Properties

Label 650.6.b.j.599.3
Level 650650
Weight 66
Character 650.599
Analytic conductor 104.249104.249
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [650,6,Mod(599,650)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(650, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("650.599");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 650=25213 650 = 2 \cdot 5^{2} \cdot 13
Weight: k k == 6 6
Character orbit: [χ][\chi] == 650.b (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: 104.249482878104.249482878
Analytic rank: 00
Dimension: 66
Coefficient field: Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x62x5+2x4390x3+32400x2135000x+281250 x^{6} - 2x^{5} + 2x^{4} - 390x^{3} + 32400x^{2} - 135000x + 281250 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 23 2^{3}
Twist minimal: no (minimal twist has level 130)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 599.3
Root 9.94525+9.94525i-9.94525 + 9.94525i of defining polynomial
Character χ\chi == 650.599
Dual form 650.6.b.j.599.4

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) == q4.00000iq2+27.8905iq316.0000q4+111.562q6240.426iq7+64.0000iq8534.880q9+544.151q11446.248iq12169.000iq13961.702q14+256.000q16+1629.30iq17+2139.52iq18+805.920q19+6705.59q212176.61iq22373.152iq231784.99q24676.000q268140.67iq27+3846.81iq281503.62q292200.08q311024.00iq32+15176.7iq33+6517.20q34+8558.08q3613109.1iq373223.68iq38+4713.49q3917099.9q4126822.4iq42+8935.58iq438706.42q441492.61q46+15749.7iq47+7139.97iq4840997.5q4945442.0q51+2704.00iq5240379.7iq5332562.7q54+15387.2q56+22477.5iq57+6014.46iq58+47562.1q5930280.0q61+8800.31iq62+128599.iq634096.00q64+60706.6q66+38769.4iq6726068.8iq68+10407.4q6910519.7q7134232.3iq721582.12iq7352436.5q7412894.7q76130828.iq7718854.0iq78+6191.23q79+97071.7q81+68399.8iq8237849.2iq83107289.q84+35742.3q8641936.6iq87+34825.7iq8849151.0q8940631.9q91+5970.43iq9261361.3iq93+62999.0q94+28559.9q9615654.2iq97+163990.iq98291056.q99+O(q100)q-4.00000i q^{2} +27.8905i q^{3} -16.0000 q^{4} +111.562 q^{6} -240.426i q^{7} +64.0000i q^{8} -534.880 q^{9} +544.151 q^{11} -446.248i q^{12} -169.000i q^{13} -961.702 q^{14} +256.000 q^{16} +1629.30i q^{17} +2139.52i q^{18} +805.920 q^{19} +6705.59 q^{21} -2176.61i q^{22} -373.152i q^{23} -1784.99 q^{24} -676.000 q^{26} -8140.67i q^{27} +3846.81i q^{28} -1503.62 q^{29} -2200.08 q^{31} -1024.00i q^{32} +15176.7i q^{33} +6517.20 q^{34} +8558.08 q^{36} -13109.1i q^{37} -3223.68i q^{38} +4713.49 q^{39} -17099.9 q^{41} -26822.4i q^{42} +8935.58i q^{43} -8706.42 q^{44} -1492.61 q^{46} +15749.7i q^{47} +7139.97i q^{48} -40997.5 q^{49} -45442.0 q^{51} +2704.00i q^{52} -40379.7i q^{53} -32562.7 q^{54} +15387.2 q^{56} +22477.5i q^{57} +6014.46i q^{58} +47562.1 q^{59} -30280.0 q^{61} +8800.31i q^{62} +128599. i q^{63} -4096.00 q^{64} +60706.6 q^{66} +38769.4i q^{67} -26068.8i q^{68} +10407.4 q^{69} -10519.7 q^{71} -34232.3i q^{72} -1582.12i q^{73} -52436.5 q^{74} -12894.7 q^{76} -130828. i q^{77} -18854.0i q^{78} +6191.23 q^{79} +97071.7 q^{81} +68399.8i q^{82} -37849.2i q^{83} -107289. q^{84} +35742.3 q^{86} -41936.6i q^{87} +34825.7i q^{88} -49151.0 q^{89} -40631.9 q^{91} +5970.43i q^{92} -61361.3i q^{93} +62999.0 q^{94} +28559.9 q^{96} -15654.2i q^{97} +163990. i q^{98} -291056. q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q96q4+176q6310q9+96q111872q14+1536q16+720q19+13808q212816q244056q26+6156q2910776q31+12048q34+4960q36+7436q39+700680q99+O(q100) 6 q - 96 q^{4} + 176 q^{6} - 310 q^{9} + 96 q^{11} - 1872 q^{14} + 1536 q^{16} + 720 q^{19} + 13808 q^{21} - 2816 q^{24} - 4056 q^{26} + 6156 q^{29} - 10776 q^{31} + 12048 q^{34} + 4960 q^{36} + 7436 q^{39}+ \cdots - 700680 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/650Z)×\left(\mathbb{Z}/650\mathbb{Z}\right)^\times.

nn 2727 301301
χ(n)\chi(n) 1-1 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 − 4.00000i − 0.707107i
33 27.8905i 1.78918i 0.446892 + 0.894588i 0.352531π0.352531\pi
−0.446892 + 0.894588i 0.647469π0.647469\pi
44 −16.0000 −0.500000
55 0 0
66 111.562 1.26514
77 − 240.426i − 1.85454i −0.374397 0.927269i 0.622150π-0.622150\pi
0.374397 0.927269i 0.377850π-0.377850\pi
88 64.0000i 0.353553i
99 −534.880 −2.20115
1010 0 0
1111 544.151 1.35593 0.677966 0.735093i 0.262862π-0.262862\pi
0.677966 + 0.735093i 0.262862π0.262862\pi
1212 − 446.248i − 0.894588i
1313 − 169.000i − 0.277350i
1414 −961.702 −1.31136
1515 0 0
1616 256.000 0.250000
1717 1629.30i 1.36735i 0.729788 + 0.683673i 0.239619π0.239619\pi
−0.729788 + 0.683673i 0.760381π0.760381\pi
1818 2139.52i 1.55645i
1919 805.920 0.512162 0.256081 0.966655i 0.417569π-0.417569\pi
0.256081 + 0.966655i 0.417569π0.417569\pi
2020 0 0
2121 6705.59 3.31809
2222 − 2176.61i − 0.958789i
2323 − 373.152i − 0.147084i −0.997292 0.0735421i 0.976570π-0.976570\pi
0.997292 0.0735421i 0.0234303π-0.0234303\pi
2424 −1784.99 −0.632569
2525 0 0
2626 −676.000 −0.196116
2727 − 8140.67i − 2.14907i
2828 3846.81i 0.927269i
2929 −1503.62 −0.332003 −0.166001 0.986126i 0.553086π-0.553086\pi
−0.166001 + 0.986126i 0.553086π0.553086\pi
3030 0 0
3131 −2200.08 −0.411182 −0.205591 0.978638i 0.565912π-0.565912\pi
−0.205591 + 0.978638i 0.565912π0.565912\pi
3232 − 1024.00i − 0.176777i
3333 15176.7i 2.42600i
3434 6517.20 0.966860
3535 0 0
3636 8558.08 1.10058
