Properties

Label 605.4.a.t.1.7
Level 605605
Weight 44
Character 605.1
Self dual yes
Analytic conductor 35.69635.696
Analytic rank 00
Dimension 1212
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] = [605,4,Mod(1,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 605=5112 605 = 5 \cdot 11^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 605.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: 35.696155553535.6961555535
Analytic rank: 00
Dimension: 1212
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x125x1158x10+264x9+1280x85073x713326x6+43166x5++123904 x^{12} - 5 x^{11} - 58 x^{10} + 264 x^{9} + 1280 x^{8} - 5073 x^{7} - 13326 x^{6} + 43166 x^{5} + \cdots + 123904 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 112 11^{2}
Twist minimal: no (minimal twist has level 55)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.7
Root 0.661955-0.661955 of defining polynomial
Character χ\chi == 605.1

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) == q+1.66196q2+1.98058q35.23790q4+5.00000q5+3.29164q68.81834q722.0008q823.0773q9+8.30978q1010.3741q1210.3377q1314.6557q14+9.90292q15+5.33888q16+48.5862q1738.3534q18+97.1627q1926.1895q2017.4655q21+196.403q2343.5745q24+25.0000q2517.1808q2699.1823q27+46.1896q28+169.043q29+16.4582q30+40.8279q31+184.879q32+80.7481q3444.0917q35+120.877q36+145.892q37+161.480q3820.4747q39110.004q40+157.333q4129.0268q42266.051q43115.386q45+326.414q46+483.044q47+10.5741q48265.237q49+41.5489q50+96.2290q51+54.1480q52344.896q53164.837q54+194.010q56+192.439q57+280.942q58772.298q5951.8706q60+800.490q61+67.8541q62+203.503q63+264.550q6451.6887q65+128.194q67254.490q68+388.994q6973.2784q70288.991q71+507.719q7225.4865q73+242.466q74+49.5146q75508.929q7634.0281q78+214.115q79+26.6944q80+426.648q81+261.481q82+518.134q83+91.4824q84+242.931q85442.166q86+334.804q87+6.39690q89191.767q90+91.1616q911028.74q92+80.8631q93+802.797q94+485.814q95+366.169q96325.571q97440.812q98+O(q100)q+1.66196 q^{2} +1.98058 q^{3} -5.23790 q^{4} +5.00000 q^{5} +3.29164 q^{6} -8.81834 q^{7} -22.0008 q^{8} -23.0773 q^{9} +8.30978 q^{10} -10.3741 q^{12} -10.3377 q^{13} -14.6557 q^{14} +9.90292 q^{15} +5.33888 q^{16} +48.5862 q^{17} -38.3534 q^{18} +97.1627 q^{19} -26.1895 q^{20} -17.4655 q^{21} +196.403 q^{23} -43.5745 q^{24} +25.0000 q^{25} -17.1808 q^{26} -99.1823 q^{27} +46.1896 q^{28} +169.043 q^{29} +16.4582 q^{30} +40.8279 q^{31} +184.879 q^{32} +80.7481 q^{34} -44.0917 q^{35} +120.877 q^{36} +145.892 q^{37} +161.480 q^{38} -20.4747 q^{39} -110.004 q^{40} +157.333 q^{41} -29.0268 q^{42} -266.051 q^{43} -115.386 q^{45} +326.414 q^{46} +483.044 q^{47} +10.5741 q^{48} -265.237 q^{49} +41.5489 q^{50} +96.2290 q^{51} +54.1480 q^{52} -344.896 q^{53} -164.837 q^{54} +194.010 q^{56} +192.439 q^{57} +280.942 q^{58} -772.298 q^{59} -51.8706 q^{60} +800.490 q^{61} +67.8541 q^{62} +203.503 q^{63} +264.550 q^{64} -51.6887 q^{65} +128.194 q^{67} -254.490 q^{68} +388.994 q^{69} -73.2784 q^{70} -288.991 q^{71} +507.719 q^{72} -25.4865 q^{73} +242.466 q^{74} +49.5146 q^{75} -508.929 q^{76} -34.0281 q^{78} +214.115 q^{79} +26.6944 q^{80} +426.648 q^{81} +261.481 q^{82} +518.134 q^{83} +91.4824 q^{84} +242.931 q^{85} -442.166 q^{86} +334.804 q^{87} +6.39690 q^{89} -191.767 q^{90} +91.1616 q^{91} -1028.74 q^{92} +80.8631 q^{93} +802.797 q^{94} +485.814 q^{95} +366.169 q^{96} -325.571 q^{97} -440.812 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+7q23q3+47q4+60q5+30q6+97q7+105q8+131q9+35q10+5q12+205q13+109q1415q15+115q16+231q17+241q18+276q19++3889q98+O(q100) 12 q + 7 q^{2} - 3 q^{3} + 47 q^{4} + 60 q^{5} + 30 q^{6} + 97 q^{7} + 105 q^{8} + 131 q^{9} + 35 q^{10} + 5 q^{12} + 205 q^{13} + 109 q^{14} - 15 q^{15} + 115 q^{16} + 231 q^{17} + 241 q^{18} + 276 q^{19}+ \cdots + 3889 q^{98}+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 1.66196 0.587590 0.293795 0.955868i 0.405082π-0.405082\pi
0.293795 + 0.955868i 0.405082π0.405082\pi
33 1.98058 0.381164 0.190582 0.981671i 0.438963π-0.438963\pi
0.190582 + 0.981671i 0.438963π0.438963\pi
44 −5.23790 −0.654738
55 5.00000 0.447214
66 3.29164 0.223968
77 −8.81834 −0.476145 −0.238073 0.971247i 0.576516π-0.576516\pi
−0.238073 + 0.971247i 0.576516π0.576516\pi
88 −22.0008 −0.972307
99 −23.0773 −0.854714
1010 8.30978 0.262778
1111 0 0
1212 −10.3741 −0.249562
1313 −10.3377 −0.220552 −0.110276 0.993901i 0.535173π-0.535173\pi
−0.110276 + 0.993901i 0.535173π0.535173\pi
1414 −14.6557 −0.279778
1515 9.90292 0.170462
1616 5.33888 0.0834200
1717 48.5862 0.693169 0.346585 0.938019i 0.387341π-0.387341\pi
0.346585 + 0.938019i 0.387341π0.387341\pi
1818 −38.3534 −0.502222
1919 97.1627 1.17319 0.586596 0.809879i 0.300468π-0.300468\pi
0.586596 + 0.809879i 0.300468π0.300468\pi
2020 −26.1895 −0.292808
2121 −17.4655 −0.181489
2222 0 0
2323 196.403 1.78056 0.890281 0.455411i 0.150508π-0.150508\pi
0.890281 + 0.455411i 0.150508π0.150508\pi
2424 −43.5745 −0.370608
2525 25.0000 0.200000
2626 −17.1808 −0.129594
2727 −99.1823 −0.706950
2828 46.1896 0.311750
2929 169.043 1.08243 0.541216 0.840884i 0.317964π-0.317964\pi
0.541216 + 0.840884i 0.317964π0.317964\pi
3030 16.4582 0.100161
3131 40.8279 0.236545 0.118273 0.992981i 0.462264π-0.462264\pi
0.118273 + 0.992981i 0.462264π0.462264\pi
3232 184.879 1.02132
