Properties

Label 403.2.h.a.222.1
Level $403$
Weight $2$
Character 403.222
Analytic conductor $3.218$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [403,2,Mod(118,403)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(403, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("403.118");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(15\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 222.1
Character \(\chi\) \(=\) 403.222
Dual form 403.2.h.a.118.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.75405 q^{2} +(1.04794 - 1.81508i) q^{3} +5.58479 q^{4} +(1.03612 + 1.79462i) q^{5} +(-2.88606 + 4.99881i) q^{6} +(2.05805 - 3.56464i) q^{7} -9.87267 q^{8} +(-0.696336 - 1.20609i) q^{9} +O(q^{10})\) \(q-2.75405 q^{2} +(1.04794 - 1.81508i) q^{3} +5.58479 q^{4} +(1.03612 + 1.79462i) q^{5} +(-2.88606 + 4.99881i) q^{6} +(2.05805 - 3.56464i) q^{7} -9.87267 q^{8} +(-0.696336 - 1.20609i) q^{9} +(-2.85353 - 4.94246i) q^{10} +(-2.89835 - 5.02008i) q^{11} +(5.85249 - 10.1368i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-5.66796 + 9.81719i) q^{14} +4.34316 q^{15} +16.0203 q^{16} +(0.558338 - 0.967070i) q^{17} +(1.91774 + 3.32163i) q^{18} +(-1.17562 + 2.03624i) q^{19} +(5.78652 + 10.0226i) q^{20} +(-4.31340 - 7.47102i) q^{21} +(7.98219 + 13.8256i) q^{22} +1.07915 q^{23} +(-10.3459 + 17.9197i) q^{24} +(0.352899 - 0.611239i) q^{25} +(-1.37702 - 2.38508i) q^{26} +3.36875 q^{27} +(11.4937 - 19.9078i) q^{28} -1.28942 q^{29} -11.9613 q^{30} +(-3.68732 + 4.17177i) q^{31} -24.3752 q^{32} -12.1491 q^{33} +(-1.53769 + 2.66336i) q^{34} +8.52955 q^{35} +(-3.88889 - 6.73575i) q^{36} +(1.12141 - 1.94234i) q^{37} +(3.23772 - 5.60790i) q^{38} +2.09587 q^{39} +(-10.2293 - 17.7177i) q^{40} +(-1.14144 - 1.97703i) q^{41} +(11.8793 + 20.5756i) q^{42} +(1.75743 - 3.04395i) q^{43} +(-16.1866 - 28.0361i) q^{44} +(1.44298 - 2.49931i) q^{45} -2.97204 q^{46} +9.81990 q^{47} +(16.7882 - 29.0780i) q^{48} +(-4.97111 - 8.61021i) q^{49} +(-0.971902 + 1.68338i) q^{50} +(-1.17020 - 2.02685i) q^{51} +(2.79239 + 4.83657i) q^{52} +(0.394310 + 0.682964i) q^{53} -9.27771 q^{54} +(6.00608 - 10.4028i) q^{55} +(-20.3184 + 35.1925i) q^{56} +(2.46395 + 4.26769i) q^{57} +3.55113 q^{58} +(0.600735 - 1.04050i) q^{59} +24.2556 q^{60} -14.8169 q^{61} +(10.1551 - 11.4893i) q^{62} -5.73236 q^{63} +35.0900 q^{64} +(-1.03612 + 1.79462i) q^{65} +33.4593 q^{66} +(-3.85317 - 6.67389i) q^{67} +(3.11820 - 5.40088i) q^{68} +(1.13088 - 1.95875i) q^{69} -23.4908 q^{70} +(6.95281 + 12.0426i) q^{71} +(6.87470 + 11.9073i) q^{72} +(0.390898 + 0.677056i) q^{73} +(-3.08842 + 5.34930i) q^{74} +(-0.739631 - 1.28108i) q^{75} +(-6.56560 + 11.3720i) q^{76} -23.8597 q^{77} -5.77213 q^{78} +(-0.613563 + 1.06272i) q^{79} +(16.5990 + 28.7502i) q^{80} +(5.61924 - 9.73281i) q^{81} +(3.14358 + 5.44484i) q^{82} +(1.22711 + 2.12541i) q^{83} +(-24.0894 - 41.7241i) q^{84} +2.31403 q^{85} +(-4.84004 + 8.38319i) q^{86} +(-1.35123 + 2.34040i) q^{87} +(28.6144 + 49.5616i) q^{88} -17.3100 q^{89} +(-3.97403 + 6.88323i) q^{90} +4.11609 q^{91} +6.02685 q^{92} +(3.70800 + 11.0645i) q^{93} -27.0445 q^{94} -4.87236 q^{95} +(-25.5436 + 44.2429i) q^{96} +1.70614 q^{97} +(13.6907 + 23.7129i) q^{98} +(-4.03644 + 6.99133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.75405 −1.94741 −0.973703 0.227820i \(-0.926840\pi\)
−0.973703 + 0.227820i \(0.926840\pi\)
\(3\) 1.04794 1.81508i 0.605026 1.04794i −0.387022 0.922071i \(-0.626496\pi\)
0.992047 0.125865i \(-0.0401705\pi\)
\(4\) 5.58479 2.79239
\(5\) 1.03612 + 1.79462i 0.463368 + 0.802577i 0.999126 0.0417943i \(-0.0133074\pi\)
−0.535758 + 0.844372i \(0.679974\pi\)
\(6\) −2.88606 + 4.99881i −1.17823 + 2.04076i
\(7\) 2.05805 3.56464i 0.777868 1.34731i −0.155300 0.987867i \(-0.549634\pi\)
0.933168 0.359440i \(-0.117032\pi\)
\(8\) −9.87267 −3.49052
\(9\) −0.696336 1.20609i −0.232112 0.402030i
\(10\) −2.85353 4.94246i −0.902366 1.56294i
\(11\) −2.89835 5.02008i −0.873884 1.51361i −0.857947 0.513739i \(-0.828260\pi\)
−0.0159376 0.999873i \(-0.505073\pi\)
\(12\) 5.85249 10.1368i 1.68947 2.92625i
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i
\(14\) −5.66796 + 9.81719i −1.51483 + 2.62376i
\(15\) 4.34316 1.12140
\(16\) 16.0203 4.00506
\(17\) 0.558338 0.967070i 0.135417 0.234549i −0.790340 0.612669i \(-0.790096\pi\)
0.925757 + 0.378120i \(0.123429\pi\)
\(18\) 1.91774 + 3.32163i 0.452016 + 0.782915i
\(19\) −1.17562 + 2.03624i −0.269706 + 0.467145i −0.968786 0.247899i \(-0.920260\pi\)
0.699080 + 0.715044i \(0.253593\pi\)
\(20\) 5.78652 + 10.0226i 1.29391 + 2.24111i
\(21\) −4.31340 7.47102i −0.941261 1.63031i
\(22\) 7.98219 + 13.8256i 1.70181 + 2.94762i
\(23\) 1.07915 0.225019 0.112510 0.993651i \(-0.464111\pi\)
0.112510 + 0.993651i \(0.464111\pi\)
\(24\) −10.3459 + 17.9197i −2.11185 + 3.65784i
\(25\) 0.352899 0.611239i 0.0705798 0.122248i
\(26\) −1.37702 2.38508i −0.270057 0.467752i
\(27\) 3.36875 0.648317
\(28\) 11.4937 19.9078i 2.17211 3.76221i
\(29\) −1.28942 −0.239439 −0.119720 0.992808i \(-0.538200\pi\)
−0.119720 + 0.992808i \(0.538200\pi\)
\(30\) −11.9613 −2.18382
\(31\) −3.68732 + 4.17177i −0.662263 + 0.749272i
\(32\) −24.3752 −4.30897
\(33\) −12.1491 −2.11489
\(34\) −1.53769 + 2.66336i −0.263712 + 0.456762i
\(35\) 8.52955 1.44176
\(36\) −3.88889 6.73575i −0.648148 1.12262i
\(37\) 1.12141 1.94234i 0.184359 0.319319i −0.759002 0.651089i \(-0.774313\pi\)
0.943360 + 0.331770i \(0.107646\pi\)
\(38\) 3.23772 5.60790i 0.525228 0.909721i
\(39\) 2.09587 0.335608
\(40\) −10.2293 17.7177i −1.61739 2.80141i
\(41\) −1.14144 1.97703i −0.178263 0.308761i 0.763023 0.646372i \(-0.223714\pi\)
−0.941286 + 0.337611i \(0.890381\pi\)
\(42\) 11.8793 + 20.5756i 1.83302 + 3.17488i
\(43\) 1.75743 3.04395i 0.268005 0.464198i −0.700342 0.713808i \(-0.746969\pi\)
0.968347 + 0.249610i \(0.0803023\pi\)
\(44\) −16.1866 28.0361i −2.44023 4.22660i
\(45\) 1.44298 2.49931i 0.215107 0.372575i
\(46\) −2.97204 −0.438204
\(47\) 9.81990 1.43238 0.716190 0.697906i \(-0.245885\pi\)
0.716190 + 0.697906i \(0.245885\pi\)
\(48\) 16.7882 29.0780i 2.42317 4.19705i
\(49\) −4.97111 8.61021i −0.710158 1.23003i
\(50\) −0.971902 + 1.68338i −0.137448 + 0.238066i
\(51\) −1.17020 2.02685i −0.163861 0.283816i
\(52\) 2.79239 + 4.83657i 0.387235 + 0.670711i
\(53\) 0.394310 + 0.682964i 0.0541626 + 0.0938124i 0.891835 0.452360i \(-0.149418\pi\)
−0.837673 + 0.546172i \(0.816084\pi\)
\(54\) −9.27771 −1.26254
\(55\) 6.00608 10.4028i 0.809860 1.40272i
\(56\) −20.3184 + 35.1925i −2.71516 + 4.70280i
\(57\) 2.46395 + 4.26769i 0.326358 + 0.565269i
\(58\) 3.55113 0.466286
\(59\) 0.600735 1.04050i 0.0782090 0.135462i −0.824268 0.566199i \(-0.808413\pi\)
0.902477 + 0.430738i \(0.141747\pi\)
\(60\) 24.2556 3.13138
\(61\) −14.8169 −1.89710 −0.948552 0.316622i \(-0.897451\pi\)
−0.948552 + 0.316622i \(0.897451\pi\)
\(62\) 10.1551 11.4893i 1.28970 1.45914i
\(63\) −5.73236 −0.722210
\(64\) 35.0900 4.38625
\(65\) −1.03612 + 1.79462i −0.128515 + 0.222595i
\(66\) 33.4593 4.11855
\(67\) −3.85317 6.67389i −0.470740 0.815346i 0.528700 0.848809i \(-0.322680\pi\)
