Properties

Label 152.4.p.a.45.9
Level 152152
Weight 44
Character 152.45
Analytic conductor 8.9688.968
Analytic rank 00
Dimension 116116
Inner twists 44

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [152,4,Mod(45,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.45"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 152=2319 152 = 2^{3} \cdot 19
Weight: k k == 4 4
Character orbit: [χ][\chi] == 152.p (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 8.968290320878.96829032087
Analytic rank: 00
Dimension: 116116
Relative dimension: 5858 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 45.9
Character χ\chi == 152.45
Dual form 152.4.p.a.125.9

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(2.55889+1.20502i)q2+(4.74696+2.74066i)q3+(5.095836.16705i)q4+(2.752861.58936i)q5+(8.8443812.7332i)q6+6.39182q7+(5.60823+21.9214i)q8+(1.522392.63686i)q9+(5.12904+7.38426i)q10+61.8197iq11+(7.28793+43.2406i)q12+(48.993928.2866i)q13+(16.3560+7.70229i)q14+(8.71179+15.0893i)q15+(12.065062.8525i)q16+(3.160695.47448i)q17+(0.718153+8.58197i)q18+(50.289965.8022i)q19+(4.2264225.0761i)q20+(30.3417+17.5178i)q21+(74.4942158.190i)q22+(36.533863.2785i)q23+(33.4570119.430i)q24+(57.4479+99.5026i)q25+(159.456+13.3435i)q26131.306iq27+(32.571639.4186i)q28+(226.243130.622i)q29+(4.1095849.1097i)q30112.649q31+(106.612+146.294i)q32+(169.426293.455i)q33+(14.6847+10.1999i)q34+(17.595710.1589i)q35+(8.5038022.8257i)q36227.883iq37+(49.3930+228.981i)q38+310.096q39+(19.4024+69.2600i)q40+(25.356243.9183i)q41+(56.531681.3885i)q42+(407.779+235.431i)q43+(381.245+315.023i)q449.67854iq45+(17.2340+205.947i)q46+(67.6767117.219i)q47+(229.529+265.292i)q48302.145q49+(27.0997323.842i)q50+(30.0073+17.3247i)q51+(424.110+158.004i)q52+(364.115210.222i)q53+(158.227+335.998i)q54+(98.2539+170.181i)q55+(35.8468+140.118i)q56+(58.3826+450.187i)q57+(736.334+61.6177i)q58+(330.020190.537i)q59+(48.6624+130.618i)q60+(291.562+168.333i)q61+(288.255135.744i)q62+(9.7308616.8543i)q63+(449.096245.880i)q64179.831q65+(787.164+546.757i)q66+(469.568271.105i)q67+(49.86778.40488i)q68+400.507iq69+(32.7838+47.1988i)q70+(513.735+889.815i)q71+(49.2658+48.1611i)q72+(335.367580.873i)q73+(274.604+583.126i)q74629.779iq75+(149.537645.457i)q76+395.140iq77+(793.501+373.673i)q78+(83.2056+144.116i)q79+(133.109153.848i)q80+(400.969+694.499i)q81+(117.806+81.8271i)q82213.128iq83+(46.5831+276.386i)q84+(17.401810.0470i)q85+(759.7611093.83i)q86+1431.96q87+(1355.17346.699i)q88+(315.321+546.152i)q89+(11.6629+24.7663i)q90+(313.160180.803i)q91+(204.071547.763i)q92+(534.738308.731i)q93+(31.9249+381.504i)q94+(33.8573261.073i)q95+(907.023402.265i)q96+(320.342554.849i)q97+(773.155364.092i)q98+(163.010+94.1139i)q99+O(q100)q+(-2.55889 + 1.20502i) q^{2} +(-4.74696 + 2.74066i) q^{3} +(5.09583 - 6.16705i) q^{4} +(2.75286 - 1.58936i) q^{5} +(8.84438 - 12.7332i) q^{6} +6.39182 q^{7} +(-5.60823 + 21.9214i) q^{8} +(1.52239 - 2.63686i) q^{9} +(-5.12904 + 7.38426i) q^{10} +61.8197i q^{11} +(-7.28793 + 43.2406i) q^{12} +(-48.9939 - 28.2866i) q^{13} +(-16.3560 + 7.70229i) q^{14} +(-8.71179 + 15.0893i) q^{15} +(-12.0650 - 62.8525i) q^{16} +(-3.16069 - 5.47448i) q^{17} +(-0.718153 + 8.58197i) q^{18} +(50.2899 - 65.8022i) q^{19} +(4.22642 - 25.0761i) q^{20} +(-30.3417 + 17.5178i) q^{21} +(-74.4942 - 158.190i) q^{22} +(36.5338 - 63.2785i) q^{23} +(-33.4570 - 119.430i) q^{24} +(-57.4479 + 99.5026i) q^{25} +(159.456 + 13.3435i) q^{26} -131.306i q^{27} +(32.5716 - 39.4186i) q^{28} +(-226.243 - 130.622i) q^{29} +(4.10958 - 49.1097i) q^{30} -112.649 q^{31} +(106.612 + 146.294i) q^{32} +(-169.426 - 293.455i) q^{33} +(14.6847 + 10.1999i) q^{34} +(17.5957 - 10.1589i) q^{35} +(-8.50380 - 22.8257i) q^{36} -227.883i q^{37} +(-49.3930 + 228.981i) q^{38} +310.096 q^{39} +(19.4024 + 69.2600i) q^{40} +(-25.3562 - 43.9183i) q^{41} +(56.5316 - 81.3885i) q^{42} +(-407.779 + 235.431i) q^{43} +(381.245 + 315.023i) q^{44} -9.67854i q^{45} +(-17.2340 + 205.947i) q^{46} +(67.6767 - 117.219i) q^{47} +(229.529 + 265.292i) q^{48} -302.145 q^{49} +(27.0997 - 323.842i) q^{50} +(30.0073 + 17.3247i) q^{51} +(-424.110 + 158.004i) q^{52} +(-364.115 - 210.222i) q^{53} +(158.227 + 335.998i) q^{54} +(98.2539 + 170.181i) q^{55} +(-35.8468 + 140.118i) q^{56} +(-58.3826 + 450.187i) q^{57} +(736.334 + 61.6177i) q^{58} +(330.020 - 190.537i) q^{59} +(48.6624 + 130.618i) q^{60} +(291.562 + 168.333i) q^{61} +(288.255 - 135.744i) q^{62} +(9.73086 - 16.8543i) q^{63} +(-449.096 - 245.880i) q^{64} -179.831 q^{65} +(787.164 + 546.757i) q^{66} +(-469.568 - 271.105i) q^{67} +(-49.8677 - 8.40488i) q^{68} +400.507i q^{69} +(-32.7838 + 47.1988i) q^{70} +(513.735 + 889.815i) q^{71} +(49.2658 + 48.1611i) q^{72} +(-335.367 - 580.873i) q^{73} +(274.604 + 583.126i) q^{74} -629.779i q^{75} +(-149.537 - 645.457i) q^{76} +395.140i q^{77} +(-793.501 + 373.673i) q^{78} +(83.2056 + 144.116i) q^{79} +(-133.109 - 153.848i) q^{80} +(400.969 + 694.499i) q^{81} +(117.806 + 81.8271i) q^{82} -213.128i q^{83} +(-46.5831 + 276.386i) q^{84} +(-17.4018 - 10.0470i) q^{85} +(759.761 - 1093.83i) q^{86} +1431.96 q^{87} +(-1355.17 - 346.699i) q^{88} +(-315.321 + 546.152i) q^{89} +(11.6629 + 24.7663i) q^{90} +(-313.160 - 180.803i) q^{91} +(-204.071 - 547.763i) q^{92} +(534.738 - 308.731i) q^{93} +(-31.9249 + 381.504i) q^{94} +(33.8573 - 261.073i) q^{95} +(-907.023 - 402.265i) q^{96} +(-320.342 - 554.849i) q^{97} +(773.155 - 364.092i) q^{98} +(163.010 + 94.1139i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 116qq27q411q68q746q8+484q944q1058q12+24q14230q1567q162q17+196q18840q20+137q222q23+77q24++55q98+O(q100) 116 q - q^{2} - 7 q^{4} - 11 q^{6} - 8 q^{7} - 46 q^{8} + 484 q^{9} - 44 q^{10} - 58 q^{12} + 24 q^{14} - 230 q^{15} - 67 q^{16} - 2 q^{17} + 196 q^{18} - 840 q^{20} + 137 q^{22} - 2 q^{23} + 77 q^{24}+ \cdots + 55 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/152Z)×\left(\mathbb{Z}/152\mathbb{Z}\right)^\times.

