Properties

Label 460.2.e.b.91.19
Level 460460
Weight 22
Character 460.91
Analytic conductor 3.6733.673
Analytic rank 00
Dimension 3232
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(91,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 460=22523 460 = 2^{2} \cdot 5 \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 460.e (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: 3.673118492983.67311849298
Analytic rank: 00
Dimension: 3232
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 91.19
Character χ\chi == 460.91
Dual form 460.2.e.b.91.18

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.341935+1.37225i)q22.41873iq3+(1.76616+0.938444i)q41.00000iq5+(3.319110.827049i)q62.44077q7+(1.891702.10273i)q82.85025q9+(1.372250.341935i)q102.59002q11+(2.26984+4.27186i)q120.482508q13+(0.8345843.34935i)q142.41873q15+(2.238653.31489i)q16+1.74316iq17+(0.9746013.91126i)q187.09763q19+(0.938444+1.76616i)q20+5.90355iq21+(0.8856203.55417i)q22+(1.733884.47143i)q23+(5.08594+4.57550i)q241.00000q25+(0.1649860.662123i)q260.362207iq27+(4.310782.29052i)q28+1.03287q29+(0.8270493.31911i)q30+2.87696iq31+(5.31434+1.93851i)q32+6.26456iq33+(2.39206+0.596048i)q34+2.44077iq35+(5.034002.67480i)q366.76257iq37+(2.426939.73974i)q38+1.16706iq39+(2.10273+1.89170i)q40+0.907172q41+(8.10117+2.01863i)q42+1.65967q43+(4.574392.43059i)q44+2.85025iq45+(5.543053.90827i)q464.40127iq47+(8.017815.41468i)q481.04266q49+(0.3419351.37225i)q50+4.21623q51+(0.8521860.452807i)q521.89738iq53+(0.4970400.123851i)q54+2.59002iq55+(4.61719+5.13228i)q56+17.1672iq57+(0.353174+1.41736i)q583.79671iq59+(4.271862.26984i)q608.17854iq61+(3.94792+0.983733i)q62+6.95679q63+(0.842973+7.95546i)q64+0.482508iq65+(8.59656+2.14207i)q66+15.6210q67+(1.635863.07870i)q68+(10.8152+4.19380i)q69+(3.34935+0.834584i)q70+11.0655iq71+(5.39180+5.99331i)q72+5.06355q73+(9.279962.31236i)q74+2.41873iq75+(12.53556.66073i)q76+6.32163q77+(1.60150+0.399057i)q78+9.79312q79+(3.314892.23865i)q809.42683q81+(0.310194+1.24487i)q82+13.5571q83+(5.5401510.4266i)q84+1.74316q85+(0.567501+2.27749i)q862.49823iq87+(4.89953+5.44612i)q88+2.55180iq89+(3.91126+0.974601i)q90+1.17769q91+(7.25850+6.27010i)q92+6.95858q93+(6.039651.50495i)q94+7.09763iq95+(4.6887412.8539i)q96+1.34364iq97+(0.3565231.43080i)q98+7.38220q99+O(q100)q+(0.341935 + 1.37225i) q^{2} -2.41873i q^{3} +(-1.76616 + 0.938444i) q^{4} -1.00000i q^{5} +(3.31911 - 0.827049i) q^{6} -2.44077 q^{7} +(-1.89170 - 2.10273i) q^{8} -2.85025 q^{9} +(1.37225 - 0.341935i) q^{10} -2.59002 q^{11} +(2.26984 + 4.27186i) q^{12} -0.482508 q^{13} +(-0.834584 - 3.34935i) q^{14} -2.41873 q^{15} +(2.23865 - 3.31489i) q^{16} +1.74316i q^{17} +(-0.974601 - 3.91126i) q^{18} -7.09763 q^{19} +(0.938444 + 1.76616i) q^{20} +5.90355i q^{21} +(-0.885620 - 3.55417i) q^{22} +(-1.73388 - 4.47143i) q^{23} +(-5.08594 + 4.57550i) q^{24} -1.00000 q^{25} +(-0.164986 - 0.662123i) q^{26} -0.362207i q^{27} +(4.31078 - 2.29052i) q^{28} +1.03287 q^{29} +(-0.827049 - 3.31911i) q^{30} +2.87696i q^{31} +(5.31434 + 1.93851i) q^{32} +6.26456i q^{33} +(-2.39206 + 0.596048i) q^{34} +2.44077i q^{35} +(5.03400 - 2.67480i) q^{36} -6.76257i q^{37} +(-2.42693 - 9.73974i) q^{38} +1.16706i q^{39} +(-2.10273 + 1.89170i) q^{40} +0.907172 q^{41} +(-8.10117 + 2.01863i) q^{42} +1.65967 q^{43} +(4.57439 - 2.43059i) q^{44} +2.85025i q^{45} +(5.54305 - 3.90827i) q^{46} -4.40127i q^{47} +(-8.01781 - 5.41468i) q^{48} -1.04266 q^{49} +(-0.341935 - 1.37225i) q^{50} +4.21623 q^{51} +(0.852186 - 0.452807i) q^{52} -1.89738i q^{53} +(0.497040 - 0.123851i) q^{54} +2.59002i q^{55} +(4.61719 + 5.13228i) q^{56} +17.1672i q^{57} +(0.353174 + 1.41736i) q^{58} -3.79671i q^{59} +(4.27186 - 2.26984i) q^{60} -8.17854i q^{61} +(-3.94792 + 0.983733i) q^{62} +6.95679 q^{63} +(-0.842973 + 7.95546i) q^{64} +0.482508i q^{65} +(-8.59656 + 2.14207i) q^{66} +15.6210 q^{67} +(-1.63586 - 3.07870i) q^{68} +(-10.8152 + 4.19380i) q^{69} +(-3.34935 + 0.834584i) q^{70} +11.0655i q^{71} +(5.39180 + 5.99331i) q^{72} +5.06355 q^{73} +(9.27996 - 2.31236i) q^{74} +2.41873i q^{75} +(12.5355 - 6.66073i) q^{76} +6.32163 q^{77} +(-1.60150 + 0.399057i) q^{78} +9.79312 q^{79} +(-3.31489 - 2.23865i) q^{80} -9.42683 q^{81} +(0.310194 + 1.24487i) q^{82} +13.5571 q^{83} +(-5.54015 - 10.4266i) q^{84} +1.74316 q^{85} +(0.567501 + 2.27749i) q^{86} -2.49823i q^{87} +(4.89953 + 5.44612i) q^{88} +2.55180i q^{89} +(-3.91126 + 0.974601i) q^{90} +1.17769 q^{91} +(7.25850 + 6.27010i) q^{92} +6.95858 q^{93} +(6.03965 - 1.50495i) q^{94} +7.09763i q^{95} +(4.68874 - 12.8539i) q^{96} +1.34364i q^{97} +(-0.356523 - 1.43080i) q^{98} +7.38220 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+4q24q416q62q852q9+24q124q13+20q1656q186q2432q25+68q26+8q2916q32+8q36+44q414q464q48++62q98+O(q100) 32 q + 4 q^{2} - 4 q^{4} - 16 q^{6} - 2 q^{8} - 52 q^{9} + 24 q^{12} - 4 q^{13} + 20 q^{16} - 56 q^{18} - 6 q^{24} - 32 q^{25} + 68 q^{26} + 8 q^{29} - 16 q^{32} + 8 q^{36} + 44 q^{41} - 4 q^{46} - 4 q^{48}+ \cdots + 62 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/460Z)×\left(\mathbb{Z}/460\mathbb{Z}\right)^\times.

