Properties

Label 168.2.ba.c.5.17
Level $168$
Weight $2$
Character 168.5
Analytic conductor $1.341$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [168,2,Mod(5,168)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(168, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("168.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 168.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.34148675396\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 5.17
Character \(\chi\) \(=\) 168.5
Dual form 168.2.ba.c.101.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.968446 + 1.03059i) q^{2} +(-1.70874 - 0.283220i) q^{3} +(-0.124224 + 1.99614i) q^{4} +(2.24840 + 1.29811i) q^{5} +(-1.36294 - 2.03529i) q^{6} +(-2.53678 + 0.751482i) q^{7} +(-2.17750 + 1.80513i) q^{8} +(2.83957 + 0.967897i) q^{9} +O(q^{10})\) \(q+(0.968446 + 1.03059i) q^{2} +(-1.70874 - 0.283220i) q^{3} +(-0.124224 + 1.99614i) q^{4} +(2.24840 + 1.29811i) q^{5} +(-1.36294 - 2.03529i) q^{6} +(-2.53678 + 0.751482i) q^{7} +(-2.17750 + 1.80513i) q^{8} +(2.83957 + 0.967897i) q^{9} +(0.839632 + 3.57432i) q^{10} +(1.63808 + 2.83724i) q^{11} +(0.777612 - 3.37570i) q^{12} +0.912635 q^{13} +(-3.23121 - 1.88661i) q^{14} +(-3.47427 - 2.85492i) q^{15} +(-3.96914 - 0.495937i) q^{16} +(-2.39448 - 4.14736i) q^{17} +(1.75247 + 3.86379i) q^{18} +(2.66693 - 4.61926i) q^{19} +(-2.87052 + 4.32685i) q^{20} +(4.54754 - 0.565618i) q^{21} +(-1.33763 + 4.43590i) q^{22} +(4.45569 + 2.57249i) q^{23} +(4.23203 - 2.46778i) q^{24} +(0.870190 + 1.50721i) q^{25} +(0.883838 + 0.940551i) q^{26} +(-4.57796 - 2.45811i) q^{27} +(-1.18493 - 5.15712i) q^{28} +1.35950 q^{29} +(-0.422391 - 6.34538i) q^{30} +(8.18469 - 4.72543i) q^{31} +(-3.33279 - 4.57083i) q^{32} +(-1.99549 - 5.31204i) q^{33} +(1.95529 - 6.48421i) q^{34} +(-6.67920 - 1.60340i) q^{35} +(-2.28480 + 5.54794i) q^{36} +(1.59746 + 0.922292i) q^{37} +(7.34333 - 1.72500i) q^{38} +(-1.55945 - 0.258476i) q^{39} +(-7.23914 + 1.23200i) q^{40} -5.91833 q^{41} +(4.98696 + 4.13887i) q^{42} -8.00125i q^{43} +(-5.86701 + 2.91738i) q^{44} +(5.12805 + 5.86230i) q^{45} +(1.66391 + 7.08330i) q^{46} +(-3.29243 + 5.70266i) q^{47} +(6.64176 + 1.97156i) q^{48} +(5.87055 - 3.81269i) q^{49} +(-0.710584 + 2.35646i) q^{50} +(2.91692 + 7.76491i) q^{51} +(-0.113371 + 1.82175i) q^{52} +(0.841712 + 1.45789i) q^{53} +(-1.90021 - 7.09853i) q^{54} +8.50565i q^{55} +(4.16733 - 6.21557i) q^{56} +(-5.86535 + 7.13777i) q^{57} +(1.31661 + 1.40109i) q^{58} +(1.50266 - 0.867561i) q^{59} +(6.13041 - 6.58047i) q^{60} +(-4.72347 + 8.18130i) q^{61} +(12.7964 + 3.85872i) q^{62} +(-7.93074 - 0.321460i) q^{63} +(1.48302 - 7.86134i) q^{64} +(2.05197 + 1.18470i) q^{65} +(3.54200 - 7.20095i) q^{66} +(-10.8634 + 6.27198i) q^{67} +(8.57615 - 4.26451i) q^{68} +(-6.88502 - 5.65766i) q^{69} +(-4.81600 - 8.43632i) q^{70} +0.603989i q^{71} +(-7.93035 + 3.01820i) q^{72} +(-1.29220 + 0.746053i) q^{73} +(0.596548 + 2.53951i) q^{74} +(-1.06005 - 2.82189i) q^{75} +(8.88938 + 5.89738i) q^{76} +(-6.28759 - 5.96647i) q^{77} +(-1.24387 - 1.85748i) q^{78} +(-0.0625152 + 0.108280i) q^{79} +(-8.28041 - 6.26745i) q^{80} +(7.12635 + 5.49683i) q^{81} +(-5.73158 - 6.09936i) q^{82} +0.246431i q^{83} +(0.564138 + 9.14777i) q^{84} -12.4332i q^{85} +(8.24600 - 7.74878i) q^{86} +(-2.32303 - 0.385038i) q^{87} +(-8.68850 - 3.22114i) q^{88} +(-1.80671 + 3.12931i) q^{89} +(-1.07538 + 10.9622i) q^{90} +(-2.31516 + 0.685829i) q^{91} +(-5.68856 + 8.57461i) q^{92} +(-15.3238 + 5.75646i) q^{93} +(-9.06563 + 2.12958i) q^{94} +(11.9926 - 6.92395i) q^{95} +(4.40031 + 8.75427i) q^{96} +5.10324i q^{97} +(9.61463 + 2.35773i) q^{98} +(1.90529 + 9.64204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.968446 + 1.03059i 0.684795 + 0.728736i
\(3\) −1.70874 0.283220i −0.986541 0.163517i
\(4\) −0.124224 + 1.99614i −0.0621120 + 0.998069i
\(5\) 2.24840 + 1.29811i 1.00551 + 0.580533i 0.909875 0.414883i \(-0.136177\pi\)
0.0956384 + 0.995416i \(0.469511\pi\)
\(6\) −1.36294 2.03529i −0.556417 0.830903i
\(7\) −2.53678 + 0.751482i −0.958814 + 0.284033i
\(8\) −2.17750 + 1.80513i −0.769863 + 0.638209i
\(9\) 2.83957 + 0.967897i 0.946524 + 0.322632i
\(10\) 0.839632 + 3.57432i 0.265515 + 1.13030i
\(11\) 1.63808 + 2.83724i 0.493900 + 0.855460i 0.999975 0.00702958i \(-0.00223760\pi\)
−0.506075 + 0.862489i \(0.668904\pi\)
\(12\) 0.777612 3.37570i 0.224477 0.974479i
\(13\) 0.912635 0.253119 0.126560 0.991959i \(-0.459606\pi\)
0.126560 + 0.991959i \(0.459606\pi\)
\(14\) −3.23121 1.88661i −0.863577 0.504218i
\(15\) −3.47427 2.85492i −0.897052 0.737138i
\(16\) −3.96914 0.495937i −0.992284 0.123984i
\(17\) −2.39448 4.14736i −0.580746 1.00588i −0.995391 0.0958985i \(-0.969428\pi\)
0.414645 0.909983i \(-0.363906\pi\)
\(18\) 1.75247 + 3.86379i 0.413061 + 0.910703i
\(19\) 2.66693 4.61926i 0.611836 1.05973i −0.379095 0.925358i \(-0.623765\pi\)
0.990931 0.134373i \(-0.0429019\pi\)
\(20\) −2.87052 + 4.32685i −0.641867 + 0.967514i
\(21\) 4.54754 0.565618i 0.992354 0.123428i
\(22\) −1.33763 + 4.43590i −0.285184 + 0.945737i
\(23\) 4.45569 + 2.57249i 0.929075 + 0.536402i 0.886519 0.462692i \(-0.153116\pi\)
0.0425563 + 0.999094i \(0.486450\pi\)
\(24\) 4.23203 2.46778i 0.863859 0.503734i
\(25\) 0.870190 + 1.50721i 0.174038 + 0.301443i
\(26\) 0.883838 + 0.940551i 0.173335 + 0.184457i
\(27\) −4.57796 2.45811i −0.881029 0.473063i
\(28\) −1.18493 5.15712i −0.223931 0.974605i
\(29\) 1.35950 0.252453 0.126227 0.992001i \(-0.459713\pi\)
0.126227 + 0.992001i \(0.459713\pi\)
\(30\) −0.422391 6.34538i −0.0771178 1.15850i
\(31\) 8.18469 4.72543i 1.47001 0.848713i 0.470580 0.882357i \(-0.344045\pi\)
0.999434 + 0.0336443i \(0.0107113\pi\)
\(32\) −3.33279 4.57083i −0.589159 0.808017i
\(33\) −1.99549 5.31204i −0.347370 0.924707i
\(34\) 1.95529 6.48421i 0.335330 1.11203i
\(35\) −6.67920 1.60340i −1.12899 0.271024i
\(36\) −2.28480 + 5.54794i −0.380800 + 0.924657i
\(37\) 1.59746 + 0.922292i 0.262620 + 0.151624i 0.625529 0.780201i \(-0.284883\pi\)
−0.362909 + 0.931825i \(0.618216\pi\)
\(38\) 7.34333 1.72500i 1.19125 0.279831i
\(39\) −1.55945 0.258476i −0.249713 0.0413894i
\(40\) −7.23914 + 1.23200i −1.14461 + 0.194797i
\(41\) −5.91833 −0.924288 −0.462144 0.886805i \(-0.652920\pi\)
−0.462144 + 0.886805i \(0.652920\pi\)
\(42\) 4.98696 + 4.13887i 0.769505 + 0.638641i
\(43\) 8.00125i 1.22018i −0.792332 0.610090i \(-0.791133\pi\)
0.792332 0.610090i \(-0.208867\pi\)
\(44\) −5.86701 + 2.91738i −0.884485 + 0.439812i
\(45\) 5.12805 + 5.86230i 0.764444 + 0.873900i
\(46\) 1.66391 + 7.08330i 0.245331 + 1.04438i
\(47\) −3.29243 + 5.70266i −0.480250 + 0.831818i −0.999743 0.0226567i \(-0.992788\pi\)
0.519493 + 0.854475i \(0.326121\pi\)
\(48\) 6.64176 + 1.97156i 0.958655 + 0.284571i
\(49\) 5.87055 3.81269i 0.838650 0.544671i
\(50\) −0.710584 + 2.35646i −0.100492 + 0.333254i
\(51\) 2.91692 + 7.76491i 0.408451 + 1.08730i
\(52\) −0.113371 + 1.82175i −0.0157218 + 0.252631i
\(53\) 0.841712 + 1.45789i 0.115618 + 0.200256i 0.918027 0.396519i \(-0.129782\pi\)
−0.802409 + 0.596775i \(0.796448\pi\)
\(54\) −1.90021 7.09853i −0.258586 0.965988i
\(55\) 8.50565i 1.14690i
\(56\) 4.16733 6.21557i 0.556883 0.830591i
\(57\) −5.86535 + 7.13777i −0.776885 + 0.945421i
\(58\) 1.31661 + 1.40109i 0.172879 + 0.183972i
\(59\) 1.50266 0.867561i 0.195630 0.112947i −0.398986 0.916957i \(-0.630638\pi\)
0.594615 + 0.804010i \(0.297304\pi\)
\(60\) 6.13041 6.58047i 0.791433 0.849535i
\(61\) −4.72347 + 8.18130i −0.604779 + 1.04751i 0.387308 + 0.921951i \(0.373405\pi\)
−0.992086 + 0.125557i \(0.959928\pi\)
\(62\) 12.7964 + 3.85872i 1.62515 + 0.490058i
\(63\) −7.93074 0.321460i −0.999180 0.0405001i
\(64\) 1.48302 7.86134i 0.185378 0.982667i
\(65\) 2.05197 + 1.18470i 0.254515 + 0.146944i
\(66\) 3.54200 7.20095i 0.435990 0.886375i
\(67\) −10.8634 + 6.27198i −1.32717 + 0.766245i −0.984862 0.173341i \(-0.944544\pi\)
−0.342313 + 0.939586i \(0.611210\pi\)
