Properties

Label 171.4.y.a.53.9
Level 171171
Weight 44
Character 171.53
Analytic conductor 10.08910.089
Analytic rank 00
Dimension 120120
Inner twists 44

Related objects

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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 53.9
Character χ\chi == 171.53
Dual form 171.4.y.a.71.9

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+(1.026760.373709i)q2+(5.213784.37488i)q4+(4.491875.35320i)q5+(9.5530616.5464i)q7+(8.08896+14.0105i)q8+(2.61152+7.17509i)q10+(21.701012.5291i)q11+(55.17059.72805i)q13+(15.9922+13.4191i)q14+(6.38540+36.2134i)q16+(47.2141+129.720i)q17+(51.002165.2517i)q19+47.5618iq20+(26.9639+4.75447i)q22+(74.2193+88.4512i)q23+(13.226275.0092i)q25+(53.0113+30.6061i)q26+(122.196+44.4758i)q28+(8.46316+3.08034i)q29+(150.55186.9205i)q31+(29.4512167.026i)q32+(96.9548115.546i)q34+(131.487+23.1847i)q35+419.365iq37+(27.9816+86.0576i)q38+(38.6664106.235i)q40+(61.5401+349.011i)q41+(15.214412.7664i)q43+(167.95829.6155i)q44+(109.26063.0814i)q46+(132.663364.487i)q47+(11.022019.0907i)q49+(41.6117+72.0735i)q50+(245.088+292.085i)q52+(202.318169.765i)q53+(164.54959.8909i)q55+309.097q56+9.84076q58+(75.360327.4289i)q59+(287.655241.371i)q61+(122.096+145.508i)q62+(54.430094.2756i)q64+(195.743+339.036i)q65+(162.434+446.284i)q67+(813.672469.774i)q68+(143.670+25.3329i)q70+(371.275311.537i)q71+(97.0717550.521i)q73+(156.720430.586i)q74+(19.5547+563.337i)q76478.765iq77+(999.614176.259i)q79+(165.175196.848i)q80+(67.2419381.348i)q82+(1116.92644.856i)q83+(906.494329.937i)q85+(20.3923+7.42221i)q86+(351.078+202.695i)q88+(20.8524118.260i)q89+(688.012+819.940i)q91+(773.927136.464i)q92+423.817iq94+(120.211+566.127i)q95+(449.8491235.95i)q97+(4.18257+23.7205i)q98+O(q100)q+(-1.02676 - 0.373709i) q^{2} +(-5.21378 - 4.37488i) q^{4} +(-4.49187 - 5.35320i) q^{5} +(9.55306 - 16.5464i) q^{7} +(8.08896 + 14.0105i) q^{8} +(2.61152 + 7.17509i) q^{10} +(21.7010 - 12.5291i) q^{11} +(-55.1705 - 9.72805i) q^{13} +(-15.9922 + 13.4191i) q^{14} +(6.38540 + 36.2134i) q^{16} +(-47.2141 + 129.720i) q^{17} +(-51.0021 - 65.2517i) q^{19} +47.5618i q^{20} +(-26.9639 + 4.75447i) q^{22} +(-74.2193 + 88.4512i) q^{23} +(13.2262 - 75.0092i) q^{25} +(53.0113 + 30.6061i) q^{26} +(-122.196 + 44.4758i) q^{28} +(-8.46316 + 3.08034i) q^{29} +(-150.551 - 86.9205i) q^{31} +(29.4512 - 167.026i) q^{32} +(96.9548 - 115.546i) q^{34} +(-131.487 + 23.1847i) q^{35} +419.365i q^{37} +(27.9816 + 86.0576i) q^{38} +(38.6664 - 106.235i) q^{40} +(61.5401 + 349.011i) q^{41} +(15.2144 - 12.7664i) q^{43} +(-167.958 - 29.6155i) q^{44} +(109.260 - 63.0814i) q^{46} +(-132.663 - 364.487i) q^{47} +(-11.0220 - 19.0907i) q^{49} +(-41.6117 + 72.0735i) q^{50} +(245.088 + 292.085i) q^{52} +(-202.318 - 169.765i) q^{53} +(-164.549 - 59.8909i) q^{55} +309.097 q^{56} +9.84076 q^{58} +(-75.3603 - 27.4289i) q^{59} +(-287.655 - 241.371i) q^{61} +(122.096 + 145.508i) q^{62} +(54.4300 - 94.2756i) q^{64} +(195.743 + 339.036i) q^{65} +(162.434 + 446.284i) q^{67} +(813.672 - 469.774i) q^{68} +(143.670 + 25.3329i) q^{70} +(371.275 - 311.537i) q^{71} +(-97.0717 - 550.521i) q^{73} +(156.720 - 430.586i) q^{74} +(-19.5547 + 563.337i) q^{76} -478.765i q^{77} +(999.614 - 176.259i) q^{79} +(165.175 - 196.848i) q^{80} +(67.2419 - 381.348i) q^{82} +(-1116.92 - 644.856i) q^{83} +(906.494 - 329.937i) q^{85} +(-20.3923 + 7.42221i) q^{86} +(351.078 + 202.695i) q^{88} +(20.8524 - 118.260i) q^{89} +(-688.012 + 819.940i) q^{91} +(773.927 - 136.464i) q^{92} +423.817i q^{94} +(-120.211 + 566.127i) q^{95} +(449.849 - 1235.95i) q^{97} +(4.18257 + 23.7205i) 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 −1.02676 0.373709i −0.363013 0.132126i 0.154073 0.988060i 0.450761π-0.450761\pi
−0.517086 + 0.855933i 0.672983π0.672983\pi
33 0 0
44 −5.21378 4.37488i −0.651723 0.546861i
55 −4.49187 5.35320i −0.401765 0.478805i 0.526792 0.849994i 0.323395π-0.323395\pi
−0.928557 + 0.371189i 0.878950π0.878950\pi
66 0 0
77 9.55306 16.5464i 0.515817 0.893421i −0.484015 0.875060i 0.660822π-0.660822\pi
0.999831 0.0183611i 0.00584486π-0.00584486\pi
88 8.08896 + 14.0105i 0.357485 + 0.619182i
99 0 0
1010 2.61152 + 7.17509i 0.0825834 + 0.226896i
1111 21.7010 12.5291i 0.594828 0.343424i −0.172176 0.985066i 0.555080π-0.555080\pi
0.767004 + 0.641642i 0.221747π0.221747\pi
1212 0 0
1313 −55.1705 9.72805i −1.17704 0.207544i −0.449291 0.893385i 0.648323π-0.648323\pi
−0.727751 + 0.685841i 0.759434π0.759434\pi
1414 −15.9922 + 13.4191i −0.305293 + 0.256171i
1515 0 0
1616 6.38540 + 36.2134i 0.0997719 + 0.565834i
1717 −47.2141 + 129.720i −0.673594 + 1.85068i −0.173198 + 0.984887i 0.555410π0.555410\pi
−0.500395 + 0.865797i 0.666812π0.666812\pi
1818 0 0
1919 −51.0021 65.2517i −0.615826 0.787883i
2020 47.5618i 0.531758i
2121 0 0
2222 −26.9639 + 4.75447i −0.261306 + 0.0460752i
2323 −74.2193 + 88.4512i −0.672861 + 0.801884i −0.989170 0.146772i 0.953112π-0.953112\pi
0.316310 + 0.948656i 0.397556π0.397556\pi
2424 0 0
2525 13.2262 75.0092i 0.105809 0.600074i
2626 53.0113 + 30.6061i 0.399860 + 0.230859i
2727 0 0
2828 −122.196 + 44.4758i −0.824747 + 0.300183i
2929 −8.46316 + 3.08034i −0.0541921 + 0.0197243i −0.368974 0.929440i 0.620291π-0.620291\pi
0.314782 + 0.949164i 0.398069π0.398069\pi
3030 0 0
3131 −150.551 86.9205i −0.872249 0.503593i −0.00415372 0.999991i 0.501322π-0.501322\pi
−0.868095 + 0.496398i 0.834656π0.834656\pi
3232 29.4512 167.026i 0.162696 0.922696i
3333 0 0
3434 96.9548 115.546i 0.489047 0.582824i
3535 −131.487 + 23.1847i −0.635011 + 0.111970i
3636 0 0
3737 419.365i 1.86333i 0.363321 + 0.931664i 0.381643π0.381643\pi
−0.363321 + 0.931664i 0.618357π0.618357\pi
3838 27.9816 + 86.0576i 0.119453 + 0.367378i
3939 0 0
4040 38.6664 106.235i 0.152842 0.419931i
4141 61.5401 + 349.011i 0.234413 + 1.32942i 0.843846 + 0.536586i 0.180286π0.180286\pi
−0.609433 + 0.792838i 0.708603π0.708603\pi
4242 0 0
4343 15.2144 12.7664i 0.0539574 0.0452756i −0.615410 0.788207i 0.711010π-0.711010\pi
0.669368 + 0.742931i 0.266565π0.266565\pi
4444 −167.958 29.6155i −0.575468 0.101471i
4545 0 0
4646 109.260 63.0814i 0.350207 0.202192i
4747 −132.663 364.487i −0.411719 1.13119i −0.956276 0.292466i 0.905524π-0.905524\pi
0.544557 0.838724i 0.316698π-0.316698\pi
4848 0 0
4949 −11.0220 19.0907i −0.0321342 0.0556580i
5050 −41.6117 + 72.0735i −0.117696 + 0.203855i
5151 0 0
5252 245.088 + 292.085i 0.653608 + 0.778939i
5353 −202.318 169.765i −0.524349 0.439981i 0.341796 0.939774i 0.388965π-0.388965\pi