nn 231231 277277 281281
χ(n)\chi(n) 1-1 11 1-1

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 0.341935 + 1.37225i 0.241785 + 0.970330i
33 2.41873i 1.39645i −0.715877 0.698227i 0.753973π-0.753973\pi
0.715877 0.698227i 0.246027π-0.246027\pi
44 −1.76616 + 0.938444i −0.883080 + 0.469222i
55 1.00000i 0.447214i
66 3.31911 0.827049i 1.35502 0.337641i
77 −2.44077 −0.922523 −0.461261 0.887264i 0.652603π-0.652603\pi
−0.461261 + 0.887264i 0.652603π0.652603\pi
88 −1.89170 2.10273i −0.668816 0.743428i
99 −2.85025 −0.950083
1010 1.37225 0.341935i 0.433945 0.108129i
1111 −2.59002 −0.780921 −0.390460 0.920620i 0.627684π-0.627684\pi
−0.390460 + 0.920620i 0.627684π0.627684\pi
1212 2.26984 + 4.27186i 0.655247 + 1.23318i
1313 −0.482508 −0.133824 −0.0669118 0.997759i 0.521315π-0.521315\pi
−0.0669118 + 0.997759i 0.521315π0.521315\pi
1414 −0.834584 3.34935i −0.223052 0.895151i
1515 −2.41873 −0.624513
1616 2.23865 3.31489i 0.559661 0.828721i
1717 1.74316i 0.422779i 0.977402 + 0.211389i 0.0677988π0.0677988\pi
−0.977402 + 0.211389i 0.932201π0.932201\pi
1818 −0.974601 3.91126i −0.229716 0.921894i
1919 −7.09763 −1.62831 −0.814154 0.580650i 0.802799π-0.802799\pi
−0.814154 + 0.580650i 0.802799π0.802799\pi
2020 0.938444 + 1.76616i 0.209842 + 0.394925i
2121 5.90355i 1.28826i
2222 −0.885620 3.55417i −0.188815 0.757751i
2323 −1.73388 4.47143i −0.361540 0.932357i
2424 −5.08594 + 4.57550i −1.03816 + 0.933970i
2525 −1.00000 −0.200000
2626 −0.164986 0.662123i −0.0323565 0.129853i
2727 0.362207i 0.0697068i
2828 4.31078 2.29052i 0.814662 0.432868i
2929 1.03287 0.191799 0.0958994 0.995391i 0.469427π-0.469427\pi
0.0958994 + 0.995391i 0.469427π0.469427\pi
3030 −0.827049 3.31911i −0.150998 0.605984i
3131 2.87696i 0.516717i 0.966049 + 0.258358i 0.0831815π0.0831815\pi
−0.966049 + 0.258358i 0.916818π0.916818\pi
3232 5.31434 + 1.93851i 0.939451 + 0.342684i
3333 6.26456i 1.09052i
3434 −2.39206 + 0.596048i −0.410235 + 0.102221i
3535 2.44077i 0.412565i
3636 5.03400 2.67480i 0.839000 0.445800i
3737 6.76257i 1.11176i −0.831263 0.555880i 0.812382π-0.812382\pi
0.831263 0.555880i 0.187618π-0.187618\pi
3838 −2.42693 9.73974i −0.393700 1.58000i
3939 1.16706i 0.186878i
4040 −2.10273 + 1.89170i −0.332471 + 0.299103i
4141 0.907172 0.141677 0.0708383 0.997488i 0.477433π-0.477433\pi
0.0708383 + 0.997488i 0.477433π0.477433\pi
4242 −8.10117 + 2.01863i −1.25004 + 0.311482i
4343 1.65967 0.253098 0.126549 0.991960i 0.459610π-0.459610\pi
0.126549 + 0.991960i 0.459610π0.459610\pi
4444 4.57439 2.43059i 0.689616 0.366425i
4545 2.85025i 0.424890i
4646 5.54305 3.90827i 0.817279 0.576243i
4747 4.40127i 0.641991i −0.947081 0.320995i 0.895983π-0.895983\pi
0.947081 0.320995i 0.104017π-0.104017\pi
4848 −8.01781 5.41468i −1.15727 0.781541i
4949 −1.04266 −0.148952
5050 −0.341935 1.37225i −0.0483570 0.194066i
5151 4.21623 0.590391
5252 0.852186 0.452807i 0.118177 0.0627930i
5353 1.89738i 0.260625i −0.991473 0.130312i 0.958402π-0.958402\pi
0.991473 0.130312i 0.0415980π-0.0415980\pi
5454 0.497040 0.123851i 0.0676385 0.0168540i
5555 2.59002i 0.349238i
5656 4.61719 + 5.13228i 0.616997 + 0.685830i
5757 17.1672i 2.27386i
5858 0.353174 + 1.41736i 0.0463740 + 0.186108i
5959 3.79671i 0.494290i −0.968978 0.247145i 0.920508π-0.920508\pi
0.968978 0.247145i 0.0794924π-0.0794924\pi
6060 4.27186 2.26984i 0.551495 0.293035i
6161 8.17854i 1.04715i −0.851978 0.523577i 0.824597π-0.824597\pi
0.851978 0.523577i 0.175403π-0.175403\pi
6262 −3.94792 + 0.983733i −0.501386 + 0.124934i
6363 6.95679 0.876473
6464 −0.842973 + 7.95546i −0.105372 + 0.994433i
6565 0.482508i 0.0598477i
6666 −8.59656 + 2.14207i −1.05816 + 0.263671i
6767 15.6210 1.90840 0.954202 0.299163i 0.0967076π-0.0967076\pi
0.954202 + 0.299163i 0.0967076π0.0967076\pi
6868 −1.63586 3.07870i −0.198377 0.373348i
6969 −10.8152 + 4.19380i −1.30199 + 0.504874i
7070 −3.34935 + 0.834584i −0.400324 + 0.0997519i
7171 11.0655i 1.31323i 0.754225 + 0.656616i 0.228013π0.228013\pi
−0.754225 + 0.656616i 0.771987π0.771987\pi
7272 5.39180 + 5.99331i 0.635430 + 0.706319i
7373 5.06355 0.592644 0.296322 0.955088i 0.404240π-0.404240\pi
0.296322 + 0.955088i 0.404240π0.404240\pi
7474 9.27996 2.31236i 1.07877 0.268806i
7575 2.41873i 0.279291i
7676 12.5355 6.66073i 1.43793 0.764038i
7777 6.32163 0.720417
7878 −1.60150 + 0.399057i −0.181334 + 0.0451844i
7979 9.79312 1.10181 0.550906 0.834567i 0.314282π-0.314282\pi
0.550906 + 0.834567i 0.314282π0.314282\pi
8080 −3.31489 2.23865i −0.370615 0.250288i
8181 −9.42683 −1.04743
8282 0.310194 + 1.24487i 0.0342552 + 0.137473i
8383 13.5571 1.48808 0.744041 0.668134i 0.232907π-0.232907\pi
0.744041 + 0.668134i 0.232907π0.232907\pi
8484 −5.54015 10.4266i −0.604480 1.13764i
8585 1.74316 0.189072
8686 0.567501 + 2.27749i 0.0611952 + 0.245588i
8787 2.49823i 0.267838i
8888 4.89953 + 5.44612i 0.522292 + 0.580559i
8989 2.55180i 0.270490i 0.990812 + 0.135245i 0.0431822π0.0431822\pi
−0.990812 + 0.135245i 0.956818π0.956818\pi
9090 −3.91126 + 0.974601i −0.412284 + 0.102732i
9191 1.17769 0.123455
9292 7.25850 + 6.27010i 0.756751 + 0.653703i
9393 6.95858 0.721571
9494 6.03965 1.50495i 0.622943 0.155224i
9595 7.09763i 0.728201i
9696 4.68874 12.8539i 0.478542 1.31190i
9797 1.34364i 0.136426i 0.997671 + 0.0682131i 0.0217298π0.0217298\pi
−0.997671 + 0.0682131i 0.978270π0.978270\pi
9898 −0.356523 1.43080i −0.0360143 0.144532i
9999 7.38220 0.741939
100100 1.76616 0.938444i 0.176616 0.0938444i
101101 −17.6082 −1.75208 −0.876039 0.482240i 0.839823π-0.839823\pi
−0.876039 + 0.482240i 0.839823π0.839823\pi
102102 1.44168 + 5.78574i 0.142748 + 0.572874i
103103 −14.8411 −1.46233 −0.731167 0.682199i 0.761024π-0.761024\pi
−0.731167 + 0.682199i 0.761024π0.761024\pi
104104 0.912758 + 1.01459i 0.0895033 + 0.0994883i
105105 5.90355 0.576128
106106 2.60368 0.648780i 0.252892 0.0630151i
107107 −13.8673 −1.34060 −0.670302 0.742088i 0.733836π-0.733836\pi
−0.670302 + 0.742088i 0.733836π0.733836\pi
108108 0.339911 + 0.639716i 0.0327079 + 0.0615567i
109109 16.3923i 1.57010i −0.619434 0.785049i 0.712638π-0.712638\pi
0.619434 0.785049i 0.287362π-0.287362\pi
110110 −3.55417 + 0.885620i −0.338876 + 0.0844405i
111111 −16.3568 −1.55252
112112 −5.46401 + 8.09086i −0.516300 + 0.764514i
113113 15.5128i 1.45932i 0.683811 + 0.729660i 0.260321π0.260321\pi
−0.683811 + 0.729660i 0.739679π0.739679\pi
114114 −23.5578 + 5.87008i −2.20639 + 0.549784i
115115 −4.47143 + 1.73388i −0.416963 + 0.161686i
116116 −1.82421 + 0.969289i −0.169374 + 0.0899962i
117117 1.37527 0.127144
118118 5.21006 1.29823i 0.479625 0.119512i
119119 4.25465i 0.390023i
120120 4.57550 + 5.08594i 0.417684 + 0.464281i
121121 −4.29179 −0.390163
122122 11.2230 2.79653i 1.01609 0.253186i
123123 2.19420i 0.197845i
124124 −2.69986 5.08117i −0.242455 0.456302i
125125 1.00000i 0.0894427i
126126 2.37877 + 9.54648i 0.211918 + 0.850468i
127127 9.72306i 0.862782i −0.902165 0.431391i 0.858023π-0.858023\pi
0.902165 0.431391i 0.141977π-0.141977\pi
128128 −11.2052 + 1.56348i −0.990405 + 0.138193i
129129 4.01430i 0.353439i
130130 −0.662123 + 0.164986i −0.0580720 + 0.0144703i
131131 8.55926i 0.747826i −0.927464 0.373913i 0.878016π-0.878016\pi
0.927464 0.373913i 0.121984π-0.121984\pi
132132 −5.87894 11.0642i −0.511696 0.963016i
133133 17.3236 1.50215
134134 5.34136 + 21.4359i 0.461423 + 1.85178i