\(68\) 8.57615 4.26451i 1.04001 0.517147i
\(69\) −6.88502 5.65766i −0.828860 0.681102i
\(70\) −4.81600 8.43632i −0.575622 1.00833i
\(71\) 0.603989i 0.0716803i 0.999358 + 0.0358401i \(0.0114107\pi\)
−0.999358 + 0.0358401i \(0.988589\pi\)
\(72\) −7.93035 + 3.01820i −0.934601 + 0.355698i
\(73\) −1.29220 + 0.746053i −0.151241 + 0.0873189i −0.573711 0.819058i \(-0.694497\pi\)
0.422470 + 0.906377i \(0.361163\pi\)
\(74\) 0.596548 + 2.53951i 0.0693473 + 0.295212i
\(75\) −1.06005 2.82189i −0.122404 0.325844i
\(76\) 8.88938 + 5.89738i 1.01968 + 0.676476i
\(77\) −6.28759 5.96647i −0.716537 0.679943i
\(78\) −1.24387 1.85748i −0.140840 0.210318i
\(79\) −0.0625152 + 0.108280i −0.00703351 + 0.0121824i −0.869521 0.493896i \(-0.835572\pi\)
0.862487 + 0.506079i \(0.168906\pi\)
\(80\) −8.28041 6.26745i −0.925778 0.700722i
\(81\) 7.12635 + 5.49683i 0.791817 + 0.610759i
\(82\) −5.73158 6.09936i −0.632947 0.673562i
\(83\) 0.246431i 0.0270493i 0.999909 + 0.0135247i \(0.00430516\pi\)
−0.999909 + 0.0135247i \(0.995695\pi\)
\(84\) 0.564138 + 9.14777i 0.0615525 + 0.998104i
\(85\) 12.4332i 1.34857i
\(86\) 8.24600 7.74878i 0.889189 0.835573i
\(87\) −2.32303 0.385038i −0.249055 0.0412804i
\(88\) −8.68850 3.22114i −0.926198 0.343375i
\(89\) −1.80671 + 3.12931i −0.191511 + 0.331706i −0.945751 0.324892i \(-0.894672\pi\)
0.754241 + 0.656598i \(0.228005\pi\)
\(90\) −1.07538 + 10.9622i −0.113355 + 1.15552i
\(91\) −2.31516 + 0.685829i −0.242695 + 0.0718944i
\(92\) −5.68856 + 8.57461i −0.593073 + 0.893964i
\(93\) −15.3238 + 5.75646i −1.58901 + 0.596917i
\(94\) −9.06563 + 2.12958i −0.935049 + 0.219649i
\(95\) 11.9926 6.92395i 1.23042 0.710382i
\(96\) 4.40031 + 8.75427i 0.449105 + 0.893479i
\(97\) 5.10324i 0.518155i 0.965857 + 0.259078i \(0.0834185\pi\)
−0.965857 + 0.259078i \(0.916581\pi\)
\(98\) 9.61463 + 2.35773i 0.971224 + 0.238167i
\(99\) 1.90529 + 9.64204i 0.191489 + 0.969061i
\(100\) −3.11670 + 1.54979i −0.311670 + 0.154979i
\(101\) −6.33114 + 3.65529i −0.629972 + 0.363715i −0.780741 0.624854i \(-0.785158\pi\)
0.150769 + 0.988569i \(0.451825\pi\)
\(102\) −5.17754 + 10.5260i −0.512653 + 1.04223i
\(103\) 0.670566 + 0.387151i 0.0660728 + 0.0381472i 0.532672 0.846321i \(-0.321188\pi\)
−0.466600 + 0.884469i \(0.654521\pi\)
\(104\) −1.98726 + 1.64742i −0.194867 + 0.161543i
\(105\) 10.9589 + 4.63148i 1.06948 + 0.451986i
\(106\) −0.687329 + 2.27934i −0.0667593 + 0.221389i
\(107\) 7.26435 12.5822i 0.702271 1.21637i −0.265397 0.964139i \(-0.585503\pi\)
0.967667 0.252229i \(-0.0811638\pi\)
\(108\) 5.47541 8.83288i 0.526872 0.849945i
\(109\) 12.8015 7.39093i 1.22616 0.707923i 0.259934 0.965626i \(-0.416299\pi\)
0.966224 + 0.257703i \(0.0829658\pi\)
\(110\) −8.76582 + 8.23726i −0.835788 + 0.785392i
\(111\) −2.46842 2.02839i −0.234292 0.192526i
\(112\) 10.4415 1.72465i 0.986632 0.162964i
\(113\) 16.2708i 1.53063i −0.643657 0.765314i \(-0.722584\pi\)
0.643657 0.765314i \(-0.277416\pi\)
\(114\) −13.0364 + 0.867790i −1.22097 + 0.0812759i
\(115\) 6.67877 + 11.5680i 0.622798 + 1.07872i
\(116\) −0.168883 + 2.71376i −0.0156804 + 0.251966i
\(117\) 2.59149 + 0.883337i 0.239584 + 0.0816646i
\(118\) 2.34934 + 0.708437i 0.216275 + 0.0652170i
\(119\) 9.19094 + 8.72154i 0.842532 + 0.799503i
\(120\) 12.7187 0.0549029i 1.16106 0.00501193i
\(121\) 0.133385 0.231029i 0.0121259 0.0210026i
\(122\) −13.0060 + 3.05519i −1.17751 + 0.276604i
\(123\) 10.1129 + 1.67619i 0.911847 + 0.151137i
\(124\) 8.41588 + 16.9248i 0.755769 + 1.51989i
\(125\) 8.46270i 0.756927i
\(126\) −7.34920 8.48465i −0.654719 0.755872i
\(127\) −1.59996 −0.141973 −0.0709867 0.997477i \(-0.522615\pi\)
−0.0709867 + 0.997477i \(0.522615\pi\)
\(128\) 9.53803 6.08490i 0.843051 0.537834i
\(129\) −2.26611 + 13.6720i −0.199520 + 1.20376i
\(130\) 0.766277 + 3.26205i 0.0672070 + 0.286101i
\(131\) −7.96684 4.59965i −0.696066 0.401874i 0.109815 0.993952i \(-0.464974\pi\)
−0.805880 + 0.592078i \(0.798308\pi\)
\(132\) 10.8514 3.32339i 0.944497 0.289264i
\(133\) −3.29414 + 13.7222i −0.285638 + 1.18987i
\(134\) −16.9844 5.12161i −1.46723 0.442439i
\(135\) −7.10217 11.4695i −0.611257 0.987138i
\(136\) 12.7005 + 4.70853i 1.08906 + 0.403753i
\(137\) −2.43936 + 1.40836i −0.208408 + 0.120325i −0.600571 0.799571i \(-0.705060\pi\)
0.392163 + 0.919896i \(0.371727\pi\)
\(138\) −0.837061 12.5748i −0.0712554 1.07043i
\(139\) −2.80505 −0.237921 −0.118960 0.992899i \(-0.537956\pi\)
−0.118960 + 0.992899i \(0.537956\pi\)
\(140\) 4.03033 13.1334i 0.340625 1.10998i
\(141\) 7.24101 8.81187i 0.609803 0.742093i
\(142\) −0.622464 + 0.584930i −0.0522360 + 0.0490863i
\(143\) 1.49497 + 2.58936i 0.125016 + 0.216533i
\(144\) −10.7906 5.24997i −0.899220 0.437497i
\(145\) 3.05670 + 1.76479i 0.253845 + 0.146558i
\(146\) −2.02030 0.609216i −0.167201 0.0504190i
\(147\) −11.1111 + 4.85224i −0.916425 + 0.400206i
\(148\) −2.03947 + 3.07417i −0.167643 + 0.252696i
\(149\) −8.67025 + 15.0173i −0.710295 + 1.23027i 0.254451 + 0.967086i \(0.418105\pi\)
−0.964746 + 0.263181i \(0.915228\pi\)
\(150\) 1.88160 3.82533i 0.153632 0.312337i
\(151\) −6.41551 11.1120i −0.522087 0.904281i −0.999670 0.0256942i \(-0.991820\pi\)
0.477583 0.878587i \(-0.341513\pi\)
\(152\) 2.53111 + 14.8726i 0.205300 + 1.20633i
\(153\) −2.78508 14.0943i −0.225160 1.13946i
\(154\) 0.0597859 12.2581i 0.00481769 0.987788i
\(155\) 24.5366 1.97082
\(156\) 0.709677 3.08078i 0.0568196 0.246660i
\(157\) −8.55356 14.8152i −0.682648 1.18238i −0.974170 0.225817i \(-0.927495\pi\)
0.291521 0.956564i \(-0.405839\pi\)
\(158\) −0.172134 + 0.0404355i −0.0136943 + 0.00321687i
\(159\) −1.02536 2.72954i −0.0813165 0.216466i
\(160\) −1.55998 14.6034i −0.123327 1.15450i
\(161\) −13.2363 3.17749i −1.04317 0.250421i
\(162\) 1.23652 + 12.6677i 0.0971499 + 0.995270i
\(163\) 21.6390 + 12.4933i 1.69489 + 0.978547i 0.950458 + 0.310853i \(0.100615\pi\)
0.744436 + 0.667694i \(0.232718\pi\)
\(164\) 0.735199 11.8138i 0.0574094 0.922503i
\(165\) 2.40897 14.5339i 0.187538 1.13146i
\(166\) −0.253969 + 0.238655i −0.0197118 + 0.0185232i
\(167\) −9.89286 −0.765532 −0.382766 0.923845i \(-0.625028\pi\)
−0.382766 + 0.923845i \(0.625028\pi\)
\(168\) −8.88125 + 9.44052i −0.685203 + 0.728352i
\(169\) −12.1671 −0.935931
\(170\) 12.8135 12.0409i 0.982751 0.923494i
\(171\) 12.0439 10.5354i 0.921021 0.805662i
\(172\) 15.9716 + 0.993948i 1.21782 + 0.0757878i
\(173\) 13.3755 + 7.72235i 1.01692 + 0.587120i 0.913211 0.407488i \(-0.133595\pi\)
0.103710 + 0.994608i \(0.466929\pi\)
\(174\) −1.85292 2.76698i −0.140469 0.209764i
\(175\) −3.34013 3.16954i −0.252490 0.239595i
\(176\) −5.09467 12.0738i −0.384026 0.910095i
\(177\) −2.81336 + 1.05685i −0.211465 + 0.0794379i
\(178\) −4.97473 + 1.16860i −0.372871 + 0.0875899i
\(179\) 6.07462 + 10.5216i 0.454038 + 0.786418i 0.998632 0.0522822i \(-0.0166495\pi\)
−0.544594 + 0.838700i \(0.683316\pi\)
\(180\) −12.3390 + 9.50805i −0.919694 + 0.708688i
\(181\) 1.41922 0.105489 0.0527447 0.998608i \(-0.483203\pi\)
0.0527447 + 0.998608i \(0.483203\pi\)
\(182\) −2.94891 1.72179i −0.218588 0.127627i
\(183\) 10.3883 12.6419i 0.767924 0.934517i
\(184\) −14.3459 + 2.44149i −1.05760 + 0.179989i
\(185\) 2.39448 + 4.14736i 0.176045 + 0.304920i
\(186\) −20.7728 10.2177i −1.52314 0.749201i
\(187\) 7.84469 13.5874i 0.573661 0.993610i
\(188\) −10.9743 7.28055i −0.800383 0.530989i
\(189\) 13.4605 + 2.79543i 0.979109 + 0.203338i
\(190\) 18.7500 + 5.65399i 1.36026 + 0.410184i
\(191\) −3.62414 2.09240i −0.262234 0.151401i 0.363119 0.931743i \(-0.381712\pi\)
−0.625353 + 0.780342i \(0.715045\pi\)
\(192\) −4.76058 + 13.0129i −0.343565 + 0.939129i
\(193\) −13.1905 22.8467i −0.949476 1.64454i −0.746531 0.665351i \(-0.768282\pi\)
−0.202946 0.979190i \(-0.565051\pi\)
\(194\) −5.25933 + 4.94221i −0.377598 + 0.354830i
\(195\) −3.17074 2.60550i −0.227061 0.186584i
\(196\) 6.88140 + 12.1921i 0.491529 + 0.870861i
\(197\) −12.6908 −0.904184 −0.452092 0.891971i \(-0.649322\pi\)
