Properties

Label 350.6.a.y.1.4
Level 350350
Weight 66
Character 350.1
Self dual yes
Analytic conductor 56.13456.134
Analytic rank 00
Dimension 55
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [350,6,Mod(1,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, 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("350.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 350=2527 350 = 2 \cdot 5^{2} \cdot 7
Weight: k k == 6 6
Character orbit: [χ][\chi] == 350.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: 56.134336934556.1343369345
Analytic rank: 00
Dimension: 55
Coefficient field: Q[x]/(x5)\mathbb{Q}[x]/(x^{5} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x5x4915x32649x2+122688x432576 x^{5} - x^{4} - 915x^{3} - 2649x^{2} + 122688x - 432576 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 22353 2^{2}\cdot 3\cdot 5^{3}
Twist minimal: no (minimal twist has level 70)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 6.918356.91835 of defining polynomial
Character χ\chi == 350.1

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) == q4.00000q2+3.91835q3+16.0000q415.6734q649.0000q764.0000q8227.647q9+337.260q11+62.6937q1224.3276q13+196.000q14+256.000q161445.07q17+910.586q181197.44q19191.999q211349.04q22+2247.26q23250.775q24+97.3103q261844.16q27784.000q28+1182.78q29+10458.6q311024.00q32+1321.50q33+5780.27q343642.34q36825.831q37+4789.75q3895.3241q39+2843.58q41+767.997q429617.84q43+5396.16q448989.03q46+10435.0q47+1003.10q48+2401.00q495662.28q51389.241q5233934.4q53+7376.64q54+3136.00q564691.99q574731.12q58+18857.8q5926489.1q6141834.6q62+11154.7q63+4096.00q645286.01q6610647.5q6723121.1q68+8805.55q69+47989.5q71+14569.4q72+37699.4q73+3303.32q7419159.0q7616525.7q77+381.296q78+62335.6q79+48092.0q8111374.3q82+369.796q833071.99q84+38471.4q86+4634.56q8721584.6q88+115397.q89+1192.05q91+35956.1q92+40980.7q9341739.9q944012.39q96136508.q979604.00q9876776.0q99+O(q100)q-4.00000 q^{2} +3.91835 q^{3} +16.0000 q^{4} -15.6734 q^{6} -49.0000 q^{7} -64.0000 q^{8} -227.647 q^{9} +337.260 q^{11} +62.6937 q^{12} -24.3276 q^{13} +196.000 q^{14} +256.000 q^{16} -1445.07 q^{17} +910.586 q^{18} -1197.44 q^{19} -191.999 q^{21} -1349.04 q^{22} +2247.26 q^{23} -250.775 q^{24} +97.3103 q^{26} -1844.16 q^{27} -784.000 q^{28} +1182.78 q^{29} +10458.6 q^{31} -1024.00 q^{32} +1321.50 q^{33} +5780.27 q^{34} -3642.34 q^{36} -825.831 q^{37} +4789.75 q^{38} -95.3241 q^{39} +2843.58 q^{41} +767.997 q^{42} -9617.84 q^{43} +5396.16 q^{44} -8989.03 q^{46} +10435.0 q^{47} +1003.10 q^{48} +2401.00 q^{49} -5662.28 q^{51} -389.241 q^{52} -33934.4 q^{53} +7376.64 q^{54} +3136.00 q^{56} -4691.99 q^{57} -4731.12 q^{58} +18857.8 q^{59} -26489.1 q^{61} -41834.6 q^{62} +11154.7 q^{63} +4096.00 q^{64} -5286.01 q^{66} -10647.5 q^{67} -23121.1 q^{68} +8805.55 q^{69} +47989.5 q^{71} +14569.4 q^{72} +37699.4 q^{73} +3303.32 q^{74} -19159.0 q^{76} -16525.7 q^{77} +381.296 q^{78} +62335.6 q^{79} +48092.0 q^{81} -11374.3 q^{82} +369.796 q^{83} -3071.99 q^{84} +38471.4 q^{86} +4634.56 q^{87} -21584.6 q^{88} +115397. q^{89} +1192.05 q^{91} +35956.1 q^{92} +40980.7 q^{93} -41739.9 q^{94} -4012.39 q^{96} -136508. q^{97} -9604.00 q^{98} -76776.0 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 5q20q214q3+80q4+56q6245q7320q8+655q9+748q11224q12456q13+980q14+1280q16780q172620q18256q19+686q21++575944q99+O(q100) 5 q - 20 q^{2} - 14 q^{3} + 80 q^{4} + 56 q^{6} - 245 q^{7} - 320 q^{8} + 655 q^{9} + 748 q^{11} - 224 q^{12} - 456 q^{13} + 980 q^{14} + 1280 q^{16} - 780 q^{17} - 2620 q^{18} - 256 q^{19} + 686 q^{21}+ \cdots + 575944 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 3.91835 0.251363 0.125681 0.992071i 0.459888π-0.459888\pi
0.125681 + 0.992071i 0.459888π0.459888\pi
44 16.0000 0.500000
55 0 0
66 −15.6734 −0.177740
77 −49.0000 −0.377964
88 −64.0000 −0.353553
99 −227.647 −0.936817
1010 0 0
1111 337.260 0.840394 0.420197 0.907433i 0.361961π-0.361961\pi
0.420197 + 0.907433i 0.361961π0.361961\pi
1212 62.6937 0.125681
1313 −24.3276 −0.0399246 −0.0199623 0.999801i 0.506355π-0.506355\pi
−0.0199623 + 0.999801i 0.506355π0.506355\pi
1414 196.000 0.267261
1515 0 0
1616 256.000 0.250000
1717 −1445.07 −1.21273 −0.606367 0.795185i 0.707374π-0.707374\pi
−0.606367 + 0.795185i 0.707374π0.707374\pi
1818 910.586 0.662430
1919 −1197.44 −0.760973 −0.380486 0.924786i 0.624243π-0.624243\pi
−0.380486 + 0.924786i 0.624243π0.624243\pi
2020 0 0
2121 −191.999 −0.0950061
2222 −1349.04 −0.594248
2323 2247.26 0.885795 0.442898 0.896572i 0.353950π-0.353950\pi
0.442898 + 0.896572i 0.353950π0.353950\pi
2424 −250.775 −0.0888701
2525 0 0
2626 97.3103 0.0282310
2727 −1844.16 −0.486843
2828 −784.000 −0.188982
2929 1182.78 0.261162 0.130581 0.991438i 0.458316π-0.458316\pi
0.130581 + 0.991438i 0.458316π0.458316\pi
3030 0 0
3131 10458.6 1.95466 0.977330 0.211721i 0.0679068π-0.0679068\pi
0.977330 + 0.211721i 0.0679068π0.0679068\pi
3232 −1024.00 −0.176777
3333 1321.50 0.211243
3434 5780.27 0.857533
3535 0 0
3636 −3642.34 −0.468408
3737 −825.831 −0.0991715 −0.0495857 0.998770i 0.515790π-0.515790\pi
−0.0495857 + 0.998770i 0.515790π0.515790\pi
3838 4789.75 0.538089
3939 −95.3241 −0.0100355