−0.999440 + 0.0334631i \(0.989346\pi\)
\(68\) 3.11820 5.40088i 0.378137 0.654953i
\(69\) 1.13088 1.95875i 0.136142 0.235806i
\(70\) −23.4908 −2.80769
\(71\) 6.95281 + 12.0426i 0.825147 + 1.42920i 0.901807 + 0.432139i \(0.142241\pi\)
−0.0766597 + 0.997057i \(0.524426\pi\)
\(72\) 6.87470 + 11.9073i 0.810191 + 1.40329i
\(73\) 0.390898 + 0.677056i 0.0457512 + 0.0792434i 0.887994 0.459855i \(-0.152099\pi\)
−0.842243 + 0.539098i \(0.818765\pi\)
\(74\) −3.08842 + 5.34930i −0.359021 + 0.621843i
\(75\) −0.739631 1.28108i −0.0854052 0.147926i
\(76\) −6.56560 + 11.3720i −0.753126 + 1.30445i
\(77\) −23.8597 −2.71907
\(78\) −5.77213 −0.653565
\(79\) −0.613563 + 1.06272i −0.0690312 + 0.119566i −0.898475 0.439024i \(-0.855324\pi\)
0.829444 + 0.558590i \(0.188657\pi\)
\(80\) 16.5990 + 28.7502i 1.85582 + 3.21437i
\(81\) 5.61924 9.73281i 0.624360 1.08142i
\(82\) 3.14358 + 5.44484i 0.347150 + 0.601282i
\(83\) 1.22711 + 2.12541i 0.134692 + 0.233294i 0.925480 0.378797i \(-0.123662\pi\)
−0.790787 + 0.612091i \(0.790329\pi\)
\(84\) −24.0894 41.7241i −2.62837 4.55247i
\(85\) 2.31403 0.250991
\(86\) −4.84004 + 8.38319i −0.521915 + 0.903983i
\(87\) −1.35123 + 2.34040i −0.144867 + 0.250917i
\(88\) 28.6144 + 49.5616i 3.05031 + 5.28329i
\(89\) −17.3100 −1.83485 −0.917427 0.397903i \(-0.869738\pi\)
−0.917427 + 0.397903i \(0.869738\pi\)
\(90\) −3.97403 + 6.88323i −0.418900 + 0.725556i
\(91\) 4.11609 0.431484
\(92\) 6.02685 0.628342
\(93\) 3.70800 + 11.0645i 0.384502 + 1.14734i
\(94\) −27.0445 −2.78942
\(95\) −4.87236 −0.499893
\(96\) −25.5436 + 44.2429i −2.60704 + 4.51552i
\(97\) 1.70614 0.173233 0.0866163 0.996242i \(-0.472395\pi\)
0.0866163 + 0.996242i \(0.472395\pi\)
\(98\) 13.6907 + 23.7129i 1.38297 + 2.39537i
\(99\) −4.03644 + 6.99133i −0.405678 + 0.702655i
\(100\) 1.97087 3.41364i 0.197087 0.341364i
\(101\) 10.4932 1.04411 0.522055 0.852912i \(-0.325166\pi\)
0.522055 + 0.852912i \(0.325166\pi\)
\(102\) 3.22280 + 5.58205i 0.319105 + 0.552705i
\(103\) 2.33045 + 4.03646i 0.229626 + 0.397724i 0.957697 0.287778i \(-0.0929164\pi\)
−0.728071 + 0.685501i \(0.759583\pi\)
\(104\) −4.93634 8.54999i −0.484048 0.838395i
\(105\) 8.93842 15.4818i 0.872300 1.51087i
\(106\) −1.08595 1.88092i −0.105477 0.182691i
\(107\) 9.27609 16.0667i 0.896753 1.55322i 0.0651337 0.997877i \(-0.479253\pi\)
0.831620 0.555346i \(-0.187414\pi\)
\(108\) 18.8138 1.81035
\(109\) 14.0939 1.34995 0.674973 0.737842i \(-0.264155\pi\)
0.674973 + 0.737842i \(0.264155\pi\)
\(110\) −16.5411 + 28.6499i −1.57713 + 2.73166i
\(111\) −2.35033 4.07089i −0.223083 0.386392i
\(112\) 32.9704 57.1065i 3.11541 5.39605i
\(113\) 7.04820 + 12.2078i 0.663039 + 1.14842i 0.979813 + 0.199916i \(0.0640668\pi\)
−0.316775 + 0.948501i \(0.602600\pi\)
\(114\) −6.78584 11.7534i −0.635553 1.10081i
\(115\) 1.11814 + 1.93667i 0.104267 + 0.180595i
\(116\) −7.20114 −0.668609
\(117\) 0.696336 1.20609i 0.0643763 0.111503i
\(118\) −1.65445 + 2.86560i −0.152305 + 0.263800i
\(119\) −2.29817 3.98055i −0.210673 0.364896i
\(120\) −42.8786 −3.91426
\(121\) −11.3008 + 19.5736i −1.02735 + 1.77942i
\(122\) 40.8063 3.69443
\(123\) −4.78462 −0.431415
\(124\) −20.5929 + 23.2984i −1.84930 + 2.09226i
\(125\) 11.8238 1.05755
\(126\) 15.7872 1.40644
\(127\) −7.46945 + 12.9375i −0.662806 + 1.14801i 0.317069 + 0.948403i \(0.397301\pi\)
−0.979875 + 0.199612i \(0.936032\pi\)
\(128\) −47.8892 −4.23285
\(129\) −3.68334 6.37973i −0.324300 0.561704i
\(130\) 2.85353 4.94246i 0.250271 0.433483i
\(131\) −2.83417 + 4.90892i −0.247622 + 0.428895i −0.962866 0.269981i \(-0.912983\pi\)
0.715243 + 0.698876i \(0.246316\pi\)
\(132\) −67.8502 −5.90560
\(133\) 4.83897 + 8.38134i 0.419592 + 0.726755i
\(134\) 10.6118 + 18.3802i 0.916722 + 1.58781i
\(135\) 3.49044 + 6.04562i 0.300409 + 0.520324i
\(136\) −5.51229 + 9.54757i −0.472675 + 0.818697i
\(137\) 1.35879 + 2.35350i 0.116089 + 0.201073i 0.918215 0.396083i \(-0.129631\pi\)
−0.802125 + 0.597156i \(0.796297\pi\)
\(138\) −3.11451 + 5.39449i −0.265125 + 0.459209i
\(139\) −2.02589 −0.171834 −0.0859168 0.996302i \(-0.527382\pi\)
−0.0859168 + 0.996302i \(0.527382\pi\)
\(140\) 47.6357 4.02595
\(141\) 10.2906 17.8239i 0.866626 1.50104i
\(142\) −19.1484 33.1660i −1.60690 2.78323i
\(143\) 2.89835 5.02008i 0.242372 0.419800i
\(144\) −11.1555 19.3219i −0.929623 1.61015i
\(145\) −1.33600 2.31402i −0.110949 0.192169i
\(146\) −1.07655 1.86465i −0.0890962 0.154319i
\(147\) −20.8376 −1.71866
\(148\) 6.26283 10.8475i 0.514802 0.891663i
\(149\) 5.04899 8.74511i 0.413630 0.716427i −0.581654 0.813436i \(-0.697594\pi\)
0.995284 + 0.0970089i \(0.0309275\pi\)
\(150\) 2.03698 + 3.52815i 0.166319 + 0.288072i
\(151\) 19.3862 1.57762 0.788812 0.614634i \(-0.210696\pi\)
0.788812 + 0.614634i \(0.210696\pi\)
\(152\) 11.6065 20.1031i 0.941415 1.63058i
\(153\) −1.55516 −0.125727
\(154\) 65.7108 5.29513
\(155\) −11.3072 2.29487i −0.908220 0.184329i
\(156\) 11.7050 0.937149
\(157\) −12.3098 −0.982432 −0.491216 0.871038i \(-0.663447\pi\)
−0.491216 + 0.871038i \(0.663447\pi\)
\(158\) 1.68978 2.92679i 0.134432 0.232843i
\(159\) 1.65284 0.131079
\(160\) −25.2557 43.7442i −1.99664 3.45828i
\(161\) 2.22095 3.84680i 0.175035 0.303170i
\(162\) −15.4757 + 26.8046i −1.21588 + 2.10597i
\(163\) 17.4732 1.36861 0.684304 0.729197i \(-0.260106\pi\)
0.684304 + 0.729197i \(0.260106\pi\)
\(164\) −6.37470 11.0413i −0.497780 0.862181i
\(165\) −12.5880 21.8030i −0.979972 1.69736i
\(166\) −3.37951 5.85349i −0.262301 0.454319i
\(167\) −0.0455449 + 0.0788861i −0.00352437 + 0.00610439i −0.867782 0.496945i \(-0.834455\pi\)
0.864258 + 0.503049i \(0.167789\pi\)
\(168\) 42.5848 + 73.7590i 3.28549 + 5.69063i
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) −6.37294 −0.488782
\(171\) 3.27451 0.250408
\(172\) 9.81485 16.9998i 0.748375 1.29622i
\(173\) −4.01072 6.94676i −0.304929 0.528153i 0.672317 0.740264i \(-0.265299\pi\)
−0.977246 + 0.212111i \(0.931966\pi\)
\(174\) 3.72135 6.44557i 0.282115 0.488637i
\(175\) −1.45257 2.51592i −0.109804 0.190185i
\(176\) −46.4322 80.4230i −3.49996 6.06211i
\(177\) −1.25906 2.18076i −0.0946369 0.163916i
\(178\) 47.6725 3.57321
\(179\) −6.64920 + 11.5168i −0.496985 + 0.860803i −0.999994 0.00347806i \(-0.998893\pi\)
0.503009 + 0.864281i \(0.332226\pi\)
\(180\) 8.05873 13.9581i 0.600662 1.04038i
\(181\) 10.7606 + 18.6379i 0.799830 + 1.38535i 0.919727 + 0.392560i \(0.128410\pi\)
−0.119897 + 0.992786i \(0.538256\pi\)
\(182\) −11.3359 −0.840274
\(183\) −15.5271 + 26.8937i −1.14780 + 1.98804i
\(184\) −10.6541 −0.785434
\(185\) 4.64767 0.341704
\(186\) −10.2120 30.4722i −0.748782 2.23433i
\(187\) −6.47303 −0.473355
\(188\) 54.8420 3.99976
\(189\) 6.93305 12.0084i 0.504305 0.873482i
\(190\) 13.4187 0.973496
\(191\) 4.45247 + 7.71191i 0.322170 + 0.558014i 0.980935 0.194334i \(-0.0622545\pi\)
−0.658766 + 0.752348i \(0.728921\pi\)
\(192\) 36.7721 63.6911i 2.65380 4.59651i
\(193\) −8.84306 + 15.3166i −0.636538 + 1.10252i 0.349649 + 0.936881i \(0.386301\pi\)
−0.986187 + 0.165635i \(0.947033\pi\)
