Properties

Label 560.4.q.n.81.1
Level 560560
Weight 44
Character 560.81
Analytic conductor 33.04133.041
Analytic rank 00
Dimension 1010
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [560,4,Mod(81,560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(560, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("560.81");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 560=2457 560 = 2^{4} \cdot 5 \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 560.q (of order 33, degree 22, 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: 33.041069603233.0410696032
Analytic rank: 00
Dimension: 1010
Relative dimension: 55 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x10)\mathbb{Q}[x]/(x^{10} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x10x9+38x85x7+1102x6137x5+11161x4+10784x3+81600x2++4096 x^{10} - x^{9} + 38 x^{8} - 5 x^{7} + 1102 x^{6} - 137 x^{5} + 11161 x^{4} + 10784 x^{3} + 81600 x^{2} + \cdots + 4096 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 28 2^{8}
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 81.1
Root 1.923113.33093i1.92311 - 3.33093i of defining polynomial
Character χ\chi == 560.81
Dual form 560.4.q.n.401.1

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+(4.48397+7.76647i)q3+(2.50000+4.33013i)q5+(12.350913.8005i)q7+(26.712046.2666i)q9+(11.556020.0155i)q11+61.0473q1344.8397q15+(0.344154+0.596093i)q17+(31.6124+54.7542i)q19+(162.56334.0419i)q21+(62.2508+107.822i)q23+(12.5000+21.6506i)q25+236.970q27+104.167q29+(140.011242.506i)q31+(103.633+179.498i)q33+(28.880787.9824i)q35+(131.936+228.519i)q37+(273.735+474.122i)q39243.366q41172.541q43+(133.560231.333i)q45+(53.690792.9951i)q47+(37.9094+340.899i)q49+(3.086365.34573i)q51+(22.4043+38.8054i)q53+115.560q55566.996q57+(228.623395.986i)q59+(236.901410.324i)q61+(308.586+940.076i)q63+(152.618+264.343i)q65+(114.727+198.713i)q671116.52q69407.688q71+(174.238301.789i)q73+(112.099194.162i)q75+(418.952+87.7317i)q77+(420.068+727.579i)q79+(341.342+591.221i)q81+885.652q833.44154q85+(467.082+809.010i)q87+(428.048+741.401i)q89+(753.991842.486i)q91+(1255.61+2174.78i)q93+(158.062+273.771i)q95+189.436q971234.74q99+O(q100)q+(-4.48397 + 7.76647i) q^{3} +(2.50000 + 4.33013i) q^{5} +(-12.3509 - 13.8005i) q^{7} +(-26.7120 - 46.2666i) q^{9} +(11.5560 - 20.0155i) q^{11} +61.0473 q^{13} -44.8397 q^{15} +(-0.344154 + 0.596093i) q^{17} +(31.6124 + 54.7542i) q^{19} +(162.563 - 34.0419i) q^{21} +(62.2508 + 107.822i) q^{23} +(-12.5000 + 21.6506i) q^{25} +236.970 q^{27} +104.167 q^{29} +(140.011 - 242.506i) q^{31} +(103.633 + 179.498i) q^{33} +(28.8807 - 87.9824i) q^{35} +(131.936 + 228.519i) q^{37} +(-273.735 + 474.122i) q^{39} -243.366 q^{41} -172.541 q^{43} +(133.560 - 231.333i) q^{45} +(-53.6907 - 92.9951i) q^{47} +(-37.9094 + 340.899i) q^{49} +(-3.08636 - 5.34573i) q^{51} +(-22.4043 + 38.8054i) q^{53} +115.560 q^{55} -566.996 q^{57} +(228.623 - 395.986i) q^{59} +(-236.901 - 410.324i) q^{61} +(-308.586 + 940.076i) q^{63} +(152.618 + 264.343i) q^{65} +(-114.727 + 198.713i) q^{67} -1116.52 q^{69} -407.688 q^{71} +(174.238 - 301.789i) q^{73} +(-112.099 - 194.162i) q^{75} +(-418.952 + 87.7317i) q^{77} +(420.068 + 727.579i) q^{79} +(-341.342 + 591.221i) q^{81} +885.652 q^{83} -3.44154 q^{85} +(-467.082 + 809.010i) q^{87} +(428.048 + 741.401i) q^{89} +(-753.991 - 842.486i) q^{91} +(1255.61 + 2174.78i) q^{93} +(-158.062 + 273.771i) q^{95} +189.436 q^{97} -1234.74 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q8q3+25q5+62q781q9+47q11+2q1380q15+2q1721q19+178q21+201q23125q25+1036q27+380q29+388q31+262q33+95q35+70q99+O(q100) 10 q - 8 q^{3} + 25 q^{5} + 62 q^{7} - 81 q^{9} + 47 q^{11} + 2 q^{13} - 80 q^{15} + 2 q^{17} - 21 q^{19} + 178 q^{21} + 201 q^{23} - 125 q^{25} + 1036 q^{27} + 380 q^{29} + 388 q^{31} + 262 q^{33} + 95 q^{35}+ \cdots - 70 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/560Z)×\left(\mathbb{Z}/560\mathbb{Z}\right)^\times.

nn 241241 337337 351351 421421
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) 11 11 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 0 0
33 −4.48397 + 7.76647i −0.862941 + 1.49466i 0.00613580 + 0.999981i 0.498047π0.498047\pi
−0.869077 + 0.494677i 0.835286π0.835286\pi
44 0 0
55 2.50000 + 4.33013i 0.223607 + 0.387298i
66 0 0
77 −12.3509 13.8005i −0.666887 0.745159i
88 0 0
99 −26.7120 46.2666i −0.989335 1.71358i
1010 0 0
1111 11.5560 20.0155i 0.316751 0.548628i −0.663057 0.748569i 0.730741π-0.730741\pi
0.979808 + 0.199940i 0.0640748π0.0640748\pi
1212 0 0
1313 61.0473 1.30242 0.651211 0.758897i 0.274261π-0.274261\pi
0.651211 + 0.758897i 0.274261π0.274261\pi
1414 0 0
1515 −44.8397 −0.771838
1616 0 0
1717 −0.344154 + 0.596093i −0.00490998 + 0.00850434i −0.868470 0.495742i 0.834896π-0.834896\pi
0.863560 + 0.504246i 0.168230π0.168230\pi
1818 0 0
1919 31.6124 + 54.7542i 0.381704 + 0.661130i 0.991306 0.131577i 0.0420041π-0.0420041\pi
−0.609602 + 0.792707i 0.708671π0.708671\pi
2020 0 0
2121 162.563 34.0419i 1.68924 0.353740i
2222 0 0
2323 62.2508 + 107.822i 0.564356 + 0.977493i 0.997109 + 0.0759809i 0.0242088π0.0242088\pi
−0.432753 + 0.901512i 0.642458π0.642458\pi
2424 0 0
2525 −12.5000 + 21.6506i −0.100000 + 0.173205i
2626 0 0
2727 236.970 1.68907
2828 0 0
2929 104.167 0.667011 0.333506 0.942748i 0.391768π-0.391768\pi
0.333506 + 0.942748i 0.391768π0.391768\pi
3030 0 0
3131 140.011 242.506i 0.811185 1.40501i −0.100850 0.994902i 0.532156π-0.532156\pi
0.912035 0.410112i 0.134510π-0.134510\pi
3232 0 0
3333 103.633 + 179.498i 0.546674 + 0.946868i
3434 0 0
3535 28.8807 87.9824i 0.139478 0.424907i
3636 0 0
3737 131.936 + 228.519i 0.586219 + 1.01536i 0.994722 + 0.102604i 0.0327174π0.0327174\pi
