# Properties

 Label 49.6.c.h.30.1 Level $49$ Weight $6$ Character 49.30 Analytic conductor $7.859$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,6,Mod(18,49)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("49.18");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$49 = 7^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 49.c (of order $$3$$, degree $$2$$, 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: $$7.85880717084$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: 8.0.54095201243136.19 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - 4x^{7} - 102x^{6} + 320x^{5} + 4283x^{4} - 9104x^{3} - 85298x^{2} + 89904x + 714364$$ x^8 - 4*x^7 - 102*x^6 + 320*x^5 + 4283*x^4 - 9104*x^3 - 85298*x^2 + 89904*x + 714364 Coefficient ring: $$\Z[a_1, \ldots, a_{9}]$$ Coefficient ring index: $$7^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 30.1 Root $$-4.10797 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 49.30 Dual form 49.6.c.h.18.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.40754 + 2.43792i) q^{2} +(-3.27401 - 5.67075i) q^{3} +(12.0377 + 20.8499i) q^{4} +(22.9955 - 39.8294i) q^{5} +18.4331 q^{6} -157.856 q^{8} +(100.062 - 173.312i) q^{9} +O(q^{10})$$ $$q+(-1.40754 + 2.43792i) q^{2} +(-3.27401 - 5.67075i) q^{3} +(12.0377 + 20.8499i) q^{4} +(22.9955 - 39.8294i) q^{5} +18.4331 q^{6} -157.856 q^{8} +(100.062 - 173.312i) q^{9} +(64.7341 + 112.123i) q^{10} +(275.890 + 477.856i) q^{11} +(78.8229 - 136.525i) q^{12} +1094.10 q^{13} -301.150 q^{15} +(-163.017 + 282.354i) q^{16} +(590.357 + 1022.53i) q^{17} +(281.681 + 487.886i) q^{18} +(583.063 - 1009.89i) q^{19} +1107.25 q^{20} -1553.30 q^{22} +(-22.1925 + 38.4386i) q^{23} +(516.823 + 895.163i) q^{24} +(504.912 + 874.533i) q^{25} +(-1539.98 + 2667.33i) q^{26} -2901.58 q^{27} +3329.02 q^{29} +(423.880 - 734.181i) q^{30} +(-4392.01 - 7607.18i) q^{31} +(-2984.61 - 5169.49i) q^{32} +(1806.53 - 3129.01i) q^{33} -3323.80 q^{34} +4818.05 q^{36} +(1278.56 - 2214.53i) q^{37} +(1641.37 + 2842.93i) q^{38} +(-3582.08 - 6204.35i) q^{39} +(-3629.99 + 6287.32i) q^{40} -12761.3 q^{41} -96.7714 q^{43} +(-6642.16 + 11504.6i) q^{44} +(-4601.94 - 7970.80i) q^{45} +(-62.4736 - 108.207i) q^{46} +(-3839.58 + 6650.34i) q^{47} +2134.88 q^{48} -2842.73 q^{50} +(3865.67 - 6695.53i) q^{51} +(13170.4 + 22811.8i) q^{52} +(5976.67 + 10351.9i) q^{53} +(4084.08 - 7073.83i) q^{54} +25377.0 q^{55} -7635.81 q^{57} +(-4685.71 + 8115.89i) q^{58} +(-4928.62 - 8536.62i) q^{59} +(-3625.15 - 6278.94i) q^{60} +(19258.9 - 33357.5i) q^{61} +24727.6 q^{62} +6370.65 q^{64} +(25159.4 - 43577.3i) q^{65} +(5085.53 + 8808.39i) q^{66} +(33774.5 + 58499.1i) q^{67} +(-14213.1 + 24617.7i) q^{68} +290.634 q^{69} -61374.6 q^{71} +(-15795.4 + 27358.4i) q^{72} +(-925.199 - 1602.49i) q^{73} +(3599.24 + 6234.07i) q^{74} +(3306.17 - 5726.45i) q^{75} +28074.9 q^{76} +20167.7 q^{78} +(4.26456 - 7.38644i) q^{79} +(7497.34 + 12985.8i) q^{80} +(-14815.2 - 25660.7i) q^{81} +(17961.9 - 31111.0i) q^{82} -95039.3 q^{83} +54302.3 q^{85} +(136.209 - 235.921i) q^{86} +(-10899.2 - 18878.0i) q^{87} +(-43551.0 - 75432.6i) q^{88} +(-26802.8 + 46423.8i) q^{89} +25909.6 q^{90} -1068.59 q^{92} +(-28758.9 + 49811.9i) q^{93} +(-10808.7 - 18721.2i) q^{94} +(-26815.7 - 46446.1i) q^{95} +(-19543.2 + 33849.9i) q^{96} +3110.79 q^{97} +110424. q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9}+O(q^{10})$$ 8 * q + 10 * q^2 - 10 * q^4 - 540 * q^8 - 220 * q^9 $$8 q + 10 q^{2} - 10 q^{4} - 540 q^{8} - 220 q^{9} + 1952 q^{11} - 8192 q^{15} + 1566 q^{16} + 5974 q^{18} + 7048 q^{22} + 7136 q^{23} - 2764 q^{25} - 6704 q^{29} - 25608 q^{30} - 27810 q^{32} + 55340 q^{36} + 9208 q^{37} - 2464 q^{39} + 40896 q^{43} - 1900 q^{44} - 56712 q^{46} - 86140 q^{50} + 67408 q^{51} + 102920 q^{53} - 31152 q^{57} - 96972 q^{58} + 87080 q^{60} - 80636 q^{64} + 63168 q^{65} + 22896 q^{67} - 307648 q^{71} - 77358 q^{72} - 17596 q^{74} + 266112 q^{78} + 90688 q^{79} + 17204 q^{81} + 545312 q^{85} + 161860 q^{86} - 154812 q^{88} - 424400 q^{92} - 247760 q^{93} - 108224 q^{95} - 84544 q^{99}+O(q^{100})$$ 8 * q + 10 * q^2 - 10 * q^4 - 540 * q^8 - 220 * q^9 + 1952 * q^11 - 8192 * q^15 + 1566 * q^16 + 5974 * q^18 + 7048 * q^22 + 7136 * q^23 - 2764 * q^25 - 6704 * q^29 - 25608 * q^30 - 27810 * q^32 + 55340 * q^36 + 9208 * q^37 - 2464 * q^39 + 40896 * q^43 - 1900 * q^44 - 56712 * q^46 - 86140 * q^50 + 67408 * q^51 + 102920 * q^53 - 31152 * q^57 - 96972 * q^58 + 87080 * q^60 - 80636 * q^64 + 63168 * q^65 + 22896 * q^67 - 307648 * q^71 - 77358 * q^72 - 17596 * q^74 + 266112 * q^78 + 90688 * q^79 + 17204 * q^81 + 545312 * q^85 + 161860 * q^86 - 154812 * q^88 - 424400 * q^92 - 247760 * q^93 - 108224 * q^95 - 84544 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.40754 + 2.43792i −0.248820 + 0.430968i −0.963199 0.268791i $$-0.913376\pi$$
0.714379 + 0.699759i $$0.246709\pi$$
$$3$$ −3.27401 5.67075i −0.210028 0.363779i 0.741695 0.670737i $$-0.234022\pi$$
−0.951723 + 0.306958i $$0.900689\pi$$
$$4$$ 12.0377 + 20.8499i 0.376178 + 0.651559i
$$5$$ 22.9955 39.8294i 0.411356 0.712490i −0.583682 0.811982i $$-0.698388\pi$$
0.995038 + 0.0994921i $$0.0317218\pi$$
$$6$$ 18.4331 0.209036
$$7$$ 0 0
$$8$$ −157.856 −0.872041
$$9$$ 100.062 173.312i 0.411777 0.713218i
$$10$$ 64.7341 + 112.123i 0.204707 + 0.354563i
$$11$$ 275.890 + 477.856i 0.687472 + 1.19074i 0.972653 + 0.232263i $$0.0746129\pi$$
−0.285181 + 0.958474i $$0.592054\pi$$
$$12$$ 78.8229 136.525i 0.158015 0.273691i
