Properties

Label 1014.6.a.o.1.3
Level 10141014
Weight 66
Character 1014.1
Self dual yes
Analytic conductor 162.629162.629
Analytic rank 00
Dimension 33
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1014,6,Mod(1,1014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1014, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1014.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 1014=23132 1014 = 2 \cdot 3 \cdot 13^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 1014.a (trivial)

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: yes
Analytic conductor: 162.629193290162.629193290
Analytic rank: 00
Dimension: 33
Coefficient field: Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x2727x6617 x^{3} - x^{2} - 727x - 6617 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 223 2^{2}\cdot 3
Twist minimal: no (minimal twist has level 78)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 18.9385-18.9385 of defining polynomial
Character χ\chi == 1014.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q4.00000q29.00000q3+16.0000q4+86.8538q5+36.0000q6+98.7774q764.0000q8+81.0000q9347.415q10+610.754q11144.000q12395.109q14781.684q15+256.000q16+1148.60q17324.000q182267.14q19+1389.66q20888.996q212443.02q22433.224q23+576.000q24+4418.59q25729.000q27+1580.44q28+7669.59q29+3126.74q307367.13q311024.00q325496.79q334594.42q34+8579.19q35+1296.00q36+10575.0q37+9068.57q385558.65q40+3699.17q41+3555.98q42+6061.57q43+9772.07q44+7035.16q45+1732.89q46+8740.69q472304.00q487050.03q4917674.4q5010337.4q51+34784.8q53+2916.00q54+53046.3q556321.75q56+20404.3q5730678.4q5811949.6q5912507.0q6045400.2q61+29468.5q62+8000.97q63+4096.00q64+21987.2q66+45698.1q67+18377.7q68+3899.01q6934316.8q70+23826.9q715184.00q72+37759.1q7342299.9q7439767.3q7536274.3q76+60328.7q7735307.0q79+22234.6q80+6561.00q8114796.7q8231484.4q8314223.9q84+99760.7q8524246.3q8669026.3q8739088.3q88+59051.5q8928140.6q906931.58q92+66304.2q9334962.7q94196910.q95+9216.00q964965.78q97+28200.1q98+49471.1q99+O(q100)q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} +86.8538 q^{5} +36.0000 q^{6} +98.7774 q^{7} -64.0000 q^{8} +81.0000 q^{9} -347.415 q^{10} +610.754 q^{11} -144.000 q^{12} -395.109 q^{14} -781.684 q^{15} +256.000 q^{16} +1148.60 q^{17} -324.000 q^{18} -2267.14 q^{19} +1389.66 q^{20} -888.996 q^{21} -2443.02 q^{22} -433.224 q^{23} +576.000 q^{24} +4418.59 q^{25} -729.000 q^{27} +1580.44 q^{28} +7669.59 q^{29} +3126.74 q^{30} -7367.13 q^{31} -1024.00 q^{32} -5496.79 q^{33} -4594.42 q^{34} +8579.19 q^{35} +1296.00 q^{36} +10575.0 q^{37} +9068.57 q^{38} -5558.65 q^{40} +3699.17 q^{41} +3555.98 q^{42} +6061.57 q^{43} +9772.07 q^{44} +7035.16 q^{45} +1732.89 q^{46} +8740.69 q^{47} -2304.00 q^{48} -7050.03 q^{49} -17674.4 q^{50} -10337.4 q^{51} +34784.8 q^{53} +2916.00 q^{54} +53046.3 q^{55} -6321.75 q^{56} +20404.3 q^{57} -30678.4 q^{58} -11949.6 q^{59} -12507.0 q^{60} -45400.2 q^{61} +29468.5 q^{62} +8000.97 q^{63} +4096.00 q^{64} +21987.2 q^{66} +45698.1 q^{67} +18377.7 q^{68} +3899.01 q^{69} -34316.8 q^{70} +23826.9 q^{71} -5184.00 q^{72} +37759.1 q^{73} -42299.9 q^{74} -39767.3 q^{75} -36274.3 q^{76} +60328.7 q^{77} -35307.0 q^{79} +22234.6 q^{80} +6561.00 q^{81} -14796.7 q^{82} -31484.4 q^{83} -14223.9 q^{84} +99760.7 q^{85} -24246.3 q^{86} -69026.3 q^{87} -39088.3 q^{88} +59051.5 q^{89} -28140.6 q^{90} -6931.58 q^{92} +66304.2 q^{93} -34962.7 q^{94} -196910. q^{95} +9216.00 q^{96} -4965.78 q^{97} +28200.1 q^{98} +49471.1 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q12q227q3+48q4+40q5+108q6+170q7192q8+243q9160q10+162q11432q12680q14360q15+768q16+418q17972q18+66q19++13122q99+O(q100) 3 q - 12 q^{2} - 27 q^{3} + 48 q^{4} + 40 q^{5} + 108 q^{6} + 170 q^{7} - 192 q^{8} + 243 q^{9} - 160 q^{10} + 162 q^{11} - 432 q^{12} - 680 q^{14} - 360 q^{15} + 768 q^{16} + 418 q^{17} - 972 q^{18} + 66 q^{19}+ \cdots + 13122 q^{99}+O(q^{100}) Copy content Toggle raw display

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 −4.00000 −0.707107
33 −9.00000 −0.577350
44 16.0000 0.500000
55 86.8538 1.55369 0.776844 0.629693i 0.216819π-0.216819\pi
0.776844 + 0.629693i 0.216819π0.216819\pi
66 36.0000 0.408248
77 98.7774 0.761925 0.380963 0.924590i 0.375593π-0.375593\pi
0.380963 + 0.924590i 0.375593π0.375593\pi
88 −64.0000 −0.353553
99 81.0000 0.333333
1010 −347.415 −1.09862
1111 610.754 1.52190 0.760948 0.648813i 0.224734π-0.224734\pi
0.760948 + 0.648813i 0.224734π0.224734\pi
1212 −144.000 −0.288675
1313 0 0
1414 −395.109 −0.538762
1515 −781.684 −0.897023
1616 256.000 0.250000
1717 1148.60 0.963936 0.481968 0.876189i 0.339922π-0.339922\pi
0.481968 + 0.876189i 0.339922π0.339922\pi
1818 −324.000 −0.235702
1919 −2267.14 −1.44077 −0.720386 0.693574i 0.756035π-0.756035\pi
−0.720386 + 0.693574i 0.756035π0.756035\pi
2020 1389.66 0.776844
2121 −888.996 −0.439898
2222 −2443.02 −1.07614
2323 −433.224 −0.170763 −0.0853813 0.996348i 0.527211π-0.527211\pi
−0.0853813 + 0.996348i 0.527211π0.527211\pi
2424 576.000 0.204124
2525 4418.59 1.41395
2626 0 0
2727 −729.000 −0.192450
2828 1580.44 0.380963
2929 7669.59 1.69347 0.846734 0.532016i 0.178566π-0.178566\pi
0.846734 + 0.532016i 0.178566π0.178566\pi
3030 3126.74 0.634291
3131 −7367.13 −1.37687 −0.688437 0.725296i 0.741703π-0.741703\pi
−0.688437 + 0.725296i 0.741703π0.741703\pi
3232 −1024.00 −0.176777
3333 −5496.79 −0.878667
3434 −4594.42 −0.681606
3535 8579.19 1.18379
3636 1296.00 0.166667