4040 0 0
4141 2843.58 0.264183 0.132092 0.991238i 0.457831π-0.457831\pi
0.132092 + 0.991238i 0.457831π0.457831\pi
4242 767.997 0.0671795
4343 −9617.84 −0.793244 −0.396622 0.917982i 0.629818π-0.629818\pi
−0.396622 + 0.917982i 0.629818π0.629818\pi
4444 5396.16 0.420197
4545 0 0
4646 −8989.03 −0.626352
4747 10435.0 0.689043 0.344522 0.938778i 0.388041π-0.388041\pi
0.344522 + 0.938778i 0.388041π0.388041\pi
4848 1003.10 0.0628406
4949 2401.00 0.142857
5050 0 0
5151 −5662.28 −0.304836
5252 −389.241 −0.0199623
5353 −33934.4 −1.65940 −0.829698 0.558212i 0.811488π-0.811488\pi
−0.829698 + 0.558212i 0.811488π0.811488\pi
5454 7376.64 0.344250
5555 0 0
5656 3136.00 0.133631
5757 −4691.99 −0.191280
5858 −4731.12 −0.184669
5959 18857.8 0.705281 0.352640 0.935759i 0.385284π-0.385284\pi
0.352640 + 0.935759i 0.385284π0.385284\pi
6060 0 0
6161 −26489.1 −0.911470 −0.455735 0.890115i 0.650624π-0.650624\pi
−0.455735 + 0.890115i 0.650624π0.650624\pi
6262 −41834.6 −1.38215
6363 11154.7 0.354083
6464 4096.00 0.125000
6565 0 0
6666 −5286.01 −0.149372
6767 −10647.5 −0.289774 −0.144887 0.989448i 0.546282π-0.546282\pi
−0.144887 + 0.989448i 0.546282π0.546282\pi
6868 −23121.1 −0.606367
6969 8805.55 0.222656
7070 0 0
7171 47989.5 1.12980 0.564899 0.825160i 0.308915π-0.308915\pi
0.564899 + 0.825160i 0.308915π0.308915\pi
7272 14569.4 0.331215
7373 37699.4 0.827993 0.413997 0.910278i 0.364132π-0.364132\pi
0.413997 + 0.910278i 0.364132π0.364132\pi
7474 3303.32 0.0701248
7575 0 0
7676 −19159.0 −0.380486
7777 −16525.7 −0.317639
7878 381.296 0.00709620
7979 62335.6 1.12375 0.561874 0.827223i 0.310081π-0.310081\pi
0.561874 + 0.827223i 0.310081π0.310081\pi
8080 0 0
8181 48092.0 0.814443
8282 −11374.3 −0.186806
8383 369.796 0.00589205 0.00294603 0.999996i 0.499062π-0.499062\pi
0.00294603 + 0.999996i 0.499062π0.499062\pi
8484 −3071.99 −0.0475031
8585 0 0
8686 38471.4 0.560908
8787 4634.56 0.0656463
8888 −21584.6 −0.297124
8989 115397. 1.54425 0.772126 0.635469i 0.219193π-0.219193\pi
0.772126 + 0.635469i 0.219193π0.219193\pi
9090 0 0
9191 1192.05 0.0150901
9292 35956.1 0.442898
9393 40980.7 0.491328
9494 −41739.9 −0.487227
9595 0 0
9696 −4012.39 −0.0444350
9797 −136508. −1.47309 −0.736544 0.676390i 0.763543π-0.763543\pi
−0.736544 + 0.676390i 0.763543π0.763543\pi
9898 −9604.00 −0.101015
9999 −76776.0 −0.787295
100100 0 0
101101 55976.1 0.546008 0.273004 0.962013i 0.411983π-0.411983\pi
0.273004 + 0.962013i 0.411983π0.411983\pi
102102 22649.1 0.215552
103103 165176. 1.53410 0.767052 0.641585i 0.221723π-0.221723\pi
0.767052 + 0.641585i 0.221723π0.221723\pi
104104 1556.97 0.0141155
105105 0 0
106106 135737. 1.17337
107107 99801.0 0.842705 0.421352 0.906897i 0.361556π-0.361556\pi
0.421352 + 0.906897i 0.361556π0.361556\pi
108108 −29506.6 −0.243422
109109 225386. 1.81703 0.908514 0.417855i 0.137218π-0.137218\pi
0.908514 + 0.417855i 0.137218π0.137218\pi
110110 0 0
111111 −3235.90 −0.0249280
112112 −12544.0 −0.0944911
113113 −104503. −0.769895 −0.384948 0.922938i 0.625781π-0.625781\pi
−0.384948 + 0.922938i 0.625781π0.625781\pi
114114 18768.0 0.135255
115115 0 0
116116 18924.5 0.130581
117117 5538.09 0.0374020
118118 −75431.4 −0.498709
119119 70808.3 0.458371
120120 0 0
121121 −47306.9 −0.293738
122122 105956. 0.644507
123123 11142.1 0.0664058
124124 167338. 0.977330
125125 0 0
126126 −44618.7 −0.250375
127127 245433. 1.35028 0.675141 0.737689i 0.264083π-0.264083\pi
0.675141 + 0.737689i 0.264083π0.264083\pi
128128 −16384.0 −0.0883883
129129 −37686.1 −0.199392
130130 0 0
131131 −101703. −0.517792 −0.258896 0.965905i 0.583359π-0.583359\pi
−0.258896 + 0.965905i 0.583359π0.583359\pi
132132 21144.0 0.105622
133133 58674.5 0.287621
134134 42589.9 0.204901
135135 0 0
136136 92484.3 0.428766
137137 63654.7 0.289754 0.144877 0.989450i 0.453721π-0.453721\pi
0.144877 + 0.989450i 0.453721π0.453721\pi
138138 −35222.2 −0.157441
139139 277917. 1.22005 0.610025 0.792382i 0.291159π-0.291159\pi
0.610025 + 0.792382i 0.291159π0.291159\pi
140140 0 0
141141 40887.9 0.173200
142142 −191958. −0.798888
143143 −8204.71 −0.0335524
144144 −58277.5 −0.234204
145145 0 0
146146 −150797. −0.585480
147147 9407.97 0.0359089
148148 −13213.3 −0.0495857
149149 456393. 1.68412 0.842060 0.539384i 0.181343π-0.181343\pi
0.842060 + 0.539384i 0.181343π0.181343\pi
150150 0 0
151151 318099. 1.13532 0.567662 0.823262i 0.307848π-0.307848\pi
0.567662 + 0.823262i 0.307848π0.307848\pi
152152 76636.1 0.269045
153153 328964. 1.13611
154154 66102.9 0.224605
155155 0 0
156156 −1525.19 −0.00501777
157157 392920. 1.27220 0.636099 0.771607i 0.280547π-0.280547\pi
0.636099 + 0.771607i 0.280547π0.280547\pi
158158 −249342. −0.794609
159159 −132967. −0.417110
160160 0 0
161161 −110116. −0.334799
162162 −192368. −0.575898
163163 −56353.1 −0.166130 −0.0830652 0.996544i 0.526471π-0.526471\pi
−0.0830652 + 0.996544i 0.526471π0.526471\pi
164164 45497.2 0.132092
165165 0 0
166166 −1479.18 −0.00416631
167167 312776. 0.867845 0.433922 0.900950i 0.357129π-0.357129\pi
0.433922 + 0.900950i 0.357129π0.357129\pi
168168 12288.0 0.0335897
169169 −370701. −0.998406
170170 0 0
171171 272593. 0.712892
172172 −153885. −0.396622