$$13$$ 1094.10 1.79555 0.897776 0.440453i $$-0.145182\pi$$
0.897776 + 0.440453i $$0.145182\pi$$
$$14$$ 0 0
$$15$$ −301.150 −0.345585
$$16$$ −163.017 + 282.354i −0.159197 + 0.275737i
$$17$$ 590.357 + 1022.53i 0.495442 + 0.858130i 0.999986 0.00525555i $$-0.00167290\pi$$
−0.504545 + 0.863386i $$0.668340\pi$$
$$18$$ 281.681 + 487.886i 0.204916 + 0.354925i
$$19$$ 583.063 1009.89i 0.370537 0.641789i −0.619111 0.785303i $$-0.712507\pi$$
0.989648 + 0.143514i $$0.0458404\pi$$
$$20$$ 1107.25 0.618972
$$21$$ 0 0
$$22$$ −1553.30 −0.684226
$$23$$ −22.1925 + 38.4386i −0.00874757 + 0.0151512i −0.870366 0.492405i $$-0.836118\pi$$
0.861618 + 0.507556i $$0.169451\pi$$
$$24$$ 516.823 + 895.163i 0.183153 + 0.317230i
$$25$$ 504.912 + 874.533i 0.161572 + 0.279850i
$$26$$ −1539.98 + 2667.33i −0.446768 + 0.773826i
$$27$$ −2901.58 −0.765993
$$28$$ 0 0
$$29$$ 3329.02 0.735057 0.367529 0.930012i $$-0.380204\pi$$
0.367529 + 0.930012i $$0.380204\pi$$
$$30$$ 423.880 734.181i 0.0859883 0.148936i
$$31$$ −4392.01 7607.18i −0.820841 1.42174i −0.905057 0.425290i $$-0.860172\pi$$
0.0842165 0.996447i $$-0.473161\pi$$
$$32$$ −2984.61 5169.49i −0.515243 0.892427i
$$33$$ 1806.53 3129.01i 0.288776 0.500175i
$$34$$ −3323.80 −0.493102
$$35$$ 0 0
$$36$$ 4818.05 0.619605
$$37$$ 1278.56 2214.53i 0.153539 0.265937i −0.778987 0.627040i $$-0.784266\pi$$
0.932526 + 0.361103i $$0.117600\pi$$
$$38$$ 1641.37 + 2842.93i 0.184394 + 0.319379i
$$39$$ −3582.08 6204.35i −0.377115 0.653183i
$$40$$ −3629.99 + 6287.32i −0.358720 + 0.621321i
$$41$$ −12761.3 −1.18559 −0.592794 0.805354i $$-0.701975\pi$$
−0.592794 + 0.805354i $$0.701975\pi$$
$$42$$ 0 0
$$43$$ −96.7714 −0.00798135 −0.00399067 0.999992i $$-0.501270\pi$$
−0.00399067 + 0.999992i $$0.501270\pi$$
$$44$$ −6642.16 + 11504.6i −0.517223 + 0.895857i
$$45$$ −4601.94 7970.80i −0.338774 0.586774i
$$46$$ −62.4736 108.207i −0.00435313 0.00753985i
$$47$$ −3839.58 + 6650.34i −0.253535 + 0.439136i −0.964497 0.264095i $$-0.914927\pi$$
0.710961 + 0.703231i $$0.248260\pi$$
$$48$$ 2134.88 0.133743
$$49$$ 0 0
$$50$$ −2842.73 −0.160809
$$51$$ 3865.67 6695.53i 0.208113 0.360462i
$$52$$ 13170.4 + 22811.8i 0.675446 + 1.16991i
$$53$$ 5976.67 + 10351.9i 0.292260 + 0.506209i 0.974344 0.225065i $$-0.0722594\pi$$
−0.682084 + 0.731274i $$0.738926\pi$$
$$54$$ 4084.08 7073.83i 0.190594 0.330119i
$$55$$ 25377.0 1.13118
$$56$$ 0 0
$$57$$ −7635.81 −0.311292
$$58$$ −4685.71 + 8115.89i −0.182897 + 0.316786i
$$59$$ −4928.62 8536.62i −0.184330 0.319268i 0.759021 0.651066i $$-0.225678\pi$$
−0.943350 + 0.331798i $$0.892345\pi$$
$$60$$ −3625.15 6278.94i −0.130001 0.225169i
$$61$$ 19258.9 33357.5i 0.662686 1.14781i −0.317221 0.948352i $$-0.602750\pi$$
0.979907 0.199454i $$-0.0639169\pi$$
$$62$$ 24727.6 0.816965
$$63$$ 0 0
$$64$$ 6370.65 0.194417
$$65$$ 25159.4 43577.3i 0.738612 1.27931i
$$66$$ 5085.53 + 8808.39i 0.143706 + 0.248907i
$$67$$ 33774.5 + 58499.1i 0.919182 + 1.59207i 0.800661 + 0.599118i $$0.204482\pi$$
0.118521 + 0.992952i $$0.462185\pi$$
$$68$$ −14213.1 + 24617.7i −0.372748 + 0.645619i
$$69$$ 290.634 0.00734893
$$70$$ 0 0
$$71$$ −61374.6 −1.44492 −0.722458 0.691415i $$-0.756988\pi$$
−0.722458 + 0.691415i $$0.756988\pi$$
$$72$$ −15795.4 + 27358.4i −0.359086 + 0.621955i
$$73$$ −925.199 1602.49i −0.0203202 0.0351956i 0.855686 0.517495i $$-0.173135\pi$$
−0.876007 + 0.482299i $$0.839802\pi$$
$$74$$ 3599.24 + 6234.07i 0.0764068 + 0.132340i
$$75$$ 3306.17 5726.45i 0.0678691 0.117553i
$$76$$ 28074.9 0.557551
$$77$$ 0 0
$$78$$ 20167.7 0.375335
$$79$$ 4.26456 7.38644i 7.68788e−5 0.000133158i −0.865987 0.500067i $$-0.833309\pi$$
0.866064 + 0.499933i $$0.166642\pi$$
$$80$$ 7497.34 + 12985.8i 0.130973 + 0.226852i
$$81$$ −14815.2 25660.7i −0.250897 0.434566i
$$82$$ 17961.9 31111.0i 0.294998 0.510951i
$$83$$ −95039.3 −1.51429 −0.757143 0.653249i $$-0.773405\pi$$
−0.757143 + 0.653249i $$0.773405\pi$$
$$84$$ 0 0
$$85$$ 54302.3 0.815212
$$86$$ 136.209 235.921i 0.00198592 0.00343971i
$$87$$ −10899.2 18878.0i −0.154382 0.267398i
$$88$$ −43551.0 75432.6i −0.599503 1.03837i
$$89$$ −26802.8 + 46423.8i −0.358678 + 0.621249i −0.987740 0.156106i $$-0.950106\pi$$
0.629062 + 0.777355i $$0.283439\pi$$
$$90$$ 25909.6 0.337175
$$91$$ 0 0
$$92$$ −1068.59 −0.0131626
$$93$$ −28758.9 + 49811.9i −0.344798 + 0.597208i
$$94$$ −10808.7 18721.2i −0.126169 0.218531i
$$95$$ −26815.7 46446.1i −0.304846 0.528008i
$$96$$ −19543.2 + 33849.9i −0.216431 + 0.374869i
$$97$$ 3110.79 0.0335693 0.0167846 0.999859i $$-0.494657\pi$$
0.0167846 + 0.999859i $$0.494657\pi$$
$$98$$ 0 0
$$99$$ 110424. 1.13234
$$100$$ −12155.9 + 21054.7i −0.121559 + 0.210547i
$$101$$ −10918.0 18910.4i −0.106497 0.184458i 0.807852 0.589386i $$-0.200630\pi$$
−0.914349 + 0.404927i $$0.867297\pi$$
$$102$$ 10882.1 + 18848.4i 0.103565 + 0.179380i
$$103$$ −32670.7 + 56587.3i −0.303435 + 0.525565i −0.976912 0.213644i $$-0.931467\pi$$
0.673477 + 0.739208i $$0.264800\pi$$
$$104$$ −172710. −1.56579
$$105$$ 0 0
$$106$$ −33649.5 −0.290880
$$107$$ 54478.7 94359.8i 0.460010 0.796760i −0.538951 0.842337i $$-0.681179\pi$$
0.998961 + 0.0455767i $$0.0145125\pi$$
$$108$$ −34928.3 60497.6i −0.288150 0.499090i
$$109$$ −43364.3 75109.2i −0.349596 0.605518i 0.636582 0.771209i $$-0.280348\pi$$
−0.986178 + 0.165691i $$0.947014\pi$$
$$110$$ −35719.0 + 61867.2i −0.281461 + 0.487504i
$$111$$ −16744.1 −0.128989
$$112$$ 0 0
$$113$$ −101496. −0.747746 −0.373873 0.927480i $$-0.621970\pi$$
−0.373873 + 0.927480i $$0.621970\pi$$
$$114$$ 10747.7 18615.5i 0.0774556 0.134157i