3737 10575.0 1.26991 0.634957 0.772547i 0.281018π-0.281018\pi
0.634957 + 0.772547i 0.281018π0.281018\pi
3838 9068.57 1.01878
3939 0 0
4040 −5558.65 −0.549312
4141 3699.17 0.343672 0.171836 0.985126i 0.445030π-0.445030\pi
0.171836 + 0.985126i 0.445030π0.445030\pi
4242 3555.98 0.311055
4343 6061.57 0.499936 0.249968 0.968254i 0.419580π-0.419580\pi
0.249968 + 0.968254i 0.419580π0.419580\pi
4444 9772.07 0.760948
4545 7035.16 0.517896
4646 1732.89 0.120747
4747 8740.69 0.577166 0.288583 0.957455i 0.406816π-0.406816\pi
0.288583 + 0.957455i 0.406816π0.406816\pi
4848 −2304.00 −0.144338
4949 −7050.03 −0.419470
5050 −17674.4 −0.999812
5151 −10337.4 −0.556529
5252 0 0
5353 34784.8 1.70098 0.850491 0.525990i 0.176305π-0.176305\pi
0.850491 + 0.525990i 0.176305π0.176305\pi
5454 2916.00 0.136083
5555 53046.3 2.36455
5656 −6321.75 −0.269381
5757 20404.3 0.831830
5858 −30678.4 −1.19746
5959 −11949.6 −0.446915 −0.223457 0.974714i 0.571734π-0.571734\pi
−0.223457 + 0.974714i 0.571734π0.571734\pi
6060 −12507.0 −0.448511
6161 −45400.2 −1.56219 −0.781094 0.624414i 0.785338π-0.785338\pi
−0.781094 + 0.624414i 0.785338π0.785338\pi
6262 29468.5 0.973597
6363 8000.97 0.253975
6464 4096.00 0.125000
6565 0 0
6666 21987.2 0.621311
6767 45698.1 1.24369 0.621844 0.783141i 0.286384π-0.286384\pi
0.621844 + 0.783141i 0.286384π0.286384\pi
6868 18377.7 0.481968
6969 3899.01 0.0985898
7070 −34316.8 −0.837069
7171 23826.9 0.560946 0.280473 0.959862i 0.409509π-0.409509\pi
0.280473 + 0.959862i 0.409509π0.409509\pi
7272 −5184.00 −0.117851
7373 37759.1 0.829305 0.414653 0.909980i 0.363903π-0.363903\pi
0.414653 + 0.909980i 0.363903π0.363903\pi
7474 −42299.9 −0.897965
7575 −39767.3 −0.816343
7676 −36274.3 −0.720386
7777 60328.7 1.15957
7878 0 0
7979 −35307.0 −0.636492 −0.318246 0.948008i 0.603094π-0.603094\pi
−0.318246 + 0.948008i 0.603094π0.603094\pi
8080 22234.6 0.388422
8181 6561.00 0.111111
8282 −14796.7 −0.243013
8383 −31484.4 −0.501649 −0.250824 0.968033i 0.580702π-0.580702\pi
−0.250824 + 0.968033i 0.580702π0.580702\pi
8484 −14223.9 −0.219949
8585 99760.7 1.49766
8686 −24246.3 −0.353508
8787 −69026.3 −0.977724
8888 −39088.3 −0.538071
8989 59051.5 0.790235 0.395117 0.918631i 0.370704π-0.370704\pi
0.395117 + 0.918631i 0.370704π0.370704\pi
9090 −28140.6 −0.366208
9191 0 0
9292 −6931.58 −0.0853813
9393 66304.2 0.794938
9494 −34962.7 −0.408118
9595 −196910. −2.23851
9696 9216.00 0.102062
9797 −4965.78 −0.0535868 −0.0267934 0.999641i 0.508530π-0.508530\pi
−0.0267934 + 0.999641i 0.508530π0.508530\pi
9898 28200.1 0.296610
9999 49471.1 0.507298
100100 70697.4 0.706974
101101 125605. 1.22519 0.612596 0.790396i 0.290125π-0.290125\pi
0.612596 + 0.790396i 0.290125π0.290125\pi
102102 41349.8 0.393525
103103 126352. 1.17351 0.586756 0.809764i 0.300405π-0.300405\pi
0.586756 + 0.809764i 0.300405π0.300405\pi
104104 0 0
105105 −77212.7 −0.683464
106106 −139139. −1.20278
107107 33067.8 0.279219 0.139610 0.990207i 0.455415π-0.455415\pi
0.139610 + 0.990207i 0.455415π0.455415\pi
108108 −11664.0 −0.0962250
109109 −147666. −1.19046 −0.595230 0.803555i 0.702939π-0.702939\pi
−0.595230 + 0.803555i 0.702939π0.702939\pi
110110 −212185. −1.67199
111111 −95174.7 −0.733186
112112 25287.0 0.190481
113113 118111. 0.870152 0.435076 0.900394i 0.356722π-0.356722\pi
0.435076 + 0.900394i 0.356722π0.356722\pi
114114 −81617.2 −0.588192
115115 −37627.1 −0.265312
116116 122713. 0.846734
117117 0 0
118118 47798.6 0.316016
119119 113456. 0.734447
120120 50027.8 0.317145
121121 211970. 1.31616
122122 181601. 1.10463
123123 −33292.5 −0.198419
124124 −117874. −0.688437
125125 112353. 0.643147
126126 −32003.9 −0.179587
127127 −322666. −1.77518 −0.887592 0.460631i 0.847623π-0.847623\pi
−0.887592 + 0.460631i 0.847623π0.847623\pi
128128 −16384.0 −0.0883883
129129 −54554.2 −0.288638
130130 0 0
131131 −357874. −1.82202 −0.911008 0.412390i 0.864694π-0.864694\pi
−0.911008 + 0.412390i 0.864694π0.864694\pi
132132 −87948.6 −0.439333
133133 −223942. −1.09776
134134 −182792. −0.879420
135135 −63316.4 −0.299008
136136 −73510.7 −0.340803
137137 −347064. −1.57982 −0.789912 0.613221i 0.789874π-0.789874\pi
−0.789912 + 0.613221i 0.789874π0.789874\pi
138138 −15596.1 −0.0697135
139139 −103030. −0.452299 −0.226149 0.974093i 0.572614π-0.572614\pi
−0.226149 + 0.974093i 0.572614π0.572614\pi
140140 137267. 0.591897
141141 −78666.2 −0.333227
142142 −95307.4 −0.396649
143143 0 0
144144 20736.0 0.0833333
145145 666133. 2.63112
146146 −151036. −0.586407
147147 63450.3 0.242181
148148 169199. 0.634957
149149 −90695.3 −0.334672 −0.167336 0.985900i 0.553516π-0.553516\pi
−0.167336 + 0.985900i 0.553516π0.553516\pi
150150 159069. 0.577242
151151 −104288. −0.372215 −0.186107 0.982529i 0.559587π-0.559587\pi
−0.186107 + 0.982529i 0.559587π0.559587\pi
152152 145097. 0.509390
153153 93036.9 0.321312
154154 −241315. −0.819940
155155 −639863. −2.13923
156156 0 0
157157 −314419. −1.01803 −0.509014 0.860758i 0.669990π-0.669990\pi
−0.509014 + 0.860758i 0.669990π0.669990\pi
158158 141228. 0.450068
159159 −313063. −0.982062
160160 −88938.3 −0.274656
161161 −42792.7 −0.130108
162162 −26244.0 −0.0785674
163163 140732. 0.414881 0.207441 0.978248i 0.433487π-0.433487\pi
0.207441 + 0.978248i 0.433487π0.433487\pi
164164 59186.7 0.171836
165165 −477417. −1.36517
166166 125937. 0.354719
167167 108944. 0.302281 0.151141 0.988512i 0.451705π-0.451705\pi
0.151141 + 0.988512i 0.451705π0.451705\pi
168168 56895.8 0.155527
169169 0 0
170170 −399043. −1.05900
