Properties

Label 975.2.n.o.824.2
Level 975975
Weight 22
Character 975.824
Analytic conductor 7.7857.785
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [975,2,Mod(749,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.749"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 975=35213 975 = 3 \cdot 5^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 975.n (of order 44, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,6,2,0,0,-4,14,-12,4,0,-4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.785414197077.78541419707
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(i)\Q(i)
Coefficient field: 8.0.619810816.2
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x82x5+14x48x3+2x2+2x+1 x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 824.2
Root 1.490941.49094i-1.49094 - 1.49094i of defining polynomial
Character χ\chi == 975.824
Dual form 975.2.n.o.749.2

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.6646400.664640i)q2+(1.290211.15558i)q3+1.11651iq4+(0.08948181.62557i)q6+(2.200732.20073i)q7+(2.07136+2.07136i)q8+(0.3292812.98187i)q9+(0.8202180.820218i)q11+(1.29021+1.44053i)q12+(0.173703+3.60136i)q132.92539iq14+0.520402q160.688845iq17+(1.763022.20073i)q18+(1.826301.82630i)q19+(0.2962885.38251i)q211.09030iq22+4.86537iq23+(5.06610+0.278871i)q24+(2.50906+2.27816i)q26+(3.020954.22775i)q27+(2.45713+2.45713i)q281.93998iq29+(0.910518+0.910518i)q31+(3.79683+3.79683i)q32+(0.1104272.00608i)q33+(0.4578340.457834i)q34+(3.32928+0.367644i)q36+(1.826301.82630i)q372.42766iq38+(4.38577+4.44579i)q39+(5.960935.96093i)q41+(3.380513.77436i)q42+2.50580q43+(0.915778+0.915778i)q44+(3.23372+3.23372i)q46+(8.628398.62839i)q47+(0.6714270.601365i)q482.68640iq49+(0.7960140.888754i)q51+(4.02095+0.193941i)q52+8.99159q53+(4.817780.802092i)q54+9.11698q56+(0.2458784.46673i)q57+(1.289391.28939i)q58+(3.46755+3.46755i)q59+13.9094q61+1.21033iq62+(5.837647.28695i)q63+6.08786iq64+(1.259931.40672i)q66+(5.39820+5.39820i)q67+0.769099q68+(5.62231+6.27734i)q69+(5.583245.58324i)q71+(6.858585.49447i)q72+(9.43292+9.43292i)q732.42766iq74+(2.03907+2.03907i)q763.61015iq77+(5.86981+0.0398898i)q78+6.07461q79+(8.783151.96375i)q817.92375q82+(3.93390+3.93390i)q83+(6.00961+0.330807i)q84+(1.665461.66546i)q86+(2.241802.50298i)q87+3.39793q88+(1.078141.07814i)q89+(8.30790+7.54335i)q915.43221q92+(0.122585+2.22693i)q9311.4696q94+(0.511175+9.28624i)q96+(7.02377+7.02377i)q97+(1.785491.78549i)q98+(2.175702.71587i)q99+O(q100)q+(0.664640 - 0.664640i) q^{2} +(1.29021 - 1.15558i) q^{3} +1.11651i q^{4} +(0.0894818 - 1.62557i) q^{6} +(2.20073 - 2.20073i) q^{7} +(2.07136 + 2.07136i) q^{8} +(0.329281 - 2.98187i) q^{9} +(0.820218 - 0.820218i) q^{11} +(1.29021 + 1.44053i) q^{12} +(0.173703 + 3.60136i) q^{13} -2.92539i q^{14} +0.520402 q^{16} -0.688845i q^{17} +(-1.76302 - 2.20073i) q^{18} +(1.82630 - 1.82630i) q^{19} +(0.296288 - 5.38251i) q^{21} -1.09030i q^{22} +4.86537i q^{23} +(5.06610 + 0.278871i) q^{24} +(2.50906 + 2.27816i) q^{26} +(-3.02095 - 4.22775i) q^{27} +(2.45713 + 2.45713i) q^{28} -1.93998i q^{29} +(-0.910518 + 0.910518i) q^{31} +(-3.79683 + 3.79683i) q^{32} +(0.110427 - 2.00608i) q^{33} +(-0.457834 - 0.457834i) q^{34} +(3.32928 + 0.367644i) q^{36} +(1.82630 - 1.82630i) q^{37} -2.42766i q^{38} +(4.38577 + 4.44579i) q^{39} +(-5.96093 - 5.96093i) q^{41} +(-3.38051 - 3.77436i) q^{42} +2.50580 q^{43} +(0.915778 + 0.915778i) q^{44} +(3.23372 + 3.23372i) q^{46} +(-8.62839 - 8.62839i) q^{47} +(0.671427 - 0.601365i) q^{48} -2.68640i q^{49} +(-0.796014 - 0.888754i) q^{51} +(-4.02095 + 0.193941i) q^{52} +8.99159 q^{53} +(-4.81778 - 0.802092i) q^{54} +9.11698 q^{56} +(0.245878 - 4.46673i) q^{57} +(-1.28939 - 1.28939i) q^{58} +(-3.46755 + 3.46755i) q^{59} +13.9094 q^{61} +1.21033i q^{62} +(-5.83764 - 7.28695i) q^{63} +6.08786i q^{64} +(-1.25993 - 1.40672i) q^{66} +(5.39820 + 5.39820i) q^{67} +0.769099 q^{68} +(5.62231 + 6.27734i) q^{69} +(-5.58324 - 5.58324i) q^{71} +(6.85858 - 5.49447i) q^{72} +(-9.43292 + 9.43292i) q^{73} -2.42766i q^{74} +(2.03907 + 2.03907i) q^{76} -3.61015i q^{77} +(5.86981 + 0.0398898i) q^{78} +6.07461 q^{79} +(-8.78315 - 1.96375i) q^{81} -7.92375 q^{82} +(-3.93390 + 3.93390i) q^{83} +(6.00961 + 0.330807i) q^{84} +(1.66546 - 1.66546i) q^{86} +(-2.24180 - 2.50298i) q^{87} +3.39793 q^{88} +(1.07814 - 1.07814i) q^{89} +(8.30790 + 7.54335i) q^{91} -5.43221 q^{92} +(-0.122585 + 2.22693i) q^{93} -11.4696 q^{94} +(-0.511175 + 9.28624i) q^{96} +(7.02377 + 7.02377i) q^{97} +(-1.78549 - 1.78549i) q^{98} +(-2.17570 - 2.71587i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+6q2+2q34q6+14q712q8+4q94q11+2q12+14q138q16+30q18+2q198q21+34q24+32q2610q2724q2812q31++28q99+O(q100) 8 q + 6 q^{2} + 2 q^{3} - 4 q^{6} + 14 q^{7} - 12 q^{8} + 4 q^{9} - 4 q^{11} + 2 q^{12} + 14 q^{13} - 8 q^{16} + 30 q^{18} + 2 q^{19} - 8 q^{21} + 34 q^{24} + 32 q^{26} - 10 q^{27} - 24 q^{28} - 12 q^{31}+ \cdots + 28 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/975Z)×\left(\mathbb{Z}/975\mathbb{Z}\right)^\times.