nn 3939 7777 9797
χ(n)\chi(n) 11 1-1 e(13)e\left(\frac{1}{3}\right)

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 −2.55889 + 1.20502i −0.904704 + 0.426040i
33 −4.74696 + 2.74066i −0.913552 + 0.527440i −0.881572 0.472049i 0.843515π-0.843515\pi
−0.0319798 + 0.999489i 0.510181π0.510181\pi
44 5.09583 6.16705i 0.636979 0.770881i
55 2.75286 1.58936i 0.246223 0.142157i −0.371811 0.928309i 0.621263π-0.621263\pi
0.618034 + 0.786152i 0.287930π0.287930\pi
66 8.84438 12.7332i 0.601784 0.866387i
77 6.39182 0.345126 0.172563 0.984999i 0.444795π-0.444795\pi
0.172563 + 0.984999i 0.444795π0.444795\pi
88 −5.60823 + 21.9214i −0.247851 + 0.968798i
99 1.52239 2.63686i 0.0563850 0.0976616i
1010 −5.12904 + 7.38426i −0.162194 + 0.233511i
1111 61.8197i 1.69448i 0.531206 + 0.847242i 0.321739π0.321739\pi
−0.531206 + 0.847242i 0.678261π0.678261\pi
1212 −7.28793 + 43.2406i −0.175320 + 1.04021i
1313 −48.9939 28.2866i −1.04527 0.603485i −0.123946 0.992289i 0.539555π-0.539555\pi
−0.921320 + 0.388804i 0.872888π0.872888\pi
1414 −16.3560 + 7.70229i −0.312237 + 0.147037i
1515 −8.71179 + 15.0893i −0.149958 + 0.259735i
1616 −12.0650 62.8525i −0.188515 0.982070i
1717 −3.16069 5.47448i −0.0450929 0.0781033i 0.842598 0.538543i 0.181025π-0.181025\pi
−0.887691 + 0.460440i 0.847692π0.847692\pi
1818 −0.718153 + 8.58197i −0.00940391 + 0.112377i
1919 50.2899 65.8022i 0.607226 0.794529i
2020 4.22642 25.0761i 0.0472528 0.280360i
2121 −30.3417 + 17.5178i −0.315290 + 0.182033i
2222 −74.4942 158.190i −0.721919 1.53301i
2323 36.5338 63.2785i 0.331210 0.573673i −0.651539 0.758615i 0.725876π-0.725876\pi
0.982749 + 0.184942i 0.0592098π0.0592098\pi
2424 −33.4570 119.430i −0.284558 1.01577i
2525 −57.4479 + 99.5026i −0.459583 + 0.796021i
2626 159.456 + 13.3435i 1.20277 + 0.100649i
2727 131.306i 0.935920i
2828 32.5716 39.4186i 0.219838 0.266051i
2929 −226.243 130.622i −1.44870 0.836408i −0.450297 0.892879i 0.648682π-0.648682\pi
−0.998404 + 0.0564711i 0.982015π0.982015\pi
3030 4.10958 49.1097i 0.0250101 0.298872i
3131 −112.649 −0.652654 −0.326327 0.945257i 0.605811π-0.605811\pi
−0.326327 + 0.945257i 0.605811π0.605811\pi
3232 106.612 + 146.294i 0.588952 + 0.808168i
3333 −169.426 293.455i −0.893738 1.54800i
3434 14.6847 + 10.1999i 0.0740709 + 0.0514489i
3535 17.5957 10.1589i 0.0849778 0.0490620i
3636 −8.50380 22.8257i −0.0393695 0.105675i
3737 227.883i 1.01253i −0.862378 0.506266i 0.831026π-0.831026\pi
0.862378 0.506266i 0.168974π-0.168974\pi
3838 −49.3930 + 228.981i −0.210858 + 0.977517i
3939 310.096 1.27321
4040 19.4024 + 69.2600i 0.0766947 + 0.273774i
4141 −25.3562 43.9183i −0.0965848 0.167290i 0.813684 0.581307i 0.197459π-0.197459\pi
−0.910269 + 0.414017i 0.864125π0.864125\pi
4242 56.5316 81.3885i 0.207691 0.299012i
4343 −407.779 + 235.431i −1.44618 + 0.834953i −0.998251 0.0591165i 0.981172π-0.981172\pi
−0.447929 + 0.894069i 0.647838π0.647838\pi
4444 381.245 + 315.023i 1.30625 + 1.07935i
4545 9.67854i 0.0320620i
4646 −17.2340 + 205.947i −0.0552394 + 0.660113i
4747 67.6767 117.219i 0.210035 0.363792i −0.741690 0.670743i 0.765975π-0.765975\pi
0.951725 + 0.306951i 0.0993088π0.0993088\pi
4848 229.529 + 265.292i 0.690201 + 0.797742i
4949 −302.145 −0.880888
5050 27.0997 323.842i 0.0766494 0.915964i
5151 30.0073 + 17.3247i 0.0823895 + 0.0475676i
5252 −424.110 + 158.004i −1.13103 + 0.421369i
5353 −364.115 210.222i −0.943680 0.544834i −0.0525679 0.998617i 0.516741π-0.516741\pi
−0.891112 + 0.453784i 0.850074π0.850074\pi
5454 158.227 + 335.998i 0.398740 + 0.846731i
5555 98.2539 + 170.181i 0.240883 + 0.417221i
5656 −35.8468 + 140.118i −0.0855397 + 0.334357i
5757 −58.3826 + 450.187i −0.135666 + 1.04612i
5858 736.334 + 61.6177i 1.66699 + 0.139496i
5959 330.020 190.537i 0.728219 0.420437i −0.0895512 0.995982i 0.528543π-0.528543\pi
0.817770 + 0.575545i 0.195210π0.195210\pi
6060 48.6624 + 130.618i 0.104705 + 0.281046i
6161 291.562 + 168.333i 0.611978 + 0.353326i 0.773739 0.633504i 0.218384π-0.218384\pi
−0.161761 + 0.986830i 0.551717π0.551717\pi
6262 288.255 135.744i 0.590459 0.278057i
6363 9.73086 16.8543i 0.0194599 0.0337055i
6464 −449.096 245.880i −0.877140 0.480235i
6565 −179.831 −0.343158
6666 787.164 + 546.757i 1.46808 + 1.01971i
6767 −469.568 271.105i −0.856223 0.494340i 0.00652287 0.999979i 0.497924π-0.497924\pi
−0.862746 + 0.505638i 0.831257π0.831257\pi
6868 −49.8677 8.40488i −0.0889316 0.0149888i
6969 400.507i 0.698773i
7070 −32.7838 + 47.1988i −0.0559774 + 0.0805906i
7171 513.735 + 889.815i 0.858720 + 1.48735i 0.873151 + 0.487450i 0.162073π0.162073\pi
−0.0144309 + 0.999896i 0.504594π0.504594\pi
7272 49.2658 + 48.1611i 0.0806393 + 0.0788312i
7373 −335.367 580.873i −0.537696 0.931316i −0.999028 0.0440884i 0.985962π-0.985962\pi
0.461332 0.887228i 0.347372π-0.347372\pi
7474 274.604 + 583.126i 0.431379 + 0.916041i
7575 629.779i 0.969609i
7676 −149.537 645.457i −0.225698 0.974197i
7777 395.140i 0.584810i
7878 −793.501 + 373.673i −1.15188 + 0.542438i
7979 83.2056 + 144.116i 0.118498 + 0.205245i 0.919173 0.393855i 0.128859π-0.128859\pi
−0.800674 + 0.599100i 0.795525π0.795525\pi
8080 −133.109 153.848i −0.186025 0.215009i
8181 400.969 + 694.499i 0.550026 + 0.952674i
8282 117.806 + 81.8271i 0.158653 + 0.110199i
8383 213.128i 0.281854i −0.990020 0.140927i 0.954992π-0.954992\pi
0.990020 0.140927i 0.0450083π-0.0450083\pi
8484 −46.5831 + 276.386i −0.0605076 + 0.359002i
8585 −17.4018 10.0470i −0.0222058 0.0128205i
8686 759.761 1093.83i 0.952642 1.37152i
8787 1431.96 1.76462
8888 −1355.17 346.699i −1.64161 0.419980i
8989 −315.321 + 546.152i −0.375550 + 0.650471i −0.990409 0.138165i 0.955879π-0.955879\pi
0.614859 + 0.788637i 0.289213π0.289213\pi
9090 11.6629 + 24.7663i 0.0136597 + 0.0290067i
9191 −313.160 180.803i −0.360748 0.208278i
9292 −204.071 547.763i −0.231260 0.620741i
9393 534.738 308.731i 0.596233 0.344235i
9494 −31.9249 + 381.504i −0.0350298 + 0.418607i
9595 33.8573 261.073i 0.0365651 0.281953i
9696 −907.023 402.265i −0.964298 0.427667i
9797 −320.342 554.849i −0.335317 0.580787i 0.648228 0.761446i 0.275510π-0.275510\pi
−0.983546 + 0.180659i 0.942177π0.942177\pi
9898 773.155 364.092i 0.796943 0.375294i
9999 163.010 + 94.1139i 0.165486 + 0.0955435i
100100 320.893 + 861.332i 0.320893 + 0.861332i
101101 863.815 + 498.724i 0.851018 + 0.491336i 0.860994 0.508615i 0.169842π-0.169842\pi
−0.00997612 + 0.999950i 0.503176π0.503176\pi
102102 −97.6621 8.17253i −0.0948038 0.00793334i
103103 −706.149 −0.675523 −0.337762 0.941232i 0.609670π-0.609670\pi
−0.337762 + 0.941232i 0.609670π0.609670\pi
104104 894.851 915.377i 0.843725 0.863077i
105105 −55.6842 + 96.4478i −0.0517545 + 0.0896414i
106106 1185.05 + 99.1672i 1.08587 + 0.0908676i
107107 1358.71i 1.22758i 0.789469 + 0.613791i 0.210356π0.210356\pi
−0.789469 + 0.613791i 0.789644π0.789644\pi
108108 −809.771 669.113i −0.721483 0.596162i
109109 383.566 221.452i 0.337055 0.194599i −0.321914 0.946769i 0.604326π-0.604326\pi
0.658969 + 0.752170i 0.270993π0.270993\pi
110110 −456.493 317.075i −0.395681 0.274836i
111111 624.548 + 1081.75i 0.534049 + 0.925000i
112112 −77.1171 401.742i −0.0650615 0.338938i
113113 −1241.51 −1.03355 −0.516776 0.856121i 0.672868π-0.672868\pi
−0.516776 + 0.856121i 0.672868π0.672868\pi
114114 −393.092 1222.33i −0.322951 1.00423i
115115 232.262i 0.188335i
116116 −1958.45 + 729.627i −1.56756 + 0.584002i
117117 −149.176 + 86.1268i −0.117875 + 0.0680549i
118118 −614.883 + 885.245i −0.479699 + 0.690622i
119119 −20.2025 34.9918i −0.0155627 0.0269554i
120120 −281.920 275.599i −0.214464 0.209655i
121121 −2490.67 −1.87128
122122 −948.921 79.4073i −0.704191 0.0589278i
123123 240.730 + 138.985i 0.176470 + 0.101885i
124124 −574.038 + 694.709i −0.415727 + 0.503119i
125125 762.562i 0.545645i
126126 −4.59030 + 54.8543i −0.00324553 + 0.0387842i
127127 938.410 1625.37i 0.655673 1.13566i −0.326052 0.945352i 0.605718π-0.605718\pi
0.981725 0.190307i 0.0609483π-0.0609483\pi
128128 1445.48 + 88.0100i 0.998152 + 0.0607739i
129129 1290.47 2235.17i 0.880774 1.52555i
130130 460.167 216.701i 0.310456 0.146199i
131131 −110.321 + 63.6936i −0.0735783 + 0.0424804i −0.536338 0.844003i 0.680193π-0.680193\pi
0.462760 + 0.886484i 0.346859π0.346859\pi
132132 −2673.12 450.538i −1.76262 0.297078i
133133 321.444 420.595i 0.209569 0.274212i
134134 1528.26 + 127.888i 0.985237 + 0.0824463i