171171 −183639. −0.480257
172172 96985.2 0.249968
173173 −401188. −1.01914 −0.509569 0.860430i 0.670195π-0.670195\pi
−0.509569 + 0.860430i 0.670195π0.670195\pi
174174 276105. 0.691355
175175 436456. 1.07732
176176 156353. 0.380474
177177 107547. 0.258026
178178 −236206. −0.558780
179179 209535. 0.488792 0.244396 0.969676i 0.421410π-0.421410\pi
0.244396 + 0.969676i 0.421410π0.421410\pi
180180 112563. 0.258948
181181 −236277. −0.536075 −0.268038 0.963408i 0.586375π-0.586375\pi
−0.268038 + 0.963408i 0.586375π0.586375\pi
182182 0 0
183183 408602. 0.901929
184184 27726.3 0.0603737
185185 918476. 1.97305
186186 −265217. −0.562106
187187 701515. 1.46701
188188 139851. 0.288583
189189 −72008.7 −0.146633
190190 787640. 1.58287
191191 509719. 1.01099 0.505496 0.862829i 0.331310π-0.331310\pi
0.505496 + 0.862829i 0.331310π0.331310\pi
192192 −36864.0 −0.0721688
193193 −58146.8 −0.112365 −0.0561827 0.998421i 0.517893π-0.517893\pi
−0.0561827 + 0.998421i 0.517893π0.517893\pi
194194 19863.1 0.0378916
195195 0 0
196196 −112801. −0.209735
197197 −91830.0 −0.168585 −0.0842925 0.996441i 0.526863π-0.526863\pi
−0.0842925 + 0.996441i 0.526863π0.526863\pi
198198 −197884. −0.358714
199199 −562291. −1.00653 −0.503267 0.864131i 0.667869π-0.667869\pi
−0.503267 + 0.864131i 0.667869π0.667869\pi
200200 −282790. −0.499906
201201 −411283. −0.718043
202202 −502421. −0.866341
203203 757582. 1.29030
204204 −165399. −0.278264
205205 321287. 0.533960
206206 −505406. −0.829798
207207 −35091.1 −0.0569208
208208 0 0
209209 −1.38467e6 −2.19270
210210 308851. 0.483282
211211 650662. 1.00612 0.503059 0.864252i 0.332208π-0.332208\pi
0.503059 + 0.864252i 0.332208π0.332208\pi
212212 556557. 0.850491
213213 −214442. −0.323862
214214 −132271. −0.197438
215215 526471. 0.776745
216216 46656.0 0.0680414
217217 −727706. −1.04907
218218 590665. 0.841782
219219 −339832. −0.478800
220220 848741. 1.18228
221221 0 0
222222 380699. 0.518441
223223 −302795. −0.407743 −0.203871 0.978998i 0.565352π-0.565352\pi
−0.203871 + 0.978998i 0.565352π0.565352\pi
224224 −101148. −0.134691
225225 357906. 0.471316
226226 −472445. −0.615290
227227 −723191. −0.931512 −0.465756 0.884913i 0.654218π-0.654218\pi
−0.465756 + 0.884913i 0.654218π0.654218\pi
228228 326469. 0.415915
229229 1.39378e6 1.75633 0.878166 0.478356i 0.158767π-0.158767\pi
0.878166 + 0.478356i 0.158767π0.158767\pi
230230 150509. 0.187604
231231 −542958. −0.669478
232232 −490854. −0.598731
233233 319385. 0.385411 0.192706 0.981257i 0.438274π-0.438274\pi
0.192706 + 0.981257i 0.438274π0.438274\pi
234234 0 0
235235 759162. 0.896736
236236 −191194. −0.223457
237237 317763. 0.367479
238238 −453824. −0.519332
239239 1.52265e6 1.72427 0.862133 0.506682i 0.169128π-0.169128\pi
0.862133 + 0.506682i 0.169128π0.169128\pi
240240 −200111. −0.224256
241241 607839. 0.674134 0.337067 0.941481i 0.390565π-0.390565\pi
0.337067 + 0.941481i 0.390565π0.390565\pi
242242 −847879. −0.930669
243243 −59049.0 −0.0641500
244244 −726403. −0.781094
245245 −612323. −0.651726
246246 133170. 0.140304
247247 0 0
248248 471496. 0.486798
249249 283359. 0.289627
250250 −449412. −0.454773
251251 1.05049e6 1.05247 0.526234 0.850340i 0.323604π-0.323604\pi
0.526234 + 0.850340i 0.323604π0.323604\pi
252252 128015. 0.126988
253253 −264593. −0.259883
254254 1.29066e6 1.25524
255255 −897846. −0.864672
256256 65536.0 0.0625000
257257 −236240. −0.223111 −0.111555 0.993758i 0.535583π-0.535583\pi
−0.111555 + 0.993758i 0.535583π0.535583\pi
258258 218217. 0.204098
259259 1.04457e6 0.967580
260260 0 0
261261 621237. 0.564489
262262 1.43150e6 1.28836
263263 928964. 0.828151 0.414076 0.910242i 0.364105π-0.364105\pi
0.414076 + 0.910242i 0.364105π0.364105\pi
264264 351794. 0.310656
265265 3.02119e6 2.64280
266266 895770. 0.776233
267267 −531464. −0.456242
268268 731170. 0.621844
269269 827650. 0.697374 0.348687 0.937239i 0.386628π-0.386628\pi
0.348687 + 0.937239i 0.386628π0.386628\pi
270270 253266. 0.211430
271271 660781. 0.546555 0.273278 0.961935i 0.411892π-0.411892\pi
0.273278 + 0.961935i 0.411892π0.411892\pi
272272 294043. 0.240984
273273 0 0
274274 1.38826e6 1.11710
275275 2.69867e6 2.15188
276276 62384.2 0.0492949
277277 1.38275e6 1.08279 0.541395 0.840769i 0.317896π-0.317896\pi
0.541395 + 0.840769i 0.317896π0.317896\pi
278278 412119. 0.319823
279279 −596738. −0.458958
280280 −549068. −0.418534
281281 1.44893e6 1.09467 0.547333 0.836915i 0.315643π-0.315643\pi
0.547333 + 0.836915i 0.315643π0.315643\pi
282282 314665. 0.235627
283283 −1.22044e6 −0.905841 −0.452921 0.891551i 0.649618π-0.649618\pi
−0.452921 + 0.891551i 0.649618π0.649618\pi
284284 381230. 0.280473
285285 1.77219e6 1.29240
286286 0 0
287287 365394. 0.261853
288288 −82944.0 −0.0589256
289289 −100565. −0.0708279
290290 −2.66453e6 −1.86048
291291 44692.0 0.0309384
292292 604146. 0.414653
293293 −2.19465e6 −1.49347 −0.746734 0.665123i 0.768379π-0.768379\pi
−0.746734 + 0.665123i 0.768379π0.768379\pi
294294 −253801. −0.171248
295295 −1.03787e6 −0.694366
296296 −676798. −0.448983
297297 −445240. −0.292889
298298 362781. 0.236649
299299 0 0
300300 −636277. −0.408172
301301 598746. 0.380914
302302 417154. 0.263196
303303 −1.13045e6 −0.707365
304304 −580389. −0.360193
305305 −3.94318e6 −2.42715
306306 −372148. −0.227202
307307 −83619.1 −0.0506360 −0.0253180 0.999679i 0.508060π-0.508060\pi
−0.0253180 + 0.999679i 0.508060π0.508060\pi
308308 965259. 0.579785
309309 −1.13716e6 −0.677528
310310 2.55945e6 1.51267