nn 301301 326326 352352
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 1-1 1-1

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 0.664640 0.664640i 0.469972 0.469972i −0.431934 0.901905i 0.642169π-0.642169\pi
0.901905 + 0.431934i 0.142169π0.142169\pi
33 1.29021 1.15558i 0.744903 0.667173i
44 1.11651i 0.558253i
55 0 0
66 0.0894818 1.62557i 0.0365308 0.663636i
77 2.20073 2.20073i 0.831797 0.831797i −0.155966 0.987762i 0.549849π-0.549849\pi
0.987762 + 0.155966i 0.0498489π0.0498489\pi
88 2.07136 + 2.07136i 0.732335 + 0.732335i
99 0.329281 2.98187i 0.109760 0.993958i
1010 0 0
1111 0.820218 0.820218i 0.247305 0.247305i −0.572559 0.819864i 0.694049π-0.694049\pi
0.819864 + 0.572559i 0.194049π0.194049\pi
1212 1.29021 + 1.44053i 0.372451 + 0.415844i
1313 0.173703 + 3.60136i 0.0481766 + 0.998839i
1414 2.92539i 0.781842i
1515 0 0
1616 0.520402 0.130100
1717 0.688845i 0.167069i −0.996505 0.0835347i 0.973379π-0.973379\pi
0.996505 0.0835347i 0.0266209π-0.0266209\pi
1818 −1.76302 2.20073i −0.415548 0.518716i
1919 1.82630 1.82630i 0.418981 0.418981i −0.465871 0.884852i 0.654259π-0.654259\pi
0.884852 + 0.465871i 0.154259π0.154259\pi
2020 0 0
2121 0.296288 5.38251i 0.0646554 1.17456i
2222 1.09030i 0.232453i
2323 4.86537i 1.01450i 0.861799 + 0.507250i 0.169338π0.169338\pi
−0.861799 + 0.507250i 0.830662π0.830662\pi
2424 5.06610 + 0.278871i 1.03411 + 0.0569242i
2525 0 0
2626 2.50906 + 2.27816i 0.492068 + 0.446784i
2727 −3.02095 4.22775i −0.581381 0.813631i
2828 2.45713 + 2.45713i 0.464353 + 0.464353i
2929 1.93998i 0.360246i −0.983644 0.180123i 0.942350π-0.942350\pi
0.983644 0.180123i 0.0576495π-0.0576495\pi
3030 0 0
3131 −0.910518 + 0.910518i −0.163534 + 0.163534i −0.784130 0.620596i 0.786891π-0.786891\pi
0.620596 + 0.784130i 0.286891π0.286891\pi
3232 −3.79683 + 3.79683i −0.671191 + 0.671191i
3333 0.110427 2.00608i 0.0192230 0.349213i
3434 −0.457834 0.457834i −0.0785179 0.0785179i
3535 0 0
3636 3.32928 + 0.367644i 0.554880 + 0.0612740i
3737 1.82630 1.82630i 0.300241 0.300241i −0.540867 0.841108i 0.681904π-0.681904\pi
0.841108 + 0.540867i 0.181904π0.181904\pi
3838 2.42766i 0.393819i
3939 4.38577 + 4.44579i 0.702285 + 0.711896i
4040 0 0
4141 −5.96093 5.96093i −0.930941 0.930941i 0.0668241 0.997765i 0.478713π-0.478713\pi
−0.997765 + 0.0668241i 0.978713π0.978713\pi
4242 −3.38051 3.77436i −0.521624 0.582396i
4343 2.50580 0.382132 0.191066 0.981577i 0.438806π-0.438806\pi
0.191066 + 0.981577i 0.438806π0.438806\pi
4444 0.915778 + 0.915778i 0.138059 + 0.138059i
4545 0 0
4646 3.23372 + 3.23372i 0.476786 + 0.476786i
4747 −8.62839 8.62839i −1.25858 1.25858i −0.951771 0.306809i 0.900739π-0.900739\pi
−0.306809 0.951771i 0.599261π-0.599261\pi
4848 0.671427 0.601365i 0.0969122 0.0867995i
4949 2.68640i 0.383772i
5050 0 0
5151 −0.796014 0.888754i −0.111464 0.124450i
5252 −4.02095 + 0.193941i −0.557605 + 0.0268948i
5353 8.99159 1.23509 0.617545 0.786536i 0.288127π-0.288127\pi
0.617545 + 0.786536i 0.288127π0.288127\pi
5454 −4.81778 0.802092i −0.655617 0.109151i
5555 0 0
5656 9.11698 1.21831
5757 0.245878 4.46673i 0.0325673 0.591633i
5858 −1.28939 1.28939i −0.169305 0.169305i
5959 −3.46755 + 3.46755i −0.451437 + 0.451437i −0.895831 0.444394i 0.853419π-0.853419\pi
0.444394 + 0.895831i 0.353419π0.353419\pi
6060 0 0
6161 13.9094 1.78091 0.890456 0.455069i 0.150385π-0.150385\pi
0.890456 + 0.455069i 0.150385π0.150385\pi
6262 1.21033i 0.153713i
6363 −5.83764 7.28695i −0.735473 0.918070i
6464 6.08786i 0.760982i
6565 0 0
6666 −1.25993 1.40672i −0.155086 0.173155i
6767 5.39820 + 5.39820i 0.659495 + 0.659495i 0.955260 0.295766i 0.0955748π-0.0955748\pi
−0.295766 + 0.955260i 0.595575π0.595575\pi
6868 0.769099 0.0932670
6969 5.62231 + 6.27734i 0.676847 + 0.755703i
7070 0 0
7171 −5.58324 5.58324i −0.662609 0.662609i 0.293386 0.955994i 0.405218π-0.405218\pi
−0.955994 + 0.293386i 0.905218π0.905218\pi
7272 6.85858 5.49447i 0.808292 0.647529i
7373 −9.43292 + 9.43292i −1.10404 + 1.10404i −0.110122 + 0.993918i 0.535124π0.535124\pi
−0.993918 + 0.110122i 0.964876π0.964876\pi
7474 2.42766i 0.282210i
7575 0 0
7676 2.03907 + 2.03907i 0.233898 + 0.233898i
7777 3.61015i 0.411415i
7878 5.86981 + 0.0398898i 0.664625 + 0.00451663i
7979 6.07461 0.683448 0.341724 0.939800i 0.388989π-0.388989\pi
0.341724 + 0.939800i 0.388989π0.388989\pi
8080 0 0
8181 −8.78315 1.96375i −0.975905 0.218194i
8282 −7.92375 −0.875032
8383 −3.93390 + 3.93390i −0.431802 + 0.431802i −0.889241 0.457439i 0.848767π-0.848767\pi
0.457439 + 0.889241i 0.348767π0.348767\pi
8484 6.00961 + 0.330807i 0.655702 + 0.0360941i
8585 0 0
8686 1.66546 1.66546i 0.179591 0.179591i
8787 −2.24180 2.50298i −0.240346 0.268348i
8888 3.39793 0.362220
8989 1.07814 1.07814i 0.114283 0.114283i −0.647653 0.761936i 0.724249π-0.724249\pi
0.761936 + 0.647653i 0.224249π0.224249\pi
9090 0 0
9191 8.30790 + 7.54335i 0.870904 + 0.790758i
9292 −5.43221 −0.566347
9393 −0.122585 + 2.22693i −0.0127114 + 0.230922i
9494 −11.4696 −1.18299
9595 0 0
9696 −0.511175 + 9.28624i −0.0521715 + 0.947773i
9797 7.02377 + 7.02377i 0.713155 + 0.713155i 0.967194 0.254039i 0.0817591π-0.0817591\pi
−0.254039 + 0.967194i 0.581759π0.581759\pi
9898 −1.78549 1.78549i −0.180362 0.180362i
9999 −2.17570 2.71587i −0.218667 0.272955i
100100 0 0
101101 −19.0737 −1.89791 −0.948954 0.315415i 0.897856π-0.897856\pi
−0.948954 + 0.315415i 0.897856π0.897856\pi
102102 −1.11976 0.0616391i −0.110873 0.00610318i
103103 −14.1165 −1.39094 −0.695470 0.718555i 0.744804π-0.744804\pi
−0.695470 + 0.718555i 0.744804π0.744804\pi
104104 −7.09991 + 7.81951i −0.696203 + 0.766766i
105105 0 0
106106 5.97618 5.97618i 0.580457 0.580457i
107107 −18.1484 −1.75447 −0.877234 0.480064i 0.840614π-0.840614\pi
−0.877234 + 0.480064i 0.840614π0.840614\pi
108108 4.72031 3.37290i 0.454212 0.324558i
109109 9.49294 9.49294i 0.909259 0.909259i −0.0869537 0.996212i 0.527713π-0.527713\pi
0.996212 + 0.0869537i 0.0277132π0.0277132\pi
110110 0 0
111111 0.245878 4.46673i 0.0233377 0.423964i
112112 1.14526 1.14526i 0.108217 0.108217i
113113 −7.29303 −0.686070 −0.343035 0.939323i 0.611455π-0.611455\pi
−0.343035 + 0.939323i 0.611455π0.611455\pi
114114 −2.80535 3.13219i −0.262745 0.293357i
115115 0 0
116116 2.16600 0.201108
117117 10.7960 + 0.667899i 0.998092 + 0.0617473i
118118 4.60935i 0.424325i
119119 −1.51596 1.51596i −0.138968 0.138968i
120120 0 0
121121 9.65448i 0.877680i
122122 9.24473 9.24473i 0.836979 0.836979i
123123 −14.5792 0.802531i −1.31456 0.0723618i
124124 −1.01660 1.01660i −0.0912933 0.0912933i
125125 0 0
126126 −8.72313 0.963274i −0.777118 0.0858152i
127127 −12.1706 −1.07996 −0.539981 0.841677i 0.681569π-0.681569\pi
−0.539981 + 0.841677i 0.681569π0.681569\pi
128128 −3.54743 3.54743i −0.313551 0.313551i
129129 3.23301 2.89565i 0.284651 0.254948i
130130 0 0
131131 9.06213i 0.791762i 0.918302 + 0.395881i 0.129561π0.129561\pi
−0.918302 + 0.395881i 0.870439π0.870439\pi
132132 2.23980 + 0.123293i 0.194949 + 0.0107313i
133133 8.03836i 0.697014i
134134 7.17572 0.619888
135135 0 0
136136 1.42684 1.42684i 0.122351 0.122351i
137137 13.0162 + 13.0162i 1.11205 + 1.11205i 0.992874 + 0.119172i 0.0380240π0.0380240\pi