173173 307297. 0.780626 0.390313 0.920682i 0.372367π-0.372367\pi
0.390313 + 0.920682i 0.372367π0.372367\pi
174174 −18538.2 −0.0464189
175175 0 0
176176 86338.5 0.210098
177177 73891.7 0.177281
178178 −461587. −1.09195
179179 −804792. −1.87738 −0.938688 0.344768i 0.887958π-0.887958\pi
−0.938688 + 0.344768i 0.887958π0.887958\pi
180180 0 0
181181 −518678. −1.17680 −0.588399 0.808571i 0.700241π-0.700241\pi
−0.588399 + 0.808571i 0.700241π0.700241\pi
182182 −4768.21 −0.0106703
183183 −103794. −0.229109
184184 −143825. −0.313176
185185 0 0
186186 −163923. −0.347422
187187 −487363. −1.01917
188188 166960. 0.344522
189189 90363.8 0.184009
190190 0 0
191191 −204063. −0.404744 −0.202372 0.979309i 0.564865π-0.564865\pi
−0.202372 + 0.979309i 0.564865π0.564865\pi
192192 16049.6 0.0314203
193193 873491. 1.68797 0.843986 0.536365i 0.180203π-0.180203\pi
0.843986 + 0.536365i 0.180203π0.180203\pi
194194 546032. 1.04163
195195 0 0
196196 38416.0 0.0714286
197197 −114332. −0.209895 −0.104948 0.994478i 0.533468π-0.533468\pi
−0.104948 + 0.994478i 0.533468π0.533468\pi
198198 307104. 0.556702
199199 −262148. −0.469261 −0.234630 0.972085i 0.575388π-0.575388\pi
−0.234630 + 0.972085i 0.575388π0.575388\pi
200200 0 0
201201 −41720.6 −0.0728384
202202 −223904. −0.386086
203203 −57956.3 −0.0987098
204204 −90596.5 −0.152418
205205 0 0
206206 −660705. −1.08478
207207 −511581. −0.829828
208208 −6227.86 −0.00998115
209209 −403848. −0.639517
210210 0 0
211211 878765. 1.35883 0.679417 0.733752i 0.262233π-0.262233\pi
0.679417 + 0.733752i 0.262233π0.262233\pi
212212 −542950. −0.829698
213213 188040. 0.283989
214214 −399204. −0.595882
215215 0 0
216216 118026. 0.172125
217217 −512474. −0.738792
218218 −901546. −1.28483
219219 147719. 0.208127
220220 0 0
221221 35155.0 0.0484179
222222 12943.6 0.0176268
223223 −540539. −0.727888 −0.363944 0.931421i 0.618570π-0.618570\pi
−0.363944 + 0.931421i 0.618570π0.618570\pi
224224 50176.0 0.0668153
225225 0 0
226226 418011. 0.544398
227227 135234. 0.174189 0.0870947 0.996200i 0.472242π-0.472242\pi
0.0870947 + 0.996200i 0.472242π0.472242\pi
228228 −75071.8 −0.0956400
229229 −118878. −0.149800 −0.0749000 0.997191i 0.523864π-0.523864\pi
−0.0749000 + 0.997191i 0.523864π0.523864\pi
230230 0 0
231231 −64753.6 −0.0798425
232232 −75698.0 −0.0923346
233233 −659512. −0.795854 −0.397927 0.917417i 0.630270π-0.630270\pi
−0.397927 + 0.917417i 0.630270π0.630270\pi
234234 −22152.4 −0.0264472
235235 0 0
236236 301726. 0.352640
237237 244253. 0.282468
238238 −283233. −0.324117
239239 467946. 0.529908 0.264954 0.964261i 0.414643π-0.414643\pi
0.264954 + 0.964261i 0.414643π0.414643\pi
240240 0 0
241241 −215104. −0.238564 −0.119282 0.992860i 0.538059π-0.538059\pi
−0.119282 + 0.992860i 0.538059π0.538059\pi
242242 189228. 0.207704
243243 636572. 0.691564
244244 −423826. −0.455735
245245 0 0
246246 −44568.6 −0.0469560
247247 29130.8 0.0303815
248248 −669353. −0.691077
249249 1448.99 0.00148104
250250 0 0
251251 −874948. −0.876593 −0.438297 0.898830i 0.644418π-0.644418\pi
−0.438297 + 0.898830i 0.644418π0.644418\pi
252252 178475. 0.177042
253253 757910. 0.744417
254254 −981734. −0.954793
255255 0 0
256256 65536.0 0.0625000
257257 227843. 0.215180 0.107590 0.994195i 0.465687π-0.465687\pi
0.107590 + 0.994195i 0.465687π0.465687\pi
258258 150744. 0.140991
259259 40465.7 0.0374833
260260 0 0
261261 −269256. −0.244661
262262 406812. 0.366134
263263 −1.56138e6 −1.39194 −0.695968 0.718073i 0.745024π-0.745024\pi
−0.695968 + 0.718073i 0.745024π0.745024\pi
264264 −84576.2 −0.0746858
265265 0 0
266266 −234698. −0.203379
267267 452165. 0.388167
268268 −170360. −0.144887
269269 −1.58500e6 −1.33551 −0.667756 0.744380i 0.732745π-0.732745\pi
−0.667756 + 0.744380i 0.732745π0.732745\pi
270270 0 0
271271 477067. 0.394599 0.197300 0.980343i 0.436783π-0.436783\pi
0.197300 + 0.980343i 0.436783π0.436783\pi
272272 −369937. −0.303184
273273 4670.88 0.00379308
274274 −254619. −0.204887
275275 0 0
276276 140889. 0.111328
277277 138751. 0.108652 0.0543258 0.998523i 0.482699π-0.482699\pi
0.0543258 + 0.998523i 0.482699π0.482699\pi
278278 −1.11167e6 −0.862706
279279 −2.38087e6 −1.83116
280280 0 0
281281 −2.51115e6 −1.89717 −0.948585 0.316522i 0.897485π-0.897485\pi
−0.948585 + 0.316522i 0.897485π0.897485\pi
282282 −163552. −0.122471
283283 2.29079e6 1.70027 0.850136 0.526563i 0.176520π-0.176520\pi
0.850136 + 0.526563i 0.176520π0.176520\pi
284284 767833. 0.564899
285285 0 0
286286 32818.9 0.0237251
287287 −139335. −0.0998519
288288 233110. 0.165607
289289 668362. 0.470725
290290 0 0
291291 −534886. −0.370279
292292 603190. 0.413997
293293 446400. 0.303777 0.151888 0.988398i 0.451465π-0.451465\pi
0.151888 + 0.988398i 0.451465π0.451465\pi
294294 −37631.9 −0.0253914
295295 0 0
296296 52853.2 0.0350624
297297 −621961. −0.409140
298298 −1.82557e6 −1.19085
299299 −54670.4 −0.0353650
300300 0 0
301301 471274. 0.299818
302302 −1.27240e6 −0.802795
303303 219334. 0.137246
304304 −306544. −0.190243
305305 0 0
306306 −1.31586e6 −0.803351
307307 132928. 0.0804956 0.0402478 0.999190i 0.487185π-0.487185\pi
0.0402478 + 0.999190i 0.487185π0.487185\pi
308308 −264412. −0.158819
309309 647219. 0.385616
310310 0 0
