Properties

Label 115.4.l.a.102.4
Level 115115
Weight 44
Character 115.102
Analytic conductor 6.7856.785
Analytic rank 00
Dimension 680680
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] = [115,4,Mod(7,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) 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("115.7"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 115=523 115 = 5 \cdot 23
Weight: k k == 4 4
Character orbit: [χ][\chi] == 115.l (of order 4444, degree 2020, 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: 6.785219650666.78521965066
Analytic rank: 00
Dimension: 680680
Relative dimension: 3434 over Q(ζ44)\Q(\zeta_{44})
Twist minimal: yes
Sato-Tate group: SU(2)[C44]\mathrm{SU}(2)[C_{44}]

Embedding invariants

Embedding label 102.4
Character χ\chi == 115.102
Dual form 115.4.l.a.53.4

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+(0.341249+4.77128i)q2+(6.157721.33953i)q3+(14.73012.11787i)q4+(11.14790.850466i)q5+(4.28996+29.8374i)q6+(31.163517.0166i)q7+(6.9972232.1657i)q8+(11.56315.28070i)q9+(0.253587+53.4802i)q10+(2.59952+2.25250i)q11+(93.5410+6.69019i)q12+(3.35434+6.14302i)q13+(70.5564+154.497i)q14+(67.506720.1699i)q15+(36.8535+10.8212i)q16+(50.486437.7936i)q17+(21.2498+56.9730i)q18+(10.4871+72.9396i)q19+(166.01211.0825i)q20+(169.102146.528i)q21+(11.6344+11.6344i)q22+(80.959874.9167i)q23207.440iq24+(123.55318.9619i)q25+(28.165418.1008i)q26+(72.0808+53.9590i)q27+(495.082+184.656i)q28+(248.606+35.7442i)q29+(73.1999+328.977i)q30+(200.632+128.938i)q31+(27.822174.5939i)q32+(19.0244+10.3881i)q33+(197.553227.988i)q34+(332.937216.203i)q35+(181.510+53.2962i)q36+(293.809+109.585i)q37+(344.43774.9277i)q38+(12.4264+42.3203i)q39+(50.6488364.532i)q40+(12.098426.4918i)q41+(641.420+856.837i)q42+(62.2309+286.071i)q43+(33.520838.6851i)q44+(124.41468.7030i)q45+(385.077360.717i)q46+(141.204141.204i)q47+(241.429+17.2674i)q48+(496.162772.043i)q49+(48.3101+595.979i)q50+(361.507165.095i)q51+(62.420183.3835i)q52+(74.6819+136.770i)q53+(232.856362.331i)q54+(30.8950+22.9000i)q55+(329.2921121.47i)q56+(33.1280+463.190i)q57+(85.70901198.37i)q58+(32.9465112.205i)q59+(1037.10+154.135i)q60+(99.1163+154.228i)q61+(546.7351001.27i)q62+(270.488361.330i)q63+(625.922+285.849i)q64+(32.1696+71.3348i)q65+(56.0568+87.2261i)q66+(497.436+35.5773i)q67+(663.629+663.629i)q68+(598.881352.868i)q69+(917.953+1662.32i)q70+(92.5491106.807i)q71+(88.9477408.886i)q72+(165.051+220.482i)q73+(623.124+1364.45i)q74+(735.407282.266i)q75+(308.9541052.20i)q76+(119.340+25.9609i)q77+(197.68273.7314i)q78+(129.779+38.1066i)q79+(420.044+89.2912i)q80+(596.335+688.207i)q81+(122.271+66.7652i)q82+(295.086791.157i)q83+(2801.22+1800.24i)q84+(594.962378.385i)q85+(1386.16+199.300i)q86+(1482.97+553.118i)q87+(90.642767.8543i)q88+(536.164344.572i)q89+(285.345+617.059i)q90+248.518iq91+(1033.88+1275.00i)q92+(1062.72+1062.72i)q93+(721.912625.540i)q94+(54.8774+822.046i)q95+(71.3999496.597i)q96+(403.4931081.81i)q97+(3514.32+2630.79i)q98+(41.9534+12.3186i)q99+O(q100)q+(-0.341249 + 4.77128i) q^{2} +(6.15772 - 1.33953i) q^{3} +(-14.7301 - 2.11787i) q^{4} +(11.1479 - 0.850466i) q^{5} +(4.28996 + 29.8374i) q^{6} +(31.1635 - 17.0166i) q^{7} +(6.99722 - 32.1657i) q^{8} +(11.5631 - 5.28070i) q^{9} +(0.253587 + 53.4802i) q^{10} +(2.59952 + 2.25250i) q^{11} +(-93.5410 + 6.69019i) q^{12} +(-3.35434 + 6.14302i) q^{13} +(70.5564 + 154.497i) q^{14} +(67.5067 - 20.1699i) q^{15} +(36.8535 + 10.8212i) q^{16} +(-50.4864 - 37.7936i) q^{17} +(21.2498 + 56.9730i) q^{18} +(-10.4871 + 72.9396i) q^{19} +(-166.012 - 11.0825i) q^{20} +(169.102 - 146.528i) q^{21} +(-11.6344 + 11.6344i) q^{22} +(-80.9598 - 74.9167i) q^{23} -207.440i q^{24} +(123.553 - 18.9619i) q^{25} +(-28.1654 - 18.1008i) q^{26} +(-72.0808 + 53.9590i) q^{27} +(-495.082 + 184.656i) q^{28} +(-248.606 + 35.7442i) q^{29} +(73.1999 + 328.977i) q^{30} +(-200.632 + 128.938i) q^{31} +(27.8221 - 74.5939i) q^{32} +(19.0244 + 10.3881i) q^{33} +(197.553 - 227.988i) q^{34} +(332.937 - 216.203i) q^{35} +(-181.510 + 53.2962i) q^{36} +(293.809 + 109.585i) q^{37} +(-344.437 - 74.9277i) q^{38} +(-12.4264 + 42.3203i) q^{39} +(50.6488 - 364.532i) q^{40} +(12.0984 - 26.4918i) q^{41} +(641.420 + 856.837i) q^{42} +(62.2309 + 286.071i) q^{43} +(-33.5208 - 38.6851i) q^{44} +(124.414 - 68.7030i) q^{45} +(385.077 - 360.717i) q^{46} +(-141.204 - 141.204i) q^{47} +(241.429 + 17.2674i) q^{48} +(496.162 - 772.043i) q^{49} +(48.3101 + 595.979i) q^{50} +(-361.507 - 165.095i) q^{51} +(62.4201 - 83.3835i) q^{52} +(74.6819 + 136.770i) q^{53} +(-232.856 - 362.331i) q^{54} +(30.8950 + 22.9000i) q^{55} +(-329.292 - 1121.47i) q^{56} +(33.1280 + 463.190i) q^{57} +(-85.7090 - 1198.37i) q^{58} +(-32.9465 - 112.205i) q^{59} +(-1037.10 + 154.135i) q^{60} +(99.1163 + 154.228i) q^{61} +(-546.735 - 1001.27i) q^{62} +(270.488 - 361.330i) q^{63} +(625.922 + 285.849i) q^{64} +(-32.1696 + 71.3348i) q^{65} +(-56.0568 + 87.2261i) q^{66} +(497.436 + 35.5773i) q^{67} +(663.629 + 663.629i) q^{68} +(-598.881 - 352.868i) q^{69} +(917.953 + 1662.32i) q^{70} +(-92.5491 - 106.807i) q^{71} +(-88.9477 - 408.886i) q^{72} +(165.051 + 220.482i) q^{73} +(-623.124 + 1364.45i) q^{74} +(735.407 - 282.266i) q^{75} +(308.954 - 1052.20i) q^{76} +(119.340 + 25.9609i) q^{77} +(-197.682 - 73.7314i) q^{78} +(-129.779 + 38.1066i) q^{79} +(420.044 + 89.2912i) q^{80} +(-596.335 + 688.207i) q^{81} +(122.271 + 66.7652i) q^{82} +(295.086 - 791.157i) q^{83} +(-2801.22 + 1800.24i) q^{84} +(-594.962 - 378.385i) q^{85} +(-1386.16 + 199.300i) q^{86} +(-1482.97 + 553.118i) q^{87} +(90.6427 - 67.8543i) q^{88} +(-536.164 - 344.572i) q^{89} +(285.345 + 617.059i) q^{90} +248.518i q^{91} +(1033.88 + 1275.00i) q^{92} +(-1062.72 + 1062.72i) q^{93} +(721.912 - 625.540i) q^{94} +(-54.8774 + 822.046i) q^{95} +(71.3999 - 496.597i) q^{96} +(-403.493 - 1081.81i) q^{97} +(3514.32 + 2630.79i) q^{98} +(41.9534 + 12.3186i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 680q18q226q322q576q622q750q822q1044q11222q12+78q1322q15+788q1622q1786q1822q2044q21944q23+10314q98+O(q100) 680 q - 18 q^{2} - 26 q^{3} - 22 q^{5} - 76 q^{6} - 22 q^{7} - 50 q^{8} - 22 q^{10} - 44 q^{11} - 222 q^{12} + 78 q^{13} - 22 q^{15} + 788 q^{16} - 22 q^{17} - 86 q^{18} - 22 q^{20} - 44 q^{21} - 944 q^{23}+ \cdots - 10314 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/115Z)×\left(\mathbb{Z}/115\mathbb{Z}\right)^\times.

