Properties

Label 416.2.bg.a.77.1
Level 416416
Weight 22
Character 416.77
Analytic conductor 3.3223.322
Analytic rank 00
Dimension 216216
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [416,2,Mod(77,416)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(416, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("416.77");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 416=2513 416 = 2^{5} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 416.bg (of order 88, degree 44, 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: 3.321776724093.32177672409
Analytic rank: 00
Dimension: 216216
Relative dimension: 5454 over Q(ζ8)\Q(\zeta_{8})
Twist minimal: yes
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

Embedding invariants

Embedding label 77.1
Character χ\chi == 416.77
Dual form 416.2.bg.a.389.1

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+(1.412100.0772002i)q2+(0.397360+0.959313i)q3+(1.98808+0.218030i)q4+(1.53059+3.69517i)q5+(0.6351741.32397i)q6+(2.05838+2.05838i)q7+(2.790550.461361i)q8+(1.35893+1.35893i)q9+(1.876095.33613i)q10+(3.54378+1.46788i)q11+(0.999143+1.82055i)q12+(2.84949+2.20917i)q13+(2.747743.06556i)q144.15302q15+(3.90493+0.866921i)q167.36012iq17+(1.814052.02387i)q18+(2.658636.41850i)q19+(2.23728+7.68001i)q20+(2.79255+1.15671i)q21+(5.117511.79922i)q22+(1.167541.16754i)q23+(1.551442.49368i)q24+(7.77604+7.77604i)q25+(3.853223.33956i)q26+(4.72157+1.95574i)q27+(3.64344+4.54101i)q28+(0.2161470.521825i)q29+(5.86450+0.320614i)q302.50053iq31+(5.447241.52564i)q323.98287iq33+(0.568203+10.3933i)q34+(4.45553+10.7566i)q35+(2.40538+2.99796i)q36+(1.41369+3.41294i)q37+(4.24977+8.85835i)q38+(3.25156+1.85571i)q39+(2.5663711.0177i)q40+(4.166474.16647i)q41+(4.032671.41781i)q42+(1.85725+4.48380i)q43+(7.36536+2.14562i)q44+(2.94152+7.10147i)q45+(1.55855+1.73882i)q46+3.77337q47+(2.38331+3.40157i)q48+1.47386iq49+(11.580910.3803i)q50+(7.06066+2.92462i)q51+(5.18334+5.01328i)q52+(2.74388+6.62432i)q53+(6.818332.39720i)q54+(10.848110.8481i)q55+(4.794356.69366i)q56+(5.10092+5.10092i)q57+(0.345507+0.720185i)q58+(3.364978.12374i)q59+(8.256540.905481i)q60+(0.246606+0.595359i)q61+(0.193041+3.53100i)q62+5.59441iq63+(7.57429+2.57490i)q64+(3.80186+13.9107i)q65+(0.307478+5.62423i)q66+(3.114721.29016i)q67+(1.6047214.6325i)q68+(1.583970.656100i)q69+(7.1220914.8455i)q70+(7.663327.66332i)q71+(3.165214.41913i)q72+(2.64357+2.64357i)q73+(1.732794.92857i)q74+(4.3697710.5496i)q75+(6.6849912.1808i)q76+(10.31594.27299i)q77+(4.734802.36944i)q788.91163iq79+(2.77342+15.7563i)q80+0.458877iq81+(6.20514+5.56184i)q82+(0.865494+2.08949i)q83+(5.80401+1.69078i)q84+(27.196911.2653i)q85+(2.276486.47497i)q86+(0.414705+0.414705i)q87+(10.56632.46123i)q88+(8.31178+8.31178i)q89+(4.701979.80093i)q90+(1.31801+10.4126i)q91+(2.066602.57571i)q92+(2.39879+0.993610i)q93+(5.328400.291305i)q94+27.7867q95+(3.628094.61938i)q968.83594iq97+(0.1137822.08124i)q98+(6.810522.82101i)q99+O(q100)q+(-1.41210 - 0.0772002i) q^{2} +(-0.397360 + 0.959313i) q^{3} +(1.98808 + 0.218030i) q^{4} +(1.53059 + 3.69517i) q^{5} +(0.635174 - 1.32397i) q^{6} +(2.05838 + 2.05838i) q^{7} +(-2.79055 - 0.461361i) q^{8} +(1.35893 + 1.35893i) q^{9} +(-1.87609 - 5.33613i) q^{10} +(-3.54378 + 1.46788i) q^{11} +(-0.999143 + 1.82055i) q^{12} +(2.84949 + 2.20917i) q^{13} +(-2.74774 - 3.06556i) q^{14} -4.15302 q^{15} +(3.90493 + 0.866921i) q^{16} -7.36012i q^{17} +(-1.81405 - 2.02387i) q^{18} +(2.65863 - 6.41850i) q^{19} +(2.23728 + 7.68001i) q^{20} +(-2.79255 + 1.15671i) q^{21} +(5.11751 - 1.79922i) q^{22} +(-1.16754 - 1.16754i) q^{23} +(1.55144 - 2.49368i) q^{24} +(-7.77604 + 7.77604i) q^{25} +(-3.85322 - 3.33956i) q^{26} +(-4.72157 + 1.95574i) q^{27} +(3.64344 + 4.54101i) q^{28} +(0.216147 - 0.521825i) q^{29} +(5.86450 + 0.320614i) q^{30} -2.50053i q^{31} +(-5.44724 - 1.52564i) q^{32} -3.98287i q^{33} +(-0.568203 + 10.3933i) q^{34} +(-4.45553 + 10.7566i) q^{35} +(2.40538 + 2.99796i) q^{36} +(1.41369 + 3.41294i) q^{37} +(-4.24977 + 8.85835i) q^{38} +(-3.25156 + 1.85571i) q^{39} +(-2.56637 - 11.0177i) q^{40} +(4.16647 - 4.16647i) q^{41} +(4.03267 - 1.41781i) q^{42} +(1.85725 + 4.48380i) q^{43} +(-7.36536 + 2.14562i) q^{44} +(-2.94152 + 7.10147i) q^{45} +(1.55855 + 1.73882i) q^{46} +3.77337 q^{47} +(-2.38331 + 3.40157i) q^{48} +1.47386i q^{49} +(11.5809 - 10.3803i) q^{50} +(7.06066 + 2.92462i) q^{51} +(5.18334 + 5.01328i) q^{52} +(2.74388 + 6.62432i) q^{53} +(6.81833 - 2.39720i) q^{54} +(-10.8481 - 10.8481i) q^{55} +(-4.79435 - 6.69366i) q^{56} +(5.10092 + 5.10092i) q^{57} +(-0.345507 + 0.720185i) q^{58} +(-3.36497 - 8.12374i) q^{59} +(-8.25654 - 0.905481i) q^{60} +(-0.246606 + 0.595359i) q^{61} +(-0.193041 + 3.53100i) q^{62} +5.59441i q^{63} +(7.57429 + 2.57490i) q^{64} +(-3.80186 + 13.9107i) q^{65} +(-0.307478 + 5.62423i) q^{66} +(-3.11472 - 1.29016i) q^{67} +(1.60472 - 14.6325i) q^{68} +(1.58397 - 0.656100i) q^{69} +(7.12209 - 14.8455i) q^{70} +(-7.66332 - 7.66332i) q^{71} +(-3.16521 - 4.41913i) q^{72} +(-2.64357 + 2.64357i) q^{73} +(-1.73279 - 4.92857i) q^{74} +(-4.36977 - 10.5496i) q^{75} +(6.68499 - 12.1808i) q^{76} +(-10.3159 - 4.27299i) q^{77} +(4.73480 - 2.36944i) q^{78} -8.91163i q^{79} +(2.77342 + 15.7563i) q^{80} +0.458877i q^{81} +(-6.20514 + 5.56184i) q^{82} +(-0.865494 + 2.08949i) q^{83} +(-5.80401 + 1.69078i) q^{84} +(27.1969 - 11.2653i) q^{85} +(-2.27648 - 6.47497i) q^{86} +(0.414705 + 0.414705i) q^{87} +(10.5663 - 2.46123i) q^{88} +(8.31178 + 8.31178i) q^{89} +(4.70197 - 9.80093i) q^{90} +(1.31801 + 10.4126i) q^{91} +(-2.06660 - 2.57571i) q^{92} +(2.39879 + 0.993610i) q^{93} +(-5.32840 - 0.291305i) q^{94} +27.7867 q^{95} +(3.62809 - 4.61938i) q^{96} -8.83594i q^{97} +(0.113782 - 2.08124i) q^{98} +(-6.81052 - 2.82101i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 216q8q38q48q98q1024q124q13+24q148q16+8q228q238q25+16q2656q278q2924q308q35+16q3648q38++112q95+O(q100) 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38}+ \cdots + 112 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/416Z)×\left(\mathbb{Z}/416\mathbb{Z}\right)^\times.

