Properties

Label 16.4.e.a.13.1
Level 1616
Weight 44
Character 16.13
Analytic conductor 0.9440.944
Analytic rank 00
Dimension 1010
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [16,4,Mod(5,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.5");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 16=24 16 = 2^{4}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 16.e (of order 44, degree 22, 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: 0.9440305600920.944030560092
Analytic rank: 00
Dimension: 1010
Relative dimension: 55 over Q(i)\Q(i)
Coefficient field: Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x102x9x8+6x7+14x680x5+56x4+96x364x2512x+1024 x^{10} - 2x^{9} - x^{8} + 6x^{7} + 14x^{6} - 80x^{5} + 56x^{4} + 96x^{3} - 64x^{2} - 512x + 1024 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 210 2^{10}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 13.1
Root 1.28199+1.53509i1.28199 + 1.53509i of defining polynomial
Character χ\chi == 16.13
Dual form 16.4.e.a.5.1

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+(2.81708+0.253099i)q2+(5.49618+5.49618i)q3+(7.871881.42600i)q4+(4.66372+4.66372i)q5+(16.874314.0921i)q624.8965iq7+(21.8148+6.00953i)q8+33.4160iq9+(11.957714.3185i)q10+(22.343122.3431i)q11+(51.1028+35.4277i)q12+(11.271411.2714i)q13+(6.30129+70.1355i)q1451.2653q15+(59.933022.4506i)q1688.4846q17+(8.4575694.1356i)q18+(37.8187+37.8187i)q19+(30.0618+43.3627i)q20+(136.836136.836i)q21+(57.2873+68.5974i)q22+48.1224iq23+(152.92886.8686i)q24+81.4994iq25+(34.6053+28.8997i)q26+(35.2635+35.2635i)q27+(35.5025195.982i)q28+(10.4432+10.4432i)q29+(144.41912.9752i)q3096.9578q31+(163.154+78.4142i)q32+245.604q33+(249.26822.3954i)q34+(116.110+116.110i)q35+(47.6513+263.047i)q36+(163.279+163.279i)q37+(116.11096.9665i)q38123.899iq39+(73.7114129.765i)q40360.519iq41+(350.844+420.110i)q42+(100.249+100.249i)q43+(144.021207.744i)q44+(155.843155.843i)q45+(12.1797135.565i)q46+220.669q47+(452.796+206.010i)q48276.837q49+(20.6274229.590i)q50+(486.327486.327i)q51+(104.80072.6542i)q52+(175.752+175.752i)q53+(90.4150108.265i)q54+208.404iq55+(149.616+543.113i)q56+415.717iq57+(32.062426.7761i)q58+(405.008405.008i)q59+(403.555+73.1044i)q60+(664.576+664.576i)q61+(273.13824.5399i)q62+831.942q63+(439.771262.193i)q64+105.133q65+(691.885+62.1621i)q66+(107.377107.377i)q67+(696.540+126.179i)q68+(264.489+264.489i)q69+(356.480297.705i)q70+215.050iq71+(200.814728.964i)q72668.587iq73+(418.644501.296i)q74+(447.935+447.935i)q75+(351.634+243.775i)q76+(556.266556.266i)q77+(31.3588+349.035i)q78822.956q79+(174.808+384.215i)q80+514.603q81+(91.2471+1015.61i)q82+(326.873+326.873i)q83+(882.0271272.28i)q84+(412.668412.668i)q85+(257.037307.783i)q86+114.795iq87+(353.139+621.682i)q88262.733iq89+(478.466+399.578i)q90+(280.619+280.619i)q91+(68.6226+378.814i)q92+(532.898532.898i)q93+(621.643+55.8512i)q94352.752q95+(1327.70465.745i)q96150.801q97+(779.87170.0671i)q98+(746.618+746.618i)q99+O(q100)q+(-2.81708 + 0.253099i) q^{2} +(5.49618 + 5.49618i) q^{3} +(7.87188 - 1.42600i) q^{4} +(-4.66372 + 4.66372i) q^{5} +(-16.8743 - 14.0921i) q^{6} -24.8965i q^{7} +(-21.8148 + 6.00953i) q^{8} +33.4160i q^{9} +(11.9577 - 14.3185i) q^{10} +(22.3431 - 22.3431i) q^{11} +(51.1028 + 35.4277i) q^{12} +(-11.2714 - 11.2714i) q^{13} +(6.30129 + 70.1355i) q^{14} -51.2653 q^{15} +(59.9330 - 22.4506i) q^{16} -88.4846 q^{17} +(-8.45756 - 94.1356i) q^{18} +(37.8187 + 37.8187i) q^{19} +(-30.0618 + 43.3627i) q^{20} +(136.836 - 136.836i) q^{21} +(-57.2873 + 68.5974i) q^{22} +48.1224i q^{23} +(-152.928 - 86.8686i) q^{24} +81.4994i q^{25} +(34.6053 + 28.8997i) q^{26} +(-35.2635 + 35.2635i) q^{27} +(-35.5025 - 195.982i) q^{28} +(10.4432 + 10.4432i) q^{29} +(144.419 - 12.9752i) q^{30} -96.9578 q^{31} +(-163.154 + 78.4142i) q^{32} +245.604 q^{33} +(249.268 - 22.3954i) q^{34} +(116.110 + 116.110i) q^{35} +(47.6513 + 263.047i) q^{36} +(-163.279 + 163.279i) q^{37} +(-116.110 - 96.9665i) q^{38} -123.899i q^{39} +(73.7114 - 129.765i) q^{40} -360.519i q^{41} +(-350.844 + 420.110i) q^{42} +(-100.249 + 100.249i) q^{43} +(144.021 - 207.744i) q^{44} +(-155.843 - 155.843i) q^{45} +(-12.1797 - 135.565i) q^{46} +220.669 q^{47} +(452.796 + 206.010i) q^{48} -276.837 q^{49} +(-20.6274 - 229.590i) q^{50} +(-486.327 - 486.327i) q^{51} +(-104.800 - 72.6542i) q^{52} +(-175.752 + 175.752i) q^{53} +(90.4150 - 108.265i) q^{54} +208.404i q^{55} +(149.616 + 543.113i) q^{56} +415.717i q^{57} +(-32.0624 - 26.7761i) q^{58} +(405.008 - 405.008i) q^{59} +(-403.555 + 73.1044i) q^{60} +(664.576 + 664.576i) q^{61} +(273.138 - 24.5399i) q^{62} +831.942 q^{63} +(439.771 - 262.193i) q^{64} +105.133 q^{65} +(-691.885 + 62.1621i) q^{66} +(-107.377 - 107.377i) q^{67} +(-696.540 + 126.179i) q^{68} +(-264.489 + 264.489i) q^{69} +(-356.480 - 297.705i) q^{70} +215.050i q^{71} +(-200.814 - 728.964i) q^{72} -668.587i q^{73} +(418.644 - 501.296i) q^{74} +(-447.935 + 447.935i) q^{75} +(351.634 + 243.775i) q^{76} +(-556.266 - 556.266i) q^{77} +(31.3588 + 349.035i) q^{78} -822.956 q^{79} +(-174.808 + 384.215i) q^{80} +514.603 q^{81} +(91.2471 + 1015.61i) q^{82} +(326.873 + 326.873i) q^{83} +(882.027 - 1272.28i) q^{84} +(412.668 - 412.668i) q^{85} +(257.037 - 307.783i) q^{86} +114.795i q^{87} +(-353.139 + 621.682i) q^{88} -262.733i q^{89} +(478.466 + 399.578i) q^{90} +(-280.619 + 280.619i) q^{91} +(68.6226 + 378.814i) q^{92} +(-532.898 - 532.898i) q^{93} +(-621.643 + 55.8512i) q^{94} -352.752 q^{95} +(-1327.70 - 465.745i) q^{96} -150.801 q^{97} +(779.871 - 70.0671i) q^{98} +(746.618 + 746.618i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q2q22q3+8q42q532q644q868q10+18q11+100q122q13+188q14124q15+280q164q17+174q1826q19196q20++4958q99+O(q100) 10 q - 2 q^{2} - 2 q^{3} + 8 q^{4} - 2 q^{5} - 32 q^{6} - 44 q^{8} - 68 q^{10} + 18 q^{11} + 100 q^{12} - 2 q^{13} + 188 q^{14} - 124 q^{15} + 280 q^{16} - 4 q^{17} + 174 q^{18} - 26 q^{19} - 196 q^{20}+ \cdots + 4958 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/16Z)×\left(\mathbb{Z}/16\mathbb{Z}\right)^\times.