nn 4747 5151
χ(n)\chi(n) e(14)e\left(\frac{1}{4}\right) e(322)e\left(\frac{3}{22}\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 −0.341249 + 4.77128i −0.120650 + 1.68690i 0.472122 + 0.881533i 0.343488π0.343488\pi
−0.592772 + 0.805371i 0.701966π0.701966\pi
33 6.15772 1.33953i 1.18505 0.257793i 0.423501 0.905896i 0.360801π-0.360801\pi
0.761553 + 0.648103i 0.224437π0.224437\pi
44 −14.7301 2.11787i −1.84127 0.264734i
55 11.1479 0.850466i 0.997103 0.0760679i
66 4.28996 + 29.8374i 0.291895 + 2.03017i
77 31.1635 17.0166i 1.68267 0.918809i 0.704855 0.709352i 0.251012π-0.251012\pi
0.977818 0.209457i 0.0671696π-0.0671696\pi
88 6.99722 32.1657i 0.309236 1.42154i
99 11.5631 5.28070i 0.428264 0.195582i
1010 0.253587 + 53.4802i 0.00801914 + 1.69119i
1111 2.59952 + 2.25250i 0.0712533 + 0.0617413i 0.689759 0.724039i 0.257716π-0.257716\pi
−0.618506 + 0.785780i 0.712262π0.712262\pi
1212 −93.5410 + 6.69019i −2.25025 + 0.160941i
1313 −3.35434 + 6.14302i −0.0715637 + 0.131059i −0.911011 0.412382i 0.864697π-0.864697\pi
0.839447 + 0.543441i 0.182879π0.182879\pi
1414 70.5564 + 154.497i 1.34693 + 2.94936i
1515 67.5067 20.1699i 1.16201 0.347190i
1616 36.8535 + 10.8212i 0.575837 + 0.169081i
1717 −50.4864 37.7936i −0.720279 0.539194i 0.175072 0.984556i 0.443984π-0.443984\pi
−0.895351 + 0.445361i 0.853075π0.853075\pi
1818 21.2498 + 56.9730i 0.278257 + 0.746037i
1919 −10.4871 + 72.9396i −0.126627 + 0.880710i 0.823159 + 0.567811i 0.192209π0.192209\pi
−0.949786 + 0.312900i 0.898700π0.898700\pi
2020 −166.012 11.0825i −1.85607 0.123906i
2121 169.102 146.528i 1.75720 1.52262i
2222 −11.6344 + 11.6344i −0.112748 + 0.112748i
2323 −80.9598 74.9167i −0.733969 0.679183i
2424 207.440i 1.76432i
2525 123.553 18.9619i 0.988427 0.151695i
2626 −28.1654 18.1008i −0.212450 0.136533i
2727 −72.0808 + 53.9590i −0.513776 + 0.384608i
2828 −495.082 + 184.656i −3.34149 + 1.24631i
2929 −248.606 + 35.7442i −1.59190 + 0.228880i −0.880547 0.473959i 0.842825π-0.842825\pi
−0.711349 + 0.702839i 0.751915π0.751915\pi
3030 73.1999 + 328.977i 0.445481 + 2.00209i
3131 −200.632 + 128.938i −1.16240 + 0.747031i −0.972071 0.234688i 0.924593π-0.924593\pi
−0.190333 + 0.981720i 0.560957π0.560957\pi
3232 27.8221 74.5939i 0.153697 0.412077i
3333 19.0244 + 10.3881i 0.100355 + 0.0547982i
3434 197.553 227.988i 0.996471 1.14999i
3535 332.937 216.203i 1.60791 1.04414i
3636 −181.510 + 53.2962i −0.840325 + 0.246742i
3737 293.809 + 109.585i 1.30546 + 0.486911i 0.903437 0.428720i 0.141035π-0.141035\pi
0.402021 + 0.915631i 0.368308π0.368308\pi
3838 −344.437 74.9277i −1.47040 0.319865i
3939 −12.4264 + 42.3203i −0.0510207 + 0.173761i
4040 50.6488 364.532i 0.200207 1.44094i
4141 12.0984 26.4918i 0.0460842 0.100910i −0.885189 0.465231i 0.845971π-0.845971\pi
0.931274 + 0.364320i 0.118699π0.118699\pi
4242 641.420 + 856.837i 2.35651 + 3.14792i
4343 62.2309 + 286.071i 0.220701 + 1.01454i 0.945510 + 0.325594i 0.105564π0.105564\pi
−0.724809 + 0.688950i 0.758072π0.758072\pi
4444 −33.5208 38.6851i −0.114851 0.132545i
4545 124.414 68.7030i 0.412145 0.227592i
4646 385.077 360.717i 1.23427 1.15619i
4747 −141.204 141.204i −0.438229 0.438229i 0.453187 0.891416i 0.350287π-0.350287\pi
−0.891416 + 0.453187i 0.850287π0.850287\pi
4848 241.429 + 17.2674i 0.725985 + 0.0519235i
4949 496.162 772.043i 1.44654 2.25085i
5050 48.3101 + 595.979i 0.136642 + 1.68568i
5151 −361.507 165.095i −0.992570 0.453292i
5252 62.4201 83.3835i 0.166464 0.222369i
5353 74.6819 + 136.770i 0.193554 + 0.354467i 0.956375 0.292143i 0.0943682π-0.0943682\pi
−0.762821 + 0.646610i 0.776186π0.776186\pi
5454 −232.856 362.331i −0.586809 0.913093i
5555 30.8950 + 22.9000i 0.0757434 + 0.0561423i
5656 −329.292 1121.47i −0.785777 2.67611i
5757 33.1280 + 463.190i 0.0769808 + 1.07633i
5858 −85.7090 1198.37i −0.194037 2.71299i
5959 −32.9465 112.205i −0.0726994 0.247592i 0.915124 0.403174i 0.132093π-0.132093\pi
−0.987823 + 0.155582i 0.950275π0.950275\pi
6060 −1037.10 + 154.135i −2.23148 + 0.331646i
6161 99.1163 + 154.228i 0.208042 + 0.323719i 0.929556 0.368680i 0.120190π-0.120190\pi
−0.721515 + 0.692399i 0.756554π0.756554\pi
6262 −546.735 1001.27i −1.11993 2.05099i
6363 270.488 361.330i 0.540926 0.722592i
6464 625.922 + 285.849i 1.22250 + 0.558299i
6565 −32.1696 + 71.3348i −0.0613869 + 0.136123i
6666 −56.0568 + 87.2261i −0.104547 + 0.162679i
6767 497.436 + 35.5773i 0.907036 + 0.0648725i 0.517057 0.855951i 0.327028π-0.327028\pi
0.389979 + 0.920824i 0.372482π0.372482\pi
6868 663.629 + 663.629i 1.18348 + 1.18348i
6969 −598.881 352.868i −1.04488 0.615657i
7070 917.953 + 1662.32i 1.56738 + 2.83836i
7171 −92.5491 106.807i −0.154698 0.178531i 0.673110 0.739542i 0.264958π-0.264958\pi
−0.827808 + 0.561011i 0.810412π0.810412\pi
7272 −88.9477 408.886i −0.145592 0.669274i
7373 165.051 + 220.482i 0.264626 + 0.353499i 0.913099 0.407739i 0.133683π-0.133683\pi
−0.648472 + 0.761238i 0.724592π0.724592\pi
7474 −623.124 + 1364.45i −0.978875 + 2.14344i
7575 735.407 282.266i 1.13223 0.434576i
7676 308.954 1052.20i 0.466308 1.58810i
7777 119.340 + 25.9609i 0.176624 + 0.0384223i
7878 −197.682 73.7314i −0.286962 0.107031i
7979 −129.779 + 38.1066i −0.184827 + 0.0542700i −0.372836 0.927897i 0.621615π-0.621615\pi
0.188009 + 0.982167i 0.439796π0.439796\pi
8080 420.044 + 89.2912i 0.587030 + 0.124788i
8181 −596.335 + 688.207i −0.818018 + 0.944043i
8282 122.271 + 66.7652i 0.164666 + 0.0899145i
8383 295.086 791.157i 0.390240 1.04627i −0.582184 0.813057i 0.697802π-0.697802\pi
0.972425 0.233218i 0.0749254π-0.0749254\pi
8484 −2801.22 + 1800.24i −3.63856 + 2.33836i
8585 −594.962 378.385i −0.759208 0.482842i
8686 −1386.16 + 199.300i −1.73807 + 0.249896i
8787 −1482.97 + 553.118i −1.82748 + 0.681614i
8888 90.6427 67.8543i 0.109802 0.0821965i
8989 −536.164 344.572i −0.638576 0.410388i 0.180900 0.983502i 0.442099π-0.442099\pi
−0.819476 + 0.573114i 0.805735π0.805735\pi
9090 285.345 + 617.059i 0.334201 + 0.722709i
9191 248.518i 0.286283i
9292 1033.88 + 1275.00i 1.17163 + 1.44486i
9393 −1062.72 + 1062.72i −1.18493 + 1.18493i
9494 721.912 625.540i 0.792123 0.686378i
9595 −54.8774 + 822.046i −0.0592663 + 0.887791i
9696 71.3999 496.597i 0.0759085 0.527956i
9797 −403.493 1081.81i −0.422356 1.13238i −0.957706 0.287750i 0.907093π-0.907093\pi
0.535349 0.844631i 0.320180π-0.320180\pi
9898 3514.32 + 2630.79i 3.62245 + 2.71173i
9999 41.9534 + 12.3186i 0.0425907 + 0.0125057i
100100 −1860.12 + 17.6406i −1.86012 + 0.0176406i
101101 306.956 + 672.139i 0.302408 + 0.662181i 0.998440 0.0558291i 0.0177802π-0.0177802\pi
−0.696032 + 0.718011i 0.745053π0.745053\pi
102102 911.077 1668.51i 0.884413 1.61968i
103103 −1554.60 + 111.187i −1.48718 + 0.106365i −0.791138 0.611638i 0.790511π-0.790511\pi
−0.696040 + 0.718003i 0.745056π0.745056\pi
104104 174.124 + 150.879i 0.164175 + 0.142259i
105105 1760.52 1777.30i 1.63628 1.65187i
106106 −678.052 + 309.656i −0.621304 + 0.283740i
107107 58.1514 267.318i 0.0525393 0.241519i −0.943387 0.331695i 0.892379π-0.892379\pi
0.995926 + 0.0901761i 0.0287430π0.0287430\pi
108108 1176.04 642.165i 1.04782 0.572152i
109109 −306.540 2132.03i −0.269369 1.87350i −0.454441 0.890777i 0.650161π-0.650161\pi
0.185073 0.982725i 0.440748π-0.440748\pi
110110 −119.805 + 139.594i −0.103845 + 0.120998i
111111 1955.99 + 281.229i 1.67256 + 0.240478i
112112 1332.63 289.895i 1.12430 0.244576i
113113 −36.9155 + 516.146i −0.0307320 + 0.429690i 0.958673 + 0.284509i 0.0918307π0.0918307\pi
−0.989405 + 0.145180i 0.953624π0.953624\pi
114114 −2221.31 −1.82496
115115 −966.249 766.314i −0.783506 0.621384i
116116 3737.70 2.99170
117117 −6.34723 + 88.7458i −0.00501540 + 0.0701244i
118118 546.607 118.907i 0.426434 0.0927651i
119119 −2216.45 318.678i −1.70741 0.245489i
120120 −176.421 2312.53i −0.134208 1.75920i
121121 −187.737 1305.74i −0.141050 0.981023i
122122 −769.689 + 420.282i −0.571183 + 0.311890i
123123 39.0120 179.335i 0.0285983 0.131464i
124124 3228.41 1474.36i 2.33806 1.06776i
125125 1361.24 316.464i 0.974024 0.226443i
126126 1631.70 + 1413.88i 1.15368 + 0.999670i
127127 −637.560 + 45.5992i −0.445467 + 0.0318604i −0.292271 0.956335i 0.594411π-0.594411\pi
−0.153196 + 0.988196i 0.548957π0.548957\pi
128128 −1272.22 + 2329.90i −0.878514 + 1.60888i
129129 766.401 + 1678.18i 0.523084 + 1.14539i
130130 −329.381 177.833i −0.222220 0.119977i
131131 2300.03 + 675.351i 1.53401 + 0.450425i 0.936274 0.351271i 0.114250π-0.114250\pi
0.597732 + 0.801696i 0.296069π0.296069\pi
132132 −258.232 193.310i −0.170274 0.127466i
133133 914.367 + 2451.51i 0.596133 + 1.59829i
134134 −339.499 + 2361.27i −0.218867 + 1.52226i
135135 −757.662 + 662.834i −0.483031 + 0.422575i
