Properties

Label 200.6.f.d.149.10
Level 200200
Weight 66
Character 200.149
Analytic conductor 32.07732.077
Analytic rank 00
Dimension 4040
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [200,6,Mod(149,200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("200.149");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 200=2352 200 = 2^{3} \cdot 5^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 200.f (of order 22, degree 11, 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: 32.076763962632.0767639626
Analytic rank: 00
Dimension: 4040
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 149.10
Character χ\chi == 200.149
Dual form 200.6.f.d.149.9

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+(4.83252+2.94053i)q20.457817q3+(14.706528.4204i)q4+(2.212411.34622i)q6195.837iq7+(12.5013+180.587i)q8242.790q9358.513iq11+(6.73290+13.0113i)q12951.826q13+(575.865+946.387i)q14+(591.435835.931i)q16+2101.46iq17+(1173.29713.933i)q182882.77iq19+89.6574iq21+(1054.22+1732.52i)q22+1537.16iq23+(5.7232882.6758i)q24+(4599.722798.88i)q26+222.403q27+(5565.762880.09i)q28+3875.11iq29+5182.92q31+(5316.20+2300.52i)q32+164.133iq33+(6179.4110155.4i)q34+(3570.61+6900.19i)q36+9494.97q37+(8476.87+13931.0i)q38+435.762q39+3802.93q41+(263.641433.272i)q42+4330.63q43+(10189.15272.49i)q44+(4520.087428.38i)q46+12506.7iq47+(270.769+382.703i)q4821545.1q49962.084iq51+(13998.1+27051.3i)q5225075.5q53+(1074.77+653.983i)q54+(35365.62448.21i)q56+1319.78iq57+(11394.918726.5i)q58+18453.8iq59+17488.7iq61+(25046.6+15240.5i)q62+47547.3iq63+(32455.4+4515.13i)q64+(482.639793.177i)q66+7490.73q67+(59724.3+30905.2i)q68703.739iq69+1056.69q71+(3035.1943844.8i)q72+55286.5iq73+(45884.7+27920.3i)q74+(81929.342395.6i)q7670210.1q77+(2105.83+1281.37i)q7889387.0q79+58896.2q81+(18377.8+11182.6i)q82103847.q83+(2548.10+1318.55i)q84+(20927.8+12734.3i)q861774.09iq87+(64742.84481.86i)q88+38137.1q89+186403.iq91+(43686.8+22606.4i)q922372.83q93+(36776.360438.8i)q94+(2433.851053.22i)q9622739.9iq97+(104117.63354.2i)q98+87043.5iq99+O(q100)q+(-4.83252 + 2.94053i) q^{2} -0.457817 q^{3} +(14.7065 - 28.4204i) q^{4} +(2.21241 - 1.34622i) q^{6} -195.837i q^{7} +(12.5013 + 180.587i) q^{8} -242.790 q^{9} -358.513i q^{11} +(-6.73290 + 13.0113i) q^{12} -951.826 q^{13} +(575.865 + 946.387i) q^{14} +(-591.435 - 835.931i) q^{16} +2101.46i q^{17} +(1173.29 - 713.933i) q^{18} -2882.77i q^{19} +89.6574i q^{21} +(1054.22 + 1732.52i) q^{22} +1537.16i q^{23} +(-5.72328 - 82.6758i) q^{24} +(4599.72 - 2798.88i) q^{26} +222.403 q^{27} +(-5565.76 - 2880.09i) q^{28} +3875.11i q^{29} +5182.92 q^{31} +(5316.20 + 2300.52i) q^{32} +164.133i q^{33} +(-6179.41 - 10155.4i) q^{34} +(-3570.61 + 6900.19i) q^{36} +9494.97 q^{37} +(8476.87 + 13931.0i) q^{38} +435.762 q^{39} +3802.93 q^{41} +(-263.641 - 433.272i) q^{42} +4330.63 q^{43} +(-10189.1 - 5272.49i) q^{44} +(-4520.08 - 7428.38i) q^{46} +12506.7i q^{47} +(270.769 + 382.703i) q^{48} -21545.1 q^{49} -962.084i q^{51} +(-13998.1 + 27051.3i) q^{52} -25075.5 q^{53} +(-1074.77 + 653.983i) q^{54} +(35365.6 - 2448.21i) q^{56} +1319.78i q^{57} +(-11394.9 - 18726.5i) q^{58} +18453.8i q^{59} +17488.7i q^{61} +(-25046.6 + 15240.5i) q^{62} +47547.3i q^{63} +(-32455.4 + 4515.13i) q^{64} +(-482.639 - 793.177i) q^{66} +7490.73 q^{67} +(59724.3 + 30905.2i) q^{68} -703.739i q^{69} +1056.69 q^{71} +(-3035.19 - 43844.8i) q^{72} +55286.5i q^{73} +(-45884.7 + 27920.3i) q^{74} +(-81929.3 - 42395.6i) q^{76} -70210.1 q^{77} +(-2105.83 + 1281.37i) q^{78} -89387.0 q^{79} +58896.2 q^{81} +(-18377.8 + 11182.6i) q^{82} -103847. q^{83} +(2548.10 + 1318.55i) q^{84} +(-20927.8 + 12734.3i) q^{86} -1774.09i q^{87} +(64742.8 - 4481.86i) q^{88} +38137.1 q^{89} +186403. i q^{91} +(43686.8 + 22606.4i) q^{92} -2372.83 q^{93} +(-36776.3 - 60438.8i) q^{94} +(-2433.85 - 1053.22i) q^{96} -22739.9i q^{97} +(104117. - 63354.2i) q^{98} +87043.5i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q2q4+66q6+3240q9+848q14110q1618918q24+18344q26+14320q31+19182q34+29656q3644904q3911608q41+23186q4475224q46125304q49++115582q96+O(q100) 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49}+ \cdots + 115582 q^{96}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/200Z)×\left(\mathbb{Z}/200\mathbb{Z}\right)^\times.

nn 101101 151151 177177
χ(n)\chi(n) 1-1 11 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −4.83252 + 2.94053i −0.854277 + 0.519817i
33 −0.457817 −0.0293689 −0.0146845 0.999892i 0.504674π-0.504674\pi
−0.0146845 + 0.999892i 0.504674π0.504674\pi
44 14.7065 28.4204i 0.459580 0.888137i
55 0 0
66 2.21241 1.34622i 0.0250892 0.0152665i
77 195.837i 1.51060i −0.655379 0.755300i 0.727491π-0.727491\pi
0.655379 0.755300i 0.272509π-0.272509\pi
88 12.5013 + 180.587i 0.0690604 + 0.997612i
99 −242.790 −0.999137
1010 0 0
1111 358.513i 0.893353i −0.894696 0.446676i 0.852608π-0.852608\pi
0.894696 0.446676i 0.147392π-0.147392\pi
1212 −6.73290 + 13.0113i −0.0134974 + 0.0260836i
1313 −951.826 −1.56207 −0.781033 0.624490i 0.785307π-0.785307\pi
−0.781033 + 0.624490i 0.785307π0.785307\pi
1414 575.865 + 946.387i 0.785237 + 1.29047i
1515 0 0
1616 −591.435 835.931i −0.577573 0.816339i
1717 2101.46i 1.76360i 0.471628 + 0.881798i 0.343667π0.343667\pi
−0.471628 + 0.881798i 0.656333π0.656333\pi
1818 1173.29 713.933i 0.853541 0.519369i
1919 2882.77i 1.83200i −0.401178 0.916000i 0.631399π-0.631399\pi
0.401178 0.916000i 0.368601π-0.368601\pi
2020 0 0
2121 89.6574i 0.0443648i
2222 1054.22 + 1732.52i 0.464380 + 0.763171i
2323 1537.16i 0.605899i 0.953007 + 0.302950i 0.0979714π0.0979714\pi
−0.953007 + 0.302950i 0.902029π0.902029\pi
2424 −5.72328 82.6758i −0.00202823 0.0292988i
2525 0 0
2626 4599.72 2798.88i 1.33444 0.811989i
2727 222.403 0.0587126
2828 −5565.76 2880.09i −1.34162 0.694241i
2929 3875.11i 0.855636i 0.903865 + 0.427818i 0.140718π0.140718\pi
−0.903865 + 0.427818i 0.859282π0.859282\pi
3030 0 0
3131 5182.92 0.968658 0.484329 0.874886i 0.339064π-0.339064\pi
0.484329 + 0.874886i 0.339064π0.339064\pi
3232 5316.20 + 2300.52i 0.917755 + 0.397147i
3333 164.133i 0.0262368i
3434 −6179.41 10155.4i −0.916748 1.50660i
3535 0 0
3636 −3570.61 + 6900.19i −0.459183 + 0.887371i
3737 9494.97 1.14022 0.570111 0.821568i 0.306900π-0.306900\pi
0.570111 + 0.821568i 0.306900π0.306900\pi
3838 8476.87 + 13931.0i 0.952306 + 1.56504i
3939 435.762 0.0458762
4040 0 0
4141 3802.93 0.353312 0.176656 0.984273i 0.443472π-0.443472\pi
0.176656 + 0.984273i 0.443472π0.443472\pi
4242 −263.641 433.272i −0.0230616 0.0378998i
