Properties

Label 325.6.b.d.274.3
Level 325325
Weight 66
Character 325.274
Analytic conductor 52.12552.125
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] = [325,6,Mod(274,325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(325, 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("325.274");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 325=5213 325 = 5^{2} \cdot 13
Weight: k k == 6 6
Character orbit: [χ][\chi] == 325.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: 52.124741439252.1247414392
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: x6+85x4+1668x2+2304 x^{6} + 85x^{4} + 1668x^{2} + 2304 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 274.3
Root 1.22183i-1.22183i of defining polynomial
Character χ\chi == 325.274
Dual form 325.6.b.d.274.4

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) == q2.22183iq216.8416iq3+27.0635q437.4193q6177.501iq7131.229iq840.6407q9353.532q11455.793iq12169.000iq13394.376q14+574.462q161545.40iq17+90.2967iq18+132.374q192989.40q21+785.489iq22+3897.96iq232210.11q24375.489q263408.06iq274803.78iq28825.458q295360.62q315475.69iq32+5954.06iq333433.62q341099.88q36+5251.49iq37294.112iq382846.24q39+17324.0q41+6641.94iq4211155.8iq439567.80q44+8660.61q46+5169.48iq479674.88iq4814699.4q4926027.1q514573.73iq5237052.1iq537572.14q5423293.2q562229.39iq57+1834.03iq58+22894.2q5956415.9q61+11910.4iq62+7213.74iq63+6216.74q64+13228.9q66+33700.6iq6741823.9iq68+65648.0q69+19320.2q71+5333.24iq72+47632.1iq73+11667.9q74+3582.49q76+62752.1iq77+6323.86iq7820458.1q7967273.0q8138491.0iq8216270.2iq8380903.5q8424786.3q86+13902.1iq87+46393.7iq88+73643.6q8929997.6q91+105492.iq92+90281.5iq93+11485.7q9492219.5q96+140209.iq97+32659.7iq98+14367.8q99+O(q100)q-2.22183i q^{2} -16.8416i q^{3} +27.0635 q^{4} -37.4193 q^{6} -177.501i q^{7} -131.229i q^{8} -40.6407 q^{9} -353.532 q^{11} -455.793i q^{12} -169.000i q^{13} -394.376 q^{14} +574.462 q^{16} -1545.40i q^{17} +90.2967i q^{18} +132.374 q^{19} -2989.40 q^{21} +785.489i q^{22} +3897.96i q^{23} -2210.11 q^{24} -375.489 q^{26} -3408.06i q^{27} -4803.78i q^{28} -825.458 q^{29} -5360.62 q^{31} -5475.69i q^{32} +5954.06i q^{33} -3433.62 q^{34} -1099.88 q^{36} +5251.49i q^{37} -294.112i q^{38} -2846.24 q^{39} +17324.0 q^{41} +6641.94i q^{42} -11155.8i q^{43} -9567.80 q^{44} +8660.61 q^{46} +5169.48i q^{47} -9674.88i q^{48} -14699.4 q^{49} -26027.1 q^{51} -4573.73i q^{52} -37052.1i q^{53} -7572.14 q^{54} -23293.2 q^{56} -2229.39i q^{57} +1834.03i q^{58} +22894.2 q^{59} -56415.9 q^{61} +11910.4i q^{62} +7213.74i q^{63} +6216.74 q^{64} +13228.9 q^{66} +33700.6i q^{67} -41823.9i q^{68} +65648.0 q^{69} +19320.2 q^{71} +5333.24i q^{72} +47632.1i q^{73} +11667.9 q^{74} +3582.49 q^{76} +62752.1i q^{77} +6323.86i q^{78} -20458.1 q^{79} -67273.0 q^{81} -38491.0i q^{82} -16270.2i q^{83} -80903.5 q^{84} -24786.3 q^{86} +13902.1i q^{87} +46393.7i q^{88} +73643.6 q^{89} -29997.6 q^{91} +105492. i q^{92} +90281.5i q^{93} +11485.7 q^{94} -92219.5 q^{96} +140209. i q^{97} +32659.7i q^{98} +14367.8 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+20q4+44q6286q91232q11+2568q143740q16+6720q197584q211044q24676q264612q2912760q31+5720q341372q36+5408q39++138896q99+O(q100) 6 q + 20 q^{4} + 44 q^{6} - 286 q^{9} - 1232 q^{11} + 2568 q^{14} - 3740 q^{16} + 6720 q^{19} - 7584 q^{21} - 1044 q^{24} - 676 q^{26} - 4612 q^{29} - 12760 q^{31} + 5720 q^{34} - 1372 q^{36} + 5408 q^{39}+ \cdots + 138896 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/325Z)×\left(\mathbb{Z}/325\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 − 2.22183i − 0.392768i −0.980527 0.196384i 0.937080π-0.937080\pi
0.980527 0.196384i 0.0629199π-0.0629199\pi
33 − 16.8416i − 1.08039i −0.841539 0.540196i 0.818350π-0.818350\pi
0.841539 0.540196i 0.181650π-0.181650\pi
44 27.0635 0.845733
55 0 0
66 −37.4193 −0.424343
77 − 177.501i − 1.36916i −0.728937 0.684580i 0.759985π-0.759985\pi
0.728937 0.684580i 0.240015π-0.240015\pi
88 − 131.229i − 0.724945i
99 −40.6407 −0.167246
1010 0 0
1111 −353.532 −0.880942 −0.440471 0.897767i 0.645188π-0.645188\pi
−0.440471 + 0.897767i 0.645188π0.645188\pi
1212 − 455.793i − 0.913723i
1313 − 169.000i − 0.277350i
1414 −394.376 −0.537763
1515 0 0
1616 574.462 0.560998
1717 − 1545.40i − 1.29694i −0.761242 0.648468i 0.775410π-0.775410\pi
0.761242 0.648468i 0.224590π-0.224590\pi
1818 90.2967i 0.0656887i
1919 132.374 0.0841236 0.0420618 0.999115i 0.486607π-0.486607\pi
0.0420618 + 0.999115i 0.486607π0.486607\pi
2020 0 0
2121 −2989.40 −1.47923
2222 785.489i 0.346006i
2323 3897.96i 1.53645i 0.640181 + 0.768224i 0.278859π0.278859\pi
−0.640181 + 0.768224i 0.721141π0.721141\pi
2424 −2210.11 −0.783224
2525 0 0
2626 −375.489 −0.108934
2727 − 3408.06i − 0.899701i
2828 − 4803.78i − 1.15795i
2929 −825.458 −0.182264 −0.0911318 0.995839i 0.529048π-0.529048\pi
−0.0911318 + 0.995839i 0.529048π0.529048\pi
3030 0 0
3131 −5360.62 −1.00187 −0.500934 0.865485i 0.667010π-0.667010\pi
−0.500934 + 0.865485i 0.667010π0.667010\pi
3232 − 5475.69i − 0.945287i
3333 5954.06i 0.951762i
3434 −3433.62 −0.509395
3535 0 0
3636 −1099.88 −0.141445
3737 5251.49i 0.630636i 0.948986 + 0.315318i 0.102111π0.102111\pi
−0.948986 + 0.315318i 0.897889π0.897889\pi
3838 − 294.112i − 0.0330411i
3939 −2846.24 −0.299647
4040 0 0
4141 17324.0 1.60949 0.804745 0.593620i 0.202302π-0.202302\pi