135135 −208.693 361.467i −0.133048 0.230445i
136136 137.734 38.5846i 0.0868426 0.0243280i
137137 933.960 1617.67i 0.582435 1.00881i −0.412755 0.910842i 0.635433π-0.635433\pi
0.995190 0.0979652i 0.0312334π-0.0312334\pi
138138 −482.621 1024.85i −0.297706 0.632183i
139139 1560.88 + 901.173i 0.952460 + 0.549903i 0.893844 0.448378i 0.147998π-0.147998\pi
0.0586157 + 0.998281i 0.481331π0.481331\pi
140140 27.0145 160.282i 0.0163082 0.0967593i
141141 741.914i 0.443123i
142142 −2386.84 1657.87i −1.41056 0.979759i
143143 1748.67 3028.79i 1.02260 1.77119i
144144 −184.101 63.8726i −0.106540 0.0369633i
145145 −830.420 −0.475605
146146 1558.13 + 1082.26i 0.883234 + 0.613485i
147147 1434.27 828.075i 0.804737 0.464615i
148148 −1405.36 1161.25i −0.780541 0.644961i
149149 −1.35824 + 0.784180i −0.000746788 + 0.000431158i −0.500373 0.865810i 0.666804π-0.666804\pi
0.499627 + 0.866241i 0.333471π0.333471\pi
150150 758.899 + 1611.54i 0.413093 + 0.877209i
151151 −2598.55 −1.40044 −0.700221 0.713926i 0.746915π-0.746915\pi
−0.700221 + 0.713926i 0.746915π0.746915\pi
152152 1160.44 + 1471.46i 0.619237 + 0.785204i
153153 −19.2473 −0.0101703
154154 −476.153 1011.12i −0.249153 0.529080i
155155 −310.105 + 179.039i −0.160698 + 0.0927793i
156156 1580.20 1912.38i 0.811006 0.981491i
157157 −2111.46 + 1219.05i −1.07333 + 0.619689i −0.929090 0.369854i 0.879408π-0.879408\pi
−0.144242 + 0.989542i 0.546074π0.546074\pi
158158 −386.578 268.513i −0.194649 0.135201i
159159 2304.58 1.14947
160160 526.001 + 233.282i 0.259900 + 0.115266i
161161 233.518 404.464i 0.114309 0.197989i
162162 −1862.92 1293.97i −0.903489 0.627554i
163163 966.960i 0.464651i 0.972638 + 0.232326i 0.0746335π0.0746335\pi
−0.972638 + 0.232326i 0.925366π0.925366\pi
164164 −400.057 67.4271i −0.190483 0.0321047i
165165 −932.814 538.560i −0.440118 0.254102i
166166 256.825 + 545.372i 0.120081 + 0.254995i
167167 −1541.94 + 2670.72i −0.714485 + 1.23752i 0.248672 + 0.968588i 0.420006π0.420006\pi
−0.963158 + 0.268937i 0.913328π0.913328\pi
168168 −213.851 763.375i −0.0982081 0.350570i
169169 501.767 + 869.086i 0.228387 + 0.395578i
170170 56.6362 + 4.73942i 0.0255518 + 0.00213822i
171171 −96.9504 232.784i −0.0433566 0.104102i
172172 −626.058 + 3714.51i −0.277537 + 1.64668i
173173 311.262 179.707i 0.136791 0.0789762i −0.430043 0.902808i 0.641502π-0.641502\pi
0.566834 + 0.823832i 0.308168π0.308168\pi
174174 −3664.22 + 1725.54i −1.59646 + 0.751799i
175175 −367.196 + 636.002i −0.158614 + 0.274727i
176176 3885.52 745.853i 1.66410 0.319436i
177177 −1044.39 + 1808.94i −0.443511 + 0.768183i
178178 148.745 1777.51i 0.0626344 0.748484i
179179 3379.39i 1.41110i 0.708658 + 0.705552i 0.249301π0.249301\pi
−0.708658 + 0.705552i 0.750699π0.750699\pi
180180 −59.6881 49.3202i −0.0247160 0.0204229i
181181 4023.87 + 2323.18i 1.65244 + 0.954039i 0.976064 + 0.217485i 0.0697854π0.0697854\pi
0.676380 + 0.736553i 0.263548π0.263548\pi
182182 1019.21 + 85.2895i 0.415105 + 0.0347367i
183183 −1845.38 −0.745432
184184 1182.26 + 1155.75i 0.473682 + 0.463061i
185185 −362.188 627.328i −0.143938 0.249308i
186186 −996.306 + 1434.38i −0.392757 + 0.565451i
187187 338.430 195.393i 0.132345 0.0764093i
188188 −378.029 1014.70i −0.146652 0.393640i
189189 839.284i 0.323010i
190190 227.962 + 708.855i 0.0870427 + 0.270662i
191191 1388.26 0.525923 0.262961 0.964806i 0.415301π-0.415301\pi
0.262961 + 0.964806i 0.415301π0.415301\pi
192192 2805.71 63.6327i 1.05461 0.0239182i
193193 1038.65 + 1798.99i 0.387376 + 0.670956i 0.992096 0.125483i 0.0400481π-0.0400481\pi
−0.604719 + 0.796439i 0.706715π0.706715\pi
194194 1488.33 + 1033.78i 0.550802 + 0.382582i
195195 853.649 492.854i 0.313493 0.180995i
196196 −1539.68 + 1863.34i −0.561107 + 0.679060i
197197 2552.51i 0.923140i −0.887104 0.461570i 0.847286π-0.847286\pi
0.887104 0.461570i 0.152714π-0.152714\pi
198198 −530.534 44.3960i −0.190421 0.0159348i
199199 −44.5813 + 77.2171i −0.0158808 + 0.0275064i −0.873857 0.486184i 0.838389π-0.838389\pi
0.857976 + 0.513690i 0.171722π0.171722\pi
200200 −1859.06 1817.37i −0.657275 0.642538i
201201 2972.03 1.04294
202202 −2811.38 235.261i −0.979248 0.0819451i
203203 −1446.11 834.909i −0.499984 0.288666i
204204 259.755 96.7726i 0.0891493 0.0332129i
205205 −139.604 80.6005i −0.0475628 0.0274604i
206206 1806.96 850.926i 0.611149 0.287800i
207207 −111.238 192.670i −0.0373505 0.0646930i
208208 −1186.78 + 3420.67i −0.395616 + 1.14029i
209209 4067.87 + 3108.90i 1.34632 + 1.02893i
210210 26.2677 313.900i 0.00863163 0.103148i
211211 143.613 82.9147i 0.0468564 0.0270525i −0.476389 0.879235i 0.658055π-0.658055\pi
0.523245 + 0.852182i 0.324721π0.324721\pi
212212 −3151.92 + 1174.26i −1.02111 + 0.380417i
213213 −4877.35 2815.94i −1.56897 0.905846i
214214 −1637.28 3476.78i −0.522999 1.11060i
215215 −748.372 + 1296.22i −0.237389 + 0.411169i
216216 2878.41 + 736.394i 0.906718 + 0.231969i
217217 −720.029 −0.225248
218218 −714.648 + 1028.88i −0.222028 + 0.319653i
219219 3183.95 + 1838.25i 0.982426 + 0.567204i
220220 1550.20 + 261.276i 0.475065 + 0.0800692i
221221 357.621i 0.108852i
222222 −2901.68 2015.48i −0.877244 0.609325i
223223 1649.50 + 2857.01i 0.495330 + 0.857937i 0.999986 0.00538423i 0.00171386π-0.00171386\pi
−0.504656 + 0.863321i 0.668381π0.668381\pi
224224 681.443 + 935.084i 0.203262 + 0.278919i
225225 174.917 + 302.964i 0.0518271 + 0.0897672i
226226 3176.88 1496.05i 0.935058 0.440335i
227227 2190.15i 0.640377i −0.947354 0.320188i 0.896254π-0.896254\pi
0.947354 0.320188i 0.103746π-0.103746\pi
228228 2478.82 + 2654.13i 0.720017 + 0.770938i
229229 5275.55i 1.52235i −0.648547 0.761175i 0.724623π-0.724623\pi
0.648547 0.761175i 0.275377π-0.275377\pi
230230 279.881 + 594.333i 0.0802384 + 0.170388i
231231 −1082.94 1875.71i −0.308452 0.534254i
232232 4132.23 4227.01i 1.16937 1.19619i
233233 351.609 + 609.005i 0.0988612 + 0.171233i 0.911214 0.411934i 0.135147π-0.135147\pi
−0.812352 + 0.583167i 0.801813π0.801813\pi
234234 277.940 400.150i 0.0776475 0.111789i
235235 430.251i 0.119432i
236236 506.675 3006.19i 0.139753 0.829180i
237237 −789.947 456.076i −0.216509 0.125001i
238238 93.8621 + 65.1957i 0.0255638 + 0.0177563i
239239 −3283.69 −0.888721 −0.444361 0.895848i 0.646569π-0.646569\pi
−0.444361 + 0.895848i 0.646569π0.646569\pi
240240 1053.51 + 365.506i 0.283348 + 0.0983055i
241241 −463.112 + 802.133i −0.123783 + 0.214398i −0.921256 0.388956i 0.872836π-0.872836\pi
0.797474 + 0.603354i 0.206169π0.206169\pi
242242 6373.35 3001.32i 1.69295 0.797240i
243243 −736.480 425.207i −0.194425 0.112251i
244244 2523.87 940.278i 0.662190 0.246701i
245245 −831.761 + 480.217i −0.216895 + 0.125224i
246246 −783.482 65.5631i −0.203061 0.0169925i
247247 −4325.22 + 1801.37i −1.11420 + 0.464043i
248248 631.759 2469.41i 0.161761 0.632290i
249249 584.112 + 1011.71i 0.148661 + 0.257488i
250250 −918.906 1951.31i −0.232467 0.493648i
251251 −5566.76 3213.97i −1.39988 0.808223i −0.405504 0.914093i 0.632904π-0.632904\pi
−0.994380 + 0.105870i 0.966237π0.966237\pi
252252 −54.3547 145.898i −0.0135874 0.0364710i
253253 3911.85 + 2258.51i 0.972080 + 0.561231i
254254 −442.673 + 5289.96i −0.109353 + 1.30678i
255255 110.141 0.0270482
256256 −3804.87 + 1516.63i −0.928924 + 0.370271i
257257 621.051 1075.69i 0.150740 0.261089i −0.780760 0.624831i 0.785168π-0.785168\pi
0.931500 + 0.363742i 0.118501π0.118501\pi
258258 −608.750 + 7274.59i −0.146896 + 1.75541i
259259 1456.58i 0.349450i
260260 −916.388 + 1109.03i −0.218584 + 0.264534i
261261 −688.863 + 397.715i −0.163370 + 0.0943217i
262262 205.546 295.924i 0.0484682 0.0697795i
263263 1023.95 + 1773.53i 0.240074 + 0.415820i 0.960735 0.277467i 0.0894950π-0.0894950\pi
−0.720661 + 0.693287i 0.756162π0.756162\pi
264264 7383.13 2068.30i 1.72121 0.482179i
265265 −1336.47 −0.309808
266266 −315.711 + 1463.60i −0.0727725 + 0.337366i
267267 3456.74i 0.792319i
268268 −4064.76 + 1514.34i −0.926474 + 0.345161i
269269 −1938.16 + 1119.00i −0.439300 + 0.253630i −0.703301 0.710893i 0.748291π-0.748291\pi
0.264001 + 0.964522i 0.414958π0.414958\pi
270270 969.598 + 673.473i 0.218548 + 0.151801i
271271 −3298.44 5713.07i −0.739359 1.28061i −0.952784 0.303648i 0.901795π-0.901795\pi
0.213426 0.976959i 0.431538π-0.431538\pi
272272 −305.951 + 264.707i −0.0682022 + 0.0590081i
273273 1982.07 0.439416
274274 −440.574 + 5264.88i −0.0971388 + 1.16081i