−0.408504 + 0.912757i 0.633949π0.633949\pi
3838 0 0
3939 −273.735 + 474.122i −1.12391 + 1.94668i
4040 0 0
4141 −243.366 −0.927009 −0.463505 0.886095i 0.653408π-0.653408\pi
−0.463505 + 0.886095i 0.653408π0.653408\pi
4242 0 0
4343 −172.541 −0.611913 −0.305956 0.952046i 0.598976π-0.598976\pi
−0.305956 + 0.952046i 0.598976π0.598976\pi
4444 0 0
4545 133.560 231.333i 0.442444 0.766336i
4646 0 0
4747 −53.6907 92.9951i −0.166630 0.288611i 0.770603 0.637315i 0.219955π-0.219955\pi
−0.937233 + 0.348704i 0.886622π0.886622\pi
4848 0 0
4949 −37.9094 + 340.899i −0.110523 + 0.993874i
5050 0 0
5151 −3.08636 5.34573i −0.00847405 0.0146775i
5252 0 0
5353 −22.4043 + 38.8054i −0.0580654 + 0.100572i −0.893597 0.448870i 0.851827π-0.851827\pi
0.835532 + 0.549443i 0.185160π0.185160\pi
5454 0 0
5555 115.560 0.283310
5656 0 0
5757 −566.996 −1.31755
5858 0 0
5959 228.623 395.986i 0.504477 0.873780i −0.495509 0.868603i 0.665019π-0.665019\pi
0.999987 0.00517746i 0.00164804π-0.00164804\pi
6060 0 0
6161 −236.901 410.324i −0.497247 0.861256i 0.502748 0.864433i 0.332322π-0.332322\pi
−0.999995 + 0.00317642i 0.998989π0.998989\pi
6262 0 0
6363 −308.586 + 940.076i −0.617113 + 1.87998i
6464 0 0
6565 152.618 + 264.343i 0.291230 + 0.504426i
6666 0 0
6767 −114.727 + 198.713i −0.209196 + 0.362338i −0.951461 0.307768i 0.900418π-0.900418\pi
0.742266 + 0.670106i 0.233751π0.233751\pi
6868 0 0
6969 −1116.52 −1.94802
7070 0 0
7171 −407.688 −0.681460 −0.340730 0.940161i 0.610674π-0.610674\pi
−0.340730 + 0.940161i 0.610674π0.610674\pi
7272 0 0
7373 174.238 301.789i 0.279356 0.483859i −0.691869 0.722023i 0.743212π-0.743212\pi
0.971225 + 0.238165i 0.0765457π0.0765457\pi
7474 0 0
7575 −112.099 194.162i −0.172588 0.298932i
7676 0 0
7777 −418.952 + 87.7317i −0.620052 + 0.129844i
7878 0 0
7979 420.068 + 727.579i 0.598244 + 1.03619i 0.993080 + 0.117438i 0.0374682π0.0374682\pi
−0.394836 + 0.918752i 0.629199π0.629199\pi
8080 0 0
8181 −341.342 + 591.221i −0.468233 + 0.811003i
8282 0 0
8383 885.652 1.17124 0.585620 0.810586i 0.300851π-0.300851\pi
0.585620 + 0.810586i 0.300851π0.300851\pi
8484 0 0
8585 −3.44154 −0.00439162
8686 0 0
8787 −467.082 + 809.010i −0.575592 + 0.996954i
8888 0 0
8989 428.048 + 741.401i 0.509809 + 0.883015i 0.999935 + 0.0113636i 0.00361722π0.00361722\pi
−0.490127 + 0.871651i 0.663049π0.663049\pi
9090 0 0
9191 −753.991 842.486i −0.868569 0.970511i
9292 0 0
9393 1255.61 + 2174.78i 1.40001 + 2.42489i
9494 0 0
9595 −158.062 + 273.771i −0.170703 + 0.295666i
9696 0 0
9797 189.436 0.198292 0.0991459 0.995073i 0.468389π-0.468389\pi
0.0991459 + 0.995073i 0.468389π0.468389\pi
9898 0 0
9999 −1234.74 −1.25349
100100 0 0
101101 −397.902 + 689.186i −0.392007 + 0.678976i −0.992714 0.120493i 0.961552π-0.961552\pi
0.600707 + 0.799469i 0.294886π0.294886\pi
102102 0 0
103103 970.353 + 1680.70i 0.928269 + 1.60781i 0.786218 + 0.617950i 0.212037π0.212037\pi
0.142052 + 0.989859i 0.454630π0.454630\pi
104104 0 0
105105 553.812 + 618.812i 0.514729 + 0.575142i
106106 0 0
107107 244.344 + 423.217i 0.220763 + 0.382373i 0.955040 0.296477i 0.0958119π-0.0958119\pi
−0.734277 + 0.678850i 0.762479π0.762479\pi
108108 0 0
109109 −815.027 + 1411.67i −0.716197 + 1.24049i 0.246300 + 0.969194i 0.420785π0.420785\pi
−0.962496 + 0.271295i 0.912548π0.912548\pi
110110 0 0
111111 −2366.38 −2.02349
112112 0 0
113113 345.925 0.287981 0.143991 0.989579i 0.454007π-0.454007\pi
0.143991 + 0.989579i 0.454007π0.454007\pi
114114 0 0
115115 −311.254 + 539.108i −0.252388 + 0.437148i
116116 0 0
117117 −1630.70 2824.45i −1.28853 2.23180i
118118 0 0
119119 12.4770 2.61278i 0.00961149 0.00201272i
120120 0 0
121121 398.419 + 690.082i 0.299338 + 0.518469i
122122 0 0
123123 1091.25 1890.09i 0.799954 1.38556i
124124 0 0
125125 −125.000 −0.0894427
126126 0 0
127127 1665.24 1.16351 0.581757 0.813362i 0.302365π-0.302365\pi
0.581757 + 0.813362i 0.302365π0.302365\pi
128128 0 0
129129 773.669 1340.03i 0.528045 0.914601i
130130 0 0
131131 338.374 + 586.080i 0.225678 + 0.390886i 0.956523 0.291658i 0.0942069π-0.0942069\pi
−0.730844 + 0.682544i 0.760874π0.760874\pi
132132 0 0
133133 365.195 1112.53i 0.238094 0.725329i
134134 0 0
135135 592.425 + 1026.11i 0.377687 + 0.654174i
136136 0 0
137137 517.117 895.673i 0.322484 0.558558i −0.658516 0.752567i 0.728816π-0.728816\pi
0.981000 + 0.194008i 0.0621489π0.0621489\pi
138138 0 0
139139 −435.826 −0.265944 −0.132972 0.991120i 0.542452π-0.542452\pi
−0.132972 + 0.991120i 0.542452π0.542452\pi
140140 0 0
141141 962.992 0.575167
142142 0 0
143143 705.462 1221.90i 0.412543 0.714546i
144144 0 0
145145 260.418 + 451.056i 0.149148 + 0.258332i
146146 0 0
147147 −2477.59 1823.00i −1.39013 1.02285i
148148 0 0
149149 −1059.97 1835.93i −0.582795 1.00943i −0.995146 0.0984057i 0.968626π-0.968626\pi
0.412351 0.911025i 0.364708π-0.364708\pi
150150 0 0
151151 −1200.20 + 2078.81i −0.646827 + 1.12034i 0.337050 + 0.941487i 0.390571π0.390571\pi
−0.983876 + 0.178850i 0.942762π0.942762\pi
152152 0 0
153153 36.7723 0.0194305
154154 0 0
155155 1400.11 0.725546
156156 0 0
157157 253.094 438.372i 0.128657 0.222840i −0.794500 0.607265i 0.792267π-0.792267\pi
0.923156 + 0.384425i 0.125600π0.125600\pi
158158 0 0
159159 −200.921 348.005i −0.100214 0.173576i
160160 0 0
161161 719.140 2190.79i 0.352026 1.07241i
162162 0 0
163163 1300.47 + 2252.49i 0.624913 + 1.08238i 0.988558 + 0.150844i 0.0481991π0.0481991\pi
−0.363644 + 0.931538i 0.618468π0.618468\pi
164164 0 0
165165 −518.167 + 897.491i −0.244480 + 0.423452i
166166 0 0
167167 −546.077 −0.253034 −0.126517 0.991964i 0.540380π-0.540380\pi
−0.126517 + 0.991964i 0.540380π0.540380\pi
