Properties

Label 338.4.c.o.191.6
Level 338338
Weight 44
Character 338.191
Analytic conductor 19.94319.943
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [338,4,Mod(191,338)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(338, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("338.191");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 338=2132 338 = 2 \cdot 13^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 338.c (of order 33, degree 22, not 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: 19.942645581919.9426455819
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x12x11+108x1063x9+7831x83348x7+317885x6+1680x5++1759886401 x^{12} - x^{11} + 108 x^{10} - 63 x^{9} + 7831 x^{8} - 3348 x^{7} + 317885 x^{6} + 1680 x^{5} + \cdots + 1759886401 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 134 13^{4}
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 191.6
Root 2.42606+4.20205i-2.42606 + 4.20205i of defining polynomial
Character χ\chi == 338.191
Dual form 338.4.c.o.315.6

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+(1.00000+1.73205i)q2+(4.074017.05638i)q3+(2.000003.46410i)q412.6646q5+(8.14801+14.1128i)q6+(14.3853+24.9160i)q7+8.00000q8+(19.695034.1128i)q9+(12.664621.9357i)q10+(26.420345.7613i)q1132.5920q1257.5411q14+(51.5957+89.3664i)q15+(8.00000+13.8564i)q16+(35.516161.5158i)q17+78.7801q18+(32.884356.9572i)q19+(25.3292+43.8715i)q20+234.423q21+(52.8406+91.5226i)q22+(22.215438.4783i)q23+(32.592056.4511i)q24+35.3924q25100.954q27+(57.541199.6641i)q28+(39.218967.9292i)q29+(103.191178.733i)q30195.024q31+(16.000027.7128i)q32+(215.273372.863i)q33+142.065q34+(182.184315.552i)q35+(78.7801+136.451i)q36+(116.595+201.948i)q37+131.537q38101.317q40+(60.2286+104.319i)q41+(234.423+406.032i)q42+(202.551350.829i)q43211.362q44+(249.430+432.025i)q45+(44.4309+76.9566i)q46400.779q47+(65.1841+112.902i)q48+(242.372+419.800i)q49+(35.3924+61.3014i)q50578.772q51+116.566q53+(100.954174.858i)q54+(334.603+579.549i)q55+(115.082+199.328i)q56535.883q57+(78.4379+135.858i)q58+(390.718676.744i)q59+412.765q60+(26.278145.5149i)q61+(195.024337.792i)q62+(566.637981.444i)q63+64.0000q64+861.091q66+(402.652697.414i)q67+(142.065+246.063i)q68+(181.012313.521i)q69+728.735q70+(200.786+347.771i)q71+(157.560272.902i)q72+323.057q73+(233.189403.895i)q74+(144.189249.742i)q75+(131.537+227.829i)q76+1520.25q77794.845q79+(101.317175.486i)q80+(120.477208.673i)q81+(120.457208.638i)q82+444.820q83+(468.845812.064i)q84+(449.798+779.073i)q85+810.205q86+(319.556553.488i)q87+(211.362366.090i)q88+(39.5736+68.5435i)q89997.720q90177.724q92+(794.529+1376.16i)q93+(400.779694.169i)q94+(416.467+721.341i)q95260.736q96+(1.948183.37434i)q97+(484.744839.601i)q982081.39q99+O(q100)q+(-1.00000 + 1.73205i) q^{2} +(4.07401 - 7.05638i) q^{3} +(-2.00000 - 3.46410i) q^{4} -12.6646 q^{5} +(8.14801 + 14.1128i) q^{6} +(14.3853 + 24.9160i) q^{7} +8.00000 q^{8} +(-19.6950 - 34.1128i) q^{9} +(12.6646 - 21.9357i) q^{10} +(26.4203 - 45.7613i) q^{11} -32.5920 q^{12} -57.5411 q^{14} +(-51.5957 + 89.3664i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-35.5161 - 61.5158i) q^{17} +78.7801 q^{18} +(-32.8843 - 56.9572i) q^{19} +(25.3292 + 43.8715i) q^{20} +234.423 q^{21} +(52.8406 + 91.5226i) q^{22} +(22.2154 - 38.4783i) q^{23} +(32.5920 - 56.4511i) q^{24} +35.3924 q^{25} -100.954 q^{27} +(57.5411 - 99.6641i) q^{28} +(39.2189 - 67.9292i) q^{29} +(-103.191 - 178.733i) q^{30} -195.024 q^{31} +(-16.0000 - 27.7128i) q^{32} +(-215.273 - 372.863i) q^{33} +142.065 q^{34} +(-182.184 - 315.552i) q^{35} +(-78.7801 + 136.451i) q^{36} +(-116.595 + 201.948i) q^{37} +131.537 q^{38} -101.317 q^{40} +(-60.2286 + 104.319i) q^{41} +(-234.423 + 406.032i) q^{42} +(-202.551 - 350.829i) q^{43} -211.362 q^{44} +(249.430 + 432.025i) q^{45} +(44.4309 + 76.9566i) q^{46} -400.779 q^{47} +(65.1841 + 112.902i) q^{48} +(-242.372 + 419.800i) q^{49} +(-35.3924 + 61.3014i) q^{50} -578.772 q^{51} +116.566 q^{53} +(100.954 - 174.858i) q^{54} +(-334.603 + 579.549i) q^{55} +(115.082 + 199.328i) q^{56} -535.883 q^{57} +(78.4379 + 135.858i) q^{58} +(-390.718 - 676.744i) q^{59} +412.765 q^{60} +(-26.2781 - 45.5149i) q^{61} +(195.024 - 337.792i) q^{62} +(566.637 - 981.444i) q^{63} +64.0000 q^{64} +861.091 q^{66} +(402.652 - 697.414i) q^{67} +(-142.065 + 246.063i) q^{68} +(-181.012 - 313.521i) q^{69} +728.735 q^{70} +(200.786 + 347.771i) q^{71} +(-157.560 - 272.902i) q^{72} +323.057 q^{73} +(-233.189 - 403.895i) q^{74} +(144.189 - 249.742i) q^{75} +(-131.537 + 227.829i) q^{76} +1520.25 q^{77} -794.845 q^{79} +(101.317 - 175.486i) q^{80} +(120.477 - 208.673i) q^{81} +(-120.457 - 208.638i) q^{82} +444.820 q^{83} +(-468.845 - 812.064i) q^{84} +(449.798 + 779.073i) q^{85} +810.205 q^{86} +(-319.556 - 553.488i) q^{87} +(211.362 - 366.090i) q^{88} +(-39.5736 + 68.5435i) q^{89} -997.720 q^{90} -177.724 q^{92} +(-794.529 + 1376.16i) q^{93} +(400.779 - 694.169i) q^{94} +(416.467 + 721.341i) q^{95} -260.736 q^{96} +(-1.94818 - 3.37434i) q^{97} +(-484.744 - 839.601i) q^{98} -2081.39 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q12q29q324q4+36q518q625q7+96q8113q936q1037q11+72q12+100q14118q1596q1699q17+452q18+81q19+2688q99+O(q100) 12 q - 12 q^{2} - 9 q^{3} - 24 q^{4} + 36 q^{5} - 18 q^{6} - 25 q^{7} + 96 q^{8} - 113 q^{9} - 36 q^{10} - 37 q^{11} + 72 q^{12} + 100 q^{14} - 118 q^{15} - 96 q^{16} - 99 q^{17} + 452 q^{18} + 81 q^{19}+ \cdots - 2688 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/338Z)×\left(\mathbb{Z}/338\mathbb{Z}\right)^\times.