136136 −1568.92 + 1359.48i −0.989221 + 0.857165i
137137 −429.115 + 429.115i −0.267604 + 0.267604i −0.828134 0.560530i 0.810597π-0.810597\pi
0.560530 + 0.828134i 0.310597π0.310597\pi
138138 1888.00 2737.01i 1.16462 1.68833i
139139 789.752i 0.481913i 0.970536 + 0.240957i 0.0774611π0.0774611\pi
−0.970536 + 0.240957i 0.922539π0.922539\pi
140140 −5362.10 + 2479.59i −3.23700 + 1.49688i
141141 −1058.64 680.349i −0.632297 0.406353i
142142 541.191 405.130i 0.319829 0.239421i
143143 −22.5569 + 8.41328i −0.0131909 + 0.00491995i
144144 483.285 69.4859i 0.279679 0.0402118i
145145 −2741.05 + 609.905i −1.56987 + 0.349309i
146146 −1108.31 + 712.265i −0.628247 + 0.403750i
147147 2021.05 5418.65i 1.13397 3.04029i
148148 −4095.76 2236.46i −2.27479 1.24213i
149149 1018.99 1175.97i 0.560260 0.646574i −0.402983 0.915208i 0.632027π-0.632027\pi
0.963242 + 0.268633i 0.0865720π0.0865720\pi
150150 1095.81 + 3605.16i 0.596485 + 1.96240i
151151 2026.18 594.940i 1.09197 0.320633i 0.314315 0.949319i 0.398225π-0.398225\pi
0.777659 + 0.628686i 0.216407π0.216407\pi
152152 2272.77 + 847.701i 1.21280 + 0.452353i
153153 −783.357 170.409i −0.413926 0.0900441i
154154 −164.591 + 560.547i −0.0861244 + 0.293313i
155155 −2126.97 + 1608.03i −1.10221 + 0.833289i
156156 272.671 597.066i 0.139943 0.306433i
157157 1952.95 + 2608.83i 0.992753 + 1.32616i 0.944918 + 0.327307i 0.106141π0.106141\pi
0.0478347 + 0.998855i 0.484768π0.484768\pi
158158 −137.530 632.217i −0.0692489 0.318332i
159159 643.077 + 742.151i 0.320750 + 0.370166i
160160 246.720 855.231i 0.121906 0.422575i
161161 −3797.82 957.012i −1.85907 0.468467i
162162 −3080.13 3080.13i −1.49382 1.49382i
163163 −542.249 38.7824i −0.260566 0.0186360i −0.0595548 0.998225i 0.518968π-0.518968\pi
−0.201011 + 0.979589i 0.564423π0.564423\pi
164164 −234.317 + 364.605i −0.111568 + 0.173603i
165165 220.918 + 99.6267i 0.104233 + 0.0470056i
166166 3674.14 + 1677.92i 1.71788 + 0.784530i
167167 −46.3081 + 61.8603i −0.0214576 + 0.0286640i −0.811142 0.584850i 0.801154π-0.801154\pi
0.789684 + 0.613514i 0.210244π0.210244\pi
168168 −3529.93 6464.58i −1.62107 2.96877i
169169 1161.30 + 1807.02i 0.528586 + 0.822495i
170170 2008.41 2709.61i 0.906106 1.22246i
171171 263.908 + 898.789i 0.118021 + 0.401942i
172172 −310.808 4345.66i −0.137784 1.92647i
173173 133.281 + 1863.52i 0.0585733 + 0.818962i 0.938812 + 0.344431i 0.111928π0.111928\pi
−0.880238 + 0.474532i 0.842617π0.842617\pi
174174 −2133.02 7264.40i −0.929333 3.16502i
175175 3527.69 2693.38i 1.52382 1.16343i
176176 71.4270 + 111.143i 0.0305910 + 0.0476005i
177177 −353.178 646.797i −0.149980 0.274668i
178178 1827.01 2440.61i 0.769329 1.02770i
179179 90.5150 + 41.3368i 0.0377956 + 0.0172607i 0.434223 0.900805i 0.357023π-0.357023\pi
−0.396428 + 0.918066i 0.629750π0.629750\pi
180180 −1978.14 + 748.511i −0.819121 + 0.309949i
181181 −85.2048 + 132.581i −0.0349902 + 0.0544458i −0.858308 0.513135i 0.828484π-0.828484\pi
0.823318 + 0.567581i 0.192120π0.192120\pi
182182 −1185.75 84.8064i −0.482932 0.0345400i
183183 816.924 + 816.924i 0.329993 + 0.329993i
184184 −2976.24 + 2079.92i −1.19245 + 0.833335i
185185 3368.57 + 971.775i 1.33871 + 0.386196i
186186 −4707.88 5433.18i −1.85590 2.14183i
187187 −46.1104 211.966i −0.0180317 0.0828904i
188188 1780.91 + 2379.01i 0.690882 + 0.922911i
189189 −1328.09 + 2908.12i −0.511136 + 1.11923i
190190 −3903.49 542.358i −1.49047 0.207088i
191191 850.294 2895.83i 0.322121 1.09704i −0.626182 0.779677i 0.715383π-0.715383\pi
0.948303 0.317366i 0.102798π-0.102798\pi
192192 4237.16 + 921.737i 1.59266 + 0.346462i
193193 2244.62 + 837.201i 0.837158 + 0.312244i 0.731231 0.682130i 0.238946π-0.238946\pi
0.105927 + 0.994374i 0.466219π0.466219\pi
194194 5299.30 1556.02i 1.96117 0.575853i
195195 −102.536 + 482.352i −0.0376553 + 0.177138i
196196 −8943.62 + 10321.5i −3.25934 + 3.76148i
197197 −1808.62 987.584i −0.654108 0.357170i 0.117679 0.993052i 0.462455π-0.462455\pi
−0.771786 + 0.635882i 0.780637π0.780637\pi
198198 −73.0923 + 195.968i −0.0262345 + 0.0703375i
199199 2871.62 1845.48i 1.02293 0.657399i 0.0822237 0.996614i 0.473798π-0.473798\pi
0.940709 + 0.339215i 0.110161π0.110161\pi
200200 254.608 4106.86i 0.0900175 1.45200i
201201 3110.73 447.255i 1.09161 0.156950i
202202 −3311.71 + 1235.21i −1.15352 + 0.430241i
203203 −7139.20 + 5344.34i −2.46834 + 1.84778i
204204 4975.39 + 3197.49i 1.70758 + 1.09740i
205205 112.342 305.619i 0.0382747 0.104124i
206206 7455.38i 2.52156i
207207 −1331.76 438.747i −0.447168 0.147319i
208208 −190.094 + 190.094i −0.0633686 + 0.0633686i
209209 −191.558 + 165.986i −0.0633988 + 0.0549354i
210210 7879.23 + 9006.46i 2.58913 + 2.95955i
211211 −60.1692 + 418.486i −0.0196314 + 0.136539i −0.997280 0.0737064i 0.976517π-0.976517\pi
0.977649 + 0.210245i 0.0674263π0.0674263\pi
212212 −810.413 2172.80i −0.262544 0.703909i
213213 −712.963 533.718i −0.229349 0.171689i
214214 1255.60 + 368.679i 0.401081 + 0.117768i
215215 937.041 + 3136.18i 0.297235 + 0.994817i
216216 1231.26 + 2696.09i 0.387856 + 0.849286i
217217 −4058.31 + 7432.23i −1.26957 + 2.32504i
218218 10277.1 735.036i 3.19292 0.228362i
219219 1311.68 + 1136.58i 0.404726 + 0.350697i
220220 −406.589 402.751i −0.124601 0.123425i
221221 401.516 183.366i 0.122212 0.0558124i
222222 −2009.30 + 9236.61i −0.607457 + 2.79243i
223223 1782.60 973.372i 0.535298 0.292295i −0.188772 0.982021i 0.560451π-0.560451\pi
0.724071 + 0.689726i 0.242269π0.242269\pi
224224 −402.298 2798.05i −0.119999 0.834609i
225225 1328.53 871.707i 0.393639 0.258284i
226226 −2450.08 352.269i −0.721137 0.103684i
227227 5347.73 1163.33i 1.56362 0.340144i 0.654296 0.756239i 0.272965π-0.272965\pi
0.909321 + 0.416095i 0.136601π0.136601\pi
228228 492.998 6893.01i 0.143200 2.00220i
229229 −3928.07 −1.13351 −0.566757 0.823885i 0.691802π-0.691802\pi
−0.566757 + 0.823885i 0.691802π0.691802\pi
230230 3986.04 4348.75i 1.14275 1.24673i
231231 769.639 0.219214
232232 −589.815 + 8246.70i −0.166911 + 2.33372i
233233 −3223.12 + 701.147i −0.906238 + 0.197140i −0.641448 0.767166i 0.721666π-0.721666\pi
−0.264790 + 0.964306i 0.585303π0.585303\pi
234234 −421.266 60.5688i −0.117688 0.0169210i
235235 −1694.23 1454.05i −0.470295 0.403624i
236236 247.669 + 1722.58i 0.0683131 + 0.475128i
237237 −748.099 + 408.493i −0.205039 + 0.111960i
238238 2276.86 10466.6i 0.620114 2.85062i
239239 −3774.03 + 1723.54i −1.02143 + 0.466472i −0.854475 0.519493i 0.826121π-0.826121\pi
−0.166955 + 0.985964i 0.553394π0.553394\pi
240240 2706.12 12.8316i 0.727831 0.00345116i
241241 3977.90 + 3446.87i 1.06323 + 0.921296i 0.997069 0.0765125i 0.0243785π-0.0243785\pi
0.0661639 + 0.997809i 0.478924π0.478924\pi
242242 6294.13 450.165i 1.67191 0.119577i
243243 −1585.10 + 2902.89i −0.418453 + 0.766339i
244244 −1133.36 2481.72i −0.297361 0.651129i
245245 4874.59 9028.67i 1.27113 2.35437i
246246 842.347 + 247.335i 0.218317 + 0.0641038i
247247 −412.892 309.087i −0.106363 0.0796225i
248248 2743.52 + 7355.67i 0.702475 + 1.88341i
249249 757.280 5267.00i 0.192734 1.34049i
250250 1045.42 + 6602.86i 0.264472 + 1.67041i
251251 −3416.76 + 2960.64i −0.859219 + 0.744518i −0.968373 0.249507i 0.919731π-0.919731\pi
0.109154 + 0.994025i 0.465186π0.465186\pi
252252 −4749.58 + 4749.58i −1.18728 + 1.18728i
253253 −41.7069 377.110i −0.0103640 0.0937102i
254254 3057.54i 0.755304i
255255 −4170.47 1533.02i −1.02418 0.376475i
256256 −6051.53 3889.08i −1.47742 0.949483i
257257 −1945.26 + 1456.21i −0.472149 + 0.353446i −0.808702 0.588218i 0.799830π-0.799830\pi
0.336553 + 0.941664i 0.390739π0.390739\pi
258258 −8268.63 + 3084.04i −1.99528 + 0.744201i
259259 11020.9 1584.57i 2.64404 0.380155i
260260 624.941 982.641i 0.149066 0.234388i
261261 −2685.91 + 1726.13i −0.636987 + 0.409366i
262262 −4007.17 + 10743.6i −0.944901 + 2.53338i
263263 −748.723 408.834i −0.175545 0.0958547i 0.389074 0.921206i 0.372795π-0.372795\pi
−0.564619 + 0.825352i 0.690977π0.690977\pi
264264 467.260 539.246i 0.108931 0.125713i
265265 948.867 + 1461.19i 0.219956 + 0.338717i
266266 −12008.9 + 3526.13i −2.76809 + 0.812785i
267267 −3763.11 1403.57i −0.862542 0.321712i
268268 −7251.95 1577.56i −1.65292 0.359571i
269269 −790.293 + 2691.49i −0.179126 + 0.610049i 0.820155 + 0.572142i 0.193887π0.193887\pi
−0.999281 + 0.0379070i 0.987931π0.987931\pi
270270 −2904.02 3841.21i −0.654566 0.865810i
271271 2866.03 6275.72i 0.642431 1.40673i −0.255595 0.966784i 0.582271π-0.582271\pi
0.898026 0.439943i 0.145001π-0.145001\pi
272272 −1451.63 1939.15i −0.323596 0.432273i
273273 332.897 + 1530.30i 0.0738016 + 0.339261i
274274 −1900.99 2193.86i −0.419136 0.483708i
275275 363.892 + 229.012i 0.0797946 + 0.0502180i