0.119172 + 0.992874i 0.461976π0.461976\pi
138138 7.90899 + 0.435362i 0.673258 + 0.0370605i
139139 −5.96375 −0.505839 −0.252919 0.967487i 0.581391π-0.581391\pi
−0.252919 + 0.967487i 0.581391π0.581391\pi
140140 0 0
141141 −21.1032 1.16166i −1.77721 0.0978291i
142142 −7.42169 −0.622815
143143 3.09638 + 2.81143i 0.258932 + 0.235104i
144144 0.171358 1.55177i 0.0142799 0.129314i
145145 0 0
146146 12.5390i 1.03774i
147147 −3.10435 3.46602i −0.256042 0.285873i
148148 2.03907 + 2.03907i 0.167611 + 0.167611i
149149 −3.10679 3.10679i −0.254518 0.254518i 0.568302 0.822820i 0.307601π-0.307601\pi
−0.822820 + 0.568302i 0.807601π0.807601\pi
150150 0 0
151151 0.0298443 + 0.0298443i 0.00242869 + 0.00242869i 0.708320 0.705891i 0.249453π-0.249453\pi
−0.705891 + 0.708320i 0.749453π0.749453\pi
152152 7.56582 0.613669
153153 −2.05405 0.226823i −0.166060 0.0183376i
154154 −2.39945 2.39945i −0.193353 0.193353i
155155 0 0
156156 −4.96375 + 4.89674i −0.397418 + 0.392053i
157157 18.6772i 1.49060i 0.666729 + 0.745300i 0.267694π0.267694\pi
−0.666729 + 0.745300i 0.732306π0.732306\pi
158158 4.03743 4.03743i 0.321201 0.321201i
159159 11.6010 10.3905i 0.920022 0.824019i
160160 0 0
161161 10.7074 + 10.7074i 0.843857 + 0.843857i
162162 −7.14282 + 4.53245i −0.561193 + 0.356103i
163163 −2.74196 + 2.74196i −0.214767 + 0.214767i −0.806289 0.591522i 0.798527π-0.798527\pi
0.591522 + 0.806289i 0.298527π0.298527\pi
164164 6.65541 6.65541i 0.519700 0.519700i
165165 0 0
166166 5.22926i 0.405870i
167167 12.0831 + 12.0831i 0.935016 + 0.935016i 0.998014 0.0629973i 0.0200660π-0.0200660\pi
−0.0629973 + 0.998014i 0.520066π0.520066\pi
168168 11.7628 10.5354i 0.907521 0.812822i
169169 −12.9397 + 1.25114i −0.995358 + 0.0962414i
170170 0 0
171171 −4.84442 6.04715i −0.370462 0.462437i
172172 2.79775i 0.213326i
173173 24.0678i 1.82984i 0.403637 + 0.914919i 0.367746π0.367746\pi
−0.403637 + 0.914919i 0.632254π0.632254\pi
174174 −3.15358 0.173593i −0.239072 0.0131601i
175175 0 0
176176 0.426843 0.426843i 0.0321745 0.0321745i
177177 −0.466843 + 8.48089i −0.0350901 + 0.637463i
178178 1.43315i 0.107419i
179179 −9.42733 −0.704632 −0.352316 0.935881i 0.614606π-0.614606\pi
−0.352316 + 0.935881i 0.614606π0.614606\pi
180180 0 0
181181 17.8034i 1.32332i −0.749806 0.661658i 0.769853π-0.769853\pi
0.749806 0.661658i 0.230147π-0.230147\pi
182182 10.5354 0.508149i 0.780934 0.0376665i
183183 17.9460 16.0734i 1.32661 1.18818i
184184 −10.0779 + 10.0779i −0.742953 + 0.742953i
185185 0 0
186186 1.39864 + 1.56158i 0.102553 + 0.114501i
187187 −0.565003 0.565003i −0.0413171 0.0413171i
188188 9.63365 9.63365i 0.702606 0.702606i
189189 −15.9524 2.65585i −1.16037 0.193185i
190190 0 0
191191 7.08269i 0.512486i −0.966612 0.256243i 0.917515π-0.917515\pi
0.966612 0.256243i 0.0824847π-0.0824847\pi
192192 7.03499 + 7.85461i 0.507707 + 0.566858i
193193 4.47645 4.47645i 0.322222 0.322222i −0.527397 0.849619i 0.676832π-0.676832\pi
0.849619 + 0.527397i 0.176832π0.176832\pi
194194 9.33656 0.670326
195195 0 0
196196 2.99939 0.214242
197197 17.0750 17.0750i 1.21654 1.21654i 0.247708 0.968835i 0.420323π-0.420323\pi
0.968835 0.247708i 0.0796775π-0.0796775\pi
198198 −3.25114 0.359015i −0.231048 0.0255141i
199199 2.76666i 0.196123i −0.995180 0.0980616i 0.968736π-0.968736\pi
0.995180 0.0980616i 0.0312642π-0.0312642\pi
200200 0 0
201201 13.2028 + 0.726769i 0.931256 + 0.0512624i
202202 −12.6772 + 12.6772i −0.891963 + 0.891963i
203203 −4.26937 4.26937i −0.299651 0.299651i
204204 0.992299 0.888754i 0.0694749 0.0622252i
205205 0 0
206206 −9.38240 + 9.38240i −0.653703 + 0.653703i
207207 14.5079 + 1.60207i 1.00837 + 0.111352i
208208 0.0903955 + 1.87416i 0.00626780 + 0.129949i
209209 2.99592i 0.207232i
210210 0 0
211211 −8.53412 −0.587513 −0.293757 0.955880i 0.594906π-0.594906\pi
−0.293757 + 0.955880i 0.594906π0.594906\pi
212212 10.0392i 0.689493i
213213 −13.6554 0.751682i −0.935654 0.0515044i
214214 −12.0621 + 12.0621i −0.824550 + 0.824550i
215215 0 0
216216 2.49973 15.0146i 0.170085 1.02162i
217217 4.00761i 0.272054i
218218 12.6188i 0.854652i
219219 −1.26997 + 23.0709i −0.0858168 + 1.55899i
220220 0 0
221221 2.48078 0.119655i 0.166875 0.00804884i
222222 −2.80535 3.13219i −0.188283 0.210219i
223223 17.3123 + 17.3123i 1.15932 + 1.15932i 0.984622 + 0.174698i 0.0558949π0.0558949\pi
0.174698 + 0.984622i 0.444105π0.444105\pi
224224 16.7116i 1.11659i
225225 0 0
226226 −4.84724 + 4.84724i −0.322434 + 0.322434i
227227 7.27653 7.27653i 0.482960 0.482960i −0.423116 0.906076i 0.639064π-0.639064\pi
0.906076 + 0.423116i 0.139064π0.139064\pi
228228 4.98713 + 0.274524i 0.330281 + 0.0181808i
229229 −15.2314 15.2314i −1.00652 1.00652i −0.999979 0.00653900i 0.997919π-0.997919\pi
−0.00653900 0.999979i 0.502081π-0.502081\pi
230230 0 0
231231 −4.17181 4.65785i −0.274485 0.306464i
232232 4.01840 4.01840i 0.263821 0.263821i
233233 10.5507i 0.691198i −0.938382 0.345599i 0.887676π-0.887676\pi
0.938382 0.345599i 0.112324π-0.112324\pi
234234 7.61938 6.73155i 0.498094 0.440055i
235235 0 0
236236 −3.87154 3.87154i −0.252016 0.252016i
237237 7.83753 7.01969i 0.509102 0.455978i
238238 −2.01514 −0.130622
239239 10.7892 + 10.7892i 0.697897 + 0.697897i 0.963957 0.266060i 0.0857218π-0.0857218\pi
−0.266060 + 0.963957i 0.585722π0.585722\pi
240240 0 0
241241 4.73192 + 4.73192i 0.304810 + 0.304810i 0.842892 0.538082i 0.180851π-0.180851\pi
−0.538082 + 0.842892i 0.680851π0.680851\pi
242242 6.41676 + 6.41676i 0.412485 + 0.412485i
243243 −13.6014 + 7.61596i −0.872528 + 0.488564i
244244 15.5299i 0.994200i
245245 0 0
246246 −10.2233 + 9.15651i −0.651814 + 0.583798i
247247 6.89439 + 6.25993i 0.438680 + 0.398310i
248248 −3.77201 −0.239523
249249 −0.529629 + 9.62149i −0.0335639 + 0.609737i
250250 0 0
251251 23.8077 1.50273 0.751365 0.659887i 0.229396π-0.229396\pi
0.751365 + 0.659887i 0.229396π0.229396\pi
252252 8.13593 6.51776i 0.512515 0.410580i
253253 3.99066 + 3.99066i 0.250891 + 0.250891i
254254 −8.08904 + 8.08904i −0.507552 + 0.507552i
255255 0 0
256256 −16.8912 −1.05570
257257 27.4019i 1.70929i 0.519217 + 0.854643i 0.326224π0.326224\pi
−0.519217 + 0.854643i 0.673776π0.673776\pi
258258 0.224224 4.07336i 0.0139596 0.253596i
259259 8.03836i 0.499480i
260260 0 0
261261 −5.78478 0.638799i −0.358069 0.0395407i
262262 6.02306 + 6.02306i 0.372106 + 0.372106i
263263 −21.4135 −1.32042 −0.660208 0.751083i 0.729532π-0.729532\pi
−0.660208 + 0.751083i 0.729532π0.729532\pi
264264 4.38404 3.92657i 0.269819 0.241664i
265265 0 0
266266 −5.34262 5.34262i −0.327577 0.327577i
267267 0.145152 2.63691i 0.00888318 0.161376i
268268 −6.02712 + 6.02712i −0.368165 + 0.368165i
269269 2.04786i 0.124860i 0.998049 + 0.0624301i 0.0198851π0.0198851\pi
−0.998049 + 0.0624301i 0.980115π0.980115\pi
270270 0 0
271271 −12.9996 12.9996i −0.789667 0.789667i 0.191772 0.981439i 0.438576π-0.438576\pi
−0.981439 + 0.191772i 0.938576π0.938576\pi
272272 0.358476i 0.0217358i
273273 19.4359 + 0.132081i 1.17631 + 0.00799393i
274274 17.3021 1.04526
275275 0 0
276276 −7.00869 + 6.27734i −0.421874 + 0.377852i
277277 −3.90482 −0.234618 −0.117309 0.993095i 0.537427π-0.537427\pi