−0.866145 + 0.499793i 0.833409π0.833409\pi
5454 0 0
5555 −164.549 59.8909i −0.403414 0.146831i
5656 309.097 0.737587
5757 0 0
5858 9.84076 0.0222785
5959 −75.3603 27.4289i −0.166289 0.0605244i 0.257534 0.966269i 0.417090π-0.417090\pi
−0.423823 + 0.905745i 0.639312π0.639312\pi
6060 0 0
6161 −287.655 241.371i −0.603778 0.506630i 0.288880 0.957365i 0.406717π-0.406717\pi
−0.892657 + 0.450736i 0.851162π0.851162\pi
6262 122.096 + 145.508i 0.250100 + 0.298058i
6363 0 0
6464 54.4300 94.2756i 0.106309 0.184132i
6565 195.743 + 339.036i 0.373521 + 0.646958i
6666 0 0
6767 162.434 + 446.284i 0.296186 + 0.813765i 0.995128 + 0.0985871i 0.0314323π0.0314323\pi
−0.698942 + 0.715178i 0.746345π0.746345\pi
6868 813.672 469.774i 1.45106 0.837771i
6969 0 0
7070 143.670 + 25.3329i 0.245312 + 0.0432551i
7171 371.275 311.537i 0.620595 0.520741i −0.277396 0.960756i 0.589471π-0.589471\pi
0.897991 + 0.440015i 0.145027π0.145027\pi
7272 0 0
7373 −97.0717 550.521i −0.155635 0.882652i −0.958203 0.286091i 0.907644π-0.907644\pi
0.802567 0.596562i 0.203467π-0.203467\pi
7474 156.720 430.586i 0.246194 0.676413i
7575 0 0
7676 −19.5547 + 563.337i −0.0295141 + 0.850252i
7777 478.765i 0.708576i
7878 0 0
7979 999.614 176.259i 1.42361 0.251021i 0.591803 0.806083i 0.298416π-0.298416\pi
0.831809 + 0.555061i 0.187305π0.187305\pi
8080 165.175 196.848i 0.230839 0.275104i
8181 0 0
8282 67.2419 381.348i 0.0905564 0.513571i
8383 −1116.92 644.856i −1.47709 0.852797i −0.477423 0.878673i 0.658429π-0.658429\pi
−0.999665 + 0.0258760i 0.991763π0.991763\pi
8484 0 0
8585 906.494 329.937i 1.15674 0.421020i
8686 −20.3923 + 7.42221i −0.0255693 + 0.00930648i
8787 0 0
8888 351.078 + 202.695i 0.425284 + 0.245538i
8989 20.8524 118.260i 0.0248354 0.140848i −0.969869 0.243628i 0.921662π-0.921662\pi
0.994704 + 0.102779i 0.0327736π0.0327736\pi
9090 0 0
9191 −688.012 + 819.940i −0.792563 + 0.944540i
9292 773.927 136.464i 0.877038 0.154645i
9393 0 0
9494 423.817i 0.465036i
9595 −120.211 + 566.127i −0.129825 + 0.611404i
9696 0 0
9797 449.849 1235.95i 0.470879 1.29373i −0.446167 0.894950i 0.647211π-0.647211\pi
0.917046 0.398780i 0.130566π-0.130566\pi
9898 4.18257 + 23.7205i 0.00431126 + 0.0244504i
9999 0 0
100100 −397.115 + 333.219i −0.397115 + 0.333219i
101101 −1155.05 203.666i −1.13793 0.200649i −0.427233 0.904142i 0.640511π-0.640511\pi
−0.710702 + 0.703493i 0.751623π0.751623\pi
102102 0 0
103103 −712.793 + 411.531i −0.681880 + 0.393684i −0.800563 0.599249i 0.795466π-0.795466\pi
0.118683 + 0.992932i 0.462133π0.462133\pi
104104 −309.977 851.656i −0.292267 0.802998i
105105 0 0
106106 144.288 + 249.915i 0.132213 + 0.228999i
107107 51.9112 89.9128i 0.0469013 0.0812355i −0.841622 0.540068i 0.818399π-0.818399\pi
0.888523 + 0.458832i 0.151732π0.151732\pi
108108 0 0
109109 −532.921 635.110i −0.468299 0.558097i 0.479262 0.877672i 0.340904π-0.340904\pi
−0.947561 + 0.319575i 0.896460π0.896460\pi
110110 146.570 + 122.987i 0.127045 + 0.106603i
111111 0 0
112112 660.201 + 240.294i 0.556992 + 0.202729i
113113 659.556 0.549078 0.274539 0.961576i 0.411475π-0.411475\pi
0.274539 + 0.961576i 0.411475π0.411475\pi
114114 0 0
115115 806.880 0.654278
116116 57.6012 + 20.9651i 0.0461047 + 0.0167807i
117117 0 0
118118 67.1262 + 56.3256i 0.0523684 + 0.0439423i
119119 1695.35 + 2020.44i 1.30599 + 1.55642i
120120 0 0
121121 −351.544 + 608.891i −0.264120 + 0.457469i
122122 205.149 + 355.329i 0.152240 + 0.263688i
123123 0 0
124124 404.672 + 1111.83i 0.293069 + 0.805201i
125125 −1217.43 + 702.886i −0.871125 + 0.502944i
126126 0 0
127127 −1670.80 294.606i −1.16740 0.205843i −0.443838 0.896107i 0.646383π-0.646383\pi
−0.723558 + 0.690264i 0.757494π0.757494\pi
128128 −1130.50 + 948.604i −0.780650 + 0.655043i
129129 0 0
130130 −74.2792 421.258i −0.0501132 0.284206i
131131 205.409 564.357i 0.136998 0.376398i −0.852155 0.523290i 0.824705π-0.824705\pi
0.989153 + 0.146892i 0.0469269π0.0469269\pi
132132 0 0
133133 −1566.91 + 220.547i −1.02156 + 0.143788i
134134 518.928i 0.334542i
135135 0 0
136136 −2199.35 + 387.805i −1.38671 + 0.244514i
137137 −1061.49 + 1265.03i −0.661964 + 0.788897i −0.987666 0.156575i 0.949955π-0.949955\pi
0.325703 + 0.945472i 0.394399π0.394399\pi
138138 0 0
139139 221.349 1255.33i 0.135069 0.766013i −0.839743 0.542984i 0.817294π-0.817294\pi
0.974812 0.223029i 0.0715944π-0.0715944\pi
140140 786.977 + 454.361i 0.475083 + 0.274290i
141141 0 0
142142 −497.633 + 181.124i −0.294088 + 0.107039i
143143 −1319.14 + 480.128i −0.771413 + 0.280771i
144144 0 0
145145 54.5051 + 31.4685i 0.0312166 + 0.0180229i
146146 −106.066 + 601.528i −0.0601236 + 0.340978i
147147 0 0
148148 1834.67 2186.48i 1.01898 1.21437i
149149 −1369.62 + 241.501i −0.753044 + 0.132782i −0.536978 0.843597i 0.680434π-0.680434\pi
−0.216067 + 0.976379i 0.569323π0.569323\pi
150150 0 0
151151 1135.54i 0.611977i −0.952035 0.305989i 0.901013π-0.901013\pi
0.952035 0.305989i 0.0989869π-0.0989869\pi
152152 501.654 1242.38i 0.267694 0.662964i
153153 0 0
154154 −178.919 + 491.575i −0.0936213 + 0.257222i
155155 210.951 + 1196.36i 0.109316 + 0.619963i
156156 0 0
157157 413.929 347.328i 0.210415 0.176559i −0.531489 0.847065i 0.678367π-0.678367\pi
0.741904 + 0.670506i 0.233923π0.233923\pi
158158 −1092.23 192.590i −0.549957 0.0969722i
159159 0 0
160160 −1026.41 + 592.600i −0.507157 + 0.292807i
161161 754.525 + 2073.04i 0.369347 + 1.01477i
162162 0 0
163163 −298.203 516.504i −0.143295 0.248194i 0.785440 0.618937i 0.212436π-0.212436\pi
−0.928736 + 0.370743i 0.879103π0.879103\pi
164164 1206.03 2088.90i 0.574237 0.994607i
165165 0 0
166166 905.821 + 1079.52i 0.423526 + 0.504739i
167167 1506.45 + 1264.06i 0.698041 + 0.585726i 0.921216 0.389053i 0.127198π-0.127198\pi
−0.223175 + 0.974778i 0.571642π0.571642\pi
168168 0 0
169169 884.647 + 321.985i 0.402661 + 0.146557i
170170 −1054.05 −0.475541
171171 0 0
172172 −135.176 −0.0599247
173173 −3837.95 1396.90i −1.68667 0.613897i −0.692470 0.721447i 0.743477π-0.743477\pi
−0.994200 + 0.107550i 0.965700π0.965700\pi
174174 0 0
175175 −1114.78 935.413i −0.481540 0.404060i
176176 592.291 + 705.865i 0.253668 + 0.302310i
177177 0 0
178178 −65.6051 + 113.631i −0.0276253 + 0.0478485i
179179 773.834 + 1340.32i 0.323123 + 0.559666i 0.981131 0.193345i 0.0619338π-0.0619338\pi
−0.658007 + 0.753012i 0.728600π0.728600\pi
180180 0 0
181181 −540.228 1484.26i −0.221850 0.609528i 0.777974 0.628297i 0.216248π-0.216248\pi
