i
\(473\) 16.0683i 0.738823i
\(474\) 1.41485 + 4.50563i 0.0649861 + 0.206950i
\(475\) −9.63396 + 5.56217i −0.442036 + 0.255210i
\(476\) −7.89406 + 15.0993i −0.361824 + 0.692075i
\(477\) 7.34829 15.6630i 0.336455 0.717160i
\(478\) −4.01665 + 6.95704i −0.183717 + 0.318208i
\(479\) −5.59729 + 9.69478i −0.255747 + 0.442966i −0.965098 0.261889i \(-0.915655\pi\)
0.709351 + 0.704855i \(0.248988\pi\)
\(480\) 11.9241 12.9824i 0.544258 0.592565i
\(481\) 15.8043 9.12464i 0.720616 0.416048i
\(482\) 3.13352 5.42741i 0.142728 0.247212i
\(483\) 13.4450 + 2.41134i 0.611769 + 0.109720i
\(484\) 4.00191 + 6.93152i 0.181905 + 0.315069i
\(485\) 15.2645 + 8.81298i 0.693126 + 0.400177i
\(486\) −4.57537 0.226492i −0.207543 0.0102739i
\(487\) −1.48332 2.56919i −0.0672158 0.116421i 0.830459 0.557080i \(-0.188078\pi\)
−0.897675 + 0.440659i \(0.854745\pi\)
\(488\) 1.84037 0.0833097
\(489\) −9.54666 + 42.8259i −0.431715 + 1.93665i
\(490\) −0.526553 6.27318i −0.0237872 0.283393i
\(491\) −20.1795 11.6507i −0.910690 0.525787i −0.0300367 0.999549i \(-0.509562\pi\)
−0.880653 + 0.473762i \(0.842896\pi\)
\(492\) −4.51070 + 20.2348i −0.203358 + 0.912256i
\(493\) 12.3586 + 7.13524i 0.556603 + 0.321355i
\(494\) 1.51976 0.877435i 0.0683773 0.0394776i
\(495\) −20.4501 29.3511i −0.919162 1.31923i
\(496\) 1.64952i 0.0740654i
\(497\) 30.4107 19.2985i 1.36411 0.865654i
\(498\) 3.78301 4.11878i 0.169521 0.184567i
\(499\) 2.29296 + 3.97152i 0.102647 + 0.177790i 0.912774 0.408464i \(-0.133935\pi\)
−0.810127 + 0.586254i \(0.800602\pi\)
\(500\) 3.71723 0.166240
\(501\) −0.660121 + 2.96127i −0.0294920 + 0.132300i
\(502\) 7.85751i 0.350698i
\(503\) −23.1383 −1.03169 −0.515844 0.856683i \(-0.672521\pi\)
−0.515844 + 0.856683i \(0.672521\pi\)
\(504\) 3.52788 8.41938i 0.157144 0.375029i
\(505\) 52.5081 2.33658
\(506\) 3.41313i 0.151732i
\(507\) 9.57875 + 8.79787i 0.425407 + 0.390727i
\(508\) 5.26039 0.233392
\(509\) 4.82853 + 8.36326i 0.214021 + 0.370695i 0.952969 0.303067i \(-0.0980106\pi\)
−0.738948 + 0.673762i \(0.764677\pi\)
\(510\) −5.11637 1.14053i −0.226557 0.0505036i
\(511\) 2.31873 + 1.21226i 0.102575 + 0.0536271i
\(512\) 19.6301i 0.867536i
\(513\) −12.2515 + 5.02459i −0.540915 + 0.221841i
\(514\) 0.776931 0.448561i 0.0342690 0.0197852i
\(515\) 26.0252 + 15.0257i 1.14681 + 0.662110i
\(516\) −10.0667 9.24604i −0.443161 0.407034i
\(517\) 13.6796 + 7.89791i 0.601627 + 0.347350i
\(518\) 0.253457 + 6.04982i 0.0111362 + 0.265814i
\(519\) −39.5384 + 12.4158i −1.73555 + 0.544992i
\(520\) 8.24748 0.361676
\(521\) 5.00035 + 8.66086i 0.219069 + 0.379439i 0.954524 0.298135i \(-0.0963646\pi\)
−0.735454 + 0.677574i \(0.763031\pi\)
\(522\) −3.38453 1.58785i −0.148137 0.0694983i
\(523\) −10.7796 6.22361i −0.471359 0.272139i 0.245449 0.969409i \(-0.421065\pi\)
−0.716809 + 0.697270i \(0.754398\pi\)
\(524\) −7.15531 12.3934i −0.312581 0.541406i
\(525\) −18.8177 + 6.78673i −0.821271 + 0.296197i
\(526\) −2.38289 + 4.12729i −0.103899 + 0.179959i
\(527\) 1.37774 0.795437i 0.0600152 0.0346498i
\(528\) 22.9848 + 5.12372i 1.00028 + 0.222981i
\(529\) −7.05755 + 12.2240i −0.306850 + 0.531480i
\(530\) −2.59320 + 4.49156i −0.112641 + 0.195101i
\(531\) −11.5370 + 8.03826i −0.500662 + 0.348831i
\(532\) −0.540075 12.8912i −0.0234152 0.558904i
\(533\) −12.6930 + 7.32833i −0.549797 + 0.317425i
\(534\) 2.14468 + 0.478089i 0.0928095 + 0.0206889i
\(535\) 10.6188i 0.459091i
\(536\) 1.81217i 0.0782737i
\(537\) −29.7445 + 32.3845i −1.28357 + 1.39750i
\(538\) −0.154356 + 0.0891175i −0.00665476 + 0.00384213i
\(539\) 22.3977 15.5656i 0.964735 0.670458i
\(540\) −30.1556 4.07740i −1.29769 0.175463i
\(541\) 6.96514 12.0640i 0.299455 0.518671i −0.676557 0.736391i \(-0.736529\pi\)
0.976011 + 0.217720i \(0.0698619\pi\)
\(542\) −3.37547 + 5.84648i −0.144989 + 0.251128i
\(543\) −11.6253 37.0212i −0.498890 1.58873i
\(544\) 9.69211 5.59574i 0.415546 0.239916i
\(545\) −1.87003 + 3.23898i −0.0801032 + 0.138743i
