Properties

Label 225.2.u.a.214.8
Level $225$
Weight $2$
Character 225.214
Analytic conductor $1.797$
Analytic rank $0$
Dimension $224$
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] = [225,2,Mod(4,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([10, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.u (of order \(30\), degree \(8\), 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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(28\) over \(\Q(\zeta_{30})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label 214.8
Character \(\chi\) \(=\) 225.214
Dual form 225.2.u.a.184.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.66066 + 0.174542i) q^{2} +(-1.65808 + 0.500767i) q^{3} +(0.771027 - 0.163887i) q^{4} +(1.94471 + 1.10368i) q^{5} +(2.66610 - 1.12101i) q^{6} +(-0.907253 - 0.523803i) q^{7} +(1.92435 - 0.625260i) q^{8} +(2.49846 - 1.66062i) q^{9} +O(q^{10})\) \(q+(-1.66066 + 0.174542i) q^{2} +(-1.65808 + 0.500767i) q^{3} +(0.771027 - 0.163887i) q^{4} +(1.94471 + 1.10368i) q^{5} +(2.66610 - 1.12101i) q^{6} +(-0.907253 - 0.523803i) q^{7} +(1.92435 - 0.625260i) q^{8} +(2.49846 - 1.66062i) q^{9} +(-3.42214 - 1.49339i) q^{10} +(0.524279 + 4.98818i) q^{11} +(-1.19636 + 0.657843i) q^{12} +(-5.17530 - 0.543946i) q^{13} +(1.59806 + 0.711504i) q^{14} +(-3.77717 - 0.856137i) q^{15} +(-4.52677 + 2.01545i) q^{16} +(-2.45762 + 0.798530i) q^{17} +(-3.85925 + 3.19382i) q^{18} +(-0.420608 - 1.29450i) q^{19} +(1.68030 + 0.532251i) q^{20} +(1.76660 + 0.414185i) q^{21} +(-1.74130 - 8.19215i) q^{22} +(-2.88655 + 6.48329i) q^{23} +(-2.87762 + 2.00038i) q^{24} +(2.56380 + 4.29266i) q^{25} +8.68934 q^{26} +(-3.31107 + 4.00460i) q^{27} +(-0.785361 - 0.255179i) q^{28} +(-2.86568 - 3.18266i) q^{29} +(6.42203 + 0.762475i) q^{30} +(-4.45370 + 4.94633i) q^{31} +(3.66103 - 2.11370i) q^{32} +(-3.36721 - 8.00826i) q^{33} +(3.94190 - 1.75504i) q^{34} +(-1.18624 - 2.01996i) q^{35} +(1.65423 - 1.68985i) q^{36} +(1.74627 - 2.40354i) q^{37} +(0.924432 + 2.07631i) q^{38} +(8.85345 - 1.68971i) q^{39} +(4.43239 + 0.907911i) q^{40} +(0.295314 - 2.80972i) q^{41} +(-3.00602 - 0.379473i) q^{42} +(0.434744 + 0.251000i) q^{43} +(1.22173 + 3.76010i) q^{44} +(6.69158 - 0.471939i) q^{45} +(3.66196 - 11.2704i) q^{46} +(-4.17729 + 3.76125i) q^{47} +(6.49648 - 5.60863i) q^{48} +(-2.95126 - 5.11173i) q^{49} +(-5.00685 - 6.68115i) q^{50} +(3.67506 - 2.55472i) q^{51} +(-4.07944 + 0.428766i) q^{52} +(13.1345 + 4.26766i) q^{53} +(4.79959 - 7.22819i) q^{54} +(-4.48576 + 10.2792i) q^{55} +(-2.07339 - 0.440712i) q^{56} +(1.34564 + 1.93576i) q^{57} +(5.31443 + 4.78514i) q^{58} +(0.192990 - 1.83618i) q^{59} +(-3.05261 - 0.0410757i) q^{60} +(1.13403 + 10.7896i) q^{61} +(6.53273 - 8.99153i) q^{62} +(-3.13658 + 0.197903i) q^{63} +(2.30683 - 1.67601i) q^{64} +(-9.46411 - 6.76966i) q^{65} +(6.98957 + 12.7113i) q^{66} +(0.899874 + 0.810250i) q^{67} +(-1.76402 + 1.01846i) q^{68} +(1.53951 - 12.1953i) q^{69} +(2.32250 + 3.14741i) q^{70} +(-3.62243 + 11.1487i) q^{71} +(3.76960 - 4.75782i) q^{72} +(0.855883 + 1.17802i) q^{73} +(-2.48045 + 4.29626i) q^{74} +(-6.40061 - 5.83371i) q^{75} +(-0.536452 - 0.929162i) q^{76} +(2.13717 - 4.80016i) q^{77} +(-14.4076 + 4.35133i) q^{78} +(-2.69159 - 2.98931i) q^{79} +(-11.0277 - 1.07662i) q^{80} +(3.48465 - 8.29802i) q^{81} +4.71753i q^{82} +(0.159783 - 0.751720i) q^{83} +(1.42998 + 0.0298251i) q^{84} +(-5.66068 - 1.15951i) q^{85} +(-0.765772 - 0.340944i) q^{86} +(6.34531 + 3.84208i) q^{87} +(4.12781 + 9.27120i) q^{88} +(-13.8694 + 10.0767i) q^{89} +(-11.0301 + 1.95169i) q^{90} +(4.41038 + 3.20433i) q^{91} +(-1.16308 + 5.47186i) q^{92} +(4.90763 - 10.4317i) q^{93} +(6.28055 - 6.97526i) q^{94} +(0.610746 - 2.98164i) q^{95} +(-5.01181 + 5.33800i) q^{96} +(11.0307 - 9.93212i) q^{97} +(5.79325 + 7.97373i) q^{98} +(9.59338 + 11.5922i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 224 q - 5 q^{2} - 10 q^{3} - 29 q^{4} - 2 q^{6} - 20 q^{8} - 8 q^{9} - 12 q^{10} + 5 q^{11} - 30 q^{12} - 5 q^{13} - 23 q^{14} + 18 q^{15} + 15 q^{16} - 20 q^{17} - 12 q^{19} - 17 q^{20} - 27 q^{21} - 5 q^{22} - 5 q^{23} - 46 q^{24} - 16 q^{25} + 72 q^{26} - 25 q^{27} - 60 q^{28} - 15 q^{29} + 2 q^{30} - 9 q^{31} - 35 q^{33} - 7 q^{34} - 46 q^{35} - 66 q^{36} - 20 q^{37} - 75 q^{38} + 32 q^{39} - q^{40} + 13 q^{41} - 140 q^{42} + 20 q^{44} + 90 q^{45} - 4 q^{46} + 20 q^{47} + 165 q^{48} + 56 q^{49} - 29 q^{50} - 6 q^{51} - 15 q^{52} - 20 q^{53} + 61 q^{54} - 44 q^{55} + 22 q^{56} - 5 q^{58} - 30 q^{59} - 149 q^{60} - 3 q^{61} + 40 q^{62} - 12 q^{64} + 45 q^{65} + 98 q^{66} + 10 q^{67} - 14 q^{69} - 12 q^{70} - 106 q^{71} + 40 q^{72} - 20 q^{73} + 82 q^{74} + 43 q^{75} + 8 q^{76} - 115 q^{77} + 110 q^{78} - 15 q^{79} - 22 q^{80} + 72 q^{81} + 65 q^{83} + 57 q^{84} - 21 q^{85} - 15 q^{86} + 115 q^{87} - 5 q^{88} + 26 q^{89} - 29 q^{90} - 54 q^{91} + 95 q^{92} + 41 q^{94} - 17 q^{95} - 47 q^{96} - 5 q^{97} - 70 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{10}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.66066 + 0.174542i −1.17426 + 0.123420i −0.671500 0.741004i \(-0.734350\pi\)
−0.502763 + 0.864424i \(0.667683\pi\)
\(3\) −1.65808 + 0.500767i −0.957293 + 0.289118i
\(4\) 0.771027 0.163887i 0.385514 0.0819434i
\(5\) 1.94471 + 1.10368i 0.869701 + 0.493579i
\(6\) 2.66610 1.12101i 1.08843 0.457650i
\(7\) −0.907253 0.523803i −0.342909 0.197979i 0.318648 0.947873i \(-0.396771\pi\)
−0.661558 + 0.749894i \(0.730104\pi\)
\(8\) 1.92435 0.625260i 0.680361 0.221063i
\(9\) 2.49846 1.66062i 0.832822 0.553541i
\(10\) −3.42214 1.49339i −1.08218 0.472253i
\(11\) 0.524279 + 4.98818i 0.158076 + 1.50399i 0.729865 + 0.683592i \(0.239583\pi\)
−0.571789 + 0.820401i \(0.693750\pi\)
\(12\) −1.19636 + 0.657843i −0.345358 + 0.189903i
\(13\) −5.17530 0.543946i −1.43537 0.150863i −0.645322 0.763910i \(-0.723277\pi\)
−0.790046 + 0.613047i \(0.789944\pi\)
\(14\) 1.59806 + 0.711504i 0.427100 + 0.190157i
\(15\) −3.77717 0.856137i −0.975262 0.221054i
\(16\) −4.52677 + 2.01545i −1.13169 + 0.503862i
\(17\) −2.45762 + 0.798530i −0.596061 + 0.193672i −0.591483 0.806318i \(-0.701457\pi\)
−0.00457814 + 0.999990i \(0.501457\pi\)
\(18\) −3.85925 + 3.19382i −0.909634 + 0.752790i
\(19\) −0.420608 1.29450i −0.0964942 0.296978i 0.891146 0.453717i \(-0.149902\pi\)
−0.987640 + 0.156738i \(0.949902\pi\)
\(20\) 1.68030 + 0.532251i 0.375727 + 0.119015i
\(21\) 1.76660 + 0.414185i 0.385504 + 0.0903826i
\(22\) −1.74130 8.19215i −0.371246 1.74657i
\(23\) −2.88655 + 6.48329i −0.601887 + 1.35186i 0.313616 + 0.949550i \(0.398459\pi\)
−0.915503 + 0.402310i \(0.868207\pi\)
\(24\) −2.87762 + 2.00038i −0.587392 + 0.408327i
\(25\) 2.56380 + 4.29266i 0.512760 + 0.858532i
\(26\) 8.68934 1.70412
\(27\) −3.31107 + 4.00460i −0.637216 + 0.770685i
\(28\) −0.785361 0.255179i −0.148419 0.0482244i
\(29\) −2.86568 3.18266i −0.532144 0.591006i 0.415795 0.909459i \(-0.363504\pi\)
−0.947939 + 0.318453i \(0.896837\pi\)
\(30\) 6.42203 + 0.762475i 1.17250 + 0.139208i
\(31\) −4.45370 + 4.94633i −0.799908 + 0.888388i −0.995736 0.0922506i \(-0.970594\pi\)
0.195828 + 0.980638i \(0.437261\pi\)
\(32\) 3.66103 2.11370i 0.647185 0.373652i
\(33\) −3.36721 8.00826i −0.586156 1.39406i
\(34\) 3.94190 1.75504i 0.676029 0.300988i
\(35\) −1.18624 2.01996i −0.200511 0.341435i
\(36\) 1.65423 1.68985i 0.275705 0.281642i
\(37\) 1.74627 2.40354i 0.287086 0.395140i −0.640979 0.767558i \(-0.721471\pi\)
0.928065 + 0.372419i \(0.121471\pi\)
\(38\) 0.924432 + 2.07631i 0.149963 + 0.336822i
\(39\) 8.85345 1.68971i 1.41769 0.270570i
\(40\) 4.43239 + 0.907911i 0.700823 + 0.143553i
\(41\) 0.295314 2.80972i 0.0461202 0.438805i −0.946959 0.321355i \(-0.895862\pi\)
0.993079 0.117449i \(-0.0374717\pi\)
\(42\) −3.00602 0.379473i −0.463838 0.0585540i
\(43\) 0.434744 + 0.251000i 0.0662979 + 0.0382771i 0.532783 0.846252i \(-0.321146\pi\)
−0.466485 + 0.884529i \(0.654480\pi\)
\(44\) 1.22173 + 3.76010i 0.184183 + 0.566856i
\(45\) 6.69158 0.471939i 0.997522 0.0703525i
\(46\) 3.66196 11.2704i 0.539927 1.66172i
\(47\) −4.17729 + 3.76125i −0.609320 + 0.548634i −0.914976 0.403508i \(-0.867791\pi\)
0.305656 + 0.952142i \(0.401124\pi\)
\(48\) 6.49648 5.60863i 0.937686 0.809536i