nn 55 1515
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −2.81708 + 0.253099i −0.995988 + 0.0894841i
33 5.49618 + 5.49618i 1.05774 + 1.05774i 0.998228 + 0.0595129i 0.0189548π0.0189548\pi
0.0595129 + 0.998228i 0.481045π0.481045\pi
44 7.87188 1.42600i 0.983985 0.178250i
55 −4.66372 + 4.66372i −0.417136 + 0.417136i −0.884215 0.467079i 0.845306π-0.845306\pi
0.467079 + 0.884215i 0.345306π0.345306\pi
66 −16.8743 14.0921i −1.14815 0.958846i
77 24.8965i 1.34429i −0.740422 0.672143i 0.765374π-0.765374\pi
0.740422 0.672143i 0.234626π-0.234626\pi
88 −21.8148 + 6.00953i −0.964087 + 0.265586i
99 33.4160i 1.23763i
1010 11.9577 14.3185i 0.378136 0.452790i
1111 22.3431 22.3431i 0.612427 0.612427i −0.331151 0.943578i 0.607437π-0.607437\pi
0.943578 + 0.331151i 0.107437π0.107437\pi
1212 51.1028 + 35.4277i 1.22934 + 0.852259i
1313 −11.2714 11.2714i −0.240471 0.240471i 0.576574 0.817045i 0.304389π-0.304389\pi
−0.817045 + 0.576574i 0.804389π0.804389\pi
1414 6.30129 + 70.1355i 0.120292 + 1.33889i
1515 −51.2653 −0.882443
1616 59.9330 22.4506i 0.936454 0.350791i
1717 −88.4846 −1.26239 −0.631196 0.775623i 0.717436π-0.717436\pi
−0.631196 + 0.775623i 0.717436π0.717436\pi
1818 −8.45756 94.1356i −0.110748 1.23266i
1919 37.8187 + 37.8187i 0.456643 + 0.456643i 0.897552 0.440909i 0.145344π-0.145344\pi
−0.440909 + 0.897552i 0.645344π0.645344\pi
2020 −30.0618 + 43.3627i −0.336101 + 0.484810i
2121 136.836 136.836i 1.42191 1.42191i
2222 −57.2873 + 68.5974i −0.555168 + 0.664773i
2323 48.1224i 0.436270i 0.975919 + 0.218135i 0.0699973π0.0699973\pi
−0.975919 + 0.218135i 0.930003π0.930003\pi
2424 −152.928 86.8686i −1.30068 0.738833i
2525 81.4994i 0.651995i
2626 34.6053 + 28.8997i 0.261025 + 0.217988i
2727 −35.2635 + 35.2635i −0.251351 + 0.251351i
2828 −35.5025 195.982i −0.239619 1.32276i
2929 10.4432 + 10.4432i 0.0668705 + 0.0668705i 0.739751 0.672881i 0.234943π-0.234943\pi
−0.672881 + 0.739751i 0.734943π0.734943\pi
3030 144.419 12.9752i 0.878903 0.0789646i
3131 −96.9578 −0.561746 −0.280873 0.959745i 0.590624π-0.590624\pi
−0.280873 + 0.959745i 0.590624π0.590624\pi
3232 −163.154 + 78.4142i −0.901307 + 0.433181i
3333 245.604 1.29558
3434 249.268 22.3954i 1.25733 0.112964i
3535 116.110 + 116.110i 0.560750 + 0.560750i
3636 47.6513 + 263.047i 0.220608 + 1.21781i
3737 −163.279 + 163.279i −0.725484 + 0.725484i −0.969717 0.244233i 0.921464π-0.921464\pi
0.244233 + 0.969717i 0.421464π0.421464\pi
3838 −116.110 96.9665i −0.495673 0.413949i
3939 123.899i 0.508713i
4040 73.7114 129.765i 0.291370 0.512941i
4141 360.519i 1.37326i −0.727008 0.686629i 0.759090π-0.759090\pi
0.727008 0.686629i 0.240910π-0.240910\pi
4242 −350.844 + 420.110i −1.28896 + 1.54344i
4343 −100.249 + 100.249i −0.355531 + 0.355531i −0.862163 0.506632i 0.830890π-0.830890\pi
0.506632 + 0.862163i 0.330890π0.330890\pi
4444 144.021 207.744i 0.493454 0.711785i
4545 −155.843 155.843i −0.516260 0.516260i
4646 −12.1797 135.565i −0.0390392 0.434520i
4747 220.669 0.684849 0.342425 0.939545i 0.388752π-0.388752\pi
0.342425 + 0.939545i 0.388752π0.388752\pi
4848 452.796 + 206.010i 1.36157 + 0.619479i
4949 −276.837 −0.807104
5050 −20.6274 229.590i −0.0583432 0.649379i
5151 −486.327 486.327i −1.33528 1.33528i
5252 −104.800 72.6542i −0.279484 0.193756i
5353 −175.752 + 175.752i −0.455498 + 0.455498i −0.897174 0.441676i 0.854384π-0.854384\pi
0.441676 + 0.897174i 0.354384π0.354384\pi
5454 90.4150 108.265i 0.227850 0.272834i
5555 208.404i 0.510931i
5656 149.616 + 543.113i 0.357024 + 1.29601i
5757 415.717i 0.966019i
5858 −32.0624 26.7761i −0.0725861 0.0606184i
5959 405.008 405.008i 0.893687 0.893687i −0.101181 0.994868i 0.532262π-0.532262\pi
0.994868 + 0.101181i 0.0322622π0.0322622\pi
6060 −403.555 + 73.1044i −0.868311 + 0.157296i
6161 664.576 + 664.576i 1.39492 + 1.39492i 0.813860 + 0.581061i 0.197362π0.197362\pi
0.581061 + 0.813860i 0.302638π0.302638\pi
6262 273.138 24.5399i 0.559493 0.0502674i
6363 831.942 1.66373
6464 439.771 262.193i 0.858928 0.512096i
6565 105.133 0.200619
6666 −691.885 + 62.1621i −1.29038 + 0.115934i
6767 −107.377 107.377i −0.195794 0.195794i 0.602400 0.798194i 0.294211π-0.294211\pi
−0.798194 + 0.602400i 0.794211π0.794211\pi
6868 −696.540 + 126.179i −1.24218 + 0.225022i
6969 −264.489 + 264.489i −0.461461 + 0.461461i
7070 −356.480 297.705i −0.608679 0.508322i
7171 215.050i 0.359461i 0.983716 + 0.179731i 0.0575226π0.0575226\pi
−0.983716 + 0.179731i 0.942477π0.942477\pi
7272 −200.814 728.964i −0.328697 1.19318i
7373 668.587i 1.07195i −0.844235 0.535974i 0.819945π-0.819945\pi
0.844235 0.535974i 0.180055π-0.180055\pi
7474 418.644 501.296i 0.657654 0.787492i
7575 −447.935 + 447.935i −0.689642 + 0.689642i
7676 351.634 + 243.775i 0.530726 + 0.367933i
7777 −556.266 556.266i −0.823277 0.823277i
7878 31.3588 + 349.035i 0.0455217 + 0.506672i
7979 −822.956 −1.17202 −0.586012 0.810303i 0.699303π-0.699303\pi
−0.586012 + 0.810303i 0.699303π0.699303\pi
8080 −174.808 + 384.215i −0.244301 + 0.536956i
8181 514.603 0.705902
8282 91.2471 + 1015.61i 0.122885 + 1.36775i
8383 326.873 + 326.873i 0.432277 + 0.432277i 0.889402 0.457125i 0.151121π-0.151121\pi
−0.457125 + 0.889402i 0.651121π0.651121\pi
8484 882.027 1272.28i 1.14568 1.65259i
8585 412.668 412.668i 0.526589 0.526589i
8686 257.037 307.783i 0.322290 0.385919i
8787 114.795i 0.141463i
8888 −353.139 + 621.682i −0.427781 + 0.753086i
8989 262.733i 0.312918i −0.987684 0.156459i 0.949992π-0.949992\pi
0.987684 0.156459i 0.0500079π-0.0500079\pi
9090 478.466 + 399.578i 0.560386 + 0.467992i
9191 −280.619 + 280.619i −0.323262 + 0.323262i
9292 68.6226 + 378.814i 0.0777652 + 0.429283i
9393 −532.898 532.898i −0.594182 0.594182i
9494 −621.643 + 55.8512i −0.682102 + 0.0612831i
9595 −352.752 −0.380964
9696 −1327.70 465.745i −1.41154 0.495155i
9797 −150.801 −0.157850 −0.0789251 0.996881i 0.525149π-0.525149\pi
−0.0789251 + 0.996881i 0.525149π0.525149\pi
9898 779.871 70.0671i 0.803866 0.0722229i
9999 746.618 + 746.618i 0.757958 + 0.757958i
100100 116.218 + 641.553i 0.116218 + 0.641553i
101101 487.985 487.985i 0.480755 0.480755i −0.424617 0.905373i 0.639591π-0.639591\pi
0.905373 + 0.424617i 0.139591π0.139591\pi
102102 1493.11 + 1246.93i 1.44941 + 1.21044i
103103 1840.58i 1.76075i −0.474275 0.880377i 0.657290π-0.657290\pi
0.474275 0.880377i 0.342710π-0.342710\pi
104104 313.620 + 178.148i 0.295701 + 0.167970i
105105 1276.33i 1.18626i
106106 450.625 539.590i 0.412911 0.494431i
107107 −79.4098 + 79.4098i −0.0717461 + 0.0717461i −0.742069 0.670323i 0.766155π-0.766155\pi
0.670323 + 0.742069i 0.266155π0.266155\pi
108108 −227.304 + 327.876i −0.202522 + 0.292129i
109109 952.979 + 952.979i 0.837421 + 0.837421i 0.988519 0.151098i 0.0482809π-0.0482809\pi
−0.151098 + 0.988519i 0.548281π0.548281\pi
110110 −52.7469 587.091i −0.0457202 0.508881i
111111 −1794.82 −1.53475
112112 −558.942 1492.12i −0.471563 1.25886i
113113 −720.469 −0.599788 −0.299894 0.953973i 0.596951π-0.596951\pi
−0.299894 + 0.953973i 0.596951π0.596951\pi
114114 −105.218 1171.11i −0.0864433 0.962144i
115115 −224.430 224.430i −0.181984 0.181984i
116116 97.0993 + 67.3153i 0.0777193 + 0.0538799i
117117 376.646 376.646i 0.297615 0.297615i
118118 −1038.43 + 1243.45i −0.810131 + 0.970072i
119119 2202.96i 1.69702i
120120 1118.34 308.080i 0.850752 0.234365i
121121 332.571i 0.249865i
122122 −2040.37 1703.96i −1.51415 1.26450i
123123 1981.48 1981.48i 1.45255 1.45255i
124124 −763.240 + 138.262i −0.552750 + 0.100131i
125125 −963.056 963.056i −0.689107 0.689107i
126126 −2343.65 + 210.564i −1.65705 + 0.148877i
127127 2622.35 1.83225 0.916124 0.400895i 0.131301π-0.131301\pi
0.916124 + 0.400895i 0.131301π0.131301\pi
128128 −1172.51 + 849.925i −0.809658 + 0.586902i
129129 −1101.97 −0.752119
130130 −296.169 + 26.6092i −0.199814 + 0.0179522i
131131 657.574 + 657.574i 0.438569 + 0.438569i 0.891530 0.452961i 0.149632π-0.149632\pi
−0.452961 + 0.891530i 0.649632π0.649632\pi
132132 1933.36 350.231i 1.27483 0.230937i
133133 941.555 941.555i 0.613858 0.613858i
134134 329.666 + 275.312i 0.212529 + 0.177488i
135135 328.919i 0.209695i
136136 1930.27 531.751i 1.21706 0.335274i