311311 −491767. −0.288309 −0.144155 0.989555i 0.546046π-0.546046\pi
−0.144155 + 0.989555i 0.546046π0.546046\pi
312312 0 0
313313 896969. 0.517508 0.258754 0.965943i 0.416688π-0.416688\pi
0.258754 + 0.965943i 0.416688π0.416688\pi
314314 1.25768e6 0.719854
315315 694915. 0.394598
316316 −564912. −0.318246
317317 3.15449e6 1.76312 0.881559 0.472074i 0.156494π-0.156494\pi
0.881559 + 0.472074i 0.156494π0.156494\pi
318318 1.25225e6 0.694423
319319 4.68423e6 2.57728
320320 355753. 0.194211
321321 −297610. −0.161207
322322 171171. 0.0920004
323323 −2.60405e6 −1.38881
324324 104976. 0.0555556
325325 0 0
326326 −562928. −0.293365
327327 1.32900e6 0.687312
328328 −236747. −0.121507
329329 863382. 0.439757
330330 1.90967e6 0.965324
331331 597196. 0.299604 0.149802 0.988716i 0.452136π-0.452136\pi
0.149802 + 0.988716i 0.452136π0.452136\pi
332332 −503750. −0.250824
333333 856572. 0.423305
334334 −435775. −0.213745
335335 3.96906e6 1.93230
336336 −227583. −0.109974
337337 −3.61808e6 −1.73541 −0.867707 0.497077i 0.834407π-0.834407\pi
−0.867707 + 0.497077i 0.834407π0.834407\pi
338338 0 0
339339 −1.06300e6 −0.502382
340340 1.59617e6 0.748828
341341 −4.49951e6 −2.09546
342342 734555. 0.339593
343343 −2.35653e6 −1.08153
344344 −387941. −0.176754
345345 338644. 0.153178
346346 1.60475e6 0.720639
347347 −1.62893e6 −0.726236 −0.363118 0.931743i 0.618288π-0.618288\pi
−0.363118 + 0.931743i 0.618288π0.618288\pi
348348 −1.10442e6 −0.488862
349349 −2.60140e6 −1.14326 −0.571628 0.820513i 0.693688π-0.693688\pi
−0.571628 + 0.820513i 0.693688π0.693688\pi
350350 −1.74583e6 −0.761782
351351 0 0
352352 −625412. −0.269036
353353 −1.30441e6 −0.557155 −0.278578 0.960414i 0.589863π-0.589863\pi
−0.278578 + 0.960414i 0.589863π0.589863\pi
354354 −430187. −0.182452
355355 2.06945e6 0.871535
356356 944824. 0.395117
357357 −1.02110e6 −0.424033
358358 −838140. −0.345628
359359 213674. 0.0875013 0.0437507 0.999042i 0.486069π-0.486069\pi
0.0437507 + 0.999042i 0.486069π0.486069\pi
360360 −450250. −0.183104
361361 2.66384e6 1.07582
362362 945110. 0.379062
363363 −1.90773e6 −0.759888
364364 0 0
365365 3.27952e6 1.28848
366366 −1.63441e6 −0.637760
367367 1.15670e6 0.448285 0.224142 0.974556i 0.428042π-0.428042\pi
0.224142 + 0.974556i 0.428042π0.428042\pi
368368 −110905. −0.0426906
369369 299633. 0.114557
370370 −3.67390e6 −1.39516
371371 3.43595e6 1.29602
372372 1.06087e6 0.397469
373373 1.97983e6 0.736810 0.368405 0.929665i 0.379904π-0.379904\pi
0.368405 + 0.929665i 0.379904π0.379904\pi
374374 −2.80606e6 −1.03733
375375 −1.01118e6 −0.371321
376376 −559404. −0.204059
377377 0 0
378378 288035. 0.103685
379379 3.86155e6 1.38090 0.690451 0.723379i 0.257412π-0.257412\pi
0.690451 + 0.723379i 0.257412π0.257412\pi
380380 −3.15056e6 −1.11925
381381 2.90399e6 1.02490
382382 −2.03888e6 −0.714879
383383 1.55518e6 0.541731 0.270866 0.962617i 0.412690π-0.412690\pi
0.270866 + 0.962617i 0.412690π0.412690\pi
384384 147456. 0.0510310
385385 5.23978e6 1.80161
386386 232587. 0.0794544
387387 490988. 0.166645
388388 −79452.4 −0.0267934
389389 −2.85249e6 −0.955763 −0.477881 0.878424i 0.658595π-0.658595\pi
−0.477881 + 0.878424i 0.658595π0.658595\pi
390390 0 0
391391 −497603. −0.164604
392392 451202. 0.148305
393393 3.22087e6 1.05194
394394 367320. 0.119208
395395 −3.06655e6 −0.988911
396396 791537. 0.253649
397397 −1.25222e6 −0.398752 −0.199376 0.979923i 0.563891π-0.563891\pi
−0.199376 + 0.979923i 0.563891π0.563891\pi
398398 2.24917e6 0.711727
399399 2.01548e6 0.633792
400400 1.13116e6 0.353487
401401 4.20050e6 1.30449 0.652244 0.758009i 0.273828π-0.273828\pi
0.652244 + 0.758009i 0.273828π0.273828\pi
402402 1.64513e6 0.507733
403403 0 0
404404 2.00968e6 0.612596
405405 569848. 0.172632
406406 −3.03033e6 −0.912377
407407 6.45870e6 1.93268
408408 661596. 0.196763
409409 650694. 0.192340 0.0961698 0.995365i 0.469341π-0.469341\pi
0.0961698 + 0.995365i 0.469341π0.469341\pi
410410 −1.28515e6 −0.377567
411411 3.12358e6 0.912111
412412 2.02163e6 0.586756
413413 −1.18035e6 −0.340516
414414 140364. 0.0402491
415415 −2.73454e6 −0.779406
416416 0 0
417417 927267. 0.261135
418418 5.53867e6 1.55047
419419 −6.82010e6 −1.89782 −0.948912 0.315541i 0.897814π-0.897814\pi
−0.948912 + 0.315541i 0.897814π0.897814\pi
420420 −1.23540e6 −0.341732
421421 3.11659e6 0.856988 0.428494 0.903545i 0.359044π-0.359044\pi
0.428494 + 0.903545i 0.359044π0.359044\pi
422422 −2.60265e6 −0.711433
423423 707996. 0.192389
424424 −2.22623e6 −0.601388
425425 5.07521e6 1.36296
426426 857767. 0.229005
427427 −4.48451e6 −1.19027
428428 529084. 0.139610
429429 0 0
430430 −2.10588e6 −0.549241
431431 4.88213e6 1.26595 0.632974 0.774173i 0.281834π-0.281834\pi
0.632974 + 0.774173i 0.281834π0.281834\pi
432432 −186624. −0.0481125
433433 −3.64275e6 −0.933705 −0.466852 0.884335i 0.654612π-0.654612\pi
−0.466852 + 0.884335i 0.654612π0.654612\pi
434434 2.91082e6 0.741808
435435 −5.99520e6 −1.51908
436436 −2.36266e6 −0.595230
437437 982180. 0.246030
438438 1.35933e6 0.338562
439439 1.70122e6 0.421308 0.210654 0.977561i 0.432441π-0.432441\pi
0.210654 + 0.977561i 0.432441π0.432441\pi
440440 −3.39497e6 −0.835995
441441 −571053. −0.139823
442442 0 0
443443 −5.85057e6 −1.41641 −0.708205 0.706007i 0.750495π-0.750495\pi
−0.708205 + 0.706007i 0.750495π0.750495\pi
444444 −1.52279e6 −0.366593
445445 5.12885e6 1.22778
446446 1.21118e6 0.288318
447447 816258. 0.193223
448448 404592. 0.0952406