$$115$$ 1020.66 + 1767.83i 0.00719674 + 0.0124651i
$$116$$ 40073.7 + 69409.6i 0.276512 + 0.478933i
$$117$$ 109477. 189620.i 0.739366 1.28062i
$$118$$ 27748.9 0.183459
$$119$$ 0 0
$$120$$ 47538.4 0.301364
$$121$$ −71705.6 + 124198.i −0.445235 + 0.771170i
$$122$$ 54215.3 + 93903.7i 0.329779 + 0.571193i
$$123$$ 41780.5 + 72365.9i 0.249006 + 0.431292i
$$124$$ 105739. 183146.i 0.617564 1.06965i
$$125$$ 190165. 1.08857
$$126$$ 0 0
$$127$$ −3094.61 −0.0170253 −0.00851267 0.999964i $$-0.502710\pi$$
−0.00851267 + 0.999964i $$0.502710\pi$$
$$128$$ 86540.5 149892.i 0.466868 0.808639i
$$129$$ 316.830 + 548.766i 0.00167630 + 0.00290344i
$$130$$ 70825.4 + 122673.i 0.367562 + 0.636636i
$$131$$ −126715. + 219478.i −0.645136 + 1.11741i 0.339134 + 0.940738i $$0.389866\pi$$
−0.984270 + 0.176671i $$0.943467\pi$$
$$132$$ 86986.0 0.434525
$$133$$ 0 0
$$134$$ −190155. −0.914842
$$135$$ −66723.3 + 115568.i −0.315096 + 0.545763i
$$136$$ −93191.6 161413.i −0.432045 0.748324i
$$137$$ 48576.4 + 84136.9i 0.221118 + 0.382988i 0.955148 0.296130i $$-0.0956960\pi$$
−0.734030 + 0.679117i $$0.762363\pi$$
$$138$$ −409.078 + 708.544i −0.00182856 + 0.00316715i
$$139$$ 210308. 0.923249 0.461624 0.887076i $$-0.347267\pi$$
0.461624 + 0.887076i $$0.347267\pi$$
$$140$$ 0 0
$$141$$ 50283.2 0.212998
$$142$$ 86387.0 149627.i 0.359524 0.622713i
$$143$$ 301851. + 522822.i 1.23439 + 2.13803i
$$144$$ 32623.6 + 56505.8i 0.131107 + 0.227084i
$$145$$ 76552.5 132593.i 0.302370 0.523721i
$$146$$ 5209.01 0.0202243
$$147$$ 0 0
$$148$$ 61563.7 0.231031
$$149$$ −70203.2 + 121595.i −0.259055 + 0.448696i −0.965989 0.258584i $$-0.916744\pi$$
0.706934 + 0.707279i $$0.250078\pi$$
$$150$$ 9307.11 + 16120.4i 0.0337743 + 0.0584988i
$$151$$ −59847.9 103660.i −0.213603 0.369971i 0.739237 0.673446i $$-0.235186\pi$$
−0.952839 + 0.303475i $$0.901853\pi$$
$$152$$ −92040.1 + 159418.i −0.323123 + 0.559666i
$$153$$ 236289. 0.816045
$$154$$ 0 0
$$155$$ −403986. −1.35063
$$156$$ 86240.0 149372.i 0.283725 0.491426i
$$157$$ −48808.4 84538.7i −0.158032 0.273720i 0.776127 0.630577i $$-0.217182\pi$$
−0.934159 + 0.356857i $$0.883848\pi$$
$$158$$ 12.0051 + 20.7934i 3.82579e−5 + 6.62647e-5i
$$159$$ 39135.3 67784.3i 0.122765 0.212636i
$$160$$ −274530. −0.847794
$$161$$ 0 0
$$162$$ 83411.8 0.249712
$$163$$ −91339.0 + 158204.i −0.269270 + 0.466389i −0.968673 0.248338i $$-0.920116\pi$$
0.699404 + 0.714727i $$0.253449\pi$$
$$164$$ −153616. 266071.i −0.445992 0.772481i
$$165$$ −83084.4 143906.i −0.237580 0.411501i
$$166$$ 133771. 231699.i 0.376784 0.652609i
$$167$$ −451674. −1.25324 −0.626619 0.779326i $$-0.715562\pi$$
−0.626619 + 0.779326i $$0.715562\pi$$
$$168$$ 0 0
$$169$$ 825757. 2.22400
$$170$$ −76432.5 + 132385.i −0.202841 + 0.351331i
$$171$$ −116685. 202104.i −0.305157 0.528547i
$$172$$ −1164.90 2017.67i −0.00300240 0.00520031i
$$173$$ −185824. + 321856.i −0.472047 + 0.817610i −0.999488 0.0319815i $$-0.989818\pi$$
0.527441 + 0.849592i $$0.323152\pi$$
$$174$$ 61364.2 0.153653
$$175$$ 0 0
$$176$$ −179900. −0.437773
$$177$$ −32272.7 + 55897.9i −0.0774287 + 0.134110i
$$178$$ −75451.8 130686.i −0.178492 0.309158i
$$179$$ −42501.7 73615.1i −0.0991457 0.171725i 0.812186 0.583399i $$-0.198278\pi$$
−0.911331 + 0.411674i $$0.864944\pi$$
$$180$$ 110794. 191900.i 0.254878 0.441462i
$$181$$ −379442. −0.860892 −0.430446 0.902616i $$-0.641644\pi$$
−0.430446 + 0.902616i $$0.641644\pi$$
$$182$$ 0 0
$$183$$ −252216. −0.556730
$$184$$ 3503.23 6067.77i 0.00762824 0.0132125i
$$185$$ −58802.4 101849.i −0.126318 0.218789i
$$186$$ −80958.5 140224.i −0.171585 0.297194i
$$187$$ −325748. + 564212.i −0.681204 + 1.17988i
$$188$$ −184878. −0.381497
$$189$$ 0 0
$$190$$ 150976. 0.303406
$$191$$ 461098. 798645.i 0.914555 1.58406i 0.107003 0.994259i $$-0.465875\pi$$
0.807552 0.589796i $$-0.200792\pi$$
$$192$$ −20857.6 36126.4i −0.0408329 0.0707247i
$$193$$ −252553. 437435.i −0.488045 0.845319i 0.511860 0.859069i $$-0.328956\pi$$
−0.999905 + 0.0137498i $$0.995623\pi$$
$$194$$ −4378.55 + 7583.88i −0.00835269 + 0.0144673i
$$195$$ −329488. −0.620516
$$196$$ 0 0
$$197$$ 251505. 0.461723 0.230861 0.972987i $$-0.425846\pi$$
0.230861 + 0.972987i $$0.425846\pi$$
$$198$$ −155426. + 269206.i −0.281748 + 0.488002i
$$199$$ 104017. + 180162.i 0.186196 + 0.322501i 0.943979 0.330006i $$-0.107051\pi$$
−0.757783 + 0.652507i $$0.773717\pi$$
$$200$$ −79703.5 138050.i −0.140897 0.244041i
$$201$$ 221156. 383053.i 0.386107 0.668757i
$$202$$ 61469.7 0.105994
$$203$$ 0 0
$$204$$ 186135. 0.313150
$$205$$ −293452. + 508274.i −0.487700 + 0.844720i
$$206$$ −91970.5 159297.i −0.151001 0.261542i
$$207$$ 4441.25 + 7692.47i 0.00720409 + 0.0124779i
$$208$$ −178357. + 308923.i −0.285846 + 0.495100i
$$209$$ 643446. 1.01893
$$210$$ 0 0
$$211$$ −640577. −0.990525 −0.495262 0.868744i $$-0.664928\pi$$
−0.495262 + 0.868744i $$0.664928\pi$$
$$212$$ −143890. + 249225.i −0.219883 + 0.380849i
$$213$$ 200941. + 348040.i 0.303472 + 0.525630i
$$214$$ 153361. + 265630.i 0.228919 + 0.396499i
$$215$$ −2225.31 + 3854.35i −0.00328318 + 0.00568663i
$$216$$ 458032. 0.667977
$$217$$ 0 0
$$218$$ 244148. 0.347945
$$219$$ −6058.22 + 10493.1i −0.00853561 + 0.0147841i
$$220$$ 305480. + 529107.i 0.425526 + 0.737033i
$$221$$ 645909. + 1.11875e6i 0.889591 + 1.54082i
$$222$$ 23567.9 40820.8i 0.0320951 0.0555903i
$$223$$ 390135. 0.525354 0.262677 0.964884i $$-0.415395\pi$$
0.262677 + 0.964884i $$0.415395\pi$$
$$224$$ 0 0
$$225$$ 202089. 0.266126
$$226$$ 142860. 247440.i 0.186054 0.322255i
