Properties

Label 735.2.p.g.509.10
Level 735735
Weight 22
Character 735.509
Analytic conductor 5.8695.869
Analytic rank 00
Dimension 6464
Inner twists 1616

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [735,2,Mod(374,735)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(735, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("735.374");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 735=3572 735 = 3 \cdot 5 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 735.p (of order 66, degree 22, not 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: 5.869004548565.86900454856
Analytic rank: 00
Dimension: 6464
Relative dimension: 3232 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 509.10
Character χ\chi == 735.509
Dual form 735.2.p.g.374.10

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+(0.451669+0.782314i)q2+(0.6979461.58520i)q3+(0.591990+1.02536i)q4+(0.01998882.23598i)q5+(1.55537+0.169975i)q62.87621q8+(2.02574+2.21277i)q9+(1.74021+1.02556i)q10+(3.519852.03219i)q11+(1.212221.65407i)q122.88298q13+(3.55843+1.52891i)q15+(0.1151170.199389i)q16+(5.775213.33432i)q17+(0.8161192.58421i)q18+(4.942422.85351i)q19+(2.304511.30318i)q20+3.67151iq22+(0.815927+1.41323i)q23+(2.00744+4.55938i)q24+(4.999200.0893892i)q25+(1.302152.25540i)q26+(4.92156+1.66682i)q275.89707iq29+(0.4111503.47437i)q30+(1.62006+0.935342i)q31+(2.772224.80163i)q32+(5.678104.16132i)q33+6.02404iq34+(3.468100.767168i)q36+(1.385410.799864i)q37+(4.464682.57768i)q38+(2.01217+4.57011i)q39+(0.0574921+6.43115i)q409.12244q417.53359iq43+(4.16743+2.40607i)q44+(4.90722+4.57375i)q45+(0.7370591.27662i)q46+(5.988103.45723i)q47+(0.3964170.0433215i)q48+(2.327923.87057i)q50+(9.316366.82771i)q51+(1.706702.95608i)q52+(0.7593251.31519i)q53+(3.52689+3.09735i)q54+(4.473577.91093i)q55+(1.07385+9.82633i)q57+(4.61336+2.66353i)q58+(0.4959250.858968i)q59+(3.674232.74356i)q60+(5.33892+3.08243i)q611.68986iq62+5.46898q64+(0.0576274+6.44628i)q65+(5.820082.56251i)q66+(8.738435.04513i)q67+(6.83773+3.94776i)q68+(2.80973+0.307054i)q694.81213iq71+(5.826466.36441i)q72+(0.2803090.485510i)q73+(1.251490.722548i)q74+(3.34747+7.98714i)q756.75699iq76+(4.484100.490034i)q78+(1.89924+3.28958i)q79+(0.4435280.261385i)q80+(0.7927368.96502i)q81+(4.120337.13661i)q824.00431iq83+(7.3400312.9799i)q85+(5.89364+3.40269i)q86+(9.34806+4.11584i)q87+(10.1238+5.84500i)q88+(5.205479.01615i)q89+(5.79455+1.77317i)q901.93208q92+(2.61342+1.91531i)q93+(5.409283.12305i)q94+(6.47917+10.9941i)q95+(5.67670+7.74581i)q96+14.5370q97+(2.63354+11.9053i)q99+O(q100)q+(-0.451669 + 0.782314i) q^{2} +(-0.697946 - 1.58520i) q^{3} +(0.591990 + 1.02536i) q^{4} +(0.0199888 - 2.23598i) q^{5} +(1.55537 + 0.169975i) q^{6} -2.87621 q^{8} +(-2.02574 + 2.21277i) q^{9} +(1.74021 + 1.02556i) q^{10} +(3.51985 - 2.03219i) q^{11} +(1.21222 - 1.65407i) q^{12} -2.88298 q^{13} +(-3.55843 + 1.52891i) q^{15} +(0.115117 - 0.199389i) q^{16} +(5.77521 - 3.33432i) q^{17} +(-0.816119 - 2.58421i) q^{18} +(-4.94242 - 2.85351i) q^{19} +(2.30451 - 1.30318i) q^{20} +3.67151i q^{22} +(-0.815927 + 1.41323i) q^{23} +(2.00744 + 4.55938i) q^{24} +(-4.99920 - 0.0893892i) q^{25} +(1.30215 - 2.25540i) q^{26} +(4.92156 + 1.66682i) q^{27} -5.89707i q^{29} +(0.411150 - 3.47437i) q^{30} +(-1.62006 + 0.935342i) q^{31} +(-2.77222 - 4.80163i) q^{32} +(-5.67810 - 4.16132i) q^{33} +6.02404i q^{34} +(-3.46810 - 0.767168i) q^{36} +(-1.38541 - 0.799864i) q^{37} +(4.46468 - 2.57768i) q^{38} +(2.01217 + 4.57011i) q^{39} +(-0.0574921 + 6.43115i) q^{40} -9.12244 q^{41} -7.53359i q^{43} +(4.16743 + 2.40607i) q^{44} +(4.90722 + 4.57375i) q^{45} +(-0.737059 - 1.27662i) q^{46} +(-5.98810 - 3.45723i) q^{47} +(-0.396417 - 0.0433215i) q^{48} +(2.32792 - 3.87057i) q^{50} +(-9.31636 - 6.82771i) q^{51} +(-1.70670 - 2.95608i) q^{52} +(-0.759325 - 1.31519i) q^{53} +(-3.52689 + 3.09735i) q^{54} +(-4.47357 - 7.91093i) q^{55} +(-1.07385 + 9.82633i) q^{57} +(4.61336 + 2.66353i) q^{58} +(-0.495925 - 0.858968i) q^{59} +(-3.67423 - 2.74356i) q^{60} +(5.33892 + 3.08243i) q^{61} -1.68986i q^{62} +5.46898 q^{64} +(-0.0576274 + 6.44628i) q^{65} +(5.82008 - 2.56251i) q^{66} +(8.73843 - 5.04513i) q^{67} +(6.83773 + 3.94776i) q^{68} +(2.80973 + 0.307054i) q^{69} -4.81213i q^{71} +(5.82646 - 6.36441i) q^{72} +(-0.280309 - 0.485510i) q^{73} +(1.25149 - 0.722548i) q^{74} +(3.34747 + 7.98714i) q^{75} -6.75699i q^{76} +(-4.48410 - 0.490034i) q^{78} +(-1.89924 + 3.28958i) q^{79} +(-0.443528 - 0.261385i) q^{80} +(-0.792736 - 8.96502i) q^{81} +(4.12033 - 7.13661i) q^{82} -4.00431i q^{83} +(-7.34003 - 12.9799i) q^{85} +(5.89364 + 3.40269i) q^{86} +(-9.34806 + 4.11584i) q^{87} +(-10.1238 + 5.84500i) q^{88} +(5.20547 - 9.01615i) q^{89} +(-5.79455 + 1.77317i) q^{90} -1.93208 q^{92} +(2.61342 + 1.91531i) q^{93} +(5.40928 - 3.12305i) q^{94} +(-6.47917 + 10.9941i) q^{95} +(-5.67670 + 7.74581i) q^{96} +14.5370 q^{97} +(-2.63354 + 11.9053i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 64q16q440q9+32q15+16q1664q2556q3032q36+56q39+32q46+40q518q60352q6448q79+40q81128q85+80q99+O(q100) 64 q - 16 q^{4} - 40 q^{9} + 32 q^{15} + 16 q^{16} - 64 q^{25} - 56 q^{30} - 32 q^{36} + 56 q^{39} + 32 q^{46} + 40 q^{51} - 8 q^{60} - 352 q^{64} - 48 q^{79} + 40 q^{81} - 128 q^{85} + 80 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/735Z)×\left(\mathbb{Z}/735\mathbb{Z}\right)^\times.

