Properties

Label 22.3.d.a.19.2
Level $22$
Weight $3$
Character 22.19
Analytic conductor $0.599$
Analytic rank $0$
Dimension $8$
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] = [22,3,Mod(7,22)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(22, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([7]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("22.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 22.d (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.599456581593\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: 8.0.64000000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 19.2
Root \(0.831254 + 1.14412i\) of defining polynomial
Character \(\chi\) \(=\) 22.19
Dual form 22.3.d.a.7.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.831254 + 1.14412i) q^{2} +(-0.295274 - 0.908759i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(-2.42545 - 1.76219i) q^{5} +(0.794285 - 1.09324i) q^{6} +(-3.70473 - 1.20374i) q^{7} +(-2.68999 + 0.874032i) q^{8} +(6.54250 - 4.75340i) q^{9} +O(q^{10})\) \(q+(0.831254 + 1.14412i) q^{2} +(-0.295274 - 0.908759i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(-2.42545 - 1.76219i) q^{5} +(0.794285 - 1.09324i) q^{6} +(-3.70473 - 1.20374i) q^{7} +(-2.68999 + 0.874032i) q^{8} +(6.54250 - 4.75340i) q^{9} -4.23984i q^{10} +(-10.2616 + 3.96233i) q^{11} +1.91105 q^{12} +(14.4340 + 19.8667i) q^{13} +(-1.70234 - 5.23927i) q^{14} +(-0.885238 + 2.72448i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(3.79692 - 5.22601i) q^{17} +(10.8770 + 3.53414i) q^{18} +(14.9139 - 4.84581i) q^{19} +(4.85090 - 3.52439i) q^{20} +3.72214i q^{21} +(-13.0634 - 8.44680i) q^{22} -30.3518 q^{23} +(1.58857 + 2.18648i) q^{24} +(-4.94794 - 15.2282i) q^{25} +(-10.7316 + 33.0285i) q^{26} +(-13.2089 - 9.59680i) q^{27} +(4.57929 - 6.30286i) q^{28} +(-14.2561 - 4.63209i) q^{29} +(-3.85300 + 1.25191i) q^{30} +(21.4645 - 15.5949i) q^{31} -5.65685i q^{32} +(6.63078 + 8.15533i) q^{33} +9.13540 q^{34} +(6.86441 + 9.44805i) q^{35} +(4.99802 + 15.3823i) q^{36} +(-1.29043 + 3.97153i) q^{37} +(17.9414 + 13.0352i) q^{38} +(13.7920 - 18.9831i) q^{39} +(8.06466 + 2.62037i) q^{40} +(41.2318 - 13.3970i) q^{41} +(-4.25858 + 3.09404i) q^{42} +56.0236i q^{43} +(-1.19479 - 21.9675i) q^{44} -24.2449 q^{45} +(-25.2301 - 34.7262i) q^{46} +(9.34350 + 28.7563i) q^{47} +(-1.18110 + 3.63504i) q^{48} +(-27.3658 - 19.8824i) q^{49} +(13.3099 - 18.3195i) q^{50} +(-5.87032 - 1.90738i) q^{51} +(-46.7093 + 15.1768i) q^{52} +(-42.1199 + 30.6019i) q^{53} -23.0899i q^{54} +(31.8713 + 8.47245i) q^{55} +11.0178 q^{56} +(-8.80735 - 12.1223i) q^{57} +(-6.55077 - 20.1612i) q^{58} +(29.1737 - 89.7875i) q^{59} +(-4.63516 - 3.36764i) q^{60} +(-54.8450 + 75.4877i) q^{61} +(35.6849 + 11.5947i) q^{62} +(-29.9600 + 9.73460i) q^{63} +(6.47214 - 4.70228i) q^{64} -73.6210i q^{65} +(-3.81884 + 14.3656i) q^{66} +54.0771 q^{67} +(7.59384 + 10.4520i) q^{68} +(8.96210 + 27.5825i) q^{69} +(-5.10366 + 15.7075i) q^{70} +(75.9613 + 55.1891i) q^{71} +(-13.4446 + 18.5050i) q^{72} +(-23.3346 - 7.58189i) q^{73} +(-5.61660 + 1.82494i) q^{74} +(-12.3778 + 8.99297i) q^{75} +31.3627i q^{76} +(42.7859 - 2.32709i) q^{77} +33.1837 q^{78} +(-45.4416 - 62.5450i) q^{79} +(3.70576 + 11.4052i) q^{80} +(17.6701 - 54.3831i) q^{81} +(49.6020 + 36.0379i) q^{82} +(-16.8251 + 23.1578i) q^{83} +(-7.07993 - 2.30041i) q^{84} +(-18.4185 + 5.98453i) q^{85} +(-64.0978 + 46.5698i) q^{86} +14.3231i q^{87} +(24.1404 - 19.6276i) q^{88} +68.2705 q^{89} +(-20.1537 - 27.7392i) q^{90} +(-29.5597 - 90.9753i) q^{91} +(18.7585 - 57.7326i) q^{92} +(-20.5099 - 14.9013i) q^{93} +(-25.1340 + 34.5939i) q^{94} +(-44.7121 - 14.5278i) q^{95} +(-5.14072 + 1.67032i) q^{96} +(-29.1342 + 21.1672i) q^{97} -47.8372i q^{98} +(-48.3018 + 74.7009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{3} + 4 q^{4} + 2 q^{5} - 20 q^{6} - 30 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{3} + 4 q^{4} + 2 q^{5} - 20 q^{6} - 30 q^{7} - 4 q^{9} - 4 q^{11} + 24 q^{12} + 30 q^{13} + 16 q^{14} + 42 q^{15} - 8 q^{16} + 30 q^{17} + 40 q^{18} - 30 q^{19} - 4 q^{20} + 24 q^{22} - 104 q^{23} - 40 q^{24} - 12 q^{25} - 96 q^{26} - 26 q^{27} - 40 q^{28} - 10 q^{29} - 60 q^{30} + 46 q^{31} - 14 q^{33} + 112 q^{34} + 70 q^{35} - 12 q^{36} + 6 q^{37} + 108 q^{38} + 130 q^{39} + 80 q^{40} + 250 q^{41} + 56 q^{42} - 12 q^{44} - 136 q^{45} - 160 q^{46} - 54 q^{47} - 8 q^{48} - 144 q^{49} - 80 q^{50} - 30 q^{51} - 40 q^{52} - 274 q^{53} - 26 q^{55} + 48 q^{56} - 130 q^{57} + 64 q^{58} + 50 q^{59} + 116 q^{60} + 50 q^{61} + 20 q^{62} - 20 q^{63} + 16 q^{64} - 136 q^{66} + 112 q^{67} + 60 q^{68} + 76 q^{69} + 4 q^{70} + 54 q^{71} - 80 q^{72} - 70 q^{73} - 40 q^{74} + 318 q^{75} + 266 q^{77} + 104 q^{78} + 370 q^{79} + 48 q^{80} + 180 q^{81} - 96 q^{82} - 150 q^{83} - 120 q^{84} - 330 q^{85} - 72 q^{86} + 72 q^{88} + 24 q^{89} + 160 q^{90} - 294 q^{91} - 112 q^{92} - 134 q^{93} - 20 q^{94} - 330 q^{95} - 18 q^{97} - 308 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).

\(n\) \(13\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.831254 + 1.14412i 0.415627 + 0.572061i
\(3\) −0.295274 0.908759i −0.0984246 0.302920i 0.889706 0.456533i \(-0.150909\pi\)
−0.988131 + 0.153613i \(0.950909\pi\)
\(4\) −0.618034 + 1.90211i −0.154508 + 0.475528i
\(5\) −2.42545 1.76219i −0.485090 0.352439i 0.318203 0.948023i \(-0.396921\pi\)
−0.803293 + 0.595584i \(0.796921\pi\)
\(6\) 0.794285 1.09324i 0.132381 0.182207i
\(7\) −3.70473 1.20374i −0.529247 0.171963i 0.0321910 0.999482i \(-0.489752\pi\)
−0.561438 + 0.827519i \(0.689752\pi\)
\(8\) −2.68999 + 0.874032i −0.336249 + 0.109254i
\(9\) 6.54250 4.75340i 0.726944 0.528156i
\(10\) 4.23984i 0.423984i
\(11\) −10.2616 + 3.96233i −0.932871 + 0.360212i
\(12\) 1.91105 0.159254
\(13\) 14.4340 + 19.8667i 1.11031 + 1.52820i 0.820965 + 0.570978i \(0.193436\pi\)
0.289340 + 0.957226i \(0.406564\pi\)
\(14\) −1.70234 5.23927i −0.121596 0.374234i
\(15\) −0.885238 + 2.72448i −0.0590158 + 0.181632i
\(16\) −3.23607 2.35114i −0.202254 0.146946i
\(17\) 3.79692 5.22601i 0.223348 0.307412i −0.682607 0.730785i \(-0.739154\pi\)
0.905955 + 0.423373i \(0.139154\pi\)
\(18\) 10.8770 + 3.53414i 0.604275 + 0.196341i
\(19\) 14.9139 4.84581i 0.784940 0.255043i 0.110992 0.993821i \(-0.464597\pi\)
0.673948 + 0.738779i \(0.264597\pi\)
\(20\) 4.85090 3.52439i 0.242545 0.176219i
\(21\) 3.72214i 0.177245i
\(22\) −13.0634 8.44680i −0.593789 0.383946i
\(23\) −30.3518 −1.31964 −0.659822 0.751422i \(-0.729369\pi\)
−0.659822 + 0.751422i \(0.729369\pi\)
\(24\) 1.58857 + 2.18648i 0.0661904 + 0.0911033i
\(25\) −4.94794 15.2282i −0.197918 0.609127i
\(26\) −10.7316 + 33.0285i −0.412754 + 1.27033i
\(27\) −13.2089 9.59680i −0.489217 0.355437i
\(28\) 4.57929 6.30286i 0.163546 0.225102i
\(29\) −14.2561 4.63209i −0.491590 0.159727i 0.0527235 0.998609i \(-0.483210\pi\)
−0.544314 + 0.838882i \(0.683210\pi\)
\(30\) −3.85300 + 1.25191i −0.128433 + 0.0417305i
\(31\) 21.4645 15.5949i 0.692404 0.503061i −0.185045 0.982730i \(-0.559243\pi\)
0.877450 + 0.479669i \(0.159243\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 6.63078 + 8.15533i 0.200933 + 0.247131i
\(34\) 9.13540 0.268688
\(35\) 6.86441 + 9.44805i 0.196126 + 0.269944i
\(36\) 4.99802 + 15.3823i 0.138834 + 0.427287i
\(37\) −1.29043 + 3.97153i −0.0348765 + 0.107339i −0.966979 0.254855i \(-0.917972\pi\)
0.932103 + 0.362194i \(0.117972\pi\)
\(38\) 17.9414 + 13.0352i 0.472142 + 0.343031i
\(39\) 13.7920 18.9831i 0.353642 0.486746i
\(40\) 8.06466 + 2.62037i 0.201617 + 0.0655092i
\(41\) 41.2318 13.3970i 1.00565 0.326757i 0.240532 0.970641i \(-0.422678\pi\)
0.765123 + 0.643884i \(0.222678\pi\)
\(42\) −4.25858 + 3.09404i −0.101395 + 0.0736676i
\(43\) 56.0236i 1.30287i 0.758703 + 0.651437i \(0.225833\pi\)
−0.758703 + 0.651437i \(0.774167\pi\)
\(44\) −1.19479 21.9675i −0.0271544 0.499262i
