Properties

Label 207.2.i.d.190.2
Level 207207
Weight 22
Character 207.190
Analytic conductor 1.6531.653
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [207,2,Mod(55,207)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(207, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("207.55");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 207=3223 207 = 3^{2} \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 207.i (of order 1111, degree 1010, 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: 1.652903321841.65290332184
Analytic rank: 00
Dimension: 2020
Relative dimension: 22 over Q(ζ11)\Q(\zeta_{11})
Coefficient field: Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x207x19+24x1870x17+209x16527x15+1115x142187x13++529 x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 Copy content Toggle raw display
Coefficient ring: Z[a1,,a4]\Z[a_1, \ldots, a_{4}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 69)
Sato-Tate group: SU(2)[C11]\mathrm{SU}(2)[C_{11}]

Embedding invariants

Embedding label 190.2
Root 0.5459350.160301i0.545935 - 0.160301i of defining polynomial
Character χ\chi == 207.190
Dual form 207.2.i.d.73.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.104892.41937i)q2+(3.322853.83478i)q4+(2.444701.57111i)q5+(0.326826+2.27313i)q7+(7.84516+2.30355i)q8+(1.099987.65055i)q10+(0.04942060.108216i)q11+(0.614381+4.27311i)q13+(5.13843+3.30227i)q14+(1.65065+11.4805i)q16+(1.686041.94579i)q17+(1.131031.30528i)q19+(14.14834.15430i)q200.316419q22+(4.00915+2.63187i)q23+(1.431093.13366i)q25+(11.0171+3.23490i)q26+(9.802936.29996i)q28+(0.9334941.07731i)q29+(5.495271.61356i)q31+(12.1951+7.83731i)q32+(2.844706.22903i)q34+(2.77235+6.07060i)q35+(5.79948+3.72710i)q37+(4.40762+1.29419i)q38+(15.5599+17.9571i)q40+(5.481803.52294i)q41+(8.283852.43236i)q43+(0.250767+0.549102i)q44+(1.93781+12.6075i)q465.91880q47+(1.65616+0.486293i)q49+(6.000286.92469i)q50+(14.344916.5549i)q52+(0.5148953.58117i)q53+(0.2908380.186910i)q55+(2.6722518.5859i)q56+(1.575003.44878i)q58+(0.3861942.68604i)q59+(12.0589+3.54081i)q61+(2.1678715.0779i)q62+(12.92098.30375i)q64+(8.21553+9.48123i)q65+(0.0349839+0.0766041i)q6713.0641q68+17.7502q70+(6.43563+14.0921i)q71+(0.455430+0.525595i)q73+(15.42509.91306i)q74+(1.24721+8.67450i)q76+(0.2621400.0769714i)q77+(1.05210+7.31752i)q79+(14.0019+30.6598i)q80+(2.4665117.1550i)q82+(2.339031.50321i)q83+(1.064807.40583i)q85+(15.0375+17.3542i)q86+(0.636992+0.735128i)q88+(12.74683.74281i)q899.91413q91+(23.4144+6.62886i)q92+(6.53962+14.3198i)q94+(4.815781.41404i)q95+(7.16897+4.60722i)q97+(3.006403.46957i)q98+O(q100)q+(1.10489 - 2.41937i) q^{2} +(-3.32285 - 3.83478i) q^{4} +(2.44470 - 1.57111i) q^{5} +(-0.326826 + 2.27313i) q^{7} +(-7.84516 + 2.30355i) q^{8} +(-1.09998 - 7.65055i) q^{10} +(-0.0494206 - 0.108216i) q^{11} +(0.614381 + 4.27311i) q^{13} +(5.13843 + 3.30227i) q^{14} +(-1.65065 + 11.4805i) q^{16} +(1.68604 - 1.94579i) q^{17} +(-1.13103 - 1.30528i) q^{19} +(-14.1483 - 4.15430i) q^{20} -0.316419 q^{22} +(-4.00915 + 2.63187i) q^{23} +(1.43109 - 3.13366i) q^{25} +(11.0171 + 3.23490i) q^{26} +(9.80293 - 6.29996i) q^{28} +(0.933494 - 1.07731i) q^{29} +(5.49527 - 1.61356i) q^{31} +(12.1951 + 7.83731i) q^{32} +(-2.84470 - 6.22903i) q^{34} +(2.77235 + 6.07060i) q^{35} +(5.79948 + 3.72710i) q^{37} +(-4.40762 + 1.29419i) q^{38} +(-15.5599 + 17.9571i) q^{40} +(5.48180 - 3.52294i) q^{41} +(-8.28385 - 2.43236i) q^{43} +(-0.250767 + 0.549102i) q^{44} +(1.93781 + 12.6075i) q^{46} -5.91880 q^{47} +(1.65616 + 0.486293i) q^{49} +(-6.00028 - 6.92469i) q^{50} +(14.3449 - 16.5549i) q^{52} +(0.514895 - 3.58117i) q^{53} +(-0.290838 - 0.186910i) q^{55} +(-2.67225 - 18.5859i) q^{56} +(-1.57500 - 3.44878i) q^{58} +(-0.386194 - 2.68604i) q^{59} +(-12.0589 + 3.54081i) q^{61} +(2.16787 - 15.0779i) q^{62} +(12.9209 - 8.30375i) q^{64} +(8.21553 + 9.48123i) q^{65} +(-0.0349839 + 0.0766041i) q^{67} -13.0641 q^{68} +17.7502 q^{70} +(-6.43563 + 14.0921i) q^{71} +(0.455430 + 0.525595i) q^{73} +(15.4250 - 9.91306i) q^{74} +(-1.24721 + 8.67450i) q^{76} +(0.262140 - 0.0769714i) q^{77} +(1.05210 + 7.31752i) q^{79} +(14.0019 + 30.6598i) q^{80} +(-2.46651 - 17.1550i) q^{82} +(-2.33903 - 1.50321i) q^{83} +(1.06480 - 7.40583i) q^{85} +(-15.0375 + 17.3542i) q^{86} +(0.636992 + 0.735128i) q^{88} +(-12.7468 - 3.74281i) q^{89} -9.91413 q^{91} +(23.4144 + 6.62886i) q^{92} +(-6.53962 + 14.3198i) q^{94} +(-4.81578 - 1.41404i) q^{95} +(-7.16897 + 4.60722i) q^{97} +(3.00640 - 3.46957i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+4q26q4+6q56q710q818q10+16q11+14q13+22q148q1611q1711q1957q20+26q224q25+14q2614q2812q29+85q98+O(q100) 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29}+ \cdots - 85 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/207Z)×\left(\mathbb{Z}/207\mathbb{Z}\right)^\times.

nn 2828 4747
χ(n)\chi(n) e(911)e\left(\frac{9}{11}\right) 11

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.10489 2.41937i 0.781275 1.71075i 0.0811848 0.996699i 0.474130π-0.474130\pi
0.700090 0.714054i 0.253143π-0.253143\pi
33 0 0
44 −3.32285 3.83478i −1.66143 1.91739i
55 2.44470 1.57111i 1.09330 0.702624i 0.135711 0.990748i 0.456668π-0.456668\pi
0.957593 + 0.288125i 0.0930317π0.0930317\pi
66 0 0
77 −0.326826 + 2.27313i −0.123529 + 0.859161i 0.829979 + 0.557794i 0.188352π0.188352\pi
−0.953508 + 0.301367i 0.902557π0.902557\pi
88 −7.84516 + 2.30355i −2.77368 + 0.814426i
99 0 0
1010 −1.09998 7.65055i −0.347845 2.41932i
1111 −0.0494206 0.108216i −0.0149009 0.0326283i 0.902035 0.431662i 0.142073π-0.142073\pi
−0.916936 + 0.399034i 0.869346π0.869346\pi
1212 0 0
1313 0.614381 + 4.27311i 0.170399 + 1.18515i 0.878044 + 0.478580i 0.158849π0.158849\pi
−0.707645 + 0.706568i 0.750242π0.750242\pi
1414 5.13843 + 3.30227i 1.37330 + 0.882568i
1515 0 0
1616 −1.65065 + 11.4805i −0.412663 + 2.87013i
1717 1.68604 1.94579i 0.408924 0.471923i −0.513507 0.858085i 0.671654π-0.671654\pi
0.922431 + 0.386162i 0.126200π0.126200\pi
1818 0 0
1919 −1.13103 1.30528i −0.259476 0.299452i 0.611031 0.791606i 0.290755π-0.290755\pi
−0.870508 + 0.492155i 0.836209π0.836209\pi
2020 −14.1483 4.15430i −3.16365 0.928931i
2121 0 0
2222 −0.316419 −0.0674607
2323 −4.00915 + 2.63187i −0.835965 + 0.548783i
2424 0 0
2525 1.43109 3.13366i 0.286219 0.626731i
2626 11.0171 + 3.23490i 2.16063 + 0.634417i
2727 0 0
2828 9.80293 6.29996i 1.85258 1.19058i
2929 0.933494 1.07731i 0.173345 0.200051i −0.662428 0.749125i 0.730474π-0.730474\pi
0.835774 + 0.549074i 0.185020π0.185020\pi
3030 0 0
3131 5.49527 1.61356i 0.986980 0.289803i 0.251877 0.967759i 0.418952π-0.418952\pi
0.735103 + 0.677956i 0.237134π0.237134\pi
