Properties

Label 95.4.e.c.26.7
Level 9595
Weight 44
Character 95.26
Analytic conductor 5.6055.605
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,4,Mod(11,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.11");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 95=519 95 = 5 \cdot 19
Weight: k k == 4 4
Character orbit: [χ][\chi] == 95.e (of order 33, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.605181450555.60518145055
Analytic rank: 00
Dimension: 2020
Relative dimension: 1010 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x203x19+66x18125x17+2555x163995x15+60229x14++2336368896 x^{20} - 3 x^{19} + 66 x^{18} - 125 x^{17} + 2555 x^{16} - 3995 x^{15} + 60229 x^{14} + \cdots + 2336368896 Copy content Toggle raw display
Coefficient ring: Z[a1,,a19]\Z[a_1, \ldots, a_{19}]
Coefficient ring index: 32 3^{2}
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 26.7
Root 1.09984+1.90498i-1.09984 + 1.90498i of defining polynomial
Character χ\chi == 95.26
Dual form 95.4.e.c.11.7

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.09984+1.90498i)q2+(4.377567.58215i)q3+(1.580712.73786i)q4+(2.50000+4.33013i)q5+(9.6292216.6783i)q633.5680q7+24.5515q8+(24.8260+43.0000i)q9+(5.49920+9.52489i)q1052.8293q1127.6785q12+(23.589640.8584i)q13+(36.919463.9463i)q14+(21.887837.9108i)q15+(14.3571+24.8672i)q16+(19.330933.4821i)q17109.219q18+(57.7308+59.3814i)q19+15.8071q20+(146.946+254.518i)q21+(58.1037100.639i)q22+(94.9663164.486i)q23+(107.476186.153i)q24+(12.5000+21.6506i)q25+103.779q26+198.322q27+(53.0611+91.9045i)q28+(51.293888.8434i)q29+96.2922q30+62.8629q31+(66.6251115.398i)q32+(231.263+400.560i)q33+(42.521873.6500i)q34+(83.9199145.354i)q35+(78.4853+135.941i)q36121.050q37+(176.61544.6659i)q38413.060q39+(61.3788+106.311i)q40+(18.6460+32.2958i)q41+(323.234+559.857i)q42+(92.8180160.765i)q43+(83.5076+144.639i)q44248.260q45+417.791q46+(142.854+247.430i)q47+(125.698217.715i)q48+783.809q4954.9920q50+(169.245+293.140i)q51+(74.5765129.170i)q52+(139.396241.441i)q53+(218.122+377.798i)q54+(132.073228.758i)q55824.145q56+(702.959+177.778i)q57+225.660q58+(49.5587+85.8381i)q59+(69.1963119.852i)q60+(192.118332.758i)q61+(69.1391+119.752i)q62+(833.3601443.42i)q63+522.821q64+235.896q65+(508.705+881.103i)q66+(275.126476.532i)q67122.226q681662.88q69+(184.597319.731i)q70+(446.673773.660i)q71+(609.517+1055.71i)q72+(97.1143+168.207i)q73+(133.135230.597i)q74+218.878q75+(71.3227+251.924i)q76+1773.37q77+(454.299786.869i)q78+(318.203+551.144i)q79+(71.7854+124.336i)q80+(197.861342.705i)q81+(41.0152+71.0405i)q82465.318q83+929.112q84+(96.6546167.411i)q85+(204.170353.632i)q86898.166q871297.04q88+(617.121+1068.88i)q89+(273.047472.930i)q90+(791.855+1371.53i)q91+(300.228520.010i)q92+(275.186476.636i)q93628.464q94+(401.456101.528i)q951166.62q96+(355.282615.367i)q97+(862.064+1493.14i)q98+(1311.542271.66i)q99+O(q100)q+(1.09984 + 1.90498i) q^{2} +(-4.37756 - 7.58215i) q^{3} +(1.58071 - 2.73786i) q^{4} +(2.50000 + 4.33013i) q^{5} +(9.62922 - 16.6783i) q^{6} -33.5680 q^{7} +24.5515 q^{8} +(-24.8260 + 43.0000i) q^{9} +(-5.49920 + 9.52489i) q^{10} -52.8293 q^{11} -27.6785 q^{12} +(23.5896 - 40.8584i) q^{13} +(-36.9194 - 63.9463i) q^{14} +(21.8878 - 37.9108i) q^{15} +(14.3571 + 24.8672i) q^{16} +(-19.3309 - 33.4821i) q^{17} -109.219 q^{18} +(-57.7308 + 59.3814i) q^{19} +15.8071 q^{20} +(146.946 + 254.518i) q^{21} +(-58.1037 - 100.639i) q^{22} +(94.9663 - 164.486i) q^{23} +(-107.476 - 186.153i) q^{24} +(-12.5000 + 21.6506i) q^{25} +103.779 q^{26} +198.322 q^{27} +(-53.0611 + 91.9045i) q^{28} +(51.2938 - 88.8434i) q^{29} +96.2922 q^{30} +62.8629 q^{31} +(66.6251 - 115.398i) q^{32} +(231.263 + 400.560i) q^{33} +(42.5218 - 73.6500i) q^{34} +(-83.9199 - 145.354i) q^{35} +(78.4853 + 135.941i) q^{36} -121.050 q^{37} +(-176.615 - 44.6659i) q^{38} -413.060 q^{39} +(61.3788 + 106.311i) q^{40} +(18.6460 + 32.2958i) q^{41} +(-323.234 + 559.857i) q^{42} +(-92.8180 - 160.765i) q^{43} +(-83.5076 + 144.639i) q^{44} -248.260 q^{45} +417.791 q^{46} +(-142.854 + 247.430i) q^{47} +(125.698 - 217.715i) q^{48} +783.809 q^{49} -54.9920 q^{50} +(-169.245 + 293.140i) q^{51} +(-74.5765 - 129.170i) q^{52} +(139.396 - 241.441i) q^{53} +(218.122 + 377.798i) q^{54} +(-132.073 - 228.758i) q^{55} -824.145 q^{56} +(702.959 + 177.778i) q^{57} +225.660 q^{58} +(49.5587 + 85.8381i) q^{59} +(-69.1963 - 119.852i) q^{60} +(192.118 - 332.758i) q^{61} +(69.1391 + 119.752i) q^{62} +(833.360 - 1443.42i) q^{63} +522.821 q^{64} +235.896 q^{65} +(-508.705 + 881.103i) q^{66} +(275.126 - 476.532i) q^{67} -122.226 q^{68} -1662.88 q^{69} +(184.597 - 319.731i) q^{70} +(-446.673 - 773.660i) q^{71} +(-609.517 + 1055.71i) q^{72} +(97.1143 + 168.207i) q^{73} +(-133.135 - 230.597i) q^{74} +218.878 q^{75} +(71.3227 + 251.924i) q^{76} +1773.37 q^{77} +(-454.299 - 786.869i) q^{78} +(318.203 + 551.144i) q^{79} +(-71.7854 + 124.336i) q^{80} +(-197.861 - 342.705i) q^{81} +(-41.0152 + 71.0405i) q^{82} -465.318 q^{83} +929.112 q^{84} +(96.6546 - 167.411i) q^{85} +(204.170 - 353.632i) q^{86} -898.166 q^{87} -1297.04 q^{88} +(-617.121 + 1068.88i) q^{89} +(-273.047 - 472.930i) q^{90} +(-791.855 + 1371.53i) q^{91} +(-300.228 - 520.010i) q^{92} +(-275.186 - 476.636i) q^{93} -628.464 q^{94} +(-401.456 - 101.528i) q^{95} -1166.62 q^{96} +(-355.282 - 615.367i) q^{97} +(862.064 + 1493.14i) q^{98} +(1311.54 - 2271.66i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q3q25q343q4+50q5+9q6+6q7+96q897q9+15q1036q11+186q12+14q13+68q14+25q15+9q16144q1722q18+96q19++2723q99+O(q100) 20 q - 3 q^{2} - 5 q^{3} - 43 q^{4} + 50 q^{5} + 9 q^{6} + 6 q^{7} + 96 q^{8} - 97 q^{9} + 15 q^{10} - 36 q^{11} + 186 q^{12} + 14 q^{13} + 68 q^{14} + 25 q^{15} + 9 q^{16} - 144 q^{17} - 22 q^{18} + 96 q^{19}+ \cdots + 2723 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/95Z)×\left(\mathbb{Z}/95\mathbb{Z}\right)^\times.