137137 2511.52i 1.56623i 0.621874 + 0.783117i 0.286371π0.286371\pi
−0.621874 + 0.783117i 0.713629π0.713629\pi
138138 678.146 812.030i 0.418316 0.500903i
139139 −1086.02 + 1086.02i −0.662697 + 0.662697i −0.956015 0.293318i 0.905241π-0.905241\pi
0.293318 + 0.956015i 0.405241π0.405241\pi
140140 1079.58 + 748.434i 0.651723 + 0.451816i
141141 1212.84 + 1212.84i 0.724393 + 0.724393i
142142 −54.4290 605.813i −0.0321661 0.358019i
143143 −503.677 −0.294543
144144 750.210 + 2002.72i 0.434149 + 1.15898i
145145 −97.4080 −0.0557882
146146 169.219 + 1883.46i 0.0959222 + 1.06765i
147147 −1521.54 1521.54i −0.853706 0.853706i
148148 −1052.48 + 1518.15i −0.584547 + 0.843183i
149149 −2284.63 + 2284.63i −1.25614 + 1.25614i −0.303214 + 0.952922i 0.598060π0.598060\pi
−0.952922 + 0.303214i 0.901940π0.901940\pi
150150 1148.50 1375.24i 0.625163 0.748587i
151151 2814.39i 1.51677i −0.651809 0.758383i 0.725990π-0.725990\pi
0.651809 0.758383i 0.274010π-0.274010\pi
152152 −1052.28 597.735i −0.561521 0.318965i
153153 2956.80i 1.56237i
154154 1707.84 + 1426.25i 0.893645 + 0.746304i
155155 452.184 452.184i 0.234325 0.234325i
156156 −176.681 975.322i −0.0906781 0.500566i
157157 −906.308 906.308i −0.460709 0.460709i 0.438179 0.898888i 0.355624π-0.355624\pi
−0.898888 + 0.438179i 0.855624π0.855624\pi
158158 2318.33 208.290i 1.16732 0.104877i
159159 −1931.93 −0.963598
160160 395.203 1126.61i 0.195272 0.556663i
161161 1198.08 0.586472
162162 −1449.68 + 130.246i −0.703070 + 0.0631670i
163163 1392.36 + 1392.36i 0.669067 + 0.669067i 0.957500 0.288433i 0.0931342π-0.0931342\pi
−0.288433 + 0.957500i 0.593134π0.593134\pi
164164 −514.101 2837.96i −0.244784 1.35127i
165165 −1145.43 + 1145.43i −0.540433 + 0.540433i
166166 −1003.56 838.097i −0.469225 0.391861i
167167 1221.66i 0.566075i −0.959109 0.283038i 0.908658π-0.908658\pi
0.959109 0.283038i 0.0913421π-0.0913421\pi
168168 −2162.73 + 3807.36i −0.993202 + 1.74848i
169169 1942.91i 0.884347i
170170 −1058.07 + 1266.96i −0.477356 + 0.571598i
171171 −1263.75 + 1263.75i −0.565155 + 0.565155i
172172 −646.193 + 932.104i −0.286464 + 0.413211i
173173 −563.418 563.418i −0.247606 0.247606i 0.572381 0.819988i 0.306020π-0.306020\pi
−0.819988 + 0.572381i 0.806020π0.806020\pi
174174 −29.0545 323.387i −0.0126587 0.140896i
175175 2029.05 0.876468
176176 837.474 1840.71i 0.358676 0.788344i
177177 4451.99 1.89058
178178 66.4976 + 740.141i 0.0280012 + 0.311662i
179179 −2202.23 2202.23i −0.919565 0.919565i 0.0774329 0.996998i 0.475328π-0.475328\pi
−0.996998 + 0.0774329i 0.975328π0.975328\pi
180180 −1449.01 1004.55i −0.600016 0.415969i
181181 121.294 121.294i 0.0498104 0.0498104i −0.681763 0.731573i 0.738786π-0.738786\pi
0.731573 + 0.681763i 0.238786π0.238786\pi
182182 719.502 861.551i 0.293039 0.350892i
183183 7305.26i 2.95093i
184184 −289.193 1049.78i −0.115867 0.420602i
185185 1522.98i 0.605251i
186186 1636.09 + 1366.34i 0.644968 + 0.538628i
187187 −1977.02 + 1977.02i −0.773124 + 0.773124i
188188 1737.08 314.675i 0.673882 0.122074i
189189 877.939 + 877.939i 0.337887 + 0.337887i
190190 993.731 89.2813i 0.379436 0.0340902i
191191 3927.65 1.48793 0.743966 0.668218i 0.232942π-0.232942\pi
0.743966 + 0.668218i 0.232942π0.232942\pi
192192 3858.12 + 976.000i 1.45019 + 0.366858i
193193 −3249.02 −1.21176 −0.605880 0.795556i 0.707179π-0.707179\pi
−0.605880 + 0.795556i 0.707179π0.707179\pi
194194 424.817 38.1675i 0.157217 0.0141251i
195195 577.833 + 577.833i 0.212202 + 0.212202i
196196 −2179.23 + 394.769i −0.794178 + 0.143866i
197197 2420.90 2420.90i 0.875545 0.875545i −0.117525 0.993070i 0.537496π-0.537496\pi
0.993070 + 0.117525i 0.0374961π0.0374961\pi
198198 −2292.25 1914.31i −0.822743 0.687093i
199199 1371.30i 0.488488i 0.969714 + 0.244244i 0.0785397π0.0785397\pi
−0.969714 + 0.244244i 0.921460π0.921460\pi
200200 −489.773 1777.89i −0.173161 0.628580i
201201 1180.33i 0.414198i
202202 −1251.18 + 1498.20i −0.435807 + 0.521847i
203203 259.998 259.998i 0.0898931 0.0898931i
204204 −4521.82 3134.81i −1.55191 1.07588i
205205 1681.36 + 1681.36i 0.572836 + 0.572836i
206206 465.849 + 5185.06i 0.157559 + 1.75369i
207207 −1608.06 −0.539941
208208 −928.580 422.480i −0.309546 0.140835i
209209 1689.98 0.559321
210210 −323.038 3595.52i −0.106151 1.18150i
211211 −1620.50 1620.50i −0.528719 0.528719i 0.391471 0.920190i 0.371966π-0.371966\pi
−0.920190 + 0.391471i 0.871966π0.871966\pi
212212 −1132.88 + 1634.12i −0.367011 + 0.529396i
213213 −1181.95 + 1181.95i −0.380217 + 0.380217i
214214 203.605 243.802i 0.0650382 0.0778784i
215215 935.068i 0.296610i
216216 557.350 981.184i 0.175569 0.309079i
217217 2413.91i 0.755148i
218218 −2925.82 2443.42i −0.908997 0.759125i
219219 3674.67 3674.67i 1.13384 1.13384i
220220 297.185 + 1640.53i 0.0910736 + 0.502749i
221221 997.347 + 997.347i 0.303569 + 0.303569i
222222 5056.15 454.268i 1.52859 0.137335i
223223 −419.617 −0.126007 −0.0630036 0.998013i 0.520068π-0.520068\pi
−0.0630036 + 0.998013i 0.520068π0.520068\pi
224224 1952.24 + 4061.97i 0.582320 + 1.21161i
225225 −2723.38 −0.806929
226226 2029.62 182.350i 0.597381 0.0536714i
227227 −2133.64 2133.64i −0.623853 0.623853i 0.322661 0.946515i 0.395423π-0.395423\pi
−0.946515 + 0.322661i 0.895423π0.895423\pi
228228 592.813 + 3272.48i 0.172193 + 0.950548i
229229 −1574.42 + 1574.42i −0.454325 + 0.454325i −0.896787 0.442462i 0.854105π-0.854105\pi
0.442462 + 0.896787i 0.354105π0.354105\pi
230230 689.039 + 575.433i 0.197539 + 0.164969i
231231 6114.67i 1.74163i
232232 −290.574 165.057i −0.0822289 0.0467091i
233233 1194.86i 0.335957i 0.985791 + 0.167978i 0.0537239π0.0537239\pi
−0.985791 + 0.167978i 0.946276π0.946276\pi
234234 −965.712 + 1156.37i −0.269789 + 0.323052i
235235 −1029.14 + 1029.14i −0.285675 + 0.285675i
236236 2610.63 3765.71i 0.720075 1.03867i
237237 −4523.12 4523.12i −1.23970 1.23970i
238238 −557.567 6205.91i −0.151856 1.69021i
239239 −4241.03 −1.14782 −0.573911 0.818917i 0.694575π-0.694575\pi
−0.573911 + 0.818917i 0.694575π0.694575\pi
240240 −3072.49 + 1150.94i −0.826367 + 0.309553i
241241 −5571.19 −1.48910 −0.744548 0.667569i 0.767335π-0.767335\pi
−0.744548 + 0.667569i 0.767335π0.767335\pi
242242 −84.1734 936.878i −0.0223590 0.248863i
243243 3780.46 + 3780.46i 0.998012 + 0.998012i
244244 6179.15 + 4283.77i 1.62123 + 1.12394i
245245 1291.09 1291.09i 0.336672 0.336672i
246246 −5080.47 + 6083.49i −1.31674 + 1.57670i
247247 852.541i 0.219619i
248248 2115.12 582.671i 0.541572 0.149192i
249249 3593.11i 0.914474i
250250 2956.75 + 2469.26i 0.748006 + 0.624678i
251251 −482.728 + 482.728i −0.121393 + 0.121393i −0.765193 0.643801i 0.777357π-0.777357\pi
0.643801 + 0.765193i 0.277357π0.277357\pi
252252 6548.95 1186.35i 1.63708 0.296560i
253253 1075.20 + 1075.20i 0.267184 + 0.267184i
254254 −7387.36 + 663.713i −1.82490 + 0.163957i
255255 4536.19 1.11399
256256 3087.94 2691.07i 0.753891 0.656999i
257257 8093.12 1.96434 0.982169 0.188002i 0.0602013π-0.0602013\pi
0.982169 + 0.188002i 0.0602013π0.0602013\pi
258258 3104.35 278.909i 0.749102 0.0673027i
259259 4065.08 + 4065.08i 0.975257 + 0.975257i
260260 827.598 149.921i 0.197406 0.0357603i
261261 −348.969 + 348.969i −0.0827610 + 0.0827610i
262262 −2018.87 1686.01i −0.476054 0.397564i
263263 410.300i 0.0961984i −0.998843 0.0480992i 0.984684π-0.984684\pi
0.998843 0.0480992i 0.0153164π-0.0153164\pi
264264 −5357.79 + 1475.96i −1.24905 + 0.344088i
265265 1639.32i 0.380009i
266266 −2414.13 + 2890.74i −0.556465 + 0.666326i
267267 1444.03 1444.03i 0.330986 0.330986i
268268 −998.378 692.139i −0.227558 0.157758i
269269 −4.77962 4.77962i −0.00108334 0.00108334i 0.706565 0.707648i 0.250244π-0.250244\pi
−0.707648 + 0.706565i 0.750244π0.750244\pi
270270 83.2490 + 926.590i 0.0187643 + 0.208854i
271271 −2833.98 −0.635247 −0.317623 0.948217i 0.602885π-0.602885\pi
−0.317623 + 0.948217i 0.602885π0.602885\pi
272272 −5303.15 + 1986.54i −1.18217 + 0.442836i
273273 −3084.67 −0.683855
274274 −635.665 7075.17i −0.140153 1.55995i
275275 1820.95 + 1820.95i 0.399300 + 0.399300i
276276 −1704.87 + 2459.19i −0.371815 + 0.536326i
277277 1525.80 1525.80i 0.330962 0.330962i −0.521989 0.852952i 0.674810π-0.674810\pi