$$227$$ −145676. 252319.i −0.187639 0.325001i 0.756823 0.653620i $$-0.226750\pi$$
−0.944463 + 0.328618i $$0.893417\pi$$
$$228$$ −91917.5 159206.i −0.117101 0.202825i
$$229$$ 615202. 1.06556e6i 0.775227 1.34273i −0.159439 0.987208i $$-0.550969\pi$$
0.934667 0.355526i $$-0.115698\pi$$
$$230$$ −5746.45 −0.00716276
$$231$$ 0 0
$$232$$ −525506. −0.641000
$$233$$ −57139.3 + 98968.1i −0.0689517 + 0.119428i −0.898440 0.439096i $$-0.855299\pi$$
0.829488 + 0.558524i $$0.188632\pi$$
$$234$$ 308187. + 533795.i 0.367938 + 0.637287i
$$235$$ 176586. + 305856.i 0.208587 + 0.361283i
$$236$$ 118658. 205522.i 0.138681 0.240203i
$$237$$ −55.8489 −6.45867e−5
$$238$$ 0 0
$$239$$ −1.14782e6 −1.29981 −0.649906 0.760014i $$-0.725192\pi$$
−0.649906 + 0.760014i $$0.725192\pi$$
$$240$$ 49092.7 85031.1i 0.0550160 0.0952905i
$$241$$ −406354. 703825.i −0.450673 0.780589i 0.547755 0.836639i $$-0.315483\pi$$
−0.998428 + 0.0560501i $$0.982149\pi$$
$$242$$ −201856. 349626.i −0.221567 0.383764i
$$243$$ −449552. + 778647.i −0.488387 + 0.845912i
$$244$$ 927332. 0.997150
$$245$$ 0 0
$$246$$ −235230. −0.247831
$$247$$ 637928. 1.10492e6i 0.665318 1.15236i
$$248$$ 693306. + 1.20084e6i 0.715806 + 1.23981i
$$249$$ 311159. + 538944.i 0.318042 + 0.550865i
$$250$$ −267664. + 463608.i −0.270857 + 0.469138i
$$251$$ −406772. −0.407537 −0.203768 0.979019i $$-0.565319\pi$$
−0.203768 + 0.979019i $$0.565319\pi$$
$$252$$ 0 0
$$253$$ −24490.8 −0.0240548
$$254$$ 4355.77 7544.41i 0.00423624 0.00733738i
$$255$$ −177786. 307935.i −0.171217 0.296557i
$$256$$ 345548. + 598507.i 0.329540 + 0.570781i
$$257$$ 848562. 1.46975e6i 0.801403 1.38807i −0.117290 0.993098i $$-0.537421\pi$$
0.918693 0.394973i $$-0.129246\pi$$
$$258$$ −1783.80 −0.00166839
$$259$$ 0 0
$$260$$ 1.21144e6 1.11140
$$261$$ 333107. 576959.i 0.302679 0.524256i
$$262$$ −356713. 617846.i −0.321045 0.556067i
$$263$$ −102847. 178136.i −0.0916859 0.158805i 0.816535 0.577296i $$-0.195892\pi$$
−0.908221 + 0.418492i $$0.862559\pi$$
$$264$$ −285173. + 493934.i −0.251825 + 0.436173i
$$265$$ 549746. 0.480892
$$266$$ 0 0
$$267$$ 351010. 0.301330
$$268$$ −813133. + 1.40839e6i −0.691551 + 1.19780i
$$269$$ −867123. 1.50190e6i −0.730635 1.26550i −0.956612 0.291364i $$-0.905891\pi$$
0.225978 0.974132i $$-0.427442\pi$$
$$270$$ −187831. 325333.i −0.156804 0.271593i
$$271$$ −184521. + 319600.i −0.152624 + 0.264352i −0.932191 0.361966i $$-0.882106\pi$$
0.779567 + 0.626318i $$0.215439\pi$$
$$272$$ −384954. −0.315491
$$273$$ 0 0
$$274$$ −273492. −0.220074
$$275$$ −278601. + 482550.i −0.222152 + 0.384779i
$$276$$ 3498.56 + 6059.69i 0.00276450 + 0.00478826i
$$277$$ −613835. 1.06319e6i −0.480676 0.832554i 0.519079 0.854727i $$-0.326275\pi$$
−0.999754 + 0.0221720i $$0.992942\pi$$
$$278$$ −296016. + 512715.i −0.229722 + 0.397891i
$$279$$ −1.75789e6 −1.35201
$$280$$ 0 0
$$281$$ 2.00671e6 1.51607 0.758035 0.652214i $$-0.226159\pi$$
0.758035 + 0.652214i $$0.226159\pi$$
$$282$$ −70775.4 + 122587.i −0.0529980 + 0.0917953i
$$283$$ 892905. + 1.54656e6i 0.662734 + 1.14789i 0.979894 + 0.199517i $$0.0639374\pi$$
−0.317160 + 0.948372i $$0.602729\pi$$
$$284$$ −738808. 1.27965e6i −0.543545 0.941448i
$$285$$ −175589. + 304130.i −0.128052 + 0.221793i
$$286$$ −1.69947e6 −1.22856
$$287$$ 0 0
$$288$$ −1.19458e6 −0.848660
$$289$$ 12885.4 22318.1i 0.00907513 0.0157186i
$$290$$ 215501. + 373258.i 0.150471 + 0.260624i
$$291$$ −10184.8 17640.5i −0.00705047 0.0122118i
$$292$$ 22274.5 38580.6i 0.0152880 0.0264796i
$$293$$ 853248. 0.580639 0.290319 0.956930i $$-0.406238\pi$$
0.290319 + 0.956930i $$0.406238\pi$$
$$294$$ 0 0
$$295$$ −453345. −0.303301
$$296$$ −201829. + 349578.i −0.133892 + 0.231908i
$$297$$ −800518. 1.38654e6i −0.526599 0.912096i
$$298$$ −197627. 342300.i −0.128916 0.223289i
$$299$$ −24280.8 + 42055.6i −0.0157067 + 0.0272048i
$$300$$ 159194. 0.102123
$$301$$ 0 0
$$302$$ 336952. 0.212594
$$303$$ −71490.9 + 123826.i −0.0447347 + 0.0774827i
$$304$$ 190099. + 329261.i 0.117977 + 0.204341i
$$305$$ −885739. 1.53414e6i −0.545200 0.944315i
$$306$$ −332585. + 576054.i −0.203048 + 0.351690i
$$307$$ −1.96068e6 −1.18730 −0.593652 0.804722i $$-0.702314\pi$$
−0.593652 + 0.804722i $$0.702314\pi$$
$$308$$ 0 0
$$309$$ 427857. 0.254919
$$310$$ 568625. 984888.i 0.336064 0.582080i
$$311$$ −431802. 747903.i −0.253153 0.438474i 0.711239 0.702950i $$-0.248134\pi$$
−0.964392 + 0.264476i $$0.914801\pi$$
$$312$$ 565454. + 979396.i 0.328860 + 0.569602i
$$313$$ −550235. + 953035.i −0.317459 + 0.549855i −0.979957 0.199209i $$-0.936163\pi$$
0.662498 + 0.749063i $$0.269496\pi$$
$$314$$ 274799. 0.157286
$$315$$ 0 0
$$316$$ 205.342 0.000115680
$$317$$ −747954. + 1.29549e6i −0.418048 + 0.724081i −0.995743 0.0921719i $$-0.970619\pi$$
0.577695 + 0.816253i $$0.303952\pi$$
$$318$$ 110169. + 190818.i 0.0610929 + 0.105816i
$$319$$ 918444. + 1.59079e6i 0.505331 + 0.875259i
$$320$$ 146496. 253739.i 0.0799746 0.138520i
$$321$$ −713454. −0.386459
$$322$$ 0 0
$$323$$ 1.37686e6 0.734318
$$324$$ 356682. 617791.i 0.188764 0.326948i
$$325$$ 552423. + 956824.i 0.290110 + 0.502486i
$$326$$ −257126. 445355.i −0.133999 0.232093i
$$327$$ −283950. + 491816.i −0.146850 + 0.254351i
$$328$$ 2.01445e6 1.03388
$$329$$ 0 0
$$330$$ 467777. 0.236458
$$331$$ 1.37008e6 2.37304e6i 0.687345 1.19052i −0.285348 0.958424i $$-0.592109\pi$$
0.972694 0.232093i $$-0.0745573\pi$$
$$332$$ −1.14405e6 1.98156e6i −0.569640 0.986646i
$$333$$ −255870. 443180.i −0.126447 0.219013i
$$334$$ 635747. 1.10115e6i 0.311830 0.540106i
$$335$$ 3.10665e6 1.51245
$$336$$ 0 0
