Properties

Label 95.2.i.b.49.6
Level $95$
Weight $2$
Character 95.49
Analytic conductor $0.759$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,2,Mod(49,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.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: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6x^{10} + 29x^{8} - 40x^{6} + 43x^{4} - 7x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.6
Root \(0.352587 + 0.203566i\) of defining polynomial
Character \(\chi\) \(=\) 95.49
Dual form 95.2.i.b.64.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.12713 + 1.22810i) q^{2} +(-1.35190 - 0.780522i) q^{3} +(2.01647 + 3.49262i) q^{4} +(-0.746759 + 2.10769i) q^{5} +(-1.91712 - 3.32055i) q^{6} -4.50527i q^{7} +4.99330i q^{8} +(-0.281570 - 0.487693i) q^{9} +O(q^{10})\) \(q+(2.12713 + 1.22810i) q^{2} +(-1.35190 - 0.780522i) q^{3} +(2.01647 + 3.49262i) q^{4} +(-0.746759 + 2.10769i) q^{5} +(-1.91712 - 3.32055i) q^{6} -4.50527i q^{7} +4.99330i q^{8} +(-0.281570 - 0.487693i) q^{9} +(-4.17691 + 3.56624i) q^{10} +2.19869 q^{11} -6.29559i q^{12} +(-3.25495 + 1.87925i) q^{13} +(5.53293 - 9.58332i) q^{14} +(2.65464 - 2.26653i) q^{15} +(-2.09935 + 3.63617i) q^{16} +(0.576674 + 0.332943i) q^{17} -1.38318i q^{18} +(-3.79804 + 2.13891i) q^{19} +(-8.86718 + 1.64194i) q^{20} +(-3.51647 + 6.09070i) q^{21} +(4.67691 + 2.70022i) q^{22} +(-0.422643 + 0.244013i) q^{23} +(3.89738 - 6.75046i) q^{24} +(-3.88470 - 3.14787i) q^{25} -9.23163 q^{26} +5.56222i q^{27} +(15.7352 - 9.08474i) q^{28} +(1.79804 + 3.11429i) q^{29} +(8.43032 - 1.56104i) q^{30} +6.83424 q^{31} +(-0.282531 + 0.163119i) q^{32} +(-2.97242 - 1.71613i) q^{33} +(0.817776 + 1.41643i) q^{34} +(9.49572 + 3.36435i) q^{35} +(1.13555 - 1.96683i) q^{36} +3.01171i q^{37} +(-10.7057 - 0.114636i) q^{38} +5.86718 q^{39} +(-10.5243 - 3.72879i) q^{40} +(-0.0362063 + 0.0627112i) q^{41} +(-14.9600 + 8.63716i) q^{42} +(-0.364199 - 0.210271i) q^{43} +(4.43359 + 7.67920i) q^{44} +(1.23817 - 0.229272i) q^{45} -1.19869 q^{46} +(-4.34986 + 2.51139i) q^{47} +(5.67623 - 3.27717i) q^{48} -13.2975 q^{49} +(-4.39738 - 11.4668i) q^{50} +(-0.519739 - 0.900215i) q^{51} +(-13.1270 - 7.57888i) q^{52} +(2.26725 - 1.30900i) q^{53} +(-6.83097 + 11.8316i) q^{54} +(-1.64189 + 4.63416i) q^{55} +22.4962 q^{56} +(6.80405 + 0.0728572i) q^{57} +8.83269i q^{58} +(6.26783 - 10.8562i) q^{59} +(13.2691 + 4.70129i) q^{60} +(-3.53293 - 6.11922i) q^{61} +(14.5374 + 8.39315i) q^{62} +(-2.19719 + 1.26855i) q^{63} +7.59607 q^{64} +(-1.53020 - 8.26377i) q^{65} +(-4.21516 - 7.30087i) q^{66} +(-4.95944 + 2.86334i) q^{67} +2.68548i q^{68} +0.761831 q^{69} +(16.0669 + 18.8181i) q^{70} +(-3.48626 + 6.03838i) q^{71} +(2.43520 - 1.40596i) q^{72} +(2.56139 + 1.47882i) q^{73} +(-3.69869 + 6.40632i) q^{74} +(2.79476 + 7.28772i) q^{75} +(-15.1290 - 8.95208i) q^{76} -9.90571i q^{77} +(12.4803 + 7.20549i) q^{78} +(5.66849 - 9.81811i) q^{79} +(-6.09622 - 7.14011i) q^{80} +(3.49673 - 6.05651i) q^{81} +(-0.154031 + 0.0889301i) q^{82} -15.6999i q^{83} -28.3634 q^{84} +(-1.13238 + 0.966822i) q^{85} +(-0.516467 - 0.894547i) q^{86} -5.61363i q^{87} +10.9787i q^{88} +(-0.668486 - 1.15785i) q^{89} +(2.91532 + 1.03290i) q^{90} +(8.46652 + 14.6644i) q^{91} +(-1.70449 - 0.984089i) q^{92} +(-9.23924 - 5.33428i) q^{93} -12.3370 q^{94} +(-1.67193 - 9.60233i) q^{95} +0.509273 q^{96} +(3.79871 + 2.19319i) q^{97} +(-28.2856 - 16.3307i) q^{98} +(-0.619085 - 1.07229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{4} - 2 q^{5} - 12 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{4} - 2 q^{5} - 12 q^{6} + 8 q^{9} + 6 q^{10} + 4 q^{11} + 22 q^{14} - 4 q^{15} - 14 q^{16} - 12 q^{19} - 40 q^{20} - 20 q^{21} + 2 q^{24} - 6 q^{25} - 44 q^{26} - 12 q^{29} + 12 q^{30} + 60 q^{31} + 10 q^{34} + 14 q^{36} + 4 q^{39} + 10 q^{40} - 12 q^{41} + 20 q^{44} + 60 q^{45} + 8 q^{46} - 4 q^{49} - 8 q^{50} - 40 q^{51} - 4 q^{54} - 18 q^{55} + 92 q^{56} + 20 q^{59} + 4 q^{60} + 2 q^{61} + 24 q^{64} - 40 q^{65} - 6 q^{66} - 36 q^{69} + 46 q^{70} + 2 q^{71} - 22 q^{74} - 56 q^{75} - 70 q^{76} + 24 q^{79} - 22 q^{80} - 14 q^{81} - 96 q^{84} + 2 q^{85} + 16 q^{86} + 36 q^{89} - 8 q^{90} + 24 q^{91} - 60 q^{94} + 46 q^{95} + 52 q^{96} - 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.12713 + 1.22810i 1.50411 + 0.868399i 0.999989 + 0.00476685i \(0.00151734\pi\)
0.504123 + 0.863632i \(0.331816\pi\)
\(3\) −1.35190 0.780522i −0.780522 0.450635i 0.0560930 0.998426i \(-0.482136\pi\)
−0.836615 + 0.547791i \(0.815469\pi\)
\(4\) 2.01647 + 3.49262i 1.00823 + 1.74631i
\(5\) −0.746759 + 2.10769i −0.333961 + 0.942587i
\(6\) −1.91712 3.32055i −0.782662 1.35561i
\(7\) 4.50527i 1.70283i −0.524490 0.851417i \(-0.675744\pi\)
0.524490 0.851417i \(-0.324256\pi\)
\(8\) 4.99330i 1.76540i
\(9\) −0.281570 0.487693i −0.0938566 0.162564i
\(10\) −4.17691 + 3.56624i −1.32086 + 1.12774i
\(11\) 2.19869 0.662930 0.331465 0.943467i \(-0.392457\pi\)
0.331465 + 0.943467i \(0.392457\pi\)
\(12\) 6.29559i 1.81738i
\(13\) −3.25495 + 1.87925i −0.902761 + 0.521209i −0.878095 0.478486i \(-0.841186\pi\)
−0.0246661 + 0.999696i \(0.507852\pi\)
\(14\) 5.53293 9.58332i 1.47874 2.56125i
\(15\) 2.65464 2.26653i 0.685426 0.585216i
\(16\) −2.09935 + 3.63617i −0.524836 + 0.909043i
\(17\) 0.576674 + 0.332943i 0.139864 + 0.0807506i 0.568299 0.822822i \(-0.307602\pi\)
−0.428435 + 0.903573i \(0.640935\pi\)
\(18\) 1.38318i 0.326020i
\(19\) −3.79804 + 2.13891i −0.871329 + 0.490699i
\(20\) −8.86718 + 1.64194i −1.98276 + 0.367149i
\(21\) −3.51647 + 6.09070i −0.767356 + 1.32910i
\(22\) 4.67691 + 2.70022i 0.997121 + 0.575688i
\(23\) −0.422643 + 0.244013i −0.0881272 + 0.0508802i −0.543416 0.839464i \(-0.682869\pi\)
0.455289 + 0.890344i \(0.349536\pi\)
\(24\) 3.89738 6.75046i 0.795550 1.37793i
\(25\) −3.88470 3.14787i −0.776941 0.629574i
\(26\) −9.23163 −1.81047
\(27\) 5.56222i 1.07045i
\(28\) 15.7352 9.08474i 2.97368 1.71685i
\(29\) 1.79804 + 3.11429i 0.333887 + 0.578309i 0.983270 0.182152i \(-0.0583062\pi\)
−0.649383 + 0.760461i \(0.724973\pi\)
\(30\) 8.43032 1.56104i 1.53916 0.285006i
\(31\) 6.83424 1.22747 0.613733 0.789514i \(-0.289667\pi\)
0.613733 + 0.789514i \(0.289667\pi\)
\(32\) −0.282531 + 0.163119i −0.0499449 + 0.0288357i
\(33\) −2.97242 1.71613i −0.517432 0.298739i
\(34\) 0.817776 + 1.41643i 0.140247 + 0.242916i
\(35\) 9.49572 + 3.36435i 1.60507 + 0.568679i
\(36\) 1.13555 1.96683i 0.189259 0.327806i
\(37\) 3.01171i 0.495123i 0.968872 + 0.247561i \(0.0796292\pi\)
−0.968872 + 0.247561i \(0.920371\pi\)
\(38\) −10.7057 0.114636i −1.73670 0.0185964i
\(39\) 5.86718 0.939500
\(40\) −10.5243 3.72879i −1.66404 0.589573i
\(41\) −0.0362063 + 0.0627112i −0.00565448 + 0.00979384i −0.868839 0.495095i \(-0.835133\pi\)
0.863184 + 0.504889i \(0.168467\pi\)
\(42\) −14.9600 + 8.63716i −2.30838 + 1.33274i
\(43\) −0.364199 0.210271i −0.0555399 0.0320660i 0.471973 0.881613i \(-0.343542\pi\)
−0.527513 + 0.849547i \(0.676875\pi\)
\(44\) 4.43359 + 7.67920i 0.668389 + 1.15768i
\(45\) 1.23817 0.229272i 0.184575 0.0341779i
\(46\) −1.19869 −0.176737
\(47\) −4.34986 + 2.51139i −0.634492 + 0.366324i −0.782490 0.622664i \(-0.786050\pi\)
0.147998 + 0.988988i \(0.452717\pi\)
\(48\) 5.67623 3.27717i 0.819293 0.473019i
\(49\) −13.2975 −1.89964
\(50\) −4.39738 11.4668i −0.621884 1.62164i
\(51\) −0.519739 0.900215i −0.0727780 0.126055i
\(52\) −13.1270 7.57888i −1.82039 1.05100i
\(53\) 2.26725 1.30900i 0.311430 0.179804i −0.336136 0.941813i \(-0.609120\pi\)
0.647566 + 0.762009i \(0.275787\pi\)
\(54\) −6.83097 + 11.8316i −0.929577 + 1.61008i
