Properties

Label 105.2.s.d.26.4
Level $105$
Weight $2$
Character 105.26
Analytic conductor $0.838$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,2,Mod(26,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.s (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: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.856615824.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 26.4
Root \(2.33086i\) of defining polynomial
Character \(\chi\) \(=\) 105.26
Dual form 105.2.s.d.101.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.01859 + 1.16543i) q^{2} +(-1.67602 + 0.437000i) q^{3} +(1.71646 + 2.97300i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.89248 - 1.07116i) q^{6} +(1.11699 - 2.39840i) q^{7} +3.33995i q^{8} +(2.61806 - 1.46484i) q^{9} +O(q^{10})\) \(q+(2.01859 + 1.16543i) q^{2} +(-1.67602 + 0.437000i) q^{3} +(1.71646 + 2.97300i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.89248 - 1.07116i) q^{6} +(1.11699 - 2.39840i) q^{7} +3.33995i q^{8} +(2.61806 - 1.46484i) q^{9} +(-2.01859 + 1.16543i) q^{10} +(-2.42019 + 1.39730i) q^{11} +(-4.17602 - 4.23270i) q^{12} -3.20486i q^{13} +(5.04991 - 3.53962i) q^{14} +(0.459555 - 1.66997i) q^{15} +(-0.459555 + 0.795973i) q^{16} +(0.440969 + 0.763780i) q^{17} +(6.99195 + 0.0942709i) q^{18} +(1.90160 + 1.09789i) q^{19} -3.43292 q^{20} +(-0.823984 + 4.50789i) q^{21} -6.51381 q^{22} +(-6.53240 - 3.77148i) q^{23} +(-1.45956 - 5.59780i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.73505 - 6.46929i) q^{26} +(-3.74778 + 3.59918i) q^{27} +(9.04771 - 0.795973i) q^{28} +8.15270i q^{29} +(2.87389 - 2.83540i) q^{30} +(-7.62645 + 4.40313i) q^{31} +(3.92965 - 2.26878i) q^{32} +(3.44566 - 3.39951i) q^{33} +2.05568i q^{34} +(1.51859 + 2.16654i) q^{35} +(8.84876 + 5.26916i) q^{36} +(-0.203727 + 0.352865i) q^{37} +(2.55903 + 4.43237i) q^{38} +(1.40052 + 5.37140i) q^{39} +(-2.89248 - 1.66997i) q^{40} +8.55098 q^{41} +(-6.91692 + 8.13927i) q^{42} -0.118062 q^{43} +(-8.30832 - 4.79681i) q^{44} +(-0.0404447 + 2.99973i) q^{45} +(-8.79081 - 15.2261i) q^{46} +(1.31486 - 2.27740i) q^{47} +(0.422382 - 1.53489i) q^{48} +(-4.50469 - 5.35796i) q^{49} -2.33086i q^{50} +(-1.07284 - 1.08741i) q^{51} +(9.52805 - 5.50102i) q^{52} +(-6.46794 + 3.73427i) q^{53} +(-11.7598 + 2.89748i) q^{54} -2.79459i q^{55} +(8.01054 + 3.73067i) q^{56} +(-3.66689 - 1.00908i) q^{57} +(-9.50142 + 16.4569i) q^{58} +(-2.04991 - 3.55054i) q^{59} +(5.75363 - 1.50019i) q^{60} +(10.7004 + 6.17786i) q^{61} -20.5262 q^{62} +(-0.588936 - 7.91537i) q^{63} +12.4147 q^{64} +(2.77549 + 1.60243i) q^{65} +(10.9173 - 2.84653i) q^{66} +(0.802125 + 1.38932i) q^{67} +(-1.51381 + 2.62200i) q^{68} +(12.5965 + 3.46641i) q^{69} +(0.540445 + 6.14316i) q^{70} -6.25869i q^{71} +(4.89248 + 8.74419i) q^{72} +(0.192022 - 0.110864i) q^{73} +(-0.822480 + 0.474859i) q^{74} +(1.21646 + 1.23297i) q^{75} +7.53794i q^{76} +(0.647967 + 7.36535i) q^{77} +(-3.43292 + 12.4749i) q^{78} +(1.56849 - 2.71671i) q^{79} +(-0.459555 - 0.795973i) q^{80} +(4.70850 - 7.67007i) q^{81} +(17.2609 + 9.96559i) q^{82} +0.666893 q^{83} +(-14.8163 + 5.28791i) q^{84} -0.881938 q^{85} +(-0.238319 - 0.137594i) q^{86} +(-3.56273 - 13.6641i) q^{87} +(-4.66689 - 8.08330i) q^{88} +(0.437271 - 0.757376i) q^{89} +(-3.57762 + 6.00807i) q^{90} +(-7.68656 - 3.57978i) q^{91} -25.8944i q^{92} +(10.8579 - 10.7125i) q^{93} +(5.30832 - 3.06476i) q^{94} +(-1.90160 + 1.09789i) q^{95} +(-5.59470 + 5.51978i) q^{96} +6.37221i q^{97} +(-2.84876 - 16.0654i) q^{98} +(-4.28939 + 7.20339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 3 q^{2} + 2 q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} + 2 q^{7} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 3 q^{2} + 2 q^{3} + 3 q^{4} - 4 q^{5} - 5 q^{6} + 2 q^{7} + 4 q^{9} - 3 q^{10} - 18 q^{12} + 12 q^{14} - q^{15} + q^{16} + 12 q^{17} + 26 q^{18} + 9 q^{19} - 6 q^{20} - 22 q^{21} - 40 q^{22} - 27 q^{23} - 7 q^{24} - 4 q^{25} + 6 q^{26} - 4 q^{27} + 3 q^{28} + 10 q^{30} - 21 q^{31} - 21 q^{32} + 4 q^{33} - q^{35} + 9 q^{36} + 7 q^{37} + 12 q^{38} + 15 q^{39} + 3 q^{40} + 30 q^{41} - 5 q^{42} + 16 q^{43} - 5 q^{45} - 7 q^{46} + 6 q^{47} + 25 q^{48} - 4 q^{49} + 12 q^{51} + 30 q^{52} - 24 q^{53} + 7 q^{54} + 21 q^{56} + 6 q^{57} - 13 q^{58} + 12 q^{59} + 9 q^{60} + 15 q^{61} - 24 q^{62} - 44 q^{63} + 38 q^{64} + 3 q^{65} - 16 q^{66} + 4 q^{67} + 13 q^{69} + 9 q^{70} + 13 q^{72} + 15 q^{73} - 54 q^{74} - q^{75} + 36 q^{77} - 6 q^{78} - 29 q^{79} + q^{80} + 28 q^{81} + 27 q^{82} - 30 q^{83} - 51 q^{84} - 24 q^{85} - 9 q^{86} - 29 q^{87} - 2 q^{88} + 3 q^{89} - 7 q^{90} - 3 q^{91} + 45 q^{93} - 24 q^{94} - 9 q^{95} - 42 q^{96} + 39 q^{98} - 34 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.01859 + 1.16543i 1.42736 + 0.824085i 0.996912 0.0785324i \(-0.0250234\pi\)
0.430445 + 0.902617i \(0.358357\pi\)
\(3\) −1.67602 + 0.437000i −0.967649 + 0.252302i
\(4\) 1.71646 + 2.97300i 0.858231 + 1.48650i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −3.89248 1.07116i −1.58910 0.437299i
\(7\) 1.11699 2.39840i 0.422181 0.906512i
\(8\) 3.33995i 1.18085i
\(9\) 2.61806 1.46484i 0.872687 0.488279i
\(10\) −2.01859 + 1.16543i −0.638333 + 0.368542i
\(11\) −2.42019 + 1.39730i −0.729714 + 0.421301i −0.818318 0.574766i \(-0.805093\pi\)
0.0886035 + 0.996067i \(0.471760\pi\)
\(12\) −4.17602 4.23270i −1.20551 1.22188i
\(13\) 3.20486i 0.888869i −0.895811 0.444434i \(-0.853405\pi\)
0.895811 0.444434i \(-0.146595\pi\)
\(14\) 5.04991 3.53962i 1.34964 0.946002i
\(15\) 0.459555 1.66997i 0.118657 0.431185i
\(16\) −0.459555 + 0.795973i −0.114889 + 0.198993i
\(17\) 0.440969 + 0.763780i 0.106951 + 0.185244i 0.914533 0.404510i \(-0.132558\pi\)
−0.807583 + 0.589754i \(0.799225\pi\)
\(18\) 6.99195 + 0.0942709i 1.64802 + 0.0222199i
\(19\) 1.90160 + 1.09789i 0.436257 + 0.251873i 0.702009 0.712168i \(-0.252287\pi\)
−0.265751 + 0.964042i \(0.585620\pi\)
\(20\) −3.43292 −0.767625
\(21\) −0.823984 + 4.50789i −0.179808 + 0.983702i
\(22\) −6.51381 −1.38875
\(23\) −6.53240 3.77148i −1.36210 0.786408i −0.372196 0.928154i \(-0.621395\pi\)
−0.989903 + 0.141746i \(0.954728\pi\)
\(24\) −1.45956 5.59780i −0.297930 1.14265i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 3.73505 6.46929i 0.732503 1.26873i
\(27\) −3.74778 + 3.59918i −0.721261 + 0.692663i
\(28\) 9.04771 0.795973i 1.70986 0.150425i
\(29\) 8.15270i 1.51392i 0.653462 + 0.756959i \(0.273316\pi\)
−0.653462 + 0.756959i \(0.726684\pi\)
\(30\) 2.87389 2.83540i 0.524698 0.517672i
\(31\) −7.62645 + 4.40313i −1.36975 + 0.790826i −0.990896 0.134630i \(-0.957015\pi\)
−0.378855 + 0.925456i \(0.623682\pi\)
\(32\) 3.92965 2.26878i 0.694671 0.401068i
\(33\) 3.44566 3.39951i 0.599812 0.591779i
\(34\) 2.05568i 0.352545i
\(35\) 1.51859 + 2.16654i 0.256688 + 0.366212i
\(36\) 8.84876 + 5.26916i 1.47479 + 0.878193i
\(37\) −0.203727 + 0.352865i −0.0334925 + 0.0580107i −0.882286 0.470714i \(-0.843996\pi\)
0.848793 + 0.528725i \(0.177330\pi\)
\(38\) 2.55903 + 4.43237i 0.415130 + 0.719026i
\(39\) 1.40052 + 5.37140i 0.224263 + 0.860113i
\(40\) −2.89248 1.66997i −0.457341 0.264046i
\(41\) 8.55098 1.33544 0.667720 0.744413i \(-0.267270\pi\)
0.667720 + 0.744413i \(0.267270\pi\)
\(42\) −6.91692 + 8.13927i −1.06730 + 1.25592i
\(43\) −0.118062 −0.0180044 −0.00900218 0.999959i \(-0.502866\pi\)
−0.00900218 + 0.999959i \(0.502866\pi\)
\(44\) −8.30832 4.79681i −1.25253 0.723146i
\(45\) −0.0404447 + 2.99973i −0.00602913 + 0.447173i
\(46\) −8.79081 15.2261i −1.29613 2.24497i
\(47\) 1.31486 2.27740i 0.191792 0.332194i −0.754052 0.656815i \(-0.771903\pi\)
0.945844 + 0.324621i \(0.105237\pi\)
\(48\) 0.422382 1.53489i 0.0609656 0.221542i
\(49\) −4.50469 5.35796i −0.643527 0.765424i
\(50\) 2.33086i 0.329634i
\(51\) −1.07284 1.08741i −0.150228 0.152267i
\(52\) 9.52805 5.50102i 1.32130 0.762854i