nn 171171
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.00000 + 1.73205i −0.353553 + 0.612372i
33 4.07401 7.05638i 0.784043 1.35800i −0.145527 0.989354i 0.546488π-0.546488\pi
0.929569 0.368647i 0.120179π-0.120179\pi
44 −2.00000 3.46410i −0.250000 0.433013i
55 −12.6646 −1.13276 −0.566379 0.824145i 0.691656π-0.691656\pi
−0.566379 + 0.824145i 0.691656π0.691656\pi
66 8.14801 + 14.1128i 0.554402 + 0.960252i
77 14.3853 + 24.9160i 0.776732 + 1.34534i 0.933816 + 0.357753i 0.116457π0.116457\pi
−0.157085 + 0.987585i 0.550210π0.550210\pi
88 8.00000 0.353553
99 −19.6950 34.1128i −0.729446 1.26344i
1010 12.6646 21.9357i 0.400490 0.693669i
1111 26.4203 45.7613i 0.724183 1.25432i −0.235126 0.971965i 0.575550π-0.575550\pi
0.959309 0.282357i 0.0911164π-0.0911164\pi
1212 −32.5920 −0.784043
1313 0 0
1414 −57.5411 −1.09846
1515 −51.5957 + 89.3664i −0.888130 + 1.53829i
1616 −8.00000 + 13.8564i −0.125000 + 0.216506i
1717 −35.5161 61.5158i −0.506702 0.877633i −0.999970 0.00775579i 0.997531π-0.997531\pi
0.493268 0.869877i 0.335802π-0.335802\pi
1818 78.7801 1.03159
1919 −32.8843 56.9572i −0.397062 0.687731i 0.596300 0.802761i 0.296637π-0.296637\pi
−0.993362 + 0.115030i 0.963303π0.963303\pi
2020 25.3292 + 43.8715i 0.283189 + 0.490498i
2121 234.423 2.43596
2222 52.8406 + 91.5226i 0.512075 + 0.886940i
2323 22.2154 38.4783i 0.201402 0.348838i −0.747579 0.664173i 0.768784π-0.768784\pi
0.948980 + 0.315335i 0.102117π0.102117\pi
2424 32.5920 56.4511i 0.277201 0.480126i
2525 35.3924 0.283139
2626 0 0
2727 −100.954 −0.719581
2828 57.5411 99.6641i 0.388366 0.672669i
2929 39.2189 67.9292i 0.251130 0.434970i −0.712707 0.701462i 0.752531π-0.752531\pi
0.963837 + 0.266492i 0.0858645π0.0858645\pi
3030 −103.191 178.733i −0.628003 1.08773i
3131 −195.024 −1.12991 −0.564957 0.825120i 0.691107π-0.691107\pi
−0.564957 + 0.825120i 0.691107π0.691107\pi
3232 −16.0000 27.7128i −0.0883883 0.153093i
3333 −215.273 372.863i −1.13558 1.96688i
3434 142.065 0.716584
3535 −182.184 315.552i −0.879848 1.52394i
3636 −78.7801 + 136.451i −0.364723 + 0.631719i
3737 −116.595 + 201.948i −0.518055 + 0.897297i 0.481725 + 0.876322i 0.340010π0.340010\pi
−0.999780 + 0.0209750i 0.993323π0.993323\pi
3838 131.537 0.561530
3939 0 0
4040 −101.317 −0.400490
4141 −60.2286 + 104.319i −0.229418 + 0.397363i −0.957636 0.287983i 0.907015π-0.907015\pi
0.728218 + 0.685345i 0.240349π0.240349\pi
4242 −234.423 + 406.032i −0.861243 + 1.49172i
4343 −202.551 350.829i −0.718344 1.24421i −0.961656 0.274260i 0.911567π-0.911567\pi
0.243312 0.969948i 0.421766π-0.421766\pi
4444 −211.362 −0.724183
4545 249.430 + 432.025i 0.826285 + 1.43117i
4646 44.4309 + 76.9566i 0.142413 + 0.246666i
4747 −400.779 −1.24382 −0.621911 0.783088i 0.713643π-0.713643\pi
−0.621911 + 0.783088i 0.713643π0.713643\pi
4848 65.1841 + 112.902i 0.196011 + 0.339500i
4949 −242.372 + 419.800i −0.706624 + 1.22391i
5050 −35.3924 + 61.3014i −0.100105 + 0.173386i
5151 −578.772 −1.58910
5252 0 0
5353 116.566 0.302105 0.151052 0.988526i 0.451734π-0.451734\pi
0.151052 + 0.988526i 0.451734π0.451734\pi
5454 100.954 174.858i 0.254410 0.440652i
5555 −334.603 + 579.549i −0.820324 + 1.42084i
5656 115.082 + 199.328i 0.274616 + 0.475649i
5757 −535.883 −1.24525
5858 78.4379 + 135.858i 0.177576 + 0.307570i
5959 −390.718 676.744i −0.862155 1.49330i −0.869844 0.493326i 0.835781π-0.835781\pi
0.00768919 0.999970i 0.497552π-0.497552\pi
6060 412.765 0.888130
6161 −26.2781 45.5149i −0.0551567 0.0955343i 0.837129 0.547006i 0.184233π-0.184233\pi
−0.892285 + 0.451472i 0.850899π0.850899\pi
6262 195.024 337.792i 0.399485 0.691929i
6363 566.637 981.444i 1.13317 1.96270i
6464 64.0000 0.125000
6565 0 0
6666 861.091 1.60595
6767 402.652 697.414i 0.734206 1.27168i −0.220864 0.975305i 0.570888π-0.570888\pi
0.955071 0.296378i 0.0957789π-0.0957789\pi
6868 −142.065 + 246.063i −0.253351 + 0.438817i
6969 −181.012 313.521i −0.315815 0.547008i
7070 728.735 1.24429
7171 200.786 + 347.771i 0.335618 + 0.581307i 0.983603 0.180345i 0.0577216π-0.0577216\pi
−0.647985 + 0.761653i 0.724388π0.724388\pi
7272 −157.560 272.902i −0.257898 0.446692i
7373 323.057 0.517958 0.258979 0.965883i 0.416614π-0.416614\pi
0.258979 + 0.965883i 0.416614π0.416614\pi
7474 −233.189 403.895i −0.366320 0.634485i
7575 144.189 249.742i 0.221993 0.384503i
7676 −131.537 + 227.829i −0.198531 + 0.343865i
7777 1520.25 2.24998
7878 0 0
7979 −794.845 −1.13199 −0.565994 0.824409i 0.691507π-0.691507\pi
−0.565994 + 0.824409i 0.691507π0.691507\pi
8080 101.317 175.486i 0.141595 0.245249i
8181 120.477 208.673i 0.165264 0.286245i
8282 −120.457 208.638i −0.162223 0.280978i
8383 444.820 0.588258 0.294129 0.955766i 0.404971π-0.404971\pi
0.294129 + 0.955766i 0.404971π0.404971\pi
8484 −468.845 812.064i −0.608991 1.05480i
8585 449.798 + 779.073i 0.573970 + 0.994145i
8686 810.205 1.01589
8787 −319.556 553.488i −0.393793 0.682070i
8888 211.362 366.090i 0.256037 0.443470i
8989 −39.5736 + 68.5435i −0.0471325 + 0.0816359i −0.888629 0.458626i 0.848342π-0.848342\pi
0.841497 + 0.540262i 0.181675π0.181675\pi
9090 −997.720 −1.16854
9191 0 0
9292 −177.724 −0.201402
9393 −794.529 + 1376.16i −0.885901 + 1.53443i
9494 400.779 694.169i 0.439757 0.761682i
9595 416.467 + 721.341i 0.449774 + 0.779032i
9696 −260.736 −0.277201
9797 −1.94818 3.37434i −0.00203925 0.00353209i 0.865004 0.501765i 0.167316π-0.167316\pi
−0.867043 + 0.498233i 0.833982π0.833982\pi
9898 −484.744 839.601i −0.499658 0.865434i
9999 −2081.39 −2.11301
100100 −70.7847 122.603i −0.0707847 0.122603i
101101 517.657 896.609i 0.509988 0.883326i −0.489945 0.871754i 0.662983π-0.662983\pi
0.999933 0.0115723i 0.00368367π-0.00368367\pi
102102 578.772 1002.46i 0.561833 0.973123i
103103 1248.51 1.19436 0.597181 0.802107i 0.296287π-0.296287\pi
0.597181 + 0.802107i 0.296287π0.296287\pi
104104 0 0
105105 −2968.87 −2.75935
106106 −116.566 + 201.898i −0.106810 + 0.185001i
107107 581.006 1006.33i 0.524934 0.909212i −0.474644 0.880178i 0.657423π-0.657423\pi
0.999578 0.0290348i 0.00924335π-0.00924335\pi
108108 201.909 + 349.716i 0.179895 + 0.311588i
109109 −1003.58 −0.881885 −0.440943 0.897535i 0.645356π-0.645356\pi
−0.440943 + 0.897535i 0.645356π0.645356\pi
110110 −669.205 1159.10i −0.580057 1.00469i
111111 950.014 + 1645.47i 0.812354 + 1.40704i
112112 −460.329 −0.388366
113113 372.206 + 644.679i 0.309860 + 0.536693i 0.978332 0.207045i 0.0663845π-0.0663845\pi
−0.668472 + 0.743738i 0.733051π0.733051\pi
114114 535.883 928.176i 0.440263 0.762559i
115115 −281.350 + 487.312i −0.228139 + 0.395149i
116116 −313.751 −0.251130
117117 0 0
118118 1562.87 1.21927
119119 1021.82 1769.84i 0.787142 1.36337i
120120 −412.765 + 714.931i −0.314001 + 0.543866i
121121 −730.563 1265.37i −0.548883 0.950694i
122122 105.112 0.0780034
123123 490.743 + 849.992i 0.359746 + 0.623099i
124124 390.048 + 675.583i 0.282479 + 0.489267i
125125 1134.85 0.812030
126126 1133.27 + 1962.89i 0.801270 + 1.38784i
127127 −841.759 + 1457.97i −0.588142 + 1.01869i 0.406334 + 0.913725i 0.366807π0.366807\pi
−0.994476 + 0.104967i 0.966526π0.966526\pi
128128 −64.0000 + 110.851i −0.0441942 + 0.0765466i
129129 −3300.78 −2.25285
130130 0 0
131131 2177.87 1.45253 0.726266 0.687414i 0.241254π-0.241254\pi
0.726266 + 0.687414i 0.241254π0.241254\pi
132132 −861.091 + 1491.45i −0.567791 + 0.983442i
133133 946.098 1638.69i 0.616821 1.06836i
134134 805.305 + 1394.83i 0.519162 + 0.899215i
135135 1278.55 0.815110
136136 −284.129 492.126i −0.179146 0.310290i
