Properties

Label 702.2.bc.a.305.10
Level 702702
Weight 22
Character 702.305
Analytic conductor 5.6055.605
Analytic rank 00
Dimension 5656
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [702,2,Mod(305,702)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(702, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("702.305");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 702=23313 702 = 2 \cdot 3^{3} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 702.bc (of order 1212, degree 44, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.605498221895.60549822189
Analytic rank: 00
Dimension: 5656
Relative dimension: 1414 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: no (minimal twist has level 234)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 305.10
Character χ\chi == 702.305
Dual form 702.2.bc.a.557.10

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.2588190.965926i)q2+(0.8660250.500000i)q4+(0.361873+1.35053i)q5+(0.7152840.715284i)q7+(0.707107+0.707107i)q8+(1.21085+0.699086i)q10+(5.617181.50512i)q11+(0.218517+3.59892i)q13+(0.876041+0.505782i)q14+(0.500000+0.866025i)q16+(1.67305+2.89781i)q17+(7.076051.89602i)q19+(0.9886570.988657i)q20+(2.90767+5.03622i)q220.580436q23+(2.63715+1.52256i)q25+(3.41974+1.14254i)q26+(0.261812+0.977097i)q28+(0.8922490.515140i)q29+(8.527142.28484i)q31+(0.9659260.258819i)q32+(3.232090.866036i)q34+(1.224860.707171i)q35+(7.82443+2.09655i)q37+(3.66283+6.34422i)q38+(0.6990861.21085i)q40+(1.157311.15731i)q41+8.38054iq43+(4.11206+4.11206i)q44+(0.150228+0.560658i)q46+(0.388741+1.45080i)q475.97674iq49+(2.153222.15322i)q50+(1.988703.00750i)q52+2.77082iq53+(4.065427.04151i)q55+1.01156q56+(0.2666560.995175i)q58+(3.10182+11.5761i)q59+2.82816q61+(4.41397+7.64523i)q621.00000iq64+(4.781381.59747i)q65+(0.802042+0.802042i)q673.34611iq68+(0.3660581.36615i)q70+(2.7149510.1323i)q71+(0.788181+0.788181i)q73+8.10045iq74+(5.18003+5.18003i)q76+(2.94129+5.09447i)q77+(0.827245+1.43283i)q79+(1.35053+0.361873i)q80+(1.41741+0.818343i)q82+(15.72244.21280i)q83+(4.51902+1.21087i)q85+(8.09498+2.16904i)q86+(5.036222.90767i)q88+(0.7837972.92517i)q89+(2.730562.41795i)q91+(0.502672+0.290218i)q92+1.50198q94+(5.121278.87030i)q95+(8.704878.70487i)q97+(5.773081.54689i)q98+O(q100)q+(0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.361873 + 1.35053i) q^{5} +(-0.715284 - 0.715284i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.21085 + 0.699086i) q^{10} +(-5.61718 - 1.50512i) q^{11} +(-0.218517 + 3.59892i) q^{13} +(-0.876041 + 0.505782i) q^{14} +(0.500000 + 0.866025i) q^{16} +(1.67305 + 2.89781i) q^{17} +(-7.07605 - 1.89602i) q^{19} +(0.988657 - 0.988657i) q^{20} +(-2.90767 + 5.03622i) q^{22} -0.580436 q^{23} +(2.63715 + 1.52256i) q^{25} +(3.41974 + 1.14254i) q^{26} +(0.261812 + 0.977097i) q^{28} +(0.892249 - 0.515140i) q^{29} +(-8.52714 - 2.28484i) q^{31} +(0.965926 - 0.258819i) q^{32} +(3.23209 - 0.866036i) q^{34} +(1.22486 - 0.707171i) q^{35} +(-7.82443 + 2.09655i) q^{37} +(-3.66283 + 6.34422i) q^{38} +(-0.699086 - 1.21085i) q^{40} +(-1.15731 - 1.15731i) q^{41} +8.38054i q^{43} +(4.11206 + 4.11206i) q^{44} +(-0.150228 + 0.560658i) q^{46} +(0.388741 + 1.45080i) q^{47} -5.97674i q^{49} +(2.15322 - 2.15322i) q^{50} +(1.98870 - 3.00750i) q^{52} +2.77082i q^{53} +(4.06542 - 7.04151i) q^{55} +1.01156 q^{56} +(-0.266656 - 0.995175i) q^{58} +(3.10182 + 11.5761i) q^{59} +2.82816 q^{61} +(-4.41397 + 7.64523i) q^{62} -1.00000i q^{64} +(-4.78138 - 1.59747i) q^{65} +(-0.802042 + 0.802042i) q^{67} -3.34611i q^{68} +(-0.366058 - 1.36615i) q^{70} +(2.71495 - 10.1323i) q^{71} +(0.788181 + 0.788181i) q^{73} +8.10045i q^{74} +(5.18003 + 5.18003i) q^{76} +(2.94129 + 5.09447i) q^{77} +(-0.827245 + 1.43283i) q^{79} +(-1.35053 + 0.361873i) q^{80} +(-1.41741 + 0.818343i) q^{82} +(15.7224 - 4.21280i) q^{83} +(-4.51902 + 1.21087i) q^{85} +(8.09498 + 2.16904i) q^{86} +(5.03622 - 2.90767i) q^{88} +(-0.783797 - 2.92517i) q^{89} +(2.73056 - 2.41795i) q^{91} +(0.502672 + 0.290218i) q^{92} +1.50198 q^{94} +(5.12127 - 8.87030i) q^{95} +(8.70487 - 8.70487i) q^{97} +(-5.77308 - 1.54689i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 56q8q7+24q11+28q168q194q284q31+24q354q3736q38+48q41+36q47+24q50+8q52+36q65+28q67+24q71+28q73+48q98+O(q100) 56 q - 8 q^{7} + 24 q^{11} + 28 q^{16} - 8 q^{19} - 4 q^{28} - 4 q^{31} + 24 q^{35} - 4 q^{37} - 36 q^{38} + 48 q^{41} + 36 q^{47} + 24 q^{50} + 8 q^{52} + 36 q^{65} + 28 q^{67} + 24 q^{71} + 28 q^{73}+ \cdots - 48 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/702Z)×\left(\mathbb{Z}/702\mathbb{Z}\right)^\times.

nn 379379 677677
χ(n)\chi(n) e(512)e\left(\frac{5}{12}\right) e(16)e\left(\frac{1}{6}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.258819 0.965926i 0.183013 0.683013i
33 0 0
44 −0.866025 0.500000i −0.433013 0.250000i
55 −0.361873 + 1.35053i −0.161835 + 0.603975i 0.836588 + 0.547833i 0.184547π0.184547\pi
−0.998423 + 0.0561429i 0.982120π0.982120\pi
66 0 0
77 −0.715284 0.715284i −0.270352 0.270352i 0.558890 0.829242i 0.311227π-0.311227\pi
−0.829242 + 0.558890i 0.811227π0.811227\pi
88 −0.707107 + 0.707107i −0.250000 + 0.250000i
99 0 0
1010 1.21085 + 0.699086i 0.382905 + 0.221070i
1111 −5.61718 1.50512i −1.69364 0.453810i −0.722317 0.691562i 0.756923π-0.756923\pi
−0.971326 + 0.237752i 0.923589π0.923589\pi
1212 0 0
1313 −0.218517 + 3.59892i −0.0606058 + 0.998162i
1414 −0.876041 + 0.505782i −0.234132 + 0.135176i
1515 0 0
1616 0.500000 + 0.866025i 0.125000 + 0.216506i
1717 1.67305 + 2.89781i 0.405775 + 0.702823i 0.994411 0.105575i 0.0336683π-0.0336683\pi
−0.588636 + 0.808398i 0.700335π0.700335\pi
1818 0 0
1919 −7.07605 1.89602i −1.62336 0.434977i −0.671372 0.741120i 0.734295π-0.734295\pi
−0.951986 + 0.306143i 0.900961π0.900961\pi
2020 0.988657 0.988657i 0.221070 0.221070i
2121 0 0
2222 −2.90767 + 5.03622i −0.619916 + 1.07373i
2323 −0.580436 −0.121029 −0.0605146 0.998167i 0.519274π-0.519274\pi
−0.0605146 + 0.998167i 0.519274π0.519274\pi
2424 0 0
2525 2.63715 + 1.52256i 0.527430 + 0.304512i
2626 3.41974 + 1.14254i 0.670666 + 0.224071i
2727 0 0
2828 0.261812 + 0.977097i 0.0494779 + 0.184654i
2929 0.892249 0.515140i 0.165687 0.0956592i −0.414864 0.909884i 0.636171π-0.636171\pi
0.580550 + 0.814224i 0.302837π0.302837\pi
3030 0 0
3131 −8.52714 2.28484i −1.53152 0.410369i −0.608005 0.793933i 0.708030π-0.708030\pi
−0.923514 + 0.383564i 0.874697π0.874697\pi
3232 0.965926 0.258819i 0.170753 0.0457532i
3333 0 0
3434 3.23209 0.866036i 0.554299 0.148524i
3535 1.22486 0.707171i 0.207038 0.119534i
3636 0 0
