Properties

Label 171.4.y.a.53.16
Level 171171
Weight 44
Character 171.53
Analytic conductor 10.08910.089
Analytic rank 00
Dimension 120120
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [171,4,Mod(53,171)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(171, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 11]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("171.53");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 171=3219 171 = 3^{2} \cdot 19
Weight: k k == 4 4
Character orbit: [χ][\chi] == 171.y (of order 1818, degree 66, 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: 10.089326611010.0893266110
Analytic rank: 00
Dimension: 120120
Relative dimension: 2020 over Q(ζ18)\Q(\zeta_{18})
Twist minimal: yes
Sato-Tate group: SU(2)[C18]\mathrm{SU}(2)[C_{18}]

Embedding invariants

Embedding label 53.16
Character χ\chi == 171.53
Dual form 171.4.y.a.71.16

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+(3.36331+1.22414i)q2+(3.68495+3.09204i)q4+(13.301915.8526i)q5+(7.77429+13.4655i)q7+(5.708119.88673i)q8+(25.332569.6004i)q10+(0.5079630.293273i)q11+(46.33978.17093i)q13+(42.6310+35.7717i)q14+(13.777878.1379i)q16+(10.694329.3824i)q17+(31.041376.7818i)q1999.5459iq20+(2.067440.364546i)q22+(15.0014+17.8779i)q23+(52.6577+298.637i)q25+(145.85284.2078i)q26+(70.2837+25.5812i)q28+(267.61797.4045i)q29+(86.4832+49.9311i)q31+(33.4537189.726i)q32+(71.936685.7307i)q34+(316.87555.8736i)q3553.8378iq37+(10.4094296.240i)q38+(80.8014+222.000i)q40+(58.8231+333.603i)q41+(199.580+167.468i)q43+(2.77863+0.489948i)q44+(72.3393+41.7651i)q46+(210.832579.255i)q47+(50.6207+87.6777i)q49+(542.678+939.946i)q50+(145.495173.394i)q52+(116.390+97.6631i)q53+(11.40604.15144i)q55+177.506q56+1019.31q58+(425.794154.976i)q59+(479.767402.572i)q61+(229.747+273.801i)q62+(27.393447.4467i)q64+(486.874+843.291i)q65+(309.378850.010i)q67+(130.26075.2055i)q68+(1134.14+199.980i)q70+(186.080156.140i)q71+(59.3899+336.817i)q73+(65.9052181.073i)q74+(123.027378.918i)q76+9.11995iq77+(551.53897.2510i)q79+(1055.41+1257.79i)q80+(210.537+1194.02i)q82+(518.748299.499i)q83+(608.041+221.309i)q85+(876.255+318.931i)q86+(5.799023.34806i)q88+(207.6851177.84i)q89+(470.284560.462i)q91+(110.559+19.4944i)q922206.30iq94+(804.281+1513.42i)q95+(71.1316195.432i)q97+(62.9230+356.854i)q98+O(q100)q+(3.36331 + 1.22414i) q^{2} +(3.68495 + 3.09204i) q^{4} +(-13.3019 - 15.8526i) q^{5} +(-7.77429 + 13.4655i) q^{7} +(-5.70811 - 9.88673i) q^{8} +(-25.3325 - 69.6004i) q^{10} +(0.507963 - 0.293273i) q^{11} +(-46.3397 - 8.17093i) q^{13} +(-42.6310 + 35.7717i) q^{14} +(-13.7778 - 78.1379i) q^{16} +(10.6943 - 29.3824i) q^{17} +(-31.0413 - 76.7818i) q^{19} -99.5459i q^{20} +(2.06744 - 0.364546i) q^{22} +(-15.0014 + 17.8779i) q^{23} +(-52.6577 + 298.637i) q^{25} +(-145.852 - 84.2078i) q^{26} +(-70.2837 + 25.5812i) q^{28} +(267.617 - 97.4045i) q^{29} +(86.4832 + 49.9311i) q^{31} +(33.4537 - 189.726i) q^{32} +(71.9366 - 85.7307i) q^{34} +(316.875 - 55.8736i) q^{35} -53.8378i q^{37} +(-10.4094 - 296.240i) q^{38} +(-80.8014 + 222.000i) q^{40} +(58.8231 + 333.603i) q^{41} +(-199.580 + 167.468i) q^{43} +(2.77863 + 0.489948i) q^{44} +(-72.3393 + 41.7651i) q^{46} +(-210.832 - 579.255i) q^{47} +(50.6207 + 87.6777i) q^{49} +(-542.678 + 939.946i) q^{50} +(-145.495 - 173.394i) q^{52} +(116.390 + 97.6631i) q^{53} +(-11.4060 - 4.15144i) q^{55} +177.506 q^{56} +1019.31 q^{58} +(-425.794 - 154.976i) q^{59} +(-479.767 - 402.572i) q^{61} +(229.747 + 273.801i) q^{62} +(27.3934 - 47.4467i) q^{64} +(486.874 + 843.291i) q^{65} +(-309.378 - 850.010i) q^{67} +(130.260 - 75.2055i) q^{68} +(1134.14 + 199.980i) q^{70} +(186.080 - 156.140i) q^{71} +(59.3899 + 336.817i) q^{73} +(65.9052 - 181.073i) q^{74} +(123.027 - 378.918i) q^{76} +9.11995i q^{77} +(551.538 - 97.2510i) q^{79} +(-1055.41 + 1257.79i) q^{80} +(-210.537 + 1194.02i) q^{82} +(-518.748 - 299.499i) q^{83} +(-608.041 + 221.309i) q^{85} +(-876.255 + 318.931i) q^{86} +(-5.79902 - 3.34806i) q^{88} +(207.685 - 1177.84i) q^{89} +(470.284 - 560.462i) q^{91} +(-110.559 + 19.4944i) q^{92} -2206.30i q^{94} +(-804.281 + 1513.42i) q^{95} +(71.1316 - 195.432i) q^{97} +(62.9230 + 356.854i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 120q36q4180q10156q13+180q16+924q19+432q22360q25624q28+324q34+1440q40+1524q43+3888q463228q496000q524464q55++5904q97+O(q100) 120 q - 36 q^{4} - 180 q^{10} - 156 q^{13} + 180 q^{16} + 924 q^{19} + 432 q^{22} - 360 q^{25} - 624 q^{28} + 324 q^{34} + 1440 q^{40} + 1524 q^{43} + 3888 q^{46} - 3228 q^{49} - 6000 q^{52} - 4464 q^{55}+ \cdots + 5904 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/171Z)×\left(\mathbb{Z}/171\mathbb{Z}\right)^\times.

nn 2020 154154
χ(n)\chi(n) 1-1 e(1118)e\left(\frac{11}{18}\right)

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 3.36331 + 1.22414i 1.18911 + 0.432800i 0.859410 0.511286i 0.170831π-0.170831\pi
0.329698 + 0.944086i 0.393053π0.393053\pi
33 0 0
44 3.68495 + 3.09204i 0.460619 + 0.386505i
55 −13.3019 15.8526i −1.18976 1.41790i −0.885079 0.465440i 0.845896π-0.845896\pi
−0.304677 0.952456i 0.598548π-0.598548\pi
66 0 0
77 −7.77429 + 13.4655i −0.419772 + 0.727067i −0.995916 0.0902812i 0.971223π-0.971223\pi
0.576144 + 0.817348i 0.304557π0.304557\pi
88 −5.70811 9.88673i −0.252265 0.436936i
99 0 0
1010 −25.3325 69.6004i −0.801084 2.20096i
1111 0.507963 0.293273i 0.0139233 0.00803864i −0.493022 0.870017i 0.664108π-0.664108\pi
0.506946 + 0.861978i 0.330775π0.330775\pi
1212 0 0
1313 −46.3397 8.17093i −0.988639 0.174324i −0.344131 0.938922i 0.611827π-0.611827\pi
−0.644508 + 0.764598i 0.722938π0.722938\pi
1414 −42.6310 + 35.7717i −0.813830 + 0.682884i
1515 0 0
1616 −13.7778 78.1379i −0.215278 1.22090i
1717 10.6943 29.3824i 0.152574 0.419193i −0.839732 0.543000i 0.817288π-0.817288\pi
0.992306 + 0.123807i 0.0395104π0.0395104\pi
1818 0 0
1919 −31.0413 76.7818i −0.374808 0.927102i
2020 99.5459i 1.11296i
2121 0 0
2222 2.06744 0.364546i 0.0200355 0.00353280i
2323 −15.0014 + 17.8779i −0.136000 + 0.162078i −0.829746 0.558141i 0.811515π-0.811515\pi
0.693746 + 0.720220i 0.255959π0.255959\pi
2424 0 0
2525 −52.6577 + 298.637i −0.421261 + 2.38909i
2626 −145.852 84.2078i −1.10015 0.635173i
2727 0 0
2828 −70.2837 + 25.5812i −0.474370 + 0.172657i
2929 267.617 97.4045i 1.71363 0.623709i 0.716369 0.697721i 0.245803π-0.245803\pi
0.997257 + 0.0740120i 0.0235803π0.0235803\pi
3030 0 0
3131 86.4832 + 49.9311i 0.501059 + 0.289287i 0.729151 0.684353i 0.239915π-0.239915\pi
−0.228092 + 0.973640i 0.573249π0.573249\pi
3232 33.4537 189.726i 0.184808 1.04810i
3333 0 0