−0.999824 + 0.0187689i 0.994025π0.994025\pi
182182 1012.84 584.763i 0.412509 0.238162i
183183 0 0
184184 −1839.60 324.371i −0.737050 0.129962i
185185 2244.94 1883.73i 0.892170 0.748620i
186186 0 0
187187 600.675 + 3406.60i 0.234897 + 1.33217i
188188 −902.916 + 2480.74i −0.350276 + 0.962376i
189189 0 0
190190 334.994 536.351i 0.127911 0.204795i
191191 1653.75i 0.626497i −0.949671 0.313248i 0.898583π-0.898583\pi
0.949671 0.313248i 0.101417π-0.101417\pi
192192 0 0
193193 1860.16 327.996i 0.693768 0.122330i 0.184364 0.982858i 0.440977π-0.440977\pi
0.509403 + 0.860528i 0.329866π0.329866\pi
194194 −923.772 + 1100.91i −0.341871 + 0.407426i
195195 0 0
196196 −26.0532 + 147.755i −0.00949460 + 0.0538465i
197197 1372.16 + 792.214i 0.496254 + 0.286512i 0.727165 0.686462i 0.240837π-0.240837\pi
−0.230911 + 0.972975i 0.574171π0.574171\pi
198198 0 0
199199 −2001.13 + 728.352i −0.712846 + 0.259455i −0.672886 0.739746i 0.734945π-0.734945\pi
−0.0399607 + 0.999201i 0.512723π0.512723\pi
200200 1157.90 421.442i 0.409380 0.149002i
201201 0 0
202202 1109.84 + 640.766i 0.386575 + 0.223189i
203203 −29.8806 + 169.461i −0.0103311 + 0.0585905i
204204 0 0
205205 1591.90 1897.15i 0.542355 0.646354i
206206 885.659 156.165i 0.299547 0.0528183i
207207 0 0
208208 2060.03i 0.686718i
209209 −1924.34 777.019i −0.636888 0.257165i
210210 0 0
211211 747.181 2052.86i 0.243782 0.669786i −0.756100 0.654456i 0.772898π-0.772898\pi
0.999882 0.0153302i 0.00487996π-0.00487996\pi
212212 312.140 + 1770.23i 0.101122 + 0.573491i
213213 0 0
214214 −86.9014 + 72.9189i −0.0277591 + 0.0232927i
215215 −136.682 24.1007i −0.0433564 0.00764490i
216216 0 0
217217 −2876.44 + 1660.71i −0.899841 + 0.519523i
218218 309.834 + 851.261i 0.0962595 + 0.264471i
219219 0 0
220220 595.907 + 1032.14i 0.182618 + 0.316304i
221221 3866.74 6697.40i 1.17695 2.03853i
222222 0 0
223223 272.714 + 325.008i 0.0818937 + 0.0975971i 0.805435 0.592684i 0.201932π-0.201932\pi
−0.723542 + 0.690281i 0.757487π0.757487\pi
224224 −2482.33 2082.92i −0.740435 0.621298i
225225 0 0
226226 −677.203 246.482i −0.199323 0.0725475i
227227 3939.83 1.15196 0.575982 0.817463i 0.304620π-0.304620\pi
0.575982 + 0.817463i 0.304620π0.304620\pi
228228 0 0
229229 1301.54 0.375580 0.187790 0.982209i 0.439867π-0.439867\pi
0.187790 + 0.982209i 0.439867π0.439867\pi
230230 −828.470 301.538i −0.237512 0.0864472i
231231 0 0
232232 −111.615 93.6564i −0.0315858 0.0265036i
233233 −2074.81 2472.66i −0.583371 0.695234i 0.390947 0.920413i 0.372148π-0.372148\pi
−0.974317 + 0.225179i 0.927703π0.927703\pi
234234 0 0
235235 −1355.27 + 2347.40i −0.376205 + 0.651606i
236236 272.914 + 472.701i 0.0752762 + 0.130382i
237237 0 0
238238 −985.657 2708.07i −0.268448 0.737555i
239239 −5423.52 + 3131.27i −1.46786 + 0.847469i −0.999352 0.0359911i 0.988541π-0.988541\pi
−0.468507 + 0.883460i 0.655208π0.655208\pi
240240 0 0
241241 7096.32 + 1251.27i 1.89674 + 0.334446i 0.995168 0.0981849i 0.0313036π-0.0313036\pi
0.901571 + 0.432631i 0.142415π0.142415\pi
242242 588.498 493.808i 0.156323 0.131170i
243243 0 0
244244 443.800 + 2516.91i 0.116440 + 0.660365i
245245 −52.6869 + 144.756i −0.0137389 + 0.0377474i
246246 0 0
247247 2179.04 + 4096.12i 0.561332 + 1.05518i
248248 2812.39i 0.720108i
249249 0 0
250250 1512.68 266.727i 0.382682 0.0674772i
251251 4223.49 5033.36i 1.06209 1.26575i 0.0994256 0.995045i 0.468299π-0.468299\pi
0.962663 0.270703i 0.0872561π-0.0872561\pi
252252 0 0
253253 −502.423 + 2849.38i −0.124850 + 0.708060i
254254 1605.40 + 926.881i 0.396583 + 0.228967i
255255 0 0
256256 696.893 253.648i 0.170140 0.0619258i
257257 −3525.46 + 1283.16i −0.855690 + 0.311446i −0.732358 0.680920i 0.761580π-0.761580\pi
−0.123332 + 0.992365i 0.539358π0.539358\pi
258258 0 0
259259 6938.97 + 4006.22i 1.66474 + 0.961136i
260260 462.684 2624.01i 0.110363 0.625901i
261261 0 0
262262 −421.811 + 502.694i −0.0994639 + 0.118537i
263263 5217.46 919.979i 1.22328 0.215697i 0.475543 0.879693i 0.342252π-0.342252\pi
0.747737 + 0.663996i 0.231141π0.231141\pi
264264 0 0
265265 1845.61i 0.427829i
266266 1691.25 + 359.119i 0.389840 + 0.0827781i
267267 0 0
268268 1105.54 3037.46i 0.251985 0.692322i
269269 −1004.71 5698.00i −0.227726 1.29150i −0.857404 0.514643i 0.827924π-0.827924\pi
0.629678 0.776856i 0.283187π-0.283187\pi
270270 0 0
271271 −1239.10 + 1039.73i −0.277750 + 0.233060i −0.771012 0.636821i 0.780249π-0.780249\pi
0.493262 + 0.869881i 0.335805π0.335805\pi
272272 −4999.07 881.471i −1.11439 0.196496i
273273 0 0
274274 1562.64 902.193i 0.344536 0.198918i
275275 −652.777 1793.49i −0.143141 0.393278i
276276 0 0
277277 −1703.14 2949.93i −0.369430 0.639871i 0.620047 0.784565i 0.287114π-0.287114\pi
−0.989476 + 0.144694i 0.953780π0.953780\pi
278278 −696.400 + 1206.20i −0.150242 + 0.260227i
279279 0 0
280280 −1388.43 1654.66i −0.296337 0.353160i
281281 −1712.42 1436.89i −0.363538 0.305045i 0.442661 0.896689i 0.354035π-0.354035\pi
−0.806199 + 0.591644i 0.798479π0.798479\pi
282282 0 0
283283 1210.23 + 440.489i 0.254208 + 0.0925242i 0.465981 0.884795i 0.345702π-0.345702\pi
−0.211773 + 0.977319i 0.567924π0.567924\pi
284284 −3298.69 −0.689229
285285 0 0
286286 1533.86 0.317131
287287 6362.77 + 2315.86i 1.30865 + 0.476309i
288288 0 0
289289 −10834.4 9091.17i −2.20526 1.85043i
290290 −44.2034 52.6796i −0.00895074 0.0106671i
291291 0 0
292292 −1902.36 + 3294.98i −0.381257 + 0.660356i
293293 4227.55 + 7322.32i 0.842921 + 1.45998i 0.887414 + 0.460972i 0.152499π0.152499\pi
−0.0444934 + 0.999010i 0.514167π0.514167\pi
294294 0 0
295295 191.676 + 526.626i 0.0378299 + 0.103937i
296296 −5875.51 + 3392.23i −1.15374 + 0.666112i
297297 0 0
298298 1496.52 + 263.876i 0.290909 + 0.0512951i
299299 4955.18 4157.89i 0.958412 0.804203i
300300 0 0
301301 −65.8935 373.700i −0.0126181 0.0715606i
302302 −424.360 + 1165.92i −0.0808581 + 0.222156i
303303 0 0
304304 2037.32 2263.62i 0.384369 0.427064i
305305 2624.08i 0.492638i
306306 0 0
307307 1792.01 315.979i 0.333144 0.0587423i −0.00457421 0.999990i 0.501456π-0.501456\pi
0.337718 + 0.941247i 0.390345π0.390345\pi
308308 −2094.54 + 2496.18i −0.387492 + 0.461795i
309309 0 0
310310 230.496 1307.21i 0.0422300 0.239498i
311311 −1489.75 860.109i −0.271628 0.156824i 0.358000 0.933722i 0.383459π-0.383459\pi
−0.629627 + 0.776898i 0.716792π0.716792\pi
312312 0 0
313313 1506.16 548.196i 0.271990 0.0989964i −0.202424 0.979298i 0.564882π-0.564882\pi
0.474415 + 0.880302i 0.342660π0.342660\pi