3333 0 0
3434 80.7481 0.407299
3535 −44.0917 −0.212939
3636 120.877 0.559614
3737 145.892 0.648229 0.324114 0.946018i 0.394934π-0.394934\pi
0.324114 + 0.946018i 0.394934π0.394934\pi
3838 161.480 0.689356
3939 −20.4747 −0.0840662
4040 −110.004 −0.434829
4141 157.333 0.599301 0.299650 0.954049i 0.403130π-0.403130\pi
0.299650 + 0.954049i 0.403130π0.403130\pi
4242 −29.0268 −0.106641
4343 −266.051 −0.943546 −0.471773 0.881720i 0.656386π-0.656386\pi
−0.471773 + 0.881720i 0.656386π0.656386\pi
4444 0 0
4545 −115.386 −0.382240
4646 326.414 1.04624
4747 483.044 1.49913 0.749566 0.661930i 0.230262π-0.230262\pi
0.749566 + 0.661930i 0.230262π0.230262\pi
4848 10.5741 0.0317967
4949 −265.237 −0.773286
5050 41.5489 0.117518
5151 96.2290 0.264211
5252 54.1480 0.144404
5353 −344.896 −0.893871 −0.446935 0.894566i 0.647485π-0.647485\pi
−0.446935 + 0.894566i 0.647485π0.647485\pi
5454 −164.837 −0.415397
5555 0 0
5656 194.010 0.462960
5757 192.439 0.447178
5858 280.942 0.636026
5959 −772.298 −1.70415 −0.852073 0.523424i 0.824655π-0.824655\pi
−0.852073 + 0.523424i 0.824655π0.824655\pi
6060 −51.8706 −0.111608
6161 800.490 1.68020 0.840101 0.542431i 0.182496π-0.182496\pi
0.840101 + 0.542431i 0.182496π0.182496\pi
6262 67.8541 0.138992
6363 203.503 0.406968
6464 264.550 0.516700
6565 −51.6887 −0.0986337
6666 0 0
6767 128.194 0.233751 0.116876 0.993147i 0.462712π-0.462712\pi
0.116876 + 0.993147i 0.462712π0.462712\pi
6868 −254.490 −0.453844
6969 388.994 0.678686
7070 −73.2784 −0.125121
7171 −288.991 −0.483055 −0.241528 0.970394i 0.577648π-0.577648\pi
−0.241528 + 0.970394i 0.577648π0.577648\pi
7272 507.719 0.831045
7373 −25.4865 −0.0408626 −0.0204313 0.999791i 0.506504π-0.506504\pi
−0.0204313 + 0.999791i 0.506504π0.506504\pi
7474 242.466 0.380893
7575 49.5146 0.0762327
7676 −508.929 −0.768134
7777 0 0
7878 −34.0281 −0.0493965
7979 214.115 0.304934 0.152467 0.988309i 0.451278π-0.451278\pi
0.152467 + 0.988309i 0.451278π0.451278\pi
8080 26.6944 0.0373066
8181 426.648 0.585251
8282 261.481 0.352143
8383 518.134 0.685212 0.342606 0.939479i 0.388690π-0.388690\pi
0.342606 + 0.939479i 0.388690π0.388690\pi
8484 91.4824 0.118828
8585 242.931 0.309995
8686 −442.166 −0.554418
8787 334.804 0.412584
8888 0 0
8989 6.39690 0.00761876 0.00380938 0.999993i 0.498787π-0.498787\pi
0.00380938 + 0.999993i 0.498787π0.498787\pi
9090 −191.767 −0.224600
9191 91.1616 0.105015
9292 −1028.74 −1.16580
9393 80.8631 0.0901625
9494 802.797 0.880874
9595 485.814 0.524668
9696 366.169 0.389292
9797 −325.571 −0.340791 −0.170395 0.985376i 0.554504π-0.554504\pi
−0.170395 + 0.985376i 0.554504π0.554504\pi
9898 −440.812 −0.454375
9999 0 0
100100 −130.948 −0.130948
101101 1255.66 1.23706 0.618528 0.785763i 0.287730π-0.287730\pi
0.618528 + 0.785763i 0.287730π0.287730\pi
102102 159.928 0.155248
103103 −1462.82 −1.39938 −0.699688 0.714449i 0.746677π-0.746677\pi
−0.699688 + 0.714449i 0.746677π0.746677\pi
104104 227.438 0.214444
105105 −87.3273 −0.0811645
106106 −573.202 −0.525230
107107 1571.15 1.41952 0.709762 0.704442i 0.248803π-0.248803\pi
0.709762 + 0.704442i 0.248803π0.248803\pi
108108 519.507 0.462867
109109 1292.93 1.13615 0.568074 0.822977i 0.307689π-0.307689\pi
0.568074 + 0.822977i 0.307689π0.307689\pi
110110 0 0
111111 288.951 0.247081
112112 −47.0800 −0.0397201
113113 999.873 0.832390 0.416195 0.909275i 0.363363π-0.363363\pi
0.416195 + 0.909275i 0.363363π0.363363\pi
114114 319.825 0.262758
115115 982.017 0.796292
116116 −885.432 −0.708709
117117 238.567 0.188509
118118 −1283.52 −1.00134
119119 −428.449 −0.330049
120120 −217.872 −0.165741
121121 0 0
122122 1330.38 0.987269
123123 311.612 0.228432
124124 −213.853 −0.154875
125125 125.000 0.0894427
126126 338.213 0.239130
127127 −646.206 −0.451508 −0.225754 0.974184i 0.572485π-0.572485\pi
−0.225754 + 0.974184i 0.572485π0.572485\pi
128128 −1039.36 −0.717717
129129 −526.937 −0.359645
130130 −85.9042 −0.0579561
131131 367.577 0.245155 0.122578 0.992459i 0.460884π-0.460884\pi
0.122578 + 0.992459i 0.460884π0.460884\pi
132132 0 0
133133 −856.814 −0.558610
134134 213.052 0.137350
135135 −495.911 −0.316157
136136 −1068.94 −0.673974
137137 −791.385 −0.493523 −0.246761 0.969076i 0.579366π-0.579366\pi
−0.246761 + 0.969076i 0.579366π0.579366\pi
138138 646.490 0.398789
139139 −1909.61 −1.16526 −0.582629 0.812739i 0.697976π-0.697976\pi
−0.582629 + 0.812739i 0.697976π0.697976\pi
140140 230.948 0.139419
141141 956.709 0.571414
142142 −480.290 −0.283838
143143 0 0
144144 −123.207 −0.0713003
145145 845.216 0.484078
146146 −42.3574 −0.0240105
147147 −525.324 −0.294748
148148 −764.167 −0.424420
149149 1969.24 1.08273 0.541363 0.840789i 0.317908π-0.317908\pi
0.541363 + 0.840789i 0.317908π0.317908\pi
150150 82.2911 0.0447936
151151 2653.58 1.43010 0.715049 0.699074i 0.246404π-0.246404\pi
0.715049 + 0.699074i 0.246404π0.246404\pi
152152 −2137.66 −1.14070
153153 −1121.24 −0.592462
154154 0 0
155155 204.139 0.105786
156156 107.245 0.0550414
157157 −2060.15 −1.04725 −0.523625 0.851949i 0.675421π-0.675421\pi
−0.523625 + 0.851949i 0.675421π0.675421\pi
158158 355.850 0.179176
159159 −683.096 −0.340711
160160 924.397 0.456750
161161 −1731.95 −0.847807
162162 709.070 0.343887
163163 −219.965 −0.105699 −0.0528496 0.998602i 0.516830π-0.516830\pi