3737 − 13109.1i − 1.57423i −0.616804 0.787117i 0.711573π-0.711573\pi
0.616804 0.787117i 0.288427π-0.288427\pi
3838 − 3223.68i − 0.362154i
3939 4713.49 0.496228
4040 0 0
4141 −17099.9 −1.58867 −0.794337 0.607477i 0.792182π-0.792182\pi
−0.794337 + 0.607477i 0.792182π0.792182\pi
4242 − 26822.4i − 2.34625i
4343 8935.58i 0.736973i 0.929633 + 0.368487i 0.120124π0.120124\pi
−0.929633 + 0.368487i 0.879876π0.879876\pi
4444 −8706.42 −0.677966
4545 0 0
4646 −1492.61 −0.104004
4747 15749.7i 1.03999i 0.854170 + 0.519995i 0.174066π0.174066\pi
−0.854170 + 0.519995i 0.825934π0.825934\pi
4848 7139.97i 0.447294i
4949 −40997.5 −2.43931
5050 0 0
5151 −45442.0 −2.44642
5252 2704.00i 0.138675i
5353 − 40379.7i − 1.97457i −0.158951 0.987286i 0.550811π-0.550811\pi
0.158951 0.987286i 0.449189π-0.449189\pi
5454 −32562.7 −1.51962
5555 0 0
5656 15387.2 0.655678
5757 22477.5i 0.916349i
5858 6014.46i 0.234761i
5959 47562.1 1.77881 0.889407 0.457116i 0.151118π-0.151118\pi
0.889407 + 0.457116i 0.151118π0.151118\pi
6060 0 0
6161 −30280.0 −1.04191 −0.520956 0.853584i 0.674424π-0.674424\pi
−0.520956 + 0.853584i 0.674424π0.674424\pi
6262 8800.31i 0.290749i
6363 128599.i 4.08212i
6464 −4096.00 −0.125000
6565 0 0
6666 60706.6 1.71544
6767 38769.4i 1.05512i 0.849517 + 0.527561i 0.176893π0.176893\pi
−0.849517 + 0.527561i 0.823107π0.823107\pi
6868 − 26068.8i − 0.683673i
6969 10407.4 0.263160
7070 0 0
7171 −10519.7 −0.247660 −0.123830 0.992303i 0.539518π-0.539518\pi
−0.123830 + 0.992303i 0.539518π0.539518\pi
7272 − 34232.3i − 0.778225i
7373 − 1582.12i − 0.0347483i −0.999849 0.0173742i 0.994469π-0.994469\pi
0.999849 0.0173742i 0.00553064π-0.00553064\pi
7474 −52436.5 −1.11315
7575 0 0
7676 −12894.7 −0.256081
7777 − 130828.i − 2.51463i
7878 − 18854.0i − 0.350886i
7979 6191.23 0.111612 0.0558058 0.998442i 0.482227π-0.482227\pi
0.0558058 + 0.998442i 0.482227π0.482227\pi
8080 0 0
8181 97071.7 1.64392
8282 68399.8i 1.12336i
8383 − 37849.2i − 0.603062i −0.953456 0.301531i 0.902502π-0.902502\pi
0.953456 0.301531i 0.0974977π-0.0974977\pi
8484 −107289. −1.65905
8585 0 0
8686 35742.3 0.521119
8787 − 41936.6i − 0.594011i
8888 34825.7i 0.479394i
8989 −49151.0 −0.657744 −0.328872 0.944374i 0.606669π-0.606669\pi
−0.328872 + 0.944374i 0.606669π0.606669\pi
9090 0 0
9191 −40631.9 −0.514356
9292 5970.43i 0.0735421i
9393 − 61361.3i − 0.735677i
9494 62999.0 0.735383
9595 0 0
9696 28559.9 0.316285
9797 − 15654.2i − 0.168928i −0.996427 0.0844641i 0.973082π-0.973082\pi
0.996427 0.0844641i 0.0269178π-0.0269178\pi
9898 163990.i 1.72485i
9999 −291056. −2.98461
100100 0 0
101101 −138108. −1.34714 −0.673572 0.739122i 0.735241π-0.735241\pi
−0.673572 + 0.739122i 0.735241π0.735241\pi
102102 181768.i 1.72988i
103103 47642.1i 0.442484i 0.975219 + 0.221242i 0.0710111π0.0710111\pi
−0.975219 + 0.221242i 0.928989π0.928989\pi
104104 10816.0 0.0980581
105105 0 0
106106 −161519. −1.39623
107107 − 186527.i − 1.57500i −0.616313 0.787501i 0.711374π-0.711374\pi
0.616313 0.787501i 0.288626π-0.288626\pi
108108 130251.i 1.07454i
109109 −14407.1 −0.116147 −0.0580736 0.998312i 0.518496π-0.518496\pi
−0.0580736 + 0.998312i 0.518496π0.518496\pi
110110 0 0
111111 365620. 2.81658
112112 − 61548.9i − 0.463634i
113113 50802.0i 0.374270i 0.982334 + 0.187135i 0.0599201π0.0599201\pi
−0.982334 + 0.187135i 0.940080π0.940080\pi
114114 89910.0 0.647957
115115 0 0
116116 24057.8 0.166001
117117 90394.7i 0.610490i
118118 − 190248.i − 1.25781i
119119 391725. 2.53580
120120 0 0
121121 135050. 0.838552
122122 121120.i 0.736742i
123123 − 476926.i − 2.84242i
124124 35201.3 0.205591
125125 0 0
126126 514395. 2.88649
127127 − 182278.i − 1.00282i −0.865209 0.501411i 0.832814π-0.832814\pi
0.865209 0.501411i 0.167186π-0.167186\pi
128128 16384.0i 0.0883883i
129129 −249218. −1.31858
130130 0 0
131131 199714. 1.01679 0.508394 0.861124i 0.330239π-0.330239\pi
0.508394 + 0.861124i 0.330239π0.330239\pi
132132 − 242826.i − 1.21300i
133133 − 193764.i − 0.949824i
134134 155078. 0.746083
135135 0 0
136136 −104275. −0.483430
137137 − 345418.i − 1.57233i −0.618017 0.786165i 0.712064π-0.712064\pi
0.618017 0.786165i 0.287936π-0.287936\pi
138138 − 41629.6i − 0.186082i
139139 −183088. −0.803754 −0.401877 0.915694i 0.631642π-0.631642\pi
−0.401877 + 0.915694i 0.631642π0.631642\pi
140140 0 0
141141 −439268. −1.86072
142142 42078.7i 0.175122i
143143 − 91961.6i − 0.376068i
144144 −136929. −0.550288
145145 0 0
146146 −6328.50 −0.0245708
147147 − 1.14344e6i − 4.36435i
148148 209746.i 0.787117i
149149 187082. 0.690344 0.345172 0.938540i 0.387821π-0.387821\pi
0.345172 + 0.938540i 0.387821π0.387821\pi
150150 0 0
151151 −10616.3 −0.0378907 −0.0189454 0.999821i 0.506031π-0.506031\pi
−0.0189454 + 0.999821i 0.506031π0.506031\pi
152152 51578.9i 0.181077i
153153 − 871480.i − 3.00974i
154154 −523312. −1.77811
155155 0 0
156156 −75415.9 −0.248114
157157 − 335884.i − 1.08753i −0.839238 0.543764i 0.816999π-0.816999\pi
0.839238 0.543764i 0.183001π-0.183001\pi
158158 − 24764.9i − 0.0789213i
159159 1.12621e6 3.53286
160160 0 0
161161 −89715.3 −0.272773
162162 − 388287.i − 1.16242i
163163 − 201881.i − 0.595150i −0.954698 0.297575i 0.903822π-0.903822\pi
0.954698 0.297575i 0.0961778π-0.0961778\pi
164164 273599. 0.794337
165165 0 0
166166 −151397. −0.426429
167167 − 446050.i − 1.23764i −0.785535 0.618818i 0.787612π-0.787612\pi
0.785535 0.618818i 0.212388π-0.212388\pi