\(55\) −1.64189 + 4.63416i −0.221393 + 0.624870i
\(56\) 22.4962 3.00618
\(57\) 6.80405 + 0.0728572i 0.901218 + 0.00965017i
\(58\) 8.83269i 1.15979i
\(59\) 6.26783 10.8562i 0.816002 1.41336i −0.0926038 0.995703i \(-0.529519\pi\)
0.908606 0.417654i \(-0.137148\pi\)
\(60\) 13.2691 + 4.70129i 1.71304 + 0.606934i
\(61\) −3.53293 6.11922i −0.452346 0.783486i 0.546185 0.837664i \(-0.316079\pi\)
−0.998531 + 0.0541782i \(0.982746\pi\)
\(62\) 14.5374 + 8.39315i 1.84625 + 1.06593i
\(63\) −2.19719 + 1.26855i −0.276820 + 0.159822i
\(64\) 7.59607 0.949509
\(65\) −1.53020 8.26377i −0.189799 1.02499i
\(66\) −4.21516 7.30087i −0.518850 0.898675i
\(67\) −4.95944 + 2.86334i −0.605892 + 0.349812i −0.771356 0.636404i \(-0.780421\pi\)
0.165464 + 0.986216i \(0.447088\pi\)
\(68\) 2.68548i 0.325662i
\(69\) 0.761831 0.0917136
\(70\) 16.0669 + 18.8181i 1.92036 + 2.24920i
\(71\) −3.48626 + 6.03838i −0.413743 + 0.716624i −0.995296 0.0968847i \(-0.969112\pi\)
0.581552 + 0.813509i \(0.302446\pi\)
\(72\) 2.43520 1.40596i 0.286991 0.165694i
\(73\) 2.56139 + 1.47882i 0.299788 + 0.173083i 0.642348 0.766413i \(-0.277961\pi\)
−0.342560 + 0.939496i \(0.611294\pi\)
\(74\) −3.69869 + 6.40632i −0.429964 + 0.744720i
\(75\) 2.79476 + 7.28772i 0.322712 + 0.841513i
\(76\) −15.1290 8.95208i −1.73542 1.02687i
\(77\) 9.90571i 1.12886i
\(78\) 12.4803 + 7.20549i 1.41311 + 0.815861i
\(79\) 5.66849 9.81811i 0.637755 1.10462i −0.348170 0.937431i \(-0.613197\pi\)
0.985924 0.167192i \(-0.0534699\pi\)
\(80\) −6.09622 7.14011i −0.681578 0.798289i
\(81\) 3.49673 6.05651i 0.388525 0.672946i
\(82\) −0.154031 + 0.0889301i −0.0170099 + 0.00982068i
\(83\) 15.6999i 1.72328i −0.507517 0.861642i \(-0.669436\pi\)
0.507517 0.861642i \(-0.330564\pi\)
\(84\) −28.3634 −3.09470
\(85\) −1.13238 + 0.966822i −0.122824 + 0.104867i
\(86\) −0.516467 0.894547i −0.0556921 0.0964615i
\(87\) 5.61363i 0.601845i
\(88\) 10.9787i 1.17034i
\(89\) −0.668486 1.15785i −0.0708594 0.122732i 0.828419 0.560109i \(-0.189241\pi\)
−0.899278 + 0.437377i \(0.855908\pi\)
\(90\) 2.91532 + 1.03290i 0.307302 + 0.108878i
\(91\) 8.46652 + 14.6644i 0.887533 + 1.53725i
\(92\) −1.70449 0.984089i −0.177706 0.102598i
\(93\) −9.23924 5.33428i −0.958065 0.553139i
\(94\) −12.3370 −1.27246
\(95\) −1.67193 9.60233i −0.171536 0.985178i
\(96\) 0.509273 0.0519775
\(97\) 3.79871 + 2.19319i 0.385701 + 0.222685i 0.680296 0.732938i \(-0.261851\pi\)
−0.294595 + 0.955622i \(0.595185\pi\)
\(98\) −28.2856 16.3307i −2.85727 1.64965i
\(99\) −0.619085 1.07229i −0.0622204 0.107769i
\(100\) 3.16095 19.9154i 0.316095 1.99154i
\(101\) 5.28430 + 9.15267i 0.525807 + 0.910725i 0.999548 + 0.0300608i \(0.00957008\pi\)
−0.473741 + 0.880664i \(0.657097\pi\)
\(102\) 2.55317i 0.252801i
\(103\) 5.75615i 0.567171i 0.958947 + 0.283585i \(0.0915239\pi\)
−0.958947 + 0.283585i \(0.908476\pi\)
\(104\) −9.38364 16.2529i −0.920142 1.59373i
\(105\) −10.2113 11.9599i −0.996525 1.16717i
\(106\) 6.43032 0.624568
\(107\) 1.30229i 0.125897i 0.998017 + 0.0629486i \(0.0200504\pi\)
−0.998017 + 0.0629486i \(0.979950\pi\)
\(108\) −19.4267 + 11.2160i −1.86934 + 1.07926i
\(109\) −6.01647 + 10.4208i −0.576273 + 0.998134i 0.419629 + 0.907696i \(0.362160\pi\)
−0.995902 + 0.0904385i \(0.971173\pi\)
\(110\) −9.18374 + 7.84106i −0.875635 + 0.747616i
\(111\) 2.35071 4.07155i 0.223120 0.386454i
\(112\) 16.3820 + 9.45813i 1.54795 + 0.893709i
\(113\) 7.74626i 0.728707i 0.931261 + 0.364353i \(0.118710\pi\)
−0.931261 + 0.364353i \(0.881290\pi\)
\(114\) 14.3836 + 8.51104i 1.34715 + 0.797132i
\(115\) −0.198691 1.07302i −0.0185281 0.100060i
\(116\) −7.25136 + 12.5597i −0.673272 + 1.16614i
\(117\) 1.83299 + 1.05828i 0.169460 + 0.0978378i
\(118\) 26.6650 15.3951i 2.45472 1.41723i
\(119\) 1.50000 2.59808i 0.137505 0.238165i
\(120\) 11.3175 + 13.2554i 1.03314 + 1.21005i
\(121\) −6.16576 −0.560523
\(122\) 17.3552i 1.57127i
\(123\) 0.0978950 0.0565197i 0.00882689 0.00509621i
\(124\) 13.7810 + 23.8694i 1.23757 + 2.14354i
\(125\) 9.53566 5.83705i 0.852896 0.522081i
\(126\) −6.23163 −0.555157
\(127\) 3.40898 1.96818i 0.302498 0.174647i −0.341066 0.940039i \(-0.610788\pi\)
0.643565 + 0.765392i \(0.277455\pi\)
\(128\) 16.7229 + 9.65499i 1.47811 + 0.853389i
\(129\) 0.328242 + 0.568531i 0.0289001 + 0.0500564i
\(130\) 6.89380 19.4574i 0.604626 1.70653i
\(131\) 8.16248 14.1378i 0.713160 1.23523i −0.250505 0.968115i \(-0.580597\pi\)
0.963665 0.267114i \(-0.0860699\pi\)
\(132\) 13.8421i 1.20480i
\(133\) 9.63635 + 17.1112i 0.835578 + 1.48373i
\(134\) −14.0659 −1.21511
\(135\) −11.7234 4.15364i −1.00899 0.357488i
\(136\) −1.66248 + 2.87951i −0.142557 + 0.246916i
\(137\) 14.2293 8.21529i 1.21569 0.701879i 0.251697 0.967806i \(-0.419011\pi\)
0.963993 + 0.265927i \(0.0856780\pi\)
\(138\) 1.62052 + 0.935605i 0.137947 + 0.0796440i
\(139\) −1.33424 2.31098i −0.113169 0.196015i 0.803877 0.594795i \(-0.202767\pi\)
−0.917046 + 0.398781i \(0.869433\pi\)
\(140\) 7.39738 + 39.9491i 0.625193 + 3.37631i
\(141\) 7.84079 0.660313
\(142\) −14.8315 + 8.56297i −1.24463 + 0.718588i
\(143\) −7.15663 + 4.13188i −0.598468 + 0.345526i
\(144\) 2.36445 0.197037
\(145\) −7.90666 + 1.46408i −0.656612 + 0.121585i
\(146\) 3.63228 + 6.29129i 0.300610 + 0.520671i
\(147\) 17.9769 + 10.3790i 1.48271 + 0.856045i
\(148\) −10.5188 + 6.07302i −0.864639 + 0.499199i
\(149\) −8.98299 + 15.5590i −0.735915 + 1.27464i 0.218405 + 0.975858i \(0.429915\pi\)
−0.954321 + 0.298784i \(0.903419\pi\)
\(150\) −3.00522 + 18.9342i −0.245375 + 1.54597i
\(151\) −12.7344 −1.03631 −0.518154 0.855288i \(-0.673380\pi\)
−0.518154 + 0.855288i \(0.673380\pi\)
\(152\) −10.6802 18.9647i −0.866278 1.53824i
\(153\) 0.374987i 0.0303159i
\(154\) 12.1652 21.0708i 0.980301 1.69793i
\(155\) −5.10353 + 14.4045i −0.409925 + 1.15699i
\(156\) 11.8310 + 20.4918i 0.947236 + 1.64066i
\(157\) −17.3674 10.0270i −1.38607 0.800245i −0.393197 0.919454i \(-0.628631\pi\)
−0.992869 + 0.119209i \(0.961964\pi\)
\(158\) 24.1153 13.9230i 1.91851 1.10765i
\(159\) −4.08680 −0.324104
\(160\) −0.132822 0.717298i −0.0105005 0.0567074i
\(161\) 1.09935 + 1.90412i 0.0866406 + 0.150066i
\(162\) 14.8760 8.58867i 1.16877 0.674790i
\(163\) 14.2331i 1.11482i −0.830236 0.557412i \(-0.811794\pi\)
0.830236 0.557412i \(-0.188206\pi\)
\(164\) −0.292035 −0.0228041
\(165\) 5.83674 4.98340i 0.454390 0.387957i
\(166\) 19.2810 33.3957i 1.49650 2.59201i
\(167\) −4.86386 + 2.80815i −0.376376 + 0.217301i −0.676241 0.736681i \(-0.736392\pi\)
0.299864 + 0.953982i \(0.403059\pi\)
\(168\) −30.4127 17.5588i −2.34639 1.35469i
\(169\) 0.563139 0.975386i 0.0433184 0.0750297i
\(170\) −3.59607 + 0.665886i −0.275806 + 0.0510711i
\(171\) 2.11254 + 1.25002i 0.161550 + 0.0955918i
\(172\) 1.69601i 0.129320i
\(173\) 9.25824 + 5.34524i 0.703891 + 0.406391i 0.808795 0.588091i \(-0.200120\pi\)
−0.104904 + 0.994482i \(0.533454\pi\)
\(174\) 6.89411 11.9409i 0.522641 0.905241i
\(175\) −14.1820 + 17.5017i −1.07206 + 1.32300i
\(176\) −4.61581 + 7.99482i −0.347930 + 0.602632i
\(177\) −16.9470 + 9.78437i −1.27382 + 0.735438i
\(178\) 3.28388i 0.246137i
\(179\) −7.68942 −0.574734 −0.287367 0.957821i \(-0.592780\pi\)
−0.287367 + 0.957821i \(0.592780\pi\)
\(180\) 3.29749 + 3.86214i 0.245780 + 0.287867i
\(181\) 3.06314 + 5.30551i 0.227681 + 0.394356i 0.957121 0.289690i \(-0.0935522\pi\)
−0.729439 + 0.684046i \(0.760219\pi\)
\(182\) 41.5910i 3.08293i
\(183\) 11.0301i 0.815371i
\(184\) −1.21843 2.11038i −0.0898239 0.155580i
\(185\) −6.34776 2.24902i −0.466696 0.165351i
\(186\) −13.1021 22.6935i −0.960691 1.66397i
\(187\) 1.26793 + 0.732039i 0.0927201 + 0.0535320i