276276 8074.26 + 6466.15i 1.76092 + 1.41021i
277277 3501.54 + 3501.54i 0.759520 + 0.759520i 0.976235 0.216715i 0.0695342π-0.0695342\pi
−0.216715 + 0.976235i 0.569534π0.569534\pi
278278 −3768.13 269.502i −0.812941 0.0581427i
279279 −1639.04 + 2550.40i −0.351710 + 0.547271i
280280 −4624.70 12222.0i −0.987066 2.60858i
281281 2419.64 + 1105.01i 0.513678 + 0.234589i 0.655351 0.755325i 0.272521π-0.272521\pi
−0.141673 + 0.989914i 0.545248π0.545248\pi
282282 3607.40 4818.92i 0.761765 1.01760i
283283 −2131.77 3904.04i −0.447775 0.820039i 0.552131 0.833758i 0.313815π-0.313815\pi
−0.999906 + 0.0137186i 0.995633π0.995633\pi
284284 1137.06 + 1769.29i 0.237577 + 0.369677i
285285 763.236 + 5135.44i 0.158632 + 1.06736i
286286 −32.4446 110.496i −0.00670801 0.0228454i
287287 −73.7709 1031.45i −0.0151727 0.212142i
288288 −72.1979 1009.46i −0.0147719 0.206538i
289289 −263.636 897.860i −0.0536608 0.182752i
290290 −1974.65 13286.4i −0.399846 2.69037i
291291 −3933.71 6120.98i −0.792434 1.23305i
292292 −1964.27 3597.29i −0.393664 0.720942i
293293 −1675.57 + 2238.30i −0.334088 + 0.446289i −0.935857 0.352381i 0.885372π-0.885372\pi
0.601769 + 0.798671i 0.294463π0.294463\pi
294294 25164.2 + 11492.1i 4.99187 + 2.27971i
295295 −462.712 1222.84i −0.0913226 0.241344i
296296 5580.73 8683.79i 1.09586 1.70519i
297297 −308.918 22.0943i −0.0603544 0.00431663i
298298 5263.18 + 5263.18i 1.02311 + 1.02311i
299299 731.782 246.041i 0.141539 0.0475884i
300300 −11430.5 + 2600.31i −2.19979 + 0.500430i
301301 6807.28 + 7856.02i 1.30354 + 1.50436i
302302 2147.20 + 9870.50i 0.409130 + 1.88074i
303303 2790.50 + 3727.67i 0.529076 + 0.706762i
304304 −1175.78 + 2574.60i −0.221828 + 0.485735i
305305 1236.11 + 1635.03i 0.232064 + 0.306956i
306306 1080.39 3679.47i 0.201836 0.687390i
307307 −463.662 100.864i −0.0861974 0.0187511i 0.169260 0.985571i 0.445862π-0.445862\pi
−0.255457 + 0.966820i 0.582226π0.582226\pi
308308 −1702.92 635.155i −0.315041 0.117504i
309309 −9423.85 + 2767.09i −1.73497 + 0.509432i
310310 −6946.52 10697.1i −1.27270 1.95986i
311311 3711.98 4283.85i 0.676808 0.781078i −0.308618 0.951186i 0.599866π-0.599866\pi
0.985425 + 0.170109i 0.0544119π0.0544119\pi
312312 1274.31 + 695.827i 0.231230 + 0.126261i
313313 −3002.25 + 8049.33i −0.542163 + 1.45359i 0.320222 + 0.947342i 0.396242π0.396242\pi
−0.862385 + 0.506252i 0.831030π0.831030\pi
314314 −13113.9 + 8427.81i −2.35688 + 1.51468i
315315 2708.09 4258.13i 0.484392 0.761646i
316316 1992.37 286.459i 0.354682 0.0509956i
317317 −5773.99 + 2153.59i −1.02303 + 0.381569i −0.804304 0.594218i 0.797462π-0.797462\pi
−0.218722 + 0.975787i 0.570189π0.570189\pi
318318 −3760.46 + 2815.05i −0.663133 + 0.496415i
319319 −726.771 467.068i −0.127559 0.0819773i
320320 7220.85 + 2654.30i 1.26143 + 0.463688i
321321 1723.96i 0.299758i
322322 5862.18 17793.9i 1.01455 3.07955i
323323 3286.11 3286.11i 0.566081 0.566081i
324324 10241.6 8874.42i 1.75611 1.52168i
325325 −297.957 + 822.596i −0.0508545 + 0.140398i
326326 370.084 2573.99i 0.0628744 0.437301i
327327 −4743.51 12717.8i −0.802192 2.15076i
328328 −767.472 574.523i −0.129197 0.0967156i
329329 −6803.24 1997.61i −1.14004 0.334747i
330330 −550.735 + 1020.07i −0.0918697 + 0.170160i
331331 3213.42 + 7036.42i 0.533613 + 1.16845i 0.964024 + 0.265816i 0.0856413π0.0856413\pi
−0.430411 + 0.902633i 0.641631π0.641631\pi
332332 −6022.23 + 11028.9i −0.995521 + 1.82316i
333333 3976.04 284.372i 0.654311 0.0467973i
334334 −279.351 242.059i −0.0457646 0.0396553i
335335 5575.64 26.4380i 0.909343 0.00431183i
336336 7817.61 3570.19i 1.26930 0.579671i
337337 82.4270 378.911i 0.0133237 0.0612480i −0.970005 0.243085i 0.921841π-0.921841\pi
0.983329 + 0.181837i 0.0582043π0.0582043\pi
338338 −9018.11 + 4924.26i −1.45124 + 0.792439i
339339 464.078 + 3227.73i 0.0743518 + 0.517128i
340340 7962.50 + 6833.71i 1.27008 + 1.09003i
341341 −811.980 116.745i −0.128948 0.0185399i
342342 −4378.44 + 952.471i −0.692277 + 0.150596i
343343 1455.80 20354.8i 0.229172 3.20424i
344344 9637.12 1.51046
345345 −6976.39 3424.43i −1.08869 0.534392i
346346 −8936.84 −1.38858
347347 426.179 5958.76i 0.0659323 0.921853i −0.851600 0.524192i 0.824367π-0.824367\pi
0.917532 0.397661i 0.130178π-0.130178\pi
348348 23015.7 5006.76i 3.54532 0.771238i
349349 −12368.4 1778.31i −1.89703 0.272752i −0.907835 0.419328i 0.862266π-0.862266\pi
−0.989199 + 0.146576i 0.953175π0.953175\pi
350350 11647.0 + 17750.7i 1.77874 + 2.71091i
351351 −89.6876 623.791i −0.0136387 0.0948589i
352352 240.347 131.239i 0.0363936 0.0198724i
353353 544.107 2501.22i 0.0820394 0.377129i −0.917761 0.397134i 0.870005π-0.870005\pi
0.999800 + 0.0200054i 0.00636835π0.00636835\pi
354354 3206.57 1464.39i 0.481433 0.219863i
355355 −1122.57 1111.97i −0.167830 0.166246i
356356 7168.01 + 6211.11i 1.06715 + 0.924687i
357357 −14075.2 + 1006.68i −2.08666 + 0.149241i
358358 −228.118 + 417.767i −0.0336771 + 0.0616750i
359359 −3049.66 6677.82i −0.448342 0.981731i −0.989991 0.141127i 0.954927π-0.954927\pi
0.541650 0.840604i 0.317800π-0.317800\pi
360360 −1339.33 4482.59i −0.196080 0.656260i
361361 1370.95 + 402.548i 0.199877 + 0.0586890i
362362 −603.507 451.779i −0.0876232 0.0655939i
363363 −2905.11 7788.91i −0.420052 1.12620i
364364 526.329 3660.70i 0.0757889 0.527123i
365365 2027.49 + 2317.55i 0.290750 + 0.332346i
366366 −4176.55 + 3619.00i −0.596480 + 0.516853i
367367 4132.87 4132.87i 0.587831 0.587831i −0.349212 0.937044i 0.613551π-0.613551\pi
0.937044 + 0.349212i 0.113551π0.113551\pi
368368 −2172.97 3637.03i −0.307809 0.515199i
369369 370.216i 0.0522295i
370370 −5786.14 + 15740.8i −0.812992 + 2.21169i
371371 4654.70 + 2991.39i 0.651375 + 0.418613i
372372 17904.7 13403.3i 2.49547 1.86808i
373373 −1022.43 + 381.347i −0.141929 + 0.0529367i −0.419425 0.907790i 0.637768π-0.637768\pi
0.277496 + 0.960727i 0.410495π0.410495\pi
374374 1027.09 147.673i 0.142004 0.0204170i
375375 7958.23 3772.12i 1.09590 0.519444i
376376 −5529.97 + 3553.90i −0.758475 + 0.487442i
377377 614.333 1647.09i 0.0839251 0.225012i
378378 −13422.3 7329.11i −1.82637 0.997271i
379379 −3970.78 + 4582.52i −0.538167 + 0.621078i −0.958085 0.286484i 0.907513π-0.907513\pi
0.419918 + 0.907562i 0.362059π0.362059\pi
380380 2549.34 11992.6i 0.344154 1.61897i
381381 −3864.84 + 1134.82i −0.519689 + 0.152595i
382382 13526.7 + 5045.19i 1.81174 + 0.675745i
383383 3590.25 + 781.011i 0.478990 + 0.104198i 0.445577 0.895244i 0.352999π-0.352999\pi
0.0334132 + 0.999442i 0.489362π0.489362\pi
384384 −4713.02 + 16051.1i −0.626329 + 2.13308i
385385 1352.48 + 187.916i 0.179035 + 0.0248755i
386386 −4760.50 + 10424.0i −0.627728 + 1.37453i
387387 2230.24 + 2979.25i 0.292944 + 0.391328i
388388 3652.38 + 16789.7i 0.477891 + 2.19683i
389389 4676.06 + 5396.46i 0.609474 + 0.703371i 0.973673 0.227951i 0.0732025π-0.0732025\pi
−0.364199 + 0.931321i 0.618657π0.618657\pi
390390 −2266.45 653.832i −0.294272 0.0848925i
391391 1255.99 + 6842.04i 0.162450 + 0.884953i
392392 −21361.6 21361.6i −2.75235 2.75235i
393393 15067.6 + 1077.66i 1.93400 + 0.138322i
394394 5329.24 8292.45i 0.681429 1.06032i
395395 −1414.36 + 535.183i −0.180163 + 0.0681721i
396396 −591.890 270.307i −0.0751101 0.0343016i
397397 6911.34 9232.47i 0.873729 1.16717i −0.111130 0.993806i 0.535447π-0.535447\pi
0.984859 0.173359i 0.0554622π-0.0554622\pi
398398 7825.36 + 14331.1i 0.985552 + 1.80490i
399399 8914.29 + 13870.9i 1.11848 + 1.74039i
400400 4758.57 + 638.181i 0.594821 + 0.0797726i
401401 −1481.13 5044.26i −0.184449 0.628176i −0.998853 0.0478776i 0.984754π-0.984754\pi
0.814404 0.580298i 0.197064π-0.197064\pi
402402 1072.45 + 14994.8i 0.133057 + 1.86038i
403403 −119.082 1664.99i −0.0147194 0.205804i
404404 −3097.99 10550.8i −0.381512 1.29931i
405405 −6062.61 + 8179.26i −0.743836 + 1.00353i
406406 −23063.1 35886.9i −2.81922 4.38679i
407407 516.924 + 946.675i 0.0629557 + 0.115295i
408408 −7839.93 + 10472.9i −0.951309 + 1.27080i
409409 −5308.15 2424.15i −0.641739 0.293072i 0.0678421 0.997696i 0.478389π-0.478389\pi
−0.709581 + 0.704624i 0.751116π0.751116\pi
410410 1419.86 + 640.308i 0.171029 + 0.0771281i
411411 −2067.56 + 3217.18i −0.248139 + 0.386111i
412412 23134.9 + 1654.64i 2.76645 + 0.197860i
413413 −2936.08 2936.08i −0.349819 0.349819i
414414 2547.85 6204.49i 0.302464 0.736555i
415415 2616.75 9070.74i 0.309522 1.07293i
416416 364.907 + 421.126i 0.0430073 + 0.0496331i
417417 1057.90 + 4863.08i 0.124234 + 0.571093i
418418 −726.598 970.621i −0.0850217 0.113576i
419419 1545.71 3384.62i 0.180221 0.394629i −0.797863 0.602839i 0.794036π-0.794036\pi
0.978084 + 0.208209i 0.0667635π0.0667635\pi
420420 −29696.9 + 22451.3i −3.45014 + 2.60836i