−0.0528496 + 0.998602i 0.516830π0.516830\pi
164164 −824.096 −0.392385
165165 0 0
166166 861.115 0.402623
167167 −990.902 −0.459151 −0.229576 0.973291i 0.573734π-0.573734\pi
−0.229576 + 0.973291i 0.573734π0.573734\pi
168168 384.254 0.176463
169169 −2090.13 −0.951357
170170 403.740 0.182150
171171 −2242.25 −1.00274
172172 1393.55 0.617775
173173 1556.90 0.684213 0.342107 0.939661i 0.388860π-0.388860\pi
0.342107 + 0.939661i 0.388860π0.388860\pi
174174 556.430 0.242430
175175 −220.458 −0.0952291
176176 0 0
177177 −1529.60 −0.649558
178178 10.6314 0.00447671
179179 −1344.51 −0.561417 −0.280708 0.959793i 0.590569π-0.590569\pi
−0.280708 + 0.959793i 0.590569π0.590569\pi
180180 604.383 0.250267
181181 −1489.71 −0.611765 −0.305882 0.952069i 0.598951π-0.598951\pi
−0.305882 + 0.952069i 0.598951π0.598951\pi
182182 151.506 0.0617055
183183 1585.44 0.640432
184184 −4321.03 −1.73125
185185 729.459 0.289897
186186 134.391 0.0529786
187187 0 0
188188 −2530.14 −0.981538
189189 874.623 0.336611
190190 807.401 0.308289
191191 4194.91 1.58918 0.794589 0.607148i 0.207686π-0.207686\pi
0.794589 + 0.607148i 0.207686π0.207686\pi
192192 523.964 0.196947
193193 −3372.22 −1.25771 −0.628854 0.777523i 0.716476π-0.716476\pi
−0.628854 + 0.777523i 0.716476π0.716476\pi
194194 −541.084 −0.200245
195195 −102.374 −0.0375956
196196 1389.29 0.506300
197197 5256.04 1.90090 0.950450 0.310878i 0.100623π-0.100623\pi
0.950450 + 0.310878i 0.100623π0.100623\pi
198198 0 0
199199 3413.08 1.21581 0.607907 0.794008i 0.292009π-0.292009\pi
0.607907 + 0.794008i 0.292009π0.292009\pi
200200 −550.020 −0.194461
201201 253.898 0.0890975
202202 2086.85 0.726881
203203 −1490.68 −0.515395
204204 −504.039 −0.172989
205205 786.666 0.268015
206206 −2431.14 −0.822259
207207 −4532.46 −1.52187
208208 −55.1919 −0.0183984
209209 0 0
210210 −145.134 −0.0476914
211211 1088.49 0.355142 0.177571 0.984108i 0.443176π-0.443176\pi
0.177571 + 0.984108i 0.443176π0.443176\pi
212212 1806.53 0.585251
213213 −572.371 −0.184123
214214 2611.19 0.834098
215215 −1330.26 −0.421966
216216 2182.09 0.687372
217217 −360.034 −0.112630
218218 2148.79 0.667590
219219 −50.4782 −0.0155753
220220 0 0
221221 −502.271 −0.152880
222222 480.224 0.145182
223223 −195.453 −0.0586929 −0.0293464 0.999569i 0.509343π-0.509343\pi
−0.0293464 + 0.999569i 0.509343π0.509343\pi
224224 −1630.33 −0.486299
225225 −576.932 −0.170943
226226 1661.74 0.489104
227227 1935.65 0.565962 0.282981 0.959126i 0.408677π-0.408677\pi
0.282981 + 0.959126i 0.408677π0.408677\pi
228228 −1007.98 −0.292785
229229 3483.24 1.00515 0.502575 0.864534i 0.332386π-0.332386\pi
0.502575 + 0.864534i 0.332386π0.332386\pi
230230 1632.07 0.467893
231231 0 0
232232 −3719.09 −1.05246
233233 −943.151 −0.265184 −0.132592 0.991171i 0.542330π-0.542330\pi
−0.132592 + 0.991171i 0.542330π0.542330\pi
234234 396.487 0.110766
235235 2415.22 0.670432
236236 4045.22 1.11577
237237 424.073 0.116230
238238 −712.064 −0.193934
239239 −402.723 −0.108996 −0.0544979 0.998514i 0.517356π-0.517356\pi
−0.0544979 + 0.998514i 0.517356π0.517356\pi
240240 52.8705 0.0142199
241241 −4356.62 −1.16446 −0.582229 0.813025i 0.697819π-0.697819\pi
−0.582229 + 0.813025i 0.697819π0.697819\pi
242242 0 0
243243 3522.93 0.930026
244244 −4192.89 −1.10009
245245 −1326.18 −0.345824
246246 517.885 0.134224
247247 −1004.44 −0.258749
248248 −898.246 −0.229995
249249 1026.21 0.261178
250250 207.744 0.0525556
251251 5231.68 1.31562 0.657810 0.753184i 0.271483π-0.271483\pi
0.657810 + 0.753184i 0.271483π0.271483\pi
252252 −1065.93 −0.266458
253253 0 0
254254 −1073.96 −0.265301
255255 481.145 0.118159
256256 −3843.78 −0.938423
257257 7412.38 1.79911 0.899555 0.436807i 0.143891π-0.143891\pi
0.899555 + 0.436807i 0.143891π0.143891\pi
258258 −875.746 −0.211324
259259 −1286.52 −0.308651
260260 270.740 0.0645792
261261 −3901.06 −0.925170
262262 610.896 0.144051
263263 −774.208 −0.181520 −0.0907599 0.995873i 0.528930π-0.528930\pi
−0.0907599 + 0.995873i 0.528930π0.528930\pi
264264 0 0
265265 −1724.48 −0.399751
266266 −1423.99 −0.328234
267267 12.6696 0.00290399
268268 −671.465 −0.153046
269269 −3400.24 −0.770692 −0.385346 0.922772i 0.625918π-0.625918\pi
−0.385346 + 0.922772i 0.625918π0.625918\pi
270270 −824.183 −0.185771
271271 1107.64 0.248281 0.124140 0.992265i 0.460383π-0.460383\pi
0.124140 + 0.992265i 0.460383π0.460383\pi
272272 259.396 0.0578242
273273 180.553 0.0400278
274274 −1315.25 −0.289989
275275 0 0
276276 −2037.51 −0.444361
277277 −7648.53 −1.65905 −0.829523 0.558473i 0.811387π-0.811387\pi
−0.829523 + 0.558473i 0.811387π0.811387\pi
278278 −3173.68 −0.684693
279279 −942.197 −0.202179
280280 970.052 0.207042
281281 −4933.48 −1.04736 −0.523678 0.851917i 0.675440π-0.675440\pi
−0.523678 + 0.851917i 0.675440π0.675440\pi
282282 1590.01 0.335757
283283 −5768.82 −1.21173 −0.605867 0.795566i 0.707174π-0.707174\pi
−0.605867 + 0.795566i 0.707174π0.707174\pi
284284 1513.71 0.316275
285285 962.195 0.199984
286286 0 0
287287 −1387.42 −0.285354
288288 −4266.52 −0.872940
289289 −2552.38 −0.519516
290290 1404.71 0.284440
291291 −644.820 −0.129897
292292 133.496 0.0267543
293293 −6038.18 −1.20394 −0.601969 0.798519i 0.705617π-0.705617\pi
−0.601969 + 0.798519i 0.705617π0.705617\pi
294294 −873.065 −0.173191
295295 −3861.49 −0.762117
296296 −3209.74 −0.630278