\(194\) −4.69880 −0.337354
\(195\) 2.17158 + 3.76128i 0.155510 + 0.269351i
\(196\) −27.7626 48.0862i −1.98304 3.43473i
\(197\) 3.12237 + 5.40811i 0.222460 + 0.385312i 0.955554 0.294815i \(-0.0952580\pi\)
−0.733094 + 0.680127i \(0.761925\pi\)
\(198\) 11.1166 19.2545i 0.790020 1.36835i
\(199\) −6.98550 12.0992i −0.495189 0.857692i 0.504796 0.863239i \(-0.331568\pi\)
−0.999985 + 0.00554643i \(0.998235\pi\)
\(200\) −3.48406 + 6.03457i −0.246360 + 0.426708i
\(201\) −16.1515 −1.13924
\(202\) −28.8987 −2.03331
\(203\) −2.65369 + 4.59632i −0.186252 + 0.322599i
\(204\) −6.53534 11.3195i −0.457565 0.792526i
\(205\) 2.36534 4.09690i 0.165203 0.286140i
\(206\) −6.41817 11.1166i −0.447175 0.774530i
\(207\) −0.751454 1.30156i −0.0522297 0.0904644i
\(208\) 8.01013 + 13.8739i 0.555402 + 0.961985i
\(209\) 13.6294 0.942768
\(210\) −24.6168 + 42.6376i −1.69872 + 2.94228i
\(211\) −4.71904 + 8.17361i −0.324872 + 0.562694i −0.981486 0.191532i \(-0.938654\pi\)
0.656615 + 0.754226i \(0.271988\pi\)
\(212\) 2.20213 + 3.81421i 0.151243 + 0.261961i
\(213\) 29.1444 1.99694
\(214\) −25.5468 + 44.2484i −1.74634 + 3.02476i
\(215\) 7.28364 0.496740
\(216\) −33.2586 −2.26296
\(217\) 7.28217 + 21.7297i 0.494346 + 1.47511i
\(218\) −38.8152 −2.62889
\(219\) 1.63854 0.110723
\(220\) 33.5427 58.0976i 2.26145 3.91694i
\(221\) 1.11668 0.0751158
\(222\) 6.47292 + 11.2114i 0.434434 + 0.752462i
\(223\) −2.74494 + 4.75438i −0.183815 + 0.318377i −0.943177 0.332292i \(-0.892178\pi\)
0.759362 + 0.650669i \(0.225511\pi\)
\(224\) −50.1653 + 86.8889i −3.35181 + 5.80551i
\(225\) −0.982945 −0.0655297
\(226\) −19.4111 33.6210i −1.29121 2.23643i
\(227\) −1.43569 2.48669i −0.0952902 0.165048i 0.814439 0.580249i \(-0.197045\pi\)
−0.909730 + 0.415201i \(0.863711\pi\)
\(228\) 13.7606 + 23.8341i 0.911321 + 1.57845i
\(229\) −12.5648 + 21.7629i −0.830306 + 1.43813i 0.0674897 + 0.997720i \(0.478501\pi\)
−0.897796 + 0.440412i \(0.854832\pi\)
\(230\) −3.07940 5.33368i −0.203050 0.351693i
\(231\) −25.0034 + 43.3072i −1.64511 + 2.84941i
\(232\) 12.7300 0.835768
\(233\) −22.4053 −1.46782 −0.733909 0.679248i \(-0.762306\pi\)
−0.733909 + 0.679248i \(0.762306\pi\)
\(234\) −1.91774 + 3.32163i −0.125367 + 0.217142i
\(235\) 10.1746 + 17.6230i 0.663719 + 1.14959i
\(236\) 3.35497 5.81099i 0.218390 0.378263i
\(237\) 1.28595 + 2.22733i 0.0835313 + 0.144680i
\(238\) 6.32928 + 10.9626i 0.410266 + 0.710602i
\(239\) 8.62992 + 14.9475i 0.558223 + 0.966871i 0.997645 + 0.0685903i \(0.0218501\pi\)
−0.439422 + 0.898281i \(0.644817\pi\)
\(240\) 69.5785 4.49127
\(241\) −1.59576 + 2.76393i −0.102792 + 0.178040i −0.912834 0.408331i \(-0.866111\pi\)
0.810042 + 0.586372i \(0.199444\pi\)
\(242\) 31.1230 53.9066i 2.00066 3.46525i
\(243\) −6.72407 11.6464i −0.431349 0.747119i
\(244\) −82.7489 −5.29746
\(245\) 10.3014 17.8425i 0.658130 1.13991i
\(246\) 13.1771 0.840140
\(247\) −2.35125 −0.149606
\(248\) 36.4037 41.1865i 2.31164 2.61535i
\(249\) 5.14371 0.325970
\(250\) −32.5634 −2.05949
\(251\) 7.35147 12.7331i 0.464021 0.803707i −0.535136 0.844766i \(-0.679740\pi\)
0.999157 + 0.0410585i \(0.0130730\pi\)
\(252\) −32.0140 −2.01669
\(253\) −3.12776 5.41744i −0.196641 0.340592i
\(254\) 20.5712 35.6304i 1.29075 2.23565i
\(255\) 2.42495 4.20014i 0.151856 0.263023i
\(256\) 61.7092 3.85683
\(257\) 7.82723 + 13.5572i 0.488249 + 0.845672i 0.999909 0.0135162i \(-0.00430247\pi\)
−0.511660 + 0.859188i \(0.670969\pi\)
\(258\) 10.1441 + 17.5701i 0.631544 + 1.09387i
\(259\) −4.61583 7.99485i −0.286814 0.496776i
\(260\) −5.78652 + 10.0226i −0.358865 + 0.621572i
\(261\) 0.897870 + 1.55516i 0.0555767 + 0.0962618i
\(262\) 7.80544 13.5194i 0.482222 0.835232i
\(263\) 2.29515 0.141525 0.0707625 0.997493i \(-0.477457\pi\)
0.0707625 + 0.997493i \(0.477457\pi\)
\(264\) 119.944 7.38206
\(265\) −0.817107 + 1.41527i −0.0501945 + 0.0869393i
\(266\) −13.3268 23.0826i −0.817116 1.41529i
\(267\) −18.1397 + 31.4189i −1.11013 + 1.92281i
\(268\) −21.5191 37.2723i −1.31449 2.27677i
\(269\) −8.97769 15.5498i −0.547379 0.948089i −0.998453 0.0556019i \(-0.982292\pi\)
0.451074 0.892487i \(-0.351041\pi\)
\(270\) −9.61284 16.6499i −0.585019 1.01328i
\(271\) 3.99290 0.242551 0.121276 0.992619i \(-0.461301\pi\)
0.121276 + 0.992619i \(0.461301\pi\)
\(272\) 8.94472 15.4927i 0.542353 0.939383i
\(273\) 4.31340 7.47102i 0.261059 0.452167i
\(274\) −3.74218 6.48164i −0.226073 0.391570i
\(275\) −4.09130 −0.246714
\(276\) 6.31574 10.9392i 0.380163 0.658462i
\(277\) −2.13754 −0.128433 −0.0642163 0.997936i \(-0.520455\pi\)
−0.0642163 + 0.997936i \(0.520455\pi\)
\(278\) 5.57940 0.334630
\(279\) 7.59914 + 1.54229i 0.454948 + 0.0923345i
\(280\) −84.2095 −5.03248
\(281\) −1.18045 −0.0704195 −0.0352098 0.999380i \(-0.511210\pi\)
−0.0352098 + 0.999380i \(0.511210\pi\)
\(282\) −28.3409 + 49.0878i −1.68767 + 2.92314i
\(283\) 6.66467 0.396174 0.198087 0.980184i \(-0.436527\pi\)
0.198087 + 0.980184i \(0.436527\pi\)
\(284\) 38.8300 + 67.2555i 2.30413 + 3.99088i
\(285\) −5.10591 + 8.84370i −0.302448 + 0.523856i
\(286\) −7.98219 + 13.8256i −0.471997 + 0.817522i
\(287\) −9.39654 −0.554661
\(288\) 16.9733 + 29.3987i 1.00016 + 1.73233i
\(289\) 7.87652 + 13.6425i 0.463325 + 0.802502i
\(290\) 3.67940 + 6.37292i 0.216062 + 0.374231i
\(291\) 1.78793 3.09678i 0.104810 0.181537i
\(292\) 2.18308 + 3.78121i 0.127755 + 0.221279i
\(293\) −10.4048 + 18.0216i −0.607853 + 1.05283i 0.383740 + 0.923441i \(0.374636\pi\)
−0.991594 + 0.129392i \(0.958697\pi\)
\(294\) 57.3878 3.34692
\(295\) 2.48974 0.144958
\(296\) −11.0713 + 19.1761i −0.643507 + 1.11459i
\(297\) −9.76381 16.9114i −0.566554 0.981300i
\(298\) −13.9052 + 24.0845i −0.805505 + 1.39518i
\(299\) 0.539577 + 0.934575i 0.0312046 + 0.0540479i
\(300\) −4.13068 7.15455i −0.238485 0.413068i
\(301\) −7.23373 12.5292i −0.416945 0.722170i
\(302\) −53.3905 −3.07228
\(303\) 10.9962 19.0459i 0.631713 1.09416i
\(304\) −18.8338 + 32.6211i −1.08019 + 1.87095i
\(305\) −15.3521 26.5906i −0.879057 1.52257i
\(306\) 4.28299 0.244843
\(307\) 3.85935 6.68459i 0.220265 0.381509i −0.734624 0.678475i \(-0.762641\pi\)
0.954888 + 0.296965i \(0.0959746\pi\)
\(308\) −133.251 −7.59270
\(309\) 9.76864 0.555718
\(310\) 31.1407 + 6.32019i 1.76867 + 0.358963i
\(311\) 7.91172 0.448633 0.224316 0.974516i \(-0.427985\pi\)
0.224316 + 0.974516i \(0.427985\pi\)
\(312\) −20.6918 −1.17144
\(313\) 7.21927 12.5041i 0.408057 0.706776i −0.586615 0.809866i \(-0.699540\pi\)
0.994672 + 0.103090i \(0.0328730\pi\)
\(314\) 33.9019 1.91319
\(315\) −5.93943 10.2874i −0.334649 0.579629i
\(316\) −3.42662 + 5.93507i −0.192762 + 0.333874i
\(317\) −0.0424106 + 0.0734573i −0.00238202 + 0.00412578i −0.867214 0.497936i \(-0.834092\pi\)
0.864832 + 0.502061i \(0.167425\pi\)
\(318\) −4.55201 −0.255264
\(319\) 3.73719 + 6.47300i 0.209242 + 0.362418i
\(320\) 36.3576 + 62.9732i 2.03245 + 3.52031i
\(321\) −19.4415 33.6736i −1.08512 1.87948i
\(322\) −6.11660 + 10.5943i −0.340865 + 0.590396i
\(323\) 1.31279 + 2.27382i 0.0730456 + 0.126519i
\(324\) 31.3823 54.3557i 1.74346 3.01976i
\(325\) 0.705798 0.0391506