\(546\) 2.96850 1.07061i 0.127040 0.0458179i
\(547\) −21.6768 37.5454i −0.926834 1.60532i −0.788584 0.614926i \(-0.789186\pi\)
−0.138250 0.990397i \(-0.544148\pi\)
\(548\) −20.2331 11.6816i −0.864316 0.499013i
\(549\) −2.74431 3.93879i −0.117124 0.168103i
\(550\) 2.49923 + 4.32879i 0.106567 + 0.184580i
\(551\) −10.8065 −0.460372
\(552\) −4.37309 4.01659i −0.186131 0.170957i
\(553\) 13.1529 + 20.7265i 0.559320 + 0.881382i
\(554\) −3.38062 1.95180i −0.143629 0.0829241i
\(555\) 39.3839 12.3673i 1.67176 0.524961i
\(556\) −22.1026 12.7610i −0.937361 0.541186i
\(557\) −31.1339 + 17.9752i −1.31919 + 0.761632i −0.983598 0.180377i \(-0.942268\pi\)
−0.335588 + 0.942009i \(0.608935\pi\)
\(558\) −0.341952 + 0.238251i −0.0144760 + 0.0100860i
\(559\) 9.66329i 0.408714i
\(560\) 13.0894 25.0367i 0.553129 1.05799i
\(561\) −6.80430 21.6685i −0.287278 0.914846i
\(562\) 0.964340 + 1.67029i 0.0406782 + 0.0704568i
\(563\) 6.11108 0.257551 0.128776 0.991674i \(-0.458895\pi\)
0.128776 + 0.991674i \(0.458895\pi\)
\(564\) 12.8195 4.02554i 0.539797 0.169506i
\(565\) 6.63207i 0.279013i
\(566\) 0.873481 0.0367151
\(567\) −23.2800 + 5.00432i −0.977667 + 0.210162i
\(568\) −15.6566 −0.656935
\(569\) 19.3045i 0.809285i −0.914475 0.404642i \(-0.867396\pi\)
0.914475 0.404642i \(-0.132604\pi\)
\(570\) 3.78720 1.18925i 0.158628 0.0498121i
\(571\) 12.7224 0.532415 0.266207 0.963916i \(-0.414229\pi\)
0.266207 + 0.963916i \(0.414229\pi\)
\(572\) 8.73631 + 15.1317i 0.365284 + 0.632690i
\(573\) −2.22558 7.08745i −0.0929751 0.296083i
\(574\) −0.203560 4.85883i −0.00849644 0.202804i
\(575\) 13.0118i 0.542628i
\(576\) 14.7720 10.2922i 0.615500 0.428843i
\(577\) 7.05520 4.07332i 0.293712 0.169575i −0.345903 0.938270i \(-0.612427\pi\)
0.639615 + 0.768696i \(0.279094\pi\)
\(578\) 1.44429 + 0.833863i 0.0600747 + 0.0346841i
\(579\) 38.5773 12.1140i 1.60322 0.503439i
\(580\) −21.5066 12.4168i −0.893012 0.515581i
\(581\) 13.4682 25.7612i 0.558755 1.06875i
\(582\) −2.15911 1.98309i −0.0894979 0.0822019i
\(583\) −22.4711 −0.930657
\(584\) −0.568693 0.985005i −0.0235327 0.0407598i
\(585\) −12.2984 17.6514i −0.508476 0.729795i
\(586\) 1.54270 + 0.890680i 0.0637285 + 0.0367937i
\(587\) 12.3041 + 21.3113i 0.507843 + 0.879610i 0.999959 + 0.00908019i \(0.00289036\pi\)
−0.492116 + 0.870530i \(0.663776\pi\)
\(588\) 3.13631 22.9887i 0.129339 0.948038i
\(589\) −0.602354 + 1.04331i −0.0248196 + 0.0429888i
\(590\) 3.65043 2.10758i 0.150286 0.0867676i
\(591\) 9.74571 + 31.0355i 0.400885 + 1.27663i
\(592\) −13.5872 + 23.5336i −0.558429 + 0.967227i
\(593\) −18.9321 + 32.7913i −0.777447 + 1.34658i 0.155962 + 0.987763i \(0.450152\pi\)
−0.933409 + 0.358814i \(0.883181\pi\)
\(594\) 2.25768 + 5.50490i 0.0926338 + 0.225869i
\(595\) −27.2236 + 1.14053i −1.11606 + 0.0467572i
\(596\) −14.0428 + 8.10762i −0.575216 + 0.332101i
\(597\) 5.31590 5.78773i 0.217565 0.236876i
\(598\) 2.05261i 0.0839375i
\(599\) 10.6529i 0.435268i 0.976030 + 0.217634i \(0.0698339\pi\)
−0.976030 + 0.217634i \(0.930166\pi\)
\(600\) 8.48740 + 1.89199i 0.346497 + 0.0772404i
\(601\) 39.8636 23.0153i 1.62607 0.938812i 0.640821 0.767691i \(-0.278594\pi\)
0.985250 0.171122i \(-0.0547391\pi\)
\(602\) 2.84140 + 1.48551i 0.115807 + 0.0605449i
\(603\) 3.87843 2.70225i 0.157942 0.110044i
\(604\) 3.21161 5.56267i 0.130679 0.226342i
\(605\) −6.39981 + 11.0848i −0.260189 + 0.450661i
\(606\) −8.52414 1.90019i −0.346270 0.0771897i
\(607\) 3.74063 2.15965i 0.151827 0.0876576i −0.422162 0.906521i \(-0.638729\pi\)
0.573989 + 0.818863i \(0.305395\pi\)
\(608\) −4.23745 + 7.33947i −0.171851 + 0.297655i
\(609\) −19.1274 3.43046i −0.775080 0.139009i
\(610\) 0.719539 + 1.24628i 0.0291333 + 0.0504603i
\(611\) 8.22672 + 4.74970i 0.332818 + 0.192152i
\(612\) −17.4905 8.20565i −0.707011 0.331694i
\(613\) 14.3838 + 24.9135i 0.580956 + 1.00624i 0.995366 + 0.0961549i \(0.0306544\pi\)
−0.414411 + 0.910090i \(0.636012\pi\)
\(614\) −6.34846 −0.256203