449449 −1.56399e6 −0.366115 −0.183058 0.983102i 0.558599π-0.558599\pi
−0.183058 + 0.983102i 0.558599π0.558599\pi
450450 −1.43162e6 −0.333271
451451 2.25928e6 0.523033
452452 1.88978e6 0.435076
453453 938596. 0.214898
454454 2.89276e6 0.658678
455455 0 0
456456 −1.30587e6 −0.294096
457457 −336948. −0.0754697 −0.0377349 0.999288i 0.512014π-0.512014\pi
−0.0377349 + 0.999288i 0.512014π0.512014\pi
458458 −5.57513e6 −1.24191
459459 −837332. −0.185510
460460 −602034. −0.132656
461461 −3.89174e6 −0.852887 −0.426444 0.904514i 0.640234π-0.640234\pi
−0.426444 + 0.904514i 0.640234π0.640234\pi
462462 2.17183e6 0.473393
463463 −6.34214e6 −1.37494 −0.687470 0.726213i 0.741279π-0.741279\pi
−0.687470 + 0.726213i 0.741279π0.741279\pi
464464 1.96341e6 0.423367
465465 5.75877e6 1.23509
466466 −1.27754e6 −0.272527
467467 −2.48691e6 −0.527677 −0.263839 0.964567i 0.584989π-0.584989\pi
−0.263839 + 0.964567i 0.584989π0.584989\pi
468468 0 0
469469 4.51394e6 0.947597
470470 −3.03665e6 −0.634088
471471 2.82977e6 0.587759
472472 764777. 0.158008
473473 3.70213e6 0.760850
474474 −1.27105e6 −0.259847
475475 −1.00176e7 −2.03718
476476 1.81530e6 0.367223
477477 2.81757e6 0.566994
478478 −6.09058e6 −1.21924
479479 −5.31079e6 −1.05760 −0.528798 0.848747i 0.677357π-0.677357\pi
−0.528798 + 0.848747i 0.677357π0.677357\pi
480480 800445. 0.158573
481481 0 0
482482 −2.43136e6 −0.476685
483483 385134. 0.0751180
484484 3.39151e6 0.658082
485485 −431297. −0.0832572
486486 236196. 0.0453609
487487 7.73506e6 1.47789 0.738944 0.673767i 0.235325π-0.235325\pi
0.738944 + 0.673767i 0.235325π0.235325\pi
488488 2.90561e6 0.552317
489489 −1.26659e6 −0.239532
490490 2.44929e6 0.460840
491491 322490. 0.0603689 0.0301844 0.999544i 0.490391π-0.490391\pi
0.0301844 + 0.999544i 0.490391π0.490391\pi
492492 −532680. −0.0992097
493493 8.80932e6 1.63239
494494 0 0
495495 4.29675e6 0.788184
496496 −1.88599e6 −0.344218
497497 2.35355e6 0.427399
498498 −1.13344e6 −0.204797
499499 −414653. −0.0745476 −0.0372738 0.999305i 0.511867π-0.511867\pi
−0.0372738 + 0.999305i 0.511867π0.511867\pi
500500 1.79765e6 0.321573
501501 −980493. −0.174522
502502 −4.20197e6 −0.744207
503503 −1.11227e7 −1.96016 −0.980080 0.198604i 0.936359π-0.936359\pi
−0.980080 + 0.198604i 0.936359π0.936359\pi
504504 −512062. −0.0897937
505505 1.09093e7 1.90357
506506 1.05837e6 0.183765
507507 0 0
508508 −5.16265e6 −0.887592
509509 754143. 0.129021 0.0645103 0.997917i 0.479451π-0.479451\pi
0.0645103 + 0.997917i 0.479451π0.479451\pi
510510 3.59138e6 0.611415
511511 3.72974e6 0.631869
512512 −262144. −0.0441942
513513 1.65275e6 0.277277
514514 944959. 0.157763
515515 1.09741e7 1.82327
516516 −872867. −0.144319
517517 5.33841e6 0.878386
518518 −4.17827e6 −0.684182
519519 3.61069e6 0.588399
520520 0 0
521521 6.34188e6 1.02358 0.511792 0.859109i 0.328982π-0.328982\pi
0.511792 + 0.859109i 0.328982π0.328982\pi
522522 −2.48495e6 −0.399154
523523 7.64810e6 1.22264 0.611321 0.791382i 0.290638π-0.290638\pi
0.611321 + 0.791382i 0.290638π0.290638\pi
524524 −5.72599e6 −0.911008
525525 −3.92811e6 −0.621993
526526 −3.71586e6 −0.585591
527527 −8.46192e6 −1.32722
528528 −1.40718e6 −0.219667
529529 −6.24866e6 −0.970840
530530 −1.20848e7 −1.86874
531531 −967921. −0.148972
532532 −3.58308e6 −0.548880
533533 0 0
534534 2.12585e6 0.322612
535535 2.87206e6 0.433820
536536 −2.92468e6 −0.439710
537537 −1.88581e6 −0.282204
538538 −3.31060e6 −0.493118
539539 −4.30584e6 −0.638390
540540 −1.01306e6 −0.149504
541541 5.40473e6 0.793927 0.396964 0.917834i 0.370064π-0.370064\pi
0.396964 + 0.917834i 0.370064π0.370064\pi
542542 −2.64312e6 −0.386473
543543 2.12650e6 0.309503
544544 −1.17617e6 −0.170401
545545 −1.28254e7 −1.84960
546546 0 0
547547 6.06535e6 0.866737 0.433368 0.901217i 0.357325π-0.357325\pi
0.433368 + 0.901217i 0.357325π0.357325\pi
548548 −5.55303e6 −0.789912
549549 −3.67742e6 −0.520729
550550 −1.07947e7 −1.52161
551551 −1.73881e7 −2.43990
552552 −249537. −0.0348568
553553 −3.48753e6 −0.484960
554554 −5.53100e6 −0.765648
555555 −8.26629e6 −1.13914
556556 −1.64847e6 −0.226149
557557 6.81169e6 0.930287 0.465143 0.885235i 0.346003π-0.346003\pi
0.465143 + 0.885235i 0.346003π0.346003\pi
558558 2.38695e6 0.324532
559559 0 0
560560 2.19627e6 0.295949
561561 −6.31363e6 −0.846978
562562 −5.79572e6 −0.774046
563563 −4.93741e6 −0.656491 −0.328245 0.944593i 0.606457π-0.606457\pi
−0.328245 + 0.944593i 0.606457π0.606457\pi
564564 −1.25866e6 −0.166614
565565 1.02584e7 1.35194
566566 4.88178e6 0.640526
567567 648078. 0.0846583
568568 −1.52492e6 −0.198324
569569 −9.18371e6 −1.18915 −0.594576 0.804039i 0.702680π-0.702680\pi
−0.594576 + 0.804039i 0.702680π0.702680\pi
570570 −7.08876e6 −0.913868
571571 1.11741e7 1.43424 0.717120 0.696949i 0.245460π-0.245460\pi
0.717120 + 0.696949i 0.245460π0.245460\pi
572572 0 0
573573 −4.58748e6 −0.583697
574574 −1.46158e6 −0.185158
575575 −1.91424e6 −0.241449
576576 331776. 0.0416667
577577 8.62732e6 1.07879 0.539394 0.842053i 0.318653π-0.318653\pi
0.539394 + 0.842053i 0.318653π0.318653\pi
578578 402262. 0.0500829
579579 523322. 0.0648742
580580 1.06581e7 1.31556
581581 −3.10994e6 −0.382219
582582 −178768. −0.0218767
583583 2.12450e7 2.58872
584584 −2.41658e6 −0.293204
585585 0 0
586586 8.77859e6 1.05604
587587 −5.86783e6 −0.702882 −0.351441 0.936210i 0.614308π-0.614308\pi
−0.351441 + 0.936210i 0.614308π0.614308\pi
588588 1.01520e6 0.121091
589589 1.67023e7 1.98376
590590 4.15149e6 0.490991
591591 826470. 0.0973326