135135 −0.362207 −0.0311738
136136 3.66540 3.29753i 0.314306 0.282761i
137137 5.34661i 0.456792i −0.973568 0.228396i 0.926652π-0.926652\pi
0.973568 0.228396i 0.0733480π-0.0733480\pi
138138 −9.45304 13.4071i −0.804696 1.14129i
139139 15.1210i 1.28255i 0.767312 + 0.641274i 0.221594π0.221594\pi
−0.767312 + 0.641274i 0.778406π0.778406\pi
140140 −2.29052 4.31078i −0.193584 0.364328i
141141 −10.6455 −0.896510
142142 −15.1847 + 3.78368i −1.27427 + 0.317519i
143143 1.24971 0.104506
144144 −6.38070 + 9.44825i −0.531725 + 0.787354i
145145 1.03287i 0.0857751i
146146 1.73141 + 6.94848i 0.143292 + 0.575060i
147147 2.52192i 0.208004i
148148 6.34629 + 11.9438i 0.521662 + 0.981773i
149149 14.6235i 1.19800i 0.800749 + 0.599000i 0.204435π0.204435\pi
−0.800749 + 0.599000i 0.795565π0.795565\pi
150150 −3.31911 + 0.827049i −0.271004 + 0.0675283i
151151 6.63114i 0.539635i −0.962911 0.269817i 0.913037π-0.913037\pi
0.962911 0.269817i 0.0869634π-0.0869634\pi
152152 13.4266 + 14.9244i 1.08904 + 1.21053i
153153 4.96844i 0.401675i
154154 2.16159 + 8.67488i 0.174186 + 0.699042i
155155 2.87696 0.231083
156156 −1.09522 2.06121i −0.0876875 0.165029i
157157 17.8150i 1.42180i −0.703296 0.710898i 0.748289π-0.748289\pi
0.703296 0.710898i 0.251711π-0.251711\pi
158158 3.34861 + 13.4387i 0.266402 + 1.06912i
159159 −4.58924 −0.363951
160160 1.93851 5.31434i 0.153253 0.420135i
161161 4.23201 + 10.9137i 0.333529 + 0.860120i
162162 −3.22337 12.9360i −0.253251 1.01635i
163163 4.03456i 0.316011i −0.987438 0.158005i 0.949494π-0.949494\pi
0.987438 0.158005i 0.0505064π-0.0505064\pi
164164 −1.60221 + 0.851330i −0.125112 + 0.0664777i
165165 6.26456 0.487695
166166 4.63564 + 18.6037i 0.359795 + 1.44393i
167167 12.1772i 0.942301i −0.882053 0.471150i 0.843839π-0.843839\pi
0.882053 0.471150i 0.156161π-0.156161\pi
168168 12.4136 11.1677i 0.957729 0.861608i
169169 −12.7672 −0.982091
170170 0.596048 + 2.39206i 0.0457148 + 0.183463i
171171 20.2300 1.54703
172172 −2.93125 + 1.55751i −0.223506 + 0.118759i
173173 21.5454 1.63807 0.819035 0.573743i 0.194509π-0.194509\pi
0.819035 + 0.573743i 0.194509π0.194509\pi
174174 3.42820 0.854233i 0.259891 0.0647592i
175175 2.44077 0.184505
176176 −5.79814 + 8.58562i −0.437051 + 0.647166i
177177 −9.18322 −0.690253
178178 −3.50171 + 0.872550i −0.262465 + 0.0654004i
179179 25.0006i 1.86863i 0.356449 + 0.934315i 0.383987π0.383987\pi
−0.356449 + 0.934315i 0.616013π0.616013\pi
180180 −2.67480 5.03400i −0.199368 0.375212i
181181 20.6924i 1.53805i −0.639217 0.769026i 0.720742π-0.720742\pi
0.639217 0.769026i 0.279258π-0.279258\pi
182182 0.402693 + 1.61609i 0.0298496 + 0.119792i
183183 −19.7817 −1.46230
184184 −6.12223 + 12.1045i −0.451337 + 0.892354i
185185 −6.76257 −0.497194
186186 2.37938 + 9.54894i 0.174465 + 0.700162i
187187 4.51482i 0.330157i
188188 4.13034 + 7.77334i 0.301236 + 0.566929i
189189 0.884062i 0.0643061i
190190 −9.73974 + 2.42693i −0.706595 + 0.176068i
191191 −3.12789 −0.226326 −0.113163 0.993576i 0.536098π-0.536098\pi
−0.113163 + 0.993576i 0.536098π0.536098\pi
192192 19.2421 + 2.03892i 1.38868 + 0.147147i
193193 19.7240 1.41976 0.709882 0.704320i 0.248748π-0.248748\pi
0.709882 + 0.704320i 0.248748π0.248748\pi
194194 −1.84382 + 0.459439i −0.132378 + 0.0329858i
195195 1.16706 0.0835746
196196 1.84151 0.978481i 0.131536 0.0698915i
197197 −10.6999 −0.762333 −0.381167 0.924506i 0.624478π-0.624478\pi
−0.381167 + 0.924506i 0.624478π0.624478\pi
198198 2.52424 + 10.1303i 0.179390 + 0.719926i
199199 −21.1502 −1.49930 −0.749649 0.661836i 0.769778π-0.769778\pi
−0.749649 + 0.661836i 0.769778π0.769778\pi
200200 1.89170 + 2.10273i 0.133763 + 0.148686i
201201 37.7829i 2.66500i
202202 −6.02086 24.1629i −0.423626 1.70009i
203203 −2.52099 −0.176939
204204 −7.44655 + 3.95670i −0.521363 + 0.277024i
205205 0.907172i 0.0633597i
206206 −5.07468 20.3657i −0.353570 1.41895i
207207 4.94200 + 12.7447i 0.343493 + 0.885816i
208208 −1.08016 + 1.59946i −0.0748959 + 0.110902i
209209 18.3830 1.27158
210210 2.01863 + 8.10117i 0.139299 + 0.559034i
211211 6.84533i 0.471252i −0.971844 0.235626i 0.924286π-0.924286\pi
0.971844 0.235626i 0.0757140π-0.0757140\pi
212212 1.78058 + 3.35107i 0.122291 + 0.230153i
213213 26.7644 1.83387
214214 −4.74173 19.0295i −0.324138 1.30083i
215215 1.65967i 0.113189i
216216 −0.761624 + 0.685185i −0.0518220 + 0.0466210i
217217 7.02198i 0.476683i
218218 22.4944 5.60510i 1.52351 0.379626i
219219 12.2474i 0.827600i
220220 −2.43059 4.57439i −0.163870 0.308405i
221221 0.841089i 0.0565778i
222222 −5.59297 22.4457i −0.375376 1.50646i
223223 9.20583i 0.616468i −0.951311 0.308234i 0.900262π-0.900262\pi
0.951311 0.308234i 0.0997379π-0.0997379\pi
224224 −12.9710 4.73146i −0.866665 0.316134i
225225 2.85025 0.190017
226226 −21.2875 + 5.30437i −1.41602 + 0.352841i
227227 15.6774 1.04055 0.520274 0.853999i 0.325830π-0.325830\pi
0.520274 + 0.853999i 0.325830π0.325830\pi
228228 −16.1105 30.3201i −1.06694 2.00800i
229229 12.3042i 0.813087i −0.913631 0.406543i 0.866734π-0.866734\pi
0.913631 0.406543i 0.133266π-0.133266\pi
230230 −3.90827 5.54305i −0.257704 0.365498i
231231 15.2903i 1.00603i
232232 −1.95387 2.17185i −0.128278 0.142589i
233233 −7.21602 −0.472737 −0.236369 0.971663i 0.575957π-0.575957\pi
−0.236369 + 0.971663i 0.575957π0.575957\pi
234234 0.470252 + 1.88722i 0.0307414 + 0.123371i
235235 −4.40127 −0.287107
236236 3.56300 + 6.70561i 0.231932 + 0.436498i
237237 23.6869i 1.53863i
238238 5.83846 1.45481i 0.378451 0.0943016i
239239 0.395962i 0.0256126i 0.999918 + 0.0128063i 0.00407649π0.00407649\pi
−0.999918 + 0.0128063i 0.995924π0.995924\pi
240240 −5.41468 + 8.01781i −0.349516 + 0.517547i
241241 3.11185i 0.200452i 0.994965 + 0.100226i 0.0319565π0.0319565\pi
−0.994965 + 0.100226i 0.968043π0.968043\pi
242242 −1.46752 5.88943i −0.0943355 0.378587i
243243 21.7143i 1.39297i
244244 7.67510 + 14.4446i 0.491348 + 0.924722i
245245 1.04266i 0.0666133i
246246 3.01100 0.750276i 0.191975 0.0478358i
247247 3.42466 0.217906
248248 6.04947 5.44233i 0.384142 0.345588i
249249 32.7909i 2.07804i
250250 −1.37225 + 0.341935i −0.0867889 + 0.0216259i
251251 13.7629 0.868704 0.434352 0.900743i 0.356977π-0.356977\pi
0.434352 + 0.900743i 0.356977π0.356977\pi
252252 −12.2868 + 6.52856i −0.773996 + 0.411260i
253253 4.49080 + 11.5811i 0.282334 + 0.728096i
254254 13.3425 3.32466i 0.837183 0.208607i
255255 4.21623i 0.264031i
256256 −5.97693 14.8417i −0.373558 0.927607i
257257 −24.5390 −1.53070 −0.765351 0.643613i 0.777435π-0.777435\pi
−0.765351 + 0.643613i 0.777435π0.777435\pi
258258 5.50864 1.37263i 0.342953 0.0854563i
259259 16.5058i 1.02562i
260260 −0.452807 0.852186i −0.0280819 0.0528503i
261261 −2.94393 −0.182225
262262 11.7455 2.92671i 0.725638 0.180813i
263263 10.3038 0.635362 0.317681 0.948198i 0.397096π-0.397096\pi
0.317681 + 0.948198i 0.397096π0.397096\pi
264264 13.1727 11.8506i 0.810723 0.729356i
265265 −1.89738 −0.116555
266266 5.92357 + 23.7724i 0.363197 + 1.45758i
267267 6.17211 0.377727
268268 −27.5891 + 14.6594i −1.68527 + 0.895465i
269269 −2.31211 −0.140972 −0.0704859 0.997513i 0.522455π-0.522455\pi
−0.0704859 + 0.997513i 0.522455π0.522455\pi
270270 −0.123851 0.497040i −0.00753735 0.0302489i
271271 21.0099i 1.27626i −0.769929 0.638129i 0.779709π-0.779709\pi
0.769929 0.638129i 0.220291π-0.220291\pi
272272 5.77838 + 3.90232i 0.350366 + 0.236613i