nn 2121 7777
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) 11

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.09984 + 1.90498i 0.388852 + 0.673511i 0.992295 0.123894i 0.0395384π-0.0395384\pi
−0.603443 + 0.797406i 0.706205π0.706205\pi
33 −4.37756 7.58215i −0.842462 1.45919i −0.887808 0.460215i 0.847772π-0.847772\pi
0.0453461 0.998971i 0.485561π-0.485561\pi
44 1.58071 2.73786i 0.197588 0.342233i
55 2.50000 + 4.33013i 0.223607 + 0.387298i
66 9.62922 16.6783i 0.655186 1.13481i
77 −33.5680 −1.81250 −0.906250 0.422742i 0.861068π-0.861068\pi
−0.906250 + 0.422742i 0.861068π0.861068\pi
88 24.5515 1.08503
99 −24.8260 + 43.0000i −0.919483 + 1.59259i
1010 −5.49920 + 9.52489i −0.173900 + 0.301203i
1111 −52.8293 −1.44806 −0.724029 0.689770i 0.757712π-0.757712\pi
−0.724029 + 0.689770i 0.757712π0.757712\pi
1212 −27.6785 −0.665842
1313 23.5896 40.8584i 0.503275 0.871699i −0.496717 0.867912i 0.665461π-0.665461\pi
0.999993 0.00378625i 0.00120520π-0.00120520\pi
1414 −36.9194 63.9463i −0.704794 1.22074i
1515 21.8878 37.9108i 0.376760 0.652568i
1616 14.3571 + 24.8672i 0.224330 + 0.388550i
1717 −19.3309 33.4821i −0.275790 0.477683i 0.694544 0.719450i 0.255606π-0.255606\pi
−0.970334 + 0.241767i 0.922273π0.922273\pi
1818 −109.219 −1.43017
1919 −57.7308 + 59.3814i −0.697071 + 0.717002i
2020 15.8071 0.176728
2121 146.946 + 254.518i 1.52696 + 2.64478i
2222 −58.1037 100.639i −0.563080 0.975283i
2323 94.9663 164.486i 0.860950 1.49121i −0.0100635 0.999949i 0.503203π-0.503203\pi
0.871013 0.491259i 0.163463π-0.163463\pi
2424 −107.476 186.153i −0.914100 1.58327i
2525 −12.5000 + 21.6506i −0.100000 + 0.173205i
2626 103.779 0.782799
2727 198.322 1.41359
2828 −53.0611 + 91.9045i −0.358129 + 0.620297i
2929 51.2938 88.8434i 0.328449 0.568890i −0.653755 0.756706i 0.726807π-0.726807\pi
0.982204 + 0.187816i 0.0601408π0.0601408\pi
3030 96.2922 0.586016
3131 62.8629 0.364210 0.182105 0.983279i 0.441709π-0.441709\pi
0.182105 + 0.983279i 0.441709π0.441709\pi
3232 66.6251 115.398i 0.368055 0.637490i
3333 231.263 + 400.560i 1.21993 + 2.11299i
3434 42.5218 73.6500i 0.214483 0.371496i
3535 −83.9199 145.354i −0.405287 0.701978i
3636 78.4853 + 135.941i 0.363358 + 0.629354i
3737 −121.050 −0.537851 −0.268925 0.963161i 0.586669π-0.586669\pi
−0.268925 + 0.963161i 0.586669π0.586669\pi
3838 −176.615 44.6659i −0.753966 0.190678i
3939 −413.060 −1.69596
4040 61.3788 + 106.311i 0.242621 + 0.420232i
4141 18.6460 + 32.2958i 0.0710248 + 0.123019i 0.899351 0.437228i 0.144040π-0.144040\pi
−0.828326 + 0.560247i 0.810706π0.810706\pi
4242 −323.234 + 559.857i −1.18752 + 2.05685i
4343 −92.8180 160.765i −0.329177 0.570151i 0.653172 0.757210i 0.273438π-0.273438\pi
−0.982349 + 0.187058i 0.940105π0.940105\pi
4444 −83.5076 + 144.639i −0.286119 + 0.495573i
4545 −248.260 −0.822410
4646 417.791 1.33913
4747 −142.854 + 247.430i −0.443348 + 0.767901i −0.997935 0.0642246i 0.979543π-0.979543\pi
0.554588 + 0.832125i 0.312876π0.312876\pi
4848 125.698 217.715i 0.377978 0.654677i
4949 783.809 2.28516
5050 −54.9920 −0.155541
5151 −169.245 + 293.140i −0.464686 + 0.804859i
5252 −74.5765 129.170i −0.198883 0.344475i
5353 139.396 241.441i 0.361274 0.625746i −0.626896 0.779103i 0.715675π-0.715675\pi
0.988171 + 0.153357i 0.0490084π0.0490084\pi
5454 218.122 + 377.798i 0.549678 + 0.952071i
5555 −132.073 228.758i −0.323795 0.560830i
5656 −824.145 −1.96663
5757 702.959 + 177.778i 1.63349 + 0.413111i
5858 225.660 0.510872
5959 49.5587 + 85.8381i 0.109356 + 0.189410i 0.915509 0.402296i 0.131788π-0.131788\pi
−0.806154 + 0.591706i 0.798455π0.798455\pi
6060 −69.1963 119.852i −0.148887 0.257879i
6161 192.118 332.758i 0.403249 0.698448i −0.590867 0.806769i 0.701214π-0.701214\pi
0.994116 + 0.108321i 0.0345475π0.0345475\pi
6262 69.1391 + 119.752i 0.141624 + 0.245300i
6363 833.360 1443.42i 1.66656 2.88657i
6464 522.821 1.02114
6565 235.896 0.450143
6666 −508.705 + 881.103i −0.948747 + 1.64328i
6767 275.126 476.532i 0.501672 0.868921i −0.498327 0.866989i 0.666052π-0.666052\pi
0.999998 0.00193131i 0.000614756π-0.000614756\pi
6868 −122.226 −0.217972
6969 −1662.88 −2.90127
7070 184.597 319.731i 0.315194 0.545931i
7171 −446.673 773.660i −0.746624 1.29319i −0.949432 0.313973i 0.898340π-0.898340\pi
0.202808 0.979219i 0.434993π-0.434993\pi
7272 −609.517 + 1055.71i −0.997670 + 1.72802i
7373 97.1143 + 168.207i 0.155704 + 0.269687i 0.933315 0.359059i 0.116902π-0.116902\pi
−0.777611 + 0.628745i 0.783569π0.783569\pi
7474 −133.135 230.597i −0.209144 0.362249i
7575 218.878 0.336985
7676 71.3227 + 251.924i 0.107648 + 0.380232i
7777 1773.37 2.62460
7878 −454.299 786.869i −0.659478 1.14225i
7979 318.203 + 551.144i 0.453173 + 0.784919i 0.998581 0.0532519i 0.0169586π-0.0169586\pi
−0.545408 + 0.838171i 0.683625π0.683625\pi
8080 −71.7854 + 124.336i −0.100323 + 0.173765i
8181 −197.861 342.705i −0.271414 0.470104i
8282 −41.0152 + 71.0405i −0.0552363 + 0.0956720i
8383 −465.318 −0.615365 −0.307683 0.951489i 0.599554π-0.599554\pi
−0.307683 + 0.951489i 0.599554π0.599554\pi
8484 929.112 1.20684
8585 96.6546 167.411i 0.123337 0.213626i
8686 204.170 353.632i 0.256002 0.443409i
8787 −898.166 −1.10682
8888 −1297.04 −1.57119
8989 −617.121 + 1068.88i −0.734996 + 1.27305i 0.219728 + 0.975561i 0.429483π0.429483\pi
−0.954725 + 0.297490i 0.903850π0.903850\pi
9090 −273.047 472.930i −0.319796 0.553903i
9191 −791.855 + 1371.53i −0.912187 + 1.57995i
9292 −300.228 520.010i −0.340227 0.589291i
9393 −275.186 476.636i −0.306833 0.531450i
9494 −628.464 −0.689586
9595 −401.456 101.528i −0.433563 0.109648i
9696 −1166.62 −1.24029
9797 −355.282 615.367i −0.371891 0.644135i 0.617965 0.786205i 0.287957π-0.287957\pi
−0.989857 + 0.142071i 0.954624π0.954624\pi
9898 862.064 + 1493.14i 0.888588 + 1.53908i
9999 1311.54 2271.66i 1.33146 2.30616i
100100 39.5176 + 68.4466i 0.0395176 + 0.0684466i
101101 −192.743 + 333.840i −0.189887 + 0.328894i −0.945212 0.326456i 0.894146π-0.894146\pi
0.755325 + 0.655350i 0.227479π0.227479\pi
102102 −744.567 −0.722776
103103 −237.487 −0.227187 −0.113594 0.993527i 0.536236π-0.536236\pi
−0.113594 + 0.993527i 0.536236π0.536236\pi
104104 579.161 1003.14i 0.546071 0.945823i
105105 −734.729 + 1272.59i −0.682878 + 1.18278i
106106 613.254 0.561929
107107 −150.931 −0.136365 −0.0681826 0.997673i 0.521720π-0.521720\pi
−0.0681826 + 0.997673i 0.521720π0.521720\pi
108108 313.488 542.977i 0.279309 0.483778i
109109 −197.545 342.158i −0.173590 0.300668i 0.766082 0.642743i 0.222204π-0.222204\pi
−0.939673 + 0.342075i 0.888870π0.888870\pi
110110 290.519 503.193i 0.251817 0.436160i
111111 529.903 + 917.819i 0.453119 + 0.784825i
112112 −481.938 834.742i −0.406597 0.704247i
113113 −1310.50 −1.09099 −0.545495 0.838114i 0.683658π-0.683658\pi
−0.545495 + 0.838114i 0.683658π0.683658\pi
114114 434.478 + 1534.65i 0.356953 + 1.26082i
115115 949.663 0.770057
116116 −162.161 280.871i −0.129795 0.224812i
117117 1171.27 + 2028.70i 0.925506 + 1.60302i
118118 −109.013 + 188.816i −0.0850464 + 0.147305i
119119 648.900 + 1123.93i 0.499870 + 0.865801i
120120 537.379 930.767i 0.408798 0.708059i
121121 1459.93 1.09687
122122 845.196 0.627217
123123 163.248 282.754i 0.119671 0.207277i
124124 99.3678 172.110i 0.0719637 0.124645i
125125 −125.000 −0.0894427
126126 3666.25 2.59219
127127 −954.294 + 1652.89i −0.666771 + 1.15488i 0.312031 + 0.950072i 0.398991π0.398991\pi
−0.978802 + 0.204809i 0.934343π0.934343\pi
128128 42.0185 + 72.7782i 0.0290152 + 0.0502558i
129129 −812.632 + 1407.52i −0.554638 + 0.960661i
130130 259.448 + 449.377i 0.175039 + 0.303177i
131131 −620.371 1074.51i −0.413756 0.716647i 0.581541 0.813517i 0.302450π-0.302450\pi
−0.995297 + 0.0968702i 0.969117π0.969117\pi
132132 1462.24 0.964177
133133 1937.91 1993.31i 1.26344 1.29957i