0.852952 + 0.521989i 0.174810π0.174810\pi
278278 2784.53 3334.27i 0.600738 0.719339i
279279 3239.94i 0.695234i
280280 −3230.70 1835.16i −0.689539 0.391684i
281281 4750.23i 1.00845i 0.863572 + 0.504226i 0.168222π0.168222\pi
−0.863572 + 0.504226i 0.831778π0.831778\pi
282282 −3723.63 3109.69i −0.786308 0.656665i
283283 644.104 644.104i 0.135293 0.135293i −0.636217 0.771510i 0.719502π-0.719502\pi
0.771510 + 0.636217i 0.219502π0.219502\pi
284284 306.662 + 1692.85i 0.0640740 + 0.353705i
285285 −1938.79 1938.79i −0.402961 0.402961i
286286 1418.90 127.480i 0.293361 0.0263569i
287287 −8975.67 −1.84605
288288 −2620.29 5451.95i −0.536118 1.11548i
289289 2916.53 0.593635
290290 274.406 24.6539i 0.0555644 0.00499216i
291291 −828.827 828.827i −0.166965 0.166965i
292292 −953.405 5263.03i −0.191075 1.05478i
293293 −1433.16 + 1433.16i −0.285755 + 0.285755i −0.835399 0.549644i 0.814763π-0.814763\pi
0.549644 + 0.835399i 0.314763π0.314763\pi
294294 4671.41 + 3901.21i 0.926675 + 0.773888i
295295 3777.69i 0.745578i
296296 2580.67 4543.13i 0.506751 0.892108i
297297 1575.79i 0.307868i
298298 5857.75 7014.23i 1.13869 1.36350i
299299 542.407 542.407i 0.104910 0.104910i
300300 −2887.34 + 4164.85i −0.555668 + 0.801526i
301301 2495.85 + 2495.85i 0.477935 + 0.477935i
302302 712.319 + 7928.36i 0.135726 + 1.51068i
303303 5364.10 1.01703
304304 3115.65 + 1417.54i 0.587811 + 0.267439i
305305 −6198.79 −1.16374
306306 748.364 + 8329.55i 0.139808 + 1.55611i
307307 −231.211 231.211i −0.0429834 0.0429834i 0.685288 0.728272i 0.259676π-0.259676\pi
−0.728272 + 0.685288i 0.759676π0.759676\pi
308308 −5172.09 3585.62i −0.956842 0.663343i
309309 10116.2 10116.2i 1.86242 1.86242i
310310 −1159.39 + 1388.29i −0.212416 + 0.254353i
311311 871.410i 0.158885i 0.996839 + 0.0794423i 0.0253140π0.0253140\pi
−0.996839 + 0.0794423i 0.974686π0.974686\pi
312312 744.577 + 2702.84i 0.135107 + 0.490443i
313313 3515.02i 0.634762i −0.948298 0.317381i 0.897197π-0.897197\pi
0.948298 0.317381i 0.102803π-0.102803\pi
314314 2782.53 + 2323.76i 0.500087 + 0.417634i
315315 −3879.95 + 3879.95i −0.694001 + 0.694001i
316316 −6478.22 + 1173.54i −1.15325 + 0.208913i
317317 4723.77 + 4723.77i 0.836951 + 0.836951i 0.988456 0.151506i 0.0484121π-0.0484121\pi
−0.151506 + 0.988456i 0.548412π0.548412\pi
318318 5442.40 488.970i 0.959732 0.0862266i
319319 466.665 0.0819067
320320 −828.174 + 3273.77i −0.144676 + 0.571904i
321321 −872.901 −0.151778
322322 −3375.09 + 303.233i −0.584119 + 0.0524799i
323323 −3346.38 3346.38i −0.576462 0.576462i
324324 4050.89 733.824i 0.694597 0.125827i
325325 918.613 918.613i 0.156786 0.156786i
326326 −4274.79 3569.98i −0.726254 0.606512i
327327 10475.5i 1.77155i
328328 2166.55 + 7864.65i 0.364718 + 1.32394i
329329 5493.90i 0.920633i
330330 2936.85 3516.67i 0.489904 0.586625i
331331 −1820.26 + 1820.26i −0.302268 + 0.302268i −0.841901 0.539633i 0.818563π-0.818563\pi
0.539633 + 0.841901i 0.318563π0.318563\pi
332332 3039.23 + 2106.99i 0.502408 + 0.348301i
333333 −5456.13 5456.13i −0.897880 0.897880i
334334 309.200 + 3441.50i 0.0506547 + 0.563804i
335335 1001.55 0.163345
336336 5128.93 11273.0i 0.832757 1.83034i
337337 74.0970 0.0119772 0.00598861 0.999982i 0.498094π-0.498094\pi
0.00598861 + 0.999982i 0.498094π0.498094\pi
338338 491.749 + 5473.33i 0.0791350 + 0.880799i
339339 −3959.83 3959.83i −0.634420 0.634420i
340340 2660.01 3836.94i 0.424292 0.612021i
341341 −2166.34 + 2166.34i −0.344029 + 0.344029i
342342 3240.23 3879.94i 0.512315 0.613460i
343343 1647.24i 0.259307i
344344 1584.46 2789.36i 0.248339 0.437187i
345345 2467.01i 0.384984i
346346 1729.80 + 1444.59i 0.268770 + 0.224456i
347347 2102.73 2102.73i 0.325305 0.325305i −0.525493 0.850798i 0.676119π-0.676119\pi
0.850798 + 0.525493i 0.176119π0.176119\pi
348348 163.698 + 903.652i 0.0252159 + 0.139198i
349349 −6612.85 6612.85i −1.01426 1.01426i −0.999897 0.0143661i 0.995427π-0.995427\pi
−0.0143661 0.999897i 0.504573π-0.504573\pi
350350 −5716.00 + 513.551i −0.872951 + 0.0784299i
351351 794.940 0.120885
352352 −1893.35 + 5397.38i −0.286693 + 0.817277i
353353 2216.90 0.334259 0.167130 0.985935i 0.446550π-0.446550\pi
0.167130 + 0.985935i 0.446550π0.446550\pi
354354 −12541.6 + 1126.80i −1.88299 + 0.169177i
355355 −1002.93 1002.93i −0.149944 0.149944i
356356 −374.658 2068.21i −0.0557776 0.307906i
357357 −12107.9 + 12107.9i −1.79500 + 1.79500i
358358 6761.23 + 5646.46i 0.998162 + 0.833589i
359359 2082.23i 0.306117i −0.988217 0.153059i 0.951088π-0.951088\pi
0.988217 0.153059i 0.0489123π-0.0489123\pi
360360 4336.23 + 2463.14i 0.634831 + 0.360608i
361361 3998.49i 0.582955i
362362 −310.995 + 372.393i −0.0451533 + 0.0540678i
363363 −1827.87 + 1827.87i −0.264293 + 0.264293i
364364 −1808.84 + 2609.16i −0.260464 + 0.375707i
365365 3118.10 + 3118.10i 0.447148 + 0.447148i
366366 −1848.95 20579.5i −0.264061 2.93909i
367367 4509.22 0.641360 0.320680 0.947188i 0.396089π-0.396089\pi
0.320680 + 0.947188i 0.396089π0.396089\pi
368368 1080.38 + 2884.12i 0.153040 + 0.408547i
369369 12047.1 1.69959
370370 385.464 + 4290.34i 0.0541603 + 0.602823i
371371 4375.61 + 4375.61i 0.612320 + 0.612320i
372372 −4954.82 3434.99i −0.690579 0.478753i
373373 −8661.56 + 8661.56i −1.20236 + 1.20236i −0.228908 + 0.973448i 0.573515π0.573515\pi
−0.973448 + 0.228908i 0.926485π0.926485\pi
374374 5069.05 6069.81i 0.700840 0.839205i
375375 10586.3i 1.45779i
376376 −4813.86 + 1326.12i −0.660254 + 0.181886i
377377 235.418i 0.0321609i
378378 −2695.43 2251.02i −0.366767 0.306296i
379379 3522.46 3522.46i 0.477405 0.477405i −0.426896 0.904301i 0.640393π-0.640393\pi
0.904301 + 0.426896i 0.140393π0.140393\pi
380380 −2776.82 + 503.025i −0.374863 + 0.0679069i
381381 14412.9 + 14412.9i 1.93804 + 1.93804i
382382 −11064.5 + 994.086i −1.48196 + 0.133146i
383383 3044.88 0.406229 0.203115 0.979155i 0.434894π-0.434894\pi
0.203115 + 0.979155i 0.434894π0.434894\pi
384384 −11115.7 1772.98i −1.47720 0.235618i
385385 5188.54 0.686837
386386 9152.75 822.325i 1.20690 0.108433i
387387 −3349.92 3349.92i −0.440016 0.440016i
388388 −1187.08 + 215.042i −0.155322 + 0.0281368i
389389 1932.73 1932.73i 0.251911 0.251911i −0.569843 0.821754i 0.692996π-0.692996\pi
0.821754 + 0.569843i 0.192996π0.192996\pi
390390 −1774.05 1481.55i −0.230340 0.192362i
391391 4258.09i 0.550744i
392392 6039.14 1663.66i 0.778119 0.214356i
393393 7228.29i 0.927784i
394394 −6207.15 + 7432.61i −0.793685 + 0.950379i
395395 3838.04 3838.04i 0.488893 0.488893i
396396 6941.96 + 4812.61i 0.880926 + 0.610714i
397397 −672.457 672.457i −0.0850117 0.0850117i 0.663322 0.748334i 0.269146π-0.269146\pi
−0.748334 + 0.663322i 0.769146π0.769146\pi
398398 −347.075 3863.07i −0.0437119 0.486528i
399399 10349.9 1.29861
400400 1829.71 + 4884.51i 0.228714 + 0.610563i
401401 −7606.74 −0.947288 −0.473644 0.880716i 0.657062π-0.657062\pi
−0.473644 + 0.880716i 0.657062π0.657062\pi
402402 298.740 + 3325.07i 0.0370641 + 0.412536i
403403 1092.85 + 1092.85i 0.135084 + 0.135084i
404404 3145.49 4537.23i 0.387361 0.558751i
405405 −2399.96 + 2399.96i −0.294457 + 0.294457i
406406 −666.631 + 798.241i −0.0814885 + 0.0975765i
407407 7296.32i 0.888612i
408408 13531.7 + 7686.54i 1.64196 + 0.932697i
409409 4981.58i 0.602257i 0.953584 + 0.301129i 0.0973634π0.0973634\pi
−0.953584 + 0.301129i 0.902637π0.902637\pi
410410 −5162.08 4310.98i −0.621797 0.519278i
411411 −13803.8 + 13803.8i −1.65667 + 1.65667i
412412 −2624.67 14488.8i −0.313855 1.73256i
413413 −10083.3 10083.3i −1.20137 1.20137i
414414 4530.03 406.998i 0.537775 0.0483161i
415415 −3048.89 −0.360637
416416 2722.81 + 955.136i 0.320906 + 0.112571i
417417 −11937.9 −1.40192
418418 −4760.80 + 427.732i −0.557077 + 0.0500503i
419419 −3433.38 3433.38i −0.400314 0.400314i 0.478030 0.878344i 0.341351π-0.341351\pi
−0.878344 + 0.478030i 0.841351π0.841351\pi
420420 1820.05 + 10047.1i 0.211450 + 1.16726i
421421 7973.72 7973.72i 0.923077 0.923077i −0.0741686 0.997246i 0.523630π-0.523630\pi
0.997246 + 0.0741686i 0.0236303π0.0236303\pi
422422 4975.22 + 4154.93i 0.573910 + 0.479286i
423423 7373.88i 0.847590i
424424 2777.81 4890.18i 0.318166 0.560114i
425425 7211.44i 0.823074i