−0.452092 + 0.891971i \(0.649322\pi\)
\(198\) −8.09180 + 11.3014i −0.575059 + 0.803153i
\(199\) 0.939591 0.542473i 0.0666058 0.0384549i −0.466327 0.884612i \(-0.654423\pi\)
0.532933 + 0.846157i \(0.321090\pi\)
\(200\) −4.61555 1.71115i −0.326369 0.120997i
\(201\) 20.3390 7.64045i 1.43461 0.538916i
\(202\) −9.89847 2.98485i −0.696454 0.210014i
\(203\) −3.44876 + 1.02164i −0.242056 + 0.0717052i
\(204\) −15.8622 + 4.85799i −1.11058 + 0.340127i
\(205\) −13.3067 7.68265i −0.929384 0.536580i
\(206\) 0.250413 + 1.06601i 0.0174471 + 0.0742726i
\(207\) 10.1623 + 11.6174i 0.706332 + 0.807467i
\(208\) −3.62237 0.452609i −0.251166 0.0313828i
\(209\) 17.4746 1.20874
\(210\) 5.83995 + 15.7794i 0.402995 + 1.08889i
\(211\) 7.89074i 0.543221i 0.962407 + 0.271610i \(0.0875562\pi\)
−0.962407 + 0.271610i \(0.912444\pi\)
\(212\) −3.01471 + 1.49907i −0.207051 + 0.102956i
\(213\) 0.171062 1.03206i 0.0117209 0.0707155i
\(214\) 20.0022 4.69865i 1.36732 0.321193i
\(215\) 10.3865 17.9900i 0.708355 1.22691i
\(216\) 14.4057 2.91128i 0.980184 0.198087i
\(217\) −17.2117 + 18.1381i −1.16841 + 1.23129i
\(218\) 20.0145 + 6.03532i 1.35556 + 0.408764i
\(219\) 2.41933 0.908832i 0.163483 0.0614132i
\(220\) −16.9785 1.05661i −1.14469 0.0712363i
\(221\) −2.18528 3.78502i −0.146998 0.254608i
\(222\) −0.300104 4.50831i −0.0201416 0.302578i
\(223\) 11.5392i 0.772720i 0.922348 + 0.386360i \(0.126268\pi\)
−0.922348 + 0.386360i \(0.873732\pi\)
\(224\) 11.8895 + 9.09069i 0.794398 + 0.607397i
\(225\) 1.01214 + 5.12210i 0.0674760 + 0.341473i
\(226\) 16.7685 15.7574i 1.11542 1.04817i
\(227\) −13.4825 + 7.78410i −0.894862 + 0.516649i −0.875530 0.483164i \(-0.839487\pi\)
−0.0193323 + 0.999813i \(0.506154\pi\)
\(228\) −13.5194 12.5947i −0.895342 0.834107i
\(229\) −1.78238 + 3.08717i −0.117783 + 0.204006i −0.918889 0.394517i \(-0.870912\pi\)
0.801106 + 0.598523i \(0.204245\pi\)
\(230\) −5.45378 + 18.0860i −0.359612 + 1.19256i
\(231\) 9.05402 + 11.9759i 0.595711 + 0.787957i
\(232\) −2.96032 + 2.45408i −0.194354 + 0.161118i
\(233\) 6.60666 + 3.81435i 0.432816 + 0.249887i 0.700546 0.713607i \(-0.252940\pi\)
−0.267729 + 0.963494i \(0.586273\pi\)
\(234\) 1.59937 + 3.52623i 0.104554 + 0.230517i
\(235\) −14.8054 + 8.54789i −0.965796 + 0.557603i
\(236\) 1.54511 + 3.10729i 0.100578 + 0.202267i
\(237\) 0.137489 0.167316i 0.00893087 0.0108683i
\(238\) −0.0873926 + 17.9184i −0.00566482 + 1.16148i
\(239\) 13.2745i 0.858658i 0.903148 + 0.429329i \(0.141250\pi\)
−0.903148 + 0.429329i \(0.858750\pi\)
\(240\) 12.3740 + 13.0546i 0.798737 + 0.842671i
\(241\) 9.92793 5.73189i 0.639514 0.369224i −0.144913 0.989444i \(-0.546290\pi\)
0.784427 + 0.620221i \(0.212957\pi\)
\(242\) 0.367272 0.0862745i 0.0236091 0.00554593i
\(243\) −10.6203 11.4110i −0.681290 0.732014i
\(244\) −15.7442 10.4450i −1.00792 0.668674i
\(245\) 18.1486 0.951816i 1.15947 0.0608093i
\(246\) 8.06631 + 12.0455i 0.514289 + 0.767994i
\(247\) 2.43393 4.21570i 0.154867 0.268238i
\(248\) −9.29216 + 25.0641i −0.590053 + 1.59157i
\(249\) 0.0697941 0.421086i 0.00442302 0.0266852i
\(250\) 8.72156 8.19567i 0.551600 0.518340i
\(251\) 1.44903i 0.0914619i −0.998954 0.0457309i \(-0.985438\pi\)
0.998954 0.0457309i \(-0.0145617\pi\)
\(252\) 1.62687 15.7909i 0.102483 0.994735i
\(253\) 16.8558i 1.05972i
\(254\) −1.54947 1.64890i −0.0972226 0.103461i
\(255\) −3.52133 + 21.2451i −0.220514 + 1.33042i
\(256\) 15.5081 + 3.93688i 0.969256 + 0.246055i
\(257\) −6.03418 + 10.4515i −0.376402 + 0.651948i −0.990536 0.137254i \(-0.956172\pi\)
0.614134 + 0.789202i \(0.289506\pi\)
\(258\) −16.2849 + 10.9052i −1.01385 + 0.678929i
\(259\) −4.74549 1.13920i −0.294870 0.0707862i
\(260\) −2.61973 + 3.94884i −0.162469 + 0.244897i
\(261\) 3.86041 + 1.31586i 0.238953 + 0.0814496i
\(262\) −2.97510 12.6650i −0.183802 0.782449i
\(263\) −21.7325 + 12.5473i −1.34008 + 0.773697i −0.986819 0.161827i \(-0.948261\pi\)
−0.353264 + 0.935524i \(0.614928\pi\)
\(264\) 13.9341 + 7.96485i 0.857584 + 0.490203i
\(265\) 4.37055i 0.268480i
\(266\) −17.3321 + 9.89432i −1.06270 + 0.606660i
\(267\) 3.97347 4.83547i 0.243172 0.295926i
\(268\) −11.1703 22.4640i −0.682332 1.37221i
\(269\) −6.61826 + 3.82105i −0.403522 + 0.232974i −0.688003 0.725708i \(-0.741512\pi\)
0.284480 + 0.958682i \(0.408179\pi\)
\(270\) 4.94227 18.4270i 0.300777 1.12143i
\(271\) −9.27850 5.35694i −0.563629 0.325411i 0.190972 0.981595i \(-0.438836\pi\)
−0.754601 + 0.656184i \(0.772169\pi\)
\(272\) 7.44718 + 17.6489i 0.451552 + 1.07012i
\(273\) 4.15024 0.516203i 0.251184 0.0312420i
\(274\) −3.81383 1.15005i −0.230402 0.0694769i
\(275\) −2.85088 + 4.93787i −0.171915 + 0.297765i
\(276\) 12.1488 13.0406i 0.731269 0.784955i
\(277\) −3.08910 + 1.78349i −0.185606 + 0.107160i −0.589924 0.807459i \(-0.700842\pi\)
0.404318 + 0.914618i \(0.367509\pi\)
\(278\) −2.71654 2.89085i −0.162927 0.173382i
\(279\) 27.8148 5.49627i 1.66523 0.329053i
\(280\) 17.4383 8.56541i 1.04214 0.511881i
\(281\) 4.26336i 0.254331i −0.991882 0.127165i \(-0.959412\pi\)
0.991882 0.127165i \(-0.0405879\pi\)
\(282\) 16.0939 1.07132i 0.958380 0.0637962i
\(283\) −11.3202 19.6072i −0.672918 1.16553i −0.977073 0.212906i \(-0.931707\pi\)
0.304154 0.952623i \(-0.401626\pi\)
\(284\) −1.20564 0.0750299i −0.0715419 0.00445221i
\(285\) −22.4533 + 8.43466i −1.33002 + 0.499626i
\(286\) −1.22077 + 4.04836i −0.0721856 + 0.239384i
\(287\) 15.0135 4.44752i 0.886220 0.262529i
\(288\) −5.03960 16.2050i −0.296961 0.954890i
\(289\) −2.96705 + 5.13907i −0.174532 + 0.302298i
\(290\) 1.14148 + 4.85930i 0.0670301 + 0.285348i
\(291\) 1.44534 8.72009i 0.0847272 0.511181i
\(292\) −1.32870 2.67209i −0.0777564 0.156372i
\(293\) 5.96057i 0.348220i −0.984726 0.174110i \(-0.944295\pi\)
0.984726 0.174110i \(-0.0557049\pi\)
\(294\) −15.7611 6.75180i −0.919208 0.393773i
\(295\) 4.50477 0.262278
\(296\) −5.14332 + 0.875323i −0.298949 + 0.0508771i
\(297\) −0.524829 17.0153i −0.0304537 0.987330i
\(298\) −23.8733 + 5.60801i −1.38295 + 0.324863i
\(299\) 4.06642 + 2.34775i 0.235167 + 0.135774i
\(300\) 5.76456 1.76547i 0.332817 0.101929i
\(301\) 6.01280 + 20.2975i 0.346572 + 1.16993i
\(302\) 5.23881 17.3731i 0.301460 0.999710i
\(303\) 11.8535 4.45282i 0.680967 0.255808i
\(304\) −12.8763 + 17.0118i −0.738505 + 0.975696i
\(305\) −21.2405 + 12.2632i −1.21623 + 0.702189i
\(306\) 11.8283 16.5199i 0.676176 0.944378i
\(307\) −5.42113 −0.309400 −0.154700 0.987961i \(-0.549441\pi\)
−0.154700 + 0.987961i \(0.549441\pi\)
\(308\) 12.6910 11.8097i 0.723136 0.672921i
\(309\) −1.03617 0.851458i −0.0589458 0.0484378i
\(310\) 23.7623 + 25.2871i 1.34961 + 1.43621i
\(311\) −12.1809 21.0979i −0.690714 1.19635i −0.971604 0.236612i \(-0.923963\pi\)
0.280890 0.959740i \(-0.409370\pi\)
\(312\) 3.86230 2.25218i 0.218660 0.127505i
\(313\) 14.1392 + 8.16327i 0.799195 + 0.461415i 0.843189 0.537617i \(-0.180675\pi\)
−0.0439948 + 0.999032i \(0.514009\pi\)
\(314\) 6.98471 23.1629i 0.394170 1.30716i
\(315\) −17.4142 11.0178i −0.981177 0.620780i
\(316\) −0.208375 0.138240i −0.0117220 0.00777660i
\(317\) 9.94185 17.2198i 0.558390 0.967160i −0.439241 0.898369i \(-0.644753\pi\)
0.997631 0.0687904i \(-0.0219140\pi\)
\(318\) 1.82002 3.70014i 0.102062 0.207493i
\(319\) 2.22697 + 3.85723i 0.124687 + 0.215964i
\(320\) 13.5393 15.7503i 0.756871 0.880467i
\(321\) −15.9764 + 19.4423i −0.891716 + 1.08516i
\(322\) −9.54396 16.7184i −0.531864 0.931680i
\(323\) −25.5436 −1.42128
\(324\) −11.8577 + 13.5423i −0.658761 + 0.752352i
\(325\) 0.794166 + 1.37554i 0.0440524 + 0.0763010i
\(326\) 8.08076 + 34.3999i 0.447552 + 1.90523i
\(327\) −23.9676 + 9.00354i −1.32541 + 0.497897i
\(328\) 12.8872 10.6833i 0.711575 0.589889i
\(329\) 4.06674 16.9406i 0.224207 0.933966i
\(330\) 17.3114 11.5927i 0.952964 0.638156i
\(331\) −1.90300 1.09870i −0.104599 0.0603900i 0.446788 0.894640i \(-0.352568\pi\)
−0.551387 + 0.834250i \(0.685901\pi\)
\(332\) −0.491910 0.0306126i −0.0269971 0.00168009i