\(326\) −48.1221 −2.66524
\(327\) 14.7694 25.5814i 0.816752 1.41466i
\(328\) 11.2691 + 19.5186i 0.622230 + 1.07773i
\(329\) 20.2098 35.0044i 1.11420 1.92986i
\(330\) 34.6679 + 60.0466i 1.90840 + 3.30545i
\(331\) 12.5755 + 21.7813i 0.691210 + 1.19721i 0.971442 + 0.237279i \(0.0762555\pi\)
−0.280231 + 0.959932i \(0.590411\pi\)
\(332\) 6.85313 + 11.8700i 0.376114 + 0.651449i
\(333\) −3.12351 −0.171167
\(334\) 0.125433 0.217256i 0.00686339 0.0118877i
\(335\) 7.98472 13.8299i 0.436252 0.755611i
\(336\) −69.1017 119.688i −3.76981 6.52950i
\(337\) 6.13735 0.334323 0.167162 0.985930i \(-0.446540\pi\)
0.167162 + 0.985930i \(0.446540\pi\)
\(338\) 1.37702 2.38508i 0.0749003 0.129731i
\(339\) 29.5442 1.60462
\(340\) 12.9233 0.700867
\(341\) 31.6298 + 6.41945i 1.71285 + 0.347632i
\(342\) −9.01817 −0.487647
\(343\) −12.1104 −0.653902
\(344\) −17.3505 + 30.0519i −0.935476 + 1.62029i
\(345\) 4.68694 0.252336
\(346\) 11.0457 + 19.1317i 0.593821 + 1.02853i
\(347\) −7.28960 + 12.6260i −0.391326 + 0.677797i −0.992625 0.121228i \(-0.961317\pi\)
0.601298 + 0.799024i \(0.294650\pi\)
\(348\) −7.54633 + 13.0706i −0.404526 + 0.700659i
\(349\) 5.17904 0.277228 0.138614 0.990347i \(-0.455735\pi\)
0.138614 + 0.990347i \(0.455735\pi\)
\(350\) 4.00044 + 6.92896i 0.213832 + 0.370368i
\(351\) 1.68438 + 2.91742i 0.0899053 + 0.155721i
\(352\) 70.6478 + 122.366i 3.76554 + 6.52211i
\(353\) −1.02602 + 1.77712i −0.0546095 + 0.0945864i −0.892038 0.451961i \(-0.850725\pi\)
0.837428 + 0.546547i \(0.184058\pi\)
\(354\) 3.46752 + 6.00592i 0.184297 + 0.319211i
\(355\) −14.4079 + 24.9553i −0.764694 + 1.32449i
\(356\) −96.6725 −5.12363
\(357\) −9.63334 −0.509850
\(358\) 18.3122 31.7177i 0.967832 1.67633i
\(359\) 2.54319 + 4.40494i 0.134224 + 0.232484i 0.925301 0.379234i \(-0.123812\pi\)
−0.791076 + 0.611717i \(0.790479\pi\)
\(360\) −14.2461 + 24.6749i −0.750833 + 1.30048i
\(361\) 6.73582 + 11.6668i 0.354517 + 0.614041i
\(362\) −29.6352 51.3298i −1.55759 2.69783i
\(363\) 23.6851 + 41.0237i 1.24314 + 2.15319i
\(364\) 22.9875 1.20487
\(365\) −0.810038 + 1.40303i −0.0423993 + 0.0734377i
\(366\) 42.7624 74.0666i 2.23523 3.87152i
\(367\) −12.8547 22.2650i −0.671009 1.16222i −0.977618 0.210386i \(-0.932528\pi\)
0.306610 0.951835i \(-0.400805\pi\)
\(368\) 17.2883 0.901217
\(369\) −1.58965 + 2.75336i −0.0827539 + 0.143334i
\(370\) −12.7999 −0.665436
\(371\) 3.24603 0.168526
\(372\) 20.7084 + 61.7930i 1.07368 + 3.20382i
\(373\) 27.0653 1.40139 0.700694 0.713462i \(-0.252874\pi\)
0.700694 + 0.713462i \(0.252874\pi\)
\(374\) 17.8270 0.921814
\(375\) 12.3906 21.4611i 0.639847 1.10825i
\(376\) −96.9486 −4.99974
\(377\) −0.644710 1.11667i −0.0332043 0.0575115i
\(378\) −19.0940 + 33.0717i −0.982087 + 1.70102i
\(379\) 1.12358 1.94610i 0.0577144 0.0999642i −0.835725 0.549149i \(-0.814952\pi\)
0.893439 + 0.449184i \(0.148285\pi\)
\(380\) −27.2111 −1.39590
\(381\) 15.6550 + 27.1152i 0.802029 + 1.38916i
\(382\) −12.2623 21.2390i −0.627395 1.08668i
\(383\) −7.99482 13.8474i −0.408516 0.707571i 0.586208 0.810161i \(-0.300620\pi\)
−0.994724 + 0.102590i \(0.967287\pi\)
\(384\) −50.1848 + 86.9226i −2.56098 + 4.43575i
\(385\) −24.7216 42.8191i −1.25993 2.18226i
\(386\) 24.3542 42.1828i 1.23960 2.14705i
\(387\) −4.89504 −0.248829
\(388\) 9.52845 0.483734
\(389\) 1.59535 2.76322i 0.0808873 0.140101i −0.822744 0.568412i \(-0.807558\pi\)
0.903631 + 0.428311i \(0.140891\pi\)
\(390\) −5.98063 10.3588i −0.302841 0.524536i
\(391\) 0.602533 1.04362i 0.0304714 0.0527780i
\(392\) 49.0781 + 85.0058i 2.47882 + 4.29344i
\(393\) 5.94005 + 10.2885i 0.299636 + 0.518984i
\(394\) −8.59917 14.8942i −0.433220 0.750359i
\(395\) −2.54291 −0.127947
\(396\) −22.5427 + 39.0451i −1.13281 + 1.96209i
\(397\) −0.357825 + 0.619771i −0.0179587 + 0.0311054i −0.874865 0.484367i \(-0.839050\pi\)
0.856906 + 0.515472i \(0.172383\pi\)
\(398\) 19.2384 + 33.3219i 0.964334 + 1.67028i
\(399\) 20.2837 1.01546
\(400\) 5.65353 9.79221i 0.282677 0.489610i
\(401\) 17.4555 0.871687 0.435844 0.900022i \(-0.356450\pi\)
0.435844 + 0.900022i \(0.356450\pi\)
\(402\) 44.4820 2.21856
\(403\) −5.45652 1.10743i −0.271809 0.0551651i
\(404\) 58.6021 2.91556
\(405\) 23.2889 1.15723
\(406\) 7.30839 12.6585i 0.362709 0.628231i
\(407\) −13.0009 −0.644432
\(408\) 11.5530 + 20.0105i 0.571961 + 0.990665i
\(409\) −9.00141 + 15.5909i −0.445091 + 0.770920i −0.998059 0.0622826i \(-0.980162\pi\)
0.552968 + 0.833203i \(0.313495\pi\)
\(410\) −6.51427 + 11.2831i −0.321717 + 0.557230i
\(411\) 5.69570 0.280948
\(412\) 13.0151 + 22.5427i 0.641206 + 1.11060i
\(413\) −2.47268 4.28281i −0.121673 0.210743i
\(414\) 2.06954 + 3.58455i 0.101712 + 0.176171i
\(415\) −2.54287 + 4.40437i −0.124824 + 0.216202i
\(416\) −12.1876 21.1096i −0.597547 1.03498i
\(417\) −2.12300 + 3.67714i −0.103964 + 0.180071i
\(418\) −37.5362 −1.83595
\(419\) −6.66221 −0.325470 −0.162735 0.986670i \(-0.552032\pi\)
−0.162735 + 0.986670i \(0.552032\pi\)
\(420\) 49.9192 86.4625i 2.43581 4.21894i
\(421\) −9.57493 16.5843i −0.466654 0.808268i 0.532621 0.846354i \(-0.321207\pi\)
−0.999274 + 0.0380861i \(0.987874\pi\)
\(422\) 12.9965 22.5105i 0.632658 1.09579i
\(423\) −6.83794 11.8437i −0.332472 0.575859i
\(424\) −3.89289 6.74268i −0.189055 0.327454i
\(425\) −0.394074 0.682556i −0.0191154 0.0331088i
\(426\) −80.2651 −3.88886
\(427\) −30.4938 + 52.8167i −1.47570 + 2.55598i
\(428\) 51.8050 89.7288i 2.50409 4.33721i
\(429\) −6.07456 10.5214i −0.293282 0.507980i
\(430\) −20.0595 −0.967355
\(431\) 5.23095 9.06026i 0.251966 0.436418i −0.712101 0.702077i \(-0.752256\pi\)
0.964067 + 0.265659i \(0.0855896\pi\)
\(432\) 53.9683 2.59655
\(433\) −4.81123 −0.231213 −0.115606 0.993295i \(-0.536881\pi\)
−0.115606 + 0.993295i \(0.536881\pi\)
\(434\) −20.0554 59.8446i −0.962692 2.87263i
\(435\) −5.60016 −0.268507
\(436\) 78.7112 3.76958
\(437\) −1.26868 + 2.19742i −0.0606891 + 0.105117i
\(438\) −4.51263 −0.215622
\(439\) −13.5014 23.3852i −0.644389 1.11611i −0.984442 0.175708i \(-0.943779\pi\)
0.340053 0.940406i \(-0.389555\pi\)
\(440\) −59.2961 + 102.704i −2.82683 + 4.89622i
\(441\) −6.92312 + 11.9912i −0.329672 + 0.571009i
\(442\) −3.07538 −0.146281
\(443\) −0.529870 0.917762i −0.0251749 0.0436042i 0.853163 0.521644i \(-0.174681\pi\)
−0.878338 + 0.478039i \(0.841348\pi\)
\(444\) −13.1261 22.7350i −0.622936 1.07896i
\(445\) −17.9353 31.0648i −0.850213 1.47261i
\(446\) 7.55971 13.0938i 0.357963 0.620009i
\(447\) −10.5820 18.3286i −0.500513 0.866914i
\(448\) 72.2169 125.083i 3.41193 5.90963i
\(449\) 18.2765 0.862521 0.431261 0.902227i \(-0.358069\pi\)
0.431261 + 0.902227i \(0.358069\pi\)
\(450\) 2.70708 0.127613
\(451\) −6.61658 + 11.4602i −0.311562 + 0.539642i
\(452\) 39.3627 + 68.1781i 1.85146 + 3.20683i
\(453\) 20.3155 35.1874i 0.954503 1.65325i
\(454\) 3.95397 + 6.84847i 0.185569 + 0.321415i
\(455\) 4.26478 + 7.38681i 0.199936 + 0.346299i
\(456\) −24.3258 42.1335i −1.13916 1.97308i
\(457\) 0.720047 0.0336824 0.0168412 0.999858i \(-0.494639\pi\)
0.0168412 + 0.999858i \(0.494639\pi\)