nn 261261 287287 353353
χ(n)\chi(n) e(78)e\left(\frac{7}{8}\right) 11 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 −1.41210 0.0772002i −0.998509 0.0545888i
33 −0.397360 + 0.959313i −0.229416 + 0.553859i −0.996107 0.0881575i 0.971902π-0.971902\pi
0.766690 + 0.642017i 0.221902π0.221902\pi
44 1.98808 + 0.218030i 0.994040 + 0.109015i
55 1.53059 + 3.69517i 0.684500 + 1.65253i 0.755577 + 0.655059i 0.227356π0.227356\pi
−0.0710768 + 0.997471i 0.522644π0.522644\pi
66 0.635174 1.32397i 0.259309 0.540510i
77 2.05838 + 2.05838i 0.777995 + 0.777995i 0.979490 0.201495i 0.0645800π-0.0645800\pi
−0.201495 + 0.979490i 0.564580π0.564580\pi
88 −2.79055 0.461361i −0.986607 0.163116i
99 1.35893 + 1.35893i 0.452978 + 0.452978i
1010 −1.87609 5.33613i −0.593270 1.68743i
1111 −3.54378 + 1.46788i −1.06849 + 0.442583i −0.846457 0.532456i 0.821269π-0.821269\pi
−0.222032 + 0.975039i 0.571269π0.571269\pi
1212 −0.999143 + 1.82055i −0.288428 + 0.525549i
1313 2.84949 + 2.20917i 0.790305 + 0.612713i
1414 −2.74774 3.06556i −0.734365 0.819304i
1515 −4.15302 −1.07231
1616 3.90493 + 0.866921i 0.976232 + 0.216730i
1717 7.36012i 1.78509i −0.450957 0.892546i 0.648917π-0.648917\pi
0.450957 0.892546i 0.351083π-0.351083\pi
1818 −1.81405 2.02387i −0.427575 0.477030i
1919 2.65863 6.41850i 0.609932 1.47251i −0.253143 0.967429i 0.581464π-0.581464\pi
0.863075 0.505076i 0.168536π-0.168536\pi
2020 2.23728 + 7.68001i 0.500271 + 1.71730i
2121 −2.79255 + 1.15671i −0.609384 + 0.252415i
2222 5.11751 1.79922i 1.09106 0.383595i
2323 −1.16754 1.16754i −0.243448 0.243448i 0.574827 0.818275i 0.305069π-0.305069\pi
−0.818275 + 0.574827i 0.805069π0.805069\pi
2424 1.55144 2.49368i 0.316687 0.509020i
2525 −7.77604 + 7.77604i −1.55521 + 1.55521i
2626 −3.85322 3.33956i −0.755679 0.654942i
2727 −4.72157 + 1.95574i −0.908666 + 0.376382i
2828 3.64344 + 4.54101i 0.688545 + 0.858171i
2929 0.216147 0.521825i 0.0401375 0.0969004i −0.902540 0.430607i 0.858299π-0.858299\pi
0.942677 + 0.333707i 0.108299π0.108299\pi
3030 5.86450 + 0.320614i 1.07071 + 0.0585358i
3131 2.50053i 0.449108i −0.974462 0.224554i 0.927908π-0.927908\pi
0.974462 0.224554i 0.0720925π-0.0720925\pi
3232 −5.44724 1.52564i −0.962945 0.269698i
3333 3.98287i 0.693329i
3434 −0.568203 + 10.3933i −0.0974460 + 1.78243i
3535 −4.45553 + 10.7566i −0.753122 + 1.81820i
3636 2.40538 + 2.99796i 0.400897 + 0.499660i
3737 1.41369 + 3.41294i 0.232409 + 0.561084i 0.996460 0.0840716i 0.0267925π-0.0267925\pi
−0.764051 + 0.645156i 0.776792π0.776792\pi
3838 −4.24977 + 8.85835i −0.689405 + 1.43701i
3939 −3.25156 + 1.85571i −0.520666 + 0.297152i
4040 −2.56637 11.0177i −0.405779 1.74205i
4141 4.16647 4.16647i 0.650693 0.650693i −0.302467 0.953160i 0.597810π-0.597810\pi
0.953160 + 0.302467i 0.0978102π0.0978102\pi
4242 4.03267 1.41781i 0.622255 0.218773i
4343 1.85725 + 4.48380i 0.283228 + 0.683773i 0.999907 0.0136304i 0.00433882π-0.00433882\pi
−0.716679 + 0.697403i 0.754339π0.754339\pi
4444 −7.36536 + 2.14562i −1.11037 + 0.323464i
4545 −2.94152 + 7.10147i −0.438496 + 1.05862i
4646 1.55855 + 1.73882i 0.229796 + 0.256375i
4747 3.77337 0.550403 0.275202 0.961387i 0.411255π-0.411255\pi
0.275202 + 0.961387i 0.411255π0.411255\pi
4848 −2.38331 + 3.40157i −0.344001 + 0.490974i
4949 1.47386i 0.210551i
5050 11.5809 10.3803i 1.63779 1.46799i
5151 7.06066 + 2.92462i 0.988690 + 0.409529i
5252 5.18334 + 5.01328i 0.718800 + 0.695217i
5353 2.74388 + 6.62432i 0.376901 + 0.909920i 0.992543 + 0.121894i 0.0388968π0.0388968\pi
−0.615642 + 0.788026i 0.711103π0.711103\pi
5454 6.81833 2.39720i 0.927858 0.326218i
5555 −10.8481 10.8481i −1.46276 1.46276i
5656 −4.79435 6.69366i −0.640672 0.894478i
5757 5.10092 + 5.10092i 0.675633 + 0.675633i
5858 −0.345507 + 0.720185i −0.0453673 + 0.0945649i
5959 −3.36497 8.12374i −0.438081 1.05762i −0.976611 0.215015i 0.931020π-0.931020\pi
0.538530 0.842607i 0.318980π-0.318980\pi
6060 −8.25654 0.905481i −1.06591 0.116897i
6161 −0.246606 + 0.595359i −0.0315746 + 0.0762279i −0.938880 0.344244i 0.888135π-0.888135\pi
0.907306 + 0.420472i 0.138135π0.138135\pi
6262 −0.193041 + 3.53100i −0.0245162 + 0.448438i
6363 5.59441i 0.704829i
6464 7.57429 + 2.57490i 0.946787 + 0.321862i
6565 −3.80186 + 13.9107i −0.471563 + 1.72541i
6666 −0.307478 + 5.62423i −0.0378480 + 0.692295i
6767 −3.11472 1.29016i −0.380524 0.157618i 0.184219 0.982885i 0.441025π-0.441025\pi
−0.564743 + 0.825267i 0.691025π0.691025\pi
6868 1.60472 14.6325i 0.194601 1.77445i
6969 1.58397 0.656100i 0.190687 0.0789852i
7070 7.12209 14.8455i 0.851252 1.77437i
7171 −7.66332 7.66332i −0.909469 0.909469i 0.0867604 0.996229i 0.472349π-0.472349\pi
−0.996229 + 0.0867604i 0.972349π0.972349\pi
7272 −3.16521 4.41913i −0.373024 0.520799i
7373 −2.64357 + 2.64357i −0.309406 + 0.309406i −0.844679 0.535273i 0.820209π-0.820209\pi
0.535273 + 0.844679i 0.320209π0.320209\pi
7474 −1.73279 4.92857i −0.201433 0.572934i
7575 −4.36977 10.5496i −0.504577 1.21816i
7676 6.68499 12.1808i 0.766821 1.39724i
7777 −10.3159 4.27299i −1.17561 0.486952i
7878 4.73480 2.36944i 0.536111 0.268286i
7979 8.91163i 1.00264i −0.865263 0.501319i 0.832848π-0.832848\pi
0.865263 0.501319i 0.167152π-0.167152\pi
8080 2.77342 + 15.7563i 0.310078 + 1.76160i
8181 0.458877i 0.0509864i
8282 −6.20514 + 5.56184i −0.685243 + 0.614202i
8383 −0.865494 + 2.08949i −0.0950003 + 0.229351i −0.964235 0.265049i 0.914612π-0.914612\pi
0.869235 + 0.494400i 0.164612π0.164612\pi
8484 −5.80401 + 1.69078i −0.633269 + 0.184479i
8585 27.1969 11.2653i 2.94992 1.22190i
8686 −2.27648 6.47497i −0.245479 0.698214i
8787 0.414705 + 0.414705i 0.0444610 + 0.0444610i
8888 10.5663 2.46123i 1.12637 0.262368i
8989 8.31178 + 8.31178i 0.881047 + 0.881047i 0.993641 0.112594i 0.0359160π-0.0359160\pi
−0.112594 + 0.993641i 0.535916π0.535916\pi
9090 4.70197 9.80093i 0.495632 1.03311i
9191 1.31801 + 10.4126i 0.138165 + 1.09154i
9292 −2.06660 2.57571i −0.215458 0.268537i
9393 2.39879 + 0.993610i 0.248743 + 0.103033i
9494 −5.32840 0.291305i −0.549582 0.0300458i
9595 27.7867 2.85086
9696 3.62809 4.61938i 0.370290 0.471463i
9797 8.83594i 0.897154i −0.893744 0.448577i 0.851931π-0.851931\pi
0.893744 0.448577i 0.148069π-0.148069\pi
9898 0.113782 2.08124i 0.0114937 0.210237i
9999 −6.81052 2.82101i −0.684483 0.283522i
100100 −17.1548 + 13.7640i −1.71548 + 1.37640i
101101 1.40230 0.580850i 0.139534 0.0577967i −0.311824 0.950140i 0.600940π-0.600940\pi
0.451358 + 0.892343i 0.350940π0.350940\pi
102102 −9.74461 4.67496i −0.964860 0.462890i
103103 0.960494 0.960494i 0.0946403 0.0946403i −0.658201 0.752842i 0.728683π-0.728683\pi
0.752842 + 0.658201i 0.228683π0.228683\pi
104104 −6.93240 7.47943i −0.679777 0.733419i
105105 −8.54849 8.54849i −0.834248 0.834248i
106106 −3.36325 9.56606i −0.326668 0.929138i
107107 5.49544 + 13.2672i 0.531265 + 1.28259i 0.930686 + 0.365819i 0.119211π0.119211\pi
−0.399421 + 0.916767i 0.630789π0.630789\pi
108108 −9.81327 + 2.85872i −0.944282 + 0.275081i
109109 6.06687 14.6467i 0.581100 1.40290i −0.310716 0.950503i 0.600569π-0.600569\pi
0.891816 0.452398i 0.149431π-0.149431\pi
110110 14.4812 + 16.1562i 1.38073 + 1.54043i
111111 −3.83582 −0.364080
112112 6.25337 + 9.82228i 0.590888 + 0.928118i
113113 7.29110i 0.685889i −0.939356 0.342945i 0.888576π-0.888576\pi
0.939356 0.342945i 0.111424π-0.111424\pi
114114 −6.80924 7.59682i −0.637744 0.711507i
115115 2.52723 6.10127i 0.235665 0.568946i
116116 0.543491 0.990303i 0.0504618 0.0919473i
117117 0.870148 + 6.87438i 0.0804452 + 0.635537i
118118 4.12453 + 11.7314i 0.379694 + 1.07996i
119119 15.1499 15.1499i 1.38879 1.38879i
120120 11.5892 + 1.91604i 1.05794 + 0.174910i
121121 2.62552 2.62552i 0.238684 0.238684i
122122 0.394195 0.821671i 0.0356887 0.0743906i
123123 2.34136 + 5.65254i 0.211113 + 0.509672i
124124 0.545189 4.97124i 0.0489594 0.446431i
125125 −22.1599 9.17893i −1.98204 0.820988i
126126 0.431890 7.89989i 0.0384758 0.703778i
127127 −4.75853 −0.422251 −0.211126 0.977459i 0.567713π-0.567713\pi
−0.211126 + 0.977459i 0.567713π0.567713\pi
128128 −10.4969 4.22076i −0.927805 0.373066i
129129 −5.03936 −0.443691
130130 6.44254 19.3498i 0.565048 1.69709i
131131 −2.56389 + 6.18978i −0.224008 + 0.540804i −0.995427 0.0955240i 0.969547π-0.969547\pi
0.771419 + 0.636328i 0.219547π0.219547\pi
132132 0.868384 7.91827i 0.0755831 0.689197i
133133 18.6842 7.73925i 1.62012 0.671078i
134134 4.29871 + 2.06230i 0.371352 + 0.178155i
135135 −14.4536 14.4536i −1.24396 1.24396i