421421 −2841.91 + 9678.67i −0.328994 + 1.12045i 0.614461 + 0.788947i 0.289374π0.289374\pi
−0.943454 + 0.331502i 0.892445π0.892445\pi
422422 −1976.18 429.892i −0.227960 0.0495896i
423423 −2378.42 887.105i −0.273387 0.101968i
424424 4921.86 1445.19i 0.563742 0.165529i
425425 −6954.40 3712.22i −0.793737 0.423692i
426426 2789.82 3219.62i 0.317294 0.366176i
427427 5713.25 + 3119.67i 0.647502 + 0.353563i
428428 −1422.72 + 3814.47i −0.160677 + 0.430793i
429429 −127.629 + 82.0222i −0.0143636 + 0.00923093i
430430 −15283.4 + 3400.67i −1.71402 + 0.381383i
431431 −12530.7 + 1801.64i −1.40042 + 0.201350i −0.800799 0.598933i 0.795592π-0.795592\pi
−0.599622 + 0.800283i 0.704682π0.704682\pi
432432 −3240.33 + 1208.58i −0.360881 + 0.134602i
433433 −6793.39 + 5085.47i −0.753971 + 0.564416i −0.905656 0.424013i 0.860621π-0.860621\pi
0.151685 + 0.988429i 0.451530π0.451530\pi
434434 −34076.4 21899.6i −3.76894 2.42215i
435435 −16061.6 + 7427.34i −1.77033 + 0.818652i
436436 32054.3i 3.52093i
437437 6313.43 5119.51i 0.691104 0.560411i
438438 −5870.54 + 5870.54i −0.640422 + 0.640422i
439439 8984.52 7785.13i 0.976783 0.846387i −0.0113582 0.999935i 0.503615π-0.503615\pi
0.988141 + 0.153548i 0.0490700π0.0490700\pi
440440 952.772 833.525i 0.103231 0.0903107i
441441 1660.25 11547.3i 0.179274 1.24688i
442442 737.875 + 1978.32i 0.0794053 + 0.212894i
443443 −7955.00 5955.04i −0.853168 0.638674i 0.0805232 0.996753i 0.474341π-0.474341\pi
−0.933691 + 0.358079i 0.883432π0.883432\pi
444444 −28216.4 8285.07i −3.01597 0.885568i
445445 −6270.17 3385.28i −0.667943 0.360624i
446446 4035.92 + 8837.44i 0.428490 + 0.938262i
447447 4699.39 8606.28i 0.497256 0.910656i
448448 24370.1 1742.98i 2.57004 0.183813i
449449 10980.0 + 9514.25i 1.15408 + 1.00001i 0.999928 + 0.0119639i 0.00380831π0.00380831\pi
0.154147 + 0.988048i 0.450737π0.450737\pi
450450 3705.80 + 6636.27i 0.388207 + 0.695193i
451451 91.1229 41.6144i 0.00951399 0.00434489i
452452 1636.90 7524.72i 0.170339 0.783037i
453453 11679.7 6377.60i 1.21139 0.661470i
454454 3725.66 + 25912.5i 0.385140 + 2.67871i
455455 211.356 + 2770.46i 0.0217769 + 0.285453i
456456 15130.6 + 2175.46i 1.55385 + 0.223410i
457457 9322.71 2028.03i 0.954263 0.207587i 0.291630 0.956531i 0.405803π-0.405803\pi
0.662633 + 0.748944i 0.269439π0.269439\pi
458458 1340.45 18742.0i 0.136758 1.91213i
459459 5678.40 0.577440
460460 12610.0 + 13334.3i 1.27814 + 1.35155i
461461 15515.3 1.56750 0.783752 0.621074i 0.213303π-0.213303\pi
0.783752 + 0.621074i 0.213303π0.213303\pi
462462 −262.639 + 3672.17i −0.0264482 + 0.369794i
463463 −224.304 + 48.7944i −0.0225147 + 0.00489777i −0.223809 0.974633i 0.571849π-0.571849\pi
0.201294 + 0.979531i 0.435485π0.435485\pi
464464 −9548.81 1372.91i −0.955371 0.137362i
465465 −10943.3 + 12750.9i −1.09136 + 1.27163i
466466 −2245.48 15617.7i −0.223219 1.55252i
467467 −11854.7 + 6473.16i −1.17467 + 0.641418i −0.943460 0.331486i 0.892450π-0.892450\pi
−0.231209 + 0.972904i 0.574268π0.574268\pi
468468 281.448 1293.80i 0.0277990 0.127790i
469469 16107.3 7355.94i 1.58585 0.724234i
470470 7515.83 7587.45i 0.737616 0.744645i
471471 15520.3 + 13448.4i 1.51834 + 1.31565i
472472 −3839.70 + 274.621i −0.374442 + 0.0267806i
473473 −482.604 + 883.824i −0.0469137 + 0.0859160i
474474 −1693.75 3708.79i −0.164127 0.359389i
475475 87.3517 + 9210.80i 0.00843783 + 0.889727i
476476 31973.7 + 9388.33i 3.07881 + 0.904020i
477477 1585.79 + 1187.11i 0.152219 + 0.113950i
478478 −6935.63 18595.1i −0.663657 1.77933i
479479 1248.17 8681.19i 0.119061 0.828087i −0.839533 0.543309i 0.817171π-0.817171\pi
0.958594 0.284778i 0.0919198π-0.0919198\pi
480480 373.623 5596.76i 0.0355281 0.532200i
481481 −1658.72 + 1437.29i −0.157237 + 0.136247i
482482 −17803.5 + 17803.5i −1.68242 + 1.68242i
483483 −24667.9 805.722i −2.32386 0.0759040i
484484 19631.4i 1.84367i
485485 −5418.16 11716.8i −0.507270 1.09697i
486486 −13309.6 8553.56i −1.24225 0.798348i
487487 −2440.03 + 1826.58i −0.227039 + 0.169960i −0.706742 0.707472i 0.749836π-0.749836\pi
0.479702 + 0.877431i 0.340745π0.340745\pi
488488 5654.39 2108.98i 0.524513 0.195633i
489489 −3390.97 + 487.547i −0.313589 + 0.0450872i
490490 41414.9 + 26339.1i 3.81823 + 2.42832i
491491 662.160 425.544i 0.0608612 0.0391131i −0.509856 0.860260i 0.670301π-0.670301\pi
0.570718 + 0.821146i 0.306665π0.306665\pi
492492 −954.462 + 2559.01i −0.0874603 + 0.234490i
493493 13902.1 + 7591.13i 1.27002 + 0.693484i
494494 1615.64 1864.55i 0.147148 0.169818i
495495 478.171 + 101.648i 0.0434186 + 0.00922973i
496496 −8789.25 + 2580.76i −0.795663 + 0.233628i
497497 −4701.65 1753.63i −0.424342 0.158271i
498498 24871.9 + 5410.56i 2.23803 + 0.486853i
499499 −4229.02 + 14402.7i −0.379393 + 1.29209i 0.519705 + 0.854345i 0.326042π0.326042\pi
−0.899098 + 0.437747i 0.855776π0.855776\pi
500500 −20721.5 + 1778.62i −1.85339 + 0.159085i
501501 −202.288 + 442.950i −0.0180391 + 0.0395001i
502502 −12960.1 17312.7i −1.15227 1.53925i
503503 1139.60 + 5238.64i 0.101018 + 0.464372i 0.999669 + 0.0257090i 0.00818434π0.00818434\pi
−0.898651 + 0.438663i 0.855452π0.855452\pi
504504 −9729.77 11228.8i −0.859917 0.992397i
505505 3993.56 + 7231.91i 0.351903 + 0.637259i
506506 1813.53 70.3070i 0.159331 0.00617693i
507507 9571.54 + 9571.54i 0.838436 + 0.838436i
508508 9487.92 + 678.590i 0.828658 + 0.0592668i
509509 5682.46 8842.09i 0.494834 0.769977i −0.500574 0.865694i 0.666878π-0.666878\pi
0.995409 + 0.0957162i 0.0305141π0.0305141\pi
510510 8737.63 19375.3i 0.758644 1.68226i
511511 8895.41 + 4062.40i 0.770078 + 0.351683i
512512 7894.16 10545.4i 0.681398 0.910241i
513513 −3179.83 5823.42i −0.273670 0.501189i
514514 −6284.16 9778.34i −0.539265 0.839113i
515515 −17236.0 + 2561.64i −1.47478 + 0.219183i
516516 −7735.01 26343.0i −0.659913 2.24746i
517517 −49.0012 685.127i −0.00416842 0.0582821i
518518 3799.55 + 53124.6i 0.322283 + 4.50610i
519519 3316.94 + 11296.5i 0.280535 + 0.955415i
520520 2069.44 + 1533.90i 0.174521 + 0.129358i
521521 4001.17 + 6225.94i 0.336457 + 0.523538i 0.967719 0.252032i 0.0810989π-0.0810989\pi
−0.631262 + 0.775570i 0.717463π0.717463\pi
522522 −7319.28 13404.3i −0.613710 1.12393i
523523 20.2508 27.0520i 0.00169313 0.00226176i −0.799694 0.600408i 0.795005π-0.795005\pi
0.801387 + 0.598146i 0.204096π0.204096\pi
524524 −32449.5 14819.2i −2.70527 1.23546i
525525 18114.7 21310.5i 1.50589 1.77156i
526526 2206.16 3432.86i 0.182877 0.284562i
527527 15002.2 + 1072.98i 1.24005 + 0.0886902i
528528 588.706 + 588.706i 0.0485230 + 0.0485230i
529529 941.965 + 12130.5i 0.0774196 + 0.996999i
530530 −7295.53 + 4028.69i −0.597920 + 0.330179i
531531 −973.487 1123.46i −0.0795589 0.0918158i
532532 −8276.75 38047.6i −0.674516 3.10070i
533533 122.158 + 163.183i 0.00992726 + 0.0132613i
534534 7980.98 17475.9i 0.646762 1.41621i
535535 420.924 3029.50i 0.0340152 0.244816i
536536 4625.04 15751.4i 0.372707 1.26932i
537537 612.738 + 133.293i 0.0492395 + 0.0107114i
538538 −12572.2 4689.18i −1.00748 0.375771i
539539 3028.81 889.340i 0.242041 0.0710697i
540540 12564.3 8159.00i 1.00126 0.650199i
541541 9236.49 10659.5i 0.734025 0.847110i −0.258894 0.965906i 0.583358π-0.583358\pi
0.992919 + 0.118796i 0.0379034π0.0379034\pi
542542 28965.2 + 15816.2i 2.29550 + 1.25344i
543543 −347.071 + 930.532i −0.0274295 + 0.0735414i
544544 −4223.81 + 2714.48i −0.332894 + 0.213938i
545545 −5230.51 23507.1i −0.411102 1.84758i
546546 −7415.11 + 1066.13i −0.581204 + 0.0835645i
547547 −845.016 + 315.175i −0.0660517 + 0.0246360i −0.382273 0.924049i 0.624859π-0.624859\pi
0.316221 + 0.948685i 0.397586π0.397586\pi
548548 7229.72 5412.10i 0.563574 0.421886i
549549 1960.53 + 1259.95i 0.152410 + 0.0979481i
550550 −1216.86 + 1658.08i −0.0943402 + 0.128547i
551551 18508.1i 1.43098i
552552 −15540.8 + 16794.3i −1.19829 + 1.29495i
553553 −3395.93 + 3395.93i −0.261139 + 0.261139i
554554 −17901.7 + 15511.9i −1.37287 + 1.18960i
555555 22044.4 + 1471.62i 1.68601 + 0.112553i
556556 1672.60 11633.2i 0.127579 0.887331i
557557 −4009.98 10751.2i −0.305042 0.817850i −0.995525 0.0945006i 0.969875π-0.969875\pi
0.690483 0.723349i 0.257398π-0.257398\pi
558558 −11609.4 8690.67i −0.880760 0.659329i
559559 −1966.08 577.294i −0.148759 0.0436797i
560560 14609.5 4365.09i 1.10244 0.329390i
561561 −567.870 1243.46i −0.0427371 0.0935811i
562562 −6098.03 + 11167.7i −0.457704 + 0.838223i
563563 −5786.45 + 413.855i −0.433161 + 0.0309803i −0.286218 0.958165i 0.592398π-0.592398\pi
−0.146943 + 0.989145i 0.546944π0.546944\pi
564564 14153.1 + 12263.7i 1.05665 + 0.915595i
565565 27.4325 + 5785.36i 0.00204264 + 0.430782i
566566 19354.7 8839.01i 1.43735 0.656416i
567567 −6872.97 + 31594.6i −0.509061 + 2.34012i