$$337$$ −2.31353e6 −1.10968 −0.554842 0.831956i $$-0.687221\pi$$
−0.554842 + 0.831956i $$0.687221\pi$$
$$338$$ −1.16228e6 + 2.01313e6i −0.553376 + 0.958475i
$$339$$ 332300. + 575560.i 0.157047 + 0.272014i
$$340$$ 653674. + 1.13220e6i 0.306665 + 0.531159i
$$341$$ 2.42343e6 4.19750e6i 1.12861 1.95481i
$$342$$ 656951. 0.303716
$$343$$ 0 0
$$344$$ 15276.0 0.00696006
$$345$$ 6683.29 11575.8i 0.00302303 0.00523604i
$$346$$ −523107. 906048.i −0.234909 0.406875i
$$347$$ 1.52963e6 + 2.64940e6i 0.681966 + 1.18120i 0.974380 + 0.224908i $$0.0722081\pi$$
−0.292414 + 0.956292i $$0.594459\pi$$
$$348$$ 262403. 454495.i 0.116150 0.201178i
$$349$$ −210232. −0.0923921 −0.0461961 0.998932i $$-0.514710\pi$$
−0.0461961 + 0.998932i $$0.514710\pi$$
$$350$$ 0 0
$$351$$ −3.17461e6 −1.37538
$$352$$ 1.64685e6 2.85243e6i 0.708430 1.22704i
$$353$$ 1.88395e6 + 3.26310e6i 0.804697 + 1.39378i 0.916495 + 0.400045i $$0.131006\pi$$
−0.111798 + 0.993731i $$0.535661\pi$$
$$354$$ −90850.0 157357.i −0.0385316 0.0667386i
$$355$$ −1.41134e6 + 2.44451e6i −0.594376 + 1.02949i
$$356$$ −1.29057e6 −0.539707
$$357$$ 0 0
$$358$$ 239291. 0.0986776
$$359$$ −503608. + 872275.i −0.206232 + 0.357205i −0.950525 0.310649i $$-0.899454\pi$$
0.744292 + 0.667854i $$0.232787\pi$$
$$360$$ 726446. + 1.25824e6i 0.295425 + 0.511691i
$$361$$ 558124. + 966700.i 0.225405 + 0.390412i
$$362$$ 534078. 925050.i 0.214207 0.371017i
$$363$$ 939058. 0.374047
$$364$$ 0 0
$$365$$ −85101.8 −0.0334354
$$366$$ 355003. 614883.i 0.138525 0.239933i
$$367$$ 763248. + 1.32198e6i 0.295802 + 0.512343i 0.975171 0.221453i $$-0.0710799\pi$$
−0.679369 + 0.733796i $$0.737747\pi$$
$$368$$ −7235.54 12532.3i −0.00278517 0.00482405i
$$369$$ −1.27691e6 + 2.21168e6i −0.488198 + 0.845583i
$$370$$ 331066. 0.125722
$$371$$ 0 0
$$372$$ −1.38476e6 −0.518822
$$373$$ −2.43149e6 + 4.21146e6i −0.904898 + 1.56733i −0.0838438 + 0.996479i $$0.526720\pi$$
−0.821054 + 0.570850i $$0.806614\pi$$
$$374$$ −917004. 1.58830e6i −0.338994 0.587155i
$$375$$ −622601. 1.07838e6i −0.228629 0.395997i
$$376$$ 606101. 1.04980e6i 0.221093 0.382945i
$$377$$ 3.64227e6 1.31983
$$378$$ 0 0
$$379$$ 630878. 0.225604 0.112802 0.993617i $$-0.464017\pi$$
0.112802 + 0.993617i $$0.464017\pi$$
$$380$$ 645597. 1.11821e6i 0.229352 0.397249i
$$381$$ 10131.8 + 17548.7i 0.00357579 + 0.00619346i
$$382$$ 1.29802e6 + 2.24824e6i 0.455118 + 0.788288i
$$383$$ −282822. + 489862.i −0.0985182 + 0.170639i −0.911072 0.412248i $$-0.864744\pi$$
0.812553 + 0.582887i $$0.198077\pi$$
$$384$$ −1.13334e6 −0.392221
$$385$$ 0 0
$$386$$ 1.42191e6 0.485741
$$387$$ −9683.12 + 16771.7i −0.00328653 + 0.00569244i
$$388$$ 37446.7 + 64859.7i 0.0126280 + 0.0218723i
$$389$$ −296106. 512870.i −0.0992140 0.171844i 0.812146 0.583455i $$-0.198300\pi$$
−0.911360 + 0.411611i $$0.864966\pi$$
$$390$$ 463766. 803266.i 0.154396 0.267423i
$$391$$ −52406.1 −0.0173356
$$392$$ 0 0
$$393$$ 1.65947e6 0.541986
$$394$$ −354003. + 613151.i −0.114886 + 0.198988i
$$395$$ −196.132 339.710i −6.32492e−5 0.000109551i
$$396$$ 1.32925e6 + 2.30233e6i 0.425961 + 0.737786i
$$397$$ −671558. + 1.16317e6i −0.213849 + 0.370397i −0.952916 0.303235i $$-0.901933\pi$$
0.739067 + 0.673632i $$0.235267\pi$$
$$398$$ −585629. −0.185317
$$399$$ 0 0
$$400$$ −329238. −0.102887
$$401$$ 1.84358e6 3.19318e6i 0.572534 0.991658i −0.423771 0.905769i $$-0.639294\pi$$
0.996305 0.0858884i $$-0.0273729\pi$$
$$402$$ 622569. + 1.07832e6i 0.192142 + 0.332800i
$$403$$ −4.80529e6 8.32300e6i −1.47386 2.55280i
$$404$$ 262854. 455276.i 0.0801236 0.138778i
$$405$$ −1.36273e6 −0.412832
$$406$$ 0 0
$$407$$ 1.41097e6 0.422214
$$408$$ −610220. + 1.05693e6i −0.181483 + 0.314338i
$$409$$ −728151. 1.26119e6i −0.215235 0.372798i 0.738110 0.674680i $$-0.235718\pi$$
−0.953345 + 0.301882i $$0.902385\pi$$
$$410$$ −826089. 1.43083e6i −0.242698 0.420366i
$$411$$ 318079. 550929.i 0.0928818 0.160876i
$$412$$ −1.57312e6 −0.456582
$$413$$ 0 0
$$414$$ −25004.9 −0.00717008
$$415$$ −2.18548e6 + 3.78536e6i −0.622911 + 1.07891i
$$416$$ −3.26545e6 5.65593e6i −0.925145 1.60240i
$$417$$ −688550. 1.19260e6i −0.193908 0.335858i
$$418$$ −905674. + 1.56867e6i −0.253531 + 0.439129i
$$419$$ −2.92192e6 −0.813080 −0.406540 0.913633i $$-0.633265\pi$$
−0.406540 + 0.913633i $$0.633265\pi$$
$$420$$ 0 0
$$421$$ 2.01999e6 0.555450 0.277725 0.960661i $$-0.410420\pi$$
0.277725 + 0.960661i $$0.410420\pi$$
$$422$$ 901636. 1.56168e6i 0.246462 0.426885i
$$423$$ 768389. + 1.33089e6i 0.208800 + 0.361652i
$$424$$ −943454. 1.63411e6i −0.254863 0.441435i
$$425$$ −596156. + 1.03257e6i −0.160099 + 0.277299i
$$426$$ −1.13133e6 −0.302040
$$427$$ 0 0
$$428$$ 2.62319e6 0.692182
$$429$$ 1.97653e6 3.42344e6i 0.518513 0.898090i
$$430$$ −6264.41 10850.3i −0.00163384 0.00282989i
$$431$$ 2.71900e6 + 4.70944e6i 0.705043 + 1.22117i 0.966676 + 0.256003i $$0.0824057\pi$$
−0.261633 + 0.965167i $$0.584261\pi$$
$$432$$ 473008. 819274.i 0.121944 0.211213i
$$433$$ −3.77335e6 −0.967179 −0.483590 0.875295i $$-0.660667\pi$$
−0.483590 + 0.875295i $$0.660667\pi$$
$$434$$ 0 0
$$435$$ −1.00253e6 −0.254025
$$436$$ 1.04401e6 1.80828e6i 0.263020 0.455565i
$$437$$ 25879.3 + 44824.3i 0.00648260 + 0.0112282i
$$438$$ −17054.3 29539.0i −0.00424766 0.00735716i
$$439$$ −1.17575e6 + 2.03646e6i −0.291175 + 0.504330i −0.974088 0.226170i $$-0.927379\pi$$
0.682913 + 0.730500i $$0.260713\pi$$
$$440$$ −4.00591e6 −0.986439
$$441$$ 0 0
$$442$$ −3.63656e6 −0.885391
$$443$$ −2.40188e6 + 4.16019e6i −0.581491 + 1.00717i 0.413812 + 0.910362i $$0.364197\pi$$