\(53\) −6.46794 + 3.73427i −0.888440 + 0.512941i −0.873432 0.486946i \(-0.838111\pi\)
−0.0150081 + 0.999887i \(0.504777\pi\)
\(54\) −11.7598 + 2.89748i −1.60031 + 0.394297i
\(55\) 2.79459i 0.376823i
\(56\) 8.01054 + 3.73067i 1.07045 + 0.498532i
\(57\) −3.66689 1.00908i −0.485692 0.133656i
\(58\) −9.50142 + 16.4569i −1.24760 + 2.16090i
\(59\) −2.04991 3.55054i −0.266875 0.462241i 0.701178 0.712986i \(-0.252658\pi\)
−0.968053 + 0.250745i \(0.919324\pi\)
\(60\) 5.75363 1.50019i 0.742791 0.193673i
\(61\) 10.7004 + 6.17786i 1.37004 + 0.790994i 0.990933 0.134358i \(-0.0428972\pi\)
0.379109 + 0.925352i \(0.376231\pi\)
\(62\) −20.5262 −2.60683
\(63\) −0.588936 7.91537i −0.0741989 0.997243i
\(64\) 12.4147 1.55183
\(65\) 2.77549 + 1.60243i 0.344257 + 0.198757i
\(66\) 10.9173 2.84653i 1.34382 0.350384i
\(67\) 0.802125 + 1.38932i 0.0979952 + 0.169733i 0.910855 0.412727i \(-0.135424\pi\)
−0.812860 + 0.582460i \(0.802090\pi\)
\(68\) −1.51381 + 2.62200i −0.183577 + 0.317964i
\(69\) 12.5965 + 3.46641i 1.51645 + 0.417307i
\(70\) 0.540445 + 6.14316i 0.0645955 + 0.734248i
\(71\) 6.25869i 0.742770i −0.928479 0.371385i \(-0.878883\pi\)
0.928479 0.371385i \(-0.121117\pi\)
\(72\) 4.89248 + 8.74419i 0.576584 + 1.03051i
\(73\) 0.192022 0.110864i 0.0224745 0.0129757i −0.488721 0.872440i \(-0.662536\pi\)
0.511195 + 0.859465i \(0.329203\pi\)
\(74\) −0.822480 + 0.474859i −0.0956114 + 0.0552012i
\(75\) 1.21646 + 1.23297i 0.140465 + 0.142371i
\(76\) 7.53794i 0.864661i
\(77\) 0.647967 + 7.36535i 0.0738427 + 0.839359i
\(78\) −3.43292 + 12.4749i −0.388702 + 1.41250i
\(79\) 1.56849 2.71671i 0.176469 0.305654i −0.764199 0.644980i \(-0.776866\pi\)
0.940669 + 0.339326i \(0.110199\pi\)
\(80\) −0.459555 0.795973i −0.0513798 0.0889925i
\(81\) 4.70850 7.67007i 0.523167 0.852230i
\(82\) 17.2609 + 9.96559i 1.90615 + 1.10051i
\(83\) 0.666893 0.0732010 0.0366005 0.999330i \(-0.488347\pi\)
0.0366005 + 0.999330i \(0.488347\pi\)
\(84\) −14.8163 + 5.28791i −1.61659 + 0.576959i
\(85\) −0.881938 −0.0956596
\(86\) −0.238319 0.137594i −0.0256986 0.0148371i
\(87\) −3.56273 13.6641i −0.381965 1.46494i
\(88\) −4.66689 8.08330i −0.497492 0.861682i
\(89\) 0.437271 0.757376i 0.0463506 0.0802816i −0.841919 0.539603i \(-0.818574\pi\)
0.888270 + 0.459322i \(0.151908\pi\)
\(90\) −3.57762 + 6.00807i −0.377114 + 0.633307i
\(91\) −7.68656 3.57978i −0.805770 0.375263i
\(92\) 25.8944i 2.69968i
\(93\) 10.8579 10.7125i 1.12591 1.11083i
\(94\) 5.30832 3.06476i 0.547511 0.316106i
\(95\) −1.90160 + 1.09789i −0.195100 + 0.112641i
\(96\) −5.59470 + 5.51978i −0.571007 + 0.563360i
\(97\) 6.37221i 0.647000i 0.946228 + 0.323500i \(0.104860\pi\)
−0.946228 + 0.323500i \(0.895140\pi\)
\(98\) −2.84876 16.0654i −0.287768 1.62285i
\(99\) −4.28939 + 7.20339i −0.431100 + 0.723968i
\(100\) 1.71646 2.97300i 0.171646 0.297300i
\(101\) −5.31267 9.20181i −0.528630 0.915614i −0.999443 0.0333808i \(-0.989373\pi\)
0.470813 0.882233i \(-0.343961\pi\)
\(102\) −0.898330 3.44535i −0.0889479 0.341140i
\(103\) −0.868777 0.501589i −0.0856031 0.0494230i 0.456587 0.889679i \(-0.349072\pi\)
−0.542191 + 0.840256i \(0.682405\pi\)
\(104\) 10.7041 1.04962
\(105\) −3.49195 2.96753i −0.340780 0.289602i
\(106\) −17.4081 −1.69083
\(107\) 11.0651 + 6.38846i 1.06971 + 0.617596i 0.928101 0.372328i \(-0.121440\pi\)
0.141606 + 0.989923i \(0.454774\pi\)
\(108\) −17.1333 4.96429i −1.64865 0.477689i
\(109\) −0.00912370 0.0158027i −0.000873892 0.00151363i 0.865588 0.500757i \(-0.166945\pi\)
−0.866462 + 0.499243i \(0.833612\pi\)
\(110\) 3.25691 5.64113i 0.310534 0.537860i
\(111\) 0.187247 0.680436i 0.0177727 0.0645841i
\(112\) 1.39575 + 1.99129i 0.131886 + 0.188159i
\(113\) 7.23027i 0.680166i −0.940395 0.340083i \(-0.889545\pi\)
0.940395 0.340083i \(-0.110455\pi\)
\(114\) −6.22592 6.31043i −0.583111 0.591026i
\(115\) 6.53240 3.77148i 0.609149 0.351692i
\(116\) −24.2380 + 13.9938i −2.25044 + 1.29929i
\(117\) −4.69460 8.39053i −0.434016 0.775705i
\(118\) 9.55611i 0.879711i
\(119\) 2.32441 0.204490i 0.213078 0.0187456i
\(120\) 5.57762 + 1.53489i 0.509165 + 0.140116i
\(121\) −1.59513 + 2.76284i −0.145012 + 0.251167i
\(122\) 14.3997 + 24.9411i 1.30369 + 2.25806i
\(123\) −14.3316 + 3.73678i −1.29224 + 0.336934i
\(124\) −26.1810 15.1156i −2.35112 1.35742i
\(125\) 1.00000 0.0894427
\(126\) 8.03601 16.6642i 0.715905 1.48457i
\(127\) 6.99561 0.620760 0.310380 0.950613i \(-0.399544\pi\)
0.310380 + 0.950613i \(0.399544\pi\)
\(128\) 17.2008 + 9.93088i 1.52035 + 0.877774i
\(129\) 0.197875 0.0515933i 0.0174219 0.00454253i
\(130\) 3.73505 + 6.46929i 0.327585 + 0.567394i
\(131\) −4.94673 + 8.56799i −0.432198 + 0.748589i −0.997062 0.0765948i \(-0.975595\pi\)
0.564864 + 0.825184i \(0.308929\pi\)
\(132\) 16.0211 + 4.40880i 1.39446 + 0.383737i
\(133\) 4.75724 3.33448i 0.412505 0.289136i
\(134\) 3.73929i 0.323025i
\(135\) −1.24309 5.04527i −0.106989 0.434227i
\(136\) −2.55098 + 1.47281i −0.218745 + 0.126293i
\(137\) 10.9111 6.29951i 0.932195 0.538203i 0.0446900 0.999001i \(-0.485770\pi\)
0.887505 + 0.460798i \(0.152437\pi\)
\(138\) 21.3874 + 21.6777i 1.82061 + 1.84532i
\(139\) 0.988113i 0.0838106i −0.999122 0.0419053i \(-0.986657\pi\)
0.999122 0.0419053i \(-0.0133428\pi\)
\(140\) −3.83452 + 8.23354i −0.324076 + 0.695861i
\(141\) −1.20850 + 4.39156i −0.101774 + 0.369836i
\(142\) 7.29408 12.6337i 0.612106 1.06020i
\(143\) 4.47814 + 7.75637i 0.374481 + 0.648620i
\(144\) −0.0371731 + 2.75708i −0.00309776 + 0.229757i
\(145\) −7.06045 4.07635i −0.586338 0.338523i
\(146\) 0.516818 0.0427722
\(147\) 9.89136 + 7.01149i 0.815826 + 0.578298i
\(148\) −1.39876 −0.114977
\(149\) −15.3604 8.86834i −1.25837 0.726523i −0.285616 0.958344i \(-0.592198\pi\)
−0.972758 + 0.231821i \(0.925532\pi\)
\(150\) 1.01859 + 3.90656i 0.0831672 + 0.318970i
\(151\) 11.2504 + 19.4862i 0.915542 + 1.58576i 0.806106 + 0.591771i \(0.201571\pi\)
0.109435 + 0.993994i \(0.465096\pi\)
\(152\) −3.66689 + 6.35124i −0.297424 + 0.515154i
\(153\) 2.27330 + 1.35368i 0.183785 + 0.109438i
\(154\) −7.27583 + 15.6228i −0.586303 + 1.25892i
\(155\) 8.80626i 0.707336i
\(156\) −13.5652 + 13.3836i −1.08609 + 1.07154i
\(157\) −10.2988 + 5.94600i −0.821931 + 0.474542i −0.851082 0.525033i \(-0.824053\pi\)
0.0291509 + 0.999575i \(0.490720\pi\)
\(158\) 6.33228 3.65594i 0.503769 0.290851i
\(159\) 9.20850 9.08518i 0.730282 0.720502i
\(160\) 4.53757i 0.358726i
\(161\) −16.3421 + 11.4546i −1.28794 + 0.902752i
\(162\) 18.4435 9.99527i 1.44906 0.785302i
\(163\) −4.26159 + 7.38130i −0.333794 + 0.578148i −0.983252 0.182249i \(-0.941662\pi\)
0.649459 + 0.760397i \(0.274996\pi\)
\(164\) 14.6774 + 25.4221i 1.14611 + 1.98513i
\(165\) 1.22124 + 4.68378i 0.0950731 + 0.364632i
\(166\) 1.34618 + 0.777218i 0.104484 + 0.0603238i
\(167\) −3.56923 −0.276195 −0.138098 0.990419i \(-0.544099\pi\)
−0.138098 + 0.990419i \(0.544099\pi\)
\(168\) −15.0561 2.75206i −1.16160 0.212326i
\(169\) 2.72886 0.209912
\(170\) −1.78027 1.02784i −0.136540 0.0788316i
\(171\) 6.58674 + 0.0888076i 0.503701 + 0.00679128i
\(172\) −0.202650 0.350999i −0.0154519 0.0267634i
\(173\) 4.27114 7.39784i 0.324729 0.562447i −0.656728 0.754127i \(-0.728060\pi\)
0.981457 + 0.191680i \(0.0613936\pi\)
\(174\) 8.73285 31.7342i 0.662036 2.40576i
\(175\) −2.63557 + 0.231865i −0.199231 + 0.0175273i
\(176\) 2.56854i 0.193611i
\(177\) 4.98727 + 5.05496i 0.374866 + 0.379954i
\(178\) 1.76534 1.01922i 0.132318 0.0763937i
\(179\) −1.06480 + 0.614760i −0.0795866 + 0.0459493i −0.539265 0.842136i \(-0.681298\pi\)
0.459679 + 0.888085i \(0.347965\pi\)
\(180\) −8.98760 + 5.02867i −0.669897 + 0.374815i
\(181\) 15.3995i 1.14464i −0.820032 0.572318i \(-0.806044\pi\)
0.820032 0.572318i \(-0.193956\pi\)
\(182\) −11.3440 16.1843i −0.840872 1.19966i
\(183\) −20.6337 5.67814i −1.52529 0.419740i
\(184\) 12.5965 21.8179i 0.928630 1.60843i
\(185\) −0.203727 0.352865i −0.0149783 0.0259432i