134134 1210.38 0.780304
135135 495.804 + 858.757i 0.316089 + 0.547482i
136136 −474.604 822.038i −0.299242 0.518303i
137137 −390.802 + 676.889i −0.243712 + 0.422121i −0.961769 0.273863i 0.911698π-0.911698\pi
0.718057 + 0.695984i 0.245032π0.245032\pi
138138 −1828.90 3167.75i −1.12816 1.95404i
139139 −245.493 + 425.206i −0.149802 + 0.259464i −0.931154 0.364626i 0.881197π-0.881197\pi
0.781352 + 0.624090i 0.214530π0.214530\pi
140140 −530.611 −0.320320
141141 2501.40 1.49401
142142 982.537 1701.80i 0.580653 1.00572i
143143 −1246.22 + 2158.52i −0.728772 + 1.26227i
144144 −1425.72 −0.825069
145145 512.938 0.293774
146146 −213.620 + 370.001i −0.121091 + 0.209736i
147147 −3431.17 5942.96i −1.92516 3.33447i
148148 −191.344 + 331.418i −0.106273 + 0.184070i
149149 −1150.47 1992.67i −0.632552 1.09561i −0.987028 0.160547i 0.948674π-0.948674\pi
0.354476 0.935065i 0.384659π-0.384659\pi
150150 240.731 + 416.958i 0.131037 + 0.226963i
151151 1088.03 0.586376 0.293188 0.956055i 0.405284π-0.405284\pi
0.293188 + 0.956055i 0.405284π0.405284\pi
152152 −1417.38 + 1457.90i −0.756346 + 0.777971i
153153 1919.64 1.01434
154154 1950.43 + 3378.24i 1.02058 + 1.76770i
155155 157.157 + 272.204i 0.0814399 + 0.141058i
156156 −652.926 + 1130.90i −0.335102 + 0.580413i
157157 944.065 + 1635.17i 0.479902 + 0.831215i 0.999734 0.0230538i 0.00733890π-0.00733890\pi
−0.519832 + 0.854268i 0.674006π0.674006\pi
158158 −699.945 + 1212.34i −0.352434 + 0.610434i
159159 −2440.86 −1.21744
160160 666.251 0.329199
161161 −3187.83 + 5521.48i −1.56047 + 2.70282i
162162 435.231 753.842i 0.211080 0.365601i
163163 2939.53 1.41253 0.706263 0.707950i 0.250380π-0.250380\pi
0.706263 + 0.707950i 0.250380π0.250380\pi
164164 117.895 0.0561347
165165 −1156.32 + 2002.80i −0.545570 + 0.944956i
166166 −511.776 886.421i −0.239286 0.414456i
167167 484.227 838.706i 0.224375 0.388629i −0.731757 0.681566i 0.761299π-0.761299\pi
0.956132 + 0.292937i 0.0946326π0.0946326\pi
168168 3607.74 + 6248.79i 1.65681 + 2.86967i
169169 −14.4393 25.0095i −0.00657226 0.0113835i
170170 425.218 0.191840
171171 −1120.17 3956.63i −0.500945 1.76942i
172172 −586.872 −0.260166
173173 −252.819 437.895i −0.111107 0.192443i 0.805110 0.593125i 0.202106π-0.202106\pi
−0.916217 + 0.400683i 0.868773π0.868773\pi
174174 −987.839 1710.99i −0.430390 0.745457i
175175 419.600 726.768i 0.181250 0.313934i
176176 −758.475 1313.72i −0.324842 0.562643i
177177 433.892 751.523i 0.184256 0.319141i
178178 −2714.94 −1.14322
179179 1467.79 0.612894 0.306447 0.951888i 0.400860π-0.400860\pi
0.306447 + 0.951888i 0.400860π0.400860\pi
180180 −392.427 + 679.703i −0.162499 + 0.281456i
181181 223.681 387.427i 0.0918569 0.159101i −0.816436 0.577436i 0.804053π-0.804053\pi
0.908292 + 0.418336i 0.137386π0.137386\pi
182182 −3483.66 −1.41882
183183 −3364.03 −1.35889
184184 2331.57 4038.39i 0.934160 1.61801i
185185 −302.625 524.162i −0.120267 0.208309i
186186 605.321 1048.45i 0.238625 0.413311i
187187 1021.24 + 1768.84i 0.399360 + 0.691713i
188188 451.619 + 782.227i 0.175201 + 0.303456i
189189 −6657.25 −2.56214
190190 −248.128 876.430i −0.0947427 0.334647i
191191 1763.01 0.667889 0.333944 0.942593i 0.391620π-0.391620\pi
0.333944 + 0.942593i 0.391620π0.391620\pi
192192 −2288.68 3964.11i −0.860267 1.49003i
193193 −1630.63 2824.34i −0.608164 1.05337i −0.991543 0.129780i 0.958573π-0.958573\pi
0.383379 0.923591i 0.374760π-0.374760\pi
194194 781.507 1353.61i 0.289221 0.500946i
195195 −1032.65 1788.60i −0.379228 0.656843i
196196 1238.97 2145.96i 0.451520 0.782056i
197197 3612.79 1.30660 0.653301 0.757098i 0.273384π-0.273384\pi
0.653301 + 0.757098i 0.273384π0.273384\pi
198198 5769.94 2.07097
199199 2332.57 4040.13i 0.830912 1.43918i −0.0664044 0.997793i 0.521153π-0.521153\pi
0.897316 0.441389i 0.145514π-0.145514\pi
200200 −306.894 + 531.556i −0.108503 + 0.187933i
201201 −4817.52 −1.69056
202202 −847.944 −0.295352
203203 −1721.83 + 2982.29i −0.595314 + 1.03111i
204204 535.052 + 926.737i 0.183633 + 0.318061i
205205 −93.2300 + 161.479i −0.0317633 + 0.0550156i
206206 −261.198 452.407i −0.0883422 0.153013i
207207 4715.27 + 8167.09i 1.58326 + 2.74228i
208208 1354.71 0.451598
209209 3049.88 3137.08i 1.00940 1.03826i
210210 −3232.34 −1.06215
211211 1021.28 + 1768.92i 0.333214 + 0.577143i 0.983140 0.182854i 0.0585336π-0.0585336\pi
−0.649926 + 0.759997i 0.725200π0.725200\pi
212212 −440.689 763.296i −0.142767 0.247280i
213213 −3910.67 + 6773.49i −1.25800 + 2.17893i
214214 −166.000 287.521i −0.0530258 0.0918435i
215215 464.090 803.827i 0.147212 0.254979i
216216 4869.10 1.53380
217217 −2110.18 −0.660131
218218 434.535 752.637i 0.135002 0.233830i
219219 850.247 1472.67i 0.262349 0.454401i
220220 −835.076 −0.255913
221221 −1824.04 −0.555194
222222 −1165.62 + 2018.91i −0.352392 + 0.610361i
223223 2894.33 + 5013.12i 0.869141 + 1.50540i 0.862876 + 0.505415i 0.168661π0.168661\pi
0.00626455 + 0.999980i 0.498006π0.498006\pi
224224 −2236.47 + 3873.68i −0.667100 + 1.15545i
225225 −620.651 1075.00i −0.183897 0.318518i
226226 −1441.34 2496.48i −0.424233 0.734794i
227227 1033.17 0.302087 0.151043 0.988527i 0.451737π-0.451737\pi
0.151043 + 0.988527i 0.451737π0.451737\pi
228228 1597.90 1643.59i 0.464139 0.477410i
229229 −5757.42 −1.66140 −0.830701 0.556719i 0.812060π-0.812060\pi
−0.830701 + 0.556719i 0.812060π0.812060\pi
230230 1044.48 + 1809.09i 0.299438 + 0.518642i
231231 −7763.04 13446.0i −2.21113 3.82979i
232232 1259.34 2181.24i 0.356378 0.617265i
233233 −1720.22 2979.51i −0.483671 0.837743i 0.516153 0.856497i 0.327364π-0.327364\pi
−0.999824 + 0.0187532i 0.994030π0.994030\pi
234234 −2576.42 + 4462.50i −0.719770 + 1.24668i
235235 −1428.54 −0.396542
236236 313.351 0.0864296
237237 2785.91 4825.33i 0.763562 1.32253i
238238 −1427.37 + 2472.28i −0.388751 + 0.673337i
239239 2674.35 0.723806 0.361903 0.932216i 0.382127π-0.382127\pi
0.361903 + 0.932216i 0.382127π0.382127\pi
240240 1256.98 0.338074
241241 −401.622 + 695.630i −0.107347 + 0.185931i −0.914695 0.404145i 0.867569π-0.867569\pi
0.807347 + 0.590076i 0.200902π0.200902\pi
242242 1605.69 + 2781.14i 0.426520 + 0.738755i
243243 945.044 1636.86i 0.249484 0.432119i
244244 −607.364 1051.99i −0.159355 0.276010i
245245 1959.52 + 3393.99i 0.510977 + 0.885038i
246246 718.186 0.186138
247247 1064.38 + 3759.57i 0.274190 + 0.968485i
248248 1543.38 0.395181
249249 2036.96 + 3528.12i 0.518422 + 0.897933i
250250 −137.480 238.122i −0.0347800 0.0602407i
251251 1659.00 2873.48i 0.417192 0.722598i −0.578463 0.815708i 0.696347π-0.696347\pi
0.995656 + 0.0931099i 0.0296808π0.0296808\pi
252252 −2634.59 4563.25i −0.658586 1.14071i
253253 −5017.00 + 8689.70i −1.24670 + 2.15936i
254254 −4198.28 −1.03710
255255 −1692.45 −0.415628
256256 1998.86 3462.12i 0.488002 0.845245i
257257 2277.91 3945.46i 0.552888 0.957629i −0.445177 0.895443i 0.646859π-0.646859\pi
0.998065 0.0621867i 0.0198074π-0.0198074\pi
258258 −3575.06 −0.862688
259259 4063.40 0.974855
260260 372.882 645.851i 0.0889430 0.154054i
261261 2546.84 + 4411.26i 0.604006 + 1.04617i
262262 1364.62 2363.59i 0.321780 0.557339i
263263 −1869.96 3238.87i −0.438429 0.759382i 0.559139 0.829074i 0.311132π-0.311132\pi
−0.997569 + 0.0696919i 0.977798π0.977798\pi
264264 5677.87 + 9834.35i 1.32367 + 2.29266i
265265 1393.96 0.323134
266266 5928.61 + 1499.34i 1.36656 + 0.345604i
267267 10805.9 2.47682
268268 −869.787 1506.52i −0.198249 0.343377i
269269 1075.30 + 1862.47i 0.243726 + 0.422145i 0.961773 0.273850i 0.0882971π-0.0882971\pi
−0.718047 + 0.695995i 0.754964π0.754964\pi
270270 −1090.61 + 1888.99i −0.245824 + 0.425779i
271271 −664.544 1151.02i −0.148960 0.258006i 0.781883 0.623425i 0.214259π-0.214259\pi
−0.930843 + 0.365418i 0.880926π0.880926\pi
272272 555.072 961.412i 0.123736 0.214317i