314314 −554.804 + 201.932i −0.0997114 + 0.0362920i
315315 0 0
316316 −5982.88 3454.22i −1.06507 0.614921i
317317 −545.188 + 3091.91i −0.0965956 + 0.547821i 0.897651 + 0.440707i 0.145272π0.145272\pi
−0.994247 + 0.107114i 0.965839π0.965839\pi
318318 0 0
319319 −145.065 + 172.882i −0.0254612 + 0.0303434i
320320 −749.168 + 132.099i −0.130874 + 0.0230767i
321321 0 0
322322 2410.48i 0.417177i
323323 10872.4 3535.17i 1.87294 0.608986i
324324 0 0
325325 −1459.39 + 4009.63i −0.249084 + 0.684352i
326326 113.160 + 641.765i 0.0192251 + 0.109031i
327327 0 0
328328 −4392.02 + 3685.34i −0.739356 + 0.620394i
329329 −7298.28 1286.88i −1.22300 0.215648i
330330 0 0
331331 −7994.76 + 4615.77i −1.32759 + 0.766483i −0.984926 0.172976i 0.944662π-0.944662\pi
−0.342662 + 0.939459i 0.611328π0.611328\pi
332332 3002.23 + 8248.56i 0.496291 + 1.36355i
333333 0 0
334334 −1074.37 1860.86i −0.176009 0.304856i
335335 1659.42 2874.19i 0.270637 0.468758i
336336 0 0
337337 4194.73 + 4999.09i 0.678046 + 0.808064i 0.989855 0.142081i 0.0453793π-0.0453793\pi
−0.311809 + 0.950145i 0.600935π0.600935\pi
338338 −787.988 661.201i −0.126807 0.106404i
339339 0 0
340340 −6169.70 2245.59i −0.984115 0.358189i
341341 −4356.14 −0.691784
342342 0 0
343343 6132.22 0.965332
344344 301.931 + 109.894i 0.0473228 + 0.0172241i
345345 0 0
346346 3418.61 + 2868.55i 0.531172 + 0.445706i
347347 6767.67 + 8065.40i 1.04700 + 1.24776i 0.968017 + 0.250885i 0.0807217π0.0807217\pi
0.0789795 + 0.996876i 0.474834π0.474834\pi
348348 0 0
349349 5270.27 9128.37i 0.808341 1.40009i −0.105671 0.994401i 0.533699π-0.533699\pi
0.914012 0.405687i 0.132968π-0.132968\pi
350350 795.038 + 1377.05i 0.121419 + 0.210303i
351351 0 0
352352 −1453.56 3993.63i −0.220100 0.604719i
353353 −5189.48 + 2996.15i −0.782459 + 0.451753i −0.837301 0.546742i 0.815868π-0.815868\pi
0.0548419 + 0.998495i 0.482535π0.482535\pi
354354 0 0
355355 −3335.44 588.128i −0.498667 0.0879284i
356356 −626.093 + 525.354i −0.0932103 + 0.0782127i
357357 0 0
358358 −293.650 1665.37i −0.0433516 0.245859i
359359 −4059.28 + 11152.8i −0.596771 + 1.63961i 0.160895 + 0.986972i 0.448562π0.448562\pi
−0.757666 + 0.652643i 0.773660π0.773660\pi
360360 0 0
361361 −1656.57 + 6655.95i −0.241518 + 0.970396i
362362 1725.87i 0.250579i
363363 0 0
364364 7174.29 1265.02i 1.03306 0.182157i
365365 −2511.02 + 2992.51i −0.360089 + 0.429138i
366366 0 0
367367 −317.137 + 1798.57i −0.0451074 + 0.255817i −0.999020 0.0442689i 0.985904π-0.985904\pi
0.953912 + 0.300086i 0.0970153π0.0970153\pi
368368 −3677.04 2122.94i −0.520866 0.300722i
369369 0 0
370370 −3008.98 + 1095.18i −0.422782 + 0.153880i
371371 −4741.75 + 1725.85i −0.663556 + 0.241515i
372372 0 0
373373 −5746.38 3317.67i −0.797685 0.460543i 0.0449763 0.998988i 0.485679π-0.485679\pi
−0.842661 + 0.538445i 0.819012π0.819012\pi
374374 656.329 3722.23i 0.0907432 0.514630i
375375 0 0
376376 4033.54 4806.99i 0.553229 0.659313i
377377 496.883 87.6139i 0.0678800 0.0119691i
378378 0 0
379379 2511.14i 0.340339i −0.985415 0.170170i 0.945568π-0.945568\pi
0.985415 0.170170i 0.0544315π-0.0544315\pi
380380 3103.49 2425.75i 0.418962 0.327470i
381381 0 0
382382 −618.020 + 1698.00i −0.0827765 + 0.227427i
383383 −1614.98 9158.99i −0.215461 1.22194i −0.880105 0.474779i 0.842528π-0.842528\pi
0.664644 0.747160i 0.268583π-0.268583\pi
384384 0 0
385385 −2562.92 + 2150.55i −0.339269 + 0.284681i
386386 −2032.51 358.386i −0.268010 0.0472574i
387387 0 0
388388 −7752.56 + 4475.94i −1.01437 + 0.585648i
389389 −3526.18 9688.09i −0.459600 1.26274i −0.925784 0.378052i 0.876594π-0.876594\pi
0.466185 0.884687i 0.345628π-0.345628\pi
390390 0 0
391391 −7969.65 13803.8i −1.03080 1.78540i
392392 178.313 308.848i 0.0229750 0.0397938i
393393 0 0
394394 −1112.81 1326.20i −0.142291 0.169576i
395395 −5433.68 4559.40i −0.692148 0.580781i
396396 0 0
397397 −4607.91 1677.14i −0.582531 0.212024i 0.0339105 0.999425i 0.489204π-0.489204\pi
−0.616441 + 0.787401i 0.711426π0.711426\pi
398398 2326.87 0.293054
399399 0 0
400400 2800.79 0.350099
401401 −2396.16 872.132i −0.298401 0.108609i 0.188481 0.982077i 0.439644π-0.439644\pi
−0.486882 + 0.873468i 0.661866π0.661866\pi
402402 0 0
403403 7460.39 + 6260.01i 0.922156 + 0.773780i
404404 5131.15 + 6115.06i 0.631891 + 0.753059i
405405 0 0
406406 94.0094 162.829i 0.0114916 0.0199041i
407407 5254.26 + 9100.64i 0.639911 + 1.10836i
408408 0 0
409409 789.489 + 2169.10i 0.0954467 + 0.262238i 0.978223 0.207555i 0.0665507π-0.0665507\pi
−0.882777 + 0.469793i 0.844329π0.844329\pi
410410 −2343.47 + 1353.00i −0.282282 + 0.162976i
411411 0 0
412412 5516.75 + 972.753i 0.659687 + 0.116321i
413413 −1173.77 + 984.910i −0.139849 + 0.117347i
414414 0 0
415415 1565.03 + 8875.73i 0.185119 + 1.04986i
416416 −3249.67 + 8928.40i −0.383001 + 1.05229i
417417 0 0
418418 1685.45 + 1516.95i 0.197221 + 0.177504i
419419 6841.40i 0.797671i 0.917022 + 0.398836i 0.130586π0.130586\pi
−0.917022 + 0.398836i 0.869414π0.869414\pi
420420 0 0
421421 1336.82 235.717i 0.154757 0.0272878i −0.0957330 0.995407i 0.530519π-0.530519\pi
0.250490 + 0.968119i 0.419408π0.419408\pi
422422 −1534.35 + 1828.56i −0.176992 + 0.210931i
423423 0 0
424424 741.947 4207.79i 0.0849815 0.481954i
425425 9105.71 + 5257.18i 1.03927 + 0.600025i
426426 0 0
427427 −6741.81 + 2453.82i −0.764073 + 0.278100i
428428 −664.012 + 241.681i −0.0749912 + 0.0272946i
429429 0 0
430430 131.332 + 75.8247i 0.0147288 + 0.00850370i
431431 2205.75 12509.4i 0.246514 1.39805i −0.570437 0.821341i 0.693226π-0.693226\pi
0.816951 0.576707i 0.195663π-0.195663\pi
432432 0 0
433433 8937.43 10651.2i 0.991929 1.18214i 0.00866258 0.999962i 0.497243π-0.497243\pi
0.983267 0.182173i 0.0583130π-0.0583130\pi
434434 3574.03 630.198i 0.395297 0.0697015i
435435 0 0
436436 5642.79i 0.619818i
437437 9556.93 + 331.742i 1.04616 + 0.0363144i
438438 0 0
439439 −2629.41 + 7224.26i −0.285866 + 0.785410i 0.710768 + 0.703427i 0.248348π0.248348\pi
−0.996634 + 0.0819832i 0.973875π0.973875\pi
440440 −491.929 2789.87i −0.0532995 0.302277i
441441 0 0
442442 −6473.08 + 5431.56i −0.696591 + 0.584509i
443443 −12954.5 2284.22i −1.38936 0.244981i −0.571594 0.820537i 0.693675π-0.693675\pi
−0.817762 + 0.575556i 0.804786π0.804786\pi
444444 0 0
445445 −726.735 + 419.580i −0.0774169 + 0.0446967i
446446 −158.553 435.620i −0.0168334 0.0462494i
447447 0 0
448448 −1039.95 1801.24i −0.109672 0.189957i
449449 3981.53 6896.21i 0.418485 0.724838i −0.577302 0.816531i 0.695894π-0.695894\pi