3232 12.1951 + 7.83731i 2.15581 + 1.38545i
3333 0 0
3434 −2.84470 6.22903i −0.487862 1.06827i
3535 2.77235 + 6.07060i 0.468613 + 1.02612i
3636 0 0
3737 5.79948 + 3.72710i 0.953429 + 0.612731i 0.922172 0.386780i 0.126413π-0.126413\pi
0.0312566 + 0.999511i 0.490049π0.490049\pi
3838 −4.40762 + 1.29419i −0.715010 + 0.209946i
3939 0 0
4040 −15.5599 + 17.9571i −2.46024 + 2.83927i
4141 5.48180 3.52294i 0.856113 0.550190i −0.0373628 0.999302i 0.511896π-0.511896\pi
0.893476 + 0.449111i 0.148259π0.148259\pi
4242 0 0
4343 −8.28385 2.43236i −1.26327 0.370931i −0.419562 0.907726i 0.637816π-0.637816\pi
−0.843712 + 0.536796i 0.819635π0.819635\pi
4444 −0.250767 + 0.549102i −0.0378045 + 0.0827803i
4545 0 0
4646 1.93781 + 12.6075i 0.285714 + 1.85888i
4747 −5.91880 −0.863345 −0.431673 0.902030i 0.642076π-0.642076\pi
−0.431673 + 0.902030i 0.642076π0.642076\pi
4848 0 0
4949 1.65616 + 0.486293i 0.236595 + 0.0694704i
5050 −6.00028 6.92469i −0.848567 0.979299i
5151 0 0
5252 14.3449 16.5549i 1.98929 2.29576i
5353 0.514895 3.58117i 0.0707263 0.491912i −0.923413 0.383807i 0.874613π-0.874613\pi
0.994140 0.108105i 0.0344782π-0.0344782\pi
5454 0 0
5555 −0.290838 0.186910i −0.0392166 0.0252030i
5656 −2.67225 18.5859i −0.357094 2.48364i
5757 0 0
5858 −1.57500 3.44878i −0.206808 0.452846i
5959 −0.386194 2.68604i −0.0502782 0.349692i −0.999395 0.0347692i 0.988930π-0.988930\pi
0.949117 0.314923i 0.101979π-0.101979\pi
6060 0 0
6161 −12.0589 + 3.54081i −1.54398 + 0.453354i −0.939296 0.343109i 0.888520π-0.888520\pi
−0.604687 + 0.796463i 0.706702π0.706702\pi
6262 2.16787 15.0779i 0.275320 1.91490i
6363 0 0
6464 12.9209 8.30375i 1.61511 1.03797i
6565 8.21553 + 9.48123i 1.01901 + 1.17600i
6666 0 0
6767 −0.0349839 + 0.0766041i −0.00427397 + 0.00935868i −0.911757 0.410730i 0.865274π-0.865274\pi
0.907483 + 0.420089i 0.138001π0.138001\pi
6868 −13.0641 −1.58426
6969 0 0
7070 17.7502 2.12155
7171 −6.43563 + 14.0921i −0.763769 + 1.67242i −0.0238577 + 0.999715i 0.507595π0.507595\pi
−0.739911 + 0.672705i 0.765132π0.765132\pi
7272 0 0
7373 0.455430 + 0.525595i 0.0533041 + 0.0615162i 0.781775 0.623560i 0.214314π-0.214314\pi
−0.728471 + 0.685076i 0.759769π0.759769\pi
7474 15.4250 9.91306i 1.79312 1.15237i
7575 0 0
7676 −1.24721 + 8.67450i −0.143064 + 0.995034i
7777 0.262140 0.0769714i 0.0298737 0.00877170i
7878 0 0
7979 1.05210 + 7.31752i 0.118371 + 0.823285i 0.959350 + 0.282218i 0.0910702π0.0910702\pi
−0.840980 + 0.541067i 0.818021π0.818021\pi
8080 14.0019 + 30.6598i 1.56546 + 3.42787i
8181 0 0
8282 −2.46651 17.1550i −0.272381 1.89445i
8383 −2.33903 1.50321i −0.256742 0.164998i 0.405938 0.913901i 0.366945π-0.366945\pi
−0.662680 + 0.748902i 0.730581π0.730581\pi
8484 0 0
8585 1.06480 7.40583i 0.115493 0.803275i
8686 −15.0375 + 17.3542i −1.62154 + 1.87135i
8787 0 0
8888 0.636992 + 0.735128i 0.0679036 + 0.0783649i
8989 −12.7468 3.74281i −1.35116 0.396737i −0.475522 0.879704i 0.657741π-0.657741\pi
−0.875638 + 0.482967i 0.839559π0.839559\pi
9090 0 0
9191 −9.91413 −1.03928
9292 23.4144 + 6.62886i 2.44112 + 0.691107i
9393 0 0
9494 −6.53962 + 14.3198i −0.674510 + 1.47697i
9595 −4.81578 1.41404i −0.494089 0.145077i
9696 0 0
9797 −7.16897 + 4.60722i −0.727898 + 0.467792i −0.851376 0.524555i 0.824232π-0.824232\pi
0.123478 + 0.992347i 0.460595π0.460595\pi
9898 3.00640 3.46957i 0.303692 0.350479i
9999 0 0
100100 −16.7722 + 4.92476i −1.67722 + 0.492476i
101101 −5.88248 3.78044i −0.585328 0.376168i 0.214206 0.976789i 0.431284π-0.431284\pi
−0.799534 + 0.600621i 0.794920π0.794920\pi
102102 0 0
103103 5.73944 + 12.5676i 0.565523 + 1.23832i 0.949147 + 0.314834i 0.101949π0.101949\pi
−0.383623 + 0.923490i 0.625324π0.625324\pi
104104 −14.6632 32.1080i −1.43785 3.14845i
105105 0 0
106106 −8.09528 5.20252i −0.786283 0.505314i
107107 7.88971 2.31663i 0.762727 0.223957i 0.122841 0.992426i 0.460800π-0.460800\pi
0.639886 + 0.768469i 0.278981π0.278981\pi
108108 0 0
109109 11.3104 13.0529i 1.08334 1.25024i 0.116958 0.993137i 0.462686π-0.462686\pi
0.966383 0.257106i 0.0827688π-0.0827688\pi
110110 −0.773550 + 0.497130i −0.0737551 + 0.0473995i
111111 0 0
112112 −25.5572 7.50428i −2.41493 0.709088i
113113 −3.11467 + 6.82019i −0.293004 + 0.641589i −0.997690 0.0679300i 0.978361π-0.978361\pi
0.704686 + 0.709519i 0.251088π0.251088\pi
114114 0 0
115115 −5.66620 + 12.7330i −0.528376 + 1.18736i
116116 −7.23310 −0.671577
117117 0 0
118118 −6.92522 2.03343i −0.637518 0.187192i
119119 3.87198 + 4.46851i 0.354944 + 0.409627i
120120 0 0
121121 7.19420 8.30255i 0.654018 0.754777i
122122 −4.75721 + 33.0871i −0.430698 + 2.99557i
123123 0 0
124124 −24.4476 15.7115i −2.19546 1.41094i
125125 0.643114 + 4.47295i 0.0575218 + 0.400073i
126126 0 0
127127 −0.834395 1.82707i −0.0740406 0.162126i 0.868992 0.494825i 0.164768π-0.164768\pi
−0.943033 + 0.332699i 0.892041π0.892041\pi
128128 −1.68761 11.7376i −0.149165 1.03747i
129129 0 0
130130 32.0159 9.40071i 2.80798 0.824496i
131131 −0.699047 + 4.86198i −0.0610760 + 0.424793i 0.936227 + 0.351396i 0.114293π0.114293\pi
−0.997303 + 0.0733967i 0.976616π0.976616\pi
132132 0 0
133133 3.33672 2.14438i 0.289330 0.185941i
134134 0.146680 + 0.169278i 0.0126712 + 0.0146234i
135135 0 0
136136 −8.74500 + 19.1489i −0.749877 + 1.64200i
137137 −7.93152 −0.677636 −0.338818 0.940852i 0.610027π-0.610027\pi
−0.338818 + 0.940852i 0.610027π0.610027\pi
138138 0 0
139139 10.7987 0.915936 0.457968 0.888969i 0.348577π-0.348577\pi
0.457968 + 0.888969i 0.348577π0.348577\pi
140140 14.0673 30.8030i 1.18890 2.60333i
141141 0 0
142142 26.9833 + 31.1403i 2.26439 + 2.61324i
143143 0.432056 0.277665i 0.0361303 0.0232196i
144144 0 0
145145 0.589538 4.10033i 0.0489585 0.340514i
146146 1.77481 0.521131i 0.146884 0.0431291i
147147 0 0
148148 −4.97822 34.6243i −0.409207 2.84610i
149149 −6.87613 15.0566i −0.563315 1.23349i −0.950281 0.311393i 0.899204π-0.899204\pi
0.386967 0.922094i 0.373523π-0.373523\pi
150150 0 0
151151 −2.68982 18.7081i −0.218895 1.52245i −0.742128 0.670258i 0.766184π-0.766184\pi
0.523234 0.852189i 0.324726π-0.324726\pi
152152 11.8799 + 7.63474i 0.963586 + 0.619259i
153153 0 0
154154 0.103414 0.719260i 0.00833333 0.0579596i
155155 10.8992 12.5784i 0.875446 1.01032i
156156 0 0
157157 −4.95301 5.71608i −0.395293 0.456193i 0.522860 0.852419i 0.324865π-0.324865\pi
−0.918153 + 0.396226i 0.870320π0.870320\pi
158158 18.8662 + 5.53963i 1.50092 + 0.440709i
159159 0 0
160160 42.1267 3.33041
161161 −4.67228 9.97346i −0.368227 0.786019i
162162 0 0
163163 0.693430 1.51840i 0.0543136 0.118930i −0.880529 0.473992i 0.842813π-0.842813\pi
0.934843 + 0.355061i 0.115540π0.115540\pi
164164 −31.7249 9.31527i −2.47730 0.727400i