3434 71.9366 85.7307i 0.362854 0.432432i
3535 316.875 55.8736i 1.53033 0.269839i
3636 0 0
3737 53.8378i 0.239213i −0.992821 0.119606i 0.961837π-0.961837\pi
0.992821 0.119606i 0.0381633π-0.0381633\pi
3838 −10.4094 296.240i −0.0444374 1.26464i
3939 0 0
4040 −80.8014 + 222.000i −0.319396 + 0.877533i
4141 58.8231 + 333.603i 0.224064 + 1.27073i 0.864466 + 0.502691i 0.167657π0.167657\pi
−0.640402 + 0.768040i 0.721232π0.721232\pi
4242 0 0
4343 −199.580 + 167.468i −0.707808 + 0.593921i −0.923983 0.382433i 0.875086π-0.875086\pi
0.216175 + 0.976355i 0.430642π0.430642\pi
4444 2.77863 + 0.489948i 0.00952033 + 0.00167869i
4545 0 0
4646 −72.3393 + 41.7651i −0.231866 + 0.133868i
4747 −210.832 579.255i −0.654318 1.79772i −0.601147 0.799138i 0.705290π-0.705290\pi
−0.0531704 0.998585i 0.516933π-0.516933\pi
4848 0 0
4949 50.6207 + 87.6777i 0.147582 + 0.255620i
5050 −542.678 + 939.946i −1.53493 + 2.65857i
5151 0 0
5252 −145.495 173.394i −0.388009 0.462411i
5353 116.390 + 97.6631i 0.301650 + 0.253114i 0.781031 0.624493i 0.214694π-0.214694\pi
−0.479381 + 0.877607i 0.659139π0.659139\pi
5454 0 0
5555 −11.4060 4.15144i −0.0279633 0.0101778i
5656 177.506 0.423576
5757 0 0
5858 1019.31 2.30763
5959 −425.794 154.976i −0.939554 0.341970i −0.173564 0.984823i 0.555528π-0.555528\pi
−0.765990 + 0.642853i 0.777751π0.777751\pi
6060 0 0
6161 −479.767 402.572i −1.00701 0.844985i −0.0190729 0.999818i 0.506071π-0.506071\pi
−0.987941 + 0.154833i 0.950516π0.950516\pi
6262 229.747 + 273.801i 0.470611 + 0.560852i
6363 0 0
6464 27.3934 47.4467i 0.0535027 0.0926694i
6565 486.874 + 843.291i 0.929066 + 1.60919i
6666 0 0
6767 −309.378 850.010i −0.564128 1.54993i −0.813527 0.581528i 0.802455π-0.802455\pi
0.249399 0.968401i 0.419767π-0.419767\pi
6868 130.260 75.2055i 0.232299 0.134118i
6969 0 0
7070 1134.14 + 199.980i 1.93652 + 0.341460i
7171 186.080 156.140i 0.311037 0.260991i −0.473883 0.880588i 0.657148π-0.657148\pi
0.784921 + 0.619596i 0.212704π0.212704\pi
7272 0 0
7373 59.3899 + 336.817i 0.0952200 + 0.540020i 0.994680 + 0.103016i 0.0328492π0.0328492\pi
−0.899460 + 0.437004i 0.856040π0.856040\pi
7474 65.9052 181.073i 0.103531 0.284450i
7575 0 0
7676 123.027 378.918i 0.185686 0.571906i
7777 9.11995i 0.0134976i
7878 0 0
7979 551.538 97.2510i 0.785479 0.138501i 0.233497 0.972357i 0.424983π-0.424983\pi
0.551982 + 0.833856i 0.313872π0.313872\pi
8080 −1055.41 + 1257.79i −1.47499 + 1.75782i
8181 0 0
8282 −210.537 + 1194.02i −0.283536 + 1.60801i
8383 −518.748 299.499i −0.686024 0.396076i 0.116097 0.993238i 0.462962π-0.462962\pi
−0.802121 + 0.597162i 0.796295π0.796295\pi
8484 0 0
8585 −608.041 + 221.309i −0.775898 + 0.282404i
8686 −876.255 + 318.931i −1.09871 + 0.399898i
8787 0 0
8888 −5.79902 3.34806i −0.00702474 0.00405574i
8989 207.685 1177.84i 0.247355 1.40282i −0.567605 0.823301i 0.692130π-0.692130\pi
0.814960 0.579518i 0.196759π-0.196759\pi
9090 0 0
9191 470.284 560.462i 0.541748 0.645631i
9292 −110.559 + 19.4944i −0.125288 + 0.0220917i
9393 0 0
9494 2206.30i 2.42088i
9595 −804.281 + 1513.42i −0.868605 + 1.63446i
9696 0 0
9797 71.1316 195.432i 0.0744569 0.204569i −0.896881 0.442272i 0.854172π-0.854172\pi
0.971338 + 0.237704i 0.0763947π0.0763947\pi
9898 62.9230 + 356.854i 0.0648590 + 0.367834i
9999 0 0
100100 −1117.44 + 937.642i −1.11744 + 0.937642i
101101 1472.31 + 259.609i 1.45050 + 0.255762i 0.842724 0.538345i 0.180950π-0.180950\pi
0.607777 + 0.794108i 0.292062π0.292062\pi
102102 0 0
103103 −592.237 + 341.928i −0.566552 + 0.327099i −0.755771 0.654836i 0.772738π-0.772738\pi
0.189219 + 0.981935i 0.439404π0.439404\pi
104104 183.728 + 504.788i 0.173231 + 0.475948i
105105 0 0
106106 271.903 + 470.949i 0.249146 + 0.431534i
107107 403.890 699.557i 0.364911 0.632044i −0.623851 0.781543i 0.714433π-0.714433\pi
0.988762 + 0.149499i 0.0477661π0.0477661\pi
108108 0 0
109109 202.419 + 241.233i 0.177873 + 0.211981i 0.847613 0.530615i 0.178039π-0.178039\pi
−0.669740 + 0.742596i 0.733594π0.733594\pi
110110 −33.2799 27.9251i −0.0288465 0.0242051i
111111 0 0
112112 1159.28 + 421.942i 0.978048 + 0.355980i
113113 −397.509 −0.330925 −0.165462 0.986216i 0.552912π-0.552912\pi
−0.165462 + 0.986216i 0.552912π0.552912\pi
114114 0 0
115115 482.957 0.391617
116116 1287.33 + 468.551i 1.03040 + 0.375033i
117117 0 0
118118 −1242.36 1042.47i −0.969227 0.813278i
119119 312.507 + 372.432i 0.240735 + 0.286897i
120120 0 0
121121 −665.328 + 1152.38i −0.499871 + 0.865802i
122122 −1120.80 1941.28i −0.831739 1.44061i
123123 0 0
124124 164.297 + 451.403i 0.118987 + 0.326913i
125125 3194.40 1844.29i 2.28573 1.31967i
126126 0 0
127127 1404.21 + 247.599i 0.981127 + 0.172999i 0.641134 0.767429i 0.278464π-0.278464\pi
0.339993 + 0.940428i 0.389575π0.389575\pi
128128 −1030.43 + 864.632i −0.711546 + 0.597058i
129129 0 0
130130 605.198 + 3432.25i 0.408303 + 2.31560i
131131 621.100 1706.46i 0.414242 1.13812i −0.540670 0.841235i 0.681829π-0.681829\pi
0.954913 0.296887i 0.0959485π-0.0959485\pi
132132 0 0
133133 1275.23 + 178.939i 0.831400 + 0.116661i
134134 3237.57i 2.08719i
135135 0 0
136136 −351.540 + 61.9861i −0.221650 + 0.0390828i
137137 −71.1041 + 84.7386i −0.0443419 + 0.0528446i −0.787760 0.615983i 0.788759π-0.788759\pi
0.743418 + 0.668827i 0.233203π0.233203\pi
138138 0 0
139139 −307.402 + 1743.37i −0.187579 + 1.06382i 0.735017 + 0.678049i 0.237174π0.237174\pi
−0.922596 + 0.385767i 0.873937π0.873937\pi
140140 1340.43 + 773.899i 0.809194 + 0.467188i
141141 0 0
142142 816.982 297.357i 0.482814 0.175730i
143143 −25.9352 + 9.43963i −0.0151665 + 0.00552015i
144144 0 0
145145 −5103.92 2946.75i −2.92315 1.68768i
146146 −212.566 + 1205.52i −0.120494 + 0.683353i
147147 0 0
148148 166.469 198.390i 0.0924570 0.110186i
149149 −1037.46 + 182.932i −0.570417 + 0.100580i −0.451415 0.892314i 0.649081π-0.649081\pi
−0.119002 + 0.992894i 0.537969π0.537969\pi
150150 0 0
151151 1020.14i 0.549789i −0.961474 0.274895i 0.911357π-0.911357\pi
0.961474 0.274895i 0.0886430π-0.0886430\pi
152152 −581.934 + 745.175i −0.310533 + 0.397643i
153153 0 0
154154 −11.1641 + 30.6732i −0.00584176 + 0.0160501i
155155 −358.853 2035.16i −0.185960 1.05463i
156156 0 0
157157 2296.68 1927.14i 1.16748 0.979634i 0.167502 0.985872i 0.446430π-0.446430\pi
0.999981 + 0.00623754i 0.00198549π0.00198549\pi
158158 1974.04 + 348.077i 0.993963 + 0.175263i
159159 0 0
160160 −3452.63 + 1993.38i −1.70597 + 0.984940i
161161 −124.110 340.988i −0.0607529 0.166917i
162162 0 0
163163 −773.278 1339.36i −0.371582 0.643599i 0.618227 0.785999i 0.287851π-0.287851\pi
−0.989809 + 0.142401i 0.954518π0.954518\pi
