Properties

Label 360.3.p.g.19.7
Level 360360
Weight 33
Character 360.19
Analytic conductor 9.8099.809
Analytic rank 00
Dimension 88
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,3,Mod(19,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 360=23325 360 = 2^{3} \cdot 3^{2} \cdot 5
Weight: k k == 3 3
Character orbit: [χ][\chi] == 360.p (of order 22, degree 11, 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: 9.809289516979.80928951697
Analytic rank: 00
Dimension: 88
Coefficient field: 8.0.53824000000.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8+6x6+36x4+96x2+256 x^{8} + 6x^{6} + 36x^{4} + 96x^{2} + 256 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 25 2^{5}
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 19.7
Root 1.345001.48020i1.34500 - 1.48020i of defining polynomial
Character χ\chi == 360.19
Dual form 360.3.p.g.19.8

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+(1.345001.48020i)q2+(0.3819663.98172i)q4+(4.35250+2.46084i)q5+7.67752q7+(6.407474.79002i)q8+(9.496633.13274i)q10+0.472136q11+4.10995q13+(10.326211.3642i)q14+(15.7082+3.04176i)q16+2.26154iq17+26.3607q19+(8.1358718.2704i)q20+(0.6350210.698854i)q229.73249q23+(12.8885+21.4216i)q25+(5.527866.08353i)q26+(2.9325530.5697i)q2841.6971iq2922.0104iq31+(16.6251+27.3424i)q32+(3.34752+3.04176i)q34+(33.4164+18.8931i)q3551.7449q37+(35.455039.0190i)q38+(16.101136.6163i)q4015.0557q419.31310iq43+(0.1803401.87991i)q44+(13.0902+14.4060i)q468.76226q47+9.94427q49+(49.0433+9.73442i)q50+(1.5698616.3647i)q5239.9002q53+(2.05497+1.16185i)q55+(49.193536.7754i)q56+(61.720056.0825i)q58+77.1935q59+14.7650iq61+(32.579729.6039i)q62+(18.1115+61.3838i)q64+(17.8885+10.1139i)q65+75.8395iq67+(9.004820.863831i)q68+(72.910524.0517i)q70+81.0705iq71+83.4249iq73+(69.5967+76.5927i)q74+(10.0689104.961i)q76+3.62483q77+100.757iq79+(75.855325.4161i)q80+(20.2499+22.2854i)q820.266939iq83+(5.56528+9.84336i)q85+(13.785212.5261i)q86+(3.025202.26154i)q8885.5542q89+31.5542q91+(3.71748+38.7521i)q92+(11.7852+12.9699i)q94+(114.735+64.8694i)q95+99.1297iq97+(13.375014.7195i)q98+O(q100)q+(1.34500 - 1.48020i) q^{2} +(-0.381966 - 3.98172i) q^{4} +(4.35250 + 2.46084i) q^{5} +7.67752 q^{7} +(-6.40747 - 4.79002i) q^{8} +(9.49663 - 3.13274i) q^{10} +0.472136 q^{11} +4.10995 q^{13} +(10.3262 - 11.3642i) q^{14} +(-15.7082 + 3.04176i) q^{16} +2.26154i q^{17} +26.3607 q^{19} +(8.13587 - 18.2704i) q^{20} +(0.635021 - 0.698854i) q^{22} -9.73249 q^{23} +(12.8885 + 21.4216i) q^{25} +(5.52786 - 6.08353i) q^{26} +(-2.93255 - 30.5697i) q^{28} -41.6971i q^{29} -22.0104i q^{31} +(-16.6251 + 27.3424i) q^{32} +(3.34752 + 3.04176i) q^{34} +(33.4164 + 18.8931i) q^{35} -51.7449 q^{37} +(35.4550 - 39.0190i) q^{38} +(-16.1011 - 36.6163i) q^{40} -15.0557 q^{41} -9.31310i q^{43} +(-0.180340 - 1.87991i) q^{44} +(-13.0902 + 14.4060i) q^{46} -8.76226 q^{47} +9.94427 q^{49} +(49.0433 + 9.73442i) q^{50} +(-1.56986 - 16.3647i) q^{52} -39.9002 q^{53} +(2.05497 + 1.16185i) q^{55} +(-49.1935 - 36.7754i) q^{56} +(-61.7200 - 56.0825i) q^{58} +77.1935 q^{59} +14.7650i q^{61} +(-32.5797 - 29.6039i) q^{62} +(18.1115 + 61.3838i) q^{64} +(17.8885 + 10.1139i) q^{65} +75.8395i q^{67} +(9.00482 - 0.863831i) q^{68} +(72.9105 - 24.0517i) q^{70} +81.0705i q^{71} +83.4249i q^{73} +(-69.5967 + 76.5927i) q^{74} +(-10.0689 - 104.961i) q^{76} +3.62483 q^{77} +100.757i q^{79} +(-75.8553 - 25.4161i) q^{80} +(-20.2499 + 22.2854i) q^{82} -0.266939i q^{83} +(-5.56528 + 9.84336i) q^{85} +(-13.7852 - 12.5261i) q^{86} +(-3.02520 - 2.26154i) q^{88} -85.5542 q^{89} +31.5542 q^{91} +(3.71748 + 38.7521i) q^{92} +(-11.7852 + 12.9699i) q^{94} +(114.735 + 64.8694i) q^{95} +99.1297i q^{97} +(13.3750 - 14.7195i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q12q4+20q1032q11+20q1472q16+32q1920q2040q25+80q26+152q34+160q3580q40192q41+88q4460q46+8q49+200q50+300q94+O(q100) 8 q - 12 q^{4} + 20 q^{10} - 32 q^{11} + 20 q^{14} - 72 q^{16} + 32 q^{19} - 20 q^{20} - 40 q^{25} + 80 q^{26} + 152 q^{34} + 160 q^{35} - 80 q^{40} - 192 q^{41} + 88 q^{44} - 60 q^{46} + 8 q^{49} + 200 q^{50}+ \cdots - 300 q^{94}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/360Z)×\left(\mathbb{Z}/360\mathbb{Z}\right)^\times.

nn 181181 217217 271271 281281
χ(n)\chi(n) 1-1 1-1 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 1.34500 1.48020i 0.672499 0.740098i
33 0 0
44 −0.381966 3.98172i −0.0954915 0.995430i
55 4.35250 + 2.46084i 0.870500 + 0.492168i
66 0 0
77 7.67752 1.09679 0.548394 0.836220i 0.315239π-0.315239\pi
0.548394 + 0.836220i 0.315239π0.315239\pi
88 −6.40747 4.79002i −0.800934 0.598752i
99 0 0
1010 9.49663 3.13274i 0.949663 0.313274i
1111 0.472136 0.0429215 0.0214607 0.999770i 0.493168π-0.493168\pi
0.0214607 + 0.999770i 0.493168π0.493168\pi
1212 0 0
1313 4.10995 0.316150 0.158075 0.987427i 0.449471π-0.449471\pi
0.158075 + 0.987427i 0.449471π0.449471\pi
1414 10.3262 11.3642i 0.737588 0.811731i
1515 0 0
1616 −15.7082 + 3.04176i −0.981763 + 0.190110i
1717 2.26154i 0.133032i 0.997785 + 0.0665159i 0.0211883π0.0211883\pi
−0.997785 + 0.0665159i 0.978812π0.978812\pi
1818 0 0
1919 26.3607 1.38740 0.693702 0.720262i 0.255978π-0.255978\pi
0.693702 + 0.720262i 0.255978π0.255978\pi
2020 8.13587 18.2704i 0.406793 0.913520i
2121 0 0
2222 0.635021 0.698854i 0.0288646 0.0317661i
2323 −9.73249 −0.423152 −0.211576 0.977362i 0.567860π-0.567860\pi
−0.211576 + 0.977362i 0.567860π0.567860\pi
2424 0 0
2525 12.8885 + 21.4216i 0.515542 + 0.856864i
2626 5.52786 6.08353i 0.212610 0.233982i
2727 0 0
2828 −2.93255 30.5697i −0.104734 1.09178i
2929 41.6971i 1.43783i −0.695097 0.718916i 0.744639π-0.744639\pi
0.695097 0.718916i 0.255361π-0.255361\pi
3030 0 0
3131 22.0104i 0.710013i −0.934864 0.355007i 0.884479π-0.884479\pi
0.934864 0.355007i 0.115521π-0.115521\pi
3232 −16.6251 + 27.3424i −0.519534 + 0.854450i
3333 0 0
3434 3.34752 + 3.04176i 0.0984566 + 0.0894637i
3535 33.4164 + 18.8931i 0.954755 + 0.539804i
3636 0 0
3737 −51.7449 −1.39851 −0.699256 0.714872i 0.746485π-0.746485\pi
−0.699256 + 0.714872i 0.746485π0.746485\pi
3838 35.4550 39.0190i 0.933027 1.02682i
3939 0 0
4040 −16.1011 36.6163i −0.402527 0.915408i
4141 −15.0557 −0.367213 −0.183606 0.983000i 0.558777π-0.558777\pi
