Properties

Label 672.2.cj.a.613.27
Level $672$
Weight $2$
Character 672.613
Analytic conductor $5.366$
Analytic rank $0$
Dimension $512$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [672,2,Mod(37,672)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(672, base_ring=CyclotomicField(24))
 
chi = DirichletCharacter(H, H._module([0, 3, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("672.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.cj (of order \(24\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.36594701583\)
Analytic rank: \(0\)
Dimension: \(512\)
Relative dimension: \(64\) over \(\Q(\zeta_{24})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label 613.27
Character \(\chi\) \(=\) 672.613
Dual form 672.2.cj.a.205.27

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.288120 - 1.38455i) q^{2} +(-0.991445 - 0.130526i) q^{3} +(-1.83397 + 0.797834i) q^{4} +(-0.308662 - 2.34452i) q^{5} +(0.104934 + 1.41032i) q^{6} +(-0.0642908 - 2.64497i) q^{7} +(1.63305 + 2.30936i) q^{8} +(0.965926 + 0.258819i) q^{9} +O(q^{10})\) \(q+(-0.288120 - 1.38455i) q^{2} +(-0.991445 - 0.130526i) q^{3} +(-1.83397 + 0.797834i) q^{4} +(-0.308662 - 2.34452i) q^{5} +(0.104934 + 1.41032i) q^{6} +(-0.0642908 - 2.64497i) q^{7} +(1.63305 + 2.30936i) q^{8} +(0.965926 + 0.258819i) q^{9} +(-3.15719 + 1.10286i) q^{10} +(-1.41092 - 1.83874i) q^{11} +(1.92242 - 0.551627i) q^{12} +(1.45857 - 0.604158i) q^{13} +(-3.64358 + 0.851082i) q^{14} +2.36475i q^{15} +(2.72692 - 2.92641i) q^{16} +(-4.68459 - 2.70465i) q^{17} +(0.0800464 - 1.41195i) q^{18} +(0.531685 + 0.407976i) q^{19} +(2.43662 + 4.05353i) q^{20} +(-0.281497 + 2.63073i) q^{21} +(-2.13932 + 2.48327i) q^{22} +(-5.21510 - 1.39738i) q^{23} +(-1.31764 - 2.50276i) q^{24} +(-0.571890 + 0.153238i) q^{25} +(-1.25673 - 1.84539i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(2.22816 + 4.79951i) q^{28} +(2.83162 + 6.83613i) q^{29} +(3.27413 - 0.681333i) q^{30} +(-0.332612 + 0.576100i) q^{31} +(-4.83746 - 2.93241i) q^{32} +(1.15884 + 2.00717i) q^{33} +(-2.39501 + 7.26532i) q^{34} +(-6.18135 + 0.967134i) q^{35} +(-1.97798 + 0.295981i) q^{36} +(1.06583 + 8.09580i) q^{37} +(0.411676 - 0.853692i) q^{38} +(-1.52495 + 0.408608i) q^{39} +(4.91029 - 4.54153i) q^{40} +(6.00126 - 6.00126i) q^{41} +(3.72349 - 0.368219i) q^{42} +(-1.49306 + 3.60456i) q^{43} +(4.05459 + 2.24653i) q^{44} +(0.308662 - 2.34452i) q^{45} +(-0.432176 + 7.62320i) q^{46} +(-11.0340 + 6.37051i) q^{47} +(-3.08557 + 2.54544i) q^{48} +(-6.99173 + 0.340095i) q^{49} +(0.376938 + 0.747662i) q^{50} +(4.29148 + 3.29297i) q^{51} +(-2.19296 + 2.27170i) q^{52} +(-0.337455 - 0.439779i) q^{53} +(-0.263658 + 1.38942i) q^{54} +(-3.87548 + 3.87548i) q^{55} +(6.00320 - 4.46783i) q^{56} +(-0.473885 - 0.473885i) q^{57} +(8.64914 - 5.89015i) q^{58} +(2.47876 - 1.90202i) q^{59} +(-1.88668 - 4.33690i) q^{60} +(-5.40788 + 7.04769i) q^{61} +(0.893474 + 0.294533i) q^{62} +(0.622468 - 2.57148i) q^{63} +(-2.66631 + 7.54260i) q^{64} +(-1.86667 - 3.23316i) q^{65} +(2.44515 - 2.18278i) q^{66} +(-7.76980 - 1.02291i) q^{67} +(10.7493 + 1.22273i) q^{68} +(4.98809 + 2.06614i) q^{69} +(3.12002 + 8.27976i) q^{70} +(-8.57151 - 8.57151i) q^{71} +(0.979696 + 2.65334i) q^{72} +(-0.159343 - 0.594678i) q^{73} +(10.9020 - 3.80826i) q^{74} +(0.586999 - 0.0772799i) q^{75} +(-1.30059 - 0.324021i) q^{76} +(-4.77271 + 3.85004i) q^{77} +(1.00511 + 1.99364i) q^{78} +(8.31378 - 4.79997i) q^{79} +(-7.70275 - 5.49006i) q^{80} +(0.866025 + 0.500000i) q^{81} +(-10.0382 - 6.57998i) q^{82} +(4.72948 - 1.95902i) q^{83} +(-1.58263 - 5.04929i) q^{84} +(-4.89516 + 11.8180i) q^{85} +(5.42088 + 1.02867i) q^{86} +(-1.91510 - 7.14725i) q^{87} +(1.94223 - 6.26107i) q^{88} +(3.85743 - 14.3961i) q^{89} +(-3.33505 + 0.248144i) q^{90} +(-1.69175 - 3.81902i) q^{91} +(10.6792 - 1.59802i) q^{92} +(0.404962 - 0.527757i) q^{93} +(11.9994 + 13.4417i) q^{94} +(0.792399 - 1.37247i) q^{95} +(4.41331 + 3.53874i) q^{96} +10.6575 q^{97} +(2.48534 + 9.58244i) q^{98} +(-0.886939 - 2.14126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 512 q+O(q^{10}) \) Copy content Toggle raw display \( 512 q - 64 q^{14} + 8 q^{16} + 8 q^{18} + 64 q^{20} + 16 q^{22} + 16 q^{23} - 40 q^{28} + 96 q^{31} + 48 q^{35} - 80 q^{38} + 64 q^{40} - 32 q^{43} - 8 q^{44} - 48 q^{50} + 24 q^{52} + 32 q^{53} - 32 q^{58} + 64 q^{59} - 48 q^{60} - 48 q^{64} + 48 q^{66} - 16 q^{67} + 72 q^{70} - 128 q^{71} - 144 q^{74} - 48 q^{78} + 24 q^{80} + 40 q^{82} - 88 q^{88} + 48 q^{91} + 128 q^{92} - 24 q^{94} - 40 q^{96} - 88 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.288120 1.38455i −0.203731 0.979027i
\(3\) −0.991445 0.130526i −0.572411 0.0753593i
\(4\) −1.83397 + 0.797834i −0.916987 + 0.398917i
\(5\) −0.308662 2.34452i −0.138038 1.04850i −0.910520 0.413466i \(-0.864318\pi\)
0.772482 0.635037i \(-0.219015\pi\)
\(6\) 0.104934 + 1.41032i 0.0428393 + 0.575759i
\(7\) −0.0642908 2.64497i −0.0242997 0.999705i
\(8\) 1.63305 + 2.30936i 0.577370 + 0.816483i
\(9\) 0.965926 + 0.258819i 0.321975 + 0.0862730i
\(10\) −3.15719 + 1.10286i −0.998390 + 0.348756i
\(11\) −1.41092 1.83874i −0.425407 0.554401i 0.530646 0.847593i \(-0.321949\pi\)
−0.956054 + 0.293192i \(0.905283\pi\)
\(12\) 1.92242 0.551627i 0.554956 0.159241i
\(13\) 1.45857 0.604158i 0.404534 0.167563i −0.171133 0.985248i \(-0.554743\pi\)
0.575666 + 0.817685i \(0.304743\pi\)
\(14\) −3.64358 + 0.851082i −0.973787 + 0.227461i
\(15\) 2.36475i 0.610577i
\(16\) 2.72692 2.92641i 0.681730 0.731604i
\(17\) −4.68459 2.70465i −1.13618 0.655974i −0.190698 0.981649i \(-0.561075\pi\)
−0.945482 + 0.325675i \(0.894408\pi\)
\(18\) 0.0800464 1.41195i 0.0188671 0.332799i
\(19\) 0.531685 + 0.407976i 0.121977 + 0.0935962i 0.667948 0.744208i \(-0.267173\pi\)
−0.545972 + 0.837804i \(0.683839\pi\)
\(20\) 2.43662 + 4.05353i 0.544845 + 0.906398i
\(21\) −0.281497 + 2.63073i −0.0614277 + 0.574073i
\(22\) −2.13932 + 2.48327i −0.456105 + 0.529434i
\(23\) −5.21510 1.39738i −1.08742 0.291374i −0.329790 0.944054i \(-0.606978\pi\)
−0.757634 + 0.652680i \(0.773645\pi\)
\(24\) −1.31764 2.50276i −0.268963 0.510874i
\(25\) −0.571890 + 0.153238i −0.114378 + 0.0306475i
\(26\) −1.25673 1.84539i −0.246465 0.361911i
\(27\) −0.923880 0.382683i −0.177801 0.0736475i
\(28\) 2.22816 + 4.79951i 0.421082 + 0.907023i
\(29\) 2.83162 + 6.83613i 0.525819 + 1.26944i 0.934240 + 0.356645i \(0.116079\pi\)
−0.408422 + 0.912793i \(0.633921\pi\)
\(30\) 3.27413 0.681333i 0.597771 0.124394i
\(31\) −0.332612 + 0.576100i −0.0597388 + 0.103471i −0.894348 0.447372i \(-0.852360\pi\)
0.834609 + 0.550842i \(0.185693\pi\)
\(32\) −4.83746 2.93241i −0.855149 0.518382i
\(33\) 1.15884 + 2.00717i 0.201728 + 0.349404i
\(34\) −2.39501 + 7.26532i −0.410740 + 1.24599i
\(35\) −6.18135 + 0.967134i −1.04484 + 0.163476i
\(36\) −1.97798 + 0.295981i −0.329663 + 0.0493302i
\(37\) 1.06583 + 8.09580i 0.175222 + 1.33094i 0.822534 + 0.568716i \(0.192560\pi\)
−0.647312 + 0.762225i \(0.724107\pi\)
\(38\) 0.411676 0.853692i 0.0667826 0.138487i
\(39\) −1.52495 + 0.408608i −0.244187 + 0.0654297i
\(40\) 4.91029 4.54153i 0.776386 0.718079i
\(41\) 6.00126 6.00126i 0.937240 0.937240i −0.0609037 0.998144i \(-0.519398\pi\)
0.998144 + 0.0609037i \(0.0193983\pi\)
\(42\) 3.72349 0.368219i 0.574548 0.0568174i
\(43\) −1.49306 + 3.60456i −0.227689 + 0.549690i −0.995895 0.0905126i \(-0.971149\pi\)
0.768206 + 0.640202i \(0.221149\pi\)
\(44\) 4.05459 + 2.24653i 0.611253 + 0.338677i
\(45\) 0.308662 2.34452i 0.0460127 0.349501i
\(46\) −0.432176 + 7.62320i −0.0637209 + 1.12398i
\(47\) −11.0340 + 6.37051i −1.60948 + 0.929234i −0.619994 + 0.784606i \(0.712865\pi\)
−0.989486 + 0.144628i \(0.953802\pi\)
\(48\) −3.08557 + 2.54544i −0.445363 + 0.367403i
\(49\) −6.99173 + 0.340095i −0.998819 + 0.0485850i
\(50\) 0.376938 + 0.747662i 0.0533071 + 0.105735i
\(51\) 4.29148 + 3.29297i 0.600928 + 0.461108i
\(52\) −2.19296 + 2.27170i −0.304108 + 0.315029i
\(53\) −0.337455 0.439779i −0.0463529 0.0604083i 0.769602 0.638524i \(-0.220455\pi\)
−0.815955 + 0.578116i \(0.803788\pi\)
\(54\) −0.263658 + 1.38942i −0.0358792 + 0.189076i