164164 −814.753 + 1411.19i −0.387936 + 0.671925i
165165 0 0
166166 −1378.08 1642.33i −0.644336 0.767889i
167167 −3156.36 2648.50i −1.46255 1.22723i −0.922730 0.385448i 0.874047π-0.874047\pi
−0.539822 0.841779i 0.681509π-0.681509\pi
168168 0 0
169169 16.0952 + 5.85818i 0.00732600 + 0.00266645i
170170 −2315.94 −1.04485
171171 0 0
172172 −1253.26 −0.555583
173173 −3385.01 1232.04i −1.48761 0.541448i −0.534794 0.844982i 0.679611π-0.679611\pi
−0.952820 + 0.303535i 0.901833π0.901833\pi
174174 0 0
175175 −3611.91 3030.75i −1.56020 1.30916i
176176 −29.9144 35.6505i −0.0128118 0.0152685i
177177 0 0
178178 2140.36 3707.20i 0.901272 1.56105i
179179 389.679 + 674.943i 0.162715 + 0.281830i 0.935841 0.352421i 0.114642π-0.114642\pi
−0.773127 + 0.634252i 0.781308π0.781308\pi
180180 0 0
181181 296.501 + 814.631i 0.121761 + 0.334536i 0.985566 0.169290i 0.0541474π-0.0541474\pi
−0.863805 + 0.503826i 0.831925π0.831925\pi
182182 2267.79 1309.31i 0.923627 0.533256i
183183 0 0
184184 262.383 + 46.2653i 0.105126 + 0.0185365i
185185 −853.467 + 716.144i −0.339179 + 0.284605i
186186 0 0
187187 −3.18474 18.0615i −0.00124541 0.00706305i
188188 1014.18 2786.43i 0.393438 1.08096i
189189 0 0
190190 −4557.69 + 4105.56i −1.74026 + 1.56762i
191191 3746.70i 1.41938i 0.704514 + 0.709690i 0.251165π0.251165\pi
−0.704514 + 0.709690i 0.748835π0.748835\pi
192192 0 0
193193 1602.36 282.539i 0.597617 0.105376i 0.133347 0.991069i 0.457428π-0.457428\pi
0.464271 + 0.885693i 0.346316π0.346316\pi
194194 478.475 570.224i 0.177075 0.211029i
195195 0 0
196196 −84.5681 + 479.610i −0.0308193 + 0.174785i
197197 319.858 + 184.670i 0.115680 + 0.0667878i 0.556724 0.830698i 0.312058π-0.312058\pi
−0.441044 + 0.897486i 0.645392π0.645392\pi
198198 0 0
199199 2623.17 954.754i 0.934429 0.340104i 0.170465 0.985364i 0.445473π-0.445473\pi
0.763963 + 0.645259i 0.223251π0.223251\pi
200200 3253.11 1184.04i 1.15015 0.418620i
201201 0 0
202202 4634.04 + 2675.47i 1.61411 + 0.931907i
203203 −768.933 + 4360.84i −0.265855 + 1.50774i
204204 0 0
205205 4506.00 5370.04i 1.53518 1.82956i
206206 −2410.45 + 425.027i −0.815261 + 0.143752i
207207 0 0
208208 3733.46i 1.24456i
209209 −38.2858 29.8988i −0.0126712 0.00989541i
210210 0 0
211211 674.084 1852.03i 0.219933 0.604261i −0.779831 0.625990i 0.784695π-0.784695\pi
0.999764 + 0.0217291i 0.00691714π0.00691714\pi
212212 126.914 + 719.767i 0.0411156 + 0.233178i
213213 0 0
214214 2214.76 1858.41i 0.707468 0.593636i
215215 5309.59 + 936.224i 1.68424 + 0.296976i
216216 0 0
217217 −1344.69 + 776.358i −0.420662 + 0.242869i
218218 385.492 + 1059.13i 0.119765 + 0.329052i
219219 0 0
220220 −29.1941 50.5656i −0.00894666 0.0154961i
221221 −735.653 + 1274.19i −0.223916 + 0.387834i
222222 0 0
223223 3862.31 + 4602.93i 1.15982 + 1.38222i 0.910352 + 0.413835i 0.135811π0.135811\pi
0.249467 + 0.968383i 0.419745π0.419745\pi
224224 2294.67 + 1925.45i 0.684459 + 0.574329i
225225 0 0
226226 −1336.95 486.608i −0.393506 0.143224i
227227 −2018.84 −0.590287 −0.295143 0.955453i 0.595367π-0.595367\pi
−0.295143 + 0.955453i 0.595367π0.595367\pi
228228 0 0
229229 4532.55 1.30794 0.653972 0.756519i 0.273101π-0.273101\pi
0.653972 + 0.756519i 0.273101π0.273101\pi
230230 1624.33 + 591.209i 0.465675 + 0.169492i
231231 0 0
232232 −2490.60 2089.86i −0.704809 0.591405i
233233 −2069.78 2466.67i −0.581957 0.693550i 0.392082 0.919930i 0.371755π-0.371755\pi
−0.974039 + 0.226381i 0.927311π0.927311\pi
234234 0 0
235235 −6378.22 + 11047.4i −1.77051 + 3.06661i
236236 −1089.84 1887.65i −0.300603 0.520660i
237237 0 0
238238 595.148 + 1635.16i 0.162091 + 0.445342i
239239 −4014.76 + 2317.92i −1.08658 + 0.627339i −0.932664 0.360745i 0.882522π-0.882522\pi
−0.153918 + 0.988084i 0.549189π0.549189\pi
240240 0 0
241241 −6641.51 1171.08i −1.77517 0.313011i −0.812356 0.583162i 0.801815π-0.801815\pi
−0.962818 + 0.270151i 0.912927π0.912927\pi
242242 −3648.38 + 3061.36i −0.969120 + 0.813188i
243243 0 0
244244 −523.147 2966.92i −0.137259 0.778432i
245245 716.565 1968.75i 0.186856 0.513382i
246246 0 0
247247 811.062 + 3811.68i 0.208934 + 0.981908i
248248 1140.05i 0.291908i
249249 0 0
250250 13001.4 2292.50i 3.28913 0.579963i
251251 −2630.37 + 3134.75i −0.661463 + 0.788301i −0.987595 0.157023i 0.949810π-0.949810\pi
0.326132 + 0.945324i 0.394255π0.394255\pi
252252 0 0
253253 −2.37703 + 13.4808i −0.000590683 + 0.00334993i
254254 4419.68 + 2551.70i 1.09179 + 0.630347i
255255 0 0
256256 −4935.94 + 1796.54i −1.20506 + 0.438608i
257257 5250.22 1910.92i 1.27432 0.463814i 0.385769 0.922595i 0.373936π-0.373936\pi
0.888549 + 0.458781i 0.151714π0.151714\pi
258258 0 0
259259 724.951 + 418.551i 0.173924 + 0.100415i
260260 −813.382 + 4612.92i −0.194015 + 1.10031i
261261 0 0
262262 4177.90 4979.03i 0.985158 1.17407i
263263 7263.49 1280.75i 1.70299 0.300283i 0.764251 0.644918i 0.223109π-0.223109\pi
0.938737 + 0.344636i 0.111998π0.111998\pi
264264 0 0
265265 3144.19i 0.728852i
266266 4069.93 + 2162.89i 0.938133 + 0.498553i
267267 0 0
268268 1488.22 4088.86i 0.339207 0.931965i
269269 −177.720 1007.90i −0.0402816 0.228448i 0.958020 0.286700i 0.0925584π-0.0925584\pi
−0.998302 + 0.0582520i 0.981447π0.981447\pi
270270 0 0
271271 −4082.96 + 3426.01i −0.915212 + 0.767954i −0.973103 0.230369i 0.926007π-0.926007\pi
0.0578917 + 0.998323i 0.481562π0.481562\pi
272272 −2443.23 430.807i −0.544641 0.0960349i
273273 0 0
274274 −342.877 + 197.960i −0.0755984 + 0.0436468i
275275 60.8338 + 167.140i 0.0133397 + 0.0366505i
276276 0 0
277277 2776.61 + 4809.22i 0.602274 + 1.04317i 0.992476 + 0.122440i 0.0390721π0.0390721\pi
−0.390201 + 0.920730i 0.627595π0.627595\pi
278278 −3168.02 + 5487.17i −0.683472 + 1.18381i
279279 0 0
280280 −2361.16 2813.92i −0.503952 0.600586i
281281 5678.68 + 4764.98i 1.20556 + 1.01158i 0.999454 + 0.0330525i 0.0105228π0.0105228\pi
0.206104 + 0.978530i 0.433922π0.433922\pi
282282 0 0
283283 3476.62 + 1265.39i 0.730260 + 0.265793i 0.680275 0.732957i 0.261860π-0.261860\pi
0.0499849 + 0.998750i 0.484083π0.484083\pi
284284 1168.49 0.244144
285285 0 0
286286 −98.7834 −0.0204237
287287 −4949.42 1801.44i −1.01796 0.370508i
288288 0 0
289289 3014.62 + 2529.57i 0.613600 + 0.514872i
290290 −13558.8 16158.7i −2.74552 3.27198i
291291 0 0
292292 −822.603 + 1424.79i −0.164860 + 0.285546i
293293 158.920 + 275.257i 0.0316867 + 0.0548830i 0.881434 0.472307i 0.156579π-0.156579\pi
−0.849747 + 0.527190i 0.823245π0.823245\pi
294294 0 0
295295 3207.09 + 8811.41i 0.632963 + 1.73905i
296296 −532.280 + 307.312i −0.104521 + 0.0603451i
297297 0 0
298298 −3713.24 654.744i −0.721819 0.127276i
299299 841.237 705.882i 0.162709 0.136529i