273273 2.84851i 0.172400i
274274 7.33690 1.82819i 0.443239 0.110445i
275275 2.59002 0.156184
276276 15.1657 17.5563i 0.912866 1.05677i
277277 −7.45198 −0.447746 −0.223873 0.974618i 0.571870π-0.571870\pi
−0.223873 + 0.974618i 0.571870π0.571870\pi
278278 −20.7499 + 5.17041i −1.24449 + 0.310101i
279279 8.20005i 0.490924i
280280 5.13228 4.61719i 0.306712 0.275930i
281281 14.8257i 0.884429i 0.896909 + 0.442215i 0.145807π0.145807\pi
−0.896909 + 0.442215i 0.854193π0.854193\pi
282282 −3.64006 14.6083i −0.216763 0.869911i
283283 −4.08320 −0.242721 −0.121360 0.992609i 0.538726π-0.538726\pi
−0.121360 + 0.992609i 0.538726π0.538726\pi
284284 −10.3843 19.5434i −0.616197 1.15969i
285285 17.1672 1.01690
286286 0.427318 + 1.71491i 0.0252679 + 0.101405i
287287 −2.21419 −0.130700
288288 −15.1472 5.52525i −0.892556 0.325578i
289289 13.9614 0.821258
290290 1.41736 0.353174i 0.0832301 0.0207391i
291291 3.24991 0.190513
292292 −8.94304 + 4.75186i −0.523352 + 0.278082i
293293 7.93619i 0.463637i −0.972759 0.231819i 0.925532π-0.925532\pi
0.972759 0.231819i 0.0744676π-0.0744676\pi
294294 −3.46071 + 0.862333i −0.201833 + 0.0502923i
295295 −3.79671 −0.221053
296296 −14.2199 + 12.7927i −0.826514 + 0.743562i
297297 0.938123i 0.0544354i
298298 −20.0671 + 5.00028i −1.16246 + 0.289658i
299299 0.836613 + 2.15750i 0.0483826 + 0.124771i
300300 −2.26984 4.27186i −0.131049 0.246636i
301301 −4.05087 −0.233488
302302 9.09961 2.26742i 0.523624 0.130475i
303303 42.5894i 2.44670i
304304 −15.8891 + 23.5278i −0.911301 + 1.34941i
305305 −8.17854 −0.468302
306306 6.81797 1.69889i 0.389757 0.0971189i
307307 26.2313i 1.49710i 0.663078 + 0.748551i 0.269250π0.269250\pi
−0.663078 + 0.748551i 0.730750π0.730750\pi
308308 −11.1650 + 5.93250i −0.636186 + 0.338035i
309309 35.8965i 2.04208i
310310 0.983733 + 3.94792i 0.0558723 + 0.224227i
311311 25.4427i 1.44272i 0.692559 + 0.721361i 0.256483π0.256483\pi
−0.692559 + 0.721361i 0.743517π0.743517\pi
312312 2.45401 2.20771i 0.138931 0.124987i
313313 27.2137i 1.53821i −0.639123 0.769105i 0.720702π-0.720702\pi
0.639123 0.769105i 0.279298π-0.279298\pi
314314 24.4468 6.09159i 1.37961 0.343768i
315315 6.95679i 0.391971i
316316 −17.2962 + 9.19030i −0.972989 + 0.516995i
317317 −19.7663 −1.11019 −0.555094 0.831788i 0.687318π-0.687318\pi
−0.555094 + 0.831788i 0.687318π0.687318\pi
318318 −1.56922 6.29760i −0.0879977 0.353152i
319319 −2.67515 −0.149780
320320 7.95546 + 0.842973i 0.444724 + 0.0471236i
321321 33.5413i 1.87209i
322322 −13.5293 + 9.53917i −0.753958 + 0.531597i
323323 12.3723i 0.688414i
324324 16.6493 8.84655i 0.924961 0.491475i
325325 0.482508 0.0267647
326326 5.53644 1.37956i 0.306635 0.0764066i
327327 −39.6485 −2.19257
328328 −1.71609 1.90754i −0.0947554 0.105326i
329329 10.7425i 0.592251i
330330 2.14207 + 8.59656i 0.117917 + 0.473225i
331331 32.1515i 1.76720i −0.468238 0.883602i 0.655111π-0.655111\pi
0.468238 0.883602i 0.344889π-0.344889\pi
332332 −23.9440 + 12.7225i −1.31410 + 0.698241i
333333 19.2750i 1.05626i
334334 16.7102 4.16382i 0.914343 0.227834i
335335 15.6210i 0.853464i
336336 19.5696 + 13.2160i 1.06761 + 0.720990i
337337 25.7071i 1.40035i 0.713970 + 0.700176i 0.246895π0.246895\pi
−0.713970 + 0.700176i 0.753105π0.753105\pi
338338 −4.36555 17.5198i −0.237455 0.952953i
339339 37.5212 2.03787
340340 −3.07870 + 1.63586i −0.166966 + 0.0887169i
341341 7.45138i 0.403515i
342342 6.91735 + 27.7607i 0.374048 + 1.50113i
343343 19.6303 1.05993
344344 −3.13960 3.48985i −0.169276 0.188160i
345345 4.19380 + 10.8152i 0.225786 + 0.582269i
346346 7.36715 + 29.5658i 0.396060 + 1.58947i
347347 6.50423i 0.349165i −0.984643 0.174583i 0.944142π-0.944142\pi
0.984643 0.174583i 0.0558576π-0.0558576\pi
348348 2.34445 + 4.41227i 0.125676 + 0.236523i
349349 13.3980 0.717177 0.358588 0.933496i 0.383258π-0.383258\pi
0.358588 + 0.933496i 0.383258π0.383258\pi
350350 0.834584 + 3.34935i 0.0446104 + 0.179030i
351351 0.174768i 0.00932841i
352352 −13.7642 5.02079i −0.733636 0.267609i
353353 −35.4004 −1.88417 −0.942087 0.335370i 0.891139π-0.891139\pi
−0.942087 + 0.335370i 0.891139π0.891139\pi
354354 −3.14007 12.6017i −0.166893 0.669773i
355355 11.0655 0.587295
356356 −2.39472 4.50688i −0.126920 0.238864i
357357 −10.2908 −0.544649
358358 −34.3071 + 8.54857i −1.81319 + 0.451806i
359359 −17.3591 −0.916179 −0.458089 0.888906i 0.651466π-0.651466\pi
−0.458089 + 0.888906i 0.651466π0.651466\pi
360360 5.99331 5.39180i 0.315875 0.284173i
361361 31.3763 1.65138
362362 28.3952 7.07546i 1.49242 0.371878i
363363 10.3807i 0.544845i
364364 −2.07999 + 1.10519i −0.109021 + 0.0579279i
365365 5.06355i 0.265038i
366366 −6.76405 27.1455i −0.353563 1.41892i
367367 −15.7816 −0.823792 −0.411896 0.911231i 0.635133π-0.635133\pi
−0.411896 + 0.911231i 0.635133π0.635133\pi
368368 −18.7038 4.26231i −0.975004 0.222188i
369369 −2.58567 −0.134604
370370 −2.31236 9.27996i −0.120214 0.482442i
371371 4.63105i 0.240432i
372372 −12.2900 + 6.53024i −0.637205 + 0.338577i
373373 32.2760i 1.67119i 0.549348 + 0.835593i 0.314876π0.314876\pi
−0.549348 + 0.835593i 0.685124π0.685124\pi
374374 6.19548 1.54378i 0.320361 0.0798268i
375375 2.41873 0.124903
376376 −9.25469 + 8.32586i −0.477274 + 0.429373i
377377 −0.498367 −0.0256672
378378 −1.21316 + 0.302292i −0.0623981 + 0.0155482i
379379 −9.04274 −0.464494 −0.232247 0.972657i 0.574608π-0.574608\pi
−0.232247 + 0.972657i 0.574608π0.574608\pi
380380 −6.66073 12.5355i −0.341688 0.643060i
381381 −23.5174 −1.20483
382382 −1.06954 4.29226i −0.0547223 0.219611i
383383 −5.57417 −0.284827 −0.142414 0.989807i 0.545486π-0.545486\pi
−0.142414 + 0.989807i 0.545486π0.545486\pi
384384 3.78164 + 27.1022i 0.192981 + 1.38306i
385385 6.32163i 0.322180i
386386 6.74433 + 27.0663i 0.343277 + 1.37764i
387387 −4.73048 −0.240464
388388 −1.26093 2.37309i −0.0640142 0.120475i
389389 4.18438i 0.212156i 0.994358 + 0.106078i 0.0338294π0.0338294\pi
−0.994358 + 0.106078i 0.966171π0.966171\pi
390390 0.399057 + 1.60150i 0.0202071 + 0.0810949i
391391 7.79442 3.02244i 0.394181 0.152851i
392392 1.97240 + 2.19244i 0.0996213 + 0.110735i
393393 −20.7025 −1.04430
394394 −3.65866 14.6829i −0.184321 0.739715i
395395 9.79312i 0.492746i
396396 −13.0382 + 6.92778i −0.655192 + 0.348134i
397397 −10.2111 −0.512481 −0.256240 0.966613i 0.582484π-0.582484\pi
−0.256240 + 0.966613i 0.582484π0.582484\pi
398398 −7.23200 29.0234i −0.362507 1.45481i
399399 41.9012i 2.09768i
400400 −2.23865 + 3.31489i −0.111932 + 0.165744i
401401 8.28754i 0.413860i 0.978356 + 0.206930i 0.0663473π0.0663473\pi
−0.978356 + 0.206930i 0.933653π0.933653\pi
402402 51.8477 12.9193i 2.58593 0.644356i
403403 1.38815i 0.0691489i
404404 31.0989 16.5243i 1.54723 0.822114i
405405 9.42683i 0.468423i
406406 −0.862015 3.45944i −0.0427811 0.171689i
407407 17.5152i 0.868196i
408408 −7.97583 8.86562i −0.394863 0.438913i
409409 −1.64792 −0.0814844 −0.0407422 0.999170i 0.512972π-0.512972\pi
−0.0407422 + 0.999170i 0.512972π0.512972\pi
410410 1.24487 0.310194i 0.0614798 0.0153194i
411411 −12.9320 −0.637888
412412 26.2117 13.9275i 1.29136 0.686159i
413413 9.26689i 0.455994i
414414 −15.7991 + 11.1395i −0.776483 + 0.547478i
415415 13.5571i 0.665490i
416416 −2.56421 0.935348i −0.125721 0.0458592i
417417 36.5736 1.79102
418418 6.28580 + 25.2261i 0.307448 + 1.23385i
419419 −27.8772 −1.36189 −0.680945 0.732334i 0.738431π-0.738431\pi