4343 4330.63 0.357174 0.178587 0.983924i 0.442847π-0.442847\pi
0.178587 + 0.983924i 0.442847π0.442847\pi
4444 −10189.1 5272.49i −0.793419 0.410567i
4545 0 0
4646 −4520.08 7428.38i −0.314957 0.517606i
4747 12506.7i 0.825842i 0.910767 + 0.412921i 0.135492π0.135492\pi
−0.910767 + 0.412921i 0.864508π0.864508\pi
4848 270.769 + 382.703i 0.0169627 + 0.0239750i
4949 −21545.1 −1.28191
5050 0 0
5151 962.084i 0.0517949i
5252 −13998.1 + 27051.3i −0.717894 + 1.38733i
5353 −25075.5 −1.22620 −0.613099 0.790006i 0.710077π-0.710077\pi
−0.613099 + 0.790006i 0.710077π0.710077\pi
5454 −1074.77 + 653.983i −0.0501568 + 0.0305198i
5555 0 0
5656 35365.6 2448.21i 1.50699 0.104323i
5757 1319.78i 0.0538039i
5858 −11394.9 18726.5i −0.444774 0.730950i
5959 18453.8i 0.690171i 0.938571 + 0.345085i 0.112150π0.112150\pi
−0.938571 + 0.345085i 0.887850π0.887850\pi
6060 0 0
6161 17488.7i 0.601774i 0.953660 + 0.300887i 0.0972827π0.0972827\pi
−0.953660 + 0.300887i 0.902717π0.902717\pi
6262 −25046.6 + 15240.5i −0.827502 + 0.503525i
6363 47547.3i 1.50930i
6464 −32455.4 + 4515.13i −0.990461 + 0.137791i
6565 0 0
6666 −482.639 793.177i −0.0136384 0.0224135i
6767 7490.73 0.203862 0.101931 0.994791i 0.467498π-0.467498\pi
0.101931 + 0.994791i 0.467498π0.467498\pi
6868 59724.3 + 30905.2i 1.56631 + 0.810513i
6969 703.739i 0.0177946i
7070 0 0
7171 1056.69 0.0248773 0.0124387 0.999923i 0.496041π-0.496041\pi
0.0124387 + 0.999923i 0.496041π0.496041\pi
7272 −3035.19 43844.8i −0.0690008 0.996752i
7373 55286.5i 1.21426i 0.794602 + 0.607130i 0.207679π0.207679\pi
−0.794602 + 0.607130i 0.792321π0.792321\pi
7474 −45884.7 + 27920.3i −0.974066 + 0.592707i
7575 0 0
7676 −81929.3 42395.6i −1.62707 0.841950i
7777 −70210.1 −1.34950
7878 −2105.83 + 1281.37i −0.0391910 + 0.0238473i
7979 −89387.0 −1.61141 −0.805706 0.592316i 0.798214π-0.798214\pi
−0.805706 + 0.592316i 0.798214π0.798214\pi
8080 0 0
8181 58896.2 0.997413
8282 −18377.8 + 11182.6i −0.301827 + 0.183658i
8383 −103847. −1.65462 −0.827310 0.561746i 0.810130π-0.810130\pi
−0.827310 + 0.561746i 0.810130π0.810130\pi
8484 2548.10 + 1318.55i 0.0394020 + 0.0203891i
8585 0 0
8686 −20927.8 + 12734.3i −0.305125 + 0.185665i
8787 1774.09i 0.0251291i
8888 64742.8 4481.86i 0.891220 0.0616953i
8989 38137.1 0.510355 0.255178 0.966894i 0.417866π-0.417866\pi
0.255178 + 0.966894i 0.417866π0.417866\pi
9090 0 0
9191 186403.i 2.35966i
9292 43686.8 + 22606.4i 0.538121 + 0.278459i
9393 −2372.83 −0.0284485
9494 −36776.3 60438.8i −0.429287 0.705498i
9595 0 0
9696 −2433.85 1053.22i −0.0269535 0.0116638i
9797 22739.9i 0.245391i −0.992444 0.122696i 0.960846π-0.960846\pi
0.992444 0.122696i 0.0391539π-0.0391539\pi
9898 104117. 63354.2i 1.09511 0.666362i
9999 87043.5i 0.892582i
100100 0 0
101101 52711.9i 0.514168i −0.966389 0.257084i 0.917238π-0.917238\pi
0.966389 0.257084i 0.0827618π-0.0827618\pi
102102 2829.04 + 4649.29i 0.0269239 + 0.0442473i
103103 38301.0i 0.355727i −0.984055 0.177863i 0.943081π-0.943081\pi
0.984055 0.177863i 0.0569185π-0.0569185\pi
104104 −11899.0 171888.i −0.107877 1.55834i
105105 0 0
106106 121178. 73735.4i 1.04751 0.637399i
107107 151431. 1.27866 0.639329 0.768933i 0.279212π-0.279212\pi
0.639329 + 0.768933i 0.279212π0.279212\pi
108108 3270.78 6320.77i 0.0269831 0.0521448i
109109 146420.i 1.18041i 0.807253 + 0.590206i 0.200953π0.200953\pi
−0.807253 + 0.590206i 0.799047π0.799047\pi
110110 0 0
111111 −4346.96 −0.0334871
112112 −163706. + 115825.i −1.23316 + 0.872482i
113113 59368.9i 0.437384i 0.975794 + 0.218692i 0.0701789π0.0701789\pi
−0.975794 + 0.218692i 0.929821π0.929821\pi
114114 −3880.85 6377.86i −0.0279682 0.0459635i
115115 0 0
116116 110132. + 56989.5i 0.759921 + 0.393233i
117117 231094. 1.56072
118118 −54264.1 89178.6i −0.358763 0.589597i
119119 411544. 2.66409
120120 0 0
121121 32519.6 0.201921
122122 −51426.1 84514.6i −0.312812 0.514082i
123123 −1741.05 −0.0103764
124124 76222.9 147300.i 0.445175 0.860300i
125125 0 0
126126 −139814. 229774.i −0.784559 1.28936i
127127 13242.9i 0.0728577i −0.999336 0.0364288i 0.988402π-0.988402\pi
0.999336 0.0364288i 0.0115982π-0.0115982\pi
128128 143565. 117256.i 0.774503 0.632571i
129129 −1982.63 −0.0104898
130130 0 0
131131 29434.9i 0.149860i −0.997189 0.0749298i 0.976127π-0.976127\pi
0.997189 0.0749298i 0.0238733π-0.0238733\pi
132132 4664.72 + 2413.83i 0.0233019 + 0.0120579i
133133 −564553. −2.76742
134134 −36199.1 + 22026.7i −0.174155 + 0.105971i
135135 0 0
136136 −379497. + 26270.9i −1.75938 + 0.121795i
137137 226821.i 1.03248i −0.856443 0.516241i 0.827331π-0.827331\pi
0.856443 0.516241i 0.172669π-0.172669\pi
138138 2069.37 + 3400.84i 0.00924996 + 0.0152016i
139139 206068.i 0.904637i −0.891856 0.452319i 0.850597π-0.850597\pi
0.891856 0.452319i 0.149403π-0.149403\pi
140140 0 0
141141 5725.76i 0.0242541i
142142 −5106.50 + 3107.24i −0.0212521 + 0.0129317i
143143 341242.i 1.39548i
144144 143595. + 202956.i 0.577075 + 0.815635i
145145 0 0
146146 −162572. 267173.i −0.631194 1.03732i
147147 9863.72 0.0376485
148148 139638. 269851.i 0.524023 1.01267i
149149 276062.i 1.01869i 0.860563 + 0.509344i 0.170112π0.170112\pi
−0.860563 + 0.509344i 0.829888π0.829888\pi
150150 0 0
151151 −88898.4 −0.317287 −0.158643 0.987336i 0.550712π-0.550712\pi
−0.158643 + 0.987336i 0.550712π0.550712\pi
152152 520591. 36038.2i 1.82763 0.126519i
153153 510215.i 1.76207i
154154 339292. 206455.i 1.15285 0.701493i
155155 0 0
156156 6408.55 12384.5i 0.0210838 0.0407444i
157157 −273937. −0.886954 −0.443477 0.896286i 0.646255π-0.646255\pi
−0.443477 + 0.896286i 0.646255π0.646255\pi
158158 431965. 262845.i 1.37659 0.837640i
159159 11480.0 0.0360122
160160 0 0
161161 301034. 0.915272
162162 −284617. + 173186.i −0.852067 + 0.518473i
163163 22520.3 0.0663902 0.0331951 0.999449i 0.489432π-0.489432\pi
0.0331951 + 0.999449i 0.489432π0.489432\pi
164164 55928.0 108081.i 0.162375 0.313790i
165165 0 0
166166 501842. 305365.i 1.41350 0.860100i
167167 4216.06i 0.0116981i 0.999983 + 0.00584906i 0.00186182π0.00186182\pi
−0.999983 + 0.00584906i 0.998138π0.998138\pi
168168 −16191.0 + 1120.83i −0.0442588 + 0.00306385i
169169 534680. 1.44005
170170 0 0
171171 699908.i 1.83042i
172172 63688.6 123078.i 0.164150 0.317219i
173173 −240365. −0.610599 −0.305299 0.952256i 0.598757π-0.598757\pi
−0.305299 + 0.952256i 0.598757π0.598757\pi
174174 5216.76 + 8573.32i 0.0130626 + 0.0214672i
175175 0 0
176176 −299692. + 212037.i −0.729279 + 0.515976i
177177 8448.47i 0.0202696i
178178 −184298. + 112143.i −0.435985 + 0.265292i
179179 245501.i 0.572691i 0.958126 + 0.286346i 0.0924406π0.0924406\pi