275275 −6151.22 3551.41i −1.34885 0.778756i
276276 2469.95 + 2040.92i 0.538671 + 0.445104i
277277 1603.05i 0.347718i −0.984771 0.173859i 0.944376π-0.944376\pi
0.984771 0.173859i 0.0556237π-0.0556237\pi
278278 −5080.05 425.107i −1.09598 0.0917131i
279279 −171.495 + 297.039i −0.0367999 + 0.0637392i
280280 124.017 + 442.697i 0.0264693 + 0.0944864i
281281 857.822 1485.79i 0.182112 0.315427i −0.760488 0.649352i 0.775040π-0.775040\pi
0.942599 + 0.333926i 0.108373π0.108373\pi
282282 −894.024 1898.48i −0.188789 0.400896i
283283 395.275 228.212i 0.0830271 0.0479357i −0.457912 0.888998i 0.651402π-0.651402\pi
0.540939 + 0.841062i 0.318069π0.318069\pi
284284 8105.44 + 1366.12i 1.69355 + 0.285438i
285285 554.792 + 1332.09i 0.115309 + 0.276864i
286286 −824.894 + 9857.52i −0.170549 + 2.03807i
287287 −162.072 280.717i −0.0333339 0.0577360i
288288 548.062 58.4035i 0.112135 0.0119495i
289289 2436.52 4220.18i 0.495933 0.858982i
290290 2124.95 1000.68i 0.430281 0.202627i
291291 3041.30 + 1755.89i 0.612660 + 0.353719i
292292 −5291.25 891.806i −1.06043 0.178729i
293293 8541.68i 1.70311i 0.524268 + 0.851553i 0.324339π0.324339\pi
−0.524268 + 0.851553i 0.675661π0.675661\pi
294294 −2672.28 + 3847.28i −0.530104 + 0.763190i
295295 605.665 1049.04i 0.119536 0.207043i
296296 4995.50 + 1278.02i 0.980938 + 0.250957i
297297 8117.29 1.58590
298298 2.53063 3.64334i 0.000491931 0.000708232i
299299 −3579.87 + 2066.84i −0.692405 + 0.399760i
300300 −3883.88 3209.25i −0.747453 0.617620i
301301 −2606.45 + 1504.83i −0.499114 + 0.288163i
302302 6649.39 3131.31i 1.26699 0.596645i
303303 −5467.32 −1.03660
304304 −4742.58 2366.94i −0.894755 0.446557i
305305 1070.17 0.200911
306306 49.2516 23.1934i 0.00920107 0.00433294i
307307 −7852.60 + 4533.70i −1.45984 + 0.842840i −0.999003 0.0446434i 0.985785π-0.985785\pi
−0.460839 + 0.887484i 0.652451π0.652451\pi
308308 2436.85 + 2013.57i 0.450819 + 0.372512i
309309 3352.06 1935.31i 0.617126 0.356298i
310310 577.778 831.826i 0.105857 0.152402i
311311 −8924.69 −1.62724 −0.813622 0.581395i 0.802507π-0.802507\pi
−0.813622 + 0.581395i 0.802507π0.802507\pi
312312 −1739.09 + 6797.73i −0.315566 + 1.23348i
313313 −2712.33 + 4697.89i −0.489808 + 0.848373i −0.999931 0.0117286i 0.996267π-0.996267\pi
0.510123 + 0.860102i 0.329600π0.329600\pi
314314 3934.01 5663.79i 0.707036 1.01792i
315315 61.8635i 0.0110654i
316316 1312.77 + 221.260i 0.233700 + 0.0393887i
317317 −4881.35 2818.25i −0.864870 0.499333i 0.000770037 1.00000i 0.499755π-0.499755\pi
−0.865640 + 0.500667i 0.833088π0.833088\pi
318318 −5897.17 + 2777.08i −1.03993 + 0.489720i
319319 8074.99 13986.3i 1.41728 2.45480i
320320 −1627.09 + 36.9019i −0.284241 + 0.00644649i
321321 −3723.75 6449.73i −0.647475 1.12146i
322322 −110.156 + 1316.37i −0.0190645 + 0.227822i
323323 −519.183 67.3303i −0.0894369 0.0115986i
324324 6326.28 + 1066.25i 1.08475 + 0.182828i
325325 5629.19 3250.01i 0.960773 0.554702i
326326 −1165.21 2474.34i −0.197960 0.420372i
327327 −1213.85 + 2102.44i −0.205278 + 0.355552i
328328 1104.95 309.540i 0.186009 0.0521082i
329329 432.577 749.245i 0.0724885 0.125554i
330330 3035.94 + 254.053i 0.506434 + 0.0423793i
331331 3650.02i 0.606112i 0.952973 + 0.303056i 0.0980069π0.0980069\pi
−0.952973 + 0.303056i 0.901993π0.901993\pi
332332 −1314.37 1086.07i −0.217276 0.179535i
333333 −600.895 346.927i −0.0988855 0.0570915i
334334 727.375 8692.16i 0.119162 1.42399i
335335 −1723.54 −0.281096
336336 1467.11 + 1695.70i 0.238206 + 0.275321i
337337 134.374 + 232.742i 0.0217205 + 0.0376210i 0.876681 0.481072i 0.159752π-0.159752\pi
−0.854961 + 0.518693i 0.826419π0.826419\pi
338338 −2331.24 1619.25i −0.375155 0.260579i
339339 5893.39 3402.55i 0.944203 0.545136i
340340 −150.637 + 56.1204i −0.0240278 + 0.00895164i
341341 6963.89i 1.10591i
342342 528.596 + 478.842i 0.0835767 + 0.0757100i
343343 −4123.65 −0.649143
344344 −2874.07 10259.4i −0.450463 1.60800i
345345 636.551 + 1102.54i 0.0993355 + 0.172054i
346346 −579.934 + 834.929i −0.0901082 + 0.129729i
347347 −5735.95 + 3311.65i −0.887383 + 0.512331i −0.873085 0.487567i 0.837884π-0.837884\pi
−0.0142971 + 0.999898i 0.504551π0.504551\pi
348348 7297.01 8830.94i 1.12402 1.36031i
349349 5975.97i 0.916580i 0.888803 + 0.458290i 0.151538π0.151538\pi
−0.888803 + 0.458290i 0.848462π0.848462\pi
350350 173.216 2069.94i 0.0264537 0.316123i
351351 −3714.20 + 6433.19i −0.564814 + 0.978286i
352352 −9043.85 + 6590.70i −1.36943 + 0.997971i
353353 1584.14 0.238854 0.119427 0.992843i 0.461894π-0.461894\pi
0.119427 + 0.992843i 0.461894π0.461894\pi
354354 492.668 5887.40i 0.0739689 0.883932i
355355 2828.48 + 1633.02i 0.422873 + 0.244146i
356356 1761.32 + 4727.70i 0.262219 + 0.703841i
357357 191.801 + 110.736i 0.0284347 + 0.0164168i
358358 −4072.25 8647.49i −0.601187 1.27663i
359359 3969.58 + 6875.51i 0.583583 + 1.01080i 0.995050 + 0.0993707i 0.0316830π0.0316830\pi
−0.411468 + 0.911424i 0.634984π0.634984\pi
360360 212.167 + 54.2795i 0.0310617 + 0.00794661i
361361 −1800.86 6618.37i −0.262554 0.964917i
362362 −13096.1 1095.91i −1.90143 0.159115i
363363 11823.1 6826.08i 1.70951 0.986986i
364364 −2710.83 + 1009.93i −0.390347 + 0.145425i
365365 −1846.44 1066.04i −0.264786 0.152874i
366366 4722.11 2223.72i 0.674396 0.317584i
367367 2360.44 4088.40i 0.335733 0.581506i −0.647893 0.761732i 0.724349π-0.724349\pi
0.983625 + 0.180226i 0.0576828π0.0576828\pi
368368 −4417.99 1532.79i −0.625825 0.217126i
369369 −154.409 −0.0217837
370370 1682.74 + 1168.82i 0.236437 + 0.164227i
371371 −2327.36 1343.70i −0.325688 0.188036i
372372 820.975 4870.99i 0.114424 0.678896i
373373 5353.86i 0.743197i −0.928394 0.371598i 0.878810π-0.878810\pi
0.928394 0.371598i 0.121190π-0.121190\pi
374374 −630.553 + 907.805i −0.0871794 + 0.125512i
375375 −2089.92 3619.85i −0.287795 0.498475i
376376 2190.07 + 2140.96i 0.300383 + 0.293648i
377377 7389.69 + 12799.3i 1.00952 + 1.74854i
378378 1011.36 + 2147.63i 0.137615 + 0.292229i
379379 11268.1i 1.52719i −0.645698 0.763593i 0.723434π-0.723434\pi
0.645698 0.763593i 0.276566π-0.276566\pi
380380 −1437.52 1539.18i −0.194061 0.207785i
381381 10287.4i 1.38331i
382382 −3552.41 + 1672.89i −0.475804 + 0.224064i
383383 1046.07 + 1811.85i 0.139561 + 0.241727i 0.927331 0.374243i 0.122098π-0.122098\pi
−0.787770 + 0.615970i 0.788764π0.788764\pi
384384 −7102.82 + 3543.78i −0.943918 + 0.470945i
385385 628.021 + 1087.76i 0.0831348 + 0.143994i
386386 −4825.62 3351.83i −0.636315 0.441978i
387387 1433.68i 0.188315i
388388 −5054.19 851.851i −0.661308 0.111459i
389389 −4810.82 2777.53i −0.627039 0.362021i 0.152565 0.988293i 0.451247π-0.451247\pi
−0.779605 + 0.626272i 0.784580π0.784580\pi
390390 −1590.49 + 2289.83i −0.206507 + 0.297308i
391391 −461.889 −0.0597410
392392 1694.50 6623.43i 0.218329 0.853403i
393393 349.125 604.702i 0.0448117 0.0776162i
394394 3075.83 + 6531.58i 0.393295 + 0.835169i
395395 458.106 + 264.488i 0.0583540 + 0.0336907i
396396 1411.08 525.702i 0.179064 0.0667109i
397397 12606.1 7278.16i 1.59366 0.920102i 0.600992 0.799255i 0.294773π-0.294773\pi
0.992671 0.120846i 0.0385608π-0.0385608\pi
398398 21.0302 251.312i 0.00264861 0.0316511i
399399 −373.171 + 2877.51i −0.0468218 + 0.361042i
400400 6947.09 + 2410.24i 0.868387 + 0.301281i
401401 −2718.61 4708.78i −0.338556 0.586397i 0.645605 0.763671i 0.276605π-0.276605\pi
−0.984161 + 0.177275i 0.943272π0.943272\pi
402402 −7605.09 + 3581.37i −0.943551 + 0.444334i
403403 5519.09 + 3186.45i 0.682197 + 0.393867i
404404 7477.51 2785.78i 0.920842 0.343063i
405405 2207.62 + 1274.57i 0.270858 + 0.156380i
406406 4706.51 + 393.849i 0.575321 + 0.0481438i
407407 14087.6 1.71572
408408 −548.070 + 560.641i −0.0665037 + 0.0680291i
409409 −2336.00 + 4046.08i −0.282415 + 0.489158i −0.971979 0.235067i 0.924469π-0.924469\pi
0.689564 + 0.724225i 0.257802π0.257802\pi
410410 454.357 + 38.0214i 0.0547295 + 0.00457986i
411411 10238.7i 1.22880i
412412 −3598.42 + 4354.85i −0.430294 + 0.520748i
413413 2109.43 1217.88i 0.251327 0.145104i
414414 516.817 + 358.976i 0.0613531 + 0.0426152i
415415 −338.738 586.712i −0.0400675 0.0693989i
416416 −1085.16 10183.2i −0.127895 1.20017i
417417 −9879.23 −1.16016
418418 −14155.5 3053.46i −1.65639 0.357296i
419419 10426.9i 1.21572i 0.794045 + 0.607859i 0.207972π0.207972\pi
−0.794045 + 0.607859i 0.792028π0.792028\pi