−0.680945 + 0.732334i 0.738431π0.738431\pi
420420 −10.4266 + 5.54015i −0.508767 + 0.270332i
421421 1.00728i 0.0490920i −0.999699 0.0245460i 0.992186π-0.992186\pi
0.999699 0.0245460i 0.00781402π-0.00781402\pi
422422 9.39353 2.34066i 0.457270 0.113942i
423423 12.5447i 0.609944i
424424 −3.98968 + 3.58926i −0.193756 + 0.174310i
425425 1.74316i 0.0845557i
426426 9.15169 + 36.7276i 0.443401 + 1.77946i
427427 19.9619i 0.966024i
428428 24.4919 13.0137i 1.18386 0.629041i
429429 3.02270i 0.145937i
430430 2.27749 0.567501i 0.109830 0.0273673i
431431 32.5335 1.56708 0.783542 0.621339i 0.213411π-0.213411\pi
0.783542 + 0.621339i 0.213411π0.213411\pi
432432 −1.20067 0.810853i −0.0577675 0.0390122i
433433 25.0052i 1.20167i −0.799373 0.600836i 0.794835π-0.794835\pi
0.799373 0.600836i 0.205165π-0.205165\pi
434434 9.63594 2.40106i 0.462540 0.115255i
435435 −2.49823 −0.119781
436436 15.3833 + 28.9514i 0.736724 + 1.38652i
437437 12.3065 + 31.7365i 0.588698 + 1.51816i
438438 16.8065 4.18780i 0.803045 0.200101i
439439 3.60464i 0.172040i 0.996293 + 0.0860201i 0.0274149π0.0274149\pi
−0.996293 + 0.0860201i 0.972585π0.972585\pi
440440 5.44612 4.89953i 0.259634 0.233576i
441441 2.97185 0.141517
442442 1.15419 0.287598i 0.0548991 0.0136796i
443443 8.90760i 0.423213i −0.977355 0.211606i 0.932131π-0.932131\pi
0.977355 0.211606i 0.0678695π-0.0678695\pi
444444 28.8888 15.3500i 1.37100 0.728477i
445445 2.55180 0.120967
446446 12.6327 3.14780i 0.598177 0.149053i
447447 35.3702 1.67295
448448 2.05750 19.4174i 0.0972077 0.917387i
449449 24.9219 1.17614 0.588069 0.808811i 0.299888π-0.299888\pi
0.588069 + 0.808811i 0.299888π0.299888\pi
450450 0.974601 + 3.91126i 0.0459431 + 0.184379i
451451 −2.34959 −0.110638
452452 −14.5579 27.3981i −0.684745 1.28870i
453453 −16.0389 −0.753575
454454 5.36067 + 21.5134i 0.251589 + 1.00968i
455455 1.17769i 0.0552109i
456456 36.0981 32.4752i 1.69045 1.52079i
457457 22.7410i 1.06378i −0.846813 0.531890i 0.821482π-0.821482\pi
0.846813 0.531890i 0.178518π-0.178518\pi
458458 16.8845 4.20725i 0.788962 0.196592i
459459 0.631385 0.0294705
460460 6.27010 7.25850i 0.292345 0.338429i
461461 37.7027 1.75599 0.877996 0.478668i 0.158880π-0.158880\pi
0.877996 + 0.478668i 0.158880π0.158880\pi
462462 20.9822 5.22830i 0.976180 0.243242i
463463 4.38605i 0.203837i −0.994793 0.101918i 0.967502π-0.967502\pi
0.994793 0.101918i 0.0324981π-0.0324981\pi
464464 2.31223 3.42384i 0.107342 0.158948i
465465 6.95858i 0.322696i
466466 −2.46741 9.90221i −0.114301 0.458711i
467467 −13.7395 −0.635788 −0.317894 0.948126i 0.602976π-0.602976\pi
−0.317894 + 0.948126i 0.602976π0.602976\pi
468468 −2.42894 + 1.29061i −0.112278 + 0.0596585i
469469 −38.1271 −1.76055
470470 −1.50495 6.03965i −0.0694181 0.278588i
471471 −43.0898 −1.98547
472472 −7.98348 + 7.18223i −0.367469 + 0.330589i
473473 −4.29859 −0.197649
474474 32.5045 8.09939i 1.49298 0.372017i
475475 7.09763 0.325661
476476 3.99275 + 7.51439i 0.183007 + 0.344422i
477477 5.40800i 0.247615i
478478 −0.543360 + 0.135393i −0.0248527 + 0.00619275i
479479 34.3897 1.57130 0.785652 0.618668i 0.212327π-0.212327\pi
0.785652 + 0.618668i 0.212327π0.212327\pi
480480 −12.8539 4.68874i −0.586699 0.214011i
481481 3.26299i 0.148780i
482482 −4.27025 + 1.06405i −0.194504 + 0.0484662i
483483 26.3973 10.2361i 1.20112 0.465757i
484484 7.58000 4.02761i 0.344545 0.183073i
485485 1.34364 0.0610116
486486 −29.7976 + 7.42489i −1.35164 + 0.336800i
487487 8.75208i 0.396594i −0.980142 0.198297i 0.936459π-0.936459\pi
0.980142 0.198297i 0.0635411π-0.0635411\pi
488488 −17.1973 + 15.4713i −0.778485 + 0.700353i
489489 −9.75850 −0.441295
490490 −1.43080 + 0.356523i −0.0646369 + 0.0161061i
491491 18.7020i 0.844009i 0.906594 + 0.422004i 0.138673π0.138673\pi
−0.906594 + 0.422004i 0.861327π0.861327\pi
492492 2.05914 + 3.87532i 0.0928331 + 0.174713i
493493 1.80046i 0.0810885i
494494 1.17101 + 4.69950i 0.0526863 + 0.211441i
495495 7.38220i 0.331805i
496496 9.53678 + 6.44049i 0.428214 + 0.289186i
497497 27.0083i 1.21149i
498498 44.9974 11.2124i 2.01638 0.502438i
499499 29.6215i 1.32604i 0.748601 + 0.663021i 0.230726π0.230726\pi
−0.748601 + 0.663021i 0.769274π0.769274\pi
500500 −0.938444 1.76616i −0.0419685 0.0789851i
501501 −29.4534 −1.31588
502502 4.70601 + 18.8861i 0.210039 + 0.842929i
503503 −18.2062 −0.811774 −0.405887 0.913923i 0.633037π-0.633037\pi
−0.405887 + 0.913923i 0.633037π0.633037\pi
504504 −13.1601 14.6283i −0.586199 0.651595i
505505 17.6082i 0.783553i
506506 −14.3566 + 10.1225i −0.638230 + 0.450000i
507507 30.8804i 1.37144i
508508 9.12454 + 17.1725i 0.404836 + 0.761905i
509509 6.43616 0.285278 0.142639 0.989775i 0.454441π-0.454441\pi
0.142639 + 0.989775i 0.454441π0.454441\pi
510510 5.78574 1.44168i 0.256197 0.0638386i
511511 −12.3589 −0.546727
512512 18.3229 13.2768i 0.809764 0.586756i
513513 2.57081i 0.113504i
514514 −8.39076 33.6738i −0.370101 1.48529i
515515 14.8411i 0.653976i
516516 3.76720 + 7.08990i 0.165842 + 0.312115i
517517 11.3994i 0.501344i
518518 −22.6502 + 5.64393i −0.995193 + 0.247980i
519519 52.1126i 2.28749i
520520 1.01459 0.912758i 0.0444925 0.0400271i
521521 16.5369i 0.724496i −0.932082 0.362248i 0.882009π-0.882009\pi
0.932082 0.362248i 0.117991π-0.117991\pi
522522 −1.00663 4.03982i −0.0440592 0.176818i
523523 9.19096 0.401893 0.200946 0.979602i 0.435598π-0.435598\pi
0.200946 + 0.979602i 0.435598π0.435598\pi
524524 8.03238 + 15.1170i 0.350896 + 0.660390i
525525 5.90355i 0.257652i
526526 3.52325 + 14.1395i 0.153621 + 0.616511i
527527 −5.01500 −0.218457
528528 20.7663 + 14.0241i 0.903737 + 0.610322i
529529 −16.9873 + 15.5059i −0.738578 + 0.674168i
530530 −0.648780 2.60368i −0.0281812 0.113097i
531531 10.8216i 0.469617i
532532 −30.5963 + 16.2573i −1.32652 + 0.704842i
533533 −0.437718 −0.0189597
534534 2.11046 + 8.46970i 0.0913286 + 0.366520i
535535 13.8673i 0.599537i
536536 −29.5501 32.8467i −1.27637 1.41876i
537537 60.4696 2.60945
538538 −0.790592 3.17280i −0.0340848 0.136789i
539539 2.70052 0.116320
540540 0.639716 0.339911i 0.0275290 0.0146274i
541541 −30.3151 −1.30335 −0.651673 0.758500i 0.725933π-0.725933\pi
−0.651673 + 0.758500i 0.725933π0.725933\pi
542542 28.8309 7.18401i 1.23839 0.308580i
543543 −50.0493 −2.14782
544544 −3.37914 + 9.26374i −0.144879 + 0.397180i
545545 −16.3923 −0.702169
546546 3.90888 0.974006i 0.167284 0.0416836i
547547 3.21629i 0.137519i −0.997633 0.0687593i 0.978096π-0.978096\pi
0.997633 0.0687593i 0.0219040π-0.0219040\pi
548548 5.01749 + 9.44297i 0.214337 + 0.403384i
549549 23.3109i 0.994884i
550550 0.885620 + 3.55417i 0.0377629 + 0.151550i
551551 −7.33091 −0.312307
552552 29.2774 + 14.8080i 1.24613 + 0.630271i
553553 −23.9027 −1.01645
554554 −2.54809 10.2260i −0.108258 0.434461i
555555 16.3568i 0.694308i
556556 −14.1902 26.7061i −0.601800 1.13259i
557557 11.5928i 0.491202i 0.969371 + 0.245601i 0.0789854π0.0789854\pi
−0.969371 + 0.245601i 0.921015π0.921015\pi
558558 11.2525 2.80389i 0.476358 0.118698i
559559 −0.800805 −0.0338705
560560 8.09086 + 5.46401i 0.341901 + 0.230897i
561561 −10.9201 −0.461048
562562 −20.3447 + 5.06944i −0.858188 + 0.213841i
563563 −0.736783 −0.0310517 −0.0155258 0.999879i 0.504942π-0.504942\pi
−0.0155258 + 0.999879i 0.504942π0.504942\pi
564564 18.8016 9.99018i 0.791690 0.420662i
565565 15.5128 0.652627