\(45\) −24.2449 −0.538776
\(46\) −25.2301 34.7262i −0.548480 0.754918i
\(47\) 9.34350 + 28.7563i 0.198798 + 0.611837i 0.999911 + 0.0133244i \(0.00424141\pi\)
−0.801113 + 0.598513i \(0.795759\pi\)
\(48\) −1.18110 + 3.63504i −0.0246062 + 0.0757300i
\(49\) −27.3658 19.8824i −0.558486 0.405764i
\(50\) 13.3099 18.3195i 0.266198 0.366391i
\(51\) −5.87032 1.90738i −0.115104 0.0373996i
\(52\) −46.7093 + 15.1768i −0.898256 + 0.291861i
\(53\) −42.1199 + 30.6019i −0.794714 + 0.577394i −0.909359 0.416013i \(-0.863427\pi\)
0.114644 + 0.993407i \(0.463427\pi\)
\(54\) 23.0899i 0.427591i
\(55\) 31.8713 + 8.47245i 0.579479 + 0.154044i
\(56\) 11.0178 0.196746
\(57\) −8.80735 12.1223i −0.154515 0.212671i
\(58\) −6.55077 20.1612i −0.112944 0.347607i
\(59\) 29.1737 89.7875i 0.494470 1.52182i −0.323312 0.946293i \(-0.604796\pi\)
0.817781 0.575529i \(-0.195204\pi\)
\(60\) −4.63516 3.36764i −0.0772527 0.0561274i
\(61\) −54.8450 + 75.4877i −0.899098 + 1.23750i 0.0716564 + 0.997429i \(0.477172\pi\)
−0.970755 + 0.240073i \(0.922828\pi\)
\(62\) 35.6849 + 11.5947i 0.575564 + 0.187012i
\(63\) −29.9600 + 9.73460i −0.475556 + 0.154517i
\(64\) 6.47214 4.70228i 0.101127 0.0734732i
\(65\) 73.6210i 1.13263i
\(66\) −3.81884 + 14.3656i −0.0578612 + 0.217660i
\(67\) 54.0771 0.807121 0.403560 0.914953i \(-0.367773\pi\)
0.403560 + 0.914953i \(0.367773\pi\)
\(68\) 7.59384 + 10.4520i 0.111674 + 0.153706i
\(69\) 8.96210 + 27.5825i 0.129886 + 0.399747i
\(70\) −5.10366 + 15.7075i −0.0729095 + 0.224392i
\(71\) 75.9613 + 55.1891i 1.06988 + 0.777312i 0.975890 0.218262i \(-0.0700387\pi\)
0.0939873 + 0.995573i \(0.470039\pi\)
\(72\) −13.4446 + 18.5050i −0.186731 + 0.257014i
\(73\) −23.3346 7.58189i −0.319653 0.103861i 0.144796 0.989462i \(-0.453747\pi\)
−0.464449 + 0.885600i \(0.653747\pi\)
\(74\) −5.61660 + 1.82494i −0.0758999 + 0.0246614i
\(75\) −12.3778 + 8.99297i −0.165037 + 0.119906i
\(76\) 31.3627i 0.412667i
\(77\) 42.7859 2.32709i 0.555662 0.0302219i
\(78\) 33.1837 0.425432
\(79\) −45.4416 62.5450i −0.575210 0.791709i 0.417950 0.908470i \(-0.362749\pi\)
−0.993160 + 0.116761i \(0.962749\pi\)
\(80\) 3.70576 + 11.4052i 0.0463220 + 0.142564i
\(81\) 17.6701 54.3831i 0.218150 0.671397i
\(82\) 49.6020 + 36.0379i 0.604902 + 0.439487i
\(83\) −16.8251 + 23.1578i −0.202712 + 0.279010i −0.898254 0.439476i \(-0.855164\pi\)
0.695542 + 0.718485i \(0.255164\pi\)
\(84\) −7.07993 2.30041i −0.0842848 0.0273858i
\(85\) −18.4185 + 5.98453i −0.216688 + 0.0704062i
\(86\) −64.0978 + 46.5698i −0.745324 + 0.541509i
\(87\) 14.3231i 0.164633i
\(88\) 24.1404 19.6276i 0.274322 0.223041i
\(89\) 68.2705 0.767085 0.383542 0.923523i \(-0.374704\pi\)
0.383542 + 0.923523i \(0.374704\pi\)
\(90\) −20.1537 27.7392i −0.223930 0.308213i
\(91\) −29.5597 90.9753i −0.324831 0.999728i
\(92\) 18.7585 57.7326i 0.203896 0.627528i
\(93\) −20.5099 14.9013i −0.220537 0.160229i
\(94\) −25.1340 + 34.5939i −0.267383 + 0.368021i
\(95\) −44.7121 14.5278i −0.470654 0.152925i
\(96\) −5.14072 + 1.67032i −0.0535492 + 0.0173992i
\(97\) −29.1342 + 21.1672i −0.300353 + 0.218219i −0.727746 0.685847i \(-0.759432\pi\)
0.427393 + 0.904066i \(0.359432\pi\)
\(98\) 47.8372i 0.488135i
\(99\) −48.3018 + 74.7009i −0.487897 + 0.754555i
\(100\) 32.0237 0.320237
\(101\) 1.45687 + 2.00522i 0.0144245 + 0.0198536i 0.816168 0.577814i \(-0.196094\pi\)
−0.801744 + 0.597668i \(0.796094\pi\)
\(102\) −2.69744 8.30188i −0.0264455 0.0813910i
\(103\) −9.38014 + 28.8691i −0.0910693 + 0.280283i −0.986209 0.165502i \(-0.947075\pi\)
0.895140 + 0.445785i \(0.147075\pi\)
\(104\) −56.1914 40.8254i −0.540302 0.392552i
\(105\) 6.55913 9.02786i 0.0624679 0.0859796i
\(106\) −70.0246 22.7524i −0.660609 0.214645i
\(107\) −72.8287 + 23.6635i −0.680642 + 0.221154i −0.628876 0.777505i \(-0.716485\pi\)
−0.0517656 + 0.998659i \(0.516485\pi\)
\(108\) 26.4177 19.1936i 0.244609 0.177718i
\(109\) 12.1116i 0.111116i −0.998455 0.0555580i \(-0.982306\pi\)
0.998455 0.0555580i \(-0.0176938\pi\)
\(110\) 16.7997 + 43.5075i 0.152724 + 0.395523i
\(111\) 3.99020 0.0359477
\(112\) 9.15859 + 12.6057i 0.0817731 + 0.112551i
\(113\) 29.3180 + 90.2315i 0.259451 + 0.798509i 0.992920 + 0.118786i \(0.0379001\pi\)
−0.733469 + 0.679723i \(0.762100\pi\)
\(114\) 6.54823 20.1534i 0.0574406 0.176784i
\(115\) 73.6169 + 53.4858i 0.640147 + 0.465094i
\(116\) 17.6215 24.2539i 0.151910 0.209086i
\(117\) 188.868 + 61.3671i 1.61426 + 0.524505i
\(118\) 126.979 41.2579i 1.07609 0.349643i
\(119\) −20.3573 + 14.7904i −0.171070 + 0.124289i
\(120\) 8.10256i 0.0675214i
\(121\) 89.5999 81.3195i 0.740495 0.672062i
\(122\) −131.957 −1.08162
\(123\) −24.3494 33.5140i −0.197962 0.272472i
\(124\) 16.3974 + 50.4661i 0.132237 + 0.406985i
\(125\) −37.9950 + 116.937i −0.303960 + 0.935493i
\(126\) −36.0419 26.1860i −0.286047 0.207825i
\(127\) 78.4228 107.940i 0.617502 0.849919i −0.379666 0.925124i \(-0.623961\pi\)
0.997168 + 0.0752049i \(0.0239611\pi\)
\(128\) 10.7600 + 3.49613i 0.0840623 + 0.0273135i
\(129\) 50.9119 16.5423i 0.394666 0.128235i
\(130\) 84.2315 61.1978i 0.647935 0.470752i
\(131\) 42.3750i 0.323473i 0.986834 + 0.161737i \(0.0517095\pi\)
−0.986834 + 0.161737i \(0.948290\pi\)
\(132\) −19.6104 + 7.57222i −0.148564 + 0.0573653i
\(133\) −61.0849 −0.459285
\(134\) 44.9518 + 61.8708i 0.335461 + 0.461723i
\(135\) 15.1260 + 46.5531i 0.112045 + 0.344838i
\(136\) −5.64599 + 17.3766i −0.0415146 + 0.127769i
\(137\) −110.042 79.9503i −0.803227 0.583579i 0.108632 0.994082i \(-0.465353\pi\)
−0.911859 + 0.410503i \(0.865353\pi\)
\(138\) −24.1080 + 33.1818i −0.174696 + 0.240448i
\(139\) −96.2740 31.2813i −0.692619 0.225045i −0.0585070 0.998287i \(-0.518634\pi\)
−0.634112 + 0.773242i \(0.718634\pi\)
\(140\) −22.2137 + 7.21767i −0.158669 + 0.0515548i
\(141\) 23.3737 16.9820i 0.165771 0.120440i
\(142\) 132.785i 0.935107i
\(143\) −226.834 146.671i −1.58625 1.02567i
\(144\) −32.3479 −0.224638
\(145\) 26.4149 + 36.3569i 0.182171 + 0.250737i
\(146\) −10.7224 33.0002i −0.0734411 0.226029i
\(147\) −9.98794 + 30.7397i −0.0679452 + 0.209114i
\(148\) −6.75678 4.90909i −0.0456539 0.0331695i
\(149\) 30.3729 41.8048i 0.203845 0.280569i −0.694839 0.719165i \(-0.744524\pi\)
0.898684 + 0.438597i \(0.144524\pi\)
\(150\) −20.5781 6.68624i −0.137188 0.0445749i
\(151\) −79.6932 + 25.8939i −0.527770 + 0.171483i −0.560769 0.827973i \(-0.689494\pi\)
0.0329987 + 0.999455i \(0.489494\pi\)
\(152\) −35.8828 + 26.0704i −0.236071 + 0.171516i
\(153\) 52.2394i 0.341434i
\(154\) 38.2285 + 47.0180i 0.248237 + 0.305311i
\(155\) −79.5424 −0.513177
\(156\) 27.5841 + 37.9662i 0.176821 + 0.243373i
\(157\) −71.8482 221.126i −0.457632 1.40845i −0.868017 0.496534i \(-0.834606\pi\)
0.410386 0.911912i \(-0.365394\pi\)
\(158\) 33.7857 103.982i 0.213833 0.658111i
\(159\) 40.2466 + 29.2409i 0.253124 + 0.183905i
\(160\) −9.96847 + 13.7204i −0.0623029 + 0.0857526i
\(161\) 112.445 + 36.5357i 0.698418 + 0.226930i
\(162\) 76.9094 24.9894i 0.474749 0.154255i
\(163\) 260.206 189.051i 1.59636 1.15982i 0.702284 0.711897i \(-0.252164\pi\)
0.894072 0.447923i \(-0.147836\pi\)
\(164\) 86.7074i 0.528704i
\(165\) −1.71136 31.4651i −0.0103719 0.190697i
\(166\) −40.4813 −0.243863
\(167\) 73.5229 + 101.196i 0.440257 + 0.605961i 0.970269 0.242028i \(-0.0778127\pi\)
−0.530012 + 0.847990i \(0.677813\pi\)
\(168\) −3.25327 10.0125i −0.0193647 0.0595984i
\(169\) −134.121 + 412.781i −0.793613 + 2.44249i
\(170\) −22.1575 16.0983i −0.130338 0.0946961i
\(171\) 74.5398 102.595i 0.435905 0.599972i
\(172\) −106.563 34.6245i −0.619553 0.201305i
\(173\) 120.522 39.1600i 0.696660 0.226358i 0.0607851 0.998151i \(-0.480640\pi\)
0.635875 + 0.771792i \(0.280640\pi\)
\(174\) −16.3874 + 11.9061i −0.0941805 + 0.0684261i
\(175\) 62.3723i 0.356413i
\(176\) 42.5232 + 11.3040i 0.241609 + 0.0642275i
\(177\) −90.2094 −0.509658
\(178\) 56.7501 + 78.1099i 0.318821 + 0.438820i