\(333\) 3.64341 + 4.16509i 0.199658 + 0.228246i
\(334\) −9.58070 10.1955i −0.524233 0.557871i
\(335\) −32.5669 −1.77932
\(336\) −18.3303 0.0102748i −1.00000 0.000560538i
\(337\) 29.4138 1.60227 0.801135 0.598484i \(-0.204230\pi\)
0.801135 + 0.598484i \(0.204230\pi\)
\(338\) −11.7832 12.5393i −0.640920 0.682046i
\(339\) −4.60822 + 27.8026i −0.250284 + 1.51003i
\(340\) 24.8184 + 1.54450i 1.34597 + 0.0837624i
\(341\) 26.8144 + 15.4813i 1.45208 + 0.838358i
\(342\) 22.5215 + 2.20934i 1.21783 + 0.119467i
\(343\) −12.0271 + 14.0836i −0.649405 + 0.760443i
\(344\) 14.4433 + 17.4227i 0.778730 + 0.939371i
\(345\) −8.13599 21.6582i −0.438027 1.16604i
\(346\) 4.99489 + 21.2633i 0.268527 + 1.14312i
\(347\) −6.43016 11.1374i −0.345189 0.597885i 0.640199 0.768209i \(-0.278852\pi\)
−0.985388 + 0.170324i \(0.945518\pi\)
\(348\) 1.05717 4.58927i 0.0566701 0.246010i
\(349\) 30.0571 1.60892 0.804460 0.594006i \(-0.202455\pi\)
0.804460 + 0.594006i \(0.202455\pi\)
\(350\) 0.0317598 6.51183i 0.00169763 0.348072i
\(351\) −4.17801 2.24335i −0.223005 0.119741i
\(352\) 7.50917 16.9433i 0.400240 0.903081i
\(353\) 12.1069 + 20.9698i 0.644387 + 1.11611i 0.984443 + 0.175705i \(0.0562206\pi\)
−0.340056 + 0.940405i \(0.610446\pi\)
\(354\) −3.81377 1.87592i −0.202700 0.0997038i
\(355\) −0.784045 + 1.35801i −0.0416128 + 0.0720755i
\(356\) −6.02209 3.99517i −0.319170 0.211744i
\(357\) −13.2348 17.5059i −0.700459 0.926510i
\(358\) −4.96044 + 16.4500i −0.262168 + 0.869409i
\(359\) 3.16884 + 1.82953i 0.167245 + 0.0965590i 0.581286 0.813699i \(-0.302550\pi\)
−0.414041 + 0.910258i \(0.635883\pi\)
\(360\) −21.7485 3.50838i −1.14625 0.184908i
\(361\) −4.72503 8.18398i −0.248686 0.430736i
\(362\) 1.37443 + 1.46263i 0.0722387 + 0.0768740i
\(363\) −0.293351 + 0.356991i −0.0153970 + 0.0187372i
\(364\) −1.08141 4.70657i −0.0566813 0.246691i
\(365\) −3.87384 −0.202766
\(366\) 23.0891 1.53697i 1.20689 0.0803385i
\(367\) −15.1950 + 8.77283i −0.793172 + 0.457938i −0.841078 0.540914i \(-0.818078\pi\)
0.0479063 + 0.998852i \(0.484745\pi\)
\(368\) −16.4094 12.4203i −0.855401 0.647454i
\(369\) −16.8055 5.72834i −0.874861 0.298205i
\(370\) −1.95529 + 6.48421i −0.101651 + 0.337098i
\(371\) −3.23082 3.06582i −0.167736 0.159169i
\(372\) −9.58711 31.3036i −0.497068 1.62302i
\(373\) 3.25687 + 1.88036i 0.168635 + 0.0973612i 0.581942 0.813230i \(-0.302293\pi\)
−0.413307 + 0.910592i \(0.635626\pi\)
\(374\) 21.6002 5.07402i 1.11692 0.262372i
\(375\) −2.39681 + 14.4605i −0.123771 + 0.746739i
\(376\) −3.12476 18.3608i −0.161147 0.946886i
\(377\) 1.24073 0.0639008
\(378\) 10.1548 + 16.5795i 0.522309 + 0.852756i
\(379\) 12.2799i 0.630774i 0.948963 + 0.315387i \(0.102134\pi\)
−0.948963 + 0.315387i \(0.897866\pi\)
\(380\) 12.3314 + 24.7991i 0.632587 + 1.27217i
\(381\) 2.73391 + 0.453140i 0.140062 + 0.0232151i
\(382\) −1.35338 5.76138i −0.0692452 0.294778i
\(383\) −3.77515 + 6.53874i −0.192901 + 0.334114i −0.946210 0.323552i \(-0.895123\pi\)
0.753309 + 0.657666i \(0.228456\pi\)
\(384\) −18.0214 + 7.69614i −0.919649 + 0.392742i
\(385\) −6.39184 21.5770i −0.325758 1.09967i
\(386\) 10.7712 35.7198i 0.548240 1.81809i
\(387\) 7.74439 22.7201i 0.393670 1.15493i
\(388\) −10.1868 0.633944i −0.517155 0.0321837i
\(389\) −18.2949 31.6877i −0.927588 1.60663i −0.787345 0.616513i \(-0.788545\pi\)
−0.140244 0.990117i \(-0.544789\pi\)
\(390\) −0.385489 5.79102i −0.0195200 0.293240i
\(391\) 24.6391i 1.24605i
\(392\) −5.90072 + 18.8992i −0.298032 + 0.954556i
\(393\) 12.3105 + 10.1160i 0.620984 + 0.510283i
\(394\) −12.2904 13.0790i −0.619181 0.658911i
\(395\) −0.281118 + 0.162304i −0.0141446 + 0.00816638i
\(396\) −19.4835 + 2.60546i −0.979084 + 0.130929i
\(397\) −3.83449 + 6.64152i −0.192447 + 0.333329i −0.946061 0.323989i \(-0.894976\pi\)
0.753613 + 0.657318i \(0.228309\pi\)
\(398\) 1.46901 + 0.442975i 0.0736348 + 0.0222043i
\(399\) 9.51522 22.5147i 0.476357 1.12714i
\(400\) −2.70642 6.41389i −0.135321 0.320695i
\(401\) 20.5062 + 11.8393i 1.02403 + 0.591224i 0.915269 0.402844i \(-0.131978\pi\)
0.108761 + 0.994068i \(0.465312\pi\)
\(402\) 27.5714 + 13.5618i 1.37514 + 0.676402i
\(403\) 7.46964 4.31260i 0.372089 0.214826i
\(404\) −6.50998 13.0919i −0.323884 0.651347i
\(405\) 8.88735 + 21.6099i 0.441616 + 1.07380i
\(406\) −4.39283 2.56485i −0.218013 0.127291i
\(407\) 6.04316i 0.299548i
\(408\) −20.3683 11.6427i −1.00838 0.576399i
\(409\) 13.5659 7.83230i 0.670793 0.387283i −0.125584 0.992083i \(-0.540080\pi\)
0.796377 + 0.604800i \(0.206747\pi\)
\(410\) −4.96922 21.1540i −0.245412 1.04472i
\(411\) 4.56710 1.71565i 0.225278 0.0846267i
\(412\) −0.856108 + 1.29045i −0.0421774 + 0.0635759i
\(413\) −3.15997 + 3.33004i −0.155492 + 0.163860i
\(414\) −2.13110 + 21.7240i −0.104738 + 1.06768i
\(415\) −0.319895 + 0.554074i −0.0157030 + 0.0271984i
\(416\) −3.04162 4.17150i −0.149128 0.204525i
\(417\) 4.79309 + 0.794445i 0.234719 + 0.0389041i
\(418\) 16.9232 + 18.0091i 0.827740 + 0.880854i
\(419\) 35.4540i 1.73204i 0.500009 + 0.866020i \(0.333330\pi\)
−0.500009 + 0.866020i \(0.666670\pi\)
\(420\) −10.6064 + 21.3001i −0.517541 + 1.03934i
\(421\) 8.00460i 0.390120i 0.980791 + 0.195060i \(0.0624902\pi\)
−0.980791 + 0.195060i \(0.937510\pi\)
\(422\) −8.13210 + 7.64175i −0.395864 + 0.371995i
\(423\) −14.8687 + 13.0064i −0.722940 + 0.632392i
\(424\) −4.46450 1.65515i −0.216815 0.0803814i
\(425\) 4.16730 7.21798i 0.202144 0.350123i
\(426\) 1.22929 0.823199i 0.0595594 0.0398841i
\(427\) 5.83434 24.3038i 0.282343 1.17614i
\(428\) 24.2134 + 16.0637i 1.17040 + 0.776466i
\(429\) −1.82115 4.84795i −0.0879261 0.234061i
\(430\) 28.5991 6.71811i 1.37917 0.323976i
\(431\) 25.8583 14.9293i 1.24555 0.719118i 0.275331 0.961350i \(-0.411213\pi\)
0.970219 + 0.242231i \(0.0778793\pi\)
\(432\) 16.9515 + 12.0269i 0.815578 + 0.578646i
\(433\) 1.70747i 0.0820557i 0.999158 + 0.0410278i \(0.0130632\pi\)
−0.999158 + 0.0410278i \(0.986937\pi\)
\(434\) −35.3615 0.172467i −1.69741 0.00827867i
\(435\) −4.72328 3.88128i −0.226464 0.186093i
\(436\) 13.1631 + 26.4716i 0.630397 + 1.26776i
\(437\) 23.7660 13.7213i 1.13688 0.656379i
\(438\) 3.27962 + 1.61318i 0.156706 + 0.0770807i
\(439\) 14.3026 + 8.25762i 0.682627 + 0.394115i 0.800844 0.598873i \(-0.204385\pi\)
−0.118217 + 0.992988i \(0.537718\pi\)
\(440\) −15.3538 18.5211i −0.731963 0.882957i
\(441\) 20.3602 5.14433i 0.969531 0.244968i
\(442\) 1.78447 5.91772i 0.0848786 0.281477i
\(443\) 7.12265 12.3368i 0.338407 0.586138i −0.645726 0.763569i \(-0.723445\pi\)
0.984133 + 0.177431i \(0.0567785\pi\)
\(444\) 4.35558 4.67534i 0.206707 0.221882i
\(445\) −8.12438 + 4.69062i −0.385133 + 0.222356i
\(446\) −11.8921 + 11.1751i −0.563109 + 0.529155i
\(447\) 19.0684 23.2051i 0.901904 1.09756i
\(448\) 2.14555 + 21.0570i 0.101368 + 0.994849i
\(449\) 2.18010i 0.102885i 0.998676 + 0.0514426i \(0.0163819\pi\)
−0.998676 + 0.0514426i \(0.983618\pi\)
\(450\) −4.29857 + 6.00357i −0.202636 + 0.283011i
\(451\) −9.69470 16.7917i −0.456506 0.790691i
\(452\) 32.4788 + 2.02123i 1.52767 + 0.0950704i
\(453\) 7.81529 + 20.8045i 0.367194 + 0.977480i
\(454\) −21.0792 6.35638i −0.989297 0.298320i
\(455\) −6.09568 1.46332i −0.285770 0.0686015i
\(456\) −0.112796 26.1302i −0.00528217 1.22366i
\(457\) −16.0855 + 27.8609i −0.752447 + 1.30328i 0.194186 + 0.980965i \(0.437793\pi\)
−0.946633 + 0.322312i \(0.895540\pi\)
\(458\) −4.90773 + 1.15286i −0.229323 + 0.0538696i
\(459\) 0.767174 + 24.8723i 0.0358086 + 1.16094i
\(460\) −23.9209 + 11.8947i −1.11532 + 0.554594i
\(461\) 13.9258i 0.648588i 0.945956 + 0.324294i \(0.105127\pi\)
−0.945956 + 0.324294i \(0.894873\pi\)
\(462\) −3.57390 + 20.9290i −0.166273 + 0.973705i
\(463\) 15.5838 0.724239 0.362120 0.932132i \(-0.382053\pi\)
0.362120 + 0.932132i \(0.382053\pi\)
\(464\) −5.39605 0.674227i −0.250505 0.0313002i
\(465\) −41.9266 6.94925i −1.94430 0.322264i
\(466\) 2.46716 + 10.5027i 0.114289 + 0.486530i