137137 883.829 + 1530.84i 0.551172 + 0.954658i 0.998190 + 0.0601334i 0.0191526π0.0191526\pi
−0.447018 + 0.894525i 0.647514π0.647514\pi
138138 724.047 0.446630
139139 −502.768 870.819i −0.306793 0.531381i 0.670866 0.741579i 0.265923π-0.265923\pi
−0.977659 + 0.210198i 0.932589π0.932589\pi
140140 −728.735 + 1262.21i −0.439924 + 0.761971i
141141 −1632.78 + 2828.05i −0.975209 + 1.68911i
142142 −803.143 −0.474635
143143 0 0
144144 630.241 0.364723
145145 −496.692 + 860.297i −0.284469 + 0.492715i
146146 −323.057 + 559.551i −0.183126 + 0.317183i
147147 1974.85 + 3420.54i 1.10805 + 1.91919i
148148 932.757 0.518055
149149 68.1369 + 118.017i 0.0374631 + 0.0648879i 0.884149 0.467205i 0.154739π-0.154739\pi
−0.846686 + 0.532093i 0.821406π0.821406\pi
150150 288.377 + 499.484i 0.156973 + 0.271885i
151151 −804.394 −0.433514 −0.216757 0.976226i 0.569548π-0.569548\pi
−0.216757 + 0.976226i 0.569548π0.569548\pi
152152 −263.074 455.658i −0.140383 0.243150i
153153 −1398.98 + 2423.11i −0.739223 + 1.28037i
154154 −1520.25 + 2633.15i −0.795490 + 1.37783i
155155 2469.90 1.27992
156156 0 0
157157 3730.07 1.89613 0.948064 0.318079i 0.103038π-0.103038\pi
0.948064 + 0.318079i 0.103038π0.103038\pi
158158 794.845 1376.71i 0.400218 0.693198i
159159 474.890 822.534i 0.236863 0.410259i
160160 202.634 + 350.972i 0.100123 + 0.173417i
161161 1278.30 0.625740
162162 240.954 + 417.345i 0.116859 + 0.202406i
163163 −1311.63 2271.80i −0.630273 1.09166i −0.987496 0.157646i 0.949610π-0.949610\pi
0.357223 0.934019i 0.383724π-0.383724\pi
164164 481.828 0.229418
165165 2726.35 + 4722.17i 1.28634 + 2.22800i
166166 −444.820 + 770.451i −0.207980 + 0.360233i
167167 639.001 1106.78i 0.296092 0.512847i −0.679146 0.734003i 0.737650π-0.737650\pi
0.975238 + 0.221156i 0.0709831π0.0709831\pi
168168 1875.38 0.861243
169169 0 0
170170 −1799.19 −0.811716
171171 −1295.31 + 2243.55i −0.579270 + 1.00332i
172172 −810.205 + 1403.32i −0.359172 + 0.622104i
173173 −534.991 926.631i −0.235113 0.407228i 0.724192 0.689598i 0.242213π-0.242213\pi
−0.959306 + 0.282370i 0.908879π0.908879\pi
174174 1278.22 0.556908
175175 509.129 + 881.836i 0.219923 + 0.380918i
176176 422.725 + 732.181i 0.181046 + 0.313581i
177177 −6367.15 −2.70387
178178 −79.1472 137.087i −0.0333277 0.0577253i
179179 −368.774 + 638.736i −0.153986 + 0.266712i −0.932689 0.360681i 0.882544π-0.882544\pi
0.778703 + 0.627392i 0.215878π0.215878\pi
180180 997.720 1728.10i 0.413142 0.715584i
181181 −1457.02 −0.598338 −0.299169 0.954200i 0.596709π-0.596709\pi
−0.299169 + 0.954200i 0.596709π0.596709\pi
182182 0 0
183183 −428.228 −0.172981
184184 177.724 307.826i 0.0712063 0.123333i
185185 1476.62 2557.59i 0.586830 1.01642i
186186 −1589.06 2752.33i −0.626427 1.08500i
187187 −3753.39 −1.46778
188188 801.558 + 1388.34i 0.310955 + 0.538591i
189189 −1452.26 2515.38i −0.558921 0.968080i
190190 −1665.87 −0.636077
191191 −287.715 498.337i −0.108997 0.188788i 0.806367 0.591415i 0.201430π-0.201430\pi
−0.915364 + 0.402627i 0.868097π0.868097\pi
192192 260.736 451.609i 0.0980053 0.169750i
193193 −1219.36 + 2112.00i −0.454775 + 0.787694i −0.998675 0.0514564i 0.983614π-0.983614\pi
0.543900 + 0.839150i 0.316947π0.316947\pi
194194 7.79271 0.00288394
195195 0 0
196196 1938.98 0.706624
197197 −1911.76 + 3311.27i −0.691408 + 1.19755i 0.279969 + 0.960009i 0.409676π0.409676\pi
−0.971377 + 0.237544i 0.923658π0.923658\pi
198198 2081.39 3605.08i 0.747062 1.29395i
199199 1078.71 + 1868.37i 0.384258 + 0.665555i 0.991666 0.128835i 0.0411238π-0.0411238\pi
−0.607408 + 0.794390i 0.707790π0.707790\pi
200200 283.139 0.100105
201201 −3280.82 5682.54i −1.15130 1.99411i
202202 1035.31 + 1793.22i 0.360616 + 0.624606i
203203 2256.70 0.780243
204204 1157.54 + 2004.92i 0.397276 + 0.688102i
205205 762.771 1321.16i 0.259874 0.450116i
206206 −1248.51 + 2162.48i −0.422271 + 0.731394i
207207 −1750.14 −0.587647
208208 0 0
209209 −3475.25 −1.15018
210210 2968.87 5142.24i 0.975579 1.68975i
211211 −1681.93 + 2913.19i −0.548762 + 0.950484i 0.449598 + 0.893231i 0.351567π0.351567\pi
−0.998360 + 0.0572525i 0.981766π0.981766\pi
212212 −233.132 403.796i −0.0755262 0.130815i
213213 3272.01 1.05255
214214 1162.01 + 2012.66i 0.371184 + 0.642910i
215215 2565.23 + 4443.11i 0.813709 + 1.40939i
216216 −807.635 −0.254410
217217 −2805.47 4859.22i −0.877640 1.52012i
218218 1003.58 1738.25i 0.311794 0.540042i
219219 1316.13 2279.61i 0.406101 0.703388i
220220 2676.82 0.820324
221221 0 0
222222 −3800.06 −1.14884
223223 1646.95 2852.61i 0.494566 0.856613i −0.505415 0.862877i 0.668660π-0.668660\pi
0.999980 + 0.00626360i 0.00199378π0.00199378\pi
224224 460.329 797.313i 0.137308 0.237824i
225225 −697.054 1207.33i −0.206534 0.357728i
226226 −1488.82 −0.438208
227227 −271.743 470.673i −0.0794547 0.137620i 0.823560 0.567229i 0.191985π-0.191985\pi
−0.903015 + 0.429609i 0.858651π0.858651\pi
228228 1071.77 + 1856.35i 0.311313 + 0.539210i
229229 3071.66 0.886379 0.443189 0.896428i 0.353847π-0.353847\pi
0.443189 + 0.896428i 0.353847π0.353847\pi
230230 −562.700 974.625i −0.161319 0.279412i
231231 6193.51 10727.5i 1.76408 3.05548i
232232 313.751 543.433i 0.0887879 0.153785i
233233 3383.06 0.951208 0.475604 0.879660i 0.342230π-0.342230\pi
0.475604 + 0.879660i 0.342230π0.342230\pi
234234 0 0
235235 5075.71 1.40895
236236 −1562.87 + 2706.97i −0.431078 + 0.746648i
237237 −3238.20 + 5608.73i −0.887527 + 1.53724i
238238 2043.64 + 3539.68i 0.556594 + 0.964049i
239239 698.550 0.189060 0.0945302 0.995522i 0.469865π-0.469865\pi
0.0945302 + 0.995522i 0.469865π0.469865\pi
240240 −825.531 1429.86i −0.222032 0.384572i
241241 −1857.72 3217.67i −0.496541 0.860034i 0.503451 0.864024i 0.332063π-0.332063\pi
−0.999992 + 0.00398962i 0.998730π0.998730\pi
242242 2922.25 0.776238
243243 −2344.53 4060.85i −0.618938 1.07203i
244244 −105.112 + 182.060i −0.0275784 + 0.0477671i
245245 3069.55 5316.61i 0.800433 1.38639i
246246 −1962.97 −0.508758
247247 0 0
248248 −1560.19 −0.399485
249249 1812.20 3138.82i 0.461219 0.798855i
250250 −1134.85 + 1965.61i −0.287096 + 0.497265i
251251 1926.42 + 3336.65i 0.484440 + 0.839074i 0.999840 0.0178750i 0.00569010π-0.00569010\pi
−0.515400 + 0.856950i 0.672357π0.672357\pi
252252 −4533.09 −1.13317
253253 −1173.88 2033.21i −0.291704 0.505245i
254254 −1683.52 2915.94i −0.415879 0.720324i
255255 7329.92 1.80007
256256 −128.000 221.703i −0.0312500 0.0541266i
257257 −2288.73 + 3964.19i −0.555513 + 0.962177i 0.442350 + 0.896842i 0.354145π0.354145\pi
−0.997863 + 0.0653345i 0.979189π0.979189\pi
258258 3300.78 5717.12i 0.796502 1.37958i
259259 −6708.98 −1.60956
260260 0 0
261261 −3089.67 −0.732743
262262 −2177.87 + 3772.19i −0.513547 + 0.889490i
263263 2411.71 4177.21i 0.565447 0.979383i −0.431561 0.902084i 0.642037π-0.642037\pi
0.997008 0.0772990i 0.0246296π-0.0246296\pi
264264 −1722.18 2982.91i −0.401489 0.695399i
265265 −1476.26 −0.342212
266266 1892.20 + 3277.38i 0.436158 + 0.755448i
267267 322.446 + 558.493i 0.0739078 + 0.128012i
268268 −3221.22 −0.734206
269269 982.898 + 1702.43i 0.222782 + 0.385870i 0.955652 0.294499i 0.0951529π-0.0951529\pi
−0.732870 + 0.680369i 0.761820π0.761820\pi
270270 −1278.55 + 2214.51i −0.288185 + 0.499151i
271271 2207.96 3824.29i 0.494922 0.857230i −0.505061 0.863084i 0.668530π-0.668530\pi
0.999983 + 0.00585389i 0.00186336π0.00186336\pi
272272 1136.52 0.253351
273273 0 0
274274 −3535.32 −0.779475
275275 935.076 1619.60i 0.205044 0.355147i
276276 −724.047 + 1254.09i −0.157908 + 0.273504i
