Properties

Label 325.6.b.i.274.5
Level 325325
Weight 66
Character 325.274
Analytic conductor 52.12552.125
Analytic rank 00
Dimension 2222
Inner twists 22

Related objects

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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: 2222
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 274.5
Character χ\chi == 325.274
Dual form 325.6.b.i.274.18

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) == q6.07859iq2+25.6203iq34.94922q4+155.735q6137.301iq7164.431iq8413.398q9+169.031q11126.800iq12+169.000iq13834.595q141157.88q16+487.128iq17+2512.87iq182385.49q19+3517.68q211027.47iq22+4144.47iq23+4212.75q24+1027.28q264365.63iq27+679.532iq28+4570.45q292957.68q31+1776.50iq32+4330.61iq33+2961.05q34+2046.00q365733.02iq37+14500.4iq384329.82q391705.07q4121382.5iq42+10922.2iq43836.570q44+25192.5q46+7912.12iq4729665.2iq482044.52q4912480.4q51836.418iq52+26431.1iq5326536.9q5422576.4q5661116.8iq5727781.9iq5811248.5q5940298.6q61+17978.5iq62+56759.8iq6326253.6q64+26324.0q66+64887.2iq672410.91iq68106182.q6947076.1q71+67975.2iq72+42771.8iq7334848.7q74+11806.3q7623208.1iq77+26319.2iq7890057.0q79+11392.9q81+10364.4iq8216427.0iq8317409.8q84+66391.5q86+117096.iq8727793.8iq88+35632.7q89+23203.8q9120511.9iq9275776.6iq93+48094.5q9445514.4q96+121030.iq97+12427.8iq9869876.9q99+O(q100)q-6.07859i q^{2} +25.6203i q^{3} -4.94922 q^{4} +155.735 q^{6} -137.301i q^{7} -164.431i q^{8} -413.398 q^{9} +169.031 q^{11} -126.800i q^{12} +169.000i q^{13} -834.595 q^{14} -1157.88 q^{16} +487.128i q^{17} +2512.87i q^{18} -2385.49 q^{19} +3517.68 q^{21} -1027.47i q^{22} +4144.47i q^{23} +4212.75 q^{24} +1027.28 q^{26} -4365.63i q^{27} +679.532i q^{28} +4570.45 q^{29} -2957.68 q^{31} +1776.50i q^{32} +4330.61i q^{33} +2961.05 q^{34} +2046.00 q^{36} -5733.02i q^{37} +14500.4i q^{38} -4329.82 q^{39} -1705.07 q^{41} -21382.5i q^{42} +10922.2i q^{43} -836.570 q^{44} +25192.5 q^{46} +7912.12i q^{47} -29665.2i q^{48} -2044.52 q^{49} -12480.4 q^{51} -836.418i q^{52} +26431.1i q^{53} -26536.9 q^{54} -22576.4 q^{56} -61116.8i q^{57} -27781.9i q^{58} -11248.5 q^{59} -40298.6 q^{61} +17978.5i q^{62} +56759.8i q^{63} -26253.6 q^{64} +26324.0 q^{66} +64887.2i q^{67} -2410.91i q^{68} -106182. q^{69} -47076.1 q^{71} +67975.2i q^{72} +42771.8i q^{73} -34848.7 q^{74} +11806.3 q^{76} -23208.1i q^{77} +26319.2i q^{78} -90057.0 q^{79} +11392.9 q^{81} +10364.4i q^{82} -16427.0i q^{83} -17409.8 q^{84} +66391.5 q^{86} +117096. i q^{87} -27793.8i q^{88} +35632.7 q^{89} +23203.8 q^{91} -20511.9i q^{92} -75776.6i q^{93} +48094.5 q^{94} -45514.4 q^{96} +121030. i q^{97} +12427.8i q^{98} -69876.9 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 22q374q4+702q62744q9+2552q111156q14+11414q167040q19+3412q2115446q24+1690q2636850q29+18136q31+28910q34+75368q36+853396q99+O(q100) 22 q - 374 q^{4} + 702 q^{6} - 2744 q^{9} + 2552 q^{11} - 1156 q^{14} + 11414 q^{16} - 7040 q^{19} + 3412 q^{21} - 15446 q^{24} + 1690 q^{26} - 36850 q^{29} + 18136 q^{31} + 28910 q^{34} + 75368 q^{36}+ \cdots - 853396 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 − 6.07859i − 1.07455i −0.843406 0.537276i 0.819453π-0.819453\pi
0.843406 0.537276i 0.180547π-0.180547\pi
33 25.6203i 1.64354i 0.569819 + 0.821770i 0.307013π0.307013\pi
−0.569819 + 0.821770i 0.692987π0.692987\pi
44 −4.94922 −0.154663
55 0 0
66 155.735 1.76607
77 − 137.301i − 1.05908i −0.848286 0.529539i 0.822365π-0.822365\pi
0.848286 0.529539i 0.177635π-0.177635\pi
88 − 164.431i − 0.908359i
99 −413.398 −1.70122
1010 0 0
1111 169.031 0.421196 0.210598 0.977573i 0.432459π-0.432459\pi
0.210598 + 0.977573i 0.432459π0.432459\pi
1212 − 126.800i − 0.254195i
1313 169.000i 0.277350i
1414 −834.595 −1.13804
1515 0 0
1616 −1157.88 −1.13074
1717 487.128i 0.408810i 0.978886 + 0.204405i 0.0655259π0.0655259\pi
−0.978886 + 0.204405i 0.934474π0.934474\pi
1818 2512.87i 1.82806i
1919 −2385.49 −1.51598 −0.757990 0.652267i 0.773818π-0.773818\pi
−0.757990 + 0.652267i 0.773818π0.773818\pi
2020 0 0
2121 3517.68 1.74064
2222 − 1027.47i − 0.452597i
2323 4144.47i 1.63361i 0.576911 + 0.816807i 0.304258π0.304258\pi
−0.576911 + 0.816807i 0.695742π0.695742\pi
2424 4212.75 1.49292
2525 0 0
2626 1027.28 0.298027
2727 − 4365.63i − 1.15249i
2828 679.532i 0.163800i
2929 4570.45 1.00917 0.504585 0.863362i 0.331646π-0.331646\pi
0.504585 + 0.863362i 0.331646π0.331646\pi
3030 0 0
3131 −2957.68 −0.552774 −0.276387 0.961046i 0.589137π-0.589137\pi
−0.276387 + 0.961046i 0.589137π0.589137\pi
3232 1776.50i 0.306683i
3333 4330.61i 0.692252i
3434 2961.05 0.439287
3535 0 0
3636 2046.00 0.263117
3737 − 5733.02i − 0.688461i −0.938885 0.344230i 0.888140π-0.888140\pi
0.938885 0.344230i 0.111860π-0.111860\pi
3838 14500.4i 1.62900i
3939 −4329.82 −0.455836
4040 0 0
4141 −1705.07 −0.158410 −0.0792051 0.996858i 0.525238π-0.525238\pi
−0.0792051 + 0.996858i 0.525238π0.525238\pi
4242 − 21382.5i − 1.87041i
4343 10922.2i 0.900821i 0.892822 + 0.450410i 0.148722π0.148722\pi
−0.892822 + 0.450410i 0.851278π0.851278\pi
4444 −836.570 −0.0651434
4545 0 0
4646 25192.5 1.75540
4747 7912.12i 0.522454i 0.965277 + 0.261227i 0.0841272π0.0841272\pi
−0.965277 + 0.261227i 0.915873π0.915873\pi
4848 − 29665.2i − 1.85842i
4949 −2044.52 −0.121647