\(615\) −31.6307 + 9.93259i −1.27547 + 0.400521i
\(616\) −11.8461 + 0.496291i −0.477293 + 0.0199961i
\(617\) 0.935498 + 0.540110i 0.0376617 + 0.0217440i 0.518713 0.854949i \(-0.326411\pi\)
−0.481051 + 0.876693i \(0.659745\pi\)
\(618\) −3.68117 3.38107i −0.148078 0.136007i
\(619\) −6.57128 3.79393i −0.264122 0.152491i 0.362091 0.932143i \(-0.382063\pi\)
−0.626214 + 0.779652i \(0.715396\pi\)
\(620\) −2.39755 + 1.38423i −0.0962881 + 0.0555920i
\(621\) −2.07534 + 15.3488i −0.0832806 + 0.615925i
\(622\) 3.23944i 0.129890i
\(623\) 11.4116 0.478089i 0.457197 0.0191542i
\(624\) 13.8227 + 3.08134i 0.553352 + 0.123352i
\(625\) 13.8854 + 24.0502i 0.555416 + 0.962010i
\(626\) 3.98316 0.159199
\(627\) 12.6667 + 11.6341i 0.505859 + 0.464620i
\(628\) 31.9741i 1.27591i
\(629\) 26.2082 1.04499
\(630\) 7.08082 0.902729i 0.282107 0.0359656i
\(631\) 35.0387 1.39487 0.697435 0.716648i \(-0.254325\pi\)
0.697435 + 0.716648i \(0.254325\pi\)
\(632\) 10.6708i 0.424462i
\(633\) 2.59388 11.6360i 0.103098 0.462491i
\(634\) −3.27786 −0.130181
\(635\) 4.20618 + 7.28531i 0.166917 + 0.289109i
\(636\) −12.9303 + 14.0780i −0.512719 + 0.558227i
\(637\) 13.4697 9.36096i 0.533687 0.370895i
\(638\) 4.85564i 0.192237i
\(639\) 23.3466 + 33.5084i 0.923578 + 1.32557i
\(640\) −22.3015 + 12.8758i −0.881544 + 0.508960i
\(641\) 26.9229 + 15.5439i 1.06339 + 0.613949i 0.926368 0.376619i \(-0.122913\pi\)
0.137023 + 0.990568i \(0.456247\pi\)
\(642\) −0.384277 + 1.72385i −0.0151662 + 0.0680350i
\(643\) 0.977928 + 0.564607i 0.0385657 + 0.0222659i 0.519159 0.854678i \(-0.326245\pi\)
−0.480593 + 0.876944i \(0.659579\pi\)
\(644\) −13.3741 6.99212i −0.527014 0.275528i
\(645\) 4.75591 21.3348i 0.187264 0.840057i
\(646\) 2.52021 0.0991564
\(647\) −13.5992 23.5545i −0.534640 0.926023i −0.999181 0.0404713i \(-0.987114\pi\)
0.464541 0.885552i \(-0.346219\pi\)
\(648\) 9.71005 + 3.58553i 0.381447 + 0.140853i
\(649\) 15.8162 + 9.13148i 0.620839 + 0.358442i
\(650\) 1.50300 + 2.60328i 0.0589526 + 0.102109i
\(651\) −1.39735 + 1.65543i −0.0547666 + 0.0648814i
\(652\) 24.2386 41.9824i 0.949256 1.64416i
\(653\) −19.3030 + 11.1446i −0.755384 + 0.436121i −0.827636 0.561265i \(-0.810315\pi\)
0.0722517 + 0.997386i \(0.476981\pi\)
\(654\) 0.420793 0.458141i 0.0164543 0.0179147i
\(655\) 11.4427 19.8193i 0.447102 0.774404i
\(656\) 10.9123 18.9007i 0.426055 0.737949i
\(657\) −1.26011 + 2.68594i −0.0491614 + 0.104788i
\(658\) −2.66128 + 1.68883i −0.103747 + 0.0658375i
\(659\) −7.69208 + 4.44103i −0.299641 + 0.172998i −0.642282 0.766469i \(-0.722012\pi\)
0.342641 + 0.939467i \(0.388679\pi\)
\(660\) 11.8409 + 37.7078i 0.460907 + 1.46778i
\(661\) 19.3670i 0.753291i −0.926358 0.376645i \(-0.877078\pi\)
0.926358 0.376645i \(-0.122922\pi\)
\(662\) 5.58945i 0.217240i
\(663\) −4.09202 13.0312i −0.158921 0.506089i
\(664\) −10.9434 + 6.31819i −0.424687 + 0.245193i
\(665\) 17.4216 11.0557i 0.675583 0.428721i
\(666\) −6.84112 + 0.582451i −0.265088 + 0.0225695i
\(667\) −6.31999 + 10.9465i −0.244711 + 0.423852i
\(668\) 1.67602 2.90295i 0.0648472 0.112319i
\(669\) −7.53803 + 8.20709i −0.291437 + 0.317304i
\(670\) −1.22718 + 0.708512i −0.0474101 + 0.0273722i
\(671\) −3.11754 + 5.39973i −0.120351 + 0.208454i
\(672\) −9.83011 + 11.6456i −0.379205 + 0.449240i
\(673\) 11.5828 + 20.0620i 0.446484 + 0.773333i 0.998154 0.0607292i \(-0.0193426\pi\)
−0.551670 + 0.834062i \(0.686009\pi\)
\(674\) 1.69310 + 0.977511i 0.0652157 + 0.0376523i
\(675\) −8.60689 20.9862i −0.331279 0.807757i
\(676\) −7.18476 12.4444i −0.276337 0.478630i
\(677\) 3.12693 0.120177 0.0600887 0.998193i \(-0.480862\pi\)
0.0600887 + 0.998193i \(0.480862\pi\)
\(678\) −0.240004 + 1.07665i −0.00921730 + 0.0413484i
\(679\) −13.5043 7.06017i −0.518247 0.270944i
\(680\) 10.2576 + 5.92220i 0.393359 + 0.227106i
\(681\) 7.43900 33.3710i 0.285063 1.27878i
\(682\) 0.468786 + 0.270654i 0.0179507 + 0.0103639i
\(683\) −27.1966 + 15.7020i −1.04065 + 0.600819i −0.920017 0.391878i \(-0.871825\pi\)