277277 −1806.11 3128.28i −0.391765 0.678557i 0.600917 0.799311i 0.294802π-0.294802\pi
−0.992682 + 0.120754i 0.961469π0.961469\pi
278278 2011.07 0.433871
279279 3841.01 + 6652.82i 0.824212 + 1.42758i
280280 −1457.47 2524.41i −0.311073 0.538795i
281281 4095.02 0.869353 0.434676 0.900587i 0.356863π-0.356863\pi
0.434676 + 0.900587i 0.356863π0.356863\pi
282282 −3265.55 5656.10i −0.689577 1.19438i
283283 −3363.10 + 5825.05i −0.706415 + 1.22355i 0.259764 + 0.965672i 0.416355π0.416355\pi
−0.966179 + 0.257874i 0.916978π0.916978\pi
284284 803.143 1391.08i 0.167809 0.290654i
285285 6786.75 1.41057
286286 0 0
287287 −3465.62 −0.712783
288288 −630.241 + 1091.61i −0.128949 + 0.223346i
289289 −66.2919 + 114.821i −0.0134932 + 0.0233709i
290290 −993.385 1720.59i −0.201150 0.348402i
291291 −31.7475 −0.00639544
292292 −646.114 1119.10i −0.129490 0.224282i
293293 −2251.72 3900.10i −0.448966 0.777632i 0.549353 0.835590i 0.314874π-0.314874\pi
−0.998319 + 0.0579584i 0.981541π0.981541\pi
294294 −7899.40 −1.56701
295295 4948.29 + 8570.69i 0.976613 + 1.69154i
296296 −932.757 + 1615.58i −0.183160 + 0.317243i
297297 −2667.24 + 4619.80i −0.521109 + 0.902586i
298298 −272.548 −0.0529808
299299 0 0
300300 −1153.51 −0.221993
301301 5827.51 10093.5i 1.11592 1.93283i
302302 804.394 1393.25i 0.153270 0.265472i
303303 −4217.88 7305.58i −0.799705 1.38513i
304304 1052.30 0.198531
305305 332.801 + 576.429i 0.0624792 + 0.108217i
306306 −2797.97 4846.22i −0.522709 0.905359i
307307 −1934.75 −0.359681 −0.179841 0.983696i 0.557558π-0.557558\pi
−0.179841 + 0.983696i 0.557558π0.557558\pi
308308 −3040.50 5266.31i −0.562496 0.974272i
309309 5086.43 8809.96i 0.936431 1.62195i
310310 −2469.90 + 4278.00i −0.452520 + 0.783787i
311311 −2655.72 −0.484219 −0.242110 0.970249i 0.577839π-0.577839\pi
−0.242110 + 0.970249i 0.577839π0.577839\pi
312312 0 0
313313 6102.36 1.10200 0.550999 0.834506i 0.314247π-0.314247\pi
0.550999 + 0.834506i 0.314247π0.314247\pi
314314 −3730.07 + 6460.67i −0.670383 + 1.16114i
315315 −7176.23 + 12429.6i −1.28360 + 2.22327i
316316 1589.69 + 2753.42i 0.282997 + 0.490165i
317317 1382.99 0.245037 0.122518 0.992466i 0.460903π-0.460903\pi
0.122518 + 0.992466i 0.460903π0.460903\pi
318318 949.781 + 1645.07i 0.167488 + 0.290097i
319319 −2072.35 3589.42i −0.363728 0.629996i
320320 −810.535 −0.141595
321321 −4734.04 8199.60i −0.823141 1.42572i
322322 −1278.30 + 2214.08i −0.221233 + 0.383186i
323323 −2335.85 + 4045.80i −0.402384 + 0.696949i
324324 −963.817 −0.165264
325325 0 0
326326 5246.50 0.891340
327327 −4088.59 + 7081.64i −0.691436 + 1.19760i
328328 −481.828 + 834.551i −0.0811114 + 0.140489i
329329 −5765.31 9985.81i −0.966115 1.67336i
330330 −10905.4 −1.81916
331331 5003.33 + 8666.02i 0.830839 + 1.43906i 0.897374 + 0.441271i 0.145472π0.145472\pi
−0.0665347 + 0.997784i 0.521194π0.521194\pi
332332 −889.641 1540.90i −0.147064 0.254723i
333333 9185.34 1.51157
334334 1278.00 + 2213.57i 0.209369 + 0.362637i
335335 −5099.44 + 8832.48i −0.831678 + 1.44051i
336336 −1875.38 + 3248.26i −0.304495 + 0.527401i
337337 11057.1 1.78730 0.893649 0.448767i 0.148137π-0.148137\pi
0.893649 + 0.448767i 0.148137π0.148137\pi
338338 0 0
339339 6065.47 0.971773
340340 1799.19 3116.29i 0.286985 0.497073i
341341 −5152.59 + 8924.55i −0.818266 + 1.41728i
342342 −2590.63 4487.10i −0.409606 0.709458i
343343 −4078.05 −0.641964
344344 −1620.41 2806.63i −0.253973 0.439894i
345345 2292.44 + 3970.63i 0.357742 + 0.619627i
346346 2139.96 0.332500
347347 4316.98 + 7477.22i 0.667860 + 1.15677i 0.978501 + 0.206240i 0.0661228π0.0661228\pi
−0.310642 + 0.950527i 0.600544π0.600544\pi
348348 −1278.22 + 2213.95i −0.196897 + 0.341035i
349349 −4684.53 + 8113.84i −0.718502 + 1.24448i 0.243092 + 0.970003i 0.421838π0.421838\pi
−0.961593 + 0.274478i 0.911495π0.911495\pi
350350 −2036.51 −0.311018
351351 0 0
352352 −1690.90 −0.256037
353353 2508.93 4345.59i 0.378291 0.655220i −0.612522 0.790453i 0.709845π-0.709845\pi
0.990814 + 0.135233i 0.0431784π0.0431784\pi
354354 6367.15 11028.2i 0.955961 1.65577i
355355 −2542.87 4404.38i −0.380174 0.658480i
356356 316.589 0.0471325
357357 −8325.79 14420.7i −1.23431 2.13788i
358358 −737.549 1277.47i −0.108885 0.188594i
359359 7268.33 1.06855 0.534273 0.845312i 0.320586π-0.320586\pi
0.534273 + 0.845312i 0.320586π0.320586\pi
360360 1995.44 + 3456.20i 0.292136 + 0.505994i
361361 1266.75 2194.07i 0.184684 0.319882i
362362 1457.02 2523.63i 0.211545 0.366406i
363363 −11905.3 −1.72139
364364 0 0
365365 −4091.39 −0.586721
366366 428.228 741.712i 0.0611580 0.105929i
367367 −5943.72 + 10294.8i −0.845394 + 1.46427i 0.0398848 + 0.999204i 0.487301π0.487301\pi
−0.885279 + 0.465061i 0.846032π0.846032\pi
368368 355.447 + 615.652i 0.0503504 + 0.0872095i
369369 4744.81 0.669391
370370 2953.25 + 5115.18i 0.414952 + 0.718718i
371371 1676.83 + 2904.36i 0.234654 + 0.406433i
372372 6356.23 0.885901
373373 7117.28 + 12327.5i 0.987986 + 1.71124i 0.627830 + 0.778350i 0.283943π0.283943\pi
0.360156 + 0.932892i 0.382723π0.382723\pi
374374 3753.39 6501.06i 0.518939 0.898828i
375375 4623.37 8007.91i 0.636666 1.10274i
376376 −3206.23 −0.439757
377377 0 0
378378 5809.03 0.790434
379379 −3960.04 + 6859.00i −0.536712 + 0.929612i 0.462366 + 0.886689i 0.347000π0.347000\pi
−0.999078 + 0.0429233i 0.986333π0.986333\pi
380380 1665.87 2885.37i 0.224887 0.389516i
381381 6858.66 + 11879.5i 0.922257 + 1.59740i
382382 1150.86 0.154144
383383 −5313.47 9203.20i −0.708892 1.22784i −0.965268 0.261260i 0.915862π-0.915862\pi
0.256376 0.966577i 0.417471π-0.417471\pi
384384 521.473 + 903.217i 0.0693002 + 0.120032i
385385 −19253.4 −2.54869
386386 −2438.72 4223.99i −0.321575 0.556983i
387387 −7978.51 + 13819.2i −1.04799 + 1.81516i
388388 −7.79271 + 13.4974i −0.00101963 + 0.00176604i
389389 −10183.7 −1.32733 −0.663667 0.748028i 0.731001π-0.731001\pi
−0.663667 + 0.748028i 0.731001π0.731001\pi
390390 0 0
391391 −3156.03 −0.408202
392392 −1938.98 + 3358.40i −0.249829 + 0.432717i
393393 8872.66 15367.9i 1.13885 1.97254i
394394 −3823.52 6622.53i −0.488899 0.846798i
395395 10066.4 1.28227
396396 4162.79 + 7210.16i 0.528252 + 0.914960i
397397 −1826.03 3162.78i −0.230846 0.399837i 0.727211 0.686414i 0.240816π-0.240816\pi
−0.958057 + 0.286577i 0.907483π0.907483\pi
398398 −4314.82 −0.543424
399399 −7708.82 13352.1i −0.967227 1.67529i
400400 −283.139 + 490.411i −0.0353924 + 0.0613014i
401401 4442.35 7694.37i 0.553217 0.958200i −0.444823 0.895619i 0.646733π-0.646733\pi
0.998040 0.0625817i 0.0199334π-0.0199334\pi
402402 13123.3 1.62818
403403 0 0
404404 −4141.26 −0.509988
405405 −1525.80 + 2642.76i −0.187204 + 0.324246i
406406 −2256.70 + 3908.72i −0.275857 + 0.477799i
407407 6160.93 + 10671.0i 0.750334 + 1.29962i
408408 −4630.17 −0.561833
409409 5733.99 + 9931.55i 0.693221 + 1.20069i 0.970777 + 0.239984i 0.0771423π0.0771423\pi
−0.277556 + 0.960709i 0.589524π0.589524\pi
410410 1525.54 + 2642.32i 0.183759 + 0.318280i
411411 14402.9 1.72857
412412 −2497.02 4324.96i −0.298590 0.517174i
413413 11241.2 19470.3i 1.33933 2.31978i
414414 1750.14 3031.32i 0.207764 0.359859i
415415 −5633.48 −0.666353
416416 0 0
417417 −8193.11 −0.962155
418418 3475.25 6019.31i 0.406651 0.704340i
419419 7957.04 13782.0i 0.927749 1.60691i 0.140669 0.990057i 0.455075π-0.455075\pi
0.787080 0.616851i 0.211592π-0.211592\pi
420420 5937.74 + 10284.5i 0.689839 + 1.19484i
421421 −3091.64 −0.357904 −0.178952 0.983858i 0.557271π-0.557271\pi
−0.178952 + 0.983858i 0.557271π0.557271\pi