5050 0 0
5151 −12480.4 −0.671895
5252 − 836.418i − 0.0428958i
5353 26431.1i 1.29249i 0.763131 + 0.646244i 0.223661π0.223661\pi
−0.763131 + 0.646244i 0.776339π0.776339\pi
5454 −26536.9 −1.23841
5555 0 0
5656 −22576.4 −0.962023
5757 − 61116.8i − 2.49157i
5858 − 27781.9i − 1.08441i
5959 −11248.5 −0.420692 −0.210346 0.977627i 0.567459π-0.567459\pi
−0.210346 + 0.977627i 0.567459π0.567459\pi
6060 0 0
6161 −40298.6 −1.38665 −0.693323 0.720627i 0.743854π-0.743854\pi
−0.693323 + 0.720627i 0.743854π0.743854\pi
6262 17978.5i 0.593984i
6363 56759.8i 1.80173i
6464 −26253.6 −0.801195
6565 0 0
6666 26324.0 0.743861
6767 64887.2i 1.76592i 0.469444 + 0.882962i 0.344454π0.344454\pi
−0.469444 + 0.882962i 0.655546π0.655546\pi
6868 − 2410.91i − 0.0632278i
6969 −106182. −2.68491
7070 0 0
7171 −47076.1 −1.10829 −0.554147 0.832419i 0.686955π-0.686955\pi
−0.554147 + 0.832419i 0.686955π0.686955\pi
7272 67975.2i 1.54532i
7373 42771.8i 0.939400i 0.882826 + 0.469700i 0.155638π0.155638\pi
−0.882826 + 0.469700i 0.844362π0.844362\pi
7474 −34848.7 −0.739787
7575 0 0
7676 11806.3 0.234466
7777 − 23208.1i − 0.446079i
7878 26319.2i 0.489820i
7979 −90057.0 −1.62349 −0.811745 0.584012i 0.801482π-0.801482\pi
−0.811745 + 0.584012i 0.801482π0.801482\pi
8080 0 0
8181 11392.9 0.192941
8282 10364.4i 0.170220i
8383 − 16427.0i − 0.261735i −0.991400 0.130868i 0.958224π-0.958224\pi
0.991400 0.130868i 0.0417763π-0.0417763\pi
8484 −17409.8 −0.269212
8585 0 0
8686 66391.5 0.967979
8787 117096.i 1.65861i
8888 − 27793.8i − 0.382597i
8989 35632.7 0.476841 0.238421 0.971162i 0.423370π-0.423370\pi
0.238421 + 0.971162i 0.423370π0.423370\pi
9090 0 0
9191 23203.8 0.293735
9292 − 20511.9i − 0.252660i
9393 − 75776.6i − 0.908506i
9494 48094.5 0.561405
9595 0 0
9696 −45514.4 −0.504046
9797 121030.i 1.30606i 0.757333 + 0.653029i 0.226502π0.226502\pi
−0.757333 + 0.653029i 0.773498π0.773498\pi
9898 12427.8i 0.130716i
9999 −69876.9 −0.716549
100100 0 0
101101 −33043.6 −0.322318 −0.161159 0.986928i 0.551523π-0.551523\pi
−0.161159 + 0.986928i 0.551523π0.551523\pi
102102 75862.9i 0.721987i
103103 − 198815.i − 1.84653i −0.384164 0.923265i 0.625510π-0.625510\pi
0.384164 0.923265i 0.374490π-0.374490\pi
104104 27788.8 0.251933
105105 0 0
106106 160664. 1.38885
107107 − 183355.i − 1.54822i −0.633049 0.774112i 0.718197π-0.718197\pi
0.633049 0.774112i 0.281803π-0.281803\pi
108108 21606.5i 0.178248i
109109 178328. 1.43765 0.718827 0.695189i 0.244679π-0.244679\pi
0.718827 + 0.695189i 0.244679π0.244679\pi
110110 0 0
111111 146881. 1.13151
112112 158978.i 1.19754i
113113 − 22426.7i − 0.165223i −0.996582 0.0826114i 0.973674π-0.973674\pi
0.996582 0.0826114i 0.0263260π-0.0263260\pi
114114 −371504. −2.67733
115115 0 0
116116 −22620.2 −0.156081
117117 − 69864.2i − 0.471835i
118118 68374.9i 0.452056i
119119 66883.1 0.432961
120120 0 0
121121 −132480. −0.822594
122122 244959.i 1.49002i
123123 − 43684.4i − 0.260354i
124124 14638.2 0.0854937
125125 0 0
126126 345020. 1.93605
127127 − 90854.6i − 0.499847i −0.968266 0.249924i 0.919594π-0.919594\pi
0.968266 0.249924i 0.0804055π-0.0804055\pi
128128 216433.i 1.16761i
129129 −279829. −1.48054
130130 0 0
131131 −78399.9 −0.399151 −0.199575 0.979882i 0.563956π-0.563956\pi
−0.199575 + 0.979882i 0.563956π0.563956\pi
132132 − 21433.1i − 0.107066i
133133 327530.i 1.60554i
134134 394423. 1.89758
135135 0 0
136136 80098.8 0.371346
137137 111261.i 0.506456i 0.967407 + 0.253228i 0.0814923π0.0814923\pi
−0.967407 + 0.253228i 0.918508π0.918508\pi
138138 645439.i 2.88508i
139139 226363. 0.993728 0.496864 0.867828i 0.334485π-0.334485\pi
0.496864 + 0.867828i 0.334485π0.334485\pi
140140 0 0
141141 −202711. −0.858675
142142 286156.i 1.19092i
143143 28566.2i 0.116819i
144144 478665. 1.92365
145145 0 0
146146 259992. 1.00943
147147 − 52381.1i − 0.199931i
148148 28374.0i 0.106479i
149149 −443036. −1.63483 −0.817416 0.576047i 0.804594π-0.804594\pi
−0.817416 + 0.576047i 0.804594π0.804594\pi
150150 0 0
151151 −1334.00 −0.00476118 −0.00238059 0.999997i 0.500758π-0.500758\pi
−0.00238059 + 0.999997i 0.500758π0.500758\pi
152152 392247.i 1.37705i
153153 − 201378.i − 0.695477i
154154 −141072. −0.479336
155155 0 0
156156 21429.2 0.0705010
157157 − 66009.4i − 0.213726i −0.994274 0.106863i 0.965919π-0.965919\pi
0.994274 0.106863i 0.0340806π-0.0340806\pi
158158 547419.i 1.74453i
159159 −677173. −2.12425
160160 0 0
161161 569039. 1.73012
162162 − 69253.0i − 0.207325i
163163 57419.5i 0.169274i 0.996412 + 0.0846371i 0.0269731π0.0269731\pi
−0.996412 + 0.0846371i 0.973027π0.973027\pi
164164 8438.78 0.0245002
165165 0 0
166166 −99852.7 −0.281248
167167 − 298875.i − 0.829275i −0.909987 0.414637i 0.863908π-0.863908\pi
0.909987 0.414637i 0.136092π-0.136092\pi
168168 − 578414.i − 1.58112i
169169 −28561.0 −0.0769231
170170 0 0
171171 986155. 2.57902
172172 − 54056.3i − 0.139324i
173173 16389.5i 0.0416342i 0.999783 + 0.0208171i 0.00662677π0.00662677\pi
−0.999783 + 0.0208171i 0.993373π0.993373\pi
174174 711779. 1.78226
175175 0 0
176176 −195717. −0.476264
177177 − 288189.i − 0.691424i
178178 − 216596.i − 0.512391i
179179 −420541. −0.981015 −0.490507 0.871437i 0.663189π-0.663189\pi
−0.490507 + 0.871437i 0.663189π0.663189\pi
180180 0 0
181181 −598369. −1.35760 −0.678801 0.734322i 0.737500π-0.737500\pi