300300 0 0
301301 −703.437 3989.39i −0.134702 0.763935i
302302 1248.80 3431.06i 0.237949 0.653759i
303303 0 0
304304 −5571.89 + 3483.38i −1.05122 + 0.657190i
305305 12960.5i 2.43317i
306306 0 0
307307 2868.16 505.735i 0.533208 0.0940189i 0.0994398 0.995044i 0.468295π-0.468295\pi
0.433768 + 0.901025i 0.357184π0.357184\pi
308308 −28.1993 + 33.6066i −0.00521689 + 0.00621725i
309309 0 0
310310 1284.39 7284.15i 0.235318 1.33455i
311311 −4209.45 2430.33i −0.767512 0.443123i 0.0644743 0.997919i 0.479463π-0.479463\pi
−0.831986 + 0.554796i 0.812796π0.812796\pi
312312 0 0
313313 −4039.58 + 1470.29i −0.729491 + 0.265513i −0.679950 0.733259i 0.737998π-0.737998\pi
−0.0495418 + 0.998772i 0.515776π0.515776\pi
314314 10083.5 3670.10i 1.81225 0.659605i
315315 0 0
316316 2333.09 + 1347.01i 0.415338 + 0.239795i
317317 710.113 4027.25i 0.125817 0.713542i −0.855003 0.518623i 0.826445π-0.826445\pi
0.980819 0.194919i 0.0624442π-0.0624442\pi
318318 0 0
319319 107.373 127.963i 0.0188456 0.0224593i
320320 −1116.54 + 196.875i −0.195051 + 0.0343927i
321321 0 0
322322 1298.78i 0.224776i
323323 −2588.00 + 90.9378i −0.445821 + 0.0156654i
324324 0 0
325325 4880.28 13408.5i 0.832951 2.28851i
326326 −961.207 5451.27i −0.163302 0.926129i
327327 0 0
328328 2962.47 2485.81i 0.498704 0.418463i
329329 9439.01 + 1664.35i 1.58173 + 0.278902i
330330 0 0
331331 −4107.97 + 2371.74i −0.682158 + 0.393844i −0.800668 0.599109i 0.795522π-0.795522\pi
0.118509 + 0.992953i 0.462188π0.462188\pi
332332 −985.498 2707.63i −0.162910 0.447592i
333333 0 0
334334 −7373.65 12771.5i −1.20799 2.09230i
335335 −9359.52 + 16211.2i −1.52646 + 2.64391i
336336 0 0
337337 3482.36 + 4150.11i 0.562897 + 0.670834i 0.970157 0.242478i 0.0779603π-0.0779603\pi
−0.407260 + 0.913312i 0.633516π0.633516\pi
338338 46.9619 + 39.4057i 0.00755738 + 0.00634139i
339339 0 0
340340 −2924.90 1064.58i −0.466544 0.169808i
341341 58.5737 0.00930189
342342 0 0
343343 −6907.33 −1.08735
344344 2794.94 + 1017.27i 0.438061 + 0.159441i
345345 0 0
346346 −9876.62 8287.47i −1.53460 1.28768i
347347 −4198.08 5003.07i −0.649466 0.774003i 0.336368 0.941731i 0.390802π-0.390802\pi
−0.985833 + 0.167728i 0.946357π0.946357\pi
348348 0 0
349349 2007.68 3477.41i 0.307934 0.533357i −0.669977 0.742382i 0.733696π-0.733696\pi
0.977910 + 0.209026i 0.0670292π0.0670292\pi
350350 −8437.88 14614.8i −1.28864 2.23199i
351351 0 0
352352 −38.6481 106.185i −0.00585213 0.0160786i
353353 2038.50 1176.93i 0.307361 0.177455i −0.338384 0.941008i 0.609880π-0.609880\pi
0.645745 + 0.763553i 0.276547π0.276547\pi
354354 0 0
355355 −4950.43 872.894i −0.740117 0.130503i
356356 4407.24 3698.12i 0.656133 0.550561i
357357 0 0
358358 484.381 + 2747.06i 0.0715094 + 0.405550i
359359 730.862 2008.03i 0.107447 0.295208i −0.874304 0.485378i 0.838682π-0.838682\pi
0.981751 + 0.190170i 0.0609041π0.0609041\pi
360360 0 0
361361 −4931.88 + 4766.81i −0.719038 + 0.694971i
362362 3102.81i 0.450498i
363363 0 0
364364 3465.94 611.139i 0.499079 0.0880011i
365365 4549.41 5421.78i 0.652403 0.777504i
366366 0 0
367367 548.074 3108.28i 0.0779543 0.442101i −0.920701 0.390268i 0.872383π-0.872383\pi
0.998656 0.0518331i 0.0165064π-0.0165064\pi
368368 1603.63 + 925.856i 0.227160 + 0.131151i
369369 0 0
370370 −3747.13 + 1363.85i −0.526498 + 0.191630i
371371 −2219.93 + 807.989i −0.310655 + 0.113069i
372372 0 0
373373 −6283.68 3627.89i −0.872270 0.503605i −0.00416822 0.999991i 0.501327π-0.501327\pi
−0.868102 + 0.496386i 0.834660π0.834660\pi
374374 11.3987 64.6451i 0.00157597 0.00893775i
375375 0 0
376376 −4523.49 + 5390.88i −0.620428 + 0.739398i
377377 −13197.2 + 2327.01i −1.80289 + 0.317897i
378378 0 0
379379 5263.86i 0.713420i 0.934215 + 0.356710i 0.116102π0.116102\pi
−0.934215 + 0.356710i 0.883898π0.883898\pi
380380 −7643.31 + 3090.03i −1.03182 + 0.417145i
381381 0 0
382382 −4586.50 + 12601.3i −0.614308 + 1.68780i
383383 −976.746 5539.40i −0.130312 0.739035i −0.978010 0.208556i 0.933124π-0.933124\pi
0.847699 0.530478i 0.177988π-0.177988\pi
384384 0 0
385385 144.575 121.312i 0.0191382 0.0160588i
386386 5735.09 + 1011.25i 0.756239 + 0.133345i
387387 0 0
388388 866.401 500.217i 0.113363 0.0654502i
389389 −2418.52 6644.84i −0.315229 0.866084i −0.991579 0.129504i 0.958662π-0.958662\pi
0.676350 0.736580i 0.263561π-0.263561\pi
390390 0 0
391391 364.867 + 631.968i 0.0471921 + 0.0817392i
392392 577.897 1000.95i 0.0744597 0.128968i
393393 0 0
394394 849.717 + 1012.65i 0.108650 + 0.129484i
395395 −8878.16 7449.66i −1.13091 0.948945i
396396 0 0
397397 9183.64 + 3342.57i 1.16099 + 0.422566i 0.849452 0.527667i 0.176933π-0.176933\pi
0.311540 + 0.950233i 0.399155π0.399155\pi
398398 9991.27 1.25833
399399 0 0
400400 24060.3 3.00754
401401 4793.19 + 1744.58i 0.596909 + 0.217257i 0.622765 0.782409i 0.286009π-0.286009\pi
−0.0258567 + 0.999666i 0.508231π0.508231\pi
402402 0 0
403403 −3599.62 3020.44i −0.444937 0.373347i
404404 4622.68 + 5509.10i 0.569275 + 0.678435i
405405 0 0
406406 −7924.45 + 13725.5i −0.968679 + 1.67780i
407407 −15.7892 27.3476i −0.00192295 0.00333064i
408408 0 0
409409 −16.0667 44.1429i −0.00194242 0.00533674i 0.938718 0.344687i 0.112015π-0.112015\pi
−0.940660 + 0.339350i 0.889793π0.889793\pi
410410 21728.7 12545.1i 2.61733 1.51112i
411411 0 0
412412 −3239.62 571.233i −0.387390 0.0683073i
413413 5397.08 4528.69i 0.643034 0.539569i
414414 0 0
415415 2152.49 + 12207.4i 0.254607 + 1.44395i
416416 −3100.47 + 8518.47i −0.365416 + 1.00397i
417417 0 0
418418 −92.1666 147.426i −0.0107847 0.0172508i
419419 4773.84i 0.556605i −0.960494 0.278302i 0.910228π-0.910228\pi
0.960494 0.278302i 0.0897717π-0.0897717\pi
420420 0 0
421421 864.150 152.373i 0.100038 0.0176394i −0.123405 0.992356i 0.539381π-0.539381\pi
0.223443 + 0.974717i 0.428270π0.428270\pi
422422 4534.31 5403.78i 0.523049 0.623345i
423423 0 0
424424 301.200 1708.19i 0.0344990 0.195653i
425425 8211.53 + 4740.93i 0.937218 + 0.541103i
426426 0 0
427427 9150.67 3330.57i 1.03708 0.377465i
428428 3651.37 1328.99i 0.412373 0.150092i
429429 0 0
430430 16711.7 + 9648.51i 1.87421 + 1.08208i
431431 −592.556 + 3360.55i −0.0662237 + 0.375573i 0.933626 + 0.358249i 0.116626π0.116626\pi
−0.999850 + 0.0173246i 0.994485π0.994485\pi
432432 0 0
433433 5080.87 6055.15i 0.563905 0.672036i −0.406463 0.913667i 0.633238π-0.633238\pi
0.970368 + 0.241631i 0.0776824π0.0776824\pi
434434 −5472.98 + 965.035i −0.605326 + 0.106735i
435435 0 0
436436 1514.82i 0.166392i
437437 1838.36 + 596.878i 0.201237 + 0.0653376i
438438 0 0
439439 5891.95 16188.0i 0.640564 1.75994i −0.00938327 0.999956i 0.502987π-0.502987\pi