165165 0 0
166166 −6.22119 + 3.99811i −0.482858 + 0.310314i
167167 14.0362 16.1987i 1.08615 1.25349i 0.120764 0.992681i 0.461465π-0.461465\pi
0.965391 0.260808i 0.0839890π-0.0839890\pi
168168 0 0
169169 −5.40863 + 1.58812i −0.416049 + 0.122163i
170170 −16.7410 10.7588i −1.28397 0.825159i
171171 0 0
172172 18.1985 + 39.8491i 1.38762 + 3.03846i
173173 2.62976 + 5.75836i 0.199937 + 0.437800i 0.982869 0.184307i 0.0590041π-0.0590041\pi
−0.782932 + 0.622107i 0.786277π0.786277\pi
174174 0 0
175175 6.65548 + 4.27722i 0.503107 + 0.323327i
176176 1.32395 0.388747i 0.0997966 0.0293029i
177177 0 0
178178 −23.1391 + 26.7039i −1.73435 + 2.00154i
179179 −6.89203 + 4.42924i −0.515134 + 0.331057i −0.772245 0.635325i 0.780866π-0.780866\pi
0.257110 + 0.966382i 0.417230π0.417230\pi
180180 0 0
181181 −6.05668 1.77840i −0.450189 0.132188i 0.0487755 0.998810i 0.484468π-0.484468\pi
−0.498965 + 0.866622i 0.666286π0.666286\pi
182182 −10.9540 + 23.9859i −0.811966 + 1.77796i
183183 0 0
184184 25.3897 29.8827i 1.87176 2.20298i
185185 20.0337 1.47291
186186 0 0
187187 −0.293890 0.0862939i −0.0214914 0.00631044i
188188 19.6673 + 22.6973i 1.43438 + 1.65537i
189189 0 0
190190 −8.74199 + 10.0888i −0.634211 + 0.731918i
191191 1.84244 12.8144i 0.133314 0.927221i −0.807878 0.589350i 0.799384π-0.799384\pi
0.941192 0.337871i 0.109707π-0.109707\pi
192192 0 0
193193 10.6093 + 6.81818i 0.763674 + 0.490784i 0.863579 0.504213i 0.168217π-0.168217\pi
−0.0999048 + 0.994997i 0.531854π0.531854\pi
194194 3.22565 + 22.4349i 0.231588 + 1.61073i
195195 0 0
196196 −3.63836 7.96689i −0.259883 0.569064i
197197 −2.06820 14.3847i −0.147353 1.02486i −0.920530 0.390673i 0.872242π-0.872242\pi
0.773176 0.634191i 0.218667π-0.218667\pi
198198 0 0
199199 −19.3561 + 5.68347i −1.37212 + 0.402890i −0.883019 0.469337i 0.844493π-0.844493\pi
−0.489100 + 0.872228i 0.662675π0.662675\pi
200200 −4.00863 + 27.8806i −0.283453 + 1.97146i
201201 0 0
202202 −15.6458 + 10.0549i −1.10083 + 0.707462i
203203 2.14377 + 2.47404i 0.150463 + 0.173644i
204204 0 0
205205 7.86642 17.2251i 0.549415 1.20305i
206206 36.7472 2.56030
207207 0 0
208208 −50.0717 −3.47185
209209 −0.0853558 + 0.186903i −0.00590419 + 0.0129284i
210210 0 0
211211 −4.88121 5.63321i −0.336036 0.387806i 0.562433 0.826843i 0.309865π-0.309865\pi
−0.898469 + 0.439036i 0.855320π0.855320\pi
212212 −15.4439 + 9.92520i −1.06069 + 0.681666i
213213 0 0
214214 3.11248 21.6478i 0.212765 1.47981i
215215 −24.0731 + 7.06849i −1.64177 + 0.482067i
216216 0 0
217217 1.87182 + 13.0188i 0.127067 + 0.883774i
218218 −19.0831 41.7861i −1.29247 2.83011i
219219 0 0
220220 0.249653 + 1.73637i 0.0168316 + 0.117066i
221221 9.35044 + 6.00917i 0.628979 + 0.404220i
222222 0 0
223223 −0.239369 + 1.66485i −0.0160293 + 0.111486i −0.996265 0.0863458i 0.972481π-0.972481\pi
0.980236 + 0.197832i 0.0633901π0.0633901\pi
224224 −21.8009 + 25.1596i −1.45663 + 1.68104i
225225 0 0
226226 13.0592 + 15.0711i 0.868684 + 1.00252i
227227 10.3447 + 3.03747i 0.686601 + 0.201604i 0.606383 0.795173i 0.292620π-0.292620\pi
0.0802184 + 0.996777i 0.474438π0.474438\pi
228228 0 0
229229 21.9077 1.44770 0.723852 0.689955i 0.242370π-0.242370\pi
0.723852 + 0.689955i 0.242370π0.242370\pi
230230 24.5453 + 27.7772i 1.61847 + 1.83157i
231231 0 0
232232 −4.84177 + 10.6020i −0.317878 + 0.696056i
233233 23.8637 + 7.00702i 1.56336 + 0.459045i 0.945061 0.326894i 0.106002π-0.106002\pi
0.618304 + 0.785939i 0.287820π0.287820\pi
234234 0 0
235235 −14.4697 + 9.29911i −0.943899 + 0.606607i
236236 −9.01709 + 10.4063i −0.586962 + 0.677391i
237237 0 0
238238 15.0891 4.43056i 0.978080 0.287190i
239239 −3.53060 2.26898i −0.228375 0.146768i 0.421450 0.906852i 0.361521π-0.361521\pi
−0.649825 + 0.760084i 0.725158π0.725158\pi
240240 0 0
241241 −11.3946 24.9507i −0.733991 1.60722i −0.793193 0.608971i 0.791583π-0.791583\pi
0.0592012 0.998246i 0.481145π-0.481145\pi
242242 −12.1381 26.5788i −0.780270 1.70855i
243243 0 0
244244 53.6481 + 34.4776i 3.43447 + 2.20720i
245245 4.81284 1.41318i 0.307481 0.0902847i
246246 0 0
247247 4.88272 5.63496i 0.310680 0.358544i
248248 −39.3944 + 25.3172i −2.50154 + 1.60764i
249249 0 0
250250 11.5323 + 3.38619i 0.729367 + 0.214161i
251251 5.36870 11.7558i 0.338869 0.742020i −0.661096 0.750301i 0.729909π-0.729909\pi
0.999966 + 0.00828064i 0.00263584π0.00263584\pi
252252 0 0
253253 0.482945 + 0.303785i 0.0303625 + 0.0190988i
254254 −5.34227 −0.335204
255255 0 0
256256 −0.788305 0.231467i −0.0492691 0.0144667i
257257 −0.940093 1.08493i −0.0586414 0.0676758i 0.725671 0.688042i 0.241529π-0.241529\pi
−0.784312 + 0.620366i 0.786984π0.786984\pi
258258 0 0
259259 −10.3676 + 11.9648i −0.644211 + 0.743459i
260260 9.05939 63.0095i 0.561840 3.90768i
261261 0 0
262262 10.9906 + 7.06320i 0.678999 + 0.436366i
263263 2.04437 + 14.2189i 0.126061 + 0.876774i 0.950478 + 0.310791i 0.100594π0.100594\pi
−0.824417 + 0.565983i 0.808497π0.808497\pi
264264 0 0
265265 −4.36767 9.56386i −0.268304 0.587503i
266266 −1.50134 10.4421i −0.0920531 0.640244i
267267 0 0
268268 0.410006 0.120389i 0.0250451 0.00735390i
269269 −2.75934 + 19.1916i −0.168240 + 1.17013i 0.714281 + 0.699859i 0.246754π0.246754\pi
−0.882520 + 0.470274i 0.844155π0.844155\pi
270270 0 0
271271 13.7459 8.83395i 0.835004 0.536624i −0.0518607 0.998654i 0.516515π-0.516515\pi
0.886864 + 0.462030i 0.152879π0.152879\pi
272272 19.5556 + 22.5684i 1.18573 + 1.36841i
273273 0 0
274274 −8.76346 + 19.1893i −0.529420 + 1.15927i
275275 −0.409837 −0.0247141
276276 0 0
277277 20.1827 1.21266 0.606332 0.795212i 0.292640π-0.292640\pi
0.606332 + 0.795212i 0.292640π0.292640\pi
278278 11.9314 26.1261i 0.715598 1.56694i
279279 0 0
280280 −35.7334 41.2386i −2.13548 2.46448i
281281 −7.16101 + 4.60210i −0.427190 + 0.274538i −0.736519 0.676417i 0.763532π-0.763532\pi
0.309329 + 0.950955i 0.399896π0.399896\pi
282282 0 0
283283 0.480803 3.34406i 0.0285808 0.198784i −0.970528 0.240987i 0.922529π-0.922529\pi
0.999109 + 0.0422038i 0.0134379π0.0134379\pi
284284 75.4246 22.1466i 4.47562 1.31416i
285285 0 0
286286 −0.194402 1.35209i −0.0114952 0.0799509i
287287 6.21649 + 13.6122i 0.366948 + 0.803503i
288288 0 0
289289 1.47597 + 10.2656i 0.0868220 + 0.603861i
290290 −9.26883 5.95672i −0.544285 0.349791i
291291 0 0
292292 0.502210 3.49295i 0.0293896 0.204409i
293293 −2.70239 + 3.11873i −0.157876 + 0.182198i −0.829177 0.558987i 0.811190π-0.811190\pi
0.671301 + 0.741185i 0.265736π0.265736\pi
294294 0 0
295295 −5.16420 5.95981i −0.300671 0.346993i
296296 −54.0834 15.8803i −3.14353 0.923024i
297297 0 0
298298 −44.0249 −2.55030
299299 −13.7094 15.5146i −0.792837 0.897231i
300300 0 0
301301 8.23643 18.0353i 0.474740 1.03954i
