Properties

Label 400.2.q.h.149.7
Level 400400
Weight 22
Character 400.149
Analytic conductor 3.1943.194
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [400,2,Mod(149,400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(400, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("400.149");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 400=2452 400 = 2^{4} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 400.q (of order 44, degree 22, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 3.194016080853.19401608085
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(i)\Q(i)
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x164x15+4x14+7x128x1128x10+28x9+17x8+56x7++256 x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 26 2^{6}
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 149.7
Root 1.320700.505727i1.32070 - 0.505727i of defining polynomial
Character χ\chi == 400.149
Dual form 400.2.q.h.349.7

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+(1.39064+0.257150i)q2+(1.663661.66366i)q3+(1.86775+0.715205i)q4+(1.885742.74137i)q6+2.89402q7+(2.41345+1.47488i)q8+2.53555iq9+(1.84462+1.84462i)q11+(1.917444.29717i)q12+(3.080113.08011i)q13+(4.02454+0.744198i)q14+(2.97696+2.67165i)q167.29875iq17+(0.652018+3.52604i)q18+(1.235931.23593i)q19+(4.814684.81468i)q21+(2.09086+3.03955i)q22+4.60490q23+(1.561456.46887i)q24+(3.491265.07536i)q26+(0.772683+0.772683i)q27+(5.40530+2.06982i)q28+(4.24680+4.24680i)q29+2.06299q31+(3.45286+4.48082i)q326.13767iq33+(1.8768810.1499i)q34+(1.81344+4.73577i)q36+(1.17899+1.17899i)q37+(2.036551.40091i)q38+10.2485iq39+4.61484iq41+(5.457387.93357i)q42+(3.03019+3.03019i)q43+(2.12601+4.76458i)q44+(6.40375+1.18415i)q46+11.7111iq47+(0.5079439.39739i)q48+1.37537q49+(12.1427+12.1427i)q51+(3.549957.95577i)q52+(2.73048+2.73048i)q53+(1.27322+0.875827i)q54+(6.98457+4.26835i)q564.11235q57+(6.99782+4.81369i)q58+(3.113063.11306i)q59+(2.349622.34962i)q61+(2.86887+0.530498i)q62+7.33795iq63+(3.64944+7.11910i)q64+(1.578308.53528i)q66+(8.243118.24311i)q67+(5.2201113.6322i)q68+(7.661017.66101i)q693.25937iq71+(3.73965+6.11942i)q7212.6877q73+(1.94272+1.33637i)q74+(3.192351.42446i)q76+(5.33839+5.33839i)q77+(2.63541+14.2520i)q78+0.113885q79+10.1776q81+(1.18671+6.41758i)q82+(9.76813+9.76813i)q83+(5.5491212.4361i)q84+(4.99310+3.43468i)q86+14.1305q87+(1.73129+7.17251i)q88+3.74593iq89+(8.913908.91390i)q91+(8.60080+3.29345i)q92+(3.432123.43212i)q93+(3.01150+16.2858i)q94+(1.7101713.1990i)q96+13.9853iq97+(1.91264+0.353676i)q98+(4.67714+4.67714i)q99+O(q100)q+(1.39064 + 0.257150i) q^{2} +(-1.66366 - 1.66366i) q^{3} +(1.86775 + 0.715205i) q^{4} +(-1.88574 - 2.74137i) q^{6} +2.89402 q^{7} +(2.41345 + 1.47488i) q^{8} +2.53555i q^{9} +(1.84462 + 1.84462i) q^{11} +(-1.91744 - 4.29717i) q^{12} +(-3.08011 - 3.08011i) q^{13} +(4.02454 + 0.744198i) q^{14} +(2.97696 + 2.67165i) q^{16} -7.29875i q^{17} +(-0.652018 + 3.52604i) q^{18} +(1.23593 - 1.23593i) q^{19} +(-4.81468 - 4.81468i) q^{21} +(2.09086 + 3.03955i) q^{22} +4.60490 q^{23} +(-1.56145 - 6.46887i) q^{24} +(-3.49126 - 5.07536i) q^{26} +(-0.772683 + 0.772683i) q^{27} +(5.40530 + 2.06982i) q^{28} +(-4.24680 + 4.24680i) q^{29} +2.06299 q^{31} +(3.45286 + 4.48082i) q^{32} -6.13767i q^{33} +(1.87688 - 10.1499i) q^{34} +(-1.81344 + 4.73577i) q^{36} +(-1.17899 + 1.17899i) q^{37} +(2.03655 - 1.40091i) q^{38} +10.2485i q^{39} +4.61484i q^{41} +(-5.45738 - 7.93357i) q^{42} +(-3.03019 + 3.03019i) q^{43} +(2.12601 + 4.76458i) q^{44} +(6.40375 + 1.18415i) q^{46} +11.7111i q^{47} +(-0.507943 - 9.39739i) q^{48} +1.37537 q^{49} +(-12.1427 + 12.1427i) q^{51} +(-3.54995 - 7.95577i) q^{52} +(-2.73048 + 2.73048i) q^{53} +(-1.27322 + 0.875827i) q^{54} +(6.98457 + 4.26835i) q^{56} -4.11235 q^{57} +(-6.99782 + 4.81369i) q^{58} +(-3.11306 - 3.11306i) q^{59} +(2.34962 - 2.34962i) q^{61} +(2.86887 + 0.530498i) q^{62} +7.33795i q^{63} +(3.64944 + 7.11910i) q^{64} +(1.57830 - 8.53528i) q^{66} +(-8.24311 - 8.24311i) q^{67} +(5.22011 - 13.6322i) q^{68} +(-7.66101 - 7.66101i) q^{69} -3.25937i q^{71} +(-3.73965 + 6.11942i) q^{72} -12.6877 q^{73} +(-1.94272 + 1.33637i) q^{74} +(3.19235 - 1.42446i) q^{76} +(5.33839 + 5.33839i) q^{77} +(-2.63541 + 14.2520i) q^{78} +0.113885 q^{79} +10.1776 q^{81} +(-1.18671 + 6.41758i) q^{82} +(9.76813 + 9.76813i) q^{83} +(-5.54912 - 12.4361i) q^{84} +(-4.99310 + 3.43468i) q^{86} +14.1305 q^{87} +(1.73129 + 7.17251i) q^{88} +3.74593i q^{89} +(-8.91390 - 8.91390i) q^{91} +(8.60080 + 3.29345i) q^{92} +(-3.43212 - 3.43212i) q^{93} +(-3.01150 + 16.2858i) q^{94} +(1.71017 - 13.1990i) q^{96} +13.9853i q^{97} +(1.91264 + 0.353676i) q^{98} +(-4.67714 + 4.67714i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+4q2+4q412q6+8q78q88q11+20q124q14+16q16+12q18+8q1920q22+24q238q2416q26+24q27+20q28+16q29++8q99+O(q100) 16 q + 4 q^{2} + 4 q^{4} - 12 q^{6} + 8 q^{7} - 8 q^{8} - 8 q^{11} + 20 q^{12} - 4 q^{14} + 16 q^{16} + 12 q^{18} + 8 q^{19} - 20 q^{22} + 24 q^{23} - 8 q^{24} - 16 q^{26} + 24 q^{27} + 20 q^{28} + 16 q^{29}+ \cdots + 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/400Z)×\left(\mathbb{Z}/400\mathbb{Z}\right)^\times.

nn 101101 177177 351351
χ(n)\chi(n) e(14)e\left(\frac{1}{4}\right) 1-1 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 1.39064 + 0.257150i 0.983329 + 0.181833i
33 −1.66366 1.66366i −0.960517 0.960517i 0.0387330 0.999250i 0.487668π-0.487668\pi
−0.999250 + 0.0387330i 0.987668π0.987668\pi
44 1.86775 + 0.715205i 0.933874 + 0.357603i
55 0 0
66 −1.88574 2.74137i −0.769851 1.11916i
77 2.89402 1.09384 0.546919 0.837186i 0.315801π-0.315801\pi
0.546919 + 0.837186i 0.315801π0.315801\pi
88 2.41345 + 1.47488i 0.853282 + 0.521450i
99 2.53555i 0.845184i
1010 0 0
1111 1.84462 + 1.84462i 0.556175 + 0.556175i 0.928216 0.372041i 0.121342π-0.121342\pi
−0.372041 + 0.928216i 0.621342π0.621342\pi
1212 −1.91744 4.29717i −0.553518 1.24048i
1313 −3.08011 3.08011i −0.854268 0.854268i 0.136388 0.990656i 0.456451π-0.456451\pi
−0.990656 + 0.136388i 0.956451π0.956451\pi
1414 4.02454 + 0.744198i 1.07560 + 0.198895i
1515 0 0
1616 2.97696 + 2.67165i 0.744241 + 0.667912i
1717 7.29875i 1.77021i −0.465393 0.885104i 0.654087π-0.654087\pi
0.465393 0.885104i 0.345913π-0.345913\pi
1818 −0.652018 + 3.52604i −0.153682 + 0.831095i
1919 1.23593 1.23593i 0.283542 0.283542i −0.550978 0.834520i 0.685745π-0.685745\pi
0.834520 + 0.550978i 0.185745π0.185745\pi
2020 0 0
2121 −4.81468 4.81468i −1.05065 1.05065i
2222 2.09086 + 3.03955i 0.445773 + 0.648034i
2323 4.60490 0.960189 0.480094 0.877217i 0.340602π-0.340602\pi
0.480094 + 0.877217i 0.340602π0.340602\pi
2424 −1.56145 6.46887i −0.318730 1.32045i
2525 0 0
2626 −3.49126 5.07536i −0.684693 0.995360i
2727 −0.772683 + 0.772683i −0.148703 + 0.148703i
2828 5.40530 + 2.06982i 1.02151 + 0.391159i
2929 −4.24680 + 4.24680i −0.788611 + 0.788611i −0.981266 0.192656i 0.938290π-0.938290\pi
0.192656 + 0.981266i 0.438290π0.438290\pi
3030 0 0
3131 2.06299 0.370524 0.185262 0.982689i 0.440687π-0.440687\pi
0.185262 + 0.982689i 0.440687π0.440687\pi
3232 3.45286 + 4.48082i 0.610386 + 0.792104i