422422 −3363.86 5826.37i −0.388033 0.672093i
423423 7893.35 + 13671.7i 0.907300 + 1.57149i
424424 932.528 0.106810
425425 −1257.00 2177.19i −0.143467 0.248492i
426426 −3272.01 + 5667.28i −0.372134 + 0.644556i
427427 756.034 1309.49i 0.0856840 0.148409i
428428 −4648.05 −0.524934
429429 0 0
430430 −10260.9 −1.15076
431431 −2498.35 + 4327.26i −0.279214 + 0.483612i −0.971190 0.238308i 0.923407π-0.923407\pi
0.691976 + 0.721921i 0.256740π0.256740\pi
432432 807.635 1398.87i 0.0899476 0.155794i
433433 920.918 + 1595.08i 0.102209 + 0.177031i 0.912594 0.408866i 0.134076π-0.134076\pi
−0.810386 + 0.585897i 0.800742π0.800742\pi
434434 11221.9 1.24117
435435 4047.06 + 7009.71i 0.446072 + 0.772620i
436436 2007.16 + 3476.50i 0.220471 + 0.381868i
437437 −2922.16 −0.319876
438438 2632.27 + 4559.23i 0.287157 + 0.497370i
439439 −4981.61 + 8628.40i −0.541593 + 0.938066i 0.457220 + 0.889354i 0.348845π0.348845\pi
−0.998813 + 0.0487128i 0.984488π0.984488\pi
440440 −2676.82 + 4636.39i −0.290028 + 0.502344i
441441 19094.1 2.06177
442442 0 0
443443 −8480.02 −0.909476 −0.454738 0.890625i 0.650267π-0.650267\pi
−0.454738 + 0.890625i 0.650267π0.650267\pi
444444 3800.06 6581.89i 0.406177 0.703519i
445445 501.184 868.076i 0.0533897 0.0924736i
446446 3293.91 + 5705.21i 0.349711 + 0.605717i
447447 1110.36 0.117491
448448 920.657 + 1594.63i 0.0970914 + 0.168167i
449449 −1725.34 2988.37i −0.181344 0.314098i 0.760994 0.648759i 0.224712π-0.224712\pi
−0.942339 + 0.334661i 0.891378π0.891378\pi
450450 2788.21 0.292084
451451 3182.51 + 5512.27i 0.332281 + 0.575527i
452452 1488.82 2578.72i 0.154930 0.268347i
453453 −3277.10 + 5676.11i −0.339893 + 0.588713i
454454 1086.97 0.112366
455455 0 0
456456 −4287.06 −0.440263
457457 −3270.61 + 5664.87i −0.334776 + 0.579850i −0.983442 0.181224i 0.941994π-0.941994\pi
0.648666 + 0.761074i 0.275327π0.275327\pi
458458 −3071.66 + 5320.27i −0.313382 + 0.542794i
459459 3585.51 + 6210.29i 0.364613 + 0.631528i
460460 2250.80 0.228139
461461 −7306.92 12656.0i −0.738215 1.27863i −0.953298 0.302030i 0.902336π-0.902336\pi
0.215083 0.976596i 0.430998π-0.430998\pi
462462 12387.0 + 21455.0i 1.24740 + 2.16055i
463463 −3680.01 −0.369383 −0.184692 0.982797i 0.559129π-0.559129\pi
−0.184692 + 0.982797i 0.559129π0.559129\pi
464464 627.503 + 1086.87i 0.0627825 + 0.108743i
465465 10062.4 17428.6i 1.00351 1.73813i
466466 −3383.06 + 5859.63i −0.336303 + 0.582494i
467467 457.544 0.0453375 0.0226687 0.999743i 0.492784π-0.492784\pi
0.0226687 + 0.999743i 0.492784π0.492784\pi
468468 0 0
469469 23169.1 2.28112
470470 −5075.71 + 8791.39i −0.498138 + 0.862801i
471471 15196.3 26320.8i 1.48665 2.57495i
472472 −3125.74 5413.95i −0.304818 0.527960i
473473 −21405.9 −2.08085
474474 −6476.40 11217.5i −0.627576 1.08699i
475475 −1163.85 2015.85i −0.112424 0.194723i
476476 −8174.55 −0.787142
477477 −2295.77 3976.39i −0.220369 0.381691i
478478 −698.550 + 1209.92i −0.0668429 + 0.115775i
479479 4885.47 8461.88i 0.466018 0.807167i −0.533229 0.845971i 0.679021π-0.679021\pi
0.999247 + 0.0388039i 0.0123548π0.0123548\pi
480480 3302.12 0.314001
481481 0 0
482482 7430.89 0.702215
483483 5207.80 9020.18i 0.490607 0.849756i
484484 −2922.25 + 5061.49i −0.274442 + 0.475347i
485485 24.6729 + 42.7347i 0.00230998 + 0.00400100i
486486 9378.13 0.875310
487487 −10125.1 17537.2i −0.942118 1.63180i −0.761421 0.648258i 0.775498π-0.775498\pi
−0.180698 0.983539i 0.557836π-0.557836\pi
488488 −210.225 364.120i −0.0195009 0.0337765i
489489 −21374.3 −1.97664
490490 6139.09 + 10633.2i 0.565992 + 0.980326i
491491 8639.72 14964.4i 0.794104 1.37543i −0.129303 0.991605i 0.541274π-0.541274\pi
0.923407 0.383823i 0.125393π-0.125393\pi
492492 1962.97 3399.97i 0.179873 0.311549i
493493 −5571.62 −0.508992
494494 0 0
495495 26360.0 2.39353
496496 1560.19 2702.33i 0.141239 0.244634i
497497 −5776.71 + 10005.6i −0.521370 + 0.903039i
498498 3624.40 + 6277.65i 0.326131 + 0.564876i
499499 16994.7 1.52462 0.762310 0.647212i 0.224065π-0.224065\pi
0.762310 + 0.647212i 0.224065π0.224065\pi
500500 −2269.69 3931.22i −0.203007 0.351619i
501501 −5206.59 9018.08i −0.464298 0.804188i
502502 −7705.67 −0.685101
503503 −1550.97 2686.35i −0.137483 0.238128i 0.789060 0.614316i 0.210568π-0.210568\pi
−0.926543 + 0.376188i 0.877235π0.877235\pi
504504 4533.09 7851.55i 0.400635 0.693920i
505505 −6555.93 + 11355.2i −0.577693 + 1.00059i
506506 4695.51 0.412531
507507 0 0
508508 6734.07 0.588142
509509 9973.82 17275.2i 0.868530 1.50434i 0.00503052 0.999987i 0.498399π-0.498399\pi
0.863499 0.504350i 0.168268π-0.168268\pi
510510 −7329.92 + 12695.8i −0.636420 + 1.10231i
511511 4647.26 + 8049.29i 0.402314 + 0.696829i
512512 512.000 0.0441942
513513 3319.81 + 5750.09i 0.285718 + 0.494878i
514514 −4577.45 7928.38i −0.392807 0.680362i
515515 −15811.9 −1.35292
516516 6601.56 + 11434.2i 0.563212 + 0.975512i
517517 −10588.7 + 18340.2i −0.900755 + 1.56015i
518518 6708.98 11620.3i 0.569065 0.985649i
519519 −8718.22 −0.737355
520520 0 0
521521 −18106.1 −1.52254 −0.761270 0.648436i 0.775424π-0.775424\pi
−0.761270 + 0.648436i 0.775424π0.775424\pi
522522 3089.67 5351.47i 0.259064 0.448712i
523523 427.606 740.635i 0.0357512 0.0619229i −0.847596 0.530642i 0.821951π-0.821951\pi
0.883347 + 0.468719i 0.155284π0.155284\pi
524524 −4355.74 7544.37i −0.363133 0.628964i
525525 8296.77 0.689716
526526 4823.42 + 8354.42i 0.399831 + 0.692528i
527527 6926.50 + 11997.1i 0.572530 + 0.991651i
528528 6888.73 0.567791
529529 5096.45 + 8827.31i 0.418875 + 0.725512i
530530 1476.26 2556.96i 0.120990 0.209561i
531531 −15390.4 + 26657.0i −1.25779 + 2.17856i
532532 −7568.79 −0.616821
533533 0 0
534534 −1289.78 −0.104521
535535 −7358.21 + 12744.8i −0.594623 + 1.02992i
536536 3221.22 5579.32i 0.259581 0.449608i
537537 3004.78 + 5204.43i 0.241463 + 0.418226i
538538 −3931.59 −0.315061
539539 12807.1 + 22182.5i 1.02345 + 1.77267i
540540 −2557.10 4429.02i −0.203778 0.352953i
541541 −12326.5 −0.979592 −0.489796 0.871837i 0.662929π-0.662929\pi
−0.489796 + 0.871837i 0.662929π0.662929\pi
542542 4415.91 + 7648.59i 0.349963 + 0.606153i
543543 −5935.90 + 10281.3i −0.469123 + 0.812544i
544544 −1136.52 + 1968.50i −0.0895730 + 0.155145i
545545 12709.9 0.998962
546546 0 0
547547 7326.20 0.572661 0.286330 0.958131i 0.407564π-0.407564\pi
0.286330 + 0.958131i 0.407564π0.407564\pi
548548 3535.32 6123.35i 0.275586 0.477329i
549549 −1035.09 + 1792.84i −0.0804677 + 0.139374i
550550 1870.15 + 3239.20i 0.144988 + 0.251127i
551551 −5158.75 −0.398857
552552 −1448.09 2508.17i −0.111658 0.193396i
553553 −11434.1 19804.4i −0.879251 1.52291i
554554 7224.46 0.554039
555555 −12031.6 20839.3i −0.920200 1.59383i
556556 −2011.07 + 3483.28i −0.153396 + 0.265690i
557557 −291.685 + 505.212i −0.0221886 + 0.0384318i −0.876907 0.480661i 0.840397π-0.840397\pi
0.854718 + 0.519093i 0.173730π0.173730\pi
558558 −15364.0 −1.16561
559559 0 0
560560 5829.88 0.439924
561561 −15291.3 + 26485.3i −1.15080 + 1.99325i
562562 −4095.02 + 7092.78i −0.307363 + 0.532368i
563563 −2719.97 4711.13i −0.203611 0.352665i 0.746078 0.665858i 0.231935π-0.231935\pi
−0.949689 + 0.313193i 0.898601π0.898601\pi
564564 13062.2 0.975209
565565 −4713.84 8164.61i −0.350996 0.607943i
566566 −6726.19 11650.1i −0.499511 0.865178i
567567 6932.39 0.513462
568568 1606.29 + 2782.17i 0.118659 + 0.205523i
569569 −9071.62 + 15712.5i −0.668369 + 1.15765i 0.309991 + 0.950739i 0.399674π0.399674\pi
−0.978360 + 0.206910i 0.933659π0.933659\pi