592592 2.70719e6 0.317479
593593 −1.28187e7 −1.49694 −0.748472 0.663166i 0.769212π-0.769212\pi
−0.748472 + 0.663166i 0.769212π0.769212\pi
594594 1.78096e6 0.207104
595595 9.85410e6 1.14110
596596 −1.45112e6 −0.167336
597597 5.06062e6 0.581123
598598 0 0
599599 −8.82262e6 −1.00469 −0.502343 0.864668i 0.667529π-0.667529\pi
−0.502343 + 0.864668i 0.667529π0.667529\pi
600600 2.54511e6 0.288621
601601 8.16061e6 0.921587 0.460793 0.887507i 0.347565π-0.347565\pi
0.460793 + 0.887507i 0.347565π0.347565\pi
602602 −2.39499e6 −0.269347
603603 3.70155e6 0.414563
604604 −1.66862e6 −0.186107
605605 1.84104e7 2.04491
606606 4.52179e6 0.500182
607607 8.03055e6 0.884654 0.442327 0.896854i 0.354153π-0.354153\pi
0.442327 + 0.896854i 0.354153π0.354153\pi
608608 2.32155e6 0.254695
609609 −6.81823e6 −0.744953
610610 1.57727e7 1.71626
611611 0 0
612612 1.48859e6 0.160656
613613 3.99383e6 0.429278 0.214639 0.976693i 0.431143π-0.431143\pi
0.214639 + 0.976693i 0.431143π0.431143\pi
614614 334476. 0.0358051
615615 −2.89158e6 −0.308282
616616 −3.86104e6 −0.409970
617617 1.20933e7 1.27888 0.639442 0.768840i 0.279166π-0.279166\pi
0.639442 + 0.768840i 0.279166π0.279166\pi
618618 4.54866e6 0.479084
619619 −1.31953e7 −1.38418 −0.692088 0.721813i 0.743309π-0.743309\pi
−0.692088 + 0.721813i 0.743309π0.743309\pi
620620 −1.02378e7 −1.06962
621621 315820. 0.0328633
622622 1.96707e6 0.203865
623623 5.83295e6 0.602100
624624 0 0
625625 −4.04979e6 −0.414699
626626 −3.58788e6 −0.365933
627627 1.24620e7 1.26596
628628 −5.03070e6 −0.509014
629629 1.21464e7 1.22412
630630 −2.77966e6 −0.279023
631631 1.16207e7 1.16188 0.580939 0.813947i 0.302686π-0.302686\pi
0.580939 + 0.813947i 0.302686π0.302686\pi
632632 2.25965e6 0.225034
633633 −5.85595e6 −0.580883
634634 −1.26180e7 −1.24671
635635 −2.80247e7 −2.75808
636636 −5.00901e6 −0.491031
637637 0 0
638638 −1.87369e7 −1.82241
639639 1.92998e6 0.186982
640640 −1.42301e6 −0.137328
641641 1.15298e7 1.10835 0.554173 0.832402i 0.313035π-0.313035\pi
0.554173 + 0.832402i 0.313035π0.313035\pi
642642 1.19044e6 0.113991
643643 2.90732e6 0.277310 0.138655 0.990341i 0.455722π-0.455722\pi
0.138655 + 0.990341i 0.455722π0.455722\pi
644644 −684683. −0.0650541
645645 −4.73824e6 −0.448454
646646 1.04162e7 0.982038
647647 4.58122e6 0.430249 0.215125 0.976587i 0.430984π-0.430984\pi
0.215125 + 0.976587i 0.430984π0.430984\pi
648648 −419904. −0.0392837
649649 −7.29829e6 −0.680157
650650 0 0
651651 6.54935e6 0.605684
652652 2.25171e6 0.207441
653653 1.95066e7 1.79019 0.895096 0.445874i 0.147107π-0.147107\pi
0.895096 + 0.445874i 0.147107π0.147107\pi
654654 −5.31598e6 −0.486003
655655 −3.10827e7 −2.83084
656656 946987. 0.0859181
657657 3.05849e6 0.276435
658658 −3.45353e6 −0.310955
659659 8.41225e6 0.754568 0.377284 0.926098i 0.376858π-0.376858\pi
0.377284 + 0.926098i 0.376858π0.376858\pi
660660 −7.63867e6 −0.682587
661661 1.64620e7 1.46548 0.732739 0.680510i 0.238242π-0.238242\pi
0.732739 + 0.680510i 0.238242π0.238242\pi
662662 −2.38879e6 −0.211852
663663 0 0
664664 2.01500e6 0.177360
665665 −1.94503e7 −1.70558
666666 −3.42629e6 −0.299322
667667 −3.32265e6 −0.289181
668668 1.74310e6 0.151141
669669 2.72515e6 0.235410
670670 −1.58762e7 −1.36634
671671 −2.77284e7 −2.37748
672672 910332. 0.0777637
673673 −9.88194e6 −0.841016 −0.420508 0.907289i 0.638148π-0.638148\pi
−0.420508 + 0.907289i 0.638148π0.638148\pi
674674 1.44723e7 1.22712
675675 −3.22115e6 −0.272114
676676 0 0
677677 −731933. −0.0613761 −0.0306881 0.999529i 0.509770π-0.509770\pi
−0.0306881 + 0.999529i 0.509770π0.509770\pi
678678 4.25200e6 0.355238
679679 −490506. −0.0408291
680680 −6.38468e6 −0.529501
681681 6.50872e6 0.537809
682682 1.79980e7 1.48171
683683 −6.46151e6 −0.530008 −0.265004 0.964247i 0.585373π-0.585373\pi
−0.265004 + 0.964247i 0.585373π0.585373\pi
684684 −2.93822e6 −0.240129
685685 −3.01439e7 −2.45455
686686 9.42614e6 0.764757
687687 −1.25440e7 −1.01402
688688 1.55176e6 0.124984
689689 0 0
690690 −1.35458e6 −0.108313
691691 −1.16211e7 −0.925877 −0.462939 0.886390i 0.653205π-0.653205\pi
−0.462939 + 0.886390i 0.653205π0.653205\pi
692692 −6.41901e6 −0.509569
693693 4.88662e6 0.386523
694694 6.51570e6 0.513526
695695 −8.94852e6 −0.702731
696696 4.41768e6 0.345678
697697 4.24888e6 0.331278
698698 1.04056e7 0.808404
699699 −2.87446e6 −0.222517
700700 6.98330e6 0.538661
701701 1.39904e6 0.107531 0.0537655 0.998554i 0.482878π-0.482878\pi
0.0537655 + 0.998554i 0.482878π0.482878\pi
702702 0 0
703703 −2.39750e7 −1.82966
704704 2.50165e6 0.190237
705705 −6.83246e6 −0.517731
706706 5.21763e6 0.393968
707707 1.24069e7 0.933504
708708 1.72075e6 0.129013
709709 −1.84802e7 −1.38067 −0.690336 0.723489i 0.742537π-0.742537\pi
−0.690336 + 0.723489i 0.742537π0.742537\pi
710710 −8.27781e6 −0.616268
711711 −2.85987e6 −0.212164
712712 −3.77930e6 −0.279390
713713 3.19162e6 0.235118
714714 4.08442e6 0.299837
715715 0 0
716716 3.35256e6 0.244396
717717 −1.37038e7 −0.995505
718718 −854694. −0.0618728
719719 −7.61846e6 −0.549598 −0.274799 0.961502i 0.588611π-0.588611\pi
−0.274799 + 0.961502i 0.588611π0.588611\pi
720720 1.80100e6 0.129474
721721 1.24807e7 0.894128
722722 −1.06554e7 −0.760721
723723 −5.47055e6 −0.389211
724724 −3.78044e6 −0.268038
725725 3.38888e7 2.39448
726726 7.63091e6 0.537322
727727 −2.55002e7 −1.78940 −0.894699 0.446670i 0.852610π-0.852610\pi
−0.894699 + 0.446670i 0.852610π0.852610\pi
728728 0 0
729729 531441. 0.0370370
730730 −1.31181e7 −0.911094
731731 6.96235e6 0.481906