−0.958126 + 0.286346i 0.907559π0.907559\pi
180180 0 0
181181 16588.7i 0.0376370i 0.999823 + 0.0188185i 0.00599048π0.00599048\pi
−0.999823 + 0.0188185i 0.994010π0.994010\pi
182182 −548123. 900796.i −1.22659 2.01580i
183183 8006.62i 0.0176735i
184184 −277592. + 19216.5i −0.604453 + 0.0418436i
185185 0 0
186186 11466.7 6977.37i 0.0243029 0.0147880i
187187 753401. 1.57551
188188 355444. + 183930.i 0.733461 + 0.379540i
189189 43554.7i 0.0886912i
190190 0 0
191191 −555884. −1.10256 −0.551278 0.834322i 0.685860π-0.685860\pi
−0.551278 + 0.834322i 0.685860π0.685860\pi
192192 14858.6 2067.10i 0.0290888 0.00404678i
193193 397154.i 0.767477i 0.923442 + 0.383738i 0.125364π0.125364\pi
−0.923442 + 0.383738i 0.874636π0.874636\pi
194194 66867.3 + 109891.i 0.127559 + 0.209632i
195195 0 0
196196 −316855. + 612321.i −0.589142 + 1.13852i
197197 −722243. −1.32592 −0.662961 0.748654i 0.730700π-0.730700\pi
−0.662961 + 0.748654i 0.730700π0.730700\pi
198198 −255954. 420640.i −0.463980 0.762513i
199199 129890. 0.232511 0.116256 0.993219i 0.462911π-0.462911\pi
0.116256 + 0.993219i 0.462911π0.462911\pi
200200 0 0
201201 −3429.38 −0.00598722
202202 155001. + 254732.i 0.267274 + 0.439242i
203203 758890. 1.29252
204204 −27342.8 14148.9i −0.0460010 0.0238039i
205205 0 0
206206 112625. + 185090.i 0.184913 + 0.303889i
207207 373209.i 0.605377i
208208 562943. + 795661.i 0.902207 + 1.27518i
209209 −1.03351e6 −1.63662
210210 0 0
211211 608872.i 0.941499i 0.882267 + 0.470749i 0.156016π0.156016\pi
−0.882267 + 0.470749i 0.843984π0.843984\pi
212212 −368775. + 712656.i −0.563536 + 1.08903i
213213 −483.772 −0.000730620
214214 −731792. + 445287.i −1.09233 + 0.664669i
215215 0 0
216216 2780.32 + 40163.1i 0.00405471 + 0.0585724i
217217 1.01501e6i 1.46325i
218218 −430552. 707577.i −0.613598 1.00840i
219219 25311.1i 0.0356615i
220220 0 0
221221 2.00023e6i 2.75485i
222222 21006.8 12782.4i 0.0286073 0.0174072i
223223 22540.8i 0.0303534i −0.999885 0.0151767i 0.995169π-0.995169\pi
0.999885 0.0151767i 0.00483108π-0.00483108\pi
224224 450528. 1.04111e6i 0.599931 1.38636i
225225 0 0
226226 −174576. 286901.i −0.227360 0.373647i
227227 −150889. −0.194354 −0.0971770 0.995267i 0.530981π-0.530981\pi
−0.0971770 + 0.995267i 0.530981π0.530981\pi
228228 37508.6 + 19409.4i 0.0477852 + 0.0247272i
229229 724516.i 0.912976i 0.889730 + 0.456488i 0.150893π0.150893\pi
−0.889730 + 0.456488i 0.849107π0.849107\pi
230230 0 0
231231 32143.3 0.0396334
232232 −699795. + 48443.7i −0.853593 + 0.0590905i
233233 336561.i 0.406138i −0.979164 0.203069i 0.934908π-0.934908\pi
0.979164 0.203069i 0.0650916π-0.0650916\pi
234234 −1.11677e6 + 679540.i −1.33329 + 0.811289i
235235 0 0
236236 524465. + 271392.i 0.612966 + 0.317188i
237237 40922.8 0.0473255
238238 −1.98879e6 + 1.21016e6i −2.27587 + 1.38484i
239239 −330500. −0.374262 −0.187131 0.982335i 0.559919π-0.559919\pi
−0.187131 + 0.982335i 0.559919π0.559919\pi
240240 0 0
241241 900033. 0.998196 0.499098 0.866546i 0.333665π-0.333665\pi
0.499098 + 0.866546i 0.333665π0.333665\pi
242242 −157152. + 95624.9i −0.172497 + 0.104962i
243243 −81007.6 −0.0880055
244244 497036. + 257199.i 0.534457 + 0.276563i
245245 0 0
246246 8413.64 5119.60i 0.00886433 0.00539384i
247247 2.74389e6i 2.86171i
248248 64793.0 + 935969.i 0.0668958 + 0.966345i
249249 47542.8 0.0485944
250250 0 0
251251 963725.i 0.965537i 0.875748 + 0.482768i 0.160369π0.160369\pi
−0.875748 + 0.482768i 0.839631π0.839631\pi
252252 1.35131e6 + 699257.i 1.34046 + 0.693643i
253253 551093. 0.541282
254254 38941.3 + 63996.8i 0.0378727 + 0.0622406i
255255 0 0
256256 −348986. + 988798.i −0.332819 + 0.942991i
257257 1.50847e6i 1.42463i 0.701857 + 0.712317i 0.252354π0.252354\pi
−0.701857 + 0.712317i 0.747646π0.747646\pi
258258 9581.11 5829.99i 0.00896121 0.00545279i
259259 1.85947e6i 1.72242i
260260 0 0
261261 940839.i 0.854898i
262262 86554.3 + 142245.i 0.0778997 + 0.128022i
263263 721202.i 0.642936i 0.946920 + 0.321468i 0.104176π0.104176\pi
−0.946920 + 0.321468i 0.895824π0.895824\pi
264264 −29640.3 + 2051.87i −0.0261742 + 0.00181192i
265265 0 0
266266 2.72821e6 1.66008e6i 2.36415 1.43855i
267267 −17459.8 −0.0149886
268268 110163. 212889.i 0.0936910 0.181058i
269269 1.43076e6i 1.20556i −0.797909 0.602778i 0.794061π-0.794061\pi
0.797909 0.602778i 0.205939π-0.205939\pi
270270 0 0
271271 −1.94059e6 −1.60514 −0.802568 0.596561i 0.796533π-0.796533\pi
−0.802568 + 0.596561i 0.796533π0.796533\pi
272272 1.75668e6 1.24288e6i 1.43969 1.01861i
273273 85338.3i 0.0693007i
274274 666975. + 1.09612e6i 0.536702 + 0.882026i
275275 0 0
276276 −20000.5 10349.6i −0.0158041 0.00817805i
277277 −1.71081e6 −1.33968 −0.669842 0.742504i 0.733638π-0.733638\pi
−0.669842 + 0.742504i 0.733638π0.733638\pi
278278 605951. + 995830.i 0.470246 + 0.772811i
279279 −1.25836e6 −0.967822
280280 0 0
281281 1.44573e6 1.09225 0.546126 0.837703i 0.316102π-0.316102\pi
0.546126 + 0.837703i 0.316102π0.316102\pi
282282 16836.8 + 27669.9i 0.0126077 + 0.0207197i
283283 1.07186e6 0.795555 0.397777 0.917482i 0.369782π-0.369782\pi
0.397777 + 0.917482i 0.369782π0.369782\pi
284284 15540.3 30031.6i 0.0114331 0.0220944i
285285 0 0
286286 −1.00343e6 1.64906e6i −0.725393 1.19212i
287287 744755.i 0.533714i
288288 −1.29072e6 558545.i −0.916963 0.396805i
289289 −2.99628e6 −2.11027
290290 0 0
291291 10410.7i 0.00720688i
292292 1.57126e6 + 813073.i 1.07843 + 0.558049i
293293 −176850. −0.120347 −0.0601735 0.998188i 0.519165π-0.519165\pi
−0.0601735 + 0.998188i 0.519165π0.519165\pi
294294 −47666.7 + 29004.6i −0.0321622 + 0.0195703i
295295 0 0
296296 118699. + 1.71467e6i 0.0787442 + 1.13750i
297297 79734.3i 0.0524510i
298298 −811769. 1.33408e6i −0.529532 0.870242i
299299 1.46311e6i 0.946455i
300300 0 0
301301 848097.i 0.539547i
302302 429604. 261409.i 0.271051 0.164931i
303303 24132.4i 0.0151006i
304304 −2.40979e6 + 1.70497e6i −1.49553 + 1.05811i
305305 0 0
306306 1.50030e6 + 2.46562e6i 0.915957 + 1.50530i
307307 2.76503e6 1.67438 0.837189 0.546914i 0.184198π-0.184198\pi
0.837189 + 0.546914i 0.184198π0.184198\pi
308308 −1.03255e6 + 1.99540e6i −0.620202 + 1.19854i
309309 17534.8i 0.0104473i
310310 0 0
311311 748055. 0.438564 0.219282 0.975662i 0.429629π-0.429629\pi
0.219282 + 0.975662i 0.429629π0.429629\pi
312312 5447.57 + 78693.0i 0.00316823 + 0.0457667i
313313 2.84259e6i 1.64003i −0.572340 0.820017i 0.693964π-0.693964\pi
0.572340 0.820017i 0.306036π-0.306036\pi
314314 1.32381e6 805520.i 0.757705 0.461054i
315315 0 0
316316 −1.31457e6 + 2.54041e6i −0.740572 + 1.43115i