\(55\) −3.87548 + 3.87548i −0.522569 + 0.522569i
\(56\) 6.00320 4.46783i 0.802212 0.597039i
\(57\) −0.473885 0.473885i −0.0627676 0.0627676i
\(58\) 8.64914 5.89015i 1.13569 0.773415i
\(59\) 2.47876 1.90202i 0.322708 0.247622i −0.434684 0.900583i \(-0.643140\pi\)
0.757392 + 0.652961i \(0.226473\pi\)
\(60\) −1.88668 4.33690i −0.243570 0.559891i
\(61\) −5.40788 + 7.04769i −0.692408 + 0.902364i −0.998772 0.0495509i \(-0.984221\pi\)
0.306364 + 0.951915i \(0.400888\pi\)
\(62\) 0.893474 + 0.294533i 0.113471 + 0.0374057i
\(63\) 0.622468 2.57148i 0.0784237 0.323977i
\(64\) −2.66631 + 7.54260i −0.333289 + 0.942825i
\(65\) −1.86667 3.23316i −0.231532 0.401025i
\(66\) 2.44515 2.18278i 0.300977 0.268682i
\(67\) −7.76980 1.02291i −0.949233 0.124969i −0.360018 0.932945i \(-0.617229\pi\)
−0.589215 + 0.807976i \(0.700563\pi\)
\(68\) 10.7493 + 1.22273i 1.30354 + 0.148278i
\(69\) 4.98809 + 2.06614i 0.600496 + 0.248734i
\(70\) 3.12002 + 8.27976i 0.372913 + 0.989620i
\(71\) −8.57151 8.57151i −1.01725 1.01725i −0.999849 0.0174029i \(-0.994460\pi\)
−0.0174029 0.999849i \(-0.505540\pi\)
\(72\) 0.979696 + 2.65334i 0.115458 + 0.312699i
\(73\) −0.159343 0.594678i −0.0186497 0.0696017i 0.955974 0.293452i \(-0.0948040\pi\)
−0.974624 + 0.223850i \(0.928137\pi\)
\(74\) 10.9020 3.80826i 1.26733 0.442701i
\(75\) 0.586999 0.0772799i 0.0677808 0.00892351i
\(76\) −1.30059 0.324021i −0.149188 0.0371678i
\(77\) −4.77271 + 3.85004i −0.543900 + 0.438753i
\(78\) 1.00511 + 1.99364i 0.113806 + 0.225735i
\(79\) 8.31378 4.79997i 0.935374 0.540038i 0.0468666 0.998901i \(-0.485076\pi\)
0.888507 + 0.458863i \(0.151743\pi\)
\(80\) −7.70275 5.49006i −0.861193 0.613807i
\(81\) 0.866025 + 0.500000i 0.0962250 + 0.0555556i
\(82\) −10.0382 6.57998i −1.10853 0.726638i
\(83\) 4.72948 1.95902i 0.519128 0.215030i −0.107706 0.994183i \(-0.534350\pi\)
0.626834 + 0.779153i \(0.284350\pi\)
\(84\) −1.58263 5.04929i −0.172679 0.550922i
\(85\) −4.89516 + 11.8180i −0.530954 + 1.28184i
\(86\) 5.42088 + 1.02867i 0.584548 + 0.110924i
\(87\) −1.91510 7.14725i −0.205320 0.766266i
\(88\) 1.94223 6.26107i 0.207042 0.667432i
\(89\) 3.85743 14.3961i 0.408887 1.52599i −0.387885 0.921708i \(-0.626794\pi\)
0.796772 0.604280i \(-0.206539\pi\)
\(90\) −3.33505 + 0.248144i −0.351545 + 0.0261567i
\(91\) −1.69175 3.81902i −0.177344 0.400342i
\(92\) 10.6792 1.59802i 1.11339 0.166606i
\(93\) 0.404962 0.527757i 0.0419926 0.0547259i
\(94\) 11.9994 + 13.4417i 1.23765 + 1.38641i
\(95\) 0.792399 1.37247i 0.0812984 0.140813i
\(96\) 4.41331 + 3.53874i 0.450432 + 0.361171i
\(97\) 10.6575 1.08211 0.541054 0.840988i \(-0.318026\pi\)
0.541054 + 0.840988i \(0.318026\pi\)
\(98\) 2.48534 + 9.58244i 0.251057 + 0.967972i
\(99\) −0.886939 2.14126i −0.0891407 0.215205i
\(100\) 0.926574 0.737307i 0.0926574 0.0737307i
\(101\) 8.33429 6.39513i 0.829293 0.636339i −0.104351 0.994541i \(-0.533277\pi\)
0.933644 + 0.358202i \(0.116610\pi\)
\(102\) 3.32283 6.89056i 0.329009 0.682267i
\(103\) 2.03746 7.60391i 0.200757 0.749235i −0.789944 0.613179i \(-0.789891\pi\)
0.990701 0.136056i \(-0.0434428\pi\)
\(104\) 3.77713 + 2.38174i 0.370378 + 0.233549i
\(105\) 6.25471 0.152032i 0.610397 0.0148368i
\(106\) −0.511670 + 0.593933i −0.0496978 + 0.0576879i
\(107\) −4.12814 + 0.543480i −0.399083 + 0.0525402i −0.327397 0.944887i \(-0.606171\pi\)
−0.0716861 + 0.997427i \(0.522838\pi\)
\(108\) 1.99969 0.0352712i 0.192420 0.00339397i
\(109\) 1.10378 8.38405i 0.105723 0.803047i −0.853638 0.520866i \(-0.825609\pi\)
0.959361 0.282180i \(-0.0910577\pi\)
\(110\) 6.48240 + 4.24920i 0.618073 + 0.405145i
\(111\) 8.16565i 0.775050i
\(112\) −7.91559 7.02448i −0.747953 0.663751i
\(113\) 10.0856i 0.948774i 0.880316 + 0.474387i \(0.157330\pi\)
−0.880316 + 0.474387i \(0.842670\pi\)
\(114\) −0.519583 + 0.792654i −0.0486634 + 0.0742389i
\(115\) −1.66649 + 12.6583i −0.155401 + 1.18039i
\(116\) −10.6472 10.2781i −0.988569 0.954300i
\(117\) 1.56524 0.206067i 0.144706 0.0190509i
\(118\) −3.34763 2.88397i −0.308175 0.265491i
\(119\) −6.85254 + 12.5645i −0.628171 + 1.15178i
\(120\) −5.46108 + 3.86176i −0.498526 + 0.352529i
\(121\) 1.45672 5.43657i 0.132429 0.494233i
\(122\) 11.3160 + 5.45692i 1.02450 + 0.494046i
\(123\) −6.73324 + 5.16660i −0.607116 + 0.465857i
\(124\) 0.150369 1.32192i 0.0135035 0.118712i
\(125\) −3.98897 9.63023i −0.356785 0.861354i
\(126\) −3.73970 0.120945i −0.333159 0.0107746i
\(127\) −11.8317 −1.04989 −0.524946 0.851136i \(-0.675914\pi\)
−0.524946 + 0.851136i \(0.675914\pi\)
\(128\) 11.2113 + 1.51847i 0.990952 + 0.134215i
\(129\) 1.95077 3.37884i 0.171756 0.297490i
\(130\) −3.93866 + 3.51604i −0.345444 + 0.308377i
\(131\) −1.40606 + 1.83242i −0.122848 + 0.160099i −0.850729 0.525605i \(-0.823839\pi\)
0.727880 + 0.685704i \(0.240506\pi\)
\(132\) −3.72668 2.75654i −0.324365 0.239926i
\(133\) 1.04490 1.43252i 0.0906045 0.124215i
\(134\) 0.822355 + 11.0524i 0.0710407 + 0.954784i
\(135\) −0.612044 + 2.28418i −0.0526763 + 0.196591i
\(136\) −1.40414 15.2352i −0.120404 1.30641i
\(137\) −1.99601 7.44922i −0.170531 0.636430i −0.997270 0.0738439i \(-0.976473\pi\)
0.826739 0.562586i \(-0.190193\pi\)
\(138\) 1.42351 7.50157i 0.121177 0.638576i
\(139\) 7.35635 17.7598i 0.623958 1.50637i −0.223061 0.974804i \(-0.571605\pi\)
0.847019 0.531563i \(-0.178395\pi\)
\(140\) 10.5648 6.70539i 0.892891 0.566709i
\(141\) 11.7712 4.87577i 0.991311 0.410614i
\(142\) −9.39809 + 14.3373i −0.788670 + 1.20316i
\(143\) −3.16881 1.82951i −0.264989 0.152991i
\(144\) 3.39142 2.12092i 0.282618 0.176743i
\(145\) 15.1535 8.74886i 1.25843 0.726553i
\(146\) −0.777453 + 0.391958i −0.0643424 + 0.0324386i
\(147\) 6.97631 + 0.575419i 0.575396 + 0.0474598i
\(148\) −8.41381 13.9971i −0.691611 1.15056i
\(149\) 6.61404 0.870754i 0.541843 0.0713350i 0.145363 0.989378i \(-0.453565\pi\)
0.396480 + 0.918043i \(0.370232\pi\)
\(150\) −0.276124 0.790466i −0.0225454 0.0645412i
\(151\) 3.77918 + 14.1041i 0.307545 + 1.14777i 0.930732 + 0.365701i \(0.119171\pi\)
−0.623187 + 0.782073i \(0.714163\pi\)
\(152\) −0.0738979 + 1.89410i −0.00599391 + 0.153632i
\(153\) −3.82495 3.82495i −0.309229 0.309229i
\(154\) 6.70570 + 5.49879i 0.540361 + 0.443105i
\(155\) 1.45335 + 0.601996i 0.116736 + 0.0483534i
\(156\) 2.47071 1.96603i 0.197815 0.157409i
\(157\) −15.6025 2.05411i −1.24522 0.163936i −0.521029 0.853539i \(-0.674452\pi\)
−0.724187 + 0.689603i \(0.757785\pi\)
\(158\) −9.04117 10.1279i −0.719277 0.805733i
\(159\) 0.277165 + 0.480064i 0.0219806 + 0.0380715i
\(160\) −5.38196 + 12.2467i −0.425481 + 0.968183i
\(161\) −3.36075 + 13.8836i −0.264864 + 1.09418i
\(162\) 0.442757 1.34312i 0.0347863 0.105525i
\(163\) −4.62009 + 6.02102i −0.361874 + 0.471603i −0.938437 0.345449i \(-0.887727\pi\)
0.576564 + 0.817052i \(0.304393\pi\)
\(164\) −6.21815 + 15.7942i −0.485556 + 1.23332i
\(165\) 4.34817 3.33647i 0.338505 0.259744i
\(166\) −4.07502 5.98379i −0.316283 0.464432i
\(167\) −16.4573 16.4573i −1.27350 1.27350i −0.944238 0.329263i \(-0.893200\pi\)
−0.329263 0.944238i \(-0.606800\pi\)
\(168\) −6.53502 + 3.64604i −0.504187 + 0.281298i
\(169\) −7.42998 + 7.42998i −0.571537 + 0.571537i
\(170\) 17.7730 + 3.37262i 1.36312 + 0.258668i
\(171\) 0.407976 + 0.531685i 0.0311987 + 0.0406590i
\(172\) −0.137612 7.80187i −0.0104928 0.594887i
\(173\) −7.30095 5.60222i −0.555081 0.425929i 0.292755 0.956188i \(-0.405428\pi\)
−0.847836 + 0.530259i \(0.822095\pi\)
\(174\) −9.34397 + 4.71082i −0.708364 + 0.357126i
\(175\) 0.442076 + 1.50278i 0.0334178 + 0.113600i
\(176\) −9.22838 0.885179i −0.695615 0.0667228i
\(177\) −2.70582 + 1.56221i −0.203382 + 0.117423i
\(178\) −21.0436 1.19301i −1.57729 0.0894198i
\(179\) −1.51954 + 11.5421i −0.113576 + 0.862694i 0.835906 + 0.548872i \(0.184943\pi\)
−0.949482 + 0.313822i \(0.898391\pi\)
\(180\) 1.30446 + 4.54606i 0.0972289 + 0.338843i
\(181\) 3.57147 8.62229i 0.265465 0.640889i −0.733794 0.679372i \(-0.762252\pi\)
0.999259 + 0.0384824i \(0.0122523\pi\)
\(182\) −4.80021 + 3.44266i −0.355815 + 0.255187i
\(183\) 6.28152 6.28152i 0.464343 0.464343i
\(184\) −5.28945 14.3256i −0.389944 1.05609i
\(185\) 18.6518 4.99774i 1.37131 0.367441i