570570 −6786.75 + 11755.0i −0.498712 + 0.863794i
571571 12916.3 0.946634 0.473317 0.880892i 0.343056π-0.343056\pi
0.473317 + 0.880892i 0.343056π0.343056\pi
572572 0 0
573573 −4688.61 −0.341832
574574 3465.62 6002.62i 0.252007 0.436489i
575575 786.257 1361.84i 0.0570247 0.0987696i
576576 −1260.48 2183.22i −0.0911807 0.157930i
577577 1345.12 0.0970504 0.0485252 0.998822i 0.484548π-0.484548\pi
0.0485252 + 0.998822i 0.484548π0.484548\pi
578578 −132.584 229.642i −0.00954111 0.0165257i
579579 9935.37 + 17208.6i 0.713126 + 1.23517i
580580 3973.54 0.284469
581581 6398.86 + 11083.2i 0.456918 + 0.791405i
582582 31.7475 54.9883i 0.00226113 0.00391639i
583583 3079.71 5334.21i 0.218779 0.378937i
584584 2584.45 0.183126
585585 0 0
586586 9006.89 0.634934
587587 4968.49 8605.67i 0.349355 0.605100i −0.636780 0.771045i 0.719734π-0.719734\pi
0.986135 + 0.165945i 0.0530674π0.0530674\pi
588588 7899.40 13682.2i 0.554023 0.959596i
589589 6413.23 + 11108.0i 0.448646 + 0.777077i
590590 −19793.2 −1.38114
591591 15577.0 + 26980.2i 1.08419 + 1.87787i
592592 −1865.51 3231.16i −0.129514 0.224324i
593593 −15740.8 −1.09005 −0.545024 0.838420i 0.683480π-0.683480\pi
−0.545024 + 0.838420i 0.683480π0.683480\pi
594594 −5334.49 9239.61i −0.368479 0.638225i
595595 −12940.9 + 22414.4i −0.891641 + 1.54437i
596596 272.548 472.067i 0.0187315 0.0324440i
597597 17578.6 1.20510
598598 0 0
599599 −6079.68 −0.414706 −0.207353 0.978266i 0.566485π-0.566485\pi
−0.207353 + 0.978266i 0.566485π0.566485\pi
600600 1153.51 1997.94i 0.0784863 0.135942i
601601 6882.14 11920.2i 0.467102 0.809045i −0.532191 0.846624i 0.678631π-0.678631\pi
0.999294 + 0.0375793i 0.0119647π0.0119647\pi
602602 11655.0 + 20187.1i 0.789075 + 1.36672i
603603 −31721.0 −2.14225
604604 1608.79 + 2786.50i 0.108379 + 0.187717i
605605 9252.30 + 16025.5i 0.621751 + 1.07690i
606606 16871.5 1.13095
607607 −8132.99 14086.8i −0.543835 0.941950i −0.998679 0.0513790i 0.983638π-0.983638\pi
0.454844 0.890571i 0.349695π-0.349695\pi
608608 −1052.30 + 1822.63i −0.0701913 + 0.121575i
609609 9193.81 15924.1i 0.611743 1.05957i
610610 −1331.21 −0.0883589
611611 0 0
612612 11191.9 0.739223
613613 6247.17 10820.4i 0.411616 0.712940i −0.583450 0.812149i 0.698298π-0.698298\pi
0.995067 + 0.0992084i 0.0316310π0.0316310\pi
614614 1934.75 3351.09i 0.127167 0.220259i
615615 −6215.07 10764.8i −0.407505 0.705820i
616616 12162.0 0.795490
617617 7233.90 + 12529.5i 0.472003 + 0.817534i 0.999487 0.0320316i 0.0101977π-0.0101977\pi
−0.527484 + 0.849565i 0.676864π0.676864\pi
618618 10172.9 + 17619.9i 0.662156 + 1.14689i
619619 7989.85 0.518803 0.259401 0.965770i 0.416475π-0.416475\pi
0.259401 + 0.965770i 0.416475π0.416475\pi
620620 −4939.81 8556.00i −0.319980 0.554221i
621621 −2242.75 + 3884.55i −0.144925 + 0.251017i
622622 2655.72 4599.85i 0.171197 0.296523i
623623 −2277.11 −0.146437
624624 0 0
625625 −18796.4 −1.20297
626626 −6102.36 + 10569.6i −0.389615 + 0.674834i
627627 −14158.2 + 24522.7i −0.901792 + 1.56195i
628628 −7460.14 12921.3i −0.474032 0.821048i
629629 16564.0 1.05000
630630 −14352.5 24859.2i −0.907644 1.57209i
631631 −9484.25 16427.2i −0.598355 1.03638i −0.993064 0.117575i 0.962488π-0.962488\pi
0.394709 0.918806i 0.370845π-0.370845\pi
632632 −6358.76 −0.400218
633633 13704.4 + 23736.7i 0.860506 + 1.49044i
634634 −1382.99 + 2395.42i −0.0866336 + 0.150054i
635635 10660.5 18464.6i 0.666222 1.15393i
636636 −3799.12 −0.236863
637637 0 0
638638 8289.40 0.514390
639639 7908.96 13698.7i 0.489630 0.848064i
640640 810.535 1403.89i 0.0500613 0.0867087i
641641 −12260.2 21235.3i −0.755459 1.30849i −0.945146 0.326649i 0.894081π-0.894081\pi
0.189687 0.981845i 0.439253π-0.439253\pi
642642 18936.2 1.16410
643643 −5887.83 10198.0i −0.361110 0.625460i 0.627034 0.778992i 0.284269π-0.284269\pi
−0.988144 + 0.153532i 0.950935π0.950935\pi
644644 −2556.60 4428.16i −0.156435 0.270954i
645645 41803.1 2.55193
646646 −4671.69 8091.61i −0.284528 0.492817i
647647 10917.4 18909.5i 0.663382 1.14901i −0.316340 0.948646i 0.602454π-0.602454\pi
0.979721 0.200365i 0.0642128π-0.0642128\pi
648648 963.817 1669.38i 0.0584295 0.101203i
649649 −41291.5 −2.49743
650650 0 0
651651 −45718.1 −2.75243
652652 −5246.50 + 9087.21i −0.315136 + 0.545832i
653653 −3663.85 + 6345.98i −0.219567 + 0.380302i −0.954676 0.297648i 0.903798π-0.903798\pi
0.735108 + 0.677950i 0.237131π0.237131\pi
654654 −8177.18 14163.3i −0.488919 0.846832i
655655 −27581.9 −1.64537
656656 −963.657 1669.10i −0.0573544 0.0993407i
657657 −6362.61 11020.4i −0.377822 0.654407i
658658 23061.2 1.36629
659659 4184.17 + 7247.20i 0.247333 + 0.428393i 0.962785 0.270269i 0.0871126π-0.0871126\pi
−0.715452 + 0.698662i 0.753779π0.753779\pi
660660 10905.4 18888.7i 0.643169 1.11400i
661661 −7591.06 + 13148.1i −0.446684 + 0.773679i −0.998168 0.0605065i 0.980728π-0.980728\pi
0.551484 + 0.834185i 0.314062π0.314062\pi
662662 −20013.3 −1.17498
663663 0 0
664664 3558.56 0.207980
665665 −11982.0 + 20753.4i −0.698708 + 1.21020i
666666 −9185.34 + 15909.5i −0.534421 + 0.925645i
667667 −1742.53 3018.15i −0.101156 0.175207i
668668 −5112.01 −0.296092
669669 −13419.4 23243.1i −0.775521 1.34324i
670670 −10198.9 17665.0i −0.588085 1.01859i
671671 −2777.10 −0.159774
672672 −3750.76 6496.51i −0.215311 0.372929i
673673 9952.15 17237.6i 0.570026 0.987314i −0.426537 0.904470i 0.640267π-0.640267\pi
0.996563 0.0828434i 0.0264001π-0.0264001\pi
674674 −11057.1 + 19151.5i −0.631905 + 1.09449i
675675 −3573.01 −0.203741
676676 0 0
677677 −10760.9 −0.610896 −0.305448 0.952209i 0.598806π-0.598806\pi
−0.305448 + 0.952209i 0.598806π0.598806\pi
678678 −6065.47 + 10505.7i −0.343574 + 0.595087i
679679 56.0501 97.0816i 0.00316790 0.00548697i
680680 3598.38 + 6232.58i 0.202929 + 0.351483i
681681 −4428.33 −0.249183
682682 −10305.2 17849.1i −0.578601 1.00217i
683683 11589.1 + 20073.0i 0.649262 + 1.12456i 0.983299 + 0.181995i 0.0582556π0.0582556\pi
−0.334037 + 0.942560i 0.608411π0.608411\pi
684684 10362.5 0.579270
685685 −11193.3 19387.4i −0.624344 1.08140i
686686 4078.05 7063.38i 0.226969 0.393121i
687687 12513.9 21674.8i 0.694959 1.20370i
688688 6481.64 0.359172
689689 0 0
690690 −9169.77 −0.505923
691691 −8675.41 + 15026.3i −0.477610 + 0.827244i −0.999671 0.0256641i 0.991830π-0.991830\pi
0.522061 + 0.852908i 0.325163π0.325163\pi
692692 −2139.96 + 3706.53i −0.117557 + 0.203614i
693693 −29941.4 51860.1i −1.64124 2.84271i
694694 −17267.9 −0.944497
695695 6367.36 + 11028.6i 0.347522 + 0.601925i
696696 −2556.45 4427.90i −0.139227 0.241148i
697697 8556.34 0.464985
698698 −9369.06 16227.7i −0.508057 0.879981i
699699 13782.6 23872.2i 0.745788 1.29174i
700700 2036.51 3527.35i 0.109961 0.190459i
701701 50.2552 0.00270772 0.00135386 0.999999i 0.499569π-0.499569\pi
0.00135386 + 0.999999i 0.499569π0.499569\pi
702702 0 0
703703 15336.5 0.822799
704704 1690.90 2928.72i 0.0905229 0.156790i
705705 20678.5 35816.1i 1.10468 1.91335i
706706 5017.86 + 8691.19i 0.267492 + 0.463311i
707707 29786.6 1.58450
708708 12734.3 + 22056.5i 0.675966 + 1.17081i
709709 12727.2 + 22044.2i 0.674163 + 1.16768i 0.976713 + 0.214550i 0.0688286π0.0688286\pi
−0.302550 + 0.953133i 0.597838π0.597838\pi
710710 10171.5 0.537647
711711 15654.5 + 27114.4i 0.825724 + 1.43020i
712712 −316.589 + 548.348i −0.0166639 + 0.0288626i
713713 −4332.55 + 7504.19i −0.227567 + 0.394157i
714714 33303.1 1.74557
715715 0 0
716716 2950.20 0.153986
717717 2845.90 4929.24i 0.148231 0.256744i
718718 −7268.33 + 12589.1i −0.377788 + 0.654348i