317317 −97492.6 −0.0544908 −0.0272454 0.999629i 0.508674π-0.508674\pi
−0.0272454 + 0.999629i 0.508674π0.508674\pi
318318 −55477.4 + 33757.3i −0.0307644 + 0.0187197i
319319 1.38928e6 0.764384
320320 0 0
321321 −69327.5 −0.0375528
322322 −1.45475e6 + 885199.i −0.781896 + 0.475774i
323323 6.05802e6 3.23091
324324 866161. 1.67385e6i 0.458391 0.885839i
325325 0 0
326326 −108830. + 66221.5i −0.0567157 + 0.0345108i
327327 67033.4i 0.0346674i
328328 47541.4 + 686761.i 0.0243999 + 0.352469i
329329 2.44927e6 1.24752
330330 0 0
331331 2.71471e6i 1.36193i −0.732317 0.680964i 0.761561π-0.761561\pi
0.732317 0.680964i 0.238439π-0.238439\pi
332332 −1.52723e6 + 2.95137e6i −0.760429 + 1.46953i
333333 −2.30529e6 −1.13924
334334 −12397.5 20374.2i −0.00608089 0.00999344i
335335 0 0
336336 74947.4 53026.5i 0.0362167 0.0256239i
337337 495886.i 0.237852i −0.992903 0.118926i 0.962055π-0.962055\pi
0.992903 0.118926i 0.0379452π-0.0379452\pi
338338 −2.58385e6 + 1.57224e6i −1.23020 + 0.748563i
339339 27180.0i 0.0128455i
340340 0 0
341341 1.85814e6i 0.865353i
342342 −2.05810e6 3.38232e6i −0.951484 1.56369i
343343 927903.i 0.425860i
344344 54138.3 + 782055.i 0.0246665 + 0.356321i
345345 0 0
346346 1.16157e6 706801.i 0.521621 0.317400i
347347 −3.14504e6 −1.40217 −0.701087 0.713076i 0.747302π-0.747302\pi
−0.701087 + 0.713076i 0.747302π0.747302\pi
348348 −50420.3 26090.7i −0.0223181 0.0115488i
349349 2.62573e6i 1.15395i 0.816762 + 0.576975i 0.195767π0.195767\pi
−0.816762 + 0.576975i 0.804233π0.804233\pi
350350 0 0
351351 −211689. −0.0917129
352352 824767. 1.90593e6i 0.354793 0.819879i
353353 536996.i 0.229369i −0.993402 0.114684i 0.963414π-0.963414\pi
0.993402 0.114684i 0.0365857π-0.0365857\pi
354354 24843.0 + 40827.4i 0.0105365 + 0.0173159i
355355 0 0
356356 560865. 1.08387e6i 0.234549 0.453265i
357357 −188412. −0.0782415
358358 −721903. 1.18639e6i −0.297695 0.489237i
359359 369981. 0.151511 0.0757553 0.997126i 0.475863π-0.475863\pi
0.0757553 + 0.997126i 0.475863π0.475863\pi
360360 0 0
361361 −5.83425e6 −2.35623
362362 −48779.5 80165.2i −0.0195644 0.0321525i
363363 −14888.0 −0.00593021
364364 5.29764e6 + 2.74134e6i 2.09570 + 1.08445i
365365 0 0
366366 23543.7 + 38692.2i 0.00918697 + 0.0150980i
367367 1.41712e6i 0.549214i 0.961557 + 0.274607i 0.0885478π0.0885478\pi
−0.961557 + 0.274607i 0.911452π0.911452\pi
368368 1.28496e6 909132.i 0.494619 0.349951i
369369 −923315. −0.353008
370370 0 0
371371 4.91072e6i 1.85230i
372372 −34896.1 + 67436.6i −0.0130743 + 0.0252661i
373373 2.16053e6 0.804060 0.402030 0.915626i 0.368305π-0.368305\pi
0.402030 + 0.915626i 0.368305π0.368305\pi
374374 −3.64083e6 + 2.21540e6i −1.34592 + 0.818979i
375375 0 0
376376 −2.25854e6 + 156349.i −0.823871 + 0.0570330i
377377 3.68843e6i 1.33656i
378378 128074. + 210479.i 0.0461033 + 0.0757669i
379379 1.60069e6i 0.572412i 0.958168 + 0.286206i 0.0923942π0.0923942\pi
−0.958168 + 0.286206i 0.907606π0.907606\pi
380380 0 0
381381 6062.84i 0.00213975i
382382 2.68632e6 1.63459e6i 0.941888 0.573128i
383383 3.07943e6i 1.07269i −0.844000 0.536344i 0.819805π-0.819805\pi
0.844000 0.536344i 0.180195π-0.180195\pi
384384 −65726.3 + 53681.6i −0.0227463 + 0.0185779i
385385 0 0
386386 −1.16784e6 1.91925e6i −0.398948 0.655638i
387387 −1.05143e6 −0.356866
388388 −646276. 334425.i −0.217941 0.112777i
389389 2.71294e6i 0.909006i −0.890745 0.454503i 0.849817π-0.849817\pi
0.890745 0.454503i 0.150183π-0.150183\pi
390390 0 0
391391 −3.23029e6 −1.06856
392392 −269341. 3.89078e6i −0.0885295 1.27885i
393393 13475.8i 0.00440122i
394394 3.49026e6 2.12378e6i 1.13270 0.689237i
395395 0 0
396396 2.47381e6 + 1.28011e6i 0.792735 + 0.410213i
397397 −4.05795e6 −1.29220 −0.646101 0.763252i 0.723601π-0.723601\pi
−0.646101 + 0.763252i 0.723601π0.723601\pi
398398 −627698. + 381947.i −0.198629 + 0.120863i
399399 258462. 0.0812762
400400 0 0
401401 5.22811e6 1.62362 0.811809 0.583923i 0.198483π-0.198483\pi
0.811809 + 0.583923i 0.198483π0.198483\pi
402402 16572.5 10084.2i 0.00511475 0.00311226i
403403 −4.93324e6 −1.51311
404404 −1.49809e6 775210.i −0.456652 0.236301i
405405 0 0
406406 −3.66735e6 + 2.23154e6i −1.10417 + 0.671876i
407407 3.40407e6i 1.01862i
408408 173740. 12027.3i 0.0516713 0.00357698i
409409 1.89554e6 0.560306 0.280153 0.959955i 0.409615π-0.409615\pi
0.280153 + 0.959955i 0.409615π0.409615\pi
410410 0 0
411411 103843.i 0.0303229i
412412 −1.08853e6 563275.i −0.315934 0.163485i
413413 3.61394e6 1.04257
414414 1.09743e6 + 1.80354e6i 0.314685 + 0.517160i
415415 0 0
416416 −5.06010e6 2.18970e6i −1.43359 0.620370i
417417 94341.5i 0.0265682i
418418 4.99445e6 3.03907e6i 1.39813 0.850745i
419419 663430.i 0.184612i −0.995731 0.0923060i 0.970576π-0.970576\pi
0.995731 0.0923060i 0.0294238π-0.0294238\pi
420420 0 0
421421 1.14330e6i 0.314381i −0.987568 0.157190i 0.949756π-0.949756\pi
0.987568 0.157190i 0.0502436π-0.0502436\pi
422422 −1.79041e6 2.94239e6i −0.489407 0.804301i
423423 3.03650e6i 0.825130i
424424 −313476. 4.52832e6i −0.0846817 1.22327i
425425 0 0
426426 2337.84 1422.55i 0.000624153 0.000379789i
427427 3.42494e6 0.909040
428428 2.22702e6 4.30372e6i 0.587645 1.13562i
429429 156226.i 0.0409837i
430430 0 0
431431 559165. 0.144993 0.0724964 0.997369i 0.476903π-0.476903\pi
0.0724964 + 0.997369i 0.476903π0.476903\pi
432432 −131537. 185914.i −0.0339108 0.0479294i
433433 4.04780e6i 1.03753i 0.854918 + 0.518764i 0.173608π0.173608\pi
−0.854918 + 0.518764i 0.826392π0.826392\pi
434434 2.98466e6 + 4.90505e6i 0.760625 + 1.25003i
435435 0 0
436436 4.16130e6 + 2.15333e6i 1.04837 + 0.542493i
437437 4.43129e6 1.11001
438438 74428.0 + 122316.i 0.0185375 + 0.0304649i
439439 4.17879e6 1.03488 0.517439 0.855720i 0.326886π-0.326886\pi
0.517439 + 0.855720i 0.326886π0.326886\pi
440440 0 0
441441 5.23095e6 1.28081
442442 5.88173e6 + 9.66614e6i 1.43202 + 2.35341i
443443 −6.19142e6 −1.49893 −0.749464 0.662045i 0.769689π-0.769689\pi
−0.749464 + 0.662045i 0.769689π0.769689\pi
444444 −63928.7 + 123542.i −0.0153900 + 0.0297411i
445445 0 0
446446 66281.9 + 108929.i 0.0157782 + 0.0259302i
447447 126386.i 0.0299178i
448448 884230. + 6.35598e6i 0.208147 + 1.49619i
449449 3.11618e6 0.729469 0.364735 0.931111i 0.381160π-0.381160\pi
0.364735 + 0.931111i 0.381160π0.381160\pi
450450 0 0
451451 1.36340e6i 0.315633i
452452 1.68728e6 + 873111.i 0.388456 + 0.201013i
453453 40699.2 0.00931837
454454 729175. 443694.i 0.166032 0.101029i
455455 0 0
456456 −238335. + 16498.9i −0.0536755 + 0.00371572i
457457 4.44694e6i 0.996026i 0.867170 + 0.498013i 0.165937π0.165937\pi