−0.117309 + 0.993095i 0.537427π0.537427\pi
278278 −3.96375 + 3.96375i −0.237730 + 0.237730i
279279 2.41523 + 3.01487i 0.144596 + 0.180495i
280280 0 0
281281 11.0540 11.0540i 0.659429 0.659429i −0.295816 0.955245i 0.595591π-0.595591\pi
0.955245 + 0.295816i 0.0955914π0.0955914\pi
282282 −14.7981 + 13.2540i −0.881216 + 0.789262i
283283 4.52473 0.268967 0.134484 0.990916i 0.457062π-0.457062\pi
0.134484 + 0.990916i 0.457062π0.457062\pi
284284 6.23372 6.23372i 0.369903 0.369903i
285285 0 0
286286 3.92657 0.189389i 0.232183 0.0111988i
287287 −26.2368 −1.54871
288288 10.0715 + 12.5719i 0.593466 + 0.740806i
289289 16.5255 0.972088
290290 0 0
291291 17.1786 + 0.945623i 1.00703 + 0.0554334i
292292 −10.5319 10.5319i −0.616334 0.616334i
293293 −7.37736 7.37736i −0.430990 0.430990i 0.457975 0.888965i 0.348575π-0.348575\pi
−0.888965 + 0.457975i 0.848575π0.848575\pi
294294 −4.36694 0.240384i −0.254685 0.0140195i
295295 0 0
296296 7.56582 0.439754
297297 −5.94551 0.989844i −0.344994 0.0574366i
298298 −4.12980 −0.239233
299299 −17.5220 + 0.845131i −1.01332 + 0.0488752i
300300 0 0
301301 5.51459 5.51459i 0.317856 0.317856i
302302 0.0396715 0.00228284
303303 −24.6091 + 22.0412i −1.41376 + 1.26623i
304304 0.950408 0.950408i 0.0545096 0.0545096i
305305 0 0
306306 −1.51596 + 1.21445i −0.0866617 + 0.0694254i
307307 1.80981 1.80981i 0.103291 0.103291i −0.653573 0.756864i 0.726731π-0.726731\pi
0.756864 + 0.653573i 0.226731π0.226731\pi
308308 4.03076 0.229674
309309 −18.2132 + 16.3127i −1.03612 + 0.927998i
310310 0 0
311311 −12.9697 −0.735445 −0.367723 0.929936i 0.619862π-0.619862\pi
−0.367723 + 0.929936i 0.619862π0.619862\pi
312312 −0.124317 + 18.2933i −0.00703806 + 1.03565i
313313 25.7774i 1.45703i −0.685032 0.728513i 0.740212π-0.740212\pi
0.685032 0.728513i 0.259788π-0.259788\pi
314314 12.4136 + 12.4136i 0.700540 + 0.700540i
315315 0 0
316316 6.78234i 0.381537i
317317 −1.18422 + 1.18422i −0.0665126 + 0.0665126i −0.739581 0.673068i 0.764976π-0.764976\pi
0.673068 + 0.739581i 0.264976π0.264976\pi
318318 0.804584 14.6165i 0.0451188 0.819650i
319319 −1.59121 1.59121i −0.0890906 0.0890906i
320320 0 0
321321 −23.4152 + 20.9718i −1.30691 + 1.17053i
322322 14.2331 0.793178
323323 −1.25804 1.25804i −0.0699989 0.0699989i
324324 2.19254 9.80644i 0.121808 0.544802i
325325 0 0
326326 3.64484i 0.201869i
327327 1.27805 23.2177i 0.0706764 1.28394i
328328 24.6944i 1.36352i
329329 −37.9775 −2.09377
330330 0 0
331331 1.79656 1.79656i 0.0987480 0.0987480i −0.656007 0.754755i 0.727756π-0.727756\pi
0.754755 + 0.656007i 0.227756π0.227756\pi
332332 −4.39223 4.39223i −0.241055 0.241055i
333333 −4.84442 6.04715i −0.265473 0.331382i
334334 16.0618 0.878863
335335 0 0
336336 0.154189 2.80107i 0.00841169 0.152811i
337337 10.2757 0.559753 0.279877 0.960036i 0.409706π-0.409706\pi
0.279877 + 0.960036i 0.409706π0.409706\pi
338338 −7.76866 + 9.43177i −0.422559 + 0.513021i
339339 −9.40954 + 8.42766i −0.511056 + 0.457728i
340340 0 0
341341 1.49365i 0.0808855i
342342 −7.23898 0.799383i −0.391439 0.0432257i
343343 9.49305 + 9.49305i 0.512576 + 0.512576i
344344 5.19041 + 5.19041i 0.279848 + 0.279848i
345345 0 0
346346 15.9964 + 15.9964i 0.859972 + 0.859972i
347347 −16.8673 −0.905482 −0.452741 0.891642i 0.649554π-0.649554\pi
−0.452741 + 0.891642i 0.649554π0.649554\pi
348348 2.79460 2.50298i 0.149806 0.134174i
349349 −14.9509 14.9509i −0.800302 0.800302i 0.182840 0.983143i 0.441471π-0.441471\pi
−0.983143 + 0.182840i 0.941471π0.941471\pi
350350 0 0
351351 14.7009 11.6139i 0.784677 0.619904i
352352 6.22846i 0.331978i
353353 6.54324 6.54324i 0.348261 0.348261i −0.511200 0.859462i 0.670799π-0.670799\pi
0.859462 + 0.511200i 0.170799π0.170799\pi
354354 5.32646 + 5.94703i 0.283098 + 0.316081i
355355 0 0
356356 1.20375 + 1.20375i 0.0637988 + 0.0637988i
357357 −3.70772 0.204097i −0.196233 0.0108019i
358358 −6.26579 + 6.26579i −0.331157 + 0.331157i
359359 13.2705 13.2705i 0.700388 0.700388i −0.264106 0.964494i 0.585077π-0.585077\pi
0.964494 + 0.264106i 0.0850767π0.0850767\pi
360360 0 0
361361 12.3293i 0.648910i
362362 −11.8329 11.8329i −0.621921 0.621921i
363363 11.1565 + 12.4563i 0.585565 + 0.653787i
364364 −8.42220 + 9.27582i −0.441443 + 0.486185i
365365 0 0
366366 1.24464 22.6106i 0.0650581 1.18188i
367367 15.3590i 0.801734i −0.916136 0.400867i 0.868709π-0.868709\pi
0.916136 0.400867i 0.131291π-0.131291\pi
368368 2.53195i 0.131987i
369369 −19.7376 + 15.8119i −1.02750 + 0.823136i
370370 0 0
371371 19.7880 19.7880i 1.02734 1.02734i
372372 −2.48639 0.136867i −0.128913 0.00709621i
373373 8.55388i 0.442903i −0.975171 0.221452i 0.928920π-0.928920\pi
0.975171 0.221452i 0.0710795π-0.0710795\pi
374374 −0.751048 −0.0388357
375375 0 0
376376 35.7449i 1.84340i
377377 6.98659 0.336981i 0.359827 0.0173554i
378378 −12.3678 + 8.83743i −0.636131 + 0.454548i
379379 12.1073 12.1073i 0.621909 0.621909i −0.324110 0.946019i 0.605065π-0.605065\pi
0.946019 + 0.324110i 0.105065π0.105065\pi
380380 0 0
381381 −15.7026 + 14.0640i −0.804467 + 0.720522i
382382 −4.70745 4.70745i −0.240854 0.240854i
383383 17.3280 17.3280i 0.885421 0.885421i −0.108658 0.994079i 0.534655π-0.534655\pi
0.994079 + 0.108658i 0.0346555π0.0346555\pi
384384 −8.67625 0.477597i −0.442758 0.0243723i
385385 0 0
386386 5.95046i 0.302870i
387387 0.825113 7.47199i 0.0419429 0.379823i
388388 −7.84208 + 7.84208i −0.398121 + 0.398121i
389389 18.7474 0.950533 0.475267 0.879842i 0.342352π-0.342352\pi
0.475267 + 0.879842i 0.342352π0.342352\pi
390390 0 0
391391 3.35148 0.169492
392392 5.56450 5.56450i 0.281050 0.281050i
393393 10.4720 + 11.6920i 0.528242 + 0.589786i
394394 22.6975i 1.14348i
395395 0 0
396396 3.03228 2.42919i 0.152378 0.122071i
397397 −18.5498 + 18.5498i −0.930988 + 0.930988i −0.997768 0.0667796i 0.978728π-0.978728\pi
0.0667796 + 0.997768i 0.478728π0.478728\pi
398398 −1.83883 1.83883i −0.0921724 0.0921724i
399399 −9.28895 10.3712i −0.465029 0.519208i
400400 0 0
401401 −20.2282 + 20.2282i −1.01015 + 1.01015i −0.0102015 + 0.999948i 0.503247π0.503247\pi
−0.999948 + 0.0102015i 0.996753π0.996753\pi
402402 9.25818 8.29210i 0.461756 0.413572i
403403 −3.43727 3.12095i −0.171223 0.155465i
404404 21.2959i 1.05951i
405405 0 0
406406 −5.67520 −0.281655
407407 2.99592i 0.148502i
408408 0.192099 3.48975i 0.00951030 0.172769i
409409 1.85494 1.85494i 0.0917210 0.0917210i −0.659758 0.751479i 0.729341π-0.729341\pi
0.751479 + 0.659758i 0.229341π0.229341\pi
410410 0 0
411411 31.8348 + 1.75239i 1.57029 + 0.0864390i
412412 15.7612i 0.776497i
413413 15.2623i 0.751007i
414414 10.7074 8.57775i 0.526238 0.421573i
415415 0 0
416416 −14.3333 13.0143i −0.702748 0.638076i
417417 −7.69448 + 6.89157i −0.376801 + 0.337482i
418418 −1.99121 1.99121i −0.0973933 0.0973933i
419419 22.6906i 1.10851i −0.832347 0.554255i 0.813003π-0.813003\pi
0.832347 0.554255i 0.186997π-0.186997\pi
420420 0 0
421421 0.559853 0.559853i 0.0272856 0.0272856i −0.693332 0.720618i 0.743858π-0.743858\pi
0.720618 + 0.693332i 0.243858π0.243858\pi
422422 −5.67212 + 5.67212i −0.276115 + 0.276115i
423423 −28.5699 + 22.8876i −1.38912 + 1.11283i
424424 18.6248 + 18.6248i 0.904500 + 0.904500i