719719 −3742.99 6483.06i −0.194145 0.336269i 0.752475 0.658621i 0.228860π-0.228860\pi
−0.946620 + 0.322352i 0.895527π0.895527\pi
720720 −7981.76 −0.413142
721721 17960.1 + 31107.9i 0.927698 + 1.60682i
722722 2533.50 + 4388.14i 0.130591 + 0.226191i
723723 −30273.5 −1.55724
724724 2914.03 + 5047.26i 0.149585 + 0.259088i
725725 1388.05 2404.17i 0.0711047 0.123157i
726726 11905.3 20620.5i 0.608604 1.05413i
727727 19443.6 0.991919 0.495959 0.868346i 0.334817π-0.334817\pi
0.495959 + 0.868346i 0.334817π0.334817\pi
728728 0 0
729729 −31700.8 −1.61057
730730 4091.39 7086.49i 0.207437 0.359292i
731731 −14387.7 + 24920.2i −0.727972 + 1.26088i
732732 856.456 + 1483.42i 0.0432452 + 0.0749030i
733733 24222.3 1.22056 0.610280 0.792186i 0.291057π-0.291057\pi
0.610280 + 0.792186i 0.291057π0.291057\pi
734734 −11887.4 20589.6i −0.597784 1.03539i
735735 −25010.7 43319.8i −1.25515 2.17398i
736736 −1421.79 −0.0712063
737737 −21276.4 36851.8i −1.06340 1.84186i
738738 −4744.81 + 8218.26i −0.236665 + 0.409916i
739739 −1805.33 + 3126.92i −0.0898647 + 0.155650i −0.907454 0.420152i 0.861977π-0.861977\pi
0.817589 + 0.575802i 0.195310π0.195310\pi
740740 −11813.0 −0.586830
741741 0 0
742742 −6707.33 −0.331852
743743 13089.8 22672.2i 0.646324 1.11947i −0.337670 0.941264i 0.609639π-0.609639\pi
0.983994 0.178201i 0.0570278π-0.0570278\pi
744744 −6356.23 + 11009.3i −0.313213 + 0.542502i
745745 −862.928 1494.63i −0.0424365 0.0735022i
746746 −28469.1 −1.39722
747747 −8760.75 15174.1i −0.429102 0.743226i
748748 7506.77 + 13002.1i 0.366945 + 0.635567i
749749 33431.7 1.63093
750750 9246.74 + 16015.8i 0.450191 + 0.779753i
751751 −6379.01 + 11048.8i −0.309951 + 0.536851i −0.978351 0.206950i 0.933646π-0.933646\pi
0.668400 + 0.743802i 0.266979π0.266979\pi
752752 3206.23 5553.36i 0.155478 0.269295i
753753 31392.9 1.51929
754754 0 0
755755 10187.3 0.491066
756756 −5809.03 + 10061.5i −0.279461 + 0.484040i
757757 −39.2371 + 67.9606i −0.00188388 + 0.00326297i −0.866966 0.498368i 0.833933π-0.833933\pi
0.865082 + 0.501631i 0.167266π0.167266\pi
758758 −7920.09 13718.0i −0.379513 0.657335i
759759 −19129.5 −0.914832
760760 3331.73 + 5770.73i 0.159019 + 0.275429i
761761 8488.84 + 14703.1i 0.404363 + 0.700377i 0.994247 0.107111i 0.0341600π-0.0341600\pi
−0.589884 + 0.807488i 0.700827π0.700827\pi
762762 −27434.6 −1.30427
763763 −14436.8 25005.2i −0.684988 1.18643i
764764 −1150.86 + 1993.35i −0.0544983 + 0.0943938i
765765 17717.6 30687.7i 0.837360 1.45035i
766766 21253.9 1.00252
767767 0 0
768768 −2085.89 −0.0980053
769769 11494.7 19909.4i 0.539024 0.933616i −0.459933 0.887954i 0.652127π-0.652127\pi
0.998957 0.0456629i 0.0145400π-0.0145400\pi
770770 19253.4 33347.9i 0.901096 1.56074i
771771 18648.6 + 32300.3i 0.871092 + 1.50878i
772772 9754.90 0.454775
773773 3016.71 + 5225.10i 0.140367 + 0.243123i 0.927635 0.373488i 0.121838π-0.121838\pi
−0.787268 + 0.616611i 0.788505π0.788505\pi
774774 −15957.0 27638.4i −0.741038 1.28351i
775775 −6902.36 −0.319923
776776 −15.5854 26.9947i −0.000720984 0.00124878i
777777 −27332.4 + 47341.1i −1.26196 + 2.18578i
778778 10183.7 17638.6i 0.469283 0.812823i
779779 7922.29 0.364372
780780 0 0
781781 21219.3 0.972196
782782 3156.03 5466.40i 0.144321 0.249972i
783783 −3959.32 + 6857.75i −0.180708 + 0.312996i
784784 −3877.95 6716.81i −0.176656 0.305977i
785785 −47239.9 −2.14785
786786 17745.3 + 30735.8i 0.805286 + 1.39480i
787787 −18827.9 32610.9i −0.852786 1.47707i −0.878684 0.477404i 0.841578π-0.841578\pi
0.0258980 0.999665i 0.491755π-0.491755\pi
788788 15294.1 0.691408
789789 −19650.7 34035.9i −0.886669 1.53576i
790790 −10066.4 + 17435.5i −0.453350 + 0.785225i
791791 −10708.6 + 18547.8i −0.481356 + 0.833733i
792792 −16651.2 −0.747062
793793 0 0
794794 7304.13 0.326466
795795 −6014.30 + 10417.1i −0.268308 + 0.464724i
796796 4314.82 7473.49i 0.192129 0.332778i
797797 −12114.0 20982.1i −0.538395 0.932527i −0.998991 0.0449170i 0.985698π-0.985698\pi
0.460596 0.887610i 0.347636π-0.347636\pi
798798 30835.3 1.36787
799799 14234.1 + 24654.2i 0.630246 + 1.09162i
800800 −566.278 980.822i −0.0250262 0.0433466i
801801 3117.61 0.137522
802802 8884.69 + 15388.7i 0.391184 + 0.677550i
803803 8535.25 14783.5i 0.375097 0.649686i
804804 −13123.3 + 22730.2i −0.575649 + 0.997053i
805805 −16189.2 −0.708812
806806 0 0
807807 16017.3 0.698682
808808 4141.26 7172.87i 0.180308 0.312303i
809809 −19987.2 + 34618.9i −0.868621 + 1.50450i −0.00521394 + 0.999986i 0.501660π0.501660\pi
−0.863407 + 0.504509i 0.831674π0.831674\pi
810810 −3051.59 5285.51i −0.132373 0.229277i
811811 13394.4 0.579953 0.289977 0.957034i 0.406352π-0.406352\pi
0.289977 + 0.957034i 0.406352π0.406352\pi
812812 −4513.40 7817.44i −0.195061 0.337855i
813813 −17990.5 31160.4i −0.776080 1.34421i
814814 −24643.7 −1.06113
815815 16611.2 + 28771.5i 0.713946 + 1.23659i
816816 4630.17 8019.70i 0.198638 0.344051i
817817 −13321.5 + 23073.5i −0.570453 + 0.988054i
818818 −22935.9 −0.980362
819819 0 0
820820 −6102.17 −0.259874
821821 −15769.6 + 27313.8i −0.670358 + 1.16109i 0.307445 + 0.951566i 0.400526π0.400526\pi
−0.977803 + 0.209528i 0.932807π0.932807\pi
822822 −14402.9 + 24946.5i −0.611142 + 1.05853i
823823 13443.2 + 23284.2i 0.569379 + 0.986193i 0.996627 + 0.0820590i 0.0261496π0.0261496\pi
−0.427249 + 0.904134i 0.640517π0.640517\pi
824824 9988.07 0.422271
825825 −7619.01 13196.5i −0.321527 0.556901i
826826 22482.3 + 38940.5i 0.947047 + 1.64033i
827827 16064.3 0.675466 0.337733 0.941242i 0.390340π-0.390340\pi
0.337733 + 0.941242i 0.390340π0.390340\pi
828828 3500.27 + 6062.65i 0.146912 + 0.254458i
829829 −3927.65 + 6802.90i −0.164551 + 0.285011i −0.936496 0.350679i 0.885951π-0.885951\pi
0.771945 + 0.635690i 0.219284π0.219284\pi
830830 5633.48 9757.47i 0.235591 0.408056i
831831 −29432.5 −1.22864
832832 0 0
833833 34432.5 1.43219
834834 8193.11 14190.9i 0.340173 0.589197i
835835 −8092.70 + 14017.0i −0.335401 + 0.580931i
836836 6950.50 + 12038.6i 0.287545 + 0.498043i
837837 19688.5 0.813065
838838 15914.1 + 27564.0i 0.656017 + 1.13626i
839839 −2603.26 4508.98i −0.107121 0.185539i 0.807482 0.589892i 0.200830π-0.200830\pi
−0.914603 + 0.404354i 0.867497π0.867497\pi
840840 −23751.0 −0.975579
841841 9118.25 + 15793.3i 0.373867 + 0.647557i
842842 3091.64 5354.88i 0.126538 0.219170i
843843 16683.1 28896.0i 0.681610 1.18058i
844844 13455.4 0.548762
845845 0 0
846846 −31573.4 −1.28312
847847 21018.7 36405.5i 0.852670 1.47687i
848848 −932.528 + 1615.19i −0.0377631 + 0.0654077i
849849 27402.5 + 47462.6i 1.10772 + 1.91862i
850850 5028.00 0.202893
851851 5180.40 + 8972.72i 0.208674 + 0.361435i
852852 −6544.01 11334.6i −0.263139 0.455770i
853853 −11007.6 −0.441842 −0.220921 0.975292i 0.570906π-0.570906\pi
−0.220921 + 0.975292i 0.570906π0.570906\pi
854854 1512.07 + 2618.98i 0.0605877 + 0.104941i
855855 16404.6 28413.7i 0.656172 1.13652i
856856 4648.05 8050.65i 0.185592 0.321455i
857857 −15769.9 −0.628576 −0.314288 0.949328i 0.601766π-0.601766\pi
−0.314288 + 0.949328i 0.601766π0.601766\pi
858858 0 0
859859 13386.6 0.531716 0.265858 0.964012i 0.414345π-0.414345\pi
0.265858 + 0.964012i 0.414345π0.414345\pi
860860 10260.9 17772.5i 0.406854 0.704693i
861861 −14118.9 + 24454.7i −0.558853 + 0.967961i
862862 −4996.69 8654.52i −0.197434 0.341965i
863863 13233.1 0.521968 0.260984 0.965343i 0.415953π-0.415953\pi
0.260984 + 0.965343i 0.415953π0.415953\pi
864864 1615.27 + 2797.73i 0.0636026 + 0.110163i
865865 6775.45 + 11735.4i 0.266326 + 0.461291i