0.804745 + 0.593620i 0.202302π0.202302\pi
4242 6641.94i 0.580994i
4343 − 11155.8i − 0.920089i −0.887896 0.460044i 0.847833π-0.847833\pi
0.887896 0.460044i 0.152167π-0.152167\pi
4444 −9567.80 −0.745042
4545 0 0
4646 8660.61 0.603467
4747 5169.48i 0.341352i 0.985327 + 0.170676i 0.0545951π0.0545951\pi
−0.985327 + 0.170676i 0.945405π0.945405\pi
4848 − 9674.88i − 0.606098i
4949 −14699.4 −0.874602
5050 0 0
5151 −26027.1 −1.40120
5252 − 4573.73i − 0.234564i
5353 − 37052.1i − 1.81186i −0.423432 0.905928i 0.639175π-0.639175\pi
0.423432 0.905928i 0.360825π-0.360825\pi
5454 −7572.14 −0.353374
5555 0 0
5656 −23293.2 −0.992566
5757 − 2229.39i − 0.0908864i
5858 1834.03i 0.0715873i
5959 22894.2 0.856240 0.428120 0.903722i 0.359176π-0.359176\pi
0.428120 + 0.903722i 0.359176π0.359176\pi
6060 0 0
6161 −56415.9 −1.94123 −0.970615 0.240639i 0.922643π-0.922643\pi
−0.970615 + 0.240639i 0.922643π0.922643\pi
6262 11910.4i 0.393502i
6363 7213.74i 0.228986i
6464 6216.74 0.189720
6565 0 0
6666 13228.9 0.373822
6767 33700.6i 0.917173i 0.888650 + 0.458586i 0.151644π0.151644\pi
−0.888650 + 0.458586i 0.848356π0.848356\pi
6868 − 41823.9i − 1.09686i
6969 65648.0 1.65996
7070 0 0
7171 19320.2 0.454848 0.227424 0.973796i 0.426970π-0.426970\pi
0.227424 + 0.973796i 0.426970π0.426970\pi
7272 5333.24i 0.121244i
7373 47632.1i 1.04615i 0.852287 + 0.523074i 0.175215π0.175215\pi
−0.852287 + 0.523074i 0.824785π0.824785\pi
7474 11667.9 0.247693
7575 0 0
7676 3582.49 0.0711461
7777 62752.1i 1.20615i
7878 6323.86i 0.117692i
7979 −20458.1 −0.368805 −0.184403 0.982851i 0.559035π-0.559035\pi
−0.184403 + 0.982851i 0.559035π0.559035\pi
8080 0 0
8181 −67273.0 −1.13927
8282 − 38491.0i − 0.632156i
8383 − 16270.2i − 0.259237i −0.991564 0.129619i 0.958625π-0.958625\pi
0.991564 0.129619i 0.0413753π-0.0413753\pi
8484 −80903.5 −1.25103
8585 0 0
8686 −24786.3 −0.361381
8787 13902.1i 0.196916i
8888 46393.7i 0.638634i
8989 73643.6 0.985508 0.492754 0.870169i 0.335990π-0.335990\pi
0.492754 + 0.870169i 0.335990π0.335990\pi
9090 0 0
9191 −29997.6 −0.379737
9292 105492.i 1.29942i
9393 90281.5i 1.08241i
9494 11485.7 0.134072
9595 0 0
9696 −92219.5 −1.02128
9797 140209.i 1.51303i 0.653976 + 0.756516i 0.273100π0.273100\pi
−0.653976 + 0.756516i 0.726900π0.726900\pi
9898 32659.7i 0.343516i
9999 14367.8 0.147334
100100 0 0
101101 −45049.4 −0.439426 −0.219713 0.975565i 0.570512π-0.570512\pi
−0.219713 + 0.975565i 0.570512π0.570512\pi
102102 57827.7i 0.550346i
103103 125731.i 1.16774i 0.811845 + 0.583872i 0.198463π0.198463\pi
−0.811845 + 0.583872i 0.801537π0.801537\pi
104104 −22177.7 −0.201064
105105 0 0
106106 −82323.6 −0.711639
107107 9971.50i 0.0841979i 0.999113 + 0.0420989i 0.0134045π0.0134045\pi
−0.999113 + 0.0420989i 0.986596π0.986596\pi
108108 − 92234.0i − 0.760907i
109109 −121034. −0.975756 −0.487878 0.872912i 0.662229π-0.662229\pi
−0.487878 + 0.872912i 0.662229π0.662229\pi
110110 0 0
111111 88443.7 0.681333
112112 − 101967.i − 0.768097i
113113 130644.i 0.962480i 0.876589 + 0.481240i 0.159813π0.159813\pi
−0.876589 + 0.481240i 0.840187π0.840187\pi
114114 −4953.33 −0.0356973
115115 0 0
116116 −22339.8 −0.154146
117117 6868.27i 0.0463856i
118118 − 50867.1i − 0.336304i
119119 −274309. −1.77571
120120 0 0
121121 −36066.0 −0.223942
122122 125347.i 0.762453i
123123 − 291764.i − 1.73888i
124124 −145077. −0.847313
125125 0 0
126126 16027.7 0.0899384
127127 − 157630.i − 0.867220i −0.901101 0.433610i 0.857240π-0.857240\pi
0.901101 0.433610i 0.142760π-0.142760\pi
128128 − 189035.i − 1.01980i
129129 −187882. −0.994056
130130 0 0
131131 −176730. −0.899774 −0.449887 0.893086i 0.648536π-0.648536\pi
−0.449887 + 0.893086i 0.648536π0.648536\pi
132132 161137.i 0.804937i
133133 − 23496.4i − 0.115179i
134134 74877.2 0.360236
135135 0 0
136136 −202801. −0.940207
137137 − 85660.1i − 0.389921i −0.980811 0.194961i 0.937542π-0.937542\pi
0.980811 0.194961i 0.0624579π-0.0624579\pi
138138 − 145859.i − 0.651981i
139139 221477. 0.972281 0.486141 0.873881i 0.338404π-0.338404\pi
0.486141 + 0.873881i 0.338404π0.338404\pi
140140 0 0
141141 87062.4 0.368793
142142 − 42926.3i − 0.178650i
143143 59746.9i 0.244329i
144144 −23346.5 −0.0938245
145145 0 0
146146 105831. 0.410893
147147 247562.i 0.944912i
148148 142124.i 0.533350i
149149 121702. 0.449089 0.224545 0.974464i 0.427911π-0.427911\pi
0.224545 + 0.974464i 0.427911π0.427911\pi
150150 0 0
151151 144774. 0.516710 0.258355 0.966050i 0.416820π-0.416820\pi
0.258355 + 0.966050i 0.416820π0.416820\pi
152152 − 17371.3i − 0.0609850i
153153 62806.1i 0.216907i
154154 139425. 0.473737
155155 0 0
156156 −77029.0 −0.253421
157157 − 548818.i − 1.77697i −0.458910 0.888483i 0.651760π-0.651760\pi
0.458910 0.888483i 0.348240π-0.348240\pi
158158 45454.4i 0.144855i
159159 −624019. −1.95751
160160 0 0
161161 691890. 2.10364
162162 149469.i 0.447471i
163163 − 1504.59i − 0.00443557i −0.999998 0.00221779i 0.999294π-0.999294\pi
0.999998 0.00221779i 0.000705944π-0.000705944\pi
164164 468847. 1.36120
165165 0 0
166166 −36149.6 −0.101820
167167 437343.i 1.21348i 0.794902 + 0.606738i 0.207522π0.207522\pi
−0.794902 + 0.606738i 0.792478π0.792478\pi
168168 392296.i 1.07236i
169169 −28561.0 −0.0769231
170170 0 0
171171 −5379.76 −0.0140693
172172 − 301915.i − 0.778150i
173173 − 511893.i − 1.30036i −0.759779 0.650181i 0.774693π-0.774693\pi