−0.678801 + 0.734322i 0.737500π0.737500\pi
182182 − 141047.i − 0.315634i
183183 − 1.03246e6i − 2.27901i
184184 681477. 1.48391
185185 0 0
186186 −460615. −0.976237
187187 82339.7i 0.172189i
188188 − 39158.8i − 0.0808044i
189189 −599405. −1.22058
190190 0 0
191191 207706. 0.411971 0.205985 0.978555i 0.433960π-0.433960\pi
0.205985 + 0.978555i 0.433960π0.433960\pi
192192 − 672623.i − 1.31680i
193193 545285.i 1.05373i 0.849948 + 0.526867i 0.176633π0.176633\pi
−0.849948 + 0.526867i 0.823367π0.823367\pi
194194 735690. 1.40343
195195 0 0
196196 10118.8 0.0188143
197197 559003.i 1.02624i 0.858317 + 0.513119i 0.171510π0.171510\pi
−0.858317 + 0.513119i 0.828490π0.828490\pi
198198 424753.i 0.769969i
199199 800588. 1.43310 0.716549 0.697536i 0.245720π-0.245720\pi
0.716549 + 0.697536i 0.245720π0.245720\pi
200200 0 0
201201 −1.66243e6 −2.90237
202202 200858.i 0.346347i
203203 − 627527.i − 1.06879i
204204 61768.0 0.103917
205205 0 0
206206 −1.20851e6 −1.98419
207207 − 1.71331e6i − 2.77914i
208208 − 195682.i − 0.313612i
209209 −403221. −0.638524
210210 0 0
211211 −971904. −1.50285 −0.751427 0.659816i 0.770634π-0.770634\pi
−0.751427 + 0.659816i 0.770634π0.770634\pi
212212 − 130814.i − 0.199900i
213213 − 1.20610e6i − 1.82153i
214214 −1.11454e6 −1.66365
215215 0 0
216216 −717843. −1.04688
217217 406092.i 0.585431i
218218 − 1.08398e6i − 1.54483i
219219 −1.09582e6 −1.54394
220220 0 0
221221 −82324.7 −0.113383
222222 − 892831.i − 1.21587i
223223 − 401286.i − 0.540371i −0.962808 0.270186i 0.912915π-0.912915\pi
0.962808 0.270186i 0.0870851π-0.0870851\pi
224224 243915. 0.324802
225225 0 0
226226 −136323. −0.177541
227227 1.30062e6i 1.67527i 0.546227 + 0.837637i 0.316064π0.316064\pi
−0.546227 + 0.837637i 0.683936π0.683936\pi
228228 302481.i 0.385354i
229229 864830. 1.08979 0.544894 0.838505i 0.316570π-0.316570\pi
0.544894 + 0.838505i 0.316570π0.316570\pi
230230 0 0
231231 594596. 0.733149
232232 − 751521.i − 0.916688i
233233 1.19230e6i 1.43878i 0.694606 + 0.719390i 0.255579π0.255579\pi
−0.694606 + 0.719390i 0.744421π0.744421\pi
234234 −424676. −0.507011
235235 0 0
236236 55671.3 0.0650655
237237 − 2.30728e6i − 2.66827i
238238 − 406555.i − 0.465240i
239239 1.23057e6 1.39352 0.696759 0.717305i 0.254625π-0.254625\pi
0.696759 + 0.717305i 0.254625π0.254625\pi
240240 0 0
241241 1.64306e6 1.82226 0.911129 0.412122i 0.135212π-0.135212\pi
0.911129 + 0.412122i 0.135212π0.135212\pi
242242 805289.i 0.883921i
243243 − 768958.i − 0.835385i
244244 199447. 0.214463
245245 0 0
246246 −265539. −0.279764
247247 − 403148.i − 0.420457i
248248 486333.i 0.502117i
249249 420863. 0.430172
250250 0 0
251251 −447259. −0.448100 −0.224050 0.974578i 0.571928π-0.571928\pi
−0.224050 + 0.974578i 0.571928π0.571928\pi
252252 − 280917.i − 0.278661i
253253 700543.i 0.688071i
254254 −552267. −0.537112
255255 0 0
256256 475490. 0.453463
257257 − 465085.i − 0.439237i −0.975586 0.219619i 0.929519π-0.929519\pi
0.975586 0.219619i 0.0704813π-0.0704813\pi
258258 1.70097e6i 1.59091i
259259 −787148. −0.729134
260260 0 0
261261 −1.88941e6 −1.71682
262262 476560.i 0.428909i
263263 − 1.88192e6i − 1.67769i −0.544369 0.838846i 0.683231π-0.683231\pi
0.544369 0.838846i 0.316769π-0.316769\pi
264264 712085. 0.628813
265265 0 0
266266 1.99092e6 1.72524
267267 912919.i 0.783707i
268268 − 321141.i − 0.273123i
269269 −39508.5 −0.0332897 −0.0166448 0.999861i 0.505298π-0.505298\pi
−0.0166448 + 0.999861i 0.505298π0.505298\pi
270270 0 0
271271 2.01156e6 1.66383 0.831916 0.554902i 0.187244π-0.187244\pi
0.831916 + 0.554902i 0.187244π0.187244\pi
272272 − 564036.i − 0.462258i
273273 594488.i 0.482766i
274274 676310. 0.544214
275275 0 0
276276 525520. 0.415256
277277 750989.i 0.588077i 0.955794 + 0.294039i 0.0949994π0.0949994\pi
−0.955794 + 0.294039i 0.905001π0.905001\pi
278278 − 1.37596e6i − 1.06781i
279279 1.22270e6 0.940392
280280 0 0
281281 −116949. −0.0883550 −0.0441775 0.999024i 0.514067π-0.514067\pi
−0.0441775 + 0.999024i 0.514067π0.514067\pi
282282 1.23219e6i 0.922691i
283283 1.08953e6i 0.808671i 0.914611 + 0.404335i 0.132497π0.132497\pi
−0.914611 + 0.404335i 0.867503π0.867503\pi
284284 232990. 0.171412
285285 0 0
286286 173642. 0.125528
287287 234108.i 0.167769i
288288 − 734400.i − 0.521737i
289289 1.18256e6 0.832875
290290 0 0
291291 −3.10081e6 −2.14656
292292 − 211687.i − 0.145290i
293293 − 2.35419e6i − 1.60204i −0.598638 0.801020i 0.704291π-0.704291\pi
0.598638 0.801020i 0.295709π-0.295709\pi
294294 −318403. −0.214837
295295 0 0
296296 −942683. −0.625369
297297 − 737926.i − 0.485424i
298298 2.69303e6i 1.75671i
299299 −700415. −0.453083
300300 0 0
301301 1.49963e6 0.954040
302302 8108.85i 0.00511613i
303303 − 846585.i − 0.529742i
304304 2.76211e6 1.71418
305305 0 0
306306 −1.22409e6 −0.747327
307307 1.40614e6i 0.851495i 0.904842 + 0.425748i 0.139989π0.139989\pi
−0.904842 + 0.425748i 0.860011π0.860011\pi
308308 114862.i 0.0689920i
309309 5.09369e6 3.03485
310310 0 0
311311 1.46661e6 0.859832 0.429916 0.902869i 0.358543π-0.358543\pi
0.429916 + 0.902869i 0.358543π0.358543\pi
312312 711955.i 0.414063i
313313 310576.i 0.179187i 0.995978 + 0.0895935i 0.0285568π0.0285568\pi
−0.995978 + 0.0895935i 0.971443π0.971443\pi
314314 −401244. −0.229659
315315 0 0