168168 429158.i 1.17312i
169169 −28561.0 −0.0769231
170170 0 0
171171 −431070. −1.12735
172172 − 142969.i − 0.368487i
173173 − 57408.8i − 0.145835i −0.997338 0.0729177i 0.976769π-0.976769\pi
0.997338 0.0729177i 0.0232311π-0.0232311\pi
174174 −167746. −0.420030
175175 0 0
176176 139303. 0.338983
177177 1.32653e6i 3.18261i
178178 196604.i 0.465095i
179179 −87439.4 −0.203974 −0.101987 0.994786i 0.532520π-0.532520\pi
−0.101987 + 0.994786i 0.532520π0.532520\pi
180180 0 0
181181 21341.6 0.0484206 0.0242103 0.999707i 0.492293π-0.492293\pi
0.0242103 + 0.999707i 0.492293π0.492293\pi
182182 162528.i 0.363705i
183183 − 844523.i − 1.86416i
184184 23881.7 0.0520021
185185 0 0
186186 −245445. −0.520202
187187 886586.i 1.85403i
188188 − 251996.i − 0.519995i
189189 −1.95723e6 −3.98553
190190 0 0
191191 307517. 0.609938 0.304969 0.952362i 0.401354π-0.401354\pi
0.304969 + 0.952362i 0.401354π0.401354\pi
192192 − 114239.i − 0.223647i
193193 − 182409.i − 0.352496i −0.984346 0.176248i 0.943604π-0.943604\pi
0.984346 0.176248i 0.0563960π-0.0563960\pi
194194 −62616.9 −0.119450
195195 0 0
196196 655959. 1.21965
197197 − 152508.i − 0.279980i −0.990153 0.139990i 0.955293π-0.955293\pi
0.990153 0.139990i 0.0447070π-0.0447070\pi
198198 1.16422e6i 2.11044i
199199 586606. 1.05006 0.525029 0.851084i 0.324054π-0.324054\pi
0.525029 + 0.851084i 0.324054π0.324054\pi
200200 0 0
201201 −1.08130e6 −1.88780
202202 552430.i 0.952574i
203203 361508.i 0.615711i
204204 727072. 1.22321
205205 0 0
206206 190568. 0.312884
207207 199592.i 0.323755i
208208 − 43264.0i − 0.0693375i
209209 438542. 0.694458
210210 0 0
211211 −207041. −0.320147 −0.160073 0.987105i 0.551173π-0.551173\pi
−0.160073 + 0.987105i 0.551173π0.551173\pi
212212 646075.i 0.987286i
213213 − 293399.i − 0.443108i
214214 −746106. −1.11369
215215 0 0
216216 521003. 0.759812
217217 528955.i 0.762552i
218218 57628.2i 0.0821285i
219219 44126.3 0.0621708
220220 0 0
221221 275352. 0.379234
222222 − 1.46248e6i − 1.99162i
223223 1.04889e6i 1.41243i 0.707998 + 0.706214i 0.249599π0.249599\pi
−0.707998 + 0.706214i 0.750401π0.750401\pi
224224 −246196. −0.327839
225225 0 0
226226 203208. 0.264649
227227 − 100709.i − 0.129719i −0.997894 0.0648593i 0.979340π-0.979340\pi
0.997894 0.0648593i 0.0206599π-0.0206599\pi
228228 − 359640.i − 0.458174i
229229 −487174. −0.613896 −0.306948 0.951726i 0.599308π-0.599308\pi
−0.306948 + 0.951726i 0.599308π0.599308\pi
230230 0 0
231231 3.64886e6 4.49911
232232 − 96231.4i − 0.117381i
233233 832844.i 1.00502i 0.864572 + 0.502509i 0.167590π0.167590\pi
−0.864572 + 0.502509i 0.832410π0.832410\pi
234234 361579. 0.431681
235235 0 0
236236 −760993. −0.889407
237237 172677.i 0.199693i
238238 − 1.56690e6i − 1.79308i
239239 −1.34919e6 −1.52785 −0.763923 0.645308i 0.776729π-0.776729\pi
−0.763923 + 0.645308i 0.776729π0.776729\pi
240240 0 0
241241 −1.66283e6 −1.84419 −0.922096 0.386962i 0.873524π-0.873524\pi
−0.922096 + 0.386962i 0.873524π0.873524\pi
242242 − 540199.i − 0.592946i
243243 729193.i 0.792185i
244244 484479. 0.520956
245245 0 0
246246 −1.90770e6 −2.00989
247247 − 136200.i − 0.142048i
248248 − 140805.i − 0.145375i
249249 1.05563e6 1.07898
250250 0 0
251251 −291273. −0.291820 −0.145910 0.989298i 0.546611π-0.546611\pi
−0.145910 + 0.989298i 0.546611π0.546611\pi
252252 − 2.05758e6i − 2.04106i
253253 − 203051.i − 0.199436i
254254 −729110. −0.709102
255255 0 0
256256 65536.0 0.0625000
257257 − 548204.i − 0.517737i −0.965913 0.258868i 0.916650π-0.916650\pi
0.965913 0.258868i 0.0833496π-0.0833496\pi
258258 996872.i 0.932374i
259259 −3.15177e6 −2.91947
260260 0 0
261261 804253. 0.730788
262262 − 798857.i − 0.718978i
263263 − 818412.i − 0.729596i −0.931087 0.364798i 0.881138π-0.881138\pi
0.931087 0.364798i 0.118862π-0.118862\pi
264264 −971306. −0.857721
265265 0 0
266266 −775055. −0.671627
267267 − 1.37085e6i − 1.17682i
268268 − 620311.i − 0.527561i
269269 939455. 0.791581 0.395790 0.918341i 0.370471π-0.370471\pi
0.395790 + 0.918341i 0.370471π0.370471\pi
270270 0 0
271271 −1.52416e6 −1.26069 −0.630345 0.776315i 0.717087π-0.717087\pi
−0.630345 + 0.776315i 0.717087π0.717087\pi
272272 417101.i 0.341837i
273273 − 1.13324e6i − 0.920274i
274274 −1.38167e6 −1.11180
275275 0 0
276276 −166518. −0.131580
277277 − 439704.i − 0.344319i −0.985069 0.172159i 0.944926π-0.944926\pi
0.985069 0.172159i 0.0550744π-0.0550744\pi
278278 732352.i 0.568340i
279279 1.17678e6 0.905074
280280 0 0
281281 −592033. −0.447280 −0.223640 0.974672i 0.571794π-0.571794\pi
−0.223640 + 0.974672i 0.571794π0.571794\pi
282282 1.75707e6i 1.31573i
283283 777226.i 0.576875i 0.957499 + 0.288437i 0.0931357π0.0931357\pi
−0.957499 + 0.288437i 0.906864π0.906864\pi
284284 168315. 0.123830
285285 0 0
286286 −367846. −0.265920
287287 4.11126e6i 2.94626i
288288 547717.i 0.389112i
289289 −1.23476e6 −0.869637
290290 0 0
291291 436604. 0.302242
292292 25314.0i 0.0173742i
293293 − 609025.i − 0.414444i −0.978294 0.207222i 0.933558π-0.933558\pi
0.978294 0.207222i 0.0664423π-0.0664423\pi
294294 −4.57376e6 −3.08606
295295 0 0
296296 838984. 0.556576
297297 − 4.42976e6i − 2.91400i
298298 − 748326.i − 0.488147i
299299 −63062.7 −0.0407938
300300 0 0
301301 2.14834e6 1.36674
302302 42465.4i 0.0267928i
303303 − 3.85189e6i − 2.41028i
304304 206315. 0.128041
305305 0 0
306306 −3.48592e6 −2.12821