−0.183606 + 0.983000i 0.558777π0.558777\pi
4242 0 0
4343 9.31310i 0.216584i −0.994119 0.108292i 0.965462π-0.965462\pi
0.994119 0.108292i 0.0345381π-0.0345381\pi
4444 −0.180340 1.87991i −0.00409863 0.0427253i
4545 0 0
4646 −13.0902 + 14.4060i −0.284569 + 0.313174i
4747 −8.76226 −0.186431 −0.0932156 0.995646i 0.529715π-0.529715\pi
−0.0932156 + 0.995646i 0.529715π0.529715\pi
4848 0 0
4949 9.94427 0.202944
5050 49.0433 + 9.73442i 0.980865 + 0.194688i
5151 0 0
5252 −1.56986 16.3647i −0.0301896 0.314705i
5353 −39.9002 −0.752834 −0.376417 0.926450i 0.622844π-0.622844\pi
−0.376417 + 0.926450i 0.622844π0.622844\pi
5454 0 0
5555 2.05497 + 1.16185i 0.0373631 + 0.0211246i
5656 −49.1935 36.7754i −0.878455 0.656704i
5757 0 0
5858 −61.7200 56.0825i −1.06414 0.966940i
5959 77.1935 1.30836 0.654182 0.756337i 0.273013π-0.273013\pi
0.654182 + 0.756337i 0.273013π0.273013\pi
6060 0 0
6161 14.7650i 0.242050i 0.992649 + 0.121025i 0.0386181π0.0386181\pi
−0.992649 + 0.121025i 0.961382π0.961382\pi
6262 −32.5797 29.6039i −0.525480 0.477483i
6363 0 0
6464 18.1115 + 61.3838i 0.282992 + 0.959122i
6565 17.8885 + 10.1139i 0.275208 + 0.155599i
6666 0 0
6767 75.8395i 1.13193i 0.824428 + 0.565966i 0.191497π0.191497\pi
−0.824428 + 0.565966i 0.808503π0.808503\pi
6868 9.00482 0.863831i 0.132424 0.0127034i
6969 0 0
7070 72.9105 24.0517i 1.04158 0.343595i
7171 81.0705i 1.14184i 0.821006 + 0.570919i 0.193413π0.193413\pi
−0.821006 + 0.570919i 0.806587π0.806587\pi
7272 0 0
7373 83.4249i 1.14281i 0.820669 + 0.571403i 0.193601π0.193601\pi
−0.820669 + 0.571403i 0.806399π0.806399\pi
7474 −69.5967 + 76.5927i −0.940497 + 1.03504i
7575 0 0
7676 −10.0689 104.961i −0.132485 1.38106i
7777 3.62483 0.0470757
7878 0 0
7979 100.757i 1.27541i 0.770281 + 0.637704i 0.220116π0.220116\pi
−0.770281 + 0.637704i 0.779884π0.779884\pi
8080 −75.8553 25.4161i −0.948191 0.317701i
8181 0 0
8282 −20.2499 + 22.2854i −0.246950 + 0.271774i
8383 0.266939i 0.00321613i −0.999999 0.00160806i 0.999488π-0.999488\pi
0.999999 0.00160806i 0.000511863π-0.000511863\pi
8484 0 0
8585 −5.56528 + 9.84336i −0.0654739 + 0.115804i
8686 −13.7852 12.5261i −0.160293 0.145652i
8787 0 0
8888 −3.02520 2.26154i −0.0343773 0.0256993i
8989 −85.5542 −0.961283 −0.480641 0.876917i 0.659596π-0.659596\pi
−0.480641 + 0.876917i 0.659596π0.659596\pi
9090 0 0
9191 31.5542 0.346749
9292 3.71748 + 38.7521i 0.0404074 + 0.421218i
9393 0 0
9494 −11.7852 + 12.9699i −0.125375 + 0.137977i
9595 114.735 + 64.8694i 1.20774 + 0.682836i
9696 0 0
9797 99.1297i 1.02196i 0.859594 + 0.510978i 0.170716π0.170716\pi
−0.859594 + 0.510978i 0.829284π0.829284\pi
9898 13.3750 14.7195i 0.136480 0.150199i
9999 0 0
100100 80.3719 59.5009i 0.803719 0.595009i
101101 105.405i 1.04361i −0.853065 0.521805i 0.825259π-0.825259\pi
0.853065 0.521805i 0.174741π-0.174741\pi
102102 0 0
103103 101.863 0.988958 0.494479 0.869190i 0.335359π-0.335359\pi
0.494479 + 0.869190i 0.335359π0.335359\pi
104104 −26.3344 19.6867i −0.253215 0.189295i
105105 0 0
106106 −53.6656 + 59.0601i −0.506280 + 0.557171i
107107 32.9962i 0.308376i −0.988042 0.154188i 0.950724π-0.950724\pi
0.988042 0.154188i 0.0492762π-0.0492762\pi
108108 0 0
109109 181.554i 1.66563i −0.553552 0.832814i 0.686728π-0.686728\pi
0.553552 0.832814i 0.313272π-0.313272\pi
110110 4.48370 1.47908i 0.0407609 0.0134462i
111111 0 0
112112 −120.600 + 23.3532i −1.07679 + 0.208511i
113113 76.6403i 0.678233i 0.940744 + 0.339116i 0.110128π0.110128\pi
−0.940744 + 0.339116i 0.889872π0.889872\pi
114114 0 0
115115 −42.3607 23.9501i −0.368354 0.208262i
116116 −166.026 + 15.9269i −1.43126 + 0.137301i
117117 0 0
118118 103.825 114.262i 0.879873 0.968318i
119119 17.3630i 0.145908i
120120 0 0
121121 −120.777 −0.998158
122122 21.8552 + 19.8589i 0.179141 + 0.162778i
123123 0 0
124124 −87.6393 + 8.40723i −0.706769 + 0.0678002i
125125 3.38228 + 124.954i 0.0270582 + 0.999634i
126126 0 0
127127 −142.962 −1.12569 −0.562843 0.826564i 0.690292π-0.690292\pi
−0.562843 + 0.826564i 0.690292π0.690292\pi
128128 115.220 + 55.7526i 0.900156 + 0.435567i
129129 0 0
130130 39.0306 12.8754i 0.300236 0.0990414i
131131 −110.138 −0.840746 −0.420373 0.907351i 0.638101π-0.638101\pi
−0.420373 + 0.907351i 0.638101π0.638101\pi
132132 0 0
133133 202.385 1.52169
134134 112.257 + 102.004i 0.837741 + 0.761223i
135135 0 0
136136 10.8328 14.4908i 0.0796531 0.106550i
137137 225.398i 1.64524i 0.568592 + 0.822620i 0.307488π0.307488\pi
−0.568592 + 0.822620i 0.692512π0.692512\pi
138138 0 0
139139 97.4164 0.700837 0.350419 0.936593i 0.386039π-0.386039\pi
0.350419 + 0.936593i 0.386039π0.386039\pi
140140 62.4633 140.271i 0.446166 1.00194i
141141 0 0
142142 120.000 + 109.040i 0.845073 + 0.767885i
143143 1.94045 0.0135696
144144 0 0
145145 102.610 181.487i 0.707655 1.25163i
146146 123.485 + 112.206i 0.845790 + 0.768536i
147147 0 0
148148 19.7648 + 206.034i 0.133546 + 1.39212i
149149 191.397i 1.28454i −0.766477 0.642271i 0.777992π-0.777992\pi
0.766477 0.642271i 0.222008π-0.222008\pi
150150 0 0
151151 68.3549i 0.452682i 0.974048 + 0.226341i 0.0726763π0.0726763\pi
−0.974048 + 0.226341i 0.927324π0.927324\pi
152152 −168.905 126.268i −1.11122 0.830711i
153153 0 0
154154 4.87539 5.36547i 0.0316584 0.0348407i
155155 54.1641 95.8004i 0.349446 0.618067i
156156 0 0
157157 −155.235 −0.988756 −0.494378 0.869247i 0.664604π-0.664604\pi
−0.494378 + 0.869247i 0.664604π0.664604\pi
158158 149.141 + 135.518i 0.943928 + 0.857710i
159159 0 0
160160 −139.646 + 78.0962i −0.872787 + 0.488101i
161161 −74.7214 −0.464108
162162 0 0
163163 90.4765i 0.555070i −0.960715 0.277535i 0.910482π-0.910482\pi
0.960715 0.277535i 0.0895175π-0.0895175\pi
164164 5.75078 + 59.9477i 0.0350657 + 0.365535i
165165 0 0
166166 −0.395122 0.359032i −0.00238025 0.00216284i
167167 100.778 0.603461 0.301730 0.953393i 0.402436π-0.402436\pi
0.301730 + 0.953393i 0.402436π0.402436\pi
168168 0 0
169169 −152.108 −0.900049
170170 7.08481 + 21.4770i 0.0416754 + 0.126335i
171171 0 0
172172 −37.0822 + 3.55729i −0.215594 + 0.0206819i
173173 −54.6556 −0.315928 −0.157964 0.987445i 0.550493π-0.550493\pi
−0.157964 + 0.987445i 0.550493π0.550493\pi
174174 0 0
175175 98.9520 + 164.465i 0.565440 + 0.939799i
176176 −7.41641 + 1.43613i −0.0421387 + 0.00815981i