3333 6.13767i 1.06843i
3434 1.87688 10.1499i 0.321882 1.74070i
3535 0 0
3636 −1.81344 + 4.73577i −0.302240 + 0.789296i
3737 −1.17899 + 1.17899i −0.193825 + 0.193825i −0.797346 0.603522i 0.793764π-0.793764\pi
0.603522 + 0.797346i 0.293764π0.293764\pi
3838 2.03655 1.40091i 0.330373 0.227258i
3939 10.2485i 1.64108i
4040 0 0
4141 4.61484i 0.720717i 0.932814 + 0.360359i 0.117346π0.117346\pi
−0.932814 + 0.360359i 0.882654π0.882654\pi
4242 −5.45738 7.93357i −0.842092 1.22418i
4343 −3.03019 + 3.03019i −0.462099 + 0.462099i −0.899343 0.437244i 0.855955π-0.855955\pi
0.437244 + 0.899343i 0.355955π0.355955\pi
4444 2.12601 + 4.76458i 0.320508 + 0.718287i
4545 0 0
4646 6.40375 + 1.18415i 0.944182 + 0.174594i
4747 11.7111i 1.70823i 0.520081 + 0.854117i 0.325902π0.325902\pi
−0.520081 + 0.854117i 0.674098π0.674098\pi
4848 −0.507943 9.39739i −0.0733152 1.35640i
4949 1.37537 0.196481
5050 0 0
5151 −12.1427 + 12.1427i −1.70031 + 1.70031i
5252 −3.54995 7.95577i −0.492290 1.10327i
5353 −2.73048 + 2.73048i −0.375061 + 0.375061i −0.869316 0.494256i 0.835441π-0.835441\pi
0.494256 + 0.869316i 0.335441π0.335441\pi
5454 −1.27322 + 0.875827i −0.173263 + 0.119185i
5555 0 0
5656 6.98457 + 4.26835i 0.933352 + 0.570382i
5757 −4.11235 −0.544694
5858 −6.99782 + 4.81369i −0.918859 + 0.632069i
5959 −3.11306 3.11306i −0.405285 0.405285i 0.474805 0.880091i 0.342518π-0.342518\pi
−0.880091 + 0.474805i 0.842518π0.842518\pi
6060 0 0
6161 2.34962 2.34962i 0.300838 0.300838i −0.540503 0.841342i 0.681766π-0.681766\pi
0.841342 + 0.540503i 0.181766π0.181766\pi
6262 2.86887 + 0.530498i 0.364347 + 0.0673733i
6363 7.33795i 0.924495i
6464 3.64944 + 7.11910i 0.456180 + 0.889888i
6565 0 0
6666 1.57830 8.53528i 0.194276 1.05062i
6767 −8.24311 8.24311i −1.00706 1.00706i −0.999975 0.00708173i 0.997746π-0.997746\pi
−0.00708173 0.999975i 0.502254π-0.502254\pi
6868 5.22011 13.6322i 0.633031 1.65315i
6969 −7.66101 7.66101i −0.922277 0.922277i
7070 0 0
7171 3.25937i 0.386816i −0.981118 0.193408i 0.938046π-0.938046\pi
0.981118 0.193408i 0.0619541π-0.0619541\pi
7272 −3.73965 + 6.11942i −0.440721 + 0.721180i
7373 −12.6877 −1.48499 −0.742494 0.669853i 0.766357π-0.766357\pi
−0.742494 + 0.669853i 0.766357π0.766357\pi
7474 −1.94272 + 1.33637i −0.225837 + 0.155350i
7575 0 0
7676 3.19235 1.42446i 0.366188 0.163397i
7777 5.33839 + 5.33839i 0.608365 + 0.608365i
7878 −2.63541 + 14.2520i −0.298401 + 1.61372i
7979 0.113885 0.0128130 0.00640652 0.999979i 0.497961π-0.497961\pi
0.00640652 + 0.999979i 0.497961π0.497961\pi
8080 0 0
8181 10.1776 1.13085
8282 −1.18671 + 6.41758i −0.131050 + 0.708703i
8383 9.76813 + 9.76813i 1.07219 + 1.07219i 0.997183 + 0.0750089i 0.0238985π0.0238985\pi
0.0750089 + 0.997183i 0.476101π0.476101\pi
8484 −5.54912 12.4361i −0.605459 1.35689i
8585 0 0
8686 −4.99310 + 3.43468i −0.538420 + 0.370371i
8787 14.1305 1.51495
8888 1.73129 + 7.17251i 0.184557 + 0.764592i
8989 3.74593i 0.397068i 0.980094 + 0.198534i 0.0636180π0.0636180\pi
−0.980094 + 0.198534i 0.936382π0.936382\pi
9090 0 0
9191 −8.91390 8.91390i −0.934430 0.934430i
9292 8.60080 + 3.29345i 0.896695 + 0.343366i
9393 −3.43212 3.43212i −0.355894 0.355894i
9494 −3.01150 + 16.2858i −0.310613 + 1.67976i
9595 0 0
9696 1.71017 13.1990i 0.174544 1.34711i
9797 13.9853i 1.41999i 0.704206 + 0.709995i 0.251303π0.251303\pi
−0.704206 + 0.709995i 0.748697π0.748697\pi
9898 1.91264 + 0.353676i 0.193206 + 0.0357267i
9999 −4.67714 + 4.67714i −0.470071 + 0.470071i
100100 0 0
101101 3.52228 + 3.52228i 0.350480 + 0.350480i 0.860288 0.509808i 0.170284π-0.170284\pi
−0.509808 + 0.860288i 0.670284π0.670284\pi
102102 −20.0085 + 13.7636i −1.98114 + 1.36280i
103103 −0.150216 −0.0148013 −0.00740063 0.999973i 0.502356π-0.502356\pi
−0.00740063 + 0.999973i 0.502356π0.502356\pi
104104 −2.89087 11.9765i −0.283473 1.17439i
105105 0 0
106106 −4.49926 + 3.09497i −0.437006 + 0.300610i
107107 −2.75062 + 2.75062i −0.265912 + 0.265912i −0.827451 0.561539i 0.810210π-0.810210\pi
0.561539 + 0.827451i 0.310210π0.310210\pi
108108 −1.99580 + 0.890550i −0.192046 + 0.0856932i
109109 6.90778 6.90778i 0.661646 0.661646i −0.294122 0.955768i 0.595027π-0.595027\pi
0.955768 + 0.294122i 0.0950273π0.0950273\pi
110110 0 0
111111 3.92288 0.372344
112112 8.61540 + 7.73181i 0.814078 + 0.730587i
113113 3.49507i 0.328788i −0.986395 0.164394i 0.947433π-0.947433\pi
0.986395 0.164394i 0.0525669π-0.0525669\pi
114114 −5.71879 1.05749i −0.535614 0.0990431i
115115 0 0
116116 −10.9693 + 4.89461i −1.01847 + 0.454454i
117117 7.80977 7.80977i 0.722014 0.722014i
118118 −3.52861 5.12966i −0.324835 0.472223i
119119 21.1228i 1.93632i
120120 0 0
121121 4.19472i 0.381338i
122122 3.87168 2.66327i 0.350526 0.241121i
123123 7.67755 7.67755i 0.692261 0.692261i
124124 3.85314 + 1.47546i 0.346022 + 0.132500i
125125 0 0
126126 −1.88695 + 10.2044i −0.168103 + 0.909083i
127127 6.25357i 0.554915i −0.960738 0.277458i 0.910508π-0.910508\pi
0.960738 0.277458i 0.0894918π-0.0894918\pi
128128 3.24437 + 10.8385i 0.286764 + 0.958001i
129129 10.0824 0.887708
130130 0 0
131131 −5.16490 + 5.16490i −0.451259 + 0.451259i −0.895772 0.444513i 0.853377π-0.853377\pi
0.444513 + 0.895772i 0.353377π0.353377\pi
132132 4.38969 11.4636i 0.382074 0.997780i
133133 3.57681 3.57681i 0.310149 0.310149i
134134 −9.34347 13.5829i −0.807153 1.17338i
135135 0 0
136136 10.7648 17.6151i 0.923075 1.51049i
137137 −18.9408 −1.61823 −0.809113 0.587654i 0.800052π-0.800052\pi
−0.809113 + 0.587654i 0.800052π0.800052\pi
138138 −8.68366 12.6237i −0.739203 1.07460i
139139 −2.79057 2.79057i −0.236693 0.236693i 0.578786 0.815479i 0.303527π-0.303527\pi
−0.815479 + 0.578786i 0.803527π0.803527\pi
140140 0 0
141141 19.4833 19.4833i 1.64079 1.64079i
142142 0.838147 4.53260i 0.0703357 0.380367i
143143 11.3633i 0.950245i
144144 −6.77410 + 7.54825i −0.564509 + 0.629021i
145145 0 0
146146 −17.6441 3.26265i −1.46023 0.270019i
147147 −2.28815 2.28815i −0.188723 0.188723i
148148 −3.04527 + 1.35883i −0.250320 + 0.111696i
149149 1.60372 + 1.60372i 0.131382 + 0.131382i 0.769740 0.638358i 0.220386π-0.220386\pi
−0.638358 + 0.769740i 0.720386π0.720386\pi
150150 0 0
151151 2.53754i 0.206502i 0.994655 + 0.103251i 0.0329245π0.0329245\pi
−0.994655 + 0.103251i 0.967076π0.967076\pi
152152 4.80571 1.16000i 0.389794 0.0940883i
153153 18.5064 1.49615
154154 6.05099 + 8.79653i 0.487603 + 0.708844i
155155 0 0
156156 −7.32980 + 19.1417i −0.586854 + 1.53256i
157157 −10.2405 10.2405i −0.817278 0.817278i 0.168435 0.985713i 0.446129π-0.446129\pi
−0.985713 + 0.168435i 0.946129π0.946129\pi
158158 0.158373 + 0.0292855i 0.0125994 + 0.00232983i
159159 9.08521 0.720504
160160 0 0
161161 13.3267 1.05029
162162 14.1534 + 2.61718i 1.11200 + 0.205625i
163163 8.02607 + 8.02607i 0.628650 + 0.628650i 0.947728 0.319078i 0.103373π-0.103373\pi
−0.319078 + 0.947728i 0.603373π0.603373\pi
164164 −3.30056 + 8.61936i −0.257731 + 0.673059i
165165 0 0
166166 11.0721 + 16.0958i 0.859358 + 1.24928i
167167 −6.82611 −0.528221 −0.264110 0.964492i 0.585078π-0.585078\pi
−0.264110 + 0.964492i 0.585078π0.585078\pi