\(179\) 61.2907 + 188.633i 0.342406 + 1.05382i 0.962958 + 0.269653i \(0.0869088\pi\)
−0.620551 + 0.784166i \(0.713091\pi\)
\(180\) 14.9842 46.1166i 0.0832454 0.256203i
\(181\) −86.4445 62.8056i −0.477594 0.346992i 0.322800 0.946467i \(-0.395376\pi\)
−0.800393 + 0.599475i \(0.795376\pi\)
\(182\) 79.5153 109.443i 0.436897 0.601337i
\(183\) 84.7944 + 27.5514i 0.463358 + 0.150554i
\(184\) 81.6463 26.5285i 0.443730 0.144176i
\(185\) 10.1285 7.35877i 0.0547485 0.0397771i
\(186\) 35.8527i 0.192756i
\(187\) −18.2552 + 68.6717i −0.0976214 + 0.367229i
\(188\) −60.4724 −0.321662
\(189\) 37.3832 + 51.4535i 0.197795 + 0.272241i
\(190\) −20.5455 63.2324i −0.108134 0.332802i
\(191\) 10.6399 32.7463i 0.0557064 0.171447i −0.919332 0.393482i \(-0.871270\pi\)
0.975039 + 0.222036i \(0.0712702\pi\)
\(192\) −6.18430 4.49315i −0.0322099 0.0234018i
\(193\) −125.780 + 173.121i −0.651710 + 0.897002i −0.999172 0.0406920i \(-0.987044\pi\)
0.347461 + 0.937694i \(0.387044\pi\)
\(194\) −48.4358 15.7378i −0.249669 0.0811225i
\(195\) −66.9038 + 21.7384i −0.343097 + 0.111479i
\(196\) 54.7316 39.7649i 0.279243 0.202882i
\(197\) 271.384i 1.37758i −0.724960 0.688791i \(-0.758142\pi\)
0.724960 0.688791i \(-0.241858\pi\)
\(198\) −125.618 + 6.83225i −0.634435 + 0.0345063i
\(199\) 249.930 1.25593 0.627966 0.778241i \(-0.283888\pi\)
0.627966 + 0.778241i \(0.283888\pi\)
\(200\) 26.6198 + 36.6391i 0.133099 + 0.183195i
\(201\) −15.9675 49.1431i −0.0794405 0.244493i
\(202\) −1.08318 + 3.33369i −0.00536228 + 0.0165034i
\(203\) 47.2392 + 34.3213i 0.232705 + 0.169070i
\(204\) 7.25611 9.98718i 0.0355692 0.0489568i
\(205\) −123.614 40.1646i −0.602995 0.195925i
\(206\) −40.8271 + 13.2655i −0.198190 + 0.0643957i
\(207\) −198.577 + 144.274i −0.959308 + 0.696978i
\(208\) 98.2262i 0.472241i
\(209\) −133.839 + 108.819i −0.640378 + 0.520666i
\(210\) 15.7813 0.0751490
\(211\) −5.23750 7.20881i −0.0248223 0.0341650i 0.796425 0.604737i \(-0.206722\pi\)
−0.821248 + 0.570572i \(0.806722\pi\)
\(212\) −32.1767 99.0297i −0.151777 0.467121i
\(213\) 27.7242 85.3265i 0.130161 0.400594i
\(214\) −87.6131 63.6546i −0.409407 0.297452i
\(215\) 98.7243 135.882i 0.459183 0.632011i
\(216\) 43.9197 + 14.2704i 0.203332 + 0.0660665i
\(217\) −98.2924 + 31.9371i −0.452960 + 0.147176i
\(218\) 13.8572 10.0679i 0.0635652 0.0461828i
\(219\) 23.4443i 0.107052i
\(220\) −35.8131 + 55.3866i −0.162787 + 0.251757i
\(221\) 158.628 0.717774
\(222\) 3.31687 + 4.56528i 0.0149408 + 0.0205643i
\(223\) −63.9823 196.917i −0.286916 0.883037i −0.985818 0.167819i \(-0.946327\pi\)
0.698902 0.715218i \(-0.253673\pi\)
\(224\) −6.80937 + 20.9571i −0.0303990 + 0.0935585i
\(225\) −104.758 76.1108i −0.465589 0.338270i
\(226\) −78.8652 + 108.549i −0.348961 + 0.480304i
\(227\) 92.3282 + 29.9992i 0.406732 + 0.132155i 0.505236 0.862981i \(-0.331406\pi\)
−0.0985035 + 0.995137i \(0.531406\pi\)
\(228\) 28.5012 9.26059i 0.125005 0.0406166i
\(229\) −46.7820 + 33.9891i −0.204288 + 0.148424i −0.685226 0.728331i \(-0.740296\pi\)
0.480937 + 0.876755i \(0.340296\pi\)
\(230\) 128.687i 0.559509i
\(231\) −14.7483 38.1950i −0.0638456 0.165346i
\(232\) 42.3975 0.182748
\(233\) −41.2848 56.8237i −0.177188 0.243879i 0.711180 0.703009i \(-0.248161\pi\)
−0.888369 + 0.459131i \(0.848161\pi\)
\(234\) 86.7861 + 267.100i 0.370881 + 1.14145i
\(235\) 28.0120 86.2122i 0.119200 0.366860i
\(236\) 152.756 + 110.983i 0.647269 + 0.470269i
\(237\) −43.4207 + 59.7634i −0.183210 + 0.252166i
\(238\) −33.8442 10.9966i −0.142202 0.0462043i
\(239\) 62.7924 20.4025i 0.262730 0.0853660i −0.174690 0.984623i \(-0.555892\pi\)
0.437420 + 0.899257i \(0.355892\pi\)
\(240\) 9.27033 6.73529i 0.0386264 0.0280637i
\(241\) 49.6438i 0.205991i 0.994682 + 0.102995i \(0.0328427\pi\)
−0.994682 + 0.102995i \(0.967157\pi\)
\(242\) 167.520 + 34.9162i 0.692230 + 0.144282i
\(243\) −201.582 −0.829556
\(244\) −109.690 150.975i −0.449549 0.618751i
\(245\) 31.3378 + 96.4477i 0.127909 + 0.393664i
\(246\) 18.1037 55.7173i 0.0735921 0.226493i
\(247\) 311.536 + 226.344i 1.26128 + 0.916374i
\(248\) −44.1090 + 60.7109i −0.177859 + 0.244802i
\(249\) 26.0129 + 8.45210i 0.104469 + 0.0339442i
\(250\) −165.373 + 53.7331i −0.661494 + 0.214932i
\(251\) 53.3991 38.7967i 0.212746 0.154569i −0.476309 0.879278i \(-0.658026\pi\)
0.689055 + 0.724709i \(0.258026\pi\)
\(252\) 63.0036i 0.250014i
\(253\) 311.458 120.264i 1.23106 0.475352i
\(254\) 188.685 0.742856
\(255\) 10.8770 + 14.9709i 0.0426549 + 0.0587094i
\(256\) 4.94427 + 15.2169i 0.0193136 + 0.0594410i
\(257\) 84.1944 259.124i 0.327605 1.00826i −0.642647 0.766163i \(-0.722164\pi\)
0.970251 0.242101i \(-0.0778364\pi\)
\(258\) 61.2472 + 44.4987i 0.237392 + 0.172475i
\(259\) 9.56137 13.1601i 0.0369165 0.0508112i
\(260\) 140.036 + 45.5003i 0.538598 + 0.175001i
\(261\) −115.289 + 37.4596i −0.441719 + 0.143523i
\(262\) −48.4822 + 35.2244i −0.185047 + 0.134444i
\(263\) 66.3839i 0.252410i 0.992004 + 0.126205i \(0.0402797\pi\)
−0.992004 + 0.126205i \(0.959720\pi\)
\(264\) −24.9648 16.1423i −0.0945636 0.0611450i
\(265\) 156.086 0.589004
\(266\) −50.7770 69.8886i −0.190891 0.262739i
\(267\) −20.1585 62.0415i −0.0755000 0.232365i
\(268\) −33.4215 + 102.861i −0.124707 + 0.383809i
\(269\) −147.830 107.405i −0.549553 0.399274i 0.278067 0.960562i \(-0.410306\pi\)
−0.827621 + 0.561288i \(0.810306\pi\)
\(270\) −40.6889 + 56.0035i −0.150700 + 0.207420i
\(271\) −380.422 123.607i −1.40377 0.456113i −0.493363 0.869823i \(-0.664233\pi\)
−0.910409 + 0.413710i \(0.864233\pi\)
\(272\) −24.5742 + 7.98463i −0.0903462 + 0.0293553i
\(273\) −73.9464 + 53.7252i −0.270866 + 0.196796i
\(274\) 192.361i 0.702047i
\(275\) 111.113 + 136.660i 0.404046 + 0.496945i
\(276\) −58.0039 −0.210159
\(277\) −27.4031 37.7171i −0.0989282 0.136163i 0.756683 0.653782i \(-0.226819\pi\)
−0.855611 + 0.517619i \(0.826819\pi\)
\(278\) −44.2385 136.152i −0.159131 0.489755i
\(279\) 66.3028 204.059i 0.237644 0.731394i
\(280\) −26.7231 19.4155i −0.0954397 0.0693410i
\(281\) −296.043 + 407.468i −1.05353 + 1.45006i −0.167826 + 0.985817i \(0.553675\pi\)
−0.885706 + 0.464246i \(0.846325\pi\)
\(282\) 38.8590 + 12.6260i 0.137798 + 0.0447732i
\(283\) −53.4612 + 17.3706i −0.188909 + 0.0613802i −0.401944 0.915664i \(-0.631665\pi\)
0.213035 + 0.977045i \(0.431665\pi\)
\(284\) −151.923 + 110.378i −0.534939 + 0.388656i
\(285\) 44.9222i 0.157622i
\(286\) −20.7465 381.446i −0.0725403 1.33373i
\(287\) −168.879 −0.588429
\(288\) −26.8893 37.0099i −0.0933656 0.128507i
\(289\) 76.4113 + 235.170i 0.264399 + 0.813737i
\(290\) −19.6393 + 60.4437i −0.0677219 + 0.208426i
\(291\) 27.8385 + 20.2259i 0.0956650 + 0.0695047i
\(292\) 28.8432 39.6993i 0.0987781 0.135956i
\(293\) 177.512 + 57.6771i 0.605843 + 0.196850i 0.595845 0.803100i \(-0.296817\pi\)
0.00999814 + 0.999950i \(0.496817\pi\)
\(294\) −43.4725 + 14.1251i −0.147866 + 0.0480445i
\(295\) −228.982 + 166.365i −0.776211 + 0.563950i
\(296\) 11.8113i 0.0399030i
\(297\) 173.569 + 46.1404i 0.584409 + 0.155355i
\(298\) 73.0774 0.245226
\(299\) −438.098 602.990i −1.46521 2.01669i
\(300\) −9.45577 29.1019i −0.0315192 0.0970062i
\(301\) 67.4377 207.552i 0.224046 0.689541i
\(302\) −95.8711 69.6545i −0.317454 0.230644i
\(303\) 1.39208 1.91604i 0.00459433 0.00632355i
\(304\) −59.6555 19.3832i −0.196235 0.0637606i
\(305\) 266.048 86.4441i 0.872288 0.283423i
\(306\) 59.7683 43.4242i 0.195321 0.141909i
\(307\) 495.856i 1.61517i 0.589755 + 0.807583i \(0.299224\pi\)
−0.589755 + 0.807583i \(0.700776\pi\)
\(308\) −22.0168 + 82.8219i −0.0714830 + 0.268902i
\(309\) 29.0048 0.0938666
\(310\) −66.1199 91.0063i −0.213290 0.293569i
\(311\) 114.991 + 353.907i 0.369747 + 1.13796i 0.946955 + 0.321366i \(0.104142\pi\)
−0.577208 + 0.816597i \(0.695858\pi\)
\(312\) −20.5087 + 63.1191i −0.0657329 + 0.202305i
\(313\) 198.463 + 144.192i 0.634068 + 0.460677i 0.857807 0.513972i \(-0.171826\pi\)
−0.223739 + 0.974649i \(0.571826\pi\)