273273 13865.6 3.07393
274274 −1719.28 −0.379071
275275 660.366 1143.79i 0.144806 0.250811i
276276 −2628.53 + 4552.74i −0.573256 + 0.992909i
277277 −1576.45 −0.341948 −0.170974 0.985276i 0.554691π-0.554691\pi
−0.170974 + 0.985276i 0.554691π0.554691\pi
278278 −1080.01 −0.233003
279279 −1560.64 + 2703.10i −0.334885 + 0.580038i
280280 −2060.36 3568.65i −0.439751 0.761671i
281281 1690.19 2927.50i 0.358821 0.621495i −0.628944 0.777451i 0.716512π-0.716512\pi
0.987764 + 0.155956i 0.0498457π0.0498457\pi
282282 2751.14 + 4765.11i 0.580950 + 1.00623i
283283 −1207.16 2090.86i −0.253563 0.439184i 0.710941 0.703251i 0.248269π-0.248269\pi
−0.964504 + 0.264068i 0.914936π0.914936\pi
284284 −2824.23 −0.590097
285285 987.595 + 3488.35i 0.205263 + 0.725024i
286286 −5482.58 −1.13354
287287 −625.909 1084.11i −0.128732 0.222971i
288288 3308.07 + 5729.75i 0.676841 + 1.17232i
289289 1709.13 2960.30i 0.347879 0.602545i
290290 564.149 + 977.135i 0.114234 + 0.197860i
291291 −3110.54 + 5387.61i −0.626608 + 1.08532i
292292 614.037 0.123061
293293 −7587.26 −1.51281 −0.756403 0.654106i 0.773045π-0.773045\pi
−0.756403 + 0.654106i 0.773045π0.773045\pi
294294 7547.47 13072.6i 1.49720 2.59323i
295295 −247.793 + 429.191i −0.0489054 + 0.0847066i
296296 −2971.96 −0.583587
297297 −10477.2 −2.04696
298298 2530.67 4383.24i 0.491938 0.852062i
299299 −4480.44 7760.34i −0.866590 1.50098i
300300 345.982 599.258i 0.0665842 0.115327i
301301 3115.71 + 5396.57i 0.596633 + 1.03340i
302302 1196.66 + 2072.68i 0.228014 + 0.394931i
303303 3374.97 0.639891
304304 −2305.50 583.060i −0.434965 0.110003i
305305 1921.18 0.360677
306306 2111.30 + 3656.87i 0.394427 + 0.683168i
307307 −890.420 1542.25i −0.165534 0.286714i 0.771311 0.636459i 0.219601π-0.219601\pi
−0.936845 + 0.349745i 0.886268π0.886268\pi
308308 2803.18 4855.25i 0.518591 0.898226i
309309 1039.61 + 1800.66i 0.191396 + 0.331508i
310310 −345.696 + 598.762i −0.0633361 + 0.109701i
311311 −2594.78 −0.473108 −0.236554 0.971618i 0.576018π-0.576018\pi
−0.236554 + 0.971618i 0.576018π0.576018\pi
312312 −10141.2 −1.84018
313313 −788.294 + 1365.36i −0.142355 + 0.246565i −0.928383 0.371625i 0.878801π-0.878801\pi
0.786028 + 0.618191i 0.212134π0.212134\pi
314314 −2076.64 + 3596.85i −0.373222 + 0.646439i
315315 8333.60 1.49062
316316 2011.94 0.358167
317317 −2136.44 + 3700.42i −0.378531 + 0.655634i −0.990849 0.134977i 0.956904π-0.956904\pi
0.612318 + 0.790612i 0.290237π0.290237\pi
318318 −2684.56 4649.79i −0.473404 0.819959i
319319 −2709.81 + 4693.54i −0.475613 + 0.823785i
320320 1307.05 + 2263.88i 0.228333 + 0.395484i
321321 660.710 + 1144.38i 0.114882 + 0.198982i
322322 −14024.4 −2.42717
323323 3104.21 + 785.054i 0.534745 + 0.135237i
324324 −1251.04 −0.214513
325325 589.740 + 1021.46i 0.100655 + 0.174340i
326326 3233.01 + 5599.74i 0.549263 + 0.951352i
327327 −1729.53 + 2995.63i −0.292487 + 0.506602i
328328 457.788 + 792.912i 0.0770643 + 0.133479i
329329 4795.31 8305.71i 0.803568 1.39182i
330330 −5087.05 −0.848585
331331 10622.8 1.76399 0.881996 0.471258i 0.156200π-0.156200\pi
0.881996 + 0.471258i 0.156200π0.156200\pi
332332 −735.532 + 1273.98i −0.121589 + 0.210598i
333333 3005.19 5205.14i 0.494545 0.856577i
334334 2130.29 0.348995
335335 2751.26 0.448709
336336 −4219.43 + 7308.26i −0.685085 + 1.18660i
337337 −2194.73 3801.38i −0.354761 0.614464i 0.632316 0.774711i 0.282104π-0.282104\pi
−0.987077 + 0.160246i 0.948771π0.948771\pi
338338 31.7617 55.0130i 0.00511128 0.00885299i
339339 5736.80 + 9936.44i 0.919116 + 1.59196i
340340 −305.565 529.254i −0.0487400 0.0844201i
341341 −3321.00 −0.527397
342342 6305.28 6485.56i 0.996931 1.02543i
343343 −14797.1 −2.32935
344344 −2278.82 3947.04i −0.357168 0.618634i
345345 −4157.21 7200.49i −0.648743 1.12366i
346346 556.120 963.229i 0.0864082 0.149663i
347347 −680.517 1178.69i −0.105280 0.182350i 0.808573 0.588396i 0.200240π-0.200240\pi
−0.913852 + 0.406046i 0.866907π0.866907\pi
348348 −1419.74 + 2459.06i −0.218695 + 0.378791i
349349 5738.02 0.880084 0.440042 0.897977i 0.354964π-0.354964\pi
0.440042 + 0.897977i 0.354964π0.354964\pi
350350 1845.97 0.281918
351351 4678.33 8103.10i 0.711426 1.23223i
352352 −3519.76 + 6096.40i −0.532965 + 0.923123i
353353 −7246.04 −1.09254 −0.546272 0.837608i 0.683953π-0.683953\pi
−0.546272 + 0.837608i 0.683953π0.683953\pi
354354 1908.85 0.286593
355355 2233.36 3868.30i 0.333901 0.578333i
356356 1950.97 + 3379.19i 0.290453 + 0.503080i
357357 5681.20 9840.12i 0.842243 1.45881i
358358 1614.34 + 2796.11i 0.238325 + 0.412791i
359359 −2417.54 4187.31i −0.355412 0.615592i 0.631776 0.775151i 0.282326π-0.282326\pi
−0.987188 + 0.159559i 0.948993π0.948993\pi
360360 −6095.17 −0.892344
361361 −193.306 6856.28i −0.0281828 0.999603i
362362 984.054 0.142875
363363 −6390.95 11069.4i −0.924071 1.60054i
364364 2503.38 + 4335.98i 0.360475 + 0.624361i
365365 −485.571 + 841.034i −0.0696328 + 0.120608i
366366 −3699.89 6408.40i −0.528406 0.915226i
367367 −6158.49 + 10666.8i −0.875941 + 1.51718i −0.0201850 + 0.999796i 0.506426π0.506426\pi
−0.855756 + 0.517379i 0.826908π0.826908\pi
368368 5453.76 0.772546
369369 −1851.63 −0.261224
370370 665.677 1152.99i 0.0935322 0.162003i
371371 −4679.25 + 8104.70i −0.654810 + 1.13416i
372372 −1739.95 −0.242506
373373 7876.55 1.09338 0.546692 0.837334i 0.315887π-0.315887\pi
0.546692 + 0.837334i 0.315887π0.315887\pi
374374 −2246.40 + 3890.88i −0.310584 + 0.537948i
375375 547.195 + 947.769i 0.0753520 + 0.130514i
376376 −3507.27 + 6074.78i −0.481047 + 0.833199i
377377 −2420.00 4191.56i −0.330600 0.572617i
378378 −7321.91 12681.9i −0.996292 1.72563i
379379 −2533.59 −0.343382 −0.171691 0.985151i 0.554923π-0.554923\pi
−0.171691 + 0.985151i 0.554923π0.554923\pi
380380 −912.554 + 938.646i −0.123192 + 0.126714i
381381 16709.9 2.24692
382382 1939.03 + 3358.49i 0.259710 + 0.449831i
383383 −3190.88 5526.77i −0.425708 0.737349i 0.570778 0.821105i 0.306642π-0.306642\pi
−0.996486 + 0.0837558i 0.973308π0.973308\pi
384384 367.877 637.181i 0.0488884 0.0846772i
385385 4433.43 + 7678.93i 0.586879 + 1.01650i
386386 3586.87 6212.65i 0.472972 0.819211i
387387 9217.21 1.21069
388388 −2246.39 −0.293925
389389 7359.94 12747.8i 0.959290 1.66154i 0.235059 0.971981i 0.424472π-0.424472\pi
0.724231 0.689557i 0.242195π-0.242195\pi
390390 2271.50 3934.35i 0.294927 0.510829i
391391 −7343.15 −0.949767
392392 19243.7 2.47947
393393 −5431.42 + 9407.50i −0.697148 + 1.20750i
394394 3973.49 + 6882.28i 0.508075 + 0.880011i
395395 −1591.02 + 2755.72i −0.202665 + 0.351026i
396396 −4146.32 7181.64i −0.526163 0.911341i
397397 −4044.15 7004.67i −0.511259 0.885527i −0.999915 0.0130502i 0.995846π-0.995846\pi
0.488656 0.872477i 0.337487π-0.337487\pi
398398 10261.8 1.29241
399399 −23596.9 5967.66i −2.96071 0.748763i
400400 −717.854 −0.0897318
401401 1567.31 + 2714.66i 0.195182 + 0.338064i 0.946960 0.321351i 0.104137π-0.104137\pi
−0.751778 + 0.659416i 0.770804π0.770804\pi
402402 −5298.50 9177.27i −0.657376 1.13861i
403403 1482.91 2568.48i 0.183298 0.317481i
404404 609.339 + 1055.41i 0.0750390 + 0.129971i
405405 989.305 1713.53i 0.121380 0.210237i
406406 −7574.94 −0.925955
407407 6394.98 0.778839
408408 −4155.21 + 7197.04i −0.504200 + 0.873300i
409409 −7719.88 + 13371.2i −0.933309 + 1.61654i −0.155688 + 0.987806i 0.549759π0.549759\pi
−0.777621 + 0.628733i 0.783574π0.783574\pi
410410 −410.152 −0.0494048
411411 6843.04 0.821271
412412 −375.397 + 650.207i −0.0448895 + 0.0777509i
413413 −1663.58 2881.41i −0.198207 0.343305i
414414 −10372.1 + 17965.0i −1.23131 + 2.13268i
415415 −1163.30 2014.89i −0.137600 0.238330i
416416 −3143.32 5444.39i −0.370466 0.641666i
417417 4298.63 0.504808
418418 9330.44 + 2359.67i 1.09179 + 0.276113i