\(49\) −2.95126 5.11173i −0.421609 0.730248i
\(50\) −5.00685 6.68115i −0.708075 0.944857i
\(51\) 3.67506 2.55472i 0.514611 0.357733i
\(52\) −4.07944 + 0.428766i −0.565716 + 0.0594592i
\(53\) 13.1345 + 4.26766i 1.80416 + 0.586208i 0.999967 0.00815559i \(-0.00259603\pi\)
0.804196 + 0.594364i \(0.202596\pi\)
\(54\) 4.79959 7.22819i 0.653141 0.983632i
\(55\) −4.48576 + 10.2792i −0.604860 + 1.38605i
\(56\) −2.07339 0.440712i −0.277068 0.0588926i
\(57\) 1.34564 + 1.93576i 0.178235 + 0.256397i
\(58\) 5.31443 + 4.78514i 0.697819 + 0.628319i
\(59\) 0.192990 1.83618i 0.0251252 0.239050i −0.974751 0.223296i \(-0.928318\pi\)
0.999876 0.0157543i \(-0.00501495\pi\)
\(60\) −3.05261 0.0410757i −0.394090 0.00530284i
\(61\) 1.13403 + 10.7896i 0.145197 + 1.38146i 0.788116 + 0.615526i \(0.211057\pi\)
−0.642919 + 0.765934i \(0.722277\pi\)
\(62\) 6.53273 8.99153i 0.829657 1.14193i
\(63\) −3.13658 + 0.197903i −0.395172 + 0.0249335i
\(64\) 2.30683 1.67601i 0.288354 0.209501i
\(65\) −9.46411 6.76966i −1.17388 0.839674i
\(66\) 6.98957 + 12.7113i 0.860356 + 1.56465i
\(67\) 0.899874 + 0.810250i 0.109937 + 0.0989878i 0.722266 0.691615i \(-0.243101\pi\)
−0.612329 + 0.790603i \(0.709767\pi\)
\(68\) −1.76402 + 1.01846i −0.213919 + 0.123506i
\(69\) 1.53951 12.1953i 0.185335 1.46814i
\(70\) 2.32250 + 3.14741i 0.277592 + 0.376188i
\(71\) −3.62243 + 11.1487i −0.429904 + 1.32311i 0.468316 + 0.883561i \(0.344861\pi\)
−0.898220 + 0.439547i \(0.855139\pi\)
\(72\) 3.76960 4.75782i 0.444252 0.560714i
\(73\) 0.855883 + 1.17802i 0.100174 + 0.137877i 0.856161 0.516709i \(-0.172843\pi\)
−0.755988 + 0.654586i \(0.772843\pi\)
\(74\) −2.48045 + 4.29626i −0.288346 + 0.499430i
\(75\) −6.40061 5.83371i −0.739079 0.673619i
\(76\) −0.536452 0.929162i −0.0615352 0.106582i
\(77\) 2.13717 4.80016i 0.243553 0.547029i
\(78\) −14.4076 + 4.35133i −1.63134 + 0.492692i
\(79\) −2.69159 2.98931i −0.302827 0.336324i 0.572455 0.819936i \(-0.305991\pi\)
−0.875282 + 0.483612i \(0.839324\pi\)
\(80\) −11.0277 1.07662i −1.23293 0.120370i
\(81\) 3.48465 8.29802i 0.387184 0.922003i
\(82\) 4.71753i 0.520964i
\(83\) 0.159783 0.751720i 0.0175385 0.0825120i −0.968508 0.248983i \(-0.919904\pi\)
0.986046 + 0.166471i \(0.0532371\pi\)
\(84\) 1.42998 + 0.0298251i 0.156023 + 0.00325418i
\(85\) −5.66068 1.15951i −0.613987 0.125766i
\(86\) −0.765772 0.340944i −0.0825753 0.0367649i
\(87\) 6.34531 + 3.84208i 0.680289 + 0.411914i
\(88\) 4.12781 + 9.27120i 0.440026 + 0.988314i
\(89\) −13.8694 + 10.0767i −1.47015 + 1.06813i −0.489582 + 0.871957i \(0.662851\pi\)
−0.980570 + 0.196170i \(0.937149\pi\)
\(90\) −11.0301 + 1.95169i −1.16267 + 0.205727i
\(91\) 4.41038 + 3.20433i 0.462334 + 0.335905i
\(92\) −1.16308 + 5.47186i −0.121259 + 0.570481i
\(93\) 4.90763 10.4317i 0.508898 1.08172i
\(94\) 6.28055 6.97526i 0.647790 0.719443i
\(95\) 0.610746 2.98164i 0.0626612 0.305910i
\(96\) −5.01181 + 5.33800i −0.511516 + 0.544808i
\(97\) 11.0307 9.93212i 1.12000 1.00845i 0.120124 0.992759i \(-0.461671\pi\)
0.999877 0.0156948i \(-0.00499602\pi\)
\(98\) 5.79325 + 7.97373i 0.585207 + 0.805468i
\(99\) 9.59338 + 11.5922i 0.964171 + 1.16506i
\(100\) 2.68027 + 2.88958i 0.268027 + 0.288958i
\(101\) 2.50555 4.33974i 0.249311 0.431820i −0.714023 0.700122i \(-0.753129\pi\)
0.963335 + 0.268302i \(0.0864624\pi\)
\(102\) −5.65711 + 4.88398i −0.560138 + 0.483586i
\(103\) −1.18993 5.59819i −0.117248 0.551606i −0.997083 0.0763276i \(-0.975681\pi\)
0.879835 0.475279i \(-0.157653\pi\)
\(104\) −10.2992 + 2.18916i −1.00992 + 0.214665i
\(105\) 2.97840 + 2.75523i 0.290663 + 0.268883i
\(106\) −22.5568 4.79460i −2.19091 0.465693i
\(107\) 3.87723i 0.374826i −0.982281 0.187413i \(-0.939990\pi\)
0.982281 0.187413i \(-0.0600103\pi\)
\(108\) −1.89662 + 3.63029i −0.182503 + 0.349325i
\(109\) 7.06738 + 5.13475i 0.676932 + 0.491820i 0.872339 0.488902i \(-0.162603\pi\)
−0.195406 + 0.980722i \(0.562603\pi\)
\(110\) 5.65516 17.8532i 0.539199 1.70224i
\(111\) −1.69185 + 4.85974i −0.160583 + 0.461266i
\(112\) 5.16262 + 0.542613i 0.487822 + 0.0512721i
\(113\) 0.731761 + 0.0769112i 0.0688383 + 0.00723520i 0.138885 0.990309i \(-0.455648\pi\)
−0.0700467 + 0.997544i \(0.522315\pi\)
\(114\) −2.57253 2.97976i −0.240939 0.279080i
\(115\) −12.7690 + 9.42232i −1.19071 + 0.878636i
\(116\) −2.73112 1.98427i −0.253578 0.184235i
\(117\) −13.8336 + 7.23519i −1.27892 + 0.668894i
\(118\) 3.08295i 0.283809i
\(119\) 2.64796 + 0.562841i 0.242738 + 0.0515955i
\(120\) −7.80392 + 0.714206i −0.712397 + 0.0651978i
\(121\) −13.8474 + 2.94336i −1.25886 + 0.267578i
\(122\) −3.76647 17.7198i −0.341000 1.60428i
\(123\) 0.917361 + 4.80663i 0.0827157 + 0.433399i
\(124\) −2.62328 + 4.54366i −0.235578 + 0.408033i
\(125\) 0.248146 + 11.1776i 0.0221949 + 0.999754i
\(126\) 5.17425 0.876116i 0.460959 0.0780506i
\(127\) −0.300994 0.414283i −0.0267089 0.0367616i 0.795454 0.606014i \(-0.207233\pi\)
−0.822163 + 0.569253i \(0.807233\pi\)
\(128\) −9.82145 + 8.84328i −0.868102 + 0.781643i
\(129\) −0.846534 0.198472i −0.0745331 0.0174745i
\(130\) 16.8983 + 9.59021i 1.48208 + 0.841117i
\(131\) 14.2428 15.8182i 1.24440 1.38205i 0.348794 0.937199i \(-0.386591\pi\)
0.895606 0.444847i \(-0.146742\pi\)
\(132\) −3.90866 5.62275i −0.340205 0.489397i
\(133\) −0.296464 + 1.39475i −0.0257067 + 0.120941i
\(134\) −1.63581 1.18848i −0.141312 0.102669i
\(135\) −10.8589 + 4.13344i −0.934581 + 0.355750i
\(136\) −4.23004 + 3.07331i −0.362723 + 0.263534i
\(137\) 8.53520 + 19.1704i 0.729211 + 1.63783i 0.769500 + 0.638647i \(0.220505\pi\)
−0.0402891 + 0.999188i \(0.512828\pi\)
\(138\) −0.428006 + 20.5210i −0.0364343 + 1.74686i
\(139\) 6.12389 + 2.72653i 0.519421 + 0.231261i 0.649665 0.760221i \(-0.274909\pi\)
−0.130243 + 0.991482i \(0.541576\pi\)
\(140\) −1.24567 1.36303i −0.105278 0.115197i
\(141\) 5.04277 8.32830i 0.424678 0.701369i
\(142\) 4.06971 19.1465i 0.341522 1.60674i
\(143\) 26.1005i 2.18263i
\(144\) −7.96307 + 12.5528i −0.663589 + 1.04607i
\(145\) −2.06030 9.35215i −0.171098 0.776654i
\(146\) −1.62694 1.80690i −0.134647 0.149540i
\(147\) 7.45322 + 6.99778i 0.614731 + 0.577167i
\(148\) 0.952516 2.13939i 0.0782963 0.175856i
\(149\) 3.63650 + 6.29859i 0.297913 + 0.516001i 0.975658 0.219296i \(-0.0703760\pi\)
−0.677745 + 0.735297i \(0.737043\pi\)
\(150\) 11.6475 + 8.57063i 0.951011 + 0.699789i
\(151\) 7.32816 12.6927i 0.596357 1.03292i −0.396997 0.917820i \(-0.629948\pi\)
0.993354 0.115101i \(-0.0367190\pi\)
\(152\) −1.61880 2.22808i −0.131302 0.180721i
\(153\) −4.81423 + 6.07629i −0.389207 + 0.491239i
\(154\) −2.71128 + 8.34445i −0.218481 + 0.672415i
\(155\) −14.1203 + 4.70375i −1.13417 + 0.377814i
\(156\) 6.54933 2.75378i 0.524366 0.220479i
\(157\) −3.03470 + 1.75208i −0.242195 + 0.139831i −0.616185 0.787601i \(-0.711323\pi\)
0.373990 + 0.927433i \(0.377989\pi\)
\(158\) 4.99157 + 4.49443i 0.397108 + 0.357558i
\(159\) −23.9152 0.498799i −1.89660 0.0395573i
\(160\) 9.45248 0.0699392i 0.747284 0.00552918i
\(161\) 6.01480 4.37001i 0.474032 0.344405i
\(162\) −4.33847 + 14.3884i −0.340862 + 1.13046i
\(163\) 6.16308 8.48275i 0.482729 0.664420i −0.496297 0.868153i \(-0.665307\pi\)
0.979027 + 0.203733i \(0.0653073\pi\)
\(164\) −0.232782 2.21477i −0.0181772 0.172944i
\(165\) 2.29027 19.2901i 0.178297 1.50173i
\(166\) −0.134138 + 1.27624i −0.0104111 + 0.0990554i
\(167\) 4.20294 + 3.78434i 0.325233 + 0.292841i 0.815531 0.578714i \(-0.196445\pi\)
−0.490298 + 0.871555i \(0.663112\pi\)
\(168\) 3.65854 0.307548i 0.282262 0.0237278i
\(169\) 13.7719 + 2.92731i 1.05938 + 0.225177i
\(170\) 9.60285 + 0.937519i 0.736505 + 0.0719044i
\(171\) −3.20055 2.53579i −0.244752 0.193917i
\(172\) 0.376335 + 0.122279i 0.0286953 + 0.00932367i
\(173\) 19.0067 1.99769i 1.44505 0.151881i 0.650699 0.759335i \(-0.274476\pi\)
0.794355 + 0.607454i \(0.207809\pi\)
\(174\) −11.2080 5.27285i −0.849676 0.399734i
\(175\) −0.0775084 5.23746i −0.00585909 0.395914i
\(176\) −12.4267 21.5237i −0.936697 1.62241i
\(177\) 0.599504 + 3.14118i 0.0450615 + 0.236105i
\(178\) 21.2735 19.1547i 1.59452 1.43571i
\(179\) 2.78128 8.55989i 0.207882 0.639796i −0.791700 0.610910i \(-0.790804\pi\)
0.999583 0.0288866i \(-0.00919617\pi\)
\(180\) 5.08205 1.46054i 0.378793 0.108862i