311311 −1.02347e6 −0.600029 −0.300015 0.953935i 0.596992π-0.596992\pi
−0.300015 + 0.953935i 0.596992π0.596992\pi
312312 6100.74 0.00354810
313313 2.03277e6 1.17281 0.586404 0.810018i 0.300543π-0.300543\pi
0.586404 + 0.810018i 0.300543π0.300543\pi
314314 −1.57168e6 −0.899580
315315 0 0
316316 997370. 0.561874
317317 2.42685e6 1.35642 0.678212 0.734866i 0.262755π-0.262755\pi
0.678212 + 0.734866i 0.262755π0.262755\pi
318318 531868. 0.294941
319319 398904. 0.219479
320320 0 0
321321 391056. 0.211824
322322 440463. 0.236739
323323 1.73038e6 0.922858
324324 769472. 0.407221
325325 0 0
326326 225412. 0.117472
327327 883144. 0.456733
328328 −181989. −0.0934029
329329 −511314. −0.260434
330330 0 0
331331 552981. 0.277422 0.138711 0.990333i 0.455704π-0.455704\pi
0.138711 + 0.990333i 0.455704π0.455704\pi
332332 5916.73 0.00294603
333333 187998. 0.0929055
334334 −1.25110e6 −0.613659
335335 0 0
336336 −49151.8 −0.0237515
337337 −202099. −0.0969371 −0.0484685 0.998825i 0.515434π-0.515434\pi
−0.0484685 + 0.998825i 0.515434π0.515434\pi
338338 1.48280e6 0.705980
339339 −409479. −0.193523
340340 0 0
341341 3.52728e6 1.64268
342342 −1.09037e6 −0.504091
343343 −117649. −0.0539949
344344 615542. 0.280454
345345 0 0
346346 −1.22919e6 −0.551986
347347 −1.04617e6 −0.466419 −0.233210 0.972426i 0.574923π-0.574923\pi
−0.233210 + 0.972426i 0.574923π0.574923\pi
348348 74152.9 0.0328231
349349 −2.72359e6 −1.19696 −0.598479 0.801139i 0.704228π-0.704228\pi
−0.598479 + 0.801139i 0.704228π0.704228\pi
350350 0 0
351351 44863.9 0.0194370
352352 −345354. −0.148562
353353 −1.73711e6 −0.741979 −0.370989 0.928637i 0.620981π-0.620981\pi
−0.370989 + 0.928637i 0.620981π0.620981\pi
354354 −295567. −0.125357
355355 0 0
356356 1.84635e6 0.772126
357357 277452. 0.115217
358358 3.21917e6 1.32751
359359 1.68699e6 0.690837 0.345419 0.938449i 0.387737π-0.387737\pi
0.345419 + 0.938449i 0.387737π0.387737\pi
360360 0 0
361361 −1.04224e6 −0.420920
362362 2.07471e6 0.832121
363363 −185365. −0.0738348
364364 19072.8 0.00754504
365365 0 0
366366 415175. 0.162005
367367 −3.25743e6 −1.26244 −0.631219 0.775605i 0.717445π-0.717445\pi
−0.631219 + 0.775605i 0.717445π0.717445\pi
368368 575298. 0.221449
369369 −647330. −0.247491
370370 0 0
371371 1.66278e6 0.627193
372372 655691. 0.245664
373373 −3.36622e6 −1.25277 −0.626384 0.779514i 0.715466π-0.715466\pi
−0.626384 + 0.779514i 0.715466π0.715466\pi
374374 1.94945e6 0.720665
375375 0 0
376376 −667838. −0.243614
377377 −28774.2 −0.0104268
378378 −361455. −0.130114
379379 4.98342e6 1.78209 0.891044 0.453917i 0.149974π-0.149974\pi
0.891044 + 0.453917i 0.149974π0.149974\pi
380380 0 0
381381 961695. 0.339410
382382 816252. 0.286197
383383 1.14076e6 0.397374 0.198687 0.980063i 0.436332π-0.436332\pi
0.198687 + 0.980063i 0.436332π0.436332\pi
384384 −64198.3 −0.0222175
385385 0 0
386386 −3.49396e6 −1.19358
387387 2.18947e6 0.743124
388388 −2.18413e6 −0.736544
389389 −4.58469e6 −1.53616 −0.768080 0.640354i 0.778788π-0.778788\pi
−0.768080 + 0.640354i 0.778788π0.778788\pi
390390 0 0
391391 −3.24744e6 −1.07423
392392 −153664. −0.0505076
393393 −398508. −0.130154
394394 457329. 0.148418
395395 0 0
396396 −1.22842e6 −0.393647
397397 4.12709e6 1.31422 0.657110 0.753795i 0.271779π-0.271779\pi
0.657110 + 0.753795i 0.271779π0.271779\pi
398398 1.04859e6 0.331817
399399 229907. 0.0722971
400400 0 0
401401 2.33931e6 0.726487 0.363243 0.931694i 0.381669π-0.381669\pi
0.363243 + 0.931694i 0.381669π0.381669\pi
402402 166882. 0.0515045
403403 −254434. −0.0780390
404404 895617. 0.273004
405405 0 0
406406 231825. 0.0697984
407407 −278520. −0.0833431
408408 362386. 0.107776
409409 5.04134e6 1.49018 0.745088 0.666966i 0.232408π-0.232408\pi
0.745088 + 0.666966i 0.232408π0.232408\pi
410410 0 0
411411 249422. 0.0728333
412412 2.64282e6 0.767052
413413 −924034. −0.266571
414414 2.04632e6 0.586777
415415 0 0
416416 24911.4 0.00705774
417417 1.08898e6 0.306675
418418 1.61539e6 0.452207
419419 66941.5 0.0186277 0.00931387 0.999957i 0.497035π-0.497035\pi
0.00931387 + 0.999957i 0.497035π0.497035\pi
420420 0 0
421421 670296. 0.184315 0.0921576 0.995744i 0.470624π-0.470624\pi
0.0921576 + 0.995744i 0.470624π0.470624\pi
422422 −3.51506e6 −0.960841
423423 −2.37548e6 −0.645508
424424 2.17180e6 0.586685
425425 0 0
426426 −752160. −0.200810
427427 1.29797e6 0.344503
428428 1.59682e6 0.421352
429429 −32149.0 −0.00843381
430430 0 0
431431 −365337. −0.0947329 −0.0473664 0.998878i 0.515083π-0.515083\pi
−0.0473664 + 0.998878i 0.515083π0.515083\pi
432432 −472105. −0.121711
433433 −1.30294e6 −0.333967 −0.166984 0.985960i 0.553403π-0.553403\pi
−0.166984 + 0.985960i 0.553403π0.553403\pi
434434 2.04989e6 0.522405
435435 0 0
436436 3.60618e6 0.908514
437437 −2.69095e6 −0.674066
438438 −590878. −0.147168
439439 5.16315e6 1.27865 0.639327 0.768935i 0.279213π-0.279213\pi
0.639327 + 0.768935i 0.279213π0.279213\pi
440440 0 0
441441 −546579. −0.133831
442442 −140620. −0.0342367
443443 −7.64624e6 −1.85114 −0.925569 0.378579i 0.876413π-0.876413\pi
−0.925569 + 0.378579i 0.876413π0.876413\pi
444444 −51774.4 −0.0124640
445445 0 0
446446 2.16216e6 0.514695
447447 1.78831e6 0.423325
448448 −200704. −0.0472456