566566 −1.39619 5.60318i −0.0586862 0.235519i
567567 23.0087 0.966274
568568 23.2678 20.9325i 0.976293 0.878309i
569569 6.35339i 0.266348i −0.991093 0.133174i 0.957483π-0.957483\pi
0.991093 0.133174i 0.0425169π-0.0425169\pi
570570 5.87008 + 23.5578i 0.245871 + 0.986728i
571571 19.7922 0.828277 0.414138 0.910214i 0.364083π-0.364083\pi
0.414138 + 0.910214i 0.364083π0.364083\pi
572572 −2.20718 + 1.17278i −0.0922868 + 0.0490363i
573573 7.56553i 0.316054i
574574 −0.757111 3.03844i −0.0316012 0.126822i
575575 1.73388 + 4.47143i 0.0723080 + 0.186471i
576576 2.40268 22.6751i 0.100112 0.944794i
577577 5.69116 0.236926 0.118463 0.992958i 0.462203π-0.462203\pi
0.118463 + 0.992958i 0.462203π0.462203\pi
578578 4.77389 + 19.1586i 0.198568 + 0.796891i
579579 47.7070i 1.98264i
580580 0.969289 + 1.82421i 0.0402475 + 0.0757463i
581581 −33.0896 −1.37279
582582 1.11126 + 4.45969i 0.0460631 + 0.184860i
583583 4.91425i 0.203527i
584584 −9.57870 10.6473i −0.396369 0.440588i
585585 1.37527i 0.0568603i
586586 10.8905 2.71366i 0.449881 0.112100i
587587 29.8611i 1.23250i −0.787551 0.616250i 0.788651π-0.788651\pi
0.787551 0.616250i 0.211349π-0.211349\pi
588588 −2.36668 4.45411i −0.0976002 0.183685i
589589 20.4196i 0.841374i
590590 −1.29823 5.21006i −0.0534473 0.214495i
591591 25.8801i 1.06456i
592592 −22.4171 15.1390i −0.921339 0.622209i
593593 −7.36795 −0.302565 −0.151283 0.988491i 0.548340π-0.548340\pi
−0.151283 + 0.988491i 0.548340π0.548340\pi
594594 −1.28734 + 0.320778i −0.0528203 + 0.0131617i
595595 −4.25465 −0.174424
596596 −13.7233 25.8274i −0.562128 1.05793i
597597 51.1566i 2.09370i
598598 −2.67457 + 1.88577i −0.109371 + 0.0771149i
599599 18.7451i 0.765903i 0.923768 + 0.382951i 0.125092π0.125092\pi
−0.923768 + 0.382951i 0.874908π0.874908\pi
600600 5.08594 4.57550i 0.207633 0.186794i
601601 21.7119 0.885645 0.442822 0.896609i 0.353977π-0.353977\pi
0.442822 + 0.896609i 0.353977π0.353977\pi
602602 −1.38514 5.55883i −0.0564540 0.226561i
603603 −44.5236 −1.81314
604604 6.22296 + 11.7117i 0.253209 + 0.476541i
605605 4.29179i 0.174486i
606606 −58.4434 + 14.5628i −2.37410 + 0.591574i
607607 37.1837i 1.50924i 0.656161 + 0.754621i 0.272179π0.272179\pi
−0.656161 + 0.754621i 0.727821π0.727821\pi
608608 −37.7192 13.7588i −1.52971 0.557995i
609609 6.09759i 0.247087i
610610 −2.79653 11.2230i −0.113228 0.454407i
611611 2.12365i 0.0859135i
612612 4.66261 + 8.77507i 0.188475 + 0.354711i
613613 16.3856i 0.661808i −0.943664 0.330904i 0.892646π-0.892646\pi
0.943664 0.330904i 0.107354π-0.107354\pi
614614 −35.9960 + 8.96942i −1.45268 + 0.361976i
615615 −2.19420 −0.0884788
616616 −11.9586 13.2927i −0.481826 0.535578i
617617 21.1275i 0.850560i 0.905062 + 0.425280i 0.139824π0.139824\pi
−0.905062 + 0.425280i 0.860176π0.860176\pi
618618 −49.2591 + 12.2743i −1.98149 + 0.493744i
619619 31.6245 1.27110 0.635548 0.772062i 0.280774π-0.280774\pi
0.635548 + 0.772062i 0.280774π0.280774\pi
620620 −5.08117 + 2.69986i −0.204065 + 0.108429i
621621 −1.61958 + 0.628025i −0.0649916 + 0.0252018i
622622 −34.9138 + 8.69975i −1.39992 + 0.348828i
623623 6.22834i 0.249533i
624624 3.86866 + 2.61262i 0.154870 + 0.104589i
625625 1.00000 0.0400000
626626 37.3441 9.30533i 1.49257 0.371916i
627627 44.4635i 1.77570i
628628 16.7184 + 31.4642i 0.667138 + 1.25556i
629629 11.7882 0.470028
630630 9.54648 2.37877i 0.380341 0.0947726i
631631 9.34449 0.371998 0.185999 0.982550i 0.440448π-0.440448\pi
0.185999 + 0.982550i 0.440448π0.440448\pi
632632 −18.5256 20.5923i −0.736909 0.819119i
633633 −16.5570 −0.658082
634634 −6.75880 27.1244i −0.268426 1.07725i
635635 −9.72306 −0.385848
636636 8.10534 4.30675i 0.321398 0.170774i
637637 0.503093 0.0199333
638638 −0.914728 3.67099i −0.0362144 0.145336i
639639 31.5394i 1.24768i
640640 1.56348 + 11.2052i 0.0618020 + 0.442923i
641641 22.8441i 0.902289i 0.892451 + 0.451145i 0.148984π0.148984\pi
−0.892451 + 0.451145i 0.851016π0.851016\pi
642642 −46.0272 + 11.4690i −1.81655 + 0.452643i
643643 38.8532 1.53222 0.766109 0.642710i 0.222190π-0.222190\pi
0.766109 + 0.642710i 0.222190π0.222190\pi
644644 −17.7163 15.3038i −0.698120 0.603056i
645645 −4.01430 −0.158063
646646 16.9779 4.23053i 0.667988 0.166448i
647647 28.2652i 1.11122i −0.831443 0.555610i 0.812485π-0.812485\pi
0.831443 0.555610i 0.187515π-0.187515\pi
648648 17.8327 + 19.8221i 0.700534 + 0.778686i
649649 9.83357i 0.386001i
650650 0.164986 + 0.662123i 0.00647130 + 0.0259706i
651651 −16.9843 −0.665666
652652 3.78621 + 7.12568i 0.148279 + 0.279063i
653653 41.8565 1.63797 0.818985 0.573815i 0.194537π-0.194537\pi
0.818985 + 0.573815i 0.194537π0.194537\pi
654654 −13.5572 54.4078i −0.530130 2.12751i
655655 −8.55926 −0.334438
656656 2.03084 3.00717i 0.0792909 0.117410i
657657 −14.4324 −0.563061
658658 −14.7414 + 3.67323i −0.574679 + 0.143197i
659659 12.5653 0.489473 0.244737 0.969590i 0.421298π-0.421298\pi
0.244737 + 0.969590i 0.421298π0.421298\pi
660660 −11.0642 + 5.87894i −0.430674 + 0.228837i
661661 40.3545i 1.56961i 0.619743 + 0.784805i 0.287237π0.287237\pi
−0.619743 + 0.784805i 0.712763π0.712763\pi
662662 44.1200 10.9937i 1.71477 0.427283i
663663 −2.03437 −0.0790082
664664 −25.6459 28.5069i −0.995252 1.10628i
665665 17.3236i 0.671782i
666666 −26.4502 + 6.59080i −1.02492 + 0.255388i
667667 −1.79087 4.61839i −0.0693429 0.178825i
668668 11.4276 + 21.5069i 0.442148 + 0.832127i
669669 −22.2664 −0.860869
670670 21.4359 5.34136i 0.828142 0.206355i
671671 21.1826i 0.817745i
672672 −11.4441 + 31.3734i −0.441466 + 1.21026i
673673 25.6709 0.989542 0.494771 0.869023i 0.335252π-0.335252\pi
0.494771 + 0.869023i 0.335252π0.335252\pi
674674 −35.2766 + 8.79015i −1.35880 + 0.338584i
675675 0.362207i 0.0139414i
676676 22.5489 11.9813i 0.867265 0.460819i
677677 31.1431i 1.19693i −0.801150 0.598463i 0.795778π-0.795778\pi
0.801150 0.598463i 0.204222π-0.204222\pi
678678 12.8298 + 51.4886i 0.492726 + 1.97741i
679679 3.27951i 0.125856i
680680 −3.29753 3.66540i −0.126455 0.140562i
681681 37.9195i 1.45308i
682682 10.2252 2.54789i 0.391542 0.0975637i
683683 42.9346i 1.64285i −0.570319 0.821423i 0.693180π-0.693180\pi
0.570319 0.821423i 0.306820π-0.306820\pi
684684 −35.7294 + 18.9847i −1.36615 + 0.725899i
685685 −5.34661 −0.204283
686686 6.71228 + 26.9377i 0.256276 + 1.02849i
687687 −29.7606 −1.13544
688688 3.71542 5.50163i 0.141649 0.209748i
689689 0.915499i 0.0348778i
690690 −13.4071 + 9.45304i −0.510401 + 0.359871i
691691 28.0597i 1.06744i −0.845660 0.533721i 0.820793π-0.820793\pi
0.845660 0.533721i 0.179207π-0.179207\pi
692692 −38.0527 + 20.2192i −1.44655 + 0.768619i
693693 −18.0182 −0.684456
694694 8.92545 2.22402i 0.338805 0.0844228i
695695 15.1210 0.573573
696696 −5.25311 + 4.72589i −0.199119 + 0.179134i
697697 1.58135i 0.0598978i
698698 4.58124 + 18.3854i 0.173402 + 0.695898i
699699 17.4536i 0.660156i
700700 −4.31078 + 2.29052i −0.162932 + 0.0865736i
701701 6.27098i 0.236852i −0.992963 0.118426i 0.962215π-0.962215\pi
0.992963 0.118426i 0.0377848π-0.0377848\pi
702702 −0.239826 + 0.0597592i −0.00905163 + 0.00225547i
703703 47.9982i 1.81029i
704704 2.18332 20.6048i 0.0822869 0.776573i
705705 10.6455i 0.400932i
706706 −12.1046 48.5783i −0.455564 1.82827i
707707 42.9774 1.61633
708708 16.2190 8.61794i 0.609549 0.323882i
709709 4.21638i 0.158349i −0.996861 0.0791747i 0.974772π-0.974772\pi