\(181\) −4.32538 13.3122i −0.321503 0.989485i −0.972994 0.230829i \(-0.925856\pi\)
0.651491 0.758656i \(-0.274144\pi\)
\(182\) −7.88343 4.55150i −0.584359 0.337380i
\(183\) −7.28336 17.3221i −0.538401 1.28048i
\(184\) −1.50099 + 14.2810i −0.110655 + 1.05281i
\(185\) 6.04873 2.74687i 0.444711 0.201954i
\(186\) −6.32913 + 18.1801i −0.464075 + 1.33303i
\(187\) −5.27169 11.8404i −0.385504 0.865856i
\(188\) −2.60438 + 3.58463i −0.189944 + 0.261436i
\(189\) 5.10160 1.89884i 0.371087 0.138120i
\(190\) −0.493818 + 5.05809i −0.0358253 + 0.366952i
\(191\) −0.171604 + 0.0764029i −0.0124168 + 0.00552832i −0.412936 0.910760i \(-0.635497\pi\)
0.400519 + 0.916289i \(0.368830\pi\)
\(192\) −2.98562 + 3.93414i −0.215469 + 0.283922i
\(193\) −13.0903 + 7.55766i −0.942257 + 0.544012i −0.890667 0.454656i \(-0.849762\pi\)
−0.0515900 + 0.998668i \(0.516429\pi\)
\(194\) −16.5847 + 18.4192i −1.19071 + 1.32242i
\(195\) 19.0823 + 6.48534i 1.36651 + 0.464425i
\(196\) −3.11325 3.45761i −0.222375 0.246972i
\(197\) 15.0743 + 4.89794i 1.07400 + 0.348964i 0.792044 0.610463i \(-0.209017\pi\)
0.281956 + 0.959427i \(0.409017\pi\)
\(198\) −17.9547 17.5762i −1.27598 1.24908i
\(199\) 6.78266 0.480810 0.240405 0.970673i \(-0.422720\pi\)
0.240405 + 0.970673i \(0.422720\pi\)
\(200\) 7.61768 + 6.65755i 0.538652 + 0.470760i
\(201\) −1.89781 0.892833i −0.133861 0.0629756i
\(202\) −3.40339 + 7.64415i −0.239462 + 0.537840i
\(203\) 0.932812 + 4.38854i 0.0654706 + 0.308015i
\(204\) 2.41488 2.57205i 0.169076 0.180080i
\(205\) 3.67532 5.13816i 0.256695 0.358865i
\(206\) 2.95319 + 9.08899i 0.205759 + 0.633260i
\(207\) 3.55437 + 20.9918i 0.247046 + 1.45903i
\(208\) 24.5236 7.96822i 1.70041 0.552496i
\(209\) 6.23668 2.77675i 0.431400 0.192072i
\(210\) −5.42702 4.05563i −0.374500 0.279865i
\(211\) 2.65847 + 1.18363i 0.183017 + 0.0814843i 0.496199 0.868209i \(-0.334729\pi\)
−0.313183 + 0.949693i \(0.601395\pi\)
\(212\) 10.8265 + 1.13791i 0.743565 + 0.0781518i
\(213\) 0.423386 20.2995i 0.0290099 1.39090i
\(214\) 0.676741 + 6.43876i 0.0462610 + 0.440144i
\(215\) 0.568430 + 0.967939i 0.0387666 + 0.0660129i
\(216\) −3.86775 + 9.77654i −0.263167 + 0.665209i
\(217\) 6.63154 2.15472i 0.450178 0.146272i
\(218\) −12.6327 7.29351i −0.855597 0.493979i
\(219\) −2.00904 1.52466i −0.135758 0.103027i
\(220\) −1.77402 + 8.66070i −0.119604 + 0.583904i
\(221\) 13.1533 2.79582i 0.884785 0.188067i
\(222\) 1.96136 8.36567i 0.131638 0.561467i
\(223\) 8.79958 0.924873i 0.589264 0.0619341i 0.194796 0.980844i \(-0.437596\pi\)
0.394468 + 0.918910i \(0.370929\pi\)
\(224\) −4.42864 −0.295901
\(225\) 13.5341 + 6.46755i 0.902271 + 0.431170i
\(226\) −1.22863 −0.0817272
\(227\) −9.38312 + 0.986206i −0.622780 + 0.0654568i −0.410662 0.911787i \(-0.634703\pi\)
−0.212117 + 0.977244i \(0.568036\pi\)
\(228\) 1.35477 + 1.27199i 0.0897221 + 0.0842395i
\(229\) 3.49092 0.742018i 0.230687 0.0490339i −0.0911178 0.995840i \(-0.529044\pi\)
0.321804 + 0.946806i \(0.395711\pi\)
\(230\) 19.5603 17.8760i 1.28977 1.17871i
\(231\) −1.13984 + 9.02928i −0.0749958 + 0.594083i
\(232\) −7.50458 4.33277i −0.492700 0.284460i
\(233\) −14.1133 + 4.58568i −0.924591 + 0.300418i −0.732349 0.680930i \(-0.761576\pi\)
−0.192242 + 0.981348i \(0.561576\pi\)
\(234\) 21.7100 14.4297i 1.41923 0.943301i
\(235\) −12.2748 + 2.70417i −0.800720 + 0.176400i
\(236\) −0.152125 1.44737i −0.00990249 0.0942159i
\(237\) 5.95982 + 3.60866i 0.387132 + 0.234408i
\(238\) −4.49559 0.472506i −0.291406 0.0306280i
\(239\) −13.7953 6.14204i −0.892341 0.397296i −0.0912427 0.995829i \(-0.529084\pi\)
−0.801098 + 0.598533i \(0.795751\pi\)
\(240\) 18.8239 3.73716i 1.21508 0.241232i
\(241\) 0.0408175 0.0181731i 0.00262928 0.00117063i −0.405422 0.914130i \(-0.632875\pi\)
0.408051 + 0.912959i \(0.366209\pi\)
\(242\) 22.4821 7.30488i 1.44521 0.469576i
\(243\) −1.62246 + 15.5038i −0.104081 + 0.994569i
\(244\) 2.64263 + 8.13318i 0.169177 + 0.520674i
\(245\) −0.0976530 13.1981i −0.00623882 0.843194i
\(246\) −2.36238 7.82205i −0.150620 0.498716i
\(247\) 1.47264 + 6.92820i 0.0937015 + 0.440831i
\(248\) −5.47774 + 12.3032i −0.347837 + 0.781254i
\(249\) 0.111503 + 1.32643i 0.00706624 + 0.0840589i
\(250\) −2.36305 18.5188i −0.149452 1.17123i
\(251\) −15.5334 −0.980459 −0.490229 0.871593i \(-0.663087\pi\)
−0.490229 + 0.871593i \(0.663087\pi\)
\(252\) −2.38595 + 0.666633i −0.150301 + 0.0419939i
\(253\) −33.8532 10.9996i −2.12833 0.691537i
\(254\) 0.572158 + 0.635446i 0.0359004 + 0.0398714i
\(255\) 9.96651 0.912124i 0.624127 0.0571194i
\(256\) 10.9506 12.1619i 0.684415 0.760120i
\(257\) −11.2520 + 6.49635i −0.701881 + 0.405231i −0.808048 0.589117i \(-0.799476\pi\)
0.106167 + 0.994348i \(0.466142\pi\)
\(258\) 1.44045 + 0.181839i 0.0896782 + 0.0113208i
\(259\) −2.84329 + 1.26592i −0.176674 + 0.0786602i
\(260\) −8.40655 3.66855i −0.521352 0.227514i
\(261\) −12.4450 3.19295i −0.770327 0.197639i
\(262\) −20.8915 + 28.7547i −1.29068 + 1.77647i
\(263\) 9.60965 + 21.5836i 0.592556 + 1.33090i 0.922169 + 0.386787i \(0.126415\pi\)
−0.329613 + 0.944116i \(0.606918\pi\)
\(264\) −11.4869 13.3053i −0.706973 0.818887i
\(265\) 20.8327 + 22.7956i 1.27974 + 1.40032i
\(266\) 0.248882 2.36796i 0.0152599 0.145189i
\(267\) 17.9505 23.6533i 1.09855 1.44756i
\(268\) 0.826617 + 0.477247i 0.0504936 + 0.0291525i
\(269\) 3.33752 + 10.2718i 0.203492 + 0.626284i 0.999772 + 0.0213557i \(0.00679826\pi\)
−0.796280 + 0.604928i \(0.793202\pi\)
\(270\) 17.3114 8.75956i 1.05354 0.533090i
\(271\) −4.28992 + 13.2030i −0.260594 + 0.802026i 0.732082 + 0.681217i \(0.238549\pi\)
−0.992676 + 0.120809i \(0.961451\pi\)
\(272\) 9.51569 8.56797i 0.576973 0.519509i
\(273\) −8.91740 3.10447i −0.539705 0.187891i
\(274\) −17.5201 30.3457i −1.05843 1.83325i
\(275\) −20.0684 + 15.0392i −1.21017 + 0.906901i
\(276\) −0.811646 9.65522i −0.0488554 0.581176i
\(277\) −32.5709 + 3.42334i −1.95700 + 0.205689i −0.997187 0.0749595i \(-0.976117\pi\)
−0.959811 + 0.280648i \(0.909451\pi\)
\(278\) −10.6456 3.45896i −0.638480 0.207455i
\(279\) −2.91341 + 19.7542i −0.174421 + 1.18265i
\(280\) −3.54574 3.14541i −0.211898 0.187974i
\(281\) −10.0529 2.13681i −0.599706 0.127471i −0.101952 0.994789i \(-0.532509\pi\)
−0.497755 + 0.867318i \(0.665842\pi\)
\(282\) −6.92068 + 14.7106i −0.412121 + 0.876006i
\(283\) 2.92241 + 2.63135i 0.173719 + 0.156418i 0.751404 0.659842i \(-0.229377\pi\)
−0.577685 + 0.816260i \(0.696044\pi\)
\(284\) −0.965868 + 9.18962i −0.0573137 + 0.545304i
\(285\) 0.480442 + 5.24964i 0.0284589 + 0.310962i
\(286\) 4.55564 + 43.3440i 0.269380 + 2.56298i
\(287\) −1.73966 + 2.39444i −0.102689 + 0.141339i
\(288\) 5.63690 11.3606i 0.332157 0.669429i
\(289\) −8.35103 + 6.06738i −0.491237 + 0.356905i
\(290\) 5.05380 + 15.1711i 0.296769 + 0.890879i
\(291\) −13.3162 + 21.9921i −0.780608 + 1.28920i
\(292\) 0.852971 + 0.768019i 0.0499164 + 0.0449449i
\(293\) 2.72338 1.57235i 0.159102 0.0918574i −0.418335 0.908293i \(-0.637386\pi\)
0.577437 + 0.816435i \(0.304053\pi\)
\(294\) −13.5987 10.3200i −0.793090 0.601875i
\(295\) 2.40186 3.35784i 0.139841 0.195501i
\(296\) 1.85761 5.71713i 0.107971 0.332302i
\(297\) −21.7116 14.4167i −1.25983 0.836541i
\(298\) −7.13835 9.82509i −0.413513 0.569152i
\(299\) 18.4653 31.9828i 1.06788 1.84962i
\(300\) −5.89111 3.44897i −0.340124 0.199127i
\(301\) −0.262949 0.455441i −0.0151561 0.0262512i
\(302\) −9.95415 + 22.3574i −0.572797 + 1.28652i
\(303\) −1.98121 + 8.45033i −0.113817 + 0.485459i
\(304\) 4.51299 + 5.01218i 0.258838 + 0.287468i
\(305\) −9.70281 + 22.2342i −0.555581 + 1.27312i
\(306\) 6.93422 10.9309i 0.396403 0.624879i
\(307\) 14.1051i 0.805020i −0.915416 0.402510i \(-0.868138\pi\)
0.915416 0.402510i \(-0.131862\pi\)
\(308\) 0.861132 4.05131i 0.0490675 0.230845i
\(309\) 4.77639 + 8.68638i 0.271720 + 0.494151i
\(310\) 22.6280 10.2759i 1.28518 0.583633i
\(311\) 20.4851 + 9.12054i 1.16160 + 0.517178i 0.894754 0.446560i \(-0.147351\pi\)
0.266848 + 0.963739i \(0.414018\pi\)
\(312\) 15.9806 8.78731i 0.904726 0.497483i
\(313\) −5.52084 12.4000i −0.312057 0.700890i 0.687627 0.726065i \(-0.258653\pi\)
−0.999683 + 0.0251741i \(0.991986\pi\)
\(314\) 4.73378 3.43929i 0.267143 0.194091i
\(315\) −6.31816 3.07690i −0.355988 0.173364i