−0.120632 + 0.992697i \(0.538492\pi\)
\(684\) 14.5773 1.24111i 0.557378 0.0474550i
\(685\) 37.3621i 1.42753i
\(686\) 0.681848 + 5.39966i 0.0260331 + 0.206160i
\(687\) −12.7790 + 13.9132i −0.487549 + 0.530822i
\(688\) 7.19462 + 12.4614i 0.274292 + 0.475088i
\(689\) −13.5138 −0.514835
\(690\) 1.01022 4.53179i 0.0384584 0.172522i
\(691\) 44.1739i 1.68045i 0.542235 + 0.840227i \(0.317578\pi\)
−0.542235 + 0.840227i \(0.682422\pi\)
\(692\) 45.7868 1.74055
\(693\) 18.7267 + 24.6132i 0.711370 + 0.934977i
\(694\) 7.83164 0.297285
\(695\) 40.8144i 1.54818i
\(696\) 6.22132 + 5.71415i 0.235819 + 0.216594i
\(697\) −21.0488 −0.797280
\(698\) −3.48043 6.02828i −0.131736 0.228174i
\(699\) −35.1266 7.83036i −1.32861 0.296171i
\(700\) 22.0820 0.925123i 0.834621 0.0349664i
\(701\) 9.69906i 0.366328i −0.983082 0.183164i \(-0.941366\pi\)
0.983082 0.183164i \(-0.0586340\pi\)
\(702\) 1.35774 + 3.31058i 0.0512446 + 0.124950i
\(703\) −17.1876 + 9.92326i −0.648242 + 0.374263i
\(704\) −20.2511 11.6920i −0.763242 0.440658i
\(705\) 15.8255 + 14.5354i 0.596023 + 0.547434i
\(706\) 1.16775 + 0.674202i 0.0439490 + 0.0253739i
\(707\) −45.3560 + 1.90019i −1.70579 + 0.0714638i
\(708\) 14.8217 4.65429i 0.557035 0.174919i
\(709\) −1.09786 −0.0412311 −0.0206156 0.999787i \(-0.506563\pi\)
−0.0206156 + 0.999787i \(0.506563\pi\)
\(710\) −6.12132 10.6024i −0.229729 0.397903i
\(711\) −22.8378 + 15.9120i −0.856485 + 0.596746i
\(712\) −4.29977 2.48247i −0.161141 0.0930346i
\(713\) 0.704553 + 1.22032i 0.0263857 + 0.0457014i
\(714\) 4.46074 + 0.800027i 0.166939 + 0.0299402i
\(715\) −13.9710 + 24.1985i −0.522486 + 0.904972i
\(716\) 42.0728 24.2908i 1.57233 0.907788i
\(717\) −46.2135 10.3018i −1.72588 0.384729i
\(718\) 0.900826 1.56028i 0.0336185 0.0582290i
\(719\) 11.3648 19.6844i 0.423835 0.734103i −0.572476 0.819921i \(-0.694017\pi\)
0.996311 + 0.0858183i \(0.0273505\pi\)
\(720\) 29.0016 + 13.6061i 1.08083 + 0.507068i
\(721\) −23.0241 12.0372i −0.857462 0.448289i
\(722\) 3.18269 1.83753i 0.118448 0.0683858i
\(723\) 36.0527 + 8.03679i 1.34081 + 0.298891i
\(724\) 42.8718i 1.59332i
\(725\) 18.5110i 0.687482i
\(726\) 1.44008 1.56790i 0.0534465 0.0581903i
\(727\) −3.47919 + 2.00871i −0.129036 + 0.0744990i −0.563129 0.826369i \(-0.690402\pi\)
0.434093 + 0.900868i \(0.357069\pi\)
\(728\) −7.12409 + 0.298463i −0.264036 + 0.0110618i
\(729\) −6.80552 26.1282i −0.252056 0.967713i
\(730\) 0.444689 0.770224i 0.0164587 0.0285073i
\(731\) 6.93885 12.0184i 0.256643 0.444518i
\(732\) 1.58900 + 5.06022i 0.0587311 + 0.187031i
\(733\) −7.20188 + 4.15801i −0.266008 + 0.153580i −0.627072 0.778961i \(-0.715747\pi\)
0.361064 + 0.932541i \(0.382413\pi\)
\(734\) −3.88296 + 6.72549i −0.143323 + 0.248242i
\(735\) 34.3457 14.0380i 1.26686 0.517801i
\(736\) 4.95640 + 8.58473i 0.182695 + 0.316437i
\(737\) −5.31698 3.06976i −0.195854 0.113076i
\(738\) 5.49435 0.467788i 0.202250 0.0172195i
\(739\) −2.28507 3.95785i −0.0840576 0.145592i 0.820932 0.571026i \(-0.193455\pi\)
−0.904989 + 0.425434i \(0.860121\pi\)
\(740\) −45.6079 −1.67658
\(741\) 7.61759 + 6.99659i 0.279839 + 0.257026i
\(742\) 2.07744 3.97361i 0.0762653 0.145876i
\(743\) 1.51258 + 0.873286i 0.0554910 + 0.0320378i 0.527489 0.849562i \(-0.323134\pi\)
−0.471998 + 0.881600i \(0.656467\pi\)
\(744\) 0.898447 0.282128i 0.0329387 0.0103433i
\(745\) −22.4571 12.9656i −0.822764 0.475023i
\(746\) 5.11954 2.95577i 0.187440 0.108218i
\(747\) 29.8408 + 13.9998i 1.09182 + 0.512226i
\(748\) 25.0929i 0.917486i
\(749\) 0.384277 + 9.17242i 0.0140412 + 0.335153i
\(750\) −0.296215 0.943307i −0.0108162 0.0344447i
\(751\) −2.91647 5.05147i −0.106423 0.184331i 0.807895 0.589326i \(-0.200607\pi\)
−0.914319 + 0.404995i \(0.867273\pi\)
\(752\) −14.1452 −0.515822
\(753\) 44.1845 13.8747i 1.61017 0.505622i
\(754\) 2.92012i 0.106345i
\(755\) 10.2719 0.373834
\(756\) 26.1957 + 2.43074i 0.952728 + 0.0884051i
\(757\) −42.0967 −1.53003 −0.765015 0.644013i \(-0.777268\pi\)