\(186\) 34.4022 8.96994i 2.52249 0.657708i
\(187\) −2.13445 1.23233i −0.156087 0.0901167i
\(188\) 9.02762 0.658407
\(189\) 4.44608 + 13.0089i 0.323405 + 0.946261i
\(190\) −5.11806 −0.371303
\(191\) 12.5795 + 7.26275i 0.910218 + 0.525514i 0.880501 0.474044i \(-0.157206\pi\)
0.0297166 + 0.999558i \(0.490540\pi\)
\(192\) −20.8072 + 5.42521i −1.50163 + 0.391531i
\(193\) 0.201572 + 0.349134i 0.0145095 + 0.0251312i 0.873189 0.487382i \(-0.162048\pi\)
−0.858679 + 0.512513i \(0.828715\pi\)
\(194\) −7.42638 + 12.8629i −0.533183 + 0.923500i
\(195\) −5.35203 1.47281i −0.383267 0.105470i
\(196\) 8.19710 22.5892i 0.585507 1.61351i
\(197\) 11.6716i 0.831564i 0.909464 + 0.415782i \(0.136492\pi\)
−0.909464 + 0.415782i \(0.863508\pi\)
\(198\) −17.0536 + 9.54168i −1.21194 + 0.678097i
\(199\) −16.0886 + 9.28875i −1.14049 + 0.658462i −0.946552 0.322552i \(-0.895459\pi\)
−0.193938 + 0.981014i \(0.562126\pi\)
\(200\) 2.89248 1.66997i 0.204529 0.118085i
\(201\) −1.95151 1.97800i −0.137649 0.139517i
\(202\) 24.7662i 1.74254i
\(203\) 19.5535 + 9.10645i 1.37239 + 0.639147i
\(204\) 1.39136 5.05605i 0.0974147 0.353994i
\(205\) −4.27549 + 7.40537i −0.298613 + 0.517213i
\(206\) −1.16913 2.02500i −0.0814574 0.141088i
\(207\) −22.6268 0.305073i −1.57267 0.0212040i
\(208\) 2.55098 + 1.47281i 0.176879 + 0.102121i
\(209\) −6.13631 −0.424457
\(210\) −3.59035 10.0599i −0.247758 0.694196i
\(211\) 6.98175 0.480644 0.240322 0.970693i \(-0.422747\pi\)
0.240322 + 0.970693i \(0.422747\pi\)
\(212\) −22.2039 12.8194i −1.52497 0.880443i
\(213\) 2.73505 + 10.4897i 0.187402 + 0.718741i
\(214\) 14.8906 + 25.7913i 1.01790 + 1.76306i
\(215\) 0.0590312 0.102245i 0.00402590 0.00697306i
\(216\) −12.0211 12.5174i −0.817931 0.851700i
\(217\) 2.04186 + 23.2095i 0.138611 + 1.57557i
\(218\) 0.0425322i 0.00288064i
\(219\) −0.273385 + 0.269724i −0.0184737 + 0.0182263i
\(220\) 8.30832 4.79681i 0.560147 0.323401i
\(221\) 2.44781 1.41324i 0.164658 0.0950651i
\(222\) 1.17098 1.15530i 0.0785908 0.0775383i
\(223\) 1.44594i 0.0968271i 0.998827 + 0.0484135i \(0.0154165\pi\)
−0.998827 + 0.0484135i \(0.984583\pi\)
\(224\) −1.05210 11.9591i −0.0702965 0.799050i
\(225\) −2.57762 1.53489i −0.171841 0.102326i
\(226\) 8.42638 14.5949i 0.560514 0.970839i
\(227\) 0.533562 + 0.924157i 0.0354138 + 0.0613385i 0.883189 0.469017i \(-0.155392\pi\)
−0.847775 + 0.530356i \(0.822058\pi\)
\(228\) −3.29408 12.6337i −0.218156 0.836688i
\(229\) −6.58058 3.79930i −0.434857 0.251065i 0.266557 0.963819i \(-0.414114\pi\)
−0.701414 + 0.712755i \(0.747447\pi\)
\(230\) 17.5816 1.15930
\(231\) −4.30466 12.0613i −0.283226 0.793574i
\(232\) −27.2296 −1.78771
\(233\) −15.5882 8.99983i −1.02121 0.589598i −0.106759 0.994285i \(-0.534047\pi\)
−0.914455 + 0.404687i \(0.867381\pi\)
\(234\) 0.302125 22.4082i 0.0197506 1.46487i
\(235\) 1.31486 + 2.27740i 0.0857720 + 0.148561i
\(236\) 7.03717 12.1887i 0.458081 0.793419i
\(237\) −1.44162 + 5.23868i −0.0936433 + 0.340289i
\(238\) 4.93034 + 2.29616i 0.319587 + 0.148838i
\(239\) 29.8816i 1.93288i −0.256892 0.966440i \(-0.582698\pi\)
0.256892 0.966440i \(-0.417302\pi\)
\(240\) 1.11806 + 1.13324i 0.0721706 + 0.0731502i
\(241\) 4.53760 2.61978i 0.292292 0.168755i −0.346683 0.937982i \(-0.612692\pi\)
0.638975 + 0.769227i \(0.279359\pi\)
\(242\) −6.43980 + 3.71802i −0.413966 + 0.239004i
\(243\) −4.53971 + 14.9128i −0.291222 + 0.956655i
\(244\) 42.4162i 2.71542i
\(245\) 6.89248 1.22219i 0.440344 0.0780830i
\(246\) −33.2845 9.15948i −2.12214 0.583987i
\(247\) 3.51859 6.09437i 0.223882 0.387776i
\(248\) −14.7062 25.4719i −0.933846 1.61747i
\(249\) −1.11772 + 0.291432i −0.0708328 + 0.0184688i
\(250\) 2.01859 + 1.16543i 0.127667 + 0.0737084i
\(251\) 15.0765 0.951620 0.475810 0.879548i \(-0.342155\pi\)
0.475810 + 0.879548i \(0.342155\pi\)
\(252\) 22.5215 15.3373i 1.41872 0.966161i
\(253\) 21.0795 1.32526
\(254\) 14.1212 + 8.15291i 0.886046 + 0.511559i
\(255\) 1.47814 0.385407i 0.0925648 0.0241351i
\(256\) 10.7329 + 18.5898i 0.670803 + 1.16187i
\(257\) −7.95478 + 13.7781i −0.496206 + 0.859453i −0.999990 0.00437591i \(-0.998607\pi\)
0.503785 + 0.863829i \(0.331940\pi\)
\(258\) 0.459555 + 0.126464i 0.0286107 + 0.00787329i
\(259\) 0.618753 + 0.882764i 0.0384475 + 0.0548523i
\(260\) 11.0020i 0.682318i
\(261\) 11.9424 + 21.3443i 0.739215 + 1.32118i
\(262\) −19.9708 + 11.5302i −1.23380 + 0.712336i
\(263\) −7.19124 + 4.15187i −0.443431 + 0.256015i −0.705052 0.709156i \(-0.749076\pi\)
0.261621 + 0.965171i \(0.415743\pi\)
\(264\) 11.3542 + 11.5083i 0.698802 + 0.708287i
\(265\) 7.46853i 0.458788i
\(266\) 13.4890 1.18670i 0.827065 0.0727611i
\(267\) −0.401900 + 1.46046i −0.0245959 + 0.0893788i
\(268\) −2.75363 + 4.76943i −0.168205 + 0.291340i
\(269\) −8.69353 15.0576i −0.530054 0.918080i −0.999385 0.0350578i \(-0.988838\pi\)
0.469332 0.883022i \(-0.344495\pi\)
\(270\) 3.37062 11.6330i 0.205129 0.707965i
\(271\) −8.82614 5.09577i −0.536150 0.309546i 0.207367 0.978263i \(-0.433510\pi\)
−0.743517 + 0.668717i \(0.766844\pi\)
\(272\) −0.810598 −0.0491497
\(273\) 14.4472 + 2.64075i 0.874382 + 0.159826i
\(274\) 29.3666 1.77410
\(275\) 2.42019 + 1.39730i 0.145943 + 0.0842601i
\(276\) 11.3158 + 43.3995i 0.681134 + 2.61234i
\(277\) −4.78018 8.27951i −0.287213 0.497468i 0.685930 0.727667i \(-0.259395\pi\)
−0.973143 + 0.230199i \(0.926062\pi\)
\(278\) 1.15158 1.99459i 0.0690670 0.119628i
\(279\) −13.5166 + 22.6992i −0.809220 + 1.35896i
\(280\) −7.23612 + 5.07200i −0.432441 + 0.303110i
\(281\) 11.9239i 0.711320i 0.934616 + 0.355660i \(0.115744\pi\)
−0.934616 + 0.355660i \(0.884256\pi\)
\(282\) −7.55753 + 7.45632i −0.450044 + 0.444017i
\(283\) 17.2940 9.98469i 1.02802 0.593528i 0.111604 0.993753i \(-0.464401\pi\)
0.916417 + 0.400225i \(0.131068\pi\)
\(284\) 18.6071 10.7428i 1.10413 0.637468i
\(285\) 2.70734 2.67108i 0.160369 0.158221i
\(286\) 20.8759i 1.23442i
\(287\) 9.55132 20.5087i 0.563797 1.21059i
\(288\) 6.96467 11.6961i 0.410397 0.689201i
\(289\) 8.11109 14.0488i 0.477123 0.826401i
\(290\) −9.50142 16.4569i −0.557942 0.966385i
\(291\) −2.78466 10.6799i −0.163239 0.626069i
\(292\) 0.659198 + 0.380588i 0.0385766 + 0.0222722i
\(293\) −3.01023 −0.175859 −0.0879297 0.996127i \(-0.528025\pi\)
−0.0879297 + 0.996127i \(0.528025\pi\)
\(294\) 11.7952 + 25.6810i 0.687907 + 1.49775i
\(295\) 4.09982 0.238700
\(296\) −1.17855 0.680436i −0.0685018 0.0395495i
\(297\) 4.04121 13.9475i 0.234495 0.809314i
\(298\) −20.6709 35.8030i −1.19743 2.07401i
\(299\) −12.0871 + 20.9354i −0.699014 + 1.21073i
\(300\) −1.57762 + 5.73289i −0.0910838 + 0.330988i
\(301\) −0.131874 + 0.283161i −0.00760109 + 0.0163212i
\(302\) 52.4461i 3.01793i
\(303\) 12.9253 + 13.1007i 0.742539 + 0.752618i
\(304\) −1.74778 + 1.00908i −0.100242 + 0.0578748i
\(305\) −10.7004 + 6.17786i −0.612701 + 0.353743i
\(306\) 3.01123 + 5.38189i 0.172141 + 0.307662i
\(307\) 20.3794i 1.16311i −0.813507 0.581556i \(-0.802444\pi\)
0.813507 0.581556i \(-0.197556\pi\)
\(308\) −20.7850 + 14.5687i −1.18433 + 0.830131i
\(309\) 1.67528 + 0.461015i 0.0953033 + 0.0262263i
\(310\) 10.2631 17.7762i 0.582905 1.00962i
\(311\) −13.6359 23.6181i −0.773222 1.33926i −0.935789 0.352562i \(-0.885311\pi\)
0.162567 0.986697i \(-0.448023\pi\)
\(312\) −17.9402 + 4.67767i −1.01566 + 0.264821i
\(313\) 0.546210 + 0.315354i 0.0308736 + 0.0178249i 0.515357 0.856975i \(-0.327659\pi\)
−0.484484 + 0.874800i \(0.660993\pi\)
\(314\) −27.7186 −1.56425
\(315\) 7.14938 + 3.44765i 0.402822 + 0.194253i
\(316\) 10.7690 0.605806
\(317\) −22.0233 12.7151i −1.23695 0.714153i −0.268480 0.963285i \(-0.586521\pi\)
−0.968470 + 0.249132i \(0.919855\pi\)
\(318\) 29.1763 7.60735i 1.63613 0.426599i
\(319\) −11.3917 19.7311i −0.637815 1.10473i
\(320\) −6.20734 + 10.7514i −0.347001 + 0.601023i
\(321\) −21.3371 5.87170i −1.19092 0.327726i
\(322\) −46.3376 + 4.07655i −2.58229 + 0.227177i