168168 0 0
169169 1529.78 0.696303
170170 0 0
171171 1688.86 2925.19i 0.755266 1.30816i
172172 0 0
173173 1510.16 + 2615.67i 0.663673 + 1.14951i 0.979643 + 0.200746i 0.0643365π0.0643365\pi
−0.315971 + 0.948769i 0.602330π0.602330\pi
174174 0 0
175175 453.177 94.8987i 0.195754 0.0409924i
176176 0 0
177177 2050.28 + 3551.18i 0.870668 + 1.50804i
178178 0 0
179179 999.583 1731.33i 0.417387 0.722936i −0.578288 0.815832i 0.696279π-0.696279\pi
0.995676 + 0.0928961i 0.0296125π0.0296125\pi
180180 0 0
181181 −681.145 −0.279719 −0.139859 0.990171i 0.544665π-0.544665\pi
−0.139859 + 0.990171i 0.544665π0.544665\pi
182182 0 0
183183 4249.03 1.71638
184184 0 0
185185 −659.678 + 1142.60i −0.262165 + 0.454083i
186186 0 0
187187 7.95408 + 13.7769i 0.00311048 + 0.00538751i
188188 0 0
189189 −2926.80 3270.31i −1.12642 1.25862i
190190 0 0
191191 −806.381 1396.69i −0.305485 0.529116i 0.671884 0.740656i 0.265485π-0.265485\pi
−0.977369 + 0.211541i 0.932152π0.932152\pi
192192 0 0
193193 −404.461 + 700.547i −0.150848 + 0.261277i −0.931540 0.363640i 0.881534π-0.881534\pi
0.780691 + 0.624917i 0.214867π0.214867\pi
194194 0 0
195195 −2737.35 −1.00526
196196 0 0
197197 3704.23 1.33967 0.669836 0.742509i 0.266364π-0.266364\pi
0.669836 + 0.742509i 0.266364π0.266364\pi
198198 0 0
199199 −183.964 + 318.635i −0.0655319 + 0.113505i −0.896930 0.442173i 0.854208π-0.854208\pi
0.831398 + 0.555678i 0.187541π0.187541\pi
200200 0 0
201201 −1028.87 1782.05i −0.361047 0.625353i
202202 0 0
203203 −1286.56 1437.56i −0.444821 0.497029i
204204 0 0
205205 −608.415 1053.81i −0.207286 0.359029i
206206 0 0
207207 3325.69 5760.27i 1.11667 1.93414i
208208 0 0
209209 1461.25 0.483620
210210 0 0
211211 1073.36 0.350205 0.175102 0.984550i 0.443974π-0.443974\pi
0.175102 + 0.984550i 0.443974π0.443974\pi
212212 0 0
213213 1828.06 3166.30i 0.588060 1.01855i
214214 0 0
215215 −431.352 747.124i −0.136828 0.236993i
216216 0 0
217217 −5075.98 + 1062.95i −1.58793 + 0.332524i
218218 0 0
219219 1562.55 + 2706.42i 0.482135 + 0.835083i
220220 0 0
221221 −21.0097 + 36.3899i −0.00639487 + 0.0110762i
222222 0 0
223223 1725.16 0.518050 0.259025 0.965871i 0.416599π-0.416599\pi
0.259025 + 0.965871i 0.416599π0.416599\pi
224224 0 0
225225 1335.60 0.395734
226226 0 0
227227 −1808.49 + 3132.40i −0.528784 + 0.915880i 0.470653 + 0.882318i 0.344018π0.344018\pi
−0.999437 + 0.0335619i 0.989315π0.989315\pi
228228 0 0
229229 −730.893 1265.94i −0.210912 0.365309i 0.741089 0.671407i 0.234310π-0.234310\pi
−0.952000 + 0.306098i 0.900977π0.900977\pi
230230 0 0
231231 1197.20 3647.17i 0.340997 1.03881i
232232 0 0
233233 −1067.66 1849.24i −0.300192 0.519947i 0.675988 0.736913i 0.263717π-0.263717\pi
−0.976179 + 0.216966i 0.930384π0.930384\pi
234234 0 0
235235 268.454 464.976i 0.0745191 0.129071i
236236 0 0
237237 −7534.29 −2.06500
238238 0 0
239239 −5952.35 −1.61099 −0.805493 0.592605i 0.798100π-0.798100\pi
−0.805493 + 0.592605i 0.798100π0.798100\pi
240240 0 0
241241 1923.78 3332.08i 0.514197 0.890615i −0.485668 0.874144i 0.661423π-0.661423\pi
0.999864 0.0164713i 0.00524321π-0.00524321\pi
242242 0 0
243243 137.960 + 238.954i 0.0364203 + 0.0630819i
244244 0 0
245245 −1570.91 + 688.094i −0.409639 + 0.179432i
246246 0 0
247247 1929.85 + 3342.60i 0.497139 + 0.861071i
248248 0 0
249249 −3971.24 + 6878.39i −1.01071 + 1.75060i
250250 0 0
251251 1731.69 0.435470 0.217735 0.976008i 0.430133π-0.430133\pi
0.217735 + 0.976008i 0.430133π0.430133\pi
252252 0 0
253253 2877.47 0.715041
254254 0 0
255255 15.4318 26.7287i 0.00378971 0.00656397i
256256 0 0
257257 2027.21 + 3511.24i 0.492039 + 0.852237i 0.999958 0.00916808i 0.00291833π-0.00291833\pi
−0.507919 + 0.861405i 0.669585π0.669585\pi
258258 0 0
259259 1524.16 4643.21i 0.365663 1.11396i
260260 0 0
261261 −2782.51 4819.46i −0.659898 1.14298i
262262 0 0
263263 −3167.91 + 5486.98i −0.742744 + 1.28647i 0.208498 + 0.978023i 0.433143π0.433143\pi
−0.951242 + 0.308447i 0.900191π0.900191\pi
264264 0 0
265265 −224.043 −0.0519353
266266 0 0
267267 −7677.42 −1.75974
268268 0 0
269269 660.817 1144.57i 0.149780 0.259426i −0.781366 0.624073i 0.785477π-0.785477\pi
0.931146 + 0.364647i 0.118810π0.118810\pi
270270 0 0
271271 −1168.00 2023.04i −0.261812 0.453471i 0.704912 0.709295i 0.250987π-0.250987\pi
−0.966723 + 0.255824i 0.917653π0.917653\pi
272272 0 0
273273 9924.02 2078.16i 2.20011 0.460719i
274274 0 0
275275 288.899 + 500.388i 0.0633501 + 0.109726i
276276 0 0
277277 3542.61 6135.99i 0.768430 1.33096i −0.169984 0.985447i 0.554372π-0.554372\pi
0.938414 0.345513i 0.112295π-0.112295\pi
278278 0 0
279279 −14959.9 −3.21013
280280 0 0
281281 2123.17 0.450738 0.225369 0.974273i 0.427641π-0.427641\pi
0.225369 + 0.974273i 0.427641π0.427641\pi
282282 0 0
283283 2945.82 5102.30i 0.618765 1.07173i −0.370946 0.928654i 0.620967π-0.620967\pi
0.989711 0.143078i 0.0457001π-0.0457001\pi
284284 0 0
285285 −1417.49 2455.16i −0.294613 0.510286i
286286 0 0
287287 3005.79 + 3358.58i 0.618210 + 0.690769i
288288 0 0
289289 2456.26 + 4254.37i 0.499952 + 0.865942i
290290 0 0
291291 −849.426 + 1471.25i −0.171114 + 0.296378i
292292 0 0
293293 −8137.75 −1.62257 −0.811284 0.584652i 0.801231π-0.801231\pi
−0.811284 + 0.584652i 0.801231π0.801231\pi
294294 0 0
295295 2286.23 0.451218
296296 0 0
297297 2738.42 4743.08i 0.535014 0.926671i
298298 0 0
299299 3800.25 + 6582.22i 0.735030 + 1.27311i
300300 0 0
301301 2131.04 + 2381.16i 0.408077 + 0.455972i
302302 0 0
303303 −3568.36 6180.58i −0.676558 1.17183i
304304 0 0
305305 1184.50 2051.62i 0.222375 0.385166i
306306 0 0
307307 4797.24 0.891833 0.445917 0.895075i 0.352878π-0.352878\pi
0.445917 + 0.895075i 0.352878π0.352878\pi