−0.765015 + 0.644013i \(0.777268\pi\)
\(758\) 5.12982i 0.186323i
\(759\) 19.1928 6.02686i 0.696653 0.218761i
\(760\) −8.96932 −0.325352
\(761\) 0.293431 + 0.508238i 0.0106369 + 0.0184236i 0.871295 0.490760i \(-0.163281\pi\)
−0.860658 + 0.509184i \(0.829947\pi\)
\(762\) −0.419185 1.33491i −0.0151855 0.0483586i
\(763\) 1.49810 2.86547i 0.0542348 0.103737i
\(764\) 8.20750i 0.296937i
\(765\) −2.62097 30.7844i −0.0947615 1.11301i
\(766\) 7.14208 4.12348i 0.258054 0.148987i
\(767\) 9.51165 + 5.49155i 0.343446 + 0.198288i
\(768\) −15.7479 + 4.94511i −0.568253 + 0.178441i
\(769\) −45.1905 26.0907i −1.62961 0.940856i −0.984208 0.177014i \(-0.943356\pi\)
−0.645403 0.763843i \(-0.723310\pi\)
\(770\) −4.96761 7.82800i −0.179020 0.282102i
\(771\) 3.89426 + 3.57679i 0.140248 + 0.128815i
\(772\) −44.6738 −1.60785
\(773\) −16.3906 28.3894i −0.589530 1.02110i −0.994294 0.106674i \(-0.965980\pi\)
0.404764 0.914421i \(-0.367354\pi\)
\(774\) −1.54415 + 3.29137i −0.0555032 + 0.118306i
\(775\) −1.78714 1.03180i −0.0641959 0.0370635i
\(776\) 3.31206 + 5.73666i 0.118896 + 0.205934i
\(777\) −33.5719 + 12.1080i −1.20439 + 0.434370i
\(778\) 5.03093 8.71383i 0.180368 0.312406i
\(779\) 13.8040 7.96973i 0.494579 0.285545i
\(780\) 7.12097 + 22.6770i 0.254972 + 0.811967i
\(781\) 26.5218 45.9371i 0.949024 1.64376i
\(782\) 1.47390 2.55287i 0.0527066 0.0912906i
\(783\) 2.95246 21.8358i 0.105512 0.780346i
\(784\) −10.4005 + 22.1001i −0.371446 + 0.789291i
\(785\) −44.2821 + 25.5663i −1.58050 + 0.912500i
\(786\) −2.57483 + 2.80336i −0.0918411 + 0.0999927i
\(787\) 40.9934i 1.46126i 0.682775 + 0.730628i \(0.260773\pi\)
−0.682775 + 0.730628i \(0.739227\pi\)
\(788\) 35.9402i 1.28032i
\(789\) −27.4164 6.11160i −0.976048 0.217579i
\(790\) 7.22614 4.17201i 0.257095 0.148434i
\(791\) 0.240004 + 5.72872i 0.00853356 + 0.203690i
\(792\) −1.14049 13.3955i −0.0405256 0.475990i
\(793\) −1.87485 + 3.24733i −0.0665778 + 0.115316i
\(794\) 1.91597 3.31856i 0.0679954 0.117771i
\(795\) −29.8361 6.65100i −1.05818 0.235887i
\(796\) −7.51921 + 4.34122i −0.266511 + 0.153870i
\(797\) −17.0441 + 29.5213i −0.603734 + 1.04570i 0.388516 + 0.921442i \(0.372988\pi\)
−0.992250 + 0.124256i \(0.960346\pi\)
\(798\) −3.22831 + 1.16431i −0.114281 + 0.0412162i
\(799\) 6.82116 + 11.8146i 0.241315 + 0.417971i
\(800\) −12.5722 7.25854i −0.444493 0.256628i
\(801\) 1.09866 + 12.9042i 0.0388193 + 0.455949i
\(802\) −2.69672 4.67086i −0.0952245 0.164934i
\(803\) 3.85340 0.135984
\(804\) −4.98268 + 1.56465i −0.175725 + 0.0551809i
\(805\) −1.01022 24.1132i −0.0356055 0.849877i
\(806\) 0.281922 + 0.162768i 0.00993027 + 0.00573324i
\(807\) −0.773687 0.710615i −0.0272351 0.0250148i
\(808\) 17.0896 + 9.86670i 0.601211 + 0.347109i
\(809\) −6.01547 + 3.47304i −0.211493 + 0.122105i −0.602005 0.798492i \(-0.705631\pi\)
0.390512 + 0.920598i \(0.372298\pi\)
\(810\) 1.36830 + 7.97738i 0.0480773 + 0.280297i
\(811\) 39.8573i 1.39958i −0.714350 0.699789i \(-0.753277\pi\)
0.714350 0.699789i \(-0.246723\pi\)
\(812\) 19.0265 + 9.94725i 0.667700 + 0.349080i
\(813\) −38.8364 8.65734i −1.36205 0.303626i
\(814\) 4.45878 + 7.72284i 0.156280 + 0.270685i
\(815\) 77.5240 2.71555
\(816\) 14.9790 + 13.7579i 0.524371 + 0.481623i
\(817\) 10.5091i 0.367665i
\(818\) −1.90071 −0.0664566
\(819\) 11.2620 + 14.8020i 0.393527 + 0.517225i
\(820\) 36.6294 1.27915
\(821\) 42.1017i 1.46936i 0.678414 + 0.734680i \(0.262668\pi\)
−0.678414 + 0.734680i \(0.737332\pi\)
\(822\) −1.35208 + 6.06535i −0.0471591 + 0.211553i
\(823\) 32.6821 1.13923 0.569614 0.821913i \(-0.307093\pi\)
0.569614 + 0.821913i \(0.307093\pi\)
\(824\) 5.64689 + 9.78070i 0.196719 + 0.340727i
\(825\) −19.9286 + 21.6974i −0.693826 + 0.755408i
\(826\) −3.07694 + 1.95261i −0.107060 + 0.0679399i
\(827\) 31.4399i 1.09327i −0.837370 0.546637i \(-0.815908\pi\)
0.837370 0.546637i \(-0.184092\pi\)
\(828\) 7.26810 15.4921i 0.252584 0.538387i