\(458\) 34.6041 59.9361i 1.61694 2.80063i
\(459\) 1.88090 3.25782i 0.0877930 0.152062i
\(460\) 6.24455 + 10.8159i 0.291154 + 0.504293i
\(461\) −9.36428 −0.436138 −0.218069 0.975933i \(-0.569976\pi\)
−0.218069 + 0.975933i \(0.569976\pi\)
\(462\) 68.8607 119.270i 3.20369 5.54895i
\(463\) −1.20273 −0.0558956 −0.0279478 0.999609i \(-0.508897\pi\)
−0.0279478 + 0.999609i \(0.508897\pi\)
\(464\) −20.6569 −0.958970
\(465\) −16.0146 + 18.1186i −0.742661 + 0.840232i
\(466\) 61.7052 2.85844
\(467\) −32.5260 −1.50513 −0.752563 0.658521i \(-0.771182\pi\)
−0.752563 + 0.658521i \(0.771182\pi\)
\(468\) 3.88889 6.73575i 0.179764 0.311360i
\(469\) −31.7200 −1.46470
\(470\) −28.0214 48.5345i −1.29253 2.23873i
\(471\) −12.8999 + 22.3433i −0.594396 + 1.02952i
\(472\) −5.93086 + 10.2725i −0.272990 + 0.472832i
\(473\) −20.3745 −0.936821
\(474\) −3.54156 6.13417i −0.162669 0.281752i
\(475\) 0.829752 + 1.43717i 0.0380717 + 0.0659420i
\(476\) −12.8348 22.2305i −0.588282 1.01893i
\(477\) 0.549144 0.951145i 0.0251436 0.0435499i
\(478\) −23.7672 41.1661i −1.08709 1.88289i
\(479\) −12.5146 + 21.6760i −0.571808 + 0.990401i 0.424572 + 0.905394i \(0.360425\pi\)
−0.996380 + 0.0850068i \(0.972909\pi\)
\(480\) −105.865 −4.83207
\(481\) 2.24282 0.102264
\(482\) 4.39479 7.61200i 0.200177 0.346717i
\(483\) −4.65482 8.06239i −0.211802 0.366851i
\(484\) −63.1127 + 109.314i −2.86876 + 4.96883i
\(485\) 1.76777 + 3.06188i 0.0802705 + 0.139033i
\(486\) 18.5184 + 32.0748i 0.840012 + 1.45494i
\(487\) −10.0926 17.4808i −0.457338 0.792132i 0.541482 0.840713i \(-0.317864\pi\)
−0.998819 + 0.0485806i \(0.984530\pi\)
\(488\) 146.282 6.62187
\(489\) 18.3108 31.7152i 0.828043 1.43421i
\(490\) −28.3704 + 49.1391i −1.28165 + 2.21988i
\(491\) −6.77906 11.7417i −0.305935 0.529894i 0.671534 0.740973i \(-0.265636\pi\)
−0.977469 + 0.211079i \(0.932302\pi\)
\(492\) −26.7211 −1.20468
\(493\) −0.719933 + 1.24696i −0.0324241 + 0.0561603i
\(494\) 6.47544 0.291344
\(495\) −16.7290 −0.751913
\(496\) −59.0719 + 66.8328i −2.65241 + 3.00088i
\(497\) 57.2368 2.56742
\(498\) −14.1660 −0.634795
\(499\) −1.34647 + 2.33216i −0.0602763 + 0.104402i −0.894589 0.446890i \(-0.852532\pi\)
0.834313 + 0.551292i \(0.185865\pi\)
\(500\) 66.0335 2.95311
\(501\) 0.0954563 + 0.165335i 0.00426467 + 0.00738663i
\(502\) −20.2463 + 35.0676i −0.903637 + 1.56515i
\(503\) 6.23632 10.8016i 0.278064 0.481620i −0.692840 0.721092i \(-0.743641\pi\)
0.970903 + 0.239471i \(0.0769740\pi\)
\(504\) 56.5938 2.52089
\(505\) 10.8722 + 18.8312i 0.483807 + 0.837979i
\(506\) 8.61401 + 14.9199i 0.382940 + 0.663271i
\(507\) 1.04794 + 1.81508i 0.0465404 + 0.0806104i
\(508\) −41.7153 + 72.2529i −1.85082 + 3.20571i
\(509\) −9.70290 16.8059i −0.430073 0.744909i 0.566806 0.823851i \(-0.308179\pi\)
−0.996879 + 0.0789424i \(0.974846\pi\)
\(510\) −6.67843 + 11.5674i −0.295726 + 0.512212i
\(511\) 3.21795 0.142354
\(512\) −74.1717 −3.27796
\(513\) −3.96038 + 6.85958i −0.174855 + 0.302858i
\(514\) −21.5566 37.3371i −0.950819 1.64687i
\(515\) −4.82926 + 8.36453i −0.212803 + 0.368585i
\(516\) −20.5706 35.6294i −0.905572 1.56850i
\(517\) −28.4615 49.2967i −1.25173 2.16807i
\(518\) 12.7122 + 22.0182i 0.558543 + 0.967424i
\(519\) −16.8119 −0.737959
\(520\) 10.2293 17.7177i 0.448585 0.776971i
\(521\) −20.5432 + 35.5819i −0.900014 + 1.55887i −0.0725394 + 0.997366i \(0.523110\pi\)
−0.827474 + 0.561504i \(0.810223\pi\)
\(522\) −2.47278 4.28298i −0.108231 0.187461i
\(523\) 19.3758 0.847246 0.423623 0.905839i \(-0.360758\pi\)
0.423623 + 0.905839i \(0.360758\pi\)
\(524\) −15.8282 + 27.4153i −0.691459 + 1.19764i
\(525\) −6.08878 −0.265736
\(526\) −6.32095 −0.275607
\(527\) 1.97562 + 5.89516i 0.0860592 + 0.256797i
\(528\) −194.632 −8.47027
\(529\) −21.8354 −0.949366
\(530\) 2.25035 3.89772i 0.0977490 0.169306i
\(531\) −1.67325 −0.0726130
\(532\) 27.0246 + 46.8080i 1.17167 + 2.02938i
\(533\) 1.14144 1.97703i 0.0494413 0.0856348i
\(534\) 49.9577 86.5293i 2.16188 3.74449i
\(535\) 38.4447 1.66211
\(536\) 38.0411 + 65.8892i 1.64313 + 2.84598i
\(537\) 13.9359 + 24.1376i 0.601377 + 1.04162i
\(538\) 24.7250 + 42.8249i 1.06597 + 1.84631i
\(539\) −28.8160 + 49.9108i −1.24119 + 2.14981i
\(540\) 19.4934 + 33.7635i 0.838861 + 1.45295i
\(541\) 3.68814 6.38805i 0.158566 0.274644i −0.775786 0.630996i \(-0.782646\pi\)
0.934352 + 0.356352i \(0.115980\pi\)
\(542\) −10.9966 −0.472346
\(543\) 45.1057 1.93567
\(544\) −13.6096 + 23.5725i −0.583507 + 1.01066i
\(545\) 14.6030 + 25.2931i 0.625522 + 1.08344i
\(546\) −11.8793 + 20.5756i −0.508387 + 0.880553i
\(547\) −15.7528 27.2847i −0.673543 1.16661i −0.976892 0.213732i \(-0.931438\pi\)
0.303349 0.952879i \(-0.401895\pi\)
\(548\) 7.58856 + 13.1438i 0.324167 + 0.561474i
\(549\) 10.3175 + 17.8704i 0.440340 + 0.762692i
\(550\) 11.2676 0.480453
\(551\) 1.51587 2.62557i 0.0645783 0.111853i
\(552\) −11.1648 + 19.3381i −0.475207 + 0.823083i
\(553\) 2.52548 + 4.37426i 0.107394 + 0.186012i
\(554\) 5.88690 0.250110
\(555\) 4.87046 8.43588i 0.206740 0.358083i
\(556\) −11.3142 −0.479827
\(557\) −19.1990 −0.813487 −0.406744 0.913542i \(-0.633336\pi\)
−0.406744 + 0.913542i \(0.633336\pi\)
\(558\) −20.9284 4.24754i −0.885970 0.179813i
\(559\) 3.51485 0.148662
\(560\) 136.646 5.77433
\(561\) −6.78331 + 11.7490i −0.286392 + 0.496045i
\(562\) 3.25101 0.137135
\(563\) −6.05079 10.4803i −0.255011 0.441691i 0.709888 0.704315i \(-0.248746\pi\)
−0.964898 + 0.262624i \(0.915412\pi\)
\(564\) 57.4709 99.5425i 2.41996 4.19149i
\(565\) −14.6056 + 25.2976i −0.614462 + 1.06428i
\(566\) −18.3548 −0.771511
\(567\) −23.1293 40.0611i −0.971340 1.68241i
\(568\) −68.6429 118.893i −2.88019 4.98864i
\(569\) 17.1246 + 29.6607i 0.717901 + 1.24344i 0.961830 + 0.273648i \(0.0882305\pi\)
−0.243928 + 0.969793i \(0.578436\pi\)
\(570\) 14.0619 24.3560i 0.588990 1.02016i
\(571\) −3.36637 5.83073i −0.140878 0.244008i 0.786949 0.617018i \(-0.211659\pi\)
−0.927828 + 0.373009i \(0.878326\pi\)
\(572\) 16.1866 28.0361i 0.676797 1.17225i
\(573\) 18.6636 0.779684
\(574\) 25.8785 1.08015
\(575\) 0.380833 0.659622i 0.0158818 0.0275081i
\(576\) −24.4344 42.3217i −1.01810 1.76340i
\(577\) 8.59766 14.8916i 0.357925 0.619945i −0.629689 0.776847i \(-0.716818\pi\)
0.987614 + 0.156903i \(0.0501509\pi\)
\(578\) −21.6923 37.5722i −0.902281 1.56280i
\(579\) 18.5339 + 32.1017i 0.770243 + 1.33410i
\(580\) −7.46126 12.9233i −0.309812 0.536610i
\(581\) 10.1018 0.419092
\(582\) −4.92404 + 8.52869i −0.204108 + 0.353526i
\(583\) 2.28569 3.95893i 0.0946637 0.163962i
\(584\) −3.85921 6.68435i −0.159695 0.276600i
\(585\) 2.88596 0.119320
\(586\) 28.6553 49.6324i 1.18374 2.05029i
\(587\) 16.8077 0.693729 0.346865 0.937915i \(-0.387246\pi\)
0.346865 + 0.937915i \(0.387246\pi\)
\(588\) −116.374 −4.79916
\(589\) −4.15981 12.4127i −0.171402 0.511456i
\(590\) −6.85686 −0.282293
\(591\) 13.0882 0.538376
\(592\) 17.9653 31.1168i 0.738368 1.27889i
\(593\) −22.1847 −0.911017 −0.455508 0.890232i \(-0.650542\pi\)
−0.455508 + 0.890232i \(0.650542\pi\)
\(594\) 26.8900 + 46.5749i 1.10331 + 1.91099i
\(595\) 4.76237 8.24868i 0.195238 0.338163i