168168 −4.51888 18.7211i −0.348639 1.44436i
169169 5.97411i 0.459547i
170170 0 0
171171 3.13377 + 3.13377i 0.239645 + 0.239645i
172172 −7.82683 + 3.49242i −0.596790 + 0.266294i
173173 5.08901 + 5.08901i 0.386910 + 0.386910i 0.873584 0.486674i 0.161790π-0.161790\pi
−0.486674 + 0.873584i 0.661790π0.661790\pi
174174 19.6504 + 3.63366i 1.48969 + 0.275467i
175175 0 0
176176 0.563193 + 10.4196i 0.0424523 + 0.785404i
177177 10.3582i 0.778567i
178178 −0.963267 + 5.20924i −0.0721999 + 0.390449i
179179 −1.63797 + 1.63797i −0.122428 + 0.122428i −0.765666 0.643238i 0.777590π-0.777590\pi
0.643238 + 0.765666i 0.277590π0.277590\pi
180180 0 0
181181 −16.7757 16.7757i −1.24693 1.24693i −0.957071 0.289855i 0.906393π-0.906393\pi
−0.289855 0.957071i 0.593607π-0.593607\pi
182182 −10.1038 14.6882i −0.748943 1.08876i
183183 −7.81797 −0.577921
184184 11.1137 + 6.79170i 0.819312 + 0.500691i
185185 0 0
186186 −3.89026 5.65540i −0.285248 0.414674i
187187 13.4635 13.4635i 0.984546 0.984546i
188188 −8.37582 + 21.8733i −0.610869 + 1.59527i
189189 −2.23616 + 2.23616i −0.162657 + 0.162657i
190190 0 0
191191 5.85815 0.423881 0.211940 0.977283i 0.432022π-0.432022\pi
0.211940 + 0.977283i 0.432022π0.432022\pi
192192 5.77235 17.9152i 0.416584 1.29292i
193193 0.0241155i 0.00173587i −1.00000 0.000867935i 0.999724π-0.999724\pi
1.00000 0.000867935i 0.000276272π-0.000276272\pi
194194 −3.59632 + 19.4485i −0.258201 + 1.39632i
195195 0 0
196196 2.56884 + 0.983671i 0.183489 + 0.0702622i
197197 14.9086 14.9086i 1.06219 1.06219i 0.0642576 0.997933i 0.479532π-0.479532\pi
0.997933 0.0642576i 0.0204679π-0.0204679\pi
198198 −7.70694 + 5.30149i −0.547708 + 0.376760i
199199 13.6525i 0.967801i −0.875123 0.483900i 0.839220π-0.839220\pi
0.875123 0.483900i 0.160780π-0.160780\pi
200200 0 0
201201 27.4275i 1.93459i
202202 3.99246 + 5.80397i 0.280909 + 0.408366i
203203 −12.2903 + 12.2903i −0.862612 + 0.862612i
204204 −31.3640 + 13.9949i −2.19592 + 0.979842i
205205 0 0
206206 −0.208897 0.0386282i −0.0145545 0.00269135i
207207 11.6760i 0.811537i
208208 −0.940405 17.3983i −0.0652053 1.20636i
209209 4.55966 0.315398
210210 0 0
211211 −2.45103 + 2.45103i −0.168736 + 0.168736i −0.786424 0.617688i 0.788070π-0.788070\pi
0.617688 + 0.786424i 0.288070π0.288070\pi
212212 −7.05271 + 3.14700i −0.484382 + 0.216137i
213213 −5.42249 + 5.42249i −0.371543 + 0.371543i
214214 −4.53243 + 3.11779i −0.309831 + 0.213128i
215215 0 0
216216 −3.00445 + 0.725211i −0.204427 + 0.0493444i
217217 5.97033 0.405293
218218 11.3826 7.82989i 0.770924 0.530307i
219219 21.1081 + 21.1081i 1.42636 + 1.42636i
220220 0 0
221221 −22.4809 + 22.4809i −1.51223 + 1.51223i
222222 5.45531 + 1.00877i 0.366136 + 0.0677042i
223223 13.9483i 0.934045i 0.884245 + 0.467023i 0.154673π0.154673\pi
−0.884245 + 0.467023i 0.845327π0.845327\pi
224224 9.99266 + 12.9676i 0.667663 + 0.866434i
225225 0 0
226226 0.898758 4.86038i 0.0597845 0.323307i
227227 −4.43883 4.43883i −0.294616 0.294616i 0.544285 0.838901i 0.316801π-0.316801\pi
−0.838901 + 0.544285i 0.816801π0.816801\pi
228228 −7.68083 2.94117i −0.508675 0.194784i
229229 5.35068 + 5.35068i 0.353583 + 0.353583i 0.861441 0.507858i 0.169562π-0.169562\pi
−0.507858 + 0.861441i 0.669562π0.669562\pi
230230 0 0
231231 17.7626i 1.16869i
232232 −16.5129 + 3.98588i −1.08413 + 0.261686i
233233 11.9370 0.782019 0.391010 0.920387i 0.372126π-0.372126\pi
0.391010 + 0.920387i 0.372126π0.372126\pi
234234 12.8689 8.85228i 0.841263 0.578692i
235235 0 0
236236 −3.58793 8.04088i −0.233554 0.523416i
237237 −0.189466 0.189466i −0.0123071 0.0123071i
238238 5.43172 29.3741i 0.352086 1.90404i
239239 16.7720 1.08489 0.542445 0.840091i 0.317499π-0.317499\pi
0.542445 + 0.840091i 0.317499π0.317499\pi
240240 0 0
241241 −22.0294 −1.41904 −0.709519 0.704686i 0.751088π-0.751088\pi
−0.709519 + 0.704686i 0.751088π0.751088\pi
242242 1.07867 5.83334i 0.0693397 0.374981i
243243 −14.6141 14.6141i −0.937495 0.937495i
244244 6.06897 2.70804i 0.388526 0.173365i
245245 0 0
246246 12.6510 8.70241i 0.806596 0.554845i
247247 −7.61360 −0.484442
248248 4.97891 + 3.04267i 0.316161 + 0.193210i
249249 32.5018i 2.05972i
250250 0 0
251251 6.63925 + 6.63925i 0.419066 + 0.419066i 0.884882 0.465816i 0.154239π-0.154239\pi
−0.465816 + 0.884882i 0.654239π0.654239\pi
252252 −5.24814 + 13.7054i −0.330602 + 0.863361i
253253 8.49432 + 8.49432i 0.534033 + 0.534033i
254254 1.60811 8.69646i 0.100902 0.545664i
255255 0 0
256256 1.72461 + 15.9068i 0.107788 + 0.994174i
257257 7.25821i 0.452755i 0.974040 + 0.226377i 0.0726883π0.0726883\pi
−0.974040 + 0.226377i 0.927312π0.927312\pi
258258 14.0210 + 2.59270i 0.872909 + 0.161414i
259259 −3.41202 + 3.41202i −0.212013 + 0.212013i
260260 0 0
261261 −10.7680 10.7680i −0.666521 0.666521i
262262 −8.51066 + 5.85435i −0.525790 + 0.361683i
263263 9.27431 0.571878 0.285939 0.958248i 0.407694π-0.407694\pi
0.285939 + 0.958248i 0.407694π0.407694\pi
264264 9.05235 14.8129i 0.557133 0.911673i
265265 0 0
266266 5.89383 4.05428i 0.361374 0.248584i
267267 6.23197 6.23197i 0.381390 0.381390i
268268 −9.50054 21.2916i −0.580338 1.30059i
269269 13.4195 13.4195i 0.818199 0.818199i −0.167648 0.985847i 0.553617π-0.553617\pi
0.985847 + 0.167648i 0.0536173π0.0536173\pi
270270 0 0
271271 22.5999 1.37285 0.686423 0.727202i 0.259180π-0.259180\pi
0.686423 + 0.727202i 0.259180π0.259180\pi
272272 19.4997 21.7281i 1.18234 1.31746i
273273 29.6595i 1.79507i
274274 −26.3399 4.87064i −1.59125 0.294246i
275275 0 0
276276 −8.82964 19.7880i −0.531482 1.19110i
277277 16.2015 16.2015i 0.973451 0.973451i −0.0262056 0.999657i 0.508342π-0.508342\pi
0.999657 + 0.0262056i 0.00834245π0.00834245\pi
278278 −3.16308 4.59827i −0.189709 0.275786i
279279 5.23082i 0.313161i
280280 0 0
281281 8.84793i 0.527824i −0.964547 0.263912i 0.914987π-0.914987\pi
0.964547 0.263912i 0.0850128π-0.0850128\pi
282282 32.1043 22.0840i 1.91178 1.31509i
283283 20.3062 20.3062i 1.20708 1.20708i 0.235109 0.971969i 0.424455π-0.424455\pi
0.971969 0.235109i 0.0755447π-0.0755447\pi
284284 2.33112 6.08768i 0.138326 0.361237i
285285 0 0
286286 2.92207 15.8022i 0.172786 0.934404i
287287 13.3555i 0.788348i
288288 −11.3614 + 8.75492i −0.669474 + 0.515888i
289289 −36.2718 −2.13364
290290 0 0
291291 23.2668 23.2668i 1.36392 1.36392i
292292 −23.6975 9.07434i −1.38679 0.531036i
293293 7.16936 7.16936i 0.418839 0.418839i −0.465965 0.884803i 0.654293π-0.654293\pi
0.884803 + 0.465965i 0.154293π0.154293\pi
294294 −2.59359 3.77039i −0.151261 0.219893i
295295 0 0
296296 −4.58430 + 1.10655i −0.266457 + 0.0643172i
297297 −2.85062 −0.165410
298298 1.81779 + 2.64259i 0.105302 + 0.153081i
299299 −14.1836 14.1836i −0.820258 0.820258i
300300 0 0
301301 −8.76943 + 8.76943i −0.505461 + 0.505461i
302302 −0.652528 + 3.52880i −0.0375488 + 0.203059i
303303 11.7198i 0.673284i
304304 6.98129 0.377349i 0.400405 0.0216425i
305305 0 0
306306 25.7357 + 4.75892i 1.47121 + 0.272049i
307307 18.4308 + 18.4308i 1.05190 + 1.05190i 0.998577 + 0.0533241i 0.0169816π0.0169816\pi
0.0533241 + 0.998577i 0.483018π0.483018\pi
308308 6.15271 + 13.7888i 0.350583 + 0.785690i