449449 4.83346e6 1.13147 0.565734 0.824588i 0.308593π-0.308593\pi
0.565734 + 0.824588i 0.308593π0.308593\pi
450450 0 0
451451 959024. 0.222018
452452 −1.67204e6 −0.384948
453453 1.24642e6 0.285378
454454 −540936. −0.123170
455455 0 0
456456 300287. 0.0676277
457457 −3.51870e6 −0.788119 −0.394060 0.919085i 0.628930π-0.628930\pi
−0.394060 + 0.919085i 0.628930π0.628930\pi
458458 475511. 0.105925
459459 2.66493e6 0.590411
460460 0 0
461461 3.55938e6 0.780049 0.390024 0.920805i 0.372467π-0.372467\pi
0.390024 + 0.920805i 0.372467π0.372467\pi
462462 259015. 0.0564572
463463 4.39317e6 0.952413 0.476207 0.879333i 0.342011π-0.342011\pi
0.476207 + 0.879333i 0.342011π0.342011\pi
464464 302792. 0.0652904
465465 0 0
466466 2.63805e6 0.562754
467467 −7.46723e6 −1.58441 −0.792205 0.610256i 0.791067π-0.791067\pi
−0.792205 + 0.610256i 0.791067π0.791067\pi
468468 88609.4 0.0187010
469469 521727. 0.109524
470470 0 0
471471 1.53960e6 0.319783
472472 −1.20690e6 −0.249354
473473 −3.24371e6 −0.666637
474474 −977012. −0.199735
475475 0 0
476476 1.13293e6 0.229185
477477 7.72504e6 1.55455
478478 −1.87178e6 −0.374702
479479 −5.07249e6 −1.01014 −0.505070 0.863078i 0.668534π-0.668534\pi
−0.505070 + 0.863078i 0.668534π0.668534\pi
480480 0 0
481481 20090.5 0.00395938
482482 860414. 0.168690
483483 −431472. −0.0841560
484484 −756910. −0.146869
485485 0 0
486486 −2.54629e6 −0.489009
487487 −8.40987e6 −1.60682 −0.803409 0.595428i 0.796983π-0.796983\pi
−0.803409 + 0.595428i 0.796983π0.796983\pi
488488 1.69530e6 0.322253
489489 −220811. −0.0417589
490490 0 0
491491 −1.07319e6 −0.200896 −0.100448 0.994942i 0.532028π-0.532028\pi
−0.100448 + 0.994942i 0.532028π0.532028\pi
492492 178274. 0.0332029
493493 −1.70920e6 −0.316720
494494 −116523. −0.0214830
495495 0 0
496496 2.67741e6 0.488665
497497 −2.35149e6 −0.427023
498498 −5795.96 −0.00104725
499499 4.34278e6 0.780758 0.390379 0.920654i 0.372344π-0.372344\pi
0.390379 + 0.920654i 0.372344π0.372344\pi
500500 0 0
501501 1.22557e6 0.218144
502502 3.49979e6 0.619845
503503 1.03452e6 0.182313 0.0911564 0.995837i 0.470944π-0.470944\pi
0.0911564 + 0.995837i 0.470944π0.470944\pi
504504 −713899. −0.125187
505505 0 0
506506 −3.03164e6 −0.526382
507507 −1.45254e6 −0.250962
508508 3.92693e6 0.675141
509509 −1.12485e6 −0.192442 −0.0962208 0.995360i 0.530675π-0.530675\pi
−0.0962208 + 0.995360i 0.530675π0.530675\pi
510510 0 0
511511 −1.84727e6 −0.312952
512512 −262144. −0.0441942
513513 2.20827e6 0.370474
514514 −911371. −0.152155
515515 0 0
516516 −602978. −0.0996959
517517 3.51930e6 0.579068
518518 −161863. −0.0265047
519519 1.20410e6 0.196220
520520 0 0
521521 −193877. −0.0312919 −0.0156460 0.999878i 0.504980π-0.504980\pi
−0.0156460 + 0.999878i 0.504980π0.504980\pi
522522 1.07702e6 0.173001
523523 6.31332e6 1.00926 0.504630 0.863336i 0.331629π-0.331629\pi
0.504630 + 0.863336i 0.331629π0.331629\pi
524524 −1.62725e6 −0.258896
525525 0 0
526526 6.24552e6 0.984247
527527 −1.51134e7 −2.37048
528528 338305. 0.0528109
529529 −1.38617e6 −0.215367
530530 0 0
531531 −4.29292e6 −0.660719
532532 938792. 0.143810
533533 −69177.3 −0.0105474
534534 −1.80866e6 −0.274476
535535 0 0
536536 681439. 0.102451
537537 −3.15346e6 −0.471902
538538 6.33999e6 0.944349
539539 809761. 0.120056
540540 0 0
541541 −4.19872e6 −0.616770 −0.308385 0.951262i 0.599789π-0.599789\pi
−0.308385 + 0.951262i 0.599789π0.599789\pi
542542 −1.90827e6 −0.279024
543543 −2.03237e6 −0.295803
544544 1.47975e6 0.214383
545545 0 0
546546 −18683.5 −0.00268211
547547 −6.84530e6 −0.978192 −0.489096 0.872230i 0.662673π-0.662673\pi
−0.489096 + 0.872230i 0.662673π0.662673\pi
548548 1.01848e6 0.144877
549549 6.03015e6 0.853881
550550 0 0
551551 −1.41631e6 −0.198737
552552 −563555. −0.0787207
553553 −3.05445e6 −0.424736
554554 −555003. −0.0768283
555555 0 0
556556 4.44667e6 0.610025
557557 9.43023e6 1.28791 0.643953 0.765065i 0.277293π-0.277293\pi
0.643953 + 0.765065i 0.277293π0.277293\pi
558558 9.52350e6 1.29482
559559 233979. 0.0316699
560560 0 0
561561 −1.90966e6 −0.256182
562562 1.00446e7 1.34150
563563 −1.27111e7 −1.69010 −0.845052 0.534685i 0.820430π-0.820430\pi
−0.845052 + 0.534685i 0.820430π0.820430\pi
564564 654207. 0.0865998
565565 0 0
566566 −9.16315e6 −1.20227
567567 −2.35651e6 −0.307830
568568 −3.07133e6 −0.399444
569569 7.92638e6 1.02635 0.513173 0.858285i 0.328470π-0.328470\pi
0.513173 + 0.858285i 0.328470π0.328470\pi
570570 0 0
571571 1.10620e6 0.141985 0.0709927 0.997477i 0.477383π-0.477383\pi
0.0709927 + 0.997477i 0.477383π0.477383\pi
572572 −131275. −0.0167762
573573 −799591. −0.101738
574574 557341. 0.0706059
575575 0 0
576576 −932440. −0.117102
577577 4.53166e6 0.566654 0.283327 0.959023i 0.408562π-0.408562\pi
0.283327 + 0.959023i 0.408562π0.408562\pi
578578 −2.67345e6 −0.332853
579579 3.42265e6 0.424293
580580 0 0
581581 −18120.0 −0.00222699
582582 2.13955e6 0.261827
583583 −1.14447e7 −1.39455
584584 −2.41276e6 −0.292740
585585 0 0
586586 −1.78560e6 −0.214803
587587 201145. 0.0240943 0.0120472 0.999927i 0.496165π-0.496165\pi
0.0120472 + 0.999927i 0.496165π0.496165\pi
588588 150527. 0.0179545
589589 −1.25236e7 −1.48744
590590 0 0
591591 −447994. −0.0527598
592592 −211413. −0.0247929