−0.995303 + 0.0968092i $$0.969136\pi$$
$$444$$ −201560. 349112.i −0.0485229 0.0840441i
$$445$$ 1.23269e6 + 2.13508e6i 0.295089 + 0.511110i
$$446$$ −549129. + 951119.i −0.130718 + 0.226411i
$$447$$ 919383. 0.217634
$$448$$ 0 0
$$449$$ −2.76805e6 −0.647975 −0.323987 0.946061i $$-0.605024\pi$$
−0.323987 + 0.946061i $$0.605024\pi$$
$$450$$ −284448. + 492679.i −0.0662174 + 0.114692i
$$451$$ −3.52071e6 6.09805e6i −0.815059 1.41172i
$$452$$ −1.22178e6 2.11619e6i −0.281285 0.487201i
$$453$$ −391885. + 678765.i −0.0897249 + 0.155408i
$$454$$ 820179. 0.186754
$$455$$ 0 0
$$456$$ 1.20536e6 0.271459
$$457$$ −120783. + 209203.i −0.0270530 + 0.0468573i −0.879235 0.476388i $$-0.841946\pi$$
0.852182 + 0.523246i $$0.175279\pi$$
$$458$$ 1.73184e6 + 2.99963e6i 0.385784 + 0.668197i
$$459$$ −1.71297e6 2.96695e6i −0.379505 0.657322i
$$460$$ −24572.7 + 42561.2i −0.00541450 + 0.00937819i
$$461$$ 990579. 0.217088 0.108544 0.994092i $$-0.465381\pi$$
0.108544 + 0.994092i $$0.465381\pi$$
$$462$$ 0 0
$$463$$ 6.20488e6 1.34518 0.672591 0.740014i $$-0.265181\pi$$
0.672591 + 0.740014i $$0.265181\pi$$
$$464$$ −542688. + 939963.i −0.117019 + 0.202682i
$$465$$ 1.32265e6 + 2.29090e6i 0.283670 + 0.491331i
$$466$$ −160851. 278602.i −0.0343131 0.0594320i
$$467$$ 3.44249e6 5.96256e6i 0.730432 1.26515i −0.226266 0.974066i $$-0.572652\pi$$
0.956699 0.291080i $$-0.0940147\pi$$
$$468$$ 5.27141e6 1.11253
$$469$$ 0 0
$$470$$ −994206. −0.207602
$$471$$ −319598. + 553561.i −0.0663823 + 0.114978i
$$472$$ 778014. + 1.34756e6i 0.160743 + 0.278415i
$$473$$ −26698.3 46242.8i −0.00548695 0.00950368i
$$474$$ 78.6093 136.155i 1.60705e−5 2.78348e-5i
$$475$$ 1.17758e6 0.239473
$$476$$ 0 0
$$477$$ 2.39214e6 0.481383
$$478$$ 1.61561e6 2.79831e6i 0.323419 0.560178i
$$479$$ 2.70644e6 + 4.68769e6i 0.538963 + 0.933512i 0.998960 + 0.0455914i $$0.0145172\pi$$
−0.459997 + 0.887921i $$0.652149\pi$$
$$480$$ 898814. + 1.55679e6i 0.178060 + 0.308409i
$$481$$ 1.39887e6 2.42292e6i 0.275686 0.477503i
$$482$$ 2.28783e6 0.448545
$$483$$ 0 0
$$484$$ −3.45268e6 −0.669950
$$485$$ 71534.3 123901.i 0.0138089 0.0239178i
$$486$$ −1.26552e6 2.19195e6i −0.243041 0.420959i
$$487$$ 1.50521e6 + 2.60711e6i 0.287591 + 0.498122i 0.973234 0.229815i $$-0.0738122\pi$$
−0.685643 + 0.727938i $$0.740479\pi$$
$$488$$ −3.04014e6 + 5.26568e6i −0.577889 + 1.00093i
$$489$$ 1.19618e6 0.226216
$$490$$ 0 0
$$491$$ −7.24498e6 −1.35623 −0.678115 0.734956i $$-0.737203\pi$$
−0.678115 + 0.734956i $$0.737203\pi$$
$$492$$ −1.00588e6 + 1.74224e6i −0.187341 + 0.324485i
$$493$$ 1.96531e6 + 3.40402e6i 0.364178 + 0.630775i
$$494$$ 1.79581e6 + 3.11044e6i 0.331088 + 0.573462i
$$495$$ 2.53927e6 4.39814e6i 0.465795 0.806781i
$$496$$ 2.86389e6 0.522700
$$497$$ 0 0
$$498$$ −1.75187e6 −0.316540
$$499$$ 2.56394e6 4.44088e6i 0.460953 0.798394i −0.538056 0.842909i $$-0.680841\pi$$
0.999009 + 0.0445152i $$0.0141743\pi$$
$$500$$ 2.28914e6 + 3.96491e6i 0.409495 + 0.709265i
$$501$$ 1.47878e6 + 2.56133e6i 0.263215 + 0.455901i
$$502$$ 572546. 991679.i 0.101403 0.175635i
$$503$$ 1.05978e7 1.86766 0.933830 0.357718i $$-0.116445\pi$$
0.933830 + 0.357718i $$0.116445\pi$$
$$504$$ 0 0
$$505$$ −1.00426e6 −0.175233
$$506$$ 34471.7 59706.8i 0.00598531 0.0103669i
$$507$$ −2.70354e6 4.68266e6i −0.467103 0.809045i
$$508$$ −37251.9 64522.1i −0.00640455 0.0110930i
$$509$$ −4.39420e6 + 7.61097e6i −0.751770 + 1.30210i 0.195194 + 0.980765i $$0.437466\pi$$
−0.946964 + 0.321340i $$0.895867\pi$$
$$510$$ 1.00096e6 0.170409
$$511$$ 0 0
$$512$$ 3.59310e6 0.605752
$$513$$ −1.69180e6 + 2.93029e6i −0.283829 + 0.491606i
$$514$$ 2.38877e6 + 4.13746e6i 0.398810 + 0.690759i
$$515$$ 1.50256e6 + 2.60251e6i 0.249640 + 0.432389i
$$516$$ −7627.81 + 13211.8i −0.00126118 + 0.00218442i
$$517$$ −4.23721e6 −0.697194
$$518$$ 0 0
$$519$$ 2.43355e6 0.396572
$$520$$ −3.97156e6 + 6.87895e6i −0.644099 + 1.11561i
$$521$$ −81066.4 140411.i −0.0130842 0.0226625i 0.859409 0.511288i $$-0.170832\pi$$
−0.872493 + 0.488626i $$0.837498\pi$$
$$522$$ 937721. + 1.62418e6i 0.150625 + 0.260890i
$$523$$ 3.57422e6 6.19073e6i 0.571383 0.989664i −0.425041 0.905174i $$-0.639740\pi$$
0.996424 0.0844904i $$-0.0269262\pi$$
$$524$$ −6.10144e6 −0.970743
$$525$$ 0 0
$$526$$ 579044. 0.0912530
$$527$$ 5.18571e6 8.98191e6i 0.813357 1.40878i
$$528$$ 588993. + 1.02017e6i 0.0919445 + 0.159252i
$$529$$ 3.21719e6 + 5.57233e6i 0.499847 + 0.865760i
$$530$$ −773788. + 1.34024e6i −0.119655 + 0.207249i
$$531$$ −1.97267e6 −0.303611
$$532$$ 0 0
$$533$$ −1.39621e7 −2.12879
$$534$$ −494060. + 855737.i −0.0749767 + 0.129863i
$$535$$ −2.50553e6 4.33971e6i −0.378456 0.655505i
$$536$$ −5.33151e6 9.23445e6i −0.801564 1.38835i
$$537$$ −278302. + 482033.i −0.0416467 + 0.0721342i
$$538$$ 4.88203e6 0.727185
$$539$$ 0 0
$$540$$ −3.21278e6 −0.474129
$$541$$ 2.41802e6 4.18813e6i 0.355195 0.615216i −0.631956 0.775004i $$-0.717748\pi$$
0.987151 + 0.159788i $$0.0510811\pi$$
$$542$$ −519440. 899696.i −0.0759516 0.131552i
$$543$$ 1.24230e6 + 2.15172e6i 0.180811 + 0.313174i
$$544$$ 3.52397e6 6.10369e6i 0.510546 0.884291i
$$545$$ −3.98874e6 −0.575234
$$546$$ 0 0
$$547$$ 9.98777e6 1.42725 0.713626 0.700527i $$-0.247052\pi$$
0.713626 + 0.700527i $$0.247052\pi$$
$$548$$ −1.16950e6 + 2.02563e6i −0.166359 + 0.288143i
$$549$$ −3.85417e6 6.67561e6i −0.545757 0.945279i
$$550$$ −784281. 1.35841e6i −0.110552 0.191481i
$$551$$ 1.94103e6 3.36196e6i 0.272366 0.471751i
$$552$$ −45878.4 −0.00640856
$$553$$ 0 0
$$554$$ 3.45598e6 0.478406
$$555$$ −385039. + 666907.i −0.0530606 + 0.0919037i