0.995787 + 0.0916928i 0.0292278π0.0292278\pi
450450 0 0
451451 5708.28 + 6802.86i 0.595992 + 0.710275i
452452 −3438.78 2885.48i −0.357847 0.300269i
453453 0 0
454454 −4045.25 1472.35i −0.418178 0.152204i
455455 7479.76 0.770674
456456 0 0
457457 3938.81 0.403172 0.201586 0.979471i 0.435390π-0.435390\pi
0.201586 + 0.979471i 0.435390π0.435390\pi
458458 −1336.36 486.396i −0.136341 0.0496240i
459459 0 0
460460 −4206.90 3530.01i −0.426408 0.357799i
461461 3222.21 + 3840.08i 0.325539 + 0.387962i 0.903847 0.427857i 0.140731π-0.140731\pi
−0.578308 + 0.815819i 0.696287π0.696287\pi
462462 0 0
463463 −5806.80 + 10057.7i −0.582861 + 1.00955i 0.412277 + 0.911059i 0.364734π0.364734\pi
−0.995138 + 0.0984871i 0.968600π0.968600\pi
464464 −165.590 286.811i −0.0165675 0.0286958i
465465 0 0
466466 1206.27 + 3314.20i 0.119913 + 0.329458i
467467 1449.35 836.781i 0.143614 0.0829156i −0.426471 0.904501i 0.640243π-0.640243\pi
0.570085 + 0.821586i 0.306910π0.306910\pi
468468 0 0
469469 8936.14 + 1575.68i 0.879813 + 0.155135i
470470 2268.78 1903.73i 0.222661 0.186835i
471471 0 0
472472 −225.294 1277.71i −0.0219703 0.124600i
473473 170.216 467.665i 0.0165466 0.0454614i
474474 0 0
475475 −5569.04 + 2962.60i −0.537948 + 0.286176i
476476 17951.1i 1.72855i
477477 0 0
478478 6738.82 1188.24i 0.644825 0.113700i
479479 −2094.64 + 2496.29i −0.199805 + 0.238118i −0.856638 0.515918i 0.827451π-0.827451\pi
0.656833 + 0.754036i 0.271895π0.271895\pi
480480 0 0
481481 4079.60 23136.6i 0.386723 2.19322i
482482 −6818.58 3936.71i −0.644353 0.372017i
483483 0 0
484484 4496.70 1636.67i 0.422305 0.153706i
485485 −8636.96 + 3143.60i −0.808627 + 0.294316i
486486 0 0
487487 16948.9 + 9785.48i 1.57706 + 0.910518i 0.995266 + 0.0971839i 0.0309835π0.0309835\pi
0.581797 + 0.813334i 0.302350π0.302350\pi
488488 1054.90 5982.63i 0.0978546 0.554961i
489489 0 0
490490 108.193 128.940i 0.00997484 0.0118876i
491491 1805.40 318.341i 0.165940 0.0292597i −0.0900607 0.995936i 0.528706π-0.528706\pi
0.256001 + 0.966677i 0.417595π0.417595\pi
492492 0 0
493493 1243.27i 0.113579i
494494 −706.588 5020.05i −0.0643540 0.457212i
495495 0 0
496496 2186.36 6006.98i 0.197924 0.543793i
497497 −1607.99 9119.39i −0.145128 0.823060i
498498 0 0
499499 13291.5 11152.9i 1.19240 1.00055i 0.192590 0.981279i 0.438311π-0.438311\pi
0.999814 0.0192670i 0.00613327π-0.00613327\pi
500500 9422.48 + 1661.44i 0.842773 + 0.148604i
501501 0 0
502502 −6217.51 + 3589.68i −0.552791 + 0.319154i
503503 4141.92 + 11379.8i 0.367155 + 1.00875i 0.976438 + 0.215798i 0.0692352π0.0692352\pi
−0.609283 + 0.792953i 0.708543π0.708543\pi
504504 0 0
505505 4098.05 + 7098.03i 0.361111 + 0.625462i
506506 1580.71 2737.86i 0.138875 0.240539i
507507 0 0
508508 7422.30 + 8845.56i 0.648251 + 0.772555i
509509 −13427.2 11266.8i −1.16926 0.981123i −0.169266 0.985570i 0.554140π-0.554140\pi
−0.999990 + 0.00444765i 0.998584π0.998584\pi
510510 0 0
511511 −10036.5 3652.98i −0.868860 0.316239i
512512 10995.8 0.949121
513513 0 0
514514 4099.32 0.351777
515515 5404.79 + 1967.18i 0.462453 + 0.168319i
516516 0 0
517517 −7445.61 6247.61i −0.633380 0.531469i
518518 −5627.48 6706.57i −0.477330 0.568860i
519519 0 0
520520 −3166.71 + 5484.90i −0.267056 + 0.462555i
521521 7187.90 + 12449.8i 0.604430 + 1.04690i 0.992141 + 0.125122i 0.0399323π0.0399323\pi
−0.387712 + 0.921781i 0.626734π0.626734\pi
522522 0 0
523523 −4579.81 12582.9i −0.382909 1.05203i −0.970126 0.242604i 0.921999π-0.921999\pi
0.587217 0.809430i 0.300224π-0.300224\pi
524524 −3539.96 + 2043.80i −0.295122 + 0.170389i
525525 0 0
526526 −5700.87 1005.22i −0.472566 0.0833261i
527527 18383.4 15425.5i 1.51953 1.27504i
528528 0 0
529529 −202.320 1147.41i −0.0166286 0.0943055i
530530 689.720 1894.99i 0.0565274 0.155308i
531531 0 0
532532 9134.38 + 5705.15i 0.744409 + 0.464943i
533533 19853.8i 1.61344i
534534 0 0
535535 −714.499 + 125.986i −0.0577393 + 0.0101810i
536536 −4938.74 + 5885.76i −0.397987 + 0.474302i
537537 0 0
538538 −1097.80 + 6225.93i −0.0879731 + 0.498920i
539539 −478.378 276.192i −0.0382286 0.0220713i
540540 0 0
541541 8538.52 3107.77i 0.678558 0.246975i 0.0203296 0.999793i 0.493528π-0.493528\pi
0.658228 + 0.752819i 0.271306π0.271306\pi
542542 1660.82 604.488i 0.131620 0.0479058i
543543 0 0
544544 20276.0 + 11706.4i 1.59803 + 0.922622i
545545 −1006.06 + 5705.66i −0.0790733 + 0.448447i
546546 0 0
547547 −4904.33 + 5844.75i −0.383353 + 0.456862i −0.922869 0.385113i 0.874162π-0.874162\pi
0.539517 + 0.841975i 0.318607π0.318607\pi
548548 11068.7 1951.72i 0.862834 0.152141i
549549 0 0
550550 2085.43i 0.161678i
551551 632.637 + 395.132i 0.0489133 + 0.0305503i
552552 0 0
553553 6632.93 18223.8i 0.510056 1.40137i
554554 646.299 + 3665.34i 0.0495643 + 0.281093i
555555 0 0
556556 −6645.99 + 5576.65i −0.506929 + 0.425364i
557557 −6839.48 1205.98i −0.520283 0.0917400i −0.0926615 0.995698i 0.529537π-0.529537\pi
−0.427622 + 0.903958i 0.640649π0.640649\pi
558558 0 0
559559 −963.576 + 556.321i −0.0729068 + 0.0420928i
560560 −1679.20 4613.56i −0.126713 0.348140i
561561 0 0
562562 1221.26 + 2115.28i 0.0916649 + 0.158768i
563563 8727.13 15115.8i 0.653294 1.13154i −0.329024 0.944322i 0.606720π-0.606720\pi
0.982318 0.187218i 0.0599469π-0.0599469\pi
564564 0 0
565565 −2962.64 3530.73i −0.220600 0.262901i
566566 −1078.00 904.550i −0.0800561 0.0671750i
567567 0 0
568568 7368.01 + 2681.74i 0.544287 + 0.198104i
569569 −16278.6 −1.19936 −0.599679 0.800240i 0.704705π-0.704705\pi
−0.599679 + 0.800240i 0.704705π0.704705\pi
570570 0 0
571571 −23492.9 −1.72180 −0.860901 0.508773i 0.830099π-0.830099\pi
−0.860901 + 0.508773i 0.830099π0.830099\pi
572572 8978.22 + 3267.80i 0.656291 + 0.238870i
573573 0 0
574574 −5667.56 4755.65i −0.412124 0.345813i
575575 5653.02 + 6737.00i 0.409995 + 0.488613i
576576 0 0
577577 2634.09 4562.37i 0.190049 0.329175i −0.755217 0.655475i 0.772469π-0.772469\pi
0.945266 + 0.326300i 0.105802π0.105802\pi
578578 7726.88 + 13383.3i 0.556048 + 0.963103i
579579 0 0
580580 −146.507 402.524i −0.0104885 0.0288170i
581581 −21340.1 + 12320.7i −1.52381 + 0.879775i
582582 0 0
583583 −6517.50 1149.21i −0.462997 0.0816389i
584584 6927.86 5813.17i 0.490885 0.411902i
585585 0 0
586586 −1604.24 9098.12i −0.113090 0.641365i
587587 −4998.01 + 13731.9i −0.351431 + 0.965549i 0.630480 + 0.776206i 0.282858π0.282858\pi
−0.981911 + 0.189343i 0.939364π0.939364\pi
588588 0 0
589589 2006.69 + 14256.8i 0.140381 + 0.997355i
590590 612.347i 0.0427287i