\(596\) 28.1975 48.8396i 1.15502 2.00055i
\(597\) −29.2814 −1.19841
\(598\) −1.48602 2.57387i −0.0607680 0.105253i
\(599\) 2.87829 + 4.98535i 0.117604 + 0.203696i 0.918818 0.394682i \(-0.129145\pi\)
−0.801214 + 0.598378i \(0.795812\pi\)
\(600\) 7.30213 + 12.6477i 0.298108 + 0.516339i
\(601\) −3.79186 + 6.56769i −0.154673 + 0.267902i −0.932940 0.360032i \(-0.882766\pi\)
0.778267 + 0.627934i \(0.216099\pi\)
\(602\) 19.9220 + 34.5060i 0.811962 + 1.40636i
\(603\) −5.36621 + 9.29454i −0.218529 + 0.378503i
\(604\) 108.268 4.40535
\(605\) −46.8361 −1.90416
\(606\) −30.2840 + 52.4534i −1.23020 + 2.13077i
\(607\) 12.5556 + 21.7470i 0.509617 + 0.882682i 0.999938 + 0.0111403i \(0.00354613\pi\)
−0.490321 + 0.871542i \(0.663121\pi\)
\(608\) 28.6561 49.6338i 1.16216 2.01291i
\(609\) 5.56179 + 9.63329i 0.225375 + 0.390361i
\(610\) 42.2804 + 73.2317i 1.71188 + 2.96507i
\(611\) 4.90995 + 8.50428i 0.198635 + 0.344046i
\(612\) −8.68525 −0.351080
\(613\) 4.95092 8.57524i 0.199966 0.346351i −0.748551 0.663077i \(-0.769250\pi\)
0.948517 + 0.316726i \(0.102584\pi\)
\(614\) −10.6288 + 18.4097i −0.428945 + 0.742954i
\(615\) −4.95745 8.58656i −0.199904 0.346244i
\(616\) 235.559 9.49095
\(617\) 20.6368 35.7440i 0.830807 1.43900i −0.0665928 0.997780i \(-0.521213\pi\)
0.897399 0.441219i \(-0.145454\pi\)
\(618\) −26.9033 −1.08221
\(619\) −15.8403 −0.636674 −0.318337 0.947978i \(-0.603124\pi\)
−0.318337 + 0.947978i \(0.603124\pi\)
\(620\) −63.1485 12.8164i −2.53611 0.514718i
\(621\) 3.63540 0.145884
\(622\) −21.7893 −0.873670
\(623\) −35.6247 + 61.7039i −1.42728 + 2.47211i
\(624\) 33.5764 1.34413
\(625\) 10.4864 + 18.1630i 0.419457 + 0.726521i
\(626\) −19.8822 + 34.4370i −0.794653 + 1.37638i
\(627\) 14.2828 24.7385i 0.570399 0.987960i
\(628\) −68.7478 −2.74334
\(629\) −1.25225 2.16896i −0.0499305 0.0864822i
\(630\) 16.3575 + 28.3320i 0.651698 + 1.12877i
\(631\) −25.0354 43.3626i −0.996645 1.72624i −0.569206 0.822195i \(-0.692749\pi\)
−0.427438 0.904044i \(-0.640584\pi\)
\(632\) 6.05750 10.4919i 0.240955 0.417346i
\(633\) 9.89049 + 17.1308i 0.393112 + 0.680889i
\(634\) 0.116801 0.202305i 0.00463876 0.00803456i
\(635\) −30.9571 −1.22849
\(636\) 9.23078 0.366024
\(637\) 4.97111 8.61021i 0.196963 0.341149i
\(638\) −10.2924 17.8270i −0.407480 0.705776i
\(639\) 9.68298 16.7714i 0.383053 0.663467i
\(640\) −49.6191 85.9428i −1.96137 3.39719i
\(641\) 8.31997 + 14.4106i 0.328619 + 0.569185i 0.982238 0.187639i \(-0.0600835\pi\)
−0.653619 + 0.756824i \(0.726750\pi\)
\(642\) 53.5428 + 92.7388i 2.11316 + 3.66011i
\(643\) −8.48555 −0.334637 −0.167319 0.985903i \(-0.553511\pi\)
−0.167319 + 0.985903i \(0.553511\pi\)
\(644\) 12.4035 21.4835i 0.488767 0.846570i
\(645\) 7.63278 13.2204i 0.300540 0.520551i
\(646\) −3.61549 6.26221i −0.142249 0.246383i
\(647\) −26.0392 −1.02371 −0.511854 0.859072i \(-0.671041\pi\)
−0.511854 + 0.859072i \(0.671041\pi\)
\(648\) −55.4769 + 96.0889i −2.17934 + 3.77473i
\(649\) −6.96455 −0.273382
\(650\) −1.94380 −0.0762422
\(651\) 47.0723 + 9.55359i 1.84491 + 0.374435i
\(652\) 97.5841 3.82169
\(653\) 33.9953 1.33034 0.665169 0.746693i \(-0.268360\pi\)
0.665169 + 0.746693i \(0.268360\pi\)
\(654\) −40.6758 + 70.4525i −1.59055 + 2.75491i
\(655\) −11.7462 −0.458961
\(656\) −18.2862 31.6726i −0.713955 1.23661i
\(657\) 0.544393 0.942916i 0.0212388 0.0367867i
\(658\) −55.6588 + 96.4038i −2.16981 + 3.75821i
\(659\) −17.2237 −0.670942 −0.335471 0.942051i \(-0.608895\pi\)
−0.335471 + 0.942051i \(0.608895\pi\)
\(660\) −70.3011 121.765i −2.73647 4.73970i
\(661\) −21.2401 36.7890i −0.826146 1.43093i −0.901040 0.433735i \(-0.857195\pi\)
0.0748944 0.997191i \(-0.476138\pi\)
\(662\) −34.6335 59.9869i −1.34607 2.33146i
\(663\) 1.17020 2.02685i 0.0454470 0.0787164i
\(664\) −12.1148 20.9835i −0.470146 0.814318i
\(665\) −10.0275 + 17.3682i −0.388851 + 0.673510i
\(666\) 8.60230 0.333332
\(667\) −1.39148 −0.0538785
\(668\) −0.254359 + 0.440562i −0.00984143 + 0.0170459i
\(669\) 5.75304 + 9.96456i 0.222426 + 0.385252i
\(670\) −21.9903 + 38.0883i −0.849560 + 1.47148i
\(671\) 42.9444 + 74.3818i 1.65785 + 2.87148i
\(672\) 105.140 + 182.108i 4.05586 + 7.02496i
\(673\) 9.90700 + 17.1594i 0.381887 + 0.661447i 0.991332 0.131381i \(-0.0419411\pi\)
−0.609445 + 0.792828i \(0.708608\pi\)
\(674\) −16.9026 −0.651063
\(675\) 1.18883 2.05911i 0.0457581 0.0792553i
\(676\) −2.79239 + 4.83657i −0.107400 + 0.186022i
\(677\) −21.5408 37.3097i −0.827880 1.43393i −0.899699 0.436512i \(-0.856214\pi\)
0.0718191 0.997418i \(-0.477120\pi\)
\(678\) −81.3662 −3.12485
\(679\) 3.51132 6.08179i 0.134752 0.233398i
\(680\) −22.8456 −0.876090
\(681\) −6.01805 −0.230612
\(682\) −87.1099 17.6795i −3.33561 0.676982i
\(683\) 2.33427 0.0893182 0.0446591 0.999002i \(-0.485780\pi\)
0.0446591 + 0.999002i \(0.485780\pi\)
\(684\) 18.2874 0.699238
\(685\) −2.81575 + 4.87702i −0.107584 + 0.186341i
\(686\) 33.3527 1.27341
\(687\) 26.3342 + 45.6122i 1.00471 + 1.74021i
\(688\) 28.1544 48.7649i 1.07338 1.85914i
\(689\) −0.394310 + 0.682964i −0.0150220 + 0.0260189i
\(690\) −12.9081 −0.491401
\(691\) 14.5034 + 25.1206i 0.551736 + 0.955634i 0.998149 + 0.0608077i \(0.0193676\pi\)
−0.446414 + 0.894827i \(0.647299\pi\)
\(692\) −22.3990 38.7962i −0.851482 1.47481i
\(693\) 16.6144 + 28.7769i 0.631128 + 1.09315i
\(694\) 20.0759 34.7725i 0.762071 1.31995i
\(695\) −2.09907 3.63570i −0.0796223 0.137910i
\(696\) 13.3402 23.1060i 0.505661 0.875830i
\(697\) −2.54924 −0.0965593
\(698\) −14.2633 −0.539875
\(699\) −23.4793 + 40.6673i −0.888067 + 1.53818i
\(700\) −8.11227 14.0509i −0.306615 0.531073i
\(701\) −20.1128 + 34.8364i −0.759650 + 1.31575i 0.183378 + 0.983042i \(0.441297\pi\)
−0.943029 + 0.332711i \(0.892037\pi\)
\(702\) −4.63885 8.03473i −0.175082 0.303251i
\(703\) 2.63671 + 4.56692i 0.0994454 + 0.172244i
\(704\) −101.703 176.155i −3.83308 6.63909i
\(705\) 42.6494 1.60627
\(706\) 2.82571 4.89427i 0.106347 0.184198i
\(707\) 21.5954 37.4044i 0.812180 1.40674i
\(708\) −7.03159 12.1791i −0.264263 0.457718i
\(709\) −31.6545 −1.18881 −0.594405 0.804166i \(-0.702613\pi\)
−0.594405 + 0.804166i \(0.702613\pi\)
\(710\) 39.6802 68.7281i 1.48917 2.57932i
\(711\) 1.70898 0.0640918
\(712\) 170.896 6.40459
\(713\) −3.97919 + 4.50198i −0.149022 + 0.168601i
\(714\) 26.5307 0.992886
\(715\) 12.0122 0.449230
\(716\) −37.1344 + 64.3186i −1.38778 + 2.40370i
\(717\) 36.1744 1.35096
\(718\) −7.00407 12.1314i −0.261390 0.452740i
\(719\) 14.3198 24.8027i 0.534039 0.924983i −0.465170 0.885221i \(-0.654007\pi\)
0.999209 0.0397618i \(-0.0126599\pi\)
\(720\) 23.1169 40.0396i 0.861516 1.49219i
\(721\) 19.1847 0.714475
\(722\) −18.5508 32.1309i −0.690389 1.19579i
\(723\) 3.34450 + 5.79284i 0.124383 + 0.215438i
\(724\) 60.0957 + 104.089i 2.23344 + 3.86843i
\(725\) −0.455036 + 0.788145i −0.0168996 + 0.0292710i
\(726\) −65.2298 112.981i −2.42090 4.19313i
\(727\) 21.1252 36.5899i 0.783489 1.35704i −0.146409 0.989224i \(-0.546771\pi\)
0.929898 0.367818i \(-0.119895\pi\)
\(728\) −40.6368 −1.50610
\(729\) 5.52989 0.204811