0.996861 0.0791747i 0.0252285π-0.0252285\pi
710710 3.78368 + 15.1847i 0.141999 + 0.569870i
711711 −27.9128 −1.04681
712712 5.36575 4.82722i 0.201090 0.180908i
713713 12.8641 4.98831i 0.481764 0.186814i
714714 −3.51880 14.1216i −0.131688 0.528489i
715715 1.24971i 0.0467363i
716716 −23.4616 44.1550i −0.876802 1.65015i
717717 0.957724 0.0357669
718718 −5.93569 23.8211i −0.221518 0.888995i
719719 10.0948i 0.376473i 0.982124 + 0.188237i 0.0602772π0.0602772\pi
−0.982124 + 0.188237i 0.939723π0.939723\pi
720720 9.44825 + 6.38070i 0.352115 + 0.237795i
721721 36.2236 1.34904
722722 10.7287 + 43.0563i 0.399280 + 1.60239i
723723 7.52672 0.279922
724724 19.4186 + 36.5461i 0.721688 + 1.35822i
725725 −1.03287 −0.0383598
726726 −14.2449 + 3.54952i −0.528679 + 0.131735i
727727 −35.0141 −1.29860 −0.649300 0.760532i 0.724938π-0.724938\pi
−0.649300 + 0.760532i 0.724938π0.724938\pi
728728 −2.22783 2.47636i −0.0825688 0.0917802i
729729 24.2406 0.897799
730730 6.94848 1.73141i 0.257175 0.0640823i
731731 2.89308i 0.107004i
732732 34.9376 18.5640i 1.29133 0.686145i
733733 10.2928i 0.380175i −0.981767 0.190087i 0.939123π-0.939123\pi
0.981767 0.190087i 0.0608771π-0.0608771\pi
734734 −5.39628 21.6563i −0.199180 0.799350i
735735 2.52192 0.0930224
736736 −0.546526 27.1238i −0.0201452 0.999797i
737737 −40.4586 −1.49031
738738 −0.884131 3.54819i −0.0325453 0.130611i
739739 23.0799i 0.849007i 0.905426 + 0.424503i 0.139551π0.139551\pi
−0.905426 + 0.424503i 0.860449π0.860449\pi
740740 11.9438 6.34629i 0.439062 0.233294i
741741 8.28332i 0.304296i
742742 −6.35498 + 1.58352i −0.233299 + 0.0581329i
743743 −11.9643 −0.438926 −0.219463 0.975621i 0.570431π-0.570431\pi
−0.219463 + 0.975621i 0.570431π0.570431\pi
744744 −13.1635 14.6320i −0.482598 0.536436i
745745 14.6235 0.535762
746746 −44.2908 + 11.0363i −1.62160 + 0.404068i
747747 −38.6410 −1.41380
748748 4.23691 + 7.97390i 0.154917 + 0.291555i
749749 33.8469 1.23674
750750 0.827049 + 3.31911i 0.0301996 + 0.121197i
751751 23.5856 0.860650 0.430325 0.902674i 0.358399π-0.358399\pi
0.430325 + 0.902674i 0.358399π0.358399\pi
752752 −14.5897 9.85287i −0.532031 0.359297i
753753 33.2886i 1.21310i
754754 −0.170409 0.683886i −0.00620594 0.0249057i
755755 −6.63114 −0.241332
756756 −0.829643 1.56140i −0.0301738 0.0567874i
757757 33.3612i 1.21253i −0.795261 0.606267i 0.792666π-0.792666\pi
0.795261 0.606267i 0.207334π-0.207334\pi
758758 −3.09203 12.4089i −0.112308 0.450713i
759759 28.0115 10.8620i 1.01675 0.394266i
760760 14.9244 13.4266i 0.541365 0.487032i
761761 20.9441 0.759223 0.379612 0.925146i 0.376058π-0.376058\pi
0.379612 + 0.925146i 0.376058π0.376058\pi
762762 −8.04144 32.2719i −0.291311 1.16909i
763763 40.0098i 1.44845i
764764 5.52436 2.93535i 0.199864 0.106197i
765765 −4.96844 −0.179634
766766 −1.90601 7.64918i −0.0688668 0.276376i
767767 1.83194i 0.0661477i
768768 −35.8981 + 14.4566i −1.29536 + 0.521657i
769769 40.2590i 1.45178i −0.687813 0.725888i 0.741429π-0.741429\pi
0.687813 0.725888i 0.258571π-0.258571\pi
770770 8.67488 2.16159i 0.312621 0.0778983i
771771 59.3533i 2.13756i
772772 −34.8358 + 18.5099i −1.25377 + 0.666185i
773773 8.99653i 0.323583i −0.986825 0.161791i 0.948273π-0.948273\pi
0.986825 0.161791i 0.0517271π-0.0517271\pi
774774 −1.61752 6.49142i −0.0581405 0.233329i
775775 2.87696i 0.103343i
776776 2.82532 2.54176i 0.101423 0.0912439i
777777 39.9232 1.43224
778778 −5.74203 + 1.43079i −0.205862 + 0.0512962i
779779 −6.43877 −0.230693
780780 −2.06121 + 1.09522i −0.0738031 + 0.0392150i
781781 28.6598i 1.02553i
782782 6.81274 + 9.66244i 0.243623 + 0.345528i
783783 0.374112i 0.0133697i
784784 −2.33415 + 3.45631i −0.0833626 + 0.123440i
785785 −17.8150 −0.635846
786786 −7.07892 28.4091i −0.252497 1.01332i
787787 17.3155 0.617232 0.308616 0.951187i 0.400134π-0.400134\pi
0.308616 + 0.951187i 0.400134π0.400134\pi
788788 18.8977 10.0412i 0.673202 0.357704i
789789 24.9222i 0.887254i
790790 13.4387 3.34861i 0.478126 0.119138i
791791 37.8630i 1.34626i
792792 −13.9649 15.5228i −0.496221 0.551579i
793793 3.94621i 0.140134i
794794 −3.49154 14.0122i −0.123910 0.497275i
795795 4.58924i 0.162764i
796796 37.3547 19.8483i 1.32400 0.703504i
797797 46.3144i 1.64054i −0.571976 0.820271i 0.693823π-0.693823\pi
0.571976 0.820271i 0.306177π-0.306177\pi
798798 57.4991 14.3275i 2.03545 0.507188i
799799 7.67212 0.271420
800800 −5.31434 1.93851i −0.187890 0.0685368i
801801 7.27326i 0.256988i
802802 −11.3726 + 2.83380i −0.401581 + 0.100065i
803803 −13.1147 −0.462808
804804 35.4571 + 66.7306i 1.25048 + 2.35341i
805805 10.9137 4.23201i 0.384657 0.149159i
806806 1.90490 0.474659i 0.0670972 0.0167192i
807807 5.59237i 0.196861i
808808 33.3093 + 37.0253i 1.17182 + 1.30254i
809809 16.4030 0.576698 0.288349 0.957525i 0.406894π-0.406894\pi
0.288349 + 0.957525i 0.406894π0.406894\pi
810810 −12.9360 + 3.22337i −0.454525 + 0.113258i
811811 10.0839i 0.354095i 0.984202 + 0.177048i 0.0566547π0.0566547\pi
−0.984202 + 0.177048i 0.943345π0.943345\pi
812812 4.45247 2.36581i 0.156251 0.0830236i
813813 −50.8172 −1.78224
814814 −24.0353 + 5.98906i −0.842436 + 0.209917i
815815 −4.03456 −0.141324
816816 9.43865 13.9763i 0.330419 0.489270i
817817 −11.7797 −0.412121
818818 −0.563482 2.26137i −0.0197017 0.0790668i
819819 −3.35671 −0.117293
820820 0.851330 + 1.60221i 0.0297297 + 0.0559517i
821821 29.6987 1.03649 0.518246 0.855232i 0.326585π-0.326585\pi
0.518246 + 0.855232i 0.326585π0.326585\pi
822822 −4.42191 17.7460i −0.154232 0.618962i
823823 25.1840i 0.877857i −0.898522 0.438929i 0.855358π-0.855358\pi
0.898522 0.438929i 0.144642π-0.144642\pi
824824 28.0748 + 31.2068i 0.978031 + 1.08714i
825825 6.26456i 0.218104i
826826 −12.7165 + 3.16868i −0.442464 + 0.110252i
827827 30.3418 1.05509 0.527544 0.849528i 0.323113π-0.323113\pi
0.527544 + 0.849528i 0.323113π0.323113\pi
828828 −20.6885 17.8714i −0.718976 0.621072i
829829 15.3213 0.532129 0.266065 0.963955i 0.414277π-0.414277\pi
0.266065 + 0.963955i 0.414277π0.414277\pi
830830 18.6037 4.63564i 0.645745 0.160905i
831831 18.0243i 0.625256i
832832 0.406741 3.83857i 0.0141012 0.133079i
833833 1.81753i 0.0629737i
834834 12.5058 + 50.1883i 0.433041 + 1.73788i
835835 −12.1772 −0.421410
836836 −32.4673 + 17.2514i −1.12291 + 0.596653i
837837 1.04205 0.0360187
838838 −9.53220 38.2546i −0.329284 1.32148i
839839 −17.8938 −0.617764 −0.308882 0.951100i 0.599955π-0.599955\pi
−0.308882 + 0.951100i 0.599955π0.599955\pi
840840 −11.1677 12.4136i −0.385323 0.428310i
841841 −27.9332 −0.963213
842842 1.38225 0.344426i 0.0476355 0.0118697i
843843 35.8594 1.23506
844844 6.42396 + 12.0900i 0.221122 + 0.416153i
845845 12.7672i 0.439205i
846846 −17.2145 + 4.28948i −0.591847 + 0.147475i
847847 10.4753 0.359934
848848 −6.28959 4.24756i −0.215985 0.145862i
849849 9.87615i 0.338949i
850850 2.39206 0.596048i 0.0820470 0.0204443i
851851 −30.2383 + 11.7255i −1.03656 + 0.401945i
852852 −47.2702 + 25.1169i −1.61945 + 0.860491i
853853 −28.3424 −0.970425 −0.485213 0.874396i 0.661258π-0.661258\pi
−0.485213 + 0.874396i 0.661258π0.661258\pi
854854 −27.3928 + 6.82568i −0.937362 + 0.233570i
855855 20.2300i 0.691852i
856856 26.2328 + 29.1593i 0.896617 + 0.996643i
857857 −0.739951 −0.0252763 −0.0126381 0.999920i 0.504023π-0.504023\pi
−0.0126381 + 0.999920i 0.504023π0.504023\pi
858858 4.14791 1.03357i 0.141607 0.0352854i