0.649947 0.759979i 0.274791π-0.274791\pi
440440 24.0624 + 136.465i 0.00260712 + 0.0147857i
441441 0 0
442442 −4034.02 + 3384.94i −0.434115 + 0.364265i
443443 6847.95 + 1207.48i 0.734438 + 0.129501i 0.528343 0.849031i 0.322813π-0.322813\pi
0.206095 + 0.978532i 0.433925π0.433925\pi
444444 0 0
445445 −21434.4 + 12375.2i −2.28334 + 1.31829i
446446 7355.50 + 20209.1i 0.780926 + 2.14558i
447447 0 0
448448 425.928 + 737.730i 0.0449179 + 0.0778001i
449449 −1530.82 + 2651.46i −0.160899 + 0.278686i −0.935192 0.354142i 0.884773π-0.884773\pi
0.774292 + 0.632828i 0.218106π0.218106\pi
450450 0 0
451451 127.717 + 152.207i 0.0133347 + 0.0158916i
452452 −1464.80 1229.11i −0.152430 0.127904i
453453 0 0
454454 −6789.98 2471.35i −0.701915 0.255476i
455455 −15140.4 −1.55999
456456 0 0
457457 −13086.6 −1.33953 −0.669766 0.742572i 0.733606π-0.733606\pi
−0.669766 + 0.742572i 0.733606π0.733606\pi
458458 15244.3 + 5548.49i 1.55529 + 0.566078i
459459 0 0
460460 1779.67 + 1493.32i 0.180386 + 0.151362i
461461 6745.89 + 8039.44i 0.681535 + 0.812221i 0.990304 0.138916i 0.0443617π-0.0443617\pi
−0.308770 + 0.951137i 0.599917π0.599917\pi
462462 0 0
463463 7339.34 12712.1i 0.736691 1.27599i −0.217286 0.976108i 0.569721π-0.569721\pi
0.953977 0.299878i 0.0969461π-0.0969461\pi
464464 −11298.2 19569.0i −1.13040 1.95790i
465465 0 0
466466 −3941.76 10829.9i −0.391842 1.07658i
467467 −4543.90 + 2623.42i −0.450250 + 0.259952i −0.707936 0.706277i 0.750373π-0.750373\pi
0.257686 + 0.966229i 0.417040π0.417040\pi
468468 0 0
469469 13851.0 + 2442.30i 1.36371 + 0.240458i
470470 −34975.5 + 29347.9i −3.43255 + 2.88025i
471471 0 0
472472 898.269 + 5094.33i 0.0875978 + 0.496792i
473473 −52.2658 + 143.599i −0.00508073 + 0.0139592i
474474 0 0
475475 24564.4 5226.90i 2.37283 0.504898i
476476 2338.68i 0.225196i
477477 0 0
478478 −16340.3 + 2881.24i −1.56358 + 0.275701i
479479 3625.56 4320.77i 0.345837 0.412153i −0.564887 0.825169i 0.691080π-0.691080\pi
0.910724 + 0.413016i 0.135525π0.135525\pi
480480 0 0
481481 −439.905 + 2494.83i −0.0417005 + 0.236495i
482482 −20903.9 12068.8i −1.97540 1.14050i
483483 0 0
484484 −6014.91 + 2189.25i −0.564887 + 0.205602i
485485 −4044.29 + 1472.00i −0.378642 + 0.137815i
486486 0 0
487487 7501.19 + 4330.81i 0.697970 + 0.402973i 0.806591 0.591110i 0.201310π-0.201310\pi
−0.108621 + 0.994083i 0.534643π0.534643\pi
488488 −1241.56 + 7041.25i −0.115170 + 0.653160i
489489 0 0
490490 4820.06 5744.32i 0.444384 0.529596i
491491 −13111.7 + 2311.95i −1.20514 + 0.212499i −0.739920 0.672695i 0.765137π-0.765137\pi
−0.465222 + 0.885194i 0.654026π0.654026\pi
492492 0 0
493493 8904.90i 0.813502i
494494 −1938.19 + 13812.7i −0.176525 + 1.25802i
495495 0 0
496496 2709.96 7445.56i 0.245324 0.674023i
497497 655.854 + 3719.53i 0.0591933 + 0.335702i
498498 0 0
499499 −6868.77 + 5763.59i −0.616209 + 0.517061i −0.896609 0.442822i 0.853977π-0.853977\pi
0.280400 + 0.959883i 0.409533π0.409533\pi
500500 17473.8 + 3081.11i 1.56291 + 0.275583i
501501 0 0
502502 −12684.1 + 7323.17i −1.12773 + 0.651094i
503503 −732.241 2011.81i −0.0649085 0.178335i 0.902998 0.429644i 0.141361π-0.141361\pi
−0.967907 + 0.251309i 0.919139π0.919139\pi
504504 0 0
505505 −15469.1 26793.2i −1.36310 2.36095i
506506 −24.4971 + 42.4303i −0.00215223 + 0.00372778i
507507 0 0
508508 4408.84 + 5254.25i 0.385060 + 0.458897i
509509 16941.6 + 14215.7i 1.47529 + 1.23792i 0.911042 + 0.412315i 0.135280π0.135280\pi
0.564251 + 0.825603i 0.309165π0.309165\pi
510510 0 0
511511 −4997.11 1818.80i −0.432601 0.157454i
512512 −8039.28 −0.693925
513513 0 0
514514 19997.4 1.71604
515515 13298.3 + 4840.19i 1.13785 + 0.414144i
516516 0 0
517517 −276.974 232.409i −0.0235615 0.0197705i
518518 1925.87 + 2295.16i 0.163355 + 0.194679i
519519 0 0
520520 5558.26 9627.19i 0.468742 0.811885i
521521 −1634.47 2830.98i −0.137442 0.238057i 0.789086 0.614283i 0.210555π-0.210555\pi
−0.926528 + 0.376227i 0.877221π0.877221\pi
522522 0 0
523523 −2224.28 6111.15i −0.185967 0.510941i 0.811316 0.584608i 0.198752π-0.198752\pi
−0.997283 + 0.0736677i 0.976530π0.976530\pi
524524 7565.16 4367.75i 0.630698 0.364134i
525525 0 0
526526 25997.2 + 4584.00i 2.15500 + 0.379985i
527527 2391.98 2007.11i 0.197716 0.165903i
528528 0 0
529529 2018.20 + 11445.8i 0.165875 + 0.940722i
530530 3848.94 10574.9i 0.315447 0.866684i
531531 0 0
532532 4145.86 + 4602.43i 0.337868 + 0.375077i
533533 15939.7i 1.29535i
534534 0 0
535535 −16462.3 + 2902.74i −1.33033 + 0.234573i
536536 −6637.85 + 7910.69i −0.534910 + 0.637481i
537537 0 0
538538 636.086 3607.42i 0.0509733 0.289084i
539539 51.4270 + 29.6914i 0.00410968 + 0.00237272i
540540 0 0
541541 20922.5 7615.15i 1.66271 0.605178i 0.671926 0.740618i 0.265467π-0.265467\pi
0.990785 + 0.135441i 0.0432450π0.0432450\pi
542542 −17926.2 + 6524.60i −1.42066 + 0.517077i
543543 0 0
544544 −5216.83 3011.94i −0.411158 0.237382i
545545 1131.62 6417.71i 0.0889415 0.504412i
546546 0 0
547547 −2657.93 + 3167.60i −0.207761 + 0.247599i −0.859855 0.510538i 0.829446π-0.829446\pi
0.652094 + 0.758138i 0.273891π0.273891\pi
548548 −524.030 + 92.4007i −0.0408494 + 0.00720285i
549549 0 0
550550 636.611i 0.0493549i
551551 −15786.1 17524.5i −1.22052 1.35494i
552552 0 0
553553 −2978.29 + 8182.77i −0.229023 + 0.629235i
554554 3451.40 + 19573.9i 0.264686 + 1.50111i
555555 0 0
556556 −6523.32 + 5473.72i −0.497573 + 0.417513i
557557 −3266.41 575.957i −0.248478 0.0438134i 0.0480217 0.998846i 0.484708π-0.484708\pi
−0.296500 + 0.955033i 0.595819π0.595819\pi
558558 0 0
559559 10616.9 6129.65i 0.803301 0.463786i
560560 −8731.69 23990.1i −0.658895 1.81030i
561561 0 0
562562 13266.1 + 22977.6i 0.995725 + 1.72465i
563563 −8843.07 + 15316.6i −0.661973 + 1.14657i 0.318123 + 0.948049i 0.396947π0.396947\pi
−0.980096 + 0.198522i 0.936386π0.936386\pi
564564 0 0
565565 5287.62 + 6301.54i 0.393720 + 0.469217i
566566 10143.9 + 8511.76i 0.753323 + 0.632113i
567567 0 0
568568 −2605.88 948.462i −0.192500 0.0700644i
569569 10925.5 0.804959 0.402480 0.915429i 0.368148π-0.368148\pi
0.402480 + 0.915429i 0.368148π0.368148\pi
570570 0 0
571571 −13116.4 −0.961305 −0.480652 0.876911i 0.659600π-0.659600\pi
−0.480652 + 0.876911i 0.659600π0.659600\pi
572572 −124.758 45.4080i −0.00911954 0.00331924i
573573 0 0
574574 −14441.2 12117.6i −1.05011 0.881149i
575575 −4549.06 5421.36i −0.329929 0.393194i
576576 0 0
577577 −4494.99 + 7785.54i −0.324313 + 0.561727i −0.981373 0.192111i 0.938467π-0.938467\pi
0.657060 + 0.753838i 0.271800π0.271800\pi
578578 7042.54 + 12198.0i 0.506801 + 0.877805i
579579 0 0
580580 −9696.22 26640.1i −0.694161 1.90719i