3737 −7.82443 + 2.09655i −1.28633 + 0.344671i −0.836265 0.548326i 0.815265π-0.815265\pi
−0.450064 + 0.892996i 0.648599π0.648599\pi
3838 −3.66283 + 6.34422i −0.594190 + 1.02917i
3939 0 0
4040 −0.699086 1.21085i −0.110535 0.191453i
4141 −1.15731 1.15731i −0.180742 0.180742i 0.610937 0.791679i 0.290793π-0.290793\pi
−0.791679 + 0.610937i 0.790793π0.790793\pi
4242 0 0
4343 8.38054i 1.27802i 0.769198 + 0.639010i 0.220656π0.220656\pi
−0.769198 + 0.639010i 0.779344π0.779344\pi
4444 4.11206 + 4.11206i 0.619916 + 0.619916i
4545 0 0
4646 −0.150228 + 0.560658i −0.0221499 + 0.0826645i
4747 0.388741 + 1.45080i 0.0567037 + 0.211621i 0.988465 0.151451i 0.0483945π-0.0483945\pi
−0.931761 + 0.363072i 0.881728π0.881728\pi
4848 0 0
4949 5.97674i 0.853820i
5050 2.15322 2.15322i 0.304512 0.304512i
5151 0 0
5252 1.98870 3.00750i 0.275784 0.417065i
5353 2.77082i 0.380601i 0.981726 + 0.190300i 0.0609462π0.0609462\pi
−0.981726 + 0.190300i 0.939054π0.939054\pi
5454 0 0
5555 4.06542 7.04151i 0.548180 0.949476i
5656 1.01156 0.135176
5757 0 0
5858 −0.266656 0.995175i −0.0350137 0.130673i
5959 3.10182 + 11.5761i 0.403822 + 1.50708i 0.806218 + 0.591619i 0.201511π0.201511\pi
−0.402395 + 0.915466i 0.631822π0.631822\pi
6060 0 0
6161 2.82816 0.362108 0.181054 0.983473i 0.442049π-0.442049\pi
0.181054 + 0.983473i 0.442049π0.442049\pi
6262 −4.41397 + 7.64523i −0.560575 + 0.970945i
6363 0 0
6464 1.00000i 0.125000i
6565 −4.78138 1.59747i −0.593057 0.198142i
6666 0 0
6767 −0.802042 + 0.802042i −0.0979851 + 0.0979851i −0.754400 0.656415i 0.772072π-0.772072\pi
0.656415 + 0.754400i 0.272072π0.272072\pi
6868 3.34611i 0.405775i
6969 0 0
7070 −0.366058 1.36615i −0.0437524 0.163286i
7171 2.71495 10.1323i 0.322205 1.20249i −0.594886 0.803810i 0.702803π-0.702803\pi
0.917091 0.398677i 0.130530π-0.130530\pi
7272 0 0
7373 0.788181 + 0.788181i 0.0922496 + 0.0922496i 0.751726 0.659476i 0.229222π-0.229222\pi
−0.659476 + 0.751726i 0.729222π0.729222\pi
7474 8.10045i 0.941658i
7575 0 0
7676 5.18003 + 5.18003i 0.594190 + 0.594190i
7777 2.94129 + 5.09447i 0.335191 + 0.580568i
7878 0 0
7979 −0.827245 + 1.43283i −0.0930723 + 0.161206i −0.908802 0.417227i 0.863002π-0.863002\pi
0.815730 + 0.578433i 0.196335π0.196335\pi
8080 −1.35053 + 0.361873i −0.150994 + 0.0404587i
8181 0 0
8282 −1.41741 + 0.818343i −0.156527 + 0.0903709i
8383 15.7224 4.21280i 1.72576 0.462415i 0.746557 0.665321i 0.231705π-0.231705\pi
0.979198 + 0.202906i 0.0650387π0.0650387\pi
8484 0 0
8585 −4.51902 + 1.21087i −0.490156 + 0.131337i
8686 8.09498 + 2.16904i 0.872904 + 0.233894i
8787 0 0
8888 5.03622 2.90767i 0.536863 0.309958i
8989 −0.783797 2.92517i −0.0830824 0.310068i 0.911862 0.410497i 0.134645π-0.134645\pi
−0.994944 + 0.100430i 0.967978π0.967978\pi
9090 0 0
9191 2.73056 2.41795i 0.286240 0.253470i
9292 0.502672 + 0.290218i 0.0524072 + 0.0302573i
9393 0 0
9494 1.50198 0.154917
9595 5.12127 8.87030i 0.525431 0.910074i
9696 0 0
9797 8.70487 8.70487i 0.883846 0.883846i −0.110077 0.993923i 0.535110π-0.535110\pi
0.993923 + 0.110077i 0.0351099π0.0351099\pi
9898 −5.77308 1.54689i −0.583170 0.156260i
9999 0 0
100100 −1.52256 2.63715i −0.152256 0.263715i
101101 −5.09573 8.82607i −0.507044 0.878227i −0.999967 0.00815327i 0.997405π-0.997405\pi
0.492922 0.870073i 0.335929π-0.335929\pi
102102 0 0
103103 −8.54265 + 4.93210i −0.841732 + 0.485974i −0.857853 0.513896i 0.828202π-0.828202\pi
0.0161205 + 0.999870i 0.494868π0.494868\pi
104104 −2.39031 2.69934i −0.234389 0.264692i
105105 0 0
106106 2.67640 + 0.717140i 0.259955 + 0.0696548i
107107 −8.58323 4.95553i −0.829773 0.479069i 0.0240022 0.999712i 0.492359π-0.492359\pi
−0.853775 + 0.520642i 0.825692π0.825692\pi
108108 0 0
109109 6.99609 6.99609i 0.670103 0.670103i −0.287636 0.957740i 0.592869π-0.592869\pi
0.957740 + 0.287636i 0.0928694π0.0928694\pi
110110 −5.74937 5.74937i −0.548180 0.548180i
111111 0 0
112112 0.261812 0.977097i 0.0247389 0.0923269i
113113 −8.78784 5.07366i −0.826691 0.477290i 0.0260276 0.999661i 0.491714π-0.491714\pi
−0.852718 + 0.522371i 0.825048π0.825048\pi
114114 0 0
115115 0.210044 0.783896i 0.0195867 0.0730987i
116116 −1.03028 −0.0956592
117117 0 0
118118 11.9845 1.10326
119119 0.876052 3.26947i 0.0803075 0.299712i
120120 0 0
121121 19.7610 + 11.4090i 1.79646 + 1.03718i
122122 0.731981 2.73179i 0.0662704 0.247325i
123123 0 0
124124 6.24230 + 6.24230i 0.560575 + 0.560575i
125125 −7.95386 + 7.95386i −0.711415 + 0.711415i
126126 0 0
127127 −13.1106 7.56941i −1.16338 0.671677i −0.211267 0.977428i 0.567759π-0.567759\pi
−0.952111 + 0.305752i 0.901092π0.901092\pi
128128 −0.965926 0.258819i −0.0853766 0.0228766i
129129 0 0
130130 −2.78055 + 4.20500i −0.243870 + 0.368803i
131131 −3.29059 + 1.89982i −0.287500 + 0.165988i −0.636814 0.771018i 0.719748π-0.719748\pi
0.349314 + 0.937006i 0.386415π0.386415\pi
132132 0 0
133133 3.70519 + 6.41758i 0.321281 + 0.556475i
134134 0.567130 + 0.982297i 0.0489925 + 0.0848576i
135135 0 0
136136 −3.23209 0.866036i −0.277149 0.0742620i
137137 −4.11536 + 4.11536i −0.351599 + 0.351599i −0.860704 0.509105i 0.829976π-0.829976\pi
0.509105 + 0.860704i 0.329976π0.329976\pi
138138 0 0
139139 −1.13838 + 1.97173i −0.0965559 + 0.167240i −0.910257 0.414044i 0.864116π-0.864116\pi
0.813701 + 0.581284i 0.197449π0.197449\pi
140140 −1.41434 −0.119534
141141 0 0
142142 −9.08440 5.24488i −0.762346 0.440141i
143143 6.64426 19.8869i 0.555621 1.66303i
144144 0 0
145145 0.372831 + 1.39143i 0.0309620 + 0.115552i
146146 0.965320 0.557328i 0.0798905 0.0461248i
147147 0 0
148148 7.82443 + 2.09655i 0.643164 + 0.172335i
149149 −13.8851 + 3.72050i −1.13751 + 0.304795i −0.777949 0.628327i 0.783740π-0.783740\pi
−0.359561 + 0.933122i 0.617073π0.617073\pi
150150 0 0
151151 −2.72013 + 0.728858i −0.221361 + 0.0593136i −0.367795 0.929907i 0.619887π-0.619887\pi
0.146434 + 0.989220i 0.453221π0.453221\pi
152152 6.34422 3.66283i 0.514584 0.297095i
153153 0 0
154154 5.68214 1.52252i 0.457880 0.122689i
155155 6.17149 10.6893i 0.495706 0.858588i
156156 0 0
157157 3.93908 + 6.82268i 0.314372 + 0.544509i 0.979304 0.202395i 0.0648726π-0.0648726\pi
−0.664931 + 0.746904i 0.731539π0.731539\pi
158158 1.16990 + 1.16990i 0.0930723 + 0.0930723i
159159 0 0
160160 1.39817i 0.110535i
161161 0.415177 + 0.415177i 0.0327205 + 0.0327205i
162162 0 0
163163 −1.79021 + 6.68116i −0.140220 + 0.523309i 0.859701 + 0.510797i 0.170650π0.170650\pi
−0.999922 + 0.0125123i 0.996017π0.996017\pi
164164 0.423606 + 1.58092i 0.0330780 + 0.123449i
165165 0 0
166166 16.2770i 1.26334i
167167 11.2080 11.2080i 0.867298 0.867298i −0.124874 0.992173i 0.539853π-0.539853\pi