568568 −4083.12 + 2229.55i −0.301627 + 0.164701i
569569 1387.68 + 9651.56i 0.102240 + 0.711097i 0.974880 + 0.222732i 0.0714975π0.0714975\pi
−0.872639 + 0.488365i 0.837593π0.837593\pi
570570 −24763.1 + 1889.15i −1.81967 + 0.138821i
571571 −25878.7 3720.80i −1.89666 0.272698i −0.907554 0.419935i 0.862053π-0.862053\pi
−0.989101 + 0.147237i 0.952962π0.952962\pi
572572 350.084 76.1561i 0.0255905 0.00556686i
573573 1356.81 18970.7i 0.0989209 1.38310i
574574 4946.52 0.359693
575575 −11423.4 7721.07i −0.828503 0.559984i
576576 8747.09 0.632747
577577 136.427 1907.50i 0.00984321 0.137626i −0.990154 0.139982i 0.955295π-0.955295\pi
0.999997 + 0.00235616i 0.000749991π0.000749991\pi
578578 4373.91 951.486i 0.314759 0.0684716i
579579 14943.2 + 2148.51i 1.07257 + 0.154213i
580580 41667.7 3178.79i 2.98303 0.227572i
581581 −4266.85 29676.6i −0.304680 2.11909i
582582 30547.3 16680.1i 2.17565 1.18799i
583583 −113.936 + 523.757i −0.00809393 + 0.0372072i
584584 8246.85 3766.21i 0.584344 0.266861i
585585 4.71672 + 994.732i 0.000333355 + 0.0703027i
586586 −10107.8 8758.43i −0.712540 0.617419i
587587 −13613.5 + 973.656i −0.957221 + 0.0684618i −0.541201 0.840894i 0.682030π-0.682030\pi
−0.416020 + 0.909355i 0.636575π0.636575\pi
588588 −41246.4 + 75537.1i −2.89281 + 5.29779i
589589 −7300.65 15986.2i −0.510727 1.11834i
590590 5992.42 1790.44i 0.418142 0.124934i
591591 −12459.9 3658.56i −0.867229 0.254641i
592592 9642.07 + 7217.96i 0.669403 + 0.501109i
593593 1667.36 + 4470.37i 0.115464 + 0.309572i 0.981808 0.189876i 0.0608087π-0.0608087\pi
−0.866344 + 0.499449i 0.833536π0.833536\pi
594594 210.836 1466.40i 0.0145635 0.101291i
595595 −24979.9 1667.59i −1.72114 0.114898i
596596 −17500.4 + 15164.2i −1.20276 + 1.04220i
597597 15210.5 15210.5i 1.04276 1.04276i
598598 924.212 + 3575.50i 0.0632004 + 0.244504i
599599 12141.7i 0.828207i 0.910230 + 0.414104i 0.135905π0.135905\pi
−0.910230 + 0.414104i 0.864095π0.864095\pi
600600 −3933.46 25630.0i −0.267638 1.74390i
601601 −8753.74 5625.69i −0.594131 0.381825i 0.208746 0.977970i 0.433062π-0.433062\pi
−0.802877 + 0.596145i 0.796698π0.796698\pi
602602 −39806.3 + 29798.6i −2.69499 + 2.01744i
603603 5939.78 2215.42i 0.401139 0.149617i
604604 −31105.9 + 4472.35i −2.09550 + 0.301287i
605605 −3203.37 14396.7i −0.215266 0.967451i
606606 −18738.0 + 12042.2i −1.25607 + 0.807229i
607607 1252.20 3357.29i 0.0837321 0.224494i −0.888336 0.459195i 0.848138π-0.848138\pi
0.972068 + 0.234700i 0.0754108π0.0754108\pi
608608 5149.08 + 2811.61i 0.343458 + 0.187543i
609609 −36802.3 + 42472.1i −2.44878 + 2.82604i
610610 −8223.02 + 5339.88i −0.545804 + 0.354435i
611611 1341.07 393.773i 0.0887952 0.0260726i
612612 11178.1 + 4169.20i 0.738310 + 0.275376i
613613 16714.3 + 3635.97i 1.10128 + 0.239569i 0.726241 0.687441i 0.241266π-0.241266\pi
0.375038 + 0.927009i 0.377629π0.377629\pi
614614 639.473 2177.84i 0.0420310 0.143144i
615615 282.385 2032.40i 0.0185152 0.133259i
616616 1670.10 3657.01i 0.109237 0.239197i
617617 −4878.11 6516.39i −0.318291 0.425187i 0.612651 0.790353i 0.290103π-0.290103\pi
−0.930942 + 0.365167i 0.881012π0.881012\pi
618618 −9986.71 45908.2i −0.650039 2.98818i
619619 8557.29 + 9875.63i 0.555648 + 0.641252i 0.962190 0.272380i 0.0878108π-0.0878108\pi
−0.406541 + 0.913632i 0.633265π0.633265\pi
620620 34736.2 19181.8i 2.25006 1.24251i
621621 9878.07 + 1031.55i 0.638315 + 0.0666580i
622622 19172.8 + 19172.8i 1.23595 + 1.23595i
623623 −22572.2 1614.40i −1.45158 0.103819i
624624 −915.910 + 1425.18i −0.0587592 + 0.0914311i
625625 14905.9 4685.61i 0.953977 0.299879i
626626 −37381.1 17071.4i −2.38666 1.08995i
627627 −957.218 + 1278.69i −0.0609691 + 0.0814452i
628628 −23242.0 42564.5i −1.47684 2.70463i
629629 −10691.7 16636.7i −0.677755 1.05461i
630630 19392.6 + 14374.1i 1.22638 + 0.909016i
631631 −596.673 2032.08i −0.0376437 0.128203i 0.938527 0.345205i 0.112190π-0.112190\pi
−0.976171 + 0.217002i 0.930372π0.930372\pi
632632 317.632 + 4441.08i 0.0199917 + 0.279520i
633633 190.069 + 2657.52i 0.0119346 + 0.166867i
634634 −8305.00 28284.2i −0.520243 1.77178i
635635 −7068.71 + 1050.56i −0.441753 + 0.0656539i
636636 −7900.83 12293.9i −0.492592 0.766488i
637637 3078.38 + 5637.63i 0.191476 + 0.350661i
638638 2476.52 3308.25i 0.153678 0.205290i
639639 −1634.17 746.302i −0.101169 0.0462023i
640640 −12201.2 + 27055.6i −0.753585 + 1.67104i
641641 −10688.7 + 16632.0i −0.658625 + 1.02484i 0.337870 + 0.941193i 0.390294π0.390294\pi
−0.996495 + 0.0836484i 0.973343π0.973343\pi
642642 8225.52 + 588.301i 0.505663 + 0.0361657i
643643 7007.02 + 7007.02i 0.429751 + 0.429751i 0.888543 0.458792i 0.151718π-0.151718\pi
−0.458792 + 0.888543i 0.651718π0.651718\pi
644644 53915.5 + 22140.2i 3.29902 + 1.35473i
645645 9971.04 + 18056.5i 0.608697 + 1.10229i
646646 14557.6 + 16800.4i 0.886627 + 1.02322i
647647 1524.11 + 7006.20i 0.0926101 + 0.425722i 0.999985 + 0.00540050i 0.00171904π0.00171904\pi
−0.907375 + 0.420321i 0.861917π0.861917\pi
648648 17964.0 + 23997.1i 1.08903 + 1.45477i
649649 167.098 365.893i 0.0101066 0.0221303i
650650 −3823.16 1702.35i −0.230703 0.102726i
651651 −15034.2 + 51201.8i −0.905126 + 3.08258i
652652 7905.26 + 1719.68i 0.474837 + 0.103295i
653653 684.764 + 255.404i 0.0410366 + 0.0153059i 0.369899 0.929072i 0.379392π-0.379392\pi
−0.328862 + 0.944378i 0.606665π0.606665\pi
654654 62299.2 18292.7i 3.72491 1.09373i
655655 26215.0 + 5572.67i 1.56382 + 0.332431i
656656 732.541 845.398i 0.0435990 0.0503159i
657657 3072.80 + 1677.88i 0.182468 + 0.0996350i
658658 11852.8 31778.5i 0.702233 1.88276i
659659 17465.6 11224.5i 1.03242 0.663494i 0.0893168 0.996003i 0.471532π-0.471532\pi
0.943100 + 0.332509i 0.107895π0.107895\pi
660660 −3043.16 1935.39i −0.179477 0.114144i
661661 10470.1 1505.37i 0.616095 0.0885811i 0.172800 0.984957i 0.444719π-0.444719\pi
0.443295 + 0.896376i 0.353809π0.353809\pi
662662 −34669.3 + 12931.0i −2.03544 + 0.759180i
663663 2226.80 1666.96i 0.130440 0.0976461i
664664 −23383.3 15027.6i −1.36664 0.878287i
665665 12278.2 + 26551.7i 0.715984 + 1.54832i
666666 19067.9i 1.10941i
667667 22804.9 + 15730.9i 1.32385 + 0.913199i
668668 813.136 813.136i 0.0470976 0.0470976i
669669 9672.88 8381.60i 0.559006 0.484381i
670670 −1776.54 + 26612.0i −0.102438 + 1.53449i
671671 −89.7434 + 624.179i −0.00516320 + 0.0359108i
672672 −6225.31 16690.7i −0.357361 0.958122i
673673 −17299.8 12950.5i −0.990877 0.741761i −0.0247140 0.999695i 0.507868π-0.507868\pi
−0.966163 + 0.257934i 0.916958π0.916958\pi
674674 1779.76 + 522.586i 0.101712 + 0.0298653i
675675 −7882.66 + 8033.60i −0.449487 + 0.458094i
676676 −13279.1 29077.2i −0.755525 1.65437i
677677 −2193.36 + 4016.84i −0.124516 + 0.228035i −0.932500 0.361170i 0.882377π-0.882377\pi
0.807983 + 0.589205i 0.200559π0.200559\pi
678678 −15558.8 + 1112.79i −0.881316 + 0.0630329i
679679 −30982.9 26846.9i −1.75113 1.51736i
680680 −16334.1 + 16489.7i −0.921152 + 0.929929i
681681 31371.5 14326.9i 1.76528 0.806178i
682682 834.112 3834.35i 0.0468325 0.215286i
683683 2722.71 1486.71i 0.152535 0.0832905i −0.401169 0.916004i 0.631396π-0.631396\pi
0.553704 + 0.832714i 0.313214π0.313214\pi
684684 −1983.88 13798.2i −0.110900 0.771327i
685685 −4418.80 + 5148.69i −0.246472 + 0.287185i
686686 96621.7 + 13892.1i 5.37760 + 0.773182i
687687 −24188.0 + 5261.77i −1.34327 + 0.292211i
688688 −802.194 + 11216.1i −0.0444526 + 0.621528i
689689 −1090.69 −0.0603075
690690 18719.6 32117.8i 1.03282 1.77203i
691691 −22009.9 −1.21171 −0.605857 0.795573i 0.707170π-0.707170\pi
−0.605857 + 0.795573i 0.707170π0.707170\pi
692692 1983.44 27732.1i 0.108958 1.52343i
693693 1517.04 330.011i 0.0831565 0.0180896i
694694 28285.5 + 4066.84i 1.54712 + 0.222443i
695695 671.657 + 8804.12i 0.0366581 + 0.480517i
696696 7414.78 + 51570.9i 0.403817 + 2.80861i
697697 −1612.03 + 880.233i −0.0876038 + 0.0478353i
698698 12705.5 58406.3i 0.688984 3.16721i
699699 −18907.9 + 8634.93i −1.02312 + 0.467243i
700700 −57667.6 + 32202.6i −3.11376 + 1.73878i
701701 −20164.3 17472.5i −1.08644 0.941407i −0.0879403 0.996126i 0.528028π-0.528028\pi
−0.998502 + 0.0547183i 0.982574π0.982574\pi
702702 3006.89 215.057i 0.161663 0.0115624i
703703 −11074.3 + 20281.1i −0.594134 + 1.08807i
704704 983.224 + 2152.96i 0.0526373 + 0.115260i
705705 −12380.3 6684.16i −0.661376 0.357078i
706706 11748.4 + 3449.63i 0.626282 + 0.183893i
707707 21003.3 + 15722.9i 1.11727 + 0.836379i
708708 3832.52 + 10275.4i 0.203439 + 0.545442i
709709 −1841.52 + 12808.0i −0.0975454 + 0.678443i 0.881107 + 0.472918i 0.156799π0.156799\pi
−0.978652 + 0.205525i 0.934110π0.934110\pi
710710 5688.61 4976.63i 0.300690 0.263056i