136136 −3.39567 + 20.5388i −0.291176 + 1.76118i
137137 −13.2945 + 13.2945i −1.13583 + 1.13583i −0.146639 + 0.989190i 0.546845π0.546845\pi
−0.989190 + 0.146639i 0.953155π0.953155\pi
138138 −2.28738 + 0.804200i −0.194714 + 0.0684580i
139139 −0.00167462 0.00404290i −0.000142040 0.000342914i 0.923808 0.382855i 0.125059π-0.125059\pi
−0.923951 + 0.382512i 0.875059π0.875059\pi
140140 −11.2032 + 20.4135i −0.946844 + 1.72526i
141141 −1.49939 + 3.61985i −0.126271 + 0.304846i
142142 10.2298 + 11.4130i 0.858466 + 0.957760i
143143 −13.3407 3.64610i −1.11561 0.304902i
144144 4.12845 + 6.48463i 0.344038 + 0.540386i
145145 2.25906 0.187605
146146 3.93708 3.52891i 0.325835 0.292055i
147147 −1.41389 0.585653i −0.116616 0.0483039i
148148 2.06640 + 7.09343i 0.169857 + 0.583076i
149149 −0.0814032 + 0.0337183i −0.00666881 + 0.00276231i −0.386015 0.922492i 0.626149π-0.626149\pi
0.379347 + 0.925255i 0.376149π0.376149\pi
150150 5.35614 + 15.2344i 0.437327 + 1.24389i
151151 −0.342580 + 0.342580i −0.0278787 + 0.0278787i −0.720909 0.693030i 0.756275π-0.756275\pi
0.693030 + 0.720909i 0.256275π0.256275\pi
152152 −10.3803 + 16.6845i −0.841952 + 1.35329i
153153 10.0019 10.0019i 0.808608 0.808608i
154154 14.2373 + 6.83030i 1.14727 + 0.550401i
155155 9.23987 3.82728i 0.742164 0.307414i
156156 −6.86896 + 2.98037i −0.549957 + 0.238620i
157157 −2.67456 + 6.45696i −0.213453 + 0.515321i −0.993949 0.109839i 0.964966π-0.964966\pi
0.780496 + 0.625160i 0.214966π0.214966\pi
158158 −0.687980 + 12.5842i −0.0547328 + 1.00114i
159159 −7.44510 −0.590435
160160 −2.69997 22.4636i −0.213452 1.77590i
161161 4.80647i 0.378803i
162162 0.0354254 0.647983i 0.00278329 0.0509104i
163163 11.5365 + 4.77857i 0.903607 + 0.374286i 0.785606 0.618727i 0.212351π-0.212351\pi
0.118001 + 0.993013i 0.462351π0.462351\pi
164164 9.19169 7.37486i 0.717750 0.575880i
165165 14.7174 6.09614i 1.14575 0.474584i
166166 1.38348 2.88376i 0.107379 0.223823i
167167 11.7216 + 11.7216i 0.907046 + 0.907046i 0.996033 0.0889869i 0.0283629π-0.0283629\pi
−0.0889869 + 0.996033i 0.528363π0.528363\pi
168168 8.32640 1.93948i 0.642396 0.149634i
169169 3.23914 + 12.5900i 0.249164 + 0.968461i
170170 −39.2746 + 13.8082i −3.01222 + 1.05904i
171171 12.3352 5.10942i 0.943299 0.390727i
172172 2.71476 + 9.31908i 0.206999 + 0.710573i
173173 10.9678 + 4.54302i 0.833868 + 0.345399i 0.758433 0.651751i 0.225965π-0.225965\pi
0.0754349 + 0.997151i 0.475965π0.475965\pi
174174 −0.553592 0.617622i −0.0419677 0.0468218i
175175 −32.0121 −2.41989
176176 −15.1107 + 2.65979i −1.13901 + 0.200489i
177177 9.13032 0.686277
178178 −11.0954 12.3788i −0.831638 0.927829i
179179 6.59163 + 2.73034i 0.492682 + 0.204075i 0.615170 0.788395i 0.289087π-0.289087\pi
−0.122488 + 0.992470i 0.539087π0.539087\pi
180180 −7.39631 + 13.4769i −0.551289 + 1.00451i
181181 −8.87929 21.4365i −0.659992 1.59336i −0.797813 0.602905i 0.794010π-0.794010\pi
0.137821 0.990457i 0.455990π-0.455990\pi
182182 −1.05732 14.8055i −0.0783735 1.09746i
183183 −0.473144 0.473144i −0.0349758 0.0349758i
184184 2.71941 + 3.79672i 0.200478 + 0.279898i
185185 −10.4476 + 10.4476i −0.768125 + 0.768125i
186186 −3.31063 1.58827i −0.242747 0.116457i
187187 10.8038 + 26.0826i 0.790051 + 1.90735i
188188 7.50177 + 0.822707i 0.547123 + 0.0600021i
189189 −13.7444 5.69313i −0.999761 0.414114i
190190 −39.2378 2.14514i −2.84661 0.155625i
191191 −24.5400 −1.77565 −0.887827 0.460178i 0.847786π-0.847786\pi
−0.887827 + 0.460178i 0.847786π0.847786\pi
192192 −5.47986 + 6.24295i −0.395475 + 0.450546i
193193 7.63410i 0.549514i −0.961514 0.274757i 0.911403π-0.911403\pi
0.961514 0.274757i 0.0885975π-0.0885975\pi
194194 −0.682137 + 12.4773i −0.0489746 + 0.895816i
195195 −11.8340 9.17473i −0.847448 0.657016i
196196 −0.321345 + 2.93015i −0.0229532 + 0.209296i
197197 0.420918 + 1.01619i 0.0299892 + 0.0724003i 0.938165 0.346189i 0.112525π-0.112525\pi
−0.908175 + 0.418590i 0.862525π0.862525\pi
198198 9.39938 + 4.50933i 0.667985 + 0.320464i
199199 1.28759 1.28759i 0.0912745 0.0912745i −0.659995 0.751270i 0.729442π-0.729442\pi
0.751270 + 0.659995i 0.229442π0.229442\pi
200200 25.2870 18.1118i 1.78806 1.28070i
201201 2.47533 2.47533i 0.174597 0.174597i
202202 −2.02503 + 0.711963i −0.142481 + 0.0500936i
203203 1.51903 0.629201i 0.106615 0.0441613i
204204 13.3995 + 7.35381i 0.938153 + 0.514870i
205205 21.7730 + 9.01866i 1.52069 + 0.629890i
206206 −1.43047 + 1.28217i −0.0996655 + 0.0893329i
207207 3.17321i 0.220554i
208208 9.21186 + 11.0969i 0.638727 + 0.769433i
209209 26.6483i 1.84330i
210210 11.4114 + 12.7313i 0.787463 + 0.878544i
211211 −14.6541 6.06993i −1.00883 0.417871i −0.183803 0.982963i 0.558841π-0.558841\pi
−0.825028 + 0.565092i 0.808841π0.808841\pi
212212 4.01076 + 13.7679i 0.275460 + 0.945585i
213213 10.3966 4.30642i 0.712365 0.295071i
214214 −6.73592 19.1589i −0.460458 1.30968i
215215 −13.7257 + 13.7257i −0.936085 + 0.936085i
216216 14.0781 3.27923i 0.957890 0.223123i
217217 5.14703 5.14703i 0.349403 0.349403i
218218 −9.69778 + 20.2143i −0.656817 + 1.36909i
219219 −1.48556 3.58646i −0.100385 0.242350i
220220 −19.2018 23.9322i −1.29458 1.61351i
221221 16.2598 20.9726i 1.09375 1.41077i
222222 5.41658 + 0.296126i 0.363537 + 0.0198747i
223223 8.92283i 0.597517i 0.954329 + 0.298758i 0.0965725π0.0965725\pi
−0.954329 + 0.298758i 0.903428π0.903428\pi
224224 −8.07213 14.3528i −0.539342 0.958990i
225225 −21.1343 −1.40895
226226 −0.562875 + 10.2958i −0.0374419 + 0.684867i
227227 5.06802 + 2.09924i 0.336376 + 0.139332i 0.544477 0.838776i 0.316728π-0.316728\pi
−0.208101 + 0.978107i 0.566728π0.566728\pi
228228 9.02888 + 11.2532i 0.597952 + 0.745260i
229229 4.07504 + 9.83803i 0.269286 + 0.650115i 0.999450 0.0331572i 0.0105562π-0.0105562\pi
−0.730164 + 0.683272i 0.760556π0.760556\pi
230230 −4.03973 + 8.42053i −0.266372 + 0.555233i
231231 8.19826 8.19826i 0.539406 0.539406i
232232 −0.843917 + 1.35645i −0.0554059 + 0.0890556i
233233 −17.7684 17.7684i −1.16405 1.16405i −0.983581 0.180466i 0.942239π-0.942239\pi
−0.180466 0.983581i 0.557761π-0.557761\pi
234234 −0.698036 9.77452i −0.0456320 0.638981i
235235 5.77549 + 13.9433i 0.376751 + 0.909558i
236236 −4.91860 16.8843i −0.320174 1.09908i
237237 8.54905 + 3.54113i 0.555320 + 0.230021i
238238 −22.5629 + 20.2237i −1.46253 + 1.31091i
239239 14.2280 0.920336 0.460168 0.887832i 0.347789π-0.347789\pi
0.460168 + 0.887832i 0.347789π0.347789\pi
240240 −16.2172 3.60034i −1.04682 0.232401i
241241 −14.3595 −0.924974 −0.462487 0.886626i 0.653043π-0.653043\pi
−0.462487 + 0.886626i 0.653043π0.653043\pi
242242 −3.91020 + 3.50482i −0.251357 + 0.225298i
243243 −14.6049 6.04955i −0.936906 0.388079i
244244 −0.620078 + 1.12985i −0.0396964 + 0.0723315i
245245 −5.44616 + 2.25587i −0.347942 + 0.144122i
246246 −2.86986 8.16273i −0.182976 0.520436i
247247 21.7553 12.4161i 1.38426 0.790015i
248248 −1.15364 + 6.97783i −0.0732565 + 0.443093i
249249 −1.66056 1.66056i −0.105234 0.105234i
250250 30.5835 + 14.6724i 1.93427 + 0.927961i
251251 26.9449 11.1610i 1.70075 0.704473i 0.700788 0.713370i 0.252832π-0.252832\pi
0.999960 + 0.00889690i 0.00283201π0.00283201\pi
252252 −1.21975 + 11.1221i −0.0768368 + 0.700629i
253253 5.85130 + 2.42369i 0.367868 + 0.152376i
254254 6.71955 + 0.367360i 0.421622 + 0.0230502i
255255 30.5667i 1.91416i
256256 14.4969 + 6.77052i 0.906056 + 0.423158i
257257 21.9848 1.37138 0.685689 0.727895i 0.259501π-0.259501\pi
0.685689 + 0.727895i 0.259501π0.259501\pi
258258 7.11611 + 0.389040i 0.443029 + 0.0242206i
259259 −4.11523 + 9.93504i −0.255708 + 0.617333i
260260 −10.5913 + 26.8266i −0.656848 + 1.66372i
261261 1.00286 0.415396i 0.0620752 0.0257124i
262262 4.09834 8.54269i 0.253196 0.527769i
263263 8.04680 8.04680i 0.496187 0.496187i −0.414062 0.910249i 0.635890π-0.635890\pi
0.910249 + 0.414062i 0.135890π0.135890\pi
264264 −1.83754 + 11.1144i −0.113093 + 0.684043i
265265 −20.2782 + 20.2782i −1.24568 + 1.24568i
266266 −26.9815 + 9.48620i −1.65434 + 0.581636i
267267 −11.2764 + 4.67083i −0.690103 + 0.285850i
268268 −5.91102 3.24404i −0.361073 0.198161i
269269 7.13058 + 2.95358i 0.434759 + 0.180083i 0.589319 0.807900i 0.299396π-0.299396\pi
−0.154560 + 0.987983i 0.549396π0.549396\pi
270270 19.2941 + 21.5258i 1.17420 + 1.31002i
271271 11.0640 0.672090 0.336045 0.941846i 0.390911π-0.390911\pi
0.336045 + 0.941846i 0.390911π0.390911\pi
272272 6.38064 28.7407i 0.386883 1.74266i
273273 −10.5127 2.87318i −0.636258 0.173893i