297297 0 0
298298 3272.78 0.636199
299299 −2030.37 −0.392706
300300 −259.353 −0.0499125
301301 2346.13 0.449265
302302 4410.12 0.840312
303303 2486.94 0.471520
304304 518.740 0.0978677
305305 4002.45 0.751409
306306 −1863.45 −0.348125
307307 9098.53 1.69147 0.845734 0.533605i 0.179163π-0.179163\pi
0.845734 + 0.533605i 0.179163π0.179163\pi
308308 0 0
309309 −2897.23 −0.533391
310310 339.271 0.0621589
311311 3814.96 0.695584 0.347792 0.937572i 0.386932π-0.386932\pi
0.347792 + 0.937572i 0.386932π0.386932\pi
312312 450.461 0.0817382
313313 2589.83 0.467687 0.233843 0.972274i 0.424870π-0.424870\pi
0.233843 + 0.972274i 0.424870π0.424870\pi
314314 −3423.88 −0.615353
315315 1017.52 0.182002
316316 −1121.51 −0.199652
317317 −6968.91 −1.23474 −0.617370 0.786673i 0.711802π-0.711802\pi
−0.617370 + 0.786673i 0.711802π0.711802\pi
318318 −1135.28 −0.200198
319319 0 0
320320 1322.75 0.231075
321321 3111.80 0.541071
322322 −2878.43 −0.498163
323323 4720.77 0.813221
324324 −2234.74 −0.383186
325325 −258.443 −0.0441103
326326 −365.572 −0.0621078
327327 2560.76 0.433059
328328 −3461.46 −0.582704
329329 −4259.64 −0.713804
330330 0 0
331331 −2383.56 −0.395808 −0.197904 0.980221i 0.563413π-0.563413\pi
−0.197904 + 0.980221i 0.563413π0.563413\pi
332332 −2713.93 −0.448634
333333 −3366.79 −0.554050
334334 −1646.83 −0.269793
335335 640.968 0.104537
336336 −93.2460 −0.0151398
337337 9836.49 1.58999 0.794997 0.606613i 0.207472π-0.207472\pi
0.794997 + 0.606613i 0.207472π0.207472\pi
338338 −3473.70 −0.559008
339339 1980.33 0.317277
340340 −1272.45 −0.202965
341341 0 0
342342 −3726.52 −0.589203
343343 5363.64 0.844342
344344 5853.35 0.917417
345345 1944.97 0.303517
346346 2587.50 0.402037
347347 −9537.02 −1.47543 −0.737715 0.675112i 0.764095π-0.764095\pi
−0.737715 + 0.675112i 0.764095π0.764095\pi
348348 −1753.67 −0.270134
349349 −10464.6 −1.60504 −0.802519 0.596626i 0.796508π-0.796508\pi
−0.802519 + 0.596626i 0.796508π0.796508\pi
350350 −366.392 −0.0559556
351351 1025.32 0.155919
352352 0 0
353353 8203.85 1.23696 0.618480 0.785800i 0.287749π-0.287749\pi
0.618480 + 0.785800i 0.287749π0.287749\pi
354354 −2542.13 −0.381674
355355 −1444.96 −0.216029
356356 −33.5063 −0.00498829
357357 −848.580 −0.125803
358358 −2234.52 −0.329883
359359 −12956.3 −1.90475 −0.952375 0.304930i 0.901367π-0.901367\pi
−0.952375 + 0.304930i 0.901367π0.901367\pi
360360 2538.59 0.371655
361361 2581.60 0.376381
362362 −2475.84 −0.359467
363363 0 0
364364 −477.496 −0.0687571
365365 −127.433 −0.0182743
366366 2634.93 0.376311
367367 −1259.31 −0.179116 −0.0895581 0.995982i 0.528545π-0.528545\pi
−0.0895581 + 0.995982i 0.528545π0.528545\pi
368368 1048.57 0.148535
369369 −3630.82 −0.512231
370370 1212.33 0.170340
371371 3041.41 0.425612
372372 −423.553 −0.0590328
373373 14100.6 1.95738 0.978691 0.205339i 0.0658297π-0.0658297\pi
0.978691 + 0.205339i 0.0658297π0.0658297\pi
374374 0 0
375375 247.573 0.0340923
376376 −10627.4 −1.45762
377377 −1747.52 −0.238732
378378 1453.58 0.197789
379379 −11911.1 −1.61434 −0.807168 0.590322i 0.799001π-0.799001\pi
−0.807168 + 0.590322i 0.799001π0.799001\pi
380380 −2544.65 −0.343520
381381 −1279.86 −0.172098
382382 6971.75 0.933785
383383 8578.16 1.14445 0.572224 0.820097i 0.306081π-0.306081\pi
0.572224 + 0.820097i 0.306081π0.306081\pi
384384 −2058.55 −0.273567
385385 0 0
386386 −5604.48 −0.739017
387387 6139.75 0.806462
388388 1705.31 0.223129
389389 −9962.68 −1.29853 −0.649265 0.760563i 0.724923π-0.724923\pi
−0.649265 + 0.760563i 0.724923π0.724923\pi
390390 −170.141 −0.0220908
391391 9542.49 1.23423
392392 5835.43 0.751871
393393 728.016 0.0934442
394394 8735.30 1.11695
395395 1070.57 0.136371
396396 0 0
397397 9843.58 1.24442 0.622211 0.782850i 0.286235π-0.286235\pi
0.622211 + 0.782850i 0.286235π0.286235\pi
398398 5672.39 0.714400
399399 −1696.99 −0.212922
400400 133.472 0.0166840
401401 4986.05 0.620926 0.310463 0.950585i 0.399516π-0.399516\pi
0.310463 + 0.950585i 0.399516π0.399516\pi
402402 421.967 0.0523528
403403 −422.068 −0.0521704
404404 −6577.01 −0.809947
405405 2133.24 0.261732
406406 −2477.44 −0.302841
407407 0 0
408408 −2117.12 −0.256894
409409 12051.2 1.45696 0.728478 0.685069i 0.240228π-0.240228\pi
0.728478 + 0.685069i 0.240228π0.240228\pi
410410 1307.40 0.157483
411411 −1567.41 −0.188113
412412 7662.10 0.916224
413413 6810.38 0.811421
414414 −7532.74 −0.894237
415415 2590.67 0.306436
416416 −1911.23 −0.225255
417417 −3782.14 −0.444154
418418 0 0
419419 811.934 0.0946673 0.0473336 0.998879i 0.484928π-0.484928\pi
0.0473336 + 0.998879i 0.484928π0.484928\pi
420420 457.412 0.0531415
421421 −13342.8 −1.54463 −0.772315 0.635240i 0.780901π-0.780901\pi
−0.772315 + 0.635240i 0.780901π0.780901\pi
422422 1809.02 0.208678
423423 −11147.3 −1.28133
424424 7588.00 0.869117
425425 1214.65 0.138634
426426 −951.255 −0.108189
427427 −7058.99 −0.800020
428428 −8229.55 −0.929416
429429 0 0
430430 −2210.83 −0.247943
431431 8448.33 0.944181 0.472090 0.881550i 0.343500π-0.343500\pi
0.472090 + 0.881550i 0.343500π0.343500\pi
432432 −529.522 −0.0589737
433433 −7630.81 −0.846913 −0.423456 0.905916i 0.639183π-0.639183\pi
−0.423456 + 0.905916i 0.639183π0.639183\pi
434434 −598.360 −0.0661802
435435 1674.02 0.184513
436436 −6772.24 −0.743880
437437 19083.1 2.08894