\(829\) 35.7122 20.6185i 1.24034 0.716109i 0.271174 0.962530i \(-0.412588\pi\)
0.969163 + 0.246421i \(0.0792547\pi\)
\(830\) −8.55721 4.94051i −0.297025 0.171488i
\(831\) 5.00594 22.4564i 0.173654 0.779005i
\(832\) −12.1788 7.03141i −0.422222 0.243770i
\(833\) 23.4742 1.97036i 0.813334 0.0682689i
\(834\) −1.47701 + 6.62578i −0.0511446 + 0.229432i
\(835\) 5.36054 0.185509
\(836\) −9.50094 16.4561i −0.328597 0.569147i
\(837\) −1.94355 1.50217i −0.0671790 0.0519226i
\(838\) 3.62173 + 2.09100i 0.125110 + 0.0722326i
\(839\) −4.04385 7.00416i −0.139609 0.241810i 0.787740 0.616009i \(-0.211251\pi\)
−0.927349 + 0.374198i \(0.877918\pi\)
\(840\) −15.8756 2.84726i −0.547760 0.0982398i
\(841\) −5.50894 + 9.54177i −0.189963 + 0.329026i
\(842\) −7.72241 + 4.45853i −0.266132 + 0.153651i
\(843\) −7.68956 + 8.37207i −0.264843 + 0.288349i
\(844\) −6.58576 + 11.4069i −0.226691 + 0.392641i
\(845\) 11.4898 19.9009i 0.395260 0.684611i
\(846\) −2.04309 2.93236i −0.0702429 0.100817i
\(847\) 5.12695 9.80654i 0.176164 0.336957i
\(848\) 17.4269 10.0615i 0.598444 0.345512i
\(849\) 1.54238 + 4.91177i 0.0529345 + 0.168572i
\(850\) 4.31700i 0.148072i
\(851\) 23.2138i 0.795759i
\(852\) −13.5181 43.0488i −0.463122 1.47483i
\(853\) −24.5887 + 14.1963i −0.841900 + 0.486071i −0.857910 0.513801i \(-0.828237\pi\)
0.0160098 + 0.999872i \(0.494904\pi\)
\(854\) −0.666631 1.05048i −0.0228117 0.0359468i
\(855\) 13.3748 + 19.1963i 0.457408 + 0.656499i
\(856\) 1.99536 3.45606i 0.0682000 0.118126i
\(857\) −25.6587 + 44.4422i −0.876485 + 1.51812i −0.0213132 + 0.999773i \(0.506785\pi\)
−0.855172 + 0.518344i \(0.826549\pi\)
\(858\) 3.14375 3.42278i 0.107326 0.116852i
\(859\) 14.5234 8.38509i 0.495532 0.286096i −0.231334 0.972874i \(-0.574309\pi\)
0.726867 + 0.686779i \(0.240976\pi\)
\(860\) −12.0751 + 20.9146i −0.411756 + 0.713183i
\(861\) 26.9628 9.72434i 0.918891 0.331405i
\(862\) −0.360816 0.624951i −0.0122894 0.0212859i
\(863\) −14.2380 8.22033i −0.484668 0.279823i 0.237692 0.971341i \(-0.423609\pi\)
−0.722360 + 0.691517i \(0.756943\pi\)
\(864\) −13.6725 10.5675i −0.465149 0.359513i
\(865\) 36.6109 + 63.4119i 1.24481 + 2.15607i
\(866\) 3.66000 0.124372
\(867\) −2.13868 + 9.59401i −0.0726333 + 0.325830i
\(868\) 2.02089 1.28245i 0.0685935 0.0435291i
\(869\) 31.3086 + 18.0760i 1.06207 + 0.613188i
\(870\) −1.43717 + 6.44710i −0.0487248 + 0.218577i
\(871\) −3.19757 1.84612i −0.108345 0.0625532i
\(872\) −1.21726 + 0.702787i −0.0412217 + 0.0237994i
\(873\) 7.33884 15.6429i 0.248382 0.529431i
\(874\) 2.23226i 0.0755074i
\(875\) −2.75373 4.33934i −0.0930929 0.146697i
\(876\) 2.21732 2.41413i 0.0749164 0.0815657i
\(877\) −3.06175 5.30311i −0.103388 0.179073i 0.809690 0.586857i \(-0.199635\pi\)
−0.913078 + 0.407784i \(0.866302\pi\)
\(878\) 5.15154 0.173856
\(879\) −2.28440 + 10.2477i −0.0770509 + 0.345647i
\(880\) 41.6074i 1.40258i
\(881\) 41.3283 1.39238 0.696192 0.717855i \(-0.254876\pi\)
0.696192 + 0.717855i \(0.254876\pi\)
\(882\) −6.08368 + 1.03601i −0.204848 + 0.0348844i
\(883\) 24.2918 0.817483 0.408741 0.912650i \(-0.365968\pi\)
0.408741 + 0.912650i \(0.365968\pi\)
\(884\) 15.0905i 0.507549i
\(885\) 18.2973 + 16.8056i 0.615056 + 0.564915i
\(886\) 2.64619 0.0889005
\(887\) 3.35036 + 5.80299i 0.112494 + 0.194845i 0.916775 0.399404i \(-0.130783\pi\)
−0.804281 + 0.594249i \(0.797449\pi\)
\(888\) 15.1421 + 3.37544i 0.508134 + 0.113272i
\(889\) −3.89690 6.14077i −0.130698 0.205955i
\(890\) 3.88234i 0.130136i
\(891\) −26.9687 + 22.4159i −0.903485 + 0.750962i
\(892\) 10.6624 6.15591i 0.357002 0.206115i
\(893\) −8.94675 5.16541i −0.299392 0.172854i
\(894\) 3.17647 + 2.91752i 0.106237 + 0.0975764i
\(895\) 67.2823 + 38.8455i 2.24900 + 1.29846i
\(896\) 18.7979 11.9290i 0.627993 0.398521i
\(897\) 11.5423 3.62448i 0.385385 0.121018i
\(898\) −9.05470 −0.302159
\(899\) −1.00232 1.73608i −0.0334294 0.0579014i
\(900\) 2.12596 + 24.9703i 0.0708653 + 0.832342i
\(901\) −16.8074 9.70376i −0.559936 0.323279i