316316 445712. 0.251094
317317 − 2.21756e6i − 1.23944i −0.784822 0.619721i 0.787246π-0.787246\pi
0.784822 0.619721i 0.212754π-0.212754\pi
318318 4.11625e6i 2.28262i
319319 772546. 0.425058
320320 0 0
321321 4.69761e6 2.54457
322322 − 3.45895e6i − 1.85911i
323323 − 1.16204e6i − 0.619747i
324324 −56386.2 −0.0298408
325325 0 0
326326 349030. 0.181894
327327 4.56882e6i 2.36284i
328328 280366.i 0.143893i
329329 1.08634e6 0.553320
330330 0 0
331331 439684. 0.220582 0.110291 0.993899i 0.464822π-0.464822\pi
0.110291 + 0.993899i 0.464822π0.464822\pi
332332 81300.7i 0.0404808i
333333 2.37002e6i 1.17123i
334334 −1.81674e6 −0.891099
335335 0 0
336336 −4.07306e6 −1.96821
337337 − 65125.6i − 0.0312376i −0.999878 0.0156188i 0.995028π-0.995028\pi
0.999878 0.0156188i 0.00497181π-0.00497181\pi
338338 173611.i 0.0826579i
339339 574579. 0.271550
340340 0 0
341341 −499939. −0.232826
342342 − 5.99443e6i − 2.77129i
343343 − 2.02690e6i − 0.930245i
344344 1.79594e6 0.818269
345345 0 0
346346 99625.0 0.0447382
347347 3.63163e6i 1.61912i 0.587039 + 0.809558i 0.300293π0.300293\pi
−0.587039 + 0.809558i 0.699707π0.699707\pi
348348 − 579534.i − 0.256526i
349349 −755061. −0.331832 −0.165916 0.986140i 0.553058π-0.553058\pi
−0.165916 + 0.986140i 0.553058π0.553058\pi
350350 0 0
351351 737791. 0.319643
352352 300283.i 0.129174i
353353 − 3.06050e6i − 1.30724i −0.756823 0.653620i 0.773249π-0.773249\pi
0.756823 0.653620i 0.226751π-0.226751\pi
354354 −1.75178e6 −0.742972
355355 0 0
356356 −176354. −0.0737497
357357 1.71356e6i 0.711590i
358358 2.55629e6i 1.05415i
359359 −3.68034e6 −1.50713 −0.753567 0.657371i 0.771668π-0.771668\pi
−0.753567 + 0.657371i 0.771668π0.771668\pi
360360 0 0
361361 3.21446e6 1.29819
362362 3.63724e6i 1.45882i
363363 − 3.39416e6i − 1.35197i
364364 −114841. −0.0454300
365365 0 0
366366 −6.27591e6 −2.44891
367367 2.22414e6i 0.861978i 0.902357 + 0.430989i 0.141835π0.141835\pi
−0.902357 + 0.430989i 0.858165π0.858165\pi
368368 − 4.79880e6i − 1.84720i
369369 704873. 0.269491
370370 0 0
371371 3.62902e6 1.36885
372372 375035.i 0.140512i
373373 3.73922e6i 1.39158i 0.718244 + 0.695791i 0.244946π0.244946\pi
−0.718244 + 0.695791i 0.755054π0.755054\pi
374374 500509. 0.185026
375375 0 0
376376 1.30099e6 0.474576
377377 772406.i 0.279893i
378378 3.64353e6i 1.31158i
379379 −656559. −0.234788 −0.117394 0.993085i 0.537454π-0.537454\pi
−0.117394 + 0.993085i 0.537454π0.537454\pi
380380 0 0
381381 2.32772e6 0.821519
382382 − 1.26256e6i − 0.442684i
383383 3.33584e6i 1.16200i 0.813902 + 0.581002i 0.197339π0.197339\pi
−0.813902 + 0.581002i 0.802661π0.802661\pi
384384 −5.54506e6 −1.91901
385385 0 0
386386 3.31456e6 1.13229
387387 − 4.51521e6i − 1.53250i
388388 − 599003.i − 0.201999i
389389 −4.44083e6 −1.48796 −0.743978 0.668204i 0.767063π-0.767063\pi
−0.743978 + 0.668204i 0.767063π0.767063\pi
390390 0 0
391391 −2.01889e6 −0.667837
392392 336181.i 0.110499i
393393 − 2.00863e6i − 0.656021i
394394 3.39795e6 1.10275
395395 0 0
396396 345836. 0.110824
397397 − 2.72643e6i − 0.868196i −0.900866 0.434098i 0.857067π-0.857067\pi
0.900866 0.434098i 0.142933π-0.142933\pi
398398 − 4.86644e6i − 1.53994i
399399 −8.39139e6 −2.63877
400400 0 0
401401 5.27026e6 1.63671 0.818353 0.574715i 0.194887π-0.194887\pi
0.818353 + 0.574715i 0.194887π0.194887\pi
402402 1.01052e7i 3.11875i
403403 − 499848.i − 0.153312i
404404 163540. 0.0498506
405405 0 0
406406 −3.81447e6 −1.14847
407407 − 969056.i − 0.289977i
408408 2.05215e6i 0.610322i
409409 −4.58065e6 −1.35400 −0.677000 0.735983i 0.736720π-0.736720\pi
−0.677000 + 0.735983i 0.736720π0.736720\pi
410410 0 0
411411 −2.85054e6 −0.832381
412412 983979.i 0.285590i
413413 1.54443e6i 0.445546i
414414 −1.04145e7 −2.98634
415415 0 0
416416 −300228. −0.0850586
417417 5.79947e6i 1.63323i
418418 2.45101e6i 0.686128i
419419 −3.94543e6 −1.09789 −0.548945 0.835858i 0.684970π-0.684970\pi
−0.548945 + 0.835858i 0.684970π0.684970\pi
420420 0 0
421421 4.17743e6 1.14869 0.574347 0.818612i 0.305256π-0.305256\pi
0.574347 + 0.818612i 0.305256π0.305256\pi
422422 5.90780e6i 1.61490i
423423 − 3.27085e6i − 0.888812i
424424 4.34609e6 1.17404
425425 0 0
426426 −7.33140e6 −1.95732
427427 5.53304e6i 1.46857i
428428 907465.i 0.239453i
429429 −731873. −0.191996
430430 0 0
431431 −7.66563e6 −1.98772 −0.993859 0.110652i 0.964706π-0.964706\pi
−0.993859 + 0.110652i 0.964706π0.964706\pi
432432 5.05488e6i 1.30317i
433433 − 5.49209e6i − 1.40773i −0.710336 0.703863i 0.751457π-0.751457\pi
0.710336 0.703863i 0.248543π-0.248543\pi
434434 2.46847e6 0.629076
435435 0 0
436436 −882586. −0.222352
437437 − 9.88658e6i − 2.47652i
438438 6.66107e6i 1.65905i
439439 2.56331e6 0.634805 0.317403 0.948291i 0.397189π-0.397189\pi
0.317403 + 0.948291i 0.397189π0.397189\pi
440440 0 0
441441 845199. 0.206949
442442 500418.i 0.121836i
443443 1.41896e6i 0.343526i 0.985138 + 0.171763i 0.0549463π0.0549463\pi
−0.985138 + 0.171763i 0.945054π0.945054\pi
444444 −726948. −0.175003
445445 0 0
446446 −2.43925e6 −0.580657
447447 − 1.13507e7i − 2.68691i
448448 3.60464e6i 0.848528i
449449 −3.56619e6 −0.834813 −0.417406 0.908720i 0.637061π-0.637061\pi
−0.417406 + 0.908720i 0.637061π0.637061\pi
450450 0 0
451451 −288210. −0.0667217
452452 110995.i 0.0255539i
453453 − 34177.5i − 0.00782519i