274274 19.7996 17.7469i 1.19614 1.07213i
275275 16.1423 38.9709i 0.973416 2.35003i
276276 3.29210 0.959028i 0.198161 0.0577267i
277277 −0.155389 0.375143i −0.00933643 0.0225401i 0.919143 0.393925i 0.128883π-0.128883\pi
−0.928479 + 0.371385i 0.878883π0.878883\pi
278278 0.00205263 + 0.00583828i 0.000123109 + 0.000350157i
279279 3.39805 3.39805i 0.203436 0.203436i
280280 17.3960 27.9612i 1.03961 1.67100i
281281 −4.47988 4.47988i −0.267247 0.267247i 0.560743 0.827990i 0.310516π-0.310516\pi
−0.827990 + 0.560743i 0.810516π0.810516\pi
282282 2.39675 4.99585i 0.142724 0.297498i
283283 −24.3596 + 10.0901i −1.44803 + 0.599792i −0.961729 0.274001i 0.911653π-0.911653\pi
−0.486297 + 0.873793i 0.661653π0.661653\pi
284284 −13.5645 16.9061i −0.804903 1.00319i
285285 −11.0413 + 26.6562i −0.654033 + 1.57897i
286286 18.5571 + 6.17859i 1.09730 + 0.365348i
287287 17.1524 1.01247
288288 −5.32919 9.47569i −0.314026 0.558360i
289289 −37.1714 −2.18655
290290 −3.19004 0.174400i −0.187325 0.0102411i
291291 8.47643 + 3.51105i 0.496897 + 0.205822i
292292 −5.83200 + 4.67925i −0.341292 + 0.273832i
293293 −3.58927 8.66526i −0.209687 0.506230i 0.783687 0.621156i 0.213337π-0.213337\pi
−0.993374 + 0.114926i 0.963337π0.963337\pi
294294 1.95135 + 0.936157i 0.113805 + 0.0545978i
295295 24.8682 24.8682i 1.44788 1.44788i
296296 −2.37036 10.1762i −0.137774 0.591479i
297297 13.8614 13.8614i 0.804320 0.804320i
298298 0.117553 0.0413295i 0.00680966 0.00239415i
299299 −0.747593 5.90617i −0.0432344 0.341562i
300300 −6.38733 21.9261i −0.368773 1.26590i
301301 −5.40643 + 13.0523i −0.311622 + 0.752321i
302302 0.510206 0.457311i 0.0293590 0.0263153i
303303 1.57605i 0.0905415i
304304 15.9461 22.7590i 0.914571 1.30532i
305305 −2.57740 −0.147582
306306 −14.8959 + 13.3516i −0.851543 + 0.763261i
307307 −10.0105 + 24.1675i −0.571330 + 1.37931i 0.329094 + 0.944297i 0.393257π0.393257\pi
−0.900423 + 0.435015i 0.856743π0.856743\pi
308308 −19.5772 10.7442i −1.11551 0.612208i
309309 0.539752 + 1.30308i 0.0307054 + 0.0741294i
310310 −13.3431 + 4.69120i −0.757839 + 0.266442i
311311 10.9898 + 10.9898i 0.623172 + 0.623172i 0.946341 0.323169i 0.104748π-0.104748\pi
−0.323169 + 0.946341i 0.604748π0.604748\pi
312312 9.92977 3.67831i 0.562163 0.208243i
313313 8.48897 8.48897i 0.479825 0.479825i −0.425251 0.905076i 0.639814π-0.639814\pi
0.905076 + 0.425251i 0.139814π0.139814\pi
314314 4.27524 8.91143i 0.241266 0.502901i
315315 −20.6723 + 8.56274i −1.16475 + 0.482456i
316316 1.94300 17.7170i 0.109302 0.996662i
317317 −15.2088 6.29971i −0.854214 0.353827i −0.0877720 0.996141i 0.527975π-0.527975\pi
−0.766442 + 0.642314i 0.777975π0.777975\pi
318318 10.5133 + 0.574764i 0.589555 + 0.0322311i
319319 2.16651i 0.121301i
320320 2.07845 + 31.9294i 0.116189 + 1.78491i
321321 −14.9110 −0.832253
322322 −0.371061 + 6.78724i −0.0206784 + 0.378238i
323323 −47.2410 19.5678i −2.62856 1.08878i
324324 −0.100049 + 0.912285i −0.00555827 + 0.0506825i
325325 −39.3363 + 4.97913i −2.18199 + 0.276192i
326326 −15.9218 7.63846i −0.881828 0.423055i
327327 11.6400 + 11.6400i 0.643696 + 0.643696i
328328 −13.5490 + 9.70447i −0.748116 + 0.535840i
329329 7.76704 + 7.76704i 0.428211 + 0.428211i
330330 −21.2531 + 7.47220i −1.16995 + 0.411331i
331331 5.20982 2.15798i 0.286358 0.118613i −0.234881 0.972024i 0.575470π-0.575470\pi
0.521239 + 0.853411i 0.325470π0.325470\pi
332332 −2.17624 + 3.96536i −0.119437 + 0.217628i
333333 −2.71686 + 6.55907i −0.148883 + 0.359435i
334334 −15.6472 17.4571i −0.856179 0.955208i
335335 13.4841i 0.736717i
336336 −11.9075 + 2.09596i −0.649606 + 0.114344i
337337 7.91469i 0.431141i 0.976488 + 0.215570i 0.0691611π0.0691611\pi
−0.976488 + 0.215570i 0.930839π0.930839\pi
338338 −3.60205 18.0285i −0.195926 0.980619i
339339 6.99445 + 2.89720i 0.379886 + 0.157354i
340340 56.5258 16.4666i 3.06554 0.893029i
341341 3.67047 + 8.86131i 0.198767 + 0.479867i
342342 −17.8131 + 6.26275i −0.963221 + 0.338651i
343343 11.3749 11.3749i 0.614187 0.614187i
344344 −3.11409 13.3691i −0.167901 0.720814i
345345 4.84880 + 4.84880i 0.261051 + 0.261051i
346346 −15.1370 7.26193i −0.813769 0.390404i
347347 32.3967 13.4191i 1.73914 0.720377i 0.740301 0.672276i 0.234683π-0.234683\pi
0.998842 0.0481013i 0.0153170π-0.0153170\pi
348348 0.734049 + 0.914885i 0.0393492 + 0.0490430i
349349 −19.8463 8.22061i −1.06235 0.440039i −0.218064 0.975934i 0.569974π-0.569974\pi
−0.844285 + 0.535895i 0.819974π0.819974\pi
350350 45.2045 + 2.47134i 2.41628 + 0.132099i
351351 −17.7746 4.85790i −0.948738 0.259295i
352352 21.5433 2.58936i 1.14826 0.138013i
353353 17.8817i 0.951747i −0.879514 0.475874i 0.842132π-0.842132\pi
0.879514 0.475874i 0.157868π-0.157868\pi
354354 −12.8930 0.704862i −0.685253 0.0374630i
355355 16.5879 40.0467i 0.880393 2.12546i
356356 14.7123 + 18.3367i 0.779749 + 0.971843i
357357 8.51354 + 20.5535i 0.450584 + 1.08781i
358358 −9.09729 4.36441i −0.480807 0.230666i
359359 19.0915 + 19.0915i 1.00761 + 1.00761i 0.999971 + 0.00763864i 0.00243148π0.00243148\pi
0.00763864 + 0.999971i 0.497569π0.497569\pi
360360 11.4848 18.4599i 0.605302 0.972920i
361361 −20.6938 20.6938i −1.08915 1.08915i
362362 10.8836 + 30.9561i 0.572028 + 1.62701i
363363 1.47542 + 3.56197i 0.0774393 + 0.186955i
364364 0.350054 + 20.9885i 0.0183478 + 1.10010i
365365 −13.8146 5.72221i −0.723091 0.299514i
366366 0.631602 + 0.704656i 0.0330144 + 0.0368329i
367367 27.3345i 1.42685i 0.700731 + 0.713426i 0.252857π0.252857\pi
−0.700731 + 0.713426i 0.747143π0.747143\pi
368368 −3.54698 5.57131i −0.184899 0.290424i
369369 11.3239 0.589499
370370 15.5597 13.9466i 0.808910 0.725048i
371371 −7.98741 + 19.2833i −0.414686 + 1.00114i
372372 4.55234 + 2.49838i 0.236028 + 0.129535i
373373 −4.59425 11.0915i −0.237881 0.574297i 0.759182 0.650879i 0.225599π-0.225599\pi
−0.997063 + 0.0765819i 0.975599π0.975599\pi
374374 −13.2425 37.6655i −0.684753 1.94764i
375375 17.6109 17.6109i 0.909424 0.909424i
376376 −10.5298 1.74089i −0.543032 0.0897794i
377377 1.76871 1.00943i 0.0910931 0.0519881i
378378 18.9691 + 9.10037i 0.975664 + 0.468073i
379379 6.44128 + 15.5506i 0.330866 + 0.798782i 0.998524 + 0.0543133i 0.0172970π0.0172970\pi
−0.667658 + 0.744468i 0.732703π0.732703\pi
380380 55.2422 + 6.05833i 2.83387 + 0.310786i
381381 1.89085 4.56492i 0.0968713 0.233868i
382382 34.6531 + 1.89449i 1.77301 + 0.0969308i
383383 9.87632i 0.504657i −0.967642 0.252328i 0.918804π-0.918804\pi
0.967642 0.252328i 0.0811963π-0.0811963\pi
384384 8.22009 8.39266i 0.419480 0.428286i
385385 44.6592i 2.27604i
386386 −0.589354 + 10.7801i −0.0299973 + 0.548695i
387387 −3.56931 + 8.61707i −0.181438 + 0.438030i
388388 1.92650 17.5666i 0.0978031 0.891807i
389389 −22.8288 + 9.45600i −1.15747 + 0.479438i −0.877031 0.480434i 0.840479π-0.840479\pi
−0.280436 + 0.959873i 0.590479π0.590479\pi
390390 16.0025 + 13.8693i 0.810319 + 0.702297i
391391 −8.59321 + 8.59321i −0.434578 + 0.434578i
392392 0.679981 4.11287i 0.0343442 0.207731i
393393 −4.91915 4.91915i −0.248138 0.248138i
394394 −0.515931 1.46746i −0.0259922 0.0739294i
395395 32.9300 13.6401i 1.65689 0.686306i
396396 −12.9248 7.09329i −0.649495 0.356451i
397397 6.42267 15.5057i 0.322344 0.778208i −0.676773 0.736192i 0.736622π-0.736622\pi
0.999117 0.0420160i 0.0133781π-0.0133781\pi
398398 −1.91761 + 1.71880i −0.0961210 + 0.0861559i
399399 20.9993i 1.05128i
400400 −37.1061 + 23.6237i −1.85530 + 1.18118i
401401 34.5147 1.72358 0.861790 0.507265i 0.169344π-0.169344\pi
0.861790 + 0.507265i 0.169344π0.169344\pi
402402 −3.68653 + 3.30433i −0.183867 + 0.164805i
403403 5.52408 7.12521i 0.275174 0.354932i
404404 2.91452 0.849034i 0.145003 0.0422410i
405405 −1.69563 + 0.702353i −0.0842565 + 0.0349002i
406406 −2.19360 + 0.771229i −0.108867 + 0.0382755i
407407 −10.0196 10.0196i −0.496653 0.496653i
408408 −18.3538 11.4188i −0.908648 0.565315i
409409 2.93014 + 2.93014i 0.144886 + 0.144886i 0.775829 0.630943i 0.217332π-0.217332\pi
−0.630943 + 0.775829i 0.717332π0.717332\pi
410410 −30.0495 14.4162i −1.48404 0.711964i
411411 −7.47090 18.0363i −0.368512 0.889667i
412412 2.11896 1.70012i 0.104393 0.0837591i
413413 9.79538 23.6481i 0.481999 1.16365i
414414 −0.244973 + 4.48091i −0.0120398 + 0.220225i
415415 −9.04573 −0.444037
416416 −12.1514 16.3812i −0.595773 0.803153i
417417 0.00454383 0.000222512
418418 2.05726 37.6302i 0.100624 1.84055i
419419 −4.11285 + 9.92930i −0.200926 + 0.485078i −0.991938 0.126722i 0.959554π-0.959554\pi
0.791012 + 0.611800i 0.209554π0.209554\pi