593593 1.56210e7 1.82420 0.912098 0.409973i 0.134462π-0.134462\pi
0.912098 + 0.409973i 0.134462π0.134462\pi
594594 2.48784e6 0.289306
595595 0 0
596596 7.30228e6 0.842060
597597 −1.02719e6 −0.117955
598598 218681. 0.0250069
599599 −2.80468e6 −0.319386 −0.159693 0.987167i 0.551050π-0.551050\pi
−0.159693 + 0.987167i 0.551050π0.551050\pi
600600 0 0
601601 7.57493e6 0.855446 0.427723 0.903910i 0.359316π-0.359316\pi
0.427723 + 0.903910i 0.359316π0.359316\pi
602602 −1.88510e6 −0.212003
603603 2.42386e6 0.271466
604604 5.08958e6 0.567662
605605 0 0
606606 −877336. −0.0970475
607607 1.71170e7 1.88562 0.942812 0.333324i 0.108170π-0.108170\pi
0.942812 + 0.333324i 0.108170π0.108170\pi
608608 1.22618e6 0.134522
609609 −227093. −0.0248120
610610 0 0
611611 −253858. −0.0275098
612612 5.26343e6 0.568055
613613 −1.57603e7 −1.69400 −0.847002 0.531590i 0.821595π-0.821595\pi
−0.847002 + 0.531590i 0.821595π0.821595\pi
614614 −531714. −0.0569190
615615 0 0
616616 1.05765e6 0.112302
617617 1.16536e7 1.23239 0.616194 0.787594i 0.288674π-0.288674\pi
0.616194 + 0.787594i 0.288674π0.288674\pi
618618 −2.58888e6 −0.272672
619619 −9.20111e6 −0.965192 −0.482596 0.875843i 0.660306π-0.660306\pi
−0.482596 + 0.875843i 0.660306π0.660306\pi
620620 0 0
621621 −4.14430e6 −0.431243
622622 4.09386e6 0.424285
623623 −5.65444e6 −0.583673
624624 −24403.0 −0.00250889
625625 0 0
626626 −8.13108e6 −0.829301
627627 −1.58242e6 −0.160751
628628 6.28672e6 0.636099
629629 1.19338e6 0.120269
630630 0 0
631631 1.50421e7 1.50395 0.751976 0.659191i 0.229101π-0.229101\pi
0.751976 + 0.659191i 0.229101π0.229101\pi
632632 −3.98948e6 −0.397305
633633 3.44331e6 0.341560
634634 −9.70742e6 −0.959137
635635 0 0
636636 −2.12747e6 −0.208555
637637 −58410.5 −0.00570351
638638 −1.59562e6 −0.155195
639639 −1.09247e7 −1.05841
640640 0 0
641641 −1.15445e7 −1.10976 −0.554879 0.831931i 0.687235π-0.687235\pi
−0.554879 + 0.831931i 0.687235π0.687235\pi
642642 −1.56422e6 −0.149782
643643 4.82038e6 0.459784 0.229892 0.973216i 0.426163π-0.426163\pi
0.229892 + 0.973216i 0.426163π0.426163\pi
644644 −1.76185e6 −0.167400
645645 0 0
646646 −6.92152e6 −0.652559
647647 7.53202e6 0.707377 0.353688 0.935363i 0.384927π-0.384927\pi
0.353688 + 0.935363i 0.384927π0.384927\pi
648648 −3.07789e6 −0.287949
649649 6.35999e6 0.592713
650650 0 0
651651 −2.00805e6 −0.185705
652652 −901650. −0.0830652
653653 4.07749e6 0.374205 0.187103 0.982340i 0.440090π-0.440090\pi
0.187103 + 0.982340i 0.440090π0.440090\pi
654654 −3.53257e6 −0.322959
655655 0 0
656656 727956. 0.0660458
657657 −8.58213e6 −0.775678
658658 2.04525e6 0.184155
659659 −1.52918e7 −1.37165 −0.685826 0.727765i 0.740559π-0.740559\pi
−0.685826 + 0.727765i 0.740559π0.740559\pi
660660 0 0
661661 2.03724e7 1.81359 0.906796 0.421570i 0.138521π-0.138521\pi
0.906796 + 0.421570i 0.138521π0.138521\pi
662662 −2.21193e6 −0.196167
663663 137750. 0.0121705
664664 −23666.9 −0.00208315
665665 0 0
666666 −751990. −0.0656941
667667 2.65802e6 0.231336
668668 5.00442e6 0.433922
669669 −2.11802e6 −0.182964
670670 0 0
671671 −8.93371e6 −0.765994
672672 196607. 0.0167949
673673 4.09627e6 0.348619 0.174309 0.984691i 0.444231π-0.444231\pi
0.174309 + 0.984691i 0.444231π0.444231\pi
674674 808397. 0.0685449
675675 0 0
676676 −5.93122e6 −0.499203
677677 7.73865e6 0.648924 0.324462 0.945899i 0.394817π-0.394817\pi
0.324462 + 0.945899i 0.394817π0.394817\pi
678678 1.63792e6 0.136841
679679 6.68889e6 0.556775
680680 0 0
681681 529895. 0.0437847
682682 −1.41091e7 −1.16155
683683 −2.24027e7 −1.83759 −0.918795 0.394734i 0.870837π-0.870837\pi
−0.918795 + 0.394734i 0.870837π0.870837\pi
684684 4.36148e6 0.356446
685685 0 0
686686 470596. 0.0381802
687687 −465805. −0.0376541
688688 −2.46217e6 −0.198311
689689 825541. 0.0662507
690690 0 0
691691 −2.60639e6 −0.207656 −0.103828 0.994595i 0.533109π-0.533109\pi
−0.103828 + 0.994595i 0.533109π0.533109\pi
692692 4.91675e6 0.390313
693693 3.76202e6 0.297570
694694 4.18466e6 0.329808
695695 0 0
696696 −296612. −0.0232095
697697 −4.10916e6 −0.320384
698698 1.08944e7 0.846377
699699 −2.58420e6 −0.200048
700700 0 0
701701 −5.34202e6 −0.410592 −0.205296 0.978700i 0.565816π-0.565816\pi
−0.205296 + 0.978700i 0.565816π0.565816\pi
702702 −179456. −0.0137440
703703 988882. 0.0754668
704704 1.38142e6 0.105049
705705 0 0
706706 6.94846e6 0.524658
707707 −2.74283e6 −0.206372
708708 1.18227e6 0.0886406
709709 −1.78376e7 −1.33266 −0.666332 0.745656i 0.732136π-0.732136\pi
−0.666332 + 0.745656i 0.732136π0.732136\pi
710710 0 0
711711 −1.41905e7 −1.05275
712712 −7.38539e6 −0.545976
713713 2.35033e7 1.73143
714714 −1.10981e6 −0.0814708
715715 0 0
716716 −1.28767e7 −0.938688
717717 1.83358e6 0.133199
718718 −6.74795e6 −0.488496
719719 −1.93072e7 −1.39283 −0.696414 0.717640i 0.745222π-0.745222\pi
−0.696414 + 0.717640i 0.745222π0.745222\pi
720720 0 0
721721 −8.09364e6 −0.579837
722722 4.16896e6 0.297636
723723 −842852. −0.0599660
724724 −8.29885e6 −0.588399
725725 0 0
726726 741460. 0.0522091
727727 −2.11119e7 −1.48147 −0.740733 0.671800i 0.765522π-0.765522\pi
−0.740733 + 0.671800i 0.765522π0.765522\pi
728728 −76291.3 −0.00533515
729729 −9.19205e6 −0.640610
730730 0 0