−0.867170 + 0.498013i 0.834063π0.834063\pi
458458 −2.13046e6 3.50124e6i −0.474581 0.779934i
459459 467371.i 0.103545i
460460 0 0
461461 7.51985e6i 1.64800i 0.566590 + 0.824000i 0.308262π0.308262\pi
−0.566590 + 0.824000i 0.691738π0.691738\pi
462462 −155333. + 94518.5i −0.0338579 + 0.0206021i
463463 4.34253e6i 0.941434i 0.882284 + 0.470717i 0.156005π0.156005\pi
−0.882284 + 0.470717i 0.843995π0.843995\pi
464464 3.23932e6 2.29187e6i 0.698489 0.494192i
465465 0 0
466466 989668. + 1.62644e6i 0.211118 + 0.346955i
467467 890290. 0.188903 0.0944515 0.995529i 0.469890π-0.469890\pi
0.0944515 + 0.995529i 0.469890π0.469890\pi
468468 3.39860e6 6.56779e6i 0.717274 1.38613i
469469 1.46696e6i 0.307955i
470470 0 0
471471 125413. 0.0260489
472472 −3.33253e6 + 230696.i −0.688523 + 0.0476634i
473473 1.55258e6i 0.319082i
474474 −197761. + 120335.i −0.0404291 + 0.0246006i
475475 0 0
476476 6.05239e6 1.16962e7i 1.22436 2.36607i
477477 6.08810e6 1.22514
478478 1.59715e6 971844.i 0.319724 0.194548i
479479 −3.93305e6 −0.783233 −0.391617 0.920128i 0.628084π-0.628084\pi
−0.391617 + 0.920128i 0.628084π0.628084\pi
480480 0 0
481481 −9.03757e6 −1.78110
482482 −4.34943e6 + 2.64657e6i −0.852736 + 0.518879i
483483 −137818. −0.0268806
484484 478251. 924219.i 0.0927988 0.179333i
485485 0 0
486486 391471. 238205.i 0.0751811 0.0457468i
487487 3.91119e6i 0.747286i −0.927573 0.373643i 0.878109π-0.878109\pi
0.927573 0.373643i 0.121891π-0.121891\pi
488488 −3.15824e6 + 218631.i −0.600337 + 0.0415587i
489489 −10310.1 −0.00194981
490490 0 0
491491 4.43336e6i 0.829907i −0.909843 0.414954i 0.863798π-0.863798\pi
0.909843 0.414954i 0.136202π-0.136202\pi
492492 −25604.8 + 49481.1i −0.00476879 + 0.00921567i
493493 −8.14339e6 −1.50900
494494 −8.06851e6 1.32599e7i −1.48756 2.44469i
495495 0 0
496496 −3.06536e6 4.33256e6i −0.559470 0.790753i
497497 206940.i 0.0375797i
498498 −229752. + 139801.i −0.0415131 + 0.0252602i
499499 4.84134e6i 0.870391i 0.900336 + 0.435196i 0.143321π0.143321\pi
−0.900336 + 0.435196i 0.856679π0.856679\pi
500500 0 0
501501 1930.18i 0.000343561i
502502 −2.83386e6 4.65722e6i −0.501903 0.824836i
503503 1.68379e6i 0.296735i 0.988932 + 0.148367i 0.0474018π0.0474018\pi
−0.988932 + 0.148367i 0.952598π0.952598\pi
504504 −8.58644e6 + 594402.i −1.50569 + 0.104233i
505505 0 0
506506 −2.66317e6 + 1.62051e6i −0.462405 + 0.281368i
507507 −244786. −0.0422927
508508 −376369. 194758.i −0.0647075 0.0334839i
509509 9.81220e6i 1.67869i 0.543595 + 0.839347i 0.317063π0.317063\pi
−0.543595 + 0.839347i 0.682937π0.682937\pi
510510 0 0
511511 1.08271e7 1.83426
512512 −1.22111e6 5.80459e6i −0.205864 0.978581i
513513 641136.i 0.107561i
514514 −4.43570e6 7.28971e6i −0.740550 1.21703i
515515 0 0
516516 −29157.7 + 56347.1i −0.00482091 + 0.00931639i
517517 4.48380e6 0.737768
518518 5.46782e6 + 8.98592e6i 0.895344 + 1.47142i
519519 110043. 0.0179326
520520 0 0
521521 −2.02601e6 −0.327000 −0.163500 0.986543i 0.552278π-0.552278\pi
−0.163500 + 0.986543i 0.552278π0.552278\pi
522522 2.76657e6 + 4.54663e6i 0.444391 + 0.730320i
523523 402702. 0.0643768 0.0321884 0.999482i 0.489752π-0.489752\pi
0.0321884 + 0.999482i 0.489752π0.489752\pi
524524 −836551. 432886.i −0.133096 0.0688724i
525525 0 0
526526 −2.12072e6 3.48523e6i −0.334209 0.549245i
527527 1.08917e7i 1.70832i
528528 137204. 97074.0i 0.0214181 0.0151537i
529529 4.07347e6 0.632886
530530 0 0
531531 4.48041e6i 0.689575i
532532 −8.30262e6 + 1.60448e7i −1.27185 + 2.45785i
533533 −3.61973e6 −0.551897
534534 84374.9 51341.1i 0.0128044 0.00779134i
535535 0 0
536536 93643.5 + 1.35273e6i 0.0140788 + 0.203376i
537537 112394.i 0.0168193i
538538 4.20721e6 + 6.91420e6i 0.626669 + 1.02988i
539539 7.72421e6i 1.14520i
540540 0 0
541541 8.47881e6i 1.24549i 0.782423 + 0.622747i 0.213984π0.213984\pi
−0.782423 + 0.622747i 0.786016π0.786016\pi
542542 9.37797e6 5.70638e6i 1.37123 0.834377i
543543 7594.57i 0.00110536i
544544 −4.83446e6 + 1.11718e7i −0.700407 + 1.61855i
545545 0 0
546546 250940. + 412399.i 0.0360237 + 0.0592020i
547547 −7.10206e6 −1.01488 −0.507441 0.861686i 0.669409π-0.669409\pi
−0.507441 + 0.861686i 0.669409π0.669409\pi
548548 −6.44634e6 3.33576e6i −0.916985 0.474508i
549549 4.24609e6i 0.601255i
550550 0 0
551551 1.11710e7 1.56752
552552 127086. 8797.63i 0.0177521 0.00122890i
553553 1.75053e7i 2.43420i
554554 8.26753e6 5.03069e6i 1.14446 0.696391i
555555 0 0
556556 −5.85654e6 3.03055e6i −0.803441 0.415753i
557557 −2.42337e6 −0.330965 −0.165482 0.986213i 0.552918π-0.552918\pi
−0.165482 + 0.986213i 0.552918π0.552918\pi
558558 6.08107e6 3.70026e6i 0.826788 0.503091i
559559 −4.12200e6 −0.557929
560560 0 0
561561 −344919. −0.0462712
562562 −6.98655e6 + 4.25123e6i −0.933086 + 0.567772i
563563 −1.03666e7 −1.37837 −0.689184 0.724586i 0.742031π-0.742031\pi
−0.689184 + 0.724586i 0.742031π0.742031\pi
564564 −162728. 84206.2i −0.0215410 0.0111467i
565565 0 0
566566 −5.17976e6 + 3.15182e6i −0.679624 + 0.413543i
567567 1.15341e7i 1.50669i
568568 13210.0 + 190825.i 0.00171804 + 0.0248179i
569569 −1.33323e7 −1.72633 −0.863165 0.504921i 0.831521π-0.831521\pi
−0.863165 + 0.504921i 0.831521π0.831521\pi
570570 0 0
571571 4.77970e6i 0.613494i 0.951791 + 0.306747i 0.0992405π0.0992405\pi
−0.951791 + 0.306747i 0.900760π0.900760\pi
572572 9.69822e6 + 5.01849e6i 1.23937 + 0.641332i
573573 254493. 0.0323809
574574 2.18997e6 + 3.59904e6i 0.277434 + 0.455940i
575575 0 0
576576 7.87987e6 1.09623e6i 0.989607 0.137672i
577577 5.73641e6i 0.717300i 0.933472 + 0.358650i 0.116763π0.116763\pi
−0.933472 + 0.358650i 0.883237π0.883237\pi
578578 1.44796e7 8.81066e6i 1.80276 1.09695i
579579 181823.i 0.0225400i
580580 0 0
581581 2.03371e7i 2.49947i
582582 −30613.0 50309.9i −0.00374626 0.00615667i
583583 8.98990e6i 1.09543i
584584 −9.98403e6 + 691151.i −1.21136 + 0.0838572i
585585 0 0
586586 854630. 520032.i 0.102810 0.0625585i
587587 −5.32016e6 −0.637279 −0.318639 0.947876i 0.603226π-0.603226\pi
−0.318639 + 0.947876i 0.603226π0.603226\pi
588588 145061. 280331.i 0.0173025 0.0334370i
589589 1.49412e7i 1.77458i
590590 0 0
591591 330655. 0.0389409
592592 −5.61566e6 7.93714e6i −0.658562 0.930808i
593593 828623.i 0.0967654i −0.998829 0.0483827i 0.984593π-0.984593\pi
0.998829 0.0483827i 0.0154067π-0.0154067\pi
594594 234461. + 385318.i 0.0272650 + 0.0448077i
595595 0 0
596596 7.84578e6 + 4.05992e6i 0.904734 + 0.468168i
597597 −59465.9 −0.00682861
598598 4.30233e6 + 7.07053e6i 0.491984 + 0.808535i
599599 −5.87196e6 −0.668676 −0.334338 0.942453i 0.608513π-0.608513\pi