425425 0 0
426426 −9.57554 + 8.57634i −0.463936 + 0.415525i
427427 30.6107 30.6107i 1.48136 1.48136i
428428 20.2627i 0.979437i
429429 7.24380 + 0.0492271i 0.349734 + 0.00237671i
430430 0 0
431431 −25.5824 25.5824i −1.23226 1.23226i −0.963094 0.269165i 0.913252π-0.913252\pi
−0.269165 0.963094i 0.586748π-0.586748\pi
432432 −1.57211 2.20013i −0.0756380 0.105854i
433433 −18.8544 −0.906087 −0.453043 0.891488i 0.649662π-0.649662\pi
−0.453043 + 0.891488i 0.649662π0.649662\pi
434434 2.66362 + 2.66362i 0.127858 + 0.127858i
435435 0 0
436436 10.5989 + 10.5989i 0.507596 + 0.507596i
437437 8.88561 + 8.88561i 0.425056 + 0.425056i
438438 14.4898 + 16.1779i 0.692349 + 0.773012i
439439 18.3463i 0.875620i 0.899068 + 0.437810i 0.144246π0.144246\pi
−0.899068 + 0.437810i 0.855754π0.855754\pi
440440 0 0
441441 −8.01052 0.884582i −0.381453 0.0421229i
442442 1.56930 1.72836i 0.0746440 0.0822095i
443443 7.32597 0.348067 0.174034 0.984740i 0.444320π-0.444320\pi
0.174034 + 0.984740i 0.444320π0.444320\pi
444444 4.98713 + 0.274524i 0.236679 + 0.0130283i
445445 0 0
446446 23.0130 1.08970
447447 −7.59854 0.418273i −0.359399 0.0197836i
448448 13.3977 + 13.3977i 0.632983 + 0.632983i
449449 20.5433 20.5433i 0.969498 0.969498i −0.0300506 0.999548i 0.509567π-0.509567\pi
0.999548 + 0.0300506i 0.00956684π0.00956684\pi
450450 0 0
451451 −9.77852 −0.460453
452452 8.14271i 0.383001i
453453 0.0729928 + 0.00401799i 0.00342950 + 0.000188782i
454454 9.67255i 0.453955i
455455 0 0
456456 9.76149 8.74289i 0.457124 0.409424i
457457 12.2258 + 12.2258i 0.571898 + 0.571898i 0.932659 0.360760i 0.117483π-0.117483\pi
−0.360760 + 0.932659i 0.617483π0.617483\pi
458458 −20.2468 −0.946070
459459 −2.91227 + 2.08096i −0.135933 + 0.0971310i
460460 0 0
461461 20.3228 + 20.3228i 0.946525 + 0.946525i 0.998641 0.0521156i 0.0165964π-0.0165964\pi
−0.0521156 + 0.998641i 0.516596π0.516596\pi
462462 −5.86855 0.323043i −0.273030 0.0150293i
463463 −6.93836 + 6.93836i −0.322453 + 0.322453i −0.849707 0.527254i 0.823221π-0.823221\pi
0.527254 + 0.849707i 0.323221π0.323221\pi
464464 1.00957i 0.0468681i
465465 0 0
466466 −7.01241 7.01241i −0.324844 0.324844i
467467 14.5021i 0.671075i −0.942027 0.335538i 0.891082π-0.891082\pi
0.942027 0.335538i 0.108918π-0.108918\pi
468468 −0.745713 + 12.0538i −0.0344706 + 0.557188i
469469 23.7599 1.09713
470470 0 0
471471 21.5829 + 24.0975i 0.994488 + 1.11035i
472472 −14.3651 −0.661206
473473 2.05531 2.05531i 0.0945031 0.0945031i
474474 0.543567 9.87471i 0.0249669 0.453560i
475475 0 0
476476 1.69258 1.69258i 0.0775792 0.0775792i
477477 2.96076 26.8118i 0.135564 1.22763i
478478 14.3419 0.655984
479479 12.9148 12.9148i 0.590095 0.590095i −0.347562 0.937657i 0.612990π-0.612990\pi
0.937657 + 0.347562i 0.112990π0.112990\pi
480480 0 0
481481 6.89439 + 6.25993i 0.314357 + 0.285428i
482482 6.29005 0.286504
483483 26.1879 + 1.44155i 1.19159 + 0.0655928i
484484 −10.7793 −0.489968
485485 0 0
486486 −3.97814 + 14.1019i −0.180452 + 0.639675i
487487 2.48442 + 2.48442i 0.112580 + 0.112580i 0.761153 0.648573i 0.224634π-0.224634\pi
−0.648573 + 0.761153i 0.724634π0.724634\pi
488488 28.8113 + 28.8113i 1.30422 + 1.30422i
489489 −0.369156 + 6.70626i −0.0166938 + 0.303268i
490490 0 0
491491 −16.8134 −0.758780 −0.379390 0.925237i 0.623866π-0.623866\pi
−0.379390 + 0.925237i 0.623866π0.623866\pi
492492 0.896031 16.2777i 0.0403962 0.733856i
493493 −1.33635 −0.0601860
494494 8.74289 0.421693i 0.393361 0.0189729i
495495 0 0
496496 −0.473835 + 0.473835i −0.0212758 + 0.0212758i
497497 −24.5744 −1.10231
498498 6.04282 + 6.74685i 0.270785 + 0.302333i
499499 11.5502 11.5502i 0.517060 0.517060i −0.399621 0.916681i 0.630858π-0.630858\pi
0.916681 + 0.399621i 0.130858π0.130858\pi
500500 0 0
501501 29.5526 + 1.62677i 1.32031 + 0.0726786i
502502 15.8236 15.8236i 0.706241 0.706241i
503503 11.9608 0.533304 0.266652 0.963793i 0.414083π-0.414083\pi
0.266652 + 0.963793i 0.414083π0.414083\pi
504504 3.00205 27.1857i 0.133722 1.21095i
505505 0 0
506506 5.30471 0.235823
507507 −15.2491 + 16.5670i −0.677235 + 0.735767i
508508 13.5885i 0.602892i
509509 −1.50135 1.50135i −0.0665461 0.0665461i 0.673050 0.739597i 0.264984π-0.264984\pi
−0.739597 + 0.673050i 0.764984π0.764984\pi
510510 0 0
511511 41.5186i 1.83667i
512512 −4.13175 + 4.13175i −0.182599 + 0.182599i
513513 −13.2383 2.20399i −0.584484 0.0973084i
514514 18.2124 + 18.2124i 0.803316 + 0.803316i
515515 0 0
516516 3.23301 + 3.60968i 0.142325 + 0.158907i
517517 −14.1543 −0.622506
518518 −5.34262 5.34262i −0.234741 0.234741i
519519 27.8122 + 31.0525i 1.22082 + 1.36305i
520520 0 0
521521 8.71097i 0.381635i 0.981626 + 0.190817i 0.0611138π0.0611138\pi
−0.981626 + 0.190817i 0.938886π0.938886\pi
522522 −4.26937 + 3.42023i −0.186865 + 0.149699i
523523 5.25678i 0.229863i −0.993373 0.114931i 0.963335π-0.963335\pi
0.993373 0.114931i 0.0366648π-0.0366648\pi
524524 −10.1179 −0.442003
525525 0 0
526526 −14.2323 + 14.2323i −0.620558 + 0.620558i
527527 0.627206 + 0.627206i 0.0273215 + 0.0273215i
528528 0.0574667 1.04397i 0.00250092 0.0454328i
529529 −0.671807 −0.0292090
530530 0 0
531531 9.19800 + 11.4816i 0.399159 + 0.498259i
532532 8.97488 0.389110
533533 20.4320 22.5029i 0.885010 0.974709i
534534 −1.65612 1.84907i −0.0716674 0.0800171i
535535 0 0
536536 22.3632i 0.965942i
537537 −12.1632 + 10.8940i −0.524882 + 0.470111i
538538 1.36109 + 1.36109i 0.0586808 + 0.0586808i
539539 −2.20344 2.20344i −0.0949088 0.0949088i
540540 0 0
541541 −7.12828 7.12828i −0.306469 0.306469i 0.537069 0.843538i 0.319531π-0.319531\pi
−0.843538 + 0.537069i 0.819531π0.819531\pi
542542 −17.2801 −0.742243
543543 −20.5732 22.9701i −0.882880 0.985741i
544544 2.61543 + 2.61543i 0.112136 + 0.112136i
545545 0 0
546546 13.0056 12.8301i 0.556590 0.549076i
547547 34.7849i 1.48730i −0.668571 0.743648i 0.733094π-0.733094\pi
0.668571 0.743648i 0.266906π-0.266906\pi
548548 −14.5326 + 14.5326i −0.620803 + 0.620803i
549549 4.58009 41.4760i 0.195473 1.77015i
550550 0 0
551551 −3.54298 3.54298i −0.150936 0.150936i
552552 −1.35681 + 24.6484i −0.0577496 + 1.04911i
553553 13.3686 13.3686i 0.568490 0.568490i
554554 −2.59530 + 2.59530i −0.110264 + 0.110264i
555555 0 0
556556 6.65856i 0.282386i
557557 −7.60755 7.60755i −0.322342 0.322342i 0.527323 0.849665i 0.323196π-0.323196\pi
−0.849665 + 0.527323i 0.823196π0.823196\pi
558558 3.60907 + 0.398540i 0.152784 + 0.0168715i
559559 0.435267 + 9.02431i 0.0184098 + 0.381688i
560560 0 0
561561 −1.38188 0.0760674i −0.0583429 0.00321157i
562562 14.6939i 0.619826i
563563 21.5401i 0.907807i 0.891051 + 0.453903i 0.149969π0.149969\pi
−0.891051 + 0.453903i 0.850031π0.850031\pi
564564 1.29700 23.5619i 0.0546134 0.992133i
565565 0 0
566566 3.00732 3.00732i 0.126407 0.126407i
567567 −23.6510 + 15.0076i −0.993248 + 0.630262i
568568 23.1298i 0.970503i
569569 30.7745 1.29013 0.645067 0.764126i 0.276829π-0.276829\pi
0.645067 + 0.764126i 0.276829π0.276829\pi
570570 0 0
571571 25.0540i 1.04848i −0.851572 0.524238i 0.824350π-0.824350\pi
0.851572 0.524238i 0.175650π-0.175650\pi
572572 −3.13898 + 3.45713i −0.131247 + 0.144550i