nn 346346 442442 491491
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\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 −0.451669 + 0.782314i −0.319378 + 0.553180i −0.980358 0.197224i 0.936807π-0.936807\pi
0.660980 + 0.750403i 0.270141π0.270141\pi
33 −0.697946 1.58520i −0.402959 0.915218i
44 0.591990 + 1.02536i 0.295995 + 0.512678i
55 0.0199888 2.23598i 0.00893927 0.999960i
66 1.55537 + 0.169975i 0.634976 + 0.0693919i
77 0 0
88 −2.87621 −1.01689
99 −2.02574 + 2.21277i −0.675247 + 0.737591i
1010 1.74021 + 1.02556i 0.550303 + 0.324311i
1111 3.51985 2.03219i 1.06127 0.612727i 0.135490 0.990779i 0.456739π-0.456739\pi
0.925785 + 0.378051i 0.123406π0.123406\pi
1212 1.21222 1.65407i 0.349938 0.477488i
1313 −2.88298 −0.799595 −0.399798 0.916603i 0.630920π-0.630920\pi
−0.399798 + 0.916603i 0.630920π0.630920\pi
1414 0 0
1515 −3.55843 + 1.52891i −0.918783 + 0.394762i
1616 0.115117 0.199389i 0.0287793 0.0498472i
1717 5.77521 3.33432i 1.40069 0.808691i 0.406230 0.913771i 0.366843π-0.366843\pi
0.994464 + 0.105080i 0.0335097π0.0335097\pi
1818 −0.816119 2.58421i −0.192361 0.609104i
1919 −4.94242 2.85351i −1.13387 0.654639i −0.188964 0.981984i 0.560513π-0.560513\pi
−0.944905 + 0.327345i 0.893846π0.893846\pi
2020 2.30451 1.30318i 0.515304 0.291400i
2121 0 0
2222 3.67151i 0.782768i
2323 −0.815927 + 1.41323i −0.170133 + 0.294678i −0.938466 0.345371i 0.887753π-0.887753\pi
0.768333 + 0.640050i 0.221086π0.221086\pi
2424 2.00744 + 4.55938i 0.409767 + 0.930680i
2525 −4.99920 0.0893892i −0.999840 0.0178778i
2626 1.30215 2.25540i 0.255373 0.442320i
2727 4.92156 + 1.66682i 0.947154 + 0.320779i
2828 0 0
2929 5.89707i 1.09506i −0.836786 0.547530i 0.815568π-0.815568\pi
0.836786 0.547530i 0.184432π-0.184432\pi
3030 0.411150 3.47437i 0.0750654 0.634331i
3131 −1.62006 + 0.935342i −0.290971 + 0.167992i −0.638380 0.769722i 0.720395π-0.720395\pi
0.347409 + 0.937714i 0.387062π0.387062\pi
3232 −2.77222 4.80163i −0.490064 0.848816i
3333 −5.67810 4.16132i −0.988430 0.724393i
3434 6.02404i 1.03311i
3535 0 0
3636 −3.46810 0.767168i −0.578017 0.127861i
3737 −1.38541 0.799864i −0.227759 0.131497i 0.381779 0.924254i 0.375312π-0.375312\pi
−0.609538 + 0.792757i 0.708645π0.708645\pi
3838 4.46468 2.57768i 0.724266 0.418155i
3939 2.01217 + 4.57011i 0.322204 + 0.731804i
4040 −0.0574921 + 6.43115i −0.00909030 + 1.01685i
4141 −9.12244 −1.42469 −0.712343 0.701832i 0.752366π-0.752366\pi
−0.712343 + 0.701832i 0.752366π0.752366\pi
4242 0 0
4343 7.53359i 1.14886i −0.818553 0.574431i 0.805223π-0.805223\pi
0.818553 0.574431i 0.194777π-0.194777\pi
4444 4.16743 + 2.40607i 0.628264 + 0.362728i
4545 4.90722 + 4.57375i 0.731526 + 0.681814i
4646 −0.737059 1.27662i −0.108673 0.188228i
4747 −5.98810 3.45723i −0.873454 0.504289i −0.00495956 0.999988i 0.501579π-0.501579\pi
−0.868495 + 0.495699i 0.834912π0.834912\pi
4848 −0.396417 0.0433215i −0.0572179 0.00625292i
4949 0 0
5050 2.32792 3.87057i 0.329217 0.547381i
5151 −9.31636 6.82771i −1.30455 0.956071i
5252 −1.70670 2.95608i −0.236676 0.409935i
5353 −0.759325 1.31519i −0.104301 0.180655i 0.809151 0.587600i 0.199927π-0.199927\pi
−0.913453 + 0.406945i 0.866594π0.866594\pi
5454 −3.52689 + 3.09735i −0.479949 + 0.421496i
5555 −4.47357 7.91093i −0.603216 1.06671i
5656 0 0
5757 −1.07385 + 9.82633i −0.142235 + 1.30153i
5858 4.61336 + 2.66353i 0.605764 + 0.349738i
5959 −0.495925 0.858968i −0.0645640 0.111828i 0.831937 0.554871i 0.187232π-0.187232\pi
−0.896500 + 0.443043i 0.853899π0.853899\pi
6060 −3.67423 2.74356i −0.474341 0.354193i
6161 5.33892 + 3.08243i 0.683578 + 0.394664i 0.801202 0.598394i 0.204194π-0.204194\pi
−0.117624 + 0.993058i 0.537528π0.537528\pi
6262 1.68986i 0.214612i
6363 0 0
6464 5.46898 0.683622
6565 −0.0576274 + 6.44628i −0.00714780 + 0.799563i
6666 5.82008 2.56251i 0.716403 0.315424i
6767 8.73843 5.04513i 1.06757 0.616361i 0.140053 0.990144i 0.455273π-0.455273\pi
0.927516 + 0.373783i 0.121939π0.121939\pi
6868 6.83773 + 3.94776i 0.829196 + 0.478737i
6969 2.80973 + 0.307054i 0.338251 + 0.0369650i
7070 0 0
7171 4.81213i 0.571095i −0.958365 0.285548i 0.907825π-0.907825\pi
0.958365 0.285548i 0.0921755π-0.0921755\pi
7272 5.82646 6.36441i 0.686655 0.750052i
7373 −0.280309 0.485510i −0.0328077 0.0568246i 0.849155 0.528143i 0.177112π-0.177112\pi
−0.881963 + 0.471319i 0.843778π0.843778\pi
7474 1.25149 0.722548i 0.145483 0.0839946i
7575 3.34747 + 7.98714i 0.386533 + 0.922276i
7676 6.75699i 0.775079i
7777 0 0
7878 −4.48410 0.490034i −0.507724 0.0554854i
7979 −1.89924 + 3.28958i −0.213681 + 0.370106i −0.952864 0.303399i 0.901879π-0.901879\pi
0.739183 + 0.673505i 0.235212π0.235212\pi
8080 −0.443528 0.261385i −0.0495879 0.0292237i
8181 −0.792736 8.96502i −0.0880817 0.996113i
8282 4.12033 7.13661i 0.455014 0.788107i
8383 4.00431i 0.439530i −0.975553 0.219765i 0.929471π-0.929471\pi
0.975553 0.219765i 0.0705291π-0.0705291\pi
8484 0 0
8585 −7.34003 12.9799i −0.796138 1.40787i
8686 5.89364 + 3.40269i 0.635527 + 0.366922i
8787 −9.34806 + 4.11584i −1.00222 + 0.441264i
8888 −10.1238 + 5.84500i −1.07920 + 0.623079i
8989 5.20547 9.01615i 0.551779 0.955710i −0.446367 0.894850i 0.647282π-0.647282\pi
0.998146 0.0608597i 0.0193842π-0.0193842\pi
9090 −5.79455 + 1.77317i −0.610799 + 0.186908i
9191 0 0
9292 −1.93208 −0.201433
9393 2.61342 + 1.91531i 0.270999 + 0.198608i
9494 5.40928 3.12305i 0.557925 0.322118i
9595 −6.47917 + 10.9941i −0.664749 + 1.12797i
9696 −5.67670 + 7.74581i −0.579376 + 0.790554i
9797 14.5370 1.47601 0.738006 0.674795i 0.235768π-0.235768\pi
0.738006 + 0.674795i 0.235768π0.235768\pi
9898 0 0
9999 −2.63354 + 11.9053i −0.264681 + 1.19653i
100100 −2.86782 5.17888i −0.286782 0.517888i
101101 −6.89867 11.9488i −0.686443 1.18895i −0.972981 0.230886i 0.925838π-0.925838\pi
0.286538 0.958069i 0.407496π-0.407496\pi
102102 9.54933 4.20445i 0.945524 0.416303i
103103 −4.15679 + 7.19978i −0.409581 + 0.709415i −0.994843 0.101429i 0.967658π-0.967658\pi
0.585262 + 0.810844i 0.300992π0.300992\pi
104104 8.29206 0.813104
105105 0 0
106106 1.37186 0.133246
107107 −5.36854 + 9.29858i −0.518996 + 0.898927i 0.480760 + 0.876852i 0.340361π0.340361\pi
−0.999756 + 0.0220754i 0.992973π0.992973\pi
108108 1.20443 + 6.03309i 0.115896 + 0.580534i
109109 −0.268338 0.464774i −0.0257021 0.0445173i 0.852888 0.522093i 0.174849π-0.174849\pi
−0.878590 + 0.477576i 0.841515π0.841515\pi
110110 8.20941 + 0.0733891i 0.782736 + 0.00699737i
111111 −0.301010 + 2.75441i −0.0285706 + 0.261437i
112112 0 0
113113 12.1028 1.13854 0.569270 0.822151i 0.307226π-0.307226\pi
0.569270 + 0.822151i 0.307226π0.307226\pi
114114 −7.20226 5.27834i −0.674553 0.494362i
115115 3.14364 + 1.85264i 0.293146 + 0.172760i
116116 6.04660 3.49101i 0.561413 0.324132i
117117 5.84018 6.37938i 0.539925 0.589774i
118118 0.895977 0.0824813
119119 0 0
120120 10.2348 4.39746i 0.934306 0.401431i
121121 2.75956 4.77971i 0.250870 0.434519i
122122 −4.82285 + 2.78447i −0.436640 + 0.252094i
123123 6.36697 + 14.4609i 0.574091 + 1.30390i
124124 −1.91812 1.10743i −0.172252 0.0994497i
125125 −0.299800 + 11.1763i −0.0268150 + 0.999640i
126126 0 0
127127 22.2883i 1.97777i 0.148697 + 0.988883i 0.452492π0.452492\pi
−0.148697 + 0.988883i 0.547508π0.547508\pi
128128 3.07427 5.32480i 0.271730 0.470650i
129129 −11.9423 + 5.25804i −1.05146 + 0.462945i
130130 −5.01699 2.95667i −0.440019 0.259317i
131131 0.0570895 0.0988819i 0.00498793 0.00863935i −0.863521 0.504313i 0.831746π-0.831746\pi
0.868509 + 0.495674i 0.165079π0.165079\pi
132132 0.905465 8.28553i 0.0788106 0.721163i
133133 0 0
134134 9.11493i 0.787410i
135135 3.82534 10.9712i 0.329233 0.944249i
136136 −16.6107 + 9.59021i −1.42436 + 0.822353i
137137 6.27188 + 10.8632i 0.535842 + 0.928106i 0.999122 + 0.0418942i 0.0133392π0.0133392\pi
−0.463280 + 0.886212i 0.653327π0.653327\pi
138138 −1.50928 + 2.05940i −0.128478 + 0.175308i