302302 −48.2339 14.1627i −2.77555 0.814975i
303303 0 0
304304 16.8522 10.8303i 0.966542 0.621159i
305305 −23.9174 + 27.6021i −1.36951 + 1.58049i
306306 0 0
307307 −9.98433 + 2.93166i −0.569836 + 0.167319i −0.553943 0.832555i 0.686877π-0.686877\pi
−0.0158931 + 0.999874i 0.505059π0.505059\pi
308308 −1.16622 0.749485i −0.0664517 0.0427059i
309309 0 0
310310 −18.3893 40.2670i −1.04444 2.28701i
311311 −5.48023 12.0000i −0.310756 0.680460i 0.688230 0.725493i 0.258388π-0.258388\pi
−0.998986 + 0.0450328i 0.985661π0.985661\pi
312312 0 0
313313 −11.5760 7.43943i −0.654313 0.420501i 0.170927 0.985284i 0.445324π-0.445324\pi
−0.825240 + 0.564782i 0.808960π0.808960\pi
314314 −19.3018 + 5.66753i −1.08927 + 0.319837i
315315 0 0
316316 24.5651 28.3496i 1.38189 1.59479i
317317 12.0651 7.75378i 0.677645 0.435496i −0.156029 0.987752i 0.549869π-0.549869\pi
0.833674 + 0.552257i 0.186233π0.186233\pi
318318 0 0
319319 −0.162716 0.0477777i −0.00911033 0.00267504i
320320 18.5416 40.6004i 1.03651 2.26963i
321321 0 0
322322 −29.2919 + 0.284406i −1.63237 + 0.0158493i
323323 −4.44676 −0.247424
324324 0 0
325325 14.2697 + 4.18996i 0.791541 + 0.232417i
326326 −2.90741 3.35533i −0.161026 0.185834i
327327 0 0
328328 −34.8903 + 40.2656i −1.92650 + 2.22329i
329329 1.93442 13.4542i 0.106648 0.741753i
330330 0 0
331331 −9.95577 6.39818i −0.547219 0.351676i 0.237638 0.971354i 0.423627π-0.423627\pi
−0.784856 + 0.619678i 0.787263π0.787263\pi
332332 2.00781 + 13.9646i 0.110193 + 0.766407i
333333 0 0
334334 −23.6821 51.8565i −1.29583 2.83746i
335335 0.0348286 + 0.242238i 0.00190289 + 0.0132349i
336336 0 0
337337 −25.6791 + 7.54006i −1.39883 + 0.410733i −0.892281 0.451480i 0.850896π-0.850896\pi
−0.506547 + 0.862213i 0.669078π0.669078\pi
338338 −2.13370 + 14.8402i −0.116058 + 0.807199i
339339 0 0
340340 −31.9379 + 20.5252i −1.73207 + 1.11314i
341341 −0.446192 0.514933i −0.0241626 0.0278852i
342342 0 0
343343 −8.32469 + 18.2285i −0.449491 + 0.984248i
344344 70.5911 3.80602
345345 0 0
346346 16.8372 0.905174
347347 3.67463 8.04631i 0.197264 0.431948i −0.784989 0.619510i 0.787331π-0.787331\pi
0.982253 + 0.187562i 0.0600585π0.0600585\pi
348348 0 0
349349 19.5011 + 22.5054i 1.04387 + 1.20469i 0.978376 + 0.206834i 0.0663160π0.0663160\pi
0.0654913 + 0.997853i 0.479139π0.479139\pi
350350 17.7017 11.3762i 0.946198 0.608084i
351351 0 0
352352 0.245433 1.70703i 0.0130816 0.0909849i
353353 −16.5145 + 4.84909i −0.878978 + 0.258091i −0.689930 0.723877i 0.742359π-0.742359\pi
−0.189048 + 0.981968i 0.560540π0.560540\pi
354354 0 0
355355 6.40705 + 44.5620i 0.340051 + 2.36511i
356356 28.0030 + 61.3180i 1.48416 + 3.24985i
357357 0 0
358358 3.10104 + 21.5682i 0.163895 + 1.13991i
359359 5.99586 + 3.85331i 0.316449 + 0.203370i 0.689217 0.724555i 0.257955π-0.257955\pi
−0.372767 + 0.927925i 0.621591π0.621591\pi
360360 0 0
361361 2.27946 15.8540i 0.119972 0.834420i
362362 −10.9946 + 12.6884i −0.577862 + 0.666888i
363363 0 0
364364 32.9432 + 38.0185i 1.72669 + 1.99271i
365365 1.93916 + 0.569389i 0.101500 + 0.0298032i
366366 0 0
367367 13.5836 0.709060 0.354530 0.935045i 0.384641π-0.384641\pi
0.354530 + 0.935045i 0.384641π0.384641\pi
368368 −23.5976 50.3714i −1.23011 2.62579i
369369 0 0
370370 22.1350 48.4690i 1.15075 2.51978i
371371 7.97218 + 2.34084i 0.413895 + 0.121531i
372372 0 0
373373 15.7544 10.1247i 0.815733 0.524240i −0.0649821 0.997886i 0.520699π-0.520699\pi
0.880715 + 0.473647i 0.157063π0.157063\pi
374374 −0.533493 + 0.615684i −0.0275863 + 0.0318363i
375375 0 0
376376 46.4339 13.6342i 2.39465 0.703131i
377377 5.17699 + 3.32705i 0.266628 + 0.171352i
378378 0 0
379379 −4.16129 9.11196i −0.213751 0.468050i 0.772137 0.635456i 0.219188π-0.219188\pi
−0.985888 + 0.167406i 0.946461π0.946461\pi
380380 10.5796 + 23.1661i 0.542722 + 1.18839i
381381 0 0
382382 −28.9672 18.6161i −1.48209 0.952482i
383383 −27.9432 + 8.20488i −1.42783 + 0.419250i −0.902147 0.431429i 0.858010π-0.858010\pi
−0.525686 + 0.850679i 0.676191π0.676191\pi
384384 0 0
385385 0.519924 0.600025i 0.0264978 0.0305801i
386386 28.2178 18.1345i 1.43625 0.923022i
387387 0 0
388388 41.4891 + 12.1823i 2.10629 + 0.618462i
389389 −1.82086 + 3.98712i −0.0923211 + 0.202155i −0.950159 0.311765i 0.899080π-0.899080\pi
0.857838 + 0.513920i 0.171807π0.171807\pi
390390 0 0
391391 −1.63850 + 12.2384i −0.0828624 + 0.618921i
392392 −14.1130 −0.712816
393393 0 0
394394 −37.0869 10.8897i −1.86841 0.548616i
395395 14.0687 + 16.2362i 0.707875 + 0.816931i
396396 0 0
397397 −0.0954283 + 0.110130i −0.00478941 + 0.00552727i −0.758139 0.652093i 0.773891π-0.773891\pi
0.753350 + 0.657620i 0.228437π0.228437\pi
398398 −7.63595 + 53.1092i −0.382756 + 2.66213i
399399 0 0
400400 33.6138 + 21.6023i 1.68069 + 1.08011i
401401 −4.79060 33.3194i −0.239231 1.66389i −0.655912 0.754837i 0.727716π-0.727716\pi
0.416681 0.909053i 0.363193π-0.363193\pi
402402 0 0
403403 10.2711 + 22.4906i 0.511640 + 1.12034i
404404 5.04947 + 35.1198i 0.251220 + 1.74728i
405405 0 0
406406 8.35425 2.45303i 0.414615 0.121742i
407407 0.116718 0.811791i 0.00578549 0.0402390i
408408 0 0
409409 −25.4633 + 16.3642i −1.25908 + 0.809160i −0.988158 0.153442i 0.950964π-0.950964\pi
−0.270920 + 0.962602i 0.587328π0.587328\pi
410410 −32.9823 38.0636i −1.62888 1.87983i
411411 0 0
412412 29.1227 63.7698i 1.43477 3.14171i
413413 6.23192 0.306653
414414 0 0
415415 −8.07995 −0.396629
416416 −25.9973 + 56.9261i −1.27462 + 2.79103i
417417 0 0
418418 0.357879 + 0.413015i 0.0175045 + 0.0202012i
419419 −15.7624 + 10.1299i −0.770044 + 0.494877i −0.865716 0.500536i 0.833136π-0.833136\pi
0.0956719 + 0.995413i 0.469500π0.469500\pi
420420 0 0
421421 −5.57819 + 38.7972i −0.271864 + 1.89086i 0.157173 + 0.987571i 0.449762π0.449762\pi
−0.429038 + 0.903287i 0.641147π0.641147\pi
422422 −19.0220 + 5.58537i −0.925978 + 0.271892i
423423 0 0
424424 4.20996 + 29.2809i 0.204454 + 1.42201i
425425 −3.68456 8.06806i −0.178727 0.391358i
426426 0 0
427427 −4.10755 28.5686i −0.198778 1.38253i
428428 −35.1001 22.5575i −1.69663 1.09036i
429429 0 0
430430 −9.49678 + 66.0515i −0.457975 + 3.18529i
431431 14.0594 16.2254i 0.677217 0.781550i −0.308271 0.951299i 0.599750π-0.599750\pi
0.985487 + 0.169749i 0.0542957π0.0542957\pi
432432 0 0
433433 0.496613 + 0.573122i 0.0238657 + 0.0275425i 0.767557 0.640981i 0.221472π-0.221472\pi
−0.743691 + 0.668523i 0.766927π0.766927\pi
434434 33.5655 + 9.85571i 1.61119 + 0.473089i
435435 0 0
436436 −87.6378 −4.19709
437437 7.96980 + 2.25633i 0.381247 + 0.107935i
438438 0 0
439439 5.44584 11.9247i 0.259916 0.569136i −0.734016 0.679132i 0.762357π-0.762357\pi
0.993932 + 0.109996i 0.0350838π0.0350838\pi