\(316\) −2.56520 1.86372i −0.144304 0.104843i
\(317\) 1.76598 8.30828i 0.0991873 0.466640i −0.900319 0.435230i \(-0.856667\pi\)
0.999507 0.0314096i \(-0.00999963\pi\)
\(318\) 39.8020 3.34587i 2.23199 0.187627i
\(319\) 14.3733 15.9631i 0.804749 0.893765i
\(320\) 6.33589 0.713363i 0.354187 0.0398782i
\(321\) 1.94159 + 6.42876i 0.108369 + 0.358819i
\(322\) −9.22577 + 8.30693i −0.514132 + 0.462927i
\(323\) 2.06739 + 2.84552i 0.115033 + 0.158329i
\(324\) 1.32683 6.96909i 0.0737126 0.387172i
\(325\) −10.9335 23.6104i −0.606479 1.30967i
\(326\) −8.75417 + 15.1627i −0.484849 + 0.839782i
\(327\) −14.2896 4.97473i −0.790217 0.275103i
\(328\) −1.18852 5.59154i −0.0656250 0.308741i
\(329\) 5.76001 1.22433i 0.317560 0.0674994i
\(330\) −0.436428 + 32.4340i −0.0240246 + 1.78543i
\(331\) 20.2595 + 4.30628i 1.11356 + 0.236695i 0.727722 0.685872i \(-0.240579\pi\)
0.385838 + 0.922566i \(0.373912\pi\)
\(332\) 0.605783i 0.0332467i
\(333\) 0.371628 8.90507i 0.0203651 0.487995i
\(334\) −7.64017 5.55091i −0.418052 0.303732i
\(335\) 0.855741 + 2.56887i 0.0467541 + 0.140352i
\(336\) −8.83176 + 1.68557i −0.481812 + 0.0919555i
\(337\) 29.0789 + 3.05632i 1.58403 + 0.166488i 0.855233 0.518243i \(-0.173414\pi\)
0.728796 + 0.684731i \(0.240080\pi\)
\(338\) −23.3813 2.45748i −1.27178 0.133669i
\(339\) −1.25183 + 0.238917i −0.0679903 + 0.0129762i
\(340\) −4.55457 + 0.0336994i −0.247006 + 0.00182761i
\(341\) −27.0082 19.6226i −1.46257 1.06262i
\(342\) 5.75763 + 3.65245i 0.311337 + 0.197502i
\(343\) 13.5168i 0.729836i
\(344\) 0.993542 + 0.211184i 0.0535682 + 0.0113863i
\(345\) 16.4536 22.0172i 0.885831 1.18537i
\(346\) −31.2150 + 6.63495i −1.67813 + 0.356697i
\(347\) 3.76397 + 17.7081i 0.202060 + 0.950619i 0.955930 + 0.293595i \(0.0948517\pi\)
−0.753870 + 0.657024i \(0.771815\pi\)
\(348\) 5.52207 + 1.92243i 0.296014 + 0.103053i
\(349\) −14.8995 + 25.8068i −0.797554 + 1.38140i 0.123650 + 0.992326i \(0.460540\pi\)
−0.921204 + 0.389079i \(0.872793\pi\)
\(350\) 1.04287 + 8.68410i 0.0557439 + 0.464185i
\(351\) 19.3141 18.9239i 1.03091 1.01009i
\(352\) 12.4629 + 17.1537i 0.664275 + 0.914296i
\(353\) 11.0712 9.96859i 0.589263 0.530575i −0.319664 0.947531i \(-0.603570\pi\)
0.908926 + 0.416956i \(0.136903\pi\)
\(354\) −1.54384 5.11178i −0.0820542 0.271688i
\(355\) −19.3491 + 17.6830i −1.02695 + 0.938517i
\(356\) −9.04223 + 10.0424i −0.479237 + 0.532247i
\(357\) −4.67238 + 0.392774i −0.247289 + 0.0207878i
\(358\) −3.12469 + 14.7005i −0.165145 + 0.776946i
\(359\) −19.7808 14.3716i −1.04399 0.758503i −0.0729299 0.997337i \(-0.523235\pi\)
−0.971061 + 0.238834i \(0.923235\pi\)
\(360\) 12.5819 5.09216i 0.663123 0.268380i
\(361\) 13.8725 10.0790i 0.730132 0.530472i
\(362\) 9.50652 + 21.3520i 0.499652 + 1.12224i
\(363\) 21.4862 11.8147i 1.12773 0.620109i
\(364\) 3.92567 + 1.74782i 0.205761 + 0.0916108i
\(365\) 0.364291 + 3.23553i 0.0190679 + 0.169355i
\(366\) 15.1186 + 27.4948i 0.790262 + 1.43718i
\(367\) −4.93498 + 23.2172i −0.257604 + 1.21193i 0.639039 + 0.769174i \(0.279332\pi\)
−0.896643 + 0.442755i \(0.854001\pi\)
\(368\) 35.1660i 1.83316i
\(369\) −3.92806 7.51039i −0.204487 0.390975i
\(370\) −9.56543 + 5.61737i −0.497283 + 0.292033i
\(371\) −9.68091 10.7517i −0.502608 0.558203i
\(372\) 2.07430 8.84741i 0.107548 0.458717i
\(373\) 7.29467 16.3841i 0.377704 0.848336i −0.620250 0.784404i \(-0.712969\pi\)
0.997954 0.0639327i \(-0.0203643\pi\)
\(374\) 10.8211 + 18.7427i 0.559547 + 0.969164i
\(375\) −6.00881 18.4091i −0.310294 0.950641i
\(376\) −5.68682 + 9.84985i −0.293275 + 0.507967i
\(377\) 13.0996 + 18.0300i 0.674662 + 0.928593i
\(378\) −8.14059 + 4.04376i −0.418707 + 0.207989i
\(379\) −8.41830 + 25.9089i −0.432419 + 1.33085i 0.463289 + 0.886207i \(0.346669\pi\)
−0.895708 + 0.444642i \(0.853331\pi\)
\(380\) −0.0177504 2.39902i −0.000910577 0.123067i
\(381\) 0.706531 + 0.536186i 0.0361967 + 0.0274697i
\(382\) 0.271640 0.156831i 0.0138983 0.00802418i
\(383\) 3.42913 + 3.08760i 0.175220 + 0.157769i 0.752075 0.659078i \(-0.229053\pi\)
−0.576854 + 0.816847i \(0.695720\pi\)
\(384\) 11.8563 19.5811i 0.605042 0.999245i
\(385\) 9.45399 6.97618i 0.481820 0.355539i
\(386\) 20.4193 14.8355i 1.03932 0.755107i
\(387\) 1.50301 0.0948329i 0.0764023 0.00482063i
\(388\) 6.87725 9.46572i 0.349139 0.480549i
\(389\) 1.94231 + 18.4798i 0.0984790 + 0.936965i 0.926507 + 0.376278i \(0.122796\pi\)
−0.828028 + 0.560687i \(0.810537\pi\)
\(390\) −32.8211 7.43926i −1.66196 0.376702i
\(391\) 1.91694 18.2385i 0.0969439 0.922360i
\(392\) −8.87543 7.99147i −0.448277 0.403630i
\(393\) −15.6945 + 33.3603i −0.791682 + 1.68280i
\(394\) −25.8882 5.50270i −1.30423 0.277222i
\(395\) −1.93513 8.78398i −0.0973669 0.441970i
\(396\) 9.29656 + 7.36564i 0.467170 + 0.370137i
\(397\) −2.65316 0.862063i −0.133158 0.0432657i 0.241680 0.970356i \(-0.422302\pi\)
−0.374838 + 0.927090i \(0.622302\pi\)
\(398\) −11.2637 + 1.18386i −0.564598 + 0.0593416i
\(399\) −0.206885 2.46108i −0.0103572 0.123208i
\(400\) −20.2574 14.2647i −1.01287 0.713233i
\(401\) −0.356389 0.617283i −0.0177972 0.0308257i 0.856990 0.515334i \(-0.172332\pi\)
−0.874787 + 0.484508i \(0.838999\pi\)
\(402\) 3.30745 + 1.15144i 0.164961 + 0.0574288i
\(403\) 25.7397 23.1762i 1.28219 1.15449i
\(404\) 1.22062 3.75668i 0.0607281 0.186902i
\(405\) 15.9350 12.2913i 0.791815 0.610761i
\(406\) −2.31507 7.12505i −0.114895 0.353610i
\(407\) 12.9048 + 7.45060i 0.639668 + 0.369313i
\(408\) 5.47474 7.21406i 0.271040 0.357149i
\(409\) −0.863901 + 8.21947i −0.0427172 + 0.406427i 0.952180 + 0.305536i \(0.0988358\pi\)
−0.994898 + 0.100890i \(0.967831\pi\)
\(410\) −5.20663 + 9.17424i −0.257137 + 0.453083i
\(411\) −23.7519 27.5119i −1.17160 1.35706i
\(412\) −1.83494 4.12134i −0.0904010 0.203044i
\(413\) −1.13689 + 1.56479i −0.0559425 + 0.0769983i
\(414\) −9.56655 34.2397i −0.470170 1.68279i
\(415\) 1.14039 1.28553i 0.0559794 0.0631042i
\(416\) −20.0966 + 8.94760i −0.985319 + 0.438692i
\(417\) −11.5193 1.45417i −0.564101 0.0712109i
\(418\) −9.87233 + 5.69979i −0.482872 + 0.278786i
\(419\) 10.5595 11.7275i 0.515863 0.572924i −0.427782 0.903882i \(-0.640705\pi\)
0.943646 + 0.330958i \(0.107372\pi\)
\(420\) 2.74798 + 1.63623i 0.134087 + 0.0798400i
\(421\) 1.18232 + 1.31310i 0.0576229 + 0.0639967i 0.771267 0.636512i \(-0.219623\pi\)
−0.713644 + 0.700508i \(0.752957\pi\)
\(422\) −4.62141 1.50159i −0.224967 0.0730961i
\(423\) −4.19079 + 16.3342i −0.203763 + 0.794198i
\(424\) 27.9438 1.35707
\(425\) −9.72867 8.50247i −0.471910 0.412430i
\(426\) 2.84001 + 33.7844i 0.137599 + 1.63686i
\(427\) 4.62275 10.3829i 0.223710 0.502462i
\(428\) −0.635427 2.98945i −0.0307145 0.144501i
\(429\) 13.0703 + 43.2767i 0.631038 + 2.08942i
\(430\) −1.11291 1.50820i −0.0536695 0.0727319i
\(431\) 10.7997 + 33.2379i 0.520201 + 1.60102i 0.773614 + 0.633657i \(0.218447\pi\)
−0.253413 + 0.967358i \(0.581553\pi\)
\(432\) 6.91740 24.8012i 0.332813 1.19325i
\(433\) −10.4999 + 3.41164i −0.504595 + 0.163953i −0.550243 0.835005i \(-0.685465\pi\)
0.0456476 + 0.998958i \(0.485465\pi\)
\(434\) −10.6366 + 4.73573i −0.510574 + 0.227322i
\(435\) 8.09939 + 14.4749i 0.388336 + 0.694018i
\(436\) 6.29066 + 2.80078i 0.301268 + 0.134133i
\(437\) 9.60672 + 1.00971i 0.459552 + 0.0483009i
\(438\) 3.60244 + 2.18127i 0.172131 + 0.104225i
\(439\) 1.09294 + 10.3987i 0.0521633 + 0.496301i 0.989147 + 0.146928i \(0.0469386\pi\)
−0.936984 + 0.349373i \(0.886395\pi\)
\(440\) −2.20501 + 22.5856i −0.105120 + 1.07672i
\(441\) −15.8623 7.87055i −0.755347 0.374788i
\(442\) −21.3551 + 6.93870i −1.01576 + 0.330040i
\(443\) 3.68612 + 2.12818i 0.175133 + 0.101113i 0.585004 0.811031i \(-0.301093\pi\)
−0.409871 + 0.912143i \(0.634426\pi\)
\(444\) −0.508015 + 4.02426i −0.0241093 + 0.190983i
\(445\) −38.0933 + 4.28896i −1.80580 + 0.203316i
\(446\) −14.4517 + 3.07180i −0.684307 + 0.145454i
\(447\) −9.18373 8.62254i −0.434376 0.407832i
\(448\) −2.97078 + 0.312241i −0.140356 + 0.0147520i
\(449\) 21.3213 1.00621 0.503106 0.864225i \(-0.332190\pi\)
0.503106 + 0.864225i \(0.332190\pi\)
\(450\) −23.6043 8.37813i −1.11272 0.394949i
\(451\) 14.1702 0.667249
\(452\) 0.576812 0.0606254i 0.0271310 0.00285158i
\(453\) −5.79457 + 24.7153i −0.272253 + 1.16123i