711711 −1299.42 + 1125.96i −0.0685403 + 0.0593905i
712712 −14835.0 + 14835.0i −0.780852 + 0.780852i
713713 25902.7 + 4591.87i 1.36054 + 0.241188i
714714 67500.2i 3.53800i
715715 −244.308 + 112.975i −0.0127784 + 0.00590911i
716716 −1245.75 800.597i −0.0650223 0.0417873i
717717 −20930.7 + 15668.5i −1.09020 + 0.816111i
718718 32902.4 12272.0i 1.71018 0.637864i
719719 2517.34 361.939i 0.130572 0.0187734i −0.0767191 0.997053i 0.524444π-0.524444\pi
0.207291 + 0.978279i 0.433535π0.433535\pi
720720 5328.54 1185.64i 0.275810 0.0613699i
721721 −46554.8 + 29918.9i −2.40470 + 1.54541i
722722 −2388.51 + 6403.84i −0.123118 + 0.330092i
723723 29112.0 + 15896.3i 1.49749 + 0.817692i
724724 1535.87 1772.49i 0.0788399 0.0909861i
725725 −30038.3 + 9130.35i −1.53875 + 0.467714i
726726 38154.5 11203.2i 1.95048 0.572711i
727727 4695.67 + 1751.39i 0.239550 + 0.0893475i 0.466372 0.884589i 0.345561π-0.345561\pi
−0.226822 + 0.973936i 0.572834π0.572834\pi
728728 7993.75 + 1738.93i 0.406962 + 0.0885291i
729729 1054.87 3592.57i 0.0535931 0.182521i
730730 −11749.6 + 8882.86i −0.595714 + 0.450369i
731731 7669.85 16794.6i 0.388071 0.849756i
732732 −10303.3 13763.5i −0.520245 0.694966i
733733 5054.49 + 23235.1i 0.254696 + 1.17082i 0.909724 + 0.415213i 0.136293π0.136293\pi
−0.655029 + 0.755604i 0.727343π0.727343\pi
734734 18308.8 + 21129.4i 0.920693 + 1.06254i
735735 17922.2 62125.7i 0.899416 3.11774i
736736 −7840.80 + 3954.77i −0.392685 + 0.198063i
737737 1212.96 + 1212.96i 0.0606240 + 0.0606240i
738738 1766.41 + 126.336i 0.0881061 + 0.00630147i
739739 19169.5 29828.4i 0.954213 1.48478i 0.0814276 0.996679i 0.474052π-0.474052\pi
0.872785 0.488105i 0.162312π-0.162312\pi
740740 −47561.4 21448.6i −2.36269 1.06549i
741741 −2956.51 1350.19i −0.146572 0.0669373i
742742 −15861.2 + 21188.1i −0.784748 + 1.04830i
743743 12220.1 + 22379.5i 0.603381 + 1.10501i 0.983643 + 0.180131i 0.0576522π0.0576522\pi
−0.380261 + 0.924879i 0.624166π0.624166\pi
744744 26747.0 + 41619.1i 1.31800 + 2.05085i
745745 10359.5 13976.3i 0.509453 0.687318i
746746 −1470.61 5008.44i −0.0721755 0.245807i
747747 −765.744 10706.5i −0.0375062 0.524405i
748748 230.295 + 3219.95i 0.0112572 + 0.157397i
749749 −2736.63 9320.10i −0.133504 0.454672i
750750 15282.1 + 39258.2i 0.744032 + 1.91134i
751751 3335.31 + 5189.84i 0.162060 + 0.252170i 0.912781 0.408449i 0.133930π-0.133930\pi
−0.750721 + 0.660619i 0.770294π0.770294\pi
752752 −3675.88 6731.88i −0.178252 0.326444i
753753 −17073.6 + 22807.6i −0.826290 + 1.10379i
754754 7649.10 + 3493.23i 0.369448 + 0.168721i
755755 22081.8 8355.56i 1.06442 0.402768i
756756 25722.0 40024.3i 1.23744 1.92549i
757757 −10418.4 745.138i −0.500215 0.0357761i −0.181047 0.983474i 0.557949π-0.557949\pi
−0.319168 + 0.947698i 0.603403π0.603403\pi
758758 −20509.5 20509.5i −0.982769 0.982769i
759759 −761.969 2266.27i −0.0364397 0.108380i
760760 26057.7 + 7517.21i 1.24370 + 0.358786i
761761 −6025.07 6953.30i −0.287002 0.331218i 0.593880 0.804553i 0.297595π-0.297595\pi
−0.880882 + 0.473336i 0.843050π0.843050\pi
762762 −4095.67 18827.5i −0.194712 0.895076i
763763 −45832.8 61225.4i −2.17465 2.90499i
764764 −18657.9 + 40855.2i −0.883535 + 1.93467i
765765 −8877.75 1233.49i −0.419576 0.0582967i
766766 −4951.59 + 16863.6i −0.233562 + 0.795438i
767767 799.794 + 173.985i 0.0376518 + 0.00819064i
768768 −42473.2 15841.7i −1.99560 0.744319i
769769 −16609.4 + 4876.97i −0.778871 + 0.228697i −0.646919 0.762559i 0.723943π-0.723943\pi
−0.131952 + 0.991256i 0.542125π0.542125\pi
770770 −1358.13 + 6388.93i −0.0635632 + 0.299014i
771771 −10027.8 + 11572.7i −0.468406 + 0.540569i
772772 −31290.5 17085.9i −1.45877 0.796548i
773773 −4196.88 + 11252.3i −0.195280 + 0.523565i −0.997276 0.0737641i 0.976499π-0.976499\pi
0.801996 + 0.597330i 0.203772π0.203772\pi
774774 −14975.9 + 9624.44i −0.695476 + 0.446955i
775775 −22343.8 + 19735.1i −1.03563 + 0.914717i
776776 −37620.4 + 5409.00i −1.74033 + 0.250221i
777777 65741.1 24520.1i 3.03532 1.13212i
778778 −27343.7 + 20469.3i −1.26005 + 0.943263i
779779 1805.42 + 1160.28i 0.0830373 + 0.0533648i
780780 2531.94 6887.95i 0.116228 0.316190i
781781 486.115i 0.0222722i
782782 −33073.9 + 3657.85i −1.51243 + 0.167269i
783783 15991.0 15991.0i 0.729849 0.729849i
784784 26639.7 23083.5i 1.21355 1.05154i
785785 23990.1 + 27422.2i 1.09075 + 1.24680i
786786 −10283.6 + 71524.1i −0.466672 + 3.24578i
787787 −208.082 557.888i −0.00942478 0.0252688i 0.932152 0.362067i 0.117929π-0.117929\pi
−0.941577 + 0.336798i 0.890656π0.890656\pi
788788 24549.7 + 18377.7i 1.10983 + 0.830809i
789789 −5158.07 1514.55i −0.232741 0.0683388i
790790 −2070.86 6930.96i −0.0932632 0.312142i
791791 7632.62 + 16713.1i 0.343091 + 0.751264i
792792 689.795 1263.26i 0.0309480 0.0566770i
793793 −1279.90 + 91.5400i −0.0573146 + 0.00409922i
794794 41692.3 + 36126.6i 1.86348 + 1.61471i
795795 7800.16 + 7726.54i 0.347979 + 0.344694i
796796 −46207.8 + 21102.4i −2.05753 + 0.939641i
797797 −3661.44 + 16831.4i −0.162729 + 0.748053i 0.821365 + 0.570403i 0.193213π0.193213\pi
−0.984094 + 0.177650i 0.943151π0.943151\pi
798798 −69224.0 + 37799.2i −3.07081 + 1.67679i
799799 1792.27 + 12465.5i 0.0793567 + 0.551938i
800800 2023.07 9743.89i 0.0894081 0.430623i
801801 −8019.31 1153.00i −0.353743 0.0508606i
802802 24573.0 5345.54i 1.08193 0.235359i
803803 −67.5824 + 944.925i −0.00297003 + 0.0415264i
804804 −46768.7 −2.05150
805805 −43151.8 7438.81i −1.88932 0.325694i
806806 7984.77 0.348947
807807 −1261.07 + 17632.1i −0.0550084 + 0.769118i
808808 23767.7 5170.34i 1.03483 0.225114i
809809 15512.6 + 2230.37i 0.674156 + 0.0969291i 0.470887 0.882194i 0.343934π-0.343934\pi
0.203270 + 0.979123i 0.434843π0.434843\pi
810810 −36956.7 31717.6i −1.60312 1.37586i
811811 −269.932 1877.42i −0.0116876 0.0812887i 0.983143 0.182839i 0.0585288π-0.0585288\pi
−0.994830 + 0.101550i 0.967620π0.967620\pi
812812 116480. 63602.9i 5.03405 2.74880i
813813 9241.67 42483.3i 0.398671 1.83266i
814814 −4693.26 + 2143.34i −0.202087 + 0.0922899i
815815 −6077.94 + 28.8198i −0.261228 + 0.00123867i
816816 −11536.3 9996.25i −0.494915 0.428847i
817817 −21518.5 + 1539.04i −0.921467 + 0.0659046i
818818 13377.7 24499.5i 0.571811 1.04719i
819819 1312.35 + 2873.64i 0.0559916 + 0.122605i
820820 −2302.07 + 4263.88i −0.0980389 + 0.181587i
821821 25546.8 + 7501.22i 1.08598 + 0.318872i 0.775268 0.631632i 0.217615π-0.217615\pi
0.310711 + 0.950504i 0.399433π0.399433\pi
822822 −14644.5 10962.8i −0.621395 0.465170i
823823 4199.60 + 11259.6i 0.177872 + 0.476894i 0.995036 0.0995108i 0.0317278π-0.0317278\pi
−0.817164 + 0.576405i 0.804455π0.804455\pi
824824 −7301.46 + 50782.8i −0.308688 + 2.14697i
825825 2547.51 + 922.750i 0.107507 + 0.0389406i
826826 15010.8 13006.9i 0.632316 0.547905i
827827 1691.54 1691.54i 0.0711252 0.0711252i −0.670649 0.741775i 0.733984π-0.733984\pi
0.741775 + 0.670649i 0.233984π0.233984\pi
828828 18687.8 + 9283.30i 0.784355 + 0.389634i
829829 26586.5i 1.11386i −0.830560 0.556929i 0.811979π-0.811979\pi
0.830560 0.556929i 0.188021π-0.188021\pi
830830 42386.1 + 15580.7i 1.77258 + 0.651581i
831831 26251.9 + 16871.1i 1.09587 + 0.704274i
832832 −3855.53 + 2886.22i −0.160657 + 0.120266i
833833 −54227.8 + 20225.9i −2.25556 + 0.841280i
834834 −23564.1 + 3388.01i −0.978368 + 0.140668i
835835 −463.630 + 728.999i −0.0192151 + 0.0302132i
836836 3173.21 2039.30i 0.131277 0.0843669i
837837 7504.31 20119.8i 0.309901 0.830876i
838838 15621.5 + 8530.00i 0.643958 + 0.351628i
839839 24456.4 28224.2i 1.00635 1.16139i 0.0194933 0.999810i 0.493795π-0.493795\pi
0.986859 0.161583i 0.0516598π-0.0516598\pi
840840 −44849.3 69064.7i −1.84220 2.83685i
841841 37126.2 10901.2i 1.52225 0.446974i
842842 −45209.9 16862.4i −1.85040 0.690163i
843843 16379.7 + 3563.18i 0.669212 + 0.145578i
844844 1772.60 6036.92i 0.0722931 0.246208i
845845 14483.0 + 19156.9i 0.589620 + 0.779904i
846846 5044.26 11045.4i 0.204995 0.448875i
847847 −28069.8 37496.9i −1.13871 1.52114i
848848 1272.28 + 5848.59i 0.0515217 + 0.236841i
849849 −18356.4 21184.4i −0.742038 0.856357i
850850 20085.2 31914.7i 0.810491 1.28784i
851851 −15577.0 30883.2i −0.627463 1.24402i
852852 9371.70 + 9371.70i 0.376842 + 0.376842i
853853 14713.2 + 1052.31i 0.590586 + 0.0422395i 0.363434 0.931620i 0.381604π-0.381604\pi
0.227152 + 0.973859i 0.427059π0.427059\pi
854854 −16834.5 + 26194.9i −0.674548 + 1.04962i
855855 3706.42 + 9795.21i 0.148254 + 0.391800i
856856 −8191.56 3740.96i −0.327082 0.149373i
857857 −5194.10 + 6938.50i −0.207033 + 0.276563i −0.892024 0.451988i 0.850715π-0.850715\pi
0.684991 + 0.728551i 0.259806π0.259806\pi
858858 −347.798 636.945i −0.0138387 0.0253437i