−0.334338 + 0.942453i 0.608513π0.608513\pi
600600 0 0
601601 3.38777e6 0.382584 0.191292 0.981533i 0.438732π-0.438732\pi
0.191292 + 0.981533i 0.438732π0.438732\pi
602602 2.49386e6 + 4.09845e6i 0.280466 + 0.460923i
603603 −1.81868e6 −0.203686
604604 −1.30739e6 + 2.52653e6i −0.145818 + 0.281794i
605605 0 0
606606 −70962.0 116620.i −0.00784955 0.0129001i
607607 4.02635e6i 0.443547i −0.975098 0.221774i 0.928815π-0.928815\pi
0.975098 0.221774i 0.0711846π-0.0711846\pi
608608 6.63187e6 1.53254e7i 0.727574 1.68133i
609609 −347432. −0.0379601
610610 0 0
611611 1.19042e7i 1.29002i
612612 −1.45005e7 7.50350e6i −1.56496 0.809814i
613613 5.30633e6 0.570352 0.285176 0.958475i 0.407948π-0.407948\pi
0.285176 + 0.958475i 0.407948π0.407948\pi
614614 −1.33621e7 + 8.13065e6i −1.43038 + 0.870370i
615615 0 0
616616 −877714. 1.26790e7i −0.0931969 1.34628i
617617 9.56854e6i 1.01189i 0.862566 + 0.505944i 0.168856π0.168856\pi
−0.862566 + 0.505944i 0.831144π0.831144\pi
618618 −51561.7 84737.4i −0.00543070 0.00892491i
619619 6.58401e6i 0.690659i −0.938481 0.345330i 0.887767π-0.887767\pi
0.938481 0.345330i 0.112233π-0.112233\pi
620620 0 0
621621 341870.i 0.0355739i
622622 −3.61499e6 + 2.19968e6i −0.374655 + 0.227973i
623623 7.46866e6i 0.770943i
624624 −257725. 364267.i −0.0264969 0.0374506i
625625 0 0
626626 8.35871e6 + 1.37369e7i 0.852518 + 1.40104i
627627 473157. 0.0480659
628628 −4.02866e6 + 7.78538e6i −0.407626 + 0.787736i
629629 1.99533e7i 2.01089i
630630 0 0
631631 −1.34839e7 −1.34816 −0.674079 0.738659i 0.735459π-0.735459\pi
−0.674079 + 0.738659i 0.735459π0.735459\pi
632632 −1.11745e6 1.61421e7i −0.111285 1.60756i
633633 278752.i 0.0276508i
634634 471135. 286680.i 0.0465503 0.0283253i
635635 0 0
636636 168831. 326266.i 0.0165505 0.0319837i
637637 2.05072e7 2.00244
638638 −6.71371e6 + 4.08521e6i −0.652996 + 0.397340i
639639 −256555. −0.0248559
640640 0 0
641641 −7.72929e6 −0.743010 −0.371505 0.928431i 0.621158π-0.621158\pi
−0.371505 + 0.928431i 0.621158π0.621158\pi
642642 335027. 203860.i 0.0320805 0.0195206i
643643 −9.41828e6 −0.898347 −0.449174 0.893444i 0.648282π-0.648282\pi
−0.449174 + 0.893444i 0.648282π0.648282\pi
644644 4.42717e6 8.55549e6i 0.420641 0.812887i
645645 0 0
646646 −2.92755e7 + 1.78138e7i −2.76009 + 1.67948i
647647 3.44122e6i 0.323185i −0.986858 0.161593i 0.948337π-0.948337\pi
0.986858 0.161593i 0.0516631π-0.0516631\pi
648648 736277. + 1.06359e7i 0.0688817 + 0.995032i
649649 6.61593e6 0.616566
650650 0 0
651651 464687.i 0.0429743i
652652 331195. 640034.i 0.0305116 0.0589636i
653653 1.39531e7 1.28053 0.640263 0.768155i 0.278825π-0.278825\pi
0.640263 + 0.768155i 0.278825π0.278825\pi
654654 197114. + 323940.i 0.0180207 + 0.0296156i
655655 0 0
656656 −2.24919e6 3.17899e6i −0.204064 0.288423i
657657 1.34230e7i 1.21321i
658658 −1.18362e7 + 7.20215e6i −1.06573 + 0.648482i
659659 1.16197e7i 1.04227i 0.853474 + 0.521135i 0.174491π0.174491\pi
−0.853474 + 0.521135i 0.825509π0.825509\pi
660660 0 0
661661 2.02640e6i 0.180394i 0.995924 + 0.0901970i 0.0287497π0.0287497\pi
−0.995924 + 0.0901970i 0.971250π0.971250\pi
662662 7.98270e6 + 1.31189e7i 0.707954 + 1.16346i
663663 915737.i 0.0809071i
664664 −1.29822e6 1.87534e7i −0.114269 1.65067i
665665 0 0
666666 1.11404e7 6.77877e6i 0.973226 0.592196i
667667 −5.95668e6 −0.518429
668668 119822. + 62003.8i 0.0103895 + 0.00537622i
669669 10319.6i 0.000891447i
670670 0 0
671671 6.26993e6 0.537596
672672 −206259. + 476637.i −0.0176193 + 0.0407160i
673673 5.84126e6i 0.497129i −0.968615 0.248564i 0.920041π-0.920041\pi
0.968615 0.248564i 0.0799587π-0.0799587\pi
674674 1.45817e6 + 2.39638e6i 0.123640 + 0.203192i
675675 0 0
676676 7.86330e6 1.51958e7i 0.661818 1.27896i
677677 −1.28265e7 −1.07557 −0.537784 0.843083i 0.680738π-0.680738\pi
−0.537784 + 0.843083i 0.680738π0.680738\pi
678678 79923.8 + 131348.i 0.00667731 + 0.0109736i
679679 −4.45331e6 −0.370688
680680 0 0
681681 69079.6 0.00570797
682682 5.46393e6 + 8.97952e6i 0.449825 + 0.739251i
683683 −7.24686e6 −0.594426 −0.297213 0.954811i 0.596057π-0.596057\pi
−0.297213 + 0.954811i 0.596057π0.596057\pi
684684 1.98916e7 + 1.02932e7i 1.62566 + 0.841224i
685685 0 0
686686 −2.72853e6 4.48411e6i −0.221370 0.363803i
687687 331695.i 0.0268131i
688688 −2.56128e6 3.62010e6i −0.206294 0.291575i
689689 2.38676e7 1.91540
690690 0 0
691691 2.08754e7i 1.66318i −0.555388 0.831592i 0.687430π-0.687430\pi
0.555388 0.831592i 0.312570π-0.312570\pi
692692 −3.53494e6 + 6.83126e6i −0.280619 + 0.542295i
693693 1.70463e7 1.34834
694694 1.51985e7 9.24808e6i 1.19785 0.728874i
695695 0 0
696696 320378. 22178.3i 0.0250691 0.00173543i
697697 7.99171e6i 0.623100i
698698 −7.72105e6 1.26889e7i −0.599843 0.985793i
699699 154083.i 0.0119279i
700700 0 0
701701 1.73225e7i 1.33142i −0.746209 0.665712i 0.768128π-0.768128\pi
0.746209 0.665712i 0.231872π-0.231872\pi
702702 1.02299e6 622478.i 0.0783482 0.0476740i
703703 2.73718e7i 2.08889i
704704 1.61873e6 + 1.16357e7i 0.123096 + 0.884831i
705705 0 0
706706 1.57905e6 + 2.59505e6i 0.119230 + 0.195945i
707707 −1.03229e7 −0.776703
708708 −240109. 124248.i −0.0180022 0.00931549i
709709 1.99424e7i 1.48991i −0.667113 0.744956i 0.732470π-0.732470\pi
0.667113 0.744956i 0.267530π-0.267530\pi
710710 0 0
711711 2.17023e7 1.61002
712712 476762. + 6.88707e6i 0.0352453 + 0.509137i
713713 7.96700e6i 0.586909i
714714 910503. 554030.i 0.0668399 0.0406713i
715715 0 0
716716 6.97723e6 + 3.61047e6i 0.508628 + 0.263197i
717717 151308. 0.0109917
718718 −1.78794e6 + 1.08794e6i −0.129432 + 0.0787579i
719719 2.44269e7 1.76217 0.881083 0.472962i 0.156815π-0.156815\pi
0.881083 + 0.472962i 0.156815π0.156815\pi
720720 0 0
721721 −7.50075e6 −0.537361
722722 2.81941e7 1.71558e7i 2.01287 1.22481i
723723 −412050. −0.0293160
724724 471457. + 243962.i 0.0334268 + 0.0172972i
725725 0 0
726726 71946.6 43778.6i 0.00506604 0.00308263i
727727 1.52812e7i 1.07231i 0.844119 + 0.536155i 0.180124π0.180124\pi
−0.844119 + 0.536155i 0.819876π0.819876\pi
728728 −3.36620e7 + 2.33027e6i −2.35402 + 0.162959i
729729 −1.42747e7 −0.994829
730730 0 0
731731 9.10064e6i 0.629910i
732732 −227551. 117750.i −0.0156964 0.00812236i
733733 7.69123e6 0.528732 0.264366 0.964422i 0.414837π-0.414837\pi
0.264366 + 0.964422i 0.414837π0.414837\pi
734734 −4.16709e6 6.84827e6i −0.285491 0.469181i
735735 0 0
736736 −3.53628e6 + 8.17188e6i −0.240631 + 0.556067i
737737 2.68552e6i 0.182121i
738738 4.46194e6 2.71504e6i 0.301566 0.183500i
739739 7.32363e6i 0.493305i 0.969104 + 0.246652i 0.0793306π0.0793306\pi