139139 2.37640i 0.201564i −0.994909 0.100782i 0.967866π-0.967866\pi
0.994909 0.100782i 0.0321344π-0.0321344\pi
140140 0 0
141141 −1.30104 + 11.9053i −0.109568 + 1.00261i
142142 3.76460 + 2.17349i 0.315918 + 0.182395i
143143 −10.1477 + 5.85876i −0.848590 + 0.489934i
144144 0.208004 + 0.658638i 0.0173337 + 0.0548865i
145145 −13.1857 0.117876i −1.09502 0.00978903i
146146 0.506428 0.0419123
147147 0 0
148148 1.89405i 0.155690i
149149 14.2621 + 8.23423i 1.16840 + 0.674575i 0.953302 0.302018i 0.0976604π-0.0976604\pi
0.215096 + 0.976593i 0.430994π0.430994\pi
150150 −7.76040 0.988771i −0.633634 0.0807328i
151151 6.57364 + 11.3859i 0.534955 + 0.926569i 0.999166 + 0.0408444i 0.0130048π0.0130048\pi
−0.464211 + 0.885725i 0.653662π0.653662\pi
152152 14.2154 + 8.20729i 1.15302 + 0.665699i
153153 −4.32099 + 19.5337i −0.349332 + 1.57921i
154154 0 0
155155 2.05902 + 3.64111i 0.165385 + 0.292461i
156156 −3.49481 + 4.76865i −0.279809 + 0.381797i
157157 −1.59406 2.76100i −0.127220 0.220352i 0.795378 0.606113i 0.207272π-0.207272\pi
−0.922599 + 0.385761i 0.873939π0.873939\pi
158158 −1.71565 2.97160i −0.136490 0.236408i
159159 −1.55488 + 2.12162i −0.123310 + 0.168255i
160160 −10.7918 + 6.10265i −0.853163 + 0.482457i
161161 0 0
162162 7.37152 + 3.42906i 0.579161 + 0.269412i
163163 −16.6965 9.63970i −1.30777 0.755040i −0.326044 0.945354i 0.605716π-0.605716\pi
−0.981723 + 0.190314i 0.939049π0.939049\pi
164164 −5.40039 9.35375i −0.421700 0.730405i
165165 −9.41813 + 12.6129i −0.733200 + 0.981915i
166166 3.13263 + 1.80863i 0.243139 + 0.140377i
167167 0.883913i 0.0683993i 0.999415 + 0.0341996i 0.0108882π0.0108882\pi
−0.999415 + 0.0341996i 0.989112π0.989112\pi
168168 0 0
169169 −4.68842 −0.360648
170170 13.4696 + 0.120413i 1.03307 + 0.00923529i
171171 16.3262 5.15598i 1.24850 0.394288i
172172 7.72462 4.45981i 0.588996 0.340057i
173173 10.8393 + 6.25807i 0.824097 + 0.475793i 0.851827 0.523823i 0.175495π-0.175495\pi
−0.0277303 + 0.999615i 0.508828π0.508828\pi
174174 1.00235 9.17212i 0.0759882 0.695337i
175175 0 0
176176 0.935758i 0.0705354i
177177 −1.01551 + 1.38566i −0.0763304 + 0.104152i
178178 4.70231 + 8.14463i 0.352453 + 0.610466i
179179 −10.5358 + 6.08284i −0.787481 + 0.454653i −0.839075 0.544016i 0.816903π-0.816903\pi
0.0515938 + 0.998668i 0.483570π0.483570\pi
180180 −1.78470 + 7.73926i −0.133023 + 0.576851i
181181 16.1773i 1.20245i 0.799081 + 0.601224i 0.205320π0.205320\pi
−0.799081 + 0.601224i 0.794680π0.794680\pi
182182 0 0
183183 1.16000 10.6146i 0.0857493 0.784657i
184184 2.34678 4.06474i 0.173007 0.299657i
185185 −1.81617 + 3.08175i −0.133528 + 0.226575i
186186 −2.67877 + 1.17943i −0.196417 + 0.0864801i
187187 13.5519 23.4726i 0.991014 1.71649i
188188 8.18658i 0.597068i
189189 0 0
190190 −5.67440 10.0344i −0.411664 0.727975i
191191 −7.16890 4.13896i −0.518723 0.299485i 0.217689 0.976018i 0.430148π-0.430148\pi
−0.736412 + 0.676533i 0.763482π0.763482\pi
192192 −3.81705 8.66945i −0.275472 0.625663i
193193 13.7918 7.96267i 0.992752 0.573166i 0.0866562 0.996238i 0.472382π-0.472382\pi
0.906096 + 0.423073i 0.139048π0.139048\pi
194194 −6.56593 + 11.3725i −0.471406 + 0.816499i
195195 10.2589 4.40781i 0.734655 0.315650i
196196 0 0
197197 23.8738 1.70094 0.850468 0.526027i 0.176319π-0.176319\pi
0.850468 + 0.526027i 0.176319π0.176319\pi
198198 −8.12421 7.43752i −0.577363 0.528562i
199199 10.5891 6.11364i 0.750643 0.433384i −0.0752829 0.997162i 0.523986π-0.523986\pi
0.825926 + 0.563778i 0.190653π0.190653\pi
200200 14.3788 + 0.257102i 1.01673 + 0.0181799i
201201 −14.0965 10.3310i −0.994292 0.728690i
202202 12.4637 0.876941
203203 0 0
204204 1.48565 13.5945i 0.104016 0.951807i
205205 −0.182347 + 20.3976i −0.0127357 + 1.42463i
206206 −3.75499 6.50384i −0.261623 0.453144i
207207 −1.47429 4.66830i −0.102471 0.324469i
208208 −0.331880 + 0.574834i −0.0230118 + 0.0398576i
209209 −23.1954 −1.60446
210210 0 0
211211 18.8640 1.29865 0.649327 0.760510i 0.275051π-0.275051\pi
0.649327 + 0.760510i 0.275051π0.275051\pi
212212 0.899025 1.55716i 0.0617453 0.106946i
213213 −7.62821 + 3.35861i −0.522677 + 0.230128i
214214 −4.84961 8.39976i −0.331512 0.574196i
215215 −16.8450 0.150588i −1.14882 0.0102700i
216216 −14.1554 4.79412i −0.963156 0.326199i
217217 0 0
218218 0.484799 0.0328348
219219 −0.573991 + 0.783207i −0.0387867 + 0.0529242i
220220 5.46322 9.27019i 0.368330 0.624996i
221221 −16.6498 + 9.61278i −1.11999 + 0.646625i
222222 −2.01886 1.47957i −0.135497 0.0993021i
223223 −19.2779 −1.29095 −0.645473 0.763783i 0.723340π-0.723340\pi
−0.645473 + 0.763783i 0.723340π0.723340\pi
224224 0 0
225225 10.3249 10.8810i 0.688326 0.725401i
226226 −5.46649 + 9.46823i −0.363625 + 0.629817i
227227 −9.96079 + 5.75087i −0.661121 + 0.381698i −0.792704 0.609607i 0.791327π-0.791327\pi
0.131583 + 0.991305i 0.457994π0.457994\pi
228228 −10.7112 + 4.71601i −0.709367 + 0.312326i
229229 15.0457 + 8.68661i 0.994245 + 0.574028i 0.906540 0.422119i 0.138714π-0.138714\pi
0.0877044 + 0.996147i 0.472047π0.472047\pi
230230 −2.86923 + 1.62253i −0.189192 + 0.106986i
231231 0 0
232232 16.9612i 1.11356i
233233 0.231425 0.400840i 0.0151611 0.0262599i −0.858345 0.513072i 0.828507π-0.828507\pi
0.873506 + 0.486813i 0.161841π0.161841\pi
234234 2.35285 + 7.45023i 0.153811 + 0.487036i
235235 −7.84999 + 13.3202i −0.512077 + 0.868911i
236236 0.587165 1.01700i 0.0382212 0.0662011i
237237 6.54021 + 0.714732i 0.424833 + 0.0464268i
238238 0 0
239239 17.3055i 1.11940i −0.828696 0.559699i 0.810917π-0.810917\pi
0.828696 0.559699i 0.189083π-0.189083\pi
240240 −0.104790 + 0.885515i −0.00676416 + 0.0571597i
241241 −3.70606 + 2.13970i −0.238729 + 0.137830i −0.614592 0.788845i 0.710679π-0.710679\pi
0.375864 + 0.926675i 0.377346π0.377346\pi
242242 2.49282 + 4.31769i 0.160245 + 0.277552i
243243 −13.6581 + 7.51375i −0.876167 + 0.482007i
244244 7.29906i 0.467274i
245245 0 0
246246 −14.1888 1.55058i −0.904642 0.0988617i
247247 14.2489 + 8.22661i 0.906636 + 0.523446i
248248 4.65963 2.69024i 0.295887 0.170830i
249249 −6.34765 + 2.79479i −0.402266 + 0.177113i
250250 −8.60798 5.28254i −0.544417 0.334097i
251251 17.4145 1.09919 0.549597 0.835430i 0.314781π-0.314781\pi
0.549597 + 0.835430i 0.314781π0.314781\pi
252252 0 0
253253 6.63247i 0.416980i
254254 −17.4364 10.0669i −1.09406 0.631656i
255255 −15.4528 + 20.6947i −0.967694 + 1.29595i
256256 8.24609 + 14.2826i 0.515381 + 0.892665i
257257 −13.3507 7.70805i −0.832796 0.480815i 0.0220130 0.999758i 0.492992π-0.492992\pi
−0.854809 + 0.518943i 0.826326π0.826326\pi
258258 1.28052 11.7175i 0.0797217 0.729500i
259259 0 0
260260 −6.64385 + 3.75704i −0.412034 + 0.233002i
261261 13.0489 + 11.9460i 0.807706 + 0.739436i
262262 0.0515711 + 0.0893238i 0.00318607 + 0.00551844i
263263 −3.10585 5.37949i −0.191515 0.331714i 0.754238 0.656602i 0.228007π-0.228007\pi
−0.945752 + 0.324888i 0.894673π0.894673\pi
264264 16.3314 + 11.9688i 1.00513 + 0.736632i
265265 −2.95591 + 1.67155i −0.181580 + 0.102682i
266266 0 0
267267 −17.9256 1.95895i −1.09703 0.119886i
268268 10.3461 + 5.97333i 0.631990 + 0.364879i
269269 2.99535 + 5.18810i 0.182630 + 0.316324i 0.942775 0.333429i 0.108206π-0.108206\pi
−0.760146 + 0.649753i 0.774872π0.774872\pi
270270 6.85512 + 7.94797i 0.417189 + 0.483698i
271271 5.40846 + 3.12257i 0.328540 + 0.189683i 0.655193 0.755462i 0.272587π-0.272587\pi
−0.326652 + 0.945145i 0.605921π0.605921\pi
272272 1.53535i 0.0930942i
273273 0 0
274274 −11.3313 −0.684546
275275 −17.7781 + 9.84467i −1.07206 + 0.593656i
276276 1.34849 + 3.06274i 0.0811695 + 0.184356i
277277 7.53810 4.35212i 0.452920 0.261494i −0.256142 0.966639i 0.582452π-0.582452\pi
0.709063 + 0.705145i 0.249118π0.249118\pi
278278 1.85909 + 1.07335i 0.111501 + 0.0643751i
279279 1.21212 5.47959i 0.0725679 0.328054i
280280 0 0
281281 4.36274i 0.260259i −0.991497 0.130130i 0.958461π-0.958461\pi