419419 −767.138 −0.0894442 −0.0447221 0.998999i 0.514240π-0.514240\pi
−0.0447221 + 0.998999i 0.514240π0.514240\pi
420420 2322.78 + 4023.17i 0.269857 + 0.467407i
421421 7115.75 + 12324.8i 0.823754 + 1.42678i 0.902868 + 0.429918i 0.141457π0.141457\pi
−0.0791144 + 0.996866i 0.525209π0.525209\pi
422422 −2246.50 + 3891.05i −0.259142 + 0.448847i
423423 −7092.98 12285.4i −0.815301 1.41214i
424424 3422.39 5927.75i 0.391995 0.678956i
425425 966.546 0.110316
426426 −17204.5 −1.95671
427427 −6449.01 + 11170.0i −0.730889 + 1.26594i
428428 −238.578 + 413.229i −0.0269441 + 0.0466686i
429429 21821.6 2.45585
430430 2041.70 0.228975
431431 2211.29 3830.07i 0.247132 0.428046i −0.715597 0.698514i 0.753845π-0.753845\pi
0.962729 + 0.270468i 0.0871784π0.0871784\pi
432432 2847.32 + 4931.70i 0.317111 + 0.549252i
433433 5356.73 9278.13i 0.594522 1.02974i −0.399092 0.916911i 0.630675π-0.630675\pi
0.993614 0.112831i 0.0359919π-0.0359919\pi
434434 −2320.86 4019.85i −0.256693 0.444606i
435435 −2245.42 3889.17i −0.247493 0.428670i
436436 −1249.04 −0.137198
437437 4284.96 + 15135.2i 0.469056 + 1.65678i
438438 3740.54 0.408059
439439 3397.02 + 5883.81i 0.369318 + 0.639678i 0.989459 0.144812i 0.0462579π-0.0462579\pi
−0.620141 + 0.784491i 0.712925π0.712925\pi
440440 −3242.60 5616.35i −0.351329 0.608520i
441441 −19458.9 + 33703.7i −2.10116 + 3.63932i
442442 −2006.15 3474.75i −0.215888 0.373930i
443443 1014.91 1757.87i 0.108848 0.188531i −0.806456 0.591295i 0.798617π-0.798617\pi
0.915304 + 0.402764i 0.131950π0.131950\pi
444444 3350.48 0.358124
445445 −6171.21 −0.657401
446446 −6366.59 + 11027.3i −0.675934 + 1.17075i
447447 −10072.5 + 17446.1i −1.06580 + 1.84602i
448448 −17550.0 −1.85081
449449 7113.41 0.747667 0.373834 0.927496i 0.378043π-0.378043\pi
0.373834 + 0.927496i 0.378043π0.378043\pi
450450 1365.23 2364.65i 0.143017 0.247713i
451451 −985.055 1706.17i −0.102848 0.178138i
452452 −2071.52 + 3587.98i −0.215567 + 0.373372i
453453 −4762.93 8249.63i −0.494000 0.855632i
454454 1136.32 + 1968.16i 0.117467 + 0.203459i
455455 −7918.55 −0.815885
456456 17258.7 + 4364.73i 1.77240 + 0.448239i
457457 −10681.0 −1.09330 −0.546650 0.837361i 0.684097π-0.684097\pi
−0.546650 + 0.837361i 0.684097π0.684097\pi
458458 −6332.24 10967.8i −0.646039 1.11897i
459459 −3833.74 6640.23i −0.389855 0.675249i
460460 1501.14 2600.05i 0.152154 0.263539i
461461 −1701.77 2947.55i −0.171929 0.297790i 0.767165 0.641449i 0.221667π-0.221667\pi
−0.939094 + 0.343660i 0.888333π0.888333\pi
462462 17076.2 29576.8i 1.71960 2.97844i
463463 16242.7 1.63038 0.815188 0.579196i 0.196633π-0.196633\pi
0.815188 + 0.579196i 0.196633π0.196633\pi
464464 2945.72 0.294723
465465 1375.93 2383.18i 0.137220 0.237672i
466466 3783.93 6553.97i 0.376153 0.651516i
467467 13443.3 1.33208 0.666040 0.745916i 0.267988π-0.267988\pi
0.666040 + 0.745916i 0.267988π0.267988\pi
468468 7405.75 0.731477
469469 −9235.43 + 15996.2i −0.909280 + 1.57492i
470470 −1571.16 2721.33i −0.154196 0.267076i
471471 8265.40 14316.1i 0.808598 1.40053i
472472 1216.74 + 2107.46i 0.118655 + 0.205516i
473473 4903.51 + 8493.13i 0.476667 + 0.825612i
474474 12256.2 1.18765
475475 −564.010 1992.18i −0.0544812 0.192436i
476476 4102.88 0.395074
477477 6921.31 + 11988.1i 0.664371 + 1.15072i
478478 2941.36 + 5094.59i 0.281453 + 0.487492i
479479 −1386.57 + 2401.61i −0.132263 + 0.229087i −0.924549 0.381064i 0.875558π-0.875558\pi
0.792285 + 0.610151i 0.208891π0.208891\pi
480480 −2916.55 5051.62i −0.277337 0.480362i
481481 −2855.52 + 4945.91i −0.270687 + 0.468844i
482482 −1766.88 −0.166969
483483 55819.6 5.25855
484484 2307.73 3997.10i 0.216729 0.375385i
485485 1776.41 3076.84i 0.166315 0.288066i
486486 4157.59 0.388049
487487 −15018.1 −1.39740 −0.698700 0.715415i 0.746238π-0.746238\pi
−0.698700 + 0.715415i 0.746238π0.746238\pi
488488 4716.79 8169.72i 0.437539 0.757840i
489489 −12868.0 22288.0i −1.19000 2.06114i
490490 −4310.32 + 7465.69i −0.397389 + 0.688297i
491491 −5124.95 8876.67i −0.471050 0.815883i 0.528402 0.848995i 0.322792π-0.322792\pi
−0.999452 + 0.0331120i 0.989458π0.989458\pi
492492 −516.094 893.901i −0.0472913 0.0819109i
493493 −3966.22 −0.362332
494494 −5991.25 + 6162.55i −0.545667 + 0.561268i
495495 13115.4 1.19090
496496 902.529 + 1563.23i 0.0817031 + 0.141514i
497497 14993.9 + 25970.2i 1.35326 + 2.34391i
498498 −4480.66 + 7760.72i −0.403179 + 0.698326i
499499 −235.153 407.297i −0.0210960 0.0365393i 0.855285 0.518158i 0.173382π-0.173382\pi
−0.876381 + 0.481619i 0.840049π0.840049\pi
500500 −197.588 + 342.233i −0.0176728 + 0.0306102i
501501 −8478.93 −0.756109
502502 7298.55 0.648904
503503 −1979.91 + 3429.31i −0.175507 + 0.303987i −0.940337 0.340246i 0.889490π-0.889490\pi
0.764830 + 0.644232i 0.222823π0.222823\pi
504504 20460.3 35438.2i 1.80828 3.13203i
505505 −1927.43 −0.169840
506506 −22071.6 −1.93913
507507 −126.417 + 218.961i −0.0110738 + 0.0191803i
508508 3016.92 + 5225.45i 0.263492 + 0.456382i
509509 −1863.91 + 3228.38i −0.162311 + 0.281131i −0.935697 0.352805i 0.885228π-0.885228\pi
0.773386 + 0.633935i 0.218561π0.218561\pi
510510 −1861.42 3224.07i −0.161618 0.279930i
511511 −3259.93 5646.36i −0.282213 0.488807i
512512 9465.99 0.817073
513513 −11449.3 + 11776.6i −0.985375 + 1.01355i
514514 10021.3 0.859966
515515 −593.717 1028.35i −0.0508006 0.0879892i
516516 2569.07 + 4449.75i 0.219180 + 0.379631i
517517 7546.85 13071.5i 0.641993 1.11196i
518518 4469.09 + 7740.69i 0.379074 + 0.656576i
519519 −2213.46 + 3833.82i −0.187206 + 0.324251i
520520 5791.61 0.488421
521521 895.157 0.0752736 0.0376368 0.999291i 0.488017π-0.488017\pi
0.0376368 + 0.999291i 0.488017π0.488017\pi
522522 −5602.24 + 9703.36i −0.469738 + 0.813610i
523523 −4418.42 + 7652.92i −0.369415 + 0.639845i −0.989474 0.144710i 0.953775π-0.953775\pi
0.620059 + 0.784555i 0.287108π0.287108\pi
524524 −3922.50 −0.327014
525525 −7347.29 −0.610785
526526 4113.32 7124.48i 0.340968 0.590574i
527527 −1215.20 2104.79i −0.100446 0.173977i
528528 −6640.54 + 11501.7i −0.547334 + 0.948010i
529529 −11953.7 20704.4i −0.982469 1.70169i
530530 1533.14 + 2655.47i 0.125651 + 0.217634i
531531 −4921.38 −0.402203
532532 −2394.16 8456.57i −0.195113 0.689170i
533533 1759.41 0.142980
534534 11884.8 + 20585.1i 0.963118 + 1.66817i
535535 −377.328 653.551i −0.0304922 0.0528140i
536536 6754.76 11699.6i 0.544331 0.942809i
537537 −6425.35 11129.0i −0.516340 0.894327i
538538 −2365.31 + 4096.84i −0.189546 + 0.328304i
539539 −41408.1 −3.30904
540540 3134.88 0.249822
541541 605.044 1047.97i 0.0480830 0.0832822i −0.840982 0.541063i 0.818022π-0.818022\pi
0.889065 + 0.457781i 0.151355π0.151355\pi
542542 1461.78 2531.88i 0.115847 0.200653i
543543 −3916.71 −0.309543
544544 −5151.70 −0.406024
545545 987.724 1710.79i 0.0776320 0.134463i
546546 15249.9 + 26413.6i 1.19530 + 2.07033i
547547 3265.72 5656.40i 0.255269 0.442139i −0.709700 0.704505i 0.751169π-0.751169\pi
0.964969 + 0.262366i 0.0845026π0.0845026\pi
548548 1235.49 + 2139.93i 0.0963091 + 0.166812i
549549 9539.06 + 16522.1i 0.741561 + 1.28442i
550550 2905.19 0.225232
551551 2314.42 + 8174.90i 0.178943 + 0.632055i
552552 −40826.3 −3.14798
553553 −10681.4 18500.8i −0.821376 1.42267i
554554 −1733.84 3003.10i −0.132967 0.230306i
555555 −2649.52 + 4589.10i −0.202641 + 0.350984i
556556 776.104 + 1344.25i 0.0591981 + 0.102534i
557557 7949.35 13768.7i 0.604712 1.04739i −0.387384 0.921918i 0.626621π-0.626621\pi
0.992097 0.125474i 0.0400453π-0.0400453\pi
558558 −6865.80 −0.520883
559559 −8758.16 −0.662667
560560 2409.69 4173.71i 0.181836 0.314949i
561561 8941.07 15486.4i 0.672892 1.16548i
562562 7435.77 0.558112
563563 −21833.4 −1.63440 −0.817202 0.576352i 0.804476π-0.804476\pi
−0.817202 + 0.576352i 0.804476π0.804476\pi
564564 3953.98 6848.49i 0.295199 0.511300i