−0.969104 + 0.246652i 0.920669π0.920669\pi
740740 0 0
741741 1.25620e6i 0.0840453i
742742 −1.44401e7 2.37312e7i −0.962856 1.58237i
743743 1.61613e7i 1.07400i −0.843582 0.537001i 0.819557π-0.819557\pi
0.843582 0.537001i 0.180443π-0.180443\pi
744744 −29663.3 428502.i −0.00196466 0.0283805i
745745 0 0
746746 −1.04408e7 + 6.35311e6i −0.686891 + 0.417965i
747747 2.52130e7 1.65319
748748 1.10799e7 2.14119e7i 0.724074 1.39927i
749749 2.96557e7i 1.93154i
750750 0 0
751751 −3.01764e7 −1.95240 −0.976199 0.216879i 0.930412π-0.930412\pi
−0.976199 + 0.216879i 0.930412π0.930412\pi
752752 1.04547e7 7.39688e6i 0.674167 0.476984i
753753 441209.i 0.0283568i
754754 1.08459e7 + 1.78244e7i 0.694767 + 1.14179i
755755 0 0
756756 −1.23784e6 640540.i −0.0787699 0.0407607i
757757 1.40193e7 0.889171 0.444586 0.895736i 0.353351π-0.353351\pi
0.444586 + 0.895736i 0.353351π0.353351\pi
758758 −4.70687e6 7.73536e6i −0.297550 0.488999i
759759 −252299. −0.0158969
760760 0 0
761761 −1.39222e7 −0.871456 −0.435728 0.900078i 0.643509π-0.643509\pi
−0.435728 + 0.900078i 0.643509π0.643509\pi
762762 −17828.0 29298.8i −0.00111228 0.00182794i
763763 2.86744e7 1.78313
764764 −8.17513e6 + 1.57984e7i −0.506712 + 0.979220i
765765 0 0
766766 9.05516e6 + 1.48814e7i 0.557602 + 0.916373i
767767 1.75648e7i 1.07809i
768768 159771. 452688.i 0.00977454 0.0276946i
769769 1.41369e7 0.862063 0.431031 0.902337i 0.358150π-0.358150\pi
0.431031 + 0.902337i 0.358150π0.358150\pi
770770 0 0
771771 690602.i 0.0418400i
772772 1.12872e7 + 5.84076e6i 0.681624 + 0.352717i
773773 −1.39310e7 −0.838558 −0.419279 0.907858i 0.637717π-0.637717\pi
−0.419279 + 0.907858i 0.637717π0.637717\pi
774774 5.08108e6 3.09178e6i 0.304862 0.185505i
775775 0 0
776776 4.10653e6 284277.i 0.244805 0.0169468i
777777 851295.i 0.0505857i
778778 7.97749e6 + 1.31104e7i 0.472517 + 0.776543i
779779 1.09630e7i 0.647268i
780780 0 0
781781 378838.i 0.0222242i
782782 1.56104e7 9.49877e6i 0.912848 0.555457i
783783 861835.i 0.0502366i
784784 1.27425e7 + 1.80103e7i 0.740399 + 1.04648i
785785 0 0
786786 −39626.0 65122.1i −0.00228783 0.00375986i
787787 −9.60345e6 −0.552701 −0.276351 0.961057i 0.589125π-0.589125\pi
−0.276351 + 0.961057i 0.589125π0.589125\pi
788788 −1.06217e7 + 2.05264e7i −0.609366 + 1.17760i
789789 330178.i 0.0188823i
790790 0 0
791791 1.16266e7 0.660712
792792 −1.57189e7 + 1.08815e6i −0.890451 + 0.0616420i
793793 1.66462e7i 0.940010i
794794 1.96101e7 1.19325e7i 1.10390 0.671709i
795795 0 0
796796 1.91024e6 3.69153e6i 0.106857 0.206502i
797797 −1.97451e7 −1.10107 −0.550534 0.834813i 0.685576π-0.685576\pi
−0.550534 + 0.834813i 0.685576π0.685576\pi
798798 −1.24902e6 + 760014.i −0.0694325 + 0.0422488i
799799 −2.62823e7 −1.45645
800800 0 0
801801 −9.25932e6 −0.509915
802802 −2.52650e7 + 1.53734e7i −1.38702 + 0.843985i
803803 1.98209e7 1.08476
804804 −50434.3 + 97464.2i −0.00275160 + 0.00531747i
805805 0 0
806806 2.38400e7 1.45063e7i 1.29261 0.786539i
807807 655027.i 0.0354059i
808808 9.51909e6 658965.i 0.512941 0.0355087i
809809 −1.73178e7 −0.930296 −0.465148 0.885233i 0.653999π-0.653999\pi
−0.465148 + 0.885233i 0.653999π0.653999\pi
810810 0 0
811811 3.16102e7i 1.68762i −0.536642 0.843810i 0.680307π-0.680307\pi
0.536642 0.843810i 0.319693π-0.319693\pi
812812 1.11606e7 2.15679e7i 0.594018 1.14794i
813813 888436. 0.0471411
814814 1.00098e7 + 1.64502e7i 0.529497 + 0.870184i
815815 0 0
816816 −804236. + 569010.i −0.0422822 + 0.0299154i
817817 1.24842e7i 0.654342i
818818 −9.16026e6 + 5.57390e6i −0.478657 + 0.291257i
819819 4.52568e7i 2.35762i
820820 0 0
821821 1.86667e7i 0.966519i 0.875477 + 0.483260i 0.160547π0.160547\pi
−0.875477 + 0.483260i 0.839453π0.839453\pi
822822 −305352. 501821.i −0.0157624 0.0259042i
823823 3.88081e7i 1.99720i 0.0528555 + 0.998602i 0.483168π0.483168\pi
−0.0528555 + 0.998602i 0.516832π0.516832\pi
824824 6.91666e6 478810.i 0.354878 0.0245666i
825825 0 0
826826 −1.74645e7 + 1.06269e7i −0.890646 + 0.541947i
827827 −2.98829e7 −1.51935 −0.759677 0.650301i 0.774643π-0.774643\pi
−0.759677 + 0.650301i 0.774643π0.774643\pi
828828 −1.06067e7 5.48861e6i −0.537657 0.278219i
829829 2.10001e7i 1.06129i 0.847594 + 0.530645i 0.178050π0.178050\pi
−0.847594 + 0.530645i 0.821950π0.821950\pi
830830 0 0
831831 783237. 0.0393451
832832 3.08919e7 4.29762e6i 1.54717 0.215239i
833833 4.52763e7i 2.26078i
834834 −277414. 455908.i −0.0138106 0.0226966i
835835 0 0
836836 −1.51993e7 + 2.93727e7i −0.752158 + 1.45354i
837837 1.15270e6 0.0568724
838838 1.95084e6 + 3.20604e6i 0.0959645 + 0.157710i
839839 7.61546e6 0.373501 0.186750 0.982407i 0.440204π-0.440204\pi
0.186750 + 0.982407i 0.440204π0.440204\pi
840840 0 0
841841 5.49468e6 0.267888
842842 3.36192e6 + 5.52503e6i 0.163421 + 0.268568i
843843 −661881. −0.0320783
844844 1.73044e7 + 8.95440e6i 0.836179 + 0.432694i
845845 0 0
846846 8.92892e6 + 1.46740e7i 0.428917 + 0.704890i
847847 6.36854e6i 0.305022i
848848 1.48306e7 + 2.09614e7i 0.708219 + 1.00099i
849849 −490713. −0.0233646
850850 0 0
851851 1.45953e7i 0.690860i
852852 −7114.62 + 13749.0i −0.000335778 + 0.000648891i
853853 −9.56553e6 −0.450128 −0.225064 0.974344i 0.572259π-0.572259\pi
−0.225064 + 0.974344i 0.572259π0.572259\pi
854854 −1.65511e7 + 1.00711e7i −0.776572 + 0.472535i
855855 0 0
856856 1.89307e6 + 2.73464e7i 0.0883046 + 1.27561i
857857 2.34556e7i 1.09092i 0.838136 + 0.545462i 0.183646π0.183646\pi
−0.838136 + 0.545462i 0.816354π0.816354\pi
858858 459388. + 754967.i 0.0213040 + 0.0350114i
859859 9.13964e6i 0.422616i 0.977420 + 0.211308i 0.0677723π0.0677723\pi
−0.977420 + 0.211308i 0.932228π0.932228\pi
860860 0 0
861861 340961.i 0.0156746i
862862 −2.70218e6 + 1.64424e6i −0.123864 + 0.0753698i
863863 1.04151e7i 0.476034i −0.971261 0.238017i 0.923503π-0.923503\pi
0.971261 0.238017i 0.0764974π-0.0764974\pi
864864 1.18234e6 + 511643.i 0.0538837 + 0.0233175i
865865 0 0
866866 −1.19027e7 1.95611e7i −0.539325 0.886336i
867867 1.37175e6 0.0619764
868868 −2.88469e7 1.49273e7i −1.29957 0.672482i
869869 3.20464e7i 1.43956i
870870 0 0
871871 −7.12987e6 −0.318446
872872 −2.64415e7 + 1.83043e6i −1.17759 + 0.0815196i
873873 5.52102e6i 0.245179i
874874 −2.14143e7 + 1.30303e7i −0.948255 + 0.577002i
875875 0 0
876876 −719350. 372238.i −0.0316723 0.0163893i
877877 −2.02537e7 −0.889210 −0.444605 0.895727i 0.646656π-0.646656\pi
−0.444605 + 0.895727i 0.646656π0.646656\pi
878878 −2.01941e7 + 1.22879e7i −0.884072 + 0.537947i
879879 80964.7 0.00353447
880880 0 0
881881 2.74936e7 1.19341 0.596707 0.802459i 0.296475π-0.296475\pi