308308 0 0
309309 −17404.1 −3.20417
310310 0 0
311311 2594.76 4494.26i 0.473105 0.819442i −0.526421 0.850224i 0.676467π-0.676467\pi
0.999526 + 0.0307823i 0.00979987π0.00979987\pi
312312 0 0
313313 1122.62 + 1944.44i 0.202729 + 0.351138i 0.949407 0.314049i 0.101686π-0.101686\pi
−0.746678 + 0.665186i 0.768352π0.768352\pi
314314 0 0
315315 −4842.11 + 1013.98i −0.866102 + 0.181368i
316316 0 0
317317 4871.13 + 8437.05i 0.863060 + 1.49486i 0.868961 + 0.494881i 0.164788π0.164788\pi
−0.00590040 + 0.999983i 0.501878π0.501878\pi
318318 0 0
319319 1203.75 2084.96i 0.211276 0.365941i
320320 0 0
321321 −4382.53 −0.762022
322322 0 0
323323 −43.5181 −0.00749663
324324 0 0
325325 −763.092 + 1321.71i −0.130242 + 0.225586i
326326 0 0
327327 −7309.12 12659.8i −1.23607 2.14094i
328328 0 0
329329 −620.252 + 1889.54i −0.103938 + 0.316637i
330330 0 0
331331 5665.38 + 9812.73i 0.940778 + 1.62948i 0.763992 + 0.645226i 0.223237π0.223237\pi
0.176786 + 0.984249i 0.443430π0.443430\pi
332332 0 0
333333 7048.54 12208.4i 1.15993 2.00906i
334334 0 0
335335 −1147.27 −0.187110
336336 0 0
337337 3637.35 0.587950 0.293975 0.955813i 0.405022π-0.405022\pi
0.293975 + 0.955813i 0.405022π0.405022\pi
338338 0 0
339339 −1551.12 + 2686.61i −0.248511 + 0.430433i
340340 0 0
341341 −3235.93 5604.79i −0.513887 0.890078i
342342 0 0
343343 5172.80 3687.24i 0.814300 0.580444i
344344 0 0
345345 −2791.31 4834.69i −0.435591 0.754467i
346346 0 0
347347 −2015.06 + 3490.19i −0.311741 + 0.539951i −0.978739 0.205108i 0.934245π-0.934245\pi
0.666998 + 0.745059i 0.267579π0.267579\pi
348348 0 0
349349 2887.69 0.442906 0.221453 0.975171i 0.428920π-0.428920\pi
0.221453 + 0.975171i 0.428920π0.428920\pi
350350 0 0
351351 14466.4 2.19988
352352 0 0
353353 262.459 454.592i 0.0395731 0.0685425i −0.845561 0.533880i 0.820734π-0.820734\pi
0.885134 + 0.465337i 0.154067π0.154067\pi
354354 0 0
355355 −1019.22 1765.34i −0.152379 0.263928i
356356 0 0
357357 −35.6545 + 108.618i −0.00528582 + 0.0161027i
358358 0 0
359359 −1642.66 2845.17i −0.241493 0.418279i 0.719646 0.694341i 0.244304π-0.244304\pi
−0.961140 + 0.276062i 0.910971π0.910971\pi
360360 0 0
361361 1430.82 2478.25i 0.208605 0.361314i
362362 0 0
363363 −7146.00 −1.03324
364364 0 0
365365 1742.38 0.249864
366366 0 0
367367 4526.98 7840.95i 0.643886 1.11524i −0.340671 0.940182i 0.610654π-0.610654\pi
0.984558 0.175061i 0.0560123π-0.0560123\pi
368368 0 0
369369 6500.80 + 11259.7i 0.917122 + 1.58850i
370370 0 0
371371 812.249 170.091i 0.113665 0.0238024i
372372 0 0
373373 2604.55 + 4511.22i 0.361551 + 0.626225i 0.988216 0.153064i 0.0489139π-0.0489139\pi
−0.626665 + 0.779289i 0.715581π0.715581\pi
374374 0 0
375375 560.497 970.809i 0.0771838 0.133686i
376376 0 0
377377 6359.12 0.868730
378378 0 0
379379 −3200.68 −0.433794 −0.216897 0.976194i 0.569594π-0.569594\pi
−0.216897 + 0.976194i 0.569594π0.569594\pi
380380 0 0
381381 −7466.90 + 12933.1i −1.00404 + 1.73906i
382382 0 0
383383 −1101.40 1907.69i −0.146943 0.254513i 0.783153 0.621829i 0.213610π-0.213610\pi
−0.930096 + 0.367316i 0.880277π0.880277\pi
384384 0 0
385385 −1427.27 1594.79i −0.188936 0.211111i
386386 0 0
387387 4608.92 + 7982.89i 0.605387 + 1.04856i
388388 0 0
389389 3120.79 5405.38i 0.406762 0.704533i −0.587762 0.809034i 0.699991π-0.699991\pi
0.994525 + 0.104500i 0.0333244π0.0333244\pi
390390 0 0
391391 −85.6955 −0.0110839
392392 0 0
393393 −6069.04 −0.778988
394394 0 0
395395 −2100.34 + 3637.89i −0.267543 + 0.463398i
396396 0 0
397397 −5203.58 9012.87i −0.657834 1.13940i −0.981175 0.193120i 0.938139π-0.938139\pi
0.323341 0.946283i 0.395194π-0.395194\pi
398398 0 0
399399 7002.92 + 7824.84i 0.878658 + 0.981785i
400400 0 0
401401 7486.63 + 12967.2i 0.932330 + 1.61484i 0.779327 + 0.626618i 0.215561π0.215561\pi
0.153003 + 0.988226i 0.451105π0.451105\pi
402402 0 0
403403 8547.30 14804.4i 1.05651 1.82992i
404404 0 0
405405 −3413.42 −0.418800
406406 0 0
407407 6098.58 0.742741
408408 0 0
409409 3529.55 6113.36i 0.426711 0.739086i −0.569867 0.821737i 0.693005π-0.693005\pi
0.996579 + 0.0826512i 0.0263387π0.0263387\pi
410410 0 0
411411 4637.48 + 8032.35i 0.556569 + 0.964006i
412412 0 0
413413 −8288.52 + 1735.68i −0.987534 + 0.206797i
414414 0 0
415415 2214.13 + 3834.99i 0.261897 + 0.453619i
416416 0 0
417417 1954.23 3384.83i 0.229494 0.397496i
418418 0 0
419419 −928.543 −0.108263 −0.0541316 0.998534i 0.517239π-0.517239\pi
−0.0541316 + 0.998534i 0.517239π0.517239\pi
420420 0 0
421421 7105.06 0.822517 0.411258 0.911519i 0.365089π-0.365089\pi
0.411258 + 0.911519i 0.365089π0.365089\pi
422422 0 0
423423 −2868.38 + 4968.18i −0.329705 + 0.571066i
424424 0 0
425425 −8.60386 14.9023i −0.000981996 0.00170087i
426426 0 0
427427 −2736.75 + 8337.24i −0.310165 + 0.944888i
428428 0 0
429429 6326.54 + 10957.9i 0.712001 + 1.23322i
430430 0 0
431431 −2159.64 + 3740.60i −0.241360 + 0.418047i −0.961102 0.276194i 0.910927π-0.910927\pi
0.719742 + 0.694241i 0.244260π0.244260\pi
432432 0 0
433433 4600.60 0.510602 0.255301 0.966862i 0.417825π-0.417825\pi
0.255301 + 0.966862i 0.417825π0.417825\pi
434434 0 0
435435 −4670.82 −0.514825
436436 0 0
437437 −3935.79 + 6816.99i −0.430834 + 0.746226i
438438 0 0
439439 961.868 + 1666.00i 0.104573 + 0.181125i 0.913564 0.406696i 0.133319π-0.133319\pi
−0.808991 + 0.587821i 0.799986π0.799986\pi
440440 0 0
441441 16784.9 7352.16i 1.81242 0.793884i
442442 0 0
443443 −2267.44 3927.32i −0.243181 0.421202i 0.718438 0.695591i 0.244858π-0.244858\pi
−0.961619 + 0.274390i 0.911524π0.911524\pi
444444 0 0
445445 −2140.24 + 3707.00i −0.227993 + 0.394896i
446446 0 0
447447 19011.6 2.01167
448448 0 0
449449 −17431.9 −1.83221 −0.916105 0.400937i 0.868684π-0.868684\pi