\(188\) −17.5427 10.1283i −1.27943 0.738680i
\(189\) 25.0593 1.82280
\(190\) 8.23621 22.4787i 0.597518 1.63078i
\(191\) 5.85517 0.423666 0.211833 0.977306i \(-0.432057\pi\)
0.211833 + 0.977306i \(0.432057\pi\)
\(192\) −10.2692 5.92891i −0.741113 0.427882i
\(193\) −2.24402 1.29559i −0.161528 0.0932584i 0.417057 0.908880i \(-0.363062\pi\)
−0.578585 + 0.815622i \(0.696395\pi\)
\(194\) 5.38692 + 9.33041i 0.386758 + 0.669885i
\(195\) −4.38137 + 12.3662i −0.313756 + 0.885561i
\(196\) −26.8140 46.4431i −1.91528 3.31737i
\(197\) 19.8628i 1.41517i 0.706629 + 0.707584i \(0.250215\pi\)
−0.706629 + 0.707584i \(0.749785\pi\)
\(198\) 3.04120i 0.216128i
\(199\) −6.38092 11.0521i −0.452331 0.783460i 0.546199 0.837655i \(-0.316074\pi\)
−0.998530 + 0.0541948i \(0.982741\pi\)
\(200\) 15.7183 19.3975i 1.11145 1.37161i
\(201\) 8.93959 0.630550
\(202\) 25.9586i 1.82644i
\(203\) 14.0307 8.10065i 0.984765 0.568554i
\(204\) 2.09607 3.63051i 0.146755 0.254186i
\(205\) −0.105138 0.123142i −0.00734318 0.00860059i
\(206\) −7.06914 + 12.2441i −0.492530 + 0.853088i
\(207\) 0.238007 + 0.137413i 0.0165426 + 0.00955089i
\(208\) 15.7808i 1.09420i
\(209\) −8.35071 + 4.70279i −0.577631 + 0.325299i
\(210\) −7.03293 37.9809i −0.485319 2.62093i
\(211\) −6.92759 + 11.9989i −0.476915 + 0.826041i −0.999650 0.0264545i \(-0.991578\pi\)
0.522735 + 0.852495i \(0.324912\pi\)
\(212\) 9.14366 + 5.27909i 0.627989 + 0.362570i
\(213\) 9.42619 5.44221i 0.645872 0.372894i
\(214\) −1.59935 + 2.77015i −0.109329 + 0.189363i
\(215\) 0.715154 0.610597i 0.0487731 0.0416424i
\(216\) −27.7738 −1.88977
\(217\) 30.7901i 2.09017i
\(218\) −25.5957 + 14.7777i −1.73356 + 1.00087i
\(219\) −2.30850 3.99844i −0.155994 0.270190i
\(220\) −19.4962 + 3.61012i −1.31443 + 0.243394i
\(221\) −2.50273 −0.168352
\(222\) 10.0006 5.77382i 0.671193 0.387514i
\(223\) 18.7893 + 10.8480i 1.25823 + 0.726437i 0.972729 0.231943i \(-0.0745083\pi\)
0.285496 + 0.958380i \(0.407842\pi\)
\(224\) 0.734898 + 1.27288i 0.0491024 + 0.0850479i
\(225\) −0.441379 + 2.78089i −0.0294253 + 0.185392i
\(226\) −9.51320 + 16.4773i −0.632808 + 1.09606i
\(227\) 8.19628i 0.544006i 0.962296 + 0.272003i \(0.0876861\pi\)
−0.962296 + 0.272003i \(0.912314\pi\)
\(228\) 13.4657 + 23.9109i 0.891786 + 1.58354i
\(229\) 16.6619 1.10105 0.550526 0.834818i \(-0.314427\pi\)
0.550526 + 0.834818i \(0.314427\pi\)
\(230\) 0.895133 2.52647i 0.0590233 0.166590i
\(231\) −7.73163 + 13.3916i −0.508704 + 0.881101i
\(232\) −15.5506 + 8.97814i −1.02095 + 0.589444i
\(233\) 10.5772 + 6.10677i 0.692937 + 0.400068i 0.804711 0.593666i \(-0.202320\pi\)
−0.111774 + 0.993734i \(0.535653\pi\)
\(234\) 2.59935 + 4.50220i 0.169925 + 0.294318i
\(235\) −2.04494 11.0435i −0.133397 0.720402i
\(236\) 50.5555 3.29088
\(237\) −15.3265 + 8.84876i −0.995563 + 0.574789i
\(238\) 6.38140 3.68430i 0.413645 0.238818i
\(239\) −2.03948 −0.131923 −0.0659614 0.997822i \(-0.521011\pi\)
−0.0659614 + 0.997822i \(0.521011\pi\)
\(240\) 2.66849 + 14.4110i 0.172250 + 0.930225i
\(241\) −8.76183 15.1759i −0.564399 0.977568i −0.997105 0.0760330i \(-0.975775\pi\)
0.432706 0.901535i \(-0.357559\pi\)
\(242\) −13.1154 7.57218i −0.843089 0.486758i
\(243\) 4.99659 2.88478i 0.320531 0.185059i
\(244\) 14.2481 24.6784i 0.912141 1.57987i
\(245\) 9.93002 28.0270i 0.634406 1.79058i
\(246\) 0.277648 0.0177022
\(247\) 8.34289 14.0995i 0.530846 0.897129i
\(248\) 34.1254i 2.16697i
\(249\) −12.2541 + 21.2247i −0.776572 + 1.34506i
\(250\) 27.4521 0.705418i 1.73622 0.0446146i
\(251\) 1.66903 + 2.89084i 0.105348 + 0.182468i 0.913880 0.405984i \(-0.133071\pi\)
−0.808532 + 0.588452i \(0.799738\pi\)
\(252\) −8.86112 5.11597i −0.558198 0.322276i
\(253\) −0.929261 + 0.536509i −0.0584222 + 0.0337301i
\(254\) 9.66849 0.606655
\(255\) 2.28549 0.423205i 0.143123 0.0265021i
\(256\) 16.1185 + 27.9181i 1.00741 + 1.74488i
\(257\) −23.8889 + 13.7922i −1.49015 + 0.860337i −0.999937 0.0112676i \(-0.996413\pi\)
−0.490210 + 0.871604i \(0.663080\pi\)
\(258\) 1.61246i 0.100387i
\(259\) 13.5686 0.843112
\(260\) 25.7766 22.0080i 1.59860 1.36488i
\(261\) 1.01255 1.75378i 0.0626750 0.108556i
\(262\) 34.7254 20.0487i 2.14534 1.23861i
\(263\) −11.8006 6.81310i −0.727658 0.420114i 0.0899066 0.995950i \(-0.471343\pi\)
−0.817565 + 0.575837i \(0.804676\pi\)
\(264\) 8.56914 14.8422i 0.527394 0.913473i
\(265\) 1.06587 + 5.75615i 0.0654758 + 0.353598i
\(266\) −0.516467 + 48.2322i −0.0316666 + 2.95731i
\(267\) 2.08707i 0.127727i
\(268\) −20.0011 11.5476i −1.22176 0.705385i
\(269\) −1.80404 + 3.12469i −0.109994 + 0.190515i −0.915768 0.401708i \(-0.868417\pi\)
0.805773 + 0.592224i \(0.201750\pi\)
\(270\) −19.8362 23.2329i −1.20719 1.41391i
\(271\) −5.28157 + 9.14795i −0.320833 + 0.555698i −0.980660 0.195719i \(-0.937296\pi\)
0.659828 + 0.751417i \(0.270629\pi\)
\(272\) −2.42128 + 1.39793i −0.146812 + 0.0847617i
\(273\) 26.4332i 1.59981i
\(274\) 40.3568 2.43804
\(275\) −8.54126 6.92119i −0.515058 0.417364i
\(276\) 1.53621 + 2.66079i 0.0924688 + 0.160161i
\(277\) 6.73487i 0.404659i −0.979317 0.202330i \(-0.935149\pi\)
0.979317 0.202330i \(-0.0648512\pi\)
\(278\) 6.55434i 0.393103i
\(279\) −1.92432 3.33301i −0.115206 0.199542i
\(280\) −16.7992 + 47.4150i −1.00395 + 2.83359i
\(281\) −11.7152 20.2912i −0.698868 1.21047i −0.968859 0.247612i \(-0.920354\pi\)
0.269992 0.962863i \(-0.412979\pi\)
\(282\) 16.6784 + 9.62928i 0.993185 + 0.573415i
\(283\) −12.7160 7.34157i −0.755886 0.436411i 0.0719306 0.997410i \(-0.477084\pi\)
−0.827817 + 0.560999i \(0.810417\pi\)
\(284\) −28.1197 −1.66860
\(285\) −5.23454 + 14.2864i −0.310067 + 0.846254i
\(286\) −20.2975 −1.20022
\(287\) 0.282531 + 0.163119i 0.0166773 + 0.00962863i
\(288\) 0.159104 + 0.0918589i 0.00937531 + 0.00541284i
\(289\) −8.27830 14.3384i −0.486959 0.843437i
\(290\) −18.6166 6.59589i −1.09320 0.387324i
\(291\) −3.42367 5.92996i −0.200699 0.347621i
\(292\) 11.9280i 0.698031i
\(293\) 18.1855i 1.06241i 0.847243 + 0.531206i \(0.178261\pi\)
−0.847243 + 0.531206i \(0.821739\pi\)
\(294\) 25.4929 + 44.1550i 1.48678 + 2.57517i
\(295\) 18.2009 + 21.3176i 1.05970 + 1.24116i
\(296\) −15.0384 −0.874089
\(297\) 12.2296i 0.709634i
\(298\) −38.2161 + 22.0641i −2.21380 + 1.27814i
\(299\) 0.917122 1.58850i 0.0530385 0.0918654i
\(300\) −19.8177 + 24.4565i −1.14418 + 1.41200i
\(301\) −0.947326 + 1.64082i −0.0546030 + 0.0945752i
\(302\) −27.0877 15.6391i −1.55872 0.899928i
\(303\) 16.4981i 0.947788i
\(304\) 0.195962 18.3006i 0.0112392 1.04961i
\(305\) 15.5357 2.87674i 0.889570 0.164722i
\(306\) 0.460522 0.797647i 0.0263263 0.0455985i
\(307\) −25.4439 14.6901i −1.45216 0.838406i −0.453559 0.891226i \(-0.649846\pi\)
−0.998604 + 0.0528200i \(0.983179\pi\)
\(308\) 34.5969 19.9745i 1.97134 1.13815i
\(309\) 4.49281 7.78177i 0.255587 0.442689i
\(310\) −28.5460 + 24.3726i −1.62131 + 1.38427i
\(311\) −0.193232 −0.0109572 −0.00547859 0.999985i \(-0.501744\pi\)
−0.00547859 + 0.999985i \(0.501744\pi\)
\(312\) 29.2966i 1.65859i
\(313\) 18.4251 10.6377i 1.04145 0.601281i 0.121206 0.992627i \(-0.461324\pi\)
0.920243 + 0.391346i \(0.127991\pi\)
\(314\) −24.6285 42.6578i −1.38986 2.40732i
\(315\) −1.03293 5.57829i −0.0581993 0.314301i
\(316\) 45.7213 2.57202
\(317\) 16.6018 9.58506i 0.932451 0.538351i 0.0448649 0.998993i \(-0.485714\pi\)
0.887586 + 0.460642i \(0.152381\pi\)
\(318\) −8.69317 5.01901i −0.487489 0.281452i
\(319\) 3.95333 + 6.84736i 0.221344 + 0.383379i
\(320\) −5.67243 + 16.0102i −0.317099 + 0.894995i
\(321\) 1.01647 1.76057i 0.0567337 0.0982656i
\(322\) 5.40043i 0.300954i
\(323\) −2.90236 0.0310783i −0.161492 0.00172924i