731731 1.38984e7 0.961994
732732 −1.66070e6 −0.114555
733733 2.35579e7 1.61948 0.809742 0.586786i 0.199607π-0.199607\pi
0.809742 + 0.586786i 0.199607π0.199607\pi
734734 1.30297e7 0.892678
735735 0 0
736736 −2.30119e6 −0.156588
737737 −3.59097e6 −0.243525
738738 2.58932e6 0.175003
739739 −8.49978e6 −0.572528 −0.286264 0.958151i 0.592413π-0.592413\pi
−0.286264 + 0.958151i 0.592413π0.592413\pi
740740 0 0
741741 114145. 0.00763678
742742 −6.65114e6 −0.443492
743743 5.28179e6 0.351001 0.175501 0.984479i 0.443846π-0.443846\pi
0.175501 + 0.984479i 0.443846π0.443846\pi
744744 −2.62276e6 −0.173711
745745 0 0
746746 1.34649e7 0.885841
747747 −84182.7 −0.00551977
748748 −7.79781e6 −0.509587
749749 −4.89025e6 −0.318512
750750 0 0
751751 1.72132e7 1.11368 0.556842 0.830619i 0.312013π-0.312013\pi
0.556842 + 0.830619i 0.312013π0.312013\pi
752752 2.67135e6 0.172261
753753 −3.42836e6 −0.220343
754754 115097. 0.00737284
755755 0 0
756756 1.44582e6 0.0920047
757757 1.95610e7 1.24066 0.620328 0.784343i 0.287000π-0.287000\pi
0.620328 + 0.784343i 0.287000π0.287000\pi
758758 −1.99337e7 −1.26013
759759 2.96976e6 0.187118
760760 0 0
761761 −2.65917e7 −1.66450 −0.832250 0.554401i 0.812948π-0.812948\pi
−0.832250 + 0.554401i 0.812948π0.812948\pi
762762 −3.84678e6 −0.239999
763763 −1.10439e7 −0.686772
764764 −3.26501e6 −0.202372
765765 0 0
766766 −4.56306e6 −0.280986
767767 −458766. −0.0281581
768768 256793. 0.0157102
769769 3.32124e6 0.202528 0.101264 0.994860i 0.467711π-0.467711\pi
0.101264 + 0.994860i 0.467711π0.467711\pi
770770 0 0
771771 892769. 0.0540883
772772 1.39759e7 0.843986
773773 −3.03574e7 −1.82732 −0.913662 0.406476i 0.866758π-0.866758\pi
−0.913662 + 0.406476i 0.866758π0.866758\pi
774774 −8.75787e6 −0.525468
775775 0 0
776776 8.73651e6 0.520815
777777 158559. 0.00942190
778778 1.83388e7 1.08623
779779 −3.40501e6 −0.201036
780780 0 0
781781 1.61849e7 0.949475
782782 1.29898e7 0.759599
783783 −2.18124e6 −0.127145
784784 614656. 0.0357143
785785 0 0
786786 1.59403e6 0.0920325
787787 −1.37541e7 −0.791583 −0.395792 0.918340i 0.629530π-0.629530\pi
−0.395792 + 0.918340i 0.629530π0.629530\pi
788788 −1.82932e6 −0.104948
789789 −6.11804e6 −0.349880
790790 0 0
791791 5.12064e6 0.290993
792792 4.91366e6 0.278351
793793 644416. 0.0363901
794794 −1.65084e7 −0.929294
795795 0 0
796796 −4.19437e6 −0.234630
797797 2.68171e6 0.149543 0.0747715 0.997201i 0.476177π-0.476177\pi
0.0747715 + 0.997201i 0.476177π0.476177\pi
798798 −919630. −0.0511217
799799 −1.50792e7 −0.835627
800800 0 0
801801 −2.62697e7 −1.44668
802802 −9.35726e6 −0.513704
803803 1.27145e7 0.695840
804804 −667530. −0.0364192
805805 0 0
806806 1.01773e6 0.0551819
807807 −6.21058e6 −0.335698
808808 −3.58247e6 −0.193043
809809 3.35759e7 1.80367 0.901834 0.432083i 0.142221π-0.142221\pi
0.901834 + 0.432083i 0.142221π0.142221\pi
810810 0 0
811811 5.24303e6 0.279917 0.139959 0.990157i 0.455303π-0.455303\pi
0.139959 + 0.990157i 0.455303π0.455303\pi
812812 −927300. −0.0493549
813813 1.86932e6 0.0991875
814814 1.11408e6 0.0589325
815815 0 0
816816 −1.44954e6 −0.0762090
817817 1.15168e7 0.603637
818818 −2.01653e7 −1.05371
819819 −271366. −0.0141366
820820 0 0
821821 −1.95688e7 −1.01323 −0.506614 0.862173i 0.669103π-0.669103\pi
−0.506614 + 0.862173i 0.669103π0.669103\pi
822822 −997687. −0.0515009
823823 6.20206e6 0.319181 0.159590 0.987183i 0.448983π-0.448983\pi
0.159590 + 0.987183i 0.448983π0.448983\pi
824824 −1.05713e7 −0.542388
825825 0 0
826826 3.69614e6 0.188494
827827 −2.30838e7 −1.17366 −0.586831 0.809710i 0.699625π-0.699625\pi
−0.586831 + 0.809710i 0.699625π0.699625\pi
828828 −8.18529e6 −0.414914
829829 2.73598e7 1.38270 0.691348 0.722522i 0.257017π-0.257017\pi
0.691348 + 0.722522i 0.257017π0.257017\pi
830830 0 0
831831 543675. 0.0273109
832832 −99645.8 −0.00499058
833833 −3.46961e6 −0.173248
834834 −4.35590e6 −0.216852
835835 0 0
836836 −6.46156e6 −0.319758
837837 −1.92874e7 −0.951613
838838 −267766. −0.0131718
839839 1.15303e7 0.565504 0.282752 0.959193i 0.408753π-0.408753\pi
0.282752 + 0.959193i 0.408753π0.408753\pi
840840 0 0
841841 −1.91122e7 −0.931795
842842 −2.68118e6 −0.130331
843843 −9.83956e6 −0.476878
844844 1.40602e7 0.679417
845845 0 0
846846 9.50194e6 0.456443
847847 2.31804e6 0.111023
848848 −8.68720e6 −0.414849
849849 8.97611e6 0.427385
850850 0 0
851851 −1.85586e6 −0.0878456
852852 3.00864e6 0.141994
853853 1.31074e7 0.616800 0.308400 0.951257i 0.400206π-0.400206\pi
0.308400 + 0.951257i 0.400206π0.400206\pi
854854 −5.19186e6 −0.243601
855855 0 0
856856 −6.38726e6 −0.297941
857857 3.48607e7 1.62138 0.810689 0.585477i 0.199093π-0.199093\pi
0.810689 + 0.585477i 0.199093π0.199093\pi
858858 128596. 0.00596361
859859 2.14838e7 0.993410 0.496705 0.867919i 0.334543π-0.334543\pi
0.496705 + 0.867919i 0.334543π0.334543\pi
860860 0 0
861861 −545965. −0.0250990
862862 1.46135e6 0.0669863
863863 3.37660e6 0.154331 0.0771654 0.997018i 0.475413π-0.475413\pi
0.0771654 + 0.997018i 0.475413π0.475413\pi
864864 1.88842e6 0.0860625
865865 0 0
866866 5.21175e6 0.236151
867867 2.61888e6 0.118323
868868 −8.19958e6 −0.369396
869869 2.10233e7 0.944390
870870 0 0
871871 259028. 0.0115691