309309 0.249910 + 0.249910i 0.0142169 + 0.0142169i
310310 0 0
311311 7.08961i 0.402015i 0.979590 + 0.201007i 0.0644215π0.0644215\pi
−0.979590 + 0.201007i 0.935578π0.935578\pi
312312 −15.1154 + 24.7342i −0.855739 + 1.40030i
313313 −22.0477 −1.24621 −0.623104 0.782139i 0.714129π-0.714129\pi
−0.623104 + 0.782139i 0.714129π0.714129\pi
314314 −11.6074 16.8741i −0.655046 0.952262i
315315 0 0
316316 0.212708 + 0.0814510i 0.0119658 + 0.00458198i
317317 6.19670 + 6.19670i 0.348042 + 0.348042i 0.859380 0.511338i 0.170850π-0.170850\pi
−0.511338 + 0.859380i 0.670850π0.670850\pi
318318 12.6342 + 2.33626i 0.708493 + 0.131011i
319319 −15.6675 −0.877211
320320 0 0
321321 9.15220 0.510826
322322 18.5326 + 3.42696i 1.03278 + 0.190977i
323323 −9.02076 9.02076i −0.501929 0.501929i
324324 19.0092 + 7.27910i 1.05607 + 0.404394i
325325 0 0
326326 9.09745 + 13.2253i 0.503861 + 0.732479i
327327 −22.9845 −1.27104
328328 −6.80636 + 11.1377i −0.375818 + 0.614975i
329329 33.8921i 1.86853i
330330 0 0
331331 −18.6174 18.6174i −1.02330 1.02330i −0.999722 0.0235823i 0.992493π-0.992493\pi
−0.0235823 0.999722i 0.507507π-0.507507\pi
332332 11.2582 + 25.2306i 0.617873 + 1.38471i
333333 −2.98939 2.98939i −0.163818 0.163818i
334334 −9.49265 1.75534i −0.519415 0.0960477i
335335 0 0
336336 −1.47000 27.1962i −0.0801949 1.48368i
337337 14.2577i 0.776666i −0.921519 0.388333i 0.873051π-0.873051\pi
0.921519 0.388333i 0.126949π-0.126949\pi
338338 −1.53624 + 8.30782i −0.0835606 + 0.451886i
339339 −5.81462 + 5.81462i −0.315807 + 0.315807i
340340 0 0
341341 3.80544 + 3.80544i 0.206076 + 0.206076i
342342 3.55209 + 5.16379i 0.192075 + 0.279226i
343343 −16.2778 −0.878919
344344 −11.7824 + 2.84402i −0.635262 + 0.153339i
345345 0 0
346346 5.76833 + 8.38561i 0.310107 + 0.450813i
347347 −23.5395 + 23.5395i −1.26367 + 1.26367i −0.314363 + 0.949303i 0.601791π0.601791\pi
−0.949303 + 0.314363i 0.898209π0.898209\pi
348348 26.3922 + 10.1062i 1.41477 + 0.541749i
349349 1.56682 1.56682i 0.0838701 0.0838701i −0.663927 0.747797i 0.731112π-0.731112\pi
0.747797 + 0.663927i 0.231112π0.231112\pi
350350 0 0
351351 4.75989 0.254064
352352 −1.89619 + 14.6347i −0.101068 + 0.780030i
353353 9.44678i 0.502801i 0.967883 + 0.251401i 0.0808912π0.0808912\pi
−0.967883 + 0.251401i 0.919109π0.919109\pi
354354 −2.66360 + 14.4044i −0.141569 + 0.765588i
355355 0 0
356356 −2.67911 + 6.99646i −0.141993 + 0.370811i
357357 −35.1412 + 35.1412i −1.85987 + 1.85987i
358358 −2.69903 + 1.85662i −0.142648 + 0.0981256i
359359 18.0452i 0.952392i 0.879339 + 0.476196i 0.157985π0.157985\pi
−0.879339 + 0.476196i 0.842015π0.842015\pi
360360 0 0
361361 15.9449i 0.839208i
362362 −19.0150 27.6427i −0.999407 1.45287i
363363 −6.97860 + 6.97860i −0.366282 + 0.366282i
364364 −10.2736 23.0242i −0.538485 1.20679i
365365 0 0
366366 −10.8720 2.01039i −0.568286 0.105085i
367367 29.1329i 1.52073i −0.649498 0.760363i 0.725021π-0.725021\pi
0.649498 0.760363i 0.274979π-0.274979\pi
368368 13.7086 + 12.3027i 0.714612 + 0.641321i
369369 −11.7012 −0.609139
370370 0 0
371371 −7.90208 + 7.90208i −0.410255 + 0.410255i
372372 −3.95566 8.86500i −0.205091 0.459629i
373373 −3.35598 + 3.35598i −0.173766 + 0.173766i −0.788632 0.614866i 0.789210π-0.789210\pi
0.614866 + 0.788632i 0.289210π0.289210\pi
374374 22.1849 15.2607i 1.14716 0.789110i
375375 0 0
376376 −17.2725 + 28.2640i −0.890759 + 1.45760i
377377 26.1612 1.34737
378378 −3.68472 + 2.53466i −0.189522 + 0.130369i
379379 −11.6507 11.6507i −0.598457 0.598457i 0.341445 0.939902i 0.389084π-0.389084\pi
−0.939902 + 0.341445i 0.889084π0.889084\pi
380380 0 0
381381 −10.4038 + 10.4038i −0.533005 + 0.533005i
382382 8.14656 + 1.50642i 0.416814 + 0.0770753i
383383 21.8044i 1.11415i −0.830461 0.557077i 0.811923π-0.811923\pi
0.830461 0.557077i 0.188077π-0.188077\pi
384384 12.6342 23.4292i 0.644734 1.19562i
385385 0 0
386386 0.00620130 0.0335359i 0.000315638 0.00170693i
387387 −7.68320 7.68320i −0.390559 0.390559i
388388 −10.0024 + 26.1210i −0.507793 + 1.32609i
389389 11.8899 + 11.8899i 0.602842 + 0.602842i 0.941066 0.338224i 0.109826π-0.109826\pi
−0.338224 + 0.941066i 0.609826π0.609826\pi
390390 0 0
391391 33.6101i 1.69973i
392392 3.31938 + 2.02851i 0.167654 + 0.102455i
393393 17.1853 0.866884
394394 24.5661 16.8987i 1.23762 0.851343i
395395 0 0
396396 −12.0808 + 5.39061i −0.607085 + 0.270888i
397397 9.23905 + 9.23905i 0.463694 + 0.463694i 0.899864 0.436170i 0.143665π-0.143665\pi
−0.436170 + 0.899864i 0.643665π0.643665\pi
398398 3.51074 18.9857i 0.175978 0.951667i
399399 −11.9012 −0.595807
400400 0 0
401401 −14.4744 −0.722818 −0.361409 0.932407i 0.617704π-0.617704\pi
−0.361409 + 0.932407i 0.617704π0.617704\pi
402402 −7.05300 + 38.1418i −0.351771 + 1.90234i
403403 −6.35422 6.35422i −0.316526 0.316526i
404404 4.05958 + 9.09789i 0.201972 + 0.452637i
405405 0 0
406406 −20.2519 + 13.9309i −1.00508 + 0.691381i
407407 −4.34958 −0.215601
408408 −47.2147 + 11.3967i −2.33748 + 0.564218i
409409 9.54117i 0.471781i 0.971780 + 0.235890i 0.0758006π0.0758006\pi
−0.971780 + 0.235890i 0.924199π0.924199\pi
410410 0 0
411411 31.5112 + 31.5112i 1.55433 + 1.55433i
412412 −0.280566 0.107436i −0.0138225 0.00529297i
413413 −9.00925 9.00925i −0.443316 0.443316i
414414 −3.00248 + 16.2371i −0.147564 + 0.798008i
415415 0 0
416416 3.16622 24.4366i 0.155237 1.19810i
417417 9.28514i 0.454695i
418418 6.34083 + 1.17252i 0.310140 + 0.0573497i
419419 −0.837667 + 0.837667i −0.0409227 + 0.0409227i −0.727272 0.686349i 0.759212π-0.759212\pi
0.686349 + 0.727272i 0.259212π0.259212\pi
420420 0 0
421421 17.9679 + 17.9679i 0.875702 + 0.875702i 0.993087 0.117385i 0.0374511π-0.0374511\pi
−0.117385 + 0.993087i 0.537451π0.537451\pi
422422 −4.03878 + 2.77822i −0.196605 + 0.135241i
423423 −29.6940 −1.44377
424424 −10.6170 + 2.56273i −0.515608 + 0.124457i
425425 0 0
426426 −8.93512 + 6.14633i −0.432908 + 0.297791i
427427 6.79986 6.79986i 0.329068 0.329068i
428428 −7.10471 + 3.17020i −0.343419 + 0.153237i
429429 −18.9047 + 18.9047i −0.912726 + 0.912726i
430430 0 0
431431 −3.85473 −0.185676 −0.0928380 0.995681i 0.529594π-0.529594\pi
−0.0928380 + 0.995681i 0.529594π0.529594\pi
432432 −4.36459 + 0.235912i −0.209991 + 0.0113503i
433433 25.5651i 1.22858i −0.789081 0.614289i 0.789443π-0.789443\pi
0.789081 0.614289i 0.210557π-0.210557\pi
434434 8.30257 + 1.53527i 0.398536 + 0.0736954i
435435 0 0
436436 17.8425 7.96151i 0.854500 0.381287i
437437 5.69135 5.69135i 0.272254 0.272254i
438438 23.9258 + 34.7817i 1.14322 + 1.66194i
439439 30.1311i 1.43808i 0.694970 + 0.719039i 0.255418π0.255418\pi
−0.694970 + 0.719039i 0.744582π0.744582\pi
440440 0 0
441441 3.48732i 0.166063i
442442 −37.0438 + 25.4819i −1.76199 + 1.21205i
443443 −20.1625 + 20.1625i −0.957948 + 0.957948i −0.999151 0.0412027i 0.986881π-0.986881\pi
0.0412027 + 0.999151i 0.486881π0.486881\pi
444444 7.32695 + 2.80567i 0.347722 + 0.133151i
445445 0 0
446446 −3.58680 + 19.3970i −0.169840 + 0.918474i
447447 5.33610i 0.252389i
448448 10.5616 + 20.6028i 0.498987 + 0.973393i
449449 36.5827 1.72644 0.863221 0.504826i 0.168443π-0.168443\pi
0.863221 + 0.504826i 0.168443π0.168443\pi