−0.916105 + 0.400937i 0.868684π0.868684\pi
450450 0 0
451451 −2812.33 + 4871.10i −0.293631 + 0.508583i
452452 0 0
453453 −10763.3 18642.6i −1.11635 1.93357i
454454 0 0
455455 1763.09 5371.09i 0.181660 0.553408i
456456 0 0
457457 981.162 + 1699.42i 0.100431 + 0.173951i 0.911862 0.410496i 0.134645π-0.134645\pi
−0.811431 + 0.584448i 0.801311π0.801311\pi
458458 0 0
459459 −81.5542 + 141.256i −0.00829330 + 0.0143644i
460460 0 0
461461 14344.4 1.44920 0.724602 0.689167i 0.242024π-0.242024\pi
0.724602 + 0.689167i 0.242024π0.242024\pi
462462 0 0
463463 −11657.8 −1.17016 −0.585081 0.810975i 0.698937π-0.698937\pi
−0.585081 + 0.810975i 0.698937π0.698937\pi
464464 0 0
465465 −6278.06 + 10873.9i −0.626103 + 1.08444i
466466 0 0
467467 −8256.88 14301.3i −0.818164 1.41710i −0.907033 0.421059i 0.861659π-0.861659\pi
0.0888691 0.996043i 0.471675π-0.471675\pi
468468 0 0
469469 4159.33 870.995i 0.409509 0.0857544i
470470 0 0
471471 2269.73 + 3931.30i 0.222046 + 0.384596i
472472 0 0
473473 −1993.88 + 3453.50i −0.193824 + 0.335713i
474474 0 0
475475 −1580.62 −0.152681
476476 0 0
477477 2393.86 0.229785
478478 0 0
479479 −7810.03 + 13527.4i −0.744988 + 1.29036i 0.205212 + 0.978718i 0.434212π0.434212\pi
−0.950200 + 0.311640i 0.899122π0.899122\pi
480480 0 0
481481 8054.32 + 13950.5i 0.763504 + 1.32243i
482482 0 0
483483 13790.1 + 15408.6i 1.29911 + 1.45159i
484484 0 0
485485 473.590 + 820.282i 0.0443394 + 0.0767981i
486486 0 0
487487 950.691 1646.65i 0.0884598 0.153217i −0.818400 0.574648i 0.805139π-0.805139\pi
0.906860 + 0.421431i 0.138472π0.138472\pi
488488 0 0
489489 −23325.1 −2.15705
490490 0 0
491491 15964.1 1.46731 0.733654 0.679524i 0.237814π-0.237814\pi
0.733654 + 0.679524i 0.237814π0.237814\pi
492492 0 0
493493 −35.8495 + 62.0932i −0.00327501 + 0.00567249i
494494 0 0
495495 −3086.84 5346.56i −0.280289 0.485475i
496496 0 0
497497 5035.33 + 5626.31i 0.454457 + 0.507796i
498498 0 0
499499 −3424.59 5931.56i −0.307226 0.532130i 0.670529 0.741884i 0.266067π-0.266067\pi
−0.977754 + 0.209753i 0.932734π0.932734\pi
500500 0 0
501501 2448.59 4241.09i 0.218354 0.378199i
502502 0 0
503503 766.190 0.0679179 0.0339590 0.999423i 0.489188π-0.489188\pi
0.0339590 + 0.999423i 0.489188π0.489188\pi
504504 0 0
505505 −3979.02 −0.350621
506506 0 0
507507 −6859.49 + 11881.0i −0.600869 + 1.04074i
508508 0 0
509509 −6802.36 11782.0i −0.592356 1.02599i −0.993914 0.110157i 0.964865π-0.964865\pi
0.401558 0.915834i 0.368469π-0.368469\pi
510510 0 0
511511 −6316.84 + 1322.79i −0.546850 + 0.114515i
512512 0 0
513513 7491.18 + 12975.1i 0.644724 + 1.11669i
514514 0 0
515515 −4851.76 + 8403.50i −0.415135 + 0.719034i
516516 0 0
517517 −2481.80 −0.211120
518518 0 0
519519 −27086.1 −2.29084
520520 0 0
521521 −9214.16 + 15959.4i −0.774817 + 1.34202i 0.160080 + 0.987104i 0.448825π0.448825\pi
−0.934897 + 0.354919i 0.884509π0.884509\pi
522522 0 0
523523 2170.06 + 3758.66i 0.181435 + 0.314254i 0.942369 0.334575i 0.108593π-0.108593\pi
−0.760935 + 0.648828i 0.775259π0.775259\pi
524524 0 0
525525 −1295.01 + 3945.11i −0.107655 + 0.327959i
526526 0 0
527527 96.3708 + 166.919i 0.00796581 + 0.0137972i
528528 0 0
529529 −1666.82 + 2887.03i −0.136996 + 0.237283i
530530 0 0
531531 −24427.9 −1.99639
532532 0 0
533533 −14856.8 −1.20736
534534 0 0
535535 −1221.72 + 2116.08i −0.0987282 + 0.171002i
536536 0 0
537537 8964.21 + 15526.5i 0.720362 + 1.24770i
538538 0 0
539539 6385.19 + 4698.19i 0.510259 + 0.375446i
540540 0 0
541541 −6308.12 10926.0i −0.501308 0.868290i −0.999999 0.00151060i 0.999519π-0.999519\pi
0.498691 0.866780i 0.333814π-0.333814\pi
542542 0 0
543543 3054.24 5290.09i 0.241381 0.418084i
544544 0 0
545545 −8150.27 −0.640586
546546 0 0
547547 −20677.8 −1.61630 −0.808151 0.588975i 0.799532π-0.799532\pi
−0.808151 + 0.588975i 0.799532π0.799532\pi
548548 0 0
549549 −12656.2 + 21921.2i −0.983887 + 1.70414i
550550 0 0
551551 3292.96 + 5703.58i 0.254601 + 0.440981i
552552 0 0
553553 4852.75 14783.4i 0.373164 1.13681i
554554 0 0
555555 −5915.96 10246.7i −0.452466 0.783694i
556556 0 0
557557 507.586 879.164i 0.0386124 0.0668786i −0.846073 0.533066i 0.821040π-0.821040\pi
0.884686 + 0.466188i 0.154373π0.154373\pi
558558 0 0
559559 −10533.2 −0.796969
560560 0 0
561561 −142.664 −0.0107366
562562 0 0
563563 2648.32 4587.03i 0.198248 0.343375i −0.749713 0.661763i 0.769808π-0.769808\pi
0.947960 + 0.318388i 0.103142π0.103142\pi
564564 0 0
565565 864.812 + 1497.90i 0.0643945 + 0.111535i
566566 0 0
567567 12375.0 2591.43i 0.916584 0.191940i
568568 0 0
569569 −7370.61 12766.3i −0.543044 0.940580i −0.998727 0.0504381i 0.983938π-0.983938\pi
0.455683 0.890142i 0.349395π-0.349395\pi
570570 0 0
571571 6830.70 11831.1i 0.500624 0.867105i −0.499376 0.866385i 0.666437π-0.666437\pi
1.00000 0.000720144i 0.000229229π-0.000229229\pi
572572 0 0
573573 14463.2 1.05446
574574 0 0
575575 −3112.54 −0.225742
576576 0 0
577577 −539.307 + 934.107i −0.0389110 + 0.0673958i −0.884825 0.465923i 0.845722π-0.845722\pi
0.845914 + 0.533319i 0.179056π0.179056\pi
578578 0 0
579579 −3627.18 6282.46i −0.260346 0.450933i
580580 0 0
581581 −10938.6 12222.5i −0.781085 0.872760i
582582 0 0
583583 517.807 + 896.868i 0.0367845 + 0.0637126i
584584 0 0
585585 8153.50 14122.3i 0.576249 0.998092i
586586 0 0
587587 −3863.36 −0.271649 −0.135824 0.990733i 0.543368π-0.543368\pi
−0.135824 + 0.990733i 0.543368π0.543368\pi
588588 0 0
589589 17704.3 1.23853
590590 0 0
591591 −16609.7 + 28768.8i −1.15606 + 2.00235i
592592 0 0
593593 4720.41 + 8175.98i 0.326887 + 0.566185i 0.981892 0.189439i 0.0606671π-0.0606671\pi
−0.655006 + 0.755624i 0.727334π0.727334\pi
594594 0 0