\(314\) 193.271 266.015i 0.615513 0.847181i
\(315\) 89.8208 + 29.1845i 0.285145 + 0.0926493i
\(316\) 147.052 47.7801i 0.465355 0.151203i
\(317\) 48.6657 35.3577i 0.153519 0.111538i −0.508374 0.861136i \(-0.669753\pi\)
0.661893 + 0.749598i \(0.269753\pi\)
\(318\) 70.3537i 0.221238i
\(319\) 164.644 8.95484i 0.516126 0.0280716i
\(320\) −23.9842 −0.0749506
\(321\) 43.0088 + 59.1966i 0.133984 + 0.184413i
\(322\) 51.6692 + 159.022i 0.160463 + 0.493856i
\(323\) 31.3025 96.3391i 0.0969117 0.298264i
\(324\) 92.5221 + 67.2212i 0.285562 + 0.207473i
\(325\) 231.115 318.102i 0.711122 0.978776i
\(326\) 432.594 + 140.558i 1.32698 + 0.431161i
\(327\) −11.0066 + 3.57625i −0.0336592 + 0.0109365i
\(328\) −99.2039 + 72.0759i −0.302451 + 0.219744i
\(329\) 117.782i 0.357999i
\(330\) 34.5773 28.1135i 0.104780 0.0851923i
\(331\) −89.7487 −0.271144 −0.135572 0.990767i \(-0.543287\pi\)
−0.135572 + 0.990767i \(0.543287\pi\)
\(332\) −33.6502 46.3156i −0.101356 0.139505i
\(333\) 10.4357 + 32.1177i 0.0313383 + 0.0964495i
\(334\) −54.6640 + 168.238i −0.163665 + 0.503708i
\(335\) −131.161 95.2943i −0.391526 0.284460i
\(336\) 8.75127 12.0451i 0.0260454 0.0358485i
\(337\) −117.112 38.0519i −0.347513 0.112914i 0.130060 0.991506i \(-0.458483\pi\)
−0.477572 + 0.878592i \(0.658483\pi\)
\(338\) −583.760 + 189.675i −1.72710 + 0.561169i
\(339\) 73.3419 53.2860i 0.216348 0.157186i
\(340\) 38.7327i 0.113920i
\(341\) −158.468 + 245.078i −0.464715 + 0.718703i
\(342\) 179.343 0.524395
\(343\) 189.642 + 261.020i 0.552893 + 0.760992i
\(344\) −48.9664 150.703i −0.142344 0.438090i
\(345\) 26.8686 82.6930i 0.0778799 0.239690i
\(346\) 144.988 + 105.340i 0.419041 + 0.304451i
\(347\) −186.940 + 257.300i −0.538731 + 0.741500i −0.988430 0.151681i \(-0.951531\pi\)
0.449698 + 0.893180i \(0.351531\pi\)
\(348\) −27.2442 8.85217i −0.0782879 0.0254373i
\(349\) 252.823 82.1472i 0.724421 0.235379i 0.0764822 0.997071i \(-0.475631\pi\)
0.647939 + 0.761692i \(0.275631\pi\)
\(350\) −71.3616 + 51.8472i −0.203890 + 0.148135i
\(351\) 400.936i 1.14227i
\(352\) 22.4143 + 58.0482i 0.0636770 + 0.164910i
\(353\) −249.501 −0.706802 −0.353401 0.935472i \(-0.614975\pi\)
−0.353401 + 0.935472i \(0.614975\pi\)
\(354\) −74.9869 103.211i −0.211828 0.291556i
\(355\) −86.9865 267.717i −0.245032 0.754132i
\(356\) −42.1935 + 129.858i −0.118521 + 0.364770i
\(357\) 19.4519 + 14.1327i 0.0544872 + 0.0395873i
\(358\) −164.872 + 226.926i −0.460536 + 0.633873i
\(359\) −535.038 173.844i −1.49036 0.484246i −0.553169 0.833069i \(-0.686581\pi\)
−0.937189 + 0.348823i \(0.886581\pi\)
\(360\) 65.2187 21.1908i 0.181163 0.0588634i
\(361\) −93.1137 + 67.6511i −0.257933 + 0.187399i
\(362\) 151.110i 0.417432i
\(363\) −100.356 57.4132i −0.276464 0.158163i
\(364\) 191.314 0.525588
\(365\) 43.2363 + 59.5097i 0.118456 + 0.163040i
\(366\) 38.9635 + 119.917i 0.106458 + 0.327643i
\(367\) 8.68220 26.7211i 0.0236572 0.0728094i −0.938531 0.345195i \(-0.887813\pi\)
0.962188 + 0.272386i \(0.0878127\pi\)
\(368\) 98.2206 + 71.3614i 0.266904 + 0.193917i
\(369\) 206.078 283.641i 0.558476 0.768676i
\(370\) 16.8387 + 5.47122i 0.0455099 + 0.0147871i
\(371\) 192.879 62.6703i 0.519890 0.168923i
\(372\) 41.0198 29.8027i 0.110268 0.0801147i
\(373\) 157.016i 0.420953i 0.977599 + 0.210477i \(0.0675016\pi\)
−0.977599 + 0.210477i \(0.932498\pi\)
\(374\) −93.7436 + 36.1975i −0.250651 + 0.0967846i
\(375\) 117.486 0.313297
\(376\) −50.2679 69.1879i −0.133691 0.184010i
\(377\) −113.748 350.081i −0.301719 0.928596i
\(378\) −27.7942 + 85.5419i −0.0735297 + 0.226301i
\(379\) −503.479 365.799i −1.32844 0.965169i −0.999785 0.0207195i \(-0.993404\pi\)
−0.328656 0.944450i \(-0.606596\pi\)
\(380\) 55.2672 76.0688i 0.145440 0.200181i
\(381\) −121.247 39.3957i −0.318235 0.103401i
\(382\) 46.3103 15.0471i 0.121231 0.0393904i
\(383\) 278.690 202.480i 0.727651 0.528670i −0.161168 0.986927i \(-0.551526\pi\)
0.888820 + 0.458257i \(0.151526\pi\)
\(384\) 10.8105i 0.0281525i
\(385\) −107.876 69.7528i −0.280197 0.181176i
\(386\) −302.627 −0.784009
\(387\) 266.302 + 366.534i 0.688120 + 0.947116i
\(388\) −22.2566 68.4986i −0.0573623 0.176543i
\(389\) −89.6214 + 275.826i −0.230389 + 0.709065i 0.767311 + 0.641276i \(0.221595\pi\)
−0.997700 + 0.0677892i \(0.978405\pi\)
\(390\) −80.4854 58.4761i −0.206373 0.149939i
\(391\) −115.243 + 158.619i −0.294740 + 0.405675i
\(392\) 90.9918 + 29.5650i 0.232122 + 0.0754210i
\(393\) 38.5087 12.5122i 0.0979865 0.0318377i
\(394\) 310.496 225.589i 0.788061 0.572560i
\(395\) 231.777i 0.586777i
\(396\) −112.237 138.043i −0.283428 0.348594i
\(397\) −238.817 −0.601554 −0.300777 0.953694i \(-0.597246\pi\)
−0.300777 + 0.953694i \(0.597246\pi\)
\(398\) 207.756 + 285.951i 0.521999 + 0.718470i
\(399\) 18.0368 + 55.5114i 0.0452049 + 0.139126i
\(400\) −19.7918 + 60.9127i −0.0494794 + 0.152282i
\(401\) 109.555 + 79.5964i 0.273205 + 0.198495i 0.715948 0.698154i \(-0.245995\pi\)
−0.442743 + 0.896648i \(0.645995\pi\)
\(402\) 42.9526 59.1192i 0.106847 0.147063i
\(403\) 619.637 + 201.332i 1.53756 + 0.499584i
\(404\) −4.71455 + 1.53185i −0.0116697 + 0.00379170i
\(405\) −138.692 + 100.765i −0.342449 + 0.248803i
\(406\) 82.5771i 0.203392i
\(407\) −2.49468 45.8673i −0.00612944 0.112696i
\(408\) 17.4582 0.0427898
\(409\) 178.874 + 246.199i 0.437345 + 0.601953i 0.969619 0.244618i \(-0.0786627\pi\)
−0.532275 + 0.846572i \(0.678663\pi\)
\(410\) −56.8013 174.816i −0.138540 0.426382i
\(411\) −40.1630 + 123.609i −0.0977203 + 0.300752i
\(412\) −49.1151 35.6842i −0.119211 0.0866121i
\(413\) −216.161 + 297.520i −0.523393 + 0.720388i
\(414\) −330.135 107.267i −0.797428 0.259100i
\(415\) 81.6170 26.5190i 0.196667 0.0639011i
\(416\) 112.383 81.6509i 0.270151 0.196276i
\(417\) 96.7264i 0.231958i
\(418\) −235.757 62.6719i −0.564012 0.149933i
\(419\) 594.131 1.41797 0.708987 0.705221i \(-0.249152\pi\)
0.708987 + 0.705221i \(0.249152\pi\)
\(420\) 13.1183 + 18.0557i 0.0312339 + 0.0429898i
\(421\) −78.8474 242.667i −0.187286 0.576407i 0.812694 0.582690i \(-0.198000\pi\)
−0.999980 + 0.00628320i \(0.998000\pi\)
\(422\) 3.89406 11.9847i 0.00922764 0.0283998i
\(423\) 197.820 + 143.725i 0.467660 + 0.339775i
\(424\) 86.5552 119.133i 0.204140 0.280974i
\(425\) −98.3696 31.9622i −0.231458 0.0752052i
\(426\) 120.670 39.2080i 0.283263 0.0920376i
\(427\) 294.053 213.642i 0.688649 0.500333i
\(428\) 153.153i 0.357835i
\(429\) −66.3107 + 249.445i −0.154570 + 0.581457i
\(430\) 237.531 0.552398
\(431\) 388.839 + 535.191i 0.902178 + 1.24174i 0.969768 + 0.244029i \(0.0784691\pi\)
−0.0675899 + 0.997713i \(0.521531\pi\)
\(432\) 20.1813 + 62.1118i 0.0467161 + 0.143777i
\(433\) 33.9998 104.641i 0.0785215 0.241664i −0.904089 0.427345i \(-0.859449\pi\)
0.982610 + 0.185681i \(0.0594490\pi\)
\(434\) −118.246 85.9107i −0.272456 0.197951i
\(435\) 25.2401 34.7400i 0.0580232 0.0798621i
\(436\) 23.0377 + 7.48541i 0.0528388 + 0.0171684i
\(437\) −452.663 + 147.079i −1.03584 + 0.336566i
\(438\) −26.8232 + 19.4882i −0.0612401 + 0.0444936i
\(439\) 549.236i 1.25111i −0.780181 0.625553i \(-0.784873\pi\)
0.780181 0.625553i \(-0.215127\pi\)
\(440\) −93.1389 + 5.06574i −0.211679 + 0.0115130i
\(441\) −273.550 −0.620295
\(442\) 131.860 + 181.490i 0.298326 + 0.410611i
\(443\) −10.8704 33.4556i −0.0245381 0.0755205i 0.938038 0.346534i \(-0.112641\pi\)
−0.962576 + 0.271013i \(0.912641\pi\)
\(444\) −2.46608 + 7.58981i −0.00555423 + 0.0170942i
\(445\) −165.587 120.306i −0.372105 0.270350i
\(446\) 172.112 236.892i 0.385901 0.531148i
\(447\) −46.9588 15.2578i −0.105053 0.0341339i
\(448\) −29.6378 + 9.62991i −0.0661558 + 0.0214953i
\(449\) 456.315 331.532i 1.01629 0.738379i 0.0507723 0.998710i \(-0.483832\pi\)
0.965519 + 0.260331i \(0.0838317\pi\)
\(450\) 183.123i 0.406940i
\(451\) −370.020 + 300.849i −0.820444 + 0.667070i
\(452\) −189.750 −0.419801
\(453\) 47.0627 + 64.7762i 0.103891 + 0.142994i