440440 2.71223 + 0.796382i 0.129300 + 0.0379660i
441441 0 0
442442 24.8696 15.9827i 1.18293 0.760221i
443443 −2.00368 + 2.31237i −0.0951976 + 0.109864i −0.801349 0.598197i 0.795884π-0.795884\pi
0.706152 + 0.708061i 0.250430π0.250430\pi
444444 0 0
445445 −37.0426 + 10.8767i −1.75599 + 0.515604i
446446 3.76340 + 2.41859i 0.178202 + 0.114524i
447447 0 0
448448 14.6526 + 32.0847i 0.692270 + 1.51586i
449449 3.18597 + 6.97630i 0.150355 + 0.329232i 0.969790 0.243940i 0.0784400π-0.0784400\pi
−0.819435 + 0.573172i 0.805713π0.805713\pi
450450 0 0
451451 −0.652151 0.419112i −0.0307086 0.0197352i
452452 36.5035 10.7184i 1.71698 0.504151i
453453 0 0
454454 18.7785 21.6716i 0.881319 1.01710i
455455 −24.2371 + 15.5762i −1.13625 + 0.730225i
456456 0 0
457457 −8.60068 2.52539i −0.402323 0.118133i 0.0743097 0.997235i 0.476325π-0.476325\pi
−0.476633 + 0.879103i 0.658143π0.658143\pi
458458 24.2056 53.0030i 1.13106 2.47667i
459459 0 0
460460 67.6560 20.5812i 3.15448 0.959602i
461461 7.53704 0.351035 0.175517 0.984476i 0.443840π-0.443840\pi
0.175517 + 0.984476i 0.443840π0.443840\pi
462462 0 0
463463 31.6291 + 9.28715i 1.46993 + 0.431610i 0.916076 0.401004i 0.131339π-0.131339\pi
0.553853 + 0.832614i 0.313157π0.313157\pi
464464 10.8272 + 12.4953i 0.502640 + 0.580078i
465465 0 0
466466 43.3194 49.9932i 2.00673 2.31589i
467467 −1.91901 + 13.3470i −0.0888010 + 0.617624i 0.896015 + 0.444024i 0.146449π0.146449\pi
−0.984816 + 0.173601i 0.944460π0.944460\pi
468468 0 0
469469 −0.162697 0.104559i −0.00751265 0.00482809i
470470 6.51058 + 45.2821i 0.300311 + 2.08871i
471471 0 0
472472 9.21716 + 20.1828i 0.424254 + 0.928987i
473473 0.146173 + 1.01665i 0.00672102 + 0.0467457i
474474 0 0
475475 −5.70891 + 1.67629i −0.261943 + 0.0769133i
476476 4.26969 29.6964i 0.195701 1.36113i
477477 0 0
478478 −9.39042 + 6.03486i −0.429508 + 0.276028i
479479 −13.6684 15.7742i −0.624524 0.720740i 0.352035 0.935987i 0.385490π-0.385490\pi
−0.976560 + 0.215247i 0.930944π0.930944\pi
480480 0 0
481481 −12.3632 + 27.0717i −0.563715 + 1.23436i
482482 −72.9548 −3.32300
483483 0 0
484484 −55.7437 −2.53380
485485 −10.2875 + 22.5265i −0.467133 + 1.02288i
486486 0 0
487487 5.41275 + 6.24665i 0.245275 + 0.283063i 0.865016 0.501744i 0.167308π-0.167308\pi
−0.619741 + 0.784806i 0.712762π0.712762\pi
488488 86.4475 55.5564i 3.91329 2.51492i
489489 0 0
490490 1.89866 13.2055i 0.0857727 0.596562i
491491 −10.6572 + 3.12922i −0.480951 + 0.141220i −0.513216 0.858259i 0.671546π-0.671546\pi
0.0322652 + 0.999479i 0.489728π0.489728\pi
492492 0 0
493493 −0.522312 3.63276i −0.0235238 0.163611i
494494 −8.23820 18.0391i −0.370654 0.811619i
495495 0 0
496496 9.45372 + 65.7520i 0.424484 + 2.95235i
497497 −29.9297 19.2347i −1.34253 0.862792i
498498 0 0
499499 0.865761 6.02150i 0.0387568 0.269559i −0.961224 0.275769i 0.911067π-0.911067\pi
0.999981 + 0.00620960i 0.00197659π0.00197659\pi
500500 15.0158 17.3292i 0.671527 0.774984i
501501 0 0
502502 −22.5099 25.9778i −1.00466 1.15944i
503503 −7.54921 2.21665i −0.336602 0.0988354i 0.109063 0.994035i 0.465215π-0.465215\pi
−0.445666 + 0.895199i 0.647033π0.647033\pi
504504 0 0
505505 −20.3204 −0.904246
506506 1.26857 0.832773i 0.0563948 0.0370213i
507507 0 0
508508 −4.23383 + 9.27080i −0.187846 + 0.411325i
509509 28.5327 + 8.37797i 1.26469 + 0.371347i 0.844238 0.535968i 0.180053π-0.180053\pi
0.420453 + 0.907315i 0.361871π0.361871\pi
510510 0 0
511511 −1.34359 + 0.863473i −0.0594369 + 0.0381978i
512512 14.1000 16.2723i 0.623140 0.719142i
513513 0 0
514514 −3.66354 + 1.07571i −0.161592 + 0.0474476i
515515 33.7764 + 21.7068i 1.48836 + 0.956514i
516516 0 0
517517 0.292510 + 0.640508i 0.0128646 + 0.0281695i
518518 17.4923 + 38.3029i 0.768569 + 1.68293i
519519 0 0
520520 −86.2926 55.4569i −3.78418 2.43194i
521521 −18.2067 + 5.34598i −0.797651 + 0.234211i −0.655066 0.755571i 0.727359π-0.727359\pi
−0.142584 + 0.989783i 0.545541π0.545541\pi
522522 0 0
523523 17.3500 20.0229i 0.758661 0.875542i −0.236717 0.971579i 0.576071π-0.576071\pi
0.995378 + 0.0960371i 0.0306168π0.0306168\pi
524524 20.9674 13.4749i 0.915966 0.588656i
525525 0 0
526526 36.6595 + 10.7642i 1.59843 + 0.469342i
527527 6.12558 13.4131i 0.266834 0.584286i
528528 0 0
529529 9.14651 21.1031i 0.397674 0.917527i
530530 −27.9643 −1.21469
531531 0 0
532532 −19.3106 5.67011i −0.837222 0.245831i
533533 18.4218 + 21.2599i 0.797938 + 0.920869i
534534 0 0
535535 15.6483 18.0591i 0.676535 0.780763i
536536 0.0979933 0.681558i 0.00423266 0.0294388i
537537 0 0
538538 43.3829 + 27.8805i 1.87037 + 1.20201i
539539 −0.0292238 0.203256i −0.00125876 0.00875485i
540540 0 0
541541 13.5708 + 29.7159i 0.583454 + 1.27759i 0.939318 + 0.343049i 0.111460π0.111460\pi
−0.355863 + 0.934538i 0.615813π0.615813\pi
542542 −6.18490 43.0170i −0.265664 1.84774i
543543 0 0
544544 35.8111 10.5151i 1.53539 0.450831i
545545 7.14297 49.6805i 0.305971 2.12808i
546546 0 0
547547 38.2357 24.5726i 1.63484 1.05065i 0.689639 0.724153i 0.257769π-0.257769\pi
0.945199 0.326494i 0.105867π-0.105867\pi
548548 26.3553 + 30.4156i 1.12584 + 1.29929i
549549 0 0
550550 −0.452824 + 0.991547i −0.0193085 + 0.0422797i
551551 −2.46200 −0.104885
552552 0 0
553553 −16.9775 −0.721957
554554 22.2997 48.8295i 0.947424 2.07457i
555555 0 0
556556 −35.8826 41.4107i −1.52176 1.75620i
557557 −12.6601 + 8.13615i −0.536425 + 0.344740i −0.780639 0.624982i 0.785106π-0.785106\pi
0.244214 + 0.969721i 0.421470π0.421470\pi
558558 0 0
559559 5.30430 36.8922i 0.224348 1.56037i
560560 −74.2699 + 21.8076i −3.13848 + 0.921539i
561561 0 0
562562 3.22206 + 22.4099i 0.135915 + 0.945307i
563563 14.1960 + 31.0849i 0.598290 + 1.31007i 0.930301 + 0.366796i 0.119545π0.119545\pi
−0.332012 + 0.943275i 0.607727π0.607727\pi
564564 0 0
565565 3.10084 + 21.5668i 0.130453 + 0.907324i
566566 −7.55928 4.85805i −0.317740 0.204199i
567567 0 0
568568 18.0268 125.379i 0.756388 5.26079i
569569 −12.0761 + 13.9366i −0.506257 + 0.584252i −0.950136 0.311835i 0.899056π-0.899056\pi
0.443879 + 0.896087i 0.353602π0.353602\pi
570570 0 0
571571 −4.34404 5.01329i −0.181792 0.209799i 0.657538 0.753422i 0.271598π-0.271598\pi
−0.839330 + 0.543622i 0.817053π0.817053\pi
572572 −2.50044 0.734196i −0.104549 0.0306983i
573573 0 0
574574 39.8015 1.66128
575575 2.50992 + 16.3297i 0.104671 + 0.680997i
576576 0 0
577577 −5.22293 + 11.4366i −0.217433 + 0.476112i −0.986646 0.162881i 0.947921π-0.947921\pi
0.769213 + 0.638993i 0.220649π0.220649\pi
578578 26.4672 + 7.77146i 1.10089 + 0.323250i
579579 0 0
580580 −17.6828 + 11.3640i −0.734237 + 0.471866i
581581 4.18144 4.82563i 0.173475 0.200201i
582582 0 0
583583 −0.412986 + 0.121264i −0.0171041 + 0.00502223i