591591 0 0
592592 −15186.6 + 2677.81i −1.05434 + 0.185908i
593593 −9960.87 + 11870.9i −0.689787 + 0.822056i −0.991330 0.131396i 0.958054π-0.958054\pi
0.301543 + 0.953453i 0.402498π0.402498\pi
594594 0 0
595595 3200.53 18151.1i 0.220519 1.25063i
596596 8197.44 + 4732.79i 0.563390 + 0.325273i
597597 0 0
598598 −6641.60 + 2417.34i −0.454173 + 0.165305i
599599 −7411.15 + 2697.44i −0.505528 + 0.183997i −0.582179 0.813061i 0.697800π-0.697800\pi
0.0766506 + 0.997058i 0.475577π0.475577\pi
600600 0 0
601601 2579.64 + 1489.35i 0.175084 + 0.101085i 0.584981 0.811047i 0.301102π-0.301102\pi
−0.409897 + 0.912132i 0.634435π0.634435\pi
602602 −71.9986 + 408.324i −0.00487449 + 0.0276446i
603603 0 0
604604 −4967.83 + 5920.43i −0.334666 + 0.398840i
605605 4838.61 853.177i 0.325153 0.0573332i
606606 0 0
607607 15489.8i 1.03577i 0.855452 + 0.517883i 0.173280π0.173280\pi
−0.855452 + 0.517883i 0.826720π0.826720\pi
608608 −12400.8 + 6596.93i −0.827168 + 0.440034i
609609 0 0
610610 980.643 2694.29i 0.0650903 0.178834i
611611 3773.31 + 21399.5i 0.249839 + 1.41691i
612612 0 0
613613 −9333.78 + 7831.97i −0.614989 + 0.516037i −0.896224 0.443602i 0.853700π-0.853700\pi
0.281235 + 0.959639i 0.409256π0.409256\pi
614614 −1958.04 345.255i −0.128697 0.0226928i
615615 0 0
616616 6707.73 3872.71i 0.438737 0.253305i
617617 4535.24 + 12460.5i 0.295919 + 0.813031i 0.995171 + 0.0981555i 0.0312943π0.0312943\pi
−0.699252 + 0.714875i 0.746484π0.746484\pi
618618 0 0
619619 −8561.76 14829.4i −0.555939 0.962915i −0.997830 0.0658460i 0.979025π-0.979025\pi
0.441891 0.897069i 0.354308π-0.354308\pi
620620 4134.10 7160.47i 0.267789 0.463825i
621621 0 0
622622 1208.18 + 1439.86i 0.0778839 + 0.0928184i
623623 −1757.57 1474.78i −0.113026 0.0948405i
624624 0 0
625625 284.623 + 103.594i 0.0182159 + 0.00663003i
626626 −1751.32 −0.111816
627627 0 0
628628 −3677.65 −0.233685
629629 −54399.8 19799.9i −3.44843 1.25513i
630630 0 0
631631 10029.9 + 8416.08i 0.632779 + 0.530965i 0.901791 0.432172i 0.142253π-0.142253\pi
−0.269012 + 0.963137i 0.586697π0.586697\pi
632632 10555.3 + 12579.3i 0.664348 + 0.791739i
633633 0 0
634634 1715.25 2970.90i 0.107447 0.186103i
635635 5927.91 + 10267.4i 0.370460 + 0.641655i
636636 0 0
637637 422.375 + 1160.47i 0.0262718 + 0.0721811i
638638 213.555 123.296i 0.0132519 0.00765099i
639639 0 0
640640 10156.1 + 1790.80i 0.627276 + 0.110606i
641641 −10507.9 + 8817.20i −0.647486 + 0.543305i −0.906307 0.422620i 0.861110π-0.861110\pi
0.258821 + 0.965925i 0.416666π0.416666\pi
642642 0 0
643643 2842.52 + 16120.7i 0.174336 + 0.988707i 0.938908 + 0.344169i 0.111839π0.111839\pi
−0.764572 + 0.644538i 0.777050π0.777050\pi
644644 5135.38 14109.4i 0.314227 0.863333i
645645 0 0
646646 −12484.5 433.364i −0.760364 0.0263939i
647647 6379.48i 0.387640i −0.981037 0.193820i 0.937912π-0.937912\pi
0.981037 0.193820i 0.0620878π-0.0620878\pi
648648 0 0
649649 −1979.05 + 348.961i −0.119699 + 0.0211062i
650650 2996.87 3571.53i 0.180842 0.215519i
651651 0 0
652652 −704.875 + 3997.54i −0.0423390 + 0.240116i
653653 9638.64 + 5564.87i 0.577625 + 0.333492i 0.760189 0.649702i 0.225106π-0.225106\pi
−0.182564 + 0.983194i 0.558440π0.558440\pi
654654 0 0
655655 −3943.79 + 1435.42i −0.235262 + 0.0856283i
656656 −12245.9 + 4457.15i −0.728846 + 0.265278i
657657 0 0
658658 7012.64 + 4048.75i 0.415473 + 0.239873i
659659 −1314.49 + 7454.85i −0.0777015 + 0.440667i 0.920993 + 0.389580i 0.127380π0.127380\pi
−0.998694 + 0.0510873i 0.983731π0.983731\pi
660660 0 0
661661 6467.72 7707.93i 0.380583 0.453561i −0.541415 0.840755i 0.682111π-0.682111\pi
0.921998 + 0.387194i 0.126556π0.126556\pi
662662 9933.63 1751.57i 0.583204 0.102835i
663663 0 0
664664 20864.9i 1.21945i
665665 8218.97 + 7397.30i 0.479275 + 0.431361i
666666 0 0
667667 355.671 977.197i 0.0206471 0.0567275i
668668 −2324.19 13181.1i −0.134619 0.763462i
669669 0 0
670670 −2777.93 + 2330.96i −0.160180 + 0.134407i
671671 −9266.57 1633.95i −0.533133 0.0940057i
672672 0 0
673673 −22460.8 + 12967.8i −1.28648 + 0.742749i −0.978024 0.208490i 0.933145π-0.933145\pi
−0.308455 + 0.951239i 0.599812π0.599812\pi
674674 −2438.77 6700.45i −0.139374 0.382926i
675675 0 0
676676 −3203.71 5548.99i −0.182278 0.315714i
677677 2879.85 4988.05i 0.163489 0.283171i −0.772629 0.634858i 0.781059π-0.781059\pi
0.936118 + 0.351687i 0.114392π0.114392\pi
678678 0 0
679679 −16153.1 19250.5i −0.912958 1.08802i
680680 11955.2 + 10031.6i 0.674206 + 0.565726i
681681 0 0
682682 4472.70 + 1627.93i 0.251127 + 0.0914026i
683683 −524.910 −0.0294072 −0.0147036 0.999892i 0.504680π-0.504680\pi
−0.0147036 + 0.999892i 0.504680π0.504680\pi
684684 0 0
685685 11540.0 0.643682
686686 −6296.30 2291.67i −0.350429 0.127546i
687687 0 0
688688 559.463 + 469.445i 0.0310019 + 0.0260137i
689689 9510.49 + 11334.2i 0.525865 + 0.626701i
690690 0 0
691691 −8123.39 + 14070.1i −0.447219 + 0.774606i −0.998204 0.0599095i 0.980919π-0.980919\pi
0.550985 + 0.834515i 0.314252π0.314252\pi
692692 13899.0 + 24073.7i 0.763525 + 1.32246i
693693 0 0
694694 −3934.64 10810.3i −0.215212 0.591290i
695695 −7714.31 + 4453.86i −0.421036 + 0.243085i
696696 0 0
697697 −48179.1 8495.28i −2.61824 0.461667i
698698 −8822.64 + 7403.07i −0.478427 + 0.401448i
699699 0 0
700700 1719.91 + 9754.08i 0.0928663 + 0.526671i
701701 8737.82 24007.0i 0.470789 1.29348i −0.446330 0.894868i 0.647269π-0.647269\pi
0.917119 0.398613i 0.130508π-0.130508\pi
702702 0 0
703703 27364.3 21388.5i 1.46808 1.14748i
704704 2727.84i 0.146036i
705705 0 0
706706 6448.02 1136.96i 0.343732 0.0606091i
707707 −14404.2 + 17166.2i −0.766230 + 0.913157i
708708 0 0
709709 5068.89 28747.1i 0.268500 1.52274i −0.490382 0.871508i 0.663143π-0.663143\pi
0.758881 0.651229i 0.225746π-0.225746\pi
710710 3204.89 + 1850.35i 0.169405 + 0.0978060i
711711 0 0
712712 1825.55 664.447i 0.0960891 0.0349736i
713713 18862.0 6865.20i 0.990725 0.360594i
714714 0 0
715715 8495.63 + 4904.95i 0.444361 + 0.256552i
716716 1829.14 10373.6i 0.0954724 0.541451i
717717 0 0
718718 8335.79 9934.21i 0.433272 0.516353i
719719 −21970.2 + 3873.95i −1.13957 + 0.200937i −0.711418 0.702769i 0.751947π-0.751947\pi
−0.428153 + 0.903706i 0.640836π0.640836\pi
720720 0 0
721721 15725.5i 0.812274i
722722 4188.28 6214.97i 0.215889 0.320356i
723723 0 0
724724 −3676.85 + 10102.1i −0.188742 + 0.518564i
725725 119.119 + 675.556i 0.00610202 + 0.0346063i
726726 0 0
727727 −3808.02 + 3195.31i −0.194266 + 0.163009i −0.734733 0.678357i 0.762692π-0.762692\pi