454454 7.90593e6 1.80017
455455 0 0
456456 −1.00495e7 −2.26324
457457 − 3.71538e6i − 0.832172i −0.909325 0.416086i 0.863402π-0.863402\pi
0.909325 0.416086i 0.136598π-0.136598\pi
458458 − 5.25694e6i − 1.17103i
459459 2.12662e6 0.471149
460460 0 0
461461 3.74184e6 0.820035 0.410018 0.912078i 0.365523π-0.365523\pi
0.410018 + 0.912078i 0.365523π0.365523\pi
462462 − 3.61431e6i − 0.787807i
463463 3.53774e6i 0.766962i 0.923549 + 0.383481i 0.125275π0.125275\pi
−0.923549 + 0.383481i 0.874725π0.874725\pi
464464 −5.29203e6 −1.14111
465465 0 0
466466 7.24748e6 1.54605
467467 − 1.97789e6i − 0.419671i −0.977737 0.209836i 0.932707π-0.932707\pi
0.977737 0.209836i 0.0672929π-0.0672929\pi
468468 345773.i 0.0729754i
469469 8.90907e6 1.87025
470470 0 0
471471 1.69118e6 0.351267
472472 1.84960e6i 0.382139i
473473 1.84619e6i 0.379422i
474474 −1.40250e7 −2.86720
475475 0 0
476476 −331019. −0.0669632
477477 − 1.09266e7i − 2.19881i
478478 − 7.48014e6i − 1.49741i
479479 2.88196e6 0.573918 0.286959 0.957943i 0.407356π-0.407356\pi
0.286959 + 0.957943i 0.407356π0.407356\pi
480480 0 0
481481 968880. 0.190945
482482 − 9.98746e6i − 1.95811i
483483 1.45789e7i 2.84353i
484484 655671. 0.127225
485485 0 0
486486 −4.67418e6 −0.897665
487487 − 2.88578e6i − 0.551366i −0.961249 0.275683i 0.911096π-0.911096\pi
0.961249 0.275683i 0.0889040π-0.0889040\pi
488488 6.62632e6i 1.25957i
489489 −1.47110e6 −0.278209
490490 0 0
491491 5.27189e6 0.986876 0.493438 0.869781i 0.335740π-0.335740\pi
0.493438 + 0.869781i 0.335740π0.335740\pi
492492 216204.i 0.0402671i
493493 2.22640e6i 0.412558i
494494 −2.45057e6 −0.451803
495495 0 0
496496 3.42464e6 0.625045
497497 6.46359e6i 1.17377i
498498 − 2.55825e6i − 0.462243i
499499 308093. 0.0553898 0.0276949 0.999616i 0.491183π-0.491183\pi
0.0276949 + 0.999616i 0.491183π0.491183\pi
500500 0 0
501501 7.65725e6 1.36295
502502 2.71870e6i 0.481507i
503503 − 4.27447e6i − 0.753291i −0.926358 0.376645i 0.877078π-0.877078\pi
0.926358 0.376645i 0.122922π-0.122922\pi
504504 9.33305e6 1.63662
505505 0 0
506506 4.25831e6 0.739368
507507 − 731740.i − 0.126426i
508508 449659.i 0.0773080i
509509 405253. 0.0693317 0.0346658 0.999399i 0.488963π-0.488963\pi
0.0346658 + 0.999399i 0.488963π0.488963\pi
510510 0 0
511511 5.87260e6 0.994898
512512 4.03553e6i 0.680340i
513513 1.04142e7i 1.74715i
514514 −2.82706e6 −0.471984
515515 0 0
516516 1.38494e6 0.228984
517517 1.33739e6i 0.220056i
518518 4.78475e6i 0.783492i
519519 −419903. −0.0684275
520520 0 0
521521 −7.00100e6 −1.12997 −0.564983 0.825102i 0.691117π-0.691117\pi
−0.564983 + 0.825102i 0.691117π0.691117\pi
522522 1.14850e7i 1.84482i
523523 7.78764e6i 1.24495i 0.782640 + 0.622475i 0.213873π0.213873\pi
−0.782640 + 0.622475i 0.786127π0.786127\pi
524524 388018. 0.0617339
525525 0 0
526526 −1.14394e7 −1.80277
527527 − 1.44077e6i − 0.225979i
528528 − 5.01433e6i − 0.782759i
529529 −1.07403e7 −1.66869
530530 0 0
531531 4.65010e6 0.715692
532532 − 1.62102e6i − 0.248318i
533533 − 288157.i − 0.0439351i
534534 5.54926e6 0.842135
535535 0 0
536536 1.06694e7 1.60409
537537 − 1.07744e7i − 1.61234i
538538 240156.i 0.0357715i
539539 −345586. −0.0512371
540540 0 0
541541 3.36678e6 0.494562 0.247281 0.968944i 0.420463π-0.420463\pi
0.247281 + 0.968944i 0.420463π0.420463\pi
542542 − 1.22274e7i − 1.78787i
543543 − 1.53304e7i − 2.23128i
544544 −865383. −0.125375
545545 0 0
546546 3.61365e6 0.518757
547547 1.32125e7i 1.88806i 0.329860 + 0.944030i 0.392999π0.392999\pi
−0.329860 + 0.944030i 0.607001π0.607001\pi
548548 − 550656.i − 0.0783301i
549549 1.66594e7 2.35900
550550 0 0
551551 −1.09028e7 −1.52988
552552 1.74596e7i 2.43886i
553553 1.23649e7i 1.71940i
554554 4.56495e6 0.631920
555555 0 0
556556 −1.12032e6 −0.153693
557557 7.47598e6i 1.02101i 0.859875 + 0.510505i 0.170541π0.170541\pi
−0.859875 + 0.510505i 0.829459π0.829459\pi
558558 − 7.43228e6i − 1.01050i
559559 −1.84585e6 −0.249843
560560 0 0
561561 −2.10956e6 −0.282999
562562 710886.i 0.0949421i
563563 − 1.32316e7i − 1.75931i −0.475617 0.879653i 0.657775π-0.657775\pi
0.475617 0.879653i 0.342225π-0.342225\pi
564564 1.00326e6 0.132805
565565 0 0
566566 6.62278e6 0.868959
567567 − 1.56426e6i − 0.204339i
568568 7.74075e6i 1.00673i
569569 9.80441e6 1.26952 0.634762 0.772708i 0.281098π-0.281098\pi
0.634762 + 0.772708i 0.281098π0.281098\pi
570570 0 0
571571 2.98442e6 0.383063 0.191532 0.981486i 0.438655π-0.438655\pi
0.191532 + 0.981486i 0.438655π0.438655\pi
572572 − 141380.i − 0.0180675i
573573 5.32149e6i 0.677091i
574574 1.42305e6 0.180276
575575 0 0
576576 1.08532e7 1.36301
577577 − 1.47218e7i − 1.84086i −0.390911 0.920429i 0.627840π-0.627840\pi
0.390911 0.920429i 0.372160π-0.372160\pi
578578 − 7.18831e6i − 0.894968i
579579 −1.39704e7 −1.73185
580580 0 0
581581 −2.25544e6 −0.277198
582582 1.88486e7i 2.30659i
583583 4.46768e6i 0.544390i
584584 7.03299e6 0.853312
585585 0 0
586586 −1.43102e7 −1.72148
587587 − 9.66987e6i − 1.15831i −0.815217 0.579156i 0.803382π-0.803382\pi
0.815217 0.579156i 0.196618π-0.196618\pi
588588 259245.i 0.0309220i
589589 7.05552e6 0.837993
590590 0 0
591591 −1.43218e7 −1.68666
592592 6.63815e6i 0.778472i
593593 1.52788e7i 1.78424i 0.451797 + 0.892121i 0.350783π0.350783\pi
−0.451797 + 0.892121i 0.649217π0.649217\pi