595595 42.5062 + 47.4951i 0.00292872 + 0.00327246i
596596 0 0
597597 −1649.78 2857.50i −0.113100 0.195896i
598598 0 0
599599 −10684.5 + 18506.0i −0.728807 + 1.26233i 0.228581 + 0.973525i 0.426592π0.426592\pi
−0.957388 + 0.288806i 0.906742π0.906742\pi
600600 0 0
601601 5801.37 0.393748 0.196874 0.980429i 0.436921π-0.436921\pi
0.196874 + 0.980429i 0.436921π0.436921\pi
602602 0 0
603603 12258.4 0.827859
604604 0 0
605605 −1992.09 + 3450.41i −0.133868 + 0.231866i
606606 0 0
607607 13370.0 + 23157.5i 0.894023 + 1.54849i 0.835009 + 0.550236i 0.185462π0.185462\pi
0.0590141 + 0.998257i 0.481204π0.481204\pi
608608 0 0
609609 16933.7 3546.04i 1.12674 0.235949i
610610 0 0
611611 −3277.68 5677.10i −0.217022 0.375894i
612612 0 0
613613 4169.87 7222.43i 0.274746 0.475875i −0.695325 0.718696i 0.744739π-0.744739\pi
0.970071 + 0.242821i 0.0780728π0.0780728\pi
614614 0 0
615615 10912.5 0.715501
616616 0 0
617617 −26639.2 −1.73818 −0.869088 0.494658i 0.835293π-0.835293\pi
−0.869088 + 0.494658i 0.835293π0.835293\pi
618618 0 0
619619 13930.2 24127.7i 0.904523 1.56668i 0.0829678 0.996552i 0.473560π-0.473560\pi
0.821556 0.570128i 0.193107π-0.193107\pi
620620 0 0
621621 14751.6 + 25550.5i 0.953237 + 1.65105i
622622 0 0
623623 4944.94 15064.3i 0.318001 0.968760i
624624 0 0
625625 −312.500 541.266i −0.0200000 0.0346410i
626626 0 0
627627 −6552.19 + 11348.7i −0.417335 + 0.722846i
628628 0 0
629629 −181.625 −0.0115133
630630 0 0
631631 10886.7 0.686833 0.343417 0.939183i 0.388416π-0.388416\pi
0.343417 + 0.939183i 0.388416π0.388416\pi
632632 0 0
633633 −4812.92 + 8336.23i −0.302206 + 0.523437i
634634 0 0
635635 4163.11 + 7210.71i 0.260170 + 0.450627i
636636 0 0
637637 −2314.27 + 20811.0i −0.143948 + 1.29444i
638638 0 0
639639 10890.2 + 18862.4i 0.674193 + 1.16774i
640640 0 0
641641 8425.73 14593.8i 0.519183 0.899251i −0.480568 0.876957i 0.659570π-0.659570\pi
0.999751 0.0222942i 0.00709704π-0.00709704\pi
642642 0 0
643643 −4793.72 −0.294006 −0.147003 0.989136i 0.546963π-0.546963\pi
−0.147003 + 0.989136i 0.546963π0.546963\pi
644644 0 0
645645 7736.69 0.472298
646646 0 0
647647 −13342.3 + 23109.5i −0.810725 + 1.40422i 0.101633 + 0.994822i 0.467593π0.467593\pi
−0.912358 + 0.409394i 0.865740π0.865740\pi
648648 0 0
649649 −5283.92 9152.01i −0.319587 0.553541i
650650 0 0
651651 14505.2 44188.7i 0.873278 2.66036i
652652 0 0
653653 −8770.94 15191.7i −0.525625 0.910409i −0.999554 0.0298466i 0.990498π-0.990498\pi
0.473929 0.880563i 0.342835π-0.342835\pi
654654 0 0
655655 −1691.87 + 2930.40i −0.100926 + 0.174810i
656656 0 0
657657 −18617.0 −1.10551
658658 0 0
659659 26285.3 1.55377 0.776883 0.629645i 0.216800π-0.216800\pi
0.776883 + 0.629645i 0.216800π0.216800\pi
660660 0 0
661661 −12522.1 + 21689.0i −0.736845 + 1.27625i 0.217064 + 0.976157i 0.430352π0.430352\pi
−0.953909 + 0.300096i 0.902981π0.902981\pi
662662 0 0
663663 −188.414 326.343i −0.0110368 0.0191163i
664664 0 0
665665 5730.39 1199.99i 0.334158 0.0699753i
666666 0 0
667667 6484.48 + 11231.4i 0.376432 + 0.651999i
668668 0 0
669669 −7735.57 + 13398.4i −0.447047 + 0.774308i
670670 0 0
671671 −10950.5 −0.630013
672672 0 0
673673 20799.4 1.19132 0.595658 0.803238i 0.296891π-0.296891\pi
0.595658 + 0.803238i 0.296891π0.296891\pi
674674 0 0
675675 −2962.12 + 5130.55i −0.168907 + 0.292555i
676676 0 0
677677 −14886.3 25783.8i −0.845089 1.46374i −0.885543 0.464556i 0.846214π-0.846214\pi
0.0404540 0.999181i 0.487120π-0.487120\pi
678678 0 0
679679 −2339.71 2614.32i −0.132238 0.147759i
680680 0 0
681681 −16218.5 28091.2i −0.912619 1.58070i
682682 0 0
683683 11945.2 20689.6i 0.669208 1.15910i −0.308918 0.951089i 0.599967π-0.599967\pi
0.978126 0.208014i 0.0666999π-0.0666999\pi
684684 0 0
685685 5171.17 0.288438
686686 0 0
687687 13109.2 0.728017
688688 0 0
689689 −1367.72 + 2368.97i −0.0756257 + 0.130987i
690690 0 0
691691 −12648.8 21908.3i −0.696356 1.20612i −0.969721 0.244214i 0.921470π-0.921470\pi
0.273365 0.961910i 0.411863π-0.411863\pi
692692 0 0
693693 15250.1 + 17040.0i 0.835937 + 0.934049i
694694 0 0
695695 −1089.56 1887.18i −0.0594670 0.103000i
696696 0 0
697697 83.7554 145.069i 0.00455160 0.00788360i
698698 0 0
699699 19149.4 1.03619
700700 0 0
701701 18659.1 1.00534 0.502670 0.864478i 0.332351π-0.332351\pi
0.502670 + 0.864478i 0.332351π0.332351\pi
702702 0 0
703703 −8341.59 + 14448.1i −0.447524 + 0.775134i
704704 0 0
705705 2407.48 + 4169.88i 0.128611 + 0.222761i
706706 0 0
707707 14425.6 3020.83i 0.767369 0.160693i
708708 0 0
709709 12847.4 + 22252.3i 0.680528 + 1.17871i 0.974820 + 0.222993i 0.0715828π0.0715828\pi
−0.294292 + 0.955715i 0.595084π0.595084\pi
710710 0 0
711711 22441.7 38870.2i 1.18373 2.05028i
712712 0 0
713713 34863.2 1.83119
714714 0 0
715715 7054.62 0.368990
716716 0 0
717717 26690.2 46228.8i 1.39019 2.40787i
718718 0 0
719719 −13627.3 23603.2i −0.706834 1.22427i −0.966025 0.258447i 0.916789π-0.916789\pi
0.259191 0.965826i 0.416544π-0.416544\pi
720720 0 0
721721 11209.8 34149.6i 0.579022 1.76394i
722722 0 0
723723 17252.3 + 29881.9i 0.887443 + 1.53710i
724724 0 0
725725 −1302.09 + 2255.28i −0.0667011 + 0.115530i
726726 0 0
727727 13194.3 0.673110 0.336555 0.941664i 0.390738π-0.390738\pi
0.336555 + 0.941664i 0.390738π0.390738\pi
728728 0 0
729729 −20906.9 −1.06218
730730 0 0
731731 59.3807 102.850i 0.00300448 0.00520391i
732732 0 0
733733 −2904.47 5030.70i −0.146356 0.253497i 0.783522 0.621364i 0.213421π-0.213421\pi
−0.929878 + 0.367868i 0.880088π0.880088\pi
734734 0 0
735735 1699.85 15285.8i 0.0853059 0.767109i
736736 0 0
737737 2651.56 + 4592.64i 0.132526 + 0.229542i
738738 0 0
739739 6968.34 12069.5i 0.346867 0.600791i −0.638824 0.769353i 0.720579π-0.720579\pi