\(454\) 15.4100 3.27550i 0.723229 0.153727i
\(455\) 5.04038 + 11.0991i 0.236297 + 0.520335i
\(456\) 3.79985 + 2.88370i 0.177944 + 0.135042i
\(457\) −23.8668 13.7795i −1.11644 0.644578i −0.175952 0.984399i \(-0.556300\pi\)
−0.940490 + 0.339820i \(0.889634\pi\)
\(458\) −5.66772 + 1.84155i −0.264835 + 0.0860501i
\(459\) 4.93957 12.4858i 0.230560 0.582786i
\(460\) −8.30101 + 9.35753i −0.387037 + 0.436297i
\(461\) −2.91533 27.7375i −0.135780 1.29186i −0.824095 0.566451i \(-0.808316\pi\)
0.688315 0.725412i \(-0.258351\pi\)
\(462\) 0.316891 15.1935i 0.0147431 0.706865i
\(463\) 1.92050 + 0.201853i 0.0892534 + 0.00938091i 0.149050 0.988830i \(-0.452379\pi\)
−0.0597965 + 0.998211i \(0.519045\pi\)
\(464\) 19.3868 + 8.63155i 0.900008 + 0.400710i
\(465\) 21.0571 14.8702i 0.976501 0.689588i
\(466\) 22.6369 10.0786i 1.04863 0.466882i
\(467\) −30.3777 + 9.87030i −1.40571 + 0.456743i −0.911033 0.412333i \(-0.864714\pi\)
−0.494678 + 0.869076i \(0.664714\pi\)
\(468\) −9.48031 + 7.84567i −0.438228 + 0.362666i
\(469\) −0.392002 1.20646i −0.0181010 0.0557091i
\(470\) 19.9123 6.63317i 0.918485 0.305965i
\(471\) 4.15439 4.42477i 0.191424 0.203883i
\(472\) −0.776708 3.65412i −0.0357509 0.168195i
\(473\) −1.02410 + 2.30018i −0.0470884 + 0.105762i
\(474\) −10.5271 4.95251i −0.483525 0.227477i
\(475\) 4.47849 5.12437i 0.205487 0.235122i
\(476\) 2.13389 0.0978067
\(477\) 39.9031 11.1489i 1.82704 0.510472i
\(478\) 23.9813 + 7.79198i 1.09688 + 0.356397i
\(479\) −21.5839 23.9713i −0.986192 1.09528i −0.995447 0.0953204i \(-0.969612\pi\)
0.00925432 0.999957i \(-0.497054\pi\)
\(480\) −15.6380 + 4.84945i −0.713772 + 0.221346i
\(481\) −10.3449 + 11.4892i −0.471686 + 0.523860i
\(482\) −0.0646119 + 0.0373037i −0.00294299 + 0.00169914i
\(483\) −7.78467 + 10.2578i −0.354215 + 0.466748i
\(484\) −10.1944 + 4.53882i −0.463380 + 0.206310i
\(485\) 32.4134 7.14074i 1.47182 0.324244i
\(486\) −0.0117085 26.0297i −0.000531108 1.18073i
\(487\) 14.6325 20.1400i 0.663064 0.912629i −0.336514 0.941678i \(-0.609248\pi\)
0.999578 + 0.0290491i \(0.00924791\pi\)
\(488\) 8.92854 + 20.0538i 0.404176 + 0.907795i
\(489\) −5.97100 + 17.1513i −0.270018 + 0.775611i
\(490\) 2.46579 + 21.9005i 0.111393 + 0.989362i
\(491\) 0.136136 1.29525i 0.00614373 0.0584537i −0.991020 0.133710i \(-0.957311\pi\)
0.997164 + 0.0752565i \(0.0239775\pi\)
\(492\) 1.49505 + 3.55570i 0.0674022 + 0.160303i
\(493\) 9.58422 + 5.53345i 0.431652 + 0.249214i
\(494\) −3.65481 11.2483i −0.164438 0.506087i
\(495\) 5.86237 + 33.1314i 0.263494 + 1.48914i
\(496\) 10.1918 31.3671i 0.457625 1.40842i
\(497\) 9.12619 8.21726i 0.409366 0.368594i
\(498\) −0.416687 2.18328i −0.0186722 0.0978352i
\(499\) −8.06259 13.9648i −0.360931 0.625151i 0.627183 0.778872i \(-0.284208\pi\)
−0.988114 + 0.153721i \(0.950874\pi\)
\(500\) 2.02319 + 8.57755i 0.0904797 + 0.383600i
\(501\) −8.86388 4.17005i −0.396009 0.186304i
\(502\) 25.7957 2.71123i 1.15132 0.121008i
\(503\) −5.46111 1.77442i −0.243499 0.0791176i 0.184725 0.982790i \(-0.440861\pi\)
−0.428224 + 0.903673i \(0.640861\pi\)
\(504\) −5.91214 + 2.34201i −0.263348 + 0.104322i
\(505\) 9.66223 5.67422i 0.429964 0.252500i
\(506\) 58.1385 + 12.3577i 2.58457 + 0.549367i
\(507\) −24.3008 + 2.04280i −1.07924 + 0.0907238i
\(508\) −0.299970 0.270094i −0.0133090 0.0119835i
\(509\) −0.116731 + 1.11062i −0.00517401 + 0.0492274i −0.996804 0.0798827i \(-0.974545\pi\)
0.991630 + 0.129110i \(0.0412121\pi\)
\(510\) −16.3918 + 3.25431i −0.725840 + 0.144103i
\(511\) −0.159451 1.51708i −0.00705371 0.0671116i
\(512\) −0.526086 + 0.724095i −0.0232499 + 0.0320008i
\(513\) 6.57661 + 2.60181i 0.290365 + 0.114873i
\(514\) 17.5519 12.7522i 0.774179 0.562474i
\(515\) 3.86451 12.2002i 0.170291 0.537604i
\(516\) −0.685227 0.0142918i −0.0301655 0.000629161i
\(517\) −20.9518 18.8651i −0.921461 0.829687i
\(518\) 4.50079 2.59853i 0.197753 0.114173i
\(519\) −30.5143 + 12.8303i −1.33943 + 0.563186i
\(520\) −22.4451 7.10969i −0.984282 0.311780i
\(521\) 1.63831 5.04221i 0.0717758 0.220903i −0.908733 0.417378i \(-0.862949\pi\)
0.980509 + 0.196474i \(0.0629493\pi\)
\(522\) 21.2242 + 3.13022i 0.928960 + 0.137006i
\(523\) −15.2951 21.0519i −0.668807 0.920533i 0.330926 0.943657i \(-0.392639\pi\)
−0.999733 + 0.0231234i \(0.992639\pi\)
\(524\) 8.38919 14.5305i 0.366484 0.634768i
\(525\) 2.75126 + 8.64531i 0.120075 + 0.377312i
\(526\) −19.7256 34.1657i −0.860077 1.48970i
\(527\) 6.99571 15.7126i 0.304738 0.684453i
\(528\) 31.3828 + 29.4651i 1.36576 + 1.28230i
\(529\) −18.3109 20.3363i −0.796127 0.884189i
\(530\) −38.5748 34.2195i −1.67558 1.48640i
\(531\) −2.56702 4.90811i −0.111399 0.212994i
\(532\) 1.12398i 0.0487307i
\(533\) −3.05667 + 14.3805i −0.132399 + 0.622889i
\(534\) −25.6811 + 42.4132i −1.11133 + 1.83540i
\(535\) 4.27921 7.54009i 0.185006 0.325987i
\(536\) 2.23829 + 0.996552i 0.0966795 + 0.0430445i
\(537\) −0.325072 + 15.5858i −0.0140279 + 0.672575i
\(538\) −7.33534 16.4755i −0.316249 0.710307i
\(539\) 23.9510 17.4014i 1.03164 0.749531i
\(540\) −7.69505 + 4.96661i −0.331142 + 0.213729i
\(541\) 34.1490 + 24.8107i 1.46818 + 1.06670i 0.981136 + 0.193321i \(0.0619258\pi\)
0.487046 + 0.873376i \(0.338074\pi\)
\(542\) 4.81961 22.6745i 0.207020 0.973953i
\(543\) 13.8381 + 19.9066i 0.593851 + 0.854275i
\(544\) −7.30958 + 8.11811i −0.313396 + 0.348061i
\(545\) 8.07691 + 17.7857i 0.345977 + 0.761856i
\(546\) 15.3506 + 3.59900i 0.656946 + 0.154023i
\(547\) 19.2695 17.3503i 0.823905 0.741847i −0.144960 0.989437i \(-0.546305\pi\)
0.968865 + 0.247591i \(0.0796388\pi\)
\(548\) 9.72264 + 13.3821i 0.415330 + 0.571653i
\(549\) 20.7507 + 25.0741i 0.885619 + 1.07014i
\(550\) 30.7018 28.4778i 1.30913 1.21430i
\(551\) −2.91463 + 5.04828i −0.124167 + 0.215064i
\(552\) −4.66268 24.4307i −0.198457 1.03984i
\(553\) 0.876142 + 4.12192i 0.0372573 + 0.175282i
\(554\) 53.4917 11.3700i 2.27264 0.483065i
\(555\) −8.65374 + 7.58354i −0.367331 + 0.321903i
\(556\) 5.16853 + 1.09860i 0.219194 + 0.0465912i
\(557\) 4.89318i 0.207331i −0.994612 0.103665i \(-0.966943\pi\)
0.994612 0.103665i \(-0.0330571\pi\)
\(558\) 1.39024 33.3134i 0.0588536 1.41027i
\(559\) −2.11340 1.53548i −0.0893873 0.0649437i
\(560\) 9.44093 + 6.75308i 0.398952 + 0.285370i
\(561\) 14.6702 + 16.9925i 0.619375 + 0.717423i
\(562\) 17.0674 + 1.79386i 0.719945 + 0.0756693i
\(563\) −24.7718 2.60362i −1.04401 0.109730i −0.433031 0.901379i \(-0.642556\pi\)
−0.610976 + 0.791649i \(0.709223\pi\)
\(564\) 2.52322 7.24779i 0.106247 0.305187i
\(565\) 1.33818 + 0.957197i 0.0562976 + 0.0402696i
\(566\) −5.31241 3.85969i −0.223297 0.162235i
\(567\) −7.50799 + 5.70314i −0.315306 + 0.239509i
\(568\) 23.7190i 0.995227i
\(569\) 23.0613 + 4.90183i 0.966780 + 0.205495i 0.664139 0.747609i \(-0.268798\pi\)
0.302641 + 0.953105i \(0.402132\pi\)
\(570\) −1.71413 8.63401i −0.0717972 0.361639i
\(571\) 36.3197 7.72000i 1.51993 0.323072i 0.629072 0.777347i \(-0.283435\pi\)
0.890861 + 0.454275i \(0.150102\pi\)
\(572\) −4.27753 20.1242i −0.178852 0.841434i
\(573\) 0.246273 0.212616i 0.0102882 0.00888214i
\(574\) 2.47106 4.28000i 0.103140 0.178644i
\(575\) −35.2311 + 4.23090i −1.46924 + 0.176441i
\(576\) 2.98031 8.01823i 0.124180 0.334093i
\(577\) 6.03334 + 8.30418i 0.251171 + 0.345707i 0.915921 0.401359i \(-0.131462\pi\)
−0.664750 + 0.747066i \(0.731462\pi\)
\(578\) 12.8092 11.5335i 0.532792 0.479728i
\(579\) 17.9201 19.0864i 0.744733 0.793203i
\(580\) −3.12124 6.87310i −0.129602 0.285390i
\(581\) −0.538717 + 0.598306i −0.0223497 + 0.0248219i
\(582\) 18.2751 38.8456i 0.757526 1.61020i
\(583\) −14.4017 + 67.7547i −0.596458 + 2.80611i
\(584\) 2.38359 + 1.73178i 0.0986337 + 0.0716616i
\(585\) −34.8876 1.19743i −1.44243 0.0495077i
\(586\) −4.24817 + 3.08647i −0.175490 + 0.127501i
\(587\) −15.5303 34.8816i −0.641003 1.43972i −0.882969 0.469432i \(-0.844459\pi\)
0.241966 0.970285i \(-0.422208\pi\)
\(588\) 6.89348 + 4.17399i 0.284282 + 0.172132i
\(589\) 8.27629 + 3.68484i 0.341018 + 0.151831i
\(590\) −3.40258 + 5.99545i −0.140082 + 0.246829i
\(591\) −27.4472 0.572466i −1.12903 0.0235481i
\(592\) −3.06077 + 14.3998i −0.125797 + 0.591828i
\(593\) 15.4532i 0.634585i −0.948328 0.317293i \(-0.897226\pi\)