\(323\) 1.93654i 0.107752i
\(324\) 30.8851 + 0.832984i 1.71584 + 0.0462769i
\(325\) −2.77549 + 1.60243i −0.153957 + 0.0888869i
\(326\) −17.2048 + 9.93319i −0.952885 + 0.550149i
\(327\) 0.0221973 + 0.0224986i 0.00122751 + 0.00124417i
\(328\) 28.5598i 1.57695i
\(329\) −3.99346 5.69739i −0.220166 0.314107i
\(330\) −2.99346 + 10.8779i −0.164784 + 0.598808i
\(331\) −5.74666 + 9.95352i −0.315865 + 0.547095i −0.979621 0.200855i \(-0.935628\pi\)
0.663756 + 0.747949i \(0.268961\pi\)
\(332\) 1.14470 + 1.98267i 0.0628233 + 0.108813i
\(333\) −0.0164793 + 1.22225i −0.000903061 + 0.0669788i
\(334\) −7.20480 4.15970i −0.394229 0.227608i
\(335\) −1.60425 −0.0876496
\(336\) −3.20949 2.72749i −0.175092 0.148797i
\(337\) −16.2041 −0.882694 −0.441347 0.897336i \(-0.645499\pi\)
−0.441347 + 0.897336i \(0.645499\pi\)
\(338\) 5.50843 + 3.18030i 0.299619 + 0.172985i
\(339\) 3.15962 + 12.1180i 0.171607 + 0.658162i
\(340\) −1.51381 2.62200i −0.0820980 0.142198i
\(341\) 12.3050 21.3128i 0.666351 1.15415i
\(342\) 13.1924 + 7.85566i 0.713364 + 0.424786i
\(343\) −17.8822 + 4.81930i −0.965550 + 0.260218i
\(344\) 0.394322i 0.0212604i
\(345\) −9.30027 + 9.17572i −0.500710 + 0.494004i
\(346\) 17.2433 9.95545i 0.927008 0.535208i
\(347\) 15.5732 8.99121i 0.836015 0.482673i −0.0198929 0.999802i \(-0.506333\pi\)
0.855908 + 0.517129i \(0.172999\pi\)
\(348\) 34.5079 34.0458i 1.84982 1.82505i
\(349\) 6.15422i 0.329428i −0.986341 0.164714i \(-0.947330\pi\)
0.986341 0.164714i \(-0.0526701\pi\)
\(350\) −5.59035 2.60354i −0.298817 0.139165i
\(351\) 11.5349 + 12.0111i 0.615687 + 0.641106i
\(352\) −6.34033 + 10.9818i −0.337941 + 0.585330i
\(353\) 14.7332 + 25.5186i 0.784169 + 1.35822i 0.929494 + 0.368836i \(0.120244\pi\)
−0.145326 + 0.989384i \(0.546423\pi\)
\(354\) 4.17602 + 16.0162i 0.221953 + 0.851251i
\(355\) 5.42019 + 3.12935i 0.287674 + 0.166088i
\(356\) 3.00223 0.159118
\(357\) −3.80639 + 1.35850i −0.201455 + 0.0718992i
\(358\) −2.86584 −0.151465
\(359\) 30.5228 + 17.6224i 1.61093 + 0.930073i 0.989154 + 0.146881i \(0.0469233\pi\)
0.621779 + 0.783192i \(0.286410\pi\)
\(360\) −10.0189 0.135083i −0.528044 0.00711950i
\(361\) −7.08928 12.2790i −0.373120 0.646262i
\(362\) 17.9471 31.0852i 0.943277 1.63380i
\(363\) 1.46610 5.32764i 0.0769502 0.279628i
\(364\) −2.55098 28.9967i −0.133708 1.51984i
\(365\) 0.221728i 0.0116058i
\(366\) −35.0335 35.5090i −1.83123 1.85608i
\(367\) 30.1613 17.4136i 1.57441 0.908984i 0.578788 0.815478i \(-0.303526\pi\)
0.995619 0.0935065i \(-0.0298076\pi\)
\(368\) 6.00400 3.46641i 0.312980 0.180699i
\(369\) 22.3870 12.5258i 1.16542 0.652067i
\(370\) 0.949718i 0.0493735i
\(371\) 1.73169 + 19.6839i 0.0899048 + 1.02194i
\(372\) 50.4853 + 13.8929i 2.61754 + 0.720314i
\(373\) −10.1371 + 17.5579i −0.524878 + 0.909115i 0.474702 + 0.880146i \(0.342556\pi\)
−0.999580 + 0.0289688i \(0.990778\pi\)
\(374\) −2.87239 4.97512i −0.148528 0.257257i
\(375\) −1.67602 + 0.437000i −0.0865491 + 0.0225666i
\(376\) 7.60641 + 4.39156i 0.392270 + 0.226477i
\(377\) 26.1283 1.34568
\(378\) −6.18622 + 31.4413i −0.318185 + 1.61716i
\(379\) −9.07202 −0.465998 −0.232999 0.972477i \(-0.574854\pi\)
−0.232999 + 0.972477i \(0.574854\pi\)
\(380\) −6.52805 3.76897i −0.334882 0.193344i
\(381\) −11.7248 + 3.05708i −0.600678 + 0.156619i
\(382\) 16.9285 + 29.3210i 0.866137 + 1.50019i
\(383\) 13.8881 24.0549i 0.709648 1.22915i −0.255339 0.966851i \(-0.582187\pi\)
0.964988 0.262295i \(-0.0844794\pi\)
\(384\) −33.1686 9.12758i −1.69263 0.465790i
\(385\) −6.70256 3.12152i −0.341594 0.159087i
\(386\) 0.939675i 0.0478282i
\(387\) −0.309095 + 0.172942i −0.0157122 + 0.00879115i
\(388\) −18.9446 + 10.9377i −0.961765 + 0.555275i
\(389\) 13.4945 7.79107i 0.684200 0.395023i −0.117236 0.993104i \(-0.537403\pi\)
0.801436 + 0.598081i \(0.204070\pi\)
\(390\) −9.08708 9.21043i −0.460142 0.466388i
\(391\) 6.65242i 0.336427i
\(392\) 17.8953 15.0454i 0.903850 0.759908i
\(393\) 4.54660 16.5218i 0.229345 0.833416i
\(394\) −13.6024 + 23.5600i −0.685279 + 1.18694i
\(395\) 1.56849 + 2.71671i 0.0789195 + 0.136693i
\(396\) −28.7782 0.388011i −1.44616 0.0194983i
\(397\) −16.3596 9.44524i −0.821067 0.474043i 0.0297174 0.999558i \(-0.490539\pi\)
−0.850784 + 0.525515i \(0.823873\pi\)
\(398\) −43.3016 −2.17051
\(399\) −6.51605 + 7.66756i −0.326211 + 0.383858i
\(400\) 0.919111 0.0459555
\(401\) −18.0127 10.3996i −0.899511 0.519333i −0.0224695 0.999748i \(-0.507153\pi\)
−0.877042 + 0.480415i \(0.840486\pi\)
\(402\) −1.63407 6.26711i −0.0814999 0.312575i
\(403\) 14.1114 + 24.4417i 0.702941 + 1.21753i
\(404\) 18.2380 31.5891i 0.907373 1.57162i
\(405\) 4.28823 + 7.91272i 0.213084 + 0.393186i
\(406\) 28.8574 + 41.1704i 1.43217 + 2.04325i
\(407\) 1.13867i 0.0564416i
\(408\) 3.63187 3.58324i 0.179805 0.177397i
\(409\) 24.9664 14.4143i 1.23451 0.712744i 0.266542 0.963823i \(-0.414119\pi\)
0.967966 + 0.251080i \(0.0807856\pi\)
\(410\) −17.2609 + 9.96559i −0.852455 + 0.492165i
\(411\) −15.5342 + 15.3262i −0.766248 + 0.755986i
\(412\) 3.44383i 0.169665i
\(413\) −10.8054 + 0.950602i −0.531697 + 0.0467761i
\(414\) −45.3187 26.9858i −2.22729 1.32628i
\(415\) −0.333446 + 0.577546i −0.0163682 + 0.0283506i
\(416\) −7.27114 12.5940i −0.356497 0.617471i
\(417\) 0.431805 + 1.65609i 0.0211456 + 0.0810992i
\(418\) −12.3867 7.15145i −0.605852 0.349789i
\(419\) 3.24500 0.158528 0.0792642 0.996854i \(-0.474743\pi\)
0.0792642 + 0.996854i \(0.474743\pi\)
\(420\) 2.82867 15.4752i 0.138025 0.755114i
\(421\) 27.9322 1.36133 0.680665 0.732594i \(-0.261691\pi\)
0.680665 + 0.732594i \(0.261691\pi\)
\(422\) 14.0933 + 8.13675i 0.686050 + 0.396091i
\(423\) 0.106358 7.88844i 0.00517131 0.383549i
\(424\) −12.4722 21.6026i −0.605706 1.04911i
\(425\) 0.440969 0.763780i 0.0213901 0.0370488i
\(426\) −6.70407 + 24.3618i −0.324813 + 1.18033i
\(427\) 26.7692 18.7632i 1.29545 0.908016i
\(428\) 43.8622i 2.12016i
\(429\) −10.8950 11.0429i −0.526014 0.533154i
\(430\) 0.238319 0.137594i 0.0114928 0.00663536i
\(431\) 33.1792 19.1560i 1.59819 0.922714i 0.606351 0.795197i \(-0.292633\pi\)
0.991836 0.127516i \(-0.0407006\pi\)
\(432\) −1.14254 4.63716i −0.0549705 0.223105i
\(433\) 28.9533i 1.39140i 0.718330 + 0.695702i \(0.244907\pi\)
−0.718330 + 0.695702i \(0.755093\pi\)
\(434\) −22.9275 + 49.2301i −1.10055 + 2.36312i
\(435\) 13.6148 + 3.74662i 0.652779 + 0.179637i
\(436\) 0.0313210 0.0542495i 0.00150000 0.00259808i
\(437\) −8.28134 14.3437i −0.396150 0.686153i
\(438\) −0.866196 + 0.225850i −0.0413885 + 0.0107915i
\(439\) −13.2197 7.63242i −0.630943 0.364275i 0.150174 0.988660i \(-0.452017\pi\)
−0.781117 + 0.624384i \(0.785350\pi\)
\(440\) 9.33379 0.444971
\(441\) −19.6421 7.42885i −0.935338 0.353755i
\(442\) 6.58816 0.313367
\(443\) 1.97776 + 1.14186i 0.0939660 + 0.0542513i 0.546247 0.837624i \(-0.316056\pi\)
−0.452281 + 0.891876i \(0.649389\pi\)
\(444\) 2.34434 0.611256i 0.111257 0.0290089i
\(445\) 0.437271 + 0.757376i 0.0207286 + 0.0359030i
\(446\) −1.68514 + 2.91875i −0.0797937 + 0.138207i
\(447\) 29.6198 + 8.15099i 1.40097 + 0.385528i
\(448\) 13.8670 29.7754i 0.655155 1.40676i
\(449\) 10.3113i 0.486619i 0.969949 + 0.243310i \(0.0782331\pi\)
−0.969949 + 0.243310i \(0.921767\pi\)
\(450\) −3.41434 6.10234i −0.160953 0.287667i
\(451\) −20.6950 + 11.9483i −0.974489 + 0.562621i
\(452\) 21.4956 12.4105i 1.01107 0.583739i
\(453\) −27.3713 27.7428i −1.28601 1.30347i
\(454\) 2.48732i 0.116736i
\(455\) 6.94346 4.86686i 0.325515 0.228162i
\(456\) 3.37028 12.2472i 0.157828 0.573529i
\(457\) −16.3987 + 28.4033i −0.767097 + 1.32865i 0.172033 + 0.985091i \(0.444966\pi\)
−0.939131 + 0.343560i \(0.888367\pi\)
\(458\) −8.85564 15.3384i −0.413797 0.716718i
\(459\) −4.40164 1.27535i −0.205451 0.0595284i
\(460\) 22.4252 + 12.9472i 1.04558 + 0.603666i
\(461\) −16.5678 −0.771637 −0.385819 0.922575i \(-0.626081\pi\)