307307 − 2.66761e6i − 1.61538i −0.589604 0.807692i 0.700716π-0.700716\pi
0.589604 0.807692i 0.299284π-0.299284\pi
308308 2.09325e6i 1.25731i
309309 −1.32876e6 −0.791682
310310 0 0
311311 −1.62320e6 −0.951634 −0.475817 0.879544i 0.657847π-0.657847\pi
−0.475817 + 0.879544i 0.657847π0.657847\pi
312312 301664.i 0.175443i
313313 − 592115.i − 0.341622i −0.985304 0.170811i 0.945361π-0.945361\pi
0.985304 0.170811i 0.0546387π-0.0546387\pi
314314 −1.34354e6 −0.768998
315315 0 0
316316 −99059.7 −0.0558058
317317 − 2.61036e6i − 1.45899i −0.683987 0.729494i 0.739756π-0.739756\pi
0.683987 0.729494i 0.260244π-0.260244\pi
318318 − 4.50484e6i − 2.49811i
319319 −818194. −0.450173
320320 0 0
321321 5.20232e6 2.81796
322322 358861.i 0.192880i
323323 1.31308e6i 0.700304i
324324 −1.55315e6 −0.821959
325325 0 0
326326 −807524. −0.420834
327327 − 401820.i − 0.207808i
328328 − 1.09440e6i − 0.561681i
329329 3.78664e6 1.92870
330330 0 0
331331 818785. 0.410771 0.205386 0.978681i 0.434155π-0.434155\pi
0.205386 + 0.978681i 0.434155π0.434155\pi
332332 605588.i 0.301531i
333333 7.01180e6i 3.46513i
334334 −1.78420e6 −0.875140
335335 0 0
336336 1.71663e6 0.829523
337337 3.28910e6i 1.57762i 0.614638 + 0.788809i 0.289302π0.289302\pi
−0.614638 + 0.788809i 0.710698π0.710698\pi
338338 114244.i 0.0543928i
339339 −1.41689e6 −0.669634
340340 0 0
341341 −1.19718e6 −0.557535
342342 1.72428e6i 0.797155i
343343 5.81600e6i 2.66925i
344344 −571877. −0.260559
345345 0 0
346346 −229635. −0.103121
347347 139108.i 0.0620195i 0.999519 + 0.0310098i 0.00987229π0.00987229\pi
−0.999519 + 0.0310098i 0.990128π0.990128\pi
348348 670985.i 0.297006i
349349 −1.41781e6 −0.623097 −0.311549 0.950230i 0.600848π-0.600848\pi
−0.311549 + 0.950230i 0.600848π0.600848\pi
350350 0 0
351351 −1.37577e6 −0.596045
352352 − 557211.i − 0.239697i
353353 − 2.45675e6i − 1.04936i −0.851300 0.524679i 0.824185π-0.824185\pi
0.851300 0.524679i 0.175815π-0.175815\pi
354354 5.30612e6 2.25045
355355 0 0
356356 786416. 0.328872
357357 1.09254e7i 4.53698i
358358 349758.i 0.144231i
359359 2.88601e6 1.18185 0.590924 0.806727i 0.298763π-0.298763\pi
0.590924 + 0.806727i 0.298763π0.298763\pi
360360 0 0
361361 −1.82659e6 −0.737690
362362 − 85366.4i − 0.0342386i
363363 3.76660e6i 1.50032i
364364 650111. 0.257178
365365 0 0
366366 −3.37809e6 −1.31816
367367 − 2.83587e6i − 1.09906i −0.835474 0.549530i 0.814807π-0.814807\pi
0.835474 0.549530i 0.185193π-0.185193\pi
368368 − 95526.9i − 0.0367711i
369369 9.14641e6 3.49691
370370 0 0
371371 −9.70831e6 −3.66192
372372 981781.i 0.367838i
373373 − 5.02691e6i − 1.87081i −0.353583 0.935403i 0.615037π-0.615037\pi
0.353583 0.935403i 0.384963π-0.384963\pi
374374 3.54634e6 1.31100
375375 0 0
376376 −1.00798e6 −0.367692
377377 254111.i 0.0920810i
378378 7.82891e6i 2.81820i
379379 −2.14892e6 −0.768462 −0.384231 0.923237i 0.625533π-0.625533\pi
−0.384231 + 0.923237i 0.625533π0.625533\pi
380380 0 0
381381 5.08381e6 1.79423
382382 − 1.23007e6i − 0.431291i
383383 − 832971.i − 0.290157i −0.989420 0.145078i 0.953657π-0.953657\pi
0.989420 0.145078i 0.0463434π-0.0463434\pi
384384 −456958. −0.158142
385385 0 0
386386 −729637. −0.249252
387387 − 4.77946e6i − 1.62219i
388388 250468.i 0.0844641i
389389 725243. 0.243002 0.121501 0.992591i 0.461229π-0.461229\pi
0.121501 + 0.992591i 0.461229π0.461229\pi
390390 0 0
391391 607976. 0.201115
392392 − 2.62384e6i − 0.862426i
393393 5.57013e6i 1.81921i
394394 −610032. −0.197976
395395 0 0
396396 4.65689e6 1.49231
397397 2.42654e6i 0.772701i 0.922352 + 0.386351i 0.126265π0.126265\pi
−0.922352 + 0.386351i 0.873735π0.873735\pi
398398 − 2.34642e6i − 0.742504i
399399 5.40417e6 1.69940
400400 0 0
401401 −2.14376e6 −0.665758 −0.332879 0.942970i 0.608020π-0.608020\pi
−0.332879 + 0.942970i 0.608020π0.608020\pi
402402 4.32519e6i 1.33487i
403403 371813.i 0.114041i
404404 2.20972e6 0.673572
405405 0 0
406406 1.44603e6 0.435374
407407 − 7.13335e6i − 2.13455i
408408 − 2.90829e6i − 0.864942i
409409 3.66144e6 1.08229 0.541145 0.840929i 0.317991π-0.317991\pi
0.541145 + 0.840929i 0.317991π0.317991\pi
410410 0 0
411411 9.63388e6 2.81317
412412 − 762273.i − 0.221242i
413413 − 1.14351e7i − 3.29888i
414414 798366. 0.228929
415415 0 0
416416 −173056. −0.0490290
417417 − 5.10642e6i − 1.43806i
418418 − 1.75417e6i − 0.491056i
419419 −3.03786e6 −0.845341 −0.422671 0.906283i 0.638907π-0.638907\pi
−0.422671 + 0.906283i 0.638907π0.638907\pi
420420 0 0
421421 −1.88663e6 −0.518777 −0.259389 0.965773i 0.583521π-0.583521\pi
−0.259389 + 0.965773i 0.583521π0.583521\pi
422422 828162.i 0.226378i
423423 − 8.42422e6i − 2.28917i
424424 2.58430e6 0.698117
425425 0 0
426426 −1.17360e6 −0.313325
427427 7.28008e6i 1.93226i
428428 2.98442e6i 0.787501i
429429 2.56485e6 0.672852
430430 0 0
431431 717193. 0.185970 0.0929850 0.995668i 0.470359π-0.470359\pi
0.0929850 + 0.995668i 0.470359π0.470359\pi
432432 − 2.08401e6i − 0.537268i
433433 − 2.64569e6i − 0.678140i −0.940761 0.339070i 0.889888π-0.889888\pi
0.940761 0.339070i 0.110112π-0.110112\pi
434434 2.11582e6 0.539206
435435 0 0
436436 230513. 0.0580736
437437 − 300731.i − 0.0753310i
438438 − 176505.i − 0.0439614i
439439 −4.47973e6 −1.10941 −0.554704 0.832048i 0.687168π-0.687168\pi
−0.554704 + 0.832048i 0.687168π0.687168\pi
440440 0 0
441441 2.19287e7 5.36929
442442 − 1.10141e6i − 0.268159i
443443 − 4.30731e6i − 1.04279i −0.853315 0.521395i 0.825412π-0.825412\pi