0.948328 0.317293i \(-0.102774\pi\)
\(594\) 38.5718 + 20.1516i 1.58262 + 0.826831i
\(595\) 4.52832 + 4.01705i 0.185643 + 0.164683i
\(596\) 3.83609 + 4.26041i 0.157132 + 0.174513i
\(597\) −11.2462 + 3.39653i −0.460276 + 0.139011i
\(598\) −25.0822 + 56.3355i −1.02569 + 2.30373i
\(599\) 5.19282 + 8.99423i 0.212173 + 0.367494i 0.952394 0.304869i \(-0.0986127\pi\)
−0.740221 + 0.672363i \(0.765279\pi\)
\(600\) −15.9646 7.22407i −0.651753 0.294921i
\(601\) −5.55662 + 9.62435i −0.226659 + 0.392585i −0.956816 0.290694i \(-0.906114\pi\)
0.730157 + 0.683280i \(0.239447\pi\)
\(602\) 0.516162 + 0.710436i 0.0210372 + 0.0289552i
\(603\) 3.59382 + 0.530029i 0.146352 + 0.0215845i
\(604\) 3.57003 10.9874i 0.145263 0.447072i
\(605\) −30.1778 9.55909i −1.22690 0.388632i
\(606\) 1.81517 14.3789i 0.0737361 0.584104i
\(607\) 11.2355 6.48681i 0.456034 0.263292i −0.254341 0.967115i \(-0.581859\pi\)
0.710375 + 0.703823i \(0.248525\pi\)
\(608\) −4.27604 3.85016i −0.173416 0.156145i
\(609\) −3.74431 6.80943i −0.151727 0.275932i
\(610\) 12.2323 38.6169i 0.495270 1.56355i
\(611\) 23.6646 17.1933i 0.957368 0.695568i
\(612\) −2.71607 + 5.47397i −0.109791 + 0.221272i
\(613\) 12.9781 17.8629i 0.524182 0.721475i −0.462048 0.886855i \(-0.652885\pi\)
0.986230 + 0.165380i \(0.0528851\pi\)
\(614\) 2.46193 + 23.4237i 0.0993556 + 0.945305i
\(615\) −3.52096 + 10.3600i −0.141979 + 0.417754i
\(616\) 1.11132 10.5735i 0.0447763 0.426018i
\(617\) −10.5709 9.51810i −0.425569 0.383184i 0.428330 0.903622i \(-0.359102\pi\)
−0.853899 + 0.520438i \(0.825769\pi\)
\(618\) −9.44810 13.5914i −0.380058 0.546727i
\(619\) 2.61966 + 0.556826i 0.105293 + 0.0223807i 0.260257 0.965539i \(-0.416193\pi\)
−0.154964 + 0.987920i \(0.549526\pi\)
\(620\) −10.1163 + 5.94085i −0.406278 + 0.238590i
\(621\) −16.4054 33.0261i −0.658327 1.32529i
\(622\) −35.6106 11.5706i −1.42786 0.463938i
\(623\) 17.8612 1.87729i 0.715596 0.0752121i
\(624\) −36.6720 + 25.4926i −1.46805 + 1.02052i
\(625\) −11.8539 + 22.0110i −0.474154 + 0.880442i
\(626\) 11.3326 + 19.6286i 0.452940 + 0.784516i
\(627\) −8.95041 + 7.72719i −0.357445 + 0.308594i
\(628\) −2.05269 + 1.84825i −0.0819112 + 0.0737532i
\(629\) −2.37238 + 7.30145i −0.0945932 + 0.291128i
\(630\) 11.0294 + 4.00690i 0.439420 + 0.159639i
\(631\) 11.7151 + 36.0554i 0.466371 + 1.43534i 0.857250 + 0.514900i \(0.172171\pi\)
−0.390879 + 0.920442i \(0.627829\pi\)
\(632\) −7.04866 4.06954i −0.280381 0.161878i
\(633\) −5.00068 0.631276i −0.198759 0.0250910i
\(634\) −1.48254 + 14.1055i −0.0588793 + 0.560199i
\(635\) −0.128113 1.13786i −0.00508399 0.0451546i
\(636\) −18.5210 + 3.53480i −0.734405 + 0.140164i
\(637\) 12.4931 + 28.0601i 0.494996 + 1.11178i
\(638\) −21.0829 + 29.0181i −0.834679 + 1.14884i
\(639\) 9.46329 + 33.8702i 0.374362 + 1.33988i
\(640\) −28.8600 + 6.35792i −1.14079 + 0.251319i
\(641\) −39.2879 + 17.4921i −1.55178 + 0.690896i −0.990599 0.136798i \(-0.956319\pi\)
−0.561179 + 0.827694i \(0.689652\pi\)
\(642\) −4.34641 10.3371i −0.171539 0.407972i
\(643\) −29.6116 + 17.0963i −1.16777 + 0.674211i −0.953153 0.302488i \(-0.902183\pi\)
−0.214614 + 0.976699i \(0.568849\pi\)
\(644\) 3.92138 4.35514i 0.154524 0.171617i
\(645\) −1.42721 1.32027i −0.0561965 0.0519856i
\(646\) −3.92990 4.36459i −0.154620 0.171723i
\(647\) −44.3154 14.3989i −1.74222 0.566080i −0.747093 0.664719i \(-0.768551\pi\)
−0.995123 + 0.0986388i \(0.968551\pi\)
\(648\) 1.51728 18.1471i 0.0596044 0.712887i
\(649\) 9.26037 0.363501
\(650\) 22.2777 + 37.3004i 0.873805 + 1.46304i
\(651\) −9.91661 + 6.89355i −0.388663 + 0.270179i
\(652\) 3.36169 7.55047i 0.131654 0.295699i
\(653\) 0.304338 + 1.43180i 0.0119097 + 0.0560306i 0.983701 0.179811i \(-0.0575486\pi\)
−0.971791 + 0.235842i \(0.924215\pi\)
\(654\) 24.5985 + 5.76718i 0.961876 + 0.225515i
\(655\) 45.1564 15.0425i 1.76441 0.587758i
\(656\) 4.32603 + 13.3141i 0.168903 + 0.519830i
\(657\) 4.09465 + 1.52195i 0.159747 + 0.0593768i
\(658\) −9.35171 + 3.03856i −0.364568 + 0.118455i
\(659\) −16.1186 + 7.17647i −0.627892 + 0.279556i −0.695911 0.718128i \(-0.744999\pi\)
0.0680183 + 0.997684i \(0.478332\pi\)
\(660\) −1.39553 15.2485i −0.0543208 0.593547i
\(661\) 6.96271 + 3.10000i 0.270818 + 0.120576i 0.537653 0.843166i \(-0.319311\pi\)
−0.266835 + 0.963742i \(0.585978\pi\)
\(662\) −34.3957 3.61513i −1.33683 0.140506i
\(663\) −20.4092 + 11.2224i −0.792626 + 0.435843i
\(664\) −0.162542 1.54648i −0.00630784 0.0600151i
\(665\) −2.11589 + 2.38519i −0.0820508 + 0.0924938i
\(666\) 0.937164 + 14.8531i 0.0363143 + 0.575548i
\(667\) 28.9061 9.39216i 1.11925 0.363666i
\(668\) 3.86078 + 2.22902i 0.149378 + 0.0862435i
\(669\) −14.1273 + 5.94006i −0.546192 + 0.229656i
\(670\) −1.86947 4.11666i −0.0722240 0.159040i
\(671\) −53.2257 + 11.3135i −2.05475 + 0.436751i
\(672\) 7.34305 2.21772i 0.283264 0.0855503i
\(673\) −19.4016 + 2.03919i −0.747876 + 0.0786050i −0.470796 0.882242i \(-0.656033\pi\)
−0.277080 + 0.960847i \(0.589367\pi\)
\(674\) −48.8236 −1.88061
\(675\) −25.6793 3.94631i −0.988397 0.151894i
\(676\) 11.0982 0.426856
\(677\) −6.63681 + 0.697557i −0.255073 + 0.0268093i −0.231202 0.972906i \(-0.574266\pi\)
−0.0238712 + 0.999715i \(0.507599\pi\)
\(678\) 2.03717 0.615257i 0.0782370 0.0236288i
\(679\) −15.2101 + 3.23301i −0.583712 + 0.124072i
\(680\) −11.6181 + 1.30810i −0.445535 + 0.0501632i
\(681\) 15.0641 6.33397i 0.577258 0.242718i
\(682\) 48.2763 + 27.8724i 1.84860 + 1.06729i
\(683\) −29.1384 + 9.46764i −1.11495 + 0.362269i −0.807838 0.589405i \(-0.799362\pi\)
−0.307111 + 0.951674i \(0.599362\pi\)
\(684\) −2.88329 1.43063i −0.110246 0.0547016i
\(685\) −4.55938 + 46.7009i −0.174205 + 1.78435i
\(686\) −2.35925 22.4467i −0.0900764 0.857020i
\(687\) −5.41665 + 2.97846i −0.206658 + 0.113635i
\(688\) −2.47386 0.260013i −0.0943151 0.00991292i
\(689\) −65.6536 29.2309i −2.50120 1.11361i
\(690\) −23.4808 + 39.4350i −0.893900 + 1.50126i
\(691\) 41.1455 18.3192i 1.56525 0.696894i 0.572817 0.819683i \(-0.305850\pi\)
0.992433 + 0.122789i \(0.0391837\pi\)
\(692\) 14.3273 4.65522i 0.544642 0.176965i
\(693\) −2.63162 15.5421i −0.0999670 0.590394i
\(694\) −9.34147 28.7501i −0.354597 1.09134i
\(695\) 8.89999 + 12.0611i 0.337596 + 0.457504i
\(696\) 14.6129 + 3.42604i 0.553901 + 0.129864i
\(697\) 1.51788 + 7.14105i 0.0574937 + 0.270487i
\(698\) 20.2387 45.4568i 0.766046 1.72057i
\(699\) 21.1046 14.6709i 0.798248 0.554904i
\(700\) −0.918111 4.02552i −0.0347013 0.152150i
\(701\) −5.06319 −0.191234 −0.0956170 0.995418i \(-0.530482\pi\)
−0.0956170 + 0.995418i \(0.530482\pi\)
\(702\) −28.7710 + 34.7973i −1.08589 + 1.31334i
\(703\) −3.84588 1.24960i −0.145050 0.0471296i
\(704\) 9.56966 + 10.6282i 0.360670 + 0.400565i
\(705\) 18.9985 10.6305i 0.715524 0.400370i
\(706\) −16.6456 + 18.4868i −0.626466 + 0.695761i
\(707\) −4.54634 + 2.62483i −0.170983 + 0.0987168i
\(708\) 0.977032 + 2.32368i 0.0367191 + 0.0873293i
\(709\) −23.0612 + 10.2675i −0.866083 + 0.385605i −0.791178 0.611586i \(-0.790532\pi\)
−0.0749047 + 0.997191i \(0.523865\pi\)
\(710\) 29.0459 32.7427i 1.09007 1.22881i
\(711\) −11.6890 2.99897i −0.438370 0.112470i
\(712\) −20.3890 + 28.0631i −0.764111 + 1.05171i
\(713\) −19.2127 43.1525i −0.719522 1.61607i
\(714\) 7.69067 1.46779i 0.287816 0.0549307i
\(715\) 28.8065 50.7579i 1.07730 1.89824i
\(716\) 0.741586 7.05572i 0.0277144 0.263685i
\(717\) 25.9494 + 3.27580i 0.969097 + 0.122337i
\(718\) 35.3576 + 20.4137i 1.31953 + 0.761833i
\(719\) −3.73536 11.4963i −0.139306 0.428738i 0.856929 0.515434i \(-0.172369\pi\)
−0.996235 + 0.0866955i \(0.972369\pi\)
\(720\) −29.3401 + 15.6229i −1.09344 + 0.582230i
\(721\) −1.85278 + 5.70227i −0.0690011 + 0.212364i
\(722\) −21.2783 + 19.1591i −0.791896 + 0.713026i
\(723\) −0.0585782 + 0.0505725i −0.00217854 + 0.00188081i
\(724\) −5.51668 9.55516i −0.205026 0.355115i
\(725\) 6.31506 20.4611i 0.234535 0.759907i
\(726\) −33.6191 + 23.3704i −1.24772 + 0.867357i
\(727\) −31.5367 + 3.31464i −1.16963 + 0.122933i −0.669361 0.742937i \(-0.733432\pi\)
−0.500269 + 0.865870i \(0.666765\pi\)
\(728\) 10.4907 + 3.40863i 0.388810 + 0.126332i
\(729\) −5.07361 26.5190i −0.187912 0.982186i
\(730\) −1.16970 5.30953i −0.0432925 0.196514i
\(731\) −1.26887 0.269706i −0.0469308 0.00997545i