0.759779 0.650181i 0.225307π-0.225307\pi
174174 30888.0 0.0773423
175175 0 0
176176 −203091. −0.494207
177177 − 385576.i − 0.925074i
178178 − 163624.i − 0.387076i
179179 424470. 0.990180 0.495090 0.868842i 0.335135π-0.335135\pi
0.495090 + 0.868842i 0.335135π0.335135\pi
180180 0 0
181181 −374185. −0.848965 −0.424482 0.905436i 0.639544π-0.639544\pi
−0.424482 + 0.905436i 0.639544π0.639544\pi
182182 66649.6i 0.149149i
183183 950136.i 2.09729i
184184 511526. 1.11384
185185 0 0
186186 200590. 0.425136
187187 546348.i 1.14252i
188188 139904.i 0.288692i
189189 −604933. −1.23184
190190 0 0
191191 −358814. −0.711683 −0.355841 0.934546i 0.615806π-0.615806\pi
−0.355841 + 0.934546i 0.615806π0.615806\pi
192192 − 104700.i − 0.204972i
193193 − 841799.i − 1.62673i −0.581755 0.813364i 0.697634π-0.697634\pi
0.581755 0.813364i 0.302366π-0.302366\pi
194194 311522. 0.594270
195195 0 0
196196 −397818. −0.739680
197197 − 694841.i − 1.27561i −0.770196 0.637807i 0.779842π-0.779842\pi
0.770196 0.637807i 0.220158π-0.220158\pi
198198 − 31922.8i − 0.0578679i
199199 552511. 0.989027 0.494513 0.869170i 0.335346π-0.335346\pi
0.494513 + 0.869170i 0.335346π0.335346\pi
200200 0 0
201201 567574. 0.990906
202202 100092.i 0.172592i
203203 146519.i 0.249548i
204204 −704382. −1.18504
205205 0 0
206206 279352. 0.458653
207207 − 158416.i − 0.256964i
208208 − 97084.1i − 0.155593i
209209 −46798.4 −0.0741080
210210 0 0
211211 −117103. −0.181076 −0.0905380 0.995893i 0.528859π-0.528859\pi
−0.0905380 + 0.995893i 0.528859π0.528859\pi
212212 − 1.00276e6i − 1.53235i
213213 − 325384.i − 0.491414i
214214 22155.0 0.0330702
215215 0 0
216216 −447237. −0.652233
217217 951512.i 1.37172i
218218 268917.i 0.383246i
219219 802203. 1.13025
220220 0 0
221221 −261173. −0.359705
222222 − 196507.i − 0.267606i
223223 885756.i 1.19276i 0.802703 + 0.596379i 0.203394π0.203394\pi
−0.802703 + 0.596379i 0.796606π0.796606\pi
224224 −971937. −1.29425
225225 0 0
226226 290268. 0.378031
227227 − 114582.i − 0.147588i −0.997273 0.0737941i 0.976489π-0.976489\pi
0.997273 0.0737941i 0.0235108π-0.0235108\pi
228228 − 60335.0i − 0.0768657i
229229 1.37389e6 1.73126 0.865630 0.500683i 0.166918π-0.166918\pi
0.865630 + 0.500683i 0.166918π0.166918\pi
230230 0 0
231231 1.05685e6 1.30312
232232 108324.i 0.132131i
233233 − 1.28998e6i − 1.55666i −0.627857 0.778329i 0.716068π-0.716068\pi
0.627857 0.778329i 0.283932π-0.283932\pi
234234 15260.1 0.0182188
235235 0 0
236236 619597. 0.724151
237237 344547.i 0.398454i
238238 609469.i 0.697444i
239239 626246. 0.709170 0.354585 0.935024i 0.384622π-0.384622\pi
0.354585 + 0.935024i 0.384622π0.384622\pi
240240 0 0
241241 876030. 0.971575 0.485788 0.874077i 0.338533π-0.338533\pi
0.485788 + 0.874077i 0.338533π0.338533\pi
242242 80132.6i 0.0879571i
243243 304829.i 0.331162i
244244 −1.52681e6 −1.64176
245245 0 0
246246 −648251. −0.682976
247247 − 22371.2i − 0.0233317i
248248 703469.i 0.726299i
249249 −274016. −0.280078
250250 0 0
251251 1.69324e6 1.69642 0.848209 0.529661i 0.177681π-0.177681\pi
0.848209 + 0.529661i 0.177681π0.177681\pi
252252 195229.i 0.193661i
253253 − 1.37805e6i − 1.35352i
254254 −350227. −0.340616
255255 0 0
256256 −221067. −0.210826
257257 775274.i 0.732188i 0.930578 + 0.366094i 0.119305π0.119305\pi
−0.930578 + 0.366094i 0.880695π0.880695\pi
258258 417442.i 0.390433i
259259 932143. 0.863442
260260 0 0
261261 33547.2 0.0304828
262262 392665.i 0.353402i
263263 − 1.64046e6i − 1.46244i −0.682143 0.731218i 0.738952π-0.738952\pi
0.682143 0.731218i 0.261048π-0.261048\pi
264264 781346. 0.689975
265265 0 0
266266 −52205.0 −0.0452385
267267 − 1.24028e6i − 1.06473i
268268 912056.i 0.775684i
269269 −1.00150e6 −0.843860 −0.421930 0.906629i 0.638647π-0.638647\pi
−0.421930 + 0.906629i 0.638647π0.638647\pi
270270 0 0
271271 −1.29197e6 −1.06864 −0.534318 0.845284i 0.679431π-0.679431\pi
−0.534318 + 0.845284i 0.679431π0.679431\pi
272272 − 887774.i − 0.727579i
273273 505208.i 0.410265i
274274 −190322. −0.153149
275275 0 0
276276 1.77666e6 1.40389
277277 − 2.50509e6i − 1.96166i −0.194873 0.980829i 0.562429π-0.562429\pi
0.194873 0.980829i 0.437571π-0.437571\pi
278278 − 492085.i − 0.381881i
279279 217859. 0.167558
280280 0 0
281281 965963. 0.729785 0.364892 0.931050i 0.381106π-0.381106\pi
0.364892 + 0.931050i 0.381106π0.381106\pi
282282 − 193438.i − 0.144850i
283283 1.70072e6i 1.26231i 0.775657 + 0.631155i 0.217419π0.217419\pi
−0.775657 + 0.631155i 0.782581π0.782581\pi
284284 522873. 0.384680
285285 0 0
286286 132748. 0.0959647
287287 − 3.07502e6i − 2.20365i
288288 222536.i 0.158095i
289289 −968403. −0.682042
290290 0 0
291291 2.36136e6 1.63467
292292 1.28909e6i 0.884762i
293293 − 507714.i − 0.345502i −0.984966 0.172751i 0.944734π-0.944734\pi
0.984966 0.172751i 0.0552656π-0.0552656\pi
294294 550042. 0.371131
295295 0 0
296296 689148. 0.457176
297297 1.20486e6i 0.792584i
298298 − 270402.i − 0.176388i
299299 658755. 0.426134
300300 0 0
301301 −1.98016e6 −1.25975
302302 − 321662.i − 0.202947i
303303 758706.i 0.474752i
304304 76043.7 0.0471932
305305 0 0
306306 139545. 0.0851940
307307 − 529122.i − 0.320413i −0.987084 0.160206i 0.948784π-0.948784\pi
0.987084 0.160206i 0.0512160π-0.0512160\pi
308308 1.69829e6i 1.02008i
309309 2.11751e6 1.26162
310310 0 0
311311 −524988. −0.307785 −0.153893 0.988088i 0.549181π-0.549181\pi