872872 −1.44247e7 −0.642416
873873 3.10756e7 1.38001
874874 1.07638e7 0.476637
875875 0 0
876876 2.36351e6 0.104063
877877 −1.58283e7 −0.694921 −0.347461 0.937695i 0.612956π-0.612956\pi
−0.347461 + 0.937695i 0.612956π0.612956\pi
878878 −2.06526e7 −0.904145
879879 1.74915e6 0.0763581
880880 0 0
881881 −1.50941e7 −0.655191 −0.327596 0.944818i 0.606238π-0.606238\pi
−0.327596 + 0.944818i 0.606238π0.606238\pi
882882 2.18632e6 0.0946328
883883 4.20608e7 1.81542 0.907708 0.419603i 0.137831π-0.137831\pi
0.907708 + 0.419603i 0.137831π0.137831\pi
884884 562480. 0.0242090
885885 0 0
886886 3.05850e7 1.30895
887887 2.83691e7 1.21070 0.605351 0.795959i 0.293033π-0.293033\pi
0.605351 + 0.795959i 0.293033π0.293033\pi
888888 207097. 0.00881338
889889 −1.20262e7 −0.510358
890890 0 0
891891 1.62195e7 0.684453
892892 −8.64862e6 −0.363944
893893 −1.24952e7 −0.524343
894894 −7.15323e6 −0.299336
895895 0 0
896896 802816. 0.0334077
897897 −214218. −0.00888944
898898 −1.93338e7 −0.800068
899899 1.23703e7 0.510482
900900 0 0
901901 4.90374e7 2.01241
902902 −3.83610e6 −0.156990
903903 1.84662e6 0.0753630
904904 6.68818e6 0.272199
905905 0 0
906906 −4.98569e6 −0.201793
907907 −1.00151e7 −0.404236 −0.202118 0.979361i 0.564783π-0.564783\pi
−0.202118 + 0.979361i 0.564783π0.564783\pi
908908 2.16375e6 0.0870947
909909 −1.27428e7 −0.511509
910910 0 0
911911 −2.06987e7 −0.826317 −0.413158 0.910659i 0.635574π-0.635574\pi
−0.413158 + 0.910659i 0.635574π0.635574\pi
912912 −1.20115e6 −0.0478200
913913 124717. 0.00495164
914914 1.40748e7 0.557284
915915 0 0
916916 −1.90204e6 −0.0749000
917917 4.98345e6 0.195707
918918 −1.06597e7 −0.417484
919919 6.79248e6 0.265301 0.132651 0.991163i 0.457651π-0.457651\pi
0.132651 + 0.991163i 0.457651π0.457651\pi
920920 0 0
921921 520861. 0.0202336
922922 −1.42375e7 −0.551578
923923 −1.16747e6 −0.0451067
924924 −1.03606e6 −0.0399213
925925 0 0
926926 −1.75727e7 −0.673458
927927 −3.76018e7 −1.43717
928928 −1.21117e6 −0.0461673
929929 −2.18354e7 −0.830085 −0.415042 0.909802i 0.636233π-0.636233\pi
−0.415042 + 0.909802i 0.636233π0.636233\pi
930930 0 0
931931 −2.87505e6 −0.108710
932932 −1.05522e7 −0.397927
933933 −4.01030e6 −0.150825
934934 2.98689e7 1.12035
935935 0 0
936936 −354438. −0.0132236
937937 3.76114e7 1.39949 0.699747 0.714391i 0.253296π-0.253296\pi
0.699747 + 0.714391i 0.253296π0.253296\pi
938938 −2.08691e6 −0.0774455
939939 7.96511e6 0.294800
940940 0 0
941941 3.13453e7 1.15398 0.576989 0.816752i 0.304227π-0.304227\pi
0.576989 + 0.816752i 0.304227π0.304227\pi
942942 −6.15840e6 −0.226121
943943 6.39025e6 0.234012
944944 4.82761e6 0.176320
945945 0 0
946946 1.29748e7 0.471383
947947 −2.16274e6 −0.0783664 −0.0391832 0.999232i 0.512476π-0.512476\pi
−0.0391832 + 0.999232i 0.512476π0.512476\pi
948948 3.90805e6 0.141234
949949 −917134. −0.0330573
950950 0 0
951951 9.50927e6 0.340954
952952 −4.53173e6 −0.162058
953953 2.60248e7 0.928230 0.464115 0.885775i 0.346372π-0.346372\pi
0.464115 + 0.885775i 0.346372π0.346372\pi
954954 −3.09002e7 −1.09923
955955 0 0
956956 7.48713e6 0.264954
957957 1.56305e6 0.0551687
958958 2.02899e7 0.714278
959959 −3.11908e6 −0.109517
960960 0 0
961961 8.07542e7 2.82070
962962 −80361.9 −0.00279971
963963 −2.27193e7 −0.789460
964964 −3.44166e6 −0.119282
965965 0 0
966966 1.72589e6 0.0595073
967967 −3.85997e7 −1.32745 −0.663725 0.747977i 0.731025π-0.731025\pi
−0.663725 + 0.747977i 0.731025π0.731025\pi
968968 3.02764e6 0.103852
969969 6.78024e6 0.231972
970970 0 0
971971 1.98202e7 0.674621 0.337310 0.941393i 0.390483π-0.390483\pi
0.337310 + 0.941393i 0.390483π0.390483\pi
972972 1.01852e7 0.345782
973973 −1.36179e7 −0.461136
974974 3.36395e7 1.13619
975975 0 0
976976 −6.78121e6 −0.227868
977977 6.29461e6 0.210976 0.105488 0.994421i 0.466360π-0.466360\pi
0.105488 + 0.994421i 0.466360π0.466360\pi
978978 883246. 0.0295280
979979 3.89187e7 1.29778
980980 0 0
981981 −5.13084e7 −1.70222
982982 4.29275e6 0.142055
983983 3.54716e7 1.17084 0.585419 0.810731i 0.300930π-0.300930\pi
0.585419 + 0.810731i 0.300930π0.300930\pi
984984 −713097. −0.0234780
985985 0 0
986986 6.83679e6 0.223955
987987 −2.00351e6 −0.0654633
988988 466093. 0.0151908
989989 −2.16138e7 −0.702652
990990 0 0
991991 −1.49772e7 −0.484446 −0.242223 0.970221i 0.577877π-0.577877\pi
−0.242223 + 0.970221i 0.577877π0.577877\pi
992992 −1.07097e7 −0.345538
993993 2.16678e6 0.0697334
994994 9.40595e6 0.301951
995995 0 0
996996 23183.8 0.000740520 0
997997 3.79210e7 1.20821 0.604104 0.796905i 0.293531π-0.293531\pi
0.604104 + 0.796905i 0.293531π0.293531\pi
998998 −1.73711e7 −0.552079
999999 1.52296e6 0.0482810
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 350.6.a.y.1.4 5
5.2 odd 4 70.6.c.d.29.2 10
5.3 odd 4 70.6.c.d.29.9 yes 10
5.4 even 2 350.6.a.z.1.2 5
15.2 even 4 630.6.g.h.379.7 10
15.8 even 4 630.6.g.h.379.2 10
20.3 even 4 560.6.g.d.449.4 10
20.7 even 4 560.6.g.d.449.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.6.c.d.29.2 10 5.2 odd 4
70.6.c.d.29.9 yes 10 5.3 odd 4
350.6.a.y.1.4 5 1.1 even 1 trivial
350.6.a.z.1.2 5 5.4 even 2
560.6.g.d.449.4 10 20.3 even 4
560.6.g.d.449.7 10 20.7 even 4
630.6.g.h.379.2 10 15.8 even 4
630.6.g.h.379.7 10 15.2 even 4