0.992173 + 0.124874i 0.0398528π0.0398528\pi
168168 0 0
169169 −12.9045 1.57285i −0.992654 0.120989i
170170 4.67843i 0.358819i
171171 0 0
172172 4.19027 7.25776i 0.319505 0.553399i
173173 2.60453 0.198018 0.0990092 0.995087i 0.468433π-0.468433\pi
0.0990092 + 0.995087i 0.468433π0.468433\pi
174174 0 0
175175 −0.797249 2.97537i −0.0602663 0.224917i
176176 −1.50512 5.61718i −0.113453 0.423411i
177177 0 0
178178 −3.02836 −0.226985
179179 −1.79612 + 3.11097i −0.134248 + 0.232525i −0.925310 0.379211i 0.876195π-0.876195\pi
0.791062 + 0.611736i 0.209529π0.209529\pi
180180 0 0
181181 16.3443i 1.21486i −0.794373 0.607430i 0.792201π-0.792201\pi
0.794373 0.607430i 0.207799π-0.207799\pi
182182 −1.62884 3.26333i −0.120738 0.241894i
183183 0 0
184184 0.410430 0.410430i 0.0302573 0.0302573i
185185 11.3258i 0.832691i
186186 0 0
187187 −5.03629 18.7957i −0.368290 1.37448i
188188 0.388741 1.45080i 0.0283519 0.105811i
189189 0 0
190190 −7.24257 7.24257i −0.525431 0.525431i
191191 25.4377i 1.84061i 0.391202 + 0.920305i 0.372059π0.372059\pi
−0.391202 + 0.920305i 0.627941π0.627941\pi
192192 0 0
193193 8.92082 + 8.92082i 0.642134 + 0.642134i 0.951080 0.308945i 0.0999760π-0.0999760\pi
−0.308945 + 0.951080i 0.599976π0.599976\pi
194194 −6.15527 10.6612i −0.441923 0.765433i
195195 0 0
196196 −2.98837 + 5.17601i −0.213455 + 0.369715i
197197 −0.680083 + 0.182228i −0.0484539 + 0.0129832i −0.282965 0.959130i 0.591318π-0.591318\pi
0.234511 + 0.972114i 0.424651π0.424651\pi
198198 0 0
199199 8.58639 4.95735i 0.608673 0.351418i −0.163773 0.986498i 0.552366π-0.552366\pi
0.772446 + 0.635081i 0.219033π0.219033\pi
200200 −2.94136 + 0.788134i −0.207985 + 0.0557295i
201201 0 0
202202 −9.84420 + 2.63775i −0.692635 + 0.185591i
203203 −1.00668 0.269740i −0.0706553 0.0189320i
204204 0 0
205205 1.98179 1.14418i 0.138414 0.0799133i
206206 2.55304 + 9.52809i 0.177879 + 0.663853i
207207 0 0
208208 −3.22602 + 1.61022i −0.223684 + 0.111649i
209209 36.8937 + 21.3006i 2.55199 + 1.47339i
210210 0 0
211211 −6.02887 −0.415045 −0.207522 0.978230i 0.566540π-0.566540\pi
−0.207522 + 0.978230i 0.566540π0.566540\pi
212212 1.38541 2.39960i 0.0951502 0.164805i
213213 0 0
214214 −7.00818 + 7.00818i −0.479069 + 0.479069i
215215 −11.3182 3.03269i −0.771893 0.206828i
216216 0 0
217217 4.46502 + 7.73364i 0.303105 + 0.524994i
218218 −4.94698 8.56842i −0.335052 0.580327i
219219 0 0
220220 −7.04151 + 4.06542i −0.474738 + 0.274090i
221221 −10.7946 + 5.38797i −0.726123 + 0.362434i
222222 0 0
223223 28.1618 + 7.54594i 1.88586 + 0.505313i 0.999069 + 0.0431328i 0.0137339π0.0137339\pi
0.886786 + 0.462181i 0.152933π0.152933\pi
224224 −0.876041 0.505782i −0.0585329 0.0337940i
225225 0 0
226226 −7.17524 + 7.17524i −0.477290 + 0.477290i
227227 −10.2562 10.2562i −0.680729 0.680729i 0.279435 0.960165i 0.409853π-0.409853\pi
−0.960165 + 0.279435i 0.909853π0.909853\pi
228228 0 0
229229 −2.55392 + 9.53135i −0.168768 + 0.629849i 0.828762 + 0.559601i 0.189046π0.189046\pi
−0.997530 + 0.0702479i 0.977621π0.977621\pi
230230 −0.702822 0.405774i −0.0463427 0.0267560i
231231 0 0
232232 −0.266656 + 0.995175i −0.0175068 + 0.0653364i
233233 2.06808 0.135484 0.0677421 0.997703i 0.478420π-0.478420\pi
0.0677421 + 0.997703i 0.478420π0.478420\pi
234234 0 0
235235 −2.10003 −0.136991
236236 3.10182 11.5761i 0.201911 0.753542i
237237 0 0
238238 −2.93133 1.69240i −0.190010 0.109702i
239239 −5.10931 + 19.0682i −0.330494 + 1.23342i 0.578179 + 0.815910i 0.303764π0.303764\pi
−0.908672 + 0.417510i 0.862903π0.862903\pi
240240 0 0
241241 −7.17107 7.17107i −0.461929 0.461929i 0.437358 0.899287i 0.355914π-0.355914\pi
−0.899287 + 0.437358i 0.855914π0.855914\pi
242242 16.1348 16.1348i 1.03718 1.03718i
243243 0 0
244244 −2.44926 1.41408i −0.156797 0.0905271i
245245 8.07176 + 2.16282i 0.515686 + 0.138178i
246246 0 0
247247 8.36988 25.0519i 0.532563 1.59401i
248248 7.64523 4.41397i 0.485472 0.280288i
249249 0 0
250250 5.62423 + 9.74145i 0.355707 + 0.616103i
251251 −4.78920 8.29514i −0.302292 0.523585i 0.674363 0.738400i 0.264418π-0.264418\pi
−0.976655 + 0.214815i 0.931085π0.931085\pi
252252 0 0
253253 3.26041 + 0.873624i 0.204980 + 0.0549243i
254254 −10.7048 + 10.7048i −0.671677 + 0.671677i
255255 0 0
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 5.77509 0.360240 0.180120 0.983645i 0.442351π-0.442351\pi
0.180120 + 0.983645i 0.442351π0.442351\pi
258258 0 0
259259 7.09632 + 4.09706i 0.440944 + 0.254579i
260260 3.34206 + 3.77414i 0.207266 + 0.234062i
261261 0 0
262262 0.983420 + 3.67017i 0.0607559 + 0.226744i
263263 3.86009 2.22862i 0.238023 0.137423i −0.376245 0.926520i 0.622785π-0.622785\pi
0.614268 + 0.789098i 0.289451π0.289451\pi
264264 0 0
265265 −3.74207 1.00269i −0.229874 0.0615945i
266266 7.15789 1.91795i 0.438878 0.117597i
267267 0 0
268268 1.09561 0.293568i 0.0669250 0.0179325i
269269 −11.4786 + 6.62715i −0.699860 + 0.404064i −0.807295 0.590148i 0.799069π-0.799069\pi
0.107435 + 0.994212i 0.465736π0.465736\pi
270270 0 0
271271 −5.62562 + 1.50738i −0.341732 + 0.0915668i −0.425604 0.904910i 0.639938π-0.639938\pi
0.0838714 + 0.996477i 0.473272π0.473272\pi
272272 −1.67305 + 2.89781i −0.101444 + 0.175706i
273273 0 0
274274 2.91000 + 5.04027i 0.175799 + 0.304494i
275275 −12.5217 12.5217i −0.755087 0.755087i
276276 0 0
277277 19.4395i 1.16800i 0.811752 + 0.584002i 0.198514π0.198514\pi
−0.811752 + 0.584002i 0.801486π0.801486\pi
278278 1.60991 + 1.60991i 0.0965559 + 0.0965559i
279279 0 0
280280 −0.366058 + 1.36615i −0.0218762 + 0.0816430i
281281 0.376063 + 1.40349i 0.0224340 + 0.0837250i 0.976235 0.216713i 0.0695337π-0.0695337\pi
−0.953801 + 0.300438i 0.902867π0.902867\pi
282282 0 0
283283 20.7333i 1.23247i −0.787564 0.616233i 0.788658π-0.788658\pi
0.787564 0.616233i 0.211342π-0.211342\pi
284284 −7.41738 + 7.41738i −0.440141 + 0.440141i
285285 0 0
286286 −17.4896 11.5650i −1.03418 0.683851i
287287 1.65561i 0.0977278i
288288 0 0
289289 2.90179 5.02604i 0.170693 0.295649i
290290 1.44051 0.0845896
291291 0 0
292292 −0.288494 1.07667i −0.0168828 0.0630076i
293293 6.14475 + 22.9325i 0.358980 + 1.33973i 0.875401 + 0.483398i 0.160598π0.160598\pi
−0.516420 + 0.856335i 0.672736π0.672736\pi
294294 0 0
295295 −16.7564 −0.975595
296296 4.05022 7.01519i 0.235414 0.407750i
297297 0 0
298298 14.3749i 0.832715i
299299 0.126835 2.08894i 0.00733508 0.120807i
300300 0 0
301301 5.99447 5.99447i 0.345515 0.345515i
302302 2.81609i 0.162048i
303303 0 0
304304 −1.89602 7.07605i −0.108744 0.405839i
305305 −1.02343 + 3.81951i −0.0586017 + 0.218705i