−0.385819 + 0.922575i \(0.626081\pi\)
\(462\) 5.36727 29.3635i 0.249708 1.36612i
\(463\) −36.5866 −1.70032 −0.850162 0.526522i \(-0.823496\pi\)
−0.850162 + 0.526522i \(0.823496\pi\)
\(464\) −6.48933 3.74662i −0.301260 0.173932i
\(465\) 3.84834 + 14.7594i 0.178462 + 0.684453i
\(466\) −20.9774 36.3339i −0.971758 1.68313i
\(467\) −20.5550 + 35.6023i −0.951171 + 1.64748i −0.208275 + 0.978070i \(0.566785\pi\)
−0.742896 + 0.669406i \(0.766549\pi\)
\(468\) 16.8869 28.3591i 0.780598 1.31090i
\(469\) 4.22812 0.371969i 0.195236 0.0171759i
\(470\) 6.12952i 0.282733i
\(471\) 14.6625 14.4661i 0.675613 0.666565i
\(472\) 11.8586 6.84658i 0.545837 0.315139i
\(473\) 0.285733 0.164968i 0.0131380 0.00758524i
\(474\) −9.01536 + 8.89463i −0.414089 + 0.408544i
\(475\) 2.19578i 0.100749i
\(476\) 4.59771 + 6.55947i 0.210736 + 0.300653i
\(477\) −11.4634 + 19.2510i −0.524872 + 0.881444i
\(478\) 34.8250 60.3186i 1.59286 2.75891i
\(479\) 8.25944 + 14.3058i 0.377383 + 0.653647i 0.990681 0.136205i \(-0.0434906\pi\)
−0.613297 + 0.789852i \(0.710157\pi\)
\(480\) −1.98292 7.60504i −0.0905074 0.347121i
\(481\) 1.13088 + 0.652916i 0.0515639 + 0.0297704i
\(482\) 12.2127 0.556274
\(483\) 22.3840 26.3397i 1.01851 1.19850i
\(484\) −10.9519 −0.497813
\(485\) −5.51850 3.18611i −0.250582 0.144674i
\(486\) −26.5436 + 24.8120i −1.20404 + 1.12550i
\(487\) 1.01601 + 1.75977i 0.0460396 + 0.0797430i 0.888127 0.459598i \(-0.152007\pi\)
−0.842087 + 0.539341i \(0.818673\pi\)
\(488\) −20.6337 + 35.7386i −0.934044 + 1.61781i
\(489\) 3.91688 14.2335i 0.177127 0.643661i
\(490\) 15.3374 + 5.56561i 0.692875 + 0.251429i
\(491\) 5.97889i 0.269824i 0.990858 + 0.134912i \(0.0430751\pi\)
−0.990858 + 0.134912i \(0.956925\pi\)
\(492\) −35.7091 36.1938i −1.60989 1.63174i
\(493\) −6.22687 + 3.59509i −0.280444 + 0.161915i
\(494\) 14.2051 8.20134i 0.639120 0.368996i
\(495\) −4.09362 7.31642i −0.183995 0.328848i
\(496\) 8.09393i 0.363428i
\(497\) −15.0109 6.99087i −0.673330 0.313583i
\(498\) −2.59587 0.714349i −0.116323 0.0320108i
\(499\) −4.24155 + 7.34658i −0.189878 + 0.328878i −0.945209 0.326465i \(-0.894143\pi\)
0.755331 + 0.655343i \(0.227476\pi\)
\(500\) 1.71646 + 2.97300i 0.0767625 + 0.132957i
\(501\) 5.98209 1.55975i 0.267260 0.0696846i
\(502\) 30.4332 + 17.5706i 1.35830 + 0.784216i
\(503\) −17.0296 −0.759312 −0.379656 0.925128i \(-0.623958\pi\)
−0.379656 + 0.925128i \(0.623958\pi\)
\(504\) 26.4369 1.96701i 1.17759 0.0876177i
\(505\) 10.6253 0.472821
\(506\) 42.5508 + 24.5667i 1.89161 + 1.09212i
\(507\) −4.57361 + 1.19251i −0.203121 + 0.0529612i
\(508\) 12.0077 + 20.7979i 0.532755 + 0.922759i
\(509\) −6.43409 + 11.1442i −0.285186 + 0.493956i −0.972654 0.232258i \(-0.925389\pi\)
0.687468 + 0.726214i \(0.258722\pi\)
\(510\) 3.43292 + 0.944697i 0.152012 + 0.0418319i
\(511\) −0.0514110 0.584381i −0.00227429 0.0258515i
\(512\) 10.3101i 0.455646i
\(513\) −11.0783 + 2.72956i −0.489119 + 0.120513i
\(514\) −32.1148 + 18.5415i −1.41652 + 0.817831i
\(515\) 0.868777 0.501589i 0.0382829 0.0221026i
\(516\) 0.493031 + 0.499723i 0.0217045 + 0.0219991i
\(517\) 7.34899i 0.323208i
\(518\) 0.220206 + 2.50305i 0.00967530 + 0.109978i
\(519\) −3.92565 + 14.2654i −0.172317 + 0.626181i
\(520\) −5.35203 + 9.26999i −0.234702 + 0.406516i
\(521\) 8.32724 + 14.4232i 0.364823 + 0.631892i 0.988748 0.149592i \(-0.0477961\pi\)
−0.623925 + 0.781485i \(0.714463\pi\)
\(522\) −0.768563 + 57.0033i −0.0336391 + 2.49497i
\(523\) 31.4934 + 18.1827i 1.37711 + 0.795075i 0.991811 0.127716i \(-0.0407646\pi\)
0.385300 + 0.922791i \(0.374098\pi\)
\(524\) −33.9635 −1.48370
\(525\) 4.31594 1.54035i 0.188363 0.0672265i
\(526\) −19.3549 −0.843912
\(527\) −6.72605 3.88329i −0.292991 0.169159i
\(528\) 1.12245 + 4.30491i 0.0488484 + 0.187347i
\(529\) 16.9482 + 29.3551i 0.736876 + 1.27631i
\(530\) 8.70407 15.0759i 0.378080 0.654855i
\(531\) −10.5678 6.29276i −0.458602 0.273083i
\(532\) 18.0790 + 8.41977i 0.783826 + 0.365043i
\(533\) 27.4047i 1.18703i
\(534\) −2.51334 + 2.47968i −0.108763 + 0.107306i
\(535\) −11.0651 + 6.38846i −0.478388 + 0.276197i
\(536\) −4.64026 + 2.67906i −0.200429 + 0.115718i
\(537\) 1.51597 1.49566i 0.0654188 0.0645427i
\(538\) 40.5268i 1.74724i
\(539\) 18.3889 + 6.67290i 0.792064 + 0.287422i
\(540\) 12.8658 12.3557i 0.553658 0.531706i
\(541\) −1.89575 + 3.28353i −0.0815046 + 0.141170i −0.903896 0.427751i \(-0.859306\pi\)
0.822392 + 0.568922i \(0.192639\pi\)
\(542\) −11.8775 20.5725i −0.510184 0.883665i
\(543\) 6.72958 + 25.8098i 0.288794 + 1.10761i
\(544\) 3.46571 + 2.00093i 0.148591 + 0.0857890i
\(545\) 0.0182474 0.000781633
\(546\) 26.0852 + 22.1678i 1.11634 + 0.948693i
\(547\) −10.9382 −0.467684 −0.233842 0.972275i \(-0.575130\pi\)
−0.233842 + 0.972275i \(0.575130\pi\)
\(548\) 37.4568 + 21.6257i 1.60008 + 0.923805i
\(549\) 37.0638 + 0.499723i 1.58184 + 0.0213277i
\(550\) 3.25691 + 5.64113i 0.138875 + 0.240538i
\(551\) −8.95077 + 15.5032i −0.381316 + 0.660458i
\(552\) −11.5776 + 42.0718i −0.492776 + 1.79069i
\(553\) −4.76379 6.79641i −0.202577 0.289013i
\(554\) 22.2839i 0.946752i
\(555\) 0.495651 + 0.502379i 0.0210392 + 0.0213248i
\(556\) 2.93766 1.69606i 0.124584 0.0719288i
\(557\) −8.42853 + 4.86622i −0.357128 + 0.206188i −0.667820 0.744322i \(-0.732773\pi\)
0.310692 + 0.950511i \(0.399439\pi\)
\(558\) −53.7389 + 30.0675i −2.27495 + 1.27286i
\(559\) 0.378374i 0.0160035i
\(560\) −2.42238 + 0.213109i −0.102364 + 0.00900551i
\(561\) 4.11591 + 1.13265i 0.173774 + 0.0478203i
\(562\) −13.8965 + 24.0694i −0.586187 + 1.01531i
\(563\) −0.235135 0.407265i −0.00990975 0.0171642i 0.861028 0.508558i \(-0.169821\pi\)
−0.870938 + 0.491393i \(0.836488\pi\)
\(564\) −15.1304 + 3.94507i −0.637107 + 0.166117i
\(565\) 6.26159 + 3.61513i 0.263427 + 0.152090i
\(566\) 46.5459 1.95647
\(567\) −13.1366 19.8602i −0.551686 0.834052i
\(568\) 20.9037 0.877100
\(569\) 5.38387 + 3.10838i 0.225703 + 0.130310i 0.608588 0.793486i \(-0.291736\pi\)
−0.382885 + 0.923796i \(0.625069\pi\)
\(570\) 8.57796 2.23659i 0.359291 0.0936805i
\(571\) −5.31121 9.19928i −0.222267 0.384978i 0.733229 0.679982i \(-0.238012\pi\)
−0.955496 + 0.295004i \(0.904679\pi\)
\(572\) −15.3731 + 26.6270i −0.642782 + 1.11333i
\(573\) −24.2572 6.67528i −1.01336 0.278864i
\(574\) 43.1817 30.2672i 1.80237 1.26333i
\(575\) 7.54296i 0.314563i
\(576\) 32.5024 18.1855i 1.35427 0.757728i
\(577\) −2.56914 + 1.48330i −0.106955 + 0.0617504i −0.552523 0.833497i \(-0.686335\pi\)
0.445568 + 0.895248i \(0.353002\pi\)
\(578\) 32.7459 18.9058i 1.36205 0.786380i
\(579\) −0.490410 0.497067i −0.0203807 0.0206574i
\(580\) 27.9876i 1.16212i
\(581\) 0.744909 1.59948i 0.0309040 0.0663576i
\(582\) 6.82566 24.8037i 0.282933 1.02815i
\(583\) 10.4358 18.0753i 0.432205 0.748601i
\(584\) 0.370280 + 0.641344i 0.0153223 + 0.0265390i
\(585\) 9.61371 + 0.129620i 0.397478 + 0.00535911i
\(586\) −6.07641 3.50821i −0.251014 0.144923i
\(587\) −18.8819 −0.779341 −0.389670 0.920954i \(-0.627411\pi\)
−0.389670 + 0.920954i \(0.627411\pi\)
\(588\) −3.86701 + 41.4419i −0.159473 + 1.70904i
\(589\) −19.3366 −0.796751
\(590\) 8.27583 + 4.77805i 0.340711 + 0.196709i
\(591\) −5.10047 19.5617i −0.209805 0.804661i
\(592\) −0.187247 0.324322i −0.00769582 0.0133296i
\(593\) −15.1472 + 26.2357i −0.622020 + 1.07737i 0.367088 + 0.930186i \(0.380355\pi\)
−0.989109 + 0.147185i \(0.952979\pi\)
\(594\) 24.4123 23.4444i 1.00165 0.961936i
\(595\) −0.985111 + 2.11524i −0.0403856 + 0.0867165i
\(596\) 60.8887i 2.49410i
\(597\) 22.9056 22.5988i 0.937462 0.924907i
\(598\) −48.7976 + 28.1733i −1.99548 + 1.15209i
\(599\) −6.29024 + 3.63167i −0.257012 + 0.148386i −0.622971 0.782245i \(-0.714075\pi\)
0.365959 + 0.930631i \(0.380741\pi\)
\(600\) −4.11806 + 4.06291i −0.168119 + 0.165868i
\(601\) 45.3302i 1.84906i −0.381110 0.924530i \(-0.624458\pi\)
0.381110 0.924530i \(-0.375542\pi\)