0.991497 0.130130i 0.0415393π-0.0415393\pi
282282 −8.72606 6.39509i −0.519629 0.380822i
283283 −3.76038 6.51316i −0.223531 0.387167i 0.732347 0.680932i 0.238425π-0.238425\pi
−0.955878 + 0.293765i 0.905092π0.905092\pi
284284 4.93415 2.84873i 0.292788 0.169041i
285285 21.9500 + 2.59752i 1.30021 + 0.153864i
286286 10.5849i 0.625897i
287287 0 0
288288 16.2407 + 3.59256i 0.956994 + 0.211694i
289289 13.7354 23.7904i 0.807963 1.39943i
290290 6.04781 10.2621i 0.355139 0.602614i
291291 −10.1461 23.0441i −0.594773 1.35087i
292292 0.331880 0.574834i 0.0194218 0.0336396i
293293 0.105885i 0.00618587i −0.999995 0.00309293i 0.999015π-0.999015\pi
0.999995 0.00309293i 0.000984513π-0.000984513\pi
294294 0 0
295295 −1.93055 + 1.09171i −0.112401 + 0.0635617i
296296 3.98472 + 2.30058i 0.231607 + 0.133718i
297297 20.7104 4.13457i 1.20174 0.239912i
298298 −12.8835 + 7.43830i −0.746322 + 0.430889i
299299 2.35230 4.07431i 0.136037 0.235623i
300300 −6.20800 + 8.16066i −0.358419 + 0.471156i
301301 0 0
302302 −11.8764 −0.683412
303303 −14.1265 + 19.2754i −0.811544 + 1.10735i
304304 −1.13791 + 0.656975i −0.0652638 + 0.0376801i
305305 6.99896 11.8761i 0.400759 0.680023i
306306 −13.3298 12.2031i −0.762016 0.697608i
307307 9.31270 0.531504 0.265752 0.964041i 0.414380π-0.414380\pi
0.265752 + 0.964041i 0.414380π0.414380\pi
308308 0 0
309309 14.3143 + 1.56431i 0.814314 + 0.0889904i
310310 −3.77849 0.0337783i −0.214604 0.00191848i
311311 12.6572 + 21.9228i 0.717722 + 1.24313i 0.961900 + 0.273400i 0.0881483π0.0881483\pi
−0.244179 + 0.969730i 0.578518π0.578518\pi
312312 −5.78741 13.1446i −0.327648 0.744167i
313313 −3.82491 + 6.62494i −0.216197 + 0.374464i −0.953642 0.300943i 0.902699π-0.902699\pi
0.737445 + 0.675407i 0.236032π0.236032\pi
314314 2.87996 0.162526
315315 0 0
316316 −4.49732 −0.252994
317317 12.3732 21.4311i 0.694950 1.20369i −0.275247 0.961374i 0.588760π-0.588760\pi
0.970197 0.242316i 0.0779071π-0.0779071\pi
318318 −0.957481 2.17467i −0.0536929 0.121949i
319319 −11.9840 20.7568i −0.670973 1.16216i
320320 0.109318 12.2285i 0.00611109 0.683595i
321321 18.4871 + 2.02032i 1.03185 + 0.112763i
322322 0 0
323323 −38.0580 −2.11760
324324 8.72305 6.12004i 0.484614 0.340002i
325325 14.4126 + 0.257707i 0.799467 + 0.0142950i
326326 15.0826 8.70792i 0.835346 0.482287i
327327 −0.549477 + 0.749757i −0.0303861 + 0.0414617i
328328 26.2381 1.44875
329329 0 0
330330 −5.61339 13.0648i −0.309007 0.719194i
331331 8.17810 14.1649i 0.449509 0.778573i −0.548845 0.835924i 0.684932π-0.684932\pi
0.998354 + 0.0573514i 0.0182655π0.0182655\pi
332332 4.10585 2.37051i 0.225338 0.130099i
333333 4.57639 1.44527i 0.250785 0.0792003i
334334 −0.691498 0.399237i −0.0378371 0.0218453i
335335 −11.1061 19.6398i −0.606793 1.07304i
336336 0 0
337337 3.59256i 0.195699i 0.995201 + 0.0978497i 0.0311964π0.0311964\pi
−0.995201 + 0.0978497i 0.968804π0.968804\pi
338338 2.11762 3.66782i 0.115183 0.199503i
339339 −8.44714 19.1855i −0.458786 1.04201i
340340 8.96380 15.2101i 0.486130 0.824884i
341341 −3.80158 + 6.58453i −0.205867 + 0.356572i
342342 −3.34046 + 15.1010i −0.180631 + 0.816571i
343343 0 0
344344 21.6682i 1.16827i
345345 0.742730 6.27635i 0.0399872 0.337907i
346346 −9.79156 + 5.65316i −0.526398 + 0.303916i
347347 −9.46440 16.3928i −0.508075 0.880012i −0.999956 0.00934990i 0.997024π-0.997024\pi
0.491881 0.870662i 0.336310π-0.336310\pi
348348 −9.75416 7.14856i −0.522878 0.383203i
349349 24.1751i 1.29406i −0.762463 0.647032i 0.776010π-0.776010\pi
0.762463 0.647032i 0.223990π-0.223990\pi
350350 0 0
351351 −14.1888 4.80540i −0.757340 0.256493i
352352 −19.5156 11.2673i −1.04019 0.600551i
353353 27.8032 16.0522i 1.47982 0.854373i 0.480078 0.877226i 0.340608π-0.340608\pi
0.999739 + 0.0228526i 0.00727484π0.00727484\pi
354354 −0.625343 1.42031i −0.0332366 0.0754884i
355355 −10.7598 0.0961889i −0.571072 0.00510518i
356356 12.3263 0.653295
357357 0 0
358358 10.9897i 0.580825i
359359 −14.7805 8.53352i −0.780085 0.450382i 0.0563756 0.998410i 0.482046π-0.482046\pi
−0.836460 + 0.548027i 0.815379π0.815379\pi
360360 −14.1142 13.1551i −0.743884 0.693333i
361361 6.78500 + 11.7520i 0.357105 + 0.618524i
362362 −12.6557 7.30678i −0.665169 0.384036i
363363 −9.50284 1.03850i −0.498770 0.0545069i
364364 0 0
365365 −1.09119 + 0.617061i −0.0571157 + 0.0322984i
366366 7.78005 + 5.70179i 0.406670 + 0.298037i
367367 −7.83753 13.5750i −0.409116 0.708609i 0.585675 0.810546i 0.300829π-0.300829\pi
−0.994791 + 0.101937i 0.967496π0.967496\pi
368368 0.187854 + 0.325373i 0.00979259 + 0.0169613i
369369 18.4797 20.1859i 0.962015 1.05084i
370370 −1.59059 2.81275i −0.0826907 0.146228i
371371 0 0
372372 −0.416753 + 3.81353i −0.0216076 + 0.197722i
373373 0.908235 + 0.524370i 0.0470266 + 0.0271508i 0.523329 0.852131i 0.324690π-0.324690\pi
−0.476302 + 0.879282i 0.658023π0.658023\pi
374374 12.2420 + 21.2037i 0.633017 + 1.09642i
375375 17.9260 7.32522i 0.925694 0.378273i
376376 17.2230 + 9.94373i 0.888211 + 0.512809i
377377 17.0012i 0.875604i
378378 0 0
379379 −19.7185 −1.01287 −0.506436 0.862278i 0.669037π-0.669037\pi
−0.506436 + 0.862278i 0.669037π0.669037\pi
380380 −15.1085 0.135064i −0.775048 0.00692865i
381381 35.3315 15.5560i 1.81009 0.796959i
382382 6.47594 3.73889i 0.331338 0.191298i
383383 −2.38931 1.37947i −0.122088 0.0704876i 0.437712 0.899115i 0.355789π-0.355789\pi
−0.559800 + 0.828628i 0.689122π0.689122\pi
384384 −10.5866 1.15693i −0.540244 0.0590392i
385385 0 0
386386 14.3860i 0.732227i
387387 16.6701 + 15.2611i 0.847391 + 0.775766i
388388 8.60577 + 14.9056i 0.436892 + 0.756719i
389389 27.6283 15.9512i 1.40081 0.808758i 0.406335 0.913724i 0.366807π-0.366807\pi
0.994476 + 0.104966i 0.0334733π0.0334733\pi
390390 −1.18534 + 10.0166i −0.0600219 + 0.507208i
391391 10.8822i 0.550339i
392392 0 0
393393 −0.196593 0.0214842i −0.00991682 0.00108374i
394394 −10.7831 + 18.6768i −0.543242 + 0.940923i
395395 7.31746 + 4.31241i 0.368181 + 0.216981i
396396 −13.7662 + 4.34751i −0.691779 + 0.218471i
397397 −9.41023 + 16.2990i −0.472286 + 0.818023i −0.999497 0.0317111i 0.989904π-0.989904\pi
0.527211 + 0.849734i 0.323238π0.323238\pi
398398 11.0454i 0.553654i
399399 0 0
400400 −0.593317 + 0.986494i −0.0296658 + 0.0493247i
401401 −2.84850 1.64458i −0.142247 0.0821266i 0.427187 0.904163i 0.359505π-0.359505\pi
−0.569435 + 0.822037i 0.692838π0.692838\pi
402402 14.4490 6.36173i 0.720652 0.317294i
403403 4.67060 2.69657i 0.232659 0.134326i
404404 8.16788 14.1472i 0.406367 0.703849i
405405 −20.0614 + 1.59334i −0.996861 + 0.0791737i
406406 0 0
407407 −6.50190 −0.322287
408408 26.7958 + 19.6379i 1.32659 + 0.972223i
409409 −3.59326 + 2.07457i −0.177675 + 0.102581i −0.586200 0.810166i 0.699377π-0.699377\pi
0.408525 + 0.912747i 0.366043π0.366043\pi
410410 −15.8750 9.35561i −0.784008 0.462041i
411411 12.8430 17.5241i 0.633497 0.864402i
412412 −9.84311 −0.484935
413413 0 0
414414 4.31797 + 0.955165i 0.212217 + 0.0469438i
415415 −8.95356 0.0800415i −0.439513 0.00392908i
416416 7.99226 + 13.8430i 0.391853 + 0.678709i
417417 −3.76708 + 1.65860i −0.184475 + 0.0812220i
418418 10.4767 18.1461i 0.512430 0.887555i
419419 22.6231 1.10521 0.552606 0.833443i 0.313633π-0.313633\pi
0.552606 + 0.833443i 0.313633π0.313633\pi
420420 0 0
421421 31.9233 1.55584 0.777922 0.628360i 0.216274π-0.216274\pi
0.777922 + 0.628360i 0.216274π0.216274\pi
422422 −8.52030 + 14.7576i −0.414762 + 0.718389i
423423 19.7804 6.24685i 0.961757 0.303732i
424424 2.18398 + 3.78276i 0.106063 + 0.183707i
425425 −29.1695 + 16.1527i −1.41493 + 0.783521i
426426 0.817941 7.48464i 0.0396294 0.362632i
427427 0 0
428428 −12.7125 −0.614481
429429 16.3698 + 11.9970i 0.790343 + 0.579221i
430430 7.72615 13.1100i 0.372588 0.632222i
431431 −21.6894 + 12.5224i −1.04474 + 0.603182i −0.921173 0.389154i 0.872767π-0.872767\pi