306306 0 0
307307 14.7696 + 14.7696i 0.842947 + 0.842947i 0.989241 0.146294i 0.0467346π-0.0467346\pi
−0.146294 + 0.989241i 0.546735π0.546735\pi
308308 5.88258i 0.335191i
309309 0 0
310310 −8.72781 8.72781i −0.495706 0.495706i
311311 14.0548 + 24.3437i 0.796976 + 1.38040i 0.921577 + 0.388195i 0.126901π0.126901\pi
−0.124602 + 0.992207i 0.539765π0.539765\pi
312312 0 0
313313 8.76521 15.1818i 0.495439 0.858125i −0.504547 0.863384i 0.668341π-0.668341\pi
0.999986 + 0.00525876i 0.00167392π0.00167392\pi
314314 7.60971 2.03902i 0.429441 0.115068i
315315 0 0
316316 1.43283 0.827245i 0.0806030 0.0465362i
317317 −21.3692 + 5.72585i −1.20021 + 0.321596i −0.802915 0.596094i 0.796719π-0.796719\pi
−0.397298 + 0.917690i 0.630052π0.630052\pi
318318 0 0
319319 −5.78727 + 1.55069i −0.324025 + 0.0868222i
320320 1.35053 + 0.361873i 0.0754969 + 0.0202293i
321321 0 0
322322 0.508485 0.293574i 0.0283368 0.0163603i
323323 −6.34429 23.6772i −0.353006 1.31744i
324324 0 0
325325 −6.05583 + 9.15819i −0.335917 + 0.508005i
326326 5.99017 + 3.45843i 0.331765 + 0.191544i
327327 0 0
328328 1.63669 0.0903709
329329 0.759675 1.31580i 0.0418822 0.0725422i
330330 0 0
331331 16.0059 16.0059i 0.879762 0.879762i −0.113748 0.993510i 0.536286π-0.536286\pi
0.993510 + 0.113748i 0.0362856π0.0362856\pi
332332 −15.7224 4.21280i −0.862878 0.231207i
333333 0 0
334334 −7.92523 13.7269i −0.433649 0.751102i
335335 −0.792945 1.37342i −0.0433232 0.0750380i
336336 0 0
337337 −26.9968 + 15.5866i −1.47061 + 0.849058i −0.999456 0.0329922i 0.989496π-0.989496\pi
−0.471156 + 0.882050i 0.656163π0.656163\pi
338338 −4.85919 + 12.0577i −0.264305 + 0.655853i
339339 0 0
340340 4.51902 + 1.21087i 0.245078 + 0.0656685i
341341 44.4595 + 25.6687i 2.40762 + 1.39004i
342342 0 0
343343 −9.28206 + 9.28206i −0.501184 + 0.501184i
344344 −5.92594 5.92594i −0.319505 0.319505i
345345 0 0
346346 0.674101 2.51578i 0.0362399 0.135249i
347347 17.6308 + 10.1791i 0.946468 + 0.546444i 0.891982 0.452071i 0.149315π-0.149315\pi
0.0544863 + 0.998515i 0.482648π0.482648\pi
348348 0 0
349349 −7.61062 + 28.4032i −0.407387 + 1.52039i 0.392224 + 0.919870i 0.371706π0.371706\pi
−0.799611 + 0.600519i 0.794961π0.794961\pi
350350 −3.08033 −0.164651
351351 0 0
352352 −5.81533 −0.309958
353353 2.96995 11.0840i 0.158075 0.589943i −0.840748 0.541427i 0.817884π-0.817884\pi
0.998822 0.0485157i 0.0154491π-0.0154491\pi
354354 0 0
355355 12.7016 + 7.33325i 0.674129 + 0.389208i
356356 −0.783797 + 2.92517i −0.0415412 + 0.155034i
357357 0 0
358358 2.54010 + 2.54010i 0.134248 + 0.134248i
359359 −25.9734 + 25.9734i −1.37083 + 1.37083i −0.511605 + 0.859221i 0.670949π0.670949\pi
−0.859221 + 0.511605i 0.829051π0.829051\pi
360360 0 0
361361 30.0211 + 17.3327i 1.58006 + 0.912248i
362362 −15.7873 4.23021i −0.829765 0.222335i
363363 0 0
364364 −3.57371 + 0.728730i −0.187313 + 0.0381958i
365365 −1.34968 + 0.779240i −0.0706457 + 0.0407873i
366366 0 0
367367 2.78625 + 4.82592i 0.145441 + 0.251911i 0.929537 0.368728i 0.120207π-0.120207\pi
−0.784096 + 0.620639i 0.786873π0.786873\pi
368368 −0.290218 0.502672i −0.0151287 0.0262036i
369369 0 0
370370 −10.9399 2.93134i −0.568738 0.152393i
371371 1.98192 1.98192i 0.102896 0.102896i
372372 0 0
373373 −1.43922 + 2.49280i −0.0745200 + 0.129072i −0.900877 0.434074i 0.857076π-0.857076\pi
0.826357 + 0.563146i 0.190409π0.190409\pi
374374 −19.4587 −1.00619
375375 0 0
376376 −1.30075 0.750990i −0.0670812 0.0387294i
377377 1.65898 + 3.32370i 0.0854418 + 0.171179i
378378 0 0
379379 5.51954 + 20.5992i 0.283520 + 1.05811i 0.949914 + 0.312511i 0.101170π0.101170\pi
−0.666394 + 0.745600i 0.732163π0.732163\pi
380380 −8.87030 + 5.12127i −0.455037 + 0.262716i
381381 0 0
382382 24.5710 + 6.58377i 1.25716 + 0.336855i
383383 −12.5372 + 3.35934i −0.640623 + 0.171654i −0.564486 0.825443i 0.690925π-0.690925\pi
−0.0761376 + 0.997097i 0.524259π0.524259\pi
384384 0 0
385385 −7.94461 + 2.12875i −0.404895 + 0.108491i
386386 10.9257 6.30797i 0.556105 0.321067i
387387 0 0
388388 −11.8911 + 3.18620i −0.603678 + 0.161755i
389389 −15.6511 + 27.1085i −0.793543 + 1.37446i 0.130216 + 0.991486i 0.458433π0.458433\pi
−0.923760 + 0.382972i 0.874901π0.874901\pi
390390 0 0
391391 −0.971100 1.68199i −0.0491106 0.0850621i
392392 4.22619 + 4.22619i 0.213455 + 0.213455i
393393 0 0
394394 0.704074i 0.0354707i
395395 −1.63572 1.63572i −0.0823021 0.0823021i
396396 0 0
397397 0.644906 2.40682i 0.0323669 0.120795i −0.947852 0.318710i 0.896750π-0.896750\pi
0.980219 + 0.197915i 0.0634170π0.0634170\pi
398398 −2.56612 9.57687i −0.128628 0.480045i
399399 0 0
400400 3.04512i 0.152256i
401401 −14.5050 + 14.5050i −0.724345 + 0.724345i −0.969487 0.245142i 0.921165π-0.921165\pi
0.245142 + 0.969487i 0.421165π0.421165\pi
402402 0 0
403403 10.0863 30.1893i 0.502434 1.50383i
404404 10.1915i 0.507044i
405405 0 0
406406 −0.521098 + 0.902568i −0.0258617 + 0.0447937i
407407 47.1068 2.33500
408408 0 0
409409 −2.53544 9.46239i −0.125369 0.467885i 0.874483 0.485056i 0.161201π-0.161201\pi
−0.999853 + 0.0171708i 0.994534π0.994534\pi
410410 −0.592273 2.21039i −0.0292503 0.109164i
411411 0 0
412412 9.86420 0.485974
413413 6.06155 10.4989i 0.298269 0.516618i
414414 0 0
415415 22.7581i 1.11715i
416416 0.720398 + 3.53285i 0.0353204 + 0.173212i
417417 0 0
418418 30.1236 30.1236i 1.47339 1.47339i
419419 1.73191i 0.0846094i 0.999105 + 0.0423047i 0.0134700π0.0134700\pi
−0.999105 + 0.0423047i 0.986530π0.986530\pi
420420 0 0
421421 0.920185 + 3.43418i 0.0448471 + 0.167372i 0.984717 0.174160i 0.0557210π-0.0557210\pi
−0.939870 + 0.341532i 0.889054π0.889054\pi
422422 −1.56039 + 5.82344i −0.0759584 + 0.283481i
423423 0 0
424424 −1.95926 1.95926i −0.0951502 0.0951502i
425425 10.1893i 0.494253i
426426 0 0
427427 −2.02294 2.02294i −0.0978967 0.0978967i
428428 4.95553 + 8.58323i 0.239535 + 0.414886i
429429 0 0
430430 −5.85872 + 10.1476i −0.282532 + 0.489360i
431431 14.3219 3.83753i 0.689860 0.184847i 0.103176 0.994663i 0.467100π-0.467100\pi
0.586684 + 0.809816i 0.300433π0.300433\pi
432432 0 0
433433 −9.94854 + 5.74379i −0.478096 + 0.276029i −0.719623 0.694365i 0.755685π-0.755685\pi
0.241527 + 0.970394i 0.422352π0.422352\pi
434434 8.62576 2.31126i 0.414050 0.110944i
435435 0 0
436436 −9.55683 + 2.56075i −0.457689 + 0.122637i
437437 4.10719 + 1.10052i 0.196474 + 0.0526450i
438438 0 0
439439 −35.2492 + 20.3511i −1.68235 + 0.971306i −0.722259 + 0.691623i 0.756896π0.756896\pi
−0.960092 + 0.279683i 0.909771π0.909771\pi
440440 2.10441 + 7.85378i 0.100324 + 0.374414i
441441 0 0
442442 2.41053 + 11.8213i 0.114657 + 0.562281i