\(602\) −0.596204 + 0.417896i −0.0242995 + 0.0170322i
\(603\) 4.13515 + 2.46235i 0.168396 + 0.100275i
\(604\) −38.6216 + 66.8946i −1.57149 + 2.72190i
\(605\) −1.59513 2.76284i −0.0648511 0.112325i
\(606\) 10.8228 + 41.5085i 0.439647 + 1.68617i
\(607\) 22.5370 + 13.0117i 0.914748 + 0.528130i 0.881956 0.471332i \(-0.156227\pi\)
0.0327925 + 0.999462i \(0.489560\pi\)
\(608\) 9.96351 0.404073
\(609\) −36.7515 6.71769i −1.48924 0.272215i
\(610\) −28.7995 −1.16606
\(611\) −7.29877 4.21394i −0.295276 0.170478i
\(612\) −0.122451 + 9.08204i −0.00494980 + 0.367120i
\(613\) −12.8525 22.2611i −0.519106 0.899118i −0.999753 0.0222040i \(-0.992932\pi\)
0.480648 0.876914i \(-0.340402\pi\)
\(614\) 23.7507 41.1375i 0.958502 1.66017i
\(615\) 3.92965 14.2799i 0.158459 0.575822i
\(616\) −24.5999 + 2.16417i −0.991157 + 0.0871971i
\(617\) 8.88258i 0.357599i 0.983886 + 0.178800i \(0.0572213\pi\)
−0.983886 + 0.178800i \(0.942779\pi\)
\(618\) 2.84441 + 2.88302i 0.114419 + 0.115972i
\(619\) −26.4112 + 15.2485i −1.06156 + 0.612890i −0.925863 0.377861i \(-0.876660\pi\)
−0.135694 + 0.990751i \(0.543327\pi\)
\(620\) 26.1810 15.1156i 1.05145 0.607057i
\(621\) 38.0563 9.37661i 1.52715 0.376271i
\(622\) 63.5669i 2.54880i
\(623\) −1.32807 1.89473i −0.0532079 0.0759108i
\(624\) −4.91911 1.35368i −0.196922 0.0541904i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0.735048 + 1.27314i 0.0293784 + 0.0508849i
\(627\) 10.2846 2.68157i 0.410726 0.107091i
\(628\) −35.3549 20.4121i −1.41081 0.814533i
\(629\) −0.359349 −0.0143282
\(630\) 10.4136 + 15.2915i 0.414890 + 0.609228i
\(631\) 44.3335 1.76489 0.882445 0.470416i \(-0.155896\pi\)
0.882445 + 0.470416i \(0.155896\pi\)
\(632\) 9.07367 + 5.23868i 0.360931 + 0.208384i
\(633\) −11.7015 + 3.05102i −0.465094 + 0.121267i
\(634\) −29.6372 51.3332i −1.17705 2.03870i
\(635\) −3.49781 + 6.05838i −0.138806 + 0.240419i
\(636\) 42.8163 + 11.7825i 1.69778 + 0.467206i
\(637\) −17.1715 + 14.4369i −0.680361 + 0.572011i
\(638\) 53.1052i 2.10245i
\(639\) −9.16797 16.3857i −0.362679 0.648206i
\(640\) −17.2008 + 9.93088i −0.679921 + 0.392553i
\(641\) −6.03197 + 3.48256i −0.238249 + 0.137553i −0.614371 0.789017i \(-0.710590\pi\)
0.376123 + 0.926570i \(0.377257\pi\)
\(642\) −36.2277 36.7195i −1.42979 1.44920i
\(643\) 25.8907i 1.02103i 0.859869 + 0.510514i \(0.170545\pi\)
−0.859869 + 0.510514i \(0.829455\pi\)
\(644\) −62.1053 28.9237i −2.44729 1.13975i
\(645\) −0.0542562 + 0.197161i −0.00213634 + 0.00776321i
\(646\) −2.25691 + 3.90908i −0.0887968 + 0.153801i
\(647\) −5.01859 8.69245i −0.197301 0.341735i 0.750351 0.661039i \(-0.229884\pi\)
−0.947652 + 0.319304i \(0.896551\pi\)
\(648\) 25.6176 + 15.7261i 1.00636 + 0.617781i
\(649\) 9.92232 + 5.72866i 0.389485 + 0.224869i
\(650\) −7.47010 −0.293001
\(651\) −13.5648 38.0073i −0.531645 1.48962i
\(652\) −29.2594 −1.14589
\(653\) −34.2946 19.8000i −1.34205 0.774833i −0.354942 0.934888i \(-0.615500\pi\)
−0.987108 + 0.160055i \(0.948833\pi\)
\(654\) 0.0185866 + 0.0712847i 0.000726792 + 0.00278745i
\(655\) −4.94673 8.56799i −0.193285 0.334779i
\(656\) −3.92965 + 6.80635i −0.153427 + 0.265744i
\(657\) 0.340329 0.571531i 0.0132775 0.0222975i
\(658\) −1.42122 16.1548i −0.0554048 0.629779i
\(659\) 17.9364i 0.698705i 0.936991 + 0.349352i \(0.113598\pi\)
−0.936991 + 0.349352i \(0.886402\pi\)
\(660\) −11.8287 + 11.6703i −0.460430 + 0.454264i
\(661\) −3.31012 + 1.91110i −0.128749 + 0.0743332i −0.562991 0.826463i \(-0.690350\pi\)
0.434242 + 0.900796i \(0.357016\pi\)
\(662\) −23.2003 + 13.3947i −0.901705 + 0.520599i
\(663\) −3.48498 + 3.43831i −0.135346 + 0.133533i
\(664\) 2.22739i 0.0864393i
\(665\) 0.509124 + 5.78714i 0.0197430 + 0.224416i
\(666\) −1.45771 + 2.44801i −0.0564852 + 0.0948585i
\(667\) 30.7478 53.2567i 1.19056 2.06211i
\(668\) −6.12645 10.6113i −0.237039 0.410564i
\(669\) −0.631874 2.42341i −0.0244297 0.0936946i
\(670\) −3.23832 1.86964i −0.125107 0.0722307i
\(671\) −34.5292 −1.33299
\(672\) 6.98946 + 19.5839i 0.269624 + 0.755464i
\(673\) 1.08304 0.0417483 0.0208741 0.999782i \(-0.493355\pi\)
0.0208741 + 0.999782i \(0.493355\pi\)
\(674\) −32.7094 18.8848i −1.25992 0.727415i
\(675\) 4.99088 + 1.44608i 0.192099 + 0.0556597i
\(676\) 4.68398 + 8.11288i 0.180153 + 0.312034i
\(677\) 15.5014 26.8492i 0.595766 1.03190i −0.397672 0.917528i \(-0.630182\pi\)
0.993438 0.114370i \(-0.0364849\pi\)
\(678\) −7.74478 + 28.1436i −0.297436 + 1.08085i
\(679\) 15.2831 + 7.11767i 0.586513 + 0.273151i
\(680\) 2.94562i 0.112960i
\(681\) −1.29812 1.31574i −0.0497439 0.0504191i
\(682\) 49.6772 28.6812i 1.90224 1.09826i
\(683\) 16.5419 9.55050i 0.632960 0.365440i −0.148937 0.988847i \(-0.547585\pi\)
0.781898 + 0.623407i \(0.214252\pi\)
\(684\) 11.0419 + 19.7348i 0.422196 + 0.754579i
\(685\) 12.5990i 0.481383i
\(686\) −41.7134 11.1124i −1.59263 0.424272i
\(687\) 12.6894 + 3.49198i 0.484133 + 0.133227i
\(688\) 0.0542562 0.0939745i 0.00206850 0.00358275i
\(689\) 11.9678 + 20.7289i 0.455937 + 0.789707i
\(690\) −29.4671 + 7.68316i −1.12179 + 0.292493i
\(691\) −14.5775 8.41632i −0.554554 0.320172i 0.196403 0.980523i \(-0.437074\pi\)
−0.750957 + 0.660351i \(0.770407\pi\)
\(692\) 29.3250 1.11477
\(693\) 12.4855 + 18.3338i 0.474283 + 0.696443i
\(694\) 41.9145 1.59105
\(695\) 0.855731 + 0.494056i 0.0324597 + 0.0187406i
\(696\) 45.6372 11.8993i 1.72987 0.451043i
\(697\) 3.77072 + 6.53107i 0.142826 + 0.247382i
\(698\) 7.17232 12.4228i 0.271476 0.470211i
\(699\) 30.0589 + 8.27184i 1.13693 + 0.312870i
\(700\) −5.21319 7.43756i −0.197040 0.281113i
\(701\) 21.8878i 0.826691i 0.910574 + 0.413345i \(0.135640\pi\)
−0.910574 + 0.413345i \(0.864360\pi\)
\(702\) 9.28603 + 37.6886i 0.350479 + 1.42247i
\(703\) −0.774814 + 0.447339i −0.0292227 + 0.0168717i
\(704\) −30.0458 + 17.3470i −1.13240 + 0.653789i
\(705\) −3.19895 3.24237i −0.120479 0.122115i
\(706\) 68.6821i 2.58489i
\(707\) −28.0038 + 2.46364i −1.05319 + 0.0926547i
\(708\) −6.46794 + 23.5038i −0.243080 + 0.883326i
\(709\) 5.41030 9.37091i 0.203188 0.351932i −0.746366 0.665536i \(-0.768203\pi\)
0.949554 + 0.313604i \(0.101536\pi\)
\(710\) 7.29408 + 12.6337i 0.273742 + 0.474135i
\(711\) 0.126874 9.41011i 0.00475816 0.352907i
\(712\) 2.52959 + 1.46046i 0.0948005 + 0.0547331i
\(713\) 66.4253 2.48765
\(714\) −9.26675 1.69384i −0.346800 0.0633905i
\(715\) −8.95628 −0.334946
\(716\) −3.65536 2.11042i −0.136607 0.0788703i
\(717\) 13.0583 + 50.0821i 0.487669 + 1.87035i
\(718\) 41.0753 + 71.1445i 1.53292 + 2.65509i
\(719\) −11.1296 + 19.2770i −0.415064 + 0.718912i −0.995435 0.0954404i \(-0.969574\pi\)
0.580371 + 0.814352i \(0.302907\pi\)
\(720\) −2.36912 1.41073i −0.0882917 0.0525749i
\(721\) −2.17342 + 1.52341i −0.0809425 + 0.0567348i
\(722\) 33.0483i 1.22993i
\(723\) −6.46025 + 6.37373i −0.240259 + 0.237042i
\(724\) 45.7827 26.4327i 1.70150 0.982362i
\(725\) 7.06045 4.07635i 0.262218 0.151392i
\(726\) 9.16844 9.04566i 0.340273 0.335716i
\(727\) 43.7899i 1.62408i 0.583604 + 0.812038i \(0.301642\pi\)
−0.583604 + 0.812038i \(0.698358\pi\)
\(728\) 11.9563 25.6727i 0.443129 0.951493i
\(729\) 1.09174 26.9779i 0.0404349 0.999182i
\(730\) −0.258409 + 0.447578i −0.00956415 + 0.0165656i
\(731\) −0.0520618 0.0901738i −0.00192558 0.00333520i
\(732\) −18.5359 71.0903i −0.685106 2.62757i
\(733\) 22.6647 + 13.0854i 0.837138 + 0.483322i 0.856290 0.516495i \(-0.172763\pi\)
−0.0191524 + 0.999817i \(0.506097\pi\)
\(734\) 81.1776 2.99632
\(735\) −11.0178 + 5.06042i −0.406398 + 0.186657i
\(736\) −34.2267 −1.26161
\(737\) −3.88259 2.24161i −0.143017 0.0825709i
\(738\) 59.7881 + 0.806109i 2.20083 + 0.0296733i
\(739\) −20.1777 34.9489i −0.742250 1.28561i −0.951469 0.307746i \(-0.900425\pi\)
0.209219 0.977869i \(-0.432908\pi\)
\(740\) 0.699378 1.21136i 0.0257096 0.0445304i
\(741\) −3.23397 + 11.7519i −0.118803 + 0.431716i
\(742\) −19.4446 + 41.7517i −0.713835 + 1.53275i