426426 3030.51 3628.81i 0.344668 0.412715i
427427 16545.6 16545.6i 1.87517 1.87517i
428428 −511.866 + 738.343i −0.0578084 + 0.0833859i
429429 −2768.30 2768.30i −0.311550 0.311550i
430430 236.665 + 2634.16i 0.0265418 + 0.295420i
431431 4800.16 0.536463 0.268232 0.963354i 0.413561π-0.413561\pi
0.268232 + 0.963354i 0.413561π0.413561\pi
432432 −1321.76 + 2905.14i −0.147207 + 0.323550i
433433 6242.32 0.692810 0.346405 0.938085i 0.387402π-0.387402\pi
0.346405 + 0.938085i 0.387402π0.387402\pi
434434 −610.959 6800.18i −0.0675737 0.752118i
435435 −535.372 535.372i −0.0590095 0.0590095i
436436 8860.69 + 6142.79i 0.973280 + 0.674739i
437437 −1819.93 + 1819.93i −0.199220 + 0.199220i
438438 −9421.79 + 11281.9i −1.02783 + 1.23075i
439439 4929.27i 0.535903i 0.963432 + 0.267951i 0.0863466π0.0863466\pi
−0.963432 + 0.267951i 0.913653π0.913653\pi
440440 −1252.41 4546.30i −0.135696 0.492582i
441441 9250.77i 0.998896i
442442 −3062.03 2557.18i −0.329516 0.275187i
443443 −7670.67 + 7670.67i −0.822674 + 0.822674i −0.986491 0.163817i 0.947619π-0.947619\pi
0.163817 + 0.986491i 0.447619π0.447619\pi
444444 −14128.6 + 2559.42i −1.51017 + 0.273569i
445445 1225.32 + 1225.32i 0.130529 + 0.130529i
446446 1182.09 106.205i 0.125502 0.0112756i
447447 −25113.5 −2.65733
448448 −6527.70 10948.8i −0.688404 1.15464i
449449 −11515.2 −1.21032 −0.605162 0.796102i 0.706892π-0.706892\pi
−0.605162 + 0.796102i 0.706892π0.706892\pi
450450 7671.99 689.286i 0.803691 0.0722073i
451451 −8055.12 8055.12i −0.841021 0.841021i
452452 −5671.44 + 1027.39i −0.590182 + 0.106912i
453453 15468.4 15468.4i 1.60434 1.60434i
454454 6550.66 + 5470.61i 0.677176 + 0.565526i
455455 2617.46i 0.269689i
456456 −2498.26 9068.79i −0.256561 0.931326i
457457 4829.89i 0.494383i 0.968967 + 0.247191i 0.0795076π0.0795076\pi
−0.968967 + 0.247191i 0.920492π0.920492\pi
458458 4036.78 4833.74i 0.411848 0.493157i
459459 3120.28 3120.28i 0.317303 0.317303i
460460 −2086.72 1446.65i −0.211508 0.146631i
461461 8265.79 + 8265.79i 0.835090 + 0.835090i 0.988208 0.153118i 0.0489315π-0.0489315\pi
−0.153118 + 0.988208i 0.548931π0.548931\pi
462462 1547.62 + 17225.5i 0.155848 + 1.73464i
463463 −5043.86 −0.506281 −0.253141 0.967430i 0.581464π-0.581464\pi
−0.253141 + 0.967430i 0.581464π0.581464\pi
464464 860.346 + 391.435i 0.0860788 + 0.0391636i
465465 4970.57 0.495709
466466 −302.418 3366.02i −0.0300628 0.334609i
467467 12438.8 + 12438.8i 1.23255 + 1.23255i 0.962982 + 0.269564i 0.0868796π0.0868796\pi
0.269564 + 0.962982i 0.413120π0.413120\pi
468468 2427.81 3502.01i 0.239798 0.345898i
469469 −2673.31 + 2673.31i −0.263203 + 0.263203i
470470 2638.70 3159.64i 0.258966 0.310093i
471471 9962.47i 0.974621i
472472 −6401.26 + 11269.1i −0.624241 + 1.09894i
473473 4479.75i 0.435474i
474474 13886.8 + 11597.2i 1.34566 + 1.12379i
475475 −3082.20 + 3082.20i −0.297729 + 0.297729i
476476 3141.42 + 17341.4i 0.302493 + 1.66984i
477477 −5872.93 5872.93i −0.563738 0.563738i
478478 11947.3 1073.40i 1.14322 0.102712i
479479 13059.7 1.24575 0.622875 0.782321i 0.285964π-0.285964\pi
0.622875 + 0.782321i 0.285964π0.285964\pi
480480 8364.14 4019.93i 0.795352 0.382258i
481481 3680.77 0.348916
482482 15694.5 1410.06i 1.48312 0.133250i
483483 6584.87 + 6584.87i 0.620335 + 0.620335i
484484 474.246 + 2617.96i 0.0445385 + 0.245864i
485485 703.292 703.292i 0.0658450 0.0658450i
486486 −11606.7 9693.04i −1.08331 0.904702i
487487 15549.3i 1.44683i 0.690414 + 0.723414i 0.257428π0.257428\pi
−0.690414 + 0.723414i 0.742572π0.742572\pi
488488 −18491.4 10503.8i −1.71530 0.974354i
489489 15305.3i 1.41540i
490490 −3310.33 + 3963.88i −0.305195 + 0.365448i
491491 −8628.34 + 8628.34i −0.793058 + 0.793058i −0.981990 0.188932i 0.939497π-0.939497\pi
0.188932 + 0.981990i 0.439497π0.439497\pi
492492 12772.4 18423.5i 1.17037 1.68821i
493493 −924.059 924.059i −0.0844169 0.0844169i
494494 215.777 + 2401.68i 0.0196524 + 0.218738i
495495 −6964.03 −0.632344
496496 −5810.98 + 2176.76i −0.526049 + 0.197056i
497497 5354.00 0.483219
498498 −909.413 10122.1i −0.0818309 0.910806i
499499 1732.42 + 1732.42i 0.155418 + 0.155418i 0.780533 0.625115i 0.214948π-0.214948\pi
−0.625115 + 0.780533i 0.714948π0.714948\pi
500500 −8954.38 6207.74i −0.800904 0.555237i
501501 6714.44 6714.44i 0.598761 0.598761i
502502 1237.71 1482.06i 0.110043 0.131768i
503503 16579.6i 1.46968i −0.678241 0.734839i 0.737258π-0.737258\pi
0.678241 0.734839i 0.262742π-0.262742\pi
504504 −18148.7 + 4999.58i −1.60398 + 0.441863i
505505 4551.65i 0.401081i
506506 −3301.07 2756.80i −0.290021 0.242203i
507507 10678.6 10678.6i 0.935410 0.935410i
508508 20642.8 3739.47i 1.80291 0.326599i
509509 −7830.92 7830.92i −0.681924 0.681924i 0.278509 0.960434i 0.410160π-0.410160\pi
−0.960434 + 0.278509i 0.910160π0.910160\pi
510510 −12778.8 + 1148.11i −1.10952 + 0.0996844i
511511 −16645.5 −1.44100
512512 −8017.86 + 8362.51i −0.692076 + 0.721825i
513513 −2667.24 −0.229555
514514 −22799.0 + 2048.36i −1.95646 + 0.175777i
515515 8583.95 + 8583.95i 0.734474 + 0.734474i
516516 −8674.61 + 1571.42i −0.740074 + 0.134065i
517517 4930.44 4930.44i 0.419420 0.419420i
518518 −12480.5 10422.8i −1.05861 0.884075i
519519 6193.30i 0.523807i
520520 −2293.47 + 631.803i −0.193414 + 0.0532815i
521521 3400.02i 0.285907i −0.989729 0.142953i 0.954340π-0.954340\pi
0.989729 0.142953i 0.0456599π-0.0456599\pi
522522 894.749 1071.40i 0.0750232 0.0898348i
523523 −2019.50 + 2019.50i −0.168847 + 0.168847i −0.786472 0.617626i 0.788095π-0.788095\pi
0.617626 + 0.786472i 0.288095π0.288095\pi
524524 6114.05 + 4238.64i 0.509720 + 0.353370i
525525 11152.0 + 11152.0i 0.927075 + 0.927075i
526526 103.847 + 1155.85i 0.00860822 + 0.0958124i
527527 8579.28 0.709144
528528 14719.8 5513.95i 1.21325 0.454477i
529529 9851.23 0.809668
530530 414.910 + 4618.09i 0.0340048 + 0.378485i
531531 13533.7 + 13533.7i 1.10605 + 1.10605i
532532 6069.15 8754.47i 0.494607 0.713448i
533533 −4063.56 + 4063.56i −0.330229 + 0.330229i
534534 −3702.47 + 4433.43i −0.300040 + 0.359276i
535535 740.691i 0.0598558i
536536 2987.69 + 1697.12i 0.240762 + 0.136762i
537537 24207.7i 1.94532i
538538 14.6743 + 12.2548i 0.00117594 + 0.000982052i
539539 −6185.39 + 6185.39i −0.494293 + 0.494293i
540540 −469.038 2589.21i −0.0373781 0.206337i
541541 −13432.6 13432.6i −1.06749 1.06749i −0.997551 0.0699388i 0.977720π-0.977720\pi
−0.0699388 0.997551i 0.522280π-0.522280\pi
542542 7983.54 717.278i 0.632699 0.0568445i
543543 1333.30 0.105373
544544 14436.6 6938.45i 1.13780 0.546845i
545545 −8888.86 −0.698637
546546 8689.75 780.726i 0.681112 0.0611941i
547547 −5376.46 5376.46i −0.420257 0.420257i 0.465035 0.885292i 0.346042π-0.346042\pi
−0.885292 + 0.465035i 0.846042π0.846042\pi
548548 3581.44 + 19770.4i 0.279181 + 1.54115i
549549 −22207.5 + 22207.5i −1.72640 + 1.72640i
550550 −5590.64 4668.88i −0.433429 0.361967i
551551 789.894i 0.0610719i
552552 4180.33 7359.24i 0.322331 0.567446i
553553 20488.7i 1.57553i
554554 −3912.13 + 4684.49i −0.300019 + 0.359251i
555555 8370.55 8370.55i 0.640198 0.640198i
556556 −7000.34 + 10097.7i −0.533958 + 0.770210i
557557 −2076.28 2076.28i −0.157944 0.157944i 0.623711 0.781655i 0.285624π-0.285624\pi
−0.781655 + 0.623711i 0.785624π0.785624\pi
558558 820.027 + 9127.18i 0.0622124 + 0.692445i
559559 2259.90 0.170990
560560 9565.61 + 4352.10i 0.721823 + 0.328410i
561561 −21732.1 −1.63553
562562 −1202.28 13381.8i −0.0902405 1.00441i
563563 −16643.1 16643.1i −1.24587 1.24587i −0.957528 0.288339i 0.906897π-0.906897\pi
−0.288339 0.957528i 0.593103π-0.593103\pi
564564 11276.8 + 7817.81i 0.841915 + 0.583669i
565565 3360.07 3360.07i 0.250193 0.250193i
566566 −1651.47 + 1977.51i −0.122644 + 0.146857i
567567 12811.8i 0.948934i
568568 −1292.35 4691.28i −0.0954679 0.346552i
569569 5659.60i 0.416982i 0.978024 + 0.208491i 0.0668551π0.0668551\pi
−0.978024 + 0.208491i 0.933145π0.933145\pi
570570 5952.43 + 4971.02i 0.437403 + 0.365286i
571571 4872.67 4872.67i 0.357119 0.357119i −0.505631 0.862750i 0.668740π-0.668740\pi
0.862750 + 0.505631i 0.168740π0.168740\pi
572572 −3964.89 + 718.244i −0.289825 + 0.0525023i
573573 21587.1 + 21587.1i 1.57385 + 1.57385i