\(454\) 42.4253 + 130.572i 0.0934479 + 0.287603i
\(455\) −88.6205 + 272.746i −0.194770 + 0.599441i
\(456\) 34.2870 + 24.9109i 0.0751907 + 0.0546293i
\(457\) 399.901 550.416i 0.875056 1.20441i −0.102710 0.994711i \(-0.532751\pi\)
0.977766 0.209700i \(-0.0672487\pi\)
\(458\) −77.7755 25.2708i −0.169816 0.0551764i
\(459\) −100.306 + 32.5914i −0.218531 + 0.0710052i
\(460\) −147.234 + 106.972i −0.320073 + 0.232547i
\(461\) 202.839i 0.439998i 0.975500 + 0.219999i \(0.0706053\pi\)
−0.975500 + 0.219999i \(0.929395\pi\)
\(462\) 31.4402 48.6236i 0.0680523 0.105246i
\(463\) −746.270 −1.61182 −0.805908 0.592041i \(-0.798322\pi\)
−0.805908 + 0.592041i \(0.798322\pi\)
\(464\) 35.2430 + 48.5079i 0.0759548 + 0.104543i
\(465\) 23.4868 + 72.2849i 0.0505092 + 0.155451i
\(466\) 30.6951 94.4698i 0.0658693 0.202725i
\(467\) −301.368 218.957i −0.645328 0.468858i 0.216348 0.976316i \(-0.430585\pi\)
−0.861677 + 0.507458i \(0.830585\pi\)
\(468\) −233.454 + 321.322i −0.498834 + 0.686586i
\(469\) −200.341 65.0947i −0.427166 0.138795i
\(470\) 121.922 39.6150i 0.259409 0.0842872i
\(471\) −179.735 + 130.585i −0.381604 + 0.277251i
\(472\) 267.027i 0.565734i
\(473\) −221.984 574.890i −0.469310 1.21541i
\(474\) −104.470 −0.220401
\(475\) −147.586 203.134i −0.310707 0.427651i
\(476\) −15.5516 47.8629i −0.0326714 0.100552i
\(477\) −130.106 + 400.425i −0.272759 + 0.839466i
\(478\) 75.5394 + 54.8826i 0.158032 + 0.114817i
\(479\) 336.874 463.668i 0.703287 0.967991i −0.296629 0.954993i \(-0.595862\pi\)
0.999916 0.0129981i \(-0.00413753\pi\)
\(480\) 15.4120 + 5.00766i 0.0321083 + 0.0104326i
\(481\) −97.5271 + 31.6885i −0.202759 + 0.0658804i
\(482\) −56.7986 + 41.2666i −0.117839 + 0.0856153i
\(483\) 112.974i 0.233900i
\(484\) 99.3031 + 220.687i 0.205172 + 0.455966i
\(485\) 107.964 0.222607
\(486\) −167.566 230.635i −0.344786 0.474557i
\(487\) 13.0777 + 40.2489i 0.0268535 + 0.0826467i 0.963585 0.267402i \(-0.0861651\pi\)
−0.936732 + 0.350049i \(0.886165\pi\)
\(488\) 81.5541 250.998i 0.167119 0.514339i
\(489\) −248.634 180.643i −0.508453 0.369413i
\(490\) −84.2984 + 116.027i −0.172038 + 0.236789i
\(491\) 582.692 + 189.328i 1.18675 + 0.385597i 0.834868 0.550450i \(-0.185544\pi\)
0.351877 + 0.936046i \(0.385544\pi\)
\(492\) 78.7962 25.6024i 0.160155 0.0520375i
\(493\) −78.3366 + 56.9149i −0.158898 + 0.115446i
\(494\) 544.585i 1.10240i
\(495\) 248.791 96.0663i 0.502608 0.194073i
\(496\) −106.126 −0.213965
\(497\) −214.983 295.898i −0.432561 0.595368i
\(498\) 11.9531 + 36.7878i 0.0240021 + 0.0738710i
\(499\) −143.126 + 440.498i −0.286826 + 0.882761i 0.699019 + 0.715103i \(0.253620\pi\)
−0.985845 + 0.167658i \(0.946380\pi\)
\(500\) −198.945 144.542i −0.397889 0.289083i
\(501\) 70.2530 96.6950i 0.140226 0.193004i
\(502\) 88.7765 + 28.8452i 0.176846 + 0.0574606i
\(503\) 717.814 233.232i 1.42707 0.463682i 0.509226 0.860633i \(-0.329932\pi\)
0.917840 + 0.396951i \(0.129932\pi\)
\(504\) 72.0839 52.3720i 0.143024 0.103913i
\(505\) 7.43085i 0.0147145i
\(506\) 396.497 + 256.376i 0.783591 + 0.506672i
\(507\) 414.721 0.817990
\(508\) 156.846 + 215.879i 0.308751 + 0.424959i
\(509\) 216.406 + 666.029i 0.425159 + 1.30850i 0.902842 + 0.429972i \(0.141477\pi\)
−0.477683 + 0.878532i \(0.658523\pi\)
\(510\) −8.08700 + 24.8892i −0.0158569 + 0.0488024i
\(511\) 77.3219 + 56.1776i 0.151315 + 0.109937i
\(512\) −13.3001 + 18.3060i −0.0259767 + 0.0357538i
\(513\) −243.499 79.1177i −0.474658 0.154226i
\(514\) 366.456 119.069i 0.712950 0.231651i
\(515\) 73.6240 53.4910i 0.142959 0.103866i
\(516\) 107.064i 0.207488i
\(517\) −209.821 258.063i −0.405844 0.499156i
\(518\) 23.0047 0.0444106
\(519\) −71.1741 97.9627i −0.137137 0.188753i
\(520\) 64.3472 + 198.040i 0.123745 + 0.380846i
\(521\) 72.6318 223.538i 0.139408 0.429055i −0.856841 0.515580i \(-0.827576\pi\)
0.996250 + 0.0865255i \(0.0275764\pi\)
\(522\) −138.693 100.766i −0.265695 0.193038i
\(523\) −381.075 + 524.505i −0.728633 + 1.00288i 0.270559 + 0.962703i \(0.412791\pi\)
−0.999193 + 0.0401744i \(0.987209\pi\)
\(524\) −80.6021 26.1892i −0.153821 0.0499794i
\(525\) 56.6814 18.4169i 0.107965 0.0350798i
\(526\) −75.9513 + 55.1819i −0.144394 + 0.104908i
\(527\) 171.386i 0.325211i
\(528\) −2.28332 41.9811i −0.00432446 0.0795097i
\(529\) 392.234 0.741463
\(530\) 129.747 + 178.582i 0.244806 + 0.336947i
\(531\) −235.927 726.109i −0.444307 1.36744i
\(532\) 37.7525 116.190i 0.0709634 0.218403i
\(533\) 861.293 + 625.766i 1.61593 + 1.17405i
\(534\) 54.2263 74.6360i 0.101547 0.139768i
\(535\) 218.342 + 70.9436i 0.408116 + 0.132605i
\(536\) −145.467 + 47.2651i −0.271394 + 0.0881812i
\(537\) 153.325 111.397i 0.285521 0.207443i
\(538\) 258.416i 0.480327i
\(539\) 359.597 + 95.5927i 0.667156 + 0.177352i
\(540\) −97.8977 −0.181292
\(541\) −194.429 267.608i −0.359388 0.494655i 0.590590 0.806972i \(-0.298895\pi\)
−0.949978 + 0.312317i \(0.898895\pi\)
\(542\) −174.806 537.998i −0.322521 0.992617i
\(543\) −31.5504 + 97.1021i −0.0581038 + 0.178825i
\(544\) −29.5628 21.4786i −0.0543433 0.0394827i
\(545\) −21.3431 + 29.3762i −0.0391616 + 0.0539013i
\(546\) −122.937 39.9445i −0.225158 0.0731584i
\(547\) −575.496 + 186.990i −1.05209 + 0.341846i −0.783490 0.621404i \(-0.786562\pi\)
−0.268604 + 0.963251i \(0.586562\pi\)
\(548\) 220.084 159.901i 0.401614 0.291789i
\(549\) 754.578i 1.37446i
\(550\) −63.9928 + 240.726i −0.116350 + 0.437683i
\(551\) −235.060 −0.426606
\(552\) −48.2160 66.3636i −0.0873478 0.120224i
\(553\) 93.0609 + 286.412i 0.168284 + 0.517924i
\(554\) 20.3741 62.7050i 0.0367764 0.113186i
\(555\) −9.67803 7.03150i −0.0174379 0.0126694i
\(556\) 119.001 163.791i 0.214031 0.294588i
\(557\) −242.301 78.7283i −0.435010 0.141343i 0.0833221 0.996523i \(-0.473447\pi\)
−0.518332 + 0.855179i \(0.673447\pi\)
\(558\) 288.583 93.7663i 0.517174 0.168040i
\(559\) −1113.00 + 808.642i −1.99106 + 1.44659i
\(560\) 46.7137i 0.0834174i
\(561\) 67.7964 3.68738i 0.120849 0.00657288i
\(562\) −712.280 −1.26740
\(563\) −594.763 818.621i −1.05642 1.45403i −0.883110 0.469166i \(-0.844554\pi\)
−0.173308 0.984868i \(-0.555446\pi\)
\(564\) 17.8559 + 54.9549i 0.0316594 + 0.0974377i
\(565\) 87.8960 270.516i 0.155568 0.478789i
\(566\) −64.3140 46.7268i −0.113629 0.0825562i
\(567\) −130.926 + 180.204i −0.230910 + 0.317821i
\(568\) −252.573 82.0658i −0.444670 0.144482i
\(569\) −418.918 + 136.115i −0.736236 + 0.239217i −0.653048 0.757316i \(-0.726510\pi\)
−0.0831875 + 0.996534i \(0.526510\pi\)
\(570\) −51.3965 + 37.3418i −0.0901694 + 0.0655119i
\(571\) 577.275i 1.01099i −0.862830 0.505495i \(-0.831310\pi\)
0.862830 0.505495i \(-0.168690\pi\)
\(572\) 419.176 340.815i 0.732825 0.595831i
\(573\) −32.9002 −0.0574175
\(574\) −140.381 193.218i −0.244567 0.336618i
\(575\) 150.179 + 462.203i 0.261181 + 0.803832i
\(576\) 19.9921 61.5293i 0.0347085 0.106822i
\(577\) 666.510 + 484.248i 1.15513 + 0.839251i 0.989155 0.146879i \(-0.0469226\pi\)
0.165976 + 0.986130i \(0.446923\pi\)
\(578\) −205.546 + 282.910i −0.355616 + 0.489463i
\(579\) 194.465 + 63.1856i 0.335864 + 0.109129i
\(580\) −85.4803 + 27.7742i −0.147380 + 0.0478866i
\(581\) 90.2084 65.5402i 0.155264 0.112806i
\(582\) 48.6635i 0.0836142i
\(583\) 310.962 480.916i 0.533382 0.824899i
\(584\) 69.3969 0.118830
\(585\) −349.950 481.665i −0.598206 0.823360i
\(586\) 81.5678 + 251.040i 0.139194 + 0.428395i
\(587\) −70.2908 + 216.333i −0.119746 + 0.368540i −0.992907 0.118891i \(-0.962066\pi\)
0.873161 + 0.487431i \(0.162066\pi\)
\(588\) −52.2975 37.9964i −0.0889414 0.0646197i
\(589\) 244.549 336.593i 0.415194 0.571465i
\(590\) −380.685 123.692i −0.645228 0.209647i
\(591\) −246.622 + 80.1325i −0.417297 + 0.135588i
\(592\) 13.5136 9.81817i 0.0228269 0.0165847i
\(593\) 154.112i 0.259885i 0.991522 + 0.129942i \(0.0414792\pi\)
−0.991522 + 0.129942i \(0.958521\pi\)
\(594\) 91.4899 + 236.939i 0.154023 + 0.398887i
\(595\) 75.4392 0.126789