443443 −10.6734 6.16232i −0.507111 0.292780i 0.224535 0.974466i 0.427914π-0.427914\pi
−0.731645 + 0.681686i 0.761247π0.761247\pi
444444 0 0
445445 4.23417 0.200719
446446 14.5776 25.2492i 0.690271 1.19558i
447447 0 0
448448 −0.715284 + 0.715284i −0.0337940 + 0.0337940i
449449 27.3580 + 7.33055i 1.29110 + 0.345950i 0.838080 0.545548i 0.183678π-0.183678\pi
0.453024 + 0.891498i 0.350345π0.350345\pi
450450 0 0
451451 4.75894 + 8.24272i 0.224090 + 0.388134i
452452 5.07366 + 8.78784i 0.238645 + 0.413345i
453453 0 0
454454 −12.5613 + 7.25224i −0.589529 + 0.340365i
455455 2.27740 + 4.56269i 0.106766 + 0.213902i
456456 0 0
457457 −29.0998 7.79727i −1.36123 0.364741i −0.496963 0.867772i 0.665551π-0.665551\pi
−0.864268 + 0.503031i 0.832218π0.832218\pi
458458 8.54557 + 4.93379i 0.399308 + 0.230541i
459459 0 0
460460 −0.573852 + 0.573852i −0.0267560 + 0.0267560i
461461 −20.1337 20.1337i −0.937718 0.937718i 0.0604534 0.998171i 0.480745π-0.480745\pi
−0.998171 + 0.0604534i 0.980745π0.980745\pi
462462 0 0
463463 0.936943 3.49672i 0.0435434 0.162506i −0.940731 0.339155i 0.889859π-0.889859\pi
0.984274 + 0.176649i 0.0565256π0.0565256\pi
464464 0.892249 + 0.515140i 0.0414216 + 0.0239148i
465465 0 0
466466 0.535258 1.99761i 0.0247953 0.0925375i
467467 −36.6235 −1.69473 −0.847366 0.531010i 0.821813π-0.821813\pi
−0.847366 + 0.531010i 0.821813π0.821813\pi
468468 0 0
469469 1.14738 0.0529809
470470 −0.543527 + 2.02847i −0.0250710 + 0.0935663i
471471 0 0
472472 −10.3789 5.99225i −0.477727 0.275816i
473473 12.6137 47.0750i 0.579979 2.16451i
474474 0 0
475475 −15.7738 15.7738i −0.723751 0.723751i
476476 −2.39342 + 2.39342i −0.109702 + 0.109702i
477477 0 0
478478 17.0961 + 9.87043i 0.781957 + 0.451463i
479479 4.87703 + 1.30680i 0.222837 + 0.0597091i 0.368510 0.929624i 0.379868π-0.379868\pi
−0.145673 + 0.989333i 0.546535π0.546535\pi
480480 0 0
481481 −5.83555 28.6177i −0.266078 1.30485i
482482 −8.78273 + 5.07071i −0.400043 + 0.230965i
483483 0 0
484484 −11.4090 19.7610i −0.518592 0.898228i
485485 8.60613 + 14.9063i 0.390784 + 0.676858i
486486 0 0
487487 −28.6137 7.66702i −1.29661 0.347426i −0.456443 0.889753i 0.650877π-0.650877\pi
−0.840167 + 0.542327i 0.817543π0.817543\pi
488488 −1.99981 + 1.99981i −0.0905271 + 0.0905271i
489489 0 0
490490 4.17825 7.23695i 0.188754 0.326932i
491491 1.97522 0.0891403 0.0445701 0.999006i 0.485808π-0.485808\pi
0.0445701 + 0.999006i 0.485808π0.485808\pi
492492 0 0
493493 2.98556 + 1.72371i 0.134463 + 0.0776322i
494494 −22.0320 14.5686i −0.991264 0.655471i
495495 0 0
496496 −2.28484 8.52714i −0.102592 0.382880i
497497 −9.18946 + 5.30554i −0.412204 + 0.237986i
498498 0 0
499499 −3.87214 1.03754i −0.173341 0.0464465i 0.171105 0.985253i 0.445266π-0.445266\pi
−0.344445 + 0.938806i 0.611933π0.611933\pi
500500 10.8652 2.91131i 0.485905 0.130198i
501501 0 0
502502 −9.25203 + 2.47907i −0.412938 + 0.110646i
503503 6.37037 3.67794i 0.284041 0.163991i −0.351211 0.936297i 0.614230π-0.614230\pi
0.635251 + 0.772305i 0.280897π0.280897\pi
504504 0 0
505505 13.7639 3.68802i 0.612485 0.164115i
506506 1.68771 2.92320i 0.0750280 0.129952i
507507 0 0
508508 7.56941 + 13.1106i 0.335838 + 0.581689i
509509 −10.0747 10.0747i −0.446552 0.446552i 0.447654 0.894207i 0.352260π-0.352260\pi
−0.894207 + 0.447654i 0.852260π0.852260\pi
510510 0 0
511511 1.12755i 0.0498797i
512512 0.707107 + 0.707107i 0.0312500 + 0.0312500i
513513 0 0
514514 1.49470 5.57831i 0.0659286 0.246049i
515515 −3.56959 13.3219i −0.157295 0.587033i
516516 0 0
517517 8.73451i 0.384143i
518518 5.79412 5.79412i 0.254579 0.254579i
519519 0 0
520520 4.51053 2.25136i 0.197800 0.0987289i
521521 28.5428i 1.25048i −0.780431 0.625242i 0.785000π-0.785000\pi
0.780431 0.625242i 0.215000π-0.215000\pi
522522 0 0
523523 7.95336 13.7756i 0.347776 0.602366i −0.638078 0.769972i 0.720270π-0.720270\pi
0.985854 + 0.167606i 0.0536037π0.0536037\pi
524524 3.79964 0.165988
525525 0 0
526526 −1.15362 4.30537i −0.0503002 0.187723i
527527 −7.64532 28.5327i −0.333035 1.24290i
528528 0 0
529529 −22.6631 −0.985352
530530 −1.93704 + 3.35505i −0.0841396 + 0.145734i
531531 0 0
532532 7.41039i 0.321281i
533533 4.41797 3.91218i 0.191364 0.169456i
534534 0 0
535535 9.79864 9.79864i 0.423632 0.423632i
536536 1.13426i 0.0489925i
537537 0 0
538538 3.43046 + 12.8027i 0.147898 + 0.551962i
539539 −8.99570 + 33.5724i −0.387472 + 1.44607i
540540 0 0
541541 20.5826 + 20.5826i 0.884913 + 0.884913i 0.994029 0.109116i 0.0348019π-0.0348019\pi
−0.109116 + 0.994029i 0.534802π0.534802\pi
542542 5.82407i 0.250165i
543543 0 0
544544 2.36605 + 2.36605i 0.101444 + 0.101444i
545545 6.91673 + 11.9801i 0.296280 + 0.513172i
546546 0 0
547547 −11.8581 + 20.5389i −0.507017 + 0.878180i 0.492950 + 0.870058i 0.335919π0.335919\pi
−0.999967 + 0.00812189i 0.997415π0.997415\pi
548548 5.62169 1.50633i 0.240147 0.0643471i
549549 0 0
550550 −15.3359 + 8.85418i −0.653924 + 0.377543i
551551 −7.29032 + 1.95344i −0.310578 + 0.0832191i
552552 0 0
553553 1.61660 0.433166i 0.0687447 0.0184201i
554554 18.7771 + 5.03130i 0.797762 + 0.213760i
555555 0 0
556556 1.97173 1.13838i 0.0836199 0.0482779i
557557 1.55296 + 5.79572i 0.0658010 + 0.245573i 0.990990 0.133933i 0.0427607π-0.0427607\pi
−0.925189 + 0.379506i 0.876094π0.876094\pi
558558 0 0
559559 −30.1609 1.83129i −1.27567 0.0774555i
560560 1.22486 + 0.707171i 0.0517596 + 0.0298834i
561561 0 0
562562 1.45300 0.0612909
563563 −17.1469 + 29.6993i −0.722656 + 1.25168i 0.237275 + 0.971442i 0.423746π0.423746\pi
−0.959932 + 0.280235i 0.909588π0.909588\pi
564564 0 0
565565 10.0322 10.0322i 0.422059 0.422059i
566566 −20.0268 5.36617i −0.841790 0.225557i
567567 0 0
568568 5.24488 + 9.08440i 0.220070 + 0.381173i
569569 −17.8407 30.9009i −0.747919 1.29543i −0.948818 0.315822i 0.897720π-0.897720\pi
0.200899 0.979612i 0.435614π-0.435614\pi
570570 0 0
571571 25.3581 14.6405i 1.06121 0.612687i 0.135440 0.990786i 0.456755π-0.456755\pi
0.925765 + 0.378099i 0.123422π0.123422\pi
572572 −15.6975 + 13.9004i −0.656347 + 0.581206i
573573 0 0
574574 1.59920 + 0.428504i 0.0667493 + 0.0178854i
575575 −1.53069 0.883747i −0.0638344 0.0368548i
576576 0 0
577577 −19.2968 + 19.2968i −0.803337 + 0.803337i −0.983616 0.180278i 0.942300π-0.942300\pi
0.180278 + 0.983616i 0.442300π0.442300\pi
578578 −4.10375 4.10375i −0.170693 0.170693i
579579 0 0
580580 0.372831 1.39143i 0.0154810 0.0577758i
581581 −14.2593 8.23262i −0.591576 0.341547i
582582 0 0
583583 4.17041 15.5642i 0.172721 0.644602i
584584 −1.11466 −0.0461248
585585 0 0
586586 23.7415 0.980753