177177 0 0
178178 −115.070 + 126.637i −0.646461 + 0.711444i
179179 106.807 0.596684 0.298342 0.954459i 0.403566π-0.403566\pi
0.298342 + 0.954459i 0.403566π0.403566\pi
180180 0 0
181181 144.778i 0.799879i 0.916542 + 0.399939i 0.130969π0.130969\pi
−0.916542 + 0.399939i 0.869031π0.869031\pi
182182 42.4403 46.7064i 0.233188 0.256629i
183183 0 0
184184 62.3607 + 46.6188i 0.338917 + 0.253363i
185185 −225.220 127.336i −1.21740 0.688302i
186186 0 0
187187 1.06775i 0.00570992i
188188 3.34689 + 34.8889i 0.0178026 + 0.185579i
189189 0 0
190190 250.338 82.5811i 1.31757 0.434638i
191191 210.809i 1.10371i 0.833939 + 0.551857i 0.186081π0.186081\pi
−0.833939 + 0.551857i 0.813919π0.813919\pi
192192 0 0
193193 108.176i 0.560496i −0.959928 0.280248i 0.909583π-0.909583\pi
0.959928 0.280248i 0.0904168π-0.0904168\pi
194194 146.731 + 133.329i 0.756347 + 0.687263i
195195 0 0
196196 −3.79837 39.5953i −0.0193795 0.202017i
197197 −308.300 −1.56497 −0.782487 0.622667i 0.786049π-0.786049\pi
−0.782487 + 0.622667i 0.786049π0.786049\pi
198198 0 0
199199 247.859i 1.24552i −0.782412 0.622761i 0.786011π-0.786011\pi
0.782412 0.622761i 0.213989π-0.213989\pi
200200 20.0269 198.995i 0.100134 0.994974i
201201 0 0
202202 −156.020 141.769i −0.772375 0.701826i
203203 320.130i 1.57700i
204204 0 0
205205 −65.5301 37.0497i −0.319659 0.180730i
206206 137.005 150.777i 0.665073 0.731926i
207207 0 0
208208 −64.5599 + 12.5015i −0.310384 + 0.0601033i
209209 12.4458 0.0595494
210210 0 0
211211 230.584 1.09281 0.546407 0.837520i 0.315995π-0.315995\pi
0.546407 + 0.837520i 0.315995π0.315995\pi
212212 15.2405 + 158.871i 0.0718892 + 0.749393i
213213 0 0
214214 −48.8409 44.3799i −0.228229 0.207383i
215215 22.9180 40.5353i 0.106595 0.188536i
216216 0 0
217217 168.985i 0.778734i
218218 −268.735 244.189i −1.23273 1.12013i
219219 0 0
220220 3.84123 8.62611i 0.0174602 0.0392096i
221221 9.29480i 0.0420579i
222222 0 0
223223 −177.782 −0.797229 −0.398615 0.917118i 0.630509π-0.630509\pi
−0.398615 + 0.917118i 0.630509π0.630509\pi
224224 −127.639 + 209.922i −0.569818 + 0.937151i
225225 0 0
226226 113.443 + 103.081i 0.501959 + 0.456110i
227227 203.301i 0.895601i 0.894134 + 0.447800i 0.147792π0.147792\pi
−0.894134 + 0.447800i 0.852208π0.852208\pi
228228 0 0
229229 81.0705i 0.354020i −0.984209 0.177010i 0.943358π-0.943358\pi
0.984209 0.177010i 0.0566425π-0.0566425\pi
230230 −92.4258 + 30.4893i −0.401851 + 0.132562i
231231 0 0
232232 −199.730 + 267.173i −0.860905 + 1.15161i
233233 56.2864i 0.241573i −0.992679 0.120786i 0.961458π-0.961458\pi
0.992679 0.120786i 0.0385416π-0.0385416\pi
234234 0 0
235235 −38.1378 21.5625i −0.162288 0.0917554i
236236 −29.4853 307.363i −0.124938 1.30239i
237237 0 0
238238 25.7007 + 23.3532i 0.107986 + 0.0981227i
239239 360.235i 1.50726i −0.657300 0.753629i 0.728301π-0.728301\pi
0.657300 0.753629i 0.271699π-0.271699\pi
240240 0 0
241241 −197.495 −0.819483 −0.409741 0.912202i 0.634381π-0.634381\pi
−0.409741 + 0.912202i 0.634381π0.634381\pi
242242 −162.445 + 178.774i −0.671260 + 0.738735i
243243 0 0
244244 58.7902 5.63974i 0.240944 0.0231137i
245245 43.2825 + 24.4713i 0.176663 + 0.0998827i
246246 0 0
247247 108.341 0.438627
248248 −105.430 + 141.031i −0.425122 + 0.568674i
249249 0 0
250250 189.506 + 163.057i 0.758024 + 0.652227i
251251 178.361 0.710600 0.355300 0.934752i 0.384379π-0.384379\pi
0.355300 + 0.934752i 0.384379π0.384379\pi
252252 0 0
253253 −4.59506 −0.0181623
254254 −192.284 + 211.612i −0.757022 + 0.833119i
255255 0 0
256256 237.495 95.5613i 0.927716 0.373286i
257257 453.183i 1.76336i −0.471849 0.881679i 0.656413π-0.656413\pi
0.471849 0.881679i 0.343587π-0.343587\pi
258258 0 0
259259 −397.272 −1.53387
260260 33.4380 75.0904i 0.128608 0.288809i
261261 0 0
262262 −148.135 + 163.026i −0.565401 + 0.622235i
263263 21.0921 0.0801981 0.0400990 0.999196i 0.487233π-0.487233\pi
0.0400990 + 0.999196i 0.487233π0.487233\pi
264264 0 0
265265 −173.666 98.1879i −0.655342 0.370520i
266266 272.207 299.569i 1.02333 1.12620i
267267 0 0
268268 301.972 28.9681i 1.12676 0.108090i
269269 92.4148i 0.343549i −0.985136 0.171775i 0.945050π-0.945050\pi
0.985136 0.171775i 0.0549501π-0.0549501\pi
270270 0 0
271271 188.799i 0.696675i −0.937369 0.348337i 0.886746π-0.886746\pi
0.937369 0.348337i 0.113254π-0.113254\pi
272272 −6.87907 35.5247i −0.0252907 0.130606i
273273 0 0
274274 333.633 + 303.159i 1.21764 + 1.10642i
275275 6.08514 + 10.1139i 0.0221278 + 0.0367779i
276276 0 0
277277 −70.1251 −0.253159 −0.126580 0.991956i 0.540400π-0.540400\pi
−0.126580 + 0.991956i 0.540400π0.540400\pi
278278 131.025 144.195i 0.471312 0.518689i
279279 0 0
280280 −123.616 281.122i −0.441487 1.00401i
281281 506.269 1.80167 0.900835 0.434161i 0.142955π-0.142955\pi
0.900835 + 0.434161i 0.142955π0.142955\pi
282282 0 0
283283 501.350i 1.77156i −0.464110 0.885778i 0.653626π-0.653626\pi
0.464110 0.885778i 0.346374π-0.346374\pi
284284 322.800 30.9662i 1.13662 0.109036i
285285 0 0
286286 2.60990 2.87225i 0.00912554 0.0100428i
287287 −115.591 −0.402755
288288 0 0
289289 283.885 0.982303
290290 −130.626 395.982i −0.450435 1.36546i
291291 0 0
292292 332.175 31.8655i 1.13758 0.109128i
293293 324.026 1.10589 0.552945 0.833218i 0.313504π-0.313504\pi
0.552945 + 0.833218i 0.313504π0.313504\pi
294294 0 0
295295 335.985 + 189.961i 1.13893 + 0.643935i
296296 331.554 + 247.859i 1.12012 + 0.837362i
297297 0 0
298298 −283.305 257.428i −0.950688 0.863853i
299299 −40.0000 −0.133779
300300 0 0
301301 71.5015i 0.237546i
302302 101.179 + 91.9372i 0.335029 + 0.304428i
303303 0 0
304304 −414.079 + 80.1830i −1.36210 + 0.263760i
305305 −36.3344 + 64.2648i −0.119129 + 0.210704i
306306 0 0
307307 9.84697i 0.0320748i −0.999871 0.0160374i 0.994895π-0.994895\pi
0.999871 0.0160374i 0.00510509π-0.00510509\pi
308308 −1.38456 14.4331i −0.00449533 0.0468606i
309309 0 0
310310 −68.9529 209.025i −0.222429 0.674273i
311311 200.417i 0.644429i 0.946667 + 0.322214i 0.104427π0.104427\pi
−0.946667 + 0.322214i 0.895573π0.895573\pi
312312 0 0
313313 261.582i 0.835727i 0.908510 + 0.417863i 0.137221π0.137221\pi
−0.908510 + 0.417863i 0.862779π0.862779\pi
314314 −208.790 + 229.778i −0.664937 + 0.731777i
315315 0 0
316316 401.187 38.4858i 1.26958 0.121791i