−0.153893 + 0.988088i 0.549181π0.549181\pi
312312 373509.i 0.217227i
313313 − 2.13481e6i − 1.23168i −0.787870 0.615842i 0.788816π-0.788816\pi
0.787870 0.615842i 0.211184π-0.211184\pi
314314 −1.21938e6 −0.697935
315315 0 0
316316 −553667. −0.311911
317317 − 1.52498e6i − 0.852348i −0.904641 0.426174i 0.859861π-0.859861\pi
0.904641 0.426174i 0.140139π-0.140139\pi
318318 1.38646e6i 0.768849i
319319 291826. 0.160564
320320 0 0
321321 167936. 0.0909667
322322 − 1.53726e6i − 0.826244i
323323 − 204570.i − 0.109103i
324324 −1.82064e6 −0.963522
325325 0 0
326326 −3342.95 −0.00174215
327327 2.03841e6i 1.05420i
328328 − 2.27341e6i − 1.16679i
329329 917585. 0.467365
330330 0 0
331331 −835573. −0.419194 −0.209597 0.977788i 0.567215π-0.567215\pi
−0.209597 + 0.977788i 0.567215π0.567215\pi
332332 − 440327.i − 0.219245i
333333 − 213424.i − 0.105471i
334334 971703. 0.476615
335335 0 0
336336 −1.71730e6 −0.829845
337337 − 1.15640e6i − 0.554670i −0.960773 0.277335i 0.910549π-0.910549\pi
0.960773 0.277335i 0.0894512π-0.0894512\pi
338338 63457.7i 0.0302129i
339339 2.20025e6 1.03986
340340 0 0
341341 1.89515e6 0.882587
342342 11952.9i 0.00552597i
343343 − 374094.i − 0.171690i
344344 −1.46397e6 −0.667014
345345 0 0
346346 −1.13734e6 −0.510740
347347 − 229963.i − 0.102526i −0.998685 0.0512630i 0.983675π-0.983675\pi
0.998685 0.0512630i 0.0163247π-0.0163247\pi
348348 376238.i 0.166538i
349349 −4.06529e6 −1.78660 −0.893301 0.449460i 0.851616π-0.851616\pi
−0.893301 + 0.449460i 0.851616π0.851616\pi
350350 0 0
351351 −575962. −0.249532
352352 1.93583e6i 0.832743i
353353 − 2.23732e6i − 0.955634i −0.878459 0.477817i 0.841428π-0.841428\pi
0.878459 0.477817i 0.158572π-0.158572\pi
354354 −856684. −0.363340
355355 0 0
356356 1.99305e6 0.833477
357357 4.61982e6i 1.91847i
358358 − 943100.i − 0.388911i
359359 −1.05065e6 −0.430250 −0.215125 0.976587i 0.569016π-0.569016\pi
−0.215125 + 0.976587i 0.569016π0.569016\pi
360360 0 0
361361 −2.45858e6 −0.992923
362362 831376.i 0.333446i
363363 607411.i 0.241945i
364364 −811839. −0.321156
365365 0 0
366366 2.11104e6 0.823747
367367 481650.i 0.186666i 0.995635 + 0.0933332i 0.0297522π0.0297522\pi
−0.995635 + 0.0933332i 0.970248π0.970248\pi
368368 2.23923e6i 0.861944i
369369 −704059. −0.269180
370370 0 0
371371 −6.57677e6 −2.48072
372372 2.44333e6i 0.915430i
373373 519900.i 0.193485i 0.995309 + 0.0967426i 0.0308424π0.0308424\pi
−0.995309 + 0.0967426i 0.969158π0.969158\pi
374374 1.21389e6 0.448747
375375 0 0
376376 678386. 0.247461
377377 139502.i 0.0505508i
378378 1.34406e6i 0.483825i
379379 5.03926e6 1.80206 0.901029 0.433759i 0.142813π-0.142813\pi
0.901029 + 0.433759i 0.142813π0.142813\pi
380380 0 0
381381 −2.65475e6 −0.936937
382382 797225.i 0.279526i
383383 − 2.06181e6i − 0.718212i −0.933297 0.359106i 0.883082π-0.883082\pi
0.933297 0.359106i 0.116918π-0.116918\pi
384384 −3.18365e6 −1.10179
385385 0 0
386386 −1.87034e6 −0.638927
387387 453379.i 0.153881i
388388 3.79455e6i 1.27962i
389389 3.43440e6 1.15074 0.575370 0.817893i 0.304858π-0.304858\pi
0.575370 + 0.817893i 0.304858π0.304858\pi
390390 0 0
391391 6.02390e6 1.99267
392392 1.92899e6i 0.634038i
393393 2.97643e6i 0.972108i
394394 −1.54382e6 −0.501021
395395 0 0
396396 388842. 0.124605
397397 1.81167e6i 0.576903i 0.957494 + 0.288452i 0.0931404π0.0931404\pi
−0.957494 + 0.288452i 0.906860π0.906860\pi
398398 − 1.22759e6i − 0.388458i
399399 −395718. −0.124438
400400 0 0
401401 546555. 0.169736 0.0848678 0.996392i 0.472953π-0.472953\pi
0.0848678 + 0.996392i 0.472953π0.472953\pi
402402 − 1.26105e6i − 0.389196i
403403 905944.i 0.277868i
404404 −1.21919e6 −0.371637
405405 0 0
406406 325541. 0.0980145
407407 − 1.85657e6i − 0.555553i
408408 3.41551e6i 1.01579i
409409 −4.17249e6 −1.23335 −0.616676 0.787217i 0.711521π-0.711521\pi
−0.616676 + 0.787217i 0.711521π0.711521\pi
410410 0 0
411411 −1.44266e6 −0.421268
412412 3.40271e6i 0.987601i
413413 − 4.06373e6i − 1.17233i
414414 −351973. −0.100927
415415 0 0
416416 −925391. −0.262175
417417 − 3.73004e6i − 1.05044i
418418 103978.i 0.0291072i
419419 2.08208e6 0.579379 0.289689 0.957121i 0.406448π-0.406448\pi
0.289689 + 0.957121i 0.406448π0.406448\pi
420420 0 0
421421 5.16730e6 1.42088 0.710442 0.703756i 0.248495π-0.248495\pi
0.710442 + 0.703756i 0.248495π0.248495\pi
422422 260183.i 0.0711209i
423423 − 210091.i − 0.0570895i
424424 −4.86232e6 −1.31350
425425 0 0
426426 −722949. −0.193012
427427 1.00139e7i 2.65786i
428428 269863.i 0.0712090i
429429 1.00624e6 0.263971
430430 0 0
431431 −5.84842e6 −1.51651 −0.758256 0.651957i 0.773948π-0.773948\pi
−0.758256 + 0.651957i 0.773948π0.773948\pi
432432 − 1.95780e6i − 0.504730i
433433 − 1.57061e6i − 0.402577i −0.979532 0.201289i 0.935487π-0.935487\pi
0.979532 0.201289i 0.0645129π-0.0645129\pi
434434 2.11410e6 0.538767
435435 0 0
436436 −3.27560e6 −0.825229
437437 515987.i 0.129251i
438438 − 1.78236e6i − 0.443925i
439439 4.17392e6 1.03367 0.516837 0.856084i 0.327109π-0.327109\pi
0.516837 + 0.856084i 0.327109π0.327109\pi
440440 0 0
441441 597395. 0.146273
442442 580281.i 0.141281i
443443 − 3.07291e6i − 0.743944i −0.928244 0.371972i 0.878682π-0.878682\pi
0.928244 0.371972i 0.121318π-0.121318\pi
444444 2.39359e6 0.576226
445445 0 0
446446 1.96800e6 0.468477
447447 − 2.04966e6i − 0.485192i
448448 − 1.10347e6i − 0.259757i