594594 −4.48554e6 −0.521614
595595 0 0
596596 2.19268e6 0.252848
597597 2.05113e7i 2.35536i
598598 4.25754e6i 0.486861i
599599 −7.95473e6 −0.905854 −0.452927 0.891548i 0.649620π-0.649620\pi
−0.452927 + 0.891548i 0.649620π0.649620\pi
600600 0 0
601601 5.48231e6 0.619123 0.309562 0.950879i 0.399818π-0.399818\pi
0.309562 + 0.950879i 0.399818π0.399818\pi
602602 − 9.11560e6i − 1.02517i
603603 − 2.68242e7i − 3.00423i
604604 6602.27 0.000736378 0
605605 0 0
606606 −5.14604e6 −0.569235
607607 − 1.49346e6i − 0.164521i −0.996611 0.0822605i 0.973786π-0.973786\pi
0.996611 0.0822605i 0.0262139π-0.0262139\pi
608608 − 4.23782e6i − 0.464926i
609609 1.60774e7 1.75660
610610 0 0
611611 −1.33715e6 −0.144903
612612 996663.i 0.107565i
613613 9.31063e6i 1.00076i 0.865807 + 0.500378i 0.166805π0.166805\pi
−0.865807 + 0.500378i 0.833195π0.833195\pi
614614 8.54733e6 0.914976
615615 0 0
616616 −3.81611e6 −0.405200
617617 245403.i 0.0259517i 0.999916 + 0.0129759i 0.00413046π0.00413046\pi
−0.999916 + 0.0129759i 0.995870π0.995870\pi
618618 − 3.09625e7i − 3.26110i
619619 −2.82756e6 −0.296610 −0.148305 0.988942i 0.547382π-0.547382\pi
−0.148305 + 0.988942i 0.547382π0.547382\pi
620620 0 0
621621 1.80932e7 1.88272
622622 − 8.91491e6i − 0.923934i
623623 − 4.89240e6i − 0.505012i
624624 5.01342e6 0.515433
625625 0 0
626626 1.88786e6 0.192546
627627 − 1.03306e7i − 1.04944i
628628 326695.i 0.0330555i
629629 2.79272e6 0.281449
630630 0 0
631631 −1.53391e7 −1.53366 −0.766828 0.641853i 0.778166π-0.778166\pi
−0.766828 + 0.641853i 0.778166π0.778166\pi
632632 1.48081e7i 1.47471i
633633 − 2.49004e7i − 2.47000i
634634 −1.34796e7 −1.33185
635635 0 0
636636 3.35148e6 0.328544
637637 − 345523.i − 0.0337388i
638638 − 4.69599e6i − 0.456747i
639639 1.94612e7 1.88546
640640 0 0
641641 1.02617e7 0.986444 0.493222 0.869904i 0.335819π-0.335819\pi
0.493222 + 0.869904i 0.335819π0.335819\pi
642642 − 2.85548e7i − 2.73427i
643643 − 5.26807e6i − 0.502486i −0.967924 0.251243i 0.919161π-0.919161\pi
0.967924 0.251243i 0.0808394π-0.0808394\pi
644644 −2.81630e6 −0.267586
645645 0 0
646646 −7.06356e6 −0.665951
647647 − 2.03948e7i − 1.91540i −0.287775 0.957698i 0.592915π-0.592915\pi
0.287775 0.957698i 0.407085π-0.407085\pi
648648 − 1.87335e6i − 0.175259i
649649 −1.90134e6 −0.177194
650650 0 0
651651 −1.04042e7 −0.962179
652652 − 284182.i − 0.0261805i
653653 − 8.69527e6i − 0.797994i −0.916952 0.398997i 0.869358π-0.869358\pi
0.916952 0.398997i 0.130642π-0.130642\pi
654654 2.77720e7 2.53900
655655 0 0
656656 1.97427e6 0.179121
657657 − 1.76818e7i − 1.59813i
658658 − 6.60342e6i − 0.594571i
659659 −1.85493e7 −1.66385 −0.831926 0.554886i 0.812762π-0.812762\pi
−0.831926 + 0.554886i 0.812762π0.812762\pi
660660 0 0
661661 1.00321e6 0.0893078 0.0446539 0.999003i 0.485782π-0.485782\pi
0.0446539 + 0.999003i 0.485782π0.485782\pi
662662 − 2.67266e6i − 0.237027i
663663 − 2.10918e6i − 0.186350i
664664 −2.70109e6 −0.237750
665665 0 0
666666 1.44063e7 1.25854
667667 1.89421e7i 1.64859i
668668 1.47920e6i 0.128258i
669669 1.02811e7 0.888122
670670 0 0
671671 −6.81171e6 −0.584049
672672 6.24916e6i 0.533824i
673673 − 653810.i − 0.0556434i −0.999613 0.0278217i 0.991143π-0.991143\pi
0.999613 0.0278217i 0.00885706π-0.00885706\pi
674674 −395872. −0.0335664
675675 0 0
676676 141355. 0.0118972
677677 − 831237.i − 0.0697033i −0.999392 0.0348516i 0.988904π-0.988904\pi
0.999392 0.0348516i 0.0110959π-0.0110959\pi
678678 − 3.49263e6i − 0.291795i
679679 1.66175e7 1.38322
680680 0 0
681681 −3.33222e7 −2.75338
682682 3.03892e6i 0.250184i
683683 − 4.86860e6i − 0.399349i −0.979862 0.199675i 0.936012π-0.936012\pi
0.979862 0.199675i 0.0639885π-0.0639885\pi
684684 −4.88070e6 −0.398879
685685 0 0
686686 −1.23207e7 −0.999597
687687 2.21572e7i 1.79111i
688688 − 1.26466e7i − 1.01860i
689689 −4.46686e6 −0.358471
690690 0 0
691691 −7.17359e6 −0.571533 −0.285767 0.958299i 0.592248π-0.592248\pi
−0.285767 + 0.958299i 0.592248π0.592248\pi
692692 − 81115.2i − 0.00643928i
693693 9.59416e6i 0.758881i
694694 2.20752e7 1.73983
695695 0 0
696696 1.92542e7 1.50661
697697 − 830589.i − 0.0647596i
698698 4.58970e6i 0.356571i
699699 −3.05470e7 −2.36469
700700 0 0
701701 −9.45026e6 −0.726355 −0.363177 0.931720i 0.618308π-0.618308\pi
−0.363177 + 0.931720i 0.618308π0.618308\pi
702702 − 4.48473e6i − 0.343474i
703703 1.36761e7i 1.04369i
704704 −4.43766e6 −0.337460
705705 0 0
706706 −1.86035e7 −1.40470
707707 4.53691e6i 0.341359i
708708 1.42631e6i 0.106938i
709709 2.98225e6 0.222807 0.111404 0.993775i 0.464465π-0.464465\pi
0.111404 + 0.993775i 0.464465π0.464465\pi
710710 0 0
711711 3.72293e7 2.76192
712712 − 5.85910e6i − 0.433143i
713713 − 1.22580e7i − 0.903019i
714714 1.04160e7 0.764640
715715 0 0
716716 2.08135e6 0.151727
717717 3.15276e7i 2.29030i
718718 2.23713e7i 1.61949i
719719 −1.65959e7 −1.19723 −0.598617 0.801036i 0.704283π-0.704283\pi
−0.598617 + 0.801036i 0.704283π0.704283\pi
720720 0 0
721721 −2.72975e7 −1.95562
722722 − 1.95394e7i − 1.39498i
723723 4.20955e7i 2.99495i
724724 2.96146e6 0.209971
725725 0 0
726726 −2.06317e7 −1.45276
727727 − 47580.6i − 0.00333882i −0.999999 0.00166941i 0.999469π-0.999469\pi
0.999999 0.00166941i 0.000531391π-0.000531391\pi
728728 − 3.81542e6i − 0.266817i
729729 2.24694e7 1.56593