\(730\) 2.23088 3.86400i 0.0825687 0.143013i
\(731\) −1.96248 3.39911i −0.0725848 0.125721i
\(732\) −86.7155 + 150.196i −3.20510 + 5.55139i
\(733\) −9.28640 16.0845i −0.343001 0.594095i 0.641988 0.766715i \(-0.278110\pi\)
−0.984988 + 0.172620i \(0.944777\pi\)
\(734\) 35.4024 + 61.3188i 1.30673 + 2.26332i
\(735\) −21.5903 37.3955i −0.796371 1.37935i
\(736\) −26.3046 −0.969601
\(737\) −22.3357 + 38.6865i −0.822745 + 1.42504i
\(738\) 4.37798 7.58288i 0.161156 0.279130i
\(739\) −3.87523 6.71210i −0.142553 0.246909i 0.785905 0.618348i \(-0.212198\pi\)
−0.928457 + 0.371439i \(0.878864\pi\)
\(740\) 25.9563 0.954171
\(741\) −2.46395 + 4.26769i −0.0905155 + 0.156778i
\(742\) −8.93973 −0.328188
\(743\) 32.2012 1.18135 0.590673 0.806911i \(-0.298862\pi\)
0.590673 + 0.806911i \(0.298862\pi\)
\(744\) −36.6079 109.236i −1.34211 4.00480i
\(745\) 20.9255 0.766651
\(746\) −74.5391 −2.72907
\(747\) 1.70896 2.96000i 0.0625275 0.108301i
\(748\) −36.1505 −1.32179
\(749\) −38.1812 66.1318i −1.39511 2.41641i
\(750\) −34.1243 + 59.1050i −1.24604 + 2.15821i
\(751\) −14.5038 + 25.1214i −0.529253 + 0.916693i 0.470165 + 0.882579i \(0.344194\pi\)
−0.999418 + 0.0341144i \(0.989139\pi\)
\(752\) 157.317 5.73677
\(753\) −15.4077 26.6870i −0.561489 0.972527i
\(754\) 1.77556 + 3.07537i 0.0646622 + 0.111998i
\(755\) 20.0865 + 34.7908i 0.731021 + 1.26617i
\(756\) 38.7196 67.0643i 1.40822 2.43910i
\(757\) −5.49564 9.51873i −0.199742 0.345964i 0.748702 0.662906i \(-0.230677\pi\)
−0.948445 + 0.316942i \(0.897344\pi\)
\(758\) −3.09439 + 5.35964i −0.112393 + 0.194671i
\(759\) −13.1108 −0.475891
\(760\) 48.1032 1.74489
\(761\) −19.4629 + 33.7107i −0.705528 + 1.22201i 0.260972 + 0.965346i \(0.415957\pi\)
−0.966501 + 0.256665i \(0.917376\pi\)
\(762\) −43.1146 74.6767i −1.56188 2.70525i
\(763\) 29.0058 50.2395i 1.05008 1.81879i
\(764\) 24.8661 + 43.0694i 0.899624 + 1.55820i
\(765\) −1.61134 2.79092i −0.0582581 0.100906i
\(766\) 22.0181 + 38.1365i 0.795547 + 1.37793i
\(767\) 1.20147 0.0433825
\(768\) 64.6673 112.007i 2.33348 4.04170i
\(769\) 14.9293 25.8583i 0.538364 0.932474i −0.460628 0.887593i \(-0.652376\pi\)
0.998992 0.0448806i \(-0.0142907\pi\)
\(770\) 68.0845 + 117.926i 2.45359 + 4.24975i
\(771\) 32.8097 1.18161
\(772\) −49.3866 + 85.5401i −1.77746 + 3.07866i
\(773\) 13.6168 0.489763 0.244882 0.969553i \(-0.421251\pi\)
0.244882 + 0.969553i \(0.421251\pi\)
\(774\) 13.4812 0.484571
\(775\) 1.24869 + 3.72605i 0.0448544 + 0.133844i
\(776\) −16.8442 −0.604672
\(777\) −19.3483 −0.694118
\(778\) −4.39367 + 7.61005i −0.157521 + 0.272834i
\(779\) 5.36761 0.192315
\(780\) 12.1278 + 21.0060i 0.434245 + 0.752134i
\(781\) 40.3033 69.8074i 1.44217 2.49790i
\(782\) −1.65941 + 2.87417i −0.0593402 + 0.102780i
\(783\) −4.34374 −0.155233
\(784\) −79.6384 137.938i −2.84423 4.92635i
\(785\) −12.7545 22.0914i −0.455228 0.788477i
\(786\) −16.3592 28.3349i −0.583513 1.01067i
\(787\) −1.91550 + 3.31775i −0.0682804 + 0.118265i −0.898144 0.439701i \(-0.855085\pi\)
0.829864 + 0.557966i \(0.188418\pi\)
\(788\) 17.4378 + 30.2031i 0.621195 + 1.07594i
\(789\) 2.40517 4.16587i 0.0856262 0.148309i
\(790\) 7.00328 0.249166
\(791\) 58.0221 2.06303
\(792\) 39.8505 69.0231i 1.41603 2.45263i
\(793\) −7.40843 12.8318i −0.263081 0.455669i
\(794\) 0.985468 1.70688i 0.0349729 0.0605749i
\(795\) 1.71255 + 2.96622i 0.0607379 + 0.105201i
\(796\) −39.0125 67.5717i −1.38276 2.39501i
\(797\) −6.70050 11.6056i −0.237344 0.411092i 0.722607 0.691259i \(-0.242944\pi\)
−0.959951 + 0.280167i \(0.909610\pi\)
\(798\) −55.8623 −1.97751
\(799\) 5.48282 9.49653i 0.193968 0.335963i
\(800\) −8.60199 + 14.8991i −0.304126 + 0.526762i
\(801\) 12.0536 + 20.8774i 0.425892 + 0.737666i
\(802\) −48.0734 −1.69753
\(803\) 2.26592 3.92468i 0.0799625 0.138499i
\(804\) −90.2027 −3.18120
\(805\) 9.20471 0.324423
\(806\) 15.0275 + 3.04992i 0.529322 + 0.107429i
\(807\) −37.6321 −1.32471
\(808\) −103.596 −3.64448
\(809\) 9.53951 16.5229i 0.335391 0.580915i −0.648169 0.761497i \(-0.724465\pi\)
0.983560 + 0.180582i \(0.0577982\pi\)
\(810\) −64.1387 −2.25361
\(811\) −17.0215 29.4821i −0.597706 1.03526i −0.993159 0.116771i \(-0.962746\pi\)
0.395452 0.918486i \(-0.370588\pi\)
\(812\) −14.8203 + 25.6695i −0.520090 + 0.900822i
\(813\) 4.18430 7.24742i 0.146750 0.254178i
\(814\) 35.8052 1.25497
\(815\) 18.1044 + 31.3577i 0.634169 + 1.09841i
\(816\) −18.7470 32.4707i −0.656275 1.13670i
\(817\) 4.13214 + 7.15708i 0.144565 + 0.250394i
\(818\) 24.7903 42.9381i 0.866773 1.50129i
\(819\) −2.86618 4.96437i −0.100153 0.173469i
\(820\) 13.2099 22.8803i 0.461311 0.799014i
\(821\) −11.2676 −0.393243 −0.196622 0.980479i \(-0.562997\pi\)
−0.196622 + 0.980479i \(0.562997\pi\)
\(822\) −15.6862 −0.547120
\(823\) 15.0980 26.1506i 0.526285 0.911552i −0.473246 0.880930i \(-0.656918\pi\)
0.999531 0.0306218i \(-0.00974876\pi\)
\(824\) −23.0078 39.8506i −0.801514 1.38826i
\(825\) −4.28741 + 7.42602i −0.149269 + 0.258541i
\(826\) 6.80988 + 11.7951i 0.236946 + 0.410403i
\(827\) −20.5037 35.5135i −0.712984 1.23493i −0.963732 0.266873i \(-0.914010\pi\)
0.250747 0.968053i \(-0.419324\pi\)
\(828\) −4.19671 7.26891i −0.145846 0.252612i
\(829\) 18.9122 0.656847 0.328423 0.944531i \(-0.393483\pi\)
0.328423 + 0.944531i \(0.393483\pi\)
\(830\) 7.00318 12.1299i 0.243084 0.421034i
\(831\) −2.24001 + 3.87980i −0.0777050 + 0.134589i
\(832\) 17.5450 + 30.3889i 0.608264 + 1.05354i
\(833\) −11.1022 −0.384670
\(834\) 5.84685 10.1270i 0.202460 0.350671i
\(835\) −0.188761 −0.00653233
\(836\) 76.1175 2.63258
\(837\) −12.4217 + 14.0536i −0.429356 + 0.485765i
\(838\) 18.3481 0.633823
\(839\) −10.6356 −0.367182 −0.183591 0.983003i \(-0.558772\pi\)
−0.183591 + 0.983003i \(0.558772\pi\)
\(840\) −88.2461 + 152.847i −3.04478 + 5.27371i
\(841\) −27.3374 −0.942669
\(842\) 26.3698 + 45.6739i 0.908765 + 1.57403i
\(843\) −1.23703 + 2.14260i −0.0426056 + 0.0737951i
\(844\) −26.3548 + 45.6479i −0.907170 + 1.57126i
\(845\) −2.07225 −0.0712874
\(846\) 18.8320 + 32.6180i 0.647459 + 1.12143i
\(847\) 46.5152 + 80.5667i 1.59828 + 2.76831i
\(848\) 6.31694 + 10.9413i 0.216925 + 0.375725i
\(849\) 6.98414 12.0969i 0.239695 0.415164i
\(850\) 1.08530 + 1.87979i 0.0372255 + 0.0644764i
\(851\) 1.21017 2.09608i 0.0414842 0.0718528i
\(852\) 162.765 5.57624
\(853\) 20.0398 0.686149 0.343075 0.939308i \(-0.388532\pi\)
0.343075 + 0.939308i \(0.388532\pi\)
\(854\) 83.9813 145.460i 2.87378 4.97754i
\(855\) 3.39280 + 5.87650i 0.116031 + 0.200972i
\(856\) −91.5798 + 158.621i −3.13013 + 5.42155i
\(857\) −8.74862 15.1531i −0.298847 0.517619i 0.677025 0.735960i \(-0.263269\pi\)
−0.975873 + 0.218341i \(0.929935\pi\)
\(858\) 16.7296 + 28.9766i 0.571140 + 0.989244i
\(859\) −8.62228 14.9342i −0.294188 0.509549i 0.680607 0.732648i \(-0.261716\pi\)
−0.974796 + 0.223099i \(0.928383\pi\)
\(860\) 40.6776 1.38709
\(861\) −9.84697 + 17.0555i −0.335584 + 0.581248i
\(862\) −14.4063 + 24.9524i −0.490680 + 0.849882i
\(863\) −22.9139 39.6880i −0.779997 1.35099i −0.931943 0.362606i \(-0.881887\pi\)
0.151945 0.988389i \(-0.451446\pi\)