449449 −5.77522e6 −1.35192 −0.675962 0.736936i 0.736272π-0.736272\pi
−0.675962 + 0.736936i 0.736272π0.736272\pi
450450 0 0
451451 −6.12459e6 −1.41787
452452 3.53567e6i 0.814001i
453453 − 2.43822e6i − 0.558249i
454454 −254582. −0.0579679
455455 0 0
456456 −292561. −0.0658876
457457 190877.i 0.0427526i 0.999772 + 0.0213763i 0.00680481π0.00680481\pi
−0.999772 + 0.0213763i 0.993195π0.993195\pi
458458 − 3.05255e6i − 0.679984i
459459 −5.26682e6 −1.16685
460460 0 0
461461 −7.30776e6 −1.60152 −0.800760 0.598986i 0.795571π-0.795571\pi
−0.800760 + 0.598986i 0.795571π0.795571\pi
462462 − 2.34814e6i − 0.511822i
463463 4.81629e6i 1.04414i 0.852902 + 0.522072i 0.174841π0.174841\pi
−0.852902 + 0.522072i 0.825159π0.825159\pi
464464 −474194. −0.102250
465465 0 0
466466 −2.86612e6 −0.611405
467467 6.73997e6i 1.43010i 0.699075 + 0.715049i 0.253595π0.253595\pi
−0.699075 + 0.715049i 0.746405π0.746405\pi
468468 185879.i 0.0392298i
469469 5.98188e6 1.25576
470470 0 0
471471 −9.24299e6 −1.91982
472472 − 3.00438e6i − 0.620727i
473473 3.94394e6i 0.810545i
474474 765526. 0.156500
475475 0 0
476476 −7.42376e6 −1.50178
477477 1.50582e6i 0.303025i
478478 − 1.39141e6i − 0.278539i
479479 7.26335e6 1.44643 0.723217 0.690621i 0.242663π-0.242663\pi
0.723217 + 0.690621i 0.242663π0.242663\pi
480480 0 0
481481 887502. 0.174907
482482 − 1.94639e6i − 0.381604i
483483 − 1.16526e7i − 2.27276i
484484 −976072. −0.189395
485485 0 0
486486 677278. 0.130070
487487 453817.i 0.0867079i 0.999060 + 0.0433539i 0.0138043π0.0138043\pi
−0.999060 + 0.0433539i 0.986196π0.986196\pi
488488 7.40340e6i 1.40728i
489489 −25339.8 −0.00479215
490490 0 0
491491 7.33509e6 1.37310 0.686550 0.727083i 0.259124π-0.259124\pi
0.686550 + 0.727083i 0.259124π0.259124\pi
492492 − 7.89616e6i − 1.47063i
493493 1.27566e6i 0.236384i
494494 −49704.9 −0.00916394
495495 0 0
496496 −3.07947e6 −0.562046
497497 − 3.42935e6i − 0.622761i
498498 608818.i 0.110005i
499499 2.82351e6 0.507620 0.253810 0.967254i 0.418316π-0.418316\pi
0.253810 + 0.967254i 0.418316π0.418316\pi
500500 0 0
501501 7.36558e6 1.31103
502502 − 3.76208e6i − 0.666299i
503503 − 5.55958e6i − 0.979765i −0.871789 0.489882i 0.837040π-0.837040\pi
0.871789 0.489882i 0.162960π-0.162960\pi
504504 946652. 0.166002
505505 0 0
506506 −3.06180e6 −0.531620
507507 481014.i 0.0831070i
508508 − 4.26601e6i − 0.733437i
509509 6.75257e6 1.15525 0.577623 0.816304i 0.303980π-0.303980\pi
0.577623 + 0.816304i 0.303980π0.303980\pi
510510 0 0
511511 8.45473e6 1.43234
512512 − 5.55793e6i − 0.936997i
513513 − 451138.i − 0.0756861i
514514 1.72253e6 0.287580
515515 0 0
516516 −5.08474e6 −0.840706
517517 − 1.82758e6i − 0.300711i
518518 − 2.07106e6i − 0.339132i
519519 −8.62112e6 −1.40490
520520 0 0
521521 6.06655e6 0.979146 0.489573 0.871962i 0.337153π-0.337153\pi
0.489573 + 0.871962i 0.337153π0.337153\pi
522522 − 74536.1i − 0.0119727i
523523 − 2.28846e6i − 0.365838i −0.983128 0.182919i 0.941445π-0.941445\pi
0.983128 0.182919i 0.0585547π-0.0585547\pi
524524 −4.78294e6 −0.760968
525525 0 0
526526 −3.64483e6 −0.574398
527527 8.28429e6i 1.29936i
528528 3.42038e6i 0.533937i
529529 −8.75775e6 −1.36067
530530 0 0
531531 −930436. −0.143202
532532 − 635894.i − 0.0974105i
533533 − 2.92776e6i − 0.446392i
534534 −2.75569e6 −0.418194
535535 0 0
536536 4.42250e6 0.664900
537537 − 7.14877e6i − 1.06978i
538538 2.22516e6i 0.331441i
539539 5.19672e6 0.770473
540540 0 0
541541 1.01976e7 1.49797 0.748986 0.662586i 0.230541π-0.230541\pi
0.748986 + 0.662586i 0.230541π0.230541\pi
542542 2.87054e6i 0.419726i
543543 6.30188e6i 0.917214i
544544 −8.46212e6 −1.22598
545545 0 0
546546 1.12249e6 0.161139
547547 9.57008e6i 1.36756i 0.729687 + 0.683781i 0.239666π0.239666\pi
−0.729687 + 0.683781i 0.760334π0.760334\pi
548548 − 2.31826e6i − 0.329770i
549549 2.29278e6 0.324662
550550 0 0
551551 −109269. −0.0153327
552552 − 8.61493e6i − 1.20338i
553553 3.63132e6i 0.504954i
554554 −5.56588e6 −0.770476
555555 0 0
556556 5.99394e6 0.822291
557557 3.80767e6i 0.520021i 0.965606 + 0.260010i 0.0837260π0.0837260\pi
−0.965606 + 0.260010i 0.916274π0.916274\pi
558558 − 484046.i − 0.0658114i
559559 −1.88533e6 −0.255187
560560 0 0
561561 9.20140e6 1.23437
562562 − 2.14621e6i − 0.286636i
563563 2.91611e6i 0.387733i 0.981028 + 0.193866i 0.0621028π0.0621028\pi
−0.981028 + 0.193866i 0.937897π0.937897\pi
564564 2.35621e6 0.311901
565565 0 0
566566 3.77871e6 0.495795
567567 1.19410e7i 1.55985i
568568 − 2.53538e6i − 0.329740i
569569 1.01859e6 0.131892 0.0659459 0.997823i 0.478994π-0.478994\pi
0.0659459 + 0.997823i 0.478994π0.478994\pi
570570 0 0
571571 5.49132e6 0.704833 0.352417 0.935843i 0.385360π-0.385360\pi
0.352417 + 0.935843i 0.385360π0.385360\pi
572572 1.61696e6i 0.206637i
573573 6.04302e6i 0.768896i
574574 −6.83217e6 −0.865524
575575 0 0
576576 −252652. −0.0317298
577577 − 6.62872e6i − 0.828877i −0.910077 0.414439i 0.863978π-0.863978\pi
0.910077 0.414439i 0.136022π-0.136022\pi
578578 2.15163e6i 0.267884i
579579 −1.41773e7 −1.75750
580580 0 0
581581 −2.88797e6 −0.354937
582582 − 5.24653e6i − 0.642044i
583583 1.30991e7i 1.59614i
584584 6.25072e6 0.758399
585585 0 0
586586 −1.12806e6 −0.135702
587587 − 9.21203e6i − 1.10347i −0.834020 0.551734i 0.813966π-0.813966\pi
0.834020 0.551734i 0.186034π-0.186034\pi
588588 6.69990e6i 0.799144i
589589 −709605. −0.0842807
590590 0 0
591591 −1.17023e7 −1.37816