\(902\) −3.58101 6.20249i −0.119235 0.206520i
\(903\) −3.33604 + 18.6009i −0.111016 + 0.619000i
\(904\) 1.24622 2.15852i 0.0414487 0.0717912i
\(905\) −59.3747 + 34.2800i −1.97368 + 1.13951i
\(906\) −1.66754 0.371725i −0.0554003 0.0123497i
\(907\) −10.1494 + 17.5793i −0.337005 + 0.583710i −0.983868 0.178897i \(-0.942747\pi\)
0.646863 + 0.762606i \(0.276081\pi\)
\(908\) −18.8873 + 32.7138i −0.626798 + 1.08565i
\(909\) −4.36668 51.2884i −0.144834 1.70113i
\(910\) −2.98746 4.70766i −0.0990332 0.156057i
\(911\) −30.3982 + 17.5504i −1.00714 + 0.581472i −0.910353 0.413833i \(-0.864190\pi\)
−0.0967861 + 0.995305i \(0.530856\pi\)
\(912\) −15.0325 3.35103i −0.497777 0.110964i
\(913\) 42.8114i 1.41685i
\(914\) 4.06380i 0.134419i
\(915\) −5.73754 + 6.24679i −0.189677 + 0.206512i
\(916\) 18.0756 10.4359i 0.597233 0.344813i
\(917\) −9.16685 + 17.5338i −0.302716 + 0.579018i
\(918\) −0.688551 + 5.09237i −0.0227256 + 0.168073i
\(919\) −16.9132 + 29.2946i −0.557916 + 0.966339i 0.439754 + 0.898118i \(0.355066\pi\)
−0.997670 + 0.0682206i \(0.978268\pi\)
\(920\) −5.24555 + 9.08557i −0.172941 + 0.299542i
\(921\) −11.2100 35.6988i −0.369384 1.17631i
\(922\) −3.14046 + 1.81314i −0.103425 + 0.0597127i
\(923\) 15.9499 27.6260i 0.524996 0.909320i
\(924\) −11.5927 32.1432i −0.381371 1.05743i
\(925\) −16.9981 29.4415i −0.558893 0.968031i
\(926\) 3.24639 + 1.87431i 0.106683 + 0.0615935i
\(927\) 12.5123 26.6703i 0.410959 0.875967i
\(928\) −7.05115 12.2130i −0.231465 0.400910i
\(929\) 32.1171 1.05373 0.526864 0.849950i \(-0.323368\pi\)
0.526864 + 0.849950i \(0.323368\pi\)
\(930\) 0.542324 + 0.498113i 0.0177835 + 0.0163338i
\(931\) −14.6486 + 10.1803i −0.480087 + 0.333644i
\(932\) 34.4348 + 19.8810i 1.12795 + 0.651222i
\(933\) −18.2161 + 5.72018i −0.596369 + 0.187270i
\(934\) −2.79439 1.61334i −0.0914351 0.0527901i
\(935\) −34.7520 + 20.0641i −1.13651 + 0.656166i
\(936\) −0.685877 8.05590i −0.0224186 0.263315i
\(937\) 13.9224i 0.454824i 0.973799 + 0.227412i \(0.0730263\pi\)
−0.973799 + 0.227412i \(0.926974\pi\)
\(938\) 1.03439 0.656416i 0.0337739 0.0214327i
\(939\) 7.03343 + 22.3982i 0.229527 + 0.730938i
\(940\) −11.8703 20.5599i −0.387166 0.670590i
\(941\) 57.2094 1.86497 0.932487 0.361203i \(-0.117634\pi\)
0.932487 + 0.361203i \(0.117634\pi\)
\(942\) 8.11394 2.54792i 0.264367 0.0830157i
\(943\) 18.6438i 0.607127i
\(944\) −16.3545 −0.532294
\(945\) 17.5795 + 38.2230i 0.571861 + 1.24339i
\(946\) 4.72200 0.153525
\(947\) 34.4861i 1.12065i −0.828274 0.560324i \(-0.810677\pi\)
0.828274 0.560324i \(-0.189323\pi\)
\(948\) 29.3401 9.21330i 0.952922 0.299234i
\(949\) 2.31739 0.0752255
\(950\) −1.63455 2.83113i −0.0530318 0.0918538i
\(951\) −5.78802 18.4321i −0.187689 0.597703i
\(952\) −9.07469 4.74434i −0.294112 0.153765i
\(953\) 2.58761i 0.0838209i 0.999121 + 0.0419104i \(0.0133444\pi\)
−0.999121 + 0.0419104i \(0.986656\pi\)
\(954\) 4.60288 + 2.15944i 0.149024 + 0.0699144i
\(955\) −11.3669 + 6.56267i −0.367824 + 0.212363i
\(956\) 45.3034 + 26.1559i 1.46522 + 0.845943i
\(957\) −27.3043 + 8.57404i −0.882624 + 0.277159i
\(958\) −2.84900 1.64487i −0.0920470 0.0531434i
\(959\) 1.35208 + 32.2731i 0.0436608 + 1.04215i
\(960\) −23.4279 21.5180i −0.756132 0.694491i
\(961\) 30.7765 0.992791
\(962\) 2.68145 + 4.64441i 0.0864535 + 0.149742i
\(963\) −10.3721 + 0.883081i −0.334238 + 0.0284569i
\(964\) −35.3426 20.4051i −1.13831 0.657203i
\(965\) −35.7209 61.8704i −1.14990 1.99168i
\(966\) −0.708619 + 3.95108i −0.0227994 + 0.127124i
\(967\) 2.79472 4.84059i 0.0898721 0.155663i −0.817585 0.575808i \(-0.804688\pi\)
0.907457 + 0.420145i \(0.138021\pi\)
\(968\) −4.16585 + 2.40515i −0.133895 + 0.0773045i
\(969\) 4.45016 + 14.1717i 0.142960 + 0.455260i
\(970\) −2.58986 + 4.48578i −0.0831555 + 0.144030i
\(971\) 8.01661 13.8852i 0.257265 0.445597i −0.708243 0.705969i \(-0.750512\pi\)
0.965508 + 0.260372i \(0.0838452\pi\)
\(972\) −1.47489 + 29.7942i −0.0473071 + 0.955650i