574574 25285.2 2271.73i 1.83865 0.165192i
575575 −3921.95 −0.284446
576576 8761.45 + 14695.4i 0.633786 + 1.06303i
577577 10652.2 0.768556 0.384278 0.923217i 0.374450π-0.374450\pi
0.384278 + 0.923217i 0.374450π0.374450\pi
578578 −8216.10 + 738.171i −0.591254 + 0.0531209i
579579 −17857.2 17857.2i −1.28173 1.28173i
580580 −766.784 + 138.904i −0.0548948 + 0.00994426i
581581 8138.01 8138.01i 0.581104 0.581104i
582582 2544.65 + 2125.10i 0.181235 + 0.151354i
583583 7853.69i 0.557919i
584584 4017.89 + 14585.1i 0.284694 + 1.03345i
585585 3513.14i 0.248291i
586586 3674.61 4400.07i 0.259039 0.310180i
587587 9903.95 9903.95i 0.696388 0.696388i −0.267242 0.963630i 0.586112π-0.586112\pi
0.963630 + 0.267242i 0.0861122π0.0861122\pi
588588 −14147.1 9807.69i −0.992208 0.687861i
589589 −3666.82 3666.82i −0.256517 0.256517i
590590 −956.129 10642.0i −0.0667173 0.742587i
591591 26611.5 1.85220
592592 −6120.09 + 13451.5i −0.424889 + 0.933875i
593593 −3528.04 −0.244316 −0.122158 0.992511i 0.538981π-0.538981\pi
−0.122158 + 0.992511i 0.538981π0.538981\pi
594594 −398.832 4439.14i −0.0275493 0.306633i
595595 −10274.0 10274.0i −0.707887 0.707887i
596596 −14726.5 + 21242.2i −1.01211 + 1.45993i
597597 −7536.93 + 7536.93i −0.516693 + 0.516693i
598598 −1390.72 + 1665.29i −0.0951018 + 0.113877i
599599 19024.9i 1.29772i 0.760907 + 0.648861i 0.224754π0.224754\pi
−0.760907 + 0.648861i 0.775246π0.775246\pi
600600 7079.74 12463.5i 0.481715 0.848034i
601601 1065.92i 0.0723460i 0.999346 + 0.0361730i 0.0115167π0.0115167\pi
−0.999346 + 0.0361730i 0.988483π0.988483\pi
602602 −7662.72 6399.32i −0.518786 0.433250i
603603 3588.11 3588.11i 0.242320 0.242320i
604604 −4013.32 22154.5i −0.270364 1.49248i
605605 −1551.02 1551.02i −0.104228 0.104228i
606606 −15111.1 + 1357.65i −1.01295 + 0.0910079i
607607 12909.7 0.863242 0.431621 0.902055i 0.357942π-0.357942\pi
0.431621 + 0.902055i 0.357942π0.357942\pi
608608 −9135.80 3204.75i −0.609384 0.213766i
609609 2858.00 0.190167
610610 17462.5 1568.91i 1.15908 0.104137i
611611 −2487.25 2487.25i −0.164687 0.164687i
612612 −4216.40 23275.6i −0.278494 1.53735i
613613 −8763.41 + 8763.41i −0.577408 + 0.577408i −0.934188 0.356781i 0.883874π-0.883874\pi
0.356781 + 0.934188i 0.383874π0.383874\pi
614614 709.859 + 592.820i 0.0466573 + 0.0389646i
615615 18482.1i 1.21182i
616616 15477.7 + 8791.93i 1.01236 + 0.575060i
617617 18921.2i 1.23459i −0.786733 0.617293i 0.788229π-0.788229\pi
0.786733 0.617293i 0.211771π-0.211771\pi
618618 −25937.6 + 31058.4i −1.68829 + 2.02161i
619619 −15116.6 + 15116.6i −0.981565 + 0.981565i −0.999833 0.0182677i 0.994185π-0.994185\pi
0.0182677 + 0.999833i 0.494185π0.494185\pi
620620 2914.73 4204.36i 0.188804 0.272340i
621621 −1696.97 1696.97i −0.109657 0.109657i
622622 −220.553 2454.83i −0.0142176 0.158247i
623623 −6541.15 −0.420651
624624 −2781.62 7425.67i −0.178452 0.476386i
625625 −1204.57 −0.0770926
626626 889.648 + 9902.09i 0.0568011 + 0.632216i
627627 9288.42 + 9288.42i 0.591617 + 0.591617i
628628 −8426.75 5841.95i −0.535452 0.371209i
629629 14447.7 14447.7i 0.915845 0.915845i
630630 9948.11 11912.1i 0.629115 0.753319i
631631 9602.80i 0.605834i −0.953017 0.302917i 0.902039π-0.902039\pi
0.953017 0.302917i 0.0979605π-0.0979605\pi
632632 17952.6 4945.58i 1.12993 0.311273i
633633 17813.1i 1.11849i
634634 −14502.8 12111.7i −0.908487 0.758699i
635635 −12229.9 + 12229.9i −0.764297 + 0.764297i
636636 −15207.9 + 2754.93i −0.948166 + 0.171761i
637637 3120.34 + 3120.34i 0.194085 + 0.194085i
638638 −1314.63 + 118.113i −0.0815781 + 0.00732935i
639639 −7186.12 −0.444880
640640 1504.44 9432.08i 0.0929194 0.582556i
641641 4450.84 0.274256 0.137128 0.990553i 0.456213π-0.456213\pi
0.137128 + 0.990553i 0.456213π0.456213\pi
642642 2459.03 220.931i 0.151169 0.0135817i
643643 6491.27 + 6491.27i 0.398119 + 0.398119i 0.877569 0.479450i 0.159164π-0.159164\pi
−0.479450 + 0.877569i 0.659164π0.659164\pi
644644 9431.15 1708.46i 0.577080 0.104539i
645645 5139.30 5139.30i 0.313736 0.313736i
646646 10274.0 + 8580.05i 0.625734 + 0.522566i
647647 5546.17i 0.337005i −0.985701 0.168503i 0.946107π-0.946107\pi
0.985701 0.168503i 0.0538932π-0.0538932\pi
648648 −11226.0 + 3092.52i −0.680551 + 0.187478i
649649 18098.3i 1.09464i
650650 −2355.31 + 2820.31i −0.142127 + 0.170187i
651651 −13267.3 + 13267.3i −0.798750 + 0.798750i
652652 12946.0 + 8974.98i 0.777613 + 0.539091i
653653 6327.58 + 6327.58i 0.379200 + 0.379200i 0.870813 0.491614i 0.163593π-0.163593\pi
−0.491614 + 0.870813i 0.663593π0.663593\pi
654654 −2651.34 29510.3i −0.158525 1.76444i
655655 −6133.49 −0.365886
656656 −8093.88 21607.0i −0.481727 1.28599i
657657 22341.5 1.32667
658658 1390.50 + 15476.7i 0.0823820 + 0.916940i
659659 15135.2 + 15135.2i 0.894663 + 0.894663i 0.994958 0.100294i 0.0319785π-0.0319785\pi
−0.100294 + 0.994958i 0.531978π0.531978\pi
660660 −7383.28 + 10650.0i −0.435445 + 0.628110i
661661 −23460.1 + 23460.1i −1.38047 + 1.38047i −0.536694 + 0.843777i 0.680327π0.680327\pi
−0.843777 + 0.536694i 0.819673π0.819673\pi
662662 4667.12 5588.53i 0.274007 0.328103i
663663 10963.2i 0.642195i
664664 −9095.03 5166.32i −0.531560 0.301946i
665665 8782.30i 0.512125i
666666 16751.3 + 13989.4i 0.974624 + 0.813932i
667667 −502.550 + 502.550i −0.0291736 + 0.0291736i
668668 −1742.08 9616.73i −0.100903 0.557009i
669669 −2306.29 2306.29i −0.133283 0.133283i
670670 −2821.45 + 253.492i −0.162690 + 0.0146168i
671671 29697.4 1.70858
672672 −11595.4 + 33055.2i −0.665630 + 1.89752i
673673 30638.5 1.75487 0.877436 0.479694i 0.159252π-0.159252\pi
0.877436 + 0.479694i 0.159252π0.159252\pi
674674 −208.737 + 18.7539i −0.0119292 + 0.00107177i
675675 −2873.96 2873.96i −0.163879 0.163879i
676676 −2770.59 15294.4i −0.157635 0.870184i
677677 −12468.9 + 12468.9i −0.707855 + 0.707855i −0.966084 0.258229i 0.916861π-0.916861\pi
0.258229 + 0.966084i 0.416861π0.416861\pi
678678 12157.4 + 10152.9i 0.688645 + 0.575104i
679679 3754.41i 0.212196i
680680 −6522.33 + 11482.2i −0.367823 + 0.647533i
681681 23453.8i 1.31975i
682682 5554.45 6651.05i 0.311864 0.373434i
683683 13838.5 13838.5i 0.775280 0.775280i −0.203744 0.979024i 0.565311π-0.565311\pi
0.979024 + 0.203744i 0.0653111π0.0653111\pi
684684 −8145.99 + 11750.2i −0.455365 + 0.656843i
685685 −11713.1 11713.1i −0.653333 0.653333i
686686 416.914 + 4640.40i 0.0232039 + 0.258267i
687687 −17306.6 −0.961116
688688 −3757.58 + 8258.89i −0.208221 + 0.457656i
689689 3961.95 0.219068
690690 624.398 + 6949.77i 0.0344499 + 0.383439i
691691 −106.012 106.012i −0.00583628 0.00583628i 0.704183 0.710019i 0.251314π-0.251314\pi
−0.710019 + 0.704183i 0.751314π0.751314\pi
692692 −5238.60 3631.73i −0.287777 0.199505i
693693 18588.2 18588.2i 1.01891 1.01891i
694694 −5391.37 + 6455.77i −0.294890 + 0.353109i
695695 10129.8i 0.552870i
696696 −689.863 2504.23i −0.0375707 0.136383i
697697 31900.4i 1.73359i
698698 20302.6 + 16955.2i 1.10095 + 0.919434i
699699 −6567.17 + 6567.17i −0.355355 + 0.355355i
700700 15972.4 2893.43i 0.862431 0.156231i
701701 7839.35 + 7839.35i 0.422380 + 0.422380i 0.886022 0.463643i 0.153458π-0.153458\pi
−0.463643 + 0.886022i 0.653458π0.653458\pi
702702 −2239.41 + 201.199i −0.120400 + 0.0108173i
703703 −12350.0 −0.662574
704704 3967.64 15684.1i 0.212409 0.839653i
705705 −11312.7 −0.604341
706706 −6245.17 + 561.095i −0.332918 + 0.0299109i
707707 −12149.1 12149.1i −0.646273 0.646273i
708708 35045.5 6348.55i 1.86030 0.336996i
709709 2728.30 2728.30i 0.144518 0.144518i −0.631146 0.775664i 0.717415π-0.717415\pi
0.775664 + 0.631146i 0.217415π0.217415\pi
710710 3079.19 + 2571.50i 0.162760 + 0.135925i
711711 27499.9i 1.45053i
712712 1578.90 + 5731.48i 0.0831066 + 0.301680i
713713 4665.84i 0.245073i
714714 31044.3 37173.3i 1.62718 1.94843i
715715 2349.01 2349.01i 0.122864 0.122864i
716716 −20476.0 14195.3i −1.06875 0.740925i
717717 −23309.5 23309.5i −1.21410 1.21410i
718718 527.011 + 5865.82i 0.0273926 + 0.304889i
719719 −32717.8 −1.69704 −0.848519 0.529166i 0.822505π-0.822505\pi
−0.848519 + 0.529166i 0.822505π0.822505\pi
720720 −12838.9 5841.37i −0.664553 0.302354i
721721 −45824.0 −2.36696
722722 1012.01 + 11264.1i 0.0521652 + 0.580616i