859859 12375.1 + 19256.1i 0.491541 + 0.764853i 0.995075 0.0991221i 0.0316034π-0.0316034\pi
−0.503534 + 0.863975i 0.667967π0.667967\pi
860860 −7160.70 48180.9i −0.283928 1.91041i
861861 −1835.92 6252.57i −0.0726690 0.247488i
862862 −4320.05 60402.3i −0.170698 2.38667i
863863 −1033.16 14445.5i −0.0407522 0.569791i −0.976276 0.216528i 0.930527π-0.930527\pi
0.935524 0.353263i 0.114928π-0.114928\pi
864864 2019.57 + 6878.04i 0.0795224 + 0.270828i
865865 3070.67 + 20661.0i 0.120700 + 0.812134i
866866 −21946.0 34148.6i −0.861148 1.33997i
867867 −2826.10 5175.62i −0.110703 0.202738i
868868 75519.9 100883.i 2.95313 3.94491i
869869 −423.199 193.269i −0.0165202 0.00754452i
870870 −29956.9 79169.1i −1.16740 3.08516i
871871 −1887.12 + 2936.42i −0.0734130 + 0.114233i
872872 −70723.2 5058.23i −2.74655 0.196437i
873873 −10378.3 10378.3i −0.402353 0.402353i
874874 22272.2 + 31870.2i 0.861978 + 1.23344i
875875 37035.9 33025.8i 1.43091 1.27597i
876876 −16914.1 19519.9i −0.652367 0.752872i
877877 5079.38 + 23349.5i 0.195574 + 0.899039i 0.965398 + 0.260782i 0.0839805π0.0839805\pi
−0.769824 + 0.638257i 0.779656π0.779656\pi
878878 34079.1 + 45524.4i 1.30993 + 1.74986i
879879 −7319.42 + 16027.3i −0.280862 + 0.615002i
880880 890.787 + 1178.27i 0.0341232 + 0.0451356i
881881 −1114.89 + 3796.95i −0.0426350 + 0.145202i −0.978060 0.208324i 0.933199π-0.933199\pi
0.935425 + 0.353526i 0.115017π0.115017\pi
882882 54529.0 + 11862.0i 2.08173 + 0.452853i
883883 −14009.5 5225.26i −0.533926 0.199144i 0.0680157 0.997684i 0.478333π-0.478333\pi
−0.601941 + 0.798540i 0.705606π0.705606\pi
884884 −6302.73 + 1850.65i −0.239801 + 0.0704118i
885885 −4487.29 6910.09i −0.170439 0.262463i
886886 31127.8 35923.4i 1.18032 1.36216i
887887 −36599.7 19984.9i −1.38545 0.756514i −0.398445 0.917192i 0.630450π-0.630450\pi
−0.987007 + 0.160678i 0.948632π0.948632\pi
888888 22732.4 60947.9i 0.859065 2.30324i
889889 −19092.7 + 12270.1i −0.720302 + 0.462910i
890890 18291.8 28761.6i 0.688925 1.08325i
891891 −3100.38 + 445.767i −0.116573 + 0.0167607i
892892 −28319.4 + 10562.6i −1.06301 + 0.396481i
893893 11780.2 8818.56i 0.441445 0.330461i
894894 39459.4 + 25359.0i 1.47620 + 0.948693i
895895 1044.21 + 383.841i 0.0389991 + 0.0143356i
896896 94256.9i 3.51440i
897897 4176.53 2495.30i 0.155463 0.0928824i
898898 −49142.1 + 49142.1i −1.82616 + 1.82616i
899899 45269.5 39226.2i 1.67944 1.45525i
900900 −21415.6 + 10026.7i −0.793171 + 0.371359i
901901 1398.60 9727.50i 0.0517139 0.359678i
902902 167.459 + 448.974i 0.00618156 + 0.0165734i
903903 52440.7 + 39256.6i 1.93258 + 1.44671i
904904 16343.9 + 4799.00i 0.601316 + 0.176562i
905905 −837.102 + 1550.47i −0.0307472 + 0.0569497i
906906 26443.7 + 57903.6i 0.969682 + 2.12331i
907907 13532.0 24782.0i 0.495393 0.907245i −0.503667 0.863898i 0.668016π-0.668016\pi
0.999060 0.0433471i 0.0138021π-0.0138021\pi
908908 −81236.5 + 5810.15i −2.96908 + 0.212353i
909909 7098.73 + 6151.08i 0.259021 + 0.224443i
910910 −13290.8 + 63.0210i −0.484160 + 0.00229574i
911911 −30513.4 + 13935.0i −1.10972 + 0.506792i −0.884041 0.467409i 0.845187π-0.845187\pi
−0.225679 + 0.974202i 0.572460π0.572460\pi
912912 −3791.37 + 17428.7i −0.137659 + 0.632808i
913913 2549.17 1391.95i 0.0924043 0.0504565i
914914 6494.95 + 45173.4i 0.235048 + 1.63479i
915915 9801.79 + 8412.26i 0.354139 + 0.303935i
916916 57861.1 + 8319.17i 2.08710 + 0.300080i
917917 83169.3 18092.4i 2.99508 0.651541i
918918 −1937.75 + 27093.3i −0.0696680 + 0.974087i
919919 6426.85 0.230688 0.115344 0.993326i 0.463203π-0.463203\pi
0.115344 + 0.993326i 0.463203π0.463203\pi
920920 −31410.1 + 25718.0i −1.12561 + 0.921628i
921921 −2990.21 −0.106982
922922 −5294.58 + 74027.9i −0.189119 + 2.64423i
923923 966.562 210.263i 0.0344689 0.00749824i
924924 −11336.9 1630.00i −0.403632 0.0580336i
925925 38379.1 + 7968.45i 1.36421 + 0.283244i
926926 −156.268 1086.87i −0.00554568 0.0385711i
927927 −17388.9 + 9495.05i −0.616101 + 0.336417i
928928 −4250.44 + 19539.0i −0.150353 + 0.691162i
929929 −12924.8 + 5902.56i −0.456458 + 0.208457i −0.630356 0.776306i 0.717091π-0.717091\pi
0.173898 + 0.984764i 0.444364π0.444364\pi
930930 −57103.9 56564.9i −2.01345 1.99445i
931931 51109.2 + 44286.4i 1.79918 + 1.55900i
932932 48961.9 3501.82i 1.72082 0.123075i
933933 17119.0 31351.1i 0.600697 1.10010i
934934 −26839.9 58771.2i −0.940287 2.05894i
935935 −694.306 2323.77i −0.0242848 0.0812786i
936936 2810.16 + 825.137i 0.0981334 + 0.0288146i
937937 −21608.0 16175.6i −0.753366 0.563963i 0.152108 0.988364i 0.451394π-0.451394\pi
−0.905474 + 0.424401i 0.860485π0.860485\pi
938938 29600.7 + 79362.5i 1.03038 + 2.76256i
939939 −7704.67 + 53587.1i −0.267766 + 1.86235i
940940 21876.7 + 25006.5i 0.759085 + 0.867683i
941941 22759.0 19720.7i 0.788439 0.683186i −0.164491 0.986379i 0.552598π-0.552598\pi
0.952929 + 0.303193i 0.0980526π0.0980526\pi
942942 −69462.6 + 69462.6i −2.40256 + 2.40256i
943943 −2964.16 + 1238.40i −0.102361 + 0.0427654i
944944 4491.69i 0.154864i
945945 −12332.3 + 33549.1i −0.424517 + 1.15487i
946946 −4052.29 2604.25i −0.139272 0.0895046i
947947 31807.8 23811.0i 1.09146 0.817058i 0.107281 0.994229i 0.465785π-0.465785\pi
0.984180 + 0.177171i 0.0566945π0.0566945\pi
948948 11884.7 4432.78i 0.407171 0.151867i
949949 −1908.06 + 274.338i −0.0652669 + 0.00938397i
950950 −43977.1 2726.40i −1.50190 0.0931115i
951951 −32669.8 + 20995.6i −1.11398 + 0.715909i
952952 −25759.5 + 69063.9i −0.876965 + 2.35123i
953953 −20340.5 11106.7i −0.691388 0.377526i 0.0948149 0.995495i 0.469774π-0.469774\pi
−0.786203 + 0.617969i 0.787956π0.787956\pi
954954 −6205.20 + 7161.18i −0.210588 + 0.243031i
955955 7016.22 33005.7i 0.237738 1.11837i
956956 59242.2 17395.1i 2.00422 0.588491i
957957 −5100.91 1902.54i −0.172298 0.0642637i
958958 40994.5 + 8917.81i 1.38254 + 0.300753i
959959 −6070.66 + 20674.8i −0.204413 + 0.696166i
960960 48019.5 + 6671.92i 1.61440 + 0.224308i
961961 11252.4 24639.3i 0.377711 0.827072i
962962 −6291.69 8404.71i −0.210865 0.281683i
963963 −739.213 3398.11i −0.0247360 0.113710i
964964 −51295.0 59197.5i −1.71380 1.97783i
965965 25734.9 + 7424.10i 0.858484 + 0.247658i
966966 12262.2 117422.i 0.408416 3.91098i
967967 10916.7 + 10916.7i 0.363039 + 0.363039i 0.864931 0.501891i 0.167362π-0.167362\pi
−0.501891 + 0.864931i 0.667362π0.667362\pi
968968 −43313.7 3097.86i −1.43818 0.102861i
969969 15833.1 24636.8i 0.524905 0.816768i
970970 57753.0 21853.3i 1.91169 0.723367i
971971 −8345.62 3811.32i −0.275822 0.125964i 0.272702 0.962099i 0.412083π-0.412083\pi
−0.548524 + 0.836135i 0.684810π0.684810\pi
972972 29496.7 39402.9i 0.973360 1.30026i
973973 13438.9 + 24611.5i 0.442786 + 0.810902i
974974 −7882.49 12265.4i −0.259313 0.403499i
975975 −732.846 + 5464.44i −0.0240716 + 0.179489i
976976 1983.86 + 6756.40i 0.0650633 + 0.221585i
977977 3812.57 + 53306.7i 0.124846 + 1.74558i 0.545276 + 0.838256i 0.316425π0.316425\pi
−0.420430 + 0.907325i 0.638121π0.638121\pi
978978 −1169.06 16345.6i −0.0382234 0.534434i
979979 −617.624 2103.43i −0.0201628 0.0686680i
980980 −90925.0 + 122670.i −2.96377 + 3.99851i
981981 −14803.2 23034.2i −0.481783 0.749669i
982982 1804.43 + 3304.57i 0.0586372 + 0.107386i
983983 −7774.92 + 10386.1i −0.252270 + 0.336993i −0.908743 0.417356i 0.862957π-0.862957\pi
0.656473 + 0.754350i 0.272048π0.272048\pi
984984 −5495.47 2509.70i −0.178038 0.0813071i
985985 −21002.4 9471.36i −0.679382 0.306378i
986986 −40963.5 + 63740.5i −1.32307 + 2.05873i
987987 −44568.3 3187.59i −1.43731 0.102798i
988988 5427.35 + 5427.35i 0.174764 + 0.174764i
989989 16393.3 27822.4i 0.527074 0.894540i
990990 −648.165 + 2246.80i −0.0208081 + 0.0721294i
991991 −915.995 1057.12i −0.0293618 0.0338853i 0.740879 0.671639i 0.234409π-0.234409\pi
−0.770241 + 0.637753i 0.779864π0.779864\pi
992992 4036.01 + 18553.2i 0.129177 + 0.593816i
993993 29212.9 + 39023.8i 0.933577 + 1.24711i
994994 9971.48 21834.5i 0.318185 0.696729i
995995 30443.1 23015.5i 0.969962 0.733306i
996996 −22309.7 + 75979.8i −0.709748 + 2.41718i
997997 −29589.0 6436.69i −0.939913 0.204466i −0.283590 0.958946i 0.591525π-0.591525\pi
−0.656323 + 0.754480i 0.727889π0.727889\pi
998998 −67276.3 25092.8i −2.13386 0.795890i
999999 −27091.1 + 7954.67i −0.857982 + 0.251926i
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 115.4.l.a.102.4 yes 680
5.3 odd 4 inner 115.4.l.a.33.31 yes 680
23.7 odd 22 inner 115.4.l.a.7.31 680
115.53 even 44 inner 115.4.l.a.53.4 yes 680
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.4.l.a.7.31 680 23.7 odd 22 inner
115.4.l.a.33.31 yes 680 5.3 odd 4 inner
115.4.l.a.53.4 yes 680 115.53 even 44 inner
115.4.l.a.102.4 yes 680 1.1 even 1 trivial