# Properties

 Label 63.6.e.d.37.1 Level $63$ Weight $6$ Character 63.37 Analytic conductor $10.104$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,6,Mod(37,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("63.37");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 63.e (of order $$3$$, degree $$2$$, 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: $$10.1041806482$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{37})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{3} + 10x^{2} + 9x + 81$$ x^4 - x^3 + 10*x^2 + 9*x + 81 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 7) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 37.1 Root $$-1.27069 + 2.20090i$$ of defining polynomial Character $$\chi$$ $$=$$ 63.37 Dual form 63.6.e.d.46.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-2.54138 + 4.40180i) q^{2} +(3.08276 + 5.33950i) q^{4} +(20.9138 - 36.2238i) q^{5} +(-127.159 - 25.2522i) q^{7} -193.986 q^{8} +O(q^{10})$$ $$q+(-2.54138 + 4.40180i) q^{2} +(3.08276 + 5.33950i) q^{4} +(20.9138 - 36.2238i) q^{5} +(-127.159 - 25.2522i) q^{7} -193.986 q^{8} +(106.300 + 184.117i) q^{10} +(36.0482 + 62.4374i) q^{11} -632.317 q^{13} +(434.314 - 495.552i) q^{14} +(394.345 - 683.025i) q^{16} +(-987.962 - 1711.20i) q^{17} +(932.463 - 1615.07i) q^{19} +257.889 q^{20} -366.449 q^{22} +(206.855 - 358.284i) q^{23} +(687.725 + 1191.17i) q^{25} +(1606.96 - 2783.34i) q^{26} +(-257.166 - 756.810i) q^{28} -731.934 q^{29} +(-3061.59 - 5302.83i) q^{31} +(-1099.42 - 1904.25i) q^{32} +10043.2 q^{34} +(-3574.10 + 4078.05i) q^{35} +(-5175.19 + 8963.69i) q^{37} +(4739.49 + 8209.03i) q^{38} +(-4056.99 + 7026.92i) q^{40} +3529.84 q^{41} -14515.2 q^{43} +(-222.256 + 384.959i) q^{44} +(1051.40 + 1821.07i) q^{46} +(-10711.7 + 18553.1i) q^{47} +(15531.7 + 6422.06i) q^{49} -6991.08 q^{50} +(-1949.28 - 3376.26i) q^{52} +(6289.73 + 10894.1i) q^{53} +3015.62 q^{55} +(24667.0 + 4898.57i) q^{56} +(1860.12 - 3221.83i) q^{58} +(-18067.0 - 31292.9i) q^{59} +(-2012.40 + 3485.58i) q^{61} +31122.6 q^{62} +36414.2 q^{64} +(-13224.2 + 22904.9i) q^{65} +(-7782.97 - 13480.5i) q^{67} +(6091.31 - 10550.5i) q^{68} +(-8867.61 - 26096.4i) q^{70} -12180.8 q^{71} +(-9794.56 - 16964.7i) q^{73} +(-26304.3 - 45560.3i) q^{74} +11498.2 q^{76} +(-3007.17 - 8849.75i) q^{77} +(-18044.9 + 31254.7i) q^{79} +(-16494.5 - 28569.3i) q^{80} +(-8970.66 + 15537.6i) q^{82} +24572.6 q^{83} -82648.2 q^{85} +(36888.7 - 63893.2i) q^{86} +(-6992.86 - 12112.0i) q^{88} +(-35121.7 + 60832.5i) q^{89} +(80404.6 + 15967.4i) q^{91} +2550.74 q^{92} +(-54444.8 - 94301.2i) q^{94} +(-39002.7 - 67554.7i) q^{95} +105758. q^{97} +(-67740.5 + 52046.4i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8}+O(q^{10})$$ 4 * q + 2 * q^2 - 12 * q^4 - 38 * q^5 - 168 * q^7 - 192 * q^8 $$4 q + 2 q^{2} - 12 q^{4} - 38 q^{5} - 168 q^{7} - 192 q^{8} + 778 q^{10} + 424 q^{11} - 1848 q^{13} + 2674 q^{14} + 2064 q^{16} - 2346 q^{17} + 360 q^{19} + 3416 q^{20} + 4252 q^{22} - 12 q^{23} - 1872 q^{25} + 1148 q^{26} + 2548 q^{28} + 14104 q^{29} - 3548 q^{31} - 8096 q^{32} + 14844 q^{34} - 27496 q^{35} - 11090 q^{37} + 20138 q^{38} - 15936 q^{40} - 7000 q^{41} - 25360 q^{43} + 5948 q^{44} + 5118 q^{46} - 22956 q^{47} + 4900 q^{49} - 59984 q^{50} + 1400 q^{52} + 3042 q^{53} - 50152 q^{55} + 57792 q^{56} + 58852 q^{58} - 65808 q^{59} + 42486 q^{61} + 98724 q^{62} + 70912 q^{64} - 3164 q^{65} - 42312 q^{67} + 5460 q^{68} - 113050 q^{70} + 4416 q^{71} + 50506 q^{73} - 47370 q^{74} + 77672 q^{76} - 65338 q^{77} - 9004 q^{79} + 68816 q^{80} - 67732 q^{82} + 208656 q^{83} - 106212 q^{85} + 86776 q^{86} + 20496 q^{88} - 26666 q^{89} + 135632 q^{91} + 20568 q^{92} - 98034 q^{94} - 198140 q^{95} + 418264 q^{97} - 98686 q^{98}+O(q^{100})$$ 4 * q + 2 * q^2 - 12 * q^4 - 38 * q^5 - 168 * q^7 - 192 * q^8 + 778 * q^10 + 424 * q^11 - 1848 * q^13 + 2674 * q^14 + 2064 * q^16 - 2346 * q^17 + 360 * q^19 + 3416 * q^20 + 4252 * q^22 - 12 * q^23 - 1872 * q^25 + 1148 * q^26 + 2548 * q^28 + 14104 * q^29 - 3548 * q^31 - 8096 * q^32 + 14844 * q^34 - 27496 * q^35 - 11090 * q^37 + 20138 * q^38 - 15936 * q^40 - 7000 * q^41 - 25360 * q^43 + 5948 * q^44 + 5118 * q^46 - 22956 * q^47 + 4900 * q^49 - 59984 * q^50 + 1400 * q^52 + 3042 * q^53 - 50152 * q^55 + 57792 * q^56 + 58852 * q^58 - 65808 * q^59 + 42486 * q^61 + 98724 * q^62 + 70912 * q^64 - 3164 * q^65 - 42312 * q^67 + 5460 * q^68 - 113050 * q^70 + 4416 * q^71 + 50506 * q^73 - 47370 * q^74 + 77672 * q^76 - 65338 * q^77 - 9004 * q^79 + 68816 * q^80 - 67732 * q^82 + 208656 * q^83 - 106212 * q^85 + 86776 * q^86 + 20496 * q^88 - 26666 * q^89 + 135632 * q^91 + 20568 * q^92 - 98034 * q^94 - 198140 * q^95 + 418264 * q^97 - 98686 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$$.