573573 −8.18460 9.13816i −0.341917 0.381752i
574574 −17.4380 + 17.4380i −0.727849 + 0.727849i
575575 0 0
576576 18.1532 + 2.00462i 0.756385 + 0.0835257i
577577 −13.6669 13.6669i −0.568959 0.568959i 0.362878 0.931837i 0.381794π-0.381794\pi
−0.931837 + 0.362878i 0.881794π0.881794\pi
578578 10.9835 10.9835i 0.456854 0.456854i
579579 0.602673 10.9484i 0.0250462 0.455002i
580580 0 0
581581 17.3149i 0.718343i
582582 12.0461 10.7891i 0.499328 0.447223i
583583 7.37507 7.37507i 0.305444 0.305444i
584584 −39.0779 −1.61705
585585 0 0
586586 −9.80659 −0.405106
587587 −5.19514 + 5.19514i −0.214426 + 0.214426i −0.806145 0.591718i 0.798450π-0.798450\pi
0.591718 + 0.806145i 0.298450π0.298450\pi
588588 3.86984 3.46602i 0.159589 0.142936i
589589 3.32575i 0.137035i
590590 0 0
591591 2.29884 41.7618i 0.0945616 1.71785i
592592 0.950408 0.950408i 0.0390615 0.0390615i
593593 −4.27083 4.27083i −0.175382 0.175382i 0.613957 0.789339i 0.289577π-0.289577\pi
−0.789339 + 0.613957i 0.789577π0.789577\pi
594594 −4.60952 + 3.29374i −0.189131 + 0.135144i
595595 0 0
596596 3.46875 3.46875i 0.142086 0.142086i
597597 −3.19709 3.56957i −0.130848 0.146093i
598598 −11.0841 + 12.2075i −0.453262 + 0.499202i
599599 17.0139i 0.695171i 0.937648 + 0.347585i 0.112998π0.112998\pi
−0.937648 + 0.347585i 0.887002π0.887002\pi
600600 0 0
601601 −36.2957 −1.48053 −0.740266 0.672314i 0.765300π-0.765300\pi
−0.740266 + 0.672314i 0.765300π0.765300\pi
602602 7.33044i 0.298767i
603603 17.8743 14.3192i 0.727896 0.583124i
604604 −0.0333213 + 0.0333213i −0.00135583 + 0.00135583i
605605 0 0
606606 −1.70675 + 31.0057i −0.0693321 + 1.25952i
607607 37.6421i 1.52785i −0.645306 0.763924i 0.723270π-0.723270\pi
0.645306 0.763924i 0.276730π-0.276730\pi
608608 13.8683i 0.562433i
609609 −10.4420 0.574794i −0.423130 0.0232918i
610610 0 0
611611 29.5752 32.5728i 1.19648 1.31775i
612612 0.253250 2.29336i 0.0102370 0.0927035i
613613 10.7888 + 10.7888i 0.435755 + 0.435755i 0.890581 0.454826i 0.150298π-0.150298\pi
−0.454826 + 0.890581i 0.650298π0.650298\pi
614614 2.40574i 0.0970879i
615615 0 0
616616 7.47791 7.47791i 0.301294 0.301294i
617617 27.1551 27.1551i 1.09322 1.09322i 0.0980399 0.995182i 0.468743π-0.468743\pi
0.995182 0.0980399i 0.0312573π-0.0312573\pi
618618 −1.26317 + 22.9474i −0.0508122 + 0.923078i
619619 −12.5227 12.5227i −0.503329 0.503329i 0.409142 0.912471i 0.365828π-0.365828\pi
−0.912471 + 0.409142i 0.865828π0.865828\pi
620620 0 0
621621 20.5696 14.6980i 0.825428 0.589811i
622622 −8.62020 + 8.62020i −0.345638 + 0.345638i
623623 4.74540i 0.190120i
624624 2.28236 + 2.31360i 0.0913676 + 0.0926179i
625625 0 0
626626 −17.1327 17.1327i −0.684761 0.684761i
627627 −3.46202 3.86537i −0.138260 0.154368i
628628 −20.8532 −0.832132
629629 −1.25804 1.25804i −0.0501611 0.0501611i
630630 0 0
631631 −0.0650570 0.0650570i −0.00258988 0.00258988i 0.705811 0.708401i 0.250583π-0.250583\pi
−0.708401 + 0.705811i 0.750583π0.750583\pi
632632 12.5827 + 12.5827i 0.500513 + 0.500513i
633633 −11.0108 + 9.86184i −0.437640 + 0.391973i
634634 1.57417i 0.0625181i
635635 0 0
636636 11.6010 + 12.9526i 0.460011 + 0.513605i
637637 9.67472 0.466637i 0.383326 0.0184888i
638638 −2.11516 −0.0837401
639639 −18.4870 + 14.8101i −0.731333 + 0.585877i
640640 0 0
641641 −5.72335 −0.226059 −0.113029 0.993592i 0.536055π-0.536055\pi
−0.113029 + 0.993592i 0.536055π0.536055\pi
642642 −1.62395 + 29.5014i −0.0640921 + 1.16433i
643643 24.0577 + 24.0577i 0.948742 + 0.948742i 0.998749 0.0500069i 0.0159243π-0.0159243\pi
−0.0500069 + 0.998749i 0.515924π0.515924\pi
644644 −11.9548 + 11.9548i −0.471086 + 0.471086i
645645 0 0
646646 −1.67228 −0.0657951
647647 33.6947i 1.32468i −0.749205 0.662338i 0.769564π-0.769564\pi
0.749205 0.662338i 0.230436π-0.230436\pi
648648 −14.1254 22.2606i −0.554898 0.874481i
649649 5.68830i 0.223285i
650650 0 0
651651 4.63110 + 5.17065i 0.181507 + 0.202654i
652652 −3.06142 3.06142i −0.119894 0.119894i
653653 −6.47341 −0.253324 −0.126662 0.991946i 0.540426π-0.540426\pi
−0.126662 + 0.991946i 0.540426π0.540426\pi
654654 −14.5820 16.2809i −0.570201 0.636632i
655655 0 0
656656 −3.10208 3.10208i −0.121116 0.121116i
657657 25.0217 + 31.2339i 0.976190 + 1.21855i
658658 −25.2414 + 25.2414i −0.984011 + 0.984011i
659659 0.908137i 0.0353760i 0.999844 + 0.0176880i 0.00563056π0.00563056\pi
−0.999844 + 0.0176880i 0.994369π0.994369\pi
660660 0 0
661661 −22.4502 22.4502i −0.873210 0.873210i 0.119610 0.992821i 0.461835π-0.461835\pi
−0.992821 + 0.119610i 0.961835π0.961835\pi
662662 2.38814i 0.0928176i
663663 3.06246 3.02111i 0.118936 0.117330i
664664 −16.2970 −0.632448
665665 0 0
666666 −7.23898 0.799383i −0.280505 0.0309754i
667667 9.43873 0.365469
668668 −13.4908 + 13.4908i −0.521976 + 0.521976i
669669 42.3423 + 2.33079i 1.63705 + 0.0901137i
670670 0 0
671671 11.4087 11.4087i 0.440429 0.440429i
672672 19.3115 + 21.5614i 0.744959 + 0.831751i
673673 40.5282 1.56225 0.781123 0.624377i 0.214647π-0.214647\pi
0.781123 + 0.624377i 0.214647π0.214647\pi
674674 6.82965 6.82965i 0.263068 0.263068i
675675 0 0
676676 −1.39690 14.4472i −0.0537270 0.555662i
677677 16.4579 0.632527 0.316264 0.948671i 0.397572π-0.397572\pi
0.316264 + 0.948671i 0.397572π0.397572\pi
678678 −0.652593 + 11.8553i −0.0250627 + 0.455301i
679679 30.9148 1.18640
680680 0 0
681681 0.979652 17.7968i 0.0375404 0.681976i
682682 0.992738 + 0.992738i 0.0380139 + 0.0380139i
683683 8.30681 + 8.30681i 0.317851 + 0.317851i 0.847941 0.530090i 0.177842π-0.177842\pi
−0.530090 + 0.847941i 0.677842π0.677842\pi
684684 6.75168 5.40883i 0.258157 0.206812i
685685 0 0
686686 12.6189 0.481793
687687 −37.2527 2.05063i −1.42128 0.0782364i
688688 1.30402 0.0497155
689689 1.56187 + 32.3820i 0.0595025 + 1.23366i
690690 0 0
691691 24.4080 24.4080i 0.928524 0.928524i −0.0690863 0.997611i 0.522008π-0.522008\pi
0.997611 + 0.0690863i 0.0220084π0.0220084\pi
692692 −26.8718 −1.02151
693693 −10.7650 1.18875i −0.408929 0.0451570i
694694 −11.2107 + 11.2107i −0.425551 + 0.425551i
695695 0 0
696696 0.541004 9.82814i 0.0205067 0.372535i
697697 −4.10615 + 4.10615i −0.155532 + 0.155532i
698698 −19.8739 −0.752239
699699 −12.1921 13.6126i −0.461149 0.514876i
700700 0 0
701701 −25.2071 −0.952058 −0.476029 0.879430i 0.657924π-0.657924\pi
−0.476029 + 0.879430i 0.657924π0.657924\pi
702702 2.05176 17.4899i 0.0774388 0.660114i
703703 6.67072i 0.251591i
704704 4.99337 + 4.99337i 0.188195 + 0.188195i
705705 0 0
706706 8.69780i 0.327346i
707707 −41.9761 + 41.9761i −1.57867 + 1.57867i
708708 −9.46897 0.521233i −0.355866 0.0195891i
709709 −3.27176 3.27176i −0.122873 0.122873i 0.642996 0.765869i 0.277691π-0.277691\pi
−0.765869 + 0.642996i 0.777691π0.777691\pi
710710 0 0
711711 2.00025 18.1137i 0.0750154 0.679318i
712712 4.46644 0.167387
713713 −4.43001 4.43001i −0.165905 0.165905i
714714 −2.59995 + 2.32865i −0.0973006 + 0.0871474i
715715 0 0
716716 10.5257i 0.393363i
717717 26.3882 + 1.45257i 0.985484 + 0.0542474i
718718 17.6402i 0.658325i
719719 −12.3985 −0.462385 −0.231192 0.972908i 0.574263π-0.574263\pi
−0.231192 + 0.972908i 0.574263π0.574263\pi
720720 0 0
721721 −31.0666 + 31.0666i −1.15698 + 1.15698i