\(186\) −0.847386 0.408635i −0.0621333 0.0299625i
\(187\) 1.63641 + 12.4298i 0.119666 + 0.908956i
\(188\) 15.1535 20.4867i 1.10519 1.49414i
\(189\) −0.952789 + 2.46824i −0.0693052 + 0.179538i
\(190\) −2.12857 0.701681i −0.154423 0.0509053i
\(191\) −10.7289 18.5830i −0.776315 1.34462i −0.934053 0.357136i \(-0.883753\pi\)
0.157738 0.987481i \(-0.449580\pi\)
\(192\) 3.62801 7.13005i 0.261829 0.514567i
\(193\) 0.347438 0.601780i 0.0250091 0.0433170i −0.853250 0.521502i \(-0.825372\pi\)
0.878259 + 0.478185i \(0.158705\pi\)
\(194\) −3.07064 14.7559i −0.220459 1.05941i
\(195\) 1.42869 + 3.44915i 0.102310 + 0.246999i
\(196\) 12.5513 6.20197i 0.896523 0.442998i
\(197\) 16.8311 + 6.97168i 1.19917 + 0.496712i 0.890730 0.454532i \(-0.150194\pi\)
0.308438 + 0.951244i \(0.400194\pi\)
\(198\) −2.70914 + 1.84495i −0.192530 + 0.131115i
\(199\) 1.26713 0.339526i 0.0898243 0.0240683i −0.213627 0.976915i \(-0.568528\pi\)
0.303451 + 0.952847i \(0.401861\pi\)
\(200\) −1.28781 1.07046i −0.0910616 0.0756928i
\(201\) 7.56982 + 2.02833i 0.533934 + 0.143067i
\(202\) −11.2557 9.69671i −0.791946 0.682258i
\(203\) 17.8993 7.92905i 1.25629 0.556510i
\(204\) −10.4977 2.61533i −0.734987 0.183110i
\(205\) −15.9225 12.2177i −1.11207 0.853324i
\(206\) −11.1150 0.630136i −0.774422 0.0439037i
\(207\) −4.67573 2.69954i −0.324986 0.187631i
\(208\) 2.20938 5.91586i 0.153193 0.410191i
\(209\) 1.55325i 0.107441i
\(210\) −2.01260 8.61617i −0.138883 0.594572i
\(211\) −14.1630 + 5.86649i −0.975018 + 0.403866i −0.812578 0.582853i \(-0.801936\pi\)
−0.162440 + 0.986718i \(0.551936\pi\)
\(212\) 0.969754 + 0.537311i 0.0666030 + 0.0369027i
\(213\) 7.37938 + 9.61699i 0.505626 + 0.658945i
\(214\) 1.94188 + 5.55905i 0.132744 + 0.380009i
\(215\) 8.91182 + 2.38791i 0.607781 + 0.162854i
\(216\) −0.624985 2.75851i −0.0425248 0.187693i
\(217\) 1.54515 + 0.842710i 0.104892 + 0.0572069i
\(218\) −11.9262 + 0.887368i −0.807743 + 0.0601001i
\(219\) 0.0803592 + 0.610388i 0.00543017 + 0.0412462i
\(220\) 4.01554 10.1995i 0.270727 0.687651i
\(221\) −8.46682 1.11468i −0.569540 0.0749814i
\(222\) −11.3058 + 2.35269i −0.758794 + 0.157902i
\(223\) 25.7871 1.72683 0.863417 0.504492i \(-0.168320\pi\)
0.863417 + 0.504492i \(0.168320\pi\)
\(224\) −7.44513 + 12.9835i −0.497449 + 0.867493i
\(225\) −0.592064 −0.0394710
\(226\) 13.9641 2.90586i 0.928875 0.193295i
\(227\) −3.82268 0.503265i −0.253720 0.0334029i 0.00259326 0.999997i \(-0.499175\pi\)
−0.256313 + 0.966594i \(0.582508\pi\)
\(228\) 1.24717 + 0.491011i 0.0825961 + 0.0325180i
\(229\) 2.18889 + 16.6263i 0.144646 + 1.09870i 0.897659 + 0.440690i \(0.145266\pi\)
−0.753013 + 0.658005i \(0.771400\pi\)
\(230\) 18.0062 1.33975i 1.18729 0.0883404i
\(231\) 5.23441 3.19414i 0.344399 0.210159i
\(232\) −11.1629 + 17.7030i −0.732883 + 1.16226i
\(233\) −13.4897 3.61455i −0.883738 0.236797i −0.211719 0.977331i \(-0.567906\pi\)
−0.672019 + 0.740534i \(0.734573\pi\)
\(234\) −0.736286 2.10778i −0.0481325 0.137790i
\(235\) 18.3416 + 23.9032i 1.19647 + 1.55928i
\(236\) −3.02849 + 5.46590i −0.197138 + 0.355800i
\(237\) −8.86918 + 3.67373i −0.576115 + 0.238635i
\(238\) 19.3705 + 5.86763i 1.25561 + 0.380342i
\(239\) 1.65418i 0.107000i 0.998568 + 0.0535001i \(0.0170377\pi\)
−0.998568 + 0.0535001i \(0.982962\pi\)
\(240\) 6.92025 + 6.44850i 0.446700 + 0.416249i
\(241\) −3.75684 2.16902i −0.242000 0.139719i 0.374096 0.927390i \(-0.377953\pi\)
−0.616095 + 0.787672i \(0.711286\pi\)
\(242\) −7.94692 0.450529i −0.510848 0.0289611i
\(243\) −0.793353 0.608761i −0.0508936 0.0390521i
\(244\) 4.29503 17.2399i 0.274961 1.10367i
\(245\) 2.95545 + 16.2873i 0.188816 + 1.04056i
\(246\) 9.09341 + 7.83393i 0.579775 + 0.499473i
\(247\) 1.02198 + 0.273839i 0.0650270 + 0.0174239i
\(248\) −1.87360 + 0.172679i −0.118973 + 0.0109651i
\(249\) −4.94473 + 1.32494i −0.313359 + 0.0839644i
\(250\) −12.1843 + 8.29760i −0.770600 + 0.524786i
\(251\) 7.39110 + 3.06149i 0.466522 + 0.193240i 0.603546 0.797328i \(-0.293754\pi\)
−0.137024 + 0.990568i \(0.543754\pi\)
\(252\) 0.910027 + 5.21266i 0.0573263 + 0.328367i
\(253\) 4.78865 + 11.5608i 0.301060 + 0.726822i
\(254\) 3.40894 + 16.3816i 0.213896 + 1.02787i
\(255\) 6.39583 11.0779i 0.400522 0.693725i
\(256\) −1.12780 15.9602i −0.0704876 0.997513i
\(257\) 1.29274 + 2.23909i 0.0806387 + 0.139670i 0.903524 0.428537i \(-0.140971\pi\)
−0.822886 + 0.568207i \(0.807637\pi\)
\(258\) −5.24023 1.72744i −0.326243 0.107546i
\(259\) 21.3446 3.33958i 1.32629 0.207511i
\(260\) 6.00295 + 4.44025i 0.372287 + 0.275372i
\(261\) 0.965813 + 7.33608i 0.0597823 + 0.454092i
\(262\) 2.94219 + 1.41881i 0.181769 + 0.0876545i
\(263\) −0.626655 + 0.167912i −0.0386412 + 0.0103539i −0.278088 0.960556i \(-0.589701\pi\)
0.239447 + 0.970910i \(0.423034\pi\)
\(264\) −2.74284 + 5.95399i −0.168810 + 0.366443i
\(265\) −0.926914 + 0.926914i −0.0569398 + 0.0569398i
\(266\) −2.28446 1.03399i −0.140069 0.0633977i
\(267\) −5.70351 + 13.7695i −0.349049 + 0.842679i
\(268\) 15.0657 4.32302i 0.920286 0.264070i
\(269\) 1.40685 10.6861i 0.0857771 0.651542i −0.893507 0.449050i \(-0.851763\pi\)
0.979284 0.202492i \(-0.0649040\pi\)
\(270\) 3.33891 + 0.189290i 0.203199 + 0.0115198i
\(271\) 1.00335 0.579282i 0.0609489 0.0351889i −0.469216 0.883083i \(-0.655463\pi\)
0.530165 + 0.847895i \(0.322130\pi\)
\(272\) −20.6894 + 6.33368i −1.25448 + 0.384036i
\(273\) 1.17880 + 4.00717i 0.0713440 + 0.242525i
\(274\) −9.73874 + 4.90985i −0.588339 + 0.296615i
\(275\) 1.08865 + 0.835353i 0.0656483 + 0.0503737i
\(276\) −10.7965 + 0.190432i −0.649871 + 0.0114626i
\(277\) 5.41715 + 7.05977i 0.325485 + 0.424180i 0.927221 0.374515i \(-0.122191\pi\)
−0.601736 + 0.798695i \(0.705524\pi\)
\(278\) −26.7089 5.06831i −1.60189 0.303977i
\(279\) −0.470384 + 0.470384i −0.0281612 + 0.0281612i
\(280\) −12.3279 12.6956i −0.736733 0.758707i
\(281\) 18.3199 + 18.3199i 1.09287 + 1.09287i 0.995221 + 0.0976504i \(0.0311327\pi\)
0.0976504 + 0.995221i \(0.468867\pi\)
\(282\) −10.1423 14.8930i −0.603964 0.886865i
\(283\) 15.3022 11.7418i 0.909621 0.697977i −0.0439856 0.999032i \(-0.514006\pi\)
0.953607 + 0.301055i \(0.0973389\pi\)
\(284\) 22.5586 + 8.88129i 1.33861 + 0.527007i
\(285\) −0.964764 + 1.25730i −0.0571477 + 0.0744763i
\(286\) −1.62006 + 4.91450i −0.0957961 + 0.290600i
\(287\) −16.2590 15.4873i −0.959738 0.914189i
\(288\) −3.91366 4.08452i −0.230615 0.240682i
\(289\) 6.13025 + 10.6179i 0.360603 + 0.624583i
\(290\) −16.4793 18.4601i −0.967696 1.08401i
\(291\) −10.5663 1.39109i −0.619410 0.0815469i
\(292\) 0.766686 + 0.963494i 0.0448669 + 0.0563842i
\(293\) −25.7712 10.6748i −1.50557 0.623626i −0.530930 0.847416i \(-0.678157\pi\)
−0.974637 + 0.223790i \(0.928157\pi\)
\(294\) −1.21331 9.82486i −0.0707619 0.572997i
\(295\) −5.22444 5.22444i −0.304179 0.304179i
\(296\) −16.9556 + 15.6822i −0.985523 + 0.911510i
\(297\) 0.599860 + 2.23871i 0.0348074 + 0.129903i
\(298\) −3.11124 8.90660i −0.180229 0.515946i
\(299\) −8.45082 + 1.11257i −0.488723 + 0.0643417i
\(300\) −1.01488 + 0.610057i −0.0585944 + 0.0352217i
\(301\) 9.62993 + 3.71735i 0.555060 + 0.214264i
\(302\) 18.4390 9.29614i 1.06104 0.534933i
\(303\) −9.09772 + 5.25257i −0.522651 + 0.301752i
\(304\) 2.64377 0.443411i 0.151631 0.0254314i
\(305\) 18.1927 + 10.5035i 1.04171 + 0.601431i
\(306\) −4.19380 + 6.39789i −0.239744 + 0.365743i
\(307\) 21.6083 8.95046i 1.23325 0.510830i 0.331653 0.943401i \(-0.392394\pi\)
0.901600 + 0.432571i \(0.142394\pi\)
\(308\) 5.68132 10.8687i 0.323723 0.619302i
\(309\) −3.01254 + 7.27291i −0.171377 + 0.413741i
\(310\) 0.414757 2.18568i 0.0235566 0.124138i
\(311\) 2.41801 + 9.02415i 0.137113 + 0.511713i 0.999980 + 0.00628214i \(0.00199968\pi\)
−0.862867 + 0.505431i \(0.831334\pi\)
\(312\) −3.43394 2.85438i −0.194408 0.161597i
\(313\) 6.47507 24.1653i 0.365992 1.36590i −0.500078 0.865980i \(-0.666695\pi\)
0.866071 0.499922i \(-0.166638\pi\)
\(314\) 1.65137 + 22.1943i 0.0931921 + 1.25250i
\(315\) −6.22104 0.665671i −0.350516 0.0375063i
\(316\) −11.4177 + 15.4360i −0.642295 + 0.868345i
\(317\) −11.2308 + 14.6363i −0.630787 + 0.822058i −0.993969 0.109661i \(-0.965024\pi\)
0.363182 + 0.931718i \(0.381690\pi\)