420420 311.041 + 834.889i 0.0361363 + 0.0969962i
421421 −3703.90 + 2138.44i −0.428781 + 0.247557i −0.698827 0.715291i 0.746294π-0.746294\pi
0.270046 + 0.962847i 0.412961π0.412961\pi
422422 −267.574 + 385.226i −0.0308657 + 0.0444372i
423423 −206.061 356.908i −0.0236857 0.0410248i
424424 6650.40 6802.94i 0.761726 0.779198i
425425 726.299 0.0828958
426426 15873.9 + 1328.35i 1.80538 + 0.151077i
427427 1863.61 + 1075.96i 0.211209 + 0.121942i
428428 8379.22 + 6923.75i 0.946319 + 0.781944i
429429 19170.0i 2.15743i
430430 353.027 4218.69i 0.0395918 0.473123i
431431 −3000.72 + 5197.39i −0.335358 + 0.580858i −0.983554 0.180617i 0.942191π-0.942191\pi
0.648195 + 0.761474i 0.275524π0.275524\pi
432432 −8252.91 + 1584.20i −0.919140 + 0.176435i
433433 −6833.50 + 11836.0i −0.758423 + 1.31363i 0.185231 + 0.982695i 0.440697π0.440697\pi
−0.943654 + 0.330932i 0.892637π0.892637\pi
434434 1842.47 867.652i 0.203782 0.0959646i
435435 3941.97 2275.90i 0.434490 0.250853i
436436 588.883 3493.95i 0.0646844 0.383784i
437437 −2326.58 5586.27i −0.254681 0.611505i
438438 −10362.5 867.152i −1.13046 0.0945985i
439439 8156.07 + 14126.7i 0.886715 + 1.53584i 0.843735 + 0.536760i 0.180352π0.180352\pi
0.0429802 + 0.999076i 0.486315π0.486315\pi
440440 −4281.63 + 1199.45i −0.463906 + 0.129958i
441441 −459.983 + 796.714i −0.0496689 + 0.0860290i
442442 −430.942 915.113i −0.0463752 0.0984785i
443443 13879.7 + 8013.44i 1.48859 + 0.859436i 0.999915 0.0130319i 0.00414829π-0.00414829\pi
0.488672 + 0.872468i 0.337482π0.337482\pi
444444 9853.78 + 1660.79i 1.05324 + 0.177517i
445445 2004.64i 0.213548i
446446 −7663.66 5323.10i −0.813643 0.565148i
447447 4.29834 7.44494i 0.000454820 0.000787771i
448448 −2870.54 1571.62i −0.302723 0.165741i
449449 13840.3 1.45471 0.727355 0.686261i 0.240749π-0.240749\pi
0.727355 + 0.686261i 0.240749π0.240749\pi
450450 −812.672 564.474i −0.0851327 0.0591323i
451451 2715.01 1567.51i 0.283470 0.163661i
452452 −6326.52 + 7656.44i −0.658350 + 0.796745i
453453 12335.2 7121.72i 1.27938 0.738648i
454454 2639.19 + 5604.36i 0.272826 + 0.579352i
455455 −1149.45 −0.118433
456456 −9541.31 3804.58i −0.979853 0.390715i
457457 5522.47 0.565274 0.282637 0.959227i 0.408791π-0.408791\pi
0.282637 + 0.959227i 0.408791π0.408791\pi
458458 6357.16 + 13499.5i 0.648582 + 1.37728i
459459 −718.831 + 415.018i −0.0730984 + 0.0422034i
460460 −1432.37 1183.57i −0.145184 0.119966i
461461 −14990.7 + 8654.86i −1.51450 + 0.874397i −0.514644 + 0.857404i 0.672076π0.672076\pi
−0.999856 + 0.0169930i 0.994591π0.994591\pi
462462 5031.41 + 3494.77i 0.506672 + 0.351929i
463463 8476.57 0.850842 0.425421 0.904996i 0.360126π-0.360126\pi
0.425421 + 0.904996i 0.360126π0.360126\pi
464464 −5480.27 + 15795.9i −0.548309 + 1.58040i
465465 981.370 1699.78i 0.0978709 0.169517i
466466 −1633.59 1134.68i −0.162392 0.112796i
467467 5033.78i 0.498792i 0.968402 + 0.249396i 0.0802320π0.0802320\pi
−0.968402 + 0.249396i 0.919768π0.919768\pi
468468 −229.028 + 1358.86i −0.0226214 + 0.134217i
469469 −3001.39 1732.86i −0.295504 0.170610i
470470 518.463 + 1100.96i 0.0508828 + 0.108050i
471471 6682.02 11573.6i 0.653697 1.13224i
472472 2326.01 + 8303.07i 0.226829 + 0.809703i
473473 −14554.3 25208.8i −1.41481 2.45053i
474474 2570.97 + 215.143i 0.249132 + 0.0208478i
475475 3658.44 + 8784.17i 0.353391 + 0.848516i
476476 −318.745 53.7225i −0.0306926 0.00517303i
477477 −1108.65 + 640.081i −0.106419 + 0.0614409i
478478 8402.61 3956.93i 0.804030 0.378631i
479479 −751.425 + 1301.51i −0.0716774 + 0.124149i −0.899637 0.436640i 0.856169π-0.856169\pi
0.827959 + 0.560788i 0.189502π0.189502\pi
480480 −3136.25 + 334.210i −0.298228 + 0.0317803i
481481 −6446.03 + 11164.8i −0.611047 + 1.05836i
482482 218.462 2610.63i 0.0206445 0.246703i
483483 2559.97i 0.241165i
484484 −12692.0 + 15360.1i −1.19197 + 1.44253i
485485 −1763.71 1018.28i −0.165126 0.0953354i
486486 2396.96 + 200.581i 0.223720 + 0.0187213i
487487 9650.47 0.897956 0.448978 0.893543i 0.351788π-0.351788\pi
0.448978 + 0.893543i 0.351788π0.351788\pi
488488 −5325.25 + 5447.39i −0.493981 + 0.505311i
489489 −2650.11 4590.12i −0.245075 0.424483i
490490 1549.71 2231.12i 0.142875 0.205697i
491491 −10592.0 + 6115.29i −0.973544 + 0.562076i −0.900315 0.435239i 0.856664π-0.856664\pi
−0.0732292 + 0.997315i 0.523330π0.523330\pi
492492 2083.85 776.346i 0.190949 0.0711390i
493493 1651.42i 0.150864i
494494 8897.06 9821.51i 0.810319 0.894515i
495495 598.324 0.0543287
496496 1359.10 + 7080.24i 0.123035 + 0.640952i
497497 3283.70 + 5687.53i 0.296366 + 0.513321i
498498 −2713.81 1884.99i −0.244195 0.169615i
499499 13405.5 7739.69i 1.20263 0.694341i 0.241494 0.970402i 0.422363π-0.422363\pi
0.961140 + 0.276061i 0.0890292π0.0890292\pi
500500 4702.76 + 3885.89i 0.420628 + 0.347565i
501501 16903.7i 1.50739i
502502 18117.6 + 1516.11i 1.61082 + 0.134796i
503503 7682.63 13306.7i 0.681017 1.17956i −0.293653 0.955912i 0.594871π-0.594871\pi
0.974671 0.223645i 0.0717955π-0.0717955\pi
504504 314.898 + 307.837i 0.0278307 + 0.0272067i
505505 3170.61 0.279387
506506 −12731.6 1065.40i −1.11855 0.0936023i
507507 −4763.73 2750.34i −0.417287 0.240921i
508508 −5241.78 14069.9i −0.457808 1.22884i
509509 5526.47 + 3190.71i 0.481251 + 0.277850i 0.720938 0.693000i 0.243711π-0.243711\pi
−0.239687 + 0.970850i 0.577045π0.577045\pi
510510 −281.839 + 132.723i −0.0244707 + 0.0115236i
511511 −2143.61 3712.83i −0.185572 0.321421i
512512 7908.68 8465.85i 0.682651 0.730744i
513513 −8640.22 6603.36i −0.743616 0.568315i
514514 −292.966 + 3500.96i −0.0251404 + 0.300429i
515515 −1943.93 + 1122.33i −0.166329 + 0.0960303i
516516 −7208.34 19348.4i −0.614979 1.65071i
517517 7246.46 + 4183.75i 0.616439 + 0.355901i
518518 1755.22 + 3727.24i 0.148880 + 0.316149i
519519 −985.032 + 1706.12i −0.0833104 + 0.144298i
520520 1008.53 3942.14i 0.0850521 0.332451i
521521 −18913.6 −1.59044 −0.795220 0.606321i 0.792645π-0.792645\pi
−0.795220 + 0.606321i 0.792645π0.792645\pi
522522 1283.47 1847.81i 0.107617 0.154935i
523523 −4850.23 2800.28i −0.405517 0.234126i 0.283345 0.959018i 0.408556π-0.408556\pi
−0.688862 + 0.724893i 0.741889π0.741889\pi
524524 −169.374 + 1004.92i −0.0141205 + 0.0837792i
525525 4025.43i 0.334637i
526526 −4757.33 3304.39i −0.394352 0.273913i
527527 356.047 + 616.692i 0.0294301 + 0.0509744i
528528 −16400.3 + 14189.4i −1.35176 + 1.16954i
529529 3414.06 + 5913.32i 0.280600 + 0.486013i
530530 3419.89 1610.48i 0.280284 0.131991i
531531 1160.29i 0.0948254i
532532 −955.810 4125.64i −0.0778940 0.336220i
533533 2868.97i 0.233150i
534534 4165.46 + 8845.43i 0.337560 + 0.716815i
535535 2159.48 + 3740.33i 0.174509 + 0.302259i
536536 8576.46 8773.18i 0.691132 0.706984i
537537 −9261.75 16041.8i −0.744272 1.28912i
538538 3611.12 5198.92i 0.289380 0.416620i
539539 18678.5i 1.49265i
540540 −3292.65 554.954i −0.262394 0.0442249i
541541 322.475 + 186.181i 0.0256272 + 0.0147959i 0.512759 0.858533i 0.328623π-0.328623\pi
−0.487132 + 0.873329i 0.661957π0.661957\pi
542542 15324.7 + 10644.4i 1.21449 + 0.843574i
543543 −25468.2 −2.01279
544544 463.916 1046.03i 0.0365630 0.0824417i
545545 703.934 1219.25i 0.0553270 0.0958292i
546546 −5071.91 + 2388.45i −0.397542 + 0.187209i
547547 −17836.0 10297.6i −1.39417 0.804924i −0.400395 0.916343i 0.631127π-0.631127\pi
−0.993774 + 0.111419i 0.964460π0.964460\pi
548548 −5216.92 14003.1i −0.406672 1.09158i
549549 887.744 512.539i 0.0690128 0.0398445i
550550 20019.8 + 1675.29i 1.55209 + 0.129881i
551551 −19972.9 + 8318.36i −1.54424 + 0.643147i
552552 −8779.67 2246.13i −0.676970 0.173192i
553553 531.835 + 921.165i 0.0408968 + 0.0708353i
554554 1931.71 + 4102.03i 0.148142 + 0.314582i
555555 3438.58 + 1985.27i 0.262990 + 0.151837i
556556 13511.6 5033.78i 1.03061 0.383957i
557557 11170.9 + 6449.52i 0.849777 + 0.490619i 0.860576 0.509323i 0.170104π-0.170104\pi
−0.0107985 + 0.999942i 0.503437π0.503437\pi
558558 80.8989 966.746i 0.00613750 0.0733434i
559559 26638.3 2.01552
560560 −850.805 983.370i −0.0642019 0.0742053i
561561 −1071.01 + 1855.04i −0.0806026 + 0.139608i
562562 −404.657 + 4835.67i −0.0303727 + 0.362955i
563563 7425.42i 0.555851i −0.960603 0.277926i 0.910353π-0.910353\pi
0.960603 0.277926i 0.0896469π-0.0896469\pi
564564 4575.42 + 3780.67i 0.341596 + 0.282260i
565565 −3417.69 + 1973.21i −0.254484 + 0.146926i