\(732\) −8.45453 12.1621i −0.312488 0.449525i
\(733\) 33.9228 + 30.5442i 1.25297 + 1.12818i 0.986401 + 0.164359i \(0.0525557\pi\)
0.266566 + 0.963817i \(0.414111\pi\)
\(734\) 4.14292 39.4173i 0.152918 1.45492i
\(735\) 6.77108 + 21.8346i 0.249755 + 0.805381i
\(736\) 3.13598 + 29.8368i 0.115594 + 1.09980i
\(737\) −3.56989 + 4.91353i −0.131499 + 0.180992i
\(738\) 7.83405 + 11.7866i 0.288375 + 0.433870i
\(739\) 30.6267 22.2516i 1.12662 0.818538i 0.141421 0.989950i \(-0.454833\pi\)
0.985200 + 0.171412i \(0.0548328\pi\)
\(740\) 4.21356 3.10922i 0.154893 0.114297i
\(741\) −5.91116 10.7501i −0.217152 0.394914i
\(742\) 17.9533 + 16.1652i 0.659087 + 0.593445i
\(743\) 9.59806 5.54144i 0.352119 0.203296i −0.313499 0.949588i \(-0.601501\pi\)
0.665618 + 0.746293i \(0.268168\pi\)
\(744\) 2.92150 23.1428i 0.107107 0.848456i
\(745\) 0.120326 + 16.2625i 0.00440842 + 0.595810i
\(746\) −9.25424 + 28.4816i −0.338822 + 1.04279i
\(747\) −0.849113 2.14349i −0.0310674 0.0784261i
\(748\) −6.00510 8.26531i −0.219568 0.302210i
\(749\) −2.03090 + 3.51763i −0.0742076 + 0.128531i
\(750\) 13.1917 + 29.5224i 0.481695 + 1.07801i
\(751\) 14.7550 + 25.5564i 0.538417 + 0.932565i 0.998990 + 0.0449433i \(0.0143107\pi\)
−0.460573 + 0.887622i \(0.652356\pi\)
\(752\) 11.3290 25.4454i 0.413127 0.927898i
\(753\) 25.7556 7.77861i 0.938587 0.283468i
\(754\) −24.9009 27.6553i −0.906838 1.00715i
\(755\) 28.2598 16.5958i 1.02848 0.603983i
\(756\) 3.62228 2.30014i 0.131741 0.0836552i
\(757\) 27.7567i 1.00883i 0.863460 + 0.504417i \(0.168293\pi\)
−0.863460 + 0.504417i \(0.831707\pi\)
\(758\) 9.45774 44.4952i 0.343520 1.61614i
\(759\) 61.6395 + 1.28562i 2.23737 + 0.0466649i
\(760\) −0.689011 6.11960i −0.0249931 0.221981i
\(761\) 31.4195 + 13.9889i 1.13896 + 0.507096i 0.887516 0.460777i \(-0.152429\pi\)
0.251440 + 0.967873i \(0.419096\pi\)
\(762\) −1.26689 0.767103i −0.0458947 0.0277892i
\(763\) −3.72231 8.36043i −0.134757 0.302668i
\(764\) −0.119790 + 0.0870322i −0.00433384 + 0.00314872i
\(765\) −16.0685 + 6.50328i −0.580959 + 0.235126i
\(766\) −6.23353 4.52892i −0.225226 0.163637i
\(767\) −1.99756 + 9.39779i −0.0721278 + 0.339335i
\(768\) −12.0668 + 25.6492i −0.435422 + 0.925534i
\(769\) 8.16868 9.07224i 0.294570 0.327153i −0.577633 0.816296i \(-0.696024\pi\)
0.872204 + 0.489143i \(0.162690\pi\)
\(770\) −14.4822 + 13.2352i −0.521903 + 0.476963i
\(771\) 15.4036 16.4061i 0.554746 0.590851i
\(772\) −8.85434 + 7.97248i −0.318675 + 0.286936i
\(773\) 29.8261 + 41.0520i 1.07277 + 1.47654i 0.867241 + 0.497888i \(0.165891\pi\)
0.205527 + 0.978651i \(0.434109\pi\)
\(774\) −2.47943 + 0.419824i −0.0891214 + 0.0150903i
\(775\) −32.6513 6.43680i −1.17287 0.231217i
\(776\) 15.0169 26.0100i 0.539074 0.933703i
\(777\) 4.08048 3.52282i 0.146387 0.126380i
\(778\) −6.45102 30.3497i −0.231280 1.08809i
\(779\) −3.76139 + 0.799509i −0.134766 + 0.0286454i
\(780\) 15.7758 + 1.87303i 0.564865 + 0.0670653i
\(781\) −57.5109 12.2243i −2.05790 0.437421i
\(782\) 30.6225i 1.09506i
\(783\) 22.2338 0.937883i 0.794570 0.0335172i
\(784\) 23.6621 + 17.1915i 0.845075 + 0.613983i
\(785\) −7.83533 + 0.0579739i −0.279655 + 0.00206918i
\(786\) 20.2404 58.1394i 0.721951 2.07376i
\(787\) 13.4754 + 1.41632i 0.480345 + 0.0504863i 0.341607 0.939843i \(-0.389029\pi\)
0.138738 + 0.990329i \(0.455695\pi\)
\(788\) 12.4254 + 1.30596i 0.442637 + 0.0465230i
\(789\) −26.7419 30.9752i −0.952038 1.10275i
\(790\) 4.74677 + 14.2494i 0.168882 + 0.506972i
\(791\) −0.623606 0.453077i −0.0221729 0.0161095i
\(792\) 25.7092 + 16.3090i 0.913535 + 0.579517i
\(793\) 56.4560i 2.00481i
\(794\) 4.55645 + 0.968504i 0.161703 + 0.0343709i
\(795\) −45.9576 27.3646i −1.62995 0.970523i
\(796\) 5.22962 1.11159i 0.185359 0.0393992i
\(797\) 5.96671 + 28.0712i 0.211352 + 0.994332i 0.948053 + 0.318113i \(0.103049\pi\)
−0.736701 + 0.676219i \(0.763617\pi\)
\(798\) 0.773127 + 4.05090i 0.0273684 + 0.143400i
\(799\) 7.26273 12.5794i 0.256937 0.445028i
\(800\) 18.4595 + 10.2965i 0.652643 + 0.364035i
\(801\) −17.9186 + 48.2081i −0.633121 + 1.70335i
\(802\) 0.699582 + 0.962892i 0.0247031 + 0.0340009i
\(803\) −5.42746 + 4.88691i −0.191531 + 0.172455i
\(804\) −1.60959 0.377372i −0.0567658 0.0133089i
\(805\) 16.5201 1.86001i 0.582257 0.0655568i
\(806\) −38.6997 + 42.9804i −1.36314 + 1.51392i
\(807\) −10.6777 15.3602i −0.375872 0.540705i
\(808\) 2.10809 9.91781i 0.0741625 0.348907i
\(809\) 2.62525 + 1.90736i 0.0922989 + 0.0670591i 0.632978 0.774170i \(-0.281833\pi\)
−0.540679 + 0.841229i \(0.681833\pi\)
\(810\) −24.3172 + 23.1930i −0.854419 + 0.814920i
\(811\) 4.01621 2.91795i 0.141028 0.102463i −0.515034 0.857170i \(-0.672221\pi\)
0.656062 + 0.754707i \(0.272221\pi\)
\(812\) 1.43845 + 3.23080i 0.0504796 + 0.113379i
\(813\) 0.501401 24.0399i 0.0175849 0.843117i
\(814\) −22.7310 10.1205i −0.796719 0.354722i
\(815\) 21.3476 9.69445i 0.747774 0.339582i
\(816\) −11.4872 + 18.9715i −0.402133 + 0.664136i
\(817\) 0.142062 0.668349i 0.00497012 0.0233826i
\(818\) 13.8005i 0.482524i
\(819\) 16.3404 + 0.681920i 0.570979 + 0.0238282i
\(820\) 1.99169 4.56400i 0.0695530 0.159382i
\(821\) 27.1215 + 30.1215i 0.946547 + 1.05125i 0.998615 + 0.0526037i \(0.0167520\pi\)
−0.0520682 + 0.998644i \(0.516581\pi\)
\(822\) 44.2458 + 41.5421i 1.54325 + 1.44895i
\(823\) −11.6246 + 26.1092i −0.405207 + 0.910110i 0.589539 + 0.807740i \(0.299309\pi\)
−0.994746 + 0.102370i \(0.967357\pi\)
\(824\) −5.79018 10.0289i −0.201710 0.349373i
\(825\) 25.7439 34.9859i 0.896287 1.21805i
\(826\) 1.61486 2.79702i 0.0561881 0.0973207i
\(827\) −25.9315 35.6917i −0.901728 1.24112i −0.969914 0.243449i \(-0.921721\pi\)
0.0681858 0.997673i \(-0.478279\pi\)
\(828\) 6.18079 + 15.6027i 0.214797 + 0.542231i
\(829\) −9.82498 + 30.2382i −0.341236 + 1.05022i 0.622333 + 0.782753i \(0.286185\pi\)
−0.963568 + 0.267463i \(0.913815\pi\)
\(830\) −1.66941 + 2.33387i −0.0579462 + 0.0810099i
\(831\) 52.2909 21.9866i 1.81395 0.762707i
\(832\) −12.8502 + 7.41906i −0.445500 + 0.257210i
\(833\) 11.3350 + 10.2060i 0.392733 + 0.353618i
\(834\) 19.3834 + 0.404279i 0.671191 + 0.0139990i
\(835\) 3.99681 + 11.9981i 0.138315 + 0.415212i
\(836\) 4.35357 3.16306i 0.150572 0.109397i
\(837\) −5.06156 34.2129i −0.174953 1.18257i
\(838\) −15.4887 + 21.3184i −0.535049 + 0.736431i
\(839\) 0.723320 + 6.88193i 0.0249718 + 0.237591i 0.999887 + 0.0150153i \(0.00477968\pi\)
−0.974915 + 0.222575i \(0.928554\pi\)
\(840\) 7.45423 + 3.43975i 0.257195 + 0.118683i
\(841\) 1.11412 10.6001i 0.0384178 0.365521i
\(842\) −2.19263 1.97425i −0.0755629 0.0680372i
\(843\) 17.7386 1.49116i 0.610949 0.0513582i
\(844\) 2.24373 + 0.476920i 0.0772325 + 0.0164163i
\(845\) 23.5515 + 20.8925i 0.810198 + 0.718723i
\(846\) 4.10845 27.8571i 0.141252 0.957746i
\(847\) 14.1049 + 4.58295i 0.484649 + 0.157472i
\(848\) −68.0581 + 7.15319i −2.33712 + 0.245642i
\(849\) −6.16329 2.89955i −0.211523 0.0995122i
\(850\) 17.6400 + 12.4216i 0.605048 + 0.426058i
\(851\) 10.5422 + 18.2595i 0.361380 + 0.625929i
\(852\) −3.00037 15.7208i −0.102791 0.538586i
\(853\) −15.1675 + 13.6569i −0.519325 + 0.467602i −0.886618 0.462503i \(-0.846951\pi\)
0.367293 + 0.930105i \(0.380285\pi\)
\(854\) −5.86456 + 18.0493i −0.200681 + 0.617633i
\(855\) −3.42546 8.46375i −0.117148 0.289454i
\(856\) −2.42428 7.46116i −0.0828601 0.255017i
\(857\) 22.6641 + 13.0851i 0.774190 + 0.446979i 0.834367 0.551209i \(-0.185833\pi\)
−0.0601773 + 0.998188i \(0.519167\pi\)
\(858\) −29.2588 69.5865i −0.998881 2.37564i
\(859\) 3.10459 29.5382i 0.105927 1.00783i −0.804442 0.594032i \(-0.797535\pi\)
0.910369 0.413798i \(-0.135798\pi\)
\(860\) 0.596907 + 0.653149i 0.0203544 + 0.0222722i
\(861\) 1.68545 4.84135i 0.0574399 0.164993i
\(862\) −23.7360 53.3119i −0.808451 1.81581i
\(863\) 19.7908 27.2397i 0.673687 0.927251i −0.326150 0.945318i \(-0.605751\pi\)
0.999837 + 0.0180675i \(0.00575137\pi\)
\(864\) −3.65743 + 21.6596i −0.124428 + 0.736873i
\(865\) 39.1674 + 17.0923i 1.33173 + 0.581157i
\(866\) 16.8414 7.49825i 0.572292 0.254801i
\(867\) 10.8083 14.2421i 0.367071 0.483688i
\(868\) 4.75996 2.74817i 0.161564 0.0932788i
\(869\) 13.5001 14.9933i 0.457959 0.508615i
\(870\) −15.9768 22.6242i −0.541664 0.767031i