\(743\) 8.82565i 0.323782i 0.986809 + 0.161891i \(0.0517593\pi\)
−0.986809 + 0.161891i \(0.948241\pi\)
\(744\) 35.7791 + 36.2647i 1.31173 + 1.32953i
\(745\) 15.3604 8.86834i 0.562762 0.324911i
\(746\) −40.9251 + 23.6281i −1.49838 + 0.865087i
\(747\) 1.74597 0.976890i 0.0638816 0.0357425i
\(748\) 8.46097i 0.309364i
\(749\) 27.6817 19.4029i 1.01147 0.708965i
\(750\) −3.89248 1.07116i −0.142133 0.0391133i
\(751\) −18.9165 + 32.7644i −0.690274 + 1.19559i 0.281475 + 0.959569i \(0.409176\pi\)
−0.971748 + 0.236020i \(0.924157\pi\)
\(752\) 1.20850 + 2.09319i 0.0440695 + 0.0763307i
\(753\) −25.2685 + 6.58843i −0.920834 + 0.240096i
\(754\) 52.7422 + 30.4507i 1.92076 + 1.10895i
\(755\) −22.5007 −0.818885
\(756\) −31.0440 + 35.5475i −1.12906 + 1.29285i
\(757\) −34.7636 −1.26351 −0.631753 0.775170i \(-0.717664\pi\)
−0.631753 + 0.775170i \(0.717664\pi\)
\(758\) −18.3127 10.5728i −0.665146 0.384022i
\(759\) −35.3296 + 9.21174i −1.28238 + 0.334365i
\(760\) −3.66689 6.35124i −0.133012 0.230384i
\(761\) 0.915074 1.58495i 0.0331714 0.0574545i −0.848963 0.528452i \(-0.822773\pi\)
0.882135 + 0.470998i \(0.156106\pi\)
\(762\) −27.2303 7.49342i −0.986448 0.271458i
\(763\) −0.0480923 + 0.00423093i −0.00174106 + 0.000153170i
\(764\) 49.8649i 1.80405i
\(765\) −2.30897 + 1.29190i −0.0834809 + 0.0467086i
\(766\) 56.0686 32.3712i 2.02584 1.16962i
\(767\) −11.3790 + 6.56967i −0.410872 + 0.237217i
\(768\) −26.1122 26.4666i −0.942243 0.955032i
\(769\) 23.5601i 0.849598i 0.905288 + 0.424799i \(0.139655\pi\)
−0.905288 + 0.424799i \(0.860345\pi\)
\(770\) −9.89179 14.1124i −0.356475 0.508577i
\(771\) 7.31132 26.5685i 0.263311 0.956842i
\(772\) −0.691982 + 1.19855i −0.0249050 + 0.0431367i
\(773\) 24.0437 + 41.6448i 0.864790 + 1.49786i 0.867255 + 0.497864i \(0.165882\pi\)
−0.00246461 + 0.999997i \(0.500785\pi\)
\(774\) −0.825487 0.0111299i −0.0296715 0.000400054i
\(775\) 7.62645 + 4.40313i 0.273950 + 0.158165i
\(776\) −21.2828 −0.764010
\(777\) −1.42281 1.20913i −0.0510430 0.0433774i
\(778\) 36.3198 1.30213
\(779\) 16.2606 + 9.38804i 0.582595 + 0.336361i
\(780\) −4.80789 18.4396i −0.172150 0.660244i
\(781\) 8.74525 + 15.1472i 0.312930 + 0.542010i
\(782\) 7.75294 13.4285i 0.277245 0.480202i
\(783\) −29.3431 30.5546i −1.04864 1.09193i
\(784\) 6.33495 1.12333i 0.226248 0.0401189i
\(785\) 11.8920i 0.424443i
\(786\) 28.4327 28.0520i 1.01416 1.00058i
\(787\) −26.1234 + 15.0823i −0.931197 + 0.537627i −0.887190 0.461404i \(-0.847346\pi\)
−0.0440072 + 0.999031i \(0.514012\pi\)
\(788\) −34.6995 + 20.0338i −1.23612 + 0.713673i
\(789\) 10.2383 10.1012i 0.364492 0.359611i
\(790\) 7.31189i 0.260145i
\(791\) −17.3411 8.07610i −0.616579 0.287153i
\(792\) −24.0589 14.3263i −0.854897 0.509064i
\(793\) 19.7992 34.2932i 0.703090 1.21779i
\(794\) −22.0156 38.1321i −0.781303 1.35326i
\(795\) 3.26375 + 12.5174i 0.115753 + 0.443946i
\(796\) −55.2309 31.8876i −1.95761 1.13022i
\(797\) −3.60475 −0.127687 −0.0638435 0.997960i \(-0.520336\pi\)
−0.0638435 + 0.997960i \(0.520336\pi\)
\(798\) −22.0892 + 7.88362i −0.781950 + 0.279077i
\(799\) 2.31925 0.0820491
\(800\) −3.92965 2.26878i −0.138934 0.0802137i
\(801\) 0.0353705 2.62339i 0.00124976 0.0926928i
\(802\) −24.2401 41.9851i −0.855948 1.48255i
\(803\) −0.309820 + 0.536624i −0.0109333 + 0.0189371i
\(804\) 2.53089 9.19699i 0.0892578 0.324353i
\(805\) −1.74895 19.8800i −0.0616423 0.700679i
\(806\) 65.7836i 2.31713i
\(807\) 21.1507 + 21.4378i 0.744539 + 0.754645i
\(808\) 30.7335 17.7440i 1.08120 0.624232i
\(809\) 18.7612 10.8318i 0.659607 0.380824i −0.132520 0.991180i \(-0.542307\pi\)
0.792127 + 0.610356i \(0.208974\pi\)
\(810\) −0.565574 + 20.9701i −0.0198723 + 0.736816i
\(811\) 27.6526i 0.971015i 0.874232 + 0.485508i \(0.161365\pi\)
−0.874232 + 0.485508i \(0.838635\pi\)
\(812\) 6.48933 + 73.7633i 0.227731 + 2.58858i
\(813\) 17.0196 + 4.68358i 0.596904 + 0.164260i
\(814\) 1.32704 2.29850i 0.0465126 0.0805623i
\(815\) −4.26159 7.38130i −0.149277 0.258556i
\(816\) 1.35858 0.354231i 0.0475597 0.0124006i
\(817\) −0.224508 0.129620i −0.00785453 0.00453481i
\(818\) 67.1957 2.34944
\(819\) −25.3677 + 1.88746i −0.886419 + 0.0659531i
\(820\) −29.3549 −1.02512
\(821\) −12.2722 7.08534i −0.428302 0.247280i 0.270321 0.962770i \(-0.412870\pi\)
−0.698623 + 0.715490i \(0.746203\pi\)
\(822\) −49.2189 + 12.8332i −1.71670 + 0.447609i
\(823\) −11.6538 20.1850i −0.406227 0.703605i 0.588237 0.808689i \(-0.299822\pi\)
−0.994463 + 0.105084i \(0.966489\pi\)
\(824\) 1.67528 2.90167i 0.0583611 0.101084i
\(825\) −4.66689 1.28427i −0.162480 0.0447125i
\(826\) −22.9194 10.6740i −0.797468 0.371397i
\(827\) 32.0877i 1.11580i −0.829908 0.557900i \(-0.811607\pi\)
0.829908 0.557900i \(-0.188393\pi\)
\(828\) −37.9311 67.7932i −1.31820 2.35598i
\(829\) 25.9947 15.0080i 0.902833 0.521251i 0.0247149 0.999695i \(-0.492132\pi\)
0.878118 + 0.478444i \(0.158799\pi\)
\(830\) −1.34618 + 0.777218i −0.0467266 + 0.0269776i
\(831\) 11.6298 + 11.7877i 0.403434 + 0.408910i
\(832\) 39.7873i 1.37938i
\(833\) 2.10588 5.80329i 0.0729645 0.201072i
\(834\) −1.05843 + 3.84621i −0.0366503 + 0.133183i
\(835\) 1.78462 3.09105i 0.0617592 0.106970i
\(836\) −10.5327 18.2432i −0.364282 0.630956i
\(837\) 12.7346 43.9510i 0.440172 1.51917i
\(838\) 6.55031 + 3.78182i 0.226277 + 0.130641i
\(839\) −28.6277 −0.988337 −0.494168 0.869366i \(-0.664527\pi\)
−0.494168 + 0.869366i \(0.664527\pi\)
\(840\) 9.91140 11.6629i 0.341976 0.402409i
\(841\) −37.4666 −1.29195
\(842\) 56.3835 + 32.5530i 1.94310 + 1.12185i
\(843\) −5.21074 19.9846i −0.179467 0.688307i
\(844\) 11.9839 + 20.7567i 0.412503 + 0.714476i
\(845\) −1.36443 + 2.36326i −0.0469378 + 0.0812986i
\(846\) 9.40813 15.7995i 0.323458 0.543200i
\(847\) 4.84468 + 6.91181i 0.166465 + 0.237493i
\(848\) 6.86441i 0.235725i
\(849\) −24.6217 + 24.2920i −0.845015 + 0.833698i
\(850\) 1.78027 1.02784i 0.0610627 0.0352545i
\(851\) 2.66165 1.53670i 0.0912401 0.0526775i
\(852\) −26.4912 + 26.1364i −0.907573 + 0.895419i
\(853\) 17.3563i 0.594269i 0.954836 + 0.297135i \(0.0960310\pi\)
−0.954836 + 0.297135i \(0.903969\pi\)
\(854\) 75.9031 6.67758i 2.59735 0.228502i
\(855\) −3.37028 + 5.65988i −0.115261 + 0.193564i
\(856\) −21.3371 + 36.9569i −0.729287 + 1.26316i
\(857\) 23.2842 + 40.3294i 0.795372 + 1.37763i 0.922602 + 0.385752i \(0.126058\pi\)
−0.127230 + 0.991873i \(0.540609\pi\)
\(858\) −9.12275 34.9883i −0.311446 1.19448i
\(859\) 31.5359 + 18.2072i 1.07599 + 0.621223i 0.929812 0.368035i \(-0.119969\pi\)
0.146178 + 0.989258i \(0.453303\pi\)
\(860\) 0.405299 0.0138206
\(861\) −7.04587 + 38.5469i −0.240123 + 1.31367i
\(862\) 89.3002 3.04158
\(863\) 2.05942 + 1.18901i 0.0701034 + 0.0404742i 0.534642 0.845079i \(-0.320446\pi\)
−0.464539 + 0.885553i \(0.653780\pi\)
\(864\) −6.56170 + 22.6464i −0.223234 + 0.770448i
\(865\) 4.27114 + 7.39784i 0.145223 + 0.251534i
\(866\) −33.7430 + 58.4447i −1.14664 + 1.98603i
\(867\) −7.45499 + 27.0906i −0.253185 + 0.920045i
\(868\) −65.4971 + 45.9087i −2.22312 + 1.55824i
\(869\) 8.76660i 0.297387i
\(870\) 23.1162 + 23.4300i 0.783713 + 0.794351i
\(871\) 4.45259 2.57070i 0.150870 0.0871049i
\(872\) 0.0527802 0.0304727i 0.00178736 0.00103193i
\(873\) 9.33426 + 16.6829i 0.315917 + 0.564629i
\(874\) 38.6054i 1.30585i
\(875\) 1.11699 2.39840i 0.0377610 0.0810809i
\(876\) −1.27114 0.349803i −0.0429480 0.0118187i
\(877\) 11.0465 19.1332i 0.373015 0.646082i −0.617012 0.786953i \(-0.711657\pi\)
0.990028 + 0.140872i \(0.0449905\pi\)
\(878\) −17.7901 30.8134i −0.600387 1.03990i
\(879\) 5.04519 1.31547i 0.170170 0.0443697i
\(880\) 2.22442 + 1.28427i 0.0749852 + 0.0432927i
\(881\) 33.5633 1.13078 0.565388 0.824825i \(-0.308727\pi\)
0.565388 + 0.824825i \(0.308727\pi\)
\(882\) −30.9915 37.8873i −1.04354 1.27573i
\(883\) −3.74124 −0.125903 −0.0629514 0.998017i \(-0.520051\pi\)
−0.0629514 + 0.998017i \(0.520051\pi\)