565565 −3276.26 5674.65i −0.243953 0.422538i
566566 2655.37 4599.23i 0.197197 0.341555i
567567 6641.80 + 11503.9i 0.491939 + 0.852063i
568568 −10966.5 18994.5i −0.810113 1.40316i
569569 −12370.9 −0.911448 −0.455724 0.890121i 0.650620π-0.650620\pi
−0.455724 + 0.890121i 0.650620π0.650620\pi
570570 −5559.03 + 5717.97i −0.408495 + 0.420174i
571571 15169.6 1.11178 0.555892 0.831254i 0.312377π-0.312377\pi
0.555892 + 0.831254i 0.312377π0.312377\pi
572572 3939.82 + 6823.97i 0.287993 + 0.498819i
573573 −7717.67 13367.4i −0.562671 0.974574i
574574 1376.80 2384.68i 0.100116 0.173406i
575575 2374.16 + 4112.16i 0.172190 + 0.298242i
576576 −12979.6 + 22481.3i −0.938916 + 1.62625i
577577 18083.0 1.30469 0.652343 0.757924i 0.273786π-0.273786\pi
0.652343 + 0.757924i 0.273786π0.273786\pi
578578 7519.08 0.541094
579579 −14276.4 + 24727.4i −1.02471 + 1.77485i
580580 810.804 1404.35i 0.0580462 0.100539i
581581 15619.8 1.11535
582582 −13684.4 −0.974632
583583 −7364.21 + 12755.2i −0.523146 + 0.906116i
584584 2384.30 + 4129.74i 0.168944 + 0.292619i
585585 −5856.36 + 10143.5i −0.413899 + 0.716894i
586586 −8344.77 14453.6i −0.588258 1.01889i
587587 −8771.98 15193.5i −0.616794 1.06832i −0.990067 0.140597i 0.955098π-0.955098\pi
0.373272 0.927722i 0.378236π-0.378236\pi
588588 −21694.7 −1.52155
589589 −3629.13 + 3732.89i −0.253881 + 0.261139i
590590 −1090.13 −0.0760678
591591 −15815.2 27392.7i −1.10076 1.90657i
592592 −1737.92 3010.17i −0.120656 0.208982i
593593 −1422.39 + 2463.65i −0.0985000 + 0.170607i −0.911064 0.412265i 0.864738π-0.864738\pi
0.812564 + 0.582872i 0.198071π0.198071\pi
594594 −11523.2 19958.8i −0.795966 1.37865i
595595 −3244.50 + 5619.64i −0.223549 + 0.387198i
596596 −7274.22 −0.499939
597597 −40843.8 −2.80004
598598 9855.52 17070.3i 0.673950 1.16732i
599599 −1217.27 + 2108.38i −0.0830324 + 0.143816i −0.904551 0.426365i 0.859794π-0.859794\pi
0.821519 + 0.570182i 0.193127π0.193127\pi
600600 5373.79 0.365640
601601 −2976.95 −0.202051 −0.101025 0.994884i 0.532212π-0.532212\pi
−0.101025 + 0.994884i 0.532212π0.532212\pi
602602 −6853.57 + 11870.7i −0.464004 + 0.803679i
603603 13660.6 + 23660.8i 0.922557 + 1.59792i
604604 1719.86 2978.88i 0.115861 0.200677i
605605 3649.84 + 6321.70i 0.245268 + 0.424816i
606606 3711.92 + 6429.24i 0.248823 + 0.430974i
607607 −10120.6 −0.676739 −0.338370 0.941013i 0.609875π-0.609875\pi
−0.338370 + 0.941013i 0.609875π0.609875\pi
608608 3006.18 + 10618.3i 0.200521 + 0.708272i
609609 30149.6 2.00612
610610 2112.99 + 3659.81i 0.140250 + 0.242920i
611611 6739.72 + 11673.5i 0.446252 + 0.772931i
612612 3034.39 5255.71i 0.200421 0.347140i
613613 12304.4 + 21311.8i 0.810717 + 1.40420i 0.912363 + 0.409382i 0.134256π0.134256\pi
−0.101646 + 0.994821i 0.532411π0.532411\pi
614614 1958.64 3392.46i 0.128737 0.222978i
615615 1632.48 0.107037
616616 43539.0 2.84779
617617 13331.8 23091.4i 0.869886 1.50669i 0.00777269 0.999970i 0.497526π-0.497526\pi
0.862113 0.506716i 0.169141π-0.169141\pi
618618 −2286.81 + 3960.88i −0.148850 + 0.257815i
619619 17935.1 1.16458 0.582288 0.812983i 0.302158π-0.302158\pi
0.582288 + 0.812983i 0.302158π0.302158\pi
620620 993.678 0.0643662
621621 18833.9 32621.2i 1.21703 2.10796i
622622 −2853.84 4943.00i −0.183969 0.318644i
623623 20715.5 35880.3i 1.33218 2.30741i
624624 −5930.33 10271.6i −0.380454 0.658966i
625625 −312.500 541.266i −0.0200000 0.0346410i
626626 −3467.99 −0.221419
627627 −37136.8 9391.90i −2.36539 0.598208i
628628 5969.16 0.379292
629629 2340.01 + 4053.01i 0.148334 + 0.256922i
630630 9165.62 + 15875.3i 0.579630 + 1.00395i
631631 −11866.4 + 20553.3i −0.748646 + 1.29669i 0.199826 + 0.979831i 0.435962π0.435962\pi
−0.948472 + 0.316861i 0.897371π0.897371\pi
632632 7812.38 + 13531.4i 0.491708 + 0.851664i
633633 8941.46 15487.1i 0.561440 0.972442i
634634 −9398.95 −0.588770
635635 −9542.94 −0.596378
636636 −3858.28 + 6682.74i −0.240552 + 0.416648i
637637 18489.7 32025.2i 1.15006 1.99197i
638638 −11921.4 −0.739772
639639 44356.5 2.74603
640640 −210.093 + 363.891i −0.0129760 + 0.0224751i
641641 −9004.39 15596.1i −0.554840 0.961010i −0.997916 0.0645264i 0.979446π-0.979446\pi
0.443076 0.896484i 0.353887π-0.353887\pi
642642 −1453.35 + 2517.28i −0.0893445 + 0.154749i
643643 8763.10 + 15178.1i 0.537454 + 0.930897i 0.999040 + 0.0438022i 0.0139471π0.0139471\pi
−0.461586 + 0.887095i 0.652720π0.652720\pi
644644 10078.0 + 17455.7i 0.616662 + 1.06809i
645645 −8126.32 −0.496083
646646 1918.62 + 6776.88i 0.116853 + 0.412744i
647647 −19408.8 −1.17935 −0.589673 0.807642i 0.700743π-0.700743\pi
−0.589673 + 0.807642i 0.700743π0.700743\pi
648648 −4857.79 8413.94i −0.294494 0.510078i
649649 −2618.15 4534.77i −0.158353 0.274276i
650650 −1297.24 + 2246.88i −0.0782799 + 0.135585i
651651 9237.44 + 15999.7i 0.556135 + 0.963254i
652652 4646.53 8048.02i 0.279098 0.483413i
653653 −21561.7 −1.29215 −0.646075 0.763274i 0.723591π-0.723591\pi
−0.646075 + 0.763274i 0.723591π0.723591\pi
654654 −7608.81 −0.454936
655655 3101.86 5372.57i 0.185038 0.320494i
656656 −535.405 + 927.348i −0.0318659 + 0.0551934i
657657 −9643.85 −0.572667
658658 21096.3 1.24988
659659 −4081.97 + 7070.18i −0.241291 + 0.417929i −0.961082 0.276262i 0.910904π-0.910904\pi
0.719791 + 0.694191i 0.244238π0.244238\pi
660660 3655.59 + 6331.67i 0.215597 + 0.373424i
661661 8599.69 14895.1i 0.506035 0.876478i −0.493941 0.869496i 0.664444π-0.664444\pi
0.999976 0.00698260i 0.00222265π-0.00222265\pi
662662 11683.4 + 20236.2i 0.685931 + 1.18807i
663663 7984.82 + 13830.1i 0.467730 + 0.810132i
664664 −11424.3 −0.667693
665665 13476.1 + 3408.10i 0.785834 + 0.198737i
666666 13220.9 0.769219
667667 −9742.36 16874.3i −0.565556 0.979571i
668668 −1530.84 2651.50i −0.0886678 0.153577i
669669 25340.2 43890.4i 1.46444 2.53648i
670670 3025.95 + 5241.09i 0.174481 + 0.302210i
671671 −10149.5 + 17579.4i −0.583928 + 1.01139i
672672 39161.1 2.24802
673673 −26519.7 −1.51896 −0.759478 0.650533i 0.774546π-0.774546\pi
−0.759478 + 0.650533i 0.774546π0.774546\pi
674674 4827.70 8361.82i 0.275899 0.477871i
675675 −2479.02 + 4293.79i −0.141359 + 0.244841i
676676 −91.2969 −0.00519441
677677 16854.5 0.956824 0.478412 0.878135i 0.341213π-0.341213\pi
0.478412 + 0.878135i 0.341213π0.341213\pi
678678 −12619.1 + 21857.0i −0.714800 + 1.23807i
679679 11926.1 + 20656.6i 0.674053 + 1.16749i
680680 2373.02 4110.19i 0.133825 0.231792i
681681 −4522.75 7833.63i −0.254496 0.440801i
682682 −3652.57 6326.44i −0.205079 0.355208i
683683 22859.4 1.28066 0.640330 0.768100i 0.278798π-0.278798\pi
0.640330 + 0.768100i 0.278798π0.278798\pi
684684 −12603.4 3187.39i −0.704535 0.178177i
685685 −3908.02 −0.217982
686686 −16274.4 28188.1i −0.905772 1.56884i
687687 25203.4 + 43653.6i 1.39967 + 2.42429i
688688 2665.19 4616.25i 0.147688 0.255804i
689689 −6576.61 11391.0i −0.363641 0.629845i
690690 9144.52 15838.8i 0.504530 0.873872i
691691 −3489.61 −0.192114 −0.0960572 0.995376i 0.530623π-0.530623\pi
−0.0960572 + 0.995376i 0.530623π0.530623\pi
692692 −1598.53 −0.0878135
693693 −44025.8 + 76254.9i −2.41328 + 4.17992i
694694 1496.92 2592.74i 0.0818764 0.141814i
695695 −2454.93 −0.133987
696696 −22051.3 −1.20094
697697 720.889 1248.62i 0.0391759 0.0678547i
698698 6310.90 + 10930.8i 0.342222 + 0.592747i
699699 −15060.7 + 26086.0i −0.814949 + 1.41153i
700700 −1326.53 2297.61i −0.0716258 0.124059i
701701 −488.502 846.110i −0.0263202 0.0455879i 0.852565 0.522621i 0.175046π-0.175046\pi
−0.878885 + 0.477033i 0.841712π0.841712\pi
702702 20581.6 1.10656
703703 6988.31 7188.12i 0.374921 0.385640i
704704 −27620.3 −1.47866
705705 6253.50 + 10831.4i 0.334072 + 0.578629i
706706 −7969.48 13803.6i −0.424838 0.735841i
707707 6469.98 11206.3i 0.344171 0.596121i
708708 −1371.71 2375.87i −0.0728136 0.126117i