420420 −15.1313 18.8589i −0.738330 0.920221i
421421 −3.72357 8.98949i −0.181476 0.438121i 0.806795 0.590831i 0.201200π-0.201200\pi
−0.988271 + 0.152710i 0.951200π0.951200\pi
422422 20.2245 + 9.70268i 0.984515 + 0.472319i
423423 5.12777 + 5.12777i 0.249321 + 0.249321i
424424 −4.60073 19.7514i −0.223431 0.959212i
425425 57.2326 + 57.2326i 2.77619 + 2.77619i
426426 −15.0136 + 5.27850i −0.727410 + 0.255744i
427427 −1.73308 + 0.717866i −0.0838698 + 0.0347400i
428428 8.03275 + 27.5744i 0.388278 + 1.33286i
429429 8.79884 11.3491i 0.424812 0.547941i
430430 20.4418 18.3225i 0.985789 0.883590i
431431 11.4632 0.552162 0.276081 0.961134i 0.410964π-0.410964\pi
0.276081 + 0.961134i 0.410964π0.410964\pi
432432 −20.1328 + 3.54379i −0.968642 + 0.170500i
433433 9.31026i 0.447422i 0.974655 + 0.223711i 0.0718172π0.0718172\pi
−0.974655 + 0.223711i 0.928183π0.928183\pi
434434 −7.66550 + 6.87080i −0.367956 + 0.329809i
435435 −0.897662 + 2.16715i −0.0430396 + 0.103907i
436436 15.2548 27.7961i 0.730574 1.33119i
437437 −10.5979 + 4.38979i −0.506966 + 0.209992i
438438 1.82089 + 5.17914i 0.0870054 + 0.247469i
439439 13.5303 + 13.5303i 0.645765 + 0.645765i 0.951967 0.306202i 0.0990582π-0.0990582\pi
−0.306202 + 0.951967i 0.599058π0.599058\pi
440440 25.2673 + 35.2771i 1.20457 + 1.68177i
441441 −2.00288 + 2.00288i −0.0953752 + 0.0953752i
442442 −24.5796 + 28.3602i −1.16913 + 1.34896i
443443 −9.44190 + 3.91096i −0.448598 + 0.185815i −0.595533 0.803331i 0.703059π-0.703059\pi
0.146935 + 0.989146i 0.453059π0.453059\pi
444444 −7.62592 0.836323i −0.361910 0.0396901i
445445 −17.9915 + 43.4354i −0.852880 + 2.05903i
446446 0.688844 12.6000i 0.0326177 0.596626i
447447 0.0914895i 0.00432730i
448448 10.2907 + 20.8909i 0.486188 + 0.987002i
449449 39.3232i 1.85578i −0.372856 0.927889i 0.621621π-0.621621\pi
0.372856 0.927889i 0.378379π-0.378379\pi
450450 29.8438 + 1.63157i 1.40685 + 0.0769130i
451451 −8.64916 + 20.8809i −0.407273 + 0.983244i
452452 1.58968 14.4953i 0.0747721 0.681801i
453453 −0.192514 0.464769i −0.00904507 0.0218367i
454454 −6.99451 3.35560i −0.328269 0.157486i
455455 −36.4591 + 20.8078i −1.70923 + 0.975483i
456456 −11.8810 16.5877i −0.556378 0.776790i
457457 −6.50267 + 6.50267i −0.304182 + 0.304182i −0.842647 0.538466i 0.819004π-0.819004\pi
0.538466 + 0.842647i 0.319004π0.319004\pi
458458 −4.99489 14.2069i −0.233396 0.663846i
459459 14.3945 + 34.7513i 0.671876 + 1.62205i
460460 6.35459 11.5788i 0.296284 0.539864i
461461 −13.8423 + 33.4183i −0.644702 + 1.55645i 0.175566 + 0.984468i 0.443824π0.443824\pi
−0.820268 + 0.571980i 0.806176π0.806176\pi
462462 −12.2097 + 10.9439i −0.568047 + 0.509156i
463463 2.61868 0.121700 0.0608501 0.998147i 0.480619π-0.480619\pi
0.0608501 + 0.998147i 0.480619π0.480619\pi
464464 1.29642 1.85031i 0.0601847 0.0858983i
465465 10.3847i 0.481580i
466466 23.7191 + 26.4626i 1.09877 + 1.22586i
467467 −16.8016 6.95946i −0.777487 0.322045i −0.0415858 0.999135i 0.513241π-0.513241\pi
−0.735901 + 0.677089i 0.763241π0.763241\pi
468468 0.231104 + 13.8565i 0.0106828 + 0.640519i
469469 −3.75564 9.06692i −0.173419 0.418671i
470470 −7.07917 20.1352i −0.326538 0.928768i
471471 −5.13148 5.13148i −0.236446 0.236446i
472472 5.64211 + 24.2221i 0.259699 + 1.11491i
473473 −13.1634 13.1634i −0.605252 0.605252i
474474 −11.7988 5.66044i −0.541936 0.259992i
475475 29.2369 + 70.5842i 1.34148 + 3.23862i
476476 33.4224 26.8161i 1.53191 1.22912i
477477 −5.27326 + 12.7308i −0.241446 + 0.582902i
478478 −20.0915 1.09841i −0.918964 0.0502400i
479479 12.8291i 0.586178i 0.956085 + 0.293089i 0.0946832π0.0946832\pi
−0.956085 + 0.293089i 0.905317π0.905317\pi
480480 22.6225 + 6.33603i 1.03257 + 0.289199i
481481 −3.51149 + 12.8482i −0.160110 + 0.585828i
482482 20.2771 + 1.10855i 0.923595 + 0.0504932i
483483 4.61091 + 1.90990i 0.209804 + 0.0869035i
484484 5.79219 4.64730i 0.263281 0.211241i
485485 32.6503 13.5242i 1.48257 0.614102i
486486 20.1566 + 9.67011i 0.914324 + 0.438645i
487487 16.8425 + 16.8425i 0.763205 + 0.763205i 0.976900 0.213695i 0.0685500π-0.0685500\pi
−0.213695 + 0.976900i 0.568550π0.568550\pi
488488 0.962840 1.54760i 0.0435857 0.0700566i
489489 −9.16828 + 9.16828i −0.414604 + 0.414604i
490490 7.86470 2.76509i 0.355291 0.124914i
491491 −14.3321 34.6008i −0.646799 1.56151i −0.817337 0.576160i 0.804551π-0.804551\pi
0.170538 0.985351i 0.445449π-0.445449\pi
492492 3.42239 + 11.7482i 0.154293 + 0.529649i
493493 −3.84069 1.59087i −0.172976 0.0716491i
494494 −31.6793 + 15.8533i −1.42532 + 0.713272i
495495 29.4838i 1.32520i
496496 2.16776 9.76437i 0.0973352 0.438433i
497497 31.5481i 1.41512i
498498 2.21669 + 2.47308i 0.0993321 + 0.110821i
499499 −9.19366 + 22.1955i −0.411565 + 0.993605i 0.573153 + 0.819448i 0.305720π0.305720\pi
−0.984718 + 0.174157i 0.944280π0.944280\pi
500500 −42.0544 23.0800i −1.88073 1.03217i
501501 −15.9024 + 6.58699i −0.710467 + 0.294285i
502502 −38.9107 + 13.6803i −1.73667 + 0.610581i
503503 −25.3873 25.3873i −1.13197 1.13197i −0.989850 0.142115i 0.954610π-0.954610\pi
−0.142115 0.989850i 0.545390π-0.545390\pi
504504 2.58104 15.6115i 0.114969 0.695389i
505505 4.29268 + 4.29268i 0.191022 + 0.191022i
506506 −8.07554 3.87422i −0.359001 0.172230i
507507 −13.3648 1.89542i −0.593554 0.0841785i
508508 −9.46034 1.03750i −0.419735 0.0460317i
509509 12.4459 + 5.15527i 0.551656 + 0.228503i 0.641058 0.767492i 0.278496π-0.278496\pi
−0.0894022 + 0.995996i 0.528496π0.528496\pi
510510 2.35976 43.1634i 0.104492 1.91131i
511511 −10.8829 −0.481432
512512 −19.9485 10.6799i −0.881605 0.471987i
513513 35.5050i 1.56758i
514514 −31.0449 1.69723i −1.36933 0.0748618i
515515 5.01931 + 2.07907i 0.221177 + 0.0916146i
516516 −10.0187 1.09873i −0.441047 0.0483689i
517517 −13.3720 + 5.53887i −0.588100 + 0.243599i
518518 6.57812 13.7116i 0.289026 0.602454i
519519 −8.71635 + 8.71635i −0.382605 + 0.382605i
520520 17.0271 37.0643i 0.746688 1.62538i
521521 −5.25194 5.25194i −0.230092 0.230092i 0.582639 0.812731i 0.302020π-0.302020\pi
−0.812731 + 0.582639i 0.802020π0.802020\pi
522522 −1.44821 + 0.509162i −0.0633862 + 0.0222854i
523523 −3.97481 9.59603i −0.173806 0.419605i 0.812839 0.582488i 0.197921π-0.197921\pi
−0.986645 + 0.162883i 0.947921π0.947921\pi
524524 −6.44678 + 11.7468i −0.281629 + 0.513160i
525525 12.7203 30.7096i 0.555161 1.34028i
526526 −11.9841 + 10.7417i −0.522533 + 0.468361i
527527 −18.4042 −0.801698
528528 3.45283 15.5528i 0.150265 0.676849i
529529 20.2737i 0.881466i
530530 30.2005 27.0695i 1.31182 1.17582i
531531 6.46687 15.6124i 0.280638 0.677521i
532532 38.8331 11.3125i 1.68363 0.490461i
533533 21.0767 2.66786i 0.912934 0.115558i
534534 16.2840 5.72516i 0.704678 0.247752i
535535 −40.6132 + 40.6132i −1.75586 + 1.75586i
536536 8.09654 + 5.03726i 0.349717 + 0.217577i
537537 −5.23851 + 5.23851i −0.226058 + 0.226058i
538538 −9.84110 4.72125i −0.424280 0.203547i
539539 −2.16345 5.22303i −0.0931864 0.224972i
540540 −25.5835 31.8862i −1.10094 1.37216i
541541 −19.5077 8.08037i −0.838703 0.347402i −0.0783613 0.996925i 0.524969π-0.524969\pi
−0.760342 + 0.649523i 0.774969π0.774969\pi
542542 −15.6235 0.854143i −0.671088 0.0366886i
543543 24.0926 1.03391
544544 −11.2289 + 40.0923i −0.481436 + 1.71894i
545545 63.4080 2.71610
546546 14.6232 + 4.86882i 0.625816 + 0.208366i
547547 3.45537 8.34201i 0.147741 0.356678i −0.832633 0.553825i 0.813168π-0.813168\pi
0.980374 + 0.197147i 0.0631676π0.0631676\pi
548548 −29.3292 + 23.5320i −1.25288 + 1.00524i
549549 −1.14417 + 0.473933i −0.0488322 + 0.0202270i
550550 −25.8031 + 53.7848i −1.10025 + 2.29339i
551551 −2.77468 2.77468i −0.118205 0.118205i
552552 −4.72283 + 1.10010i −0.201017 + 0.0468233i
553553 18.3435 18.3435i 0.780046 0.780046i
554554 0.190465 + 0.541737i 0.00809207 + 0.0230162i
555555 −5.87107 14.1740i −0.249213 0.601653i
556556 −0.00244781 0.00840273i −0.000103810 0.000356355i
557557 2.38893 5.76739i 0.101222 0.244372i −0.865153 0.501508i 0.832779π-0.832779\pi
0.966375 + 0.257136i 0.0827788π0.0827788\pi
558558 −5.06073 + 4.53607i −0.214238 + 0.192027i
559559 −4.61326 + 16.8795i −0.195120 + 0.713927i
560560 −26.7236 + 38.1411i −1.12928 + 1.61176i
561561 −29.3144 −1.23766
562562 5.98021 + 6.67191i 0.252260 + 0.281437i
563563 −14.1161 5.84709i −0.594923 0.246425i 0.0648438 0.997895i 0.479345π-0.479345\pi
−0.659767 + 0.751470i 0.729345π0.729345\pi
564564 −3.77014 + 6.86963i −0.158752 + 0.289264i
565565 26.9419 11.1597i 1.13345 0.469492i