438438 −83.8925 −0.00915191
439439 −1738.52 −0.189009 −0.0945043 0.995524i 0.530127π-0.530127\pi
−0.0945043 + 0.995524i 0.530127π0.530127\pi
440440 0 0
441441 6120.95 0.660938
442442 −834.752 −0.0898305
443443 1631.42 0.174968 0.0874841 0.996166i 0.472117π-0.472117\pi
0.0874841 + 0.996166i 0.472117π0.472117\pi
444444 −1513.50 −0.161773
445445 31.9845 0.00340721
446446 −324.834 −0.0344873
447447 3900.24 0.412696
448448 −2332.89 −0.246024
449449 2261.67 0.237717 0.118858 0.992911i 0.462077π-0.462077\pi
0.118858 + 0.992911i 0.462077π0.462077\pi
450450 −958.835 −0.100444
451451 0 0
452452 −5237.24 −0.544998
453453 5255.63 0.545102
454454 3216.96 0.332554
455455 455.808 0.0469640
456456 −4233.81 −0.434795
457457 6364.73 0.651486 0.325743 0.945458i 0.394386π-0.394386\pi
0.325743 + 0.945458i 0.394386π0.394386\pi
458458 5788.99 0.590616
459459 −4818.89 −0.490036
460460 −5143.71 −0.521363
461461 2491.39 0.251704 0.125852 0.992049i 0.459834π-0.459834\pi
0.125852 + 0.992049i 0.459834π0.459834\pi
462462 0 0
463463 −12869.2 −1.29175 −0.645877 0.763442i 0.723508π-0.723508\pi
−0.645877 + 0.763442i 0.723508π0.723508\pi
464464 902.501 0.0902965
465465 404.315 0.0403219
466466 −1567.47 −0.155819
467467 12857.1 1.27400 0.636998 0.770866i 0.280176π-0.280176\pi
0.636998 + 0.770866i 0.280176π0.280176\pi
468468 −1249.59 −0.123424
469469 −1130.45 −0.111300
470470 4013.99 0.393939
471471 −4080.31 −0.399174
472472 16991.2 1.65695
473473 0 0
474474 704.790 0.0682955
475475 2429.07 0.234639
476476 2244.18 0.216096
477477 7959.27 0.764004
478478 −669.308 −0.0640448
479479 5115.67 0.487977 0.243989 0.969778i 0.421544π-0.421544\pi
0.243989 + 0.969778i 0.421544π0.421544\pi
480480 1830.85 0.174097
481481 −1508.19 −0.142968
482482 −7240.50 −0.684224
483483 −3430.28 −0.323153
484484 0 0
485485 −1627.85 −0.152406
486486 5854.96 0.546474
487487 3968.67 0.369276 0.184638 0.982807i 0.440889π-0.440889\pi
0.184638 + 0.982807i 0.440889π0.440889\pi
488488 −17611.4 −1.63367
489489 −435.659 −0.0402887
490490 −2204.06 −0.203203
491491 −42.2164 −0.00388024 −0.00194012 0.999998i 0.500618π-0.500618\pi
−0.00194012 + 0.999998i 0.500618π0.500618\pi
492492 −1632.19 −0.149563
493493 8213.16 0.750309
494494 −1669.34 −0.152039
495495 0 0
496496 217.975 0.0197326
497497 2548.42 0.230005
498498 1705.51 0.153465
499499 −158.607 −0.0142289 −0.00711447 0.999975i 0.502265π-0.502265\pi
−0.00711447 + 0.999975i 0.502265π0.502265\pi
500500 −654.738 −0.0585616
501501 −1962.56 −0.175012
502502 8694.82 0.773045
503503 8842.46 0.783828 0.391914 0.920002i 0.371813π-0.371813\pi
0.391914 + 0.920002i 0.371813π0.371813\pi
504504 −4477.24 −0.395698
505505 6278.29 0.553228
506506 0 0
507507 −4139.68 −0.362623
508508 3384.76 0.295619
509509 11018.9 0.959539 0.479770 0.877394i 0.340720π-0.340720\pi
0.479770 + 0.877394i 0.340720π0.340720\pi
510510 799.642 0.0694289
511511 224.749 0.0194565
512512 1926.73 0.166309
513513 −9636.82 −0.829388
514514 12319.0 1.05714
515515 −7314.08 −0.625820
516516 2760.05 0.235473
517517 0 0
518518 −2138.14 −0.181360
519519 3083.57 0.260797
520520 1137.19 0.0959022
521521 −21660.3 −1.82141 −0.910704 0.413060i 0.864460π-0.864460\pi
−0.910704 + 0.413060i 0.864460π0.864460\pi
522522 −6483.38 −0.543621
523523 13269.4 1.10943 0.554715 0.832040i 0.312827π-0.312827\pi
0.554715 + 0.832040i 0.312827π0.312827\pi
524524 −1925.33 −0.160512
525525 −436.636 −0.0362979
526526 −1286.70 −0.106659
527527 1983.67 0.163966
528528 0 0
529529 26407.3 2.17040
530530 −2866.01 −0.234890
531531 17822.5 1.45656
532532 4487.91 0.365743
533533 −1626.47 −0.132177
534534 21.0563 0.00170636
535535 7855.76 0.634830
536536 −2820.36 −0.227278
537537 −2662.92 −0.213992
538538 −5651.04 −0.452851
539539 0 0
540540 2597.54 0.207000
541541 −6801.60 −0.540524 −0.270262 0.962787i 0.587110π-0.587110\pi
−0.270262 + 0.962787i 0.587110π0.587110\pi
542542 1840.84 0.145887
543543 −2950.50 −0.233183
544544 8982.59 0.707951
545545 6464.65 0.508101
546546 300.071 0.0235199
547547 24734.6 1.93341 0.966704 0.255898i 0.0823712π-0.0823712\pi
0.966704 + 0.255898i 0.0823712π0.0823712\pi
548548 4145.20 0.323128
549549 −18473.1 −1.43609
550550 0 0
551551 16424.7 1.26990
552552 −8558.17 −0.659891
553553 −1888.14 −0.145193
554554 −12711.5 −0.974838
555555 1444.76 0.110498
556556 10002.3 0.762938
557557 −19430.2 −1.47807 −0.739033 0.673670i 0.764717π-0.764717\pi
−0.739033 + 0.673670i 0.764717π0.764717\pi
558558 −1565.89 −0.118798
559559 2750.37 0.208101
560560 −235.400 −0.0177633
561561 0 0
562562 −8199.22 −0.615415
563563 −12323.1 −0.922483 −0.461242 0.887275i 0.652596π-0.652596\pi
−0.461242 + 0.887275i 0.652596π0.652596\pi
564564 −5011.15 −0.374127
565565 4999.36 0.372256
566566 −9587.53 −0.712003
567567 −3762.32 −0.278664
568568 6358.04 0.469678
569569 −19071.5 −1.40513 −0.702564 0.711620i 0.747962π-0.747962\pi
−0.702564 + 0.711620i 0.747962π0.747962\pi
570570 1599.13 0.117509
571571 4453.84 0.326423 0.163211 0.986591i 0.447815π-0.447815\pi
0.163211 + 0.986591i 0.447815π0.447815\pi
572572 0 0
573573 8308.37 0.605737
574574 −2305.83 −0.167671
575575 4910.09 0.356113
576576 −6105.10 −0.441631
577577 3184.19 0.229739 0.114870 0.993381i 0.463355π-0.463355\pi
0.114870 + 0.993381i 0.463355π0.463355\pi
578578 −4241.95 −0.305262