0.853315 0.521395i 0.174588π-0.174588\pi
444444 −5.84992e6 −1.40829
445445 0 0
446446 4.19555e6 0.998738
447447 5.21780e6i 1.23515i
448448 984783.i 0.231817i
449449 25272.9 0.00591615 0.00295808 0.999996i 0.499058π-0.499058\pi
0.00295808 + 0.999996i 0.499058π0.499058\pi
450450 0 0
451451 −9.30495e6 −2.15413
452452 − 812832.i − 0.187135i
453453 − 296095.i − 0.0677932i
454454 −402835. −0.0917250
455455 0 0
456456 −1.43856e6 −0.323978
457457 1.14360e6i 0.256143i 0.991765 + 0.128072i 0.0408787π0.0408787\pi
−0.991765 + 0.128072i 0.959121π0.959121\pi
458458 1.94869e6i 0.434090i
459459 1.32636e7 2.93853
460460 0 0
461461 −8.34911e6 −1.82973 −0.914867 0.403755i 0.867705π-0.867705\pi
−0.914867 + 0.403755i 0.867705π0.867705\pi
462462 − 1.45954e7i − 3.18135i
463463 3.41596e6i 0.740561i 0.928920 + 0.370280i 0.120738π0.120738\pi
−0.928920 + 0.370280i 0.879262π0.879262\pi
464464 −384925. −0.0830007
465465 0 0
466466 3.33138e6 0.710655
467467 5.67105e6i 1.20329i 0.798763 + 0.601646i 0.205488π0.205488\pi
−0.798763 + 0.601646i 0.794512π0.794512\pi
468468 − 1.44632e6i − 0.305245i
469469 9.32116e6 1.95676
470470 0 0
471471 9.36797e6 1.94578
472472 3.04397e6i 0.628906i
473473 4.86231e6i 0.999286i
474474 690706. 0.141204
475475 0 0
476476 −6.26760e6 −1.26790
477477 2.15983e7i 4.34633i
478478 5.39677e6i 1.08035i
479479 6.16340e6 1.22739 0.613694 0.789544i 0.289683π-0.289683\pi
0.613694 + 0.789544i 0.289683π0.289683\pi
480480 0 0
481481 −2.21544e6 −0.436614
482482 6.65133e6i 1.30404i
483483 − 2.50220e6i − 0.488039i
484484 −2.16080e6 −0.419276
485485 0 0
486486 2.91677e6 0.560160
487487 − 7.32701e6i − 1.39992i −0.714180 0.699962i 0.753200π-0.753200\pi
0.714180 0.699962i 0.246800π-0.246800\pi
488488 − 1.93792e6i − 0.368371i
489489 5.63056e6 1.06483
490490 0 0
491491 8.89739e6 1.66555 0.832777 0.553608i 0.186750π-0.186750\pi
0.832777 + 0.553608i 0.186750π0.186750\pi
492492 7.63081e6i 1.42121i
493493 − 2.44984e6i − 0.453963i
494494 −544802. −0.100443
495495 0 0
496496 −563220. −0.102795
497497 2.52920e6i 0.459295i
498498 − 4.22254e6i − 0.762957i
499499 −3.02237e6 −0.543371 −0.271686 0.962386i 0.587581π-0.587581\pi
−0.271686 + 0.962386i 0.587581π0.587581\pi
500500 0 0
501501 1.24406e7 2.21435
502502 1.16509e6i 0.206348i
503503 7.48799e6i 1.31961i 0.751437 + 0.659805i 0.229361π0.229361\pi
−0.751437 + 0.659805i 0.770639π0.770639\pi
504504 −8.23032e6 −1.44325
505505 0 0
506506 −812205. −0.141023
507507 − 796581.i − 0.137629i
508508 2.91644e6i 0.501411i
509509 −4.87997e6 −0.834878 −0.417439 0.908705i 0.637072π-0.637072\pi
−0.417439 + 0.908705i 0.637072π0.637072\pi
510510 0 0
511511 −380383. −0.0644420
512512 − 262144.i − 0.0441942i
513513 − 6.56073e6i − 1.10067i
514514 −2.19281e6 −0.366095
515515 0 0
516516 3.98749e6 0.659288
517517 8.57024e6i 1.41015i
518518 1.26071e7i 2.06438i
519519 1.60116e6 0.260925
520520 0 0
521521 −3.79679e6 −0.612805 −0.306403 0.951902i 0.599125π-0.599125\pi
−0.306403 + 0.951902i 0.599125π0.599125\pi
522522 − 3.21701e6i − 0.516745i
523523 5.66643e6i 0.905848i 0.891549 + 0.452924i 0.149619π0.149619\pi
−0.891549 + 0.452924i 0.850381π0.850381\pi
524524 −3.19543e6 −0.508394
525525 0 0
526526 −3.27365e6 −0.515902
527527 − 3.58459e6i − 0.562228i
528528 3.88522e6i 0.606500i
529529 6.29710e6 0.978366
530530 0 0
531531 −2.54400e7 −3.91544
532532 3.10022e6i 0.474912i
533533 2.88989e6i 0.440619i
534534 −5.48338e6 −0.832138
535535 0 0
536536 −2.48124e6 −0.373042
537537 − 2.43873e6i − 0.364945i
538538 − 3.75782e6i − 0.559732i
539539 −2.23088e7 −3.30754
540540 0 0
541541 1.15648e7 1.69881 0.849403 0.527745i 0.176962π-0.176962\pi
0.849403 + 0.527745i 0.176962π0.176962\pi
542542 6.09665e6i 0.891442i
543543 595228.i 0.0866330i
544544 1.66840e6 0.241715
545545 0 0
546546 −4.53298e6 −0.650732
547547 − 1.28104e7i − 1.83060i −0.402776 0.915299i 0.631955π-0.631955\pi
0.402776 0.915299i 0.368045π-0.368045\pi
548548 5.52669e6i 0.786165i
549549 1.61961e7 2.29340
550550 0 0
551551 −1.21179e6 −0.170039
552552 666073.i 0.0930410i
553553 − 1.48853e6i − 0.206988i
554554 −1.75881e6 −0.243470
555555 0 0
556556 2.92941e6 0.401877
557557 3.51737e6i 0.480374i 0.970727 + 0.240187i 0.0772088π0.0772088\pi
−0.970727 + 0.240187i 0.922791π0.922791\pi
558558 − 4.70711e6i − 0.639984i
559559 1.51011e6 0.204400
560560 0 0
561561 −2.47273e7 −3.31719
562562 2.36813e6i 0.316275i
563563 − 9.45258e6i − 1.25684i −0.777875 0.628419i 0.783702π-0.783702\pi
0.777875 0.628419i 0.216298π-0.216298\pi
564564 7.02829e6 0.930362
565565 0 0
566566 3.10891e6 0.407912
567567 − 2.33385e7i − 3.04871i
568568 − 673259.i − 0.0875611i
569569 −1.11315e7 −1.44136 −0.720679 0.693269i 0.756170π-0.756170\pi
−0.720679 + 0.693269i 0.756170π0.756170\pi
570570 0 0
571571 4.92935e6 0.632702 0.316351 0.948642i 0.397542π-0.397542\pi
0.316351 + 0.948642i 0.397542π0.397542\pi
572572 1.47139e6i 0.188034i
573573 8.57680e6i 1.09129i
574574 1.64450e7 2.08332
575575 0 0
576576 2.19087e6 0.275144
577577 1.09437e7i 1.36843i 0.729279 + 0.684217i 0.239856π0.239856\pi
−0.729279 + 0.684217i 0.760144π0.760144\pi
578578 4.93904e6i 0.614926i
579579 5.08749e6 0.630677
580580 0 0
581581 −9.09993e6 −1.11840
582582 − 1.74642e6i − 0.213718i
583583 − 2.19727e7i − 2.67739i
584584 101256. 0.0122854
585585 0 0
586586 −2.43610e6 −0.293056