0.985691 + 0.168562i 0.0539122π0.0539122\pi
740740 0 0
741741 −34613.6 −1.71601
742742 0 0
743743 −32424.2 −1.60098 −0.800489 0.599347i 0.795427π-0.795427\pi
−0.800489 + 0.599347i 0.795427π0.795427\pi
744744 0 0
745745 5299.87 9179.65i 0.260634 0.451431i
746746 0 0
747747 −23657.6 40976.1i −1.15875 2.00701i
748748 0 0
749749 2822.74 8599.19i 0.137704 0.419503i
750750 0 0
751751 −17644.2 30560.6i −0.857316 1.48491i −0.874480 0.485062i 0.838797π-0.838797\pi
0.0171639 0.999853i 0.494536π-0.494536\pi
752752 0 0
753753 −7764.83 + 13449.1i −0.375785 + 0.650879i
754754 0 0
755755 −12002.0 −0.578539
756756 0 0
757757 2079.86 0.0998595 0.0499298 0.998753i 0.484100π-0.484100\pi
0.0499298 + 0.998753i 0.484100π0.484100\pi
758758 0 0
759759 −12902.5 + 22347.8i −0.617038 + 1.06874i
760760 0 0
761761 −6125.72 10610.1i −0.291797 0.505407i 0.682438 0.730944i 0.260920π-0.260920\pi
−0.974235 + 0.225537i 0.927586π0.927586\pi
762762 0 0
763763 29548.1 6187.60i 1.40198 0.293586i
764764 0 0
765765 91.9307 + 159.229i 0.00434479 + 0.00752539i
766766 0 0
767767 13956.8 24173.9i 0.657042 1.13803i
768768 0 0
769769 4335.87 0.203323 0.101661 0.994819i 0.467584π-0.467584\pi
0.101661 + 0.994819i 0.467584π0.467584\pi
770770 0 0
771771 −36359.9 −1.69840
772772 0 0
773773 −15199.7 + 26326.7i −0.707240 + 1.22498i 0.258637 + 0.965975i 0.416727π0.416727\pi
−0.965877 + 0.259001i 0.916607π0.916607\pi
774774 0 0
775775 3500.28 + 6062.66i 0.162237 + 0.281003i
776776 0 0
777777 29227.0 + 32657.4i 1.34944 + 1.50782i
778778 0 0
779779 −7693.37 13325.3i −0.353843 0.612874i
780780 0 0
781781 −4711.23 + 8160.10i −0.215853 + 0.373868i
782782 0 0
783783 24684.4 1.12663
784784 0 0
785785 2530.94 0.115074
786786 0 0
787787 17637.1 30548.4i 0.798850 1.38365i −0.121515 0.992590i 0.538775π-0.538775\pi
0.920365 0.391059i 0.127891π-0.127891\pi
788788 0 0
789789 −28409.6 49206.9i −1.28189 2.22030i
790790 0 0
791791 −4272.49 4773.94i −0.192051 0.214592i
792792 0 0
793793 −14462.2 25049.2i −0.647625 1.12172i
794794 0 0
795795 1004.60 1740.02i 0.0448171 0.0776255i
796796 0 0
797797 −27524.0 −1.22328 −0.611638 0.791138i 0.709489π-0.709489\pi
−0.611638 + 0.791138i 0.709489π0.709489\pi
798798 0 0
799799 73.9116 0.00327260
800800 0 0
801801 22868.1 39608.7i 1.00874 1.74720i
802802 0 0
803803 −4026.97 6974.92i −0.176972 0.306525i
804804 0 0
805805 11284.2 2363.01i 0.494059 0.103460i
806806 0 0
807807 5926.17 + 10264.4i 0.258502 + 0.447739i
808808 0 0
809809 3533.68 6120.51i 0.153569 0.265990i −0.778968 0.627064i 0.784257π-0.784257\pi
0.932537 + 0.361074i 0.117590π0.117590\pi
810810 0 0
811811 37757.5 1.63483 0.817413 0.576052i 0.195407π-0.195407\pi
0.817413 + 0.576052i 0.195407π0.195407\pi
812812 0 0
813813 20949.1 0.903713
814814 0 0
815815 −6502.36 + 11262.4i −0.279470 + 0.484056i
816816 0 0
817817 −5454.43 9447.34i −0.233569 0.404554i
818818 0 0
819819 −18838.3 + 57389.1i −0.803742 + 2.44852i
820820 0 0
821821 12653.7 + 21916.9i 0.537902 + 0.931673i 0.999017 + 0.0443325i 0.0141161π0.0141161\pi
−0.461115 + 0.887340i 0.652551π0.652551\pi
822822 0 0
823823 −12742.4 + 22070.5i −0.539699 + 0.934786i 0.459221 + 0.888322i 0.348129π0.348129\pi
−0.998920 + 0.0464643i 0.985205π0.985205\pi
824824 0 0
825825 −5181.67 −0.218670
826826 0 0
827827 −34985.7 −1.47107 −0.735534 0.677488i 0.763069π-0.763069\pi
−0.735534 + 0.677488i 0.763069π0.763069\pi
828828 0 0
829829 −1949.04 + 3375.84i −0.0816564 + 0.141433i −0.903962 0.427614i 0.859354π-0.859354\pi
0.822305 + 0.569047i 0.192688π0.192688\pi
830830 0 0
831831 31770.0 + 55027.2i 1.32622 + 2.29708i
832832 0 0
833833 −190.161 139.919i −0.00790957 0.00581983i
834834 0 0
835835 −1365.19 2364.58i −0.0565802 0.0979997i
836836 0 0
837837 33178.4 57466.7i 1.37015 2.37317i
838838 0 0
839839 −22118.8 −0.910161 −0.455081 0.890450i 0.650390π-0.650390\pi
−0.455081 + 0.890450i 0.650390π0.650390\pi
840840 0 0
841841 −13538.2 −0.555096
842842 0 0
843843 −9520.22 + 16489.5i −0.388961 + 0.673699i
844844 0 0
845845 3824.45 + 6624.13i 0.155698 + 0.269677i
846846 0 0
847847 4602.65 14021.5i 0.186717 0.568814i
848848 0 0
849849 26417.9 + 45757.2i 1.06792 + 1.84968i
850850 0 0
851851 −16426.2 + 28451.0i −0.661672 + 1.14605i
852852 0 0
853853 33152.4 1.33074 0.665368 0.746516i 0.268275π-0.268275\pi
0.665368 + 0.746516i 0.268275π0.268275\pi
854854 0 0
855855 16888.6 0.675530
856856 0 0
857857 5173.12 8960.11i 0.206197 0.357143i −0.744317 0.667827i 0.767225π-0.767225\pi
0.950513 + 0.310684i 0.100558π0.100558\pi
858858 0 0
859859 −5952.82 10310.6i −0.236447 0.409538i 0.723245 0.690591i 0.242650π-0.242650\pi
−0.959692 + 0.281053i 0.909316π0.909316\pi
860860 0 0
861861 −39562.2 + 8284.63i −1.56594 + 0.327920i
862862 0 0
863863 15401.2 + 26675.6i 0.607487 + 1.05220i 0.991653 + 0.128935i 0.0411558π0.0411558\pi
−0.384166 + 0.923264i 0.625511π0.625511\pi
864864 0 0
865865 −7550.80 + 13078.4i −0.296803 + 0.514079i
866866 0 0
867867 −44055.3 −1.72572
868868 0 0
869869 19417.2 0.757977
870870 0 0
871871 −7003.77 + 12130.9i −0.272461 + 0.471917i
872872 0 0
873873 −5060.22 8764.56i −0.196177 0.339789i
874874 0 0
875875 1543.87 + 1725.07i 0.0596482 + 0.0666490i
876876 0 0
877877 10846.6 + 18786.9i 0.417634 + 0.723363i 0.995701 0.0926262i 0.0295262π-0.0295262\pi
−0.578067 + 0.815989i 0.696193π0.696193\pi
878878 0 0
879879 36489.5 63201.6i 1.40018 2.42518i
880880 0 0
881881 −29963.1 −1.14584 −0.572918 0.819612i 0.694189π-0.694189\pi
−0.572918 + 0.819612i 0.694189π0.694189\pi
882882 0 0
883883 4090.61 0.155900 0.0779501 0.996957i 0.475163π-0.475163\pi
0.0779501 + 0.996957i 0.475163π0.475163\pi