\(318\) 0.584817 0.522065i 0.0327949 0.0292760i
\(319\) 8.57471 14.8518i 0.480091 0.831543i
\(320\) 18.5068 + 3.92311i 1.03456 + 0.219308i
\(321\) 4.16377 0.232399
\(322\) 20.1909 + 0.652991i 1.12520 + 0.0363898i
\(323\) −1.38729 3.34922i −0.0771911 0.186356i
\(324\) −1.98719 0.226042i −0.110399 0.0125579i
\(325\) −0.741560 + 0.569019i −0.0411344 + 0.0315635i
\(326\) 9.66756 + 4.66199i 0.535437 + 0.258204i
\(327\) −2.18868 + 8.16826i −0.121034 + 0.451706i
\(328\) 23.6594 + 4.05874i 1.30637 + 0.224107i
\(329\) 17.5592 + 28.7751i 0.968069 + 1.58643i
\(330\) −5.87231 5.05897i −0.323260 0.278487i
\(331\) 13.8510 1.82352i 0.761318 0.100229i 0.260137 0.965572i \(-0.416232\pi\)
0.501181 + 0.865342i \(0.332899\pi\)
\(332\) −7.11078 + 7.36613i −0.390255 + 0.404269i
\(333\) −1.06583 + 8.09580i −0.0584072 + 0.443647i
\(334\) −18.0443 + 27.5276i −0.987340 + 1.50624i
\(335\) 18.5322i 1.01252i
\(336\) 6.93100 + 7.99758i 0.378117 + 0.436304i
\(337\) 30.7038i 1.67254i −0.548315 0.836272i \(-0.684730\pi\)
0.548315 0.836272i \(-0.315270\pi\)
\(338\) 12.4279 + 8.14647i 0.675990 + 0.443110i
\(339\) 1.31644 9.99932i 0.0714990 0.543089i
\(340\) −0.451177 25.5793i −0.0244685 1.38723i
\(341\) 1.52859 0.201242i 0.0827776 0.0108979i
\(342\) 0.618600 0.718054i 0.0334501 0.0388279i
\(343\) 1.34904 + 18.4711i 0.0728416 + 0.997344i
\(344\) −10.7625 + 2.43841i −0.580273 + 0.131470i
\(345\) 3.30447 12.3324i 0.177907 0.663956i
\(346\) −5.65302 + 11.7227i −0.303908 + 0.630215i
\(347\) 26.1412 20.0589i 1.40333 1.07682i 0.417578 0.908641i \(-0.362879\pi\)
0.985757 0.168175i \(-0.0537874\pi\)
\(348\) 9.21456 + 11.5799i 0.493952 + 0.620750i
\(349\) 1.84418 + 4.45225i 0.0987169 + 0.238324i 0.965521 0.260325i \(-0.0838298\pi\)
−0.866804 + 0.498649i \(0.833830\pi\)
\(350\) 1.95331 1.04506i 0.104409 0.0558607i
\(351\) −1.57874 −0.0842670
\(352\) 1.43330 + 13.0322i 0.0763952 + 0.694619i
\(353\) −4.41603 + 7.64879i −0.235042 + 0.407104i −0.959285 0.282440i \(-0.908856\pi\)
0.724243 + 0.689545i \(0.242189\pi\)
\(354\) 2.94256 + 3.29625i 0.156395 + 0.175194i
\(355\) −17.4504 + 22.7418i −0.926172 + 1.20701i
\(356\) 4.41130 + 29.4797i 0.233798 + 1.56242i
\(357\) 8.43391 11.5626i 0.446370 0.611955i
\(358\) 16.4184 1.22161i 0.867739 0.0645641i
\(359\) −5.05253 + 18.8563i −0.266663 + 0.995198i 0.694562 + 0.719432i \(0.255598\pi\)
−0.961225 + 0.275766i \(0.911069\pi\)
\(360\) 5.91842 3.11591i 0.311928 0.164223i
\(361\) −4.80132 17.9188i −0.252701 0.943093i
\(362\) −12.9670 2.46064i −0.681532 0.129328i
\(363\) −2.15387 + 5.19991i −0.113049 + 0.272925i
\(364\) 6.14958 + 5.65425i 0.322325 + 0.296363i
\(365\) −1.34505 + 0.557139i −0.0704033 + 0.0291620i
\(366\) −10.5069 6.88727i −0.549206 0.360003i
\(367\) −12.0996 6.98569i −0.631593 0.364650i 0.149776 0.988720i \(-0.452145\pi\)
−0.781369 + 0.624070i \(0.785478\pi\)
\(368\) −18.3105 + 11.4510i −0.954501 + 0.596925i
\(369\) 7.35002 4.24353i 0.382627 0.220910i
\(370\) −12.2936 24.3845i −0.639113 1.26769i
\(371\) −1.14151 + 0.920831i −0.0592641 + 0.0478072i
\(372\) −0.321628 + 1.29099i −0.0166756 + 0.0669345i
\(373\) −30.9653 + 4.07667i −1.60332 + 0.211082i −0.878462 0.477812i \(-0.841430\pi\)
−0.724863 + 0.688893i \(0.758097\pi\)
\(374\) 16.7382 5.84696i 0.865512 0.302339i
\(375\) 2.69785 + 10.0685i 0.139316 + 0.519936i
\(376\) −32.7309 15.0783i −1.68797 0.777602i
\(377\) 8.26021 + 8.26021i 0.425423 + 0.425423i
\(378\) 3.69192 + 0.608039i 0.189892 + 0.0312742i
\(379\) −0.203780 0.0844084i −0.0104675 0.00433577i 0.377444 0.926033i \(-0.376803\pi\)
−0.387911 + 0.921697i \(0.626803\pi\)
\(380\) −0.358231 + 3.14929i −0.0183769 + 0.161555i
\(381\) 11.7305 + 1.54434i 0.600969 + 0.0791191i
\(382\) −22.6379 + 20.2088i −1.15826 + 1.03397i
\(383\) −11.7963 20.4318i −0.602762 1.04401i −0.992401 0.123047i \(-0.960734\pi\)
0.389639 0.920968i \(-0.372600\pi\)
\(384\) −10.9172 2.96886i −0.557117 0.151504i
\(385\) 10.4997 + 10.0014i 0.535113 + 0.509717i
\(386\) −0.933299 0.307661i −0.0475037 0.0156595i
\(387\) −2.37511 + 3.09530i −0.120734 + 0.157343i
\(388\) −19.5456 + 8.50293i −0.992278 + 0.431671i
\(389\) −26.6690 + 20.4639i −1.35217 + 1.03756i −0.357561 + 0.933890i \(0.616391\pi\)
−0.994612 + 0.103668i \(0.966942\pi\)
\(390\) 4.36390 2.97186i 0.220975 0.150486i
\(391\) 20.6512 + 20.6512i 1.04438 + 1.04438i
\(392\) −12.2032 15.5911i −0.616357 0.787467i
\(393\) 1.63321 1.63321i 0.0823846 0.0823846i
\(394\) 4.80328 25.3123i 0.241986 1.27521i
\(395\) −13.8198 18.0103i −0.695349 0.906196i
\(396\) 3.33499 + 3.21938i 0.167590 + 0.161780i
\(397\) 8.65144 + 6.63848i 0.434203 + 0.333176i 0.802626 0.596482i \(-0.203435\pi\)
−0.368423 + 0.929658i \(0.620102\pi\)
\(398\) −0.835176 1.65658i −0.0418636 0.0830369i
\(399\) −1.22294 + 1.28388i −0.0612238 + 0.0642743i
\(400\) −1.11106 + 2.09145i −0.0555532 + 0.104573i
\(401\) 29.1711 16.8419i 1.45673 0.841045i 0.457885 0.889012i \(-0.348607\pi\)
0.998849 + 0.0479662i \(0.0152740\pi\)
\(402\) 0.627311 11.0652i 0.0312874 0.551883i
\(403\) −0.137081 + 1.04123i −0.00682847 + 0.0518674i
\(404\) −10.1826 + 18.3779i −0.506605 + 0.914334i
\(405\) 0.904952 2.18475i 0.0449674 0.108561i
\(406\) −16.1353 22.4980i −0.800783 1.11656i
\(407\) 13.3823 13.3823i 0.663335 0.663335i
\(408\) −0.596466 + 15.2882i −0.0295295 + 0.756877i
\(409\) −11.1083 + 2.97646i −0.549270 + 0.147176i −0.522772 0.852473i \(-0.675102\pi\)
−0.0264976 + 0.999649i \(0.508435\pi\)
\(410\) −12.3285 + 25.5657i −0.608863 + 1.26260i
\(411\) 1.00662 + 7.64602i 0.0496528 + 0.377150i
\(412\) 2.33001 + 15.5709i 0.114791 + 0.767124i
\(413\) −5.19016 6.43398i −0.255391 0.316595i
\(414\) −2.39048 + 7.25159i −0.117486 + 0.356396i
\(415\) −6.05278 10.4837i −0.297119 0.514625i
\(416\) −8.82739 1.35453i −0.432798 0.0664111i
\(417\) −9.61154 + 16.6477i −0.470679 + 0.815240i
\(418\) −2.15056 + 0.447522i −0.105187 + 0.0218890i
\(419\) 0.662805 + 1.60015i 0.0323802 + 0.0781726i 0.939242 0.343254i \(-0.111529\pi\)
−0.906862 + 0.421427i \(0.861529\pi\)
\(420\) −11.3497 + 5.26904i −0.553807 + 0.257103i
\(421\) 1.35123 + 0.559697i 0.0658548 + 0.0272780i 0.415368 0.909654i \(-0.363653\pi\)
−0.349513 + 0.936932i \(0.613653\pi\)
\(422\) 12.2031 + 17.9191i 0.594037 + 0.872289i
\(423\) −12.3069 + 3.29762i −0.598381 + 0.160336i
\(424\) 0.464530 1.49749i 0.0225596 0.0727243i
\(425\) 3.09352 + 0.828907i 0.150058 + 0.0402079i
\(426\) 11.1891 12.9880i 0.542113 0.629270i
\(427\) 18.9886 + 13.8506i 0.918923 + 0.670276i
\(428\) 7.13730 4.29030i 0.344994 0.207380i
\(429\) 2.90290 + 2.22747i 0.140153 + 0.107543i
\(430\) 0.738523 13.0269i 0.0356148 0.628212i
\(431\) 25.1019 + 14.4926i 1.20912 + 0.698084i 0.962566 0.271047i \(-0.0873697\pi\)
0.246550 + 0.969130i \(0.420703\pi\)
\(432\) −3.63924 + 1.66011i −0.175093 + 0.0798719i
\(433\) 33.0493i 1.58825i −0.607754 0.794125i \(-0.707930\pi\)
0.607754 0.794125i \(-0.292070\pi\)
\(434\) 0.721588 2.38215i 0.0346373 0.114347i
\(435\) −16.1658 + 6.69609i −0.775090 + 0.321053i
\(436\) 4.66478 + 16.2568i 0.223402 + 0.778558i
\(437\) −2.20269 2.87061i −0.105369 0.137320i
\(438\) 0.821962 0.287126i 0.0392749 0.0137194i
\(439\) −9.35360 2.50629i −0.446423 0.119619i 0.0286021 0.999591i \(-0.490894\pi\)
−0.475025 + 0.879972i \(0.657561\pi\)
\(440\) −15.2787 2.62104i −0.728384 0.124953i
\(441\) −6.84152 1.48109i −0.325787 0.0705280i
\(442\) 0.896128 + 12.0439i 0.0426244 + 0.572871i
\(443\) 0.529622 + 4.02288i 0.0251631 + 0.191133i 0.999410 0.0343520i \(-0.0109367\pi\)
−0.974247 + 0.225485i \(0.927603\pi\)
\(444\) 6.51484 + 14.9756i 0.309181 + 0.710710i
\(445\) −34.9427 4.60030i −1.65644 0.218075i
\(446\) −7.42978 35.7036i −0.351810 1.69062i
\(447\) −6.67111 −0.315533
\(448\) 20.1214 + 6.56739i 0.950645 + 0.310280i
\(449\) −26.3581 −1.24392 −0.621958 0.783051i \(-0.713663\pi\)
−0.621958 + 0.783051i \(0.713663\pi\)
\(450\) 0.170585 + 0.819744i 0.00804147 + 0.0386431i
\(451\) −19.5021 2.56749i −0.918316 0.120899i
\(452\) −8.04664 18.4967i −0.378482 0.870013i
\(453\) −1.90589 14.4767i −0.0895467 0.680175i
\(454\) 0.404592 + 5.43770i 0.0189884 + 0.255204i