579579 −6678.97 −0.479393
580580 −4427.16 −0.316944
581581 −4569.08 −0.326260
582582 −1071.66 −0.0763262
583583 0 0
584584 560.724 0.0397310
585585 1192.83 0.0843036
586586 −10035.2 −0.707422
587587 23915.2 1.68158 0.840788 0.541365i 0.182092π-0.182092\pi
0.840788 + 0.541365i 0.182092π0.182092\pi
588588 2751.60 0.192983
589589 3966.95 0.277513
590590 −6417.62 −0.447812
591591 10410.0 0.724554
592592 778.899 0.0540752
593593 −6201.48 −0.429451 −0.214725 0.976674i 0.568886π-0.568886\pi
−0.214725 + 0.976674i 0.568886π0.568886\pi
594594 0 0
595595 −2142.25 −0.147603
596596 −10314.7 −0.708902
597597 6759.90 0.463424
598598 −3374.38 −0.230750
599599 −8540.80 −0.582584 −0.291292 0.956634i 0.594085π-0.594085\pi
−0.291292 + 0.956634i 0.594085π0.594085\pi
600600 −1089.36 −0.0741216
601601 8219.57 0.557875 0.278938 0.960309i 0.410018π-0.410018\pi
0.278938 + 0.960309i 0.410018π0.410018\pi
602602 3899.16 0.263984
603603 −2958.36 −0.199790
604604 −13899.2 −0.936340
605605 0 0
606606 4133.18 0.277061
607607 24499.1 1.63820 0.819100 0.573651i 0.194473π-0.194473\pi
0.819100 + 0.573651i 0.194473π0.194473\pi
608608 17963.4 1.19821
609609 −2952.42 −0.196450
610610 6651.89 0.441520
611611 −4993.58 −0.330636
612612 5872.93 0.387907
613613 −9816.60 −0.646800 −0.323400 0.946262i 0.604826π-0.604826\pi
−0.323400 + 0.946262i 0.604826π0.604826\pi
614614 15121.3 0.993889
615615 1558.06 0.102158
616616 0 0
617617 −4396.62 −0.286874 −0.143437 0.989659i 0.545815π-0.545815\pi
−0.143437 + 0.989659i 0.545815π0.545815\pi
618618 −4815.07 −0.313415
619619 −7477.57 −0.485540 −0.242770 0.970084i 0.578056π-0.578056\pi
−0.242770 + 0.970084i 0.578056π0.578056\pi
620620 −1069.26 −0.0692623
621621 −19479.7 −1.25877
622622 6340.29 0.408718
623623 −56.4100 −0.00362764
624624 −109.312 −0.00701281
625625 625.000 0.0400000
626626 4304.19 0.274808
627627 0 0
628628 10790.9 0.685674
629629 7088.33 0.449332
630630 1691.07 0.106942
631631 2168.51 0.136810 0.0684050 0.997658i 0.478209π-0.478209\pi
0.0684050 + 0.997658i 0.478209π0.478209\pi
632632 −4710.70 −0.296490
633633 2155.85 0.135367
634634 −11582.0 −0.725521
635635 −3231.03 −0.201920
636636 3577.99 0.223077
637637 2741.95 0.170549
638638 0 0
639639 6669.13 0.412874
640640 −5196.82 −0.320973
641641 21985.0 1.35469 0.677344 0.735666i 0.263131π-0.263131\pi
0.677344 + 0.735666i 0.263131π0.263131\pi
642642 5171.67 0.317928
643643 28532.7 1.74995 0.874976 0.484166i 0.160877π-0.160877\pi
0.874976 + 0.484166i 0.160877π0.160877\pi
644644 9071.79 0.555091
645645 −2634.69 −0.160838
646646 7845.70 0.477841
647647 −28479.4 −1.73051 −0.865255 0.501331i 0.832844π-0.832844\pi
−0.865255 + 0.501331i 0.832844π0.832844\pi
648648 −9386.60 −0.569044
649649 0 0
650650 −429.521 −0.0259188
651651 −713.078 −0.0429304
652652 1152.16 0.0692053
653653 2776.35 0.166381 0.0831905 0.996534i 0.473489π-0.473489\pi
0.0831905 + 0.996534i 0.473489π0.473489\pi
654654 4255.86 0.254461
655655 1837.88 0.109637
656656 839.983 0.0499937
657657 588.159 0.0349258
658658 −7079.33 −0.419424
659659 −6085.26 −0.359709 −0.179854 0.983693i 0.557563π-0.557563\pi
−0.179854 + 0.983693i 0.557563π0.557563\pi
660660 0 0
661661 −18103.8 −1.06529 −0.532645 0.846339i 0.678802π-0.678802\pi
−0.532645 + 0.846339i 0.678802π0.678802\pi
662662 −3961.37 −0.232573
663663 −994.790 −0.0582722
664664 −11399.4 −0.666236
665665 −4284.07 −0.249818
666666 −5595.45 −0.325554
667667 33200.6 1.92734
668668 5190.25 0.300624
669669 −387.112 −0.0223716
670670 1065.26 0.0614247
671671 0 0
672672 −3229.00 −0.185359
673673 −5229.86 −0.299548 −0.149774 0.988720i 0.547855π-0.547855\pi
−0.149774 + 0.988720i 0.547855π0.547855\pi
674674 16347.8 0.934264
675675 −2479.56 −0.141390
676676 10947.9 0.622890
677677 7280.29 0.413300 0.206650 0.978415i 0.433744π-0.433744\pi
0.206650 + 0.978415i 0.433744π0.433744\pi
678678 3291.22 0.186429
679679 2870.99 0.162266
680680 −5344.68 −0.301410
681681 3833.71 0.215724
682682 0 0
683683 −4696.64 −0.263122 −0.131561 0.991308i 0.541999π-0.541999\pi
−0.131561 + 0.991308i 0.541999π0.541999\pi
684684 11744.7 0.656535
685685 −3956.93 −0.220710
686686 8914.13 0.496127
687687 6898.86 0.383126
688688 −1420.42 −0.0787106
689689 3565.45 0.197145
690690 3232.45 0.178344
691691 −12179.0 −0.670495 −0.335248 0.942130i 0.608820π-0.608820\pi
−0.335248 + 0.942130i 0.608820π0.608820\pi
692692 −8154.89 −0.447980
693693 0 0
694694 −15850.1 −0.866948
695695 −9548.03 −0.521119
696696 −7365.96 −0.401158
697697 7644.22 0.415417
698698 −17391.7 −0.943105
699699 −1867.99 −0.101078
700700 1154.74 0.0623501
701701 −12610.0 −0.679422 −0.339711 0.940530i 0.610329π-0.610329\pi
−0.339711 + 0.940530i 0.610329π0.610329\pi
702702 1704.04 0.0916164
703703 14175.2 0.760497
704704 0 0
705705 4783.54 0.255544
706706 13634.4 0.726826
707707 −11072.8 −0.589018
708708 8011.90 0.425291
709709 3325.26 0.176140 0.0880698 0.996114i 0.471930π-0.471930\pi
0.0880698 + 0.996114i 0.471930π0.471930\pi
710710 −2401.45 −0.126936
711711 −4941.19 −0.260632
712712 −140.737 −0.00740778
713713 8018.74 0.421184
714714 −1410.30 −0.0739205
715715 0 0
716716 7042.43 0.367581
717717 −797.627 −0.0415452
718718 −21532.7 −1.11921
719719 19063.2 0.988787 0.494393 0.869238i 0.335390π-0.335390\pi
0.494393 + 0.869238i 0.335390π0.335390\pi