730730 0 0
731731 −5.32051e6 −0.368264
732732 5.10988e6i 0.352479i
733733 6.02222e6i 0.413996i 0.978341 + 0.206998i 0.0663694π0.0663694\pi
−0.978341 + 0.206998i 0.933631π0.933631\pi
734734 1.35196e7 0.926241
735735 0 0
736736 −7.36265e6 −0.501002
737737 1.09679e7i 0.743800i
738738 − 4.28463e6i − 0.289583i
739739 −8.15662e6 −0.549413 −0.274707 0.961528i 0.588581π-0.588581\pi
−0.274707 + 0.961528i 0.588581π0.588581\pi
740740 0 0
741741 1.03287e7 0.691038
742742 − 2.20593e7i − 1.47090i
743743 473118.i 0.0314411i 0.999876 + 0.0157205i 0.00500421π0.00500421\pi
−0.999876 + 0.0157205i 0.994996π0.994996\pi
744744 −1.24600e7 −0.825249
745745 0 0
746746 2.27292e7 1.49533
747747 6.79087e6i 0.445270i
748748 − 407517.i − 0.0266313i
749749 −2.51748e7 −1.63969
750750 0 0
751751 5.49506e6 0.355527 0.177764 0.984073i 0.443114π-0.443114\pi
0.177764 + 0.984073i 0.443114π0.443114\pi
752752 − 9.16129e6i − 0.590761i
753753 − 1.14589e7i − 0.736470i
754754 4.69514e6 0.300760
755755 0 0
756756 2.96659e6 0.188778
757757 − 6.82041e6i − 0.432585i −0.976329 0.216292i 0.930604π-0.930604\pi
0.976329 0.216292i 0.0693964π-0.0693964\pi
758758 3.99095e6i 0.252292i
759759 −1.79481e7 −1.13087
760760 0 0
761761 1.14435e7 0.716304 0.358152 0.933663i 0.383407π-0.383407\pi
0.358152 + 0.933663i 0.383407π0.383407\pi
762762 − 1.41492e7i − 0.882766i
763763 − 2.44846e7i − 1.52259i
764764 −1.02798e6 −0.0637167
765765 0 0
766766 2.02772e7 1.24863
767767 − 1.90100e6i − 0.116679i
768768 1.21822e7i 0.745284i
769769 5.05628e6 0.308330 0.154165 0.988045i 0.450731π-0.450731\pi
0.154165 + 0.988045i 0.450731π0.450731\pi
770770 0 0
771771 1.19156e7 0.721904
772772 − 2.69874e6i − 0.162974i
773773 3.54919e6i 0.213639i 0.994278 + 0.106820i 0.0340667π0.0340667\pi
−0.994278 + 0.106820i 0.965933π0.965933\pi
774774 −2.74461e7 −1.64675
775775 0 0
776776 1.99010e7 1.18637
777777 − 2.01669e7i − 1.19836i
778778 2.69940e7i 1.59889i
779779 4.06743e6 0.240147
780780 0 0
781781 −7.95731e6 −0.466809
782782 1.22720e7i 0.717626i
783783 − 1.99529e7i − 1.16306i
784784 2.36731e6 0.137551
785785 0 0
786786 −1.22096e7 −0.704929
787787 − 2.14355e7i − 1.23367i −0.787094 0.616833i 0.788415π-0.788415\pi
0.787094 0.616833i 0.211585π-0.211585\pi
788788 − 2.76663e6i − 0.158721i
789789 4.82153e7 2.75735
790790 0 0
791791 −3.07921e6 −0.174984
792792 1.14899e7i 0.650883i
793793 − 6.81047e6i − 0.384586i
794794 −1.65728e7 −0.932923
795795 0 0
796796 −3.96228e6 −0.221648
797797 − 1.94471e7i − 1.08445i −0.840235 0.542223i 0.817583π-0.817583\pi
0.840235 0.542223i 0.182417π-0.182417\pi
798798 5.10078e7i 2.83550i
799799 −3.85422e6 −0.213584
800800 0 0
801801 −1.47305e7 −0.811214
802802 − 3.20357e7i − 1.75873i
803803 7.22975e6i 0.395671i
804804 8.22772e6 0.448889
805805 0 0
806806 −3.03837e6 −0.164742
807807 − 1.01222e6i − 0.0547129i
808808 5.43338e6i 0.292780i
809809 −1.45681e7 −0.782585 −0.391292 0.920266i 0.627972π-0.627972\pi
−0.391292 + 0.920266i 0.627972π0.627972\pi
810810 0 0
811811 1.86252e7 0.994371 0.497185 0.867644i 0.334367π-0.334367\pi
0.497185 + 0.867644i 0.334367π0.334367\pi
812812 3.10577e6i 0.165302i
813813 5.15366e7i 2.73457i
814814 −5.89049e6 −0.311595
815815 0 0
816816 1.44508e7 0.759740
817817 − 2.60548e7i − 1.36563i
818818 2.78439e7i 1.45494i
819819 −9.59241e6 −0.499710
820820 0 0
821821 1.61122e7 0.834252 0.417126 0.908849i 0.363037π-0.363037\pi
0.417126 + 0.908849i 0.363037π0.363037\pi
822822 1.73272e7i 0.894438i
823823 − 1.15862e7i − 0.596269i −0.954524 0.298134i 0.903636π-0.903636\pi
0.954524 0.298134i 0.0963643π-0.0963643\pi
824824 −3.26913e7 −1.67731
825825 0 0
826826 9.38794e6 0.478762
827827 − 8.40345e6i − 0.427262i −0.976914 0.213631i 0.931471π-0.931471\pi
0.976914 0.213631i 0.0685289π-0.0685289\pi
828828 8.47957e6i 0.429831i
829829 4.77193e6 0.241161 0.120581 0.992704i 0.461524π-0.461524\pi
0.120581 + 0.992704i 0.461524π0.461524\pi
830830 0 0
831831 −1.92405e7 −0.966528
832832 − 4.43685e6i − 0.222212i
833833 − 995943.i − 0.0497304i
834834 3.52526e7 1.75499
835835 0 0
836836 1.99563e6 0.0987561
837837 1.29121e7i 0.637067i
838838 2.39826e7i 1.17974i
839839 2.32624e7 1.14091 0.570453 0.821330i 0.306768π-0.306768\pi
0.570453 + 0.821330i 0.306768π0.306768\pi
840840 0 0
841841 377863. 0.0184223
842842 − 2.53929e7i − 1.23433i
843843 − 2.99627e6i − 0.145215i
844844 4.81016e6 0.232436
845845 0 0
846846 −1.98822e7 −0.955075
847847 1.81896e7i 0.871192i
848848 − 3.06041e7i − 1.46147i
849849 −2.79140e7 −1.32908
850850 0 0
851851 2.37603e7 1.12468
852852 5.96927e6i 0.281723i
853853 − 6.88858e6i − 0.324158i −0.986778 0.162079i 0.948180π-0.948180\pi
0.986778 0.162079i 0.0518200π-0.0518200\pi
854854 3.36330e7 1.57805
855855 0 0
856856 −3.01492e7 −1.40634
857857 − 782343.i − 0.0363869i −0.999834 0.0181935i 0.994209π-0.994209\pi
0.999834 0.0181935i 0.00579148π-0.00579148\pi
858858 4.44876e6i 0.206310i
859859 −1.23216e7 −0.569751 −0.284875 0.958565i 0.591952π-0.591952\pi
−0.284875 + 0.958565i 0.591952π0.591952\pi
860860 0 0
861861 −5.99790e6 −0.275735
862862 4.65962e7i 2.13591i
863863 − 7.42942e6i − 0.339569i −0.985481 0.169785i 0.945693π-0.945693\pi
0.985481 0.169785i 0.0543072π-0.0543072\pi
864864 7.75554e6 0.353450
865865 0 0
866866 −3.33842e7 −1.51268