\(467\) −16.6230 9.59729i −0.769220 0.444110i 0.0633760 0.997990i \(-0.479813\pi\)
−0.832596 + 0.553880i \(0.813147\pi\)
\(468\) −2.08519 + 5.06325i −0.0963879 + 0.234049i
\(469\) 22.8448 24.0743i 1.05488 1.11165i
\(470\) −23.1476 6.98008i −1.06772 0.321967i
\(471\) 10.4198 + 27.7378i 0.480121 + 1.27809i
\(472\) −1.70598 + 4.60161i −0.0785243 + 0.211806i
\(473\) 22.7015 13.1067i 1.04381 0.602647i
\(474\) 0.305584 0.0203418i 0.0140360 0.000934328i
\(475\) 9.28294 0.425931
\(476\) −18.5511 + 17.2630i −0.850290 + 0.791246i
\(477\) 0.979016 + 4.95447i 0.0448261 + 0.226850i
\(478\) −13.6806 + 12.8557i −0.625735 + 0.588004i
\(479\) −3.02090 5.23235i −0.138028 0.239072i 0.788722 0.614750i \(-0.210743\pi\)
−0.926750 + 0.375678i \(0.877410\pi\)
\(480\) −1.47038 + 25.3952i −0.0671133 + 1.15913i
\(481\) 1.45790 + 0.841716i 0.0664743 + 0.0383790i
\(482\) 15.5219 + 4.68058i 0.707003 + 0.213195i
\(483\) 21.7174 + 9.17829i 0.988178 + 0.417626i
\(484\) 0.444596 + 0.294954i 0.0202089 + 0.0134070i
\(485\) −6.62457 + 11.4741i −0.300806 + 0.521012i
\(486\) 1.47487 21.9960i 0.0669013 0.997760i
\(487\) 11.1385 + 19.2925i 0.504735 + 0.874227i 0.999985 + 0.00547672i \(0.00174330\pi\)
−0.495250 + 0.868751i \(0.664923\pi\)
\(488\) −4.48293 26.3413i −0.202933 1.19241i
\(489\) −33.4370 27.4763i −1.51207 1.24252i
\(490\) 18.5569 + 17.7820i 0.838315 + 0.803308i
\(491\) −4.63965 −0.209384 −0.104692 0.994505i \(-0.533386\pi\)
−0.104692 + 0.994505i \(0.533386\pi\)
\(492\) −4.60217 + 19.9785i −0.207482 + 0.900699i
\(493\) −3.25530 5.63834i −0.146611 0.253938i
\(494\) 6.70178 1.57429i 0.301527 0.0708308i
\(495\) −8.23260 + 24.1524i −0.370028 + 1.08557i
\(496\) −34.8297 + 14.6968i −1.56390 + 0.659906i
\(497\) −0.453886 1.53219i −0.0203596 0.0687281i
\(498\) 0.501558 0.335870i 0.0224754 0.0150507i
\(499\) −16.8940 9.75377i −0.756280 0.436639i 0.0716782 0.997428i \(-0.477165\pi\)
−0.827959 + 0.560789i \(0.810498\pi\)
\(500\) 16.8927 + 1.05127i 0.755466 + 0.0470143i
\(501\) 16.9043 + 2.80185i 0.755229 + 0.125178i
\(502\) 1.49335 1.40331i 0.0666516 0.0626326i
\(503\) 33.9146 1.51218 0.756090 0.654468i \(-0.227107\pi\)
0.756090 + 0.654468i \(0.227107\pi\)
\(504\) 17.8495 13.6160i 0.795079 0.606506i
\(505\) −18.9799 −0.844594
\(506\) −17.3714 + 16.3239i −0.772252 + 0.725688i
\(507\) 20.7904 + 3.44596i 0.923333 + 0.153041i
\(508\) 0.198753 3.19374i 0.00881825 0.141699i
\(509\) −20.9128 12.0740i −0.926946 0.535172i −0.0411013 0.999155i \(-0.513087\pi\)
−0.885844 + 0.463983i \(0.846420\pi\)
\(510\) −25.3052 + 16.9457i −1.12053 + 0.750367i
\(511\) 2.71739 2.86364i 0.120210 0.126680i
\(512\) 10.9615 + 19.7951i 0.484432 + 0.874829i
\(513\) −23.5637 + 14.5912i −1.04036 + 0.644216i
\(514\) −16.6150 + 3.90297i −0.732856 + 0.172153i
\(515\) 1.00513 + 1.74094i 0.0442914 + 0.0767150i
\(516\) −27.0098 6.22187i −1.18904 0.273903i
\(517\) −21.5731 −0.948782
\(518\) −3.42171 5.99390i −0.150341 0.263357i
\(519\) −20.6681 16.9837i −0.907230 0.745501i
\(520\) −6.60670 + 1.12437i −0.289723 + 0.0493069i
\(521\) −2.98225 5.16541i −0.130655 0.226301i 0.793274 0.608864i \(-0.208375\pi\)
−0.923929 + 0.382564i \(0.875041\pi\)
\(522\) 2.38249 + 5.25283i 0.104279 + 0.229910i
\(523\) 6.49701 11.2532i 0.284095 0.492066i −0.688295 0.725431i \(-0.741640\pi\)
0.972389 + 0.233365i \(0.0749737\pi\)
\(524\) 10.1712 15.3315i 0.444332 0.669761i
\(525\) 4.80973 + 6.36191i 0.209914 + 0.277656i
\(526\) −33.9778 10.2459i −1.48150 0.446743i
\(527\) −39.1961 22.6299i −1.70741 0.985774i
\(528\) 5.28593 + 22.0738i 0.230041 + 0.960640i
\(529\) 1.73544 + 3.00587i 0.0754539 + 0.130690i
\(530\) −4.50423 + 4.23264i −0.195651 + 0.183854i
\(531\) 5.10662 1.00908i 0.221609 0.0437905i
\(532\) −26.9822 8.28018i −1.16983 0.358991i
\(533\) −5.40127 −0.233955
\(534\) 8.83147 0.587882i 0.382175 0.0254402i
\(535\) 32.6663 18.8599i 1.41229 0.815383i
\(536\) 12.3333 33.2671i 0.532718 1.43692i
\(537\) −7.40002 19.6990i −0.319335 0.850076i
\(538\) −10.3474 3.12022i −0.446106 0.134522i
\(539\) 20.4340 + 10.4107i 0.880153 + 0.448418i
\(540\) 23.7770 12.7521i 1.02320 0.548764i
\(541\) −18.7480 10.8242i −0.806039 0.465367i 0.0395397 0.999218i \(-0.487411\pi\)
−0.845578 + 0.533851i \(0.820744\pi\)
\(542\) −3.46492 14.7502i −0.148831 0.633576i
\(543\) −2.42507 0.401950i −0.104070 0.0172493i
\(544\) −10.9766 + 24.7670i −0.470617 + 1.06188i
\(545\) 38.3770 1.64389
\(546\) 4.55128 + 3.77727i 0.194777 + 0.161652i
\(547\) 15.8930i 0.679536i 0.940509 + 0.339768i \(0.110349\pi\)
−0.940509 + 0.339768i \(0.889651\pi\)
\(548\) −2.50826 5.04424i −0.107148 0.215479i
\(549\) −21.3313 + 18.6596i −0.910398 + 0.796370i
\(550\) −7.84984 + 1.84398i −0.334718 + 0.0786275i
\(551\) 3.62570 6.27989i 0.154460 0.267532i
\(552\) 25.2049 0.108802i 1.07279 0.00463093i
\(553\) 0.0772175 0.321661i 0.00328362 0.0136784i
\(554\) −4.82967 1.45637i −0.205193 0.0618753i
\(555\) −2.91692 7.76491i −0.123816 0.329602i
\(556\) 0.348454 5.59926i 0.0147778 0.237462i
\(557\) 20.3420 + 35.2334i 0.861919 + 1.49289i 0.870074 + 0.492921i \(0.164071\pi\)
−0.00815471 + 0.999967i \(0.502596\pi\)
\(558\) 32.6015 + 23.3427i 1.38013 + 0.988176i
\(559\) 7.30223i 0.308851i
\(560\) 25.7155 + 9.67658i 1.08668 + 0.408910i
\(561\) −17.2528 + 20.9956i −0.728412 + 0.886433i
\(562\) 4.39377 4.12883i 0.185340 0.174164i
\(563\) 38.8739 22.4439i 1.63834 0.945896i 0.656936 0.753947i \(-0.271852\pi\)
0.981405 0.191950i \(-0.0614810\pi\)
\(564\) 16.6902 + 15.5487i 0.702784 + 0.654718i
\(565\) 21.1213 36.5832i 0.888581 1.53907i
\(566\) 9.24394 30.6550i 0.388552 1.28853i
\(567\) −22.2088 8.58895i −0.932681 0.360702i
\(568\) −1.09028 1.31519i −0.0457470 0.0551840i
\(569\) −12.8893 7.44164i −0.540347 0.311970i 0.204872 0.978789i \(-0.434322\pi\)
−0.745220 + 0.666819i \(0.767655\pi\)
\(570\) −30.4374 14.9715i −1.27488 0.627089i
\(571\) 6.27344 3.62197i 0.262535 0.151575i −0.362955 0.931807i \(-0.618232\pi\)
0.625490 + 0.780232i \(0.284899\pi\)
\(572\) −5.35444 + 2.66251i −0.223880 + 0.111325i
\(573\) 5.60010 + 4.60179i 0.233948 + 0.192243i
\(574\) 19.1233 + 11.1656i 0.798193 + 0.466042i
\(575\) 8.95423i 0.373417i
\(576\) 11.8201 20.8874i 0.492505 0.870310i
\(577\) 20.2309 11.6803i 0.842223 0.486258i −0.0157961 0.999875i \(-0.505028\pi\)
0.858019 + 0.513617i \(0.171695\pi\)
\(578\) −8.16969 + 1.91911i −0.339814 + 0.0798246i
\(579\) 16.0686 + 42.7748i 0.667786 + 1.77766i
\(580\) −3.90247 + 5.88237i −0.162041 + 0.244252i
\(581\) −0.185188 0.625142i −0.00768291 0.0259353i
\(582\) 10.3866 6.95539i 0.430537 0.288310i
\(583\) −2.75758 + 4.77627i −0.114207 + 0.197813i
\(584\) 1.46705 3.95712i 0.0607069 0.163747i
\(585\) 4.68003 + 5.35014i 0.193496 + 0.221201i
\(586\) 6.14289 5.77249i 0.253761 0.238459i
\(587\) 8.33175i 0.343888i 0.985107 + 0.171944i \(0.0550048\pi\)
−0.985107 + 0.171944i \(0.944995\pi\)
\(588\) −8.30548 22.7820i −0.342512 0.939513i
\(589\) 50.4096i 2.07709i
\(590\) 4.36262 + 4.64256i 0.179606 + 0.191131i
\(591\) 21.6853 + 3.59430i 0.892014 + 0.147850i
\(592\) −5.88313 4.45294i −0.241795 0.183015i
\(593\) −19.8845 + 34.4410i −0.816560 + 1.41432i 0.0916424 + 0.995792i \(0.470788\pi\)
−0.908202 + 0.418531i \(0.862545\pi\)
\(594\) 17.0275 17.0193i 0.698648 0.698311i
\(595\) 9.34332 + 31.5403i 0.383039 + 1.29303i
\(596\) −28.8996 19.1725i −1.18377 0.785338i
\(597\) −1.75915 + 0.660834i −0.0719974 + 0.0270461i
\(598\) 1.51855 + 6.46447i 0.0620980 + 0.264352i
\(599\) −12.0202 + 6.93989i −0.491134 + 0.283556i −0.725045 0.688702i \(-0.758181\pi\)
0.233911 + 0.972258i \(0.424848\pi\)
\(600\) 7.40214 + 4.23113i 0.302191 + 0.172735i
\(601\) 17.2223i 0.702512i 0.936279 + 0.351256i \(0.114245\pi\)
−0.936279 + 0.351256i \(0.885755\pi\)
\(602\) −15.0952 + 25.8537i −0.615236 + 1.05372i
\(603\) −36.9180 + 7.29510i −1.50342 + 0.297080i
\(604\) 22.9780 11.4259i 0.934963 0.464912i
\(605\) 0.599803 0.346296i 0.0243855 0.0140790i
\(606\) 16.0685 + 7.90378i 0.652739 + 0.321069i