\(455\) −8.43161 + 5.14514i −0.395280 + 0.241208i
\(456\) 0.320495 1.86825i 0.0150086 0.0874887i
\(457\) −24.2171 6.48896i −1.13283 0.303541i −0.356765 0.934194i \(-0.616120\pi\)
−0.776064 + 0.630654i \(0.782787\pi\)
\(458\) 22.3893 7.82100i 1.04618 0.365451i
\(459\) 3.29297 + 4.29148i 0.153703 + 0.200309i
\(460\) −7.04289 24.5445i −0.328376 1.14439i
\(461\) −24.9203 + 10.3223i −1.16065 + 0.480759i −0.878093 0.478490i \(-0.841184\pi\)
−0.282562 + 0.959249i \(0.591184\pi\)
\(462\) −5.93060 6.32702i −0.275916 0.294360i
\(463\) 27.2787i 1.26775i −0.773436 0.633874i \(-0.781464\pi\)
0.773436 0.633874i \(-0.218536\pi\)
\(464\) 27.7270 + 10.3551i 1.28719 + 0.480724i
\(465\) −1.36234 0.786545i −0.0631768 0.0364752i
\(466\) −1.11789 + 19.7186i −0.0517853 + 0.913446i
\(467\) 10.7453 + 8.24516i 0.497233 + 0.381540i 0.826714 0.562622i \(-0.190207\pi\)
−0.329481 + 0.944162i \(0.606874\pi\)
\(468\) −2.70619 + 1.62672i −0.125094 + 0.0751951i
\(469\) −2.20605 + 20.6167i −0.101866 + 0.951989i
\(470\) 27.8107 32.2819i 1.28281 1.48905i
\(471\) 15.2009 + 4.07307i 0.700421 + 0.187677i
\(472\) 8.44040 + 2.61827i 0.388501 + 0.120516i
\(473\) 8.73442 2.34038i 0.401609 0.107611i
\(474\) 7.64187 + 11.2214i 0.351003 + 0.515415i
\(475\) −0.366583 0.151844i −0.0168200 0.00696706i
\(476\) 2.54300 28.5101i 0.116558 1.30676i
\(477\) −0.212133 0.512134i −0.00971289 0.0234490i
\(478\) 2.29030 0.476602i 0.104756 0.0217993i
\(479\) −8.03535 + 13.9176i −0.367145 + 0.635913i −0.989118 0.147125i \(-0.952998\pi\)
0.621973 + 0.783039i \(0.286331\pi\)
\(480\) 6.93443 11.4394i 0.316512 0.522135i
\(481\) 6.44573 + 11.1643i 0.293900 + 0.509050i
\(482\) −1.92070 + 5.82649i −0.0874853 + 0.265389i
\(483\) 5.14418 13.3262i 0.234068 0.606363i
\(484\) 1.66588 + 11.1327i 0.0757220 + 0.506034i
\(485\) −3.28958 24.9868i −0.149372 1.13459i
\(486\) −0.614282 + 1.27384i −0.0278644 + 0.0577824i
\(487\) 15.8921 4.25829i 0.720142 0.192961i 0.119907 0.992785i \(-0.461740\pi\)
0.600235 + 0.799824i \(0.295074\pi\)
\(488\) −25.1070 0.979545i −1.13654 0.0443419i
\(489\) 5.36647 5.36647i 0.242680 0.242680i
\(490\) 21.6991 8.78467i 0.980266 0.396851i
\(491\) 9.86195 23.8089i 0.445064 1.07448i −0.529085 0.848569i \(-0.677465\pi\)
0.974148 0.225910i \(-0.0725354\pi\)
\(492\) 8.22650 14.8474i 0.370879 0.669373i
\(493\) 5.22437 39.6830i 0.235294 1.78723i
\(494\) 0.0846916 1.49388i 0.00381045 0.0672130i
\(495\) −4.74647 + 2.74038i −0.213338 + 0.123171i
\(496\) 0.778903 + 2.54434i 0.0349738 + 0.114244i
\(497\) −22.1203 + 23.2225i −0.992232 + 1.04167i
\(498\) 3.25912 + 6.46450i 0.146045 + 0.289681i
\(499\) −12.6630 9.71665i −0.566873 0.434977i 0.285149 0.958483i \(-0.407957\pi\)
−0.852022 + 0.523506i \(0.824624\pi\)
\(500\) 14.9990 + 14.4791i 0.670776 + 0.647523i
\(501\) 14.1684 + 18.4646i 0.632996 + 0.824936i
\(502\) 2.10928 11.1154i 0.0941417 0.496107i
\(503\) −13.9989 + 13.9989i −0.624181 + 0.624181i −0.946598 0.322417i \(-0.895505\pi\)
0.322417 + 0.946598i \(0.395505\pi\)
\(504\) 6.95501 2.76185i 0.309801 0.123023i
\(505\) −17.5660 17.5660i −0.781677 0.781677i
\(506\) 14.6269 9.96104i 0.650243 0.442822i
\(507\) 8.33622 6.39661i 0.370225 0.284083i
\(508\) 21.6990 9.43972i 0.962737 0.418820i
\(509\) −15.0853 + 19.6596i −0.668645 + 0.871395i −0.997329 0.0730450i \(-0.976728\pi\)
0.328684 + 0.944440i \(0.393395\pi\)
\(510\) −17.1807 5.66360i −0.760775 0.250789i
\(511\) −1.56266 + 0.459691i −0.0691280 + 0.0203355i
\(512\) −21.7728 + 6.15995i −0.962231 + 0.272234i
\(513\) −0.335087 0.580388i −0.0147945 0.0256248i
\(514\) 2.72767 2.43499i 0.120312 0.107403i
\(515\) −18.4564 2.42983i −0.813287 0.107071i
\(516\) −0.881914 + 7.75309i −0.0388241 + 0.341311i
\(517\) 27.2818 + 11.3005i 1.19985 + 0.496995i
\(518\) −10.7736 28.5905i −0.473366 1.25620i
\(519\) 6.50726 + 6.50726i 0.285637 + 0.285637i
\(520\) 4.41819 9.59072i 0.193750 0.420581i
\(521\) −1.59988 5.97085i −0.0700922 0.261588i 0.921984 0.387229i \(-0.126568\pi\)
−0.992076 + 0.125642i \(0.959901\pi\)
\(522\) 9.87892 3.45089i 0.432388 0.151041i
\(523\) 14.2637 1.87786i 0.623710 0.0821129i 0.187954 0.982178i \(-0.439814\pi\)
0.435756 + 0.900065i \(0.356481\pi\)
\(524\) 1.11672 4.48241i 0.0487840 0.195815i
\(525\) −0.242142 1.54763i −0.0105679 0.0675440i
\(526\) 0.413034 + 0.819259i 0.0180092 + 0.0357214i
\(527\) 3.11630 1.79920i 0.135748 0.0783742i
\(528\) 9.03389 + 2.08215i 0.393149 + 0.0906140i
\(529\) 5.32605 + 3.07500i 0.231567 + 0.133695i
\(530\) 1.55042 + 1.01630i 0.0673461 + 0.0441452i
\(531\) 2.88658 1.19566i 0.125267 0.0518873i
\(532\) −0.773410 + 3.46086i −0.0335316 + 0.150047i
\(533\) 5.12753 12.3790i 0.222098 0.536192i
\(534\) 20.7079 + 3.92955i 0.896117 + 0.170048i
\(535\) 2.54841 + 9.51078i 0.110177 + 0.411187i
\(536\) −10.3262 19.6138i −0.446023 0.847186i
\(537\) 3.01308 11.2450i 0.130024 0.485256i
\(538\) −15.2008 + 1.13101i −0.655352 + 0.0487615i
\(539\) 10.4901 + 12.3761i 0.451840 + 0.533078i
\(540\) −0.699923 4.67743i −0.0301199 0.201285i
\(541\) 22.5979 29.4501i 0.971558 1.26616i 0.00763712 0.999971i \(-0.497569\pi\)
0.963921 0.266188i \(-0.0857643\pi\)
\(542\) −1.09113 1.22228i −0.0468680 0.0525015i
\(543\) −4.66635 + 8.08235i −0.200252 + 0.346847i
\(544\) 14.7304 + 26.8208i 0.631559 + 1.14993i
\(545\) −19.9973 −0.856591
\(546\) 5.20850 2.78665i 0.222903 0.119258i
\(547\) 0.249191 + 0.601601i 0.0106547 + 0.0257226i 0.929117 0.369785i \(-0.120569\pi\)
−0.918463 + 0.395508i \(0.870569\pi\)
\(548\) 9.60387 + 12.0692i 0.410257 + 0.515570i
\(549\) −7.04769 + 5.40788i −0.300788 + 0.230803i
\(550\) 0.842928 1.74798i 0.0359426 0.0745341i
\(551\) −1.28345 + 4.78990i −0.0546768 + 0.204057i
\(552\) 3.37434 + 14.8934i 0.143621 + 0.633906i
\(553\) −13.2303 21.6811i −0.562608 0.921975i
\(554\) 8.21383 9.53439i 0.348972 0.405077i
\(555\) −19.1446 + 2.52043i −0.812642 + 0.106986i
\(556\) 0.678021 + 38.4402i 0.0287545 + 1.63023i
\(557\) 4.56128 34.6463i 0.193267 1.46801i −0.569848 0.821750i \(-0.692998\pi\)
0.763115 0.646262i \(-0.223669\pi\)
\(558\) 0.786799 + 0.515745i 0.0333078 + 0.0218332i
\(559\) 6.15953i 0.260520i
\(560\) −14.0258 + 20.7265i −0.592699 + 0.875854i
\(561\) 12.5370i 0.529314i
\(562\) 20.0865 30.6431i 0.847298 1.29260i
\(563\) 4.97147 37.7621i 0.209523 1.59148i −0.486643 0.873601i \(-0.661779\pi\)
0.696166 0.717881i \(-0.254888\pi\)
\(564\) −17.6979 + 18.3335i −0.745218 + 0.771979i
\(565\) 23.6459 3.11305i 0.994792 0.130967i
\(566\) −20.6660 17.8037i −0.868656 0.748344i
\(567\) 1.26681 2.32276i 0.0532009 0.0975466i
\(568\) 5.79704 33.7924i 0.243238 1.41790i
\(569\) 3.38834 12.6455i 0.142047 0.530126i −0.857822 0.513946i \(-0.828183\pi\)
0.999869 0.0161794i \(-0.00515030\pi\)
\(570\) 2.01877 + 0.973512i 0.0845571 + 0.0407759i
\(571\) 24.0305 18.4393i 1.00565 0.771659i 0.0319445 0.999490i \(-0.489830\pi\)
0.973701 + 0.227831i \(0.0731634\pi\)
\(572\) 7.27115 + 0.827094i 0.304022 + 0.0345825i
\(573\) 8.21153 + 19.8244i 0.343042 + 0.828176i
\(574\) −16.7585 + 26.9736i −0.699486 + 1.12586i
\(575\) 3.19660 0.133307
\(576\) −4.52763 + 6.59550i −0.188651 + 0.274812i
\(577\) −20.9025 + 36.2042i −0.870183 + 1.50720i −0.00837693 + 0.999965i \(0.502666\pi\)
−0.861807 + 0.507237i \(0.830667\pi\)
\(578\) 12.9348 11.5469i 0.538017 0.480287i
\(579\) −0.423013 + 0.551282i −0.0175798 + 0.0229105i
\(580\) −20.8109 + 28.1351i −0.864127 + 1.16825i
\(581\) −5.48560 12.3834i −0.227581 0.513750i
\(582\) 1.11834 + 15.0305i 0.0463567 + 0.623033i
\(583\) −0.332520 + 1.24098i −0.0137716 + 0.0513963i
\(584\) 1.11311 1.33912i 0.0460608 0.0554131i
\(585\) −0.966258 3.60613i −0.0399499 0.149095i
\(586\) −7.35460 + 38.7571i −0.303816 + 1.60104i
\(587\) −1.03090 + 2.48882i −0.0425499 + 0.102724i −0.943726 0.330729i \(-0.892705\pi\)
0.901176 + 0.433454i \(0.142705\pi\)
\(588\) −13.2535 + 4.51063i −0.546563 + 0.186015i
\(589\) −0.411880 + 0.170606i −0.0169712 + 0.00702971i
\(590\) −5.72825 + 8.73878i −0.235828 + 0.359770i
\(591\) −15.7772 9.10894i −0.648985 0.374692i
\(592\) 26.5981 + 18.9575i 1.09317 + 0.779150i
\(593\) −0.868236 + 0.501276i −0.0356542 + 0.0205849i −0.517721 0.855549i \(-0.673220\pi\)