732732 6.53763e6 0.450965
733733 −1.27470e7 −0.876293 −0.438147 0.898903i 0.644365π-0.644365\pi
−0.438147 + 0.898903i 0.644365π0.644365\pi
734734 −4.62678e6 −0.316985
735735 5.51090e6 0.376274
736736 443621. 0.0301868
737737 2.79103e7 1.89276
738738 −1.19853e6 −0.0810043
739739 1.54752e7 1.04238 0.521190 0.853441i 0.325488π-0.325488\pi
0.521190 + 0.853441i 0.325488π0.325488\pi
740740 1.46956e7 0.986526
741741 0 0
742742 −1.37438e7 −0.916425
743743 −3.52596e6 −0.234318 −0.117159 0.993113i 0.537379π-0.537379\pi
−0.117159 + 0.993113i 0.537379π0.537379\pi
744744 −4.24347e6 −0.281053
745745 −7.87723e6 −0.519976
746746 −7.91931e6 −0.521003
747747 −2.55023e6 −0.167216
748748 1.12242e7 0.733505
749749 3.26635e6 0.212744
750750 4.04471e6 0.262563
751751 −8.20700e6 −0.530988 −0.265494 0.964113i 0.585535π-0.585535\pi
−0.265494 + 0.964113i 0.585535π0.585535\pi
752752 2.23762e6 0.144292
753753 −9.45443e6 −0.607642
754754 0 0
755755 −9.05785e6 −0.578306
756756 −1.15214e6 −0.0733163
757757 −1.27038e7 −0.805736 −0.402868 0.915258i 0.631987π-0.631987\pi
−0.402868 + 0.915258i 0.631987π0.631987\pi
758758 −1.54462e7 −0.976446
759759 2.38134e6 0.150043
760760 1.26022e7 0.791433
761761 1.41876e7 0.888073 0.444037 0.896009i 0.353546π-0.353546\pi
0.444037 + 0.896009i 0.353546π0.353546\pi
762762 −1.16160e7 −0.724716
763763 −1.45861e7 −0.907041
764764 8.15551e6 0.505496
765765 8.08061e6 0.499219
766766 −6.22072e6 −0.383062
767767 0 0
768768 −589824. −0.0360844
769769 1.10700e7 0.675045 0.337522 0.941318i 0.390411π-0.390411\pi
0.337522 + 0.941318i 0.390411π0.390411\pi
770770 −2.09591e7 −1.27393
771771 2.12616e6 0.128813
772772 −930349. −0.0561827
773773 −5.17639e6 −0.311586 −0.155793 0.987790i 0.549793π-0.549793\pi
−0.155793 + 0.987790i 0.549793π0.549793\pi
774774 −1.96395e6 −0.117836
775775 −3.25523e7 −1.94683
776776 317810. 0.0189458
777777 −9.40110e6 −0.558633
778778 1.14100e7 0.675826
779779 −8.38655e6 −0.495153
780780 0 0
781781 1.45524e7 0.853701
782782 1.99041e6 0.116393
783783 −5.59113e6 −0.325908
784784 −1.80481e6 −0.104868
785785 −2.73085e7 −1.58170
786786 −1.28835e7 −0.743835
787787 1.43044e7 0.823252 0.411626 0.911353i 0.364961π-0.364961\pi
0.411626 + 0.911353i 0.364961π0.364961\pi
788788 −1.46928e6 −0.0842925
789789 −8.36068e6 −0.478133
790790 1.22662e7 0.699266
791791 1.16667e7 0.662990
792792 −3.16615e6 −0.179357
793793 0 0
794794 5.00886e6 0.281960
795795 −2.71907e7 −1.52582
796796 −8.99666e6 −0.503267
797797 1.27192e7 0.709275 0.354638 0.935004i 0.384604π-0.384604\pi
0.354638 + 0.935004i 0.384604π0.384604\pi
798798 −8.06193e6 −0.448159
799799 1.00396e7 0.556351
800800 −4.52463e6 −0.249953
801801 4.78317e6 0.263412
802802 −1.68020e7 −0.922412
803803 2.30615e7 1.26212
804804 −6.58053e6 −0.359022
805805 −3.71671e6 −0.202148
806806 0 0
807807 −7.44885e6 −0.402629
808808 −8.03873e6 −0.433171
809809 5.39790e6 0.289970 0.144985 0.989434i 0.453687π-0.453687\pi
0.144985 + 0.989434i 0.453687π0.453687\pi
810810 −2.27939e6 −0.122069
811811 −1.46019e7 −0.779576 −0.389788 0.920905i 0.627452π-0.627452\pi
−0.389788 + 0.920905i 0.627452π0.627452\pi
812812 1.21213e7 0.645148
813813 −5.94703e6 −0.315554
814814 −2.58348e7 −1.36661
815815 1.22231e7 0.644597
816816 −2.64638e6 −0.139132
817817 −1.37425e7 −0.720293
818818 −2.60278e6 −0.136005
819819 0 0
820820 5.14059e6 0.266980
821821 −2.73956e7 −1.41848 −0.709240 0.704967i 0.750962π-0.750962\pi
−0.709240 + 0.704967i 0.750962π0.750962\pi
822822 −1.24943e7 −0.644960
823823 −2.28175e7 −1.17427 −0.587136 0.809488i 0.699745π-0.699745\pi
−0.587136 + 0.809488i 0.699745π0.699745\pi
824824 −8.08650e6 −0.414899
825825 −2.42880e7 −1.24239
826826 4.72141e6 0.240781
827827 1.17556e7 0.597698 0.298849 0.954300i 0.403397π-0.403397\pi
0.298849 + 0.954300i 0.403397π0.403397\pi
828828 −561458. −0.0284604
829829 2.04885e7 1.03544 0.517718 0.855551i 0.326781π-0.326781\pi
0.517718 + 0.855551i 0.326781π0.326781\pi
830830 1.09382e7 0.551123
831831 −1.24447e7 −0.625149
832832 0 0
833833 −8.09770e6 −0.404342
834834 −3.70907e6 −0.184650
835835 9.46218e6 0.469651
836836 −2.21547e7 −1.09635
837837 5.37064e6 0.264979
838838 2.72804e7 1.34196
839839 2.38084e7 1.16769 0.583843 0.811867i 0.301549π-0.301549\pi
0.583843 + 0.811867i 0.301549π0.301549\pi
840840 4.94161e6 0.241641
841841 3.83114e7 1.86783
842842 −1.24664e7 −0.605982
843843 −1.30404e7 −0.632006
844844 1.04106e7 0.503059
845845 0 0
846846 −2.83198e6 −0.136039
847847 2.09378e7 1.00282
848848 8.90491e6 0.425246
849849 1.09840e7 0.522988
850850 −2.03008e7 −0.963755
851851 −4.58133e6 −0.216854
852852 −3.43107e6 −0.161931
853853 9.87851e6 0.464857 0.232428 0.972614i 0.425333π-0.425333\pi
0.232428 + 0.972614i 0.425333π0.425333\pi
854854 1.79380e7 0.841648
855855 −1.59497e7 −0.746170
856856 −2.11634e6 −0.0987189
857857 1.97784e6 0.0919898 0.0459949 0.998942i 0.485354π-0.485354\pi
0.0459949 + 0.998942i 0.485354π0.485354\pi
858858 0 0
859859 −5.87858e6 −0.271825 −0.135913 0.990721i 0.543397π-0.543397\pi
−0.135913 + 0.990721i 0.543397π0.543397\pi
860860 8.42354e6 0.388372
861861 −3.28855e6 −0.151181
862862 −1.95285e7 −0.895160
863863 1.96178e7 0.896651 0.448325 0.893870i 0.352021π-0.352021\pi
0.448325 + 0.893870i 0.352021π0.352021\pi
864864 746496. 0.0340207
865865 −3.48447e7 −1.58342
866866 1.45710e7 0.660229
867867 905089. 0.0408925
868868 −1.16433e7 −0.524537
869869 −2.15639e7 −0.968675
870870 2.39808e7 1.07415
871871 0 0
872872 9.45063e6 0.420891