581581 8065.80 4656.79i 0.575948 0.332524i
582582 0 0
583583 87.7639 + 15.4751i 0.00623467 + 0.00109934i
584584 2991.01 2509.76i 0.211933 0.177833i
585585 0 0
586586 197.542 + 1120.32i 0.0139256 + 0.0789758i
587587 6445.89 17709.9i 0.453237 1.24526i −0.477196 0.878797i 0.658347π-0.658347\pi
0.930433 0.366462i 0.119431π-0.119431\pi
588588 0 0
589589 1149.25 8190.26i 0.0803974 0.572960i
590590 33561.4i 2.34187i
591591 0 0
592592 −4206.77 + 741.768i −0.292056 + 0.0514974i
593593 5754.77 6858.27i 0.398516 0.474933i −0.529051 0.848590i 0.677452π-0.677452\pi
0.927567 + 0.373657i 0.121896π0.121896\pi
594594 0 0
595595 1747.06 9908.08i 0.120374 0.682675i
596596 −4388.63 2533.78i −0.301620 0.174140i
597597 0 0
598598 3693.44 1344.30i 0.252568 0.0919274i
599599 −9574.28 + 3484.75i −0.653079 + 0.237701i −0.647246 0.762281i 0.724079π-0.724079\pi
−0.00583382 + 0.999983i 0.501857π0.501857\pi
600600 0 0
601601 −1647.80 951.360i −0.111839 0.0645704i 0.443037 0.896503i 0.353901π-0.353901\pi
−0.554876 + 0.831933i 0.687234π0.687234\pi
602602 2517.71 14278.6i 0.170456 0.966701i
603603 0 0
604604 3154.33 3759.18i 0.212496 0.253243i
605605 27118.3 4781.69i 1.82234 0.321328i
606606 0 0
607607 3728.13i 0.249292i 0.992201 + 0.124646i 0.0397795π0.0397795\pi
−0.992201 + 0.124646i 0.960221π0.960221\pi
608608 −15605.9 + 3320.68i −1.04096 + 0.221499i
609609 0 0
610610 −15865.5 + 43590.1i −1.05307 + 2.89330i
611611 5036.81 + 28565.2i 0.333498 + 1.89136i
612612 0 0
613613 −3839.31 + 3221.57i −0.252966 + 0.212264i −0.760448 0.649398i 0.775021π-0.775021\pi
0.507482 + 0.861662i 0.330576π0.330576\pi
614614 10265.6 + 1810.10i 0.674733 + 0.118974i
615615 0 0
616616 90.1665 52.0577i 0.00589759 0.00340497i
617617 −7116.73 19553.0i −0.464358 1.27581i −0.922178 0.386767i 0.873592π-0.873592\pi
0.457820 0.889045i 0.348630π-0.348630\pi
618618 0 0
619619 6410.57 + 11103.4i 0.416256 + 0.720977i 0.995559 0.0941351i 0.0300086π-0.0300086\pi
−0.579303 + 0.815112i 0.696675π0.696675\pi
620620 4970.43 8609.04i 0.321964 0.557657i
621621 0 0
622622 −11182.6 13326.9i −0.720871 0.859101i
623623 14245.6 + 11953.5i 0.916111 + 0.768708i
624624 0 0
625625 −36108.8 13142.5i −2.31096 0.841122i
626626 −15386.2 −0.982359
627627 0 0
628628 14421.9 0.916398
629629 −1581.88 575.759i −0.100276 0.0364976i
630630 0 0
631631 18059.7 + 15153.9i 1.13937 + 0.956047i 0.999418 0.0341111i 0.0108600π-0.0108600\pi
0.139954 + 0.990158i 0.455304π0.455304\pi
632632 −4109.73 4897.79i −0.258665 0.308265i
633633 0 0
634634 7318.26 12675.6i 0.458431 0.794025i
635635 −14753.5 25553.8i −0.922007 1.59696i
636636 0 0
637637 −1629.34 4476.57i −0.101345 0.278443i
638638 517.774 298.937i 0.0321299 0.0185502i
639639 0 0
640640 27413.3 + 4833.70i 1.69313 + 0.298545i
641641 6448.66 5411.07i 0.397358 0.333423i −0.422113 0.906543i 0.638712π-0.638712\pi
0.819472 + 0.573120i 0.194267π0.194267\pi
642642 0 0
643643 −525.679 2981.27i −0.0322407 0.182846i 0.964435 0.264321i 0.0851479π-0.0851479\pi
−0.996675 + 0.0814754i 0.974037π0.974037\pi
644644 597.012 1640.28i 0.0365304 0.100366i
645645 0 0
646646 −8815.56 2862.23i −0.536909 0.174324i
647647 8844.45i 0.537421i 0.963221 + 0.268710i 0.0865975π0.0865975\pi
−0.963221 + 0.268710i 0.913403π0.913403\pi
648648 0 0
649649 −261.738 + 46.1515i −0.0158307 + 0.00279138i
650650 32827.8 39122.6i 1.98094 2.36079i
651651 0 0
652652 1291.86 7326.48i 0.0775966 0.440072i
653653 −5428.18 3133.96i −0.325300 0.187812i 0.328452 0.944521i 0.393473π-0.393473\pi
−0.653753 + 0.756708i 0.726806π0.726806\pi
654654 0 0
655655 −35313.5 + 12853.1i −2.10659 + 0.766734i
656656 25256.6 9192.63i 1.50321 0.547122i
657657 0 0
658658 29708.9 + 17152.4i 1.76014 + 1.01622i
659659 1752.32 9937.90i 0.103582 0.587444i −0.888195 0.459467i 0.848041π-0.848041\pi
0.991777 0.127977i 0.0408484π-0.0408484\pi
660660 0 0
661661 −6084.26 + 7250.94i −0.358019 + 0.426670i −0.914749 0.404024i 0.867611π-0.867611\pi
0.556730 + 0.830694i 0.312056π0.312056\pi
662662 −16719.7 + 2948.14i −0.981616 + 0.173085i
663663 0 0
664664 6838.30i 0.399665i
665665 −14126.3 22595.8i −0.823749 1.31764i
666666 0 0
667667 −2273.22 + 6245.63i −0.131963 + 0.362566i
668668 −3441.76 19519.2i −0.199350 1.13057i
669669 0 0
670670 −51323.7 + 43065.7i −2.95942 + 2.48324i
671671 −361.767 63.7893i −0.0208135 0.00366998i
672672 0 0
673673 −2930.86 + 1692.13i −0.167870 + 0.0969196i −0.581581 0.813489i 0.697566π-0.697566\pi
0.413711 + 0.910408i 0.364232π0.364232\pi
674674 6631.91 + 18221.0i 0.379008 + 1.04132i
675675 0 0
676676 41.1964 + 71.3542i 0.00234390 + 0.00405975i
677677 −6198.39 + 10735.9i −0.351881 + 0.609476i −0.986579 0.163284i 0.947791π-0.947791\pi
0.634698 + 0.772760i 0.281124π0.281124\pi
678678 0 0
679679 2078.59 + 2477.17i 0.117480 + 0.140007i
680680 5658.78 + 4748.28i 0.319124 + 0.267777i
681681 0 0
682682 197.001 + 71.7027i 0.0110610 + 0.00402586i
683683 18080.6 1.01293 0.506466 0.862260i 0.330951π-0.330951\pi
0.506466 + 0.862260i 0.330951π0.330951\pi
684684 0 0
685685 2289.14 0.127684
686686 −23231.5 8455.56i −1.29298 0.470605i
687687 0 0
688688 15835.4 + 13287.5i 0.877497 + 0.736307i
689689 −4595.49 5476.69i −0.254099 0.302823i
690690 0 0
691691 9026.08 15633.6i 0.496915 0.860682i −0.503079 0.864241i 0.667799π-0.667799\pi
0.999994 + 0.00355848i 0.00113270π0.00113270\pi
692692 −8664.06 15006.6i −0.475951 0.824372i
693693 0 0
694694 −7994.94 21965.9i −0.437297 1.20146i
695695 31725.8 18316.9i 1.73155 0.999713i
696696 0 0
697697 10431.1 + 1839.29i 0.566868 + 0.0999541i
698698 11009.3 9237.90i 0.597003 0.500945i
699699 0 0
700700 −3938.50 22336.3i −0.212659 1.20605i
701701 5123.61 14077.0i 0.276057 0.758460i −0.721743 0.692161i 0.756659π-0.756659\pi
0.997800 0.0662989i 0.0211191π-0.0211191\pi
702702 0 0
703703 −4133.76 + 1671.19i −0.221775 + 0.0896589i
704704 32.1349i 0.00172036i
705705 0 0
706706 8296.84 1462.96i 0.442289 0.0779874i
707707 −14941.9 + 17807.1i −0.794837 + 0.947250i
708708 0 0
709709 4549.43 25801.1i 0.240984 1.36669i −0.588654 0.808385i 0.700342π-0.700342\pi
0.829638 0.558302i 0.188547π-0.188547\pi
710710 −15581.3 8995.85i −0.823598 0.475505i
711711 0 0
712712 −12830.5 + 4669.91i −0.675341 + 0.245804i
713713 −2190.03 + 797.105i −0.115031 + 0.0418679i
714714 0 0
715715 494.629 + 285.574i 0.0258714 + 0.0149369i
716716 −651.005 + 3692.04i −0.0339794 + 0.192706i
717717 0 0
718718 4916.23 5858.93i 0.255532 0.304531i
719719 25947.0 4575.16i 1.34584 0.237308i 0.546135 0.837697i 0.316099π-0.316099\pi
0.799708 + 0.600389i 0.204988π0.204988\pi
720720 0 0