587587 5.15867 19.2524i 0.212921 0.794633i −0.773967 0.633226i 0.781730π-0.781730\pi
0.986888 0.161407i 0.0516030π-0.0516030\pi
588588 0 0
589589 56.0064 + 32.3353i 2.30770 + 1.33235i
590590 −4.33687 + 16.1854i −0.178546 + 0.666344i
591591 0 0
592592 −5.72788 5.72788i −0.235414 0.235414i
593593 −3.24522 + 3.24522i −0.133265 + 0.133265i −0.770593 0.637328i 0.780040π-0.780040\pi
0.637328 + 0.770593i 0.280040π0.280040\pi
594594 0 0
595595 4.09850 + 2.36627i 0.168022 + 0.0970075i
596596 13.8851 + 3.72050i 0.568755 + 0.152397i
597597 0 0
598598 −1.98494 0.663172i −0.0811701 0.0271191i
599599 36.4947 21.0702i 1.49113 0.860906i 0.491185 0.871055i 0.336564π-0.336564\pi
0.999949 + 0.0101486i 0.00323046π0.00323046\pi
600600 0 0
601601 −2.31955 4.01758i −0.0946164 0.163880i 0.814832 0.579697i 0.196829π-0.196829\pi
−0.909448 + 0.415817i 0.863496π0.863496\pi
602602 −4.23873 7.34169i −0.172758 0.299225i
603603 0 0
604604 2.72013 + 0.728858i 0.110681 + 0.0296568i
605605 −22.5592 + 22.5592i −0.917163 + 0.917163i
606606 0 0
607607 −5.75071 + 9.96053i −0.233414 + 0.404285i −0.958811 0.284046i 0.908323π-0.908323\pi
0.725396 + 0.688331i 0.241656π0.241656\pi
608608 −7.32567 −0.297095
609609 0 0
610610 3.42448 + 1.97712i 0.138653 + 0.0800514i
611611 −5.30627 + 1.08202i −0.214669 + 0.0437740i
612612 0 0
613613 −3.05394 11.3975i −0.123347 0.460339i 0.876428 0.481533i 0.159920π-0.159920\pi
−0.999775 + 0.0211942i 0.993253π0.993253\pi
614614 18.0890 10.4437i 0.730014 0.421474i
615615 0 0
616616 −5.68214 1.52252i −0.228940 0.0613443i
617617 30.8124 8.25615i 1.24046 0.332380i 0.421815 0.906682i 0.361393π-0.361393\pi
0.818644 + 0.574302i 0.194726π0.194726\pi
618618 0 0
619619 −22.3895 + 5.99924i −0.899909 + 0.241130i −0.678977 0.734160i 0.737576π-0.737576\pi
−0.220932 + 0.975289i 0.570910π0.570910\pi
620620 −10.6893 + 6.17149i −0.429294 + 0.247853i
621621 0 0
622622 27.1518 7.27531i 1.08869 0.291713i
623623 −1.53169 + 2.65297i −0.0613659 + 0.106289i
624624 0 0
625625 −0.250846 0.434477i −0.0100338 0.0173791i
626626 −12.3959 12.3959i −0.495439 0.495439i
627627 0 0
628628 7.87815i 0.314372i
629629 −19.1661 19.1661i −0.764202 0.764202i
630630 0 0
631631 6.12810 22.8704i 0.243956 0.910456i −0.729949 0.683501i 0.760456π-0.760456\pi
0.973905 0.226955i 0.0728770π-0.0728770\pi
632632 −0.428214 1.59811i −0.0170334 0.0635696i
633633 0 0
634634 22.1230i 0.878617i
635635 14.9671 14.9671i 0.593951 0.593951i
636636 0 0
637637 21.5098 + 1.30602i 0.852250 + 0.0517464i
638638 5.99142i 0.237203i
639639 0 0
640640 0.699086 1.21085i 0.0276338 0.0478631i
641641 28.7047 1.13377 0.566884 0.823798i 0.308149π-0.308149\pi
0.566884 + 0.823798i 0.308149π0.308149\pi
642642 0 0
643643 5.90865 + 22.0514i 0.233014 + 0.869621i 0.979034 + 0.203697i 0.0652959π0.0652959\pi
−0.746020 + 0.665924i 0.768037π0.768037\pi
644644 −0.151965 0.567142i −0.00598827 0.0223485i
645645 0 0
646646 −24.5125 −0.964430
647647 18.5692 32.1627i 0.730029 1.26445i −0.226841 0.973932i 0.572840π-0.572840\pi
0.956870 0.290516i 0.0938270π-0.0938270\pi
648648 0 0
649649 69.6938i 2.73572i
650650 7.27876 + 8.21980i 0.285497 + 0.322407i
651651 0 0
652652 4.89095 4.89095i 0.191544 0.191544i
653653 44.4676i 1.74015i −0.492917 0.870076i 0.664069π-0.664069\pi
0.492917 0.870076i 0.335931π-0.335931\pi
654654 0 0
655655 −1.37499 5.13153i −0.0537253 0.200506i
656656 0.423606 1.58092i 0.0165390 0.0617245i
657657 0 0
658658 −1.07434 1.07434i −0.0418822 0.0418822i
659659 0.414343i 0.0161405i −0.999967 0.00807026i 0.997431π-0.997431\pi
0.999967 0.00807026i 0.00256887π-0.00256887\pi
660660 0 0
661661 −20.1566 20.1566i −0.784000 0.784000i 0.196503 0.980503i 0.437042π-0.437042\pi
−0.980503 + 0.196503i 0.937042π0.937042\pi
662662 −11.3179 19.6031i −0.439881 0.761896i
663663 0 0
664664 −8.13850 + 14.0963i −0.315835 + 0.547043i
665665 −10.0080 + 2.68162i −0.388092 + 0.103989i
666666 0 0
667667 −0.517893 + 0.299006i −0.0200529 + 0.0115776i
668668 −15.3104 + 4.10240i −0.592376 + 0.158727i
669669 0 0
670670 −1.53185 + 0.410458i −0.0591806 + 0.0158574i
671671 −15.8863 4.25671i −0.613282 0.164328i
672672 0 0
673673 3.60027 2.07862i 0.138780 0.0801248i −0.429002 0.903303i 0.641135π-0.641135\pi
0.567783 + 0.823179i 0.307801π0.307801\pi
674674 8.06823 + 30.1111i 0.310777 + 1.15983i
675675 0 0
676676 10.3892 + 7.81438i 0.399585 + 0.300553i
677677 −17.6062 10.1649i −0.676659 0.390669i 0.121936 0.992538i 0.461090π-0.461090\pi
−0.798595 + 0.601869i 0.794423π0.794423\pi
678678 0 0
679679 −12.4529 −0.477899
680680 2.33922 4.05164i 0.0897048 0.155373i
681681 0 0
682682 36.3010 36.3010i 1.39004 1.39004i
683683 9.85750 + 2.64131i 0.377187 + 0.101067i 0.442431 0.896802i 0.354116π-0.354116\pi
−0.0652445 + 0.997869i 0.520783π0.520783\pi
684684 0 0
685685 −4.06868 7.04716i −0.155456 0.269258i
686686 6.56341 + 11.3682i 0.250592 + 0.434038i
687687 0 0
688688 −7.25776 + 4.19027i −0.276699 + 0.159753i
689689 −9.97196 0.605472i −0.379901 0.0230666i
690690 0 0
691691 40.8703 + 10.9512i 1.55478 + 0.416602i 0.931006 0.365004i 0.118932π-0.118932\pi
0.623773 + 0.781606i 0.285599π0.285599\pi
692692 −2.25559 1.30226i −0.0857445 0.0495046i
693693 0 0
694694 14.3954 14.3954i 0.546444 0.546444i
695695 −2.25093 2.25093i −0.0853826 0.0853826i
696696 0 0
697697 1.41743 5.28992i 0.0536890 0.200370i
698698 25.4656 + 14.7026i 0.963888 + 0.556501i
699699 0 0
700700 −0.797249 + 2.97537i −0.0301332 + 0.112458i
701701 16.7670 0.633280 0.316640 0.948546i 0.397445π-0.397445\pi
0.316640 + 0.948546i 0.397445π0.397445\pi
702702 0 0
703703 59.3412 2.23810
704704 −1.50512 + 5.61718i −0.0567263 + 0.211705i
705705 0 0
706706 −9.93766 5.73751i −0.374009 0.215934i
707707 −2.66825 + 9.95805i −0.100350 + 0.374511i
708708 0 0
709709 9.05848 + 9.05848i 0.340198 + 0.340198i 0.856442 0.516244i 0.172670π-0.172670\pi
−0.516244 + 0.856442i 0.672670π0.672670\pi
710710 10.3708 10.3708i 0.389208 0.389208i
711711 0 0
712712 2.62264 + 1.51418i 0.0982875 + 0.0567463i
713713 4.94946 + 1.32620i 0.185359 + 0.0496667i
714714 0 0
715715 24.4535 + 16.1698i 0.914508 + 0.604717i
716716 3.11097 1.79612i 0.116262 0.0671242i
717717 0 0
718718 18.3660 + 31.8108i 0.685413 + 1.18717i
719719 8.63433 + 14.9551i 0.322006 + 0.557731i 0.980902 0.194503i 0.0623095π-0.0623095\pi
−0.658896 + 0.752234i 0.728976π0.728976\pi
720720 0 0
721721 9.63828 + 2.58257i 0.358948 + 0.0961799i
722722 24.5122 24.5122i 0.912248 0.912248i
723723 0 0
724724 −8.17213 + 14.1545i −0.303715 + 0.526050i
725725 3.13732 0.116517
726726 0 0