867867 3.02976e7i 1.36886i
868868 − 2.00984e6i − 0.0905445i
869869 −1.52224e7 −0.683807
870870 0 0
871871 −1.09659e7 −0.489779
872872 − 2.93226e7i − 1.30591i
873873 − 5.00334e7i − 2.22190i
874874 −6.00965e7 −2.66116
875875 0 0
876876 5.42348e6 0.238791
877877 7.95778e6i 0.349376i 0.984624 + 0.174688i 0.0558917π0.0558917\pi
−0.984624 + 0.174688i 0.944108π0.944108\pi
878878 − 1.55813e7i − 0.682132i
879879 6.03151e7 2.63302
880880 0 0
881881 3.11775e7 1.35333 0.676663 0.736293i 0.263426π-0.263426\pi
0.676663 + 0.736293i 0.263426π0.263426\pi
882882 − 5.13761e6i − 0.222377i
883883 − 2.20671e7i − 0.952452i −0.879323 0.476226i 0.842004π-0.842004\pi
0.879323 0.476226i 0.157996π-0.157996\pi
884884 407443. 0.0175362
885885 0 0
886886 8.62524e6 0.369137
887887 1.08566e6i 0.0463323i 0.999732 + 0.0231662i 0.00737468π0.00737468\pi
−0.999732 + 0.0231662i 0.992625π0.992625\pi
888888 − 2.41518e7i − 1.02782i
889889 −1.24744e7 −0.529378
890890 0 0
891891 1.92576e6 0.0812657
892892 1.98605e6i 0.0835755i
893893 − 1.88743e7i − 0.792030i
894894 −6.89962e7 −2.88723
895895 0 0
896896 2.97164e7 1.23659
897897 − 1.79448e7i − 0.744660i
898898 2.16774e7i 0.897050i
899899 −1.35179e7 −0.557842
900900 0 0
901901 −1.28754e7 −0.528381
902902 1.75191e6i 0.0716960i
903903 3.84208e7i 1.56800i
904904 −3.68764e6 −0.150082
905905 0 0
906906 −207751. −0.00840857
907907 3.82701e7i 1.54469i 0.635203 + 0.772345i 0.280916π0.280916\pi
−0.635203 + 0.772345i 0.719084π0.719084\pi
908908 − 6.43706e6i − 0.259103i
909909 1.36601e7 0.548334
910910 0 0
911911 −4.01079e7 −1.60116 −0.800579 0.599227i 0.795475π-0.795475\pi
−0.800579 + 0.599227i 0.795475π0.795475\pi
912912 7.07660e7i 2.81733i
913913 − 2.77666e6i − 0.110242i
914914 −2.25843e7 −0.894212
915915 0 0
916916 −4.28023e6 −0.168550
917917 1.07644e7i 0.422732i
918918 − 1.29269e7i − 0.506275i
919919 −1.38759e6 −0.0541967 −0.0270984 0.999633i 0.508627π-0.508627\pi
−0.0270984 + 0.999633i 0.508627π0.508627\pi
920920 0 0
921921 −3.60256e7 −1.39947
922922 − 2.27451e7i − 0.881171i
923923 − 7.95587e6i − 0.307385i
924924 −2.94279e6 −0.113391
925925 0 0
926926 2.15045e7 0.824141
927927 8.21897e7i 3.14136i
928928 8.11940e6i 0.309495i
929929 7.82980e6 0.297654 0.148827 0.988863i 0.452450π-0.452450\pi
0.148827 + 0.988863i 0.452450π0.452450\pi
930930 0 0
931931 4.87717e6 0.184414
932932 − 5.90094e6i − 0.222526i
933933 3.75749e7i 1.41317i
934934 −1.20228e7 −0.450959
935935 0 0
936936 −1.14878e7 −0.428595
937937 5.19939e7i 1.93465i 0.253532 + 0.967327i 0.418408π0.418408\pi
−0.253532 + 0.967327i 0.581592π0.581592\pi
938938 − 5.41546e7i − 2.00968i
939939 −7.95703e6 −0.294501
940940 0 0
941941 2.54802e7 0.938055 0.469028 0.883184i 0.344605π-0.344605\pi
0.469028 + 0.883184i 0.344605π0.344605\pi
942942 − 1.02800e7i − 0.377455i
943943 − 7.06662e6i − 0.258781i
944944 1.30244e7 0.475694
945945 0 0
946946 1.12222e7 0.407709
947947 6.45145e6i 0.233767i 0.993146 + 0.116883i 0.0372903π0.0372903\pi
−0.993146 + 0.116883i 0.962710π0.962710\pi
948948 1.14193e7i 0.412683i
949949 −7.22843e6 −0.260543
950950 0 0
951951 5.68143e7 2.03707
952952 − 1.09976e7i − 0.393284i
953953 2.82313e7i 1.00693i 0.864016 + 0.503465i 0.167942π0.167942\pi
−0.864016 + 0.503465i 0.832058π0.832058\pi
954954 −6.64181e7 −2.36274
955955 0 0
956956 −6.09038e6 −0.215526
957957 1.97928e7i 0.698599i
958958 − 1.75183e7i − 0.616705i
959959 1.52762e7 0.536377
960960 0 0
961961 −1.98813e7 −0.694441
962962 − 5.88942e6i − 0.205180i
963963 7.57986e7i 2.63388i
964964 −8.13185e6 −0.281836
965965 0 0
966966 8.86193e7 3.05552
967967 5.33839e7i 1.83588i 0.396722 + 0.917939i 0.370148π0.370148\pi
−0.396722 + 0.917939i 0.629852π0.629852\pi
968968 2.17837e7i 0.747211i
969969 2.97717e7 1.01858
970970 0 0
971971 3.29212e7 1.12054 0.560270 0.828310i 0.310697π-0.310697\pi
0.560270 + 0.828310i 0.310697π0.310697\pi
972972 3.80574e6i 0.129203i
973973 − 3.10798e7i − 1.05244i
974974 −1.75414e7 −0.592472
975975 0 0
976976 4.66610e7 1.56794
977977 4.57380e7i 1.53300i 0.642247 + 0.766498i 0.278003π0.278003\pi
−0.642247 + 0.766498i 0.721997π0.721997\pi
978978 8.94223e6i 0.298950i
979979 6.02302e6 0.200843
980980 0 0
981981 −7.37205e7 −2.44577
982982 − 3.20457e7i − 1.06045i
983983 − 5.78671e7i − 1.91006i −0.296505 0.955031i 0.595821π-0.595821\pi
0.296505 0.955031i 0.404179π-0.404179\pi
984984 −7.18305e6 −0.236495
985985 0 0
986986 1.35333e7 0.443315
987987 2.78323e7i 0.909404i
988988 1.99527e6i 0.0650292i
989989 −4.52667e7 −1.47159
990990 0 0
991991 −4.51653e7 −1.46090 −0.730451 0.682965i 0.760690π-0.760690\pi
−0.730451 + 0.682965i 0.760690π0.760690\pi
992992 − 5.25432e6i − 0.169526i
993993 1.12648e7i 0.362536i
994994 3.92895e7 1.26128
995995 0 0
996996 −2.08294e6 −0.0665318
997997 1.89237e7i 0.602933i 0.953477 + 0.301467i 0.0974761π0.0974761\pi
−0.953477 + 0.301467i 0.902524π0.902524\pi
998998 − 1.87277e6i − 0.0595193i
999999 −2.50282e7 −0.793445
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.i.274.5 22
5.2 odd 4 325.6.a.k.1.9 yes 11
5.3 odd 4 325.6.a.j.1.3 11
5.4 even 2 inner 325.6.b.i.274.18 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
325.6.a.j.1.3 11 5.3 odd 4
325.6.a.k.1.9 yes 11 5.2 odd 4
325.6.b.i.274.5 22 1.1 even 1 trivial
325.6.b.i.274.18 22 5.4 even 2 inner