\(596\) 60.7459 + 83.6095i 0.101923 + 0.140284i
\(597\) −73.7979 227.127i −0.123615 0.380446i
\(598\) 325.724 1002.47i 0.544689 1.67638i
\(599\) −357.063 259.422i −0.596099 0.433091i 0.248393 0.968659i \(-0.420097\pi\)
−0.844492 + 0.535568i \(0.820097\pi\)
\(600\) 25.4360 35.0096i 0.0423933 0.0583493i
\(601\) 1074.30 + 349.062i 1.78753 + 0.580802i 0.999397 0.0347090i \(-0.0110504\pi\)
0.788128 + 0.615511i \(0.211050\pi\)
\(602\) 293.523 95.3713i 0.487579 0.158424i
\(603\) 353.799 257.050i 0.586731 0.426285i
\(604\) 167.589i 0.277465i
\(605\) −360.621 + 39.3441i −0.596067 + 0.0650315i
\(606\) 3.34935 0.00552699
\(607\) 156.362 + 215.214i 0.257599 + 0.354554i 0.918154 0.396223i \(-0.129679\pi\)
−0.660556 + 0.750777i \(0.729679\pi\)
\(608\) −27.4120 84.3655i −0.0450856 0.138759i
\(609\) 17.2413 53.0632i 0.0283108 0.0871317i
\(610\) 320.056 + 232.534i 0.524682 + 0.381204i
\(611\) −436.429 + 600.692i −0.714286 + 0.983130i
\(612\) 99.3653 + 32.2857i 0.162362 + 0.0527545i
\(613\) −206.889 + 67.2223i −0.337503 + 0.109661i −0.472865 0.881135i \(-0.656780\pi\)
0.135362 + 0.990796i \(0.456780\pi\)
\(614\) −567.320 + 412.182i −0.923974 + 0.671306i
\(615\) 124.195i 0.201943i
\(616\) −113.060 + 43.6561i −0.183539 + 0.0708704i
\(617\) 828.147 1.34222 0.671108 0.741360i \(-0.265819\pi\)
0.671108 + 0.741360i \(0.265819\pi\)
\(618\) 24.1103 + 33.1850i 0.0390135 + 0.0536975i
\(619\) 110.604 + 340.406i 0.178683 + 0.549928i 0.999782 0.0208561i \(-0.00663920\pi\)
−0.821100 + 0.570784i \(0.806639\pi\)
\(620\) 49.1599 151.299i 0.0792902 0.244030i
\(621\) 400.913 + 291.280i 0.645593 + 0.469051i
\(622\) −309.326 + 425.750i −0.497308 + 0.684486i
\(623\) −252.924 82.1799i −0.405977 0.131910i
\(624\) −89.2639 + 29.0036i −0.143051 + 0.0464802i
\(625\) −25.6267 + 18.6189i −0.0410027 + 0.0297902i
\(626\) 346.926i 0.554195i
\(627\) 138.410 + 89.4960i 0.220749 + 0.142737i
\(628\) 465.011 0.740464
\(629\) 15.8556 + 21.8234i 0.0252077 + 0.0346954i
\(630\) 41.2732 + 127.026i 0.0655130 + 0.201628i
\(631\) 193.271 594.828i 0.306293 0.942674i −0.672898 0.739735i \(-0.734951\pi\)
0.979191 0.202939i \(-0.0650493\pi\)
\(632\) 176.904 + 128.528i 0.279911 + 0.203368i
\(633\) −5.00457 + 6.88820i −0.00790612 + 0.0108818i
\(634\) 80.9071 + 26.2883i 0.127614 + 0.0414642i
\(635\) −380.421 + 123.606i −0.599088 + 0.194656i
\(636\) −80.4933 + 58.4818i −0.126562 + 0.0919525i
\(637\) 830.650i 1.30400i
\(638\) 147.106 + 180.929i 0.230574 + 0.283588i
\(639\) 759.313 1.18828
\(640\) −19.9369 27.4408i −0.0311515 0.0428763i
\(641\) −184.027 566.377i −0.287094 0.883583i −0.985763 0.168139i \(-0.946224\pi\)
0.698670 0.715444i \(-0.253776\pi\)
\(642\) −31.9769 + 98.4148i −0.0498082 + 0.153294i
\(643\) −594.110 431.646i −0.923965 0.671300i 0.0205425 0.999789i \(-0.493461\pi\)
−0.944508 + 0.328489i \(0.893461\pi\)
\(644\) −138.990 + 191.303i −0.215823 + 0.297055i
\(645\) −152.635 49.5941i −0.236644 0.0768902i
\(646\) 136.244 44.2684i 0.210904 0.0685269i
\(647\) −740.468 + 537.981i −1.14446 + 0.831501i −0.987735 0.156141i \(-0.950095\pi\)
−0.156728 + 0.987642i \(0.550095\pi\)
\(648\) 161.735i 0.249590i
\(649\) 56.3992 + 1036.96i 0.0869016 + 1.59778i
\(650\) 556.063 0.855482
\(651\) 58.0463 + 79.8939i 0.0891649 + 0.122725i
\(652\) 198.780 + 611.781i 0.304877 + 0.938314i
\(653\) 146.502 450.888i 0.224353 0.690487i −0.774004 0.633181i \(-0.781749\pi\)
0.998357 0.0573062i \(-0.0182511\pi\)
\(654\) −13.2409 9.62010i −0.0202461 0.0147096i
\(655\) 74.6730 102.779i 0.114005 0.156914i
\(656\) −164.927 53.5881i −0.251414 0.0816892i
\(657\) −188.707 + 61.3145i −0.287225 + 0.0933249i
\(658\) 134.757 97.9063i 0.204797 0.148794i
\(659\) 482.603i 0.732326i −0.930551 0.366163i \(-0.880671\pi\)
0.930551 0.366163i \(-0.119329\pi\)
\(660\) 60.9078 + 16.1913i 0.0922845 + 0.0245323i
\(661\) 45.0509 0.0681557 0.0340779 0.999419i \(-0.489151\pi\)
0.0340779 + 0.999419i \(0.489151\pi\)
\(662\) −74.6040 102.684i −0.112695 0.155111i
\(663\) −46.8387 144.155i −0.0706466 0.217428i
\(664\) 25.0188 77.0000i 0.0376789 0.115964i
\(665\) 148.158 + 107.643i 0.222794 + 0.161870i
\(666\) −28.0719 + 38.6376i −0.0421500 + 0.0580144i
\(667\) 432.699 + 140.592i 0.648724 + 0.210783i
\(668\) −237.925 + 77.3065i −0.356175 + 0.115728i
\(669\) −160.058 + 116.289i −0.239250 + 0.173825i
\(670\) 229.278i 0.342207i
\(671\) 263.689 991.936i 0.392979 1.47830i
\(672\) 21.0556 0.0313327
\(673\) −179.880 247.583i −0.267280 0.367880i 0.654189 0.756331i \(-0.273010\pi\)
−0.921469 + 0.388451i \(0.873010\pi\)
\(674\) −53.8135 165.621i −0.0798421 0.245729i
\(675\) −80.7852 + 248.631i −0.119682 + 0.368343i
\(676\) −702.265 510.225i −1.03885 0.754771i
\(677\) −64.6416 + 88.9715i −0.0954824 + 0.131420i −0.854085 0.520133i \(-0.825882\pi\)
0.758603 + 0.651553i \(0.225882\pi\)
\(678\) 121.931 + 39.6179i 0.179840 + 0.0584335i
\(679\) 133.414 43.3489i 0.196486 0.0638422i
\(680\) 44.3149 32.1967i 0.0651690 0.0473481i
\(681\) 92.7621i 0.136215i
\(682\) −412.126 + 22.4152i −0.604290 + 0.0328668i
\(683\) −490.810 −0.718610 −0.359305 0.933220i \(-0.616986\pi\)
−0.359305 + 0.933220i \(0.616986\pi\)
\(684\) 149.080 + 205.191i 0.217953 + 0.299986i
\(685\) 126.014 + 387.831i 0.183962 + 0.566177i
\(686\) −140.998 + 433.948i −0.205537 + 0.632578i
\(687\) 44.7015 + 32.4775i 0.0650676 + 0.0472744i
\(688\) 131.719 181.296i 0.191452 0.263512i
\(689\) −1215.91 395.074i −1.76475 0.573403i
\(690\) 116.946 37.9979i 0.169486 0.0550694i
\(691\) 632.920 459.843i 0.915947 0.665475i −0.0265646 0.999647i \(-0.508457\pi\)
0.942512 + 0.334172i \(0.108457\pi\)
\(692\) 253.449i 0.366256i
\(693\) 268.865 218.604i 0.387973 0.315445i
\(694\) −449.778 −0.648095
\(695\) 178.384 + 245.525i 0.256668 + 0.353273i
\(696\) −12.5189 38.5291i −0.0179869 0.0553579i
\(697\) 86.5408 266.345i 0.124162 0.382131i
\(698\) 304.147 + 220.975i 0.435740 + 0.316584i
\(699\) −39.4487 + 54.2965i −0.0564360 + 0.0776775i
\(700\) −118.639 38.5482i −0.169484 0.0550688i
\(701\) −298.888 + 97.1146i −0.426374 + 0.138537i −0.514340 0.857586i \(-0.671963\pi\)
0.0879664 + 0.996123i \(0.471963\pi\)
\(702\) 458.720 333.279i 0.653447 0.474757i
\(703\) 65.4841i 0.0931495i
\(704\) −47.7823 + 73.8976i −0.0678726 + 0.104968i
\(705\) −86.6173 −0.122861
\(706\) −207.399 285.460i −0.293766 0.404334i
\(707\) −2.98357 9.18247i −0.00422004 0.0129879i
\(708\) 55.7525 171.589i 0.0787465 0.242357i
\(709\) −53.5936 38.9380i −0.0755904 0.0549197i 0.549348 0.835593i \(-0.314876\pi\)
−0.624939 + 0.780674i \(0.714876\pi\)
\(710\) 233.993 322.064i 0.329568 0.453611i
\(711\) −594.603 193.198i −0.836291 0.271728i
\(712\) −183.647 + 59.6706i −0.257932 + 0.0838071i
\(713\) −651.488 + 473.334i −0.913728 + 0.663862i
\(714\) 34.0032i 0.0476235i
\(715\) 291.711 + 755.468i 0.407987 + 1.05660i
\(716\) −396.682 −0.554025
\(717\) −37.0819 51.0388i −0.0517181 0.0711839i
\(718\) −245.853 756.658i −0.342414 1.05384i
\(719\) −310.081 + 954.330i −0.431267 + 1.32730i 0.465598 + 0.884997i \(0.345839\pi\)
−0.896864 + 0.442306i \(0.854161\pi\)
\(720\) 78.4582 + 57.0032i 0.108970 + 0.0791711i
\(721\) 69.5017 95.6609i 0.0963963 0.132678i
\(722\) −154.802 50.2983i −0.214408 0.0696652i
\(723\) 45.1142 14.6585i 0.0623987 0.0202746i
\(724\) 172.889 125.611i 0.238797 0.173496i
\(725\) 240.014i 0.331054i
\(726\) −17.7338 162.545i −0.0244267 0.223891i
\(727\) 364.375 0.501204 0.250602 0.968090i \(-0.419371\pi\)
0.250602 + 0.968090i \(0.419371\pi\)
\(728\) 159.031 + 218.887i 0.218449 + 0.300669i
\(729\) −99.5094 306.258i −0.136501 0.420108i
\(730\) −32.1460 + 98.9353i −0.0440356 + 0.135528i
\(731\) 292.780 + 212.717i 0.400519 + 0.290994i
\(732\) −104.812 + 144.261i −0.143185 + 0.197078i
\(733\) 900.076 + 292.452i 1.22793 + 0.398980i 0.849965 0.526838i \(-0.176623\pi\)
0.377969 + 0.925818i \(0.376623\pi\)
\(734\) 37.7893 12.2785i 0.0514841 0.0167282i