0.482067 + 0.876134i \(0.339886\pi\)
\(594\) 2.92678 1.47556i 0.120087 0.0605428i
\(595\) 31.5728 + 12.1878i 1.29436 + 0.499649i
\(596\) −11.4353 + 6.87385i −0.468406 + 0.281564i
\(597\) −1.30060 + 0.171228i −0.0532302 + 0.00700789i
\(598\) 3.97526 + 11.3801i 0.162561 + 0.465365i
\(599\) 7.85279 + 29.3070i 0.320856 + 1.19745i 0.918412 + 0.395624i \(0.129472\pi\)
−0.597556 + 0.801827i \(0.703862\pi\)
\(600\) 1.13706 + 1.22939i 0.0464205 + 0.0501897i
\(601\) 20.7560 + 20.7560i 0.846656 + 0.846656i 0.989714 0.143058i \(-0.0456936\pi\)
−0.143058 + 0.989714i \(0.545694\pi\)
\(602\) 2.37229 14.4042i 0.0966874 0.587071i
\(603\) −7.24031 2.99903i −0.294848 0.122130i
\(604\) −18.1836 22.8514i −0.739882 0.929809i
\(605\) −13.1958 1.73726i −0.536485 0.0706296i
\(606\) 9.89370 + 11.0829i 0.401904 + 0.450212i
\(607\) −0.456878 0.791335i −0.0185441 0.0321193i 0.856604 0.515974i \(-0.172570\pi\)
−0.875149 + 0.483854i \(0.839236\pi\)
\(608\) −1.37565 3.53268i −0.0557899 0.143269i
\(609\) −18.7811 + 5.52488i −0.761050 + 0.223880i
\(610\) 9.30105 28.2150i 0.376588 1.14239i
\(611\) −12.2451 + 15.9581i −0.495383 + 0.645596i
\(612\) 10.0665 + 3.96318i 0.406916 + 0.160202i
\(613\) −17.6376 + 13.5338i −0.712375 + 0.546624i −0.900146 0.435588i \(-0.856540\pi\)
0.187771 + 0.982213i \(0.439874\pi\)
\(614\) −18.6182 27.3391i −0.751369 1.10332i
\(615\) 14.1915 + 14.1915i 0.572257 + 0.572257i
\(616\) −16.6852 4.73460i −0.672266 0.190763i
\(617\) 20.8467 20.8467i 0.839257 0.839257i −0.149504 0.988761i \(-0.547768\pi\)
0.988761 + 0.149504i \(0.0477676\pi\)
\(618\) 10.9377 + 2.07555i 0.439979 + 0.0834908i
\(619\) 3.92029 + 5.10903i 0.157570 + 0.205349i 0.865466 0.500967i \(-0.167022\pi\)
−0.707896 + 0.706316i \(0.750356\pi\)
\(620\) −3.14569 + 0.0554848i −0.126334 + 0.00222832i
\(621\) 4.28337 + 3.28675i 0.171886 + 0.131893i
\(622\) 11.7977 5.94791i 0.473046 0.238489i
\(623\) −38.3254 9.27726i −1.53547 0.371686i
\(624\) −2.96265 + 5.57687i −0.118601 + 0.223253i
\(625\) −23.9108 + 13.8049i −0.956431 + 0.552196i
\(626\) −35.3237 2.00258i −1.41182 0.0800391i
\(627\) −0.202740 + 1.53996i −0.00809665 + 0.0615002i
\(628\) 30.2534 8.68104i 1.20724 0.346411i
\(629\) 16.9033 40.8082i 0.673979 1.62713i
\(630\) 0.870747 + 8.80515i 0.0346914 + 0.350806i
\(631\) 27.4214 27.4214i 1.09163 1.09163i 0.0962739 0.995355i \(-0.469308\pi\)
0.995355 0.0962739i \(-0.0306925\pi\)
\(632\) 24.6617 + 11.3610i 0.980988 + 0.451915i
\(633\) 14.8075 3.96766i 0.588546 0.157700i
\(634\) 23.5006 + 11.3327i 0.933328 + 0.450078i
\(635\) 3.65199 + 27.7396i 0.144925 + 1.10081i
\(636\) −0.891324 0.659293i −0.0353433 0.0261427i
\(637\) −9.99244 + 4.72016i −0.395915 + 0.187020i
\(638\) −23.0337 7.59303i −0.911912 0.300611i
\(639\) −6.06097 10.4979i −0.239768 0.415291i
\(640\) 0.0995795 26.7540i 0.00393623 1.05754i
\(641\) 13.7147 23.7545i 0.541697 0.938248i −0.457109 0.889411i \(-0.651115\pi\)
0.998807 0.0488370i \(-0.0155515\pi\)
\(642\) −1.19966 5.76495i −0.0473469 0.227525i
\(643\) 9.76526 + 23.5754i 0.385104 + 0.929724i 0.990961 + 0.134150i \(0.0428304\pi\)
−0.605857 + 0.795574i \(0.707170\pi\)
\(644\) −4.91330 28.1435i −0.193611 1.10901i
\(645\) −8.52389 3.53071i −0.335628 0.139022i
\(646\) −4.23747 + 2.88576i −0.166721 + 0.113539i
\(647\) −5.60190 + 1.50102i −0.220233 + 0.0590113i −0.367248 0.930123i \(-0.619700\pi\)
0.147015 + 0.989134i \(0.453033\pi\)
\(648\) 0.259580 + 2.81649i 0.0101973 + 0.110642i
\(649\) −6.99466 1.87421i −0.274564 0.0735693i
\(650\) 1.00150 + 0.862784i 0.0392819 + 0.0338412i
\(651\) −1.42194 1.03718i −0.0557301 0.0406504i
\(652\) 3.66935 14.7285i 0.143703 0.576811i
\(653\) 30.6378 + 23.5092i 1.19895 + 0.919986i 0.998219 0.0596609i \(-0.0190020\pi\)
0.200730 + 0.979647i \(0.435669\pi\)
\(654\) 11.9400 + 0.676904i 0.466890 + 0.0264690i
\(655\) 4.73014 + 2.73095i 0.184822 + 0.106707i
\(656\) −1.19721 33.9272i −0.0467432 1.32463i
\(657\) 0.615655i 0.0240190i
\(658\) 34.7816 32.6023i 1.35593 1.27097i
\(659\) −5.82990 + 2.41482i −0.227101 + 0.0940682i −0.493332 0.869841i \(-0.664221\pi\)
0.266232 + 0.963909i \(0.414221\pi\)
\(660\) −5.31248 + 9.58812i −0.206788 + 0.373217i
\(661\) 4.67030 + 6.08645i 0.181653 + 0.236735i 0.875300 0.483580i \(-0.160664\pi\)
−0.693647 + 0.720315i \(0.743997\pi\)
\(662\) −6.51549 18.6520i −0.253232 0.724931i
\(663\) 8.24889 + 2.21028i 0.320360 + 0.0858403i
\(664\) 12.2476 + 7.72293i 0.475297 + 0.299708i
\(665\) −3.68110 2.00763i −0.142747 0.0778527i
\(666\) 11.5161 0.856858i 0.446242 0.0332026i
\(667\) −5.21449 39.6080i −0.201906 1.53363i
\(668\) 43.3124 + 17.0520i 1.67581 + 0.659763i
\(669\) −25.5665 3.36589i −0.988458 0.130133i
\(670\) 25.6589 5.33950i 0.991288 0.206283i
\(671\) 20.5889 0.794827
\(672\) 9.07612 11.9006i 0.350119 0.459075i
\(673\) −13.5409 −0.521964 −0.260982 0.965344i \(-0.584046\pi\)
−0.260982 + 0.965344i \(0.584046\pi\)
\(674\) −42.5111 + 8.84638i −1.63747 + 0.340750i
\(675\) 0.586999 + 0.0772799i 0.0225936 + 0.00297450i
\(676\) 7.69850 19.5543i 0.296096 0.752088i
\(677\) −0.691021 5.24882i −0.0265581 0.201729i 0.973022 0.230713i \(-0.0741059\pi\)
−0.999580 + 0.0289846i \(0.990773\pi\)
\(678\) −14.2239 + 1.05833i −0.546265 + 0.0406448i
\(679\) −0.685181 28.1888i −0.0262948 1.08179i
\(680\) −35.2860 + 7.99459i −1.35315 + 0.306579i
\(681\) 3.72428 + 0.997919i 0.142715 + 0.0382403i
\(682\) −0.719047 2.05843i −0.0275337 0.0788213i
\(683\) 22.0275 + 28.7068i 0.842858 + 1.09843i 0.993941 + 0.109913i \(0.0350572\pi\)
−0.151083 + 0.988521i \(0.548276\pi\)
\(684\) −1.17241 0.649599i −0.0448284 0.0248380i
\(685\) −16.8488 + 6.97899i −0.643758 + 0.266653i
\(686\) 25.1855 7.18970i 0.961586 0.274504i
\(687\) 16.7697i 0.639806i
\(688\) 6.47698 + 14.1986i 0.246933 + 0.541318i
\(689\) −0.757896 0.437572i −0.0288735 0.0166702i
\(690\) −18.0270 1.02199i −0.686276 0.0389065i
\(691\) −23.3232 17.8965i −0.887257 0.680816i 0.0610621 0.998134i \(-0.480551\pi\)
−0.948319 + 0.317318i \(0.897218\pi\)
\(692\) 17.8594 + 4.44937i 0.678913 + 0.169140i
\(693\) −5.60655 + 2.48359i −0.212975 + 0.0943438i
\(694\) −35.3044 30.4146i −1.34014 1.15452i
\(695\) −43.9089 11.7654i −1.66556 0.446286i
\(696\) 13.3781 16.0945i 0.507097 0.610059i
\(697\) −44.3448 + 11.8821i −1.67968 + 0.450068i
\(698\) 5.63303 3.83615i 0.213213 0.145200i
\(699\) 12.9025 + 5.34438i 0.488016 + 0.202143i
\(700\) −2.00973 2.40336i −0.0759605 0.0908384i
\(701\) 6.00012 + 14.4856i 0.226621 + 0.547113i 0.995762 0.0919670i \(-0.0293154\pi\)
−0.769141 + 0.639080i \(0.779315\pi\)
\(702\) 0.454867 + 2.18585i 0.0171678 + 0.0824996i
\(703\) −2.73621 + 4.73925i −0.103198 + 0.178744i
\(704\) 17.6308 5.73932i 0.664487 0.216309i
\(705\) −15.0647 26.0928i −0.567369 0.982712i
\(706\) 11.8625 + 3.91046i 0.446451 + 0.147172i
\(707\) −17.4507 21.6328i −0.656303 0.813585i
\(708\) 3.71603 5.02384i 0.139657 0.188808i
\(709\) −5.81147 44.1425i −0.218255 1.65781i −0.653077 0.757291i \(-0.726522\pi\)
0.434823 0.900516i \(-0.356811\pi\)
\(710\) 36.5151 + 17.6087i 1.37039 + 0.660841i
\(711\) 9.27282 2.48464i 0.347758 0.0931815i
\(712\) 39.5453 14.6014i 1.48202 0.547210i
\(713\) 2.53964 2.53964i 0.0951102 0.0951102i
\(714\) −18.4389 8.34579i −0.690060 0.312333i
\(715\) −3.31124 + 7.99404i −0.123833 + 0.298960i
\(716\) −6.42185 22.3802i −0.239996 0.836386i
\(717\) 0.215914 1.64003i 0.00806346 0.0612480i
\(718\) 27.5633 + 1.56262i 1.02865 + 0.0583166i
\(719\) −8.24447 + 4.75994i −0.307467 + 0.177516i −0.645792 0.763513i \(-0.723473\pi\)
0.338326 + 0.941029i \(0.390139\pi\)
\(720\) −6.01935 7.29661i −0.224328 0.271928i
\(721\) −20.2431 4.90016i −0.753892 0.182491i
\(722\) −23.4261 + 11.8104i −0.871830 + 0.439539i
\(723\) 3.44159 + 2.64083i 0.127994 + 0.0982134i
\(724\) 0.329175 + 18.6625i 0.0122337 + 0.693586i
\(725\) −2.66693 3.47561i −0.0990472 0.129081i
\(726\) 7.82013 + 1.48396i 0.290232 + 0.0550748i
\(727\) −23.2576 + 23.2576i −0.862578 + 0.862578i −0.991637 0.129059i \(-0.958804\pi\)
0.129059 + 0.991637i \(0.458804\pi\)
\(728\) 6.05680 10.1435i 0.224480 0.375944i
\(729\) 0.707107 + 0.707107i 0.0261891 + 0.0261891i