450450 0 0
451451 −8.51265 + 8.51265i −0.400845 + 0.400845i
452452 2.49969 6.52791i 0.117576 0.307047i
453453 4.22161 4.22161i 0.198349 0.198349i
454454 −5.03136 7.31426i −0.236134 0.343275i
455455 0 0
456456 −9.92493 6.06523i −0.464777 0.284031i
457457 −16.7340 −0.782785 −0.391392 0.920224i 0.628006π-0.628006\pi
−0.391392 + 0.920224i 0.628006π0.628006\pi
458458 6.06493 + 8.81679i 0.283396 + 0.411982i
459459 5.63962 + 5.63962i 0.263235 + 0.263235i
460460 0 0
461461 11.8377 11.8377i 0.551335 0.551335i −0.375491 0.926826i 0.622526π-0.622526\pi
0.926826 + 0.375491i 0.122526π0.122526\pi
462462 4.56764 24.7013i 0.212506 1.14921i
463463 32.2711i 1.49976i −0.661572 0.749882i 0.730110π-0.730110\pi
0.661572 0.749882i 0.269890π-0.269890\pi
464464 −23.9885 + 1.29661i −1.11364 + 0.0601938i
465465 0 0
466466 16.6000 + 3.06960i 0.768982 + 0.142197i
467467 −1.22565 1.22565i −0.0567163 0.0567163i 0.678180 0.734896i 0.262769π-0.262769\pi
−0.734896 + 0.678180i 0.762769π0.762769\pi
468468 20.1723 9.00109i 0.932464 0.416076i
469469 −23.8558 23.8558i −1.10156 1.10156i
470470 0 0
471471 34.0734i 1.57002i
472472 −2.92180 12.1046i −0.134487 0.557159i
473473 −11.1791 −0.514016
474474 −0.214757 0.312200i −0.00986413 0.0143398i
475475 0 0
476476 15.1071 39.4520i 0.692433 1.80828i
477477 −6.92328 6.92328i −0.316995 0.316995i
478478 23.3238 + 4.31292i 1.06680 + 0.197268i
479479 −28.8399 −1.31773 −0.658865 0.752261i 0.728963π-0.728963\pi
−0.658865 + 0.752261i 0.728963π0.728963\pi
480480 0 0
481481 7.26282 0.331156
482482 −30.6349 5.66486i −1.39538 0.258027i
483483 −22.1711 22.1711i −1.00882 1.00882i
484484 3.00009 7.83468i 0.136368 0.356122i
485485 0 0
486486 −16.5649 24.0809i −0.751399 1.09233i
487487 32.1668 1.45762 0.728808 0.684718i 0.240075π-0.240075\pi
0.728808 + 0.684718i 0.240075π0.240075\pi
488488 9.13611 2.20527i 0.413572 0.0998278i
489489 26.7054i 1.20766i
490490 0 0
491491 −5.43607 5.43607i −0.245326 0.245326i 0.573723 0.819049i 0.305499π-0.305499\pi
−0.819049 + 0.573723i 0.805499π0.805499\pi
492492 19.8307 8.84870i 0.894039 0.398930i
493493 30.9963 + 30.9963i 1.39600 + 1.39600i
494494 −10.5878 1.95784i −0.476366 0.0880873i
495495 0 0
496496 6.14144 + 5.51157i 0.275759 + 0.247477i
497497 9.43268i 0.423114i
498498 8.35783 45.1982i 0.374524 2.02538i
499499 17.1282 17.1282i 0.766762 0.766762i −0.210773 0.977535i 0.567598π-0.567598\pi
0.977535 + 0.210773i 0.0675981π0.0675981\pi
500500 0 0
501501 11.3564 + 11.3564i 0.507365 + 0.507365i
502502 7.52551 + 10.9401i 0.335880 + 0.488280i
503503 23.5180 1.04862 0.524308 0.851529i 0.324324π-0.324324\pi
0.524308 + 0.851529i 0.324324π0.324324\pi
504504 −10.8226 + 17.7097i −0.482078 + 0.788855i
505505 0 0
506506 9.62821 + 13.9968i 0.428026 + 0.622235i
507507 9.93890 9.93890i 0.441402 0.441402i
508508 4.47259 11.6801i 0.198439 0.518221i
509509 −20.3147 + 20.3147i −0.900434 + 0.900434i −0.995474 0.0950391i 0.969702π-0.969702\pi
0.0950391 + 0.995474i 0.469702π0.469702\pi
510510 0 0
511511 −36.7186 −1.62434
512512 −1.69212 + 22.5641i −0.0747820 + 0.997200i
513513 1.90997i 0.0843271i
514514 −1.86645 + 10.0935i −0.0823256 + 0.445207i
515515 0 0
516516 18.8314 + 7.21100i 0.829007 + 0.317447i
517517 −21.6025 + 21.6025i −0.950077 + 0.950077i
518518 −5.62229 + 3.86748i −0.247029 + 0.169928i
519519 16.9328i 0.743268i
520520 0 0
521521 35.5082i 1.55564i −0.628487 0.777820i 0.716325π-0.716325\pi
0.628487 0.777820i 0.283675π-0.283675\pi
522522 −12.2054 17.7434i −0.534215 0.776606i
523523 −0.677766 + 0.677766i −0.0296366 + 0.0296366i −0.721770 0.692133i 0.756671π-0.756671\pi
0.692133 + 0.721770i 0.256671π0.256671\pi
524524 −13.3407 + 5.95276i −0.582791 + 0.260048i
525525 0 0
526526 12.8972 + 2.38489i 0.562345 + 0.103986i
527527 15.0572i 0.655904i
528528 16.3977 18.2716i 0.713618 0.795170i
529529 −1.79485 −0.0780371
530530 0 0
531531 7.89332 7.89332i 0.342541 0.342541i
532532 9.23874 4.12243i 0.400550 0.178730i
533533 14.2142 14.2142i 0.615686 0.615686i
534534 10.2690 7.06386i 0.444382 0.305683i
535535 0 0
536536 −7.73667 32.0519i −0.334173 1.38443i
537537 5.45007 0.235188
538538 22.1124 15.2108i 0.953334 0.655784i
539539 2.53704 + 2.53704i 0.109278 + 0.109278i
540540 0 0
541541 5.37099 5.37099i 0.230917 0.230917i −0.582158 0.813075i 0.697792π-0.697792\pi
0.813075 + 0.582158i 0.197792π0.197792\pi
542542 31.4283 + 5.81157i 1.34996 + 0.249628i
543543 55.8181i 2.39539i
544544 32.7044 25.2016i 1.40219 1.08051i
545545 0 0
546546 −7.62693 + 41.2456i −0.326403 + 1.76515i
547547 −8.86782 8.86782i −0.379161 0.379161i 0.491639 0.870799i 0.336398π-0.336398\pi
−0.870799 + 0.491639i 0.836398π0.836398\pi
548548 −35.3767 13.5466i −1.51122 0.578682i
549549 5.95760 + 5.95760i 0.254264 + 0.254264i
550550 0 0
551551 10.4975i 0.447209i
552552 −7.19034 29.7885i −0.306041 1.26788i
553553 0.329585 0.0140154
554554 26.6966 18.3641i 1.13423 0.780218i
555555 0 0
556556 −3.21625 7.20791i −0.136399 0.305684i
557557 22.8089 + 22.8089i 0.966446 + 0.966446i 0.999455 0.0330091i 0.0105090π-0.0105090\pi
−0.0330091 + 0.999455i 0.510509π0.510509\pi
558558 −1.34510 + 7.27417i −0.0569428 + 0.307940i
559559 18.6666 0.789513
560560 0 0
561561 −44.7973 −1.89135
562562 2.27525 12.3043i 0.0959755 0.519024i
563563 20.9711 + 20.9711i 0.883826 + 0.883826i 0.993921 0.110095i 0.0351156π-0.0351156\pi
−0.110095 + 0.993921i 0.535116π0.535116\pi
564564 50.3244 22.4553i 2.11904 0.945538i
565565 0 0
566566 33.4603 23.0168i 1.40644 0.967469i
567567 29.4543 1.23696
568568 4.80719 7.86630i 0.201705 0.330063i
569569 8.05295i 0.337597i 0.985651 + 0.168799i 0.0539888π0.0539888\pi
−0.985651 + 0.168799i 0.946011π0.946011\pi
570570 0 0
571571 −22.5040 22.5040i −0.941762 0.941762i 0.0566333 0.998395i 0.481963π-0.481963\pi
−0.998395 + 0.0566333i 0.981963π0.981963\pi
572572 8.12708 21.2237i 0.339810 0.887409i
573573 −9.74599 9.74599i −0.407144 0.407144i
574574 −3.43436 + 18.5726i −0.143347 + 0.775206i
575575 0 0
576576 −18.0509 + 9.25334i −0.752119 + 0.385556i
577577 15.9819i 0.665334i −0.943044 0.332667i 0.892051π-0.892051\pi
0.943044 0.332667i 0.107949π-0.107949\pi
578578 −50.4410 9.32730i −2.09807 0.387965i
579579 −0.0401200 + 0.0401200i −0.00166733 + 0.00166733i
580580 0 0
581581 28.2692 + 28.2692i 1.17280 + 1.17280i
582582 38.3388 26.3727i 1.58919 1.09318i
583583 −10.0734 −0.417199
584584 −30.6212 18.7129i −1.26711 0.774347i
585585 0 0
586586 11.8136 8.12638i 0.488015 0.335698i
587587 −5.25752 + 5.25752i −0.217001 + 0.217001i −0.807233 0.590232i 0.799036π-0.799036\pi
0.590232 + 0.807233i 0.299036π0.299036\pi
588588 −2.63719 5.91018i −0.108756 0.243732i
589589 2.54971 2.54971i 0.105059 0.105059i
590590 0 0
591591 −49.6057 −2.04050
592592 −6.65965 + 0.359964i −0.273710 + 0.0147944i
593593 3.96571i 0.162852i 0.996679 + 0.0814260i 0.0259474π0.0259474\pi
−0.996679 + 0.0814260i 0.974053π0.974053\pi
594594 −3.96418 0.733038i −0.162652 0.0300769i
595595 0 0
596596 1.84835 + 4.14233i 0.0757115 + 0.169676i
597597 −22.7132 + 22.7132i −0.929589 + 0.929589i
598598 −16.0769 23.3716i −0.657435 0.955734i