566566 35.1772 12.3677i 1.47861 0.519852i
567567 −0.944544 + 0.944544i −0.0396671 + 0.0396671i
568568 17.8493 + 24.9204i 0.748940 + 1.04564i
569569 −9.26813 + 9.26813i −0.388540 + 0.388540i −0.874167 0.485626i 0.838592π-0.838592\pi
0.485626 + 0.874167i 0.338592π0.338592\pi
570570 17.6494 36.7889i 0.739252 1.54092i
571571 −15.0164 + 6.21999i −0.628416 + 0.260298i −0.674080 0.738659i 0.735460π-0.735460\pi
0.0456640 + 0.998957i 0.485460π0.485460\pi
572572 −25.7275 10.1574i −1.07572 0.424703i
573573 9.75123 23.5416i 0.407364 0.983463i
574574 −24.2209 1.32417i −1.01096 0.0552696i
575575 18.1576 0.757226
576576 6.79385 + 13.7921i 0.283077 + 0.574670i
577577 2.07845i 0.0865269i −0.999064 0.0432634i 0.986225π-0.986225\pi
0.999064 0.0432634i 0.0137755π-0.0137755\pi
578578 52.4899 + 2.86964i 2.18329 + 0.119361i
579579 7.32349 + 3.03349i 0.304354 + 0.126067i
580580 4.49120 + 0.492543i 0.186487 + 0.0204517i
581581 −6.08247 + 2.51944i −0.252344 + 0.104524i
582582 −11.6986 5.61236i −0.484921 0.232640i
583583 −19.4474 19.4474i −0.805430 0.805430i
584584 8.59663 6.15735i 0.355731 0.254793i
585585 −24.0702 + 13.7372i −0.995179 + 0.567963i
586586 4.39946 + 12.5133i 0.181740 + 0.516922i
587587 −29.1093 + 12.0574i −1.20147 + 0.497664i −0.891473 0.453074i 0.850327π-0.850327\pi
−0.309995 + 0.950738i 0.600327π0.600327\pi
588588 −2.68324 1.47260i −0.110655 0.0607288i
589589 −16.0496 6.64797i −0.661313 0.273925i
590590 −37.0364 + 33.1967i −1.52476 + 1.36669i
591591 −1.14210 −0.0469796
592592 2.56159 + 14.5528i 0.105281 + 0.598118i
593593 3.87908 0.159295 0.0796473 0.996823i 0.474621π-0.474621\pi
0.0796473 + 0.996823i 0.474621π0.474621\pi
594594 −20.6439 + 18.5037i −0.847028 + 0.759214i
595595 79.1699 + 32.7932i 3.24565 + 1.34439i
596596 −0.169188 + 0.0492864i −0.00693020 + 0.00201885i
597597 0.723562 + 1.74683i 0.0296134 + 0.0714931i
598598 0.599722 + 8.39784i 0.0245244 + 0.343413i
599599 −6.88889 6.88889i −0.281472 0.281472i 0.552224 0.833696i 0.313779π-0.313779\pi
−0.833696 + 0.552224i 0.813779π0.813779\pi
600600 7.32689 + 31.4550i 0.299119 + 1.28415i
601601 −10.1124 + 10.1124i −0.412494 + 0.412494i −0.882607 0.470112i 0.844213π-0.844213\pi
0.470112 + 0.882607i 0.344213π0.344213\pi
602602 8.64209 18.0138i 0.352225 0.734188i
603603 −2.47946 5.98595i −0.100971 0.243767i
604604 −0.755769 + 0.606384i −0.0307518 + 0.0246734i
605605 13.7203 + 5.68315i 0.557811 + 0.231053i
606606 0.121671 2.22554i 0.00494255 0.0904065i
607607 11.0109 0.446920 0.223460 0.974713i 0.428265π-0.428265\pi
0.223460 + 0.974713i 0.428265π0.428265\pi
608608 −24.2745 + 30.9070i −0.984463 + 1.25344i
609609 1.70724i 0.0691809i
610610 3.63956 + 0.198976i 0.147362 + 0.00805631i
611611 10.7522 + 8.33602i 0.434986 + 0.337239i
612612 22.0653 17.7039i 0.891939 0.715638i
613613 4.91732 + 11.8715i 0.198609 + 0.479484i 0.991536 0.129832i 0.0414439π-0.0414439\pi
−0.792927 + 0.609316i 0.791444π0.791444\pi
614614 16.0016 33.3542i 0.645773 1.34607i
615615 −17.3034 + 17.3034i −0.697741 + 0.697741i
616616 26.8156 + 16.6833i 1.08043 + 0.672190i
617617 −19.4321 + 19.4321i −0.782306 + 0.782306i −0.980220 0.197913i 0.936584π-0.936584\pi
0.197913 + 0.980220i 0.436584π0.436584\pi
618618 −0.661589 1.88175i −0.0266130 0.0756951i
619619 3.56961 1.47858i 0.143475 0.0594291i −0.309791 0.950805i 0.600259π-0.600259\pi
0.453265 + 0.891376i 0.350259π0.350259\pi
620620 19.2041 5.59437i 0.771253 0.224675i
621621 7.79600 + 3.22921i 0.312843 + 0.129584i
622622 −14.6703 16.3671i −0.588224 0.656261i
623623 34.2176i 1.37090i
624624 −14.3058 + 4.42757i −0.572692 + 0.177245i
625625 40.9488i 1.63795i
626626 −12.6427 + 11.3320i −0.505302 + 0.452916i
627627 −25.5641 10.5890i −1.02093 0.422883i
628628 −6.72505 + 12.2538i −0.268359 + 0.488981i
629629 25.1197 10.4049i 1.00159 0.414871i
630630 29.8525 10.4956i 1.18935 0.418154i
631631 17.7394 17.7394i 0.706193 0.706193i −0.259539 0.965733i 0.583571π-0.583571\pi
0.965733 + 0.259539i 0.0835707π0.0835707\pi
632632 −4.11148 + 24.8683i −0.163546 + 0.989209i
633633 11.6459 11.6459i 0.462884 0.462884i
634634 20.9901 + 10.0700i 0.833625 + 0.399930i
635635 −7.28336 17.5836i −0.289031 0.697783i
636636 −14.8015 1.62325i −0.586916 0.0643662i
637637 −3.25601 + 4.19974i −0.129008 + 0.166400i
638638 0.167255 3.05934i 0.00662169 0.121120i
639639 20.8279i 0.823939i
640640 −0.470031 45.2481i −0.0185796 1.78859i
641641 43.3388 1.71178 0.855891 0.517157i 0.173010π-0.173010\pi
0.855891 + 0.517157i 0.173010π0.173010\pi
642642 21.0560 + 1.15114i 0.831012 + 0.0454317i
643643 −30.2147 12.5153i −1.19155 0.493557i −0.303291 0.952898i 0.598085π-0.598085\pi
−0.888260 + 0.459341i 0.848085π0.848085\pi
644644 1.04795 9.55565i 0.0412951 0.376545i
645645 −7.71319 18.6213i −0.303707 0.733213i
646646 65.1985 + 31.2789i 2.56520 + 1.23065i
647647 −13.6398 + 13.6398i −0.536236 + 0.536236i −0.922421 0.386186i 0.873792π-0.873792\pi
0.386186 + 0.922421i 0.373792π0.373792\pi
648648 0.211708 1.28052i 0.00831668 0.0503035i
649649 23.8494 + 23.8494i 0.936170 + 0.936170i
650650 55.9314 3.99427i 2.19381 0.156668i
651651 2.89239 + 6.98284i 0.113362 + 0.273679i
652652 21.8936 + 12.0155i 0.857419 + 0.470562i
653653 −41.8250 17.3245i −1.63674 0.677960i −0.640778 0.767726i 0.721388π-0.721388\pi
−0.995963 + 0.0897662i 0.971388π0.971388\pi
654654 −15.5383 17.3356i −0.607598 0.677875i
655655 −26.7966 −1.04703
656656 19.8817 12.6578i 0.776252 0.494202i
657657 −7.18487 −0.280308
658658 −10.3683 11.5675i −0.404197 0.450948i
659659 10.8562 + 4.49680i 0.422899 + 0.175170i 0.583975 0.811772i 0.301497π-0.301497\pi
−0.161077 + 0.986942i 0.551497π0.551497\pi
660660 30.5885 8.91079i 1.19066 0.346852i
661661 −33.2622 + 13.7776i −1.29375 + 0.535888i −0.920101 0.391682i 0.871893π-0.871893\pi
−0.373648 + 0.927570i 0.621893π0.621893\pi
662662 −7.52341 + 2.64509i −0.292406 + 0.102804i
663663 13.6583 + 23.9319i 0.530443 + 0.929436i
664664 3.37921 5.43150i 0.131139 0.210783i
665665 57.1957 + 57.1957i 2.21795 + 2.21795i
666666 4.34285 9.05236i 0.168282 0.350772i
667667 −0.861609 + 0.356890i −0.0333616 + 0.0138188i
668668 20.7479 + 25.8592i 0.802759 + 1.00052i
669669 −8.55979 3.54558i −0.330940 0.137080i
670670 −1.04098 + 19.0410i −0.0402165 + 0.735618i
671671 2.47181i 0.0954231i
672672 16.9764 2.04045i 0.654879 0.0787120i
673673 1.79896 0.0693449 0.0346724 0.999399i 0.488961π-0.488961\pi
0.0346724 + 0.999399i 0.488961π0.488961\pi
674674 0.611016 11.1764i 0.0235355 0.430498i
675675 21.5072 51.9230i 0.827813 1.99852i
676676 3.69467 + 25.7361i 0.142103 + 0.989852i
677677 −22.3917 + 9.27493i −0.860582 + 0.356465i −0.768935 0.639327i 0.779213π-0.779213\pi
−0.0916466 + 0.995792i 0.529213π0.529213\pi
678678 −9.65323 4.63112i −0.370730 0.177857i
679679 18.1877 18.1877i 0.697981 0.697981i
680680 −81.0916 + 18.8888i −3.10972 + 0.724353i
681681 −4.02766 + 4.02766i −0.154340 + 0.154340i
682682 −4.49900 12.7965i −0.172276 0.490002i
683683 15.8660 6.57193i 0.607097 0.251468i −0.0578898 0.998323i 0.518437π-0.518437\pi
0.664987 + 0.746855i 0.268437π0.268437\pi
684684 25.6374 7.46849i 0.980272 0.285565i
685685 −69.4741 28.7771i −2.65447 1.09952i
686686 −16.9407 + 15.1844i −0.646799 + 0.579743i
687687 −11.0570 −0.421851
688688 3.36533 + 19.1190i 0.128302 + 0.728904i
689689 −6.81559 + 24.9376i −0.259653 + 0.950047i
690690 −6.47269 7.22135i −0.246411 0.274912i
691691 2.84020 6.85686i 0.108046 0.260847i −0.860604 0.509275i 0.829914π-0.829914\pi
0.968651 + 0.248427i 0.0799138π0.0799138\pi
692692 20.8144 + 11.4232i 0.791244 + 0.434245i
693693 −8.21193 19.8253i −0.311945 0.753103i
694694 −46.7834 + 16.4482i −1.77587 + 0.624365i
695695 0.0123760 0.0123760i 0.000469450 0.000469450i
696696 −0.965925 1.34858i −0.0366133 0.0511179i
697697 −30.6657 30.6657i −1.16155 1.16155i
698698 27.3904 + 13.1405i 1.03674 + 0.497376i
699699 24.1059 9.98500i 0.911770 0.377667i
700700 −63.6426 6.97959i −2.40547 0.263804i
701701 −2.34365 + 5.65807i −0.0885183 + 0.213702i −0.961939 0.273264i 0.911897π-0.911897\pi
0.873421 + 0.486967i 0.161897π0.161897\pi
702702 24.7246 + 8.23207i 0.933169 + 0.310699i
703703 25.6644 0.967953
704704 −30.6213 + 1.99330i −1.15408 + 0.0751251i
705705 −15.6709 −0.590200
706706 −1.38047 + 25.2508i −0.0519547 + 0.950328i
707707 4.08207 + 1.69085i 0.153522 + 0.0635909i
708708 18.1518 + 1.99068i 0.682186 + 0.0748143i
709709 −7.89990 19.0720i −0.296687 0.716265i −0.999986 0.00537098i 0.998290π-0.998290\pi