\(864\) −82.1141 −2.79358
\(865\) 8.31119 14.3954i 0.282589 0.489458i
\(866\) 13.2504 0.450265
\(867\) 33.0163 1.12129
\(868\) 40.6693 + 121.356i 1.38041 + 4.11908i
\(869\) 7.11327 0.241301
\(870\) 15.4231 0.522892
\(871\) 3.85317 6.67389i 0.130560 0.226136i
\(872\) −139.144 −4.71201
\(873\) −1.18805 2.05776i −0.0402094 0.0696447i
\(874\) 3.49400 6.05179i 0.118186 0.204705i
\(875\) 24.3340 42.1477i 0.822638 1.42485i
\(876\) 9.15092 0.309181
\(877\) 13.3582 + 23.1370i 0.451073 + 0.781282i 0.998453 0.0556025i \(-0.0177080\pi\)
−0.547380 + 0.836884i \(0.684375\pi\)
\(878\) 37.1836 + 64.4040i 1.25489 + 2.17353i
\(879\) 21.8071 + 37.7709i 0.735534 + 1.27398i
\(880\) 96.2190 166.656i 3.24354 5.61798i
\(881\) −6.69233 11.5915i −0.225470 0.390526i 0.730990 0.682388i \(-0.239059\pi\)
−0.956460 + 0.291862i \(0.905725\pi\)
\(882\) 19.0666 33.0243i 0.642006 1.11199i
\(883\) 1.73280 0.0583135 0.0291567 0.999575i \(-0.490718\pi\)
0.0291567 + 0.999575i \(0.490718\pi\)
\(884\) 6.23640 0.209753
\(885\) 2.60909 4.51907i 0.0877034 0.151907i
\(886\) 1.45929 + 2.52756i 0.0490257 + 0.0849150i
\(887\) −8.47149 + 14.6730i −0.284445 + 0.492673i −0.972474 0.233010i \(-0.925143\pi\)
0.688030 + 0.725683i \(0.258476\pi\)
\(888\) 23.2040 + 40.1906i 0.778676 + 1.34871i
\(889\) 30.7449 + 53.2518i 1.03115 + 1.78601i
\(890\) 49.3946 + 85.5540i 1.65571 + 2.86778i
\(891\) −65.1460 −2.18247
\(892\) −15.3299 + 26.5522i −0.513284 + 0.889033i
\(893\) −11.5445 + 19.9956i −0.386322 + 0.669129i
\(894\) 29.1434 + 50.4779i 0.974702 + 1.68823i
\(895\) −27.5576 −0.921148
\(896\) −98.5583 + 170.708i −3.29260 + 5.70295i
\(897\) 2.26177 0.0755182
\(898\) −50.3344 −1.67968
\(899\) 4.75451 5.37916i 0.158572 0.179405i
\(900\) −5.48954 −0.182985
\(901\) 0.880632 0.0293381
\(902\) 18.2224 31.5621i 0.606739 1.05090i
\(903\) −30.3219 −1.00905
\(904\) −69.5845 120.524i −2.31435 4.00857i
\(905\) −22.2986 + 38.6224i −0.741231 + 1.28385i
\(906\) −55.9498 + 96.9078i −1.85881 + 3.21955i
\(907\) −27.5969 −0.916340 −0.458170 0.888864i \(-0.651495\pi\)
−0.458170 + 0.888864i \(0.651495\pi\)
\(908\) −8.01803 13.8876i −0.266088 0.460877i
\(909\) −7.30677 12.6557i −0.242350 0.419763i
\(910\) −11.7454 20.3436i −0.389356 0.674385i
\(911\) 27.3306 47.3381i 0.905505 1.56838i 0.0852666 0.996358i \(-0.472826\pi\)
0.820238 0.572022i \(-0.193841\pi\)
\(912\) 39.4731 + 68.3695i 1.30709 + 2.26394i
\(913\) 7.11316 12.3204i 0.235411 0.407744i
\(914\) −1.98304 −0.0655933
\(915\) −64.3519 −2.12741
\(916\) −70.1718 + 121.541i −2.31854 + 4.01583i
\(917\) 11.6657 + 20.2056i 0.385235 + 0.667247i
\(918\) −5.18010 + 8.97219i −0.170969 + 0.296126i
\(919\) −3.57419 6.19068i −0.117902 0.204212i 0.801034 0.598618i \(-0.204283\pi\)
−0.918936 + 0.394407i \(0.870950\pi\)
\(920\) −11.0390 19.1201i −0.363945 0.630371i
\(921\) −8.08869 14.0100i −0.266531 0.461646i
\(922\) 25.7897 0.849338
\(923\) −6.95281 + 12.0426i −0.228855 + 0.396388i
\(924\) −139.639 + 241.862i −4.59378 + 7.95666i
\(925\) −0.791489 1.37090i −0.0260240 0.0450749i
\(926\) 3.31238 0.108851
\(927\) 3.24555 5.62146i 0.106598 0.184633i
\(928\) 31.4299 1.03174
\(929\) 15.3742 0.504411 0.252205 0.967674i \(-0.418844\pi\)
0.252205 + 0.967674i \(0.418844\pi\)
\(930\) 44.1051 49.8996i 1.44626 1.63627i
\(931\) 23.3766 0.766137
\(932\) −125.129 −4.09872
\(933\) 8.29097 14.3604i 0.271434 0.470138i
\(934\) 89.5783 2.93109
\(935\) −6.70685 11.6166i −0.219337 0.379904i
\(936\) −6.87470 + 11.9073i −0.224706 + 0.389203i
\(937\) −14.9935 + 25.9695i −0.489817 + 0.848388i −0.999931 0.0117187i \(-0.996270\pi\)
0.510114 + 0.860107i \(0.329603\pi\)
\(938\) 87.3585 2.85236
\(939\) −15.1307 26.2071i −0.493770 0.855235i
\(940\) 56.8231 + 98.4204i 1.85336 + 3.21012i
\(941\) 9.26659 + 16.0502i 0.302082 + 0.523221i 0.976607 0.215030i \(-0.0689850\pi\)
−0.674525 + 0.738252i \(0.735652\pi\)
\(942\) 35.5270 61.5345i 1.15753 2.00490i
\(943\) −1.23179 2.13352i −0.0401126 0.0694771i
\(944\) 9.62392 16.6691i 0.313232 0.542534i
\(945\) 28.7340 0.934716
\(946\) 56.1124 1.82437
\(947\) 13.2033 22.8688i 0.429049 0.743135i −0.567740 0.823208i \(-0.692182\pi\)
0.996789 + 0.0800728i \(0.0255153\pi\)
\(948\) 7.18174 + 12.4391i 0.233252 + 0.404005i
\(949\) −0.390898 + 0.677056i −0.0126891 + 0.0219782i
\(950\) −2.28518 3.95805i −0.0741410 0.128416i
\(951\) 0.0888871 + 0.153957i 0.00288236 + 0.00499240i
\(952\) 22.6891 + 39.2987i 0.735358 + 1.27368i
\(953\) −53.5158 −1.73355 −0.866773 0.498703i \(-0.833810\pi\)
−0.866773 + 0.498703i \(0.833810\pi\)
\(954\) −1.51237 + 2.61950i −0.0489648 + 0.0848094i
\(955\) −9.22662 + 15.9810i −0.298566 + 0.517132i
\(956\) 48.1963 + 83.4784i 1.55878 + 2.69988i
\(957\) 15.6653 0.506388
\(958\) 34.4659 59.6967i 1.11354 1.92871i
\(959\) 11.1858 0.361209
\(960\) 152.402 4.91874
\(961\) −3.80728 30.7653i −0.122816 0.992430i
\(962\) −6.17684 −0.199149
\(963\) −25.8371 −0.832589
\(964\) −8.91196 + 15.4360i −0.287035 + 0.497159i
\(965\) −36.6500 −1.17981
\(966\) 12.8196 + 22.2042i 0.412464 + 0.714409i
\(967\) −19.1947 + 33.2462i −0.617260 + 1.06913i 0.372724 + 0.927942i \(0.378424\pi\)
−0.989983 + 0.141183i \(0.954909\pi\)
\(968\) 111.569 193.244i 3.58597 6.21109i
\(969\) 5.50287 0.176778
\(970\) −4.86854 8.43255i −0.156319 0.270753i
\(971\) 14.5990 + 25.2862i 0.468505 + 0.811474i 0.999352 0.0359937i \(-0.0114596\pi\)
−0.530848 + 0.847467i \(0.678126\pi\)
\(972\) −37.5525 65.0428i −1.20450 2.08625i
\(973\) −4.16937 + 7.22157i −0.133664 + 0.231513i
\(974\) 27.7954 + 48.1431i 0.890622 + 1.54260i
\(975\) 0.739631 1.28108i 0.0236871 0.0410273i
\(976\) −237.370 −7.59802
\(977\) −49.1526 −1.57253 −0.786265 0.617890i \(-0.787988\pi\)
−0.786265 + 0.617890i \(0.787988\pi\)
\(978\) −50.4288 + 87.3453i −1.61254 + 2.79299i
\(979\) 50.1703 + 86.8975i 1.60345 + 2.77726i
\(980\) 57.5309 99.6464i 1.83776 3.18309i
\(981\) −9.81405 16.9984i −0.313339 0.542718i
\(982\) 18.6699 + 32.3372i 0.595779 + 1.03192i
\(983\) 3.95940 + 6.85788i 0.126285 + 0.218732i 0.922235 0.386631i \(-0.126361\pi\)
−0.795949 + 0.605363i \(0.793028\pi\)
\(984\) 47.2370 1.50586
\(985\) −6.47032 + 11.2069i −0.206162 + 0.357082i
\(986\) 1.98273 3.43419i 0.0631430 0.109367i
\(987\) −42.3571 73.3647i −1.34824 2.33522i
\(988\) −13.1312 −0.417759
\(989\) 1.89653 3.28489i 0.0603063 0.104454i
\(990\) 46.0725 1.46428
\(991\) −24.0440 −0.763783 −0.381891 0.924207i \(-0.624727\pi\)
−0.381891 + 0.924207i \(0.624727\pi\)
\(992\) 89.8793 101.688i 2.85367 3.22859i
\(993\) 52.7131 1.67280
\(994\) −157.633 −4.99982
\(995\) 14.4757 25.0726i 0.458910 0.794855i
\(996\) 28.7265 0.910235
\(997\) −4.28344 7.41913i −0.135658 0.234966i 0.790191 0.612861i \(-0.209981\pi\)
−0.925849 + 0.377895i \(0.876648\pi\)
\(998\) 3.70825 6.42287i 0.117382 0.203312i
\(999\) 3.77775 6.54326i 0.119523 0.207020i
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 403.2.h.a.222.1 yes 30
31.25 even 3 inner 403.2.h.a.118.1 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
403.2.h.a.118.1 30 31.25 even 3 inner
403.2.h.a.222.1 yes 30 1.1 even 1 trivial