$$556$$ 2.53162e6 + 4.38490e6i 0.347305 + 0.601551i
$$557$$ −873096. 1.51225e6i −0.119241 0.206531i 0.800226 0.599698i $$-0.204713\pi$$
−0.919467 + 0.393167i $$0.871379\pi$$
$$558$$ 2.47429e6 4.28560e6i 0.336407 0.582674i
$$559$$ −105877. −0.0143309
$$560$$ 0 0
$$561$$ 4.26600e6 0.572287
$$562$$ −2.82452e6 + 4.89221e6i −0.377228 + 0.653378i
$$563$$ 377609. + 654038.i 0.0502078 + 0.0869625i 0.890037 0.455888i $$-0.150678\pi$$
−0.839829 + 0.542851i $$0.817345\pi$$
$$564$$ 605293. + 1.04840e6i 0.0801250 + 0.138781i
$$565$$ −2.33396e6 + 4.04254e6i −0.307590 + 0.532762i
$$566$$ −5.02719e6 −0.659605
$$567$$ 0 0
$$568$$ 9.68836e6 1.26003
$$569$$ 2.19767e6 3.80648e6i 0.284565 0.492882i −0.687938 0.725769i $$-0.741484\pi$$
0.972504 + 0.232888i $$0.0748174\pi$$
$$570$$ −494297. 856148.i −0.0637237 0.110373i
$$571$$ −5.80520e6 1.00549e7i −0.745121 1.29059i −0.950138 0.311829i $$-0.899059\pi$$
0.205018 0.978758i $$-0.434275\pi$$
$$572$$ −7.26718e6 + 1.25871e7i −0.928700 + 1.60856i
$$573$$ −6.03855e6 −0.768327
$$574$$ 0 0
$$575$$ −44821.1 −0.00565344
$$576$$ 637458. 1.10411e6i 0.0800563 0.138662i
$$577$$ −5.33214e6 9.23554e6i −0.666748 1.15484i −0.978808 0.204779i $$-0.934352\pi$$
0.312060 0.950062i $$-0.398981\pi$$
$$578$$ 36273.3 + 62827.2i 0.00451614 + 0.00782218i
$$579$$ −1.65372e6 + 2.86433e6i −0.205006 + 0.355081i
$$580$$ 3.68606e6 0.454980
$$581$$ 0 0
$$582$$ 57341.7 0.00701719
$$583$$ −3.29781e6 + 5.71197e6i −0.401841 + 0.696009i
$$584$$ 146049. + 252963.i 0.0177201 + 0.0306920i
$$585$$ −5.03498e6 8.72084e6i −0.608286 1.05358i
$$586$$ −1.20098e6 + 2.08015e6i −0.144474 + 0.250237i
$$587$$ −1.39482e7 −1.67079 −0.835396 0.549648i $$-0.814762\pi$$
−0.835396 + 0.549648i $$0.814762\pi$$
$$588$$ 0 0
$$589$$ −1.02433e7 −1.21661
$$590$$ 638099. 1.10522e6i 0.0754672 0.130713i
$$591$$ −823430. 1.42622e6i −0.0969746 0.167965i
$$592$$ 416856. + 722015.i 0.0488857 + 0.0846724i
$$593$$ −5.89663e6 + 1.02133e7i −0.688600 + 1.19269i 0.283691 + 0.958916i $$0.408441\pi$$
−0.972291 + 0.233774i $$0.924892\pi$$
$$594$$ 4.50703e6 0.524113
$$595$$ 0 0
$$596$$ −3.38033e6 −0.389802
$$597$$ 681102. 1.17970e6i 0.0782125 0.135468i
$$598$$ −68352.3 118390.i −0.00781628 0.0135382i
$$599$$ 2.19029e6 + 3.79369e6i 0.249421 + 0.432011i 0.963365 0.268192i $$-0.0864262\pi$$
−0.713944 + 0.700203i $$0.753093\pi$$
$$600$$ −521899. + 903956.i −0.0591846 + 0.102511i
$$601$$ 688570. 0.0777610 0.0388805 0.999244i $$-0.487621\pi$$
0.0388805 + 0.999244i $$0.487621\pi$$
$$602$$ 0 0
$$603$$ 1.35181e7 1.51399
$$604$$ 1.44086e6 2.49564e6i 0.160705 0.278349i
$$605$$ 3.29781e6 + 5.71198e6i 0.366301 + 0.634451i
$$606$$ −201252. 348579.i −0.0222617 0.0385584i
$$607$$ 4.68660e6 8.11742e6i 0.516281 0.894224i −0.483541 0.875322i $$-0.660650\pi$$
0.999821 0.0189023i $$-0.00601715\pi$$
$$608$$ −6.96085e6 −0.763666
$$609$$ 0 0
$$610$$ 4.98684e6 0.542626
$$611$$ −4.20087e6 + 7.27612e6i −0.455236 + 0.788492i
$$612$$ 2.84437e6 + 4.92659e6i 0.306978 + 0.531701i
$$613$$ 1.08342e6 + 1.87655e6i 0.116452 + 0.201701i 0.918359 0.395748i $$-0.129515\pi$$
−0.801907 + 0.597449i $$0.796181\pi$$
$$614$$ 2.75974e6 4.78000e6i 0.295424 0.511690i
$$615$$ 3.84306e6 0.409722
$$616$$ 0 0
$$617$$ −5.07951e6 −0.537166 −0.268583 0.963256i $$-0.586555\pi$$
−0.268583 + 0.963256i $$0.586555\pi$$
$$618$$ −602224. + 1.04308e6i −0.0634288 + 0.109862i
$$619$$ 1.09517e6 + 1.89689e6i 0.114883 + 0.198983i 0.917733 0.397198i $$-0.130017\pi$$
−0.802850 + 0.596181i $$0.796684\pi$$
$$620$$ −4.86306e6 8.42306e6i −0.508078 0.880016i
$$621$$ 64393.4 111533.i 0.00670058 0.0116057i
$$622$$ 2.43111e6 0.251958
$$623$$ 0 0
$$624$$ 2.33577e6 0.240142
$$625$$ 2.79509e6 4.84124e6i 0.286217 0.495743i
$$626$$ −1.54895e6 2.68286e6i −0.157980 0.273629i
$$627$$ −2.10665e6 3.64882e6i −0.214005 0.370667i
$$628$$ 1.17508e6 2.03530e6i 0.118896 0.205935i
$$629$$ 3.01923e6 0.304278
$$630$$ 0 0
$$631$$ −7.18693e6 −0.718572 −0.359286 0.933228i $$-0.616980\pi$$
−0.359286 + 0.933228i $$0.616980\pi$$
$$632$$ −673.188 + 1166.00i −6.70415e−5 + 0.000116119i
$$633$$ 2.09725e6 + 3.63255e6i 0.208038 + 0.360332i
$$634$$ −2.10554e6 3.64691e6i −0.208037 0.360331i
$$635$$ −71162.1 + 123256.i −0.00700349 + 0.0121304i
$$636$$ 1.88439e6 0.184726
$$637$$ 0 0
$$638$$ −5.17097e6 −0.502945
$$639$$ −6.14125e6 + 1.06370e7i −0.594983 + 1.03054i
$$640$$ −3.98009e6 6.89371e6i −0.384098 0.665278i
$$641$$ 8.82500e6 + 1.52854e7i 0.848340 + 1.46937i 0.882689 + 0.469958i $$0.155731\pi$$
−0.0343490 + 0.999410i $$0.510936\pi$$
$$642$$ 1.00421e6 1.73935e6i 0.0961586 0.166552i
$$643$$ 898309. 0.0856837 0.0428419 0.999082i $$-0.486359\pi$$
0.0428419 + 0.999082i $$0.486359\pi$$
$$644$$ 0 0
$$645$$ 29142.7 0.00275823
$$646$$ −1.93798e6 + 3.35669e6i −0.182713 + 0.316468i
$$647$$ 693210. + 1.20068e6i 0.0651035 + 0.112763i 0.896740 0.442558i $$-0.145929\pi$$
−0.831636 + 0.555321i $$0.812596\pi$$
$$648$$ 2.33867e6 + 4.05070e6i 0.218792 + 0.378959i
$$649$$ 2.71952e6 4.71034e6i 0.253443 0.438976i
$$650$$ −3.11022e6 −0.288741
$$651$$ 0 0
$$652$$ −4.39804e6 −0.405173
$$653$$ 8.77125e6 1.51923e7i 0.804968 1.39425i −0.111345 0.993782i $$-0.535516\pi$$
0.916313 0.400464i $$-0.131151\pi$$
$$654$$ −799341. 1.38450e6i −0.0730782 0.126575i
$$655$$ 5.82778e6 + 1.00940e7i 0.530762 + 0.919307i
$$656$$ 2.08031e6 3.60320e6i 0.188742 0.326910i
$$657$$ −370308. −0.0334696
$$658$$ 0 0
$$659$$ 9.87522e6 0.885795 0.442898 0.896572i $$-0.353950\pi$$
0.442898 + 0.896572i $$0.353950\pi$$
$$660$$ 2.00029e6 3.46460e6i 0.178744 0.309595i