723723 −30620.3 30620.3i −1.57508 1.57508i
724724 781.844 1127.77i 0.0401340 0.0578914i
725725 −851.111 + 851.111i −0.0435993 + 0.0435993i
726726 4686.62 5611.88i 0.239582 0.286882i
727727 25847.2i 1.31859i 0.751883 + 0.659297i 0.229146π0.229146\pi
−0.751883 + 0.659297i 0.770854π0.770854\pi
728728 4435.26 7808.03i 0.225799 0.397507i
729729 27662.0i 1.40537i
730730 −9573.13 7994.75i −0.485366 0.405341i
731731 8870.50 8870.50i 0.448820 0.448820i
732732 10417.3 + 57506.1i 0.526004 + 2.90367i
733733 10131.9 + 10131.9i 0.510547 + 0.510547i 0.914694 0.404147i 0.132432π-0.132432\pi
−0.404147 + 0.914694i 0.632432π0.632432\pi
734734 −12702.8 + 1141.28i −0.638787 + 0.0573915i
735735 14192.1 0.712223
736736 −3773.48 7851.36i −0.188984 0.393213i
737737 −4798.27 −0.239819
738738 −33937.7 + 3049.11i −1.69277 + 0.152086i
739739 19163.7 + 19163.7i 0.953921 + 0.953921i 0.998984 0.0450633i 0.0143490π-0.0143490\pi
−0.0450633 + 0.998984i 0.514349π0.514349\pi
740740 −2171.76 11988.7i −0.107886 0.595558i
741741 4685.72 4685.72i 0.232300 0.232300i
742742 −13433.9 11219.0i −0.664656 0.555070i
743743 23322.1i 1.15155i −0.817607 0.575777i 0.804699π-0.804699\pi
0.817607 0.575777i 0.195301π-0.195301\pi
744744 14827.5 + 8422.59i 0.730650 + 0.415037i
745745 21309.8i 1.04796i
746746 22208.1 26592.5i 1.08994 1.30512i
747747 −10922.8 + 10922.8i −0.534999 + 0.534999i
748748 −12743.6 + 18382.1i −0.622933 + 0.898552i
749749 1977.03 + 1977.03i 0.0964473 + 0.0964473i
750750 2679.37 + 29822.3i 0.130449 + 1.45194i
751751 25994.0 1.26303 0.631515 0.775364i 0.282434π-0.282434\pi
0.631515 + 0.775364i 0.282434π0.282434\pi
752752 13225.4 4954.16i 0.641330 0.240239i
753753 −5306.32 −0.256804
754754 59.5842 + 663.192i 0.00287789 + 0.0320319i
755755 13125.5 + 13125.5i 0.632698 + 0.632698i
756756 8162.97 + 5659.09i 0.392704 + 0.272247i
757757 22145.0 22145.0i 1.06324 1.06324i 0.0653808 0.997860i 0.479174π-0.479174\pi
0.997860 0.0653808i 0.0208262π-0.0208262\pi
758758 −9031.52 + 10814.6i −0.432770 + 0.518210i
759759 11819.0i 0.565222i
760760 7695.22 2119.87i 0.367283 0.101179i
761761 16497.5i 0.785853i 0.919570 + 0.392926i 0.128537π0.128537\pi
−0.919570 + 0.392926i 0.871463π0.871463\pi
762762 −44250.1 36954.4i −2.10369 1.75684i
763763 23725.9 23725.9i 1.12573 1.12573i
764764 30918.0 5600.84i 1.46410 0.265224i
765765 13789.7 + 13789.7i 0.651723 + 0.651723i
766766 −8577.66 + 770.656i −0.404600 + 0.0363511i
767767 −9130.02 −0.429812
768768 31762.5 + 2181.27i 1.49236 + 0.102487i
769769 −24867.3 −1.16611 −0.583055 0.812433i 0.698143π-0.698143\pi
−0.583055 + 0.812433i 0.698143π0.698143\pi
770770 −14616.5 + 1313.21i −0.684082 + 0.0614610i
771771 44481.2 + 44481.2i 2.07776 + 2.07776i
772772 −25575.9 + 4633.11i −1.19235 + 0.215996i
773773 1881.72 1881.72i 0.0875559 0.0875559i −0.661972 0.749528i 0.730280π-0.730280\pi
0.749528 + 0.661972i 0.230280π0.230280\pi
774774 10284.9 + 8589.14i 0.477625 + 0.398876i
775775 7902.00i 0.366256i
776776 3289.68 906.240i 0.152181 0.0419228i
777777 44684.8i 2.06314i
778778 −4955.49 + 5933.84i −0.228359 + 0.273443i
779779 13634.4 13634.4i 0.627089 0.627089i
780780 5372.62 + 3724.64i 0.246629 + 0.170979i
781781 4804.89 + 4804.89i 0.220144 + 0.220144i
782782 1077.72 + 11995.4i 0.0492828 + 0.548535i
783783 −736.525 −0.0336159
784784 −16591.7 + 6215.16i −0.755815 + 0.283125i
785785 8453.54 0.384356
786786 −1829.47 20362.7i −0.0830219 0.924062i
787787 −7790.94 7790.94i −0.352881 0.352881i 0.508300 0.861180i 0.330274π-0.330274\pi
−0.861180 + 0.508300i 0.830274π0.830274\pi
788788 15604.9 22509.3i 0.705457 1.01759i
789789 2255.08 2255.08i 0.101753 0.101753i
790790 −9840.66 + 11783.5i −0.443184 + 0.530680i
791791 17937.2i 0.806286i
792792 −20774.1 11800.5i −0.932041 0.529435i
793793 14981.4i 0.670877i
794794 2064.56 + 1724.17i 0.0922778 + 0.0770634i
795795 9009.98 9009.98i 0.401951 0.401951i
796796 1955.48 + 10794.7i 0.0870730 + 0.480665i
797797 −4209.84 4209.84i −0.187102 0.187102i 0.607340 0.794442i 0.292237π-0.292237\pi
−0.794442 + 0.607340i 0.792237π0.792237\pi
798798 −29156.5 + 2619.55i −1.29340 + 0.116205i
799799 −19525.8 −0.864549
800800 −6390.71 13296.9i −0.282432 0.587648i
801801 8779.50 0.387276
802802 21428.8 1925.26i 0.943488 0.0847672i
803803 −14938.3 14938.3i −0.656490 0.656490i
804804 −1683.15 9291.39i −0.0738308 0.407565i
805805 −5587.51 + 5587.51i −0.244639 + 0.244639i
806806 −3355.25 2802.05i −0.146630 0.122454i
807807 52.5393i 0.00229178i
808808 −7712.73 + 13577.8i −0.335808 + 0.591172i
809809 27554.3i 1.19747i 0.800946 + 0.598737i 0.204330π0.204330\pi
−0.800946 + 0.598737i 0.795670π0.795670\pi
810810 6153.46 7368.32i 0.266927 0.319625i
811811 3406.54 3406.54i 0.147497 0.147497i −0.629502 0.776999i 0.716741π-0.716741\pi
0.776999 + 0.629502i 0.216741π0.216741\pi
812812 1675.92 2417.43i 0.0724300 0.104477i
813813 −15576.1 15576.1i −0.671926 0.671926i
814814 −1846.69 20554.3i −0.0795166 0.885047i
815815 −12987.1 −0.558184
816816 −40065.4 18228.7i −1.71884 0.782026i
817817 −7582.59 −0.324701
818818 −1260.83 14033.5i −0.0538924 0.599841i
819819 −9377.16 9377.16i −0.400079 0.400079i
820820 15633.1 + 10837.8i 0.665770 + 0.461554i
821821 −9839.14 + 9839.14i −0.418256 + 0.418256i −0.884602 0.466346i 0.845570π-0.845570\pi
0.466346 + 0.884602i 0.345570π0.345570\pi
822822 35392.7 42380.1i 1.50178 1.79827i
823823 36653.5i 1.55244i −0.630461 0.776221i 0.717134π-0.717134\pi
0.630461 0.776221i 0.282866π-0.282866\pi
824824 11061.0 + 40151.9i 0.467632 + 1.69752i
825825 20016.5i 0.844711i
826826 30957.5 + 25853.3i 1.30405 + 1.08905i
827827 −22223.2 + 22223.2i −0.934431 + 0.934431i −0.997979 0.0635475i 0.979759π-0.979759\pi
0.0635475 + 0.997979i 0.479759π0.479759\pi
828828 −12658.4 + 2293.09i −0.531294 + 0.0962446i
829829 14715.5 + 14715.5i 0.616516 + 0.616516i 0.944636 0.328120i 0.106415π-0.106415\pi
−0.328120 + 0.944636i 0.606415π0.606415\pi
830830 8588.98 771.672i 0.359190 0.0322713i
831831 16772.2 0.700145
832832 −7912.13 2001.55i −0.329692 0.0834031i
833833 24495.8 1.01888
834834 33630.0 3021.47i 1.39630 0.125450i
835835 5697.46 + 5697.46i 0.236130 + 0.236130i
836836 13303.3 2409.91i 0.550364 0.0996991i
837837 3419.07 3419.07i 0.141195 0.141195i
838838 10541.1 + 8803.12i 0.434530 + 0.362886i
839839 11010.0i 0.453050i −0.974005 0.226525i 0.927263π-0.927263\pi
0.974005 0.226525i 0.0727365π-0.0727365\pi
840840 −7670.13 27842.8i −0.315053 1.14365i
841841 24170.9i 0.991057i
842842 −20444.5 + 24480.8i −0.836773 + 1.00197i
843843 −26108.1 + 26108.1i −1.06668 + 1.06668i
844844 −15067.2 10445.5i −0.614496 0.426007i
845845 9061.20 + 9061.20i 0.368893 + 0.368893i
846846 −1866.32 20772.8i −0.0758458 0.844190i
847847 8279.85 0.335890
848848 −6587.61 + 14479.1i −0.266768 + 0.586338i
849849 7080.22 0.286210
850850 1825.21 + 20315.2i 0.0736520 + 0.819772i
851851 −7857.37 7857.37i −0.316507 0.316507i
852852 −7618.74 + 10989.7i −0.306354 + 0.441901i
853853 12809.9 12809.9i 0.514190 0.514190i −0.401617 0.915808i 0.631552π-0.631552\pi
0.915808 + 0.401617i 0.131552π0.131552\pi
854854 −42422.7 + 50798.0i −1.69985 + 2.03545i
855855 11787.6i 0.471493i
856856 1255.09 2209.52i 0.0501147 0.0882243i
857857 38510.8i 1.53501i −0.641043 0.767505i 0.721498π-0.721498\pi
0.641043 0.767505i 0.278502π-0.278502\pi
858858 8499.18 + 7097.87i 0.338178 + 0.282421i
859859 23234.6 23234.6i 0.922882 0.922882i −0.0743503 0.997232i 0.523688π-0.523688\pi
0.997232 + 0.0743503i 0.0236883π0.0236883\pi
860860 −1333.41 7360.74i −0.0528707 0.291860i
861861 −49331.9 49331.9i −1.95264 1.95264i
862862 −13522.4 + 1214.92i −0.534311 + 0.0480049i
863863 −22079.5 −0.870911 −0.435456 0.900210i 0.643413π-0.643413\pi
−0.435456 + 0.900210i 0.643413π0.643413\pi
864864 2988.22 8518.55i 0.117664 0.335425i
865865 5255.26 0.206571
866866 −17585.1 + 1579.93i −0.690031 + 0.0619955i
867867 16029.8 + 16029.8i 0.627912 + 0.627912i
868868 3442.24 + 19002.0i 0.134605 + 0.743054i
869869 −18387.4 + 18387.4i −0.717779 + 0.717779i
870870 1643.69 + 1372.68i 0.0640531 + 0.0534923i
871871 2420.58i 0.0941656i
872872 −26516.0 15062.1i −1.02975 0.584939i
873873 5039.15i 0.195360i