599599 8.31600i 0.339783i −0.985463 0.169891i 0.945658π-0.945658\pi
0.985463 0.169891i 0.0543417π-0.0543417\pi
600600 0 0
601601 46.0550i 1.87862i −0.343068 0.939310i 0.611466π-0.611466\pi
0.343068 0.939310i 0.388534π-0.388534\pi
602602 −14.4502 + 9.94004i −0.588944 + 0.405126i
603603 20.9009 20.9009i 0.851149 0.851149i
604604 −1.81486 + 4.73948i −0.0738456 + 0.192847i
605605 0 0
606606 3.01374 16.2980i 0.122425 0.662060i
607607 5.05760i 0.205282i 0.994718 + 0.102641i 0.0327292π0.0327292\pi
−0.994718 + 0.102641i 0.967271π0.967271\pi
608608 9.80549 + 1.27048i 0.397665 + 0.0515249i
609609 40.8940 1.65711
610610 0 0
611611 36.0713 36.0713i 1.45929 1.45929i
612612 34.5652 + 13.2359i 1.39722 + 0.535028i
613613 −31.2000 + 31.2000i −1.26016 + 1.26016i −0.309141 + 0.951016i 0.600042π0.600042\pi
−0.951016 + 0.309141i 0.899958π0.899958\pi
614614 20.8911 + 30.3701i 0.843096 + 1.22564i
615615 0 0
616616 5.01041 + 20.7574i 0.201875 + 0.836339i
617617 30.7412 1.23759 0.618796 0.785551i 0.287621π-0.287621\pi
0.618796 + 0.785551i 0.287621π0.287621\pi
618618 0.283269 + 0.411798i 0.0113948 + 0.0165649i
619619 16.8766 + 16.8766i 0.678329 + 0.678329i 0.959622 0.281293i 0.0907632π-0.0907632\pi
−0.281293 + 0.959622i 0.590763π0.590763\pi
620620 0 0
621621 −3.55813 + 3.55813i −0.142783 + 0.142783i
622622 −1.82309 + 9.85908i −0.0730994 + 0.395313i
623623 10.8408i 0.434328i
624624 −27.3804 + 30.5095i −1.09609 + 1.22136i
625625 0 0
626626 −30.6603 5.66956i −1.22543 0.226601i
627627 −7.58574 7.58574i −0.302945 0.302945i
628628 −11.8026 26.4506i −0.470974 1.05550i
629629 8.60515 + 8.60515i 0.343110 + 0.343110i
630630 0 0
631631 30.7318i 1.22342i 0.791084 + 0.611708i 0.209517π0.209517\pi
−0.791084 + 0.611708i 0.790483π0.790483\pi
632632 0.274855 + 0.167967i 0.0109331 + 0.00668136i
633633 8.15539 0.324147
634634 7.02389 + 10.2109i 0.278954 + 0.405525i
635635 0 0
636636 16.9689 + 6.49779i 0.672860 + 0.257654i
637637 −4.23628 4.23628i −0.167848 0.167848i
638638 −21.7878 4.02890i −0.862588 0.159506i
639639 8.26430 0.326931
640640 0 0
641641 22.1658 0.875496 0.437748 0.899098i 0.355776π-0.355776\pi
0.437748 + 0.899098i 0.355776π0.355776\pi
642642 12.7274 + 2.35349i 0.502310 + 0.0928848i
643643 0.975773 + 0.975773i 0.0384807 + 0.0384807i 0.726085 0.687605i 0.241338π-0.241338\pi
−0.687605 + 0.726085i 0.741338π0.741338\pi
644644 24.8909 + 9.53133i 0.980839 + 0.375587i
645645 0 0
646646 −10.2249 14.8643i −0.402294 0.584828i
647647 −23.2610 −0.914484 −0.457242 0.889342i 0.651163π-0.651163\pi
−0.457242 + 0.889342i 0.651163π0.651163\pi
648648 24.5632 + 15.0108i 0.964932 + 0.589681i
649649 11.4848i 0.450819i
650650 0 0
651651 −9.93263 9.93263i −0.389290 0.389290i
652652 9.25038 + 20.7310i 0.362273 + 0.811887i
653653 −23.9372 23.9372i −0.936735 0.936735i 0.0613792 0.998115i 0.480450π-0.480450\pi
−0.998115 + 0.0613792i 0.980450π0.980450\pi
654654 −31.9631 5.91046i −1.24985 0.231117i
655655 0 0
656656 −12.3292 + 13.7382i −0.481376 + 0.536387i
657657 32.1704i 1.25509i
658658 −8.71535 + 47.1316i −0.339760 + 1.83738i
659659 14.1064 14.1064i 0.549508 0.549508i −0.376790 0.926299i 0.622972π-0.622972\pi
0.926299 + 0.376790i 0.122972π0.122972\pi
660660 0 0
661661 −3.04121 3.04121i −0.118289 0.118289i 0.645484 0.763774i 0.276656π-0.276656\pi
−0.763774 + 0.645484i 0.776656π0.776656\pi
662662 −21.1026 30.6775i −0.820175 1.19232i
663663 74.8014 2.90505
664664 9.16800 + 37.9817i 0.355787 + 1.47398i
665665 0 0
666666 −3.38844 4.92588i −0.131299 0.190874i
667667 −19.5561 + 19.5561i −0.757215 + 0.757215i
668668 −12.7495 4.88207i −0.493291 0.188893i
669669 23.2052 23.2052i 0.897166 0.897166i
670670 0 0
671671 8.66835 0.334638
672672 4.94928 38.1981i 0.190923 1.47353i
673673 25.3628i 0.977662i −0.872378 0.488831i 0.837423π-0.837423\pi
0.872378 0.488831i 0.162577π-0.162577\pi
674674 3.66637 19.8273i 0.141223 0.763719i
675675 0 0
676676 −4.27271 + 11.1581i −0.164335 + 0.429159i
677677 9.36526 9.36526i 0.359936 0.359936i −0.503853 0.863789i 0.668085π-0.668085\pi
0.863789 + 0.503853i 0.168085π0.168085\pi
678678 −9.58126 + 6.59080i −0.367966 + 0.253118i
679679 40.4737i 1.55324i
680680 0 0
681681 14.7695i 0.565967i
682682 4.31342 + 6.27056i 0.165169 + 0.240112i
683683 −4.20530 + 4.20530i −0.160911 + 0.160911i −0.782970 0.622059i 0.786296π-0.786296\pi
0.622059 + 0.782970i 0.286296π0.286296\pi
684684 3.61180 + 8.09438i 0.138101 + 0.309496i
685685 0 0
686686 −22.6365 4.18584i −0.864267 0.159816i
687687 17.8035i 0.679245i
688688 −17.1163 + 0.925163i −0.652554 + 0.0352715i
689689 16.8204 0.640804
690690 0 0
691691 5.79295 5.79295i 0.220374 0.220374i −0.588282 0.808656i 0.700195π-0.700195\pi
0.808656 + 0.588282i 0.200195π0.200195\pi
692692 5.86530 + 13.1447i 0.222965 + 0.499686i
693693 −13.5358 + 13.5358i −0.514181 + 0.514181i
694694 −38.7881 + 26.6817i −1.47238 + 1.01282i
695695 0 0
696696 34.1032 + 20.8408i 1.29268 + 0.789969i
697697 33.6826 1.27582
698698 2.58179 1.77598i 0.0977223 0.0672217i
699699 −19.8592 19.8592i −0.751142 0.751142i
700700 0 0
701701 −0.258991 + 0.258991i −0.00978196 + 0.00978196i −0.711981 0.702199i 0.752202π-0.752202\pi
0.702199 + 0.711981i 0.252202π0.252202\pi
702702 6.61929 + 1.22401i 0.249829 + 0.0461972i
703703 2.91430i 0.109915i
704704 −6.40023 + 19.8639i −0.241218 + 0.748649i
705705 0 0
706706 −2.42924 + 13.1370i −0.0914257 + 0.494419i
707707 10.1936 + 10.1936i 0.383368 + 0.383368i
708708 −7.40821 + 19.3464i −0.278418 + 0.727083i
709709 0.751674 + 0.751674i 0.0282297 + 0.0282297i 0.721081 0.692851i 0.243646π-0.243646\pi
−0.692851 + 0.721081i 0.743646π0.743646\pi
710710 0 0
711711 0.288761i 0.0108294i
712712 −5.52481 + 9.04060i −0.207051 + 0.338811i
713713 9.49986 0.355773
714714 −57.9052 + 39.8321i −2.16705 + 1.49068i
715715 0 0
716716 −4.23081 + 1.88783i −0.158113 + 0.0705516i
717717 −27.9029 27.9029i −1.04205 1.04205i
718718 −4.64034 + 25.0944i −0.173176 + 0.936515i
719719 −39.6557 −1.47891 −0.739455 0.673206i 0.764917π-0.764917\pi
−0.739455 + 0.673206i 0.764917π0.764917\pi
720720 0 0
721721 −0.434730 −0.0161902
722722 −4.10025 + 22.1736i −0.152595 + 0.825218i
723723 36.6495 + 36.6495i 1.36301 + 1.36301i
724724 −19.3347 43.3308i −0.718567 1.61037i
725725 0 0
726726 −11.4993 + 7.91016i −0.426778 + 0.293574i
727727 22.2952 0.826881 0.413441 0.910531i 0.364327π-0.364327\pi
0.413441 + 0.910531i 0.364327π0.364327\pi
728728 −8.36625 34.6602i −0.310074 1.28459i
729729 18.0930i 0.670112i
730730 0 0
731731 22.1166 + 22.1166i 0.818011 + 0.818011i
732732 −14.6020 5.59145i −0.539705 0.206666i
733733 28.2309 + 28.2309i 1.04273 + 1.04273i 0.999045 + 0.0436851i 0.0139098π0.0139098\pi
0.0436851 + 0.999045i 0.486090π0.486090\pi
734734 7.49154 40.5134i 0.276518 1.49538i
735735 0 0
736736 15.9001 + 20.6337i 0.586086 + 0.760570i
737737 30.4109i 1.12020i
738738 −16.2721 3.00896i −0.598985 0.110761i
739739 5.45140 5.45140i 0.200533 0.200533i −0.599695 0.800228i 0.704712π-0.704712\pi
0.800228 + 0.599695i 0.204712π0.204712\pi
740740 0 0
741741 12.6665 + 12.6665i 0.465314 + 0.465314i
742742 −13.0210 + 8.95691i −0.478014 + 0.328819i