$$661$$ 4.03396e6 + 6.98702e6i 0.359110 + 0.621997i 0.987812 0.155649i $$-0.0497468\pi$$
−0.628702 + 0.777646i $$0.716414\pi$$
$$662$$ 3.85687e6 + 6.68029e6i 0.342050 + 0.592448i
$$663$$ 4.22942e6 7.32557e6i 0.373677 0.647228i
$$664$$ 1.50025e7 1.32052
$$665$$ 0 0
$$666$$ 1.44059e6 0.125850
$$667$$ −73879.3 + 127963.i −0.00642996 + 0.0111370i
$$668$$ −5.43710e6 9.41734e6i −0.471440 0.816558i
$$669$$ −1.27730e6 2.21236e6i −0.110339 0.191113i
$$670$$ −4.37272e6 + 7.57377e6i −0.376326 + 0.651816i
$$671$$ 2.12534e7 1.82231
$$672$$ 0 0
$$673$$ −1.12772e7 −0.959762 −0.479881 0.877334i $$-0.659320\pi$$
−0.479881 + 0.877334i $$0.659320\pi$$
$$674$$ 3.25637e6 5.64020e6i 0.276111 0.478239i
$$675$$ −1.46504e6 2.53753e6i −0.123763 0.214364i
$$676$$ 9.94020e6 + 1.72169e7i 0.836621 + 1.44907i
$$677$$ −2.60186e6 + 4.50655e6i −0.218179 + 0.377897i −0.954251 0.299006i $$-0.903345\pi$$
0.736073 + 0.676903i $$0.236678\pi$$
$$678$$ −1.87090e6 −0.156306
$$679$$ 0 0
$$680$$ −8.57196e6 −0.710899
$$681$$ −953891. + 1.65219e6i −0.0788190 + 0.136518i
$$682$$ 6.82212e6 + 1.18163e7i 0.561640 + 0.972790i
$$683$$ −3.02957e6 5.24737e6i −0.248502 0.430418i 0.714608 0.699525i $$-0.246605\pi$$
−0.963110 + 0.269107i $$0.913272\pi$$
$$684$$ 2.80922e6 4.86572e6i 0.229586 0.397655i
$$685$$ 4.46816e6 0.363833
$$686$$ 0 0
$$687$$ −8.05671e6 −0.651277
$$688$$ 15775.4 27323.8i 0.00127060 0.00220075i
$$689$$ 6.53906e6 + 1.13260e7i 0.524768 + 0.908924i
$$690$$ 18813.9 + 32586.7i 0.00150438 + 0.00260566i
$$691$$ −3.68249e6 + 6.37826e6i −0.293391 + 0.508168i −0.974609 0.223912i $$-0.928117\pi$$
0.681219 + 0.732080i $$0.261450\pi$$
$$692$$ −8.94754e6 −0.710295
$$693$$ 0 0
$$694$$ −8.61204e6 −0.678746
$$695$$ 4.83614e6 8.37644e6i 0.379784 0.657806i
$$696$$ 1.72051e6 + 2.98001e6i 0.134628 + 0.233182i
$$697$$ −7.53370e6 1.30488e7i −0.587390 1.01739i
$$698$$ 295909. 512529.i 0.0229890 0.0398181i
$$699$$ 748298. 0.0579271
$$700$$ 0 0
$$701$$ 7.80919e6 0.600221 0.300110 0.953904i $$-0.402977\pi$$
0.300110 + 0.953904i $$0.402977\pi$$
$$702$$ 4.46838e6 7.73946e6i 0.342222 0.592745i
$$703$$ −1.49096e6 2.58243e6i −0.113783 0.197079i
$$704$$ 1.75760e6 + 3.04426e6i 0.133656 + 0.231499i
$$705$$ 1.15629e6 2.00275e6i 0.0876180 0.151759i
$$706$$ −1.06069e7 −0.800898
$$707$$ 0 0
$$708$$ −1.55395e6 −0.116508
$$709$$ −8.78251e6 + 1.52118e7i −0.656150 + 1.13649i 0.325454 + 0.945558i $$0.394483\pi$$
−0.981604 + 0.190927i $$0.938851\pi$$
$$710$$ −3.97303e6 6.88149e6i −0.295785 0.512314i
$$711$$ −853.439 1478.20i −6.33138e−5 0.000109663i
$$712$$ 4.23099e6 7.32829e6i 0.312782 0.541755i
$$713$$ 389879. 0.0287214
$$714$$ 0 0
$$715$$ 2.77649e7 2.03110
$$716$$ 1.02324e6 1.77231e6i 0.0745928 0.129198i
$$717$$ 3.75799e6 + 6.50902e6i 0.272997 + 0.472844i
$$718$$ −1.41769e6 2.45552e6i −0.102629 0.177759i
$$719$$ 4.04610e6 7.00805e6i 0.291887 0.505563i −0.682369 0.731008i $$-0.739050\pi$$
0.974256 + 0.225445i $$0.0723836\pi$$
$$720$$ 3.00079e6 0.215727
$$721$$ 0 0
$$722$$ −3.14232e6 −0.224341
$$723$$ −2.66081e6 + 4.60866e6i −0.189308 + 0.327890i
$$724$$ −4.56760e6 7.91131e6i −0.323848 0.560922i
$$725$$ 1.68086e6 + 2.91133e6i 0.118764 + 0.205706i
$$726$$ −1.32176e6 + 2.28935e6i −0.0930702 + 0.161202i
$$727$$ 1.51986e7 1.06652 0.533258 0.845952i $$-0.320967\pi$$
0.533258 + 0.845952i $$0.320967\pi$$
$$728$$ 0 0
$$729$$ −1.31285e6 −0.0914944
$$730$$ 119784. 207472.i 0.00831938 0.0144096i
$$731$$ −57129.7 98951.6i −0.00395429 0.00684903i
$$732$$ −3.03609e6 5.25866e6i −0.209429 0.362742i
$$733$$ −2.91701e6 + 5.05241e6i −0.200530 + 0.347327i −0.948699 0.316180i $$-0.897600\pi$$
0.748170 + 0.663507i $$0.230933\pi$$
$$734$$ −4.29720e6 −0.294405
$$735$$ 0 0
$$736$$ 264944. 0.0180285
$$737$$ −1.86361e7 + 3.22787e7i −1.26382 + 2.18901i
$$738$$ −3.59461e6 6.22604e6i −0.242946 0.420796i
$$739$$ −3.23860e6 5.60941e6i −0.218145 0.377838i 0.736096 0.676877i $$-0.236667\pi$$
−0.954241 + 0.299039i $$0.903334\pi$$
$$740$$ 1.41569e6 2.45205e6i 0.0950361 0.164607i
$$741$$ −8.35433e6 −0.558941
$$742$$ 0 0
$$743$$ −1.50899e7 −1.00280 −0.501401 0.865215i $$-0.667182\pi$$
−0.501401 + 0.865215i $$0.667182\pi$$
$$744$$ 4.53978e6 7.86312e6i 0.300678 0.520790i
$$745$$ 3.22872e6 + 5.59230e6i 0.213127 + 0.369148i
$$746$$ −6.84481e6 1.18556e7i −0.450313 0.779965i
$$747$$ −9.50979e6 + 1.64714e7i −0.623548 + 1.08002i
$$748$$ −1.56850e7 −1.02502
$$749$$ 0 0
$$750$$ 3.50534e6 0.227550
$$751$$ 1.06998e6 1.85327e6i 0.0692273 0.119905i −0.829334 0.558753i $$-0.811280\pi$$
0.898561 + 0.438848i $$0.144613\pi$$
$$752$$ −1.25184e6 2.16824e6i −0.0807240 0.139818i
$$753$$ 1.33177e6 + 2.30670e6i 0.0855940 + 0.148253i
$$754$$ −5.12663e6 + 8.87958e6i −0.328400 + 0.568806i
$$755$$ −5.50494e6 −0.351467
$$756$$ 0 0
$$757$$ 2.10943e7 1.33791 0.668954 0.743304i $$-0.266742\pi$$
0.668954 + 0.743304i $$0.266742\pi$$
$$758$$ −887984. + 1.53803e6i −0.0561348 + 0.0972283i
$$759$$ 80183.2 + 138881.i 0.00505218 + 0.00875063i
$$760$$ 4.23302e6 + 7.33181e6i 0.265838 + 0.460444i
$$761$$ −4.89979e6 + 8.48669e6i −0.306701 + 0.531222i −0.977639 0.210292i $$-0.932559\pi$$
0.670937 + 0.741514i $$0.265892\pi$$
$$762$$ −57043.3 −0.00355891
$$763$$ 0 0
$$764$$ 2.22022e7 1.37614
$$765$$ 5.43358e6 9.41124e6i 0.335686 0.581424i
$$766$$ −796165. 1.37900e6i −0.0490265 0.0849164i
$$767$$ −5.39239e6 9.33990e6i −0.330973 0.573263i
$$768$$ 2.26265e6 3.91903e6i 0.138425 0.239759i
$$769$$ −3.23493e7 −1.97265 −0.986323 0.164825i $$-0.947294\pi$$
−0.986323 + 0.164825i $$0.947294\pi$$
$$770$$