874874 4666.26 5587.51i 0.180593 0.216247i
875875 −23976.7 + 23976.7i −0.926356 + 0.926356i
876876 23686.5 34166.7i 0.913576 1.31779i
877877 4082.13 + 4082.13i 0.157176 + 0.157176i 0.781314 0.624138i 0.214550π-0.214550\pi
−0.624138 + 0.781314i 0.714550π0.714550\pi
878878 −1247.59 13886.2i −0.0479547 0.533753i
879879 −15753.9 −0.604510
880880 4678.80 + 12490.3i 0.179230 + 0.478463i
881881 7132.59 0.272762 0.136381 0.990656i 0.456453π-0.456453\pi
0.136381 + 0.990656i 0.456453π0.456453\pi
882882 2341.36 + 26060.2i 0.0893853 + 0.994889i
883883 19170.0 + 19170.0i 0.730601 + 0.730601i 0.970739 0.240138i 0.0771926π-0.0771926\pi
−0.240138 + 0.970739i 0.577193π0.577193\pi
884884 9273.21 + 6428.78i 0.352819 + 0.244596i
885885 −20762.9 + 20762.9i −0.788628 + 0.788628i
886886 19667.4 23550.3i 0.745757 0.892989i
887887 45045.7i 1.70517i 0.522589 + 0.852585i 0.324966π0.324966\pi
−0.522589 + 0.852585i 0.675034π0.675034\pi
888888 39153.7 10786.0i 1.47963 0.407607i
889889 65287.3i 2.46306i
890890 −3761.94 3141.69i −0.141686 0.118325i
891891 11497.8 11497.8i 0.432314 0.432314i
892892 −3303.17 + 598.374i −0.123989 + 0.0224608i
893893 8345.43 + 8345.43i 0.312731 + 0.312731i
894894 70746.8 6356.21i 2.64667 0.237789i
895895 20541.1 0.767167
896896 21160.2 + 29191.4i 0.788964 + 1.08841i
897897 5962.34 0.221936
898898 32439.2 2914.49i 1.20547 0.108305i
899899 −1012.55 1012.55i −0.0375643 0.0375643i
900900 −21438.2 + 3883.55i −0.794006 + 0.143835i
901901 15551.4 15551.4i 0.575017 0.575017i
902902 24730.6 + 20653.2i 0.912905 + 0.762389i
903903 27435.3i 1.01106i
904904 15716.9 4329.68i 0.578247 0.159295i
905905 1131.36i 0.0415554i
906906 −39660.6 + 47490.7i −1.45435 + 1.74147i
907907 −33658.2 + 33658.2i −1.23220 + 1.23220i −0.269079 + 0.963118i 0.586719π0.586719\pi
−0.963118 + 0.269079i 0.913281π0.913281\pi
908908 −19838.3 13753.2i −0.725065 0.502661i
909909 16306.5 + 16306.5i 0.594997 + 0.594997i
910910 662.476 + 7373.59i 0.0241328 + 0.268607i
911911 −42503.8 −1.54579 −0.772895 0.634534i 0.781192π-0.781192\pi
−0.772895 + 0.634534i 0.781192π0.781192\pi
912912 9333.11 + 24915.2i 0.338871 + 0.904632i
913913 14606.7 0.529477
914914 −1222.44 13606.2i −0.0442394 0.492399i
915915 −34069.7 34069.7i −1.23094 1.23094i
916916 −10148.5 + 14638.7i −0.366066 + 0.528033i
917917 16371.3 16371.3i 0.589562 0.589562i
918918 −8000.34 + 9579.82i −0.287637 + 0.344424i
919919 8819.41i 0.316568i 0.987394 + 0.158284i 0.0505961π0.0505961\pi
−0.987394 + 0.158284i 0.949404π0.949404\pi
920920 6244.60 + 3547.17i 0.223781 + 0.127116i
921921 2541.55i 0.0909305i
922922 −25377.5 21193.3i −0.906467 0.757012i
923923 2423.92 2423.92i 0.0864402 0.0864402i
924924 −8719.53 48134.0i −0.310445 1.71374i
925925 −13307.1 13307.1i −0.473012 0.473012i
926926 14209.0 1276.60i 0.504250 0.0453041i
927927 61504.8 2.17916
928928 −2522.73 884.950i −0.0892380 0.0313038i
929929 −14155.6 −0.499925 −0.249963 0.968256i 0.580418π-0.580418\pi
−0.249963 + 0.968256i 0.580418π0.580418\pi
930930 −14002.5 + 1258.05i −0.493721 + 0.0443581i
931931 −10469.6 10469.6i −0.368558 0.368558i
932932 1703.87 + 9405.80i 0.0598844 + 0.330577i
933933 −4789.43 + 4789.43i −0.168059 + 0.168059i
934934 −38189.4 31892.9i −1.33790 1.11731i
935935 18440.6i 0.644996i
936936 −5952.99 + 10479.9i −0.207884 + 0.365969i
937937 38518.7i 1.34296i 0.741023 + 0.671479i 0.234341π0.234341\pi
−0.741023 + 0.671479i 0.765659π0.765659\pi
938938 6854.32 8207.55i 0.238594 0.285699i
939939 19319.2 19319.2i 0.671414 0.671414i
940940 −6633.71 + 9568.82i −0.230179 + 0.332022i
941941 27998.2 + 27998.2i 0.969942 + 0.969942i 0.999561 0.0296196i 0.00942960π-0.00942960\pi
−0.0296196 + 0.999561i 0.509430π0.509430\pi
942942 2521.49 + 28065.1i 0.0872130 + 0.970711i
943943 17349.0 0.599112
944944 15180.7 33366.0i 0.523399 1.15039i
945945 −8188.93 −0.281890
946946 −1133.82 12619.8i −0.0389680 0.433727i
947947 −32839.5 32839.5i −1.12687 1.12687i −0.990684 0.136181i 0.956517π-0.956517\pi
−0.136181 0.990684i 0.543483π-0.543483\pi
948948 −42055.4 29155.5i −1.44082 0.998867i
949949 −7535.92 + 7535.92i −0.257773 + 0.257773i
950950 7902.71 9462.92i 0.269892 0.323176i
951951 51925.4i 1.77055i
952952 −13238.7 48057.1i −0.450704 1.63607i
953953 20600.1i 0.700211i 0.936710 + 0.350106i 0.113854π0.113854\pi
−0.936710 + 0.350106i 0.886146π0.886146\pi
954954 18031.0 + 15058.1i 0.611922 + 0.511031i
955955 −18317.5 + 18317.5i −0.620670 + 0.620670i
956956 −33384.9 + 6047.72i −1.12944 + 0.204600i
957957 2564.88 + 2564.88i 0.0866360 + 0.0866360i
958958 −36790.3 + 3305.41i −1.24075 + 0.111475i
959959 62528.2 2.10547
960960 −22545.0 + 13441.4i −0.757955 + 0.451896i
961961 −20390.2 −0.684441
962962 −10369.0 + 931.599i −0.347516 + 0.0312224i
963963 −2653.56 2653.56i −0.0887951 0.0887951i
964964 −43855.8 + 7944.53i −1.46525 + 0.265432i
965965 15152.5 15152.5i 0.505469 0.505469i
966966 −20216.7 16883.5i −0.673356 0.562336i
967967 38210.9i 1.27071i −0.772219 0.635356i 0.780853π-0.780853\pi
0.772219 0.635356i 0.219147π-0.219147\pi
968968 −1998.59 7254.96i −0.0663607 0.240892i
969969 36784.6i 1.21950i
970970 −1803.23 + 2159.23i −0.0596888 + 0.0714730i
971971 37224.9 37224.9i 1.23028 1.23028i 0.266427 0.963855i 0.414157π-0.414157\pi
0.963855 0.266427i 0.0858430π-0.0858430\pi
972972 35150.3 + 24368.4i 1.15992 + 0.804133i
973973 27038.1 + 27038.1i 0.890854 + 0.890854i
974974 −3935.51 43803.6i −0.129468 1.44102i
975975 10097.7 0.331678
976976 54750.2 + 24909.9i 1.79560 + 0.816953i
977977 7985.95 0.261508 0.130754 0.991415i 0.458260π-0.458260\pi
0.130754 + 0.991415i 0.458260π0.458260\pi
978978 −3873.76 43116.3i −0.126656 1.40972i
979979 −5870.28 5870.28i −0.191639 0.191639i
980980 8322.21 12004.4i 0.271269 0.391292i
981981 −31844.8 + 31844.8i −1.03642 + 1.03642i
982982 22122.9 26490.5i 0.718910 0.860842i
983983 10703.1i 0.347279i 0.984809 + 0.173639i 0.0555527π0.0555527\pi
−0.984809 + 0.173639i 0.944447π0.944447\pi
984984 −31317.8 + 55133.3i −1.01461 + 1.78616i
985985 22580.9i 0.730442i
986986 2837.03 + 2369.27i 0.0916322 + 0.0765243i
987987 30195.4 30195.4i 0.973791 0.973791i
988988 −1215.72 6711.10i −0.0391471 0.216102i
989989 −4824.23 4824.23i −0.155108 0.155108i
990990 19618.2 1762.59i 0.629807 0.0565847i
991991 −23945.4 −0.767558 −0.383779 0.923425i 0.625377π-0.625377\pi
−0.383779 + 0.923425i 0.625377π0.625377\pi
992992 15819.0 7602.87i 0.506306 0.243338i
993993 −20009.0 −0.639442
994994 −15082.6 + 1355.09i −0.481280 + 0.0432404i
995995 −6395.37 6395.37i −0.203766 0.203766i
996996 5123.78 + 28284.5i 0.163005 + 0.899829i
997997 −14292.5 + 14292.5i −0.454010 + 0.454010i −0.896683 0.442673i 0.854030π-0.854030\pi
0.442673 + 0.896683i 0.354030π0.354030\pi
998998 −5318.83 4441.88i −0.168702 0.140887i
999999 11515.6i 0.364702i
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 16.4.e.a.13.1 yes 10
3.2 odd 2 144.4.k.a.109.5 10
4.3 odd 2 64.4.e.a.17.1 10
8.3 odd 2 128.4.e.a.33.5 10
8.5 even 2 128.4.e.b.33.1 10
12.11 even 2 576.4.k.a.145.4 10
16.3 odd 4 128.4.e.a.97.5 10
16.5 even 4 inner 16.4.e.a.5.1 10
16.11 odd 4 64.4.e.a.49.1 10
16.13 even 4 128.4.e.b.97.1 10
32.3 odd 8 1024.4.b.k.513.2 10
32.5 even 8 1024.4.a.n.1.2 10
32.11 odd 8 1024.4.a.m.1.2 10
32.13 even 8 1024.4.b.j.513.2 10
32.19 odd 8 1024.4.b.k.513.9 10
32.21 even 8 1024.4.a.n.1.9 10
32.27 odd 8 1024.4.a.m.1.9 10
32.29 even 8 1024.4.b.j.513.9 10
48.5 odd 4 144.4.k.a.37.5 10
48.11 even 4 576.4.k.a.433.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.4.e.a.5.1 10 16.5 even 4 inner
16.4.e.a.13.1 yes 10 1.1 even 1 trivial
64.4.e.a.17.1 10 4.3 odd 2
64.4.e.a.49.1 10 16.11 odd 4
128.4.e.a.33.5 10 8.3 odd 2
128.4.e.a.97.5 10 16.3 odd 4
128.4.e.b.33.1 10 8.5 even 2
128.4.e.b.97.1 10 16.13 even 4
144.4.k.a.37.5 10 48.5 odd 4
144.4.k.a.109.5 10 3.2 odd 2
576.4.k.a.145.4 10 12.11 even 2
576.4.k.a.433.4 10 48.11 even 4
1024.4.a.m.1.2 10 32.11 odd 8
1024.4.a.m.1.9 10 32.27 odd 8
1024.4.a.n.1.2 10 32.5 even 8
1024.4.a.n.1.9 10 32.21 even 8
1024.4.b.j.513.2 10 32.13 even 8
1024.4.b.j.513.9 10 32.29 even 8
1024.4.b.k.513.2 10 32.3 odd 8
1024.4.b.k.513.9 10 32.19 odd 8