0.703299 0.710894i 0.251710π-0.251710\pi
710710 −26.5154 + 55.2695i −0.995106 + 2.07423i
711711 12.1103 12.1103i 0.454173 0.454173i
712712 −19.3597 27.0291i −0.725534 1.01296i
713713 −2.91946 + 2.91946i −0.109334 + 0.109334i
714714 −10.4353 29.6809i −0.390530 1.11078i
715715 −6.94624 54.8770i −0.259775 2.05228i
716716 12.5094 + 6.86531i 0.467498 + 0.256569i
717717 −5.65366 + 13.6491i −0.211140 + 0.509737i
718718 −25.4853 28.4330i −0.951103 1.06111i
719719 23.3731i 0.871669i 0.900027 + 0.435834i 0.143547π0.143547\pi
−0.900027 + 0.435834i 0.856453π0.856453\pi
720720 −17.6428 + 25.1806i −0.657510 + 0.938427i
721721 3.95412 0.147259
722722 27.6243 + 30.8194i 1.02807 + 1.14698i
723723 5.70588 13.7752i 0.212204 0.512306i
724724 −12.9789 44.5534i −0.482359 1.65581i
725725 2.37696 + 5.73850i 0.0882783 + 0.213123i
726726 −1.80846 5.14378i −0.0671182 0.190904i
727727 −26.1047 26.1047i −0.968169 0.968169i 0.0313402 0.999509i 0.490022π-0.490022\pi
−0.999509 + 0.0313402i 0.990022π0.990022\pi
728728 1.12601 29.6650i 0.0417325 1.09946i
729729 10.6334 10.6334i 0.393830 0.393830i
730730 19.0660 + 9.14686i 0.705663 + 0.338540i
731731 33.0013 13.6696i 1.22060 0.505588i
732732 −0.837489 1.04381i −0.0309545 0.0385802i
733733 21.3849 + 8.85792i 0.789870 + 0.327175i 0.740891 0.671625i 0.234403π-0.234403\pi
0.0489784 + 0.998800i 0.484403π0.484403\pi
734734 2.11023 38.5992i 0.0778901 1.42472i
735735 6.12097i 0.225775i
736736 4.57861 + 8.14110i 0.168770 + 0.300085i
737737 12.9317 0.476345
738738 −15.9906 0.874209i −0.588620 0.0321801i
739739 −20.5537 8.51360i −0.756078 0.313178i −0.0288595 0.999583i 0.509188π-0.509188\pi
−0.727219 + 0.686406i 0.759188π0.759188\pi
740740 −23.0486 + 18.4928i −0.847284 + 0.679810i
741741 3.26620 + 25.8038i 0.119987 + 0.947926i
742742 12.7677 26.6134i 0.468719 0.977010i
743743 −6.66455 6.66455i −0.244499 0.244499i 0.574210 0.818708i 0.305309π-0.305309\pi
−0.818708 + 0.574210i 0.805309π0.805309\pi
744744 −6.23551 3.87942i −0.228605 0.142226i
745745 −0.249190 0.249190i −0.00912961 0.00912961i
746746 5.63130 + 16.0171i 0.206177 + 0.586426i
747747 −4.01563 + 1.66333i −0.146924 + 0.0608579i
748748 15.7920 + 54.2099i 0.577413 + 1.98211i
749749 −15.9972 + 38.6206i −0.584524 + 1.41117i
750750 −26.2280 + 23.5089i −0.957712 + 0.858424i
751751 32.4068i 1.18254i −0.806474 0.591270i 0.798627π-0.798627\pi
0.806474 0.591270i 0.201373π-0.201373\pi
752752 14.7347 + 3.27122i 0.537321 + 0.119289i
753753 30.2835i 1.10359i
754754 −2.57553 + 1.28887i −0.0937952 + 0.0469380i
755755 −1.79024 0.741541i −0.0651535 0.0269875i
756756 −26.0838 14.3151i −0.948658 0.520635i
757757 2.39182 + 5.77436i 0.0869321 + 0.209873i 0.961367 0.275271i 0.0887675π-0.0887675\pi
−0.874435 + 0.485143i 0.838767π0.838767\pi
758758 −7.89525 22.4564i −0.286768 0.815652i
759759 −4.65015 + 4.65015i −0.168790 + 0.168790i
760760 −77.5401 12.8197i −2.81268 0.465020i
761761 −10.4572 10.4572i −0.379075 0.379075i 0.491694 0.870768i 0.336378π-0.336378\pi
−0.870768 + 0.491694i 0.836378π0.836378\pi
762762 −3.02249 + 6.30017i −0.109493 + 0.228231i
763763 42.6364 17.6606i 1.54354 0.639356i
764764 −48.7875 5.35045i −1.76507 0.193573i
765765 52.2677 + 21.6500i 1.88974 + 0.782756i
766766 −0.762454 + 13.9464i −0.0275486 + 0.503904i
767767 8.35831 30.5823i 0.301801 1.10426i
768768 −12.2555 + 11.2167i −0.442234 + 0.404749i
769769 45.4420i 1.63868i −0.573307 0.819341i 0.694340π-0.694340\pi
0.573307 0.819341i 0.305660π-0.305660\pi
770770 −3.44770 + 63.0635i −0.124246 + 2.27265i
771771 −8.73591 + 21.0903i −0.314616 + 0.759550i
772772 1.66446 15.1772i 0.0599052 0.546239i
773773 −0.646635 1.56111i −0.0232578 0.0561494i 0.911824 0.410581i 0.134674π-0.134674\pi
−0.935082 + 0.354432i 0.884674π0.884674\pi
774774 5.70547 11.8927i 0.205079 0.427472i
775775 19.4442 + 19.4442i 0.698456 + 0.698456i
776776 −4.07656 + 24.6571i −0.146340 + 0.885138i
777777 −7.89558 7.89558i −0.283252 0.283252i
778778 32.9667 11.5905i 1.18191 0.415539i
779779 −15.6654 37.8196i −0.561271 1.35503i
780780 −21.5265 20.8202i −0.770773 0.745484i
781781 38.4060 + 15.9083i 1.37427 + 0.569243i
782782 12.7979 11.4711i 0.457653 0.410206i
783783 2.88656i 0.103157i
784784 −1.27772 + 5.75531i −0.0456328 + 0.205547i
785785 −27.9532 −0.997693
786786 6.56659 + 7.32611i 0.234223 + 0.261314i
787787 13.7217 33.1272i 0.489127 1.18086i −0.466033 0.884768i 0.654317π-0.654317\pi
0.955160 0.296090i 0.0956830π-0.0956830\pi
788788 0.615260 + 2.11203i 0.0219177 + 0.0752380i
789789 4.52192 + 10.9169i 0.160985 + 0.388651i
790790 −47.5536 + 16.7190i −1.69188 + 0.594835i
791791 15.0079 15.0079i 0.533618 0.533618i
792792 17.7036 + 11.0143i 0.629069 + 0.391375i
793793 −2.01795 + 1.15167i −0.0716594 + 0.0408971i
794794 −10.2665 + 21.3998i −0.364345 + 0.759451i
795795 −11.3954 27.5109i −0.404153 0.975712i
796796 2.84056 2.27909i 0.100681 0.0807803i
797797 −4.73476 + 11.4307i −0.167714 + 0.404897i −0.985282 0.170934i 0.945321π-0.945321\pi
0.817569 + 0.575831i 0.195321π0.195321\pi
798798 1.62115 29.6531i 0.0573880 1.04971i
799799 27.7725i 0.982520i
800800 54.2214 30.4945i 1.91702 1.07814i
801801 22.5903i 0.798190i
802802 −48.7383 2.66454i −1.72101 0.0940881i
803803 5.48777 13.2487i 0.193659 0.467535i
804804 5.46086 4.38147i 0.192590 0.154522i
805805 17.7607 7.35673i 0.625983 0.259291i
806806 −8.35065 + 9.63508i −0.294139 + 0.339381i
807807 −5.66682 + 5.66682i −0.199481 + 0.199481i
808808 −4.18115 + 0.973924i −0.147092 + 0.0342625i
809809 4.40985 + 4.40985i 0.155042 + 0.155042i 0.780366 0.625323i 0.215033π-0.215033\pi
−0.625323 + 0.780366i 0.715033π0.715033\pi
810810 2.44863 0.860893i 0.0860361 0.0302487i
811811 −31.5144 + 13.0537i −1.10662 + 0.458377i −0.859772 0.510678i 0.829395π-0.829395\pi
−0.246847 + 0.969054i 0.579395π0.579395\pi
812812 3.15713 0.919710i 0.110794 0.0322755i
813813 −4.39640 + 10.6138i −0.154188 + 0.372244i
814814 13.3752 + 14.9222i 0.468800 + 0.523024i
815815 49.9433i 1.74944i
816816 25.0359 + 17.5415i 0.876433 + 0.614074i
817817 33.7170 1.17961
818818 −3.91146 4.36387i −0.136761 0.152579i
819819 −12.3590 + 15.9412i −0.431858 + 0.557030i
820820 41.3201 + 22.6770i 1.44296 + 0.791914i
821821 −6.60418 + 2.73554i −0.230487 + 0.0954710i −0.494938 0.868928i 0.664809π-0.664809\pi
0.264451 + 0.964399i 0.414809π0.414809\pi
822822 9.15728 + 26.0460i 0.319397 + 0.908457i
823823 5.40923 + 5.40923i 0.188554 + 0.188554i 0.795071 0.606517i 0.207434π-0.207434\pi
−0.606517 + 0.795071i 0.707434π0.707434\pi
824824 −3.12344 + 2.23717i −0.108810 + 0.0779355i
825825 30.9710 + 30.9710i 1.07827 + 1.07827i
826826 −15.6577 + 32.6374i −0.544803 + 1.13560i
827827 10.2653 + 24.7826i 0.356959 + 0.861776i 0.995724 + 0.0923740i 0.0294455π0.0294455\pi
−0.638765 + 0.769402i 0.720554π0.720554\pi
828828 0.691854 6.30860i 0.0240436 0.219239i
829829 14.1391 34.1349i 0.491072 1.18555i −0.463103 0.886304i 0.653264π-0.653264\pi
0.954175 0.299248i 0.0967359π-0.0967359\pi
830830 12.7735 + 0.698332i 0.443375 + 0.0242395i
831831 0.421624 0.0146260
832832 15.8945 + 24.0700i 0.551041 + 0.834478i
833833 10.8478 0.375853
834834 −0.00641637 0.000350785i −0.000222181 1.21467e-5i
835835 −25.3724 + 61.2543i −0.878047 + 2.11979i
836836 −5.81012 + 52.9790i −0.200947 + 1.83232i
837837 4.89037 + 11.8064i 0.169036 + 0.408089i
838838 6.57432 13.7037i 0.227106 0.473387i
839839 −16.1260 16.1260i −0.556733 0.556733i 0.371643 0.928376i 0.378795π-0.378795\pi
−0.928376 + 0.371643i 0.878795π0.878795\pi
840840 19.9110 + 27.7989i 0.686996 + 0.959153i
841841 20.2805 + 20.2805i 0.699328 + 0.699328i
842842 4.56408 + 12.9816i 0.157289 + 0.447374i
843843 6.07773 2.51748i 0.209328 0.0867066i
844844 −27.8101 15.2625i −0.957264 0.525358i
845845 −41.5644 + 31.2393i −1.42986 + 1.07466i
846846 −6.84508 7.63681i −0.235339 0.262559i
847847 10.8086 0.371389
848848 4.97190 + 28.2462i 0.170736 + 0.969979i
849849 27.3778i 0.939605i
850850 −76.4001 85.2369i −2.62050 2.92360i
851851 2.33420 5.63527i 0.0800155 0.193174i
852852 21.6082 6.29474i 0.740286 0.215654i
853853 46.7452 19.3625i 1.60053 0.662959i 0.609035 0.793143i 0.291557π-0.291557\pi
0.991490 + 0.130184i 0.0415567π0.0415567\pi
854854 2.50271 0.879908i 0.0856411 0.0301098i
855855 37.7603 + 37.7603i 1.29138 + 1.29138i
856856 −9.21433 39.5581i −0.314939 1.35207i
857857 30.7848 30.7848i 1.05159 1.05159i 0.0529934 0.998595i 0.483124π-0.483124\pi
0.998595 0.0529934i 0.0168762π-0.0168762\pi