866866 −3683.67 −0.144545
867867 540.147 + 935.563i 0.0211584 + 0.0366475i
868868 −11221.9 + 19436.9i −0.438820 + 0.760059i
869869 −21000.0 + 36373.1i −0.819767 + 1.41988i
870870 −16188.2 −0.630841
871871 0 0
872872 −8028.64 −0.311794
873873 −76.7388 + 132.916i −0.00297505 + 0.00515293i
874874 2922.16 5061.32i 0.113093 0.195883i
875875 16325.1 + 28275.8i 0.630729 + 1.09245i
876876 −10529.1 −0.406101
877877 −17860.3 30934.9i −0.687684 1.19110i −0.972585 0.232547i 0.925294π-0.925294\pi
0.284901 0.958557i 0.408039π-0.408039\pi
878878 −9963.22 17256.8i −0.382964 0.663313i
879879 −36694.1 −1.40803
880880 −5353.64 9272.78i −0.205081 0.355211i
881881 −263.170 + 455.824i −0.0100641 + 0.0174315i −0.871014 0.491259i 0.836537π-0.836537\pi
0.860950 + 0.508690i 0.169870π0.169870\pi
882882 −19094.1 + 33071.9i −0.728947 + 1.26257i
883883 39626.2 1.51022 0.755112 0.655596i 0.227583π-0.227583\pi
0.755112 + 0.655596i 0.227583π0.227583\pi
884884 0 0
885885 80637.5 3.06282
886886 8480.02 14687.8i 0.321548 0.556938i
887887 18332.2 31752.3i 0.693951 1.20196i −0.276582 0.960990i 0.589202π-0.589202\pi
0.970533 0.240968i 0.0774650π-0.0774650\pi
888888 7600.11 + 13163.8i 0.287211 + 0.497463i
889889 −48435.7 −1.82731
890890 1002.37 + 1736.15i 0.0377522 + 0.0653887i
891891 −6366.08 11026.4i −0.239362 0.414588i
892892 −13175.6 −0.494566
893893 13179.3 + 22827.3i 0.493874 + 0.855415i
894894 −1110.36 + 1923.20i −0.0415392 + 0.0719480i
895895 4670.38 8089.34i 0.174429 0.302119i
896896 −3682.63 −0.137308
897897 0 0
898898 6901.34 0.256460
899899 −7648.64 + 13247.8i −0.283756 + 0.491479i
900900 −2788.21 + 4829.33i −0.103267 + 0.178864i
901901 −4139.97 7170.64i −0.153077 0.265137i
902902 −12730.0 −0.469916
903903 −47482.6 82242.3i −1.74986 3.03084i
904904 2977.65 + 5157.43i 0.109552 + 0.189750i
905905 18452.6 0.677772
906906 −6554.21 11352.2i −0.240341 0.416283i
907907 17715.0 30683.3i 0.648530 1.12329i −0.334944 0.942238i 0.608717π-0.608717\pi
0.983474 0.181049i 0.0579493π-0.0579493\pi
908908 −1086.97 + 1882.69i −0.0397273 + 0.0688098i
909909 −40781.1 −1.48804
910910 0 0
911911 −1970.18 −0.0716521 −0.0358261 0.999358i 0.511406π-0.511406\pi
−0.0358261 + 0.999358i 0.511406π0.511406\pi
912912 4287.06 7425.41i 0.155657 0.269605i
913913 11752.3 20355.6i 0.426006 0.737865i
914914 −6541.22 11329.7i −0.236723 0.410016i
915915 5423.34 0.195945
916916 −6143.31 10640.5i −0.221595 0.383813i
917917 31329.3 + 54263.9i 1.12823 + 1.95415i
918918 −14342.0 −0.515640
919919 −3499.62 6061.52i −0.125617 0.217575i 0.796357 0.604827i 0.206758π-0.206758\pi
−0.921974 + 0.387252i 0.873424π0.873424\pi
920920 −2250.80 + 3898.50i −0.0806594 + 0.139706i
921921 −7882.19 + 13652.4i −0.282005 + 0.488448i
922922 29227.7 1.04399
923923 0 0
924924 −49548.1 −1.76408
925925 −4126.56 + 7147.41i −0.146681 + 0.254060i
926926 3680.01 6373.96i 0.130597 0.226200i
927927 −24589.4 42590.1i −0.871222 1.50900i
928928 −2510.01 −0.0887879
929929 −11816.3 20466.4i −0.417309 0.722801i 0.578358 0.815783i 0.303694π-0.303694\pi
−0.995668 + 0.0929817i 0.970360π0.970360\pi
930930 20124.8 + 34857.2i 0.709590 + 1.22905i
931931 31880.9 1.12229
932932 −6766.11 11719.3i −0.237802 0.411885i
933933 −10819.4 + 18739.8i −0.379649 + 0.657571i
934934 −457.544 + 792.489i −0.0160292 + 0.0277634i
935935 47535.2 1.66264
936936 0 0
937937 −30872.4 −1.07637 −0.538183 0.842828i 0.680889π-0.680889\pi
−0.538183 + 0.842828i 0.680889π0.680889\pi
938938 −23169.1 + 40130.0i −0.806499 + 1.39690i
939939 24861.0 43060.6i 0.864014 1.49652i
940940 −10151.4 17582.8i −0.352237 0.610092i
941941 −6690.77 −0.231788 −0.115894 0.993262i 0.536973π-0.536973\pi
−0.115894 + 0.993262i 0.536973π0.536973\pi
942942 30392.7 + 52641.6i 1.05122 + 1.82076i
943943 2676.01 + 4634.98i 0.0924102 + 0.160059i
944944 12503.0 0.431078
945945 18392.3 + 31856.3i 0.633122 + 1.09660i
946946 21405.9 37076.0i 0.735692 1.27426i
947947 −10738.6 + 18599.7i −0.368486 + 0.638237i −0.989329 0.145698i 0.953457π-0.953457\pi
0.620843 + 0.783935i 0.286791π0.286791\pi
948948 25905.6 0.887527
949949 0 0
950950 4655.41 0.158991
951951 5634.33 9758.94i 0.192119 0.332761i
952952 8174.55 14158.7i 0.278297 0.482024i
953953 3925.25 + 6798.73i 0.133422 + 0.231094i 0.924994 0.379983i 0.124070π-0.124070\pi
−0.791571 + 0.611077i 0.790737π0.790737\pi
954954 9183.08 0.311649
955955 3643.80 + 6311.25i 0.123467 + 0.213851i
956956 −1397.10 2419.85i −0.0472651 0.0818656i
957957 −33771.1 −1.14071
958958 9770.94 + 16923.8i 0.329525 + 0.570753i
959959 −25428.2 + 44043.0i −0.856226 + 1.48303i
960960 −3302.12 + 5719.45i −0.111016 + 0.192286i
961961 8243.39 0.276707
962962 0 0
963963 −45771.7 −1.53164
964964 −7430.89 + 12870.7i −0.248270 + 0.430017i
965965 15442.7 26747.6i 0.515150 0.892266i
966966 10415.6 + 18040.4i 0.346912 + 0.600869i
967967 44143.2 1.46799 0.733997 0.679152i 0.237652π-0.237652\pi
0.733997 + 0.679152i 0.237652π0.237652\pi
968968 −5844.51 10123.0i −0.194060 0.336121i
969969 19032.5 + 32965.2i 0.630972 + 1.09288i
970970 −98.6916 −0.00326680
971971 −14315.9 24795.8i −0.473139 0.819500i 0.526389 0.850244i 0.323546π-0.323546\pi
−0.999527 + 0.0307439i 0.990212π0.990212\pi
972972 −9378.13 + 16243.4i −0.309469 + 0.536016i
973973 14464.9 25053.9i 0.476591 0.825481i
974974 40500.4 1.33236
975975 0 0
976976 840.898 0.0275784
977977 4652.80 8058.88i 0.152360 0.263896i −0.779734 0.626110i 0.784646π-0.784646\pi
0.932095 + 0.362215i 0.117979π0.117979\pi
978978 21374.3 37021.3i 0.698849 1.21044i
979979 2091.09 + 3621.88i 0.0682651 + 0.118239i
980980 −24556.4 −0.800433
981981 19765.5 + 34234.9i 0.643287 + 1.11421i
982982 17279.4 + 29928.9i 0.561516 + 0.972574i
983983 −28467.2 −0.923666 −0.461833 0.886967i 0.652808π-0.652808\pi
−0.461833 + 0.886967i 0.652808π0.652808\pi
984984 3925.94 + 6799.93i 0.127190 + 0.220299i
985985 24211.7 41935.9i 0.783197 1.35654i
986986 5571.62 9650.33i 0.179956 0.311693i
987987 −93951.6 −3.02990
988988 0 0
989989 −17999.1 −0.578703
990990 −26360.0 + 45656.9i −0.846240 + 1.46573i
991991 −7749.06 + 13421.8i −0.248393 + 0.430229i −0.963080 0.269215i 0.913236π-0.913236\pi
0.714687 + 0.699444i 0.246569π0.246569\pi
992992 3120.39 + 5404.67i 0.0998713 + 0.172982i
993993 81534.3 2.60565
994994 −11553.4 20011.1i −0.368664 0.638545i
995995 −13661.4 23662.2i −0.435272 0.753912i
996996 −14497.6 −0.461219
997997 −630.399 1091.88i −0.0200250 0.0346844i 0.855839 0.517242i 0.173041π-0.173041\pi
−0.875864 + 0.482558i 0.839708π0.839708\pi
998998 −16994.7 + 29435.6i −0.539035 + 0.933636i
999999 11770.7 20387.5i 0.372782 0.645678i
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 338.4.c.o.191.6 12
13.2 odd 12 338.4.e.i.23.5 24
13.3 even 3 inner 338.4.c.o.315.6 12
13.4 even 6 338.4.a.n.1.1 6
13.5 odd 4 338.4.e.i.147.12 24
13.6 odd 12 338.4.b.h.337.1 12
13.7 odd 12 338.4.b.h.337.7 12
13.8 odd 4 338.4.e.i.147.5 24
13.9 even 3 338.4.a.o.1.1 yes 6
13.10 even 6 338.4.c.p.315.6 12
13.11 odd 12 338.4.e.i.23.12 24
13.12 even 2 338.4.c.p.191.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
338.4.a.n.1.1 6 13.4 even 6
338.4.a.o.1.1 yes 6 13.9 even 3
338.4.b.h.337.1 12 13.6 odd 12
338.4.b.h.337.7 12 13.7 odd 12
338.4.c.o.191.6 12 1.1 even 1 trivial
338.4.c.o.315.6 12 13.3 even 3 inner
338.4.c.p.191.6 12 13.12 even 2
338.4.c.p.315.6 12 13.10 even 6
338.4.e.i.23.5 24 13.2 odd 12
338.4.e.i.23.12 24 13.11 odd 12
338.4.e.i.147.5 24 13.8 odd 4
338.4.e.i.147.12 24 13.5 odd 4