727727 12.1283 + 7.00226i 0.449813 + 0.259700i 0.707751 0.706462i 0.249710π-0.249710\pi
−0.257938 + 0.966161i 0.583043π0.583043\pi
728728 −0.221045 + 3.64054i −0.00819245 + 0.134928i
729729 0 0
730730 0.403364 + 1.50538i 0.0149292 + 0.0557165i
731731 −24.2852 + 14.0211i −0.898222 + 0.518589i
732732 0 0
733733 6.57489 + 1.76174i 0.242849 + 0.0650712i 0.378190 0.925728i 0.376546π-0.376546\pi
−0.135341 + 0.990799i 0.543213π0.543213\pi
734734 5.38262 1.44227i 0.198676 0.0532351i
735735 0 0
736736 −0.560658 + 0.150228i −0.0206661 + 0.00553747i
737737 5.71238 3.29805i 0.210418 0.121485i
738738 0 0
739739 −17.1161 + 4.58625i −0.629626 + 0.168708i −0.559500 0.828830i 0.689007π-0.689007\pi
−0.0701262 + 0.997538i 0.522340π0.522340\pi
740740 −5.66291 + 9.80845i −0.208173 + 0.360566i
741741 0 0
742742 −1.40143 2.42735i −0.0514481 0.0891108i
743743 −21.9872 21.9872i −0.806631 0.806631i 0.177491 0.984122i 0.443202π-0.443202\pi
−0.984122 + 0.177491i 0.943202π0.943202\pi
744744 0 0
745745 20.0986i 0.736354i
746746 2.03537 + 2.03537i 0.0745200 + 0.0745200i
747747 0 0
748748 −5.03629 + 18.7957i −0.184145 + 0.687238i
749749 2.59484 + 9.68407i 0.0948133 + 0.353848i
750750 0 0
751751 5.74389i 0.209598i −0.994493 0.104799i 0.966580π-0.966580\pi
0.994493 0.104799i 0.0334199π-0.0334199\pi
752752 −1.06206 + 1.06206i −0.0387294 + 0.0387294i
753753 0 0
754754 3.63983 0.742213i 0.132555 0.0270298i
755755 3.93738i 0.143296i
756756 0 0
757757 −13.1210 + 22.7262i −0.476891 + 0.825999i −0.999649 0.0264817i 0.991570π-0.991570\pi
0.522759 + 0.852481i 0.324903π0.324903\pi
758758 21.3259 0.774591
759759 0 0
760760 2.65097 + 9.89354i 0.0961606 + 0.358876i
761761 0.967626 + 3.61123i 0.0350764 + 0.130907i 0.981244 0.192771i 0.0617473π-0.0617473\pi
−0.946167 + 0.323678i 0.895081π0.895081\pi
762762 0 0
763763 −10.0084 −0.362328
764764 12.7189 22.0297i 0.460152 0.797007i
765765 0 0
766766 12.9795i 0.468969i
767767 −42.3394 + 8.63362i −1.52879 + 0.311742i
768768 0 0
769769 34.6441 34.6441i 1.24930 1.24930i 0.293266 0.956031i 0.405258π-0.405258\pi
0.956031 0.293266i 0.0947421π-0.0947421\pi
770770 8.22486i 0.296403i
771771 0 0
772772 −3.26525 12.1861i −0.117519 0.438586i
773773 −1.60335 + 5.98377i −0.0576683 + 0.215221i −0.988747 0.149597i 0.952202π-0.952202\pi
0.931079 + 0.364818i 0.118869π0.118869\pi
774774 0 0
775775 −19.0085 19.0085i −0.682806 0.682806i
776776 12.3105i 0.441923i
777777 0 0
778778 22.1340 + 22.1340i 0.793543 + 0.793543i
779779 5.99491 + 10.3835i 0.214790 + 0.372027i
780780 0 0
781781 −30.5007 + 52.8288i −1.09140 + 1.89036i
782782 −1.87602 + 0.502678i −0.0670864 + 0.0179757i
783783 0 0
784784 5.17601 2.98837i 0.184857 0.106727i
785785 −10.6397 + 2.85089i −0.379746 + 0.101753i
786786 0 0
787787 −19.0056 + 5.09254i −0.677477 + 0.181529i −0.581121 0.813817i 0.697386π-0.697386\pi
−0.0963566 + 0.995347i 0.530719π0.530719\pi
788788 0.680083 + 0.182228i 0.0242270 + 0.00649159i
789789 0 0
790790 −2.00334 + 1.15663i −0.0712757 + 0.0411511i
791791 2.65669 + 9.91492i 0.0944612 + 0.352534i
792792 0 0
793793 −0.618001 + 10.1783i −0.0219459 + 0.361443i
794794 −2.15790 1.24586i −0.0765809 0.0442140i
795795 0 0
796796 −9.91471 −0.351418
797797 −2.20478 + 3.81880i −0.0780974 + 0.135269i −0.902429 0.430839i 0.858218π-0.858218\pi
0.824332 + 0.566107i 0.191551π0.191551\pi
798798 0 0
799799 −3.55377 + 3.55377i −0.125723 + 0.125723i
800800 2.94136 + 0.788134i 0.103993 + 0.0278647i
801801 0 0
802802 10.2566 + 17.7649i 0.362172 + 0.627301i
803803 −3.24105 5.61366i −0.114374 0.198102i
804804 0 0
805805 −0.710950 + 0.410467i −0.0250577 + 0.0144671i
806806 −26.5501 17.5562i −0.935186 0.618390i
807807 0 0
808808 9.84420 + 2.63775i 0.346318 + 0.0927956i
809809 −17.1929 9.92632i −0.604470 0.348991i 0.166328 0.986070i 0.446809π-0.446809\pi
−0.770798 + 0.637080i 0.780142π0.780142\pi
810810 0 0
811811 6.11440 6.11440i 0.214706 0.214706i −0.591557 0.806263i 0.701487π-0.701487\pi
0.806263 + 0.591557i 0.201487π0.201487\pi
812812 0.736944 + 0.736944i 0.0258617 + 0.0258617i
813813 0 0
814814 12.1921 45.5017i 0.427334 1.59483i
815815 −8.37528 4.83547i −0.293373 0.169379i
816816 0 0
817817 15.8897 59.3011i 0.555910 2.07468i
818818 −9.79619 −0.342516
819819 0 0
820820 −2.28837 −0.0799133
821821 −8.40409 + 31.3645i −0.293305 + 1.09463i 0.649250 + 0.760575i 0.275083π0.275083\pi
−0.942554 + 0.334053i 0.891584π0.891584\pi
822822 0 0
823823 2.45985 + 1.42019i 0.0857448 + 0.0495048i 0.542259 0.840211i 0.317569π-0.317569\pi
−0.456515 + 0.889716i 0.650902π0.650902\pi
824824 2.55304 9.52809i 0.0889395 0.331927i
825825 0 0
826826 −8.57233 8.57233i −0.298269 0.298269i
827827 0.354454 0.354454i 0.0123256 0.0123256i −0.700917 0.713243i 0.747226π-0.747226\pi
0.713243 + 0.700917i 0.247226π0.247226\pi
828828 0 0
829829 −12.9034 7.44977i −0.448153 0.258741i 0.258897 0.965905i 0.416641π-0.416641\pi
−0.707050 + 0.707164i 0.749974π0.749974\pi
830830 21.9826 + 5.89022i 0.763027 + 0.204452i
831831 0 0
832832 3.59892 + 0.218517i 0.124770 + 0.00757573i
833833 17.3195 9.99940i 0.600084 0.346459i
834834 0 0
835835 11.0808 + 19.1926i 0.383468 + 0.664186i
836836 −21.3006 36.8937i −0.736696 1.27600i
837837 0 0
838838 1.67290 + 0.448252i 0.0577893 + 0.0154846i
839839 8.50311 8.50311i 0.293560 0.293560i −0.544925 0.838485i 0.683442π-0.683442\pi
0.838485 + 0.544925i 0.183442π0.183442\pi
840840 0 0
841841 −13.9693 + 24.1955i −0.481699 + 0.834327i
842842 3.55532 0.122524
843843 0 0
844844 5.22116 + 3.01444i 0.179720 + 0.103761i
845845 6.79398 16.8587i 0.233720 0.579958i
846846 0 0
847847 −5.97405 22.2955i −0.205271 0.766081i
848848 −2.39960 + 1.38541i −0.0824025 + 0.0475751i
849849 0 0
850850 9.84209 + 2.63718i 0.337581 + 0.0904545i
851851 4.54158 1.21691i 0.155683 0.0417152i
852852 0 0
853853 −11.7087 + 3.13735i −0.400900 + 0.107421i −0.453635 0.891188i 0.649873π-0.649873\pi
0.0527349 + 0.998609i 0.483206π0.483206\pi
854854 −2.47758 + 1.43043i −0.0847811 + 0.0489484i
855855 0 0
856856 9.57335 2.56517i 0.327211 0.0876758i
857857 23.9473 41.4780i 0.818025 1.41686i −0.0891105 0.996022i 0.528402π-0.528402\pi
0.907135 0.420839i 0.138264π-0.138264\pi
858858 0 0
859859 −26.9704 46.7142i −0.920220 1.59387i −0.799074 0.601232i 0.794677π-0.794677\pi
−0.121145 0.992635i 0.538657π-0.538657\pi
860860 8.28548 + 8.28548i 0.282532 + 0.282532i
861861 0 0
862862 14.8271i 0.505012i
863863 −23.3989 23.3989i −0.796508 0.796508i 0.186035 0.982543i 0.440436π-0.440436\pi
−0.982543 + 0.186035i 0.940436π0.940436\pi
864864 0 0
865865 −0.942509 + 3.51749i −0.0320463 + 0.119598i