−0.123569 + 0.992336i 0.539434π0.539434\pi
432432 0.898900 0.789423i 0.0432483 0.0379812i
433433 −5.10220 −0.245196 −0.122598 0.992456i 0.539123π-0.539123\pi
−0.122598 + 0.992456i 0.539123π0.539123\pi
434434 0 0
435435 9.01607 + 20.9843i 0.432288 + 1.00612i
436436 0.317706 0.550283i 0.0152154 0.0263538i
437437 8.06531 4.65651i 0.385816 0.222751i
438438 −0.353460 0.802792i −0.0168890 0.0383589i
439439 −9.77568 5.64399i −0.466568 0.269373i 0.248234 0.968700i 0.420150π-0.420150\pi
−0.714802 + 0.699327i 0.753483π0.753483\pi
440440 12.8669 + 22.7535i 0.613407 + 1.08473i
441441 0 0
442442 17.3672i 0.826073i
443443 10.9591 18.9817i 0.520681 0.901847i −0.479029 0.877799i 0.659011π-0.659011\pi
0.999711 0.0240479i 0.00765541π-0.00765541\pi
444444 −3.00245 + 1.32194i −0.142490 + 0.0627366i
445445 −20.0559 11.8196i −0.950739 0.560301i
446446 8.70725 15.0814i 0.412300 0.714125i
447447 3.09875 28.3554i 0.146566 1.34116i
448448 0 0
449449 0.449397i 0.0212083i −0.999944 0.0106042i 0.996625π-0.996625\pi
0.999944 0.0106042i 0.00337548π-0.00337548\pi
450450 3.84894 + 12.9919i 0.181441 + 0.612446i
451451 −32.1096 + 18.5385i −1.51198 + 0.872944i
452452 7.16476 + 12.4097i 0.337002 + 0.583705i
453453 13.4609 18.3673i 0.632448 0.862970i
454454 10.3900i 0.487625i
455455 0 0
456456 3.08861 28.2626i 0.144638 1.32352i
457457 −8.04787 4.64644i −0.376463 0.217351i 0.299815 0.953997i 0.403075π-0.403075\pi
−0.676278 + 0.736646i 0.736408π0.736408\pi
458458 −13.5913 + 7.84695i −0.635081 + 0.366664i
459459 33.9807 6.78382i 1.58608 0.316641i
460460 −0.0386201 + 4.32009i −0.00180067 + 0.201425i
461461 −20.8668 −0.971863 −0.485931 0.873997i 0.661519π-0.661519\pi
−0.485931 + 0.873997i 0.661519π0.661519\pi
462462 0 0
463463 2.45294i 0.113998i −0.998374 0.0569989i 0.981847π-0.981847\pi
0.998374 0.0569989i 0.0181532π-0.0181532\pi
464464 −1.17581 0.678854i −0.0545856 0.0315150i
465465 4.33482 5.80527i 0.201023 0.269213i
466466 0.209055 + 0.362094i 0.00968429 + 0.0167737i
467467 6.91084 + 3.98997i 0.319795 + 0.184634i 0.651301 0.758819i 0.274223π-0.274223\pi
−0.331506 + 0.943453i 0.607557π0.607557\pi
468468 9.99847 + 2.21173i 0.462179 + 0.102237i
469469 0 0
470470 −6.87495 12.1575i −0.317118 0.560782i
471471 −3.26418 + 4.45395i −0.150405 + 0.205227i
472472 1.42639 + 2.47057i 0.0656547 + 0.113717i
473473 −15.3097 26.5171i −0.703939 1.21926i
474474 −3.51316 + 4.79368i −0.161365 + 0.220181i
475475 24.4531 + 14.7071i 1.12198 + 0.674806i
476476 0 0
477477 4.44841 + 0.984021i 0.203679 + 0.0450552i
478478 13.5383 + 7.81635i 0.619228 + 0.357511i
479479 −6.94646 12.0316i −0.317392 0.549739i 0.662551 0.749017i 0.269474π-0.269474\pi
−0.979943 + 0.199278i 0.936140π0.936140\pi
480480 17.2060 + 12.8478i 0.785343 + 0.586420i
481481 3.99410 + 2.30599i 0.182115 + 0.105144i
482482 3.86574i 0.176080i
483483 0 0
484484 6.53454 0.297024
485485 0.290578 32.5045i 0.0131945 1.47595i
486486 0.290831 14.0787i 0.0131924 0.638621i
487487 −22.9590 + 13.2554i −1.04037 + 0.600659i −0.919939 0.392062i 0.871762π-0.871762\pi
−0.120433 + 0.992721i 0.538428π0.538428\pi
488488 −15.3559 8.86571i −0.695127 0.401332i
489489 −3.62767 + 33.1953i −0.164049 + 1.50114i
490490 0 0
491491 2.54611i 0.114905i 0.998348 + 0.0574523i 0.0182977π0.0182977\pi
−0.998348 + 0.0574523i 0.981702π0.981702\pi
492492 −11.0584 + 15.0891i −0.498552 + 0.680271i
493493 −19.6627 34.0568i −0.885565 1.53384i
494494 −12.8716 + 7.43141i −0.579120 + 0.334355i
495495 26.5674 + 6.12651i 1.19412 + 0.275366i
496496 0.430695i 0.0193388i
497497 0 0
498498 0.680632 6.22818i 0.0304999 0.279091i
499499 −14.8248 + 25.6773i −0.663649 + 1.14947i 0.316001 + 0.948759i 0.397660π0.397660\pi
−0.979650 + 0.200714i 0.935674π0.935674\pi
500500 −11.6372 + 6.30886i −0.520431 + 0.282141i
501501 1.40118 0.616924i 0.0626002 0.0275621i
502502 −7.86560 + 13.6236i −0.351059 + 0.608052i
503503 31.2378i 1.39283i −0.717642 0.696413i 0.754778π-0.754778\pi
0.717642 0.696413i 0.245222π-0.245222\pi
504504 0 0
505505 −26.8553 + 15.1864i −1.19504 + 0.675787i
506506 −5.18867 2.99568i −0.230665 0.133174i
507507 3.27226 + 7.43210i 0.145326 + 0.330071i
508508 −22.8534 + 13.1944i −1.01396 + 0.585408i
509509 −19.0072 + 32.9214i −0.842478 + 1.45921i 0.0453160 + 0.998973i 0.485571π0.485571\pi
−0.887794 + 0.460242i 0.847763π0.847763\pi
510510 −9.21019 21.4361i −0.407834 0.949208i
511511 0 0
512512 −2.60093 −0.114946
513513 −19.5681 22.2818i −0.863953 0.983766i
514514 12.0602 6.96298i 0.531954 0.307124i
515515 16.0155 + 9.43841i 0.705725 + 0.415906i
516516 −12.4611 9.13238i −0.548568 0.402031i
517517 −28.1030 −1.23597
518518 0 0
519519 2.35507 21.5503i 0.103376 0.945953i
520520 0.165749 18.5409i 0.00726856 0.813071i
521521 19.5707 + 33.8974i 0.857407 + 1.48507i 0.874394 + 0.485217i 0.161259π0.161259\pi
−0.0169866 + 0.999856i 0.505407π0.505407\pi
522522 −15.2393 + 4.81271i −0.667005 + 0.210647i
523523 −3.98588 + 6.90375i −0.174290 + 0.301880i −0.939915 0.341407i 0.889096π-0.889096\pi
0.765625 + 0.643287i 0.222430π0.222430\pi
524524 0.135186 0.00590561
525525 0 0
526526 5.61127 0.244663
527527 −6.23745 + 10.8036i −0.271708 + 0.470612i
528528 −1.48337 + 0.653109i −0.0645553 + 0.0284229i
529529 10.1685 + 17.6124i 0.442110 + 0.765757i
530530 0.0274218 3.06744i 0.00119113 0.133241i
531531 2.90532 + 0.642677i 0.126080 + 0.0278898i
532532 0 0
533533 26.2998 1.13917
534534 9.62895 13.1386i 0.416685 0.568564i
535535 20.6841 + 12.1898i 0.894252 + 0.527011i
536536 −25.1336 + 14.5109i −1.08560 + 0.626774i
537537 16.9959 + 12.4559i 0.733429 + 0.537510i
538538 −5.41163 −0.233312
539539 0 0
540540 13.5139 2.57248i 0.581547 0.110702i
541541 4.04174 7.00049i 0.173768 0.300975i −0.765966 0.642881i 0.777739π-0.777739\pi
0.939734 + 0.341906i 0.111072π0.111072\pi
542542 −4.88567 + 2.82074i −0.209857 + 0.121161i
543543 25.6443 11.2909i 1.10050 0.484537i
544544 −32.0203 18.4869i −1.37286 0.792621i
545545 −1.04459 + 0.590707i −0.0447453 + 0.0253031i
546546 0 0
547547 37.0430i 1.58384i −0.610623 0.791922i 0.709081π-0.709081\pi
0.610623 0.791922i 0.290919π-0.290919\pi
548548 −7.42577 + 12.8618i −0.317213 + 0.549429i
549549 −17.6360 + 5.56962i −0.752685 + 0.237705i
550550 0.328193 18.3546i 0.0139942 0.782642i
551551 −16.8273 + 29.1458i −0.716869 + 1.24165i
552552 −8.08137 0.883153i −0.343966 0.0375895i
553553 0 0
554554 7.86288i 0.334062i
555555 6.15279 + 0.728108i 0.261171 + 0.0309065i
556556 2.43666 1.40680i 0.103337 0.0596618i
557557 −4.44428 7.69772i −0.188310 0.326163i 0.756377 0.654136i 0.226968π-0.226968\pi
−0.944687 + 0.327973i 0.893634π0.893634\pi
558558 3.73928 + 3.42322i 0.158296 + 0.144917i
559559 21.7192i 0.918624i
560560 0 0
561561 −46.6674 5.09993i −1.97030 0.215319i
562562 3.41303 + 1.97051i 0.143970 + 0.0831211i
563563 −34.1282 + 19.7039i −1.43833 + 0.830421i −0.997734 0.0672831i 0.978567π-0.978567\pi
−0.440598 + 0.897704i 0.645234π0.645234\pi
564564 −12.9774 + 5.71379i −0.546447 + 0.240594i
565565 0.241922 27.0617i 0.0101777 1.13849i
566566 6.79378 0.285564
567567 0 0
568568 13.8407i 0.580744i
569569 −15.1146 8.72640i −0.633636 0.365830i 0.148523 0.988909i 0.452548π-0.452548\pi
−0.782159 + 0.623079i 0.785881π0.785881\pi
570570 −11.9462 + 15.9986i −0.500372 + 0.670107i
571571 9.69444 + 16.7913i 0.405700 + 0.702692i 0.994403 0.105657i 0.0336946π-0.0336946\pi
−0.588703 + 0.808349i 0.700361π0.700361\pi
572572 −12.0146 6.93665i −0.502357 0.290036i
573573 −1.55760 + 14.2529i −0.0650696 + 0.595425i
574574 0 0
575575 4.20531 6.99207i 0.175374 0.291590i
576576 −11.0787 + 12.1016i −0.461614 + 0.504234i
577577 20.8653 + 36.1397i 0.868633 + 1.50452i 0.863394 + 0.504531i 0.168335π0.168335\pi
0.00523985 + 0.999986i 0.498332π0.498332\pi
578578 12.4077 + 21.4907i 0.516092 + 0.893897i
579579 −22.2484 16.3052i −0.924610 0.677622i
580580 −7.68495 13.5899i −0.319100 0.564288i