722722 8.19454 + 8.19454i 0.304969 + 0.304969i
723723 11.5733 + 0.637067i 0.430414 + 0.0236928i
724724 19.8776 0.738745
725725 0 0
726726 15.6940 + 0.863901i 0.582460 + 0.0320624i
727727 14.6064 0.541722 0.270861 0.962619i 0.412692π-0.412692\pi
0.270861 + 0.962619i 0.412692π0.412692\pi
728728 1.58365 + 32.8336i 0.0586940 + 1.21689i
729729 −8.74777 + 25.5436i −0.323992 + 0.946060i
730730 0 0
731731 1.72611i 0.0638425i
732732 17.9460 + 20.0368i 0.663303 + 0.740582i
733733 −24.5952 24.5952i −0.908445 0.908445i 0.0877014 0.996147i 0.472048π-0.472048\pi
−0.996147 + 0.0877014i 0.972048π0.972048\pi
734734 −10.2082 10.2082i −0.376792 0.376792i
735735 0 0
736736 −18.4730 18.4730i −0.680923 0.680923i
737737 8.85540 0.326193
738738 −2.60914 + 23.6276i −0.0960437 + 0.869745i
739739 32.1016 + 32.1016i 1.18088 + 1.18088i 0.979518 + 0.201357i 0.0645352π0.0645352\pi
0.201357 + 0.979518i 0.435465π0.435465\pi
740740 0 0
741741 16.1290 + 0.109609i 0.592515 + 0.00402659i
742742 26.3039i 0.965645i
743743 31.6922 31.6922i 1.16268 1.16268i 0.178788 0.983888i 0.442782π-0.442782\pi
0.983888 0.178788i 0.0572177π-0.0572177\pi
744744 −4.86669 + 4.35886i −0.178421 + 0.159803i
745745 0 0
746746 −5.68526 5.68526i −0.208152 0.208152i
747747 10.4350 + 13.0258i 0.381798 + 0.476588i
748748 0.630829 0.630829i 0.0230654 0.0230654i
749749 −39.9396 + 39.9396i −1.45936 + 1.45936i
750750 0 0
751751 8.44360i 0.308111i −0.988062 0.154056i 0.950766π-0.950766\pi
0.988062 0.154056i 0.0492335π-0.0492335\pi
752752 −4.49023 4.49023i −0.163742 0.163742i
753753 30.7169 27.5117i 1.11939 1.00258i
754754 4.41960 4.86754i 0.160952 0.177265i
755755 0 0
756756 2.96528 17.8110i 0.107846 0.647778i
757757 33.4040i 1.21409i 0.794667 + 0.607045i 0.207645π0.207645\pi
−0.794667 + 0.607045i 0.792355π0.792355\pi
758758 16.0940i 0.584559i
759759 9.76031 + 0.537270i 0.354277 + 0.0195017i
760760 0 0
761761 −2.45709 + 2.45709i −0.0890694 + 0.0890694i −0.750238 0.661168i 0.770061π-0.770061\pi
0.661168 + 0.750238i 0.270061π0.270061\pi
762762 −1.08904 + 19.7841i −0.0394519 + 0.716701i
763763 41.7827i 1.51264i
764764 7.90787 0.286097
765765 0 0
766766 23.0338i 0.832245i
767767 −13.0902 11.8856i −0.472661 0.429164i
768768 −21.7932 + 19.5191i −0.786396 + 0.704336i
769769 −10.9256 + 10.9256i −0.393987 + 0.393987i −0.876106 0.482119i 0.839867π-0.839867\pi
0.482119 + 0.876106i 0.339867π0.339867\pi
770770 0 0
771771 31.6651 + 35.3542i 1.14039 + 1.27325i
772772 4.99798 + 4.99798i 0.179881 + 0.179881i
773773 −28.7466 + 28.7466i −1.03394 + 1.03394i −0.0345388 + 0.999403i 0.510996π0.510996\pi
−0.999403 + 0.0345388i 0.989004π0.989004\pi
774774 −4.41779 5.51459i −0.158794 0.198218i
775775 0 0
776776 29.0974i 1.04454i
777777 −9.28895 10.3712i −0.333239 0.372064i
778778 12.4603 12.4603i 0.446724 0.446724i
779779 −21.7728 −0.780093
780780 0 0
781781 −9.15895 −0.327733
782782 2.22753 2.22753i 0.0796564 0.0796564i
783783 −8.20177 + 5.86058i −0.293107 + 0.209440i
784784 1.39801i 0.0499289i
785785 0 0
786786 14.7311 + 0.810896i 0.525442 + 0.0289237i
787787 17.0605 17.0605i 0.608141 0.608141i −0.334319 0.942460i 0.608506π-0.608506\pi
0.942460 + 0.334319i 0.108506π0.108506\pi
788788 19.0643 + 19.0643i 0.679139 + 0.679139i
789789 −27.6280 + 24.7450i −0.983581 + 0.880946i
790790 0 0
791791 −16.0500 + 16.0500i −0.570671 + 0.570671i
792792 1.11887 10.1322i 0.0397574 0.360032i
793793 2.41610 + 50.0927i 0.0857984 + 1.77884i
794794 24.6579i 0.875076i
795795 0 0
796796 3.08899 0.109486
797797 43.7007i 1.54796i 0.633212 + 0.773979i 0.281736π0.281736\pi
−0.633212 + 0.773979i 0.718264π0.718264\pi
798798 −13.0669 0.719287i −0.462564 0.0254625i
799799 −5.94362 + 5.94362i −0.210270 + 0.210270i
800800 0 0
801801 −2.85987 3.56990i −0.101049 0.126136i
802802 26.8890i 0.949483i
803803 15.4741i 0.546069i
804804 −0.811442 + 14.7411i −0.0286174 + 0.519877i
805805 0 0
806806 −4.35886 + 0.210239i −0.153534 + 0.00740536i
807807 2.36646 + 2.64217i 0.0833034 + 0.0930087i
808808 −39.5085 39.5085i −1.38990 1.38990i
809809 37.8152i 1.32951i 0.747060 + 0.664757i 0.231465π0.231465\pi
−0.747060 + 0.664757i 0.768535π0.768535\pi
810810 0 0
811811 −33.4507 + 33.4507i −1.17461 + 1.17461i −0.193514 + 0.981098i 0.561988π0.561988\pi
−0.981098 + 0.193514i 0.938012π0.938012\pi
812812 4.76678 4.76678i 0.167281 0.167281i
813813 −31.7942 1.75016i −1.11507 0.0613806i
814814 −1.99121 1.99121i −0.0697919 0.0697919i
815815 0 0
816816 −0.414247 0.462509i −0.0145015 0.0161911i
817817 4.57634 4.57634i 0.160106 0.160106i
818818 2.46574i 0.0862126i
819819 25.2290 22.2892i 0.881571 0.778848i
820820 0 0
821821 −9.07369 9.07369i −0.316674 0.316674i 0.530814 0.847488i 0.321886π-0.321886\pi
−0.847488 + 0.530814i 0.821886π0.821886\pi
822822 22.3234 19.9940i 0.778617 0.697369i
823823 45.6468 1.59115 0.795574 0.605856i 0.207169π-0.207169\pi
0.795574 + 0.605856i 0.207169π0.207169\pi
824824 −29.2403 29.2403i −1.01863 1.01863i
825825 0 0
826826 10.1439 + 10.1439i 0.352952 + 0.352952i
827827 4.08085 + 4.08085i 0.141905 + 0.141905i 0.774491 0.632585i 0.218006π-0.218006\pi
−0.632585 + 0.774491i 0.718006π0.718006\pi
828828 −1.78872 + 16.1982i −0.0621625 + 0.562926i
829829 33.3484i 1.15824i −0.815243 0.579119i 0.803397π-0.803397\pi
0.815243 0.579119i 0.196603π-0.196603\pi
830830 0 0
831831 −5.03803 + 4.51232i −0.174767 + 0.156531i
832832 −21.9246 + 1.05748i −0.760099 + 0.0366616i
833833 −1.85052 −0.0641166
834834 −0.533647 + 9.69448i −0.0184787 + 0.335693i
835835 0 0
836836 3.34497 0.115688
837837 6.60007 + 1.09882i 0.228132 + 0.0379807i
838838 −15.0811 15.0811i −0.520968 0.520968i
839839 24.9303 24.9303i 0.860690 0.860690i −0.130728 0.991418i 0.541732π-0.541732\pi
0.991418 + 0.130728i 0.0417315π0.0417315\pi
840840 0 0
841841 25.2365 0.870223
842842 0.744202i 0.0256469i
843843 1.48823 27.0358i 0.0512573 0.931164i
844844 9.52840i 0.327981i
845845 0 0
846846 −3.77670 + 34.2008i −0.129846 + 1.17585i
847847 21.2469 + 21.2469i 0.730052 + 0.730052i
848848 4.67924 0.160686
849849 5.83785 5.22868i 0.200355 0.179448i
850850 0 0
851851 8.88561 + 8.88561i 0.304595 + 0.304595i
852852 0.839258 15.2464i 0.0287525 0.522331i
853853 15.5260 15.5260i 0.531602 0.531602i −0.389447 0.921049i 0.627334π-0.627334\pi
0.921049 + 0.389447i 0.127334π0.127334\pi
854854 40.6903i 1.39239i
855855 0 0
856856 −37.5917 37.5917i −1.28486 1.28486i
857857 7.92513i 0.270717i −0.990797 0.135359i 0.956781π-0.956781\pi
0.990797 0.135359i 0.0432187π-0.0432187\pi
858858 4.84724 4.78181i 0.165482 0.163248i
859859 −28.7269 −0.980148 −0.490074 0.871681i 0.663030π-0.663030\pi
−0.490074 + 0.871681i 0.663030π0.663030\pi
860860 0 0
861861 −33.8509 + 30.3186i −1.15364 + 1.03326i
862862 −34.0061 −1.15825
863863 −3.03332 + 3.03332i −0.103255 + 0.103255i −0.756847 0.653592i 0.773261π-0.773261\pi
0.653592 + 0.756847i 0.273261π0.273261\pi
864864 27.5221 + 4.58204i 0.936320 + 0.155884i
865865 0 0
866866 −12.5314 + 12.5314i −0.425835 + 0.425835i
867867 21.3213 19.0965i 0.724111 0.648551i
868868 −4.47452 −0.151875
869869 4.98251 4.98251i 0.169020 0.169020i
870870 0 0
871871 −18.5032 + 20.3786i −0.626957 + 0.690501i