566566 −736.465 + 1060.29i −0.0546924 + 0.0787406i
567567 2562.92 + 4439.11i 0.189828 + 0.328792i
568568 −22387.1 + 6271.50i −1.65377 + 0.463286i
569569 1865.19 0.137421 0.0687106 0.997637i 0.478111π-0.478111\pi
0.0687106 + 0.997637i 0.478111π0.478111\pi
570570 −3024.86 2740.14i −0.222276 0.201354i
571571 10029.2i 0.735044i −0.930015 0.367522i 0.880206π-0.880206\pi
0.930015 0.367522i 0.119794π-0.119794\pi
572572 −9767.74 26218.3i −0.714003 1.91651i
573573 −6590.03 + 3804.75i −0.480458 + 0.277392i
574574 752.996 + 523.024i 0.0547552 + 0.0380324i
575575 4197.58 + 7270.43i 0.304437 + 0.527300i
576576 −1332.05 + 809.877i −0.0963581 + 0.0585848i
577577 −17785.1 −1.28320 −0.641599 0.767040i 0.721729π-0.721729\pi
−0.641599 + 0.767040i 0.721729π0.721729\pi
578578 −1149.37 + 13735.0i −0.0827120 + 0.988412i
579579 −9860.85 5693.16i −0.707777 0.408635i
580580 −4231.68 + 5121.24i −0.302950 + 0.366635i
581581 1362.28i 0.0972750i
582582 −9898.24 828.301i −0.704975 0.0589935i
583583 12995.8 22509.5i 0.923213 1.59905i
584584 14614.4 4094.05i 1.03553 0.290091i
585585 −273.773 + 474.189i −0.0193490 + 0.0335134i
586586 −10292.9 21857.2i −0.725592 1.54081i
587587 −6144.71 + 3547.65i −0.432060 + 0.249450i −0.700224 0.713923i 0.746916π-0.746916\pi
0.268164 + 0.963373i 0.413583π0.413583\pi
588588 2202.01 13064.9i 0.154438 0.916307i
589589 −5665.08 + 7412.52i −0.396308 + 0.518553i
590590 −285.708 + 3414.22i −0.0199363 + 0.238240i
591591 6995.54 + 12116.6i 0.486901 + 0.843336i
592592 −14323.0 + 2749.40i −0.994377 + 0.190878i
593593 1904.63 3298.91i 0.131895 0.228448i −0.792512 0.609856i 0.791227π-0.791227\pi
0.924407 + 0.381408i 0.124561π0.124561\pi
594594 −20771.3 + 9781.54i −1.43477 + 0.675659i
595595 −111.229 64.2183i −0.00766380 0.00442470i
596596 −2.08529 + 12.3724i −0.000143317 + 0.000850323i
597597 488.728i 0.0335047i
598598 6669.90 9602.64i 0.456108 0.656658i
599599 6335.15 10972.8i 0.432132 0.748474i −0.564925 0.825142i 0.691095π-0.691095\pi
0.997057 + 0.0766680i 0.0244281π0.0244281\pi
600600 13805.6 + 3531.95i 0.939355 + 0.240319i
601601 4805.35 0.326147 0.163073 0.986614i 0.447859π-0.447859\pi
0.163073 + 0.986614i 0.447859π0.447859\pi
602602 4856.25 6991.54i 0.328781 0.473345i
603603 −1429.74 + 825.459i −0.0965562 + 0.0557467i
604604 −13241.8 + 16025.4i −0.892052 + 1.07957i
605605 −6856.46 + 3958.58i −0.460752 + 0.266015i
606606 13990.3 6588.26i 0.937816 0.441633i
607607 9703.21 0.648832 0.324416 0.945915i 0.394832π-0.394832\pi
0.324416 + 0.945915i 0.394832π0.394832\pi
608608 14988.0 + 341.821i 0.999740 + 0.0228004i
609609 9152.80 0.609015
610610 −2738.45 + 1289.58i −0.181765 + 0.0855961i
611611 −6631.48 + 3828.69i −0.439085 + 0.253506i
612612 −98.0808 + 118.699i −0.00647824 + 0.00784006i
613613 13966.3 8063.43i 0.920216 0.531287i 0.0365118 0.999333i 0.488375π-0.488375\pi
0.883704 + 0.468046i 0.155042π0.155042\pi
614614 14630.7 21063.8i 0.961641 1.38447i
615615 883.593 0.0579348
616616 −8662.02 2216.04i −0.566563 0.144946i
617617 −4323.51 + 7488.54i −0.282104 + 0.488618i −0.971903 0.235383i 0.924366π-0.924366\pi
0.689799 + 0.724001i 0.257699π0.257699\pi
618618 −6245.45 + 8991.56i −0.406519 + 0.585264i
619619 3788.37i 0.245989i −0.992407 0.122995i 0.960750π-0.960750\pi
0.992407 0.122995i 0.0392498π-0.0392498\pi
620620 −476.100 + 2824.79i −0.0308397 + 0.182978i
621621 −8308.84 4797.11i −0.536912 0.309986i
622622 22837.3 10754.5i 1.47217 0.693271i
623623 −2015.47 + 3490.90i −0.129612 + 0.224494i
624624 −3741.30 19490.3i −0.240019 1.25038i
625625 −5968.99 10338.6i −0.382016 0.661670i
626626 1279.48 15289.8i 0.0816904 0.976205i
627627 −27830.4 3609.19i −1.77263 0.229884i
628628 −3241.70 + 19233.6i −0.205984 + 1.22214i
629629 −1247.54 + 720.266i −0.0790820 + 0.0456580i
630630 74.5470 + 158.302i 0.00471432 + 0.0100109i
631631 −4423.47 + 7661.68i −0.279074 + 0.483370i −0.971155 0.238450i 0.923361π-0.923361\pi
0.692081 + 0.721820i 0.256694π0.256694\pi
632632 −3625.87 + 1015.75i −0.228211 + 0.0639307i
633633 −454.482 + 787.185i −0.0285372 + 0.0494278i
634634 15886.9 + 1329.44i 0.995188 + 0.0832790i
635635 5965.90i 0.372834i
636636 11743.8 14212.5i 0.732187 0.886103i
637637 14803.2 + 8546.66i 0.920763 + 0.531603i
638638 −3809.18 + 45519.9i −0.236375 + 2.82469i
639639 3128.43 0.193676
640640 4119.07 2055.11i 0.254407 0.126930i
641641 −9320.92 16144.3i −0.574344 0.994792i −0.996113 0.0880891i 0.971924π-0.971924\pi
0.421769 0.906703i 0.361409π-0.361409\pi
642642 17300.7 + 12016.9i 1.06356 + 0.738739i
643643 13897.4 8023.65i 0.852346 0.492102i −0.00909547 0.999959i 0.502895π-0.502895\pi
0.861442 + 0.507856i 0.169562π0.169562\pi
644644 −1304.38 3501.20i −0.0798136 0.214234i
645645 8204.12i 0.500832i
646646 1409.67 453.337i 0.0858554 0.0276104i
647647 −7100.80 −0.431470 −0.215735 0.976452i 0.569215π-0.569215\pi
−0.215735 + 0.976452i 0.569215π0.569215\pi
648648 −17473.1 + 4894.90i −1.05927 + 0.296743i
649649 11778.9 + 20401.7i 0.712425 + 1.23396i
650650 −10488.1 + 15099.7i −0.632889 + 0.911169i
651651 3417.94 1973.35i 0.205775 0.118804i
652652 5963.29 + 4927.47i 0.358191 + 0.295973i
653653 23545.3i 1.41103i 0.708696 + 0.705514i 0.249284π0.249284\pi
−0.708696 + 0.705514i 0.750716π0.750716\pi
654654 572.603 6842.64i 0.0342363 0.409126i
655655 −202.464 + 350.679i −0.0120778 + 0.0209193i
656656 −2454.45 + 2123.57i −0.146083 + 0.126390i
657657 −2042.24 −0.121272
658658 −204.058 + 2438.50i −0.0120897 + 0.144472i
659659 3758.22 + 2169.81i 0.222154 + 0.128261i 0.606947 0.794742i 0.292394π-0.292394\pi
−0.384793 + 0.923003i 0.625727π0.625727\pi
660660 −8074.79 + 3008.29i −0.476228 + 0.177421i
661661 −18725.6 10811.2i −1.10188 0.636169i −0.165164 0.986266i 0.552815π-0.552815\pi
−0.936713 + 0.350097i 0.886149π0.886149\pi
662662 −4398.36 9339.99i −0.258228 0.548352i
663663 −980.116 1697.61i −0.0574126 0.0994416i
664664 4672.07 + 1195.27i 0.273060 + 0.0698578i
665665 216.409 1668.73i 0.0126195 0.0973091i
666666 1955.68 + 163.655i 0.113785 + 0.00952175i
667667 −16531.1 + 9544.22i −0.959649 + 0.554054i
668668 8612.99 + 23118.8i 0.498872 + 1.33906i
669669 −15660.2 9041.41i −0.905019 0.522513i
670670 4410.35 2076.91i 0.254308 0.119758i
671671 −10406.3 + 18024.3i −0.598705 + 1.03699i
672672 −5797.52 2571.20i −0.332804 0.147599i
673673 −17333.9 −0.992827 −0.496413 0.868086i 0.665350π-0.665350\pi
−0.496413 + 0.868086i 0.665350π0.665350\pi
674674 −624.308 433.638i −0.0356787 0.0247821i
675675 13065.3 + 7543.25i 0.745012 + 0.430133i
676676 7916.62 + 1334.29i 0.450422 + 0.0759157i
677677 14293.2i 0.811421i −0.914002 0.405711i 0.867024π-0.867024\pi
0.914002 0.405711i 0.132976π-0.132976\pi
678678 −10980.4 + 15808.4i −0.621974 + 0.895455i
679679 −2047.57 3546.49i −0.115727 0.200444i
680680 317.837 325.127i 0.0179243 0.0183354i
681681 6002.46 + 10396.6i 0.337760 + 0.585018i
682682 8391.66 + 17819.8i 0.471163 + 1.00052i
683683 18942.7i 1.06123i 0.847613 + 0.530615i 0.178039π0.178039\pi
−0.847613 + 0.530615i 0.821961π0.821961\pi
684684 −1929.64 588.332i −0.107868 0.0328881i
685685 5937.61i 0.331189i
686686 10552.0 4969.09i 0.587282 0.276561i
687687 14458.5 + 25042.8i 0.802947 + 1.39075i
688688 19717.3 + 22789.5i 1.09261 + 1.26285i
689689 11892.9 + 20599.2i 0.657598 + 1.13899i
690690 −2957.45 2054.21i −0.163171 0.113337i
691691 2165.53i 0.119220i −0.998222 0.0596098i 0.981014π-0.981014\pi
0.998222 0.0596098i 0.0189856π-0.0189856\pi
692692 477.876 2835.33i 0.0262516 0.155756i
693693 1041.93 + 601.559i 0.0571135 + 0.0329745i
694694 10687.0 15386.1i 0.584545 0.841568i
695695 5729.16 0.312690
696696 −8030.74 + 31390.5i −0.437363 + 1.70956i
697697 −160.286 + 277.624i −0.00871058 + 0.0150872i
698698 −7201.19 15291.9i −0.390500 0.829234i
699699 −3338.14 1927.28i −0.180630 0.104287i
700700 2051.09 + 5505.48i 0.110748 + 0.297268i
701701 −10719.2 + 6188.71i −0.577542 + 0.333444i −0.760156 0.649741i 0.774877π-0.774877\pi
0.182614 + 0.983185i 0.441544π0.441544\pi
702702 1752.09 20937.5i 0.0941998 1.12569i
703703 −14995.2 11460.2i −0.804486 0.614835i
704704 15200.3 27762.9i 0.813751 1.48630i
705705 1179.17 + 2042.38i 0.0629931 + 0.109107i
706706 −4053.65 + 1908.93i −0.216092 + 0.101761i
707707 5521.35 + 3187.75i 0.293708 + 0.169572i
708708 5833.78 + 15658.9i 0.309671 + 0.831211i