\(884\) 8.40314 + 4.85156i 0.282628 + 0.163176i
\(885\) −6.87136 + 1.79162i −0.230978 + 0.0602246i
\(886\) 2.66151 + 4.60988i 0.0894153 + 0.154872i
\(887\) 13.7685 23.8478i 0.462302 0.800730i −0.536773 0.843726i \(-0.680357\pi\)
0.999075 + 0.0429963i \(0.0136904\pi\)
\(888\) 2.27262 + 0.625396i 0.0762641 + 0.0209869i
\(889\) 7.81399 16.7783i 0.262073 0.562726i
\(890\) 2.03844i 0.0683286i
\(891\) −0.678096 + 25.1422i −0.0227171 + 0.842295i
\(892\) −4.29877 + 2.48189i −0.143933 + 0.0831000i
\(893\) 5.00068 2.88714i 0.167341 0.0966146i
\(894\) 50.2907 + 50.9733i 1.68197 + 1.70480i
\(895\) 1.22952i 0.0410983i
\(896\) 43.0313 30.1618i 1.43758 1.00764i
\(897\) 11.1094 40.3702i 0.370931 1.34792i
\(898\) −12.0171 + 20.8142i −0.401015 + 0.694579i
\(899\) −35.8974 62.1762i −1.19725 2.07369i
\(900\) 0.138843 10.2978i 0.00462811 0.343261i
\(901\) −5.70432 3.29339i −0.190038 0.109719i
\(902\) −55.6995 −1.85459
\(903\) 0.0972815 0.532212i 0.00323733 0.0177109i
\(904\) 24.1487 0.803174
\(905\) 13.3364 + 7.69975i 0.443316 + 0.255949i
\(906\) −22.9189 87.9005i −0.761431 2.92030i
\(907\) −19.3650 33.5412i −0.643005 1.11372i −0.984758 0.173928i \(-0.944354\pi\)
0.341754 0.939790i \(-0.388979\pi\)
\(908\) −1.83168 + 3.17256i −0.0607864 + 0.105285i
\(909\) −27.3880 16.3087i −0.908404 0.540926i
\(910\) 19.6880 1.73205i 0.652650 0.0574169i
\(911\) 23.3967i 0.775167i −0.921835 0.387583i \(-0.873310\pi\)
0.921835 0.387583i \(-0.126690\pi\)
\(912\) 2.48834 2.45502i 0.0823973 0.0812938i
\(913\) −1.61401 + 0.931847i −0.0534158 + 0.0308396i
\(914\) −66.2043 + 38.2231i −2.18984 + 1.26431i
\(915\) 15.2343 15.0303i 0.503629 0.496885i
\(916\) 26.0854i 0.861886i
\(917\) 15.0241 + 21.4346i 0.496139 + 0.707833i
\(918\) −7.39876 7.70422i −0.244195 0.254277i
\(919\) 4.32329 7.48816i 0.142612 0.247012i −0.785867 0.618395i \(-0.787783\pi\)
0.928480 + 0.371383i \(0.121116\pi\)
\(920\) 12.5965 + 21.8179i 0.415296 + 0.719313i
\(921\) 8.90578 + 34.1561i 0.293455 + 1.12548i
\(922\) −33.4434 19.3086i −1.10140 0.635894i
\(923\) −20.0583 −0.660225
\(924\) 28.4694 33.5005i 0.936574 1.10208i
\(925\) 0.407453 0.0133970
\(926\) −73.8532 42.6392i −2.42697 1.40121i
\(927\) −3.00926 0.0405732i −0.0988370 0.00133260i
\(928\) 18.4967 + 32.0373i 0.607185 + 1.05168i
\(929\) −6.27980 + 10.8769i −0.206034 + 0.356861i −0.950462 0.310842i \(-0.899389\pi\)
0.744428 + 0.667703i \(0.232722\pi\)
\(930\) −9.43292 + 34.2782i −0.309318 + 1.12403i
\(931\) −2.68366 15.1344i −0.0879535 0.496009i
\(932\) 61.7914i 2.02405i
\(933\) 33.1751 + 33.6254i 1.08610 + 1.10085i
\(934\) −82.9840 + 47.9108i −2.71532 + 1.56769i
\(935\) 2.13445 1.23233i 0.0698041 0.0403014i
\(936\) 28.0239 15.6797i 0.915990 0.512508i
\(937\) 11.3901i 0.372097i 0.982541 + 0.186048i \(0.0595681\pi\)
−0.982541 + 0.186048i \(0.940432\pi\)
\(938\) 8.96833 + 4.17673i 0.292826 + 0.136375i
\(939\) −1.05327 0.289846i −0.0343720 0.00945875i
\(940\) −4.51381 + 7.81815i −0.147224 + 0.255000i
\(941\) 21.0434 + 36.4482i 0.685994 + 1.18818i 0.973123 + 0.230285i \(0.0739658\pi\)
−0.287129 + 0.957892i \(0.592701\pi\)
\(942\) 46.4568 12.1130i 1.51365 0.394664i
\(943\) −55.8584 32.2499i −1.81900 1.05020i
\(944\) 3.76818 0.122644
\(945\) −13.4891 2.65405i −0.438801 0.0863361i
\(946\) 0.769036 0.0250035
\(947\) −12.6504 7.30370i −0.411082 0.237338i 0.280172 0.959950i \(-0.409608\pi\)
−0.691255 + 0.722611i \(0.742942\pi\)
\(948\) −18.0491 + 4.70607i −0.586207 + 0.152846i
\(949\) −0.355304 0.615405i −0.0115337 0.0199769i
\(950\) 2.55903 4.43237i 0.0830259 0.143805i
\(951\) 42.4679 + 11.6866i 1.37711 + 0.378965i
\(952\) 0.682986 + 7.76340i 0.0221357 + 0.251613i
\(953\) 28.8817i 0.935570i 0.883842 + 0.467785i \(0.154948\pi\)
−0.883842 + 0.467785i \(0.845052\pi\)
\(954\) −45.5756 + 25.5001i −1.47556 + 0.825596i
\(955\) −12.5795 + 7.26275i −0.407062 + 0.235017i
\(956\) 88.8379 51.2906i 2.87322 1.65886i
\(957\) 27.7152 + 28.0914i 0.895906 + 0.908066i
\(958\) 38.5032i 1.24398i
\(959\) −2.92127 33.2056i −0.0943326 1.07226i
\(960\) 5.70523 20.7322i 0.184136 0.669128i
\(961\) 23.2751 40.3137i 0.750811 1.30044i
\(962\) 1.52186 + 2.63594i 0.0490667 + 0.0849860i
\(963\) 38.3273 + 0.516758i 1.23508 + 0.0166523i
\(964\) 15.5772 + 8.99352i 0.501709 + 0.289662i
\(965\) −0.403145 −0.0129777
\(966\) 75.8811 27.0819i 2.44144 0.871346i
\(967\) 0.409782 0.0131777 0.00658885 0.999978i \(-0.497903\pi\)
0.00658885 + 0.999978i \(0.497903\pi\)
\(968\) −9.22774 5.32764i −0.296591 0.171237i
\(969\) −0.846268 3.24567i −0.0271860 0.104266i
\(970\) −7.42638 12.8629i −0.238447 0.413002i
\(971\) 2.64865 4.58759i 0.0849991 0.147223i −0.820392 0.571802i \(-0.806245\pi\)
0.905391 + 0.424579i \(0.139578\pi\)
\(972\) −52.1279 + 12.1007i −1.67200 + 0.388129i
\(973\) −2.36989 1.10371i −0.0759753 0.0353832i
\(974\) 4.73634i 0.151762i
\(975\) 3.95151 3.89859i 0.126550 0.124855i
\(976\) −9.83482 + 5.67814i −0.314805 + 0.181753i
\(977\) −24.1247 + 13.9284i −0.771818 + 0.445610i −0.833523 0.552485i \(-0.813680\pi\)
0.0617045 + 0.998094i \(0.480346\pi\)
\(978\) 24.4947 24.1667i 0.783255 0.772765i
\(979\) 2.44399i 0.0781102i
\(980\) 15.4642 + 18.3935i 0.493987 + 0.587558i
\(981\) −0.0470348 0.0280077i −0.00150171 0.000894219i
\(982\) −6.96799 + 12.0689i −0.222357 + 0.385134i
\(983\) 0.330614 + 0.572640i 0.0105449 + 0.0182644i 0.871250 0.490840i \(-0.163310\pi\)
−0.860705 + 0.509104i \(0.829977\pi\)
\(984\) −12.4806 47.8667i −0.397868 1.52594i
\(985\) −10.1079 5.83578i −0.322063 0.185943i
\(986\) −16.7593 −0.533725
\(987\) 9.18286 + 7.80378i 0.292294 + 0.248397i
\(988\) 24.1581 0.768571
\(989\) 0.771231 + 0.445270i 0.0245237 + 0.0141588i
\(990\) 0.263449 19.5397i 0.00837295 0.621011i
\(991\) 25.3374 + 43.8856i 0.804868 + 1.39407i 0.916380 + 0.400309i \(0.131097\pi\)
−0.111513 + 0.993763i \(0.535570\pi\)
\(992\) −19.9795 + 34.6055i −0.634350 + 1.09873i
\(993\) 5.28182 19.1935i 0.167614 0.609089i
\(994\) −22.1534 31.6058i −0.702663 1.00248i
\(995\) 18.5775i 0.588946i
\(996\) −2.78496 2.82276i −0.0882447 0.0894425i
\(997\) 5.21879 3.01307i 0.165281 0.0954249i −0.415078 0.909786i \(-0.636246\pi\)
0.580359 + 0.814361i \(0.302912\pi\)
\(998\) −17.1239 + 9.88647i −0.542047 + 0.312951i
\(999\) −0.506503 2.05571i −0.0160250 0.0650398i
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 105.2.s.d.26.4 yes 8
3.2 odd 2 105.2.s.c.26.1 8
5.2 odd 4 525.2.q.e.299.1 16
5.3 odd 4 525.2.q.e.299.8 16
5.4 even 2 525.2.t.f.26.1 8
7.2 even 3 735.2.b.c.146.1 8
7.3 odd 6 105.2.s.c.101.1 yes 8
7.4 even 3 735.2.s.k.521.1 8
7.5 odd 6 735.2.b.d.146.1 8
7.6 odd 2 735.2.s.l.656.4 8
15.2 even 4 525.2.q.f.299.8 16
15.8 even 4 525.2.q.f.299.1 16
15.14 odd 2 525.2.t.g.26.4 8
21.2 odd 6 735.2.b.d.146.8 8
21.5 even 6 735.2.b.c.146.8 8
21.11 odd 6 735.2.s.l.521.4 8
21.17 even 6 inner 105.2.s.d.101.4 yes 8
21.20 even 2 735.2.s.k.656.1 8
35.3 even 12 525.2.q.f.374.8 16
35.17 even 12 525.2.q.f.374.1 16
35.24 odd 6 525.2.t.g.101.4 8
105.17 odd 12 525.2.q.e.374.8 16
105.38 odd 12 525.2.q.e.374.1 16
105.59 even 6 525.2.t.f.101.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.2.s.c.26.1 8 3.2 odd 2
105.2.s.c.101.1 yes 8 7.3 odd 6
105.2.s.d.26.4 yes 8 1.1 even 1 trivial
105.2.s.d.101.4 yes 8 21.17 even 6 inner
525.2.q.e.299.1 16 5.2 odd 4
525.2.q.e.299.8 16 5.3 odd 4
525.2.q.e.374.1 16 105.38 odd 12
525.2.q.e.374.8 16 105.17 odd 12
525.2.q.f.299.1 16 15.8 even 4
525.2.q.f.299.8 16 15.2 even 4
525.2.q.f.374.1 16 35.17 even 12
525.2.q.f.374.8 16 35.3 even 12
525.2.t.f.26.1 8 5.4 even 2
525.2.t.f.101.1 8 105.59 even 6
525.2.t.g.26.4 8 15.14 odd 2
525.2.t.g.101.4 8 35.24 odd 6
735.2.b.c.146.1 8 7.2 even 3
735.2.b.c.146.8 8 21.5 even 6
735.2.b.d.146.1 8 7.5 odd 6
735.2.b.d.146.8 8 21.2 odd 6
735.2.s.k.521.1 8 7.4 even 3
735.2.s.k.656.1 8 21.20 even 2
735.2.s.l.521.4 8 21.11 odd 6
735.2.s.l.656.4 8 7.6 odd 2