0.540466 + 0.841366i 0.318248π0.318248\pi
728728 −17053.1 3006.92i −0.868171 0.153082i
729729 0 0
730730 3696.53 2134.19i 0.187418 0.108206i
731731 937.715 + 2576.35i 0.0474455 + 0.130355i
732732 0 0
733733 −8489.19 14703.7i −0.427770 0.740919i 0.568905 0.822403i 0.307367π-0.307367\pi
−0.996675 + 0.0814843i 0.974034π0.974034\pi
734734 997.766 1728.18i 0.0501747 0.0869051i
735735 0 0
736736 12587.8 + 15001.5i 0.630424 + 0.751310i
737737 9116.52 + 7649.67i 0.455646 + 0.382333i
738738 0 0
739739 −6175.36 2247.65i −0.307394 0.111882i 0.183717 0.982979i 0.441187π-0.441187\pi
−0.491111 + 0.871097i 0.663409π0.663409\pi
740740 −19945.8 −0.990839
741741 0 0
742742 5513.59 0.272790
743743 5534.49 + 2014.39i 0.273271 + 0.0994626i 0.475021 0.879975i 0.342440π-0.342440\pi
−0.201750 + 0.979437i 0.564663π0.564663\pi
744744 0 0
745745 7444.95 + 6247.06i 0.366124 + 0.307214i
746746 4660.29 + 5553.92i 0.228720 + 0.272578i
747747 0 0
748748 11771.7 20389.2i 0.575422 0.996659i
749749 −991.821 1717.89i −0.0483850 0.0838053i
750750 0 0
751751 3929.29 + 10795.6i 0.190921 + 0.524552i 0.997810 0.0661524i 0.0210723π-0.0210723\pi
−0.806888 + 0.590704i 0.798850π0.798850\pi
752752 12352.2 7131.56i 0.598988 0.345826i
753753 0 0
754754 −542.920 95.7314i −0.0262228 0.00462378i
755755 −6078.75 + 5100.67i −0.293018 + 0.245871i
756756 0 0
757757 1749.49 + 9921.88i 0.0839980 + 0.476376i 0.997568 + 0.0696954i 0.0222027π0.0222027\pi
−0.913570 + 0.406681i 0.866686π0.866686\pi
758758 −938.435 + 2578.33i −0.0449677 + 0.123548i
759759 0 0
760760 −8904.09 + 2895.17i −0.424981 + 0.138182i
761761 19688.7i 0.937862i −0.883235 0.468931i 0.844639π-0.844639\pi
0.883235 0.468931i 0.155361π-0.155361\pi
762762 0 0
763763 −15599.8 + 2750.67i −0.740172 + 0.130512i
764764 −7234.95 + 8622.28i −0.342606 + 0.408302i
765765 0 0
766766 −1764.61 + 10007.6i −0.0832348 + 0.472048i
767767 3890.84 + 2246.37i 0.183168 + 0.105752i
768768 0 0
769769 −15579.7 + 5670.55i −0.730584 + 0.265911i −0.680412 0.732830i 0.738199π-0.738199\pi
−0.0501719 + 0.998741i 0.515977π0.515977\pi
770770 3435.18 1250.30i 0.160773 0.0585166i
771771 0 0
772772 −11133.4 6427.88i −0.519042 0.299669i
773773 −5068.11 + 28742.7i −0.235818 + 1.33739i 0.605066 + 0.796175i 0.293147π0.293147\pi
−0.840884 + 0.541215i 0.817965π0.817965\pi
774774 0 0
775775 −8511.04 + 10143.1i −0.394485 + 0.470129i
776776 20955.1 3694.95i 0.969387 0.170929i
777777 0 0
778778 11265.1i 0.519117i
779779 19634.9 21815.9i 0.903072 1.00338i
780780 0 0
781781 4153.78 11412.4i 0.190312 0.522878i
782782 3024.28 + 17151.5i 0.138297 + 0.784319i
783783 0 0
784784 620.959 521.047i 0.0282871 0.0237357i
785785 −3718.63 655.694i −0.169075 0.0298124i
786786 0 0
787787 −7153.14 + 4129.87i −0.323992 + 0.187057i −0.653171 0.757211i 0.726562π-0.726562\pi
0.329178 + 0.944268i 0.393228π0.393228\pi
788788 −3688.28 10133.5i −0.166738 0.458109i
789789 0 0
790790 3875.18 + 6712.01i 0.174523 + 0.302282i
791791 6300.78 10913.3i 0.283224 0.490558i
792792 0 0
793793 13522.0 + 16114.9i 0.605524 + 0.721635i
794794 4104.44 + 3444.04i 0.183452 + 0.153935i
795795 0 0
796796 13619.9 + 4957.25i 0.606464 + 0.220735i
797797 8216.48 0.365173 0.182586 0.983190i 0.441553π-0.441553\pi
0.182586 + 0.983190i 0.441553π0.441553\pi
798798 0 0
799799 53544.7 2.37081
800800 −12139.0 4418.22i −0.536471 0.195259i
801801 0 0
802802 2134.35 + 1790.94i 0.0939734 + 0.0788530i
803803 −9004.09 10730.7i −0.395700 0.471577i
804804 0 0
805805 7708.18 13351.0i 0.337488 0.584546i
806806 −5320.59 9215.53i −0.232518 0.402733i
807807 0 0
808808 −6489.67 17830.2i −0.282557 0.776318i
809809 35978.4 20772.2i 1.56358 0.902732i 0.566687 0.823933i 0.308225π-0.308225\pi
0.996891 0.0787991i 0.0251086π-0.0251086\pi
810810 0 0
811811 35857.3 + 6322.62i 1.55255 + 0.273757i 0.883132 0.469125i 0.155431π-0.155431\pi
0.669422 + 0.742882i 0.266542π0.266542\pi
812812 897.166 752.811i 0.0387738 0.0325351i
813813 0 0
814814 −1993.85 11307.7i −0.0858533 0.486898i
815815 −1425.46 + 3916.41i −0.0612657 + 0.168326i
816816 0 0
817817 −1608.99 341.651i −0.0689002 0.0146302i
818818 2522.18i 0.107807i
819819 0 0
820820 −16599.6 + 2926.96i −0.706931 + 0.124651i
821821 4890.72 5828.53i 0.207902 0.247768i −0.652010 0.758210i 0.726074π-0.726074\pi
0.859912 + 0.510443i 0.170518π0.170518\pi
822822 0 0
823823 3366.90 19094.6i 0.142604 0.808745i −0.826657 0.562707i 0.809760π-0.809760\pi
0.969260 0.246038i 0.0791289π-0.0791289\pi
824824 −11531.5 6657.73i −0.487524 0.281472i
825825 0 0
826826 1573.25 572.615i 0.0662715 0.0241209i
827827 30831.8 11221.9i 1.29641 0.471853i 0.400581 0.916261i 0.368808π-0.368808\pi
0.895824 + 0.444409i 0.146586π0.146586\pi
828828 0 0
829829 16458.5 + 9502.34i 0.689540 + 0.398106i 0.803440 0.595386i 0.203001π-0.203001\pi
−0.113900 + 0.993492i 0.536334π0.536334\pi
830830 1710.03 9698.08i 0.0715134 0.405573i
831831 0 0
832832 −3920.05 + 4671.73i −0.163345 + 0.194667i
833833 2996.83 528.423i 0.124651 0.0219793i
834834 0 0
835835 13742.4i 0.569549i
836836 6633.74 + 12470.0i 0.274441 + 0.515889i
837837 0 0
838838 2556.69 7024.45i 0.105393 0.289565i
839839 −7538.49 42752.9i −0.310200 1.75923i −0.597959 0.801527i 0.704021π-0.704021\pi
0.287759 0.957703i 0.407090π-0.407090\pi
840840 0 0
841841 −18620.9 + 15624.8i −0.763497 + 0.640650i
842842 −1460.68 257.557i −0.0597842 0.0105416i
843843 0 0
844844 −12876.7 + 7434.35i −0.525158 + 0.303200i
845845 −2250.07 6182.01i −0.0916031 0.251677i
846846 0 0
847847 6716.64 + 11633.6i 0.272475 + 0.471941i
848848 4855.88 8410.63i 0.196641 0.340592i
849849 0 0
850850 −7384.69 8800.73i −0.297992 0.355132i
851851 −37093.3 31125.0i −1.49417 1.25376i
852852 0 0
853853 184.023 + 66.9791i 0.00738669 + 0.00268853i 0.345711 0.938341i 0.387638π-0.387638\pi
−0.338324 + 0.941030i 0.609860π0.609860\pi
854854 7839.21 0.314113
855855 0 0
856856 1679.63 0.0670661
857857 12538.9 + 4563.79i 0.499792 + 0.181909i 0.579600 0.814901i 0.303209π-0.303209\pi
−0.0798086 + 0.996810i 0.525431π0.525431\pi
858858 0 0
859859 −636.366 533.975i −0.0252765 0.0212095i 0.630062 0.776545i 0.283030π-0.283030\pi
−0.655338 + 0.755335i 0.727474π0.727474\pi
860860 607.191 + 723.623i 0.0240756 + 0.0286922i
861861 0 0
862862 −6939.66 + 12019.8i −0.274206 + 0.474939i
863863 −18598.3 32213.3i −0.733598 1.27063i −0.955336 0.295522i 0.904506π-0.904506\pi
0.221738 0.975106i 0.428827π-0.428827\pi
864864 0 0
865865 9761.68 + 26820.0i 0.383708 + 1.05423i