743743 −52.5667 −1.92849 −0.964243 0.265020i 0.914621π-0.914621\pi
−0.964243 + 0.265020i 0.914621π0.914621\pi
744744 −3.22126 13.3452i −0.118097 0.489259i
745745 0 0
746746 −5.52994 + 3.80396i −0.202466 + 0.139273i
747747 −24.7676 + 24.7676i −0.906200 + 0.906200i
748748 34.7755 15.5172i 1.27152 0.567365i
749749 −7.96035 + 7.96035i −0.290865 + 0.290865i
750750 0 0
751751 31.0189 1.13190 0.565948 0.824441i 0.308510π-0.308510\pi
0.565948 + 0.824441i 0.308510π0.308510\pi
752752 −31.2878 + 34.8634i −1.14095 + 1.27134i
753753 22.0910i 0.805040i
754754 36.3807 + 6.72735i 1.32491 + 0.244996i
755755 0 0
756756 −5.77590 + 2.57727i −0.210068 + 0.0937345i
757757 −2.47389 + 2.47389i −0.0899152 + 0.0899152i −0.750634 0.660719i 0.770252π-0.770252\pi
0.660719 + 0.750634i 0.270252π0.270252\pi
758758 −13.2059 19.1979i −0.479662 0.697300i
759759 28.2634i 1.02590i
760760 0 0
761761 2.48375i 0.0900358i −0.998986 0.0450179i 0.985666π-0.985666\pi
0.998986 0.0450179i 0.0143345π-0.0143345\pi
762762 −17.1433 + 11.7926i −0.621037 + 0.427202i
763763 19.9913 19.9913i 0.723733 0.723733i
764764 10.9415 + 4.18978i 0.395851 + 0.151581i
765765 0 0
766766 5.60701 30.3221i 0.202590 1.09558i
767767 19.1771i 0.692444i
768768 23.5944 29.3327i 0.851388 1.05845i
769769 −43.4690 −1.56753 −0.783767 0.621055i 0.786704π-0.786704\pi
−0.783767 + 0.621055i 0.786704π0.786704\pi
770770 0 0
771771 12.0752 12.0752i 0.434879 0.434879i
772772 0.0172475 0.0450416i 0.000620752 0.00162108i
773773 −0.297026 + 0.297026i −0.0106833 + 0.0106833i −0.712428 0.701745i 0.752405π-0.752405\pi
0.701745 + 0.712428i 0.252405π0.252405\pi
774774 −8.70881 12.6603i −0.313032 0.455064i
775775 0 0
776776 −20.6267 + 33.7527i −0.740454 + 1.21165i
777777 11.3529 0.407283
778778 13.4771 + 19.5920i 0.483176 + 0.702409i
779779 5.70363 + 5.70363i 0.204354 + 0.204354i
780780 0 0
781781 6.01231 6.01231i 0.215137 0.215137i
782782 8.64283 46.7394i 0.309067 1.67140i
783783 6.56286i 0.234537i
784784 4.09442 + 3.67450i 0.146229 + 0.131232i
785785 0 0
786786 23.8985 + 4.41920i 0.852433 + 0.157628i
787787 23.6931 + 23.6931i 0.844567 + 0.844567i 0.989449 0.144882i 0.0462802π-0.0462802\pi
−0.144882 + 0.989449i 0.546280π0.546280\pi
788788 38.5081 17.1827i 1.37179 0.612110i
789789 −15.4293 15.4293i −0.549299 0.549299i
790790 0 0
791791 10.1148i 0.359641i
792792 −18.1863 + 4.38979i −0.646221 + 0.155984i
793793 −14.4742 −0.513993
794794 10.4723 + 15.2240i 0.371650 + 0.540279i
795795 0 0
796796 9.76435 25.4994i 0.346088 0.903804i
797797 −38.2292 38.2292i −1.35415 1.35415i −0.880963 0.473186i 0.843104π-0.843104\pi
−0.473186 0.880963i 0.656896π-0.656896\pi
798798 −16.5503 3.06040i −0.585874 0.108337i
799799 85.4762 3.02393
800800 0 0
801801 −9.49801 −0.335596
802802 −20.1287 3.72210i −0.710768 0.131432i
803803 −23.4041 23.4041i −0.825913 0.825913i
804804 −19.6163 + 51.2277i −0.691814 + 1.80666i
805805 0 0
806806 −7.20243 10.4704i −0.253695 0.368804i
807807 −44.6509 −1.57179
808808 3.30588 + 13.6958i 0.116300 + 0.481816i
809809 53.8310i 1.89260i −0.323296 0.946298i 0.604791π-0.604791\pi
0.323296 0.946298i 0.395209π-0.395209\pi
810810 0 0
811811 27.0549 + 27.0549i 0.950025 + 0.950025i 0.998809 0.0487847i 0.0155348π-0.0155348\pi
−0.0487847 + 0.998809i 0.515535π0.515535\pi
812812 −31.7454 + 14.1651i −1.11404 + 0.497098i
813813 −37.5986 37.5986i −1.31864 1.31864i
814814 −6.04870 1.11850i −0.212007 0.0392033i
815815 0 0
816816 −68.5892 + 3.70735i −2.40110 + 0.129783i
817817 7.49020i 0.262049i
818818 −2.45351 + 13.2683i −0.0857851 + 0.463916i
819819 22.6017 22.6017i 0.789766 0.789766i
820820 0 0
821821 −24.2170 24.2170i −0.845180 0.845180i 0.144347 0.989527i 0.453892π-0.453892\pi
−0.989527 + 0.144347i 0.953892π0.953892\pi
822822 35.7175 + 51.9238i 1.24579 + 1.81105i
823823 41.3013 1.43967 0.719836 0.694144i 0.244217π-0.244217\pi
0.719836 + 0.694144i 0.244217π0.244217\pi
824824 −0.362539 0.221552i −0.0126296 0.00771812i
825825 0 0
826826 −10.2119 14.8453i −0.355317 0.516535i
827827 15.7264 15.7264i 0.546862 0.546862i −0.378670 0.925532i 0.623618π-0.623618\pi
0.925532 + 0.378670i 0.123618π0.123618\pi
828828 −8.35072 + 21.8078i −0.290208 + 0.757873i
829829 20.7323 20.7323i 0.720061 0.720061i −0.248556 0.968618i 0.579956π-0.579956\pi
0.968618 + 0.248556i 0.0799560π0.0799560\pi
830830 0 0
831831 −53.9075 −1.87003
832832 10.6869 33.1682i 0.370503 1.14990i
833833 10.0385i 0.347813i
834834 −2.38767 + 12.9123i −0.0826784 + 0.447115i
835835 0 0
836836 8.51629 + 3.26109i 0.294542 + 0.112787i
837837 −1.59404 + 1.59404i −0.0550980 + 0.0550980i
838838 −1.38030 + 0.949485i −0.0476816 + 0.0327994i
839839 43.6919i 1.50841i −0.656638 0.754206i 0.728022π-0.728022\pi
0.656638 0.754206i 0.271978π-0.271978\pi
840840 0 0
841841 7.07060i 0.243814i
842842 20.3664 + 29.6073i 0.701872 + 1.02033i
843843 −14.7200 + 14.7200i −0.506983 + 0.506983i
844844 −6.33090 + 2.82492i −0.217919 + 0.0972377i
845845 0 0
846846 −41.2936 7.63582i −1.41970 0.262525i
847847 12.1396i 0.417122i
848848 −15.4234 + 0.833659i −0.529643 + 0.0286280i
849849 −67.5654 −2.31884
850850 0 0
851851 −5.42913 + 5.42913i −0.186108 + 0.186108i
852852 −14.0060 + 6.24965i −0.479839 + 0.214109i
853853 35.0610 35.0610i 1.20046 1.20046i 0.226439 0.974025i 0.427292π-0.427292\pi
0.974025 0.226439i 0.0727084π-0.0727084\pi
854854 11.2047 7.70756i 0.383418 0.263747i
855855 0 0
856856 −10.6953 + 2.58162i −0.365558 + 0.0882381i
857857 −45.3397 −1.54878 −0.774388 0.632711i 0.781942π-0.781942\pi
−0.774388 + 0.632711i 0.781942π0.781942\pi
858858 −31.1509 + 21.4282i −1.06347 + 0.731547i
859859 −32.1229 32.1229i −1.09602 1.09602i −0.994871 0.101147i 0.967749π-0.967749\pi
−0.101147 0.994871i 0.532251π-0.532251\pi
860860 0 0
861861 22.2190 22.2190i 0.757221 0.757221i
862862 −5.36054 0.991245i −0.182581 0.0337619i
863863 36.9142i 1.25657i 0.777981 + 0.628287i 0.216244π0.216244\pi
−0.777981 + 0.628287i 0.783756π0.783756\pi
864864 −6.13022 0.794285i −0.208554 0.0270221i
865865 0 0
866866 6.57406 35.5517i 0.223396 1.20810i
867867 60.3441 + 60.3441i 2.04939 + 2.04939i
868868 11.1511 + 4.27002i 0.378492 + 0.144934i
869869 0.210075 + 0.210075i 0.00712630 + 0.00712630i
870870 0 0
871871 50.7793i 1.72059i
872872 26.8597 6.48338i 0.909585 0.219555i
873873 −35.4604 −1.20015
874874 9.37813 6.45107i 0.317220 0.218211i
875875 0 0
876876 24.3280 + 54.5213i 0.821967 + 1.84210i
877877 15.7178 + 15.7178i 0.530753 + 0.530753i 0.920796 0.390044i 0.127540π-0.127540\pi
−0.390044 + 0.920796i 0.627540π0.627540\pi
878878 −7.74821 + 41.9014i −0.261490 + 1.41410i
879879 −23.8548 −0.804603
880880 0 0
881881 1.16748 0.0393335 0.0196667 0.999807i 0.493739π-0.493739\pi
0.0196667 + 0.999807i 0.493739π0.493739\pi
882882 −0.896765 + 4.84960i −0.0301956 + 0.163294i
883883 32.2410 + 32.2410i 1.08500 + 1.08500i 0.996035 + 0.0889621i 0.0283550π0.0283550\pi
0.0889621 + 0.996035i 0.471645π0.471645\pi
884884 −58.0672 + 25.9102i −1.95301 + 0.871455i
885885 0 0
886886 −33.2235 + 22.8539i −1.11616 + 0.767792i
887887 −42.7282 −1.43467 −0.717336 0.696728i 0.754639π-0.754639\pi