709709 −2196.86 + 3805.07i −0.116368 + 0.201555i −0.918326 0.395826i 0.870458π-0.870458\pi
0.801958 + 0.597380i 0.203792π0.203792\pi
710710 9825.37 0.519352
711711 −31598.9 −1.66674
712712 −15151.3 + 26242.7i −0.797496 + 1.38130i
713713 5969.86 10340.1i 0.313567 0.543113i
714714 24993.6 1.31003
715715 −12462.2 −0.651833
716716 2320.15 4018.62i 0.121101 0.209752i
717717 −11707.1 20277.4i −0.609779 1.05617i
718718 5317.82 9210.73i 0.276406 0.478749i
719719 16137.8 + 27951.5i 0.837050 + 1.44981i 0.892350 + 0.451344i 0.149055π0.149055\pi
−0.0552997 + 0.998470i 0.517611π0.517611\pi
720720 −3564.30 6173.54i −0.184491 0.319548i
721721 7971.96 0.411777
722722 12848.4 7909.05i 0.662285 0.407679i
723723 7032.49 0.361745
724724 −707.148 1224.82i −0.0362997 0.0628729i
725725 1282.34 + 2221.09i 0.0656898 + 0.113778i
726726 14058.0 24349.2i 0.718654 1.24474i
727727 6895.02 + 11942.5i 0.351750 + 0.609248i 0.986556 0.163423i 0.0522535π-0.0522535\pi
−0.634806 + 0.772671i 0.718920π0.718920\pi
728728 −19441.3 + 33673.2i −0.989754 + 1.71430i
729729 −27232.4 −1.38355
730730 −2136.20 −0.108307
731731 −3588.52 + 6215.49i −0.181568 + 0.314485i
732732 −5317.54 + 9210.26i −0.268500 + 0.465056i
733733 31204.5 1.57240 0.786198 0.617975i 0.212047π-0.212047\pi
0.786198 + 0.617975i 0.212047π0.212047\pi
734734 −27093.4 −1.36245
735735 17155.8 29714.8i 0.860956 1.49122i
736736 −12654.3 21917.9i −0.633754 1.09769i
737737 −14534.7 + 25174.9i −0.726449 + 1.25825i
738738 −2036.49 3527.31i −0.101578 0.175938i
739739 −1349.20 2336.88i −0.0671598 0.116324i 0.830490 0.557033i 0.188060π-0.188060\pi
−0.897650 + 0.440709i 0.854727π0.854727\pi
740740 −1913.44 −0.0950535
741741 23846.3 24528.1i 1.18221 1.21601i
742742 −20585.7 −1.01850
743743 10259.2 + 17769.4i 0.506558 + 0.877384i 0.999971 + 0.00758908i 0.00241570π0.00241570\pi
−0.493413 + 0.869795i 0.664251π0.664251\pi
744744 −6756.24 11702.1i −0.332924 0.576642i
745745 5752.35 9963.37i 0.282886 0.489972i
746746 8662.94 + 15004.7i 0.425165 + 0.736407i
747747 11552.0 20008.7i 0.565818 0.980025i
748748 6457.12 0.315636
749749 5066.45 0.247162
750750 −1203.65 + 2084.79i −0.0586016 + 0.101501i
751751 −3646.10 + 6315.24i −0.177161 + 0.306853i −0.940907 0.338665i 0.890025π-0.890025\pi
0.763746 + 0.645517i 0.223358π0.223358\pi
752752 −8203.85 −0.397824
753753 −29049.5 −1.40587
754754 5323.22 9220.09i 0.257109 0.445326i
755755 2720.08 + 4711.32i 0.131118 + 0.227103i
756756 −10523.2 + 18226.6i −0.506248 + 0.876847i
757757 5277.93 + 9141.64i 0.253408 + 0.438915i 0.964462 0.264222i 0.0851153π-0.0851153\pi
−0.711054 + 0.703137i 0.751782π0.751782\pi
758758 −2786.55 4826.44i −0.133525 0.231272i
759759 87848.9 4.20120
760760 −9856.36 2492.67i −0.470431 0.118972i
761761 −9699.72 −0.462043 −0.231021 0.972949i 0.574207π-0.574207\pi
−0.231021 + 0.972949i 0.574207π0.574207\pi
762762 18378.2 + 31832.0i 0.873717 + 1.51332i
763763 6631.18 + 11485.5i 0.314633 + 0.544960i
764764 2786.80 4826.87i 0.131967 0.228573i
765765 4799.10 + 8312.29i 0.226813 + 0.392852i
766766 7018.91 12157.1i 0.331075 0.573439i
767767 4676.28 0.220144
768768 −35000.5 −1.64449
769769 −13647.8 + 23638.8i −0.639992 + 1.10850i 0.345442 + 0.938440i 0.387729π0.387729\pi
−0.985434 + 0.170059i 0.945604π0.945604\pi
770770 −9752.13 + 16891.2i −0.456418 + 0.790540i
771771 −39886.7 −1.86315
772772 −10310.2 −0.480664
773773 11898.4 20608.7i 0.553631 0.958916i −0.444378 0.895839i 0.646575π-0.646575\pi
0.998009 0.0630769i 0.0200913π-0.0200913\pi
774774 10137.5 + 17558.6i 0.470779 + 0.815414i
775775 −785.787 + 1361.02i −0.0364210 + 0.0630831i
776776 −8722.72 15108.2i −0.403515 0.698908i
777777 −17787.8 30809.3i −0.821278 1.42249i
778778 32379.0 1.49209
779779 −2994.22 757.238i −0.137714 0.0348278i
780780 −6529.26 −0.299724
781781 23597.4 + 40871.9i 1.08115 + 1.87262i
782782 −8076.28 13988.5i −0.369319 0.639679i
783783 10172.7 17619.6i 0.464293 0.804179i
784784 11253.2 + 19491.1i 0.512628 + 0.887898i
785785 −4720.33 + 8175.84i −0.214619 + 0.371730i
786786 −23894.8 −1.08435
787787 38347.5 1.73690 0.868451 0.495775i 0.165116π-0.165116\pi
0.868451 + 0.495775i 0.165116π0.165116\pi
788788 5710.76 9891.32i 0.258169 0.447162i
789789 −16371.8 + 28356.7i −0.738720 + 1.27950i
790790 −6999.45 −0.315227
791791 43990.9 1.97742
792792 32200.4 55772.6i 1.44468 2.50227i
793793 −9063.98 15699.3i −0.405891 0.703023i
794794 8895.83 15408.0i 0.397608 0.688678i
795795 −6102.15 10569.2i −0.272228 0.471512i
796796 −7374.21 12772.5i −0.328357 0.568731i
797797 10845.2 0.482006 0.241003 0.970524i 0.422524π-0.422524\pi
0.241003 + 0.970524i 0.422524π0.422524\pi
798798 −14584.6 51515.1i −0.646977 2.28523i
799799 11046.0 0.489084
800800 1665.63 + 2884.95i 0.0736110 + 0.127498i
801801 −30641.3 53072.3i −1.35163 2.34110i
802802 −3447.58 + 5971.39i −0.151793 + 0.262914i
803803 −5130.48 8886.25i −0.225468 0.390522i
804804 −7615.09 + 13189.7i −0.334034 + 0.578564i
805805 −31878.3 −1.39573
806806 6523.86 0.285103
807807 9414.37 16306.2i 0.410659 0.711282i
808808 −4732.13 + 8196.28i −0.206034 + 0.356862i
809809 −25939.8 −1.12731 −0.563656 0.826009i 0.690606π-0.690606\pi
−0.563656 + 0.826009i 0.690606π0.690606\pi
810810 4352.31 0.188796
811811 −12557.6 + 21750.4i −0.543720 + 0.941750i 0.454966 + 0.890509i 0.349651π0.349651\pi
−0.998686 + 0.0512418i 0.983682π0.983682\pi
812812 5443.41 + 9428.26i 0.235254 + 0.407472i
813813 −5818.16 + 10077.3i −0.250986 + 0.434721i
814814 7033.45 + 12182.3i 0.302853 + 0.524557i
815815 7348.82 + 12728.5i 0.315850 + 0.547069i
816816 −9719.43 −0.416971
817817 14904.9 + 3769.46i 0.638259 + 0.161416i
818818 −33962.5 −1.45168
819819 −39317.3 68099.5i −1.67748 2.90548i
820820 294.739 + 510.502i 0.0125521 + 0.0217409i
821821 843.782 1461.47i 0.0358687 0.0621264i −0.847534 0.530741i 0.821914π-0.821914\pi
0.883402 + 0.468615i 0.155247π0.155247\pi
822822 7526.25 + 13035.8i 0.319353 + 0.553135i
823823 −5845.12 + 10124.0i −0.247567 + 0.428799i −0.962850 0.270036i 0.912965π-0.912965\pi
0.715283 + 0.698835i 0.246298π0.246298\pi
824824 −5830.67 −0.246506
825825 −11563.2 −0.487973
826826 3659.35 6338.18i 0.154147 0.266990i
827827 −23331.4 + 40411.2i −0.981032 + 1.69920i −0.322643 + 0.946521i 0.604571π0.604571\pi
−0.658390 + 0.752677i 0.728762π0.728762\pi
828828 29813.8 1.25133
829829 38751.9 1.62353 0.811767 0.583982i 0.198506π-0.198506\pi
0.811767 + 0.583982i 0.198506π0.198506\pi
830830 2558.88 4432.11i 0.107012 0.185350i
831831 6901.00 + 11952.9i 0.288078 + 0.498966i
832832 12333.1 21361.6i 0.513912 0.890122i
833833 −15151.8 26243.6i −0.630225 1.09158i
834834 4727.81 + 8188.80i 0.196296 + 0.339994i
835835 4842.27 0.200687
836836 −3767.93 13308.9i −0.155881 0.550598i
837837 12467.1 0.514845
838838 −843.728 1461.38i −0.0347806 0.0602417i
839839 −11551.6 20008.0i −0.475336 0.823306i 0.524265 0.851555i 0.324340π-0.324340\pi
−0.999601 + 0.0282492i 0.991007π0.991007\pi
840840 −18038.7 + 31244.0i −0.740946 + 1.28336i
841841 6932.40 + 12007.3i 0.284243 + 0.492323i
842842 −15652.4 + 27110.7i −0.640637 + 1.10961i
843843 −29595.7 −1.20917
844844 6457.40 0.263357
845845 72.1963 125.048i 0.00293921 0.00509085i
846846 15602.3 27023.9i 0.634063 1.09823i
847847 −49007.0 −1.98808
848848 8005.30 0.324178
849849 −10568.8 + 18305.8i −0.427234 + 0.739990i
850850 1063.05 + 1841.25i 0.0428967 + 0.0742992i
851851 −11495.7 + 19911.1i −0.463063 + 0.802048i
852852 12363.3 + 21413.8i 0.497134 + 0.861061i
853853 17640.0 + 30553.3i 0.708066 + 1.22641i 0.965574 + 0.260130i 0.0837655π0.0837655\pi
−0.257507 + 0.966276i 0.582901π0.582901\pi
854854 −28371.5 −1.13683
855855 14332.3 14742.1i 0.573279 0.589670i
856856 −3705.59 −0.147961
857857 696.225 + 1205.90i 0.0277510 + 0.0480661i 0.879567 0.475774i 0.157832π-0.157832\pi