\(324\) 28.2042 1.56690
\(325\) 18.5601 + 2.94584i 1.02953 + 0.163406i
\(326\) 17.4797 30.2758i 0.968112 1.67682i
\(327\) 16.2674 9.39197i 0.899588 0.519377i
\(328\) −0.313136 0.180789i −0.0172900 0.00998240i
\(329\) 11.3145 + 19.5973i 0.623789 + 1.08043i
\(330\) 18.5357 3.43226i 1.02035 0.188939i
\(331\) −20.6070 −1.13266 −0.566331 0.824178i \(-0.691638\pi\)
−0.566331 + 0.824178i \(0.691638\pi\)
\(332\) 54.8337 31.6583i 3.00939 1.73747i
\(333\) 1.46879 0.848007i 0.0804893 0.0464705i
\(334\) −13.7948 −0.754816
\(335\) −2.33151 12.5912i −0.127384 0.687930i
\(336\) −14.7646 25.5730i −0.805473 1.39512i
\(337\) 8.83982 + 5.10368i 0.481536 + 0.278015i 0.721056 0.692876i \(-0.243657\pi\)
−0.239520 + 0.970891i \(0.576990\pi\)
\(338\) 2.39575 1.38318i 0.130311 0.0752353i
\(339\) 6.04613 10.4722i 0.328381 0.568772i
\(340\) −5.66015 2.00540i −0.306965 0.108758i
\(341\) 15.0264 0.813725
\(342\) 2.95850 + 5.25339i 0.159977 + 0.284071i
\(343\) 28.3719i 1.53194i
\(344\) 1.04994 1.81856i 0.0566092 0.0980500i
\(345\) −0.568904 + 1.60570i −0.0306287 + 0.0864481i
\(346\) 13.1290 + 22.7401i 0.705820 + 1.22252i
\(347\) −4.71213 2.72055i −0.252960 0.146047i 0.368159 0.929763i \(-0.379988\pi\)
−0.621119 + 0.783716i \(0.713322\pi\)
\(348\) 19.6063 11.3197i 1.05101 0.606800i
\(349\) 1.55114 0.0830304 0.0415152 0.999138i \(-0.486781\pi\)
0.0415152 + 0.999138i \(0.486781\pi\)
\(350\) −51.6609 + 19.8114i −2.76139 + 1.05896i
\(351\) −10.4528 18.1048i −0.557928 0.966360i
\(352\) −0.621199 + 0.358649i −0.0331100 + 0.0191161i
\(353\) 32.9335i 1.75287i 0.481517 + 0.876437i \(0.340086\pi\)
−0.481517 + 0.876437i \(0.659914\pi\)
\(354\) −48.0648 −2.55461
\(355\) −10.1236 11.8572i −0.537307 0.629313i
\(356\) 2.69596 4.66954i 0.142886 0.247485i
\(357\) −4.05571 + 2.34157i −0.214651 + 0.123929i
\(358\) −16.3564 9.44339i −0.864464 0.499098i
\(359\) −1.74864 + 3.02873i −0.0922894 + 0.159850i −0.908474 0.417941i \(-0.862752\pi\)
0.816185 + 0.577791i \(0.196085\pi\)
\(360\) 1.14483 + 6.18255i 0.0603376 + 0.325849i
\(361\) 9.85017 16.2473i 0.518430 0.855120i
\(362\) 15.0474i 0.790873i
\(363\) 8.33551 + 4.81251i 0.437501 + 0.252591i
\(364\) −34.1449 + 59.1408i −1.78968 + 3.09982i
\(365\) −5.02963 + 4.29429i −0.263263 + 0.224773i
\(366\) −13.5461 + 23.4626i −0.708068 + 1.22641i
\(367\) 16.8909 9.75196i 0.881697 0.509048i 0.0104794 0.999945i \(-0.496664\pi\)
0.871218 + 0.490897i \(0.163331\pi\)
\(368\) 2.04907i 0.106815i
\(369\) 0.0407784 0.00212284
\(370\) −10.7405 12.5797i −0.558372 0.653986i
\(371\) −5.89738 10.2146i −0.306177 0.530314i
\(372\) 43.0256i 2.23077i
\(373\) 23.5158i 1.21760i −0.793322 0.608802i \(-0.791650\pi\)
0.793322 0.608802i \(-0.208350\pi\)
\(374\) 1.79804 + 3.11429i 0.0929743 + 0.161036i
\(375\) −17.4473 + 0.448330i −0.900972 + 0.0231517i
\(376\) −12.5401 21.7201i −0.646708 1.12013i
\(377\) −11.7050 6.75791i −0.602841 0.348050i
\(378\) 53.3046 + 30.7754i 2.74169 + 1.58292i
\(379\) 7.05148 0.362210 0.181105 0.983464i \(-0.442033\pi\)
0.181105 + 0.983464i \(0.442033\pi\)
\(380\) 30.1659 25.2022i 1.54748 1.29285i
\(381\) −6.14483 −0.314809
\(382\) 12.4547 + 7.19075i 0.637240 + 0.367911i
\(383\) 2.67090 + 1.54204i 0.136476 + 0.0787947i 0.566684 0.823935i \(-0.308226\pi\)
−0.430207 + 0.902730i \(0.641560\pi\)
\(384\) −15.0719 26.1052i −0.769133 1.33218i
\(385\) 20.8781 + 7.39717i 1.06405 + 0.376995i
\(386\) −3.18222 5.51177i −0.161971 0.280542i
\(387\) 0.236823i 0.0120384i
\(388\) 17.6900i 0.898072i
\(389\) 4.69542 + 8.13270i 0.238067 + 0.412345i 0.960160 0.279452i \(-0.0901528\pi\)
−0.722092 + 0.691797i \(0.756819\pi\)
\(390\) −24.5067 + 20.9238i −1.24094 + 1.05952i
\(391\) −0.324970 −0.0164344
\(392\) 66.3984i 3.35362i
\(393\) −22.0698 + 12.7420i −1.11327 + 0.642749i
\(394\) −24.3936 + 42.2509i −1.22893 + 2.12857i
\(395\) 16.4605 + 19.2792i 0.828219 + 0.970040i
\(396\) 2.49673 4.32446i 0.125465 0.217312i
\(397\) 23.1744 + 13.3797i 1.16309 + 0.671510i 0.952042 0.305966i \(-0.0989794\pi\)
0.211047 + 0.977476i \(0.432313\pi\)
\(398\) 31.3456i 1.57122i
\(399\) 0.328242 30.6541i 0.0164326 1.53462i
\(400\) 19.6015 7.51699i 0.980077 0.375849i
\(401\) 12.5851 21.7980i 0.628468 1.08854i −0.359391 0.933187i \(-0.617016\pi\)
0.987859 0.155352i \(-0.0496511\pi\)
\(402\) 19.0157 + 10.9787i 0.948417 + 0.547569i
\(403\) −22.2451 + 12.8432i −1.10811 + 0.639767i
\(404\) −21.3112 + 36.9121i −1.06027 + 1.83645i
\(405\) 10.1540 + 11.8928i 0.504558 + 0.590956i
\(406\) 39.7937 1.97493
\(407\) 6.62183i 0.328232i
\(408\) 4.49504 2.59521i 0.222538 0.128482i
\(409\) −14.1608 24.5271i −0.700204 1.21279i −0.968395 0.249423i \(-0.919759\pi\)
0.268191 0.963366i \(-0.413574\pi\)
\(410\) −0.0724126 0.391060i −0.00357621 0.0193131i
\(411\) −25.6489 −1.26516
\(412\) −20.1041 + 11.6071i −0.990457 + 0.571840i
\(413\) −48.9102 28.2383i −2.40671 1.38952i
\(414\) 0.337515 + 0.584593i 0.0165880 + 0.0287312i
\(415\) 33.0904 + 11.7240i 1.62435 + 0.575509i
\(416\) 0.613083 1.06189i 0.0300589 0.0520635i
\(417\) 4.16563i 0.203992i
\(418\) −23.5386 0.252049i −1.15131 0.0123281i
\(419\) −13.0449 −0.637287 −0.318643 0.947875i \(-0.603227\pi\)
−0.318643 + 0.947875i \(0.603227\pi\)
\(420\) 21.1806 59.7811i 1.03351 2.91702i
\(421\) −1.66248 + 2.87951i −0.0810246 + 0.140339i −0.903690 0.428187i \(-0.859153\pi\)
0.822666 + 0.568525i \(0.192486\pi\)
\(422\) −29.4718 + 17.0156i −1.43467 + 0.828305i
\(423\) 2.44958 + 1.41426i 0.119102 + 0.0687638i
\(424\) 6.53621 + 11.3210i 0.317426 + 0.549798i
\(425\) −1.19215 3.10868i −0.0578276 0.150793i
\(426\) 26.7344 1.29528
\(427\) −27.5688 + 15.9168i −1.33415 + 0.770270i
\(428\) −4.54841 + 2.62603i −0.219856 + 0.126934i
\(429\) 12.9001 0.622823
\(430\) 2.27110 0.420541i 0.109522 0.0202803i
\(431\) −0.0242034 0.0419216i −0.00116584 0.00201929i 0.865442 0.501009i \(-0.167038\pi\)
−0.866608 + 0.498990i \(0.833704\pi\)
\(432\) −20.2252 11.6770i −0.973085 0.561811i
\(433\) 8.28676 4.78436i 0.398236 0.229922i −0.287486 0.957785i \(-0.592820\pi\)
0.685723 + 0.727863i \(0.259486\pi\)
\(434\) 37.8134 65.4948i 1.81510 3.14385i
\(435\) 11.8318 + 4.19203i 0.567291 + 0.200992i
\(436\) −48.5280 −2.32407
\(437\) 1.08329 1.83076i 0.0518209 0.0875773i
\(438\) 11.3403i 0.541861i
\(439\) −11.1257 + 19.2703i −0.531002 + 0.919723i 0.468343 + 0.883547i \(0.344851\pi\)
−0.999345 + 0.0361764i \(0.988482\pi\)
\(440\) −23.1397 8.19846i −1.10314 0.390846i
\(441\) 3.74417 + 6.48509i 0.178294 + 0.308814i
\(442\) −5.32364 3.07361i −0.253220 0.146197i
\(443\) −17.4207 + 10.0579i −0.827684 + 0.477863i −0.853059 0.521815i \(-0.825255\pi\)
0.0253753 + 0.999678i \(0.491922\pi\)
\(444\) 18.9605 0.899827
\(445\) 2.93959 0.544325i 0.139350 0.0258035i
\(446\) 26.6449 + 46.1504i 1.26167 + 2.18528i
\(447\) 24.2883 14.0229i 1.14880 0.663258i
\(448\) 34.2224i 1.61686i
\(449\) 12.4973 0.589783 0.294891 0.955531i \(-0.404717\pi\)
0.294891 + 0.955531i \(0.404717\pi\)
\(450\) −4.35408 + 5.37326i −0.205254 + 0.253298i
\(451\) −0.0796065 + 0.137883i −0.00374852 + 0.00649263i
\(452\) −27.0548 + 15.6201i −1.27255 + 0.734707i
\(453\) 17.2156 + 9.93945i 0.808861 + 0.466996i
\(454\) −10.0659 + 17.4346i −0.472415 + 0.818246i
\(455\) −37.2305 + 6.89399i −1.74539 + 0.323195i
\(456\) −0.363798 + 33.9746i −0.0170364 + 1.59101i
\(457\) 28.3179i 1.32465i −0.749215 0.662327i \(-0.769569\pi\)
0.749215 0.662327i \(-0.230431\pi\)
\(458\) 35.4422 + 20.4626i 1.65610 + 0.956153i
\(459\) −1.85190 + 3.20759i −0.0864394 + 0.149717i
\(460\) 3.34700 2.85766i 0.156054 0.133239i
\(461\) −2.65976 + 4.60683i −0.123877 + 0.214562i −0.921293 0.388868i \(-0.872866\pi\)