\(735\) 78.3946 56.9570i 0.106659 0.0774925i
\(736\) 171.696i 0.233282i
\(737\) −554.916 + 214.271i −0.752939 + 0.290734i
\(738\) 495.823 0.671847
\(739\) 126.126 + 173.598i 0.170672 + 0.234909i 0.885781 0.464103i \(-0.153623\pi\)
−0.715110 + 0.699012i \(0.753623\pi\)
\(740\) 7.73747 + 23.8135i 0.0104560 + 0.0321804i
\(741\) 113.704 349.945i 0.153447 0.472261i
\(742\) 232.034 + 168.583i 0.312714 + 0.227200i
\(743\) 25.6695 35.3310i 0.0345484 0.0475518i −0.791393 0.611307i \(-0.790644\pi\)
0.825942 + 0.563755i \(0.190644\pi\)
\(744\) 68.1958 + 22.1582i 0.0916610 + 0.0297825i
\(745\) −147.336 + 47.8724i −0.197767 + 0.0642583i
\(746\) −179.645 + 130.520i −0.240811 + 0.174959i
\(747\) 231.486i 0.309888i
\(748\) −119.339 77.1649i −0.159544 0.103162i
\(749\) 298.295 0.398258
\(750\) 97.6609 + 134.419i 0.130215 + 0.179225i
\(751\) 157.978 + 486.208i 0.210357 + 0.647414i 0.999451 + 0.0331403i \(0.0105508\pi\)
−0.789093 + 0.614273i \(0.789449\pi\)
\(752\) 37.3740 115.025i 0.0496995 0.152959i
\(753\) −51.0243 37.0713i −0.0677613 0.0492315i
\(754\) 305.982 421.148i 0.405811 0.558551i
\(755\) 238.922 + 77.6305i 0.316453 + 0.102822i
\(756\) −120.974 + 39.3070i −0.160019 + 0.0519934i
\(757\) 700.963 509.280i 0.925975 0.672760i −0.0190290 0.999819i \(-0.506057\pi\)
0.945004 + 0.327059i \(0.106057\pi\)
\(758\) 880.114i 1.16110i
\(759\) −201.256 247.529i −0.265160 0.326126i
\(760\) 132.973 0.174965
\(761\) 770.228 + 1060.13i 1.01213 + 1.39307i 0.917580 + 0.397552i \(0.130140\pi\)
0.0945463 + 0.995520i \(0.469860\pi\)
\(762\) −55.7139 171.470i −0.0731153 0.225026i
\(763\) −14.5793 + 44.8703i −0.0191078 + 0.0588078i
\(764\) 55.7114 + 40.4767i 0.0729206 + 0.0529799i
\(765\) −92.0559 + 126.704i −0.120335 + 0.165626i
\(766\) 463.325 + 150.543i 0.604863 + 0.196532i
\(767\) 2204.87 716.406i 2.87467 0.934036i
\(768\) 12.3686 8.98631i 0.0161049 0.0117009i
\(769\) 1207.32i 1.56999i 0.619503 + 0.784994i \(0.287334\pi\)
−0.619503 + 0.784994i \(0.712666\pi\)
\(770\) −9.86649 181.406i −0.0128136 0.235592i
\(771\) −260.341 −0.337667
\(772\) −251.560 346.243i −0.325855 0.448501i
\(773\) −247.836 762.760i −0.320615 0.986753i −0.973381 0.229193i \(-0.926391\pi\)
0.652766 0.757560i \(-0.273609\pi\)
\(774\) −197.995 + 609.365i −0.255807 + 0.787294i
\(775\) −343.687 249.703i −0.443467 0.322198i
\(776\) 59.8700 82.4040i 0.0771521 0.106191i
\(777\) −14.7826 4.80316i −0.0190252 0.00618167i
\(778\) −390.077 + 126.744i −0.501385 + 0.162910i
\(779\) 550.006 399.603i 0.706042 0.512969i
\(780\) 140.694i 0.180377i
\(781\) −998.160 265.344i −1.27805 0.339749i
\(782\) −277.276 −0.354573
\(783\) 143.854 + 197.998i 0.183721 + 0.252871i
\(784\) 41.8113 + 128.682i 0.0533307 + 0.164135i
\(785\) −215.402 + 662.941i −0.274398 + 0.844510i
\(786\) 46.3260 + 33.6578i 0.0589390 + 0.0428217i
\(787\) −196.270 + 270.143i −0.249390 + 0.343256i −0.915298 0.402778i \(-0.868045\pi\)
0.665907 + 0.746034i \(0.268045\pi\)
\(788\) 516.202 + 167.724i 0.655079 + 0.212848i
\(789\) 60.3270 19.6014i 0.0764601 0.0248434i
\(790\) −265.181 + 192.665i −0.335672 + 0.243880i
\(791\) 369.574i 0.467224i
\(792\) 64.6405 243.162i 0.0816168 0.307023i
\(793\) −2291.32 −2.88943
\(794\) −198.518 273.236i −0.250022 0.344126i
\(795\) −46.0881 141.845i −0.0579725 0.178421i
\(796\) −154.465 + 475.396i −0.194052 + 0.597231i
\(797\) −651.319 473.211i −0.817213 0.593740i 0.0986995 0.995117i \(-0.468532\pi\)
−0.915913 + 0.401377i \(0.868532\pi\)
\(798\) −48.5188 + 66.7804i −0.0608005 + 0.0836847i
\(799\) 185.757 + 60.3563i 0.232487 + 0.0755397i
\(800\) −86.1436 + 27.9898i −0.107680 + 0.0349872i
\(801\) 446.660 324.517i 0.557628 0.405140i
\(802\) 191.509i 0.238790i
\(803\) 269.492 14.6574i 0.335607 0.0182534i
\(804\) 103.344 0.128537
\(805\) −208.347 286.766i −0.258817 0.356231i
\(806\) 284.727 + 876.299i 0.353259 + 1.08722i
\(807\) −53.9547 + 166.056i −0.0668584 + 0.205769i
\(808\) −5.67161 4.12066i −0.00701932 0.00509983i
\(809\) 698.652 961.612i 0.863600 1.18864i −0.117099 0.993120i \(-0.537360\pi\)
0.980699 0.195523i \(-0.0626404\pi\)
\(810\) −230.576 74.9187i −0.284662 0.0924922i
\(811\) 838.169 272.338i 1.03350 0.335805i 0.257328 0.966324i \(-0.417158\pi\)
0.776174 + 0.630519i \(0.217158\pi\)
\(812\) −94.4783 + 68.6425i −0.116353 + 0.0845351i
\(813\) 382.210i 0.470123i
\(814\) 50.4041 40.9816i 0.0619215 0.0503459i
\(815\) −964.261 −1.18314
\(816\) 14.5122 + 19.9744i 0.0177846 + 0.0244784i
\(817\) 271.479 + 835.528i 0.332288 + 1.02268i
\(818\) −132.992 + 409.307i −0.162582 + 0.500376i
\(819\) −625.836 454.696i −0.764146 0.555185i
\(820\) 152.795 210.305i 0.186336 0.256469i
\(821\) −981.725 318.982i −1.19577 0.388528i −0.357565 0.933888i \(-0.616393\pi\)
−0.838202 + 0.545360i \(0.816393\pi\)
\(822\) −174.810 + 56.7991i −0.212664 + 0.0690987i
\(823\) −650.900 + 472.906i −0.790886 + 0.574613i −0.908226 0.418479i \(-0.862563\pi\)
0.117340 + 0.993092i \(0.462563\pi\)
\(824\) 85.8563i 0.104195i
\(825\) 91.3822 141.327i 0.110766 0.171305i
\(826\) −520.085 −0.629643
\(827\) −37.9422 52.2230i −0.0458793 0.0631475i 0.785461 0.618911i \(-0.212426\pi\)
−0.831340 + 0.555764i \(0.812426\pi\)
\(828\) −151.699 466.882i −0.183212 0.563867i
\(829\) 188.558 580.323i 0.227453 0.700028i −0.770581 0.637343i \(-0.780034\pi\)
0.998033 0.0626852i \(-0.0199664\pi\)
\(830\) 98.1854 + 71.3359i 0.118296 + 0.0859468i
\(831\) −26.1844 + 36.0397i −0.0315095 + 0.0433691i
\(832\) 186.837 + 60.7071i 0.224564 + 0.0729653i
\(833\) −207.812 + 67.5221i −0.249474 + 0.0810589i
\(834\) −110.667 + 80.4042i −0.132694 + 0.0964079i
\(835\) 375.006i 0.449109i
\(836\) −124.269 321.831i −0.148648 0.384965i
\(837\) −433.183 −0.517542
\(838\) 493.874 + 679.759i 0.589348 + 0.811168i
\(839\) −195.113 600.497i −0.232554 0.715729i −0.997436 0.0715585i \(-0.977203\pi\)
0.764882 0.644170i \(-0.222797\pi\)
\(840\) −9.75337 + 30.0178i −0.0116112 + 0.0357355i
\(841\) −498.603 362.256i −0.592869 0.430745i
\(842\) 212.099 291.929i 0.251899 0.346709i
\(843\) 457.704 + 148.717i 0.542946 + 0.176414i
\(844\) 16.9489 5.50704i 0.0200817 0.00652493i
\(845\) 1052.70 764.833i 1.24580 0.905128i
\(846\) 345.803i 0.408750i
\(847\) −429.830 + 193.412i −0.507474 + 0.228349i
\(848\) 208.252 0.245580
\(849\) 31.5714 + 43.4543i 0.0371866 + 0.0511829i
\(850\) −45.2014 139.116i −0.0531781 0.163665i
\(851\) 39.1669 120.543i 0.0460246 0.141649i
\(852\) 145.166 + 105.469i 0.170383 + 0.123790i
\(853\) 253.913 349.481i 0.297671 0.409709i −0.633816 0.773484i \(-0.718512\pi\)
0.931487 + 0.363775i \(0.118512\pi\)
\(854\) 488.866 + 158.842i 0.572442 + 0.185998i
\(855\) −361.585 + 117.486i −0.422907 + 0.137411i
\(856\) 175.226 127.309i 0.204703 0.148726i
\(857\) 137.536i 0.160485i 0.996775 + 0.0802425i \(0.0255695\pi\)
−0.996775 + 0.0802425i \(0.974431\pi\)
\(858\) −340.517 + 131.485i −0.396873 + 0.153246i
\(859\) −64.8174 −0.0754568 −0.0377284 0.999288i \(-0.512012\pi\)
−0.0377284 + 0.999288i \(0.512012\pi\)
\(860\) 197.449 + 271.765i 0.229591 + 0.316006i
\(861\) 49.8656 + 153.471i 0.0579159 + 0.178247i
\(862\) −289.100 + 889.759i −0.335383 + 1.03220i
\(863\) 817.704 + 594.097i 0.947513 + 0.688409i 0.950217 0.311588i \(-0.100861\pi\)
−0.00270429 + 0.999996i \(0.500861\pi\)
\(864\) −54.2877 + 74.7206i −0.0628330 + 0.0864822i
\(865\) −361.328 117.403i −0.417720 0.135726i
\(866\) 147.984 48.0830i 0.170883 0.0555231i
\(867\) 191.151 138.879i 0.220474 0.160183i
\(868\) 206.701i 0.238135i
\(869\) 714.127 + 461.756i 0.821780 + 0.531365i
\(870\) 60.7278 0.0698020
\(871\) 780.547 + 1074.33i 0.896150 + 1.23345i
\(872\) 10.5860 + 32.5803i 0.0121399 + 0.0373627i
\(873\) −89.9940 + 276.973i −0.103086 + 0.317266i
\(874\) −544.555 395.642i −0.623060 0.452680i
\(875\) 281.522 387.482i 0.321740 0.442837i
\(876\) −44.5937 14.4894i −0.0509061 0.0165404i
\(877\) 628.136 204.094i 0.716233 0.232718i 0.0718438 0.997416i \(-0.477112\pi\)