−0.851816 + 0.523841i 0.824499π0.824499\pi
858858 24000.3 + 41569.8i 0.954962 + 1.65404i
859859 20190.4 34970.8i 0.801964 1.38904i −0.116358 0.993207i 0.537122π-0.537122\pi
0.918322 0.395835i 0.129545π-0.129545\pi
860860 −1467.18 2541.23i −0.0581749 0.100762i
861861 −5479.90 + 9491.47i −0.216904 + 0.375689i
862862 9728.25 0.384392
863863 −23185.3 −0.914527 −0.457263 0.889331i 0.651170π-0.651170\pi
−0.457263 + 0.889331i 0.651170π0.651170\pi
864864 13213.2 22885.9i 0.520280 0.901151i
865865 1264.09 2189.48i 0.0496884 0.0860629i
866866 23566.2 0.924724
867867 −29927.3 −1.17230
868868 −3335.58 + 5777.39i −0.130434 + 0.225919i
869869 −16810.5 29116.6i −0.656221 1.13661i
870870 4939.19 8554.93i 0.192476 0.333379i
871871 −12980.2 22482.4i −0.504958 0.874613i
872872 −4850.03 8400.49i −0.188352 0.326235i
873873 35281.0 1.36779
874874 −24119.4 + 24809.0i −0.933468 + 0.960157i
875875 4196.00 0.162115
876876 −2687.98 4655.72i −0.103674 0.179569i
877877 −19168.1 33200.1i −0.738038 1.27832i −0.953378 0.301780i 0.902419π-0.902419\pi
0.215339 0.976539i 0.430914π-0.430914\pi
878878 −7472.35 + 12942.5i −0.287220 + 0.497480i
879879 33213.7 + 57527.8i 1.27448 + 2.20747i
880880 3792.37 6568.59i 0.145274 0.251622i
881881 39178.2 1.49824 0.749120 0.662435i 0.230477π-0.230477\pi
0.749120 + 0.662435i 0.230477π0.230477\pi
882882 −85606.5 −3.26817
883883 13737.3 23793.8i 0.523554 0.906822i −0.476070 0.879407i 0.657939π-0.657939\pi
0.999624 0.0274144i 0.00872738π-0.00872738\pi
884884 −2883.26 + 4993.96i −0.109700 + 0.190006i
885885 4338.92 0.164804
886886 4464.95 0.169304
887887 25920.2 44895.0i 0.981188 1.69947i 0.323405 0.946261i 0.395173π-0.395173\pi
0.657784 0.753207i 0.271494π-0.271494\pi
888888 13009.9 + 22533.9i 0.491649 + 0.851562i
889889 32033.7 55484.0i 1.20852 2.09322i
890890 −6787.34 11756.0i −0.255632 0.442767i
891891 10452.9 + 18104.9i 0.393024 + 0.680737i
892892 18300.3 0.686928
893893 −6445.67 22767.2i −0.241541 0.853163i
894894 −44312.5 −1.65776
895895 3669.48 + 6355.73i 0.137047 + 0.237373i
896896 −1410.48 2443.02i −0.0525901 0.0910887i
897897 −39226.7 + 67942.7i −1.46014 + 2.52903i
898898 7823.61 + 13550.9i 0.290732 + 0.503562i
899899 3224.48 5584.96i 0.119624 0.207196i
900900 −3924.27 −0.145343
901901 −10778.6 −0.398544
902902 2166.81 3753.02i 0.0799853 0.138539i
903903 27278.4 47247.6i 1.00528 1.74120i
904904 −32174.9 −1.18376
905905 2236.81 0.0821593
906906 10476.9 18146.5i 0.384185 0.665429i
907907 −9593.37 16616.2i −0.351205 0.608304i 0.635256 0.772302i 0.280895π-0.280895\pi
−0.986461 + 0.163997i 0.947561π0.947561\pi
908908 1633.13 2828.67i 0.0596888 0.103384i
909909 −9570.07 16575.9i −0.349196 0.604825i
910910 −8709.14 15084.7i −0.317258 0.549508i
911911 15917.9 0.578906 0.289453 0.957192i 0.406527π-0.406527\pi
0.289453 + 0.957192i 0.406527π0.406527\pi
912912 5671.60 + 20033.0i 0.205927 + 0.727368i
913913 24582.4 0.891085
914914 −11747.4 20347.2i −0.425132 0.736350i
915915 −8410.08 14566.7i −0.303856 0.526295i
916916 −9100.79 + 15763.0i −0.328273 + 0.568586i
917917 20824.6 + 36069.3i 0.749934 + 1.29892i
918918 8432.99 14606.4i 0.303192 0.525144i
919919 −980.295 −0.0351871 −0.0175936 0.999845i 0.505600π-0.505600\pi
−0.0175936 + 0.999845i 0.505600π0.505600\pi
920920 23315.7 0.835538
921921 −7795.73 + 13502.6i −0.278912 + 0.483090i
922922 3743.34 6483.66i 0.133710 0.231592i
923923 −42147.4 −1.50303
924924 −49084.3 −1.74757
925925 1513.12 2620.81i 0.0537851 0.0931585i
926926 17864.4 + 30942.1i 0.633975 + 1.09808i
927927 5895.86 10211.9i 0.208895 0.361816i
928928 −6834.91 11838.4i −0.241775 0.418766i
929929 22729.3 + 39368.3i 0.802718 + 1.39035i 0.917821 + 0.396995i 0.129947π0.129947\pi
−0.115103 + 0.993354i 0.536720π0.536720\pi
930930 6053.21 0.213433
931931 −45249.9 + 46543.7i −1.59292 + 1.63846i
932932 −10876.7 −0.382271
933933 11358.8 + 19674.0i 0.398575 + 0.690352i
934934 14785.5 + 25609.2i 0.517982 + 0.897171i
935935 −5106.20 + 8844.19i −0.178599 + 0.309343i
936936 28756.5 + 49807.8i 1.00421 + 1.73934i
937937 18517.2 32072.7i 0.645604 1.11822i −0.338558 0.940946i 0.609939π-0.609939\pi
0.984162 0.177273i 0.0567276π-0.0567276\pi
938938 −40629.9 −1.41430
939939 13803.2 0.479713
940940 −2258.10 + 3911.14i −0.0783521 + 0.135710i
941941 −13043.1 + 22591.2i −0.451851 + 0.782629i −0.998501 0.0547324i 0.982569π-0.982569\pi
0.546650 + 0.837361i 0.315903π0.315903\pi
942942 36362.5 1.25770
943943 7082.97 0.244595
944944 −1423.04 + 2464.77i −0.0490634 + 0.0849804i
945945 −16643.1 28826.7i −0.572911 0.992311i
946946 −10786.1 + 18682.2i −0.370706 + 0.642082i
947947 −21419.6 37099.9i −0.734999 1.27306i −0.954724 0.297494i 0.903849π-0.903849\pi
0.219725 0.975562i 0.429484π-0.429484\pi
948948 −8807.40 15254.9i −0.301742 0.522632i
949949 9163.55 0.313447
950950 3174.73 3265.50i 0.108423 0.111523i
951951 37409.5 1.27559
952952 15931.5 + 27594.1i 0.542376 + 0.939424i
953953 24043.7 + 41644.9i 0.817262 + 1.41554i 0.907692 + 0.419637i 0.137843π0.137843\pi
−0.0904297 + 0.995903i 0.528824π0.528824\pi
954954 −15224.7 + 26369.9i −0.516684 + 0.894923i
955955 4407.52 + 7634.05i 0.149344 + 0.258672i
956956 4227.37 7322.02i 0.143016 0.247710i
957957 47449.5 1.60274
958958 −6100.03 −0.205723
959959 13118.4 22721.8i 0.441727 0.765094i
960960 11443.4 19820.6i 0.384723 0.666360i
961961 −25839.3 −0.867351
962962 −12562.5 −0.421029
963963 3747.02 6490.03i 0.125385 0.217174i
964964 1269.69 + 2199.17i 0.0424212 + 0.0734757i
965965 8153.17 14121.7i 0.271979 0.471082i
966966 61392.6 + 106335.i 2.04480 + 3.54169i
967967 29688.3 + 51421.6i 0.987291 + 1.71004i 0.631277 + 0.775558i 0.282531π0.282531\pi
0.356014 + 0.934481i 0.384135π0.384135\pi
968968 35843.6 1.19014
969969 −7636.45 26973.2i −0.253166 0.894225i
970970 7815.07 0.258687
971971 18380.4 + 31835.8i 0.607473 + 1.05217i 0.991655 + 0.128916i 0.0411499π0.0411499\pi
−0.384183 + 0.923257i 0.625517π0.625517\pi
972972 −2987.67 5174.80i −0.0985901 0.170763i
973973 8240.69 14273.3i 0.271515 0.470278i
974974 −16517.5 28609.1i −0.543382 0.941165i
975975 5163.24 8943.00i 0.169596 0.293749i
976976 11033.0 0.361843
977977 −18904.8 −0.619056 −0.309528 0.950890i 0.600171π-0.600171\pi
−0.309528 + 0.950890i 0.600171π0.600171\pi
978978 28305.4 49026.3i 0.925466 1.60295i
979979 32602.1 56468.4i 1.06432 1.84345i
980980 12389.7 0.403852
981981 19617.0 0.638454
982982 11273.2 19525.8i 0.366337 0.634515i
983983 10770.5 + 18655.0i 0.349466 + 0.605292i 0.986155 0.165828i 0.0530298π-0.0530298\pi
−0.636689 + 0.771121i 0.719696π0.719696\pi
984984 4007.99 6942.04i 0.129847 0.224902i
985985 9031.97 + 15643.8i 0.292165 + 0.506045i
986986 −4362.21 7555.57i −0.140894 0.244035i
987987 −83966.9 −2.70790
988988 11975.7 + 3028.65i 0.385624 + 0.0975244i
989989 −35258.3 −1.13362
990990 14424.9 + 24984.6i 0.463083 + 0.802083i
991991 −23250.3 40270.7i −0.745277 1.29086i −0.950065 0.312051i 0.898984π-0.898984\pi
0.204788 0.978806i 0.434349π-0.434349\pi
992992 4188.25 7254.26i 0.134049 0.232180i
993993 −46501.9 80543.6i −1.48609 2.57399i
994994 −32981.8 + 57126.1i −1.05243 + 1.82287i
995995 23325.7 0.743190
996996 12879.3 0.409736
997997 −27345.1 + 47363.2i −0.868635 + 1.50452i −0.00524355 + 0.999986i 0.501669π0.501669\pi
−0.863392 + 0.504534i 0.831664π0.831664\pi
998998 517.261 895.922i 0.0164064 0.0284168i
999999 −24006.8 −0.760302
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 95.4.e.c.26.7 yes 20
19.7 even 3 1805.4.a.r.1.4 10
19.11 even 3 inner 95.4.e.c.11.7 20
19.12 odd 6 1805.4.a.p.1.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.4.e.c.11.7 20 19.11 even 3 inner
95.4.e.c.26.7 yes 20 1.1 even 1 trivial
1805.4.a.p.1.7 10 19.12 odd 6
1805.4.a.r.1.4 10 19.7 even 3