0.797416 + 0.603430i \(0.206200\pi\)
\(462\) −32.8924 + 18.9904i −1.53029 + 0.883515i
\(463\) 17.9327i 0.833401i 0.909044 + 0.416701i \(0.136814\pi\)
−0.909044 + 0.416701i \(0.863186\pi\)
\(464\) −15.0988 −0.700944
\(465\) 18.1425 15.4900i 0.841338 0.718333i
\(466\) 14.9995 + 25.9798i 0.694836 + 1.20349i
\(467\) 28.7791i 1.33174i 0.746069 + 0.665868i \(0.231939\pi\)
−0.746069 + 0.665868i \(0.768061\pi\)
\(468\) 8.53593i 0.394574i
\(469\) 12.9001 + 22.3436i 0.595672 + 1.03173i
\(470\) 9.21274 26.0025i 0.424952 1.19941i
\(471\) 15.6527 + 27.1112i 0.721237 + 1.24922i
\(472\) 54.2083 + 31.2972i 2.49514 + 1.44057i
\(473\) −0.800762 0.462320i −0.0368191 0.0212575i
\(474\) −43.4687 −1.99658
\(475\) 21.4872 + 3.64671i 0.985902 + 0.167323i
\(476\) 12.0988 0.554548
\(477\) −1.27678 0.737147i −0.0584595 0.0337516i
\(478\) −4.33824 2.50469i −0.198427 0.114562i
\(479\) −4.02574 6.97279i −0.183941 0.318595i 0.759278 0.650766i \(-0.225552\pi\)
−0.943219 + 0.332171i \(0.892219\pi\)
\(480\) −0.380304 + 1.07339i −0.0173584 + 0.0489933i
\(481\) −5.65976 9.80298i −0.258063 0.446978i
\(482\) 43.0417i 1.96049i
\(483\) 3.43226i 0.156173i
\(484\) −12.4330 21.5347i −0.565138 0.978849i
\(485\) −7.45928 + 6.36872i −0.338708 + 0.289189i
\(486\) 14.1712 0.642819
\(487\) 1.09761i 0.0497376i 0.999691 + 0.0248688i \(0.00791680\pi\)
−0.999691 + 0.0248688i \(0.992083\pi\)
\(488\) 30.5551 17.6410i 1.38316 0.798571i
\(489\) −11.1093 + 19.2418i −0.502379 + 0.870145i
\(490\) 55.5425 47.4221i 2.50915 2.14231i
\(491\) −6.55267 + 11.3496i −0.295718 + 0.512199i −0.975152 0.221538i \(-0.928892\pi\)
0.679434 + 0.733737i \(0.262226\pi\)
\(492\) 0.394804 + 0.227940i 0.0177991 + 0.0102763i
\(493\) 2.39458i 0.107846i
\(494\) 35.0621 19.7456i 1.57752 0.888395i
\(495\) 2.72235 0.504099i 0.122361 0.0226576i
\(496\) −14.3474 + 24.8505i −0.644219 + 1.11582i
\(497\) 27.2046 + 15.7066i 1.22029 + 0.704536i
\(498\) −52.1322 + 30.0985i −2.33610 + 1.34875i
\(499\) 12.0703 20.9064i 0.540342 0.935900i −0.458542 0.888673i \(-0.651628\pi\)
0.998884 0.0472275i \(-0.0150386\pi\)
\(500\) 39.6150 + 21.5343i 1.77163 + 0.963042i
\(501\) 8.76729 0.391694
\(502\) 8.19895i 0.365937i
\(503\) 16.4214 9.48090i 0.732194 0.422733i −0.0870300 0.996206i \(-0.527738\pi\)
0.819224 + 0.573473i \(0.194404\pi\)
\(504\) −6.33424 10.9712i −0.282150 0.488697i
\(505\) −23.2371 + 4.30282i −1.03404 + 0.191473i
\(506\) −2.63555 −0.117165
\(507\) −1.52262 + 0.879086i −0.0676220 + 0.0390416i
\(508\) 13.7482 + 7.93753i 0.609978 + 0.352171i
\(509\) 10.9803 + 19.0184i 0.486692 + 0.842974i 0.999883 0.0152997i \(-0.00487025\pi\)
−0.513191 + 0.858274i \(0.671537\pi\)
\(510\) 5.38129 + 1.90660i 0.238287 + 0.0844257i
\(511\) 6.66248 11.5398i 0.294731 0.510489i
\(512\) 40.5609i 1.79255i
\(513\) −11.8971 21.1255i −0.525268 0.932714i
\(514\) −67.7531 −2.98846
\(515\) −12.1322 4.29846i −0.534608 0.189413i
\(516\) −1.32378 + 2.29285i −0.0582761 + 0.100937i
\(517\) −9.56399 + 5.52177i −0.420624 + 0.242847i
\(518\) 28.8622 + 16.6636i 1.26813 + 0.732157i
\(519\) −8.34417 14.4525i −0.366268 0.634395i
\(520\) 41.2635 7.64077i 1.80952 0.335070i
\(521\) 6.56968 0.287823 0.143912 0.989591i \(-0.454032\pi\)
0.143912 + 0.989591i \(0.454032\pi\)
\(522\) 4.30764 2.48702i 0.188540 0.108854i
\(523\) −3.63538 + 2.09889i −0.158964 + 0.0917779i −0.577372 0.816481i \(-0.695922\pi\)
0.418408 + 0.908259i \(0.362588\pi\)
\(524\) 65.8375 2.87613
\(525\) 32.8332 12.5912i 1.43296 0.549524i
\(526\) −16.7344 28.9848i −0.729653 1.26380i
\(527\) 3.94113 + 2.27541i 0.171678 + 0.0991186i
\(528\) 12.4803 7.20549i 0.543134 0.313579i
\(529\) −11.3809 + 19.7123i −0.494822 + 0.857058i
\(530\) −4.80189 + 13.5531i −0.208581 + 0.588709i
\(531\) −7.05933 −0.306349
\(532\) −40.3316 + 68.1603i −1.74860 + 2.95513i
\(533\) 0.272162i 0.0117887i
\(534\) −2.56314 + 4.43949i −0.110918 + 0.192115i
\(535\) −2.74482 0.972497i −0.118669 0.0420447i
\(536\) −14.2975 24.7640i −0.617558 1.06964i
\(537\) 10.3954 + 6.00176i 0.448593 + 0.258995i
\(538\) −7.67486 + 4.43108i −0.330887 + 0.191038i
\(539\) −29.2371 −1.25933
\(540\) −9.13282 49.3212i −0.393014 2.12245i
\(541\) 2.31505 + 4.00978i 0.0995316 + 0.172394i 0.911491 0.411320i \(-0.134932\pi\)
−0.811959 + 0.583714i \(0.801599\pi\)
\(542\) −22.4692 + 12.9726i −0.965136 + 0.557221i
\(543\) 9.56340i 0.410405i
\(544\) −0.217238 −0.00931400
\(545\) −17.4710 20.4627i −0.748376 0.876525i
\(546\) 32.4627 56.2271i 1.38928 2.40630i
\(547\) −32.9435 + 19.0199i −1.40856 + 0.813233i −0.995250 0.0973563i \(-0.968961\pi\)
−0.413312 + 0.910590i \(0.635628\pi\)
\(548\) 57.3858 + 33.1317i 2.45140 + 1.41532i
\(549\) −1.98953 + 3.44597i −0.0849113 + 0.147071i
\(550\) −9.66849 25.2118i −0.412266 1.07504i
\(551\) −13.4902 7.98236i −0.574701 0.340060i
\(552\) 3.80405i 0.161911i
\(553\) −44.2333 25.5381i −1.88099 1.08599i
\(554\) 8.27110 14.3260i 0.351406 0.608652i
\(555\) 6.82615 + 7.99503i 0.289754 + 0.339370i
\(556\) 5.38092 9.32002i 0.228202 0.395257i
\(557\) 31.5498 18.2153i 1.33681 0.771807i 0.350476 0.936572i \(-0.386020\pi\)
0.986333 + 0.164765i \(0.0526866\pi\)
\(558\) 9.45302i 0.400178i
\(559\) 1.58060 0.0668523
\(560\) −32.1682 + 27.4651i −1.35935 + 1.16061i
\(561\) −1.14275 1.97929i −0.0482468 0.0835659i
\(562\) 57.5496i 2.42758i
\(563\) 20.6856i 0.871795i −0.899996 0.435897i \(-0.856431\pi\)
0.899996 0.435897i \(-0.143569\pi\)
\(564\) 15.8107 + 27.3849i 0.665750 + 1.15311i
\(565\) −16.3267 5.78459i −0.686870 0.243359i
\(566\) −18.0324 31.2330i −0.757958 1.31282i
\(567\) −27.2862 15.7537i −1.14591 0.661594i
\(568\) −30.1515 17.4080i −1.26513 0.730422i
\(569\) 27.1132 1.13664 0.568322 0.822806i \(-0.307593\pi\)
0.568322 + 0.822806i \(0.307593\pi\)
\(570\) −28.6797 + 23.9606i −1.20126 + 1.00360i
\(571\) 46.4687 1.94466 0.972328 0.233622i \(-0.0750578\pi\)
0.972328 + 0.233622i \(0.0750578\pi\)
\(572\) −28.8622 16.6636i −1.20679 0.696741i
\(573\) −7.91564 4.57009i −0.330680 0.190918i
\(574\) 0.400654 + 0.693954i 0.0167230 + 0.0289651i
\(575\) 2.40996 + 0.382507i 0.100502 + 0.0159516i
\(576\) −2.13882 3.70455i −0.0891177 0.154356i
\(577\) 18.0398i 0.751008i 0.926821 + 0.375504i \(0.122530\pi\)
−0.926821 + 0.375504i \(0.877470\pi\)
\(578\) 40.6664i 1.69150i
\(579\) 2.02247 + 3.50302i 0.0840509 + 0.145580i
\(580\) −21.0570 24.6627i −0.874344 1.02406i
\(581\) −70.7322 −2.93447
\(582\) 16.8184i 0.697147i
\(583\) 4.98497 2.87808i 0.206457 0.119198i
\(584\) −7.38419 + 12.7898i −0.305560 + 0.529245i
\(585\) −3.59932 + 3.07310i −0.148814 + 0.127057i
\(586\) −22.3337 + 38.6831i −0.922597 + 1.59798i
\(587\) −22.5458 13.0168i −0.930565 0.537262i −0.0435750 0.999050i \(-0.513875\pi\)
−0.886990 + 0.461788i \(0.847208\pi\)
\(588\) 83.7156i 3.45237i
\(589\) −25.9567 + 14.6178i −1.06953 + 0.602316i
\(590\) 12.5357 + 67.6980i 0.516085 + 2.78708i
\(591\) 15.5034 26.8526i 0.637724 1.10457i
\(592\) −10.9511 6.32263i −0.450088 0.259858i
\(593\) 15.7236 9.07803i 0.645691 0.372790i −0.141112 0.989994i \(-0.545068\pi\)
0.786804 + 0.617203i \(0.211734\pi\)
\(594\) −15.0192 + 26.0140i −0.616245 + 1.06737i
\(595\) 4.35580 + 5.10167i 0.178570 + 0.209148i
\(596\) −72.4556 −2.96790
\(597\) 19.9218i 0.815345i
\(598\) 3.90168 2.25264i 0.159552 0.0921172i
\(599\) 20.0357 + 34.7028i 0.818635 + 1.41792i 0.906688 + 0.421802i \(0.138602\pi\)
−0.0880531 + 0.996116i \(0.528065\pi\)
\(600\) −36.3898 + 13.9551i −1.48561 + 0.569715i
\(601\) 15.0473 0.613793 0.306897 0.951743i \(-0.400709\pi\)
0.306897 + 0.951743i \(0.400709\pi\)