317317 322.341 1.01685 0.508425 0.861107i 0.330228π-0.330228\pi
0.508425 + 0.861107i 0.330228π0.330228\pi
318318 0 0
319319 19.6867i 0.0617138i
320320 −72.2256 + 311.743i −0.225705 + 0.974196i
321321 0 0
322322 −100.500 + 110.602i −0.312112 + 0.343485i
323323 59.6157i 0.184569i
324324 0 0
325325 52.9712 + 88.0416i 0.162988 + 0.270897i
326326 −133.923 121.691i −0.410807 0.373284i
327327 0 0
328328 96.4692 + 72.1172i 0.294113 + 0.219870i
329329 −67.2724 −0.204475
330330 0 0
331331 −61.0883 −0.184557 −0.0922783 0.995733i 0.529415π-0.529415\pi
−0.0922783 + 0.995733i 0.529415π0.529415\pi
332332 −1.06287 + 0.101961i −0.00320143 + 0.000307113i
333333 0 0
334334 135.546 149.171i 0.405826 0.446620i
335335 −186.629 + 330.091i −0.557101 + 0.985348i
336336 0 0
337337 114.960i 0.341129i 0.985347 + 0.170564i 0.0545591π0.0545591\pi
−0.985347 + 0.170564i 0.945441π0.945441\pi
338338 −204.585 + 225.150i −0.605282 + 0.666125i
339339 0 0
340340 41.3192 + 18.3996i 0.121527 + 0.0541164i
341341 10.3919i 0.0304748i
342342 0 0
343343 −299.851 −0.874201
344344 −44.6099 + 59.6734i −0.129680 + 0.173469i
345345 0 0
346346 −73.5116 + 80.9010i −0.212461 + 0.233818i
347347 143.967i 0.414892i −0.978246 0.207446i 0.933485π-0.933485\pi
0.978246 0.207446i 0.0665151π-0.0665151\pi
348348 0 0
349349 35.9526i 0.103016i −0.998673 0.0515080i 0.983597π-0.983597\pi
0.998673 0.0515080i 0.0164028π-0.0164028\pi
350350 376.530 + 74.7362i 1.07580 + 0.213532i
351351 0 0
352352 −7.84930 + 12.9093i −0.0222991 + 0.0366742i
353353 252.536i 0.715400i 0.933837 + 0.357700i 0.116439π0.116439\pi
−0.933837 + 0.357700i 0.883561π0.883561\pi
354354 0 0
355355 −199.502 + 352.860i −0.561976 + 0.993971i
356356 32.6788 + 340.653i 0.0917943 + 0.956890i
357357 0 0
358358 143.654 158.095i 0.401269 0.441605i
359359 594.152i 1.65502i −0.561452 0.827509i 0.689757π-0.689757\pi
0.561452 0.827509i 0.310243π-0.310243\pi
360360 0 0
361361 333.885 0.924890
362362 214.300 + 194.726i 0.591989 + 0.537917i
363363 0 0
364364 −12.0526 125.640i −0.0331116 0.345165i
365365 −205.295 + 363.107i −0.562453 + 0.994814i
366366 0 0
367367 88.9062 0.242251 0.121126 0.992637i 0.461350π-0.461350\pi
0.121126 + 0.992637i 0.461350π0.461350\pi
368368 152.880 29.6039i 0.415435 0.0804455i
369369 0 0
370370 −491.402 + 162.103i −1.32811 + 0.438117i
371371 −306.334 −0.825699
372372 0 0
373373 83.6542 0.224274 0.112137 0.993693i 0.464230π-0.464230\pi
0.112137 + 0.993693i 0.464230π0.464230\pi
374374 1.58049 + 1.43613i 0.00422590 + 0.00383991i
375375 0 0
376376 56.1440 + 41.9714i 0.149319 + 0.111626i
377377 171.373i 0.454570i
378378 0 0
379379 −135.135 −0.356556 −0.178278 0.983980i 0.557053π-0.557053\pi
−0.178278 + 0.983980i 0.557053π0.557053\pi
380380 214.467 481.620i 0.564387 1.26742i
381381 0 0
382382 312.039 + 283.538i 0.816857 + 0.742246i
383383 −498.526 −1.30164 −0.650818 0.759234i 0.725574π-0.725574\pi
−0.650818 + 0.759234i 0.725574π0.725574\pi
384384 0 0
385385 15.7771 + 8.92013i 0.0409794 + 0.0231692i
386386 −160.122 145.496i −0.414823 0.376933i
387387 0 0
388388 394.707 37.8642i 1.01729 0.0975880i
389389 308.420i 0.792854i −0.918066 0.396427i 0.870250π-0.870250\pi
0.918066 0.396427i 0.129750π-0.129750\pi
390390 0 0
391391 22.0104i 0.0562926i
392392 −63.7177 47.6332i −0.162545 0.121513i
393393 0 0
394394 −414.663 + 456.345i −1.05244 + 1.15824i
395395 −247.947 + 438.546i −0.627715 + 1.11024i
396396 0 0
397397 297.682 0.749828 0.374914 0.927060i 0.377672π-0.377672\pi
0.374914 + 0.927060i 0.377672π0.377672\pi
398398 −366.880 333.370i −0.921810 0.837612i
399399 0 0
400400 −267.615 297.291i −0.669038 0.743228i
401401 −148.663 −0.370729 −0.185365 0.982670i 0.559347π-0.559347\pi
−0.185365 + 0.982670i 0.559347π0.559347\pi
402402 0 0
403403 90.4616i 0.224470i
404404 −419.692 + 40.2610i −1.03884 + 0.0996559i
405405 0 0
406406 −473.856 430.574i −1.16713 1.06053i
407407 −24.4306 −0.0600261
408408 0 0
409409 442.387 1.08163 0.540815 0.841141i 0.318116π-0.318116\pi
0.540815 + 0.841141i 0.318116π0.318116\pi
410410 −142.979 + 47.1657i −0.348728 + 0.115038i
411411 0 0
412412 −38.9081 405.589i −0.0944371 0.984439i
413413 592.654 1.43500
414414 0 0
415415 0.656893 1.16185i 0.00158287 0.00279964i
416416 −68.3282 + 112.376i −0.164250 + 0.270134i
417417 0 0
418418 16.7396 18.4223i 0.0400469 0.0440724i
419419 −536.184 −1.27968 −0.639838 0.768510i 0.720999π-0.720999\pi
−0.639838 + 0.768510i 0.720999π0.720999\pi
420420 0 0
421421 514.582i 1.22228i 0.791521 + 0.611142i 0.209290π0.209290\pi
−0.791521 + 0.611142i 0.790710π0.790710\pi
422422 310.134 341.309i 0.734915 0.808789i
423423 0 0
424424 255.659 + 191.123i 0.602970 + 0.450761i
425425 −48.4458 + 29.1480i −0.113990 + 0.0685834i
426426 0 0
427427 113.359i 0.265477i
428428 −131.382 + 12.6034i −0.306967 + 0.0294473i
429429 0 0
430430 −29.1755 88.4430i −0.0678500 0.205681i
431431 86.8151i 0.201427i 0.994915 + 0.100714i 0.0321126π0.0321126\pi
−0.994915 + 0.100714i 0.967887π0.967887\pi
432432 0 0
433433 494.017i 1.14092i 0.821327 + 0.570458i 0.193234π0.193234\pi
−0.821327 + 0.570458i 0.806766π0.806766\pi
434434 −250.132 227.285i −0.576340 0.523698i
435435 0 0
436436 −722.895 + 69.3473i −1.65802 + 0.159053i
437437 −256.555 −0.587082
438438 0 0
439439 524.700i 1.19522i −0.801789 0.597608i 0.796118π-0.796118\pi
0.801789 0.597608i 0.203882π-0.203882\pi
440440 −7.60190 17.2879i −0.0172770 0.0392906i
441441 0 0
442442 13.7581 + 12.5015i 0.0311270 + 0.0282839i
443443 496.575i 1.12094i 0.828176 + 0.560469i 0.189379π0.189379\pi
−0.828176 + 0.560469i 0.810621π0.810621\pi
444444 0 0
445445 −372.375 210.535i −0.836797 0.473112i
446446 −239.116 + 263.153i −0.536136 + 0.590028i
447447 0 0
448448 139.051 + 471.275i 0.310382 + 1.05195i
449449 332.158 0.739773 0.369886 0.929077i 0.379397π-0.379397\pi
0.369886 + 0.929077i 0.379397π0.379397\pi
450450 0 0
451451 −7.10835 −0.0157613
452452 305.160 29.2740i 0.675133 0.0647655i
453453 0 0
454454 300.926 + 273.440i 0.662833 + 0.602290i
455455 137.340 + 77.6497i 0.301845 + 0.170659i
456456 0 0
457457 252.788i 0.553147i −0.960993 0.276574i 0.910801π-0.910801\pi
0.960993 0.276574i 0.0891990π-0.0891990\pi
458458 −120.000 109.040i −0.262010 0.238078i