587587 7.96444e6i 0.954025i 0.878896 + 0.477013i 0.158280π0.158280\pi
−0.878896 + 0.477013i 0.841720π0.841720\pi
588588 1.82950e7i 2.18218i
589589 −1.77309e6 −0.210592
590590 0 0
591591 4.25352e6 0.500934
592592 − 3.35593e6i − 0.393558i
593593 1.19793e7i 1.39892i 0.714671 + 0.699460i 0.246576π0.246576\pi
−0.714671 + 0.699460i 0.753424π0.753424\pi
594594 −1.77190e7 −2.06051
595595 0 0
596596 −2.99330e6 −0.345172
597597 1.63607e7i 1.87874i
598598 252251.i 0.0288456i
599599 −7.45663e6 −0.849132 −0.424566 0.905397i 0.639573π-0.639573\pi
−0.424566 + 0.905397i 0.639573π0.639573\pi
600600 0 0
601601 −1.04196e7 −1.17670 −0.588351 0.808606i 0.700223π-0.700223\pi
−0.588351 + 0.808606i 0.700223π0.700223\pi
602602 − 8.59337e6i − 0.966434i
603603 − 2.07370e7i − 2.32248i
604604 169862. 0.0189454
605605 0 0
606606 −1.54075e7 −1.70432
607607 571939.i 0.0630054i 0.999504 + 0.0315027i 0.0100293π0.0100293\pi
−0.999504 + 0.0315027i 0.989971π0.989971\pi
608608 − 825262.i − 0.0905384i
609609 −1.00826e7 −1.10162
610610 0 0
611611 2.66171e6 0.288441
612612 1.39437e7i 1.50487i
613613 1.61323e7i 1.73398i 0.498323 + 0.866991i 0.333949π0.333949\pi
−0.498323 + 0.866991i 0.666051π0.666051\pi
614614 −1.06704e7 −1.14225
615615 0 0
616616 8.37299e6 0.889055
617617 − 6.39133e6i − 0.675894i −0.941165 0.337947i 0.890268π-0.890268\pi
0.941165 0.337947i 0.109732π-0.109732\pi
618618 5.31505e6i 0.559804i
619619 −1.27062e7 −1.33287 −0.666435 0.745563i 0.732181π-0.732181\pi
−0.666435 + 0.745563i 0.732181π0.732181\pi
620620 0 0
621621 −3.03771e6 −0.316095
622622 6.49278e6i 0.672907i
623623 1.18172e7i 1.21981i
624624 1.20665e6 0.124057
625625 0 0
626626 −2.36846e6 −0.241563
627627 1.22312e7i 1.24251i
628628 5.37414e6i 0.543764i
629629 2.13587e7 2.15252
630630 0 0
631631 −694354. −0.0694237 −0.0347118 0.999397i 0.511051π-0.511051\pi
−0.0347118 + 0.999397i 0.511051π0.511051\pi
632632 396239.i 0.0394607i
633633 − 5.77447e6i − 0.572799i
634634 −1.04414e7 −1.03166
635635 0 0
636636 −1.80193e7 −1.76643
637637 6.92857e6i 0.676542i
638638 3.27278e6i 0.318321i
639639 5.62676e6 0.545138
640640 0 0
641641 −8.71863e6 −0.838114 −0.419057 0.907960i 0.637639π-0.637639\pi
−0.419057 + 0.907960i 0.637639π0.637639\pi
642642 − 2.08093e7i − 1.99260i
643643 − 5.98737e6i − 0.571096i −0.958364 0.285548i 0.907824π-0.907824\pi
0.958364 0.285548i 0.0921756π-0.0921756\pi
644644 1.43544e6 0.136387
645645 0 0
646646 5.25234e6 0.495189
647647 − 1.09581e7i − 1.02914i −0.857448 0.514571i 0.827951π-0.827951\pi
0.857448 0.514571i 0.172049π-0.172049\pi
648648 6.21259e6i 0.581212i
649649 2.58810e7 2.41195
650650 0 0
651651 −1.47528e7 −1.36434
652652 3.23009e6i 0.297575i
653653 − 6.47503e6i − 0.594236i −0.954841 0.297118i 0.903975π-0.903975\pi
0.954841 0.297118i 0.0960255π-0.0960255\pi
654654 −1.60728e6 −0.146942
655655 0 0
656656 −4.37758e6 −0.397169
657657 846247.i 0.0764863i
658658 − 1.51466e7i − 1.36380i
659659 −501723. −0.0450039 −0.0225020 0.999747i 0.507163π-0.507163\pi
−0.0225020 + 0.999747i 0.507163π0.507163\pi
660660 0 0
661661 4.00659e6 0.356674 0.178337 0.983969i 0.442928π-0.442928\pi
0.178337 + 0.983969i 0.442928π0.442928\pi
662662 − 3.27514e6i − 0.290459i
663663 7.67969e6i 0.678516i
664664 2.42235e6 0.213215
665665 0 0
666666 2.80472e7 2.45021
667667 561077.i 0.0488324i
668668 7.13681e6i 0.618818i
669669 −2.92540e7 −2.52708
670670 0 0
671671 −1.64769e7 −1.41276
672672 − 6.86652e6i − 0.586562i
673673 − 8.17473e6i − 0.695722i −0.937546 0.347861i 0.886908π-0.886908\pi
0.937546 0.347861i 0.113092π-0.113092\pi
674674 1.31564e7 1.11554
675675 0 0
676676 456976. 0.0384615
677677 1.00935e6i 0.0846392i 0.999104 + 0.0423196i 0.0134748π0.0134748\pi
−0.999104 + 0.0423196i 0.986525π0.986525\pi
678678 5.66757e6i 0.473503i
679679 −3.76368e6 −0.313284
680680 0 0
681681 2.80882e6 0.232090
682682 4.78870e6i 0.394237i
683683 − 1.99189e7i − 1.63386i −0.576739 0.816928i 0.695675π-0.695675\pi
0.576739 0.816928i 0.304325π-0.304325\pi
684684 6.89712e6 0.563674
685685 0 0
686686 2.32640e7 1.88745
687687 − 1.35875e7i − 1.09837i
688688 2.28751e6i 0.184243i
689689 −6.82417e6 −0.547648
690690 0 0
691691 −677407. −0.0539703 −0.0269851 0.999636i 0.508591π-0.508591\pi
−0.0269851 + 0.999636i 0.508591π0.508591\pi
692692 918541.i 0.0729177i
693693 6.99772e7i 5.53508i
694694 556432. 0.0438544
695695 0 0
696696 2.68394e6 0.210015
697697 − 2.78609e7i − 2.17227i
698698 5.67126e6i 0.440596i
699699 −2.32284e7 −1.79815
700700 0 0
701701 1.04542e7 0.803518 0.401759 0.915745i 0.368399π-0.368399\pi
0.401759 + 0.915745i 0.368399π0.368399\pi
702702 5.50310e6i 0.421468i
703703 − 1.05649e7i − 0.806263i
704704 −2.22884e6 −0.169492
705705 0 0
706706 −9.82700e6 −0.742009
707707 3.32046e7i 2.49833i
708708 − 2.12245e7i − 1.59131i
709709 2.25125e7 1.68193 0.840964 0.541091i 0.181989π-0.181989\pi
0.840964 + 0.541091i 0.181989π0.181989\pi
710710 0 0
711711 −3.31157e6 −0.245674
712712 − 3.14566e6i − 0.232548i
713713 820964.i 0.0604784i
714714 4.37017e7 3.20813
715715 0 0
716716 1.39903e6 0.101987
717717 − 3.76297e7i − 2.73358i
718718 − 1.15440e7i − 0.835693i
719719 2.77678e6 0.200317 0.100159 0.994971i 0.468065π-0.468065\pi
0.100159 + 0.994971i 0.468065π0.468065\pi
720720 0 0
721721 1.14544e7 0.820603
722722 7.30637e6i 0.521625i
723723 − 4.63772e7i − 3.29958i
724724 −341466. −0.0242103
725725 0 0
726726 1.50664e7 1.06089