720720 −616.034 −0.0318865
721721 12899.6 0.666306
722722 4290.50 0.221158
723723 −8628.64 −0.443849
724724 7802.97 0.400546
725725 4226.08 0.216486
726726 0 0
727727 8017.43 0.409009 0.204505 0.978866i 0.434442π-0.434442\pi
0.204505 + 0.978866i 0.434442π0.434442\pi
728728 −2005.63 −0.102106
729729 −4542.02 −0.230759
730730 −211.787 −0.0107378
731731 −12926.4 −0.654037
732732 −8304.38 −0.419315
733733 −8712.10 −0.439003 −0.219501 0.975612i 0.570443π-0.570443\pi
−0.219501 + 0.975612i 0.570443π0.570443\pi
734734 −2092.92 −0.105247
735735 −2626.62 −0.131815
736736 36310.9 1.81853
737737 0 0
738738 −6034.27 −0.300982
739739 −22769.9 −1.13343 −0.566715 0.823914i 0.691786π-0.691786\pi
−0.566715 + 0.823914i 0.691786π0.691786\pi
740740 −3820.84 −0.189806
741741 −1989.38 −0.0986259
742742 5054.69 0.250086
743743 −8449.10 −0.417184 −0.208592 0.978003i 0.566888π-0.566888\pi
−0.208592 + 0.978003i 0.566888π0.566888\pi
744744 −1779.05 −0.0876656
745745 9846.18 0.484210
746746 23434.6 1.15014
747747 −11957.1 −0.585660
748748 0 0
749749 −13855.0 −0.675900
750750 411.455 0.0200323
751751 −9469.75 −0.460128 −0.230064 0.973176i 0.573894π-0.573894\pi
−0.230064 + 0.973176i 0.573894π0.573894\pi
752752 2578.91 0.125058
753753 10361.8 0.501467
754754 −2904.30 −0.140277
755755 13267.9 0.639560
756756 −4581.19 −0.220392
757757 38387.6 1.84309 0.921545 0.388271i 0.126927π-0.126927\pi
0.921545 + 0.388271i 0.126927π0.126927\pi
758758 −19795.8 −0.948567
759759 0 0
760760 −10688.3 −0.510138
761761 −1865.95 −0.0888841 −0.0444420 0.999012i 0.514151π-0.514151\pi
−0.0444420 + 0.999012i 0.514151π0.514151\pi
762762 −2127.08 −0.101123
763763 −11401.5 −0.540972
764764 −21972.5 −1.04050
765765 −5606.19 −0.264957
766766 14256.5 0.672466
767767 7983.80 0.375852
768768 −7612.93 −0.357693
769769 29983.8 1.40604 0.703019 0.711171i 0.251835π-0.251835\pi
0.703019 + 0.711171i 0.251835π0.251835\pi
770770 0 0
771771 14680.8 0.685755
772772 17663.4 0.823470
773773 6987.07 0.325107 0.162553 0.986700i 0.448027π-0.448027\pi
0.162553 + 0.986700i 0.448027π0.448027\pi
774774 10204.0 0.473869
775775 1020.70 0.0473091
776776 7162.82 0.331353
777777 −2548.07 −0.117647
778778 −16557.5 −0.763003
779779 15286.9 0.703095
780780 536.224 0.0246152
781781 0 0
782782 15859.2 0.725222
783783 −16766.1 −0.765225
784784 −1416.07 −0.0645075
785785 −10300.8 −0.468344
786786 1209.93 0.0549069
787787 −17890.6 −0.810332 −0.405166 0.914243i 0.632786π-0.632786\pi
−0.405166 + 0.914243i 0.632786π0.632786\pi
788788 −27530.6 −1.24459
789789 −1533.38 −0.0691888
790790 1779.25 0.0801301
791791 −8817.21 −0.396339
792792 0 0
793793 −8275.25 −0.370571
794794 16359.6 0.731210
795795 −3415.48 −0.152371
796796 −17877.4 −0.796040
797797 −2164.72 −0.0962087 −0.0481043 0.998842i 0.515318π-0.515318\pi
−0.0481043 + 0.998842i 0.515318π0.515318\pi
798798 −2820.32 −0.125111
799799 23469.3 1.03915
800800 4621.99 0.204265
801801 −147.623 −0.00651186
802802 8286.59 0.364850
803803 0 0
804804 −1329.89 −0.0583355
805805 −8659.76 −0.379151
806806 −701.458 −0.0306548
807807 −6734.46 −0.293760
808808 −27625.5 −1.20280
809809 −24725.8 −1.07455 −0.537277 0.843406i 0.680547π-0.680547\pi
−0.537277 + 0.843406i 0.680547π0.680547\pi
810810 3545.35 0.153791
811811 −26049.1 −1.12788 −0.563938 0.825817i 0.690714π-0.690714\pi
−0.563938 + 0.825817i 0.690714π0.690714\pi
812812 7808.04 0.337449
813813 2193.77 0.0946357
814814 0 0
815815 −1099.82 −0.0472702
816816 513.755 0.0220405
817817 −25850.3 −1.10696
818818 20028.6 0.856093
819819 −2103.76 −0.0897575
820820 −4120.48 −0.175480
821821 −12835.8 −0.545645 −0.272822 0.962064i 0.587957π-0.587957\pi
−0.272822 + 0.962064i 0.587957π0.587957\pi
822822 −2604.96 −0.110533
823823 7513.40 0.318227 0.159113 0.987260i 0.449136π-0.449136\pi
0.159113 + 0.987260i 0.449136π0.449136\pi
824824 32183.2 1.36062
825825 0 0
826826 11318.5 0.476783
827827 −10033.8 −0.421896 −0.210948 0.977497i 0.567655π-0.567655\pi
−0.210948 + 0.977497i 0.567655π0.567655\pi
828828 23740.6 0.996428
829829 1442.57 0.0604374 0.0302187 0.999543i 0.490380π-0.490380\pi
0.0302187 + 0.999543i 0.490380π0.490380\pi
830830 4305.58 0.180059
831831 −15148.6 −0.632368
832832 −2734.85 −0.113959
833833 −12886.9 −0.536018
834834 −6285.74 −0.260980
835835 −4954.51 −0.205339
836836 0 0
837837 −4049.40 −0.167226
838838 1349.40 0.0556255
839839 −33081.1 −1.36125 −0.680624 0.732633i 0.738291π-0.738291\pi
−0.680624 + 0.732633i 0.738291π0.738291\pi
840840 1921.27 0.0789168
841841 4186.59 0.171659
842842 −22175.2 −0.907609
843843 −9771.18 −0.399214
844844 −5701.42 −0.232525
845845 −10450.7 −0.425460
846846 −18526.4 −0.752896
847847 0 0
848848 −1841.36 −0.0745667
849849 −11425.6 −0.461869
850850 2018.70 0.0814599
851851 28653.6 1.15421
852852 2998.03 0.120552
853853 −3320.28 −0.133276 −0.0666378 0.997777i 0.521227π-0.521227\pi
−0.0666378 + 0.997777i 0.521227π0.521227\pi
854854 −11731.7 −0.470084
855855 −11211.3 −0.448441
856856 −34566.6 −1.38021
857857 −14357.0 −0.572259 −0.286130 0.958191i 0.592369π-0.592369\pi
−0.286130 + 0.958191i 0.592369π0.592369\pi
858858 0 0
859859 −36024.5 −1.43090 −0.715448 0.698666i 0.753778π-0.753778\pi
−0.715448 + 0.698666i 0.753778π0.753778\pi
860860 6967.76 0.276278
861861 −2747.90 −0.108767
862862 14040.8 0.554791