709709 −30096.3 17376.1i −1.59421 0.920415i −0.992574 0.121641i 0.961184π-0.961184\pi
−0.601632 0.798774i 0.705482π-0.705482\pi
710710 −9205.59 770.339i −0.486591 0.0407188i
711711 506.687 0.0267261
712712 −10204.0 9975.22i −0.537095 0.525052i
713713 −4115.48 + 7128.23i −0.216166 + 0.374410i
714714 −624.238 52.2373i −0.0327192 0.00273800i
715715 11117.1i 0.581476i
716716 20840.9 + 17220.8i 1.08779 + 0.898844i
717717 15587.5 8999.47i 0.811893 0.468747i
718718 −18442.9 12810.2i −0.958609 0.665841i
719719 986.626 + 1708.89i 0.0511752 + 0.0886380i 0.890478 0.455026i 0.150370π-0.150370\pi
−0.839303 + 0.543664i 0.817037π0.817037\pi
720720 −608.321 + 116.771i −0.0314872 + 0.00604419i
721721 −4513.57 −0.233140
722722 12583.5 + 14765.6i 0.648627 + 0.761106i
723723 5076.92i 0.261152i
724724 34832.2 12976.9i 1.78802 0.666135i
725725 25994.4 15007.9i 1.33160 0.768797i
726726 −22028.4 + 31714.3i −1.12611 + 1.62125i
727727 −11470.7 19867.9i −0.585180 1.01356i −0.994853 0.101329i 0.967691π-0.967691\pi
0.409673 0.912232i 0.365643π-0.365643\pi
728728 5719.73 5850.92i 0.291191 0.297870i
729729 −16991.0 −0.863230
730730 6009.43 + 502.879i 0.304684 + 0.0254964i
731731 2577.73 + 1488.25i 0.130425 + 0.0753009i
732732 −9403.73 + 11380.5i −0.474825 + 0.574640i
733733 25024.7i 1.26100i 0.776191 + 0.630498i 0.217149π0.217149\pi
−0.776191 + 0.630498i 0.782851π0.782851\pi
734734 −1113.48 + 13306.1i −0.0559936 + 0.669126i
735735 2632.22 4559.14i 0.132097 0.228798i
736736 13152.2 1401.55i 0.658691 0.0701925i
737737 16759.7 29028.6i 0.837652 1.45086i
738738 395.115 186.066i 0.0197078 0.00928075i
739739 10350.8 5976.04i 0.515237 0.297473i −0.219746 0.975557i 0.570523π-0.570523\pi
0.734984 + 0.678085i 0.237190π0.237190\pi
740740 −5714.41 963.127i −0.283873 0.0478449i
741741 15594.7 20405.0i 0.773124 1.01160i
742742 7574.64 + 633.858i 0.374762 + 0.0313607i
743743 777.408 + 1346.51i 0.0383854 + 0.0664854i 0.884580 0.466389i 0.154445π-0.154445\pi
−0.846194 + 0.532874i 0.821112π0.821112\pi
744744 3768.88 + 13453.6i 0.185718 + 0.662949i
745745 −2.49269 + 4.31747i −0.000122584 + 0.000212322i
746746 6451.53 + 13699.9i 0.316632 + 0.672373i
747747 −561.991 324.465i −0.0275263 0.0158923i
748748 519.587 3082.80i 0.0253984 0.150693i
749749 8684.61i 0.423670i
750750 9709.89 + 6744.39i 0.472740 + 0.328360i
751751 15585.9 26995.6i 0.757307 1.31169i −0.186912 0.982377i 0.559848π-0.559848\pi
0.944219 0.329317i 0.106819π-0.106819\pi
752752 −8184.05 2839.40i −0.396864 0.137689i
753753 35233.6 1.70516
754754 −34332.9 23847.3i −1.65826 1.15181i
755755 −7153.43 + 4130.03i −0.344821 + 0.199082i
756756 −5175.90 4276.85i −0.249002 0.205751i
757757 17756.7 10251.9i 0.852549 0.492219i −0.00896105 0.999960i 0.502852π-0.502852\pi
0.861510 + 0.507740i 0.169519π0.169519\pi
758758 13578.3 + 28833.8i 0.650643 + 1.38165i
759759 −24759.2 −1.18406
760760 5533.20 + 2206.35i 0.264093 + 0.105306i
761761 30533.3 1.45444 0.727222 0.686403i 0.240811π-0.240811\pi
0.727222 + 0.686403i 0.240811π0.240811\pi
762762 −12396.6 26324.4i −0.589347 1.25149i
763763 2451.68 1415.48i 0.116326 0.0671609i
764764 7074.36 8561.49i 0.335002 0.405424i
765765 −52.9849 + 30.5909i −0.00250415 + 0.00144577i
766766 −4860.11 3375.79i −0.229247 0.159232i
767767 −21558.6 −1.01491
768768 13905.0 17627.2i 0.653325 0.828213i
769769 8105.11 14038.5i 0.380075 0.658309i −0.610997 0.791633i 0.709231π-0.709231\pi
0.991073 + 0.133323i 0.0425648π0.0425648\pi
770770 −2917.82 2026.69i −0.136560 0.0948529i
771771 6808.35i 0.318024i
772772 16387.3 + 2761.97i 0.763978 + 0.128764i
773773 −21339.9 12320.6i −0.992942 0.573275i −0.0867894 0.996227i 0.527661π-0.527661\pi
−0.906152 + 0.422951i 0.860994π0.860994\pi
774774 −1727.62 3668.62i −0.0802298 0.170369i
775775 6471.42 11208.8i 0.299949 0.519526i
776776 13959.6 3910.63i 0.645774 0.180906i
777777 3991.99 + 6914.34i 0.184314 + 0.319241i
778778 15657.3 + 1310.23i 0.721521 + 0.0603781i
779779 −4165.08 540.149i −0.191565 0.0248432i
780780 1310.59 7776.00i 0.0601626 0.356956i
781781 −55008.1 + 31758.9i −2.52029 + 1.45509i
782782 1181.92 556.587i 0.0540479 0.0254521i
783783 −17151.4 + 29707.1i −0.782811 + 1.35587i
784784 3645.37 + 18990.5i 0.166061 + 0.865094i
785785 −3875.04 + 6711.76i −0.176186 + 0.305163i
786786 −164.691 + 1968.07i −0.00747372 + 0.0893113i
787787 16195.9i 0.733570i 0.930306 + 0.366785i 0.119542π0.119542\pi
−0.930306 + 0.366785i 0.880458π0.880458\pi
788788 −15741.4 13007.1i −0.711631 0.588021i
789789 −9721.29 5612.59i −0.438640 0.253249i
790790 −1490.96 124.766i −0.0671467 0.00561895i
791791 −7935.49 −0.356705
792792 −2977.31 + 3045.60i −0.133578 + 0.136642i
793793 −9523.17 16494.6i −0.426453 0.738639i
794794 −23487.4 + 33814.7i −1.04979 + 1.51138i
795795 6344.19 3662.82i 0.283025 0.163405i
796796 249.023 + 668.421i 0.0110884 + 0.0297633i
797797 13372.3i 0.594319i 0.954828 + 0.297160i 0.0960393π0.0960393\pi
−0.954828 + 0.297160i 0.903961π0.903961\pi
798798 −2512.57 7812.92i −0.111459 0.346585i
799799 −855.620 −0.0378844
800800 −20681.3 + 2203.87i −0.913991 + 0.0973982i
801801 960.085 + 1662.92i 0.0423507 + 0.0733536i
802802 12630.8 + 8773.24i 0.556122 + 0.386277i
803803 35909.4 20732.3i 1.57810 0.911117i
804804 15145.0 18328.6i 0.664330 0.803982i
805805 1484.58i 0.0649993i
806806 −17962.5 1503.13i −0.784989 0.0656892i
807807 6133.57 10623.7i 0.267549 0.463408i
808808 −15777.2 + 16139.1i −0.686931 + 0.702687i
809809 −31075.8 −1.35052 −0.675259 0.737581i 0.735968π-0.735968\pi
−0.675259 + 0.737581i 0.735968π0.735968\pi
810810 −7184.95 601.249i −0.311671 0.0260811i
811811 38107.1 + 22001.2i 1.64997 + 0.952608i 0.977083 + 0.212860i 0.0682778π0.0682778\pi
0.672884 + 0.739748i 0.265055π0.265055\pi
812812 −12518.0 + 4663.64i −0.541006 + 0.201554i
813813 31315.1 + 18079.8i 1.35089 + 0.779934i
814814 −36048.7 + 16975.9i −1.55222 + 0.730966i
815815 1536.85 + 2661.90i 0.0660534 + 0.114408i
816816 726.865 2095.06i 0.0311830 0.0898795i
817817 −5015.26 + 38672.6i −0.214763 + 1.65604i
818818 1101.95 13168.4i 0.0471014 0.562864i
819819 −953.505 + 550.507i −0.0406815 + 0.0234875i
820820 −1208.47 + 450.219i −0.0514652 + 0.0191736i
821821 12045.0 + 6954.20i 0.512027 + 0.295619i 0.733666 0.679510i 0.237807π-0.237807\pi
−0.221640 + 0.975129i 0.571141π0.571141\pi
822822 −12337.8 26199.6i −0.523517 1.11170i
823823 −3643.46 + 6310.66i −0.154317 + 0.267285i −0.932810 0.360368i 0.882651π-0.882651\pi
0.778493 + 0.627653i 0.215984π0.215984\pi
824824 3960.24 15479.8i 0.167429 0.654446i
825825 38932.8 1.64299
826826 −3930.22 + 5658.32i −0.165557 + 0.238351i
827827 −3443.56 1988.14i −0.144794 0.0835967i 0.425853 0.904792i 0.359974π-0.359974\pi
−0.570647 + 0.821196i 0.693307π0.693307\pi
828828 −1755.05 295.803i −0.0736622 0.0124153i
829829 36952.6i 1.54815i −0.633094 0.774075i 0.718215π-0.718215\pi
0.633094 0.774075i 0.281785π-0.281785\pi
830830 1573.80 + 1093.14i 0.0658160 + 0.0457151i
831831 4393.41 + 7609.61i 0.183400 + 0.317659i
832832 15047.8 + 24750.0i 0.627030 + 1.03131i
833833 954.986 + 1654.08i 0.0397218 + 0.0688002i
834834 25279.8 11904.7i 1.04960 0.494276i
835835 9802.82i 0.406276i
836836 39901.9 9244.30i 1.65076 0.382441i
837837 14791.4i 0.610832i
838838 −12564.6 26681.2i −0.517945 1.09987i
839839 10745.5 + 18611.8i 0.442166 + 0.765854i 0.997850 0.0655394i 0.0208768π-0.0208768\pi
−0.555684 + 0.831394i 0.687543π0.687543\pi
840840 −1801.98 1761.58i −0.0740170 0.0723573i
841841 21929.5 + 37983.0i 0.899156 + 1.55738i
842842 6900.98 9935.33i 0.282451 0.406644i
843843 9403.99i 0.384212i
844844 220.486 1308.18i 0.00899224 0.0533526i
845845 2762.58 + 1594.98i 0.112468 + 0.0649337i
846846 957.371 + 664.980i 0.0389067 + 0.0270242i
847847 −15919.9 −0.645826
848848 −8819.93 + 25421.9i −0.357167 + 1.02947i
849849 −1250.90 + 2166.63i −0.0505664 + 0.0875836i
850850 −1858.52 + 875.208i −0.0749961 + 0.0353169i
851851 −14420.1 8325.43i −0.580862 0.335361i
852852 −42220.2 + 15729.3i −1.69770 + 0.632485i
853853 27559.1 15911.3i 1.10622 0.638677i 0.168372 0.985723i 0.446149π-0.446149\pi
0.937848 + 0.347047i 0.112816π0.112816\pi
854854 −6065.33 507.557i −0.243034 0.0203375i
855855 −636.869 486.733i −0.0254742 0.0194689i
856856 −29784.8 7619.94i −1.18928 0.304257i
857857 −11832.5 20494.5i −0.471633 0.816893i 0.527840 0.849344i 0.323002π-0.323002\pi