727727 2.76872e6i 0.194287i 0.995270 + 0.0971434i 0.0309705π0.0309705\pi
−0.995270 + 0.0971434i 0.969029π0.969029\pi
728728 − 2.60044e6i − 0.181852i
729729 3.25086e6 0.226558
730730 0 0
731731 −1.45587e7 −1.00770
732732 1.35124e7i 0.932081i
733733 1.80998e7i 1.24427i 0.782911 + 0.622133i 0.213734π0.213734\pi
−0.782911 + 0.622133i 0.786266π0.786266\pi
734734 −1.13435e7 −0.777152
735735 0 0
736736 −382108. −0.0260011
737737 2.10964e7i 1.43067i
738738 − 3.65857e7i − 2.47269i
739739 3.57016e6 0.240479 0.120239 0.992745i 0.461634π-0.461634\pi
0.120239 + 0.992745i 0.461634π0.461634\pi
740740 0 0
741741 3.79870e6 0.254149
742742 3.88332e7i 2.58937i
743743 1.73285e7i 1.15157i 0.817603 + 0.575783i 0.195303π0.195303\pi
−0.817603 + 0.575783i 0.804697π0.804697\pi
744744 3.92712e6 0.260101
745745 0 0
746746 −2.01076e7 −1.32286
747747 2.02448e7i 1.32743i
748748 − 1.41854e7i − 0.927015i
749749 −4.48457e7 −2.92090
750750 0 0
751751 3.04634e6 0.197096 0.0985480 0.995132i 0.468580π-0.468580\pi
0.0985480 + 0.995132i 0.468580π0.468580\pi
752752 4.03193e6i 0.259997i
753753 − 8.12374e6i − 0.522118i
754754 1.01644e6 0.0651111
755755 0 0
756756 3.13156e7 1.99277
757757 − 8.98398e6i − 0.569808i −0.958556 0.284904i 0.908038π-0.908038\pi
0.958556 0.284904i 0.0919618π-0.0919618\pi
758758 8.59568e6i 0.543384i
759759 5.66320e6 0.356827
760760 0 0
761761 1.31757e7 0.824731 0.412366 0.911018i 0.364703π-0.364703\pi
0.412366 + 0.911018i 0.364703π0.364703\pi
762762 − 2.03352e7i − 1.26871i
763763 3.46382e6i 0.215399i
764764 −4.92027e6 −0.304969
765765 0 0
766766 −3.33188e6 −0.205172
767767 − 8.03799e6i − 0.493354i
768768 1.82783e6i 0.111824i
769769 −3.53661e6 −0.215661 −0.107830 0.994169i 0.534390π-0.534390\pi
−0.107830 + 0.994169i 0.534390π0.534390\pi
770770 0 0
771771 1.52897e7 0.926322
772772 2.91855e6i 0.176248i
773773 3.14397e7i 1.89247i 0.323479 + 0.946235i 0.395147π0.395147\pi
−0.323479 + 0.946235i 0.604853π0.604853\pi
774774 −1.91179e7 −1.14706
775775 0 0
776776 1.00187e6 0.0597251
777777 − 8.79044e7i − 5.22346i
778778 − 2.90097e6i − 0.171828i
779779 −1.37812e7 −0.813659
780780 0 0
781781 −5.72429e6 −0.335810
782782 − 2.43191e6i − 0.142210i
783783 1.22404e7i 0.713498i
784784 −1.04953e7 −0.609827
785785 0 0
786786 2.22805e7 1.28638
787787 1.27213e7i 0.732139i 0.930588 + 0.366069i 0.119297π0.119297\pi
−0.930588 + 0.366069i 0.880703π0.880703\pi
788788 2.44013e6i 0.139990i
789789 2.28259e7 1.30538
790790 0 0
791791 1.22141e7 0.694097
792792 − 1.86276e7i − 1.05522i
793793 5.11731e6i 0.288974i
794794 9.70617e6 0.546382
795795 0 0
796796 −9.38569e6 −0.525029
797797 1.84237e7i 1.02738i 0.857977 + 0.513689i 0.171721π0.171721\pi
−0.857977 + 0.513689i 0.828279π0.828279\pi
798798 − 2.16167e7i − 1.20166i
799799 −2.56610e7 −1.42203
800800 0 0
801801 2.62899e7 1.44780
802802 8.57506e6i 0.470762i
803803 − 860915.i − 0.0471164i
804804 1.73008e7 0.943899
805805 0 0
806806 1.48725e6 0.0806394
807807 2.62019e7i 1.41628i
808808 − 8.83888e6i − 0.476287i
809809 −2.10360e7 −1.13004 −0.565018 0.825079i 0.691131π-0.691131\pi
−0.565018 + 0.825079i 0.691131π0.691131\pi
810810 0 0
811811 3.53571e7 1.88767 0.943833 0.330424i 0.107192π-0.107192\pi
0.943833 + 0.330424i 0.107192π0.107192\pi
812812 − 5.78412e6i − 0.307856i
813813 − 4.25097e7i − 2.25560i
814814 −2.85334e7 −1.50936
815815 0 0
816816 −1.16331e7 −0.611606
817817 7.20136e6i 0.377450i
818818 − 1.46458e7i − 0.765295i
819819 2.17332e7 1.13218
820820 0 0
821821 1.72038e7 0.890770 0.445385 0.895339i 0.353067π-0.353067\pi
0.445385 + 0.895339i 0.353067π0.353067\pi
822822 − 3.85355e7i − 1.98921i
823823 947098.i 0.0487411i 0.999703 + 0.0243705i 0.00775815π0.00775815\pi
−0.999703 + 0.0243705i 0.992242π0.992242\pi
824824 −3.04909e6 −0.156442
825825 0 0
826826 −4.57405e7 −2.33266
827827 − 3.05385e7i − 1.55269i −0.630308 0.776345i 0.717072π-0.717072\pi
0.630308 0.776345i 0.282928π-0.282928\pi
828828 − 3.19346e6i − 0.161877i
829829 1.57415e7 0.795538 0.397769 0.917486i 0.369785π-0.369785\pi
0.397769 + 0.917486i 0.369785π0.369785\pi
830830 0 0
831831 1.22636e7 0.616047
832832 692224.i 0.0346688i
833833 − 6.67971e7i − 3.33538i
834834 −2.04257e7 −1.01686
835835 0 0
836836 −7.01668e6 −0.347229
837837 1.79101e7i 0.883659i
838838 1.21514e7i 0.597746i
839839 −2.07700e7 −1.01867 −0.509333 0.860570i 0.670108π-0.670108\pi
−0.509333 + 0.860570i 0.670108π0.670108\pi
840840 0 0
841841 −1.82503e7 −0.889774
842842 7.54651e6i 0.366831i
843843 − 1.65121e7i − 0.800263i
844844 3.31265e6 0.160073
845845 0 0
846846 −3.36969e7 −1.61869
847847 − 3.24694e7i − 1.55513i
848848 − 1.03372e7i − 0.493643i
849849 −2.16772e7 −1.03213
850850 0 0
851851 −4.89169e6 −0.231545
852852 4.69438e6i 0.221554i
853853 1.91838e7i 0.902740i 0.892337 + 0.451370i 0.149064π0.149064\pi
−0.892337 + 0.451370i 0.850936π0.850936\pi
854854 2.91203e7 1.36632
855855 0 0
856856 1.19377e7 0.556847
857857 2.64211e7i 1.22885i 0.788975 + 0.614425i 0.210612π0.210612\pi
−0.788975 + 0.614425i 0.789388π0.789388\pi
858858 − 1.02594e7i − 0.475778i
859859 3.30576e7 1.52858 0.764289 0.644873i 0.223090π-0.223090\pi
0.764289 + 0.644873i 0.223090π0.223090\pi
860860 0 0
861861 −1.14665e8 −5.27137
862862 − 2.86877e6i − 0.131501i
863863 − 1.19324e7i − 0.545380i −0.962102 0.272690i 0.912087π-0.912087\pi
0.962102 0.272690i 0.0879133π-0.0879133\pi