858858 −13.3010 + 15.3469i −0.454090 + 0.523934i
859859 −38.9837 + 16.1476i −1.33011 + 0.550948i −0.930686 0.365820i 0.880789π-0.880789\pi
−0.399421 + 0.916768i 0.630789π0.630789\pi
860860 −30.2804 + 24.2952i −1.03255 + 0.828459i
861861 −6.81566 + 16.4545i −0.232277 + 0.560767i
862862 −16.1872 0.884960i −0.551338 0.0301418i
863863 35.8690i 1.22099i 0.792018 + 0.610497i 0.209030π0.209030\pi
−0.792018 + 0.610497i 0.790970π0.790970\pi
864864 28.7033 3.44994i 0.976505 0.117369i
865865 47.4814i 1.61442i
866866 0.718754 13.1471i 0.0244242 0.446755i
867867 14.7704 35.6590i 0.501630 1.21104i
868868 11.3549 9.11051i 0.385411 0.309231i
869869 13.0812 + 31.5809i 0.443750 + 1.07131i
870870 1.43490 2.99094i 0.0486476 0.101402i
871871 −6.02517 10.5572i −0.204155 0.357718i
872872 −23.6873 + 38.0733i −0.802153 + 1.28932i
873873 12.0075 12.0075i 0.406391 0.406391i
874874 15.3042 5.38068i 0.517673 0.182004i
875875 −26.7198 64.5072i −0.903293 2.18074i
876876 −2.17146 7.45406i −0.0733667 0.251849i
877877 4.72801 11.4144i 0.159653 0.385438i −0.823729 0.566984i 0.808110π-0.808110\pi
0.983382 + 0.181546i 0.0581102π0.0581102\pi
878878 −18.0616 20.1507i −0.609551 0.680054i
879879 9.73893 0.328486
880880 −32.9567 51.7657i −1.11097 1.74502i
881881 24.1680i 0.814239i 0.913375 + 0.407119i 0.133467π0.133467\pi
−0.913375 + 0.407119i 0.866533π0.866533\pi
882882 2.98290 2.67365i 0.100439 0.0900265i
883883 −8.10395 3.35677i −0.272720 0.112964i 0.242132 0.970243i 0.422153π-0.422153\pi
−0.514852 + 0.857279i 0.672153π0.672153\pi
884884 36.8983 38.1500i 1.24103 1.28312i
885885 13.9748 + 33.7381i 0.469757 + 1.13409i
886886 13.6349 4.79377i 0.458073 0.161050i
887887 0.999959 + 0.999959i 0.0335754 + 0.0335754i 0.723695 0.690120i 0.242442π-0.242442\pi
−0.690120 + 0.723695i 0.742442π0.742442\pi
888888 10.7040 + 1.76970i 0.359204 + 0.0593872i
889889 −9.79487 9.79487i −0.328509 0.328509i
890890 28.7591 59.9463i 0.964008 2.00941i
891891 −0.673578 1.62616i −0.0225657 0.0544784i
892892 −1.94544 + 17.7393i −0.0651382 + 0.593956i
893893 10.0320 24.2194i 0.335708 0.810472i
894894 −0.00706301 + 0.129193i −0.000236222 + 0.00432085i
895895 28.5362i 0.953861i
896896 −12.9187 30.2946i −0.431584 1.01207i
897897 5.96293 + 1.62970i 0.199096 + 0.0544142i
898898 −3.03576 + 55.5285i −0.101305 + 1.85301i
899899 −1.30484 0.540481i −0.0435187 0.0180260i
900900 −42.0166 4.60790i −1.40055 0.153597i
901901 48.7558 20.1953i 1.62429 0.672803i
902902 13.8255 28.8183i 0.460340 0.959546i
903903 −10.3729 10.3729i −0.345189 0.345189i
904904 −3.36383 + 20.3462i −0.111879 + 0.676703i
905905 65.6209 65.6209i 2.18131 2.18131i
906906 0.235969 + 0.671164i 0.00783955 + 0.0222979i
907907 13.3795 + 32.3009i 0.444259 + 1.07254i 0.974439 + 0.224651i 0.0721241π0.0721241\pi
−0.530181 + 0.847885i 0.677876π0.677876\pi
908908 9.61793 + 5.27844i 0.319182 + 0.175171i
909909 2.69497 + 1.11629i 0.0893863 + 0.0370250i
910910 53.0905 26.5681i 1.75993 0.880723i
911911 56.5416i 1.87331i −0.350256 0.936654i 0.613905π-0.613905\pi
0.350256 0.936654i 0.386095π-0.386095\pi
912912 15.4966 + 24.3408i 0.513144 + 0.806004i
913913 8.67512i 0.287105i
914914 9.68445 8.68044i 0.320333 0.287123i
915915 1.02416 2.47254i 0.0338576 0.0817395i
916916 5.95653 + 20.4473i 0.196809 + 0.675597i
917917 −18.0184 + 7.46346i −0.595019 + 0.246465i
918918 −17.6437 50.1838i −0.582328 1.65631i
919919 38.1443 + 38.1443i 1.25827 + 1.25827i 0.951920 + 0.306345i 0.0991062π0.0991062\pi
0.306345 + 0.951920i 0.400894π0.400894\pi
920920 −9.86723 + 15.8599i −0.325313 + 0.522885i
921921 −19.2064 19.2064i −0.632873 0.632873i
922922 22.1267 46.1216i 0.728705 1.51893i
923923 −4.90695 38.7661i −0.161514 1.27600i
924924 18.0863 14.5113i 0.594995 0.477388i
925925 −37.5321 15.5463i −1.23405 0.511159i
926926 −3.69785 0.202162i −0.121519 0.00664347i
927927 2.61050 0.0857400
928928 −1.97352 + 2.51274i −0.0647841 + 0.0824848i
929929 18.4449i 0.605157i −0.953124 0.302578i 0.902153π-0.902153\pi
0.953124 0.302578i 0.0978474π-0.0978474\pi
930930 0.801703 14.6643i 0.0262889 0.480862i
931931 9.45997 + 3.91845i 0.310038 + 0.128422i
932932 −31.4510 39.1991i −1.03021 1.28401i
933933 −14.9095 + 6.17572i −0.488115 + 0.202184i
934934 23.1884 + 11.1246i 0.758747 + 0.364007i
935935 −79.8437 + 79.8437i −2.61117 + 2.61117i
936936 0.743384 19.5847i 0.0242983 0.640147i
937937 −20.9082 20.9082i −0.683040 0.683040i 0.277644 0.960684i 0.410447π-0.410447\pi
−0.960684 + 0.277644i 0.910447π0.910447\pi
938938 4.60339 + 13.0934i 0.150306 + 0.427514i
939939 4.77039 + 11.5168i 0.155676 + 0.375835i
940940 8.44209 + 28.9795i 0.275351 + 0.945209i
941941 8.46495 20.4362i 0.275949 0.666201i −0.723766 0.690045i 0.757591π-0.757591\pi
0.999716 + 0.0238445i 0.00759067π0.00759067\pi
942942 6.85004 + 7.64234i 0.223186 + 0.249001i
943943 −9.72901 −0.316820
944944 −6.09730 34.6398i −0.198450 1.12743i
945945 59.5019i 1.93560i
946946 17.5718 + 19.6043i 0.571310 + 0.637390i
947947 −10.9113 + 26.3423i −0.354571 + 0.856009i 0.641473 + 0.767146i 0.278324π0.278324\pi
−0.996044 + 0.0888638i 0.971676π0.971676\pi
948948 16.2241 + 8.90400i 0.526935 + 0.289188i
949949 −13.3729 + 1.69272i −0.434102 + 0.0549479i
950950 −35.8365 101.929i −1.16269 3.30703i
951951 12.0868 12.0868i 0.391941 0.391941i
952952 −49.2662 + 35.2870i −1.59673 + 1.14366i
953953 13.7265 13.7265i 0.444646 0.444646i −0.448924 0.893570i 0.648193π-0.648193\pi
0.893570 + 0.448924i 0.148193π0.148193\pi
954954 8.42921 17.5701i 0.272906 0.568853i
955955 −37.5607 90.6796i −1.21544 2.93432i
956956 28.2865 + 3.10214i 0.914851 + 0.100330i
957957 −2.07836 0.860885i −0.0671839 0.0278285i
958958 0.990411 18.1161i 0.0319987 0.585304i
959959 −54.7304 −1.76734
960960 −31.4562 10.6936i −1.01524 0.345134i
961961 24.7474 0.798302
962962 5.95047 17.8719i 0.191851 0.576214i
963963 −10.5613 + 25.4972i −0.340332 + 0.821635i
964964 −28.5478 3.13079i −0.919461 0.100836i
965965 28.2093 11.6847i 0.908089 0.376143i
966966 −6.36364 3.05294i −0.204747 0.0982268i
967967 −1.82965 1.82965i −0.0588375 0.0588375i 0.677076 0.735913i 0.263247π-0.263247\pi
−0.735913 + 0.677076i 0.763247π0.763247\pi
968968 −8.53795 + 6.11532i −0.274420 + 0.196554i
969969 37.5434 37.5434i 1.20607 1.20607i
970970 −47.1497 + 16.5770i −1.51389 + 0.532255i
971971 11.6728 + 28.1805i 0.374597 + 0.904357i 0.992958 + 0.118463i 0.0377967π0.0377967\pi
−0.618362 + 0.785894i 0.712203π0.712203\pi
972972 −27.7168 15.2113i −0.889015 0.487903i
973973 0.00487481 0.0117688i 0.000156279 0.000377292i
974974 −22.4831 25.0836i −0.720404 0.803729i
975975 10.8542 39.7144i 0.347611 1.27188i
976976 −1.47911 + 2.11104i −0.0473450 + 0.0675729i
977977 −26.9686 −0.862803 −0.431402 0.902160i 0.641981π-0.641981\pi
−0.431402 + 0.902160i 0.641981π0.641981\pi
978978 13.6544 12.2388i 0.436619 0.391353i
979979 −41.6558 17.2544i −1.33133 0.551453i
980980 −11.3193 + 3.29743i −0.361580 + 0.105333i
981981 28.1484 11.6594i 0.898709 0.372258i
982982 17.5672 + 49.9663i 0.560593 + 1.59449i
983983 −3.17050 + 3.17050i −0.101123 + 0.101123i −0.755858 0.654735i 0.772780π-0.772780\pi
0.654735 + 0.755858i 0.272780π0.272780\pi
984984 −3.92580 16.8539i −0.125150 0.537282i
985985 −3.11073 + 3.11073i −0.0991160 + 0.0991160i
986986 5.30065 + 2.54297i 0.168807 + 0.0809848i
987987 −10.5373 + 4.36471i −0.335407 + 0.138930i
988988 45.9583 19.9408i 1.46213 0.634402i
989989 3.06659 7.40341i 0.0975119 0.235415i
990990 −2.27616 + 41.6343i −0.0723411 + 1.32322i
991991 −37.0589 −1.17722 −0.588608 0.808419i 0.700324π-0.700324\pi
−0.588608 + 0.808419i 0.700324π0.700324\pi
992992 −3.81491 + 13.6210i −0.121124 + 0.432466i
993993 5.85534i 0.185814i
994994 −2.43552 + 44.5492i −0.0772499 + 1.41301i
995995 6.72861 + 2.78708i 0.213311 + 0.0883565i
996996 −2.93927 3.66337i −0.0931344 0.116078i
997997 −11.9236 + 4.93891i −0.377624 + 0.156417i −0.563418 0.826172i 0.690514π-0.690514\pi
0.185795 + 0.982589i 0.440514π0.440514\pi
998998 14.6959 30.6326i 0.465191 0.969657i
999999 −13.3496 13.3496i −0.422364 0.422364i
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 416.2.bg.a.77.1 216
13.12 even 2 inner 416.2.bg.a.77.54 yes 216
32.5 even 8 inner 416.2.bg.a.389.54 yes 216
416.389 even 8 inner 416.2.bg.a.389.1 yes 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
416.2.bg.a.77.1 216 1.1 even 1 trivial
416.2.bg.a.77.54 yes 216 13.12 even 2 inner
416.2.bg.a.389.1 yes 216 416.389 even 8 inner
416.2.bg.a.389.54 yes 216 32.5 even 8 inner