866866 2.97320 + 11.0962i 0.101034 + 0.377063i
867867 0 0
868868 8.93004i 0.303105i
869869 6.80336 6.80336i 0.230788 0.230788i
870870 0 0
871871 −2.71123 3.06175i −0.0918665 0.103743i
872872 9.89396i 0.335052i
873873 0 0
874874 2.12604 3.68241i 0.0719144 0.124559i
875875 11.3785 0.384665
876876 0 0
877877 2.46001 + 9.18088i 0.0830686 + 0.310016i 0.994941 0.100456i 0.0320303π-0.0320303\pi
−0.911873 + 0.410473i 0.865364π0.865364\pi
878878 10.5345 + 39.3153i 0.355523 + 1.32683i
879879 0 0
880880 8.13083 0.274090
881881 −12.5122 + 21.6718i −0.421548 + 0.730143i −0.996091 0.0883317i 0.971846π-0.971846\pi
0.574543 + 0.818474i 0.305180π0.305180\pi
882882 0 0
883883 36.5915i 1.23140i −0.787980 0.615701i 0.788873π-0.788873\pi
0.787980 0.615701i 0.211127π-0.211127\pi
884884 12.0424 + 0.731182i 0.405029 + 0.0245923i
885885 0 0
886886 −8.71483 + 8.71483i −0.292780 + 0.292780i
887887 48.8136i 1.63900i 0.573079 + 0.819500i 0.305749π0.305749\pi
−0.573079 + 0.819500i 0.694251π0.694251\pi
888888 0 0
889889 3.96353 + 14.7921i 0.132933 + 0.496111i
890890 1.09588 4.08989i 0.0367341 0.137094i
891891 0 0
892892 −20.6159 20.6159i −0.690271 0.690271i
893893 11.0030i 0.368202i
894894 0 0
895895 −3.55149 3.55149i −0.118713 0.118713i
896896 0.505782 + 0.876041i 0.0168970 + 0.0292665i
897897 0 0
898898 14.1615 24.5285i 0.472577 0.818527i
899899 −8.78535 + 2.35403i −0.293008 + 0.0785112i
900900 0 0
901901 −8.02931 + 4.63572i −0.267495 + 0.154438i
902902 9.19356 2.46341i 0.306112 0.0820225i
903903 0 0
904904 9.80156 2.62632i 0.325995 0.0873501i
905905 22.0734 + 5.91456i 0.733745 + 0.196606i
906906 0 0
907907 7.29873 4.21392i 0.242350 0.139921i −0.373906 0.927467i 0.621982π-0.621982\pi
0.616256 + 0.787546i 0.288648π0.288648\pi
908908 3.75404 + 14.0103i 0.124582 + 0.464947i
909909 0 0
910910 4.99666 1.01889i 0.165638 0.0337758i
911911 −7.11409 4.10732i −0.235700 0.136082i 0.377499 0.926010i 0.376784π-0.376784\pi
−0.613199 + 0.789929i 0.710118π0.710118\pi
912912 0 0
913913 −94.6562 −3.13266
914914 −15.0632 + 26.0902i −0.498245 + 0.862986i
915915 0 0
916916 6.97743 6.97743i 0.230541 0.230541i
917917 3.71262 + 0.994793i 0.122601 + 0.0328510i
918918 0 0
919919 11.5951 + 20.0833i 0.382488 + 0.662488i 0.991417 0.130736i 0.0417341π-0.0417341\pi
−0.608929 + 0.793224i 0.708401π0.708401\pi
920920 0.405774 + 0.702822i 0.0133780 + 0.0231714i
921921 0 0
922922 −24.6586 + 14.2366i −0.812087 + 0.468859i
923923 35.8722 + 11.9850i 1.18075 + 0.394491i
924924 0 0
925925 −23.8263 6.38424i −0.783404 0.209912i
926926 −3.13507 1.81003i −0.103025 0.0594814i
927927 0 0
928928 0.728518 0.728518i 0.0239148 0.0239148i
929929 4.98880 + 4.98880i 0.163677 + 0.163677i 0.784194 0.620516i 0.213077π-0.213077\pi
−0.620516 + 0.784194i 0.713077π0.713077\pi
930930 0 0
931931 −11.3320 + 42.2917i −0.371392 + 1.38605i
932932 −1.79101 1.03404i −0.0586664 0.0338711i
933933 0 0
934934 −9.47885 + 35.3755i −0.310157 + 1.15752i
935935 27.2066 0.889752
936936 0 0
937937 −46.7071 −1.52585 −0.762927 0.646484i 0.776239π-0.776239\pi
−0.762927 + 0.646484i 0.776239π0.776239\pi
938938 0.296963 1.10828i 0.00969618 0.0361867i
939939 0 0
940940 1.81868 + 1.05001i 0.0593187 + 0.0342476i
941941 −10.1255 + 37.7889i −0.330082 + 1.23188i 0.579022 + 0.815312i 0.303435π0.303435\pi
−0.909104 + 0.416570i 0.863232π0.863232\pi
942942 0 0
943943 0.671745 + 0.671745i 0.0218750 + 0.0218750i
944944 −8.47432 + 8.47432i −0.275816 + 0.275816i
945945 0 0
946946 −42.2063 24.3678i −1.37224 0.792266i
947947 49.7829 + 13.3393i 1.61773 + 0.433469i 0.950333 0.311236i 0.100743π-0.100743\pi
0.667394 + 0.744705i 0.267410π0.267410\pi
948948 0 0
949949 −3.00883 + 2.66437i −0.0976708 + 0.0864891i
950950 −19.3189 + 11.1538i −0.626787 + 0.361876i
951951 0 0
952952 1.69240 + 2.93133i 0.0548511 + 0.0950048i
953953 16.8331 + 29.1557i 0.545276 + 0.944446i 0.998589 + 0.0530947i 0.0169085π0.0169085\pi
−0.453313 + 0.891351i 0.649758π0.649758\pi
954954 0 0
955955 −34.3544 9.20524i −1.11168 0.297875i
956956 13.9589 13.9589i 0.451463 0.451463i
957957 0 0
958958 2.52454 4.37263i 0.0815641 0.141273i
959959 5.88730 0.190111
960960 0 0
961961 40.6449 + 23.4663i 1.31112 + 0.756978i
962962 −29.1529 1.77009i −0.939927 0.0570699i
963963 0 0
964964 2.62479 + 9.79587i 0.0845389 + 0.315504i
965965 −15.2760 + 8.81963i −0.491753 + 0.283914i
966966 0 0
967967 41.2138 + 11.0432i 1.32535 + 0.355126i 0.850979 0.525200i 0.176010π-0.176010\pi
0.474369 + 0.880326i 0.342676π0.342676\pi
968968 −22.0406 + 5.90575i −0.708410 + 0.189818i
969969 0 0
970970 16.6258 4.45486i 0.533821 0.143037i
971971 19.5275 11.2742i 0.626666 0.361806i −0.152794 0.988258i 0.548827π-0.548827\pi
0.779460 + 0.626452i 0.215494π0.215494\pi
972972 0 0
973973 2.22461 0.596082i 0.0713177 0.0191095i
974974 −14.8115 + 25.6543i −0.474592 + 0.822018i
975975 0 0
976976 1.41408 + 2.44926i 0.0452635 + 0.0783987i
977977 −16.8832 16.8832i −0.540141 0.540141i 0.383429 0.923570i 0.374743π-0.374743\pi
−0.923570 + 0.383429i 0.874743π0.874743\pi
978978 0 0
979979 17.6109i 0.562847i
980980 −5.90894 5.90894i −0.188754 0.188754i
981981 0 0
982982 0.511224 1.90791i 0.0163138 0.0608839i
983983 −6.76555 25.2494i −0.215788 0.805330i −0.985888 0.167407i 0.946461π-0.946461\pi
0.770100 0.637923i 0.220206π-0.220206\pi
984984 0 0
985985 0.984416i 0.0313661i
986986 2.43770 2.43770i 0.0776322 0.0776322i
987987 0 0
988988 −19.7745 + 17.5106i −0.629109 + 0.557087i
989989 4.86436i 0.154678i
990990 0 0
991991 −5.16138 + 8.93977i −0.163957 + 0.283981i −0.936284 0.351243i 0.885759π-0.885759\pi
0.772328 + 0.635224i 0.219092π0.219092\pi
992992 −8.82795 −0.280288
993993 0 0
994994 2.74635 + 10.2495i 0.0871089 + 0.325095i
995995 3.58787 + 13.3901i 0.113743 + 0.424495i
996996 0 0
997997 34.0368 1.07796 0.538978 0.842320i 0.318811π-0.318811\pi
0.538978 + 0.842320i 0.318811π0.318811\pi
998998 −2.00437 + 3.47166i −0.0634471 + 0.109894i
999999 0 0
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 702.2.bc.a.305.10 56
3.2 odd 2 234.2.z.a.227.7 yes 56
9.4 even 3 234.2.y.a.149.10 yes 56
9.5 odd 6 702.2.bb.a.71.3 56
13.11 odd 12 702.2.bb.a.89.3 56
39.11 even 12 234.2.y.a.11.10 56
117.50 even 12 inner 702.2.bc.a.557.10 56
117.76 odd 12 234.2.z.a.167.7 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
234.2.y.a.11.10 56 39.11 even 12
234.2.y.a.149.10 yes 56 9.4 even 3
234.2.z.a.167.7 yes 56 117.76 odd 12
234.2.z.a.227.7 yes 56 3.2 odd 2
702.2.bb.a.71.3 56 9.5 odd 6
702.2.bb.a.89.3 56 13.11 odd 12
702.2.bc.a.305.10 56 1.1 even 1 trivial
702.2.bc.a.557.10 56 117.50 even 12 inner