\(730\) 1.15892 + 1.70177i 0.0428937 + 0.0629855i
\(731\) 16.7434 12.8477i 0.619278 0.475188i
\(732\) −6.50853 + 16.5318i −0.240562 + 0.611031i
\(733\) 1.59105 2.07350i 0.0587668 0.0765863i −0.763045 0.646345i \(-0.776297\pi\)
0.821812 + 0.569759i \(0.192963\pi\)
\(734\) −6.18594 + 18.7652i −0.228327 + 0.692637i
\(735\) −0.804241 16.5337i −0.0296649 0.609856i
\(736\) 21.1301 + 22.0526i 0.778867 + 0.812870i
\(737\) 9.08167 + 15.7299i 0.334527 + 0.579419i
\(738\) −7.99308 8.95384i −0.294229 0.329595i
\(739\) 10.4361 + 1.37393i 0.383897 + 0.0505410i 0.320005 0.947416i \(-0.396315\pi\)
0.0638920 + 0.997957i \(0.479649\pi\)
\(740\) −30.2196 + 24.0468i −1.11089 + 0.883977i
\(741\) −0.977494 0.404891i −0.0359091 0.0148740i
\(742\) 1.60383 + 1.31517i 0.0588785 + 0.0482814i
\(743\) 34.7918 + 34.7918i 1.27639 + 1.27639i 0.942676 + 0.333710i \(0.108301\pi\)
0.333710 + 0.942676i \(0.391699\pi\)
\(744\) 1.88011 + 0.0733520i 0.0689280 + 0.00268922i
\(745\) −4.08301 15.2380i −0.149590 0.558277i
\(746\) 14.5661 + 41.6986i 0.533302 + 1.52669i
\(747\) 5.07536 0.668184i 0.185698 0.0244476i
\(748\) −12.9180 21.4903i −0.472330 0.785763i
\(749\) 1.70289 + 10.8839i 0.0622223 + 0.397688i
\(750\) 13.1631 6.63625i 0.480648 0.242322i
\(751\) 12.4912 7.21179i 0.455810 0.263162i −0.254471 0.967080i \(-0.581901\pi\)
0.710281 + 0.703918i \(0.248568\pi\)
\(752\) −11.4462 + 49.6620i −0.417401 + 1.81099i
\(753\) −6.92826 4.00003i −0.252480 0.145769i
\(754\) 9.05677 13.8166i 0.329828 0.503172i
\(755\) 31.9009 13.2138i 1.16099 0.480898i
\(756\) −0.221853 5.28685i −0.00806872 0.192281i
\(757\) −4.00043 + 9.65790i −0.145398 + 0.351022i −0.979754 0.200203i \(-0.935840\pi\)
0.834356 + 0.551226i \(0.185840\pi\)
\(758\) −0.0581549 + 0.306464i −0.00211228 + 0.0111313i
\(759\) −3.23869 12.0870i −0.117557 0.438729i
\(760\) 4.46357 0.411381i 0.161911 0.0149224i
\(761\) −2.05860 + 7.68282i −0.0746243 + 0.278502i −0.993148 0.116864i \(-0.962716\pi\)
0.918524 + 0.395366i \(0.129382\pi\)
\(762\) −1.24155 16.6864i −0.0449766 0.604484i
\(763\) −22.2465 2.38045i −0.805379 0.0861781i
\(764\) 34.5026 + 25.5208i 1.24826 + 0.923311i
\(765\) −7.78707 + 10.1483i −0.281542 + 0.366913i
\(766\) −24.8901 + 22.2194i −0.899316 + 0.802819i
\(767\) 2.46632 4.27179i 0.0890537 0.154246i
\(768\) −0.965072 + 15.9709i −0.0348240 + 0.576299i
\(769\) −41.3627 −1.49158 −0.745788 0.666183i \(-0.767927\pi\)
−0.745788 + 0.666183i \(0.767927\pi\)
\(770\) 10.8223 17.4189i 0.390007 0.627735i
\(771\) −0.989418 2.38867i −0.0356330 0.0860257i
\(772\) −0.157071 + 1.38085i −0.00565312 + 0.0496977i
\(773\) −16.9749 + 13.0253i −0.610543 + 0.468486i −0.867162 0.498026i \(-0.834058\pi\)
0.256618 + 0.966513i \(0.417392\pi\)
\(774\) 4.96993 + 2.39665i 0.178640 + 0.0861457i
\(775\) 0.101937 0.380435i 0.00366169 0.0136656i
\(776\) 17.4042 + 24.6121i 0.624776 + 0.883522i
\(777\) −21.5979 + 0.524977i −0.774821 + 0.0188334i
\(778\) 36.0172 + 31.0286i 1.29128 + 1.11243i
\(779\) 5.63915 0.742409i 0.202044 0.0265996i
\(780\) −5.37202 5.18580i −0.192349 0.185681i
\(781\) −3.66711 + 27.8545i −0.131220 + 0.996712i
\(782\) 22.6427 34.5427i 0.809700 1.23524i
\(783\) 7.39938i 0.264432i
\(784\) −18.0706 + 21.3881i −0.645380 + 0.763861i
\(785\) 37.2145i 1.32824i
\(786\) −2.73183 1.79071i −0.0974411 0.0638724i
\(787\) −2.68457 + 20.3914i −0.0956947 + 0.726874i 0.874582 + 0.484877i \(0.161136\pi\)
−0.970277 + 0.241997i \(0.922198\pi\)
\(788\) −36.4301 + 0.642567i −1.29777 + 0.0228905i
\(789\) 0.643211 0.0846803i 0.0228989 0.00301470i
\(790\) −20.9545 + 24.3233i −0.745526 + 0.865386i
\(791\) 26.6761 0.648412i 0.948494 0.0230549i
\(792\) 3.49653 5.54504i 0.124244 0.197035i
\(793\) −3.62984 + 13.5467i −0.128899 + 0.481059i
\(794\) 6.69868 13.8911i 0.237727 0.492975i
\(795\) 1.03997 0.797997i 0.0368839 0.0283020i
\(796\) −2.05299 + 1.63364i −0.0727664 + 0.0579028i
\(797\) −19.8873 48.0122i −0.704444 1.70068i −0.713437 0.700719i \(-0.752863\pi\)
0.00899271 0.999960i \(-0.497137\pi\)
\(798\) 2.12995 + 1.32332i 0.0753994 + 0.0468451i
\(799\) 68.9199 2.43821
\(800\) 3.21585 + 0.935736i 0.113697 + 0.0330833i
\(801\) 7.45199 12.9072i 0.263303 0.456054i
\(802\) −31.7233 35.5364i −1.12019 1.25483i
\(803\) −0.868638 + 1.13203i −0.0306536 + 0.0399485i
\(804\) −15.5011 + 2.31956i −0.546682 + 0.0818046i
\(805\) 33.5878 + 3.59401i 1.18382 + 0.126672i
\(806\) 1.48114 0.110204i 0.0521708 0.00388176i
\(807\) −2.78963 + 10.4110i −0.0981995 + 0.366485i
\(808\) 28.3790 + 8.80335i 0.998369 + 0.309701i
\(809\) 8.61906 + 32.1668i 0.303030 + 1.13092i 0.934628 + 0.355627i \(0.115733\pi\)
−0.631598 + 0.775296i \(0.717601\pi\)
\(810\) −3.28563 0.623485i −0.115445 0.0219070i
\(811\) 8.59513 20.7505i 0.301816 0.728648i −0.698104 0.715996i \(-0.745973\pi\)
0.999920 0.0126515i \(-0.00402722\pi\)
\(812\) −26.5008 + 28.8224i −0.929997 + 1.01147i
\(813\) −1.07037 + 0.443363i −0.0375396 + 0.0155494i
\(814\) −22.3842 14.6728i −0.784565 0.514280i
\(815\) 15.5425 + 8.97345i 0.544429 + 0.314326i
\(816\) 21.3391 3.57899i 0.747019 0.125290i
\(817\) −2.26441 + 1.30736i −0.0792216 + 0.0457386i
\(818\) 7.32158 + 14.5224i 0.255993 + 0.507765i
\(819\) −0.645672 4.12675i −0.0225616 0.144200i
\(820\) 38.9491 + 9.70353i 1.36016 + 0.338862i
\(821\) 27.6783 3.64391i 0.965978 0.127173i 0.368998 0.929430i \(-0.379701\pi\)
0.596979 + 0.802257i \(0.296367\pi\)
\(822\) 10.2963 3.59668i 0.359124 0.125449i
\(823\) −9.11084 34.0021i −0.317584 1.18524i −0.921560 0.388237i \(-0.873084\pi\)
0.603976 0.797003i \(-0.293582\pi\)
\(824\) 20.8874 7.71231i 0.727649 0.268671i
\(825\) −0.970304 0.970304i −0.0337817 0.0337817i
\(826\) −7.41279 + 9.03980i −0.257924 + 0.314535i
\(827\) 34.0519 + 14.1048i 1.18410 + 0.490470i 0.885829 0.464011i \(-0.153590\pi\)
0.298271 + 0.954481i \(0.403590\pi\)
\(828\) 10.7290 + 1.22042i 0.372857 + 0.0424125i
\(829\) 29.6031 + 3.89733i 1.02816 + 0.135360i 0.625689 0.780073i \(-0.284818\pi\)
0.402471 + 0.915433i \(0.368151\pi\)
\(830\) −12.7713 + 11.4010i −0.443299 + 0.395733i
\(831\) −4.44932 7.70645i −0.154345 0.267334i
\(832\) 0.667932 + 12.6123i 0.0231564 + 0.437251i
\(833\) 33.6732 + 17.3170i 1.16671 + 0.599998i
\(834\) 25.8189 + 8.51116i 0.894034 + 0.294717i
\(835\) −33.5047 + 43.6642i −1.15948 + 1.51106i
\(836\) 1.23924 + 2.84862i 0.0428599 + 0.0985217i
\(837\) 0.527757 0.404962i 0.0182420 0.0139975i
\(838\) 2.02453 1.37873i 0.0699362 0.0476273i
\(839\) −27.6185 27.6185i −0.953495 0.953495i 0.0454703 0.998966i \(-0.485521\pi\)
−0.998966 + 0.0454703i \(0.985521\pi\)
\(840\) 10.5653 + 14.1961i 0.364539 + 0.489812i
\(841\) −18.2086 + 18.2086i −0.627881 + 0.627881i
\(842\) 0.385615 2.03211i 0.0132892 0.0700310i
\(843\) −15.7719 20.5544i −0.543213 0.707929i
\(844\) 21.2940 22.0587i 0.732970 0.759291i
\(845\) 19.7131 + 15.1264i 0.678152 + 0.520364i
\(846\) 8.11158 + 16.0894i 0.278882 + 0.553165i
\(847\) −14.4732 3.50347i −0.497305 0.120381i
\(848\) −2.20719 0.211712i −0.0757952 0.00727021i
\(849\) −16.7039 + 9.64400i −0.573276 + 0.330981i
\(850\) 0.256361 4.52197i 0.00879310 0.155102i
\(851\) 5.75450 43.7098i 0.197262 1.49835i
\(852\) −21.2063 11.7498i −0.726517 0.402541i
\(853\) 2.34114 5.65202i 0.0801592 0.193521i −0.878719 0.477339i \(-0.841601\pi\)
0.958878 + 0.283818i \(0.0916012\pi\)
\(854\) 13.7059 30.2813i 0.469005 1.03621i
\(855\) 1.12062 1.12062i 0.0383244 0.0383244i
\(856\) −7.99655 8.64585i −0.273316 0.295509i
\(857\) 35.5933 9.53719i 1.21584 0.325784i 0.406791 0.913521i \(-0.366648\pi\)
0.809052 + 0.587737i \(0.199981\pi\)
\(858\) 2.24767 4.66099i 0.0767342 0.159124i
\(859\) −5.51009 41.8533i −0.188002 1.42802i −0.781864 0.623449i \(-0.785731\pi\)
0.593862 0.804567i \(-0.297602\pi\)
\(860\) −18.2492 + 2.73078i −0.622293 + 0.0931188i
\(861\) 14.0984 + 17.4771i 0.480472 + 0.595617i
\(862\) 12.8334 38.9305i 0.437108 1.32598i
\(863\) 0.364820 + 0.631887i 0.0124186 + 0.0215097i 0.872168 0.489207i \(-0.162714\pi\)
−0.859749 + 0.510716i \(0.829380\pi\)
\(864\) 3.34704 + 4.56041i 0.113869 + 0.155148i
\(865\) −10.8810 + 18.8465i −0.369965 + 0.640799i
\(866\) −45.7586 + 9.52217i −1.55494 + 0.323576i