872872 39.3265 1.33176
873873 23.2568 18.6312i 0.787123 0.630570i
874874 11.8115 0.399529
875875 0 0
876876 −25.7588 1.41793i −0.870310 0.0479075i
877877 −0.402259 0.402259i −0.0135833 0.0135833i 0.700283 0.713866i 0.253057π-0.253057\pi
−0.713866 + 0.700283i 0.753057π0.753057\pi
878878 12.1937 + 12.1937i 0.411517 + 0.411517i
879879 −18.0435 0.993228i −0.608591 0.0335007i
880880 0 0
881881 38.6903 1.30351 0.651755 0.758430i 0.274033π-0.274033\pi
0.651755 + 0.758430i 0.274033π0.274033\pi
882882 −5.91204 + 4.73619i −0.199069 + 0.159476i
883883 −23.4454 −0.789000 −0.394500 0.918896i 0.629082π-0.629082\pi
−0.394500 + 0.918896i 0.629082π0.629082\pi
884884 0.133595 + 2.76981i 0.00449329 + 0.0931587i
885885 0 0
886886 4.86914 4.86914i 0.163582 0.163582i
887887 37.0936 1.24548 0.622740 0.782429i 0.286019π-0.286019\pi
0.622740 + 0.782429i 0.286019π0.286019\pi
888888 9.76149 8.74289i 0.327574 0.293392i
889889 −26.7841 + 26.7841i −0.898309 + 0.898309i
890890 0 0
891891 −8.81480 + 5.59339i −0.295307 + 0.187386i
892892 −19.3293 + 19.3293i −0.647194 + 0.647194i
893893 −31.5160 −1.05464
894894 −5.32830 + 4.77230i −0.178205 + 0.159610i
895895 0 0
896896 −15.6138 −0.521622
897897 −21.6304 + 21.3384i −0.722218 + 0.712468i
898898 27.3078i 0.911273i
899899 1.76639 + 1.76639i 0.0589124 + 0.0589124i
900900 0 0
901901 6.19381i 0.206346i
902902 −6.49920 + 6.49920i −0.216400 + 0.216400i
903903 0.742440 13.4875i 0.0247069 0.448837i
904904 −15.1065 15.1065i −0.502433 0.502433i
905905 0 0
906906 0.0511845 0.0458435i 0.00170049 0.00152305i
907907 −23.1351 −0.768189 −0.384094 0.923294i 0.625486π-0.625486\pi
−0.384094 + 0.923294i 0.625486π0.625486\pi
908908 8.12429 + 8.12429i 0.269614 + 0.269614i
909909 −6.28062 + 56.8755i −0.208315 + 1.88644i
910910 0 0
911911 51.2489i 1.69795i 0.528432 + 0.848976i 0.322780π0.322780\pi
−0.528432 + 0.848976i 0.677220π0.677220\pi
912912 0.127955 2.32450i 0.00423702 0.0769717i
913913 6.45332i 0.213574i
914914 16.2515 0.537552
915915 0 0
916916 17.0059 17.0059i 0.561892 0.561892i
917917 19.9433 + 19.9433i 0.658585 + 0.658585i
918918 −0.552517 + 3.31870i −0.0182358 + 0.109533i
919919 52.3805 1.72787 0.863936 0.503602i 0.167992π-0.167992\pi
0.863936 + 0.503602i 0.167992π0.167992\pi
920920 0 0
921921 0.243658 4.42640i 0.00802880 0.145855i
922922 27.0147 0.889680
923923 19.1375 21.0771i 0.629917 0.693761i
924924 5.20052 4.65785i 0.171085 0.153232i
925925 0 0
926926 9.22303i 0.303088i
927927 −4.64830 + 42.0936i −0.152670 + 1.38254i
928928 7.36579 + 7.36579i 0.241794 + 0.241794i
929929 −35.5168 35.5168i −1.16527 1.16527i −0.983305 0.181963i 0.941755π-0.941755\pi
−0.181963 0.983305i 0.558245π-0.558245\pi
930930 0 0
931931 −4.90617 4.90617i −0.160793 0.160793i
932932 11.7799 0.385864
933933 −16.7337 + 14.9875i −0.547835 + 0.490669i
934934 −9.63865 9.63865i −0.315386 0.315386i
935935 0 0
936936 20.9789 + 23.7458i 0.685718 + 0.776157i
937937 28.4360i 0.928962i 0.885583 + 0.464481i 0.153759π0.153759\pi
−0.885583 + 0.464481i 0.846241π0.846241\pi
938938 15.7918 15.7918i 0.515621 0.515621i
939939 −29.7878 33.2583i −0.972089 1.08534i
940940 0 0
941941 −7.42076 7.42076i −0.241910 0.241910i 0.575730 0.817640i 0.304718π-0.304718\pi
−0.817640 + 0.575730i 0.804718π0.804718\pi
942942 30.3610 + 1.67127i 0.989215 + 0.0544528i
943943 29.0021 29.0021i 0.944439 0.944439i
944944 −1.80452 + 1.80452i −0.0587321 + 0.0587321i
945945 0 0
946946 2.73208i 0.0888275i
947947 −0.253519 0.253519i −0.00823827 0.00823827i 0.702976 0.711214i 0.251854π-0.251854\pi
−0.711214 + 0.702976i 0.751854π0.751854\pi
948948 7.83753 + 8.75065i 0.254551 + 0.284208i
949949 −35.6099 32.3329i −1.15595 1.04957i
950950 0 0
951951 −0.159434 + 2.89636i −0.00517001 + 0.0939209i
952952 6.28019i 0.203542i
953953 52.1909i 1.69063i −0.534268 0.845315i 0.679413π-0.679413\pi
0.534268 0.845315i 0.320587π-0.320587\pi
954954 −15.8524 19.7880i −0.513239 0.640662i
955955 0 0
956956 −12.0462 + 12.0462i −0.389603 + 0.389603i
957957 −3.89176 0.214227i −0.125803 0.00692499i
958958 17.1675i 0.554656i
959959 57.2900 1.84999
960960 0 0
961961 29.3419i 0.946513i
962962 8.74289 0.421693i 0.281882 0.0135959i
963963 −5.97591 + 54.1161i −0.192571 + 1.74387i
964964 −5.28322 + 5.28322i −0.170161 + 0.170161i
965965 0 0
966966 18.3636 16.4474i 0.590841 0.529187i
967967 −18.9172 18.9172i −0.608336 0.608336i 0.334175 0.942511i 0.391542π-0.391542\pi
−0.942511 + 0.334175i 0.891542π0.891542\pi
968968 −19.9979 + 19.9979i −0.642756 + 0.642756i
969969 −3.07689 0.169372i −0.0988438 0.00544100i
970970 0 0
971971 30.9230i 0.992367i 0.868218 + 0.496183i 0.165266π0.165266\pi
−0.868218 + 0.496183i 0.834734π0.834734\pi
972972 −8.50327 15.1860i −0.272742 0.487091i
973973 −13.1246 + 13.1246i −0.420755 + 0.420755i
974974 3.30249 0.105819
975975 0 0
976976 7.23846 0.231698
977977 14.2630 14.2630i 0.456313 0.456313i −0.441130 0.897443i 0.645422π-0.645422\pi
0.897443 + 0.441130i 0.145422π0.145422\pi
978978 4.21190 + 4.70261i 0.134682 + 0.150373i
979979 1.76862i 0.0565255i
980980 0 0
981981 −25.1809 31.4326i −0.803964 1.00357i
982982 −11.1749 + 11.1749i −0.356605 + 0.356605i
983983 23.7893 + 23.7893i 0.758760 + 0.758760i 0.976097 0.217337i 0.0697369π-0.0697369\pi
−0.217337 + 0.976097i 0.569737π0.569737\pi
984984 −28.5363 31.8610i −0.909704 1.01569i
985985 0 0
986986 −0.888190 + 0.888190i −0.0282857 + 0.0282857i
987987 −48.9989 + 43.8859i −1.55965 + 1.39690i
988988 −6.98925 + 7.69763i −0.222358 + 0.244894i
989989 12.1917i 0.387672i
990990 0 0
991991 −47.6939 −1.51505 −0.757523 0.652809i 0.773591π-0.773591\pi
−0.757523 + 0.652809i 0.773591π0.773591\pi
992992 6.91417i 0.219525i
993993 0.241875 4.39401i 0.00767566 0.139440i
994994 −16.3331 + 16.3331i −0.518055 + 0.518055i
995995 0 0
996996 −10.7425 0.591334i −0.340388 0.0187371i
997997 51.2235i 1.62226i 0.584863 + 0.811132i 0.301148π0.301148\pi
−0.584863 + 0.811132i 0.698852π0.698852\pi
998998 15.3535i 0.486007i
999999 −13.2383 2.20399i −0.418840 0.0697310i
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 975.2.n.o.824.2 8
3.2 odd 2 975.2.n.n.824.3 8
5.2 odd 4 975.2.o.o.551.2 yes 8
5.3 odd 4 975.2.o.l.551.3 yes 8
5.4 even 2 975.2.n.m.824.3 8
13.8 odd 4 975.2.n.p.749.2 8
15.2 even 4 975.2.o.m.551.3 yes 8
15.8 even 4 975.2.o.n.551.2 yes 8
15.14 odd 2 975.2.n.p.824.2 8
39.8 even 4 975.2.n.m.749.3 8
65.8 even 4 975.2.o.n.476.2 yes 8
65.34 odd 4 975.2.n.n.749.3 8
65.47 even 4 975.2.o.m.476.3 yes 8
195.8 odd 4 975.2.o.l.476.3 8
195.47 odd 4 975.2.o.o.476.2 yes 8
195.164 even 4 inner 975.2.n.o.749.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
975.2.n.m.749.3 8 39.8 even 4
975.2.n.m.824.3 8 5.4 even 2
975.2.n.n.749.3 8 65.34 odd 4
975.2.n.n.824.3 8 3.2 odd 2
975.2.n.o.749.2 8 195.164 even 4 inner
975.2.n.o.824.2 8 1.1 even 1 trivial
975.2.n.p.749.2 8 13.8 odd 4
975.2.n.p.824.2 8 15.14 odd 2
975.2.o.l.476.3 8 195.8 odd 4
975.2.o.l.551.3 yes 8 5.3 odd 4
975.2.o.m.476.3 yes 8 65.47 even 4
975.2.o.m.551.3 yes 8 15.2 even 4
975.2.o.n.476.2 yes 8 65.8 even 4
975.2.o.n.551.2 yes 8 15.8 even 4
975.2.o.o.476.2 yes 8 195.47 odd 4
975.2.o.o.551.2 yes 8 5.2 odd 4