\(973\) 1.47701 + 35.2551i 0.0473507 + 1.13023i
\(974\) 0.755007 0.435904i 0.0241920 0.0139673i
\(975\) −11.9848 + 13.0486i −0.383821 + 0.417888i
\(976\) 5.58353i 0.178724i
\(977\) 43.9026i 1.40457i −0.711896 0.702285i \(-0.752163\pi\)
0.711896 0.702285i \(-0.247837\pi\)
\(978\) −12.5852 2.80547i −0.402431 0.0897091i
\(979\) 14.5674 8.41048i 0.465576 0.268800i
\(980\) −40.8502 + 3.42884i −1.30491 + 0.109530i
\(981\) 3.31926 + 1.55723i 0.105976 + 0.0497185i
\(982\) 3.42377 5.93015i 0.109257 0.189239i
\(983\) −9.08808 + 15.7410i −0.289865 + 0.502061i −0.973777 0.227503i \(-0.926944\pi\)
0.683912 + 0.729564i \(0.260277\pi\)
\(984\) −12.1611 2.71094i −0.387683 0.0864215i
\(985\) 49.7749 28.7376i 1.58596 0.915655i
\(986\) −2.09683 + 3.63181i −0.0667766 + 0.115660i
\(987\) −14.1959 11.9828i −0.451861 0.381417i
\(988\) −5.71374 9.89649i −0.181778 0.314849i
\(989\) 10.6453 + 6.14604i 0.338499 + 0.195433i
\(990\) 8.62540 6.00965i 0.274133 0.190999i
\(991\) −23.8146 41.2481i −0.756496 1.31029i −0.944627 0.328145i \(-0.893576\pi\)
0.188131 0.982144i \(-0.439757\pi\)
\(992\) −1.57213 −0.0499151
\(993\) 31.4307 9.86979i 0.997423 0.313208i
\(994\) 5.67123 + 8.93677i 0.179880 + 0.283457i
\(995\) −12.0246 6.94242i −0.381206 0.220090i
\(996\) −26.8210 24.6345i −0.849856 0.780574i
\(997\) 28.4838 + 16.4451i 0.902090 + 0.520822i 0.877878 0.478885i \(-0.158959\pi\)
0.0242120 + 0.999707i \(0.492292\pi\)
\(998\) −1.16711 + 0.673830i −0.0369442 + 0.0213297i
\(999\) −15.3552 37.4406i −0.485818 1.18457i
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 63.2.i.b.5.3 10
3.2 odd 2 189.2.i.b.152.3 10
4.3 odd 2 1008.2.ca.b.257.4 10
7.2 even 3 441.2.o.d.293.3 10
7.3 odd 6 63.2.s.b.59.3 yes 10
7.4 even 3 441.2.s.b.374.3 10
7.5 odd 6 441.2.o.c.293.3 10
7.6 odd 2 441.2.i.b.68.3 10
9.2 odd 6 63.2.s.b.47.3 yes 10
9.4 even 3 567.2.p.d.404.3 10
9.5 odd 6 567.2.p.c.404.3 10
9.7 even 3 189.2.s.b.89.3 10
12.11 even 2 3024.2.ca.b.2609.1 10
21.2 odd 6 1323.2.o.c.881.3 10
21.5 even 6 1323.2.o.d.881.3 10
21.11 odd 6 1323.2.s.b.962.3 10
21.17 even 6 189.2.s.b.17.3 10
21.20 even 2 1323.2.i.b.1097.3 10
28.3 even 6 1008.2.df.b.689.5 10
36.7 odd 6 3024.2.df.b.1601.1 10
36.11 even 6 1008.2.df.b.929.5 10
63.2 odd 6 441.2.o.c.146.3 10
63.11 odd 6 441.2.i.b.227.3 10
63.16 even 3 1323.2.o.d.440.3 10
63.20 even 6 441.2.s.b.362.3 10
63.25 even 3 1323.2.i.b.521.3 10
63.31 odd 6 567.2.p.c.80.3 10
63.34 odd 6 1323.2.s.b.656.3 10
63.38 even 6 inner 63.2.i.b.38.3 yes 10
63.47 even 6 441.2.o.d.146.3 10
63.52 odd 6 189.2.i.b.143.3 10
63.59 even 6 567.2.p.d.80.3 10
63.61 odd 6 1323.2.o.c.440.3 10
84.59 odd 6 3024.2.df.b.17.1 10
252.115 even 6 3024.2.ca.b.2033.1 10
252.227 odd 6 1008.2.ca.b.353.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.i.b.5.3 10 1.1 even 1 trivial
63.2.i.b.38.3 yes 10 63.38 even 6 inner
63.2.s.b.47.3 yes 10 9.2 odd 6
63.2.s.b.59.3 yes 10 7.3 odd 6
189.2.i.b.143.3 10 63.52 odd 6
189.2.i.b.152.3 10 3.2 odd 2
189.2.s.b.17.3 10 21.17 even 6
189.2.s.b.89.3 10 9.7 even 3
441.2.i.b.68.3 10 7.6 odd 2
441.2.i.b.227.3 10 63.11 odd 6
441.2.o.c.146.3 10 63.2 odd 6
441.2.o.c.293.3 10 7.5 odd 6
441.2.o.d.146.3 10 63.47 even 6
441.2.o.d.293.3 10 7.2 even 3
441.2.s.b.362.3 10 63.20 even 6
441.2.s.b.374.3 10 7.4 even 3
567.2.p.c.80.3 10 63.31 odd 6
567.2.p.c.404.3 10 9.5 odd 6
567.2.p.d.80.3 10 63.59 even 6
567.2.p.d.404.3 10 9.4 even 3
1008.2.ca.b.257.4 10 4.3 odd 2
1008.2.ca.b.353.4 10 252.227 odd 6
1008.2.df.b.689.5 10 28.3 even 6
1008.2.df.b.929.5 10 36.11 even 6
1323.2.i.b.521.3 10 63.25 even 3
1323.2.i.b.1097.3 10 21.20 even 2
1323.2.o.c.440.3 10 63.61 odd 6
1323.2.o.c.881.3 10 21.2 odd 6
1323.2.o.d.440.3 10 63.16 even 3
1323.2.o.d.881.3 10 21.5 even 6
1323.2.s.b.656.3 10 63.34 odd 6
1323.2.s.b.962.3 10 21.11 odd 6
3024.2.ca.b.2033.1 10 252.115 even 6
3024.2.ca.b.2609.1 10 12.11 even 2
3024.2.df.b.17.1 10 84.59 odd 6
3024.2.df.b.1601.1 10 36.7 odd 6