863863 24955.0 0.984332 0.492166 0.870501i 0.336205π-0.336205\pi
0.492166 + 0.870501i 0.336205π0.336205\pi
864864 −18336.8 −0.722025
865865 7784.50 0.305989
866866 −12682.1 −0.497637
867867 −5055.21 −0.198021
868868 1885.82 0.0737431
869869 0 0
870870 2782.15 0.108418
871871 −1325.23 −0.0515542
872872 −28445.5 −1.10469
873873 7513.29 0.291279
874874 31715.2 1.22744
875875 −1102.29 −0.0425877
876876 264.400 0.0101978
877877 −24077.3 −0.927062 −0.463531 0.886081i 0.653418π-0.653418\pi
−0.463531 + 0.886081i 0.653418π0.653418\pi
878878 −2889.33 −0.111060
879879 −11959.1 −0.458898
880880 0 0
881881 −37851.9 −1.44752 −0.723759 0.690052i 0.757587π-0.757587\pi
−0.723759 + 0.690052i 0.757587π0.757587\pi
882882 10172.7 0.388361
883883 −34000.9 −1.29583 −0.647917 0.761711i 0.724359π-0.724359\pi
−0.647917 + 0.761711i 0.724359π0.724359\pi
884884 2630.85 0.100096
885885 −7648.00 −0.290491
886886 2711.34 0.102810
887887 −14809.0 −0.560582 −0.280291 0.959915i 0.590431π-0.590431\pi
−0.280291 + 0.959915i 0.590431π0.590431\pi
888888 −6357.15 −0.240239
889889 5698.46 0.214983
890890 53.1568 0.00200204
891891 0 0
892892 1023.77 0.0384285
893893 46933.8 1.75877
894894 6482.02 0.242496
895895 −6722.56 −0.251073
896896 9165.47 0.341737
897897 −4021.31 −0.149685
898898 3758.79 0.139680
899899 6901.67 0.256044
900900 3021.92 0.111923
901901 −16757.2 −0.619604
902902 0 0
903903 4646.71 0.171243
904904 −21998.0 −0.809339
905905 −7448.56 −0.273590
906906 8734.62 0.320296
907907 16421.9 0.601191 0.300595 0.953752i 0.402815π-0.402815\pi
0.300595 + 0.953752i 0.402815π0.402815\pi
908908 −10138.7 −0.370557
909909 −28977.2 −1.05733
910910 757.532 0.0275956
911911 −23657.8 −0.860394 −0.430197 0.902735i 0.641556π-0.641556\pi
−0.430197 + 0.902735i 0.641556π0.641556\pi
912912 1027.41 0.0373036
913913 0 0
914914 10577.9 0.382807
915915 7927.19 0.286410
916916 −18244.9 −0.658109
917917 −3241.41 −0.116729
918918 −8008.78 −0.287940
919919 11134.2 0.399654 0.199827 0.979831i 0.435962π-0.435962\pi
0.199827 + 0.979831i 0.435962π0.435962\pi
920920 −21605.2 −0.774240
921921 18020.4 0.644726
922922 4140.58 0.147899
923923 2987.51 0.106539
924924 0 0
925925 3647.29 0.129646
926926 −21388.0 −0.759021
927927 33757.8 1.19607
928928 31252.6 1.10551
929929 386.886 0.0136634 0.00683172 0.999977i 0.497825π-0.497825\pi
0.00683172 + 0.999977i 0.497825π0.497825\pi
930930 671.954 0.0236927
931931 −25771.1 −0.907213
932932 4940.13 0.173626
933933 7555.85 0.265131
934934 21367.9 0.748587
935935 0 0
936936 −5248.66 −0.183288
937937 −40709.8 −1.41935 −0.709676 0.704528i 0.751159π-0.751159\pi
−0.709676 + 0.704528i 0.751159π0.751159\pi
938938 −1878.76 −0.0653985
939939 5129.38 0.178265
940940 −12650.7 −0.438957
941941 −33033.8 −1.14439 −0.572195 0.820117i 0.693908π-0.693908\pi
−0.572195 + 0.820117i 0.693908π0.693908\pi
942942 −6781.29 −0.234550
943943 30900.8 1.06709
944944 −4123.20 −0.142160
945945 4373.11 0.150537
946946 0 0
947947 −11956.8 −0.410288 −0.205144 0.978732i 0.565766π-0.565766\pi
−0.205144 + 0.978732i 0.565766π0.565766\pi
948948 −2221.25 −0.0761002
949949 263.473 0.00901231
950950 4037.00 0.137871
951951 −13802.5 −0.470638
952952 9426.23 0.320910
953953 46066.0 1.56582 0.782909 0.622136i 0.213735π-0.213735\pi
0.782909 + 0.622136i 0.213735π0.213735\pi
954954 13228.0 0.448921
955955 20974.5 0.710702
956956 2109.43 0.0713637
957957 0 0
958958 8502.02 0.286730
959959 6978.70 0.234989
960960 2619.82 0.0880775
961961 −28124.1 −0.944046
962962 −2506.54 −0.0840065
963963 −36257.9 −1.21329
964964 22819.5 0.762415
965965 −16861.1 −0.562465
966966 −5700.96 −0.189881
967967 14540.7 0.483555 0.241778 0.970332i 0.422270π-0.422270\pi
0.241778 + 0.970332i 0.422270π0.422270\pi
968968 0 0
969969 9349.88 0.309970
970970 −2705.42 −0.0895524
971971 −30945.6 −1.02275 −0.511375 0.859357i 0.670864π-0.670864\pi
−0.511375 + 0.859357i 0.670864π0.670864\pi
972972 −18452.8 −0.608923
973973 16839.6 0.554832
974974 6595.75 0.216983
975975 −511.869 −0.0168132
976976 4273.72 0.140162
977977 4588.59 0.150258 0.0751290 0.997174i 0.476063π-0.476063\pi
0.0751290 + 0.997174i 0.476063π0.476063\pi
978978 −724.046 −0.0236732
979979 0 0
980980 6946.43 0.226424
981981 −29837.3 −0.971083
982982 −70.1617 −0.00227999
983983 −1752.33 −0.0568571 −0.0284285 0.999596i 0.509050π-0.509050\pi
−0.0284285 + 0.999596i 0.509050π0.509050\pi
984984 −6855.71 −0.222106
985985 26280.2 0.850108
986986 13649.9 0.440874
987987 −8436.58 −0.272076
988988 5261.17 0.169413
989989 −52253.4 −1.68004
990990 0 0
991991 −23938.4 −0.767335 −0.383668 0.923471i 0.625339π-0.625339\pi
−0.383668 + 0.923471i 0.625339π0.625339\pi
992992 7548.24 0.241589
993993 −4720.84 −0.150867
994994 4235.36 0.135148
995995 17065.4 0.543729
996996 −5375.18 −0.171003
997997 −31948.4 −1.01486 −0.507430 0.861693i 0.669404π-0.669404\pi
−0.507430 + 0.861693i 0.669404π0.669404\pi
998998 −263.598 −0.00836078
999999 −14469.9 −0.458265
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 605.4.a.t.1.7 12
11.7 odd 10 55.4.g.b.16.3 24
11.8 odd 10 55.4.g.b.31.3 yes 24
11.10 odd 2 605.4.a.p.1.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.4.g.b.16.3 24 11.7 odd 10
55.4.g.b.31.3 yes 24 11.8 odd 10
605.4.a.p.1.6 12 11.10 odd 2
605.4.a.t.1.7 12 1.1 even 1 trivial