581581 0 0
582582 22.6104 + 2.47093i 0.937232 + 0.102423i
583583 −5.34542 3.08618i −0.221385 0.127817i
584584 0.806229 + 1.39643i 0.0333620 + 0.0577847i
585585 −14.1474 13.1860i −0.584924 0.545175i
586586 0.0828353 + 0.0478250i 0.00342190 + 0.00197563i
587587 19.5477i 0.806820i −0.915019 0.403410i 0.867825π-0.867825\pi
0.915019 0.403410i 0.132175π-0.132175\pi
588588 0 0
589589 10.6760 0.439897
590590 0.0179095 2.00338i 0.000737323 0.0824780i
591591 −16.6626 37.8448i −0.685408 1.55673i
592592 −0.318968 + 0.184156i −0.0131095 + 0.00756877i
593593 −2.27890 1.31572i −0.0935832 0.0540303i 0.452478 0.891776i 0.350540π-0.350540\pi
−0.546061 + 0.837745i 0.683873π0.683873\pi
594594 −6.11973 + 18.0695i −0.251096 + 0.741401i
595595 0 0
596596 19.4983i 0.798683i
597597 −17.0820 12.5189i −0.699120 0.512366i
598598 2.12493 + 3.68048i 0.0868947 + 0.150506i
599599 −27.0326 + 15.6073i −1.10452 + 0.637697i −0.937405 0.348240i 0.886779π-0.886779\pi
−0.167118 + 0.985937i 0.553446π0.553446\pi
600600 −9.62804 22.9727i −0.393063 0.937857i
601601 15.6798i 0.639593i −0.947486 0.319797i 0.896385π-0.896385\pi
0.947486 0.319797i 0.103615π-0.103615\pi
602602 0 0
603603 −6.53806 + 29.5563i −0.266251 + 1.20363i
604604 −7.78305 + 13.4806i −0.316688 + 0.548519i
605605 −10.6322 6.26587i −0.432259 0.254744i
606606 −8.69897 19.7575i −0.353371 0.802592i
607607 −2.40692 + 4.16891i −0.0976940 + 0.169211i −0.910730 0.413003i 0.864480π-0.864480\pi
0.813036 + 0.582214i 0.197813π0.197813\pi
608608 31.6422i 1.28326i
609609 0 0
610610 6.12962 + 10.8394i 0.248181 + 0.438876i
611611 17.2636 + 9.96713i 0.698410 + 0.403227i
612612 −22.5870 + 7.13319i −0.913025 + 0.288342i
613613 34.7031 20.0359i 1.40165 0.809240i 0.407084 0.913391i 0.366546π-0.366546\pi
0.994562 + 0.104150i 0.0332123π0.0332123\pi
614614 −4.20626 + 7.28546i −0.169751 + 0.294017i
615615 32.4616 13.9474i 1.30898 0.562412i
616616 0 0
617617 −18.4205 −0.741583 −0.370791 0.928716i 0.620913π-0.620913\pi
−0.370791 + 0.928716i 0.620913π0.620913\pi
618618 −7.68912 + 10.4918i −0.309302 + 0.422040i
619619 9.54440 5.51046i 0.383622 0.221484i −0.295771 0.955259i 0.595577π-0.595577\pi
0.679393 + 0.733775i 0.262243π0.262243\pi
620620 −2.51452 + 4.26673i −0.100986 + 0.171356i
621621 −6.37123 + 5.59528i −0.255668 + 0.224531i
622622 −22.8674 −0.916899
623623 0 0
624624 1.14286 + 0.124895i 0.0457512 + 0.00499981i
625625 24.9840 + 0.893749i 0.999361 + 0.0357500i
626626 −3.45519 5.98457i −0.138097 0.239191i
627627 16.1892 + 36.7695i 0.646533 + 1.46843i
628628 1.88734 3.26897i 0.0753131 0.130446i
629629 −10.6680 −0.425362
630630 0 0
631631 16.0604 0.639355 0.319678 0.947526i 0.396425π-0.396425\pi
0.319678 + 0.947526i 0.396425π0.396425\pi
632632 5.46261 9.46152i 0.217291 0.376359i
633633 −13.1661 29.9033i −0.523305 1.18855i
634634 11.1772 + 19.3595i 0.443904 + 0.768865i
635635 49.8361 + 0.445517i 1.97769 + 0.0176798i
636636 −3.09588 0.338326i −0.122760 0.0134155i
637637 0 0
638638 21.6511 0.857177
639639 10.6482 + 9.74814i 0.421235 + 0.385631i
640640 −11.8447 6.98045i −0.468202 0.275926i
641641 34.4615 19.8964i 1.36115 0.785859i 0.371372 0.928484i 0.378888π-0.378888\pi
0.989777 + 0.142625i 0.0455542π0.0455542\pi
642642 −9.93057 + 13.5502i −0.391929 + 0.534784i
643643 −22.4164 −0.884016 −0.442008 0.897011i 0.645734π-0.645734\pi
−0.442008 + 0.897011i 0.645734π0.645734\pi
644644 0 0
645645 11.5182 + 26.8078i 0.453527 + 1.05556i
646646 17.1896 29.7733i 0.676317 1.17142i
647647 −22.1456 + 12.7858i −0.870633 + 0.502660i −0.867558 0.497335i 0.834312π-0.834312\pi
−0.00307433 + 0.999995i 0.500979π0.500979\pi
648648 2.28008 + 25.7853i 0.0895698 + 1.01294i
649649 −3.49116 2.01563i −0.137040 0.0791202i
650650 −6.71134 + 11.1588i −0.263240 + 0.437684i
651651 0 0
652652 22.8264i 0.893952i
653653 8.49921 14.7211i 0.332600 0.576080i −0.650421 0.759574i 0.725408π-0.725408\pi
0.983021 + 0.183494i 0.0587409π0.0587409\pi
654654 −0.338364 0.768506i −0.0132311 0.0300510i
655655 −0.219957 0.129627i −0.00859442 0.00506496i
656656 −1.05015 + 1.81891i −0.0410014 + 0.0710166i
657657 1.64216 + 0.363257i 0.0640667 + 0.0141720i
658658 0 0
659659 2.82840i 0.110179i −0.998481 0.0550894i 0.982456π-0.982456\pi
0.998481 0.0550894i 0.0175444π-0.0175444\pi
660660 −18.5082 2.19022i −0.720430 0.0852541i
661661 −12.6301 + 7.29200i −0.491254 + 0.283626i −0.725095 0.688649i 0.758204π-0.758204\pi
0.233840 + 0.972275i 0.424871π0.424871\pi
662662 7.38760 + 12.7957i 0.287127 + 0.497319i
663663 26.8589 + 19.6842i 1.04311 + 0.764469i
664664 11.5172i 0.446956i
665665 0 0
666666 −0.936361 + 4.23296i −0.0362833 + 0.164024i
667667 8.33391 + 4.81158i 0.322690 + 0.186305i
668668 −0.906326 + 0.523268i −0.0350668 + 0.0202458i
669669 13.4550 + 30.5595i 0.520199 + 1.18150i
670670 20.3808 + 0.182197i 0.787378 + 0.00703887i
671671 25.0563 0.967286
672672 0 0
673673 13.2666i 0.511390i −0.966757 0.255695i 0.917696π-0.917696\pi
0.966757 0.255695i 0.0823043π-0.0823043\pi
674674 −2.81051 1.62265i −0.108257 0.0625022i
675675 −24.4549 8.77269i −0.941268 0.337661i
676676 −2.77550 4.80730i −0.106750 0.184896i
677677 23.6762 + 13.6695i 0.909950 + 0.525360i 0.880415 0.474204i 0.157264π-0.157264\pi
0.0295351 + 0.999564i 0.490597π0.490597\pi
678678 18.8244 + 2.05718i 0.722946 + 0.0790055i
679679 0 0
680680 21.1115 + 37.3329i 0.809588 + 1.43165i
681681 16.0684 + 11.7761i 0.615742 + 0.451261i
682682 −3.43411 5.94806i −0.131499 0.227763i
683683 −2.53669 4.39367i −0.0970637 0.168119i 0.813404 0.581699i 0.197612π-0.197612\pi
−0.910468 + 0.413579i 0.864278π0.864278\pi
684684 14.9517 + 13.6879i 0.571692 + 0.523370i
685685 24.4153 13.8066i 0.932859 0.527524i
686686 0 0
687687 3.26900 29.9132i 0.124720 1.14126i
688688 −1.50211 0.867245i −0.0572675 0.0330634i
689689 2.18912 + 3.79167i 0.0833988 + 0.144451i
690690 4.57461 + 3.41588i 0.174152 + 0.130040i
691691 29.6673 + 17.1284i 1.12860 + 0.651596i 0.943582 0.331140i 0.107433π-0.107433\pi
0.185016 + 0.982736i 0.440766π0.440766\pi
692692 14.8189i 0.563329i
693693 0 0
694694 17.0991 0.649073
695695 −5.31358 0.0475014i −0.201556 0.00180183i
696696 26.8870 11.8380i 1.01915 0.448719i
697697 −52.6840 + 30.4171i −1.99555 + 1.15213i
698698 18.9125 + 10.9192i 0.715850 + 0.413296i
699699 −0.796935 0.0870911i −0.0301428 0.00329409i
700700 0 0
701701 17.6912i 0.668188i 0.942540 + 0.334094i 0.108430π0.108430\pi
−0.942540 + 0.334094i 0.891570π0.891570\pi
702702 10.1680 8.92961i 0.383765 0.337026i
703703 4.56484 + 7.90653i 0.172166 + 0.298200i
704704 19.2500 11.1140i 0.725511 0.418874i
705705 26.5940 + 3.14708i 1.00159 + 0.118526i
706706 29.0012i 1.09147i
707707 0 0
708708 −2.02196 0.220965i −0.0759900 0.00830439i
709709 −7.80875 + 13.5251i −0.293264 + 0.507948i −0.974579 0.224042i 0.928075π-0.928075\pi
0.681316 + 0.731990i 0.261408π0.261408\pi
710710 4.93513 8.37412i 0.185212 0.314275i
711711 −3.43172 10.8664i −0.128700 0.407522i
712712 −14.9720 + 25.9323i −0.561101 + 0.971856i
713713 3.05268i 0.114324i
714714 0 0
715715 12.8972 + 22.8071i 0.482328 + 0.852936i
716716 −12.4741 7.20195i −0.466181 0.269150i
717717 −27.4327 + 12.0783i −1.02449 + 0.451072i
718718 13.3518 7.70866i 0.498284 0.287685i
719719 −8.07179 + 13.9808i −0.301027 + 0.521394i −0.976369 0.216111i 0.930663π-0.930663\pi
0.675342 + 0.737505i 0.263996π0.263996\pi
720720 1.47686 0.451928i 0.0550393 0.0168424i
721721 0 0
722722 −12.2583 −0.456207
723723 5.97849 + 4.38147i 0.222342 + 0.162949i
724724 −16.5875 + 9.57678i −0.616468 + 0.355918i
725725 −0.527135 + 29.4807i −0.0195773 + 1.09488i
726726 5.10457 6.96515i 0.189448 0.258501i
727727 −16.8426 −0.624657 −0.312329 0.949974i 0.601109π-0.601109\pi
−0.312329 + 0.949974i 0.601109π0.601109\pi
728728 0 0
729729 21.4434 + 16.4067i 0.794201 + 0.607655i
730730 0.0101229 1.13236i 0.000374666 0.0419106i