\(867\) −4.69189 11.3272i −0.159345 0.384693i
\(868\) −3.50611 0.312733i −0.119005 0.0106149i
\(869\) −20.5559 8.51455i −0.697313 0.288836i
\(870\) 13.9288 + 20.4531i 0.472229 + 0.693425i
\(871\) −11.9508 + 3.20220i −0.404937 + 0.108502i
\(872\) 21.1643 11.1425i 0.716715 0.377334i
\(873\) 10.2944 + 2.75837i 0.348412 + 0.0933567i
\(874\) −3.33987 + 3.87682i −0.112973 + 0.131136i
\(875\) −25.2152 + 11.1698i −0.852430 + 0.377610i
\(876\) −0.634365 1.05532i −0.0214332 0.0356561i
\(877\) −31.3438 24.0509i −1.05840 0.812143i −0.0756646 0.997133i \(-0.524108\pi\)
−0.982740 + 0.184991i \(0.940775\pi\)
\(878\) −0.775134 + 13.6727i −0.0261595 + 0.461430i
\(879\) 24.1573 + 13.9472i 0.814807 + 0.470429i
\(880\) 0.773131 + 21.9094i 0.0260622 + 0.738565i
\(881\) 8.83317i 0.297597i −0.988868 0.148799i \(-0.952459\pi\)
0.988868 0.148799i \(-0.0475406\pi\)
\(882\) −0.0794673 + 9.89918i −0.00267580 + 0.333323i
\(883\) −22.4955 + 9.31792i −0.757032 + 0.313573i −0.727607 0.685994i \(-0.759368\pi\)
−0.0294251 + 0.999567i \(0.509368\pi\)
\(884\) 16.4173 4.71083i 0.552172 0.158442i
\(885\) 4.49782 + 5.86167i 0.151192 + 0.197038i
\(886\) 5.41730 1.89236i 0.181998 0.0635751i
\(887\) 54.7122 + 14.6601i 1.83705 + 0.492237i 0.998608 0.0527465i \(-0.0167975\pi\)
0.838447 + 0.544984i \(0.183464\pi\)
\(888\) 18.8575 13.3349i 0.632815 0.447490i
\(889\) 0.760668 + 31.2944i 0.0255120 + 1.04958i
\(890\) 3.69834 + 49.7055i 0.123969 + 1.66613i
\(891\) −0.302518 2.29785i −0.0101347 0.0769810i
\(892\) −47.2929 + 20.5738i −1.58348 + 0.688863i
\(893\) −8.46565 1.11452i −0.283292 0.0372961i
\(894\) 1.92208 + 9.23650i 0.0642839 + 0.308915i
\(895\) 27.5297 0.920215
\(896\) 3.29553 29.7513i 0.110096 0.993921i
\(897\) 8.52374 0.284599
\(898\) 7.59429 + 36.4942i 0.253425 + 1.21783i
\(899\) −4.88013 0.642481i −0.162761 0.0214279i
\(900\) 1.08583 0.472369i 0.0361944 0.0157456i
\(901\) 0.391387 + 2.97288i 0.0130390 + 0.0990410i
\(902\) 2.06410 + 27.7414i 0.0687269 + 0.923687i
\(903\) −9.06234 4.94251i −0.301576 0.164476i
\(904\) −23.2913 + 16.4703i −0.774658 + 0.547793i
\(905\) −21.3175 5.71202i −0.708619 0.189874i
\(906\) −19.4946 + 6.80984i −0.647666 + 0.226242i
\(907\) 24.7475 + 32.2515i 0.821726 + 1.07089i 0.996274 + 0.0862456i \(0.0274870\pi\)
−0.174548 + 0.984649i \(0.555846\pi\)
\(908\) 7.41221 2.12689i 0.245983 0.0705832i
\(909\) 9.70549 4.02015i 0.321911 0.133340i
\(910\) 9.55304 + 10.1916i 0.316680 + 0.337848i
\(911\) 45.1339i 1.49535i −0.664063 0.747676i \(-0.731169\pi\)
0.664063 0.747676i \(-0.268831\pi\)
\(912\) −2.67903 + 0.0945367i −0.0887115 + 0.00313042i
\(913\) −10.2750 5.93229i −0.340054 0.196330i
\(914\) −2.00688 + 35.3995i −0.0663815 + 1.17091i
\(915\) −16.6660 12.7883i −0.550963 0.422768i
\(916\) −17.2794 28.7458i −0.570927 0.949788i
\(917\) 4.93708 + 3.60119i 0.163037 + 0.118922i
\(918\) 4.99302 5.79576i 0.164794 0.191288i
\(919\) −6.09925 1.63429i −0.201196 0.0539102i 0.156814 0.987628i \(-0.449878\pi\)
−0.358009 + 0.933718i \(0.616544\pi\)
\(920\) −31.9540 + 16.8230i −1.05349 + 0.554638i
\(921\) −22.5917 + 6.05344i −0.744423 + 0.199468i
\(922\) 21.4719 + 31.5294i 0.707138 + 1.03837i
\(923\) −17.6807 7.32357i −0.581966 0.241058i
\(924\) −7.05137 + 10.0342i −0.231973 + 0.330100i
\(925\) −1.85012 4.46658i −0.0608315 0.146860i
\(926\) −37.7688 + 7.85953i −1.24116 + 0.258280i
\(927\) 3.93607 6.81747i 0.129278 0.223915i
\(928\) 6.34851 41.3730i 0.208400 1.35813i
\(929\) −1.05911 1.83443i −0.0347481 0.0601856i 0.848128 0.529791i \(-0.177730\pi\)
−0.882876 + 0.469605i \(0.844396\pi\)
\(930\) −0.696497 + 2.11285i −0.0228391 + 0.0692829i
\(931\) −3.85615 2.67164i −0.126380 0.0875594i
\(932\) 27.6235 4.13354i 0.904839 0.135399i
\(933\) −1.21944 9.26256i −0.0399227 0.303243i
\(934\) 8.31992 17.2530i 0.272236 0.564536i
\(935\) 28.6368 7.67321i 0.936524 0.250941i
\(936\) 3.03199 + 3.27818i 0.0991036 + 0.107151i
\(937\) 0.595163 0.595163i 0.0194431 0.0194431i −0.697318 0.716762i \(-0.745624\pi\)
0.716762 + 0.697318i \(0.245624\pi\)
\(938\) 29.1805 2.88568i 0.952776 0.0942206i
\(939\) −9.57387 + 23.1134i −0.312432 + 0.754276i
\(940\) −52.7088 29.2044i −1.71917 0.952541i
\(941\) −1.96129 + 14.8975i −0.0639362 + 0.485644i 0.929281 + 0.369373i \(0.120427\pi\)
−0.993218 + 0.116271i \(0.962906\pi\)
\(942\) 1.25970 22.2200i 0.0410433 0.723967i
\(943\) −39.6833 + 22.9112i −1.29227 + 0.746090i
\(944\) 1.19329 12.4406i 0.0388382 0.404906i
\(945\) 6.08093 + 1.47199i 0.197813 + 0.0478837i
\(946\) −5.75694 11.4190i −0.187174 0.371263i
\(947\) 28.1285 + 21.5838i 0.914055 + 0.701379i 0.954629 0.297798i \(-0.0962521\pi\)
−0.0405742 + 0.999177i \(0.512919\pi\)
\(948\) 13.3348 13.8137i 0.433095 0.448647i
\(949\) −0.591692 0.771108i −0.0192071 0.0250312i
\(950\) −0.104616 + 0.551302i −0.00339418 + 0.0178866i
\(951\) 13.0452 13.0452i 0.423019 0.423019i
\(952\) −40.2065 + 4.69341i −1.30310 + 0.152114i
\(953\) −14.5432 14.5432i −0.471100 0.471100i 0.431171 0.902270i \(-0.358101\pi\)
−0.902270 + 0.431171i \(0.858101\pi\)
\(954\) −0.647957 + 0.441265i −0.0209784 + 0.0142865i
\(955\) −40.2566 + 30.8900i −1.30267 + 0.999576i
\(956\) −1.31976 3.03373i −0.0426842 0.0981177i
\(957\) −10.4399 + 13.6055i −0.337474 + 0.439805i
\(958\) 21.5849 + 7.11543i 0.697375 + 0.229889i
\(959\) −19.5746 + 5.75831i −0.632098 + 0.185945i
\(960\) −17.8364 6.30517i −0.575667 0.203498i
\(961\) 15.2787 + 26.4636i 0.492863 + 0.853663i
\(962\) 13.6005 12.1411i 0.438496 0.391445i
\(963\) −4.12814 0.543480i −0.133028 0.0175134i
\(964\) 8.62047 + 0.980578i 0.277647 + 0.0315823i
\(965\) −1.51813 0.628829i −0.0488703 0.0202427i
\(966\) −19.9330 3.28285i −0.641332 0.105624i
\(967\) −26.6986 26.6986i −0.858570 0.858570i 0.132600 0.991170i \(-0.457667\pi\)
−0.991170 + 0.132600i \(0.957667\pi\)
\(968\) 14.9339 5.51407i 0.479994 0.177229i
\(969\) 0.938263 + 3.50165i 0.0301414 + 0.112489i
\(970\) −33.6478 + 11.7538i −1.08036 + 0.377391i
\(971\) −14.0478 + 1.84942i −0.450814 + 0.0593508i −0.352515 0.935806i \(-0.614673\pi\)
−0.0982990 + 0.995157i \(0.531340\pi\)
\(972\) 1.94068 + 0.483488i 0.0622473 + 0.0155079i
\(973\) −47.4471 18.3155i −1.52108 0.587169i
\(974\) −10.4747 20.7766i −0.335630 0.665726i
\(975\) 0.809488 0.467358i 0.0259244 0.0149674i
\(976\) 5.87759 + 35.0442i 0.188137 + 1.12174i
\(977\) −30.7626 17.7608i −0.984184 0.568219i −0.0806534 0.996742i \(-0.525701\pi\)
−0.903531 + 0.428523i \(0.859034\pi\)
\(978\) −8.97635 5.88397i −0.287032 0.188149i
\(979\) −31.9133 + 13.2189i −1.01995 + 0.422479i
\(980\) −18.4148 27.5125i −0.588239 0.878856i
\(981\) 3.23612 7.81269i 0.103321 0.249440i
\(982\) −35.8061 6.79459i −1.14262 0.216824i
\(983\) 13.5574 + 50.5969i 0.432414 + 1.61379i 0.747179 + 0.664622i \(0.231408\pi\)
−0.314765 + 0.949170i \(0.601926\pi\)
\(984\) −22.9273 7.11220i −0.730894 0.226729i
\(985\) 11.1501 41.6129i 0.355273 1.32590i
\(986\) −56.4485 + 4.20005i −1.79769 + 0.133757i
\(987\) −13.6531 30.8209i −0.434582 0.981040i
\(988\) −2.09276 + 0.313158i −0.0665797 + 0.00996287i
\(989\) 12.8234 16.7118i 0.407760 0.531403i
\(990\) 5.16175 + 5.78218i 0.164051 + 0.183770i
\(991\) −9.27524 + 16.0652i −0.294638 + 0.510328i −0.974901 0.222641i \(-0.928532\pi\)
0.680263 + 0.732968i \(0.261866\pi\)
\(992\) 3.29836 1.81151i 0.104723 0.0575154i
\(993\) −13.9705 −0.443340
\(994\) 38.5260 + 23.9359i 1.22197 + 0.759201i
\(995\) −1.18714 2.86601i −0.0376349 0.0908587i
\(996\) 8.01142 6.37497i 0.253852 0.201999i
\(997\) −33.5057 + 25.7098i −1.06114 + 0.814238i −0.983165 0.182717i \(-0.941511\pi\)
−0.0779705 + 0.996956i \(0.524844\pi\)
\(998\) −9.80476 + 20.3321i −0.310364 + 0.643602i
\(999\) 2.11343 7.88742i 0.0668659 0.249547i
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 672.2.cj.a.613.27 yes 512
7.2 even 3 inner 672.2.cj.a.37.16 512
32.13 even 8 inner 672.2.cj.a.109.16 yes 512
224.205 even 24 inner 672.2.cj.a.205.27 yes 512
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
672.2.cj.a.37.16 512 7.2 even 3 inner
672.2.cj.a.109.16 yes 512 32.13 even 8 inner
672.2.cj.a.205.27 yes 512 224.205 even 24 inner
672.2.cj.a.613.27 yes 512 1.1 even 1 trivial