\(607\) 7.37230 + 4.25640i 0.299233 + 0.172762i 0.642098 0.766622i \(-0.278064\pi\)
−0.342865 + 0.939385i \(0.611398\pi\)
\(608\) −30.0022 + 3.20492i −1.21675 + 0.129977i
\(609\) 6.18239 0.768959i 0.250523 0.0311598i
\(610\) −33.2086 10.0139i −1.34458 0.405453i
\(611\) −3.00479 + 5.20445i −0.121561 + 0.210549i
\(612\) 28.4802 3.80855i 1.15124 0.153951i
\(613\) −36.3973 + 21.0140i −1.47007 + 0.848747i −0.999436 0.0335801i \(-0.989309\pi\)
−0.470637 + 0.882327i \(0.655976\pi\)
\(614\) −5.25007 5.58695i −0.211876 0.225471i
\(615\) 20.5619 + 16.8964i 0.829134 + 0.681328i
\(616\) 24.4615 + 1.64209i 0.985581 + 0.0661619i
\(617\) 16.0083i 0.644471i 0.946660 + 0.322236i \(0.104434\pi\)
−0.946660 + 0.322236i \(0.895566\pi\)
\(618\) −0.125975 1.89246i −0.00506745 0.0761259i
\(619\) 10.1543 + 17.5878i 0.408136 + 0.706913i 0.994681 0.103004i \(-0.0328455\pi\)
−0.586545 + 0.809917i \(0.699512\pi\)
\(620\) −3.04803 + 48.9784i −0.122412 + 1.96702i
\(621\) −14.0745 22.7293i −0.564790 0.912096i
\(622\) 9.94672 32.9856i 0.398827 1.32260i
\(623\) 2.23161 9.29609i 0.0894075 0.372440i
\(624\) 6.06150 + 1.79932i 0.242654 + 0.0720304i
\(625\) 15.3365 26.5636i 0.613460 1.06254i
\(626\) 5.28008 + 22.4774i 0.211035 + 0.898377i
\(627\) −29.8595 4.94915i −1.19247 0.197650i
\(628\) 30.6357 15.2337i 1.22250 0.607890i
\(629\) 8.83363i 0.352220i
\(630\) −5.50990 28.6169i −0.219520 1.14013i
\(631\) −28.0435 −1.11639 −0.558197 0.829708i \(-0.688507\pi\)
−0.558197 + 0.829708i \(0.688507\pi\)
\(632\) −0.0593316 0.348627i −0.00236008 0.0138676i
\(633\) 2.23481 13.4832i 0.0888259 0.535909i
\(634\) 27.3747 6.43048i 1.08719 0.255387i
\(635\) −3.59734 2.07693i −0.142756 0.0824203i
\(636\) 5.57591 1.70769i 0.221099 0.0677144i
\(637\) 5.35767 3.47960i 0.212279 0.137867i
\(638\) −1.81851 + 6.03062i −0.0719957 + 0.238754i
\(639\) −0.584599 + 1.71507i −0.0231264 + 0.0678471i
\(640\) 29.3441 1.29984i 1.15993 0.0513805i
\(641\) 9.80778 5.66252i 0.387384 0.223656i −0.293642 0.955915i \(-0.594867\pi\)
0.681026 + 0.732259i \(0.261534\pi\)
\(642\) −35.5093 + 2.36374i −1.40144 + 0.0932893i
\(643\) 32.8892 1.29702 0.648512 0.761204i \(-0.275392\pi\)
0.648512 + 0.761204i \(0.275392\pi\)
\(644\) 7.98698 26.0268i 0.314731 1.02560i
\(645\) −22.8430 + 27.7985i −0.899441 + 1.09457i
\(646\) −24.7376 26.3249i −0.973288 1.03574i
\(647\) −13.6188 23.5884i −0.535409 0.927356i −0.999143 0.0413818i \(-0.986824\pi\)
0.463734 0.885974i \(-0.346509\pi\)
\(648\) −25.4401 + 0.894624i −0.999382 + 0.0351441i
\(649\) 4.92296 + 2.84227i 0.193243 + 0.111569i
\(650\) −0.648504 + 2.15059i −0.0254364 + 0.0843531i
\(651\) 34.5474 26.1185i 1.35402 1.02366i
\(652\) −27.6263 + 41.6424i −1.08193 + 1.63084i
\(653\) 12.2895 21.2860i 0.480926 0.832987i −0.518835 0.854874i \(-0.673634\pi\)
0.999760 + 0.0218870i \(0.00696741\pi\)
\(654\) −32.4903 15.9813i −1.27047 0.624918i
\(655\) −11.9417 20.6837i −0.466602 0.808179i
\(656\) 23.4907 + 2.93512i 0.917156 + 0.114597i
\(657\) −4.39140 + 0.867753i −0.171325 + 0.0338543i
\(658\) 21.3972 12.2149i 0.834150 0.476188i
\(659\) 12.1725 0.474172 0.237086 0.971489i \(-0.423808\pi\)
0.237086 + 0.971489i \(0.423808\pi\)
\(660\) 28.7125 + 6.61410i 1.11763 + 0.257453i
\(661\) 4.00322 + 6.93378i 0.155707 + 0.269693i 0.933316 0.359055i \(-0.116901\pi\)
−0.777609 + 0.628748i \(0.783568\pi\)
\(662\) −0.710650 3.02524i −0.0276202 0.117579i
\(663\) 2.66208 + 7.08653i 0.103387 + 0.275218i
\(664\) −0.444840 0.536604i −0.0172631 0.0208243i
\(665\) −25.2195 + 26.5768i −0.977970 + 1.03060i
\(666\) −0.764045 + 7.78852i −0.0296062 + 0.301799i
\(667\) 6.05752 + 3.49731i 0.234548 + 0.135416i
\(668\) 1.22893 19.7475i 0.0475487 0.764054i
\(669\) 3.26812 19.7174i 0.126353 0.762319i
\(670\) −31.5393 33.5631i −1.21847 1.29666i
\(671\) −30.9497 −1.19480
\(672\) −17.7413 18.9009i −0.684386 0.729120i
\(673\) 18.1260 0.698706 0.349353 0.936991i \(-0.386401\pi\)
0.349353 + 0.936991i \(0.386401\pi\)
\(674\) 28.4856 + 30.3135i 1.09723 + 1.16763i
\(675\) −0.278803 9.03898i −0.0107311 0.347910i
\(676\) 1.51145 24.2872i 0.0581325 0.934123i
\(677\) −39.1458 22.6008i −1.50449 0.868620i −0.999986 0.00521277i \(-0.998341\pi\)
−0.504508 0.863407i \(-0.668326\pi\)
\(678\) −33.1158 + 22.1761i −1.27180 + 0.851668i
\(679\) −3.83499 12.9458i −0.147173 0.496815i
\(680\) 22.4435 + 27.0733i 0.860670 + 1.03821i
\(681\) 25.2426 9.48249i 0.967298 0.363370i
\(682\) 10.0134 + 42.6274i 0.383435 + 1.63229i
\(683\) −6.38047 11.0513i −0.244142 0.422866i 0.717748 0.696303i \(-0.245173\pi\)
−0.961890 + 0.273437i \(0.911840\pi\)
\(684\) 19.5340 + 25.3501i 0.746900 + 0.969284i
\(685\) −7.31285 −0.279410
\(686\) −26.1620 + 1.24417i −0.998871 + 0.0475025i
\(687\) 3.91996 4.77036i 0.149556 0.182000i
\(688\) −3.96811 + 31.7581i −0.151283 + 1.21077i
\(689\) 0.768176 + 1.33052i 0.0292652 + 0.0506888i
\(690\) 14.4414 29.3596i 0.549775 1.11770i
\(691\) −7.47003 + 12.9385i −0.284173 + 0.492203i −0.972408 0.233285i \(-0.925052\pi\)
0.688235 + 0.725488i \(0.258386\pi\)
\(692\) −17.0764 + 25.7401i −0.649149 + 0.978490i
\(693\) −12.0791 23.0280i −0.458848 0.874761i
\(694\) 5.25077 17.4128i 0.199316 0.660980i
\(695\) −6.30686 3.64127i −0.239233 0.138121i
\(696\) 5.75345 3.35495i 0.218084 0.127169i
\(697\) 14.1713 + 24.5454i 0.536776 + 0.929724i
\(698\) 29.1087 + 30.9765i 1.10178 + 1.17248i
\(699\) −10.2087 8.38887i −0.386130 0.317296i
\(700\) 6.74177 6.27362i 0.254815 0.237121i
\(701\) −14.3141 −0.540636 −0.270318 0.962771i \(-0.587129\pi\)
−0.270318 + 0.962771i \(0.587129\pi\)
\(702\) −1.73420 6.47837i −0.0654531 0.244510i
\(703\) 8.52061 4.91938i 0.321361 0.185538i
\(704\) 24.7338 8.66982i 0.932190 0.326756i
\(705\) 27.7194 10.4129i 1.04397 0.392173i
\(706\) −9.88634 + 32.7854i −0.372077 + 1.23389i
\(707\) 13.3139 14.0304i 0.500719 0.527668i
\(708\) −1.76014 5.74715i −0.0661499 0.215991i
\(709\) 5.67964 + 3.27914i 0.213303 + 0.123151i 0.602846 0.797858i \(-0.294033\pi\)
−0.389542 + 0.921009i \(0.627367\pi\)
\(710\) −2.15885 + 0.507128i −0.0810202 + 0.0190322i
\(711\) −0.282320 + 0.246959i −0.0105878 + 0.00926170i
\(712\) −1.71470 10.0754i −0.0642610 0.377592i
\(713\) 48.6246 1.82100
\(714\) 5.22418 30.5931i 0.195510 1.14492i
\(715\) 7.76255i 0.290303i
\(716\) −21.7571 + 10.8188i −0.813101 + 0.404316i
\(717\) 3.75961 22.6827i 0.140405 0.847100i
\(718\) 1.18336 + 5.03757i 0.0441626 + 0.188001i
\(719\) 19.5665 33.8902i 0.729708 1.26389i −0.227299 0.973825i \(-0.572990\pi\)
0.957007 0.290066i \(-0.0936772\pi\)
\(720\) −17.4466 25.8115i −0.650196 0.961936i
\(721\) −1.99202 0.478202i −0.0741866 0.0178092i
\(722\) 3.85838 12.7953i 0.143594 0.476192i
\(723\) −18.5876 + 6.98252i −0.691281 + 0.259683i
\(724\) −0.176301 + 2.83295i −0.00655216 + 0.105286i
\(725\) 1.18303 + 2.04906i 0.0439365 + 0.0761002i
\(726\) −0.652006 + 0.0434019i −0.0241982 + 0.00161080i
\(727\) 34.4829i 1.27890i 0.768833 + 0.639450i \(0.220838\pi\)
−0.768833 + 0.639450i \(0.779162\pi\)
\(728\) 3.80325 5.67255i 0.140958 0.210239i
\(729\) 14.9154 + 22.5062i 0.552423 + 0.833564i
\(730\) −3.75161 3.99234i −0.138853 0.147763i
\(731\) −33.1841 + 19.1588i −1.22736 + 0.708615i
\(732\) 23.9445 + 22.3069i 0.885015 + 0.824486i
\(733\) −9.89201 + 17.1335i −0.365370 + 0.632839i −0.988835 0.149012i \(-0.952391\pi\)
0.623466 + 0.781851i \(0.285724\pi\)
\(734\) −23.7567 7.16376i −0.876876 0.264419i
\(735\) −31.2808 3.51365i −1.15381 0.129603i
\(736\) −3.09143 28.9398i −0.113952 1.06673i
\(737\) −35.5902 20.5480i −1.31098 0.756896i
\(738\) −10.3717 22.8672i −0.381787 0.841752i
\(739\) 6.03595 3.48486i 0.222036 0.128193i −0.384857 0.922976i \(-0.625749\pi\)
0.606893 + 0.794784i \(0.292416\pi\)
\(740\) −8.57615 + 4.26451i −0.315266 + 0.156766i
\(741\) −5.35292 + 6.51418i −0.196645 + 0.239305i
\(742\) 0.0307204 6.29872i 0.00112778 0.231233i
\(743\) 45.3956i 1.66540i 0.553723 + 0.832701i \(0.313207\pi\)