\(871\) −4.21638 4.68277i −0.142867 0.158670i
\(872\) 16.8107 + 5.46212i 0.569282 + 0.184971i
\(873\) 11.0664 43.1329i 0.374540 1.45983i
\(874\) −16.1297 −0.545596
\(875\) 5.62972 10.2709i 0.190319 0.347219i
\(876\) −1.79889 0.846298i −0.0607790 0.0285937i
\(877\) 22.2232 49.9142i 0.750426 1.68548i 0.0225776 0.999745i \(-0.492813\pi\)
0.727848 0.685738i \(-0.240521\pi\)
\(878\) −3.63001 17.0779i −0.122507 0.576350i
\(879\) −3.72821 + 3.97086i −0.125749 + 0.133934i
\(880\) −0.411181 55.5723i −0.0138609 1.87334i
\(881\) 6.86980 + 21.1431i 0.231449 + 0.712328i 0.997573 + 0.0696342i \(0.0221832\pi\)
−0.766123 + 0.642694i \(0.777817\pi\)
\(882\) 27.7156 + 10.3017i 0.933233 + 0.346875i
\(883\) −23.1899 + 7.53485i −0.780401 + 0.253568i −0.672012 0.740541i \(-0.734569\pi\)
−0.108390 + 0.994108i \(0.534569\pi\)
\(884\) 9.68334 4.31130i 0.325686 0.145005i
\(885\) −2.30098 + 6.77034i −0.0773465 + 0.227582i
\(886\) −6.49284 2.89080i −0.218131 0.0971183i
\(887\) −45.7513 4.80865i −1.53618 0.161459i −0.701689 0.712483i \(-0.747570\pi\)
−0.834489 + 0.551025i \(0.814237\pi\)
\(888\) −0.217115 + 10.4097i −0.00728591 + 0.349327i
\(889\) 0.0560753 + 0.533521i 0.00188070 + 0.0178937i
\(890\) 62.5114 13.7714i 2.09539 0.461618i
\(891\) 43.2190 + 13.0316i 1.44789 + 0.436575i
\(892\) 6.63314 2.15524i 0.222094 0.0721627i
\(893\) 6.62593 + 3.82548i 0.221728 + 0.128015i
\(894\) 16.7560 + 12.7162i 0.560406 + 0.425292i
\(895\) 14.8561 13.5769i 0.496585 0.453825i
\(896\) 13.5427 2.87859i 0.452429 0.0961668i
\(897\) −14.6010 + 62.2769i −0.487514 + 2.07937i
\(898\) −35.4073 + 3.72146i −1.18156 + 0.124187i
\(899\) 28.5054 0.950709
\(900\) 11.4951 + 2.76860i 0.383169 + 0.0922867i
\(901\) −35.6875 −1.18892
\(902\) −23.5319 + 2.47330i −0.783526 + 0.0823519i
\(903\) 0.664060 + 0.623482i 0.0220985 + 0.0207482i
\(904\) 1.45626 0.309537i 0.0484343 0.0102950i
\(905\) 6.28069 30.6621i 0.208777 1.01924i
\(906\) 5.30895 42.0551i 0.176378 1.39719i
\(907\) 14.3340 + 8.27574i 0.475952 + 0.274791i 0.718728 0.695291i \(-0.244725\pi\)
−0.242776 + 0.970082i \(0.578058\pi\)
\(908\) −7.07301 + 2.29816i −0.234726 + 0.0762672i
\(909\) −0.946648 15.0035i −0.0313983 0.497633i
\(910\) −10.3076 17.5521i −0.341694 0.581847i
\(911\) 0.424712 + 4.04087i 0.0140714 + 0.133880i 0.999302 0.0373514i \(-0.0118921\pi\)
−0.985231 + 0.171231i \(0.945225\pi\)
\(912\) −9.99284 6.05065i −0.330896 0.200357i
\(913\) 3.83349 + 0.402916i 0.126870 + 0.0133346i
\(914\) 42.0397 + 18.7173i 1.39055 + 0.619113i
\(915\) 4.95391 41.7249i 0.163771 1.37938i
\(916\) 2.56999 1.14423i 0.0849148 0.0378065i
\(917\) −21.2075 + 6.89073i −0.700333 + 0.227552i
\(918\) −6.02365 + 21.5968i −0.198810 + 0.712800i
\(919\) 9.59939 + 29.5439i 0.316655 + 0.974563i 0.975068 + 0.221906i \(0.0712279\pi\)
−0.658413 + 0.752657i \(0.728772\pi\)
\(920\) −18.6806 + 26.1158i −0.615880 + 0.861012i
\(921\) 7.06336 + 23.3874i 0.232746 + 0.770641i
\(922\) 9.68273 + 45.5536i 0.318884 + 1.50023i
\(923\) 24.8115 55.7274i 0.816679 1.83429i
\(924\) 0.600934 + 7.14862i 0.0197693 + 0.235172i
\(925\) 14.7947 + 1.33396i 0.486446 + 0.0438605i
\(926\) −3.22453 −0.105965
\(927\) −12.2695 12.0109i −0.402983 0.394488i
\(928\) −17.2185 5.59464i −0.565226 0.183653i
\(929\) 10.7178 + 11.9033i 0.351640 + 0.390536i 0.892852 0.450351i \(-0.148701\pi\)
−0.541212 + 0.840886i \(0.682034\pi\)
\(930\) −32.3732 + 28.3696i −1.06156 + 0.930277i
\(931\) −5.37581 + 5.97044i −0.176185 + 0.195673i
\(932\) −10.1302 + 5.84866i −0.331825 + 0.191579i
\(933\) −38.5332 4.86435i −1.26152 0.159252i
\(934\) 48.7242 21.6934i 1.59430 0.709830i
\(935\) 2.81606 28.8444i 0.0920950 0.943313i
\(936\) −22.0968 + 22.5726i −0.722257 + 0.737810i
\(937\) −8.05137 + 11.0818i −0.263027 + 0.362025i −0.920020 0.391871i \(-0.871828\pi\)
0.656993 + 0.753896i \(0.271828\pi\)
\(938\) 0.861560 + 1.93510i 0.0281309 + 0.0631831i
\(939\) 15.3635 + 17.7956i 0.501370 + 0.580737i
\(940\) −9.02104 + 4.09667i −0.294234 + 0.133619i
\(941\) −5.19170 + 49.3957i −0.169244 + 1.61025i 0.499197 + 0.866489i \(0.333628\pi\)
−0.668441 + 0.743765i \(0.733038\pi\)
\(942\) −6.12671 + 8.07315i −0.199619 + 0.263037i
\(943\) 17.3638 + 10.0250i 0.565443 + 0.326459i
\(944\) 2.82710 + 8.70092i 0.0920142 + 0.283191i
\(945\) 12.0168 + 1.93783i 0.390908 + 0.0630375i
\(946\) 1.29921 3.99856i 0.0422410 0.130004i
\(947\) 13.4147 12.0787i 0.435919 0.392504i −0.421744 0.906715i \(-0.638582\pi\)
0.857664 + 0.514211i \(0.171915\pi\)
\(948\) 5.18659 + 1.80564i 0.168453 + 0.0586444i
\(949\) −3.78867 6.56217i −0.122985 0.213017i
\(950\) −6.54282 + 9.29151i −0.212277 + 0.301456i
\(951\) 1.23238 + 14.6601i 0.0399625 + 0.475388i
\(952\) 5.44753 0.572558i 0.176555 0.0185567i
\(953\) −0.946134 0.307417i −0.0306483 0.00995823i 0.293653 0.955912i \(-0.405129\pi\)
−0.324301 + 0.945954i \(0.605129\pi\)
\(954\) −64.3194 + 25.4793i −2.08242 + 0.824921i
\(955\) −0.418043 0.0408133i −0.0135276 0.00132069i
\(956\) −11.6431 2.47482i −0.376565 0.0800414i
\(957\) −15.8383 + 33.6659i −0.511978 + 1.08826i
\(958\) 40.0275 + 36.0409i 1.29323 + 1.16443i
\(959\) 2.29791 21.8631i 0.0742033 0.705997i
\(960\) −10.1482 + 4.35562i −0.327531 + 0.140577i
\(961\) −1.39040 13.2288i −0.0448516 0.426735i
\(962\) 15.1740 20.8852i 0.489229 0.673365i
\(963\) −6.43862 9.68713i −0.207482 0.312163i
\(964\) 0.0284930 0.0207014i 0.000917699 0.000666747i
\(965\) −33.7980 + 0.250072i −1.08800 + 0.00805011i
\(966\) 11.1372 18.3935i 0.358335 0.591802i
\(967\) −0.332935 0.299776i −0.0107065 0.00964014i 0.663760 0.747946i \(-0.268960\pi\)
−0.674466 + 0.738305i \(0.735626\pi\)
\(968\) −24.8070 + 14.3223i −0.797326 + 0.460337i
\(969\) −4.85285 3.68282i −0.155896 0.118309i
\(970\) −52.5813 + 17.5158i −1.68828 + 0.562400i
\(971\) −0.744588 + 2.29161i −0.0238950 + 0.0735411i −0.962293 0.272015i \(-0.912310\pi\)
0.938398 + 0.345557i \(0.112310\pi\)
\(972\) 1.28990 + 12.2197i 0.0413737 + 0.391948i
\(973\) −4.12775 5.68136i −0.132330 0.182136i
\(974\) −20.7844 + 35.9996i −0.665975 + 1.15350i
\(975\) 29.9518 + 33.6728i 0.959226 + 1.07839i
\(976\) −26.8792 46.5562i −0.860384 1.49023i
\(977\) −13.2366 + 29.7299i −0.423476 + 0.951142i 0.568260 + 0.822849i \(0.307617\pi\)
−0.991736 + 0.128294i \(0.959050\pi\)
\(978\) 6.92216 29.5247i 0.221346 0.944097i
\(979\) −57.5358 63.9000i −1.83885 2.04225i
\(980\) −2.23828 10.1601i −0.0714994 0.324552i
\(981\) 26.1845 + 1.09274i 0.836007 + 0.0348884i
\(982\) 2.17473i 0.0693983i
\(983\) 6.11836 28.7846i 0.195145 0.918087i −0.766170 0.642638i \(-0.777840\pi\)
0.961316 0.275449i \(-0.0888266\pi\)
\(984\) 4.77072 + 8.67606i 0.152085 + 0.276583i
\(985\) 23.9094 + 26.1622i 0.761818 + 0.833598i
\(986\) −16.8819 7.51633i −0.537631 0.239369i
\(987\) −8.93746 + 4.91446i −0.284482 + 0.156429i
\(988\) 2.27088 + 5.10049i 0.0722464 + 0.162268i
\(989\) −2.88222 + 2.09405i −0.0916491 + 0.0665870i
\(990\) −15.5182 53.9967i −0.493201 1.71613i
\(991\) −28.0855 20.4053i −0.892166 0.648196i 0.0442761 0.999019i \(-0.485902\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(992\) −5.85008 + 27.5224i −0.185740 + 0.873838i
\(993\) −35.7483 + 3.00511i −1.13444 + 0.0953641i
\(994\) −13.7212 + 15.2390i −0.435211 + 0.483351i
\(995\) 13.1903 + 7.48586i 0.418161 + 0.237318i
\(996\) 0.303356 + 1.00444i 0.00961221 + 0.0318268i
\(997\) 37.5854 33.8421i 1.19034 1.07179i 0.194482 0.980906i \(-0.437698\pi\)
0.995862 0.0908836i \(-0.0289691\pi\)
\(998\) 15.8267 + 21.7835i 0.500984 + 0.689546i
\(999\) 3.84317 + 14.9514i 0.121593 + 0.473042i
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 225.2.u.a.214.8 yes 224
3.2 odd 2 675.2.y.a.289.21 224
9.4 even 3 inner 225.2.u.a.139.21 yes 224
9.5 odd 6 675.2.y.a.64.8 224
25.9 even 10 inner 225.2.u.a.34.21 224
75.59 odd 10 675.2.y.a.559.8 224
225.59 odd 30 675.2.y.a.334.21 224
225.184 even 30 inner 225.2.u.a.184.8 yes 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.u.a.34.21 224 25.9 even 10 inner
225.2.u.a.139.21 yes 224 9.4 even 3 inner
225.2.u.a.184.8 yes 224 225.184 even 30 inner
225.2.u.a.214.8 yes 224 1.1 even 1 trivial
675.2.y.a.64.8 224 9.5 odd 6
675.2.y.a.289.21 224 3.2 odd 2
675.2.y.a.334.21 224 225.59 odd 30
675.2.y.a.559.8 224 75.59 odd 10