584584 −4.78365 3.07427i −0.197949 0.127214i
585585 0 0
586586 4.55952 + 9.98395i 0.188352 + 0.412433i
587587 −0.454966 0.996237i −0.0187785 0.0411191i 0.900010 0.435868i 0.143559π-0.143559\pi
−0.918789 + 0.394749i 0.870831π0.870831\pi
588588 0 0
589589 −8.32147 5.34788i −0.342880 0.220356i
590590 −20.1249 + 5.90919i −0.828527 + 0.243278i
591591 0 0
592592 −52.3620 + 60.4290i −2.15206 + 2.48361i
593593 −1.95340 + 1.25538i −0.0802167 + 0.0515521i −0.580134 0.814521i 0.697000π-0.697000\pi
0.499918 + 0.866073i 0.333364π0.333364\pi
594594 0 0
595595 16.4864 + 4.84084i 0.675876 + 0.198455i
596596 −34.8904 + 76.3994i −1.42917 + 3.12944i
597597 0 0
598598 −52.6829 + 16.0263i −2.15436 + 0.655364i
599599 43.0508 1.75901 0.879504 0.475892i 0.157875π-0.157875\pi
0.879504 + 0.475892i 0.157875π0.157875\pi
600600 0 0
601601 −12.7347 3.73926i −0.519461 0.152527i 0.0114837 0.999934i 0.496345π-0.496345\pi
−0.530944 + 0.847407i 0.678163π0.678163\pi
602602 −34.5337 39.8540i −1.40749 1.62433i
603603 0 0
604604 −62.8036 + 72.4793i −2.55544 + 2.94914i
605605 4.54342 31.6002i 0.184716 1.28473i
606606 0 0
607607 −27.6867 17.7932i −1.12377 0.722203i −0.159520 0.987195i 0.550995π-0.550995\pi
−0.964251 + 0.264991i 0.914631π0.914631\pi
608608 −3.56315 24.7822i −0.144505 1.00505i
609609 0 0
610610 40.3537 + 88.3623i 1.63387 + 3.57769i
611611 −3.63640 25.2917i −0.147113 1.02319i
612612 0 0
613613 38.7731 11.3848i 1.56603 0.459828i 0.620188 0.784454i 0.287057π-0.287057\pi
0.945843 + 0.324626i 0.105238π0.105238\pi
614614 −3.93880 + 27.3950i −0.158957 + 1.10557i
615615 0 0
616616 −1.87923 + 1.20770i −0.0757162 + 0.0486598i
617617 19.6464 + 22.6732i 0.790935 + 0.912788i 0.997848 0.0655717i 0.0208871π-0.0208871\pi
−0.206913 + 0.978359i 0.566342π0.566342\pi
618618 0 0
619619 11.0046 24.0967i 0.442313 0.968530i −0.548855 0.835918i 0.684936π-0.684936\pi
0.991168 0.132613i 0.0423366π-0.0423366\pi
620620 −84.4517 −3.39166
621621 0 0
622622 −35.0876 −1.40688
623623 12.6739 27.7519i 0.507768 1.11186i
624624 0 0
625625 19.8796 + 22.9423i 0.795185 + 0.917692i
626626 −30.7889 + 19.7868i −1.23057 + 0.790841i
627627 0 0
628628 −5.46176 + 37.9874i −0.217948 + 1.51586i
629629 17.0303 5.00054i 0.679041 0.199385i
630630 0 0
631631 −2.28418 15.8868i −0.0909316 0.632443i −0.983416 0.181365i 0.941948π-0.941948\pi
0.892484 0.451079i 0.148961π-0.148961\pi
632632 −25.1101 54.9835i −0.998827 2.18713i
633633 0 0
634634 −5.42865 37.7571i −0.215599 1.49953i
635635 −4.91038 3.15571i −0.194863 0.125231i
636636 0 0
637637 −1.06047 + 7.37574i −0.0420174 + 0.292237i
638638 −0.295375 + 0.340881i −0.0116940 + 0.0134956i
639639 0 0
640640 −22.5668 26.0435i −0.892031 1.02946i
641641 −44.9585 13.2010i −1.77575 0.521408i −0.781074 0.624438i 0.785328π-0.785328\pi
−0.994678 + 0.103030i 0.967146π0.967146\pi
642642 0 0
643643 −27.2328 −1.07396 −0.536979 0.843596i 0.680435π-0.680435\pi
−0.536979 + 0.843596i 0.680435π0.680435\pi
644644 −22.7207 + 51.0575i −0.895321 + 2.01195i
645645 0 0
646646 −4.91317 + 10.7584i −0.193306 + 0.423282i
647647 23.7997 + 6.98823i 0.935664 + 0.274736i 0.713806 0.700343i 0.246970π-0.246970\pi
0.221858 + 0.975079i 0.428788π0.428788\pi
648648 0 0
649649 −0.271586 + 0.174538i −0.0106607 + 0.00685121i
650650 25.9035 29.8943i 1.01602 1.17255i
651651 0 0
652652 −8.12689 + 2.38627i −0.318274 + 0.0934535i
653653 24.7733 + 15.9208i 0.969455 + 0.623031i 0.926599 0.376050i 0.122718π-0.122718\pi
0.0428558 + 0.999081i 0.486354π0.486354\pi
654654 0 0
655655 5.92976 + 12.9844i 0.231695 + 0.507341i
656656 31.3967 + 68.7491i 1.22583 + 2.68420i
657657 0 0
658658 −30.4133 19.5455i −1.18563 0.761961i
659659 13.4131 3.93844i 0.522500 0.153420i −0.00983813 0.999952i 0.503132π-0.503132\pi
0.532338 + 0.846532i 0.321313π0.321313\pi
660660 0 0
661661 16.2537 18.7578i 0.632196 0.729593i −0.345779 0.938316i 0.612385π-0.612385\pi
0.977975 + 0.208723i 0.0669308π0.0669308\pi
662662 −26.4796 + 17.0174i −1.02916 + 0.661400i
663663 0 0
664664 21.8128 + 6.40481i 0.846501 + 0.248555i
665665 4.78822 10.4847i 0.185679 0.406580i
666666 0 0
667667 −0.907174 + 6.77593i −0.0351259 + 0.262365i
668668 −108.758 −4.20799
669669 0 0
670670 0.624545 + 0.183383i 0.0241283 + 0.00708470i
671671 0.979129 + 1.12998i 0.0377989 + 0.0436222i
672672 0 0
673673 −5.82979 + 6.72793i −0.224722 + 0.259343i −0.856903 0.515478i 0.827614π-0.827614\pi
0.632181 + 0.774821i 0.282160π0.282160\pi
674674 −10.1303 + 70.4581i −0.390206 + 2.71395i
675675 0 0
676676 24.0622 + 15.4638i 0.925468 + 0.594762i
677677 0.401463 + 2.79223i 0.0154295 + 0.107314i 0.996081 0.0884485i 0.0281909π-0.0281909\pi
−0.980651 + 0.195763i 0.937282π0.937282\pi
678678 0 0
679679 −8.12978 17.8017i −0.311992 0.683168i
680680 8.70616 + 60.5527i 0.333866 + 2.32209i
681681 0 0
682682 −1.73881 + 0.510560i −0.0665823 + 0.0195503i
683683 2.95100 20.5247i 0.112917 0.785355i −0.852140 0.523314i 0.824695π-0.824695\pi
0.965057 0.262041i 0.0843956π-0.0843956\pi
684684 0 0
685685 −19.3902 + 12.4613i −0.740862 + 0.476123i
686686 34.9037 + 40.2810i 1.33263 + 1.53794i
687687 0 0
688688 41.5985 91.0880i 1.58593 3.47270i
689689 15.6191 0.595040
690690 0 0
691691 1.36601 0.0519655 0.0259827 0.999662i 0.491729π-0.491729\pi
0.0259827 + 0.999662i 0.491729π0.491729\pi
692692 13.3437 29.2187i 0.507253 1.11073i
693693 0 0
694694 −15.4069 17.7806i −0.584840 0.674941i
695695 26.3997 16.9660i 1.00140 0.643558i
696696 0 0
697697 2.38761 16.6062i 0.0904373 0.629005i
698698 75.9955 22.3143i 2.87647 0.844608i
699699 0 0
700700 −5.71301 39.7348i −0.215931 1.50184i
701701 −12.5045 27.3810i −0.472288 1.03417i −0.984512 0.175315i 0.943906π-0.943906\pi
0.512224 0.858852i 0.328822π-0.328822\pi
702702 0 0
703703 −1.69449 11.7854i −0.0639087 0.444495i
704704 −1.53716 0.987870i −0.0579337 0.0372317i
705705 0 0
706706 −6.51494 + 45.3124i −0.245193 + 1.70535i
707707 10.5160 12.1361i 0.395493 0.456424i
708708 0 0
709709 25.9980 + 30.0033i 0.976375 + 1.12680i 0.991913 + 0.126918i 0.0405085π0.0405085\pi
−0.0155379 + 0.999879i 0.504946π0.504946\pi
710710 114.891 + 33.7351i 4.31179 + 1.26605i
711711 0 0
712712 108.623 4.07080
713713 −17.7847 + 20.9318i −0.666041 + 0.783903i
714714 0 0
715715 0.620004 1.35762i 0.0231868 0.0507721i
716716 39.8863 + 11.7117i 1.49062 + 0.437686i
717717 0 0
718718 15.9473 10.2487i 0.595149 0.382479i
719719 −6.00668 + 6.93208i −0.224011 + 0.258523i −0.856619 0.515950i 0.827439π-0.827439\pi
0.632608 + 0.774473i 0.281985π0.281985\pi
720720 0 0
721721 −30.4436 + 8.93904i −1.13378 + 0.332907i
722722 −35.8381 23.0318i −1.33376 0.857153i
723723 0 0
724724 13.3057 + 29.1354i 0.494502 + 1.08281i