721721 10633.0i 0.549229i
722722 −22422.7 + 9994.90i −1.15580 + 0.515196i
723723 0 0
724724 −1426.28 + 3918.67i −0.0732144 + 0.201155i
725725 14996.5 + 85049.2i 0.768214 + 4.35676i
726726 0 0
727727 −2045.11 + 1716.05i −0.104331 + 0.0875443i −0.693461 0.720494i 0.743915π-0.743915\pi
0.589130 + 0.808038i 0.299471π0.299471\pi
728728 −8225.57 1450.39i −0.418763 0.0738393i
729729 0 0
730730 21938.1 12666.0i 1.11228 0.642176i
731731 2786.23 + 7655.11i 0.140975 + 0.387325i
732732 0 0
733733 −13594.0 23545.5i −0.685002 1.18646i −0.973436 0.228959i 0.926468π-0.926468\pi
0.288434 0.957500i 0.406865π-0.406865\pi
734734 5648.32 9783.18i 0.284037 0.491967i
735735 0 0
736736 2890.05 + 3444.22i 0.144740 + 0.172494i
737737 −406.438 341.042i −0.0203139 0.0170454i
738738 0 0
739739 −1733.94 631.102i −0.0863111 0.0314147i 0.298504 0.954408i 0.403512π-0.403512\pi
−0.384815 + 0.922994i 0.625735π0.625735\pi
740740 −5359.33 −0.266234
741741 0 0
742742 −8455.41 −0.418339
743743 −25271.5 9198.07i −1.24781 0.454165i −0.368148 0.929767i 0.620008π-0.620008\pi
−0.879660 + 0.475602i 0.842230π0.842230\pi
744744 0 0
745745 16700.1 + 14013.1i 0.821269 + 0.689126i
746746 −16692.9 19893.8i −0.819264 0.976360i
747747 0 0
748748 44.1114 76.4033i 0.00215625 0.00373473i
749749 6279.91 + 10877.1i 0.306359 + 0.530630i
750750 0 0
751751 −5931.55 16296.8i −0.288209 0.791849i −0.996317 0.0857445i 0.972673π-0.972673\pi
0.708108 0.706104i 0.249549π-0.249549\pi
752752 −42357.0 + 24454.8i −2.05399 + 1.18587i
753753 0 0
754754 −47234.7 8328.75i −2.28141 0.402275i
755755 −16171.9 + 13569.8i −0.779544 + 0.654115i
756756 0 0
757757 −1788.97 10145.7i −0.0858931 0.487124i −0.997160 0.0753083i 0.976006π-0.976006\pi
0.911267 0.411816i 0.135105π-0.135105\pi
758758 −6443.72 + 17704.0i −0.308768 + 0.848334i
759759 0 0
760760 19553.7 687.085i 0.933275 0.0327937i
761761 22833.9i 1.08769i −0.839187 0.543843i 0.816969π-0.816969\pi
0.839187 0.543843i 0.183031π-0.183031\pi
762762 0 0
763763 −4821.98 + 850.246i −0.228791 + 0.0403420i
764764 −11584.9 + 13806.4i −0.548598 + 0.653793i
765765 0 0
766766 3495.93 19826.4i 0.164899 0.935191i
767767 18464.9 + 10660.7i 0.869266 + 0.501871i
768768 0 0
769769 23430.0 8527.84i 1.09871 0.399898i 0.271870 0.962334i 0.412358π-0.412358\pi
0.826841 + 0.562436i 0.190136π0.190136\pi
770770 634.753 231.031i 0.0297077 0.0108127i
771771 0 0
772772 6778.23 + 3913.41i 0.316002 + 0.182444i
773773 −340.976 + 1933.77i −0.0158655 + 0.0899779i −0.991712 0.128478i 0.958991π-0.958991\pi
0.975847 + 0.218456i 0.0701020π0.0701020\pi
774774 0 0
775775 −19465.3 + 23197.8i −0.902210 + 1.07521i
776776 −2338.21 + 412.290i −0.108166 + 0.0190726i
777777 0 0
778778 25309.2i 1.16630i
779779 23788.7 14872.0i 1.09412 0.684011i
780780 0 0
781781 48.7304 133.886i 0.00223266 0.00613419i
782782 453.540 + 2572.15i 0.0207398 + 0.117622i
783783 0 0
784784 6153.51 5163.41i 0.280317 0.235214i
785785 −61100.2 10773.6i −2.77804 0.489843i
786786 0 0
787787 −23562.3 + 13603.7i −1.06723 + 0.616163i −0.927422 0.374016i 0.877980π-0.877980\pi
−0.139803 + 0.990179i 0.544647π0.544647\pi
788788 607.653 + 1669.51i 0.0274705 + 0.0754746i
789789 0 0
790790 −20740.5 35923.7i −0.934070 1.61786i
791791 3090.35 5352.65i 0.138913 0.240605i
792792 0 0
793793 18942.8 + 22575.2i 0.848272 + 1.01093i
794794 26795.6 + 22484.2i 1.19766 + 1.00495i
795795 0 0
796796 12618.4 + 4592.71i 0.561868 + 0.204503i
797797 13880.4 0.616899 0.308449 0.951241i 0.400190π-0.400190\pi
0.308449 + 0.951241i 0.400190π0.400190\pi
798798 0 0
799799 −19274.6 −0.853425
800800 54897.4 + 19981.0i 2.42615 + 0.883045i
801801 0 0
802802 13985.3 + 11735.1i 0.615760 + 0.516684i
803803 128.947 + 153.673i 0.00566681 + 0.00675344i
804804 0 0
805805 −3754.65 + 6503.24i −0.164390 + 0.284732i
806806 −8409.17 14565.1i −0.367494 0.636519i
807807 0 0
808808 −5837.44 16038.2i −0.254159 0.698296i
809809 −9580.31 + 5531.20i −0.416348 + 0.240379i −0.693514 0.720443i 0.743938π-0.743938\pi
0.277165 + 0.960822i 0.410605π0.410605\pi
810810 0 0
811811 6132.92 + 1081.40i 0.265544 + 0.0468225i 0.304835 0.952405i 0.401399π-0.401399\pi
−0.0392909 + 0.999228i 0.512510π0.512510\pi
812812 −16317.4 + 13691.9i −0.705206 + 0.591738i
813813 0 0
814814 −19.6264 111.307i −0.000845091 0.00479275i
815815 −10946.2 + 30074.4i −0.470464 + 1.29259i
816816 0 0
817817 19053.7 + 10125.7i 0.815918 + 0.433604i
818818 168.134i 0.00718665i
819819 0 0
820820 33208.8 5855.60i 1.41427 0.249374i
821821 9106.86 10853.1i 0.387128 0.461361i −0.536923 0.843631i 0.680413π-0.680413\pi
0.924050 + 0.382271i 0.124858π0.124858\pi
822822 0 0
823823 973.517 5521.09i 0.0412329 0.233843i −0.957226 0.289342i 0.906564π-0.906564\pi
0.998459 + 0.0554984i 0.0176748π0.0176748\pi
824824 6761.11 + 3903.53i 0.285843 + 0.165031i
825825 0 0
826826 23695.8 8624.57i 0.998163 0.363301i
827827 13477.3 4905.34i 0.566690 0.206258i −0.0427566 0.999086i 0.513614π-0.513614\pi
0.609446 + 0.792827i 0.291392π0.291392\pi
828828 0 0
829829 17268.0 + 9969.69i 0.723453 + 0.417686i 0.816022 0.578020i 0.196175π-0.196175\pi
−0.0925691 + 0.995706i 0.529508π0.529508\pi
830830 −7704.11 + 43692.2i −0.322185 + 1.82720i
831831 0 0
832832 −1657.08 + 1974.84i −0.0690494 + 0.0822898i
833833 3117.54 549.706i 0.129671 0.0228646i
834834 0 0
835835 85266.3i 3.53385i
836836 −48.6332 228.557i −0.00201198 0.00945551i
837837 0 0
838838 5843.87 16055.9i 0.240899 0.661864i
839839 −6999.02 39693.4i −0.288001 1.63334i −0.694364 0.719624i 0.744314π-0.744314\pi
0.406362 0.913712i 0.366797π-0.366797\pi
840840 0 0
841841 43448.0 36457.2i 1.78146 1.49482i
842842 3092.93 + 545.367i 0.126591 + 0.0223214i
843843 0 0
844844 8210.53 4740.35i 0.334855 0.193329i
845845 −121.230 333.075i −0.00493541 0.0135599i
846846 0 0
847847 −10344.9 17917.9i −0.419664 0.726879i
848848 6027.58 10440.1i 0.244090 0.422776i
849849 0 0
850850 21814.3 + 25997.3i 0.880264 + 1.04906i
851851 962.508 + 807.640i 0.0387713 + 0.0325329i
852852 0 0
853853 −21299.9 7752.55i −0.854978 0.311187i −0.122910 0.992418i 0.539223π-0.539223\pi
−0.732068 + 0.681231i 0.761445π0.761445\pi
854854 34853.6 1.39656
855855 0 0
856856 −9221.78 −0.368217
857857 9943.89 + 3619.28i 0.396355 + 0.144262i 0.532505 0.846427i 0.321251π-0.321251\pi
−0.136150 + 0.990688i 0.543473π0.543473\pi
858858 0 0
859859 9275.48 + 7783.06i 0.368423 + 0.309144i 0.808137 0.588994i 0.200476π-0.200476\pi
−0.439714 + 0.898138i 0.644920π0.644920\pi
860860 16670.7 + 19867.4i 0.661009 + 0.787759i
861861 0 0
862862 −6106.74 + 10577.2i −0.241295 + 0.417936i