731731 −25.1194 43.5081i −0.929075 1.60920i
732732 11.5705 5.09435i 0.427658 0.188292i
733733 11.0872 19.2035i 0.409514 0.709299i −0.585321 0.810801i 0.699032π-0.699032\pi
0.994835 + 0.101503i 0.0323650π0.0323650\pi
734734 14.1599 0.522651
735735 0 0
736736 9.04773 0.333504
737737 20.5053 35.5162i 0.755323 1.30826i
738738 7.44499 + 23.5743i 0.274054 + 0.867782i
739739 −21.2262 36.7649i −0.780820 1.35242i −0.931465 0.363831i 0.881468π-0.881468\pi
0.150645 0.988588i 0.451865π-0.451865\pi
740740 −4.23505 0.0378598i −0.155683 0.00139175i
741741 3.09588 28.3291i 0.113730 1.04070i
742742 0 0
743743 24.5486 0.900600 0.450300 0.892877i 0.351317π-0.351317\pi
0.450300 + 0.892877i 0.351317π0.351317\pi
744744 −7.51675 5.50883i −0.275577 0.201963i
745745 18.6967 31.7252i 0.684992 1.16232i
746746 −0.820444 + 0.473684i −0.0300386 + 0.0173428i
747747 8.86064 + 8.11171i 0.324194 + 0.296792i
748748 32.0904 1.17334
749749 0 0
750750 −2.36599 + 17.3323i −0.0863938 + 0.632887i
751751 −12.6883 + 21.9768i −0.463003 + 0.801944i −0.999109 0.0422062i 0.986561π-0.986561\pi
0.536106 + 0.844151i 0.319895π0.319895\pi
752752 −1.37867 + 0.795973i −0.0502748 + 0.0290261i
753753 −12.1544 27.6055i −0.442930 1.00600i
754754 −13.3002 7.67890i −0.484366 0.279649i
755755 25.5900 14.4709i 0.931314 0.526651i
756756 0 0
757757 18.9214i 0.687709i −0.939023 0.343854i 0.888267π-0.888267\pi
0.939023 0.343854i 0.111733π-0.111733\pi
758758 8.90625 15.4261i 0.323489 0.560300i
759759 10.5138 4.62910i 0.381627 0.168026i
760760 18.6355 31.6214i 0.675980 1.14703i
761761 5.12909 8.88384i 0.185929 0.322039i −0.757960 0.652301i 0.773804π-0.773804\pi
0.943889 + 0.330262i 0.107137π0.107137\pi
762762 −3.78845 + 34.6665i −0.137241 + 1.25583i
763763 0 0
764764 9.80090i 0.354584i
765765 43.5906 + 10.0521i 1.57602 + 0.363435i
766766 2.15836 1.24613i 0.0779846 0.0450244i
767767 1.42974 + 2.47639i 0.0516250 + 0.0894172i
768768 16.8856 23.0402i 0.609306 0.831393i
769769 17.8947i 0.645298i −0.946519 0.322649i 0.895427π-0.895427\pi
0.946519 0.322649i 0.104573π-0.104573\pi
770770 0 0
771771 −2.90074 + 26.5434i −0.104468 + 0.955939i
772772 16.3291 + 9.42764i 0.587699 + 0.339308i
773773 −8.93898 + 5.16092i −0.321513 + 0.185626i −0.652067 0.758162i 0.726098π-0.726098\pi
0.330554 + 0.943787i 0.392764π0.392764\pi
774774 −19.4684 + 6.14831i −0.699776 + 0.220996i
775775 8.18261 4.53114i 0.293928 0.162764i
776776 −41.8116 −1.50095
777777 0 0
778778 28.8187i 1.03320i
779779 45.0869 + 26.0309i 1.61541 + 0.932655i
780780 10.5927 + 7.90964i 0.379281 + 0.283211i
781781 −9.77915 16.9380i −0.349926 0.606089i
782782 −8.51334 4.91518i −0.304436 0.175766i
783783 9.82935 29.0228i 0.351272 1.03719i
784784 0 0
785785 −6.20540 + 3.50911i −0.221480 + 0.125245i
786786 0.105603 0.144094i 0.00376672 0.00513966i
787787 6.26338 + 10.8485i 0.223265 + 0.386707i 0.955798 0.294025i 0.0949950π-0.0949950\pi
−0.732532 + 0.680732i 0.761662π0.761662\pi
788788 14.1330 + 24.4791i 0.503468 + 0.872033i
789789 −6.35987 + 8.67800i −0.226417 + 0.308945i
790790 −6.67873 + 3.77677i −0.237619 + 0.134371i
791791 0 0
792792 7.57462 34.2422i 0.269152 1.21674i
793793 −15.3920 8.88657i −0.546586 0.315571i
794794 −8.50062 14.7235i −0.301676 0.522518i
795795 4.71281 + 3.51908i 0.167146 + 0.124809i
796796 12.5373 + 7.23842i 0.444373 + 0.256559i
797797 23.4184i 0.829521i 0.909931 + 0.414761i 0.136135π0.136135\pi
−0.909931 + 0.414761i 0.863865π0.863865\pi
798798 0 0
799799 −46.1100 −1.63126
800800 13.4297 + 24.2521i 0.474811 + 0.857442i
801801 9.40574 + 29.7829i 0.332336 + 1.05233i
802802 2.57316 1.48562i 0.0908615 0.0524589i
803803 −1.97329 1.13928i −0.0696360 0.0402044i
804804 2.24792 20.5698i 0.0792780 0.725440i
805805 0 0
806806 4.87184i 0.171603i
807807 6.13360 8.36925i 0.215913 0.294612i
808808 19.8420 + 34.3674i 0.698040 + 1.20904i
809809 −9.50469 + 5.48754i −0.334167 + 0.192932i −0.657690 0.753289i 0.728466π-0.728466\pi
0.323522 + 0.946220i 0.395133π0.395133\pi
810810 7.81464 16.4140i 0.274579 0.576730i
811811 35.5390i 1.24794i −0.781448 0.623971i 0.785518π-0.785518\pi
0.781448 0.623971i 0.214482π-0.214482\pi
812812 0 0
813813 1.17511 10.7529i 0.0412127 0.377121i
814814 2.93671 5.08653i 0.102932 0.178283i
815815 −21.8879 + 37.1402i −0.766700 + 1.30097i
816816 −2.43384 + 1.07159i −0.0852015 + 0.0375132i
817817 −21.4972 + 37.2342i −0.752090 + 1.30266i
818818 3.74808i 0.131048i
819819 0 0
820820 −21.0227 + 11.8882i −0.734146 + 0.415154i
821821 −39.5091 22.8106i −1.37888 0.796094i −0.386851 0.922142i 0.626437π-0.626437\pi
−0.992024 + 0.126048i 0.959771π0.959771\pi
822822 7.90860 + 17.9623i 0.275844 + 0.626509i
823823 12.0190 6.93918i 0.418956 0.241885i −0.275674 0.961251i 0.588901π-0.588901\pi
0.694631 + 0.719366i 0.255568π0.255568\pi
824824 11.9558 20.7081i 0.416501 0.721400i
825825 28.0140 + 21.3109i 0.975321 + 0.741949i
826826 0 0
827827 12.3739 0.430283 0.215141 0.976583i 0.430979π-0.430979\pi
0.215141 + 0.976583i 0.430979π0.430979\pi
828828 3.91390 4.27526i 0.136017 0.148576i
829829 −9.24010 + 5.33478i −0.320922 + 0.185284i −0.651803 0.758388i 0.725987π-0.725987\pi
0.330881 + 0.943672i 0.392654π0.392654\pi
830830 4.10666 6.96834i 0.142544 0.241875i
831831 −12.1602 8.91187i −0.421832 0.309149i
832832 −15.7670 −0.546621
833833 0 0
834834 0.403928 3.69618i 0.0139869 0.127988i
835835 1.97641 + 0.0176684i 0.0683965 + 0.000611440i
836836 −13.7315 23.7836i −0.474912 0.822572i
837837 −9.53226 + 1.90299i −0.329483 + 0.0657771i
838838 −10.2182 + 17.6984i −0.352981 + 0.611381i
839839 −17.5497 −0.605883 −0.302941 0.953009i 0.597969π-0.597969\pi
−0.302941 + 0.953009i 0.597969π0.597969\pi
840840 0 0
841841 −5.77548 −0.199154
842842 −14.4188 + 24.9740i −0.496903 + 0.860662i
843843 −6.91583 + 3.04496i −0.238194 + 0.104874i
844844 11.1673 + 19.3424i 0.384395 + 0.665791i
845845 −0.0937160 + 10.4832i −0.00322393 + 0.360633i
846846 −4.04721 + 18.2960i −0.139146 + 0.629030i
847847 0 0
848848 −0.349645 −0.0120069
849849 −7.70015 + 10.5068i −0.264268 + 0.360592i
850850 0.538484 30.1154i 0.0184698 1.03295i
851851 2.26078 1.30526i 0.0774986 0.0447438i
852852 −7.95960 5.83337i −0.272691 0.199848i
853853 29.6157 1.01402 0.507011 0.861940i 0.330750π-0.330750\pi
0.507011 + 0.861940i 0.330750π0.330750\pi
854854 0 0
855855 −11.2023 36.6082i −0.383112 1.25197i
856856 15.4410 26.7447i 0.527764 0.914114i
857857 38.6264 22.3010i 1.31945 0.761787i 0.335812 0.941929i 0.390989π-0.390989\pi
0.983641 + 0.180142i 0.0576558π0.0576558\pi
858858 −16.7792 + 7.38768i −0.572832 + 0.252211i
859859 5.57093 + 3.21638i 0.190078 + 0.109741i 0.592019 0.805924i 0.298331π-0.298331\pi
−0.401941 + 0.915665i 0.631664π0.631664\pi
860860 −9.81763 17.3612i −0.334778 0.592013i
861861 0 0
862862 22.6239i 0.770573i
863863 −26.6755 + 46.2033i −0.908045 + 1.57278i −0.0912683 + 0.995826i 0.529092π0.529092\pi
−0.816777 + 0.576954i 0.804241π0.804241\pi
864864 −5.64021 28.2523i −0.191884 0.961162i
865865 14.2096 24.1114i 0.483140 0.819811i
866866 2.30451 3.99152i 0.0783104 0.135638i
867867 −47.2991 5.16897i −1.60636 0.175547i
868868 0 0
869869 15.4384i 0.523713i
870870 −20.4886 2.42458i −0.694630 0.0822010i
871871 −25.1927 + 14.5450i −0.853623 + 0.492839i
872872 0.771796 + 1.33679i 0.0261363 + 0.0452694i
873873 −29.4483 + 32.1671i −0.996673 + 1.08869i
874874 8.41281i 0.284567i
875875 0 0
876876 −1.14286 0.124895i −0.0386138 0.00421982i
877877 −30.7320 17.7431i −1.03774 0.599142i −0.118551 0.992948i 0.537825π-0.537825\pi
−0.919194 + 0.393806i 0.871158π0.871158\pi
878878 8.83075 5.09844i 0.298023 0.172064i
879879 −0.167849 + 0.0739020i −0.00566141 + 0.00249265i
880880 −2.09233 0.0187047i −0.0705326 0.000630535i
881881 −25.0114 −0.842655 −0.421327 0.906909i 0.638436π-0.638436\pi
−0.421327 + 0.906909i 0.638436π0.638436\pi
882882 0 0