\(602\) −4.03018 + 2.32683i −0.164258 + 0.0948344i
\(603\) 2.79286 + 1.61246i 0.113734 + 0.0656643i
\(604\) −25.6784 44.4763i −1.04484 1.80972i
\(605\) 4.60433 12.9955i 0.187193 0.528342i
\(606\) 20.2613 35.0936i 0.823059 1.42558i
\(607\) 29.3860i 1.19274i −0.802709 0.596370i \(-0.796609\pi\)
0.802709 0.596370i \(-0.203391\pi\)
\(608\) 0.724166 1.22384i 0.0293688 0.0496333i
\(609\) −25.2910 −1.02484
\(610\) 36.5794 + 12.9602i 1.48106 + 0.524741i
\(611\) 9.43905 16.3489i 0.381863 0.661406i
\(612\) 1.30969 0.756148i 0.0529410 0.0305655i
\(613\) −30.0578 17.3539i −1.21402 0.700917i −0.250390 0.968145i \(-0.580559\pi\)
−0.963633 + 0.267229i \(0.913892\pi\)
\(614\) −36.0818 62.4955i −1.45614 2.52211i
\(615\) 0.0460220 + 0.248539i 0.00185579 + 0.0100220i
\(616\) 49.4622 1.99289
\(617\) 9.29031 5.36376i 0.374014 0.215937i −0.301197 0.953562i \(-0.597386\pi\)
0.675210 + 0.737625i \(0.264053\pi\)
\(618\) 19.1136 11.0352i 0.768862 0.443903i
\(619\) 36.1437 1.45274 0.726370 0.687304i \(-0.241206\pi\)
0.726370 + 0.687304i \(0.241206\pi\)
\(620\) −60.6004 + 11.2214i −2.43377 + 0.450663i
\(621\) −1.35725 2.35083i −0.0544647 0.0943357i
\(622\) −0.411031 0.237309i −0.0164808 0.00951521i
\(623\) −5.21644 + 3.01171i −0.208992 + 0.120662i
\(624\) −12.3172 + 21.3341i −0.493084 + 0.854046i
\(625\) 5.18184 + 24.4571i 0.207274 + 0.978283i
\(626\) 52.2569 2.08861
\(627\) 14.9600 + 0.160191i 0.597445 + 0.00639739i
\(628\) 80.8768i 3.22734i
\(629\) −1.00273 + 1.73678i −0.0399814 + 0.0692499i
\(630\) 4.65352 13.1343i 0.185401 0.523284i
\(631\) 15.7882 + 27.3460i 0.628519 + 1.08863i 0.987849 + 0.155417i \(0.0496720\pi\)
−0.359330 + 0.933211i \(0.616995\pi\)
\(632\) 49.0248 + 28.3045i 1.95010 + 1.12589i
\(633\) 18.7309 10.8143i 0.744485 0.429829i
\(634\) 47.0857 1.87001
\(635\) 1.60262 + 8.65483i 0.0635979 + 0.343456i
\(636\) −8.24090 14.2737i −0.326773 0.565987i
\(637\) 43.2827 24.9893i 1.71492 0.990111i
\(638\) 19.4204i 0.768859i
\(639\) 3.92650 0.155330
\(640\) −32.8377 + 28.0368i −1.29802 + 1.10825i
\(641\) −9.91331 + 17.1704i −0.391552 + 0.678188i −0.992654 0.120984i \(-0.961395\pi\)
0.601102 + 0.799172i \(0.294728\pi\)
\(642\) 4.32432 2.49665i 0.170667 0.0985349i
\(643\) 11.6540 + 6.72843i 0.459588 + 0.265343i 0.711871 0.702310i \(-0.247848\pi\)
−0.252283 + 0.967654i \(0.581181\pi\)
\(644\) −4.43359 + 7.67920i −0.174708 + 0.302603i
\(645\) −1.44340 + 0.267276i −0.0568340 + 0.0105240i
\(646\) −6.13555 3.63051i −0.241400 0.142840i
\(647\) 4.19511i 0.164927i 0.996594 + 0.0824634i \(0.0262787\pi\)
−0.996594 + 0.0824634i \(0.973721\pi\)
\(648\) 30.2420 + 17.4602i 1.18802 + 0.685902i
\(649\) 13.7810 23.8694i 0.540953 0.936957i
\(650\) 35.8621 + 29.0600i 1.40663 + 1.13983i
\(651\) −24.0324 + 41.6253i −0.941904 + 1.63143i
\(652\) 49.7109 28.7006i 1.94683 1.12400i
\(653\) 12.1680i 0.476170i 0.971244 + 0.238085i \(0.0765196\pi\)
−0.971244 + 0.238085i \(0.923480\pi\)
\(654\) 46.1372 1.80411
\(655\) 23.7028 + 27.7615i 0.926143 + 1.08473i
\(656\) −0.152019 0.263305i −0.00593535 0.0102803i
\(657\) 1.66556i 0.0649798i
\(658\) 55.5814i 2.16679i
\(659\) 4.12236 + 7.14013i 0.160584 + 0.278140i 0.935078 0.354441i \(-0.115329\pi\)
−0.774494 + 0.632581i \(0.781996\pi\)
\(660\) 29.1748 + 10.3367i 1.13563 + 0.402355i
\(661\) −10.5599 18.2902i −0.410731 0.711407i 0.584239 0.811582i \(-0.301393\pi\)
−0.994970 + 0.100175i \(0.968060\pi\)
\(662\) −43.8338 25.3075i −1.70365 0.983603i
\(663\) 3.38345 + 1.95344i 0.131402 + 0.0758652i
\(664\) 78.3941 3.04228
\(665\) −43.2611 + 7.53250i −1.67759 + 0.292098i
\(666\) 4.16576 0.161420
\(667\) −1.51986 0.877489i −0.0588490 0.0339765i
\(668\) −19.6156 11.3251i −0.758951 0.438180i
\(669\) −16.9342 29.3310i −0.654716 1.13400i
\(670\) 10.5038 29.6465i 0.405798 1.14534i
\(671\) −7.76783 13.4543i −0.299874 0.519397i
\(672\) 2.29442i 0.0885090i
\(673\) 30.2802i 1.16722i 0.812036 + 0.583608i \(0.198359\pi\)
−0.812036 + 0.583608i \(0.801641\pi\)
\(674\) 12.5357 + 21.7124i 0.482856 + 0.836331i
\(675\) 17.5091 21.6076i 0.673927 0.831676i
\(676\) 4.54221 0.174700
\(677\) 49.9003i 1.91783i 0.283701 + 0.958913i \(0.408438\pi\)
−0.283701 + 0.958913i \(0.591562\pi\)
\(678\) 25.7219 14.8505i 0.987842 0.570331i
\(679\) 9.88092 17.1142i 0.379195 0.656785i
\(680\) −4.82763 5.65430i −0.185131 0.216832i
\(681\) 6.39738 11.0806i 0.245148 0.424609i
\(682\) 31.9632 + 18.4539i 1.22393 + 0.706638i
\(683\) 3.11357i 0.119137i −0.998224 0.0595687i \(-0.981027\pi\)
0.998224 0.0595687i \(-0.0189725\pi\)
\(684\) −0.105997 + 9.89894i −0.00405290 + 0.378496i
\(685\) 6.68942 + 36.1258i 0.255590 + 1.38029i
\(686\) −34.8436 + 60.3509i −1.33034 + 2.30421i
\(687\) −22.5254 13.0050i −0.859396 0.496172i
\(688\) 1.52916 0.882861i 0.0582987 0.0336588i
\(689\) −4.91985 + 8.52143i −0.187431 + 0.324641i
\(690\) −3.18210 + 2.71687i −0.121140 + 0.103430i
\(691\) −30.2831 −1.15202 −0.576012 0.817441i \(-0.695392\pi\)
−0.576012 + 0.817441i \(0.695392\pi\)
\(692\) 43.1140i 1.63895i
\(693\) −4.83094 + 2.78915i −0.183512 + 0.105951i
\(694\) −6.68222 11.5740i −0.253654 0.439341i
\(695\) 5.86718 1.08643i 0.222555 0.0412105i
\(696\) 28.0305 1.06250
\(697\) −0.0417585 + 0.0241093i −0.00158172 + 0.000913204i
\(698\) 3.29948 + 1.90495i 0.124887 + 0.0721035i
\(699\) −9.53293 16.5115i −0.360569 0.624523i
\(700\) −89.7243 14.2409i −3.39126 0.538257i
\(701\) −22.2849 + 38.5987i −0.841691 + 1.45785i 0.0467733 + 0.998906i \(0.485106\pi\)
−0.888464 + 0.458946i \(0.848227\pi\)
\(702\) 51.3483i 1.93802i
\(703\) −6.44177 11.4386i −0.242956 0.431415i
\(704\) 16.7014 0.629458
\(705\) −5.85518 + 16.5259i −0.220519 + 0.622403i
\(706\) −40.4457 + 70.0540i −1.52219 + 2.63652i
\(707\) 41.2353 23.8072i 1.55081 0.895363i
\(708\) −68.3462 39.4597i −2.56861 1.48299i
\(709\) 4.67176 + 8.09172i 0.175452 + 0.303891i 0.940317 0.340299i \(-0.110528\pi\)
−0.764866 + 0.644190i \(0.777195\pi\)
\(710\) −6.97252 37.6546i −0.261674 1.41315i
\(711\) −6.38429 −0.239430
\(712\) 5.78150 3.33795i 0.216671 0.125095i
\(713\) −2.88844 + 1.66764i −0.108173 + 0.0624538i
\(714\) −11.5027 −0.430479
\(715\) −3.36445 18.1695i −0.125823 0.679500i
\(716\) −15.5055 26.8562i −0.579466 1.00366i
\(717\) 2.75718 + 1.59186i 0.102969 + 0.0594490i
\(718\) −7.43916 + 4.29500i −0.277627 + 0.160288i
\(719\) 12.6987 21.9948i 0.473581 0.820267i −0.525961 0.850508i \(-0.676294\pi\)
0.999543 + 0.0302417i \(0.00962768\pi\)
\(720\) −1.76567 + 4.98352i −0.0658027 + 0.185725i
\(721\) 25.9330 0.965797
\(722\) 40.9059 22.4631i 1.52236 0.835992i
\(723\) 27.3552i 1.01735i
\(724\) −12.3534 + 21.3968i −0.459112 + 0.795205i
\(725\) 2.81854 17.7581i 0.104678 0.659519i
\(726\) 11.8205 + 20.4737i 0.438700 + 0.759851i
\(727\) 27.2259 + 15.7189i 1.00975 + 0.582980i 0.911119 0.412143i \(-0.135220\pi\)
0.0986328 + 0.995124i \(0.468553\pi\)
\(728\) −73.2240 + 42.2759i −2.71386 + 1.56685i
\(729\) −29.9869 −1.11063
\(730\) −15.9725 + 2.95764i −0.591170 + 0.109467i
\(731\) −0.140016 0.242515i −0.00517869 0.00896975i
\(732\) −38.5241 + 22.2419i −1.42389 + 0.822085i
\(733\) 25.3946i 0.937971i 0.883206 + 0.468985i \(0.155380\pi\)
−0.883206 + 0.468985i \(0.844620\pi\)
\(734\) 47.9056 1.76823
\(735\) −35.3001 + 30.1392i −1.30206 + 1.11170i
\(736\) 0.0796065 0.137883i 0.00293434 0.00508242i
\(737\) −10.9043 + 6.29559i −0.401664 + 0.231901i
\(738\) 0.0867411 + 0.0500800i 0.00319299 + 0.00184347i
\(739\) 17.7541 30.7510i 0.653095 1.13119i −0.329273 0.944235i \(-0.606804\pi\)
0.982368 0.186959i \(-0.0598631\pi\)
\(740\) −4.94505 26.7054i −0.181784 0.981710i