−0.717336 + 0.696728i 0.754639π0.754639\pi
888888 9.46766 + 5.78579i 0.317714 + 0.194159i
889889 18.0980i 0.606987i
890890 0 0
891891 18.7739 + 18.7739i 0.628949 + 0.628949i
892892 −9.97588 + 26.0518i −0.334017 + 0.872280i
893893 14.4741 + 14.4741i 0.484356 + 0.484356i
894894 1.37218 7.42058i 0.0458925 0.248181i
895895 0 0
896896 9.38928 + 31.3670i 0.313674 + 1.04790i
897897 47.1935i 1.57574i
898898 50.8732 + 9.40724i 1.69766 + 0.313924i
899899 −8.76109 + 8.76109i −0.292199 + 0.292199i
900900 0 0
901901 19.9291 + 19.9291i 0.663935 + 0.663935i
902902 −14.0270 + 9.64899i −0.467050 + 0.321276i
903903 29.1788 0.971008
904904 5.15482 8.43516i 0.171447 0.280549i
905905 0 0
906906 6.95632 4.78514i 0.231108 0.158976i
907907 1.23335 1.23335i 0.0409528 0.0409528i −0.686334 0.727287i 0.740781π-0.740781\pi
0.727287 + 0.686334i 0.240781π0.240781\pi
908908 −5.11594 11.4653i −0.169779 0.380489i
909909 −8.93093 + 8.93093i −0.296220 + 0.296220i
910910 0 0
911911 23.9284 0.792785 0.396392 0.918081i 0.370262π-0.370262\pi
0.396392 + 0.918081i 0.370262π0.370262\pi
912912 −12.2423 10.9867i −0.405383 0.363807i
913913 36.0371i 1.19265i
914914 −23.2710 4.30316i −0.769735 0.142336i
915915 0 0
916916 6.16689 + 13.8206i 0.203760 + 0.456644i
917917 −14.9473 + 14.9473i −0.493605 + 0.493605i
918918 6.39245 + 9.29291i 0.210982 + 0.306712i
919919 45.3844i 1.49709i 0.663082 + 0.748546i 0.269248π0.269248\pi
−0.663082 + 0.748546i 0.730752π0.730752\pi
920920 0 0
921921 61.3253i 2.02074i
922922 19.5060 13.4179i 0.642395 0.441893i
923923 −10.0392 + 10.0392i −0.330444 + 0.330444i
924924 12.7039 33.1760i 0.417927 1.09141i
925925 0 0
926926 8.29851 44.8774i 0.272706 1.47476i
927927 0.380882i 0.0125098i
928928 −33.6927 4.36553i −1.10602 0.143305i
929929 6.51036 0.213598 0.106799 0.994281i 0.465940π-0.465940\pi
0.106799 + 0.994281i 0.465940π0.465940\pi
930930 0 0
931931 1.69986 1.69986i 0.0557107 0.0557107i
932932 22.2953 + 8.53741i 0.730307 + 0.279652i
933933 11.7947 11.7947i 0.386142 0.386142i
934934 −1.38926 2.01961i −0.0454579 0.0660837i
935935 0 0
936936 30.3670 7.32996i 0.992575 0.239587i
937937 −40.2986 −1.31650 −0.658248 0.752801i 0.728702π-0.728702\pi
−0.658248 + 0.752801i 0.728702π0.728702\pi
938938 −27.0402 39.3092i −0.882894 1.28349i
939939 36.6799 + 36.6799i 1.19700 + 1.19700i
940940 0 0
941941 1.10649 1.10649i 0.0360705 0.0360705i −0.688841 0.724912i 0.741880π-0.741880\pi
0.724912 + 0.688841i 0.241880π0.241880\pi
942942 −8.76198 + 47.3837i −0.285481 + 1.54385i
943943 21.2509i 0.692025i
944944 −0.950465 17.5844i −0.0309350 0.572325i
945945 0 0
946946 −15.5461 2.87471i −0.505447 0.0934649i
947947 8.83833 + 8.83833i 0.287207 + 0.287207i 0.835975 0.548768i 0.184903π-0.184903\pi
−0.548768 + 0.835975i 0.684903π0.684903\pi
948948 −0.218368 0.489382i −0.00709225 0.0158944i
949949 39.0796 + 39.0796i 1.26858 + 1.26858i
950950 0 0
951951 20.6185i 0.668600i
952952 31.1536 50.9786i 1.00969 1.65223i
953953 −14.9610 −0.484636 −0.242318 0.970197i 0.577908π-0.577908\pi
−0.242318 + 0.970197i 0.577908π0.577908\pi
954954 −7.84746 11.4081i −0.254071 0.369351i
955955 0 0
956956 31.3258 + 11.9954i 1.01315 + 0.387959i
957957 26.0654 + 26.0654i 0.842576 + 0.842576i
958958 −40.1059 7.41620i −1.29576 0.239606i
959959 −54.8152 −1.77008
960960 0 0
961961 −26.7441 −0.862712
962962 10.1000 + 1.86764i 0.325636 + 0.0602150i
963963 −6.97433 6.97433i −0.224745 0.224745i
964964 −41.1453 15.7555i −1.32520 0.507452i
965965 0 0
966966 −25.1307 36.5333i −0.808568 1.17544i
967967 −3.95287 −0.127116 −0.0635578 0.997978i 0.520245π-0.520245\pi
−0.0635578 + 0.997978i 0.520245π0.520245\pi
968968 6.18672 10.1237i 0.198849 0.325389i
969969 30.0150i 0.964221i
970970 0 0
971971 −29.0538 29.0538i −0.932380 0.932380i 0.0654740 0.997854i 0.479144π-0.479144\pi
−0.997854 + 0.0654740i 0.979144π0.979144\pi
972972 −16.8434 37.7475i −0.540251 1.21075i
973973 −8.07597 8.07597i −0.258904 0.258904i
974974 44.7323 + 8.27169i 1.43332 + 0.265042i
975975 0 0
976976 13.2721 0.717377i 0.424830 0.0229627i
977977 25.8962i 0.828494i −0.910164 0.414247i 0.864045π-0.864045\pi
0.910164 0.414247i 0.135955π-0.135955\pi
978978 6.86729 37.1375i 0.219592 1.18753i
979979 −6.90984 + 6.90984i −0.220839 + 0.220839i
980980 0 0
981981 17.5151 + 17.5151i 0.559213 + 0.559213i
982982 −6.16172 8.95749i −0.196628 0.285845i
983983 −22.0151 −0.702173 −0.351087 0.936343i 0.614188π-0.614188\pi
−0.351087 + 0.936343i 0.614188π0.614188\pi
984984 29.8528 7.20585i 0.951673 0.229714i
985985 0 0
986986 35.1340 + 51.0754i 1.11889 + 1.62657i
987987 56.3850 56.3850i 1.79476 1.79476i
988988 −14.2203 5.44529i −0.452407 0.173238i
989989 −13.9537 + 13.9537i −0.443702 + 0.443702i
990990 0 0
991991 −54.3207 −1.72556 −0.862778 0.505583i 0.831277π-0.831277\pi
−0.862778 + 0.505583i 0.831277π0.831277\pi
992992 7.12321 + 9.24388i 0.226162 + 0.293493i
993993 61.9461i 1.96580i
994994 2.42562 13.1174i 0.0769359 0.416060i
995995 0 0
996996 23.2454 60.7051i 0.736560 1.92351i
997997 8.14405 8.14405i 0.257925 0.257925i −0.566285 0.824210i 0.691620π-0.691620\pi
0.824210 + 0.566285i 0.191620π0.191620\pi
998998 28.2236 19.4146i 0.893402 0.614557i
999999 1.82197i 0.0576446i
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 400.2.q.h.149.7 16
4.3 odd 2 1600.2.q.g.49.7 16
5.2 odd 4 80.2.l.a.21.4 16
5.3 odd 4 400.2.l.h.101.5 16
5.4 even 2 400.2.q.g.149.2 16
15.2 even 4 720.2.t.c.181.5 16
16.3 odd 4 1600.2.q.h.849.2 16
16.13 even 4 400.2.q.g.349.2 16
20.3 even 4 1600.2.l.i.1201.2 16
20.7 even 4 320.2.l.a.241.7 16
20.19 odd 2 1600.2.q.h.49.2 16
40.27 even 4 640.2.l.a.481.2 16
40.37 odd 4 640.2.l.b.481.7 16
60.47 odd 4 2880.2.t.c.2161.6 16
80.3 even 4 1600.2.l.i.401.2 16
80.13 odd 4 400.2.l.h.301.5 16
80.19 odd 4 1600.2.q.g.849.7 16
80.27 even 4 640.2.l.a.161.2 16
80.29 even 4 inner 400.2.q.h.349.7 16
80.37 odd 4 640.2.l.b.161.7 16
80.67 even 4 320.2.l.a.81.7 16
80.77 odd 4 80.2.l.a.61.4 yes 16
160.67 even 8 5120.2.a.t.1.8 8
160.77 odd 8 5120.2.a.s.1.8 8
160.147 even 8 5120.2.a.u.1.1 8
160.157 odd 8 5120.2.a.v.1.1 8
240.77 even 4 720.2.t.c.541.5 16
240.227 odd 4 2880.2.t.c.721.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
80.2.l.a.21.4 16 5.2 odd 4
80.2.l.a.61.4 yes 16 80.77 odd 4
320.2.l.a.81.7 16 80.67 even 4
320.2.l.a.241.7 16 20.7 even 4
400.2.l.h.101.5 16 5.3 odd 4
400.2.l.h.301.5 16 80.13 odd 4
400.2.q.g.149.2 16 5.4 even 2
400.2.q.g.349.2 16 16.13 even 4
400.2.q.h.149.7 16 1.1 even 1 trivial
400.2.q.h.349.7 16 80.29 even 4 inner
640.2.l.a.161.2 16 80.27 even 4
640.2.l.a.481.2 16 40.27 even 4
640.2.l.b.161.7 16 80.37 odd 4
640.2.l.b.481.7 16 40.37 odd 4
720.2.t.c.181.5 16 15.2 even 4
720.2.t.c.541.5 16 240.77 even 4
1600.2.l.i.401.2 16 80.3 even 4
1600.2.l.i.1201.2 16 20.3 even 4
1600.2.q.g.49.7 16 4.3 odd 2
1600.2.q.g.849.7 16 80.19 odd 4
1600.2.q.h.49.2 16 20.19 odd 2
1600.2.q.h.849.2 16 16.3 odd 4
2880.2.t.c.721.7 16 240.227 odd 4
2880.2.t.c.2161.6 16 60.47 odd 4
5120.2.a.s.1.8 8 160.77 odd 8
5120.2.a.t.1.8 8 160.67 even 8
5120.2.a.u.1.1 8 160.147 even 8
5120.2.a.v.1.1 8 160.157 odd 8