459459 0 0
460460 −79.1822 + 177.817i −0.172135 + 0.386558i
461461 832.716i 1.80633i 0.429299 + 0.903163i 0.358761π0.358761\pi
−0.429299 + 0.903163i 0.641239π0.641239\pi
462462 0 0
463463 −854.205 −1.84494 −0.922468 0.386074i 0.873831π-0.873831\pi
−0.922468 + 0.386074i 0.873831π0.873831\pi
464464 126.833 + 654.987i 0.273347 + 1.41161i
465465 0 0
466466 −83.3150 75.7051i −0.178788 0.162457i
467467 102.726i 0.219970i 0.993933 + 0.109985i 0.0350802π0.0350802\pi
−0.993933 + 0.109985i 0.964920π0.964920\pi
468468 0 0
469469 582.259i 1.24149i
470470 −83.2120 + 27.4499i −0.177047 + 0.0584040i
471471 0 0
472472 −494.615 369.758i −1.04791 0.783386i
473473 4.39705i 0.00929608i
474474 0 0
475475 339.751 + 564.688i 0.715265 + 1.18882i
476476 69.1347 6.63208i 0.145241 0.0139329i
477477 0 0
478478 −533.218 484.515i −1.11552 1.01363i
479479 268.772i 0.561111i −0.959838 0.280556i 0.909481π-0.909481\pi
0.959838 0.280556i 0.0905187π-0.0905187\pi
480480 0 0
481481 −212.669 −0.442139
482482 −265.631 + 292.332i −0.551101 + 0.606498i
483483 0 0
484484 46.1327 + 480.901i 0.0953156 + 0.993596i
485485 −243.942 + 431.462i −0.502973 + 0.889612i
486486 0 0
487487 504.065 1.03504 0.517520 0.855671i 0.326855π-0.326855\pi
0.517520 + 0.855671i 0.326855π0.326855\pi
488488 70.7248 94.6066i 0.144928 0.193866i
489489 0 0
490490 94.4371 31.1528i 0.192729 0.0635772i
491491 −130.020 −0.264807 −0.132403 0.991196i 0.542269π-0.542269\pi
−0.132403 + 0.991196i 0.542269π0.542269\pi
492492 0 0
493493 94.2997 0.191277
494494 145.718 160.366i 0.294976 0.324627i
495495 0 0
496496 66.9505 + 345.744i 0.134981 + 0.697065i
497497 622.421i 1.25236i
498498 0 0
499499 664.184 1.33103 0.665515 0.746384i 0.268212π-0.268212\pi
0.665515 + 0.746384i 0.268212π0.268212\pi
500500 496.241 61.1955i 0.992482 0.122391i
501501 0 0
502502 239.895 264.009i 0.477878 0.525914i
503503 550.015 1.09347 0.546735 0.837306i 0.315871π-0.315871\pi
0.546735 + 0.837306i 0.315871π0.315871\pi
504504 0 0
505505 259.384 458.774i 0.513631 0.908463i
506506 −6.18034 + 6.80159i −0.0122141 + 0.0134419i
507507 0 0
508508 54.6067 + 569.235i 0.107493 + 1.12054i
509509 349.843i 0.687314i 0.939095 + 0.343657i 0.111666π0.111666\pi
−0.939095 + 0.343657i 0.888334π0.888334\pi
510510 0 0
511511 640.496i 1.25342i
512512 177.981 480.070i 0.347619 0.937636i
513513 0 0
514514 −670.800 609.530i −1.30506 1.18586i
515515 443.358 + 250.668i 0.860888 + 0.486733i
516516 0 0
517517 −4.13698 −0.00800189
518518 −534.330 + 588.041i −1.03153 + 1.13522i
519519 0 0
520520 −66.1746 150.491i −0.127259 0.289406i
521521 −29.7771 −0.0571537 −0.0285769 0.999592i 0.509098π-0.509098\pi
−0.0285769 + 0.999592i 0.509098π0.509098\pi
522522 0 0
523523 603.023i 1.15301i 0.817094 + 0.576504i 0.195584π0.195584\pi
−0.817094 + 0.576504i 0.804416π0.804416\pi
524524 42.0689 + 438.538i 0.0802841 + 0.836904i
525525 0 0
526526 28.3688 31.2205i 0.0539331 0.0593545i
527527 49.7774 0.0944543
528528 0 0
529529 −434.279 −0.820943
530530 −378.917 + 124.997i −0.714938 + 0.235843i
531531 0 0
532532 −77.3040 805.839i −0.145308 1.51473i
533533 −61.8782 −0.116094
534534 0 0
535535 81.1985 143.616i 0.151773 0.268442i
536536 363.272 485.939i 0.677747 0.906603i
537537 0 0
538538 −136.792 124.298i −0.254260 0.231036i
539539 4.69505 0.00871066
540540 0 0
541541 163.368i 0.301974i −0.988536 0.150987i 0.951755π-0.951755\pi
0.988536 0.150987i 0.0482451π-0.0482451\pi
542542 −279.460 253.934i −0.515608 0.468513i
543543 0 0
544544 −61.8359 37.5983i −0.113669 0.0691145i
545545 446.774 790.212i 0.819769 1.44993i
546546 0 0
547547 524.218i 0.958350i 0.877719 + 0.479175i 0.159064π0.159064\pi
−0.877719 + 0.479175i 0.840936π0.840936\pi
548548 897.471 86.0943i 1.63772 0.157106i
549549 0 0
550550 23.1551 + 4.59597i 0.0421002 + 0.00835631i
551551 1099.16i 1.99485i
552552 0 0
553553 773.566i 1.39885i
554554 −94.3181 + 103.799i −0.170249 + 0.187363i
555555 0 0
556556 −37.2098 387.885i −0.0669240 0.697635i
557557 589.515 1.05837 0.529187 0.848505i 0.322497π-0.322497\pi
0.529187 + 0.848505i 0.322497π0.322497\pi
558558 0 0
559559 38.2763i 0.0684728i
560560 −582.380 195.132i −1.03996 0.348451i
561561 0 0
562562 680.931 749.378i 1.21162 1.33341i
563563 557.763i 0.990698i −0.868694 0.495349i 0.835040π-0.835040\pi
0.868694 0.495349i 0.164960π-0.164960\pi
564564 0 0
565565 −188.599 + 333.577i −0.333804 + 0.590402i
566566 −742.097 674.315i −1.31113 1.19137i
567567 0 0
568568 388.329 519.457i 0.683678 0.914538i
569569 542.715 0.953805 0.476903 0.878956i 0.341759π-0.341759\pi
0.476903 + 0.878956i 0.341759π0.341759\pi
570570 0 0
571571 −476.695 −0.834842 −0.417421 0.908713i 0.637066π-0.637066\pi
−0.417421 + 0.908713i 0.637066π0.637066\pi
572572 −0.741187 7.72634i −0.00129578 0.0135076i
573573 0 0
574574 −155.469 + 171.097i −0.270852 + 0.298078i
575575 −125.438 208.486i −0.218152 0.362584i
576576 0 0
577577 865.659i 1.50027i −0.661282 0.750137i 0.729987π-0.729987\pi
0.661282 0.750137i 0.270013π-0.270013\pi
578578 381.825 420.206i 0.660597 0.727001i
579579 0 0
580580 −761.823 339.242i −1.31349 0.584900i
581581 2.04943i 0.00352741i
582582 0 0
583583 −18.8383 −0.0323127
584584 399.607 534.543i 0.684258 0.915313i
585585 0 0
586586 435.813 479.622i 0.743709 0.818467i
587587 567.091i 0.966083i 0.875597 + 0.483041i 0.160468π0.160468\pi
−0.875597 + 0.483041i 0.839532π0.839532\pi
588588 0 0
589589 580.209i 0.985075i
590590 733.078 241.827i 1.24250 0.409876i
591591 0 0
592592 812.820 157.396i 1.37301 0.265871i
593593 421.774i 0.711254i 0.934628 + 0.355627i 0.115733π0.115733\pi
−0.934628 + 0.355627i 0.884267π0.884267\pi
594594 0 0
595595 −42.7276 + 75.5725i −0.0718110 + 0.127013i
596596 −762.089 + 73.1071i −1.27867 + 0.122663i
597597 0 0
598598 −53.7999 + 59.2079i −0.0899664 + 0.0990098i
599599 120.444i 0.201075i −0.994933 0.100538i 0.967944π-0.967944\pi
0.994933 0.100538i 0.0320563π-0.0320563\pi
600600 0 0
601601 340.158 0.565986 0.282993 0.959122i 0.408673π-0.408673\pi
0.282993 + 0.959122i 0.408673π0.408673\pi
602602 −105.836 96.1693i −0.175808 0.159750i
603603 0 0
604604 272.170 26.1093i 0.450613 0.0432273i
605605 −525.682 297.213i −0.868897 0.491261i
606606 0 0
607607 115.621 0.190479 0.0952396 0.995454i 0.469638π-0.469638\pi