0.644389 + 0.764698i \(0.277112\pi\)
\(878\) 628.393 456.554i 0.715710 0.519994i
\(879\) 178.346i 0.202897i
\(880\) −83.2179 102.351i −0.0945658 0.116308i
\(881\) 1527.49 1.73382 0.866909 0.498466i \(-0.166103\pi\)
0.866909 + 0.498466i \(0.166103\pi\)
\(882\) −227.389 312.975i −0.257811 0.354847i
\(883\) −0.133623 0.411250i −0.000151329 0.000465742i 0.950981 0.309250i \(-0.100078\pi\)
−0.951132 + 0.308784i \(0.900078\pi\)
\(884\) −98.0375 + 301.728i −0.110902 + 0.341322i
\(885\) 218.799 + 158.966i 0.247230 + 0.179623i
\(886\) 29.2412 40.2471i 0.0330037 0.0454256i
\(887\) −939.334 305.208i −1.05900 0.344090i −0.272806 0.962069i \(-0.587952\pi\)
−0.786195 + 0.617979i \(0.787952\pi\)
\(888\) −10.7336 + 3.48756i −0.0120874 + 0.00392743i
\(889\) −420.466 + 305.486i −0.472965 + 0.343629i
\(890\) 289.456i 0.325232i
\(891\) 34.1603 + 628.072i 0.0383392 + 0.704906i
\(892\) 414.102 0.464240
\(893\) 278.695 + 383.591i 0.312089 + 0.429554i
\(894\) −21.5778 66.4098i −0.0241363 0.0742839i
\(895\) 183.751 565.527i 0.205308 0.631874i
\(896\) −35.6543 25.9044i −0.0397928 0.0289112i
\(897\) −418.614 + 576.172i −0.466682 + 0.642333i
\(898\) 758.627 + 246.493i 0.844796 + 0.274491i
\(899\) −378.238 + 122.897i −0.420732 + 0.136704i
\(900\) 209.515 152.222i 0.232795 0.169135i
\(901\) 336.312i 0.373265i
\(902\) −651.789 173.267i −0.722604 0.192092i
\(903\) −208.527 −0.230927
\(904\) −157.730 217.097i −0.174481 0.240152i
\(905\) 98.9912 + 304.664i 0.109383 + 0.336645i
\(906\) −34.9909 + 107.691i −0.0386213 + 0.118864i
\(907\) −581.102 422.195i −0.640685 0.465485i 0.219400 0.975635i \(-0.429590\pi\)
−0.860086 + 0.510150i \(0.829590\pi\)
\(908\) −114.124 + 157.078i −0.125687 + 0.172993i
\(909\) 19.0632 + 6.19401i 0.0209716 + 0.00681409i
\(910\) −385.721 + 125.328i −0.423869 + 0.137723i
\(911\) −275.435 + 200.115i −0.302343 + 0.219665i −0.728604 0.684935i \(-0.759831\pi\)
0.426261 + 0.904600i \(0.359831\pi\)
\(912\) 59.9358i 0.0657191i
\(913\) 80.8935 304.302i 0.0886018 0.333299i
\(914\) 962.162 1.05269
\(915\) −157.114 216.249i −0.171709 0.236337i
\(916\) −35.7383 109.991i −0.0390156 0.120078i
\(917\) 51.0084 156.988i 0.0556253 0.171197i
\(918\) −120.668 87.6706i −0.131447 0.0955017i
\(919\) 590.474 812.718i 0.642518 0.884350i −0.356229 0.934399i \(-0.615938\pi\)
0.998747 + 0.0500487i \(0.0159377\pi\)
\(920\) −244.777 79.5330i −0.266062 0.0864489i
\(921\) 450.614 146.413i 0.489266 0.158972i
\(922\) −232.073 + 168.611i −0.251706 + 0.182875i
\(923\) 2305.70i 2.49804i
\(924\) 81.7662 4.44719i 0.0884915 0.00481298i
\(925\) 66.8642 0.0722856
\(926\) −620.340 853.825i −0.669914 0.922057i
\(927\) 75.8569 + 233.464i 0.0818305 + 0.251849i
\(928\) −26.2031 + 80.6447i −0.0282361 + 0.0869017i
\(929\) 273.837 + 198.954i 0.294765 + 0.214159i 0.725332 0.688399i \(-0.241686\pi\)
−0.430567 + 0.902559i \(0.641686\pi\)
\(930\) −63.1793 + 86.9589i −0.0679347 + 0.0935042i
\(931\) −504.477 163.914i −0.541865 0.176063i
\(932\) 133.601 43.4094i 0.143348 0.0465767i
\(933\) 287.662 208.999i 0.308319 0.224007i
\(934\) 526.811i 0.564037i
\(935\) 165.290 134.391i 0.176781 0.143733i
\(936\) −561.692 −0.600098
\(937\) 16.1676 + 22.2528i 0.0172547 + 0.0237490i 0.817557 0.575847i \(-0.195328\pi\)
−0.800303 + 0.599596i \(0.795328\pi\)
\(938\) −92.0578 283.325i −0.0981426 0.302052i
\(939\) 72.4348 222.931i 0.0771404 0.237414i
\(940\) 146.673 + 106.564i 0.156035 + 0.113366i
\(941\) −389.897 + 536.648i −0.414344 + 0.570295i −0.964271 0.264917i \(-0.914655\pi\)
0.549927 + 0.835212i \(0.314655\pi\)
\(942\) −298.812 97.0898i −0.317210 0.103068i
\(943\) −1251.46 + 406.625i −1.32711 + 0.431203i
\(944\) −305.511 + 221.967i −0.323635 + 0.235134i
\(945\) 190.674i 0.201772i
\(946\) 473.220 731.856i 0.500232 0.773632i
\(947\) −730.987 −0.771898 −0.385949 0.922520i \(-0.626126\pi\)
−0.385949 + 0.922520i \(0.626126\pi\)
\(948\) −86.8413 119.527i −0.0916048 0.126083i
\(949\) −186.185 573.018i −0.196191 0.603813i
\(950\) 109.729 337.712i 0.115505 0.355487i
\(951\) −46.5013 33.7852i −0.0488973 0.0355260i
\(952\) 41.8337 57.5791i 0.0439429 0.0604823i
\(953\) 362.664 + 117.837i 0.380550 + 0.123648i 0.493045 0.870004i \(-0.335884\pi\)
−0.112494 + 0.993652i \(0.535884\pi\)
\(954\) −566.287 + 183.998i −0.593592 + 0.192870i
\(955\) −83.5119 + 60.6750i −0.0874471 + 0.0635340i
\(956\) 132.048i 0.138125i
\(957\) −56.7529 146.978i −0.0593029 0.153582i
\(958\) 810.521 0.846055
\(959\) 311.437 + 428.656i 0.324752 + 0.446982i
\(960\) 7.08190 + 21.7958i 0.00737698 + 0.0227040i
\(961\) −79.4400 + 244.491i −0.0826639 + 0.254413i
\(962\) −117.325 85.2418i −0.121960 0.0886090i
\(963\) −363.999 + 501.002i −0.377985 + 0.520252i
\(964\) −94.4281 30.6815i −0.0979544 0.0318273i
\(965\) 610.147 198.249i 0.632276 0.205439i
\(966\) 129.256 93.9098i 0.133805 0.0972151i
\(967\) 1791.77i 1.85292i −0.376396 0.926459i \(-0.622837\pi\)
0.376396 0.926459i \(-0.377163\pi\)
\(968\) −169.947 + 297.062i −0.175565 + 0.306882i
\(969\) −96.7919 −0.0998884
\(970\) 89.7458 + 123.524i 0.0925214 + 0.127345i
\(971\) −194.009 597.098i −0.199803 0.614931i −0.999887 0.0150426i \(-0.995212\pi\)
0.800084 0.599888i \(-0.204788\pi\)
\(972\) 124.585 383.432i 0.128173 0.394477i
\(973\) 319.014 + 231.777i 0.327867 + 0.238209i
\(974\) −35.1789 + 48.4196i −0.0361179 + 0.0497121i
\(975\) −357.321 116.100i −0.366483 0.119077i
\(976\) 354.964 115.335i 0.363693 0.118171i
\(977\) −382.101 + 277.613i −0.391096 + 0.284148i −0.765905 0.642954i \(-0.777709\pi\)
0.374808 + 0.927102i \(0.377709\pi\)
\(978\) 434.628i 0.444404i
\(979\) −700.563 + 270.510i −0.715591 + 0.276313i
\(980\) −202.822 −0.206962
\(981\) −57.5715 79.2404i −0.0586866 0.0807751i
\(982\) 267.750 + 824.051i 0.272658 + 0.839156i
\(983\) 145.406 447.515i 0.147921 0.455254i −0.849454 0.527663i \(-0.823069\pi\)
0.997375 + 0.0724086i \(0.0230686\pi\)
\(984\) 94.7920 + 68.8704i 0.0963333 + 0.0699902i
\(985\) −478.230 + 658.228i −0.485513 + 0.668251i
\(986\) −130.235 42.3160i −0.132084 0.0429168i
\(987\) −107.035 + 34.7778i −0.108445 + 0.0352359i
\(988\) −623.073 + 452.689i −0.630640 + 0.458187i
\(989\) 1700.42i 1.71933i
\(990\) 316.720 + 204.792i 0.319919 + 0.206861i
\(991\) 1639.02 1.65391 0.826955 0.562269i \(-0.190071\pi\)
0.826955 + 0.562269i \(0.190071\pi\)
\(992\) −88.2180 121.422i −0.0889295 0.122401i
\(993\) 26.5004 + 81.5600i 0.0266873 + 0.0821349i
\(994\) 159.839 491.933i 0.160804 0.494902i
\(995\) −606.194 440.425i −0.609240 0.442639i
\(996\) −32.1537 + 44.2558i −0.0322828 + 0.0444335i
\(997\) 123.947 + 40.2729i 0.124320 + 0.0403941i 0.370516 0.928826i \(-0.379181\pi\)
−0.246196 + 0.969220i \(0.579181\pi\)
\(998\) −622.958 + 202.411i −0.624206 + 0.202817i
\(999\) 55.1591 40.0754i 0.0552143 0.0401155i
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 22.3.d.a.19.2 yes 8
3.2 odd 2 198.3.j.a.19.1 8
4.3 odd 2 176.3.n.b.129.1 8
11.2 odd 10 242.3.b.d.241.7 8
11.3 even 5 242.3.d.d.215.2 8
11.4 even 5 242.3.d.c.161.1 8
11.5 even 5 242.3.d.e.233.1 8
11.6 odd 10 242.3.d.d.233.2 8
11.7 odd 10 inner 22.3.d.a.7.2 8
11.8 odd 10 242.3.d.e.215.1 8
11.9 even 5 242.3.b.d.241.3 8
11.10 odd 2 242.3.d.c.239.1 8
33.2 even 10 2178.3.d.l.1693.1 8
33.20 odd 10 2178.3.d.l.1693.5 8
33.29 even 10 198.3.j.a.73.1 8
44.7 even 10 176.3.n.b.161.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.3.d.a.7.2 8 11.7 odd 10 inner
22.3.d.a.19.2 yes 8 1.1 even 1 trivial
176.3.n.b.129.1 8 4.3 odd 2
176.3.n.b.161.1 8 44.7 even 10
198.3.j.a.19.1 8 3.2 odd 2
198.3.j.a.73.1 8 33.29 even 10
242.3.b.d.241.3 8 11.9 even 5
242.3.b.d.241.7 8 11.2 odd 10
242.3.d.c.161.1 8 11.4 even 5
242.3.d.c.239.1 8 11.10 odd 2
242.3.d.d.215.2 8 11.3 even 5
242.3.d.d.233.2 8 11.6 odd 10
242.3.d.e.215.1 8 11.8 odd 10
242.3.d.e.233.1 8 11.5 even 5
2178.3.d.l.1693.1 8 33.2 even 10
2178.3.d.l.1693.5 8 33.20 odd 10