\(741\) −22.2838 + 12.5493i −0.818614 + 0.461011i
\(742\) 28.9703i 1.06353i
\(743\) 14.8176 + 8.55493i 0.543604 + 0.313850i 0.746538 0.665342i \(-0.231714\pi\)
−0.202934 + 0.979192i \(0.565048\pi\)
\(744\) 26.6357 46.1343i 0.976511 1.69137i
\(745\) −26.0854 30.5522i −0.955695 1.11934i
\(746\) 28.8798 50.0213i 1.05737 1.83141i
\(747\) −7.65671 + 4.42060i −0.280144 + 0.161741i
\(748\) 5.90453i 0.215891i
\(749\) 5.86718 0.214382
\(750\) −37.6632 20.4733i −1.37527 0.747581i
\(751\) 3.72562 + 6.45297i 0.135950 + 0.235472i 0.925960 0.377622i \(-0.123258\pi\)
−0.790010 + 0.613094i \(0.789925\pi\)
\(752\) 21.0891i 0.769041i
\(753\) 5.21086i 0.189894i
\(754\) −16.5988 28.7500i −0.604493 1.04701i
\(755\) 9.50949 26.8401i 0.346086 0.976810i
\(756\) 50.5313 + 87.5228i 1.83781 + 3.18317i
\(757\) −46.5640 26.8838i −1.69240 0.977107i −0.952574 0.304306i \(-0.901575\pi\)
−0.739824 0.672801i \(-0.765091\pi\)
\(758\) 14.9994 + 8.65994i 0.544804 + 0.314543i
\(759\) 1.67503 0.0607997
\(760\) 47.9473 8.34845i 1.73923 0.302830i
\(761\) 23.3939 0.848029 0.424014 0.905655i \(-0.360621\pi\)
0.424014 + 0.905655i \(0.360621\pi\)
\(762\) −13.0709 7.54647i −0.473508 0.273380i
\(763\) 46.9487 + 27.1058i 1.69966 + 0.981297i
\(764\) 11.8068 + 20.4499i 0.427154 + 0.739852i
\(765\) 0.790355 + 0.280025i 0.0285754 + 0.0101243i
\(766\) 3.78757 + 6.56027i 0.136851 + 0.237032i
\(767\) 47.1152i 1.70123i
\(768\) 50.3235i 1.81589i
\(769\) −6.62236 11.4703i −0.238808 0.413628i 0.721564 0.692347i \(-0.243423\pi\)
−0.960373 + 0.278719i \(0.910090\pi\)
\(770\) 35.3261 + 41.3753i 1.27307 + 1.49106i
\(771\) 43.0606 1.55079
\(772\) 10.4500i 0.376105i
\(773\) 15.4198 8.90262i 0.554611 0.320205i −0.196369 0.980530i \(-0.562915\pi\)
0.750980 + 0.660325i \(0.229582\pi\)
\(774\) −0.290843 + 0.503755i −0.0104541 + 0.0181071i
\(775\) −26.5490 21.5133i −0.953668 0.772781i
\(776\) −10.9512 + 18.9681i −0.393127 + 0.680916i
\(777\) −18.3434 10.5906i −0.658068 0.379935i
\(778\) 23.0658i 0.826949i
\(779\) 0.00337965 0.315621i 0.000121088 0.0113083i
\(780\) −52.0253 + 9.63354i −1.86280 + 0.344936i
\(781\) −7.66521 + 13.2765i −0.274283 + 0.475072i
\(782\) −0.691255 0.399096i −0.0247192 0.0142716i
\(783\) −17.3224 + 10.0011i −0.619051 + 0.357409i
\(784\) 27.9160 48.3520i 0.997001 1.72686i
\(785\) 34.1031 29.1172i 1.21719 1.03924i
\(786\) −62.5939 −2.23265
\(787\) 43.5779i 1.55339i −0.629880 0.776693i \(-0.716896\pi\)
0.629880 0.776693i \(-0.283104\pi\)
\(788\) −69.3734 + 40.0527i −2.47132 + 1.42682i
\(789\) 10.6356 + 18.4213i 0.378636 + 0.655816i
\(790\) 11.3370 + 61.2246i 0.403351 + 2.17827i
\(791\) 34.8990 1.24087
\(792\) 5.35425 3.09128i 0.190255 0.109844i
\(793\) 22.9991 + 13.2785i 0.816721 + 0.471534i
\(794\) 32.8634 + 56.9210i 1.16628 + 2.02005i
\(795\) 3.05185 8.61370i 0.108238 0.305497i
\(796\) 25.7338 44.5723i 0.912111 1.57982i
\(797\) 16.1311i 0.571395i −0.958320 0.285697i \(-0.907775\pi\)
0.958320 0.285697i \(-0.0922252\pi\)
\(798\) 38.3446 64.8023i 1.35738 2.29398i
\(799\) −3.34460 −0.118323
\(800\) 1.61103 + 0.255700i 0.0569584 + 0.00904038i
\(801\) −0.376451 + 0.652032i −0.0133012 + 0.0230384i
\(802\) 53.5403 30.9115i 1.89057 1.09152i
\(803\) 5.63170 + 3.25147i 0.198739 + 0.114742i
\(804\) 18.0264 + 31.2226i 0.635742 + 1.10114i
\(805\) −4.83424 + 0.895159i −0.170385 + 0.0315502i
\(806\) −63.0912 −2.22229
\(807\) 4.87777 2.81618i 0.171706 0.0991344i
\(808\) −45.7021 + 26.3861i −1.60779 + 0.928259i
\(809\) −28.7134 −1.00951 −0.504755 0.863263i \(-0.668417\pi\)
−0.504755 + 0.863263i \(0.668417\pi\)
\(810\) 6.99346 + 37.7677i 0.245725 + 1.32702i
\(811\) −10.7711 18.6561i −0.378225 0.655104i 0.612579 0.790409i \(-0.290132\pi\)
−0.990804 + 0.135305i \(0.956799\pi\)
\(812\) 56.5850 + 32.6694i 1.98575 + 1.14647i
\(813\) 14.2804 8.24477i 0.500834 0.289157i
\(814\) −8.13228 + 14.0855i −0.285036 + 0.493697i
\(815\) 29.9990 + 10.6287i 1.05082 + 0.372307i
\(816\) 4.36445 0.152786
\(817\) 1.83299 + 0.0196275i 0.0641282 + 0.000686680i
\(818\) 69.5634i 2.43223i
\(819\) 4.76783 8.25813i 0.166602 0.288562i
\(820\) 0.218080 0.615520i 0.00761568 0.0214949i
\(821\) −16.6602 28.8563i −0.581445 1.00709i −0.995308 0.0967536i \(-0.969154\pi\)
0.413863 0.910339i \(-0.364179\pi\)
\(822\) −54.5586 31.4994i −1.90295 1.09867i
\(823\) −32.2499 + 18.6195i −1.12416 + 0.649035i −0.942460 0.334319i \(-0.891494\pi\)
−0.181701 + 0.983354i \(0.558160\pi\)
\(824\) −28.7422 −1.00128
\(825\) 6.14483 + 16.0234i 0.213935 + 0.557864i
\(826\) −69.3590 120.133i −2.41331 4.17997i
\(827\) 25.1591 14.5256i 0.874868 0.505105i 0.00590503 0.999983i \(-0.498120\pi\)
0.868963 + 0.494877i \(0.164787\pi\)
\(828\) 1.10836i 0.0385181i
\(829\) −34.5380 −1.19956 −0.599778 0.800166i \(-0.704744\pi\)
−0.599778 + 0.800166i \(0.704744\pi\)
\(830\) 55.9895 + 65.5769i 1.94342 + 2.27621i
\(831\) −5.25672 + 9.10490i −0.182353 + 0.315845i
\(832\) −24.7249 + 14.2749i −0.857180 + 0.494893i
\(833\) −7.66832 4.42731i −0.265692 0.153397i
\(834\) −5.11581 + 8.86085i −0.177146 + 0.306826i
\(835\) −2.28658 12.3485i −0.0791302 0.427338i
\(836\) −33.2640 19.6829i −1.15046 0.680746i
\(837\) 38.0136i 1.31394i
\(838\) −27.7483 16.0205i −0.958550 0.553419i
\(839\) −22.3622 + 38.7324i −0.772028 + 1.33719i 0.164422 + 0.986390i \(0.447424\pi\)
−0.936450 + 0.350801i \(0.885909\pi\)
\(840\) 59.7194 50.9883i 2.06051 1.75926i
\(841\) 8.03413 13.9155i 0.277039 0.479845i
\(842\) −7.07266 + 4.08340i −0.243740 + 0.140723i
\(843\) 36.5758i 1.25974i
\(844\) −55.8770 −1.92337
\(845\) 1.63528 + 1.91530i 0.0562554 + 0.0658883i
\(846\) 3.47372 + 6.01665i 0.119429 + 0.206857i
\(847\) 27.7784i 0.954478i
\(848\) 10.9921i 0.377471i
\(849\) 11.4605 + 19.8502i 0.393324 + 0.681257i
\(850\) 1.28192 8.07666i 0.0439694 0.277027i
\(851\) −0.734898 1.27288i −0.0251920 0.0436338i
\(852\) 38.0152 + 21.9481i 1.30238 + 0.751929i
\(853\) 14.0818 + 8.13013i 0.482152 + 0.278370i 0.721313 0.692610i \(-0.243539\pi\)
−0.239161 + 0.970980i \(0.576872\pi\)
\(854\) −78.1900 −2.67561
\(855\) −4.21222 + 3.51911i −0.144055 + 0.120351i
\(856\) −6.50273 −0.222259
\(857\) −14.4089 8.31896i −0.492197 0.284170i 0.233288 0.972408i \(-0.425051\pi\)
−0.725485 + 0.688237i \(0.758385\pi\)
\(858\) 27.4403 + 15.8426i 0.936795 + 0.540859i
\(859\) 20.1362 + 34.8769i 0.687038 + 1.18999i 0.972792 + 0.231682i \(0.0744229\pi\)
−0.285753 + 0.958303i \(0.592244\pi\)
\(860\) 3.57467 + 1.26651i 0.121895 + 0.0431878i
\(861\) −0.254637 0.441044i −0.00867799 0.0150307i
\(862\) 0.118897i 0.00404965i
\(863\) 32.9634i 1.12209i −0.827786 0.561044i \(-0.810400\pi\)
0.827786 0.561044i \(-0.189600\pi\)
\(864\) −0.907306 1.57150i −0.0308672 0.0534635i
\(865\) −18.1798 + 15.5219i −0.618131 + 0.527759i
\(866\) 23.5027 0.798655
\(867\) 25.8456i 0.877762i
\(868\) 107.538 62.0873i 3.65009 2.10738i
\(869\) 12.4633 21.5870i 0.422787 0.732288i
\(870\) 20.0196 + 23.4476i 0.678727 + 0.794950i
\(871\) 10.7618 18.6400i 0.364651 0.631594i
\(872\) −52.0343 30.0420i −1.76210 1.01735i
\(873\) 2.47014i 0.0836016i
\(874\) 4.55267 2.56389i 0.153996 0.0867248i
\(875\) −26.2975 42.9608i −0.889018 1.45234i
\(876\) 9.31004 16.1255i 0.314557 0.544829i
\(877\) 0.184636 + 0.106600i 0.00623472 + 0.00359962i 0.503114 0.864220i \(-0.332188\pi\)
−0.496879 + 0.867820i \(0.665521\pi\)
\(878\) −47.3319 + 27.3271i −1.59737 + 0.922244i
\(879\) 14.1942 24.5851i 0.478759 0.829236i
\(880\) −13.4037 15.6989i −0.451839 0.529210i
\(881\) 51.8661 1.74741 0.873707 0.486453i \(-0.161710\pi\)
0.873707 + 0.486453i \(0.161710\pi\)
\(882\) 18.3929i 0.619321i