−0.553723 + 0.832701i \(0.686793\pi\)
\(744\) 22.9765 40.1962i 0.842360 1.47366i
\(745\) −38.9883 + 22.5099i −1.42842 + 0.824700i
\(746\) 1.21623 + 5.17752i 0.0445295 + 0.189562i
\(747\) −0.238520 + 0.699759i −0.00872698 + 0.0256028i
\(748\) 26.1478 + 17.3470i 0.956060 + 0.634268i
\(749\) −8.97277 + 37.3774i −0.327858 + 1.36574i
\(750\) −17.2240 + 11.5341i −0.628933 + 0.421167i
\(751\) −10.3669 + 17.9560i −0.378293 + 0.655223i −0.990814 0.135231i \(-0.956822\pi\)
0.612521 + 0.790455i \(0.290156\pi\)
\(752\) 15.8963 21.0018i 0.579677 0.765857i
\(753\) −0.410394 + 2.47601i −0.0149556 + 0.0902309i
\(754\) 1.20158 + 1.27868i 0.0437590 + 0.0465668i
\(755\) 33.3122i 1.21236i
\(756\) −7.25219 + 26.5218i −0.263760 + 0.964588i
\(757\) 30.3555i 1.10329i 0.834079 + 0.551645i \(0.186000\pi\)
−0.834079 + 0.551645i \(0.814000\pi\)
\(758\) −12.6555 + 11.8924i −0.459668 + 0.431951i
\(759\) 4.77390 28.8022i 0.173282 1.04545i
\(760\) −13.6153 + 36.7251i −0.493880 + 1.33216i
\(761\) −6.12394 + 10.6070i −0.221993 + 0.384503i −0.955413 0.295273i \(-0.904589\pi\)
0.733420 + 0.679775i \(0.237923\pi\)
\(762\) 2.18064 + 3.25638i 0.0789964 + 0.117966i
\(763\) −26.9204 + 28.3693i −0.974585 + 1.02704i
\(764\) 4.62693 6.97436i 0.167396 0.252324i
\(765\) 12.0341 35.3050i 0.435092 1.27645i
\(766\) −10.3948 + 2.44180i −0.375579 + 0.0882259i
\(767\) 1.37138 0.791767i 0.0495177 0.0285890i
\(768\) −25.3843 11.1193i −0.915976 0.401233i
\(769\) 19.0816i 0.688100i −0.938951 0.344050i \(-0.888201\pi\)
0.938951 0.344050i \(-0.111799\pi\)
\(770\) 16.0468 27.4835i 0.578288 0.990437i
\(771\) 13.2709 16.1499i 0.477940 0.581624i
\(772\) 47.2437 23.4920i 1.70034 0.845497i
\(773\) 9.07434 5.23907i 0.326381 0.188436i −0.327852 0.944729i \(-0.606325\pi\)
0.654233 + 0.756293i \(0.272991\pi\)
\(774\) 30.9151 14.0220i 1.11122 0.504009i
\(775\) 14.2445 + 8.22405i 0.511677 + 0.295417i
\(776\) −9.21200 11.1123i −0.330691 0.398908i
\(777\) 7.78616 + 3.29061i 0.279327 + 0.118050i
\(778\) 14.9393 49.5423i 0.535601 1.77618i
\(779\) −15.7838 + 27.3383i −0.565512 + 0.979496i
\(780\) 5.59483 6.00557i 0.200327 0.215034i
\(781\) −1.71366 + 0.989382i −0.0613196 + 0.0354029i
\(782\) 25.3928 23.8616i 0.908044 0.853291i
\(783\) −6.22375 3.34180i −0.222419 0.119426i
\(784\) −25.1919 + 12.2217i −0.899710 + 0.436489i
\(785\) 44.4139i 1.58520i
\(786\) 1.49668 + 22.4839i 0.0533847 + 0.801973i
\(787\) −6.93206 12.0067i −0.247101 0.427992i 0.715619 0.698491i \(-0.246145\pi\)
−0.962720 + 0.270499i \(0.912811\pi\)
\(788\) 1.57651 25.3327i 0.0561607 0.902438i
\(789\) 40.6888 15.2849i 1.44856 0.544157i
\(790\) −0.439516 0.132535i −0.0156373 0.00471537i
\(791\) 12.2272 + 41.2755i 0.434750 + 1.46759i
\(792\) −21.5539 17.5563i −0.765885 0.623834i
\(793\) −4.31081 + 7.46654i −0.153081 + 0.265145i
\(794\) −10.5582 + 2.48018i −0.374695 + 0.0880184i
\(795\) 1.23783 7.46812i 0.0439011 0.264867i
\(796\) 0.966132 + 1.94294i 0.0342436 + 0.0688657i
\(797\) 29.4639i 1.04366i 0.853048 + 0.521832i \(0.174751\pi\)
−0.853048 + 0.521832i \(0.825249\pi\)
\(798\) 32.4184 11.9980i 1.14760 0.424725i
\(799\) 31.5346 1.11561
\(800\) 3.98906 9.00072i 0.141035 0.318223i
\(801\) −8.15912 + 7.13719i −0.288288 + 0.252180i
\(802\) 7.65775 + 32.5991i 0.270404 + 1.15111i
\(803\) −4.23346 2.44419i −0.149396 0.0862536i
\(804\) 12.7248 + 41.5487i 0.448769 + 1.46531i
\(805\) −25.6357 24.3265i −0.903540 0.857395i
\(806\) 11.6785 + 3.52160i 0.411356 + 0.124043i
\(807\) 12.3911 4.65476i 0.436186 0.163855i
\(808\) 7.18781 19.3879i 0.252866 0.682065i
\(809\) −42.7554 + 24.6848i −1.50320 + 0.867873i −0.503207 + 0.864166i \(0.667847\pi\)
−0.999993 + 0.00370713i \(0.998820\pi\)
\(810\) −13.6639 + 30.0872i −0.480102 + 1.05716i
\(811\) 0.180195 0.00632751 0.00316376 0.999995i \(-0.498993\pi\)
0.00316376 + 0.999995i \(0.498993\pi\)
\(812\) −1.61092 7.01112i −0.0565321 0.246042i
\(813\) 14.3373 + 11.7815i 0.502832 + 0.413194i
\(814\) −6.22801 + 5.85247i −0.218291 + 0.205129i
\(815\) 32.4353 + 56.1796i 1.13616 + 1.96788i
\(816\) −7.72676 32.2666i −0.270491 1.12956i
\(817\) −36.9598 21.3388i −1.29306 0.746549i
\(818\) 21.2098 + 6.39574i 0.741582 + 0.223622i
\(819\) −7.23787 0.293375i −0.252912 0.0102514i
\(820\) 16.9887 25.6077i 0.593270 0.894261i
\(821\) −11.4858 + 19.8940i −0.400857 + 0.694304i −0.993830 0.110918i \(-0.964621\pi\)
0.592973 + 0.805223i \(0.297954\pi\)
\(822\) 6.19112 + 3.04528i 0.215940 + 0.106216i
\(823\) −22.0638 38.2157i −0.769097 1.33212i −0.938053 0.346492i \(-0.887373\pi\)
0.168956 0.985624i \(-0.445960\pi\)
\(824\) −2.15902 + 0.367435i −0.0752129 + 0.0128002i
\(825\) 6.26992 7.63011i 0.218290 0.265646i
\(826\) −6.49216 0.0316639i −0.225891 0.00110173i
\(827\) 19.7749 0.687641 0.343821 0.939035i \(-0.388279\pi\)
0.343821 + 0.939035i \(0.388279\pi\)
\(828\) −24.4524 + 18.8423i −0.849780 + 0.654814i
\(829\) 13.8197 + 23.9365i 0.479979 + 0.831349i 0.999736 0.0229656i \(-0.00731081\pi\)
−0.519757 + 0.854314i \(0.673977\pi\)
\(830\) −0.880823 + 0.206911i −0.0305738 + 0.00718199i
\(831\) 5.78358 2.17263i 0.200630 0.0753676i
\(832\) 1.35346 7.17453i 0.0469227 0.248732i
\(833\) −29.8695 15.2179i −1.03492 0.527267i
\(834\) 3.82310 + 5.70908i 0.132383 + 0.197689i
\(835\) −22.2431 12.8420i −0.769753 0.444417i
\(836\) −2.17076 + 34.8817i −0.0750774 + 1.20641i
\(837\) −49.0848 + 1.51400i −1.69662 + 0.0523313i
\(838\) −36.5385 + 34.3353i −1.26220 + 1.18609i
\(839\) −28.3920 −0.980200 −0.490100 0.871666i \(-0.663040\pi\)
−0.490100 + 0.871666i \(0.663040\pi\)
\(840\) −32.2234 + 9.69717i −1.11181 + 0.334584i
\(841\) −27.1518 −0.936267
\(842\) −8.24945 + 7.75203i −0.284295 + 0.267152i
\(843\) −1.20747 + 7.28496i −0.0415874 + 0.250907i
\(844\) −15.7510 0.980219i −0.542172 0.0337405i
\(845\) −27.3565 15.7943i −0.941091 0.543339i
\(846\) −27.8037 2.72752i −0.955912 0.0937739i
\(847\) −0.164754 + 0.686307i −0.00566101 + 0.0235818i
\(848\) −2.61785 6.20399i −0.0898973 0.213046i
\(849\) 13.7902 + 36.7097i 0.473277 + 1.25987i
\(850\) 11.4746 2.69545i 0.393574 0.0924532i
\(851\) 4.74518 + 8.21889i 0.162663 + 0.281740i
\(852\) 2.03888 + 0.469669i 0.0698509 + 0.0160906i
\(853\) 30.7041 1.05129 0.525645 0.850704i \(-0.323824\pi\)
0.525645 + 0.850704i \(0.323824\pi\)
\(854\) 30.6974 17.5241i 1.05044 0.599663i
\(855\) 40.7556 8.05342i 1.39381 0.275421i
\(856\) 6.89440 + 40.5109i 0.235646 + 1.38463i
\(857\) 11.5192 + 19.9518i 0.393487 + 0.681539i 0.992907 0.118895i \(-0.0379353\pi\)
−0.599420 + 0.800435i \(0.704602\pi\)
\(858\) 3.23255 6.57184i 0.110357 0.224359i
\(859\) −26.3268 + 45.5994i −0.898260 + 1.55583i −0.0685424 + 0.997648i \(0.521835\pi\)
−0.829717 + 0.558184i \(0.811498\pi\)
\(860\) 34.6202 + 22.9677i 1.18054 + 0.783193i
\(861\) −26.9138 + 3.34751i −0.917220 + 0.114083i
\(862\) 40.4283 + 12.1910i 1.37699 + 0.415228i
\(863\) 22.4451 + 12.9587i 0.764040 + 0.441119i 0.830744 0.556654i \(-0.187915\pi\)
−0.0667045 + 0.997773i \(0.521248\pi\)
\(864\) 4.02177 + 29.1174i 0.136824 + 0.990595i
\(865\) 20.0490 + 34.7258i 0.681685 + 1.18071i
\(866\) −1.75970 + 1.65359i −0.0597969 + 0.0561913i
\(867\) 6.52539 7.94100i 0.221614 0.269691i
\(868\) −34.0680 36.6102i −1.15634 1.24263i
\(869\) −0.409620 −0.0138954
\(870\) −0.574242 8.62656i −0.0194686 0.292468i
\(871\) −9.91432 + 5.72403i −0.335934 + 0.193951i
\(872\) −14.5336 + 39.2021i −0.492171 + 1.32755i
\(873\) −4.93941 + 14.4910i −0.167174 + 0.490446i
\(874\) 37.1571 + 11.2046i 1.25686 + 0.379002i
\(875\) 6.35957 + 21.4681i 0.214993 + 0.725753i
\(876\) 1.51362 + 4.94222i 0.0511403 + 0.166982i
\(877\) 39.8660 + 23.0166i 1.34618 + 0.777216i 0.987706 0.156324i \(-0.0499644\pi\)
0.358472 + 0.933540i \(0.383298\pi\)
\(878\) 5.34111 + 22.7372i 0.180254 + 0.767342i
\(879\) −1.68815 + 10.1851i −0.0569400 + 0.343533i
\(880\) 4.21826 33.7601i 0.142198 1.13805i
\(881\) −25.6170 −0.863060 −0.431530 0.902099i \(-0.642026\pi\)
−0.431530 + 0.902099i \(0.642026\pi\)