864864 −8.33605e6 −0.379906
865865 0 0
866866 −1.05828e7 −0.479518
867867 − 3.44381e7i − 1.55593i
868868 − 8.46328e6i − 0.381276i
869869 3.36897e6 0.151338
870870 0 0
871871 6.55203e6 0.292638
872872 − 922051.i − 0.0410643i
873873 8.37313e6i 0.371837i
874874 −1.20292e6 −0.0532671
875875 0 0
876876 −706020. −0.0310854
877877 3.88434e6i 0.170537i 0.996358 + 0.0852684i 0.0271748π0.0271748\pi
−0.996358 + 0.0852684i 0.972825π0.972825\pi
878878 1.79189e7i 0.784469i
879879 1.69860e7 0.741513
880880 0 0
881881 −8.93397e6 −0.387797 −0.193899 0.981022i 0.562113π-0.562113\pi
−0.193899 + 0.981022i 0.562113π0.562113\pi
882882 − 8.77148e7i − 3.79666i
883883 4.32552e6i 0.186697i 0.995634 + 0.0933484i 0.0297570π0.0297570\pi
−0.995634 + 0.0933484i 0.970243π0.970243\pi
884884 −4.40563e6 −0.189617
885885 0 0
886886 −1.72292e7 −0.737364
887887 3.55552e7i 1.51738i 0.651453 + 0.758689i 0.274160π0.274160\pi
−0.651453 + 0.758689i 0.725840π0.725840\pi
888888 2.33997e7i 0.995812i
889889 −4.38242e7 −1.85977
890890 0 0
891891 5.28217e7 2.22904
892892 − 1.67822e7i − 0.706214i
893893 1.26930e7i 0.532643i
894894 2.08712e7 0.873380
895895 0 0
896896 3.93913e6 0.163919
897897 − 1.75885e6i − 0.0729874i
898898 − 101092.i − 0.00418335i
899899 3.30807e6 0.136514
900900 0 0
901901 6.57906e7 2.69993
902902 3.72198e7i 1.52320i
903903 5.99184e7i 2.44535i
904904 −3.25133e6 −0.132324
905905 0 0
906906 −1.18438e6 −0.0479370
907907 2.44157e7i 0.985486i 0.870175 + 0.492743i 0.164006π0.164006\pi
−0.870175 + 0.492743i 0.835994π0.835994\pi
908908 1.61134e6i 0.0648593i
909909 7.38709e7 2.96527
910910 0 0
911911 3.00267e7 1.19870 0.599352 0.800486i 0.295425π-0.295425\pi
0.599352 + 0.800486i 0.295425π0.295425\pi
912912 5.75424e6i 0.229087i
913913 − 2.05957e7i − 0.817711i
914914 4.57439e6 0.181120
915915 0 0
916916 7.79478e6 0.306948
917917 − 4.80164e7i − 1.88567i
918918 − 5.30544e7i − 2.07785i
919919 1.30118e7 0.508216 0.254108 0.967176i 0.418218π-0.418218\pi
0.254108 + 0.967176i 0.418218π0.418218\pi
920920 0 0
921921 7.44009e7 2.89021
922922 3.33964e7i 1.29382i
923923 1.77782e6i 0.0686886i
924924 −5.83817e7 −2.24956
925925 0 0
926926 1.36639e7 0.523656
927927 − 2.54828e7i − 0.973975i
928928 1.53970e6i 0.0586904i
929929 5.16678e7 1.96418 0.982089 0.188419i 0.0603362π-0.0603362\pi
0.982089 + 0.188419i 0.0603362π0.0603362\pi
930930 0 0
931931 −3.30407e7 −1.24932
932932 − 1.33255e7i − 0.502509i
933933 − 4.52717e7i − 1.70264i
934934 2.26842e7 0.850857
935935 0 0
936936 −5.78526e6 −0.215841
937937 − 4.04703e6i − 0.150587i −0.997161 0.0752936i 0.976011π-0.976011\pi
0.997161 0.0752936i 0.0239894π-0.0239894\pi
938938 − 3.72846e7i − 1.38364i
939939 1.65144e7 0.611221
940940 0 0
941941 −4.43008e7 −1.63094 −0.815470 0.578799i 0.803521π-0.803521\pi
−0.815470 + 0.578799i 0.803521π0.803521\pi
942942 − 3.74719e7i − 1.37587i
943943 6.38088e6i 0.233669i
944944 1.21759e7 0.444704
945945 0 0
946946 1.94492e7 0.706602
947947 − 3.60463e7i − 1.30613i −0.757303 0.653064i 0.773483π-0.773483\pi
0.757303 0.653064i 0.226517π-0.226517\pi
948948 − 2.76283e6i − 0.0998464i
949949 −267379. −0.00963745
950950 0 0
951951 7.28042e7 2.61039
952952 2.50704e7i 0.896539i
953953 1.31248e7i 0.468123i 0.972222 + 0.234061i 0.0752017π0.0752017\pi
−0.972222 + 0.234061i 0.924798π0.924798\pi
954954 8.63931e7 3.07332
955955 0 0
956956 2.15871e7 0.763923
957957 − 2.28198e7i − 0.805439i
958958 − 2.46536e7i − 0.867894i
959959 −8.30473e7 −2.91594
960960 0 0
961961 −2.37888e7 −0.830929
962962 8.86176e6i 0.308733i
963963 9.97693e7i 3.46682i
964964 2.66053e7 0.922096
965965 0 0
966966 −1.00088e7 −0.345096
967967 2.48150e7i 0.853390i 0.904396 + 0.426695i 0.140322π0.140322\pi
−0.904396 + 0.426695i 0.859678π0.859678\pi
968968 8.64318e6i 0.296473i
969969 −3.66226e7 −1.25297
970970 0 0
971971 −3.54227e6 −0.120569 −0.0602843 0.998181i 0.519201π-0.519201\pi
−0.0602843 + 0.998181i 0.519201π0.519201\pi
972972 − 1.16671e7i − 0.396093i
973973 4.40191e7i 1.49059i
974974 −2.93080e7 −0.989896
975975 0 0
976976 −7.75167e6 −0.260478
977977 9.16916e6i 0.307322i 0.988124 + 0.153661i 0.0491063π0.0491063\pi
−0.988124 + 0.153661i 0.950894π0.950894\pi
978978 − 2.25222e7i − 0.752947i
979979 −2.67456e7 −0.891857
980980 0 0
981981 7.70604e6 0.255658
982982 − 3.55895e7i − 1.17772i
983983 3.05912e7i 1.00975i 0.863193 + 0.504874i 0.168461π0.168461\pi
−0.863193 + 0.504874i 0.831539π0.831539\pi
984984 3.05233e7 1.00495
985985 0 0
986986 −9.79936e6 −0.321000
987987 1.05611e8i 3.45078i
988988 2.17921e6i 0.0710242i
989989 3.33433e6 0.108397
990990 0 0
991991 3.47852e7 1.12515 0.562575 0.826746i 0.309811π-0.309811\pi
0.562575 + 0.826746i 0.309811π0.309811\pi
992992 2.25288e6i 0.0726874i
993993 2.28363e7i 0.734942i
994994 1.01168e7 0.324771
995995 0 0
996996 −1.68902e7 −0.539492
997997 − 4.21812e7i − 1.34394i −0.740577 0.671972i 0.765448π-0.765448\pi
0.740577 0.671972i 0.234552π-0.234552\pi
998998 1.20895e7i 0.384222i
999999 −1.06717e8 −3.38314
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 650.6.b.j.599.3 6
5.2 odd 4 650.6.a.j.1.3 3
5.3 odd 4 130.6.a.f.1.1 3
5.4 even 2 inner 650.6.b.j.599.4 6
20.3 even 4 1040.6.a.l.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
130.6.a.f.1.1 3 5.3 odd 4
650.6.a.j.1.3 3 5.2 odd 4
650.6.b.j.599.3 6 1.1 even 1 trivial
650.6.b.j.599.4 6 5.4 even 2 inner
1040.6.a.l.1.3 3 20.3 even 4