725725 −2.04000 4.46698i −0.0757637 0.165899i
726726 0 0
727727 −3.19987 2.05643i −0.118676 0.0762687i 0.479956 0.877293i 0.340653π-0.340653\pi
−0.598632 + 0.801024i 0.704289π0.704289\pi
728728 77.7779 22.8376i 2.88264 0.846419i
729729 0 0
730730 3.52012 4.06244i 0.130286 0.150358i
731731 −18.6997 + 12.0176i −0.691634 + 0.444486i
732732 0 0
733733 −39.2138 11.5142i −1.44839 0.425287i −0.539384 0.842060i 0.681343π-0.681343\pi
−0.909011 + 0.416773i 0.863161π0.863161\pi
734734 15.0084 32.8638i 0.553971 1.21303i
735735 0 0
736736 −69.5187 + 0.674985i −2.56249 + 0.0248803i
737737 0.0100187 0.000369044
738738 0 0
739739 28.0767 + 8.24407i 1.03282 + 0.303263i 0.753856 0.657039i 0.228191π-0.228191\pi
0.278962 + 0.960302i 0.410010π0.410010\pi
740740 −66.5690 76.8248i −2.44713 2.82413i
741741 0 0
742742 14.4717 16.7013i 0.531274 0.613123i
743743 −1.23262 + 8.57306i −0.0452204 + 0.314515i 0.954639 + 0.297765i 0.0962411π0.0962411\pi
−0.999860 + 0.0167502i 0.994668π0.994668\pi
744744 0 0
745745 −40.4658 26.0058i −1.48255 0.952778i
746746 −7.08863 49.3025i −0.259533 1.80509i
747747 0 0
748748 0.645636 + 1.41374i 0.0236068 + 0.0516916i
749749 2.68742 + 18.6914i 0.0981964 + 0.682971i
750750 0 0
751751 −6.59622 + 1.93683i −0.240700 + 0.0706758i −0.399857 0.916577i 0.630940π-0.630940\pi
0.159158 + 0.987253i 0.449122π0.449122\pi
752752 9.76987 67.9509i 0.356270 2.47792i
753753 0 0
754754 13.7694 8.84903i 0.501450 0.322263i
755755 −35.9685 41.5098i −1.30903 1.51070i
756756 0 0
757757 −1.31155 + 2.87190i −0.0476692 + 0.104381i −0.931968 0.362540i 0.881910π-0.881910\pi
0.884299 + 0.466921i 0.154637π0.154637\pi
758758 −26.6430 −0.967717
759759 0 0
760760 41.0378 1.48860
761761 −7.11532 + 15.5804i −0.257930 + 0.564788i −0.993652 0.112495i 0.964116π-0.964116\pi
0.735722 + 0.677284i 0.236843π0.236843\pi
762762 0 0
763763 25.9744 + 29.9760i 0.940336 + 1.08521i
764764 −55.2627 + 35.5152i −1.99933 + 1.28489i
765765 0 0
766766 −11.0236 + 76.6706i −0.398298 + 2.77022i
767767 11.2405 3.30050i 0.405870 0.119174i
768768 0 0
769769 3.01514 + 20.9707i 0.108729 + 0.756224i 0.969120 + 0.246590i 0.0793101π0.0793101\pi
−0.860391 + 0.509634i 0.829781π0.829781\pi
770770 −0.877223 1.92085i −0.0316129 0.0692227i
771771 0 0
772772 −9.10694 63.3401i −0.327766 2.27966i
773773 −4.49268 2.88727i −0.161590 0.103848i 0.457346 0.889289i 0.348800π-0.348800\pi
−0.618937 + 0.785441i 0.712436π0.712436\pi
774774 0 0
775775 2.80791 19.5294i 0.100863 0.701518i
776776 45.6287 52.6584i 1.63798 1.89033i
777777 0 0
778778 7.63448 + 8.81066i 0.273709 + 0.315877i
779779 −10.7985 3.17073i −0.386897 0.113603i
780780 0 0
781781 1.84304 0.0659491
782782 27.7988 + 17.4862i 0.994084 + 0.625305i
783783 0 0
784784 −8.31664 + 18.2109i −0.297023 + 0.650390i
785785 −21.0893 6.19236i −0.752708 0.221015i
786786 0 0
787787 36.6862 23.5768i 1.30772 0.840423i 0.313693 0.949525i 0.398434π-0.398434\pi
0.994031 + 0.109102i 0.0347975π0.0347975\pi
788788 −48.2896 + 55.7292i −1.72025 + 1.98527i
789789 0 0
790790 54.8257 16.0983i 1.95061 0.572751i
791791 −14.4852 9.30907i −0.515034 0.330992i
792792 0 0
793793 −22.5390 49.3536i −0.800385 1.75260i
794794 0.161008 + 0.352558i 0.00571396 + 0.0125118i
795795 0 0
796796 86.1124 + 55.3410i 3.05217 + 1.96151i
797797 −11.1289 + 3.26774i −0.394205 + 0.115749i −0.472827 0.881155i 0.656766π-0.656766\pi
0.0786214 + 0.996905i 0.474948π0.474948\pi
798798 0 0
799799 −9.97930 + 11.5167i −0.353042 + 0.407432i
800800 42.0117 26.9993i 1.48534 0.954570i
801801 0 0
802802 −85.9050 25.2240i −3.03341 0.890690i
803803 0.0343701 0.0752600i 0.00121289 0.00265587i
804804 0 0
805805 −27.0918 17.0415i −0.954860 0.600632i
806806 65.7615 2.31635
807807 0 0
808808 54.8574 + 16.1076i 1.92988 + 0.566663i
809809 −5.11925 5.90793i −0.179983 0.207712i 0.658588 0.752504i 0.271154π-0.271154\pi
−0.838571 + 0.544792i 0.816609π0.816609\pi
810810 0 0
811811 −7.54232 + 8.70430i −0.264847 + 0.305649i −0.872560 0.488507i 0.837542π-0.837542\pi
0.607713 + 0.794157i 0.292087π0.292087\pi
812812 2.36397 16.4418i 0.0829590 0.576993i
813813 0 0
814814 −1.83506 1.17932i −0.0643189 0.0413353i
815815 −0.690351 4.80149i −0.0241819 0.168189i
816816 0 0
817817 6.19438 + 13.5638i 0.216714 + 0.474538i
818818 11.4571 + 79.6858i 0.400588 + 2.78615i
819819 0 0
820820 −92.1932 + 27.0704i −3.21953 + 0.945339i
821821 −0.0743036 + 0.516793i −0.00259321 + 0.0180362i −0.991077 0.133291i 0.957446π-0.957446\pi
0.988484 + 0.151327i 0.0483547π0.0483547\pi
822822 0 0
823823 −28.0088 + 18.0002i −0.976327 + 0.627447i −0.928470 0.371407i 0.878876π-0.878876\pi
−0.0478569 + 0.998854i 0.515239π0.515239\pi
824824 −73.9768 85.3738i −2.57711 2.97414i
825825 0 0
826826 6.88558 15.0773i 0.239580 0.524607i
827827 −24.2079 −0.841791 −0.420895 0.907109i 0.638284π-0.638284\pi
−0.420895 + 0.907109i 0.638284π0.638284\pi
828828 0 0
829829 26.4851 0.919866 0.459933 0.887954i 0.347873π-0.347873\pi
0.459933 + 0.887954i 0.347873π0.347873\pi
830830 −8.92746 + 19.5484i −0.309876 + 0.678535i
831831 0 0
832832 43.4212 + 50.1108i 1.50536 + 1.73728i
833833 3.73857 2.40263i 0.129534 0.0832463i
834834 0 0
835835 8.86442 61.6534i 0.306766 2.13360i
836836 1.00036 0.293731i 0.0345981 0.0101589i
837837 0 0
838838 7.09223 + 49.3275i 0.244997 + 1.70399i
839839 16.0962 + 35.2458i 0.555703 + 1.21682i 0.954067 + 0.299593i 0.0968510π0.0968510\pi
−0.398364 + 0.917228i 0.630422π0.630422\pi
840840 0 0
841841 3.83795 + 26.6935i 0.132343 + 0.920465i
842842 87.7014 + 56.3623i 3.02239 + 1.94237i
843843 0 0
844844 −5.38258 + 37.4367i −0.185276 + 1.28862i
845845 −10.7274 + 12.3801i −0.369033 + 0.425887i
846846 0 0
847847 16.5215 + 19.0668i 0.567685 + 0.655144i
848848 40.2638 + 11.8225i 1.38267 + 0.405987i
849849 0 0
850850 −23.5907 −0.809153
851851 −33.0602 + 0.320995i −1.13329 + 0.0110036i
852852 0 0
853853 3.66776 8.03127i 0.125582 0.274985i −0.836390 0.548135i 0.815338π-0.815338\pi
0.961972 + 0.273149i 0.0880654π0.0880654\pi
854854 −73.6565 21.6275i −2.52047 0.740078i
855855 0 0
856856 −56.5596 + 36.3486i −1.93317 + 1.24237i
857857 −0.448206 + 0.517257i −0.0153104 + 0.0176692i −0.763353 0.645981i 0.776448π-0.776448\pi
0.748043 + 0.663651i 0.230994π0.230994\pi
858858 0 0
859859 −12.1210 + 3.55905i −0.413563 + 0.121433i −0.481894 0.876230i 0.660051π-0.660051\pi
0.0683306 + 0.997663i 0.478233π0.478233\pi
860860 107.097 + 68.8272i 3.65199 + 2.34699i
861861 0 0
862862 −23.7212 51.9421i −0.807946 1.76916i
863863 2.36065 + 5.16909i 0.0803573 + 0.175958i 0.945546 0.325488i 0.105529π-0.105529\pi
−0.865189 + 0.501446i 0.832801π0.832801\pi
864864 0 0
865865 15.4760 + 9.94583i 0.526200 + 0.338168i