\(882\) 25.0194 + 16.0009i 0.842447 + 0.538779i
\(883\) 54.2412i 1.82536i −0.408674 0.912680i \(-0.634009\pi\)
0.408674 0.912680i \(-0.365991\pi\)
\(884\) 7.82690 3.89194i 0.263247 0.130900i
\(885\) −7.69747 1.27584i −0.258748 0.0428869i
\(886\) 19.6120 4.60700i 0.658880 0.154775i
\(887\) 17.2509 29.8794i 0.579228 1.00325i −0.416340 0.909209i \(-0.636687\pi\)
0.995568 0.0940438i \(-0.0299794\pi\)
\(888\) 9.03650 0.0390078i 0.303245 0.00130902i
\(889\) 4.05875 1.20234i 0.136126 0.0403252i
\(890\) −12.7021 3.83029i −0.425776 0.128391i
\(891\) −3.92229 + 29.2234i −0.131402 + 0.979021i
\(892\) −23.0338 1.43344i −0.771228 0.0479952i
\(893\) 17.5614 + 30.4172i 0.587669 + 1.01787i
\(894\) 42.3816 2.82121i 1.41745 0.0943552i
\(895\) 31.5422i 1.05434i
\(896\) −19.6232 + 22.6037i −0.655566 + 0.755138i
\(897\) −6.28352 5.16338i −0.209800 0.172400i
\(898\) −2.24678 + 2.11131i −0.0749762 + 0.0704553i
\(899\) 11.1271 6.42424i 0.371110 0.214260i
\(900\) −10.3501 + 1.38408i −0.345005 + 0.0461361i
\(901\) 4.03092 6.98176i 0.134289 0.232596i
\(902\) 7.91654 26.2531i 0.263592 0.874133i
\(903\) −4.52565 36.3860i −0.150604 1.21085i
\(904\) 29.3709 + 35.4297i 0.976862 + 1.17837i
\(905\) 3.19096 + 1.84230i 0.106071 + 0.0612402i
\(906\) −13.8722 + 28.2024i −0.460872 + 0.936961i
\(907\) 11.9718 6.91190i 0.397516 0.229506i −0.287896 0.957662i \(-0.592956\pi\)
0.685412 + 0.728156i \(0.259622\pi\)
\(908\) −13.8633 27.8798i −0.460070 0.925224i
\(909\) −21.5157 + 4.25156i −0.713630 + 0.141015i
\(910\) −4.39525 7.69928i −0.145701 0.255229i
\(911\) 22.6663i 0.750969i 0.926829 + 0.375484i \(0.122524\pi\)
−0.926829 + 0.375484i \(0.877476\pi\)
\(912\) 26.8203 25.4220i 0.888108 0.841805i
\(913\) −0.699183 + 0.403674i −0.0231396 + 0.0133596i
\(914\) −44.2910 + 10.4042i −1.46502 + 0.344142i
\(915\) 39.7676 14.9389i 1.31468 0.493864i
\(916\) −5.94100 3.94137i −0.196296 0.130227i
\(917\) 23.6667 + 5.68140i 0.781543 + 0.187616i
\(918\) −24.8901 + 24.8781i −0.821497 + 0.821101i
\(919\) −6.58509 + 11.4057i −0.217222 + 0.376240i −0.953958 0.299941i \(-0.903033\pi\)
0.736736 + 0.676181i \(0.236366\pi\)
\(920\) −35.4247 13.1332i −1.16792 0.432989i
\(921\) 9.26329 + 1.53537i 0.305236 + 0.0505922i
\(922\) −14.3517 + 13.4864i −0.472649 + 0.444150i
\(923\) 0.551221i 0.0181437i
\(924\) −25.0303 + 16.5854i −0.823437 + 0.545619i
\(925\) 3.21028i 0.105553i
\(926\) 15.0920 + 16.0605i 0.495955 + 0.527779i
\(927\) 1.52940 + 1.74838i 0.0502320 + 0.0574245i
\(928\) −4.53093 6.21406i −0.148735 0.203987i
\(929\) 27.9226 48.3634i 0.916111 1.58675i 0.110844 0.993838i \(-0.464645\pi\)
0.805267 0.592912i \(-0.202022\pi\)
\(930\) −33.4418 49.9390i −1.09660 1.63756i
\(931\) −1.95547 37.2858i −0.0640881 1.22199i
\(932\) −8.43468 + 12.7140i −0.276287 + 0.416460i
\(933\) 14.8386 + 39.5006i 0.485793 + 1.29319i
\(934\) −6.20762 26.4259i −0.203120 0.864682i
\(935\) 35.2760 20.3666i 1.15365 0.666058i
\(936\) −7.23752 + 2.75451i −0.236566 + 0.0900341i
\(937\) 32.0973i 1.04857i −0.851541 0.524287i \(-0.824332\pi\)
0.851541 0.524287i \(-0.175668\pi\)
\(938\) 46.9347 + 0.228912i 1.53247 + 0.00747424i
\(939\) −21.8482 17.9534i −0.712989 0.585887i
\(940\) −15.2236 30.6154i −0.496539 0.998565i
\(941\) 24.3540 14.0608i 0.793919 0.458370i −0.0474212 0.998875i \(-0.515100\pi\)
0.841341 + 0.540505i \(0.181767\pi\)
\(942\) −18.4952 + 37.6012i −0.602607 + 1.22511i
\(943\) −26.3702 15.2249i −0.858733 0.495790i
\(944\) −6.39452 + 2.69825i −0.208124 + 0.0878204i
\(945\) 26.6358 + 23.7585i 0.866462 + 0.772864i
\(946\) 35.4928 + 10.7027i 1.15397 + 0.347976i
\(947\) −10.9973 + 19.0479i −0.357365 + 0.618974i −0.987520 0.157495i \(-0.949658\pi\)
0.630155 + 0.776469i \(0.282991\pi\)
\(948\) 0.316906 + 0.295232i 0.0102926 + 0.00958868i
\(949\) −1.17931 + 0.680874i −0.0382820 + 0.0221021i
\(950\) 8.99003 + 9.56689i 0.291675 + 0.310391i
\(951\) −21.8650 + 26.6084i −0.709021 + 0.862836i
\(952\) −35.7568 2.40035i −1.15888 0.0777956i
\(953\) 48.0977i 1.55804i −0.627001 0.779018i \(-0.715718\pi\)
0.627001 0.779018i \(-0.284282\pi\)
\(954\) −4.15789 + 5.80710i −0.134617 + 0.188012i
\(955\) −5.43234 9.40909i −0.175786 0.304471i
\(956\) −26.4978 1.64901i −0.857000 0.0533329i
\(957\) −2.71287 7.22173i −0.0876947 0.233445i
\(958\) 2.46682 8.18055i 0.0796993 0.264301i
\(959\) 5.12976 5.40584i 0.165649 0.174564i
\(960\) −27.5959 + 23.0785i −0.890655 + 0.744855i
\(961\) 29.1595 50.5057i 0.940628 1.62921i
\(962\) 0.544430 + 2.31765i 0.0175531 + 0.0747239i
\(963\) 32.8059 28.6970i 1.05716 0.924747i
\(964\) 10.2084 + 20.5296i 0.328789 + 0.661213i
\(965\) 68.4912i 2.20481i
\(966\) 11.5731 + 31.2704i 0.372360 + 1.00611i
\(967\) 11.0279 0.354635 0.177317 0.984154i \(-0.443258\pi\)
0.177317 + 0.984154i \(0.443258\pi\)
\(968\) 0.126592 + 0.743842i 0.00406882 + 0.0239080i
\(969\) 43.6473 + 7.23446i 1.40215 + 0.232404i
\(970\) −18.2406 + 4.28484i −0.585671 + 0.137578i
\(971\) −2.36459 1.36519i −0.0758832 0.0438112i 0.461578 0.887099i \(-0.347283\pi\)
−0.537461 + 0.843288i \(0.680617\pi\)
\(972\) 24.0972 19.7820i 0.772917 0.634507i
\(973\) 7.11580 2.10794i 0.228122 0.0675775i
\(974\) −9.09556 + 30.1630i −0.291441 + 0.966485i
\(975\) −0.967443 2.57535i −0.0309830 0.0824773i
\(976\) 22.8055 30.1301i 0.729987 0.964442i
\(977\) 21.7078 12.5330i 0.694494 0.400967i −0.110799 0.993843i \(-0.535341\pi\)
0.805294 + 0.592876i \(0.202008\pi\)
\(978\) −4.06517 61.0691i −0.129990 1.95277i
\(979\) −11.8381 −0.378348
\(980\) −0.354540 + 36.3454i −0.0113254 + 1.16101i
\(981\) 43.5044 8.59658i 1.38899 0.274468i
\(982\) −4.49325 4.78157i −0.143385 0.152586i
\(983\) −12.9850 22.4907i −0.414157 0.717342i 0.581182 0.813773i \(-0.302590\pi\)
−0.995340 + 0.0964318i \(0.969257\pi\)
\(984\) −25.0465 + 14.6051i −0.798454 + 0.465595i
\(985\) −28.5340 16.4741i −0.909169 0.524909i
\(986\) 2.65823 8.81530i 0.0846552 0.280736i
\(987\) −11.7469 + 27.7953i −0.373909 + 0.884734i
\(988\) 8.11276 + 5.38216i 0.258101 + 0.171229i
\(989\) 20.5832 35.6511i 0.654507 1.13364i
\(990\) −32.8640 + 14.9059i −1.04449 + 0.473740i
\(991\) −9.31944 16.1417i −0.296042 0.512759i 0.679185 0.733967i \(-0.262333\pi\)
−0.975227 + 0.221208i \(0.929000\pi\)
\(992\) −48.8770 21.6620i −1.55185 0.687769i
\(993\) 2.94056 + 2.41636i 0.0933159 + 0.0766808i
\(994\) 1.13949 1.95161i 0.0361425 0.0619014i
\(995\) 2.81676 0.0892974
\(996\) 0.831876 + 0.191628i 0.0263590 + 0.00607196i
\(997\) 12.6672 + 21.9402i 0.401173 + 0.694853i 0.993868 0.110575i \(-0.0352691\pi\)
−0.592694 + 0.805427i \(0.701936\pi\)
\(998\) −6.30883 26.8568i −0.199703 0.850137i
\(999\) −5.04600 8.14894i −0.159648 0.257821i
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 168.2.ba.c.5.17 yes 48
3.2 odd 2 inner 168.2.ba.c.5.8 yes 48
4.3 odd 2 672.2.bi.c.593.24 48
7.3 odd 6 inner 168.2.ba.c.101.2 yes 48
8.3 odd 2 672.2.bi.c.593.1 48
8.5 even 2 inner 168.2.ba.c.5.23 yes 48
12.11 even 2 672.2.bi.c.593.9 48
21.17 even 6 inner 168.2.ba.c.101.23 yes 48
24.5 odd 2 inner 168.2.ba.c.5.2 48
24.11 even 2 672.2.bi.c.593.16 48
28.3 even 6 672.2.bi.c.17.16 48
56.3 even 6 672.2.bi.c.17.9 48
56.45 odd 6 inner 168.2.ba.c.101.8 yes 48
84.59 odd 6 672.2.bi.c.17.1 48
168.59 odd 6 672.2.bi.c.17.24 48
168.101 even 6 inner 168.2.ba.c.101.17 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.2.ba.c.5.2 48 24.5 odd 2 inner
168.2.ba.c.5.8 yes 48 3.2 odd 2 inner
168.2.ba.c.5.17 yes 48 1.1 even 1 trivial
168.2.ba.c.5.23 yes 48 8.5 even 2 inner
168.2.ba.c.101.2 yes 48 7.3 odd 6 inner
168.2.ba.c.101.8 yes 48 56.45 odd 6 inner
168.2.ba.c.101.17 yes 48 168.101 even 6 inner
168.2.ba.c.101.23 yes 48 21.17 even 6 inner
672.2.bi.c.17.1 48 84.59 odd 6
672.2.bi.c.17.9 48 56.3 even 6
672.2.bi.c.17.16 48 28.3 even 6
672.2.bi.c.17.24 48 168.59 odd 6
672.2.bi.c.593.1 48 8.3 odd 2
672.2.bi.c.593.9 48 12.11 even 2
672.2.bi.c.593.16 48 24.11 even 2
672.2.bi.c.593.24 48 4.3 odd 2