859859 30.7839i 1.05033i −0.851000 0.525166i 0.824003π-0.824003\pi
0.851000 0.525166i 0.175997π-0.175997\pi
860860 1.55751 + 2.93125i 0.0531107 + 0.0999548i
861861 5.35554i 0.182516i
862862 11.1244 + 44.6442i 0.378897 + 1.52059i
863863 12.5426i 0.426955i 0.976948 + 0.213478i 0.0684790π0.0684790\pi
−0.976948 + 0.213478i 0.931521π0.931521\pi
864864 0.702143 1.92489i 0.0238874 0.0654861i
865865 21.5454i 0.732567i
866866 34.3134 8.55015i 1.16602 0.290546i
867867 33.7688i 1.14685i
868868 6.58973 + 12.4019i 0.223670 + 0.420949i
869869 −25.3644 −0.860428
870870 −0.854233 3.42820i −0.0289612 0.116227i
871871 −7.53723 −0.255389
872872 −34.4686 + 31.0092i −1.16725 + 1.05011i
873873 3.82971i 0.129616i
874874 −39.3425 + 27.7394i −1.33078 + 0.938300i
875875 2.44077i 0.0825129i
876876 11.4935 + 21.6308i 0.388328 + 0.730837i
877877 −11.7013 −0.395126 −0.197563 0.980290i 0.563303π-0.563303\pi
−0.197563 + 0.980290i 0.563303π0.563303\pi
878878 −4.94648 + 1.23255i −0.166936 + 0.0415967i
879879 −19.1955 −0.647448
880880 8.58562 + 5.79814i 0.289421 + 0.195455i
881881 7.76026i 0.261450i −0.991419 0.130725i 0.958270π-0.958270\pi
0.991419 0.130725i 0.0417305π-0.0417305\pi
882882 1.01618 + 4.07813i 0.0342166 + 0.137318i
883883 49.0477i 1.65059i −0.564704 0.825294i 0.691010π-0.691010\pi
0.564704 0.825294i 0.308990π-0.308990\pi
884884 0.789315 + 1.48550i 0.0265475 + 0.0499627i
885885 9.18322i 0.308691i
886886 12.2235 3.04582i 0.410656 0.102326i
887887 1.36114i 0.0457026i −0.999739 0.0228513i 0.992726π-0.992726\pi
0.999739 0.0228513i 0.00727443π-0.00727443\pi
888888 30.9421 + 34.3940i 1.03835 + 1.15419i
889889 23.7317i 0.795936i
890890 0.872550 + 3.50171i 0.0292479 + 0.117378i
891891 24.4157 0.817956
892892 8.63915 + 16.2590i 0.289260 + 0.544390i
893893 31.2385i 1.04536i
894894 12.0943 + 48.5369i 0.404494 + 1.62332i
895895 25.0006 0.835677
896896 27.3492 3.81609i 0.913671 0.127487i
897897 5.21840 2.02354i 0.174237 0.0675640i
898898 8.52169 + 34.1992i 0.284372 + 1.14124i
899899 2.97152i 0.0991057i
900900 −5.03400 + 2.67480i −0.167800 + 0.0891600i
901901 3.30744 0.110187
902902 −0.803409 3.22424i −0.0267506 0.107355i
903903 9.79797i 0.326056i
904904 32.6192 29.3455i 1.08490 0.976015i
905905 −20.6924 −0.687838
906906 −5.48428 22.0095i −0.182203 0.731216i
907907 −13.2300 −0.439294 −0.219647 0.975579i 0.570491π-0.570491\pi
−0.219647 + 0.975579i 0.570491π0.570491\pi
908908 −27.6889 + 14.7124i −0.918888 + 0.488248i
909909 50.1877 1.66462
910910 1.61609 0.402693i 0.0535728 0.0133492i
911911 −12.0129 −0.398004 −0.199002 0.979999i 0.563770π-0.563770\pi
−0.199002 + 0.979999i 0.563770π0.563770\pi
912912 56.9074 + 38.4314i 1.88439 + 1.27259i
913913 −35.1131 −1.16207
914914 31.2065 7.77596i 1.03222 0.257206i
915915 19.7817i 0.653962i
916916 11.5468 + 21.7313i 0.381518 + 0.718021i
917917 20.8911i 0.689886i
918918 0.215893 + 0.866420i 0.00712553 + 0.0285961i
919919 21.1075 0.696273 0.348136 0.937444i 0.386815π-0.386815\pi
0.348136 + 0.937444i 0.386815π0.386815\pi
920920 12.1045 + 6.12223i 0.399073 + 0.201844i
921921 63.4465 2.09063
922922 12.8919 + 51.7377i 0.424572 + 1.70389i
923923 5.33918i 0.175741i
924924 14.3491 + 27.0052i 0.472051 + 0.888404i
925925 6.76257i 0.222352i
926926 6.01877 1.49974i 0.197789 0.0492847i
927927 42.3007 1.38934
928928 5.48901 + 2.00223i 0.180186 + 0.0657264i
929929 −16.4375 −0.539295 −0.269648 0.962959i 0.586907π-0.586907\pi
−0.269648 + 0.962959i 0.586907π0.586907\pi
930930 9.54894 2.37938i 0.313122 0.0780231i
931931 7.40043 0.242539
932932 12.7447 6.77183i 0.417465 0.221819i
933933 61.5389 2.01469
934934 −4.69802 18.8541i −0.153724 0.616925i
935935 −4.51482 −0.147651
936936 −2.60159 2.89182i −0.0850356 0.0945221i
937937 22.1718i 0.724322i 0.932115 + 0.362161i 0.117961π0.117961\pi
−0.932115 + 0.362161i 0.882039π0.882039\pi
938938 −13.0370 52.3201i −0.425673 1.70831i
939939 −65.8226 −2.14804
940940 7.77334 4.13034i 0.253538 0.134717i
941941 14.7090i 0.479500i −0.970835 0.239750i 0.922935π-0.922935\pi
0.970835 0.239750i 0.0770654π-0.0770654\pi
942942 −14.7339 59.1301i −0.480057 1.92656i
943943 −1.57293 4.05635i −0.0512217 0.132093i
944944 −12.5857 8.49950i −0.409629 0.276635i
945945 0.884062 0.0287585
946946 −1.46984 5.89875i −0.0477886 0.191785i
947947 10.0702i 0.327237i −0.986524 0.163619i 0.947683π-0.947683\pi
0.986524 0.163619i 0.0523166π-0.0523166\pi
948948 22.2288 + 41.8349i 0.721959 + 1.35873i
949949 −2.44320 −0.0793097
950950 2.42693 + 9.73974i 0.0787400 + 0.315999i
951951 47.8094i 1.55032i
952952 −8.94639 + 8.04850i −0.289954 + 0.260853i
953953 22.9968i 0.744938i −0.928045 0.372469i 0.878511π-0.878511\pi
0.928045 0.372469i 0.121489π-0.121489\pi
954954 −7.42115 + 1.84919i −0.240268 + 0.0598696i
955955 3.12789i 0.101216i
956956 −0.371588 0.699332i −0.0120180 0.0226180i
957957 6.47046i 0.209160i
958958 11.7590 + 47.1914i 0.379918 + 1.52468i
959959 13.0498i 0.421401i
960960 2.03892 19.2421i 0.0658060 0.621036i
961961 22.7231 0.733004
962962 −4.47765 + 1.11573i −0.144365 + 0.0359726i
963963 39.5253 1.27369
964964 −2.92030 5.49602i −0.0940564 0.177015i
965965 19.7240i 0.634938i
966966 23.0727 + 32.7237i 0.742350 + 1.05287i
967967 16.1903i 0.520646i 0.965522 + 0.260323i 0.0838290π0.0838290\pi
−0.965522 + 0.260323i 0.916171π0.916171\pi
968968 8.11877 + 9.02450i 0.260947 + 0.290058i
969969 −29.9253 −0.961338
970970 0.459439 + 1.84382i 0.0147517 + 0.0592014i
971971 −56.0221 −1.79784 −0.898918 0.438118i 0.855645π-0.855645\pi
−0.898918 + 0.438118i 0.855645π0.855645\pi
972972 −20.3777 38.3510i −0.653614 1.23011i
973973 36.9069i 1.18318i
974974 12.0101 2.99264i 0.384827 0.0958905i
975975 1.16706i 0.0373757i
976976 −27.1109 18.3089i −0.867800 0.586052i
977977 27.2869i 0.872984i −0.899708 0.436492i 0.856221π-0.856221\pi
0.899708 0.436492i 0.143779π-0.143779\pi
978978 −3.33678 13.3911i −0.106698 0.428201i
979979 6.60921i 0.211231i
980980 −0.978481 1.84151i −0.0312564 0.0588249i
981981 46.7221i 1.49172i
982982 −25.6639 + 6.39487i −0.818967 + 0.204069i
983983 49.0064 1.56306 0.781531 0.623866i 0.214439π-0.214439\pi
0.781531 + 0.623866i 0.214439π0.214439\pi
984984 −4.61382 + 4.15077i −0.147083 + 0.132322i
985985 10.6999i 0.340926i
986986 −2.47068 + 0.615640i −0.0786826 + 0.0196060i
987987 25.9831 0.827051
988988 −6.04850 + 3.21385i −0.192428 + 0.102246i
989989 −2.87768 7.42111i −0.0915050 0.235977i
990990 10.1303 2.52424i 0.321961 0.0802255i
991991 7.65834i 0.243275i −0.992575 0.121638i 0.961185π-0.961185\pi
0.992575 0.121638i 0.0388146π-0.0388146\pi
992992 −5.57702 + 15.2891i −0.177071 + 0.485430i
993993 −77.7657 −2.46782
994994 37.0622 9.23507i 1.17554 0.292919i
995995 21.1502i 0.670506i
996996 30.7724 + 57.9139i 0.975061 + 1.83507i
997997 60.3120 1.91010 0.955050 0.296445i 0.0958010π-0.0958010\pi
0.955050 + 0.296445i 0.0958010π0.0958010\pi
998998 −40.6482 + 10.1286i −1.28670 + 0.320617i
999999 −2.44945 −0.0774971
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 460.2.e.b.91.19 yes 32
4.3 odd 2 inner 460.2.e.b.91.17 32
23.22 odd 2 inner 460.2.e.b.91.20 yes 32
92.91 even 2 inner 460.2.e.b.91.18 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.e.b.91.17 32 4.3 odd 2 inner
460.2.e.b.91.18 yes 32 92.91 even 2 inner
460.2.e.b.91.19 yes 32 1.1 even 1 trivial
460.2.e.b.91.20 yes 32 23.22 odd 2 inner