866866 1.93530 0.568255i 0.0657641 0.0193101i
867867 0 0
868868 43.7044 50.4376i 1.48342 1.71196i
869869 0.739876 0.475490i 0.0250986 0.0161299i
870870 0 0
871871 −0.348831 0.102426i −0.0118197 0.00347058i
872872 −58.6640 + 128.456i −1.98661 + 4.35008i
873873 0 0
874874 14.2646 16.7889i 0.482509 0.567893i
875875 −10.3778 −0.350833
876876 0 0
877877 21.7361 + 6.38228i 0.733974 + 0.215514i 0.627298 0.778779i 0.284161π-0.284161\pi
0.106677 + 0.994294i 0.465979π0.465979\pi
878878 −22.8333 26.3510i −0.770585 0.889303i
879879 0 0
880880 2.62590 3.03045i 0.0885191 0.102157i
881881 −3.21562 + 22.3652i −0.108337 + 0.753501i 0.861149 + 0.508353i 0.169746π0.169746\pi
−0.969486 + 0.245148i 0.921164π0.921164\pi
882882 0 0
883883 34.5835 + 22.2255i 1.16383 + 0.747947i 0.972345 0.233549i 0.0750341π-0.0750341\pi
0.191483 + 0.981496i 0.438670π0.438670\pi
884884 −8.02634 55.8244i −0.269955 1.87758i
885885 0 0
886886 3.38063 + 7.40255i 0.113575 + 0.248693i
887887 −0.776455 5.40036i −0.0260708 0.181326i 0.972625 0.232380i 0.0746512π-0.0746512\pi
−0.998696 + 0.0510534i 0.983742π0.983742\pi
888888 0 0
889889 4.42586 1.29955i 0.148439 0.0435855i
890890 −14.6132 + 101.637i −0.489837 + 3.40689i
891891 0 0
892892 7.17970 4.61411i 0.240394 0.154492i
893893 6.69434 + 7.72569i 0.224018 + 0.258530i
894894 0 0
895895 −9.89011 + 21.6563i −0.330590 + 0.723891i
896896 27.2326 0.909776
897897 0 0
898898 20.3984 0.680703
899899 3.39150 7.42635i 0.113113 0.247683i
900900 0 0
901901 −6.10007 7.03986i −0.203223 0.234532i
902902 −1.73454 + 1.11472i −0.0577540 + 0.0371162i
903903 0 0
904904 8.72450 60.6802i 0.290173 2.01819i
905905 −17.6008 + 5.16807i −0.585072 + 0.171793i
906906 0 0
907907 −4.00188 27.8337i −0.132880 0.924202i −0.941774 0.336247i 0.890842π-0.890842\pi
0.808894 0.587955i 0.200067π-0.200067\pi
908908 −22.7258 49.7626i −0.754183 1.65143i
909909 0 0
910910 10.9054 + 75.8485i 0.361509 + 2.51435i
911911 48.0980 + 30.9107i 1.59356 + 1.02412i 0.970239 + 0.242151i 0.0778530π0.0778530\pi
0.623320 + 0.781967i 0.285783π0.285783\pi
912912 0 0
913913 −0.0470745 + 0.327410i −0.00155794 + 0.0108357i
914914 −15.6127 + 18.0180i −0.516421 + 0.595981i
915915 0 0
916916 −72.7962 84.0113i −2.40525 2.77581i
917917 −10.8234 3.17804i −0.357421 0.104948i
918918 0 0
919919 16.3674 0.539909 0.269955 0.962873i 0.412991π-0.412991\pi
0.269955 + 0.962873i 0.412991π0.412991\pi
920920 15.1212 112.944i 0.498532 3.72367i
921921 0 0
922922 8.32759 18.2349i 0.274255 0.600534i
923923 −64.1709 18.8423i −2.11221 0.620201i
924924 0 0
925925 19.9790 12.8397i 0.656907 0.422168i
926926 57.4157 66.2613i 1.88680 2.17748i
927927 0 0
928928 19.8272 5.82181i 0.650861 0.191110i
929929 −32.1390 20.6545i −1.05445 0.677651i −0.105928 0.994374i 0.533781π-0.533781\pi
−0.948518 + 0.316723i 0.897418π0.897418\pi
930930 0 0
931931 −1.23842 2.71177i −0.0405877 0.0888746i
932932 −52.4253 114.795i −1.71725 3.76025i
933933 0 0
934934 30.1710 + 19.3897i 0.987225 + 0.634451i
935935 −0.854051 + 0.250772i −0.0279305 + 0.00820112i
936936 0 0
937937 −9.21800 + 10.6381i −0.301139 + 0.347533i −0.886071 0.463549i 0.846576π-0.846576\pi
0.584932 + 0.811082i 0.301121π0.301121\pi
938938 −0.432730 + 0.278098i −0.0141291 + 0.00908023i
939939 0 0
940940 83.7407 + 24.5885i 2.73132 + 0.801988i
941941 18.0891 39.6097i 0.589689 1.29124i −0.345940 0.938256i 0.612440π-0.612440\pi
0.935630 0.352983i 0.114833π-0.114833\pi
942942 0 0
943943 −12.7054 + 28.5514i −0.413745 + 0.929760i
944944 31.4746 1.02441
945945 0 0
946946 2.62116 + 0.769643i 0.0852214 + 0.0250233i
947947 20.1689 + 23.2762i 0.655403 + 0.756375i 0.982019 0.188782i 0.0604540π-0.0604540\pi
−0.326616 + 0.945157i 0.605908π0.605908\pi
948948 0 0
949949 −1.96612 + 2.26902i −0.0638229 + 0.0736556i
950950 −2.25215 + 15.6641i −0.0730695 + 0.508210i
951951 0 0
952952 −40.6697 26.1368i −1.31811 0.847100i
953953 7.63117 + 53.0760i 0.247198 + 1.71930i 0.614261 + 0.789103i 0.289454π0.289454\pi
−0.367063 + 0.930196i 0.619637π0.619637\pi
954954 0 0
955955 −15.6288 34.2222i −0.505734 1.10740i
956956 3.03063 + 21.0785i 0.0980177 + 0.681728i
957957 0 0
958958 −53.2656 + 15.6402i −1.72093 + 0.505312i
959959 2.59223 18.0294i 0.0837075 0.582198i
960960 0 0
961961 1.51558 0.974001i 0.0488895 0.0314194i
962962 51.8365 + 59.8225i 1.67127 + 1.92875i
963963 0 0
964964 −57.8178 + 126.603i −1.86219 + 4.07762i
965965 36.6487 1.17976
966966 0 0
967967 −35.8006 −1.15127 −0.575635 0.817707i 0.695245π-0.695245\pi
−0.575635 + 0.817707i 0.695245π0.695245\pi
968968 −37.3143 + 81.7070i −1.19933 + 2.62616i
969969 0 0
970970 43.1335 + 49.7787i 1.38493 + 1.59830i
971971 17.7167 11.3859i 0.568557 0.365390i −0.224558 0.974461i 0.572094π-0.572094\pi
0.793116 + 0.609071i 0.208458π0.208458\pi
972972 0 0
973973 −3.52931 + 24.5469i −0.113144 + 0.786937i
974974 21.0934 6.19359i 0.675878 0.198456i
975975 0 0
976976 −20.7454 144.287i −0.664043 4.61852i
977977 17.6014 + 38.5417i 0.563119 + 1.23306i 0.950381 + 0.311088i 0.100693π0.100693\pi
−0.387262 + 0.921970i 0.626579π0.626579\pi
978978 0 0
979979 0.224924 + 1.56438i 0.00718860 + 0.0499978i
980980 −21.4116 13.7604i −0.683968 0.439560i
981981 0 0
982982 −4.20423 + 29.2411i −0.134162 + 0.933120i
983983 18.1016 20.8903i 0.577351 0.666299i −0.389682 0.920949i 0.627415π-0.627415\pi
0.967033 + 0.254651i 0.0819605π0.0819605\pi
984984 0 0
985985 −27.6561 31.9168i −0.881196 1.01695i
986986 −9.36610 2.75013i −0.298277 0.0875821i
987987 0 0
988988 −37.8334 −1.20364
989989 39.6128 12.0503i 1.25961 0.383179i
990990 0 0
991991 −18.8737 + 41.3276i −0.599543 + 1.31282i 0.329958 + 0.943996i 0.392966π0.392966\pi
−0.929501 + 0.368820i 0.879762π0.879762\pi
992992 79.6613 + 23.3907i 2.52925 + 0.742654i
993993 0 0
994994 −79.6048 + 51.1589i −2.52491 + 1.62266i
995995 −38.3906 + 44.3051i −1.21706 + 1.40457i
996996 0 0
997997 12.5546 3.68635i 0.397607 0.116748i −0.0768154 0.997045i 0.524475π-0.524475\pi
0.474422 + 0.880297i 0.342657π0.342657\pi
998998 −13.6117 8.74769i −0.430870 0.276903i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 207.2.i.d.190.2 20
3.2 odd 2 69.2.e.c.52.1 yes 20
23.2 even 11 4761.2.a.bt.1.10 10
23.4 even 11 inner 207.2.i.d.73.2 20
23.21 odd 22 4761.2.a.bu.1.10 10
69.2 odd 22 1587.2.a.u.1.1 10
69.44 even 22 1587.2.a.t.1.1 10
69.50 odd 22 69.2.e.c.4.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.2.e.c.4.1 20 69.50 odd 22
69.2.e.c.52.1 yes 20 3.2 odd 2
207.2.i.d.73.2 20 23.4 even 11 inner
207.2.i.d.190.2 20 1.1 even 1 trivial
1587.2.a.t.1.1 10 69.44 even 22
1587.2.a.u.1.1 10 69.2 odd 22
4761.2.a.bt.1.10 10 23.2 even 11
4761.2.a.bu.1.10 10 23.21 odd 22