863863 873.926 + 1513.68i 0.0344714 + 0.0597062i 0.882746 0.469850i 0.155692π-0.155692\pi
−0.848275 + 0.529556i 0.822359π0.822359\pi
864864 0 0
865865 25495.9 + 70049.5i 1.00218 + 2.75347i
866866 24500.9 14145.6i 0.961402 0.555066i
867867 0 0
868868 −7355.65 1297.00i −0.287635 0.0507178i
869869 251.640 211.151i 0.00982313 0.00824258i
870870 0 0
871871 7391.11 + 41917.1i 0.287530 + 1.63066i
872872 1229.58 3378.25i 0.0477510 0.131195i
873873 0 0
874874 5452.30 + 4257.90i 0.211015 + 0.164789i
875875 57352.2i 2.21584i
876876 0 0
877877 −38701.9 + 6824.19i −1.49016 + 0.262755i −0.858630 0.512596i 0.828684π-0.828684\pi
−0.631530 + 0.775351i 0.717573π0.717573\pi
878878 39632.9 47232.7i 1.52340 1.81552i
879879 0 0
880880 −167.235 + 948.438i −0.00640625 + 0.0363316i
881881 −34092.5 19683.3i −1.30375 0.752722i −0.322707 0.946499i 0.604593π-0.604593\pi
−0.981046 + 0.193777i 0.937926π0.937926\pi
882882 0 0
883883 11453.2 4168.64i 0.436503 0.158874i −0.114416 0.993433i 0.536500π-0.536500\pi
0.550919 + 0.834559i 0.314277π0.314277\pi
884884 −6650.69 + 2420.65i −0.253040 + 0.0920988i
885885 0 0
886886 21553.6 + 12444.0i 0.817278 + 0.471856i
887887 1295.85 7349.15i 0.0490535 0.278196i −0.950408 0.311006i 0.899334π-0.899334\pi
0.999462 + 0.0328091i 0.0104453π0.0104453\pi
888888 0 0
889889 −14250.7 + 16983.4i −0.537632 + 0.640725i
890890 −87239.4 + 15382.7i −3.28570 + 0.579357i
891891 0 0
892892 28904.0i 1.08495i
893893 −37931.7 + 34168.8i −1.42143 + 1.28042i
894894 0 0
895895 5516.12 15155.4i 0.206015 0.566022i
896896 −3631.83 20597.1i −0.135414 0.767970i
897897 0 0
898898 −8394.38 + 7043.72i −0.311942 + 0.261751i
899899 28007.9 + 4938.54i 1.03906 + 0.183214i
900900 0 0
901901 4114.29 2375.39i 0.152128 0.0878309i
902902 243.227 + 668.261i 0.00897847 + 0.0246681i
903903 0 0
904904 2269.02 + 3930.07i 0.0834808 + 0.144593i
905905 8969.96 15536.4i 0.329471 0.570661i
906906 0 0
907907 −14099.2 16802.7i −0.516158 0.615133i 0.443510 0.896270i 0.353733π-0.353733\pi
−0.959668 + 0.281136i 0.909289π0.909289\pi
908908 −7439.32 6242.33i −0.271897 0.228149i
909909 0 0
910910 −50921.9 18534.0i −1.85499 0.675162i
911911 24183.3 0.879505 0.439752 0.898119i 0.355066π-0.355066\pi
0.439752 + 0.898119i 0.355066π0.355066\pi
912912 0 0
913913 −351.340 −0.0127357
914914 −44014.3 16019.9i −1.59285 0.579750i
915915 0 0
916916 16702.2 + 14014.8i 0.602464 + 0.505527i
917917 18149.6 + 21629.9i 0.653603 + 0.778934i
918918 0 0
919919 24138.2 41808.5i 0.866425 1.50069i 0.000800280 1.00000i 0.499745π-0.499745\pi
0.865625 0.500693i 0.166921π-0.166921\pi
920920 −2756.77 4774.86i −0.0987913 0.171112i
921921 0 0
922922 12847.1 + 35297.0i 0.458889 + 1.26079i
923923 −9898.70 + 5715.02i −0.353001 + 0.203805i
924924 0 0
925925 16077.9 + 2834.97i 0.571502 + 0.100771i
926926 40245.9 33770.3i 1.42825 1.19845i
927927 0 0
928928 −9527.35 54032.3i −0.337016 1.91131i
929929 −12132.2 + 33333.0i −0.428466 + 1.17720i 0.518278 + 0.855212i 0.326573π0.326573\pi
−0.946744 + 0.321988i 0.895649π0.895649\pi
930930 0 0
931931 5160.72 6608.38i 0.181671 0.232632i
932932 15489.4i 0.544392i
933933 0 0
934934 −18494.0 + 3260.99i −0.647903 + 0.114243i
935935 −243.959 + 290.739i −0.00853295 + 0.0101692i
936936 0 0
937937 5916.58 33554.6i 0.206282 1.16988i −0.689128 0.724640i 0.742006π-0.742006\pi
0.895410 0.445243i 0.146883π-0.146883\pi
938938 43595.4 + 25169.8i 1.51753 + 0.876144i
939939 0 0
940940 −57662.4 + 20987.4i −2.00079 + 0.728227i
941941 18113.4 6592.72i 0.627501 0.228392i −0.00864207 0.999963i 0.502751π-0.502751\pi
0.636143 + 0.771571i 0.280529π0.280529\pi
942942 0 0
943943 −6846.55 3952.86i −0.236431 0.136503i
944944 −6243.02 + 35405.9i −0.215247 + 1.22072i
945945 0 0
946946 −351.572 + 418.987i −0.0120831 + 0.0144000i
947947 −33803.9 + 5960.54i −1.15996 + 0.204532i −0.720319 0.693643i 0.756005π-0.756005\pi
−0.439638 + 0.898175i 0.644893π0.644893\pi
948948 0 0
949949 16093.2i 0.550484i
950950 89016.1 + 12490.7i 3.04007 + 0.426580i
951951 0 0
952952 1898.31 5215.55i 0.0646265 0.177560i
953953 160.465 + 910.044i 0.00545434 + 0.0309331i 0.987413 0.158160i 0.0505562π-0.0505562\pi
−0.981959 + 0.189093i 0.939445π0.939445\pi
954954 0 0
955955 59394.7 49838.1i 2.01253 1.68872i
956956 −21961.3 3872.37i −0.742970 0.131006i
957957 0 0
958958 17483.1 10093.9i 0.589618 0.340416i
959959 −588.261 1616.23i −0.0198081 0.0544222i
960960 0 0
961961 −9909.27 17163.4i −0.332626 0.576126i
962962 −4533.56 + 7852.36i −0.151942 + 0.263171i
963963 0 0
964964 −20852.6 24851.2i −0.696698 0.830293i
965965 −25793.3 21643.2i −0.860431 0.721988i
966966 0 0
967967 24660.1 + 8975.53i 0.820077 + 0.298483i 0.717780 0.696270i 0.245159π-0.245159\pi
0.102297 + 0.994754i 0.467381π0.467381\pi
968968 15191.1 0.504400
969969 0 0
970970 −15404.1 −0.509893
971971 18612.1 + 6774.26i 0.615131 + 0.223889i 0.630747 0.775989i 0.282749π-0.282749\pi
−0.0156160 + 0.999878i 0.504971π0.504971\pi
972972 0 0
973973 −21085.4 17692.8i −0.694725 0.582943i
974974 19927.3 + 23748.4i 0.655555 + 0.781260i
975975 0 0
976976 −24846.0 + 43034.5i −0.814857 + 1.41137i
977977 −9613.30 16650.7i −0.314797 0.545245i 0.664597 0.747202i 0.268603π-0.268603\pi
−0.979394 + 0.201957i 0.935270π0.935270\pi
978978 0 0
979979 −239.932 659.208i −0.00783276 0.0215203i
980980 8727.95 5039.09i 0.284494 0.164253i
981981 0 0
982982 −46929.0 8274.85i −1.52501 0.268901i
983983 −31572.8 + 26492.7i −1.02443 + 0.859601i −0.990178 0.139813i 0.955350π-0.955350\pi
−0.0342541 + 0.999413i 0.510906π0.510906\pi
984984 0 0
985985 −1327.22 7527.02i −0.0429326 0.243483i
986986 10900.9 29949.9i 0.352084 0.967343i
987987 0 0
988988 −8797.14 + 16553.7i −0.283274 + 0.533039i
989989 6080.33i 0.195494i
990990 0 0
991991 −3507.79 + 618.518i −0.112441 + 0.0198263i −0.229585 0.973289i 0.573737π-0.573737\pi
0.117145 + 0.993115i 0.462626π0.462626\pi
992992 12366.4 14737.7i 0.395800 0.471696i
993993 0 0
994994 −2347.40 + 13312.8i −0.0749046 + 0.424805i
995995 −50028.3 28883.9i −1.59397 0.920282i
996996 0 0
997997 448.486 163.236i 0.0142464 0.00518528i −0.334887 0.942258i 0.608698π-0.608698\pi
0.349134 + 0.937073i 0.386476π0.386476\pi
998998 −30157.3 + 10976.3i −0.956524 + 0.348146i
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 171.4.y.a.53.16 yes 120
3.2 odd 2 inner 171.4.y.a.53.5 120
19.14 odd 18 inner 171.4.y.a.71.5 yes 120
57.14 even 18 inner 171.4.y.a.71.16 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
171.4.y.a.53.5 120 3.2 odd 2 inner
171.4.y.a.53.16 yes 120 1.1 even 1 trivial
171.4.y.a.71.5 yes 120 19.14 odd 18 inner
171.4.y.a.71.16 yes 120 57.14 even 18 inner