0.596707 + 0.802459i 0.296475π0.296475\pi
882882 −2.52787e7 + 1.53818e7i −1.09417 + 0.665787i
883883 3.50971e7 1.51485 0.757425 0.652922i 0.226457π-0.226457\pi
0.757425 + 0.652922i 0.226457π0.226457\pi
884884 −5.68472e7 2.94164e7i −2.44669 1.26607i
885885 0 0
886886 2.99202e7 1.82061e7i 1.28050 0.779169i
887887 1.77301e7i 0.756660i 0.925671 + 0.378330i 0.123502π0.123502\pi
−0.925671 + 0.378330i 0.876498π0.876498\pi
888888 −54342.4 785005.i −0.00231263 0.0334072i
889889 −2.59346e6 −0.110059
890890 0 0
891891 2.11151e7i 0.891042i
892892 −640618. 331497.i −0.0269580 0.0139498i
893893 3.60538e7 1.51294
894894 371641. + 610762.i 0.0155518 + 0.0255581i
895895 0 0
896896 −2.29630e7 2.81153e7i −0.955562 1.16996i
897897 669837.i 0.0277964i
898898 −1.50590e7 + 9.16323e6i −0.623169 + 0.379191i
899899 2.00844e7i 0.828818i
900900 0 0
901901 5.26953e7i 2.16252i
902902 4.00912e6 + 6.58866e6i 0.164071 + 0.269638i
903903 388273.i 0.0158459i
904904 −1.07213e7 + 742186.i −0.436339 + 0.0302059i
905905 0 0
906906 −196680. + 119677.i −0.00796047 + 0.00484385i
907907 1.04686e7 0.422542 0.211271 0.977428i 0.432240π-0.432240\pi
0.211271 + 0.977428i 0.432240π0.432240\pi
908908 −2.21906e6 + 4.28833e6i −0.0893211 + 0.172613i
909909 1.27979e7i 0.513725i
910910 0 0
911911 −4.87147e7 −1.94475 −0.972376 0.233420i 0.925008π-0.925008\pi
−0.972376 + 0.233420i 0.925008π0.925008\pi
912912 1.10324e6 780563.i 0.0439222 0.0310757i
913913 3.72304e7i 1.47816i
914914 −1.30764e7 2.14899e7i −0.517752 0.850882i
915915 0 0
916916 2.05910e7 + 1.06551e7i 0.810847 + 0.419585i
917917 −5.76445e6 −0.226378
918918 −1.37432e6 2.25858e6i −0.0538246 0.0884563i
919919 2.63015e7 1.02729 0.513643 0.858004i 0.328296π-0.328296\pi
0.513643 + 0.858004i 0.328296π0.328296\pi
920920 0 0
921921 −1.26587e6 −0.0491747
922922 −2.21124e7 3.63399e7i −0.856659 1.40785i
923923 −1.00579e6 −0.0388600
924924 472718. 913526.i 0.0182147 0.0351998i
925925 0 0
926926 −1.27693e7 2.09854e7i −0.489374 0.804246i
927927 9.29911e6i 0.355420i
928928 −8.91478e6 + 2.06009e7i −0.339813 + 0.785264i
929929 −4.91045e7 −1.86673 −0.933366 0.358925i 0.883143π-0.883143\pi
−0.933366 + 0.358925i 0.883143π0.883143\pi
930930 0 0
931931 6.21096e7i 2.34847i
932932 −9.56519e6 4.94965e6i −0.360706 0.186653i
933933 −342472. −0.0128802
934934 −4.30234e6 + 2.61792e6i −0.161376 + 0.0981951i
935935 0 0
936936 2.88897e6 + 4.17327e7i 0.107784 + 1.55699i
937937 3.24439e7i 1.20721i −0.797282 0.603607i 0.793729π-0.793729\pi
0.797282 0.603607i 0.206271π-0.206271\pi
938938 4.31365e6 + 7.08912e6i 0.160080 + 0.263079i
939939 1.30138e6i 0.0481660i
940940 0 0
941941 5.58017e6i 0.205435i −0.994711 0.102717i 0.967246π-0.967246\pi
0.994711 0.102717i 0.0327537π-0.0327537\pi
942942 −606060. + 368780.i −0.0222530 + 0.0135407i
943943 5.84573e6i 0.214072i
944944 1.54261e7 1.09142e7i 0.563413 0.398624i
945945 0 0
946946 4.56542e6 + 7.50290e6i 0.165864 + 0.272585i
947947 2.29821e7 0.832748 0.416374 0.909193i 0.363301π-0.363301\pi
0.416374 + 0.909193i 0.363301π0.363301\pi
948948 601834. 1.16304e6i 0.0217498 0.0420315i
949949 5.26231e7i 1.89675i
950950 0 0
951951 44633.7 0.00160034
952952 5.14482e6 + 7.43195e7i 0.183983 + 2.65773i
953953 2.98158e7i 1.06344i 0.846920 + 0.531721i 0.178455π0.178455\pi
−0.846920 + 0.531721i 0.821545π0.821545\pi
954954 −2.94209e7 + 1.79023e7i −1.04661 + 0.636850i
955955 0 0
956956 −4.86051e6 + 9.39292e6i −0.172003 + 0.332396i
957957 −636034. −0.0224492
958958 1.90066e7 1.15653e7i 0.669099 0.407138i
959959 −4.44200e7 −1.55967
960960 0 0
961961 −1.76649e6 −0.0617026
962962 4.36742e7 2.65752e7i 1.52156 0.925848i
963963 −3.67659e7 −1.27756
964964 1.32364e7 2.55793e7i 0.458750 0.886534i
965965 0 0
966966 666009. 405259.i 0.0229635 0.0139730i
967967 4.13822e6i 0.142314i −0.997465 0.0711570i 0.977331π-0.977331\pi
0.997465 0.0711570i 0.0226691π-0.0226691\pi
968968 406536. + 5.87262e6i 0.0139447 + 0.201439i
969969 −2.77346e6 −0.0948884
970970 0 0
971971 5.43256e7i 1.84908i 0.381081 + 0.924542i 0.375552π0.375552\pi
−0.381081 + 0.924542i 0.624448π0.624448\pi
972972 −1.19134e6 + 2.30227e6i −0.0404456 + 0.0781609i
973973 −4.03558e7 −1.36655
974974 1.15010e7 + 1.89009e7i 0.388452 + 0.638389i
975975 0 0
976976 1.46194e7 1.03434e7i 0.491251 0.347568i
977977 2.00334e7i 0.671456i 0.941959 + 0.335728i 0.108982π0.108982\pi
−0.941959 + 0.335728i 0.891018π0.891018\pi
978978 49824.0 30317.3i 0.00166568 0.00101355i
979979 1.36726e7i 0.455927i
980980 0 0
981981 3.55493e7i 1.17939i
982982 1.30364e7 + 2.14243e7i 0.431400 + 0.708971i
983983 2.92947e6i 0.0966953i −0.998831 0.0483476i 0.984604π-0.984604\pi
0.998831 0.0483476i 0.0153955π-0.0153955\pi
984984 −21765.3 314410.i −0.000716599 0.0103516i
985985 0 0
986986 3.93531e7 2.39459e7i 1.28910 0.784402i
987987 −1.12132e6 −0.0366383
988988 7.79825e7 + 4.03532e7i 2.54158 + 1.31518i
989989 6.65688e6i 0.216411i
990990 0 0
991991 5.27467e7 1.70613 0.853064 0.521807i 0.174742π-0.174742\pi
0.853064 + 0.521807i 0.174742π0.174742\pi
992992 2.75535e7 + 1.19234e7i 0.888990 + 0.384700i
993993 1.24284e6i 0.0399984i
994994 608513. + 1.00004e6i 0.0195346 + 0.0321035i
995995 0 0
996996 699191. 1.35118e6i 0.0223330 0.0431585i
997997 1.04084e7 0.331625 0.165812 0.986157i 0.446975π-0.446975\pi
0.165812 + 0.986157i 0.446975π0.446975\pi
998998 −1.42361e7 2.33959e7i −0.452444 0.743555i
999999 2.11171e6 0.0669454
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 200.6.f.d.149.10 40
4.3 odd 2 800.6.f.d.49.21 40
5.2 odd 4 200.6.d.d.101.5 yes 20
5.3 odd 4 200.6.d.c.101.16 yes 20
5.4 even 2 inner 200.6.f.d.149.31 40
8.3 odd 2 800.6.f.d.49.19 40
8.5 even 2 inner 200.6.f.d.149.32 40
20.3 even 4 800.6.d.d.401.11 20
20.7 even 4 800.6.d.b.401.10 20
20.19 odd 2 800.6.f.d.49.20 40
40.3 even 4 800.6.d.d.401.10 20
40.13 odd 4 200.6.d.c.101.15 20
40.19 odd 2 800.6.f.d.49.22 40
40.27 even 4 800.6.d.b.401.11 20
40.29 even 2 inner 200.6.f.d.149.9 40
40.37 odd 4 200.6.d.d.101.6 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.6.d.c.101.15 20 40.13 odd 4
200.6.d.c.101.16 yes 20 5.3 odd 4
200.6.d.d.101.5 yes 20 5.2 odd 4
200.6.d.d.101.6 yes 20 40.37 odd 4
200.6.f.d.149.9 40 40.29 even 2 inner
200.6.f.d.149.10 40 1.1 even 1 trivial
200.6.f.d.149.31 40 5.4 even 2 inner
200.6.f.d.149.32 40 8.5 even 2 inner
800.6.d.b.401.10 20 20.7 even 4
800.6.d.b.401.11 20 40.27 even 4
800.6.d.d.401.10 20 40.3 even 4
800.6.d.d.401.11 20 20.3 even 4
800.6.f.d.49.19 40 8.3 odd 2
800.6.f.d.49.20 40 20.19 odd 2
800.6.f.d.49.21 40 4.3 odd 2
800.6.f.d.49.22 40 40.19 odd 2