\(883\) 36.0657 20.8225i 1.21371 0.700734i 0.250142 0.968209i \(-0.419523\pi\)
0.963565 + 0.267475i \(0.0861892\pi\)
\(884\) −5.04667 8.74109i −0.169738 0.293995i
\(885\) −7.96707 43.0256i −0.267810 1.44629i
\(886\) −49.4083 −1.65990
\(887\) −3.54486 + 2.04663i −0.119025 + 0.0687190i −0.558330 0.829619i \(-0.688558\pi\)
0.439306 + 0.898338i \(0.355225\pi\)
\(888\) 20.3305 + 11.7378i 0.682246 + 0.393895i
\(889\) −8.86718 15.3584i −0.297396 0.515104i
\(890\) 6.92139 + 2.45226i 0.232006 + 0.0822000i
\(891\) 7.68823 13.3164i 0.257565 0.446116i
\(892\) 87.4987i 2.92967i
\(893\) 11.1493 18.8423i 0.373097 0.630533i
\(894\) 68.8859 2.30389
\(895\) 5.74214 16.2069i 0.191939 0.541737i
\(896\) 43.4984 75.3414i 1.45318 2.51698i
\(897\) −2.47972 + 1.43167i −0.0827955 + 0.0478020i
\(898\) 26.5834 + 15.3479i 0.887099 + 0.512167i
\(899\) 12.2882 + 21.2838i 0.409835 + 0.709855i
\(900\) −10.6026 + 4.06600i −0.353421 + 0.135533i
\(901\) 1.74328 0.0580772
\(902\) −0.338668 + 0.195530i −0.0112764 + 0.00651043i
\(903\) 2.56139 1.47882i 0.0852377 0.0492120i
\(904\) −38.6794 −1.28646
\(905\) −13.4698 + 2.49421i −0.447751 + 0.0829102i
\(906\) 24.4133 + 42.2851i 0.811078 + 1.40483i
\(907\) 7.28090 + 4.20363i 0.241758 + 0.139579i 0.615985 0.787758i \(-0.288758\pi\)
−0.374226 + 0.927337i \(0.622092\pi\)
\(908\) −28.6265 + 16.5275i −0.950005 + 0.548486i
\(909\) 2.97580 5.15423i 0.0987009 0.170955i
\(910\) −87.6609 31.0584i −2.90593 1.02958i
\(911\) 8.87918 0.294180 0.147090 0.989123i \(-0.453009\pi\)
0.147090 + 0.989123i \(0.453009\pi\)
\(912\) −14.5490 + 24.5877i −0.481764 + 0.814181i
\(913\) 34.5192i 1.14242i
\(914\) 34.7772 60.2359i 1.15033 1.99243i
\(915\) −23.2481 8.23685i −0.768558 0.272302i
\(916\) 33.5983 + 58.1939i 1.11012 + 1.92278i
\(917\) −63.6948 36.7742i −2.10339 1.21439i
\(918\) −7.87849 + 4.54865i −0.260029 + 0.150128i
\(919\) 45.9834 1.51685 0.758427 0.651758i \(-0.225968\pi\)
0.758427 + 0.651758i \(0.225968\pi\)
\(920\) 5.35790 0.992125i 0.176645 0.0327094i
\(921\) 22.9319 + 39.7191i 0.755630 + 1.30879i
\(922\) −11.3153 + 6.53290i −0.372650 + 0.215150i
\(923\) 26.2062i 0.862587i
\(924\) −62.3623 −2.05157
\(925\) 9.48048 11.6996i 0.311716 0.384681i
\(926\) −22.0231 + 38.1452i −0.723725 + 1.25353i
\(927\) 2.80724 1.62076i 0.0922017 0.0532327i
\(928\) −1.01600 0.586589i −0.0333519 0.0192557i
\(929\) −11.0889 + 19.2065i −0.363814 + 0.630145i −0.988585 0.150663i \(-0.951859\pi\)
0.624771 + 0.780808i \(0.285192\pi\)
\(930\) 57.6148 10.6686i 1.88926 0.349836i
\(931\) 50.5044 28.4421i 1.65521 0.932152i
\(932\) 49.2564i 1.61345i
\(933\) 0.261231 + 0.150822i 0.00855233 + 0.00493769i
\(934\) −35.3436 + 61.2170i −1.15648 + 2.00308i
\(935\) −2.48975 + 2.12574i −0.0814234 + 0.0695192i
\(936\) −5.28430 + 9.15267i −0.172723 + 0.299165i
\(937\) −29.7284 + 17.1637i −0.971186 + 0.560714i −0.899598 0.436720i \(-0.856140\pi\)
−0.0715882 + 0.997434i \(0.522807\pi\)
\(938\) 63.3706i 2.06912i
\(939\) −33.2120 −1.08383
\(940\) 34.4474 29.4111i 1.12355 0.959286i
\(941\) −16.8606 29.2035i −0.549641 0.952006i −0.998299 0.0583025i \(-0.981431\pi\)
0.448658 0.893704i \(-0.351902\pi\)
\(942\) 76.8923i 2.50529i
\(943\) 0.0353393i 0.00115080i
\(944\) 26.3167 + 45.5818i 0.856535 + 1.48356i
\(945\) −18.7133 + 52.8173i −0.608743 + 1.71815i
\(946\) −1.13555 1.96683i −0.0369200 0.0639473i
\(947\) −19.1794 11.0732i −0.623248 0.359832i 0.154885 0.987933i \(-0.450499\pi\)
−0.778132 + 0.628100i \(0.783833\pi\)
\(948\) −61.8108 35.6865i −2.00752 1.15904i
\(949\) −11.1163 −0.360849
\(950\) 41.2277 + 34.1456i 1.33760 + 1.10783i
\(951\) −29.9254 −0.970398
\(952\) 12.9730 + 7.48995i 0.420457 + 0.242751i
\(953\) 32.2999 + 18.6484i 1.04630 + 0.604079i 0.921610 0.388117i \(-0.126874\pi\)
0.124686 + 0.992196i \(0.460208\pi\)
\(954\) −1.81058 3.13602i −0.0586198 0.101532i
\(955\) −4.37240 + 12.3409i −0.141488 + 0.399342i
\(956\) −4.11254 7.12313i −0.133009 0.230378i
\(957\) 12.3426i 0.398981i
\(958\) 19.7761i 0.638936i
\(959\) −37.0121 64.1069i −1.19518 2.07012i
\(960\) 20.1649 17.2167i 0.650819 0.555668i
\(961\) 15.7069 0.506674
\(962\) 27.8030i 0.896405i
\(963\) 0.635118 0.366686i 0.0204664 0.0118163i
\(964\) 35.3359 61.2036i 1.13809 1.97123i
\(965\) 4.40644 3.76221i 0.141848 0.121110i
\(966\) 4.21516 7.30087i 0.135621 0.234902i
\(967\) −16.1718 9.33679i −0.520050 0.300251i 0.216905 0.976193i \(-0.430404\pi\)
−0.736955 + 0.675942i \(0.763737\pi\)
\(968\) 30.7875i 0.989547i
\(969\) 3.89946 + 2.30738i 0.125269 + 0.0741236i
\(970\) −23.6883 + 4.38638i −0.760587 + 0.140838i
\(971\) −14.2903 + 24.7515i −0.458598 + 0.794314i −0.998887 0.0471649i \(-0.984981\pi\)
0.540290 + 0.841479i \(0.318315\pi\)
\(972\) 20.1509 + 11.6341i 0.646341 + 0.373165i
\(973\) −10.4116 + 6.01113i −0.333780 + 0.192708i
\(974\) −1.34798 + 2.33477i −0.0431921 + 0.0748109i
\(975\) −22.7922 18.4691i −0.729936 0.591485i
\(976\) 29.6674 0.949630
\(977\) 58.1909i 1.86169i −0.365411 0.930846i \(-0.619072\pi\)
0.365411 0.930846i \(-0.380928\pi\)
\(978\) −47.2618 + 27.2866i −1.51127 + 0.872530i
\(979\) −1.46980 2.54576i −0.0469749 0.0813628i
\(980\) 117.911 21.8337i 3.76654 0.697451i
\(981\) 6.77622 0.216348
\(982\) −27.8768 + 16.0947i −0.889586 + 0.513602i
\(983\) −41.6320 24.0363i −1.32786 0.766638i −0.342888 0.939376i \(-0.611405\pi\)
−0.984968 + 0.172738i \(0.944738\pi\)
\(984\) 0.282220 + 0.488819i 0.00899684 + 0.0155830i
\(985\) −41.8647 14.8327i −1.33392 0.472610i
\(986\) −2.94078 + 5.09359i −0.0936536 + 0.162213i
\(987\) 35.3249i 1.12440i
\(988\) 66.0674 + 0.707444i 2.10188 + 0.0225068i
\(989\) 0.205235 0.00652609
\(990\) 6.40989 + 2.27104i 0.203720 + 0.0721784i
\(991\) −19.1976 + 33.2512i −0.609832 + 1.05626i 0.381436 + 0.924395i \(0.375430\pi\)
−0.991268 + 0.131865i \(0.957904\pi\)
\(992\) −1.93089 + 1.11480i −0.0613057 + 0.0353949i
\(993\) 27.8587 + 16.0842i 0.884069 + 0.510417i
\(994\) 38.5785 + 66.8200i 1.22364 + 2.11940i
\(995\) 28.0593 5.19576i 0.889540 0.164717i
\(996\) −98.8399 −3.13186
\(997\) −32.7546 + 18.9109i −1.03735 + 0.598914i −0.919081 0.394068i \(-0.871067\pi\)
−0.118268 + 0.992982i \(0.537734\pi\)
\(998\) 51.3504 29.6472i 1.62547 0.938465i
\(999\) −16.7518 −0.530004
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 95.2.i.b.49.6 yes 12
3.2 odd 2 855.2.be.d.334.1 12
5.2 odd 4 475.2.e.g.201.1 12
5.3 odd 4 475.2.e.g.201.6 12
5.4 even 2 inner 95.2.i.b.49.1 12
15.14 odd 2 855.2.be.d.334.6 12
19.7 even 3 inner 95.2.i.b.64.1 yes 12
19.8 odd 6 1805.2.b.g.1084.6 6
19.11 even 3 1805.2.b.f.1084.1 6
57.26 odd 6 855.2.be.d.64.6 12
95.7 odd 12 475.2.e.g.26.1 12
95.8 even 12 9025.2.a.bt.1.6 6
95.27 even 12 9025.2.a.bt.1.1 6
95.49 even 6 1805.2.b.f.1084.6 6
95.64 even 6 inner 95.2.i.b.64.6 yes 12
95.68 odd 12 9025.2.a.bu.1.1 6
95.83 odd 12 475.2.e.g.26.6 12
95.84 odd 6 1805.2.b.g.1084.1 6
95.87 odd 12 9025.2.a.bu.1.6 6
285.254 odd 6 855.2.be.d.64.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.i.b.49.1 12 5.4 even 2 inner
95.2.i.b.49.6 yes 12 1.1 even 1 trivial
95.2.i.b.64.1 yes 12 19.7 even 3 inner
95.2.i.b.64.6 yes 12 95.64 even 6 inner
475.2.e.g.26.1 12 95.7 odd 12
475.2.e.g.26.6 12 95.83 odd 12
475.2.e.g.201.1 12 5.2 odd 4
475.2.e.g.201.6 12 5.3 odd 4
855.2.be.d.64.1 12 285.254 odd 6
855.2.be.d.64.6 12 57.26 odd 6
855.2.be.d.334.1 12 3.2 odd 2
855.2.be.d.334.6 12 15.14 odd 2
1805.2.b.f.1084.1 6 19.11 even 3
1805.2.b.f.1084.6 6 95.49 even 6
1805.2.b.g.1084.1 6 95.84 odd 6
1805.2.b.g.1084.6 6 19.8 odd 6
9025.2.a.bt.1.1 6 95.27 even 12
9025.2.a.bt.1.6 6 95.8 even 12
9025.2.a.bu.1.1 6 95.68 odd 12
9025.2.a.bu.1.6 6 95.87 odd 12