0.0952396 + 0.995454i 0.469638π0.469638\pi
608608 −438.248 + 720.764i −0.720803 + 1.18547i
609609 0 0
610610 46.2550 + 140.218i 0.0758279 + 0.229866i
611611 −36.0124 −0.0589401
612612 0 0
613613 1095.63 1.78733 0.893663 0.448738i 0.148126π-0.148126\pi
0.893663 + 0.448738i 0.148126π0.148126\pi
614614 −14.5755 13.2442i −0.0237385 0.0215703i
615615 0 0
616616 −23.2260 17.3630i −0.0377046 0.0281867i
617617 716.775i 1.16171i −0.814007 0.580855i 0.802718π-0.802718\pi
0.814007 0.580855i 0.197282π-0.197282\pi
618618 0 0
619619 118.584 0.191573 0.0957864 0.995402i 0.469463π-0.469463\pi
0.0957864 + 0.995402i 0.469463π0.469463\pi
620620 −402.139 179.074i −0.648612 0.288829i
621621 0 0
622622 296.657 + 269.561i 0.476941 + 0.433378i
623623 −656.844 −1.05432
624624 0 0
625625 −292.771 + 552.187i −0.468433 + 0.883499i
626626 387.193 + 351.828i 0.618520 + 0.562025i
627627 0 0
628628 59.2944 + 618.101i 0.0944178 + 0.984238i
629629 117.023i 0.186046i
630630 0 0
631631 1168.62i 1.85201i −0.377515 0.926004i 0.623221π-0.623221\pi
0.377515 0.926004i 0.376779π-0.376779\pi
632632 482.629 645.600i 0.763654 1.02152i
633633 0 0
634634 433.548 477.128i 0.683830 0.752569i
635635 −622.243 351.807i −0.979910 0.554026i
636636 0 0
637637 40.8704 0.0641608
638638 −29.1402 26.4786i −0.0456743 0.0415025i
639639 0 0
640640 364.297 + 526.201i 0.569215 + 0.822189i
641641 244.158 0.380902 0.190451 0.981697i 0.439005π-0.439005\pi
0.190451 + 0.981697i 0.439005π0.439005\pi
642642 0 0
643643 868.847i 1.35124i −0.737250 0.675620i 0.763876π-0.763876\pi
0.737250 0.675620i 0.236124π-0.236124\pi
644644 28.5410 + 297.520i 0.0443184 + 0.461987i
645645 0 0
646646 88.2430 + 80.1830i 0.136599 + 0.124122i
647647 35.1333 0.0543019 0.0271510 0.999631i 0.491357π-0.491357\pi
0.0271510 + 0.999631i 0.491357π0.491357\pi
648648 0 0
649649 36.4458 0.0561569
650650 201.565 + 40.0079i 0.310100 + 0.0615507i
651651 0 0
652652 −360.252 + 34.5589i −0.552534 + 0.0530045i
653653 −580.068 −0.888313 −0.444157 0.895949i 0.646497π-0.646497\pi
−0.444157 + 0.895949i 0.646497π0.646497\pi
654654 0 0
655655 −479.375 271.031i −0.731870 0.413788i
656656 236.498 45.7960i 0.360516 0.0698109i
657657 0 0
658658 −90.4812 + 99.5764i −0.137509 + 0.151332i
659659 992.788 1.50651 0.753253 0.657731i 0.228483π-0.228483\pi
0.753253 + 0.657731i 0.228483π0.228483\pi
660660 0 0
661661 719.647i 1.08872i −0.838850 0.544362i 0.816772π-0.816772\pi
0.838850 0.544362i 0.183228π-0.183228\pi
662662 −82.1635 + 90.4226i −0.124114 + 0.136590i
663663 0 0
664664 −1.27864 + 1.71040i −0.00192566 + 0.00257591i
665665 880.879 + 498.036i 1.32463 + 0.748926i
666666 0 0
667667 405.817i 0.608421i
668668 −38.4938 401.270i −0.0576254 0.600703i
669669 0 0
670670 237.585 + 720.219i 0.354605 + 1.07495i
671671 6.97110i 0.0103891i
672672 0 0
673673 189.591i 0.281711i 0.990030 + 0.140855i 0.0449852π0.0449852\pi
−0.990030 + 0.140855i 0.955015π0.955015\pi
674674 170.164 + 154.621i 0.252469 + 0.229409i
675675 0 0
676676 58.1002 + 605.653i 0.0859471 + 0.895936i
677677 −327.192 −0.483297 −0.241649 0.970364i 0.577688π-0.577688\pi
−0.241649 + 0.970364i 0.577688π0.577688\pi
678678 0 0
679679 761.070i 1.12087i
680680 82.8093 36.4132i 0.121778 0.0535489i
681681 0 0
682682 −15.3821 13.9771i −0.0225544 0.0204943i
683683 673.539i 0.986148i −0.869987 0.493074i 0.835873π-0.835873\pi
0.869987 0.493074i 0.164127π-0.164127\pi
684684 0 0
685685 −554.668 + 981.044i −0.809734 + 1.43218i
686686 −403.299 + 443.839i −0.587899 + 0.646995i
687687 0 0
688688 28.3282 + 146.292i 0.0411748 + 0.212634i
689689 −163.988 −0.238008
690690 0 0
691691 237.036 0.343033 0.171516 0.985181i 0.445133π-0.445133\pi
0.171516 + 0.985181i 0.445133π0.445133\pi
692692 20.8766 + 217.623i 0.0301685 + 0.314485i
693693 0 0
694694 −213.100 193.636i −0.307061 0.279014i
695695 424.005 + 239.726i 0.610079 + 0.344930i
696696 0 0
697697 34.0491i 0.0488510i
698698 −53.2170 48.3562i −0.0762421 0.0692782i
699699 0 0
700700 617.057 456.819i 0.881509 0.652599i
701701 476.306i 0.679466i −0.940522 0.339733i 0.889663π-0.889663\pi
0.940522 0.339733i 0.110337π-0.110337\pi
702702 0 0
703703 −1364.03 −1.94030
704704 8.55107 + 28.9815i 0.0121464 + 0.0411669i
705705 0 0
706706 373.803 + 339.661i 0.529467 + 0.481106i
707707 809.246i 1.14462i
708708 0 0
709709 964.778i 1.36076i −0.732860 0.680380i 0.761815π-0.761815\pi
0.732860 0.680380i 0.238185π-0.238185\pi
710710 253.973 + 769.897i 0.357708 + 1.08436i
711711 0 0
712712 548.186 + 409.806i 0.769924 + 0.575570i
713713 214.216i 0.300443i
714714 0 0
715715 8.44582 + 4.77514i 0.0118123 + 0.00667852i
716716 −40.7965 425.274i −0.0569783 0.593958i
717717 0 0
718718 −879.461 799.132i −1.22488 1.11300i
719719 899.974i 1.25170i 0.779943 + 0.625851i 0.215248π0.215248\pi
−0.779943 + 0.625851i 0.784752π0.784752\pi
720720 0 0
721721 782.053 1.08468
722722 449.075 494.216i 0.621987 0.684510i
723723 0 0
724724 576.466 55.3003i 0.796224 0.0763816i
725725 893.220 537.415i 1.23203 0.741262i
726726 0 0
727727 908.888 1.25019 0.625095 0.780549i 0.285060π-0.285060\pi
0.625095 + 0.780549i 0.285060π0.285060\pi
728728 −202.183 151.145i −0.277723 0.207617i
729729 0 0
730730 261.348 + 792.255i 0.358012 + 1.08528i
731731 21.0619 0.0288125
732732 0 0
733733 433.283 0.591109 0.295554 0.955326i 0.404496π-0.404496\pi
0.295554 + 0.955326i 0.404496π0.404496\pi
734734 119.579 131.599i 0.162914 0.179290i
735735 0 0
736736 161.803 266.110i 0.219842 0.361562i
737737 35.8065i 0.0485842i
738738 0 0
739739 −886.138 −1.19910 −0.599552 0.800336i 0.704655π-0.704655\pi
−0.599552 + 0.800336i 0.704655π0.704655\pi
740740 −420.990 + 945.400i −0.568905 + 1.27757i
741741 0 0
742742 −412.019 + 453.435i −0.555281 + 0.611099i
743743 −895.305 −1.20499 −0.602493 0.798124i 0.705826π-0.705826\pi
−0.602493 + 0.798124i 0.705826π0.705826\pi
744744 0 0
745745 470.997 833.055i 0.632211 1.11820i
746746 112.515 123.825i 0.150824 0.165985i
747747 0 0
748748 4.25150 0.407846i 0.00568382 0.000545248i
749749 253.329i 0.338223i
750750 0 0
751751 1297.13i 1.72720i 0.504176 + 0.863601i 0.331796π0.331796\pi
−0.504176 + 0.863601i 0.668204π0.668204\pi
752752 137.639 26.6527i 0.183031 0.0354425i
753753 0 0