592592 3.01678e6i 0.353785i
593593 − 1.40550e6i − 0.164133i −0.996627 0.0820664i 0.973848π-0.973848\pi
0.996627 0.0820664i 0.0261520π-0.0261520\pi
594594 2.67699e6 0.311302
595595 0 0
596596 3.29368e6 0.379810
597597 − 9.30518e6i − 1.06854i
598598 − 1.46364e6i − 0.167372i
599599 9.54275e6 1.08669 0.543346 0.839509i 0.317157π-0.317157\pi
0.543346 + 0.839509i 0.317157π0.317157\pi
600600 0 0
601601 −1.61935e6 −0.182875 −0.0914377 0.995811i 0.529146π-0.529146\pi
−0.0914377 + 0.995811i 0.529146π0.529146\pi
602602 4.39958e6i 0.494789i
603603 − 1.36962e6i − 0.153393i
604604 3.91807e6 0.436999
605605 0 0
606606 1.68572e6 0.186467
607607 − 1.02926e7i − 1.13385i −0.823770 0.566924i 0.808133π-0.808133\pi
0.823770 0.566924i 0.191867π-0.191867\pi
608608 − 724837.i − 0.0795209i
609609 2.46762e6 0.269610
610610 0 0
611611 873642. 0.0946739
612612 1.69975e6i 0.183445i
613613 − 2.64065e6i − 0.283831i −0.989879 0.141916i 0.954674π-0.954674\pi
0.989879 0.141916i 0.0453262π-0.0453262\pi
614614 −1.17562e6 −0.125848
615615 0 0
616616 8.23490e6 0.874393
617617 1.18557e7i 1.25376i 0.779114 + 0.626882i 0.215669π0.215669\pi
−0.779114 + 0.626882i 0.784331π0.784331\pi
618618 − 4.70475e6i − 0.495524i
619619 1.38298e7 1.45074 0.725370 0.688359i 0.241669π-0.241669\pi
0.725370 + 0.688359i 0.241669π0.241669\pi
620620 0 0
621621 1.32845e7 1.38234
622622 1.16643e6i 0.120888i
623623 − 1.30718e7i − 1.34932i
624624 −1.63506e6 −0.168101
625625 0 0
626626 −4.74320e6 −0.483766
627627 788161.i 0.0800656i
628628 − 1.48529e7i − 1.50284i
629629 8.11565e6 0.817894
630630 0 0
631631 −621762. −0.0621657 −0.0310829 0.999517i 0.509896π-0.509896\pi
−0.0310829 + 0.999517i 0.509896π0.509896\pi
632632 2.68469e6i 0.267363i
633633 1.97220e6i 0.195633i
634634 −3.38825e6 −0.334775
635635 0 0
636636 −1.68881e7 −1.65553
637637 2.48420e6i 0.242571i
638638 − 648388.i − 0.0630642i
639639 −785188. −0.0760714
640640 0 0
641641 −4.56137e6 −0.438481 −0.219240 0.975671i 0.570358π-0.570358\pi
−0.219240 + 0.975671i 0.570358π0.570358\pi
642642 − 373126.i − 0.0357288i
643643 1.30425e7i 1.24404i 0.783003 + 0.622018i 0.213687π0.213687\pi
−0.783003 + 0.622018i 0.786313π0.786313\pi
644644 1.87249e7 1.77912
645645 0 0
646646 −454521. −0.0428521
647647 − 2.42397e6i − 0.227649i −0.993501 0.113825i 0.963690π-0.963690\pi
0.993501 0.113825i 0.0363102π-0.0363102\pi
648648 8.82817e6i 0.825911i
649649 −8.09384e6 −0.754298
650650 0 0
651651 1.60250e7 1.48199
652652 − 40719.5i − 0.00375131i
653653 1.21724e7i 1.11711i 0.829469 + 0.558553i 0.188643π0.188643\pi
−0.829469 + 0.558553i 0.811357π0.811357\pi
654654 4.52900e6 0.414055
655655 0 0
656656 9.95198e6 0.902921
657657 − 1.93580e6i − 0.174964i
658658 − 2.03872e6i − 0.183566i
659659 2.00313e6 0.179678 0.0898392 0.995956i 0.471365π-0.471365\pi
0.0898392 + 0.995956i 0.471365π0.471365\pi
660660 0 0
661661 −1.32025e7 −1.17531 −0.587657 0.809110i 0.699950π-0.699950\pi
−0.587657 + 0.809110i 0.699950π0.699950\pi
662662 1.85650e6i 0.164646i
663663 4.39857e6i 0.388622i
664664 −2.13512e6 −0.187933
665665 0 0
666666 −474193. −0.0414256
667667 − 3.21760e6i − 0.280038i
668668 1.18360e7i 1.02628i
669669 1.49176e7 1.28865
670670 0 0
671671 1.99448e7 1.71011
672672 1.63690e7i 1.39830i
673673 1.25393e7i 1.06718i 0.845744 + 0.533590i 0.179157π0.179157\pi
−0.845744 + 0.533590i 0.820843π0.820843\pi
674674 −2.56933e6 −0.217857
675675 0 0
676676 −772960. −0.0650564
677677 2.58077e6i 0.216410i 0.994129 + 0.108205i 0.0345103π0.0345103\pi
−0.994129 + 0.108205i 0.965490π0.965490\pi
678678 − 4.88858e6i − 0.408422i
679679 2.48872e7 2.07158
680680 0 0
681681 −1.92975e6 −0.159453
682682 − 4.21070e6i − 0.346652i
683683 2.33466e6i 0.191502i 0.995405 + 0.0957509i 0.0305252π0.0305252\pi
−0.995405 + 0.0957509i 0.969475π0.969475\pi
684684 −145595. −0.0118989
685685 0 0
686686 −831175. −0.0674345
687687 − 2.31385e7i − 1.87044i
688688 − 6.40859e6i − 0.516168i
689689 −6.26181e6 −0.502518
690690 0 0
691691 −9.56099e6 −0.761742 −0.380871 0.924628i 0.624376π-0.624376\pi
−0.380871 + 0.924628i 0.624376π0.624376\pi
692692 − 1.38536e7i − 1.09976i
693693 − 2.55029e6i − 0.201723i
694694 −510938. −0.0402689
695695 0 0
696696 1.82435e6 0.142753
697697 − 2.67725e7i − 2.08741i
698698 9.03238e6i 0.701720i
699699 −2.17254e7 −1.68180
700700 0 0
701701 1.75263e7 1.34708 0.673542 0.739149i 0.264772π-0.264772\pi
0.673542 + 0.739149i 0.264772π0.264772\pi
702702 1.27969e6i 0.0980082i
703703 695160.i 0.0530513i
704704 −2.19782e6 −0.167132
705705 0 0
706706 −4.97095e6 −0.375342
707707 7.99629e6i 0.601645i
708708 − 1.04350e7i − 0.782366i
709709 1.04230e7 0.778714 0.389357 0.921087i 0.372697π-0.372697\pi
0.389357 + 0.921087i 0.372697π0.372697\pi
710710 0 0
711711 831430. 0.0616811
712712 − 9.66418e6i − 0.714439i
713713 − 2.08955e7i − 1.53932i
714714 1.02645e7 0.753512
715715 0 0
716716 1.14876e7 0.837428
717717 − 1.05470e7i − 0.766181i
718718 2.33436e6i 0.168988i
719719 1.40272e7 1.01193 0.505964 0.862554i 0.331137π-0.331137\pi
0.505964 + 0.862554i 0.331137π0.331137\pi
720720 0 0
721721 2.23172e7 1.59883
722722 5.46254e6i 0.389988i
723723 − 1.47538e7i − 1.04968i
724724 −1.01267e7 −0.717998
725725 0 0
726726 1.34956e6 0.0950281
727727 1.43818e7i 1.00920i 0.863354 + 0.504599i 0.168360π0.168360\pi
−0.863354 + 0.504599i 0.831640π0.831640\pi
728728 3.93655e6i 0.275288i