884884 0 0
885885 −10251.4 + 17755.9i −0.389375 + 0.674417i
886886 0 0
887887 −14409.7 24958.3i −0.545468 0.944778i −0.998577 0.0533229i 0.983019π-0.983019\pi
0.453110 0.891455i 0.350315π-0.350315\pi
888888 0 0
889889 −20567.3 22981.2i −0.775933 0.867003i
890890 0 0
891891 7889.07 + 13664.3i 0.296626 + 0.513771i
892892 0 0
893893 3394.58 5879.59i 0.127206 0.220328i
894894 0 0
895895 9995.83 0.373323
896896 0 0
897897 −68160.8 −2.53715
898898 0 0
899899 14584.5 25261.2i 0.541070 0.937160i
900900 0 0
901901 −15.4211 26.7101i −0.000570200 0.000987616i
902902 0 0
903903 −28048.7 + 5873.62i −1.03367 + 0.216458i
904904 0 0
905905 −1702.86 2949.44i −0.0625470 0.108335i
906906 0 0
907907 −10319.4 + 17873.7i −0.377784 + 0.654340i −0.990739 0.135777i 0.956647π-0.956647\pi
0.612956 + 0.790117i 0.289980π0.289980\pi
908908 0 0
909909 42515.1 1.55130
910910 0 0
911911 15080.1 0.548435 0.274218 0.961668i 0.411581π-0.411581\pi
0.274218 + 0.961668i 0.411581π0.411581\pi
912912 0 0
913913 10234.6 17726.8i 0.370991 0.642576i
914914 0 0
915915 10622.6 + 18398.8i 0.383794 + 0.664750i
916916 0 0
917917 3908.99 11908.4i 0.140770 0.428843i
918918 0 0
919919 −1082.14 1874.33i −0.0388429 0.0672778i 0.845950 0.533262i 0.179034π-0.179034\pi
−0.884793 + 0.465984i 0.845701π0.845701\pi
920920 0 0
921921 −21510.7 + 37257.6i −0.769600 + 1.33299i
922922 0 0
923923 −24888.3 −0.887549
924924 0 0
925925 −6596.78 −0.234487
926926 0 0
927927 51840.2 89789.9i 1.83674 3.18132i
928928 0 0
929929 −6819.56 11811.8i −0.240842 0.417151i 0.720112 0.693858i 0.244090π-0.244090\pi
−0.960954 + 0.276707i 0.910757π0.910757\pi
930930 0 0
931931 −19864.0 + 8700.91i −0.699267 + 0.306295i
932932 0 0
933933 23269.7 + 40304.3i 0.816523 + 1.41426i
934934 0 0
935935 −39.7704 + 68.8843i −0.00139105 + 0.00240937i
936936 0 0
937937 6568.49 0.229011 0.114505 0.993423i 0.463472π-0.463472\pi
0.114505 + 0.993423i 0.463472π0.463472\pi
938938 0 0
939939 −20135.2 −0.699774
940940 0 0
941941 −4727.25 + 8187.84i −0.163766 + 0.283652i −0.936216 0.351424i 0.885698π-0.885698\pi
0.772450 + 0.635075i 0.219031π0.219031\pi
942942 0 0
943943 −15149.7 26240.1i −0.523163 0.906145i
944944 0 0
945945 6843.87 20849.2i 0.235588 0.717697i
946946 0 0
947947 17038.4 + 29511.3i 0.584660 + 1.01266i 0.994918 + 0.100691i 0.0321053π0.0321053\pi
−0.410258 + 0.911969i 0.634561π0.634561\pi
948948 0 0
949949 10636.7 18423.4i 0.363839 0.630188i
950950 0 0
951951 −87368.1 −2.97908
952952 0 0
953953 −32862.3 −1.11702 −0.558508 0.829499i 0.688626π-0.688626\pi
−0.558508 + 0.829499i 0.688626π0.688626\pi
954954 0 0
955955 4031.90 6983.46i 0.136617 0.236628i
956956 0 0
957957 10795.2 + 18697.8i 0.364638 + 0.631572i
958958 0 0
959959 −18747.6 + 3925.90i −0.631275 + 0.132194i
960960 0 0
961961 −24310.7 42107.4i −0.816042 1.41343i
962962 0 0
963963 13053.9 22610.0i 0.436817 0.756590i
964964 0 0
965965 −4044.61 −0.134923
966966 0 0
967967 −57597.8 −1.91543 −0.957715 0.287720i 0.907103π-0.907103\pi
−0.957715 + 0.287720i 0.907103π0.907103\pi
968968 0 0
969969 195.134 337.982i 0.00646915 0.0112049i
970970 0 0
971971 −14092.8 24409.5i −0.465768 0.806734i 0.533468 0.845820i 0.320889π-0.320889\pi
−0.999236 + 0.0390865i 0.987555π0.987555\pi
972972 0 0
973973 5382.85 + 6014.63i 0.177355 + 0.198171i
974974 0 0
975975 −6843.37 11853.1i −0.224783 0.389335i
976976 0 0
977977 −22131.8 + 38333.4i −0.724727 + 1.25526i 0.234359 + 0.972150i 0.424701π0.424701\pi
−0.959086 + 0.283114i 0.908633π0.908633\pi
978978 0 0
979979 19786.0 0.645929
980980 0 0
981981 87084.1 2.83423
982982 0 0
983983 73.6999 127.652i 0.00239131 0.00414187i −0.864827 0.502070i 0.832572π-0.832572\pi
0.867219 + 0.497928i 0.165905π0.165905\pi
984984 0 0
985985 9260.57 + 16039.8i 0.299560 + 0.518853i
986986 0 0
987987 −11893.8 13289.8i −0.383571 0.428591i
988988 0 0
989989 −10740.8 18603.6i −0.345337 0.598141i
990990 0 0
991991 6243.42 10813.9i 0.200130 0.346635i −0.748440 0.663202i 0.769197π-0.769197\pi
0.948570 + 0.316567i 0.102530π0.102530\pi
992992 0 0
993993 −101614. −3.24734
994994 0 0
995995 −1839.64 −0.0586135
996996 0 0
997997 3310.57 5734.08i 0.105162 0.182147i −0.808642 0.588301i 0.799797π-0.799797\pi
0.913805 + 0.406154i 0.133130π0.133130\pi
998998 0 0
999999 31264.8 + 54152.2i 0.990164 + 1.71501i
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 560.4.q.n.81.1 10
4.3 odd 2 35.4.e.c.11.2 10
7.2 even 3 inner 560.4.q.n.401.1 10
12.11 even 2 315.4.j.g.46.4 10
20.3 even 4 175.4.k.d.74.3 20
20.7 even 4 175.4.k.d.74.8 20
20.19 odd 2 175.4.e.d.151.4 10
28.3 even 6 245.4.a.n.1.4 5
28.11 odd 6 245.4.a.m.1.4 5
28.19 even 6 245.4.e.o.226.2 10
28.23 odd 6 35.4.e.c.16.2 yes 10
28.27 even 2 245.4.e.o.116.2 10
84.11 even 6 2205.4.a.bu.1.2 5
84.23 even 6 315.4.j.g.226.4 10
84.59 odd 6 2205.4.a.bt.1.2 5
140.23 even 12 175.4.k.d.149.8 20
140.39 odd 6 1225.4.a.bg.1.2 5
140.59 even 6 1225.4.a.bf.1.2 5
140.79 odd 6 175.4.e.d.51.4 10
140.107 even 12 175.4.k.d.149.3 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.4.e.c.11.2 10 4.3 odd 2
35.4.e.c.16.2 yes 10 28.23 odd 6
175.4.e.d.51.4 10 140.79 odd 6
175.4.e.d.151.4 10 20.19 odd 2
175.4.k.d.74.3 20 20.3 even 4
175.4.k.d.74.8 20 20.7 even 4
175.4.k.d.149.3 20 140.107 even 12
175.4.k.d.149.8 20 140.23 even 12
245.4.a.m.1.4 5 28.11 odd 6
245.4.a.n.1.4 5 28.3 even 6
245.4.e.o.116.2 10 28.27 even 2
245.4.e.o.226.2 10 28.19 even 6
315.4.j.g.46.4 10 12.11 even 2
315.4.j.g.226.4 10 84.23 even 6
560.4.q.n.81.1 10 1.1 even 1 trivial
560.4.q.n.401.1 10 7.2 even 3 inner
1225.4.a.bf.1.2 5 140.59 even 6
1225.4.a.bg.1.2 5 140.39 odd 6
2205.4.a.bt.1.2 5 84.59 odd 6
2205.4.a.bu.1.2 5 84.11 even 6