754754 −253.666 230.496i −0.336427 0.305698i
755755 −168.210 + 297.515i −0.222795 + 0.394060i
756756 0 0
757757 −421.694 −0.557060 −0.278530 0.960428i 0.589847π-0.589847\pi
−0.278530 + 0.960428i 0.589847π0.589847\pi
758758 −181.756 + 200.026i −0.239783 + 0.263886i
759759 0 0
760760 −424.435 965.231i −0.558468 1.27004i
761761 −1415.76 −1.86039 −0.930196 0.367063i 0.880363π-0.880363\pi
−0.930196 + 0.367063i 0.880363π0.880363\pi
762762 0 0
763763 1393.88i 1.82684i
764764 839.384 80.5220i 1.09867 0.105395i
765765 0 0
766766 −670.517 + 737.917i −0.875348 + 0.963339i
767767 317.261 0.413639
768768 0 0
769769 −414.210 −0.538635 −0.269318 0.963051i 0.586798π-0.586798\pi
−0.269318 + 0.963051i 0.586798π0.586798\pi
770770 34.4237 11.3557i 0.0447061 0.0147476i
771771 0 0
772772 −430.726 + 41.3195i −0.557935 + 0.0535226i
773773 727.056 0.940564 0.470282 0.882516i 0.344152π-0.344152\pi
0.470282 + 0.882516i 0.344152π0.344152\pi
774774 0 0
775775 471.498 283.682i 0.608385 0.366042i
776776 474.833 635.171i 0.611898 0.818519i
777777 0 0
778778 −456.522 414.824i −0.586790 0.533193i
779779 −396.879 −0.509473
780780 0 0
781781 38.2763i 0.0490094i
782782 −32.5797 29.6039i −0.0416621 0.0378567i
783783 0 0
784784 −156.207 + 30.2481i −0.199243 + 0.0385818i
785785 −675.659 382.008i −0.860713 0.486634i
786786 0 0
787787 1030.11i 1.30890i −0.756104 0.654451i 0.772900π-0.772900\pi
0.756104 0.654451i 0.227100π-0.227100\pi
788788 117.760 + 1227.56i 0.149442 + 1.55782i
789789 0 0
790790 315.646 + 956.854i 0.399552 + 1.21121i
791791 588.407i 0.743878i
792792 0 0
793793 60.6835i 0.0765239i
794794 400.381 440.627i 0.504258 0.554946i
795795 0 0
796796 −986.906 + 94.6737i −1.23983 + 0.118937i
797797 371.202 0.465750 0.232875 0.972507i 0.425187π-0.425187\pi
0.232875 + 0.972507i 0.425187π0.425187\pi
798798 0 0
799799 19.8162i 0.0248013i
800800 −799.991 3.73224i −0.999989 0.00466530i
801801 0 0
802802 −199.951 + 220.050i −0.249315 + 0.274376i
803803 39.3879i 0.0490509i
804804 0 0
805805 −325.225 183.877i −0.404006 0.228419i
806806 −133.901 121.671i −0.166130 0.150956i
807807 0 0
808808 −504.890 + 675.378i −0.624864 + 0.835863i
809809 −77.7771 −0.0961398 −0.0480699 0.998844i 0.515307π-0.515307\pi
−0.0480699 + 0.998844i 0.515307π0.515307\pi
810810 0 0
811811 −1407.90 −1.73600 −0.868000 0.496564i 0.834595π-0.834595\pi
−0.868000 + 0.496564i 0.834595π0.834595\pi
812812 −1274.67 + 122.279i −1.56979 + 0.150590i
813813 0 0
814814 −32.8591 + 36.1621i −0.0403675 + 0.0444252i
815815 222.648 393.799i 0.273188 0.483189i
816816 0 0
817817 245.500i 0.300489i
818818 595.009 654.820i 0.727395 0.800513i
819819 0 0
820820 −122.491 + 275.074i −0.149380 + 0.335456i
821821 820.275i 0.999116i 0.866280 + 0.499558i 0.166504π0.166504\pi
−0.866280 + 0.499558i 0.833496π0.833496\pi
822822 0 0
823823 1385.41 1.68336 0.841681 0.539976i 0.181567π-0.181567\pi
0.841681 + 0.539976i 0.181567π0.181567\pi
824824 −652.683 487.924i −0.792091 0.592141i
825825 0 0
826826 797.118 877.245i 0.965034 1.06204i
827827 258.898i 0.313057i 0.987673 + 0.156529i 0.0500303π0.0500303\pi
−0.987673 + 0.156529i 0.949970π0.949970\pi
828828 0 0
829829 1299.31i 1.56732i 0.621190 + 0.783660i 0.286649π0.286649\pi
−0.621190 + 0.783660i 0.713351π0.713351\pi
830830 −0.836249 2.53502i −0.00100753 0.00305424i
831831 0 0
832832 74.4371 + 252.284i 0.0894677 + 0.303226i
833833 22.4894i 0.0269980i
834834 0 0
835835 438.636 + 247.998i 0.525313 + 0.297004i
836836 −4.75388 49.5558i −0.00568646 0.0592773i
837837 0 0
838838 −721.166 + 793.658i −0.860580 + 0.947086i
839839 804.961i 0.959429i 0.877425 + 0.479715i 0.159260π0.159260\pi
−0.877425 + 0.479715i 0.840740π0.840740\pi
840840 0 0
841841 −897.650 −1.06736
842842 761.683 + 692.111i 0.904611 + 0.821985i
843843 0 0
844844 −88.0751 918.120i −0.104354 1.08782i
845845 −662.052 374.314i −0.783493 0.442975i
846846 0 0
847847 −927.268 −1.09477
848848 626.760 121.367i 0.739104 0.143121i
849849 0 0
850850 −22.0148 + 110.913i −0.0258997 + 0.130486i
851851 503.607 0.591782
852852 0 0
853853 −470.811 −0.551948 −0.275974 0.961165i 0.589000π-0.589000\pi
−0.275974 + 0.961165i 0.589000π0.589000\pi
854854 167.793 + 152.467i 0.196479 + 0.178533i
855855 0 0
856856 −158.053 + 211.423i −0.184641 + 0.246989i
857857 266.105i 0.310508i −0.987875 0.155254i 0.950380π-0.950380\pi
0.987875 0.155254i 0.0496196π-0.0496196\pi
858858 0 0
859859 1442.02 1.67872 0.839360 0.543576i 0.182930π-0.182930\pi
0.839360 + 0.543576i 0.182930π0.182930\pi
860860 −170.154 75.7701i −0.197854 0.0881048i
861861 0 0
862862 128.503 + 116.766i 0.149076 + 0.135459i
863863 −364.495 −0.422358 −0.211179 0.977447i 0.567730π-0.567730\pi
−0.211179 + 0.977447i 0.567730π0.567730\pi
864864 0 0
865865 −237.889 134.499i −0.275016 0.155490i
866866 731.242 + 664.451i 0.844391 + 0.767265i
867867 0 0
868868 −672.852 + 64.5466i −0.775176 + 0.0743625i
869869 47.5711i 0.0547424i
870870 0 0
871871 311.696i 0.357860i
872872 −869.645 + 1163.30i −0.997299 + 1.33406i
873873 0 0
874874 −345.066 + 379.752i −0.394812 + 0.434499i
875875 25.9675 + 959.338i 0.0296771 + 1.09639i
876876 0 0
877877 −77.4289 −0.0882883 −0.0441442 0.999025i 0.514056π-0.514056\pi
−0.0441442 + 0.999025i 0.514056π0.514056\pi
878878 −776.659 705.719i −0.884577 0.803781i
879879 0 0
880880 −35.8140 11.9998i −0.0406977 0.0136362i
881881 −724.932 −0.822851 −0.411426 0.911443i 0.634969π-0.634969\pi
−0.411426 + 0.911443i 0.634969π0.634969\pi
882882 0 0
883883 493.342i 0.558711i −0.960188 0.279356i 0.909879π-0.909879\pi
0.960188 0.279356i 0.0901208π-0.0901208\pi
884884 37.0093 3.55030i 0.0418657 0.00401618i
885885 0 0
886886 735.029 + 667.892i 0.829604 + 0.753828i
887887 1514.47 1.70741 0.853705 0.520758i 0.174351π-0.174351\pi
0.853705 + 0.520758i 0.174351π0.174351\pi
888888 0 0
889889 −1097.59 −1.23464
890890 −812.476 + 268.019i −0.912895 + 0.301145i
891891 0 0
892892 67.9067 + 707.879i 0.0761286 + 0.793586i
893893 −230.979 −0.258655
894894 0 0
895895 464.876 + 262.834i 0.519414 + 0.293669i
896896 884.604 + 428.041i 0.987281 + 0.477725i
897897 0 0
898898 446.751 491.659i 0.497496 0.547505i
899899 −917.771 −1.02088
900900 0 0
901901 90.2359i 0.100151i
902902 −9.56071 + 10.5218i −0.0105995 + 0.0116649i