729729 −1.12135e7 −0.781490
730730 0 0
731731 −1.72402e7 −1.19330
732732 2.57140e7i 1.77375i
733733 1.55999e7i 1.07241i 0.844087 + 0.536207i 0.180143π0.180143\pi
−0.844087 + 0.536207i 0.819857π0.819857\pi
734734 1.07014e6 0.0733166
735735 0 0
736736 2.13440e7 1.45238
737737 − 1.19143e7i − 0.807976i
738738 1.56430e6i 0.105725i
739739 −1.09689e7 −0.738840 −0.369420 0.929263i 0.620444π-0.620444\pi
−0.369420 + 0.929263i 0.620444π0.620444\pi
740740 0 0
741741 −376767. −0.0252074
742742 1.46125e7i 0.974348i
743743 − 2.14327e7i − 1.42431i −0.702021 0.712156i 0.747719π-0.747719\pi
0.702021 0.712156i 0.252281π-0.252281\pi
744744 1.18476e7 0.784687
745745 0 0
746746 1.15513e6 0.0759948
747747 661231.i 0.0433563i
748748 1.47861e7i 0.966271i
749749 1.76995e6 0.115280
750750 0 0
751751 −2.79453e7 −1.80804 −0.904022 0.427486i 0.859399π-0.859399\pi
−0.904022 + 0.427486i 0.859399π0.859399\pi
752752 2.96967e6i 0.191498i
753753 − 2.85169e7i − 1.83280i
754754 309951. 0.0198547
755755 0 0
756756 −1.63716e7 −1.04180
757757 9.90774e6i 0.628398i 0.949357 + 0.314199i 0.101736π0.101736\pi
−0.949357 + 0.314199i 0.898264π0.898264\pi
758758 − 1.11964e7i − 0.707790i
759759 −2.32087e7 −1.46233
760760 0 0
761761 −7.18134e6 −0.449515 −0.224757 0.974415i 0.572159π-0.572159\pi
−0.224757 + 0.974415i 0.572159π0.572159\pi
762762 5.89840e6i 0.367999i
763763 2.14836e7i 1.33597i
764764 −9.71076e6 −0.601894
765765 0 0
766766 −4.58100e6 −0.282091
767767 − 3.86912e6i − 0.237478i
768768 3.72313e6i 0.227775i
769769 −4.84119e6 −0.295213 −0.147607 0.989046i 0.547157π-0.547157\pi
−0.147607 + 0.989046i 0.547157π0.547157\pi
770770 0 0
771771 1.30569e7 0.791050
772772 − 2.27820e7i − 1.37578i
773773 − 1.57169e7i − 0.946059i −0.881046 0.473030i 0.843160π-0.843160\pi
0.881046 0.473030i 0.156840π-0.156840\pi
774774 1.00733e6 0.0604394
775775 0 0
776776 1.83995e7 1.09686
777777 − 1.56988e7i − 0.932855i
778778 − 7.63066e6i − 0.451974i
779779 2.29324e6 0.135396
780780 0 0
781781 −6.83033e6 −0.400695
782782 − 1.33841e7i − 0.782658i
783783 2.81321e6i 0.163983i
784784 −8.44427e6 −0.490650
785785 0 0
786786 6.61313e6 0.381813
787787 − 1.32624e6i − 0.0763281i −0.999271 0.0381640i 0.987849π-0.987849\pi
0.999271 0.0381640i 0.0121509π-0.0121509\pi
788788 − 1.88048e7i − 1.07883i
789789 −2.76281e7 −1.58000
790790 0 0
791791 2.31893e7 1.31779
792792 − 1.88547e6i − 0.106809i
793793 9.53429e6i 0.538400i
794794 4.02523e6 0.226589
795795 0 0
796796 1.49529e7 0.836453
797797 − 2.03514e7i − 1.13488i −0.823416 0.567438i 0.807935π-0.807935\pi
0.823416 0.567438i 0.192065π-0.192065\pi
798798 879218.i 0.0488753i
799799 7.98891e6 0.442711
800800 0 0
801801 −2.99293e6 −0.164822
802802 − 1.21435e6i − 0.0666667i
803803 − 1.68395e7i − 0.921595i
804804 1.53605e7 0.838042
805805 0 0
806806 2.01285e6 0.109138
807807 1.68669e7i 0.911699i
808808 5.91179e6i 0.318560i
809809 −2.72733e7 −1.46510 −0.732548 0.680716i 0.761669π-0.761669\pi
−0.732548 + 0.680716i 0.761669π0.761669\pi
810810 0 0
811811 −2.97325e7 −1.58738 −0.793688 0.608325i 0.791842π-0.791842\pi
−0.793688 + 0.608325i 0.791842π0.791842\pi
812812 3.96532e6i 0.211051i
813813 2.17589e7i 1.15454i
814814 −4.12499e6 −0.218203
815815 0 0
816816 −1.49516e7 −0.786070
817817 − 1.47674e6i − 0.0774012i
818818 9.27058e6i 0.484422i
819819 1.21912e6 0.0635093
820820 0 0
821821 4.79065e6 0.248048 0.124024 0.992279i 0.460420π-0.460420\pi
0.124024 + 0.992279i 0.460420π0.460420\pi
822822 3.20534e6i 0.165460i
823823 − 9.06060e6i − 0.466291i −0.972442 0.233146i 0.925098π-0.925098\pi
0.972442 0.233146i 0.0749019π-0.0749019\pi
824824 1.64995e7 0.846551
825825 0 0
826826 −9.02893e6 −0.460454
827827 3.26848e7i 1.66181i 0.556414 + 0.830906i 0.312177π0.312177\pi
−0.556414 + 0.830906i 0.687823π0.687823\pi
828828 − 4.28728e6i − 0.217323i
829829 −1.08535e6 −0.0548506 −0.0274253 0.999624i 0.508731π-0.508731\pi
−0.0274253 + 0.999624i 0.508731π0.508731\pi
830830 0 0
831831 −4.21897e7 −2.11936
832832 − 1.05063e6i − 0.0526188i
833833 2.27165e7i 1.13430i
834834 −8.28751e6 −0.412581
835835 0 0
836836 −1.26653e6 −0.0626756
837837 1.82693e7i 0.901381i
838838 − 4.62603e6i − 0.227561i
839839 −1.30918e7 −0.642089 −0.321045 0.947064i 0.604034π-0.604034\pi
−0.321045 + 0.947064i 0.604034π0.604034\pi
840840 0 0
841841 −1.98298e7 −0.966780
842842 − 1.14809e7i − 0.558078i
843843 − 1.62684e7i − 0.788453i
844844 −3.16921e6 −0.153142
845845 0 0
846846 −466787. −0.0224229
847847 6.40174e6i 0.306612i
848848 − 2.12851e7i − 1.01645i
849849 2.86429e7 1.36379
850850 0 0
851851 −2.04701e7 −0.968938
852852 − 8.80603e6i − 0.415605i
853853 2.08437e7i 0.980848i 0.871484 + 0.490424i 0.163158π0.163158\pi
−0.871484 + 0.490424i 0.836842π0.836842\pi
854854 2.22491e7 1.04392
855855 0 0
856856 1.30855e6 0.0610388
857857 − 2.39931e7i − 1.11592i −0.829866 0.557962i 0.811583π-0.811583\pi
0.829866 0.557962i 0.188417π-0.188417\pi
858858 − 2.23569e6i − 0.103679i
859859 −3.57929e7 −1.65506 −0.827531 0.561419i 0.810255π-0.810255\pi
−0.827531 + 0.561419i 0.810255π0.810255\pi
860860 0 0
861861 −5.17883e7 −2.38081
862862 1.29942e7i 0.595637i
863863 − 3.10281e6i − 0.141817i −0.997483 0.0709086i 0.977410π-0.977410\pi
0.997483 0.0709086i 0.0225899π-0.0225899\pi
864864 −1.86615e7 −0.850475
865865 0 0
866866 −3.48963e6 −0.158119
867867 1.63095e7i 0.736873i
868868 2.57512e7i 1.16011i