873873 −402228. −0.0178623
874874 −3.92872e6 −0.173969
875875 1.10979e7 0.490030
876876 −5.43731e6 −0.239400
877877 1.90004e7 0.834189 0.417095 0.908863i 0.363048π-0.363048\pi
0.417095 + 0.908863i 0.363048π0.363048\pi
878878 −6.80489e6 −0.297910
879879 1.97518e7 0.862254
880880 1.35799e7 0.591138
881881 −6.81302e6 −0.295733 −0.147866 0.989007i 0.547241π-0.547241\pi
−0.147866 + 0.989007i 0.547241π0.547241\pi
882882 2.28421e6 0.0988701
883883 −2.84750e7 −1.22903 −0.614513 0.788906i 0.710648π-0.710648\pi
−0.614513 + 0.788906i 0.710648π0.710648\pi
884884 0 0
885885 9.34085e6 0.400893
886886 2.34023e7 1.00155
887887 3.43992e7 1.46804 0.734022 0.679126i 0.237641π-0.237641\pi
0.734022 + 0.679126i 0.237641π0.237641\pi
888888 6.09118e6 0.259220
889889 −3.18721e7 −1.35256
890890 −2.05154e7 −0.868170
891891 4.00716e6 0.169099
892892 −4.84472e6 −0.203871
893893 −1.98164e7 −0.831564
894894 −3.26503e6 −0.136629
895895 1.81989e7 0.759430
896896 −1.61837e6 −0.0673453
897897 0 0
898898 6.25596e6 0.258883
899899 −5.65029e7 −2.33169
900900 5.72649e6 0.235658
901901 3.99540e7 1.63964
902902 −9.03713e6 −0.369840
903903 −5.38872e6 −0.219921
904904 −7.55912e6 −0.307645
905905 −2.05216e7 −0.832894
906906 −3.75438e6 −0.151956
907907 −2.13493e7 −0.861719 −0.430859 0.902419i 0.641789π-0.641789\pi
−0.430859 + 0.902419i 0.641789π0.641789\pi
908908 −1.15711e7 −0.465756
909909 1.01740e7 0.408397
910910 0 0
911911 −7.55882e6 −0.301758 −0.150879 0.988552i 0.548210π-0.548210\pi
−0.150879 + 0.988552i 0.548210π0.548210\pi
912912 5.22350e6 0.207957
913913 −1.92292e7 −0.763457
914914 1.34779e6 0.0533651
915915 3.54886e7 1.40132
916916 2.23005e7 0.878166
917917 −3.53499e7 −1.38824
918918 3.34933e6 0.131175
919919 −4.56027e7 −1.78115 −0.890577 0.454832i 0.849699π-0.849699\pi
−0.890577 + 0.454832i 0.849699π0.849699\pi
920920 2.40814e6 0.0938019
921921 752572. 0.0292347
922922 1.55670e7 0.603082
923923 0 0
924924 −8.68733e6 −0.334739
925925 4.67264e7 1.79559
926926 2.53686e7 0.972229
927927 1.02345e7 0.391171
928928 −7.85366e6 −0.299366
929929 4.74157e7 1.80253 0.901266 0.433267i 0.142639π-0.142639\pi
0.901266 + 0.433267i 0.142639π0.142639\pi
930930 −2.30351e7 −0.873338
931931 1.59834e7 0.604360
932932 5.11016e6 0.192706
933933 4.42590e6 0.166455
934934 9.94765e6 0.373124
935935 6.09292e7 2.27928
936936 0 0
937937 4.02496e7 1.49766 0.748829 0.662764i 0.230617π-0.230617\pi
0.748829 + 0.662764i 0.230617π0.230617\pi
938938 −1.80558e7 −0.670052
939939 −8.07272e6 −0.298783
940940 1.21466e7 0.448368
941941 −8.70389e6 −0.320434 −0.160217 0.987082i 0.551219π-0.551219\pi
−0.160217 + 0.987082i 0.551219π0.551219\pi
942942 −1.13191e7 −0.415608
943943 −1.60257e6 −0.0586864
944944 −3.05911e6 −0.111729
945945 −6.25423e6 −0.227821
946946 −1.48085e7 −0.538002
947947 −9.78178e6 −0.354440 −0.177220 0.984171i 0.556710π-0.556710\pi
−0.177220 + 0.984171i 0.556710π0.556710\pi
948948 5.08421e6 0.183740
949949 0 0
950950 4.00703e7 1.44050
951951 −2.83904e7 −1.01794
952952 −7.26119e6 −0.259666
953953 1.18962e7 0.424303 0.212151 0.977237i 0.431953π-0.431953\pi
0.212151 + 0.977237i 0.431953π0.431953\pi
954954 −1.12703e7 −0.400925
955955 4.42711e7 1.57077
956956 2.43623e7 0.862133
957957 −4.21581e7 −1.48799
958958 2.12431e7 0.747834
959959 −3.42821e7 −1.20371
960960 −3.20178e6 −0.112128
961961 2.56455e7 0.895781
962962 0 0
963963 2.67849e6 0.0930731
964964 9.72543e6 0.337067
965965 −5.05028e6 −0.174581
966966 −1.54054e6 −0.0531165
967967 −7.21381e6 −0.248084 −0.124042 0.992277i 0.539586π-0.539586\pi
−0.124042 + 0.992277i 0.539586π0.539586\pi
968968 −1.35661e7 −0.465335
969969 2.34365e7 0.801830
970970 1.72519e6 0.0588717
971971 9.17081e6 0.312147 0.156074 0.987745i 0.450116π-0.450116\pi
0.156074 + 0.987745i 0.450116π0.450116\pi
972972 −944784. −0.0320750
973973 −1.01770e7 −0.344618
974974 −3.09402e7 −1.04502
975975 0 0
976976 −1.16224e7 −0.390547
977977 −2.18053e7 −0.730845 −0.365423 0.930842i 0.619076π-0.619076\pi
−0.365423 + 0.930842i 0.619076π0.619076\pi
978978 5.06635e6 0.169375
979979 3.60660e7 1.20265
980980 −9.79716e6 −0.325863
981981 −1.19610e7 −0.396820
982982 −1.28996e6 −0.0426872
983983 −1.96569e7 −0.648831 −0.324415 0.945915i 0.605168π-0.605168\pi
−0.324415 + 0.945915i 0.605168π0.605168\pi
984984 2.13072e6 0.0701518
985985 −7.97579e6 −0.261929
986986 −3.52373e7 −1.15428
987987 −7.77044e6 −0.253894
988988 0 0
989989 −2.62602e6 −0.0853703
990990 −1.71870e7 −0.557330
991991 2.15229e7 0.696173 0.348087 0.937462i 0.386832π-0.386832\pi
0.348087 + 0.937462i 0.386832π0.386832\pi
992992 7.54394e6 0.243399
993993 −5.37477e6 −0.172976
994994 −9.41421e6 −0.302216
995995 −4.88372e7 −1.56384
996996 4.53375e6 0.144814
997997 −1.16375e6 −0.0370783 −0.0185392 0.999828i 0.505902π-0.505902\pi
−0.0185392 + 0.999828i 0.505902π0.505902\pi
998998 1.65861e6 0.0527131
999999 −7.70915e6 −0.244395
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 1014.6.a.o.1.3 3
13.5 odd 4 78.6.b.a.25.4 yes 6
13.8 odd 4 78.6.b.a.25.3 6
13.12 even 2 1014.6.a.q.1.1 3
39.5 even 4 234.6.b.c.181.3 6
39.8 even 4 234.6.b.c.181.4 6
52.31 even 4 624.6.c.d.337.1 6
52.47 even 4 624.6.c.d.337.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.6.b.a.25.3 6 13.8 odd 4
78.6.b.a.25.4 yes 6 13.5 odd 4
234.6.b.c.181.3 6 39.5 even 4
234.6.b.c.181.4 6 39.8 even 4
624.6.c.d.337.1 6 52.31 even 4
624.6.c.d.337.6 6 52.47 even 4
1014.6.a.o.1.3 3 1.1 even 1 trivial
1014.6.a.q.1.1 3 13.12 even 2