−0.999473 + 0.0324509i 0.989669π0.989669\pi
858858 −23100.3 49054.0i −0.919152 1.95184i
859859 25238.7 + 14571.5i 1.00248 + 0.578783i 0.908982 0.416836i 0.136861π-0.136861\pi
0.0935000 + 0.995619i 0.470194π0.470194\pi
860860 4180.26 + 11220.6i 0.165751 + 0.444904i
861861 1538.70 + 888.369i 0.0609045 + 0.0351632i
862862 1415.52 16915.5i 0.0559312 0.668380i
863863 −49067.9 −1.93545 −0.967724 0.252014i 0.918907π-0.918907\pi
−0.967724 + 0.252014i 0.918907π0.918907\pi
864864 19209.3 13998.8i 0.756381 0.551212i
865865 571.240 989.417i 0.0224540 0.0388915i
866866 3223.54 38521.5i 0.126490 1.51156i
867867 26710.7i 1.04630i
868868 −3669.14 + 4440.45i −0.143478 + 0.173639i
869869 −8909.22 + 5143.74i −0.347785 + 0.200793i
870870 −7344.55 + 10573.9i −0.286211 + 0.412058i
871871 15337.3 + 26565.0i 0.596654 + 1.03343i
872872 2703.41 + 9650.25i 0.104987 + 0.374769i
873873 −1950.75 −0.0756275
874874 12685.1 + 11491.1i 0.490937 + 0.444727i
875875 4874.16i 0.188316i
876876 27561.5 10268.1i 1.06303 0.396036i
877877 6393.42 3691.24i 0.246169 0.142126i −0.371840 0.928297i 0.621273π-0.621273\pi
0.618009 + 0.786171i 0.287940π0.287940\pi
878878 −37893.5 26320.5i −1.45654 1.01170i
879879 −23409.8 40547.0i −0.898286 1.55588i
880880 9510.85 8228.73i 0.364330 0.315216i
881881 22901.8 0.875802 0.437901 0.899023i 0.355722π-0.355722\pi
0.437901 + 0.899023i 0.355722π0.355722\pi
882882 216.986 2593.00i 0.00828379 0.0989917i
883883 −4238.68 2447.20i −0.161543 0.0932671i 0.417049 0.908884i 0.363064π-0.363064\pi
−0.578592 + 0.815617i 0.696398π0.696398\pi
884884 2205.47 + 1822.38i 0.0839116 + 0.0693362i
885885 6639.68i 0.252192i
886886 −45173.0 3780.15i −1.71288 0.143337i
887887 20720.0 35888.1i 0.784341 1.35852i −0.145052 0.989424i 0.546335π-0.546335\pi
0.929392 0.369094i 0.120332π-0.120332\pi
888888 −27216.0 + 7624.27i −1.02850 + 0.288123i
889889 5998.15 10389.1i 0.226289 0.391945i
890890 −2415.64 5129.64i −0.0909801 0.193198i
891891 −42933.7 + 24787.8i −1.61429 + 0.932011i
892892 26024.9 + 4386.33i 0.976882 + 0.164647i
893893 −4309.84 10348.2i −0.161504 0.387783i
894894 −2.02764 + 24.2304i −7.58550e−5 + 0.000906471i
895895 5371.08 + 9302.98i 0.200598 + 0.347446i
896896 9239.23 + 562.544i 0.344488 + 0.0209746i
897897 11329.0 19622.4i 0.421699 0.730404i
898898 −35415.8 + 16677.9i −1.31608 + 0.619765i
899899 25486.0 + 14714.3i 0.945500 + 0.545885i
900900 2759.74 + 465.137i 0.102213 + 0.0172273i
901901 2657.78i 0.0982726i
902902 −5058.53 + 7282.75i −0.186730 + 0.268835i
903903 8248.47 14286.8i 0.303978 0.526505i
904904 6962.66 27215.6i 0.256167 1.00130i
905905 14769.5 0.542493
906906 −22982.5 + 33087.9i −0.842763 + 1.21332i
907907 −12042.1 + 6952.48i −0.440849 + 0.254524i −0.703958 0.710242i 0.748585π-0.748585\pi
0.263109 + 0.964766i 0.415252π0.415252\pi
908908 −13506.8 11160.7i −0.493654 0.407907i
909909 2630.13 1518.51i 0.0959693 0.0554079i
910910 2941.30 1385.11i 0.107146 0.0504571i
911911 −47260.7 −1.71879 −0.859395 0.511313i 0.829159π-0.829159\pi
−0.859395 + 0.511313i 0.829159π0.829159\pi
912912 28999.8 1762.01i 1.05294 0.0639758i
913913 13175.5 0.477597
914914 −14131.4 + 6654.71i −0.511406 + 0.240829i
915915 −5080.05 + 2932.97i −0.183543 + 0.105968i
916916 −32534.6 26883.3i −1.17355 0.969705i
917917 −705.149 + 407.118i −0.0253937 + 0.0146611i
918918 1339.30 1928.19i 0.0481521 0.0693245i
919919 22188.4 0.796438 0.398219 0.917290i 0.369628π-0.369628\pi
0.398219 + 0.917290i 0.369628π0.369628\pi
920920 5091.51 + 1302.58i 0.182459 + 0.0466791i
921921 24850.6 43042.6i 0.889095 1.53996i
922922 27930.1 40210.9i 0.997646 1.43631i
923923 58127.3i 2.07290i
924924 −17086.1 2879.75i −0.608324 0.102529i
925925 22674.9 + 13091.4i 0.805996 + 0.465342i
926926 −21690.6 + 10214.5i −0.769760 + 0.362493i
927927 −1075.04 + 1862.02i −0.0380894 + 0.0659727i
928928 −5011.03 47023.8i −0.177258 1.66340i
929929 −15325.1 26543.9i −0.541228 0.937435i −0.998834 0.0482796i 0.984626π-0.984626\pi
0.457606 0.889155i 0.348707π-0.348707\pi
930930 −462.938 + 5532.13i −0.0163229 + 0.195060i
931931 −15194.8 + 19881.8i −0.534898 + 0.699892i
932932 5547.50 + 934.996i 0.194973 + 0.0328614i
933933 42365.1 24459.5i 1.48657 0.858273i
934934 −6065.83 12880.9i −0.212505 0.451259i
935935 621.100 1075.78i 0.0217242 0.0376274i
936936 −1051.41 3753.17i −0.0367161 0.131064i
937937 −25506.0 + 44177.7i −0.889268 + 1.54026i −0.0485257 + 0.998822i 0.515452π0.515452\pi
−0.840742 + 0.541435i 0.817881π0.817881\pi
938938 9768.37 + 817.434i 0.340031 + 0.0284543i
939939 29734.3i 1.03338i
940940 −2653.38 2192.49i −0.0920677 0.0760756i
941941 −9061.27 5231.53i −0.313910 0.181236i 0.334765 0.942302i 0.391343π-0.391343\pi
−0.648675 + 0.761066i 0.724676π0.724676\pi
942942 −3152.08 + 37667.5i −0.109024 + 1.30284i
943943 −3705.44 −0.127959
944944 −15957.4 18443.7i −0.550180 0.635903i
945945 −1333.93 2310.43i −0.0459181 0.0795325i
946946 67620.0 + 46968.2i 2.32401 + 1.61424i
947947 −3818.37 + 2204.54i −0.131025 + 0.0756471i −0.564080 0.825720i 0.690769π-0.690769\pi
0.433055 + 0.901368i 0.357436π0.357436\pi
948948 −6838.08 + 2547.55i −0.234273 + 0.0872792i
949949 37945.6i 1.29796i
950950 −19946.7 18069.2i −0.681217 0.617097i
951951 30895.4 1.05347
952952 880.370 246.626i 0.0299716 0.00839621i
953953 19342.4 + 33502.1i 0.657464 + 1.13876i 0.981270 + 0.192637i 0.0617041π0.0617041\pi
−0.323806 + 0.946123i 0.604963π0.604963\pi
954954 2065.61 2973.85i 0.0701012 0.100924i
955955 3821.69 2206.45i 0.129494 0.0747635i
956956 −16733.1 + 20250.7i −0.566097 + 0.685098i
957957 88523.1i 2.99012i
958958 354.467 4235.89i 0.0119544 0.142855i
959959 5969.70 10339.8i 0.201013 0.348165i
960960 7622.58 4634.46i 0.256269 0.155809i
961961 −17101.3 −0.574043
962962 3040.76 36337.2i 0.101911 1.21784i
963963 3582.73 + 2068.49i 0.119888 + 0.0692171i
964964 2586.85 + 6943.57i 0.0864284 + 0.231989i
965965 5718.51 + 3301.58i 0.190762 + 0.110136i
966966 −3084.82 6550.67i −0.102746 0.218183i
967967 −18421.0 31906.1i −0.612595 1.06105i −0.990801 0.135325i 0.956792π-0.956792\pi
0.378206 0.925721i 0.376541π-0.376541\pi
968968 13968.3 54599.0i 0.463798 1.81289i
969969 2649.07 1103.29i 0.0878229 0.0365766i
970970 5740.19 + 480.349i 0.190007 + 0.0159001i
971971 26691.1 15410.1i 0.882140 0.509304i 0.0107765 0.999942i 0.496570π-0.496570\pi
0.871363 + 0.490638i 0.163236π0.163236\pi
972972 −6375.25 + 2375.12i −0.210377 + 0.0783767i
973973 9976.84 + 5760.13i 0.328718 + 0.189786i
974974 −24694.5 + 11629.0i −0.812384 + 0.382565i
975975 −17814.3 + 30855.3i −0.585144 + 1.01350i
976976 7062.48 20356.3i 0.231624 0.667613i
977977 13392.6 0.438555 0.219278 0.975662i 0.429630π-0.429630\pi
0.219278 + 0.975662i 0.429630π0.429630\pi
978978 12312.5 + 8552.16i 0.402568 + 0.279620i
979979 −33762.9 19493.0i −1.10221 0.636364i
980980 −1276.99 + 7576.62i −0.0416245 + 0.246965i
981981 1348.55i 0.0438897i
982982 19734.7 28412.0i 0.641302 0.923281i
983983 2753.68 + 4769.51i 0.0893476 + 0.154754i 0.907236 0.420623i 0.138188π-0.138188\pi
−0.817888 + 0.575378i 0.804855π0.804855\pi
984984 −4396.82 + 4497.67i −0.142445 + 0.145712i
985985 −4056.86 7026.68i −0.131231 0.227298i
986986 −1990.00 4225.80i −0.0642743 0.136488i
987987 4742.18i 0.152933i
988988 −10931.4 + 35853.3i −0.351999 + 1.15450i
989989 34404.9i 1.10618i
990990 −1531.05 + 720.995i −0.0491514 + 0.0231462i
991991 −13422.3 23248.1i −0.430245 0.745206i 0.566649 0.823959i 0.308239π-0.308239\pi
−0.996894 + 0.0787530i 0.974906π0.974906\pi
992992 −12009.7 16479.8i −0.384382 0.527454i
993993 −10003.4 17326.5i −0.319687 0.553715i
994994 −15256.2 10596.8i −0.486819 0.338140i
995995 283.424i 0.00903028i
996996 9215.81 + 1553.27i 0.293187 + 0.0494148i
997997 −2888.90 1667.91i −0.0917676 0.0529821i 0.453414 0.891300i 0.350206π-0.350206\pi
−0.545182 + 0.838318i 0.683539π0.683539\pi
998998 −24976.8 + 35959.0i −0.792211 + 1.14054i
999999 −29922.3 −0.947649
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 152.4.p.a.45.9 116
8.5 even 2 inner 152.4.p.a.45.48 yes 116
19.11 even 3 inner 152.4.p.a.125.48 yes 116
152.125 even 6 inner 152.4.p.a.125.9 yes 116
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
152.4.p.a.45.9 116 1.1 even 1 trivial
152.4.p.a.45.48 yes 116 8.5 even 2 inner
152.4.p.a.125.9 yes 116 152.125 even 6 inner
152.4.p.a.125.48 yes 116 19.11 even 3 inner