869869 7.23259e6 0.324896
870870 0 0
871871 5.69541e6 0.254378
872872 1.58832e7i 0.707369i
873873 − 5.69821e6i − 0.253048i
874874 1.14644e6 0.0507658
875875 0 0
876876 2.17104e7 0.955889
877877 − 3.29223e7i − 1.44541i −0.691155 0.722706i 0.742898π-0.742898\pi
0.691155 0.722706i 0.257102π-0.257102\pi
878878 − 9.27376e6i − 0.405994i
879879 −8.55074e6 −0.373277
880880 0 0
881881 7.18368e6 0.311822 0.155911 0.987771i 0.450169π-0.450169\pi
0.155911 + 0.987771i 0.450169π0.450169\pi
882882 − 1.32731e6i − 0.0574515i
883883 − 1.55599e7i − 0.671593i −0.941935 0.335797i 0.890995π-0.890995\pi
0.941935 0.335797i 0.109005π-0.109005\pi
884884 −7.06823e6 −0.304215
885885 0 0
886886 −6.82749e6 −0.292198
887887 1.70664e7i 0.728336i 0.931333 + 0.364168i 0.118647π0.118647\pi
−0.931333 + 0.364168i 0.881353π0.881353\pi
888888 − 1.16064e7i − 0.493929i
889889 −2.79794e7 −1.18736
890890 0 0
891891 2.37832e7 1.00363
892892 2.39716e7i 1.00875i
893893 684303.i 0.0287157i
894894 −4.55401e6 −0.190568
895895 0 0
896896 −3.35537e7 −1.39627
897897 − 1.10945e7i − 0.460391i
898898 1.28316e7i 0.530993i
899899 4.42496e6 0.182604
900900 0 0
901901 −5.72604e7 −2.34986
902902 1.36078e7i 0.556893i
903903 3.33491e7i 1.36102i
904904 1.71442e7 0.697745
905905 0 0
906906 −5.41732e6 −0.219262
907907 2.26122e7i 0.912691i 0.889803 + 0.456345i 0.150842π0.150842\pi
−0.889803 + 0.456345i 0.849158π0.849158\pi
908908 − 3.10099e6i − 0.124820i
909909 1.83084e6 0.0734920
910910 0 0
911911 2.42960e7 0.969927 0.484963 0.874534i 0.338833π-0.338833\pi
0.484963 + 0.874534i 0.338833π0.338833\pi
912912 − 1.28070e6i − 0.0509871i
913913 5.75203e6i 0.228373i
914914 424096. 0.0167919
915915 0 0
916916 3.71822e7 1.46419
917917 3.13698e7i 1.23193i
918918 1.17020e7i 0.458303i
919919 2.72862e7 1.06575 0.532873 0.846195i 0.321112π-0.321112\pi
0.532873 + 0.846195i 0.321112π0.321112\pi
920920 0 0
921921 −8.91128e6 −0.346171
922922 1.62366e7i 0.629026i
923923 − 3.26512e6i − 0.126152i
924924 2.86020e7 1.10209
925925 0 0
926926 1.07010e7 0.410106
927927 − 5.10978e6i − 0.195300i
928928 4.51995e6i 0.172291i
929929 2.89100e7 1.09903 0.549515 0.835484i 0.314813π-0.314813\pi
0.549515 + 0.835484i 0.314813π0.314813\pi
930930 0 0
931931 −1.94582e6 −0.0735746
932932 − 3.49113e7i − 1.31652i
933933 8.84165e6i 0.332529i
934934 1.49751e7 0.561696
935935 0 0
936936 901317. 0.0336270
937937 1.09147e7i 0.406127i 0.979166 + 0.203063i 0.0650897π0.0650897\pi
−0.979166 + 0.203063i 0.934910π0.934910\pi
938938 − 1.32907e7i − 0.493221i
939939 −3.59538e7 −1.33070
940940 0 0
941941 4.12025e7 1.51687 0.758437 0.651746i 0.225963π-0.225963\pi
0.758437 + 0.651746i 0.225963π0.225963\pi
942942 2.05364e7i 0.754043i
943943 6.75282e7i 2.47290i
944944 1.31519e7 0.480349
945945 0 0
946946 8.76276e6 0.318356
947947 1.50182e6i 0.0544180i 0.999630 + 0.0272090i 0.00866197π0.00866197\pi
−0.999630 + 0.0272090i 0.991338π0.991338\pi
948948 9.32465e6i 0.336986i
949949 8.04983e6 0.290149
950950 0 0
951951 −2.56832e7 −0.920869
952952 3.59973e7i 1.28729i
953953 − 2.96005e6i − 0.105576i −0.998606 0.0527882i 0.983189π-0.983189\pi
0.998606 0.0527882i 0.0168108π-0.0168108\pi
954954 3.34569e6 0.119018
955955 0 0
956956 1.69484e7 0.599768
957957 − 4.91483e6i − 0.173472i
958958 − 1.61379e7i − 0.568113i
959959 −1.52047e7 −0.533865
960960 0 0
961961 107057. 0.00373946
962962 − 1.97188e6i − 0.0686978i
963963 − 405249.i − 0.0140817i
964964 2.37084e7 0.821693
965965 0 0
966966 −2.58900e7 −0.892667
967967 4.68047e7i 1.60962i 0.593532 + 0.804810i 0.297733π0.297733\pi
−0.593532 + 0.804810i 0.702267π0.702267\pi
968968 4.73291e6i 0.162345i
969969 −3.44530e6 −0.117874
970970 0 0
971971 3.91779e7 1.33350 0.666750 0.745281i 0.267685π-0.267685\pi
0.666750 + 0.745281i 0.267685π0.267685\pi
972972 8.24972e6i 0.280074i
973973 − 3.93123e7i − 1.33121i
974974 1.00831e6 0.0340561
975975 0 0
976976 −3.24088e7 −1.08903
977977 3.27316e6i 0.109706i 0.998494 + 0.0548530i 0.0174690π0.0174690\pi
−0.998494 + 0.0548530i 0.982531π0.982531\pi
978978 56300.7i 0.00188220i
979979 −2.60354e7 −0.868175
980980 0 0
981981 4.91890e6 0.163191
982982 − 1.62973e7i − 0.539309i
983983 2.58761e7i 0.854111i 0.904225 + 0.427055i 0.140449π0.140449\pi
−0.904225 + 0.427055i 0.859551π0.859551\pi
984984 −3.82880e7 −1.26059
985985 0 0
986986 2.83431e6 0.0928441
987987 − 1.54536e7i − 0.504937i
988988 − 605441.i − 0.0197324i
989989 4.34849e7 1.41367
990990 0 0
991991 −4.94262e6 −0.159872 −0.0799362 0.996800i 0.525472π-0.525472\pi
−0.0799362 + 0.996800i 0.525472π0.525472\pi
992992 2.93531e7i 0.947053i
993993 1.40724e7i 0.452893i
994994 −7.61944e6 −0.244600
995995 0 0
996996 −7.41583e6 −0.236871
997997 − 2.01815e6i − 0.0643007i −0.999483 0.0321503i 0.989764π-0.989764\pi
0.999483 0.0321503i 0.0102355π-0.0102355\pi
998998 − 6.27337e6i − 0.199377i
999999 1.78974e7 0.567383
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 325.6.b.d.274.3 6
5.2 odd 4 325.6.a.d.1.2 3
5.3 odd 4 65.6.a.b.1.2 3
5.4 even 2 inner 325.6.b.d.274.4 6
15.8 even 4 585.6.a.c.1.2 3
20.3 even 4 1040.6.a.k.1.1 3
65.38 odd 4 845.6.a.c.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.6.a.b.1.2 3 5.3 odd 4
325.6.a.d.1.2 3 5.2 odd 4
325.6.b.d.274.3 6 1.1 even 1 trivial
325.6.b.d.274.4 6 5.4 even 2 inner
585.6.a.c.1.2 3 15.8 even 4
845.6.a.c.1.2 3 65.38 odd 4
1040.6.a.k.1.1 3 20.3 even 4