903903 0 0
904904 367.108 491.071i 0.406093 0.543220i
905905 −356.276 + 630.147i −0.393675 + 0.696295i
906906 0 0
907907 851.570i 0.938887i −0.882963 0.469443i 0.844455π-0.844455\pi
0.882963 0.469443i 0.155545π-0.155545\pi
908908 809.489 77.6542i 0.891508 0.0855223i
909909 0 0
910910 299.658 98.8510i 0.329295 0.108627i
911911 517.728i 0.568308i −0.958779 0.284154i 0.908287π-0.908287\pi
0.958779 0.284154i 0.0917127π-0.0917127\pi
912912 0 0
913913 0.126031i 0.000138041i
914914 −374.177 340.000i −0.409383 0.371991i
915915 0 0
916916 −322.800 + 30.9662i −0.352402 + 0.0338059i
917917 −845.585 −0.922121
918918 0 0
919919 657.730i 0.715701i −0.933779 0.357851i 0.883510π-0.883510\pi
0.933779 0.357851i 0.116490π-0.116490\pi
920920 156.704 + 356.368i 0.170330 + 0.387357i
921921 0 0
922922 1232.58 + 1120.00i 1.33686 + 1.21475i
923923 333.195i 0.360992i
924924 0 0
925925 −666.917 1108.46i −0.720991 1.19833i
926926 −1148.90 + 1264.39i −1.24072 + 1.36543i
927927 0 0
928928 1140.10 + 693.218i 1.22856 + 0.747002i
929929 −1206.28 −1.29847 −0.649237 0.760586i 0.724912π-0.724912\pi
−0.649237 + 0.760586i 0.724912π0.724912\pi
930930 0 0
931931 262.138 0.281566
932932 −224.117 + 21.4995i −0.240469 + 0.0230681i
933933 0 0
934934 152.055 + 138.166i 0.162799 + 0.147929i
935935 −2.62757 + 4.64740i −0.00281024 + 0.00497048i
936936 0 0
937937 216.730i 0.231302i 0.993290 + 0.115651i 0.0368954π0.0368954\pi
−0.993290 + 0.115651i 0.963105π0.963105\pi
938938 861.858 + 783.136i 0.918825 + 0.834900i
939939 0 0
940940 −71.2886 + 160.090i −0.0758389 + 0.170309i
941941 749.322i 0.796304i −0.917320 0.398152i 0.869652π-0.869652\pi
0.917320 0.398152i 0.130348π-0.130348\pi
942942 0 0
943943 146.530 0.155387
944944 −1212.57 + 234.804i −1.28450 + 0.248733i
945945 0 0
946946 −6.50850 5.91402i −0.00688002 0.00625160i
947947 114.160i 0.120549i −0.998182 0.0602743i 0.980802π-0.980802\pi
0.998182 0.0602743i 0.0191976π-0.0191976\pi
948948 0 0
949949 342.872i 0.361298i
950950 1292.81 + 256.606i 1.36086 + 0.270112i
951951 0 0
952952 83.1691 111.253i 0.0873625 0.116862i
953953 820.680i 0.861154i −0.902554 0.430577i 0.858310π-0.858310\pi
0.902554 0.430577i 0.141690π-0.141690\pi
954954 0 0
955955 −518.768 + 917.548i −0.543212 + 0.960783i
956956 −1434.35 + 137.597i −1.50037 + 0.143930i
957957 0 0
958958 −397.836 361.498i −0.415278 0.377347i
959959 1730.50i 1.80448i
960960 0 0
961961 476.542 0.495881
962962 −286.039 + 314.792i −0.297338 + 0.327226i
963963 0 0
964964 75.4365 + 786.371i 0.0782536 + 0.815738i
965965 266.203 470.835i 0.275858 0.487912i
966966 0 0
967967 1108.56 1.14639 0.573194 0.819420i 0.305704π-0.305704\pi
0.573194 + 0.819420i 0.305704π0.305704\pi
968968 773.876 + 578.524i 0.799459 + 0.597649i
969969 0 0
970970 310.547 + 941.397i 0.320152 + 0.970513i
971971 1372.41 1.41340 0.706698 0.707516i 0.250184π-0.250184\pi
0.706698 + 0.707516i 0.250184π0.250184\pi
972972 0 0
973973 747.916 0.768670
974974 677.966 746.115i 0.696063 0.766032i
975975 0 0
976976 −44.9117 231.932i −0.0460161 0.237635i
977977 927.224i 0.949052i −0.880241 0.474526i 0.842619π-0.842619\pi
0.880241 0.474526i 0.157381π-0.157381\pi
978978 0 0
979979 −40.3932 −0.0412597
980980 80.9053 181.686i 0.0825564 0.185394i
981981 0 0
982982 −174.877 + 192.455i −0.178082 + 0.195983i
983983 354.106 0.360230 0.180115 0.983646i 0.442353π-0.442353\pi
0.180115 + 0.983646i 0.442353π0.442353\pi
984984 0 0
985985 −1341.88 758.677i −1.36231 0.770230i
986986 126.833 139.582i 0.128634 0.141564i
987987 0 0
988988 −41.3826 431.383i −0.0418852 0.436623i
989989 90.6396i 0.0916478i
990990 0 0
991991 537.545i 0.542427i −0.962519 0.271213i 0.912575π-0.912575\pi
0.962519 0.271213i 0.0874249π-0.0874249\pi
992992 601.817 + 365.925i 0.606671 + 0.368876i
993993 0 0
994994 921.305 + 837.154i 0.926866 + 0.842207i
995995 609.941 1078.81i 0.613006 1.08423i
996996 0 0
997997 −441.759 −0.443088 −0.221544 0.975150i 0.571110π-0.571110\pi
−0.221544 + 0.975150i 0.571110π0.571110\pi
998998 893.326 983.123i 0.895116 0.985094i
999999 0 0
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 360.3.p.g.19.7 8
3.2 odd 2 40.3.e.c.19.2 yes 8
4.3 odd 2 1440.3.p.g.559.8 8
5.4 even 2 inner 360.3.p.g.19.2 8
8.3 odd 2 inner 360.3.p.g.19.1 8
8.5 even 2 1440.3.p.g.559.1 8
12.11 even 2 160.3.e.c.79.7 8
15.2 even 4 200.3.g.h.51.3 8
15.8 even 4 200.3.g.h.51.6 8
15.14 odd 2 40.3.e.c.19.7 yes 8
20.19 odd 2 1440.3.p.g.559.2 8
24.5 odd 2 160.3.e.c.79.8 8
24.11 even 2 40.3.e.c.19.8 yes 8
40.19 odd 2 inner 360.3.p.g.19.8 8
40.29 even 2 1440.3.p.g.559.7 8
48.5 odd 4 1280.3.h.m.1279.3 16
48.11 even 4 1280.3.h.m.1279.15 16
48.29 odd 4 1280.3.h.m.1279.14 16
48.35 even 4 1280.3.h.m.1279.2 16
60.23 odd 4 800.3.g.h.751.2 8
60.47 odd 4 800.3.g.h.751.7 8
60.59 even 2 160.3.e.c.79.2 8
120.29 odd 2 160.3.e.c.79.1 8
120.53 even 4 800.3.g.h.751.1 8
120.59 even 2 40.3.e.c.19.1 8
120.77 even 4 800.3.g.h.751.8 8
120.83 odd 4 200.3.g.h.51.5 8
120.107 odd 4 200.3.g.h.51.4 8
240.29 odd 4 1280.3.h.m.1279.1 16
240.59 even 4 1280.3.h.m.1279.4 16
240.149 odd 4 1280.3.h.m.1279.16 16
240.179 even 4 1280.3.h.m.1279.13 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.3.e.c.19.1 8 120.59 even 2
40.3.e.c.19.2 yes 8 3.2 odd 2
40.3.e.c.19.7 yes 8 15.14 odd 2
40.3.e.c.19.8 yes 8 24.11 even 2
160.3.e.c.79.1 8 120.29 odd 2
160.3.e.c.79.2 8 60.59 even 2
160.3.e.c.79.7 8 12.11 even 2
160.3.e.c.79.8 8 24.5 odd 2
200.3.g.h.51.3 8 15.2 even 4
200.3.g.h.51.4 8 120.107 odd 4
200.3.g.h.51.5 8 120.83 odd 4
200.3.g.h.51.6 8 15.8 even 4
360.3.p.g.19.1 8 8.3 odd 2 inner
360.3.p.g.19.2 8 5.4 even 2 inner
360.3.p.g.19.7 8 1.1 even 1 trivial
360.3.p.g.19.8 8 40.19 odd 2 inner
800.3.g.h.751.1 8 120.53 even 4
800.3.g.h.751.2 8 60.23 odd 4
800.3.g.h.751.7 8 60.47 odd 4
800.3.g.h.751.8 8 120.77 even 4
1280.3.h.m.1279.1 16 240.29 odd 4
1280.3.h.m.1279.2 16 48.35 even 4
1280.3.h.m.1279.3 16 48.5 odd 4
1280.3.h.m.1279.4 16 240.59 even 4
1280.3.h.m.1279.13 16 240.179 even 4
1280.3.h.m.1279.14 16 48.29 odd 4
1280.3.h.m.1279.15 16 48.11 even 4
1280.3.h.m.1279.16 16 240.149 odd 4
1440.3.p.g.559.1 8 8.5 even 2
1440.3.p.g.559.2 8 20.19 odd 2
1440.3.p.g.559.7 8 40.29 even 2
1440.3.p.g.559.8 8 4.3 odd 2