866866 −13157.0 + 7596.21i −0.516274 + 0.298071i
867867 0 0
868868 22262.6 + 3925.49i 0.870554 + 0.153502i
869869 19484.3 16349.3i 0.760597 0.638217i
870870 0 0
871871 −4620.10 26201.9i −0.179732 1.01931i
872872 4587.43 12603.9i 0.178154 0.489473i
873873 0 0
874874 −9688.67 3912.13i −0.374970 0.151407i
875875 26858.9i 1.03771i
876876 0 0
877877 8374.99 1476.74i 0.322467 0.0568596i −0.0100718 0.999949i 0.503206π-0.503206\pi
0.332538 + 0.943090i 0.392095π0.392095\pi
878878 5399.54 6434.92i 0.207546 0.247344i
879879 0 0
880880 1118.14 6341.30i 0.0428325 0.242915i
881881 −647.493 373.830i −0.0247612 0.0142959i 0.487568 0.873085i 0.337884π-0.337884\pi
−0.512329 + 0.858789i 0.671217π0.671217\pi
882882 0 0
883883 27766.7 10106.3i 1.05824 0.385167i 0.246472 0.969150i 0.420729π-0.420729\pi
0.811766 + 0.583983i 0.198506π0.198506\pi
884884 −49460.7 + 18002.2i −1.88184 + 0.684933i
885885 0 0
886886 12447.4 + 7186.53i 0.471986 + 0.272502i
887887 1018.01 5773.41i 0.0385359 0.218548i −0.959459 0.281850i 0.909052π-0.909052\pi
0.997994 + 0.0633019i 0.0201631π0.0201631\pi
888888 0 0
889889 −20835.9 + 24831.3i −0.786067 + 0.936798i
890890 902.981 159.220i 0.0340090 0.00599670i
891891 0 0
892892 2887.62i 0.108391i
893893 −17017.3 + 27246.1i −0.637697 + 1.02100i
894894 0 0
895895 3699.04 10163.0i 0.138151 0.379567i
896896 4896.21 + 27767.8i 0.182557 + 1.03533i
897897 0 0
898898 −6665.24 + 5592.80i −0.247686 + 0.207833i
899899 1541.88 + 271.875i 0.0572020 + 0.0100863i
900900 0 0
901901 31574.1 18229.3i 1.16746 0.674035i
902902 −3318.72 9118.11i −0.122507 0.336585i
903903 0 0
904904 5335.12 + 9240.70i 0.196287 + 0.339979i
905905 −5518.93 + 9559.07i −0.202713 + 0.351110i
906906 0 0
907907 20538.0 + 24476.3i 0.751879 + 0.896054i 0.997305 0.0733610i 0.0233725π-0.0233725\pi
−0.245427 + 0.969415i 0.578928π0.578928\pi
908908 −20541.4 17236.3i −0.750761 0.629963i
909909 0 0
910910 −7679.90 2795.25i −0.279765 0.101826i
911911 46413.8 1.68799 0.843994 0.536353i 0.180199π-0.180199\pi
0.843994 + 0.536353i 0.180199π0.180199\pi
912912 0 0
913913 −32317.9 −1.17148
914914 −4044.20 1471.97i −0.146357 0.0532696i
915915 0 0
916916 −6785.93 5694.07i −0.244774 0.205390i
917917 −7375.79 8790.12i −0.265616 0.316549i
918918 0 0
919919 −4163.77 + 7211.85i −0.149456 + 0.258865i −0.931026 0.364952i 0.881086π-0.881086\pi
0.781571 + 0.623817i 0.214419π0.214419\pi
920920 6526.82 + 11304.8i 0.233895 + 0.405117i
921921 0 0
922922 −1873.35 5147.00i −0.0669150 0.183848i
923923 −23514.1 + 13575.9i −0.838543 + 0.484133i
924924 0 0
925925 31456.2 + 5546.58i 1.11813 + 0.197157i
926926 9720.81 8156.73i 0.344974 0.289467i
927927 0 0
928928 265.246 + 1504.29i 0.00938269 + 0.0532119i
929929 −8010.52 + 22008.7i −0.282903 + 0.777269i 0.714110 + 0.700033i 0.246831π0.246831\pi
−0.997013 + 0.0772353i 0.975391π0.975391\pi
930930 0 0
931931 −683.555 + 1692.87i −0.0240629 + 0.0595936i
932932 21969.0i 0.772123i
933933 0 0
934934 −1800.84 + 317.536i −0.0630891 + 0.0111243i
935935 15538.0 18517.5i 0.543474 0.647688i
936936 0 0
937937 −7508.84 + 42584.7i −0.261796 + 1.48472i 0.516209 + 0.856462i 0.327343π0.327343\pi
−0.778006 + 0.628257i 0.783769π0.783769\pi
938938 −8586.39 4957.36i −0.298887 0.172562i
939939 0 0
940940 17335.7 6309.67i 0.601519 0.218935i
941941 36138.5 13153.4i 1.25195 0.455672i 0.370889 0.928677i 0.379053π-0.379053\pi
0.881059 + 0.473006i 0.156831π0.156831\pi
942942 0 0
943943 −35437.9 20460.1i −1.22377 0.706545i
944944 512.088 2904.20i 0.0176558 0.100131i
945945 0 0
946946 −349.541 + 416.567i −0.0120133 + 0.0143169i
947947 2254.56 397.540i 0.0773636 0.0136413i −0.134832 0.990868i 0.543050π-0.543050\pi
0.212196 + 0.977227i 0.431938π0.431938\pi
948948 0 0
949949 31316.9i 1.07122i
950950 6825.20 960.669i 0.233093 0.0328087i
951951 0 0
952952 −14593.8 + 40096.0i −0.496834 + 1.36504i
953953 −433.779 2460.08i −0.0147445 0.0836200i 0.976548 0.215302i 0.0690735π-0.0690735\pi
−0.991292 + 0.131682i 0.957962π0.957962\pi
954954 0 0
955955 −8852.83 + 7428.41i −0.299970 + 0.251704i
956956 41976.0 + 7401.50i 1.42008 + 0.250399i
957957 0 0
958958 3083.57 1780.30i 0.103993 0.0600406i
959959 10791.3 + 29648.7i 0.363366 + 0.998339i
960960 0 0
961961 214.842 + 372.118i 0.00721165 + 0.0124910i
962962 −12835.1 + 22231.0i −0.430167 + 0.745070i
963963 0 0
964964 −31524.5 37569.4i −1.05325 1.25522i
965965 −10111.4 8484.49i −0.337304 0.283031i
966966 0 0
967967 −51551.3 18763.1i −1.71435 0.623973i −0.717025 0.697047i 0.754497π-0.754497\pi
−0.997327 + 0.0730739i 0.976719π0.976719\pi
968968 −11374.5 −0.377676
969969 0 0
970970 10042.8 0.332429
971971 14110.5 + 5135.79i 0.466351 + 0.169738i 0.564499 0.825434i 0.309070π-0.309070\pi
−0.0981477 + 0.995172i 0.531292π0.531292\pi
972972 0 0
973973 −18656.6 15654.8i −0.614701 0.515795i
974974 −13745.5 16381.3i −0.452192 0.538901i
975975 0 0
976976 6904.08 11958.2i 0.226429 0.392186i
977977 14086.4 + 24398.3i 0.461272 + 0.798946i 0.999025 0.0441562i 0.0140599π-0.0140599\pi
−0.537753 + 0.843103i 0.680727π0.680727\pi
978978 0 0
979979 −1029.17 2827.62i −0.0335980 0.0923096i
980980 907.989 524.228i 0.0295966 0.0170876i
981981 0 0
982982 −1972.68 347.836i −0.0641045 0.0113034i
983983 −7916.63 + 6642.84i −0.256868 + 0.215538i −0.762123 0.647432i 0.775843π-0.775843\pi
0.505255 + 0.862970i 0.331398π0.331398\pi
984984 0 0
985985 −1922.66 10903.9i −0.0621940 0.352719i
986986 −464.622 + 1276.54i −0.0150067 + 0.0412305i
987987 0 0
988988 6559.01 30889.3i 0.211204 0.994657i
989989 2293.24i 0.0737318i
990990 0 0
991991 22751.5 4011.70i 0.729288 0.128593i 0.203338 0.979109i 0.434821π-0.434821\pi
0.525950 + 0.850516i 0.323710π0.323710\pi
992992 −18951.9 + 22585.9i −0.606575 + 0.722888i
993993 0 0
994994 −1756.98 + 9964.32i −0.0560644 + 0.317957i
995995 12887.8 + 7440.80i 0.410625 + 0.237074i
996996 0 0
997997 806.496 293.541i 0.0256188 0.00932450i −0.329179 0.944268i 0.606772π-0.606772\pi
0.354798 + 0.934943i 0.384550π0.384550\pi
998998 −17815.1 + 6484.16i −0.565057 + 0.205664i
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.53.9 120
3.2 odd 2 inner 171.4.y.a.53.12 yes 120
19.14 odd 18 inner 171.4.y.a.71.12 yes 120
57.14 even 18 inner 171.4.y.a.71.9 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
171.4.y.a.53.9 120 1.1 even 1 trivial
171.4.y.a.53.12 yes 120 3.2 odd 2 inner
171.4.y.a.71.9 yes 120 57.14 even 18 inner
171.4.y.a.71.12 yes 120 19.14 odd 18 inner