883883 30.1344i 1.01410i 0.861916 + 0.507051i 0.169264π0.169264\pi
−0.861916 + 0.507051i 0.830736π0.830736\pi
884884 −19.7130 11.3813i −0.663021 0.382796i
885885 3.07800 + 2.29836i 0.103466 + 0.0772584i
886886 9.89976 + 17.1469i 0.332589 + 0.576061i
887887 7.84535 + 4.52951i 0.263421 + 0.152086i 0.625894 0.779908i 0.284734π-0.284734\pi
−0.362473 + 0.931994i 0.618068π0.618068\pi
888888 0.865767 7.92227i 0.0290532 0.265854i
889889 0 0
890890 18.3052 10.3515i 0.613592 0.346982i
891891 −21.0089 29.9445i −0.703825 1.00318i
892892 −11.4123 19.7668i −0.382113 0.661840i
893893 19.7305 + 34.1742i 0.660255 + 1.14359i
894894 20.7832 + 15.2315i 0.695095 + 0.509416i
895895 13.3905 + 23.6794i 0.447595 + 0.791514i
896896 0 0
897897 −8.10039 0.885232i −0.270464 0.0295570i
898898 0.351569 + 0.202979i 0.0117320 + 0.00677349i
899899 5.51578 + 9.55361i 0.183962 + 0.318631i
900900 17.2692 + 4.14524i 0.575638 + 0.138175i
901901 −8.77052 5.06366i −0.292188 0.168695i
902902 33.4931i 1.11520i
903903 0 0
904904 −34.8104 −1.15778
905905 36.1720 + 0.323365i 1.20240 + 0.0107490i
906906 8.28912 + 18.8266i 0.275387 + 0.625471i
907907 −8.21292 + 4.74173i −0.272705 + 0.157447i −0.630116 0.776501i 0.716993π-0.716993\pi
0.357411 + 0.933947i 0.383660π0.383660\pi
908908 −11.7934 6.80891i −0.391377 0.225962i
909909 40.4150 + 8.94009i 1.34048 + 0.296524i
910910 0 0
911911 56.8415i 1.88324i −0.336672 0.941622i 0.609301π-0.609301\pi
0.336672 0.941622i 0.390699π-0.390699\pi
912912 1.83564 + 1.34529i 0.0607842 + 0.0445471i
913913 −8.13751 14.0946i −0.269312 0.466463i
914914 7.26995 4.19731i 0.240469 0.138835i
915915 −23.7109 2.80590i −0.783859 0.0927602i
916916 20.5695i 0.679637i
917917 0 0
918918 −10.0410 + 29.6476i −0.331402 + 0.978518i
919919 28.6839 49.6820i 0.946195 1.63886i 0.192853 0.981228i 0.438226π-0.438226\pi
0.753341 0.657630i 0.228441π-0.228441\pi
920920 −9.04177 5.32860i −0.298098 0.175679i
921921 −6.49977 14.7625i −0.214175 0.486442i
922922 9.42488 16.3244i 0.310392 0.537615i
923923 13.8733i 0.456645i
924924 0 0
925925 6.85442 + 4.12252i 0.225372 + 0.135548i
926926 1.91897 + 1.10792i 0.0630613 + 0.0364084i
927927 −7.51088 23.7829i −0.246690 0.781134i
928928 −28.3156 + 16.3480i −0.929504 + 0.536649i
929929 5.14668 8.91430i 0.168857 0.292469i −0.769161 0.639055i 0.779326π-0.779326\pi
0.938018 + 0.346586i 0.112659π0.112659\pi
930930 2.58364 + 6.01326i 0.0847208 + 0.197182i
931931 0 0
932932 0.548005 0.0179505
933933 25.9182 35.3651i 0.848522 1.15780i
934934 −6.24283 + 3.60430i −0.204271 + 0.117936i
935935 −52.2134 30.7710i −1.70756 1.00632i
936936 −16.7976 + 18.3485i −0.549046 + 0.599738i
937937 29.0347 0.948522 0.474261 0.880384i 0.342715π-0.342715\pi
0.474261 + 0.880384i 0.342715π0.342715\pi
938938 0 0
939939 13.1715 + 1.43941i 0.429835 + 0.0469735i
940940 −18.3050 0.163640i −0.597044 0.00533735i
941941 −7.48583 12.9658i −0.244031 0.422674i 0.717828 0.696221i 0.245137π-0.245137\pi
−0.961859 + 0.273546i 0.911803π0.911803\pi
942942 −2.01006 4.56532i −0.0654912 0.148746i
943943 7.44325 12.8921i 0.242386 0.419824i
944944 −0.228358 −0.00743242
945945 0 0
946946 27.6596 0.899292
947947 −7.25429 + 12.5648i −0.235733 + 0.408301i −0.959485 0.281758i 0.909082π-0.909082\pi
0.723753 + 0.690059i 0.242416π0.242416\pi
948948 3.13888 + 7.12916i 0.101946 + 0.231544i
949949 0.808126 + 1.39972i 0.0262329 + 0.0454367i
950950 −22.5502 + 12.4873i −0.731626 + 0.405140i
951951 −42.6085 4.65637i −1.38167 0.150993i
952952 0 0
953953 −34.9591 −1.13244 −0.566218 0.824256i 0.691594π-0.691594\pi
−0.566218 + 0.824256i 0.691594π0.691594\pi
954954 −2.77903 + 3.03561i −0.0899743 + 0.0982813i
955955 −9.39793 + 15.9468i −0.304110 + 0.516025i
956956 17.7443 10.2447i 0.573891 0.331336i
957957 −24.5396 + 33.4842i −0.793254 + 1.08239i
958958 12.5500 0.405473
959959 0 0
960960 −19.4610 + 8.36156i −0.628101 + 0.269868i
961961 −13.7503 + 23.8162i −0.443557 + 0.768264i
962962 −3.60802 + 2.08309i −0.116327 + 0.0671616i
963963 −9.70038 30.7159i −0.312590 0.989805i
964964 −4.38790 2.53336i −0.141325 0.0815939i
965965 −17.5287 30.9972i −0.564268 0.997836i
966966 0 0
967967 46.6810i 1.50116i −0.660779 0.750581i 0.729774π-0.729774\pi
0.660779 0.750581i 0.270226π-0.270226\pi
968968 −7.93709 + 13.7474i −0.255108 + 0.441860i
969969 26.5624 + 60.3297i 0.853308 + 1.93807i
970970 25.2975 + 14.9086i 0.812253 + 0.478686i
971971 0.656690 1.13742i 0.0210742 0.0365016i −0.855296 0.518140i 0.826625π-0.826625\pi
0.876370 + 0.481638i 0.159958π0.159958\pi
972972 −15.7897 9.55635i −0.506456 0.306520i
973973 0 0
974974 23.9482i 0.767350i
975975 −9.65070 23.0268i −0.309070 0.737447i
976976 1.22920 0.709680i 0.0393458 0.0227163i
977977 −26.5376 45.9645i −0.849013 1.47053i −0.882090 0.471081i 0.843864π-0.843864\pi
0.0330769 0.999453i 0.489469π-0.489469\pi
978978 −24.3306 17.8313i −0.778008 0.570181i
979979 42.3140i 1.35236i
980980 0 0
981981 1.57202 + 0.347743i 0.0501908 + 0.0111026i
982982 −1.99186 1.15000i −0.0635629 0.0366980i
983983 18.2849 10.5568i 0.583198 0.336709i −0.179206 0.983812i 0.557353π-0.557353\pi
0.762403 + 0.647102i 0.224019π0.224019\pi
984984 −18.3128 41.5927i −0.583789 1.32593i
985985 0.477209 53.3812i 0.0152051 1.70087i
986986 35.5242 1.13132
987987 0 0
988988 19.4803i 0.619750i
989989 10.6467 + 6.14686i 0.338545 + 0.195459i
990990 −16.7925 + 18.0169i −0.533702 + 0.572614i
991991 26.8174 + 46.4491i 0.851883 + 1.47551i 0.879507 + 0.475887i 0.157873π0.157873\pi
−0.0276234 + 0.999618i 0.508794π0.508794\pi
992992 8.98233 + 5.18595i 0.285189 + 0.164654i
993993 −28.1621 3.07763i −0.893698 0.0976657i
994994 0 0
995995 −13.4583 23.7993i −0.426657 0.754488i
996996 −6.62340 4.85411i −0.209871 0.153808i
997997 19.4435 + 33.6771i 0.615781 + 1.06656i 0.990247 + 0.139323i 0.0444927π0.0444927\pi
−0.374466 + 0.927241i 0.622174π0.622174\pi
998998 −13.3918 23.1953i −0.423910 0.734234i
999999 −5.48513 6.24580i −0.173542 0.197608i
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 735.2.p.g.509.10 64
3.2 odd 2 inner 735.2.p.g.509.21 64
5.4 even 2 inner 735.2.p.g.509.23 64
7.2 even 3 735.2.g.c.734.24 yes 32
7.3 odd 6 inner 735.2.p.g.374.12 64
7.4 even 3 inner 735.2.p.g.374.9 64
7.5 odd 6 735.2.g.c.734.21 yes 32
7.6 odd 2 inner 735.2.p.g.509.11 64
15.14 odd 2 inner 735.2.p.g.509.12 64
21.2 odd 6 735.2.g.c.734.11 yes 32
21.5 even 6 735.2.g.c.734.10 yes 32
21.11 odd 6 inner 735.2.p.g.374.22 64
21.17 even 6 inner 735.2.p.g.374.23 64
21.20 even 2 inner 735.2.p.g.509.24 64
35.4 even 6 inner 735.2.p.g.374.24 64
35.9 even 6 735.2.g.c.734.9 32
35.19 odd 6 735.2.g.c.734.12 yes 32
35.24 odd 6 inner 735.2.p.g.374.21 64
35.34 odd 2 inner 735.2.p.g.509.22 64
105.44 odd 6 735.2.g.c.734.22 yes 32
105.59 even 6 inner 735.2.p.g.374.10 64
105.74 odd 6 inner 735.2.p.g.374.11 64
105.89 even 6 735.2.g.c.734.23 yes 32
105.104 even 2 inner 735.2.p.g.509.9 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
735.2.g.c.734.9 32 35.9 even 6
735.2.g.c.734.10 yes 32 21.5 even 6
735.2.g.c.734.11 yes 32 21.2 odd 6
735.2.g.c.734.12 yes 32 35.19 odd 6
735.2.g.c.734.21 yes 32 7.5 odd 6
735.2.g.c.734.22 yes 32 105.44 odd 6
735.2.g.c.734.23 yes 32 105.89 even 6
735.2.g.c.734.24 yes 32 7.2 even 3
735.2.p.g.374.9 64 7.4 even 3 inner
735.2.p.g.374.10 64 105.59 even 6 inner
735.2.p.g.374.11 64 105.74 odd 6 inner
735.2.p.g.374.12 64 7.3 odd 6 inner
735.2.p.g.374.21 64 35.24 odd 6 inner
735.2.p.g.374.22 64 21.11 odd 6 inner
735.2.p.g.374.23 64 21.17 even 6 inner
735.2.p.g.374.24 64 35.4 even 6 inner
735.2.p.g.509.9 64 105.104 even 2 inner
735.2.p.g.509.10 64 1.1 even 1 trivial
735.2.p.g.509.11 64 7.6 odd 2 inner
735.2.p.g.509.12 64 15.14 odd 2 inner
735.2.p.g.509.21 64 3.2 odd 2 inner
735.2.p.g.509.22 64 35.34 odd 2 inner
735.2.p.g.509.23 64 5.4 even 2 inner
735.2.p.g.509.24 64 21.20 even 2 inner