 $$n$$ $$10$$ $$29$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.54138 + 4.40180i −0.449257 + 0.778136i −0.998338 0.0576333i $$-0.981645\pi$$
0.549081 + 0.835769i $$0.314978\pi$$
$$3$$ 0 0
$$4$$ 3.08276 + 5.33950i 0.0963363 + 0.166859i
$$5$$ 20.9138 36.2238i 0.374118 0.647991i −0.616077 0.787686i $$-0.711279\pi$$
0.990195 + 0.139695i $$0.0446123\pi$$
$$6$$ 0 0
$$7$$ −127.159 25.2522i −0.980846 0.194784i
$$8$$ −193.986 −1.07163
$$9$$ 0 0
$$10$$ 106.300 + 184.117i 0.336150 + 0.582229i
$$11$$ 36.0482 + 62.4374i 0.0898260 + 0.155583i 0.907437 0.420187i $$-0.138036\pi$$
−0.817611 + 0.575770i $$0.804702\pi$$
$$12$$ 0 0
$$13$$ −632.317 −1.03771 −0.518856 0.854862i $$-0.673642\pi$$
−0.518856 + 0.854862i $$0.673642\pi$$
$$14$$ 434.314 495.552i 0.592220 0.675724i
$$15$$ 0 0
$$16$$ 394.345 683.025i 0.385102 0.667017i
$$17$$ −987.962 1711.20i −0.829121 1.43608i −0.898728 0.438506i $$-0.855508\pi$$
0.0696071 0.997574i $$-0.477825\pi$$
$$18$$ 0 0
$$19$$ 932.463 1615.07i 0.592581 1.02638i −0.401303 0.915945i $$-0.631443\pi$$
0.993883 0.110434i $$-0.0352242\pi$$
$$20$$ 257.889 0.144164
$$21$$ 0 0
$$22$$ −366.449 −0.161420
$$23$$ 206.855 358.284i 0.0815356 0.141224i −0.822374 0.568947i $$-0.807351\pi$$
0.903910 + 0.427723i $$0.140684\pi$$
$$24$$ 0 0
$$25$$ 687.725 + 1191.17i 0.220072 + 0.381176i
$$26$$ 1606.96 2783.34i 0.466199 0.807481i
$$27$$ 0 0
$$28$$ −257.166 756.810i −0.0619896 0.182428i
$$29$$ −731.934 −0.161613 −0.0808066 0.996730i $$-0.525750\pi$$
−0.0808066 + 0.996730i $$0.525750\pi$$
$$30$$ 0 0
$$31$$ −3061.59 5302.83i −0.572193 0.991067i −0.996340 0.0854740i $$-0.972760\pi$$
0.424148 0.905593i $$-0.360574\pi$$
$$32$$ −1099.42 1904.25i −0.189797 0.328738i
$$33$$ 0 0
$$34$$ 10043.2 1.48995
$$35$$ −3574.10 + 4078.05i −0.493170 + 0.562707i
$$36$$ 0 0
$$37$$ −5175.19 + 8963.69i −0.621473 + 1.07642i 0.367739 + 0.929929i $$0.380132\pi$$
−0.989212 + 0.146493i $$0.953201\pi$$
$$38$$ 4739.49 + 8209.03i 0.532442 + 0.922216i
$$39$$ 0 0
$$40$$ −4056.99 + 7026.92i −0.400917 + 0.694408i
$$41$$ 3529.84 0.327941 0.163970 0.986465i $$-0.447570\pi$$
0.163970 + 0.986465i $$0.447570\pi$$
$$42$$ 0 0
$$43$$ −14515.2 −1.19716 −0.598581 0.801062i $$-0.704269\pi$$
−0.598581 + 0.801062i $$0.704269\pi$$
$$44$$ −222.256 + 384.959i −0.0173070 + 0.0299766i
$$45$$ 0 0
$$46$$ 1051.40 + 1821.07i 0.0732608 + 0.126892i
$$47$$ −10711.7 + 18553.1i −0.707314 + 1.22510i 0.258536 + 0.966002i $$0.416760\pi$$
−0.965850 + 0.259102i $$0.916574\pi$$
$$48$$ 0 0
$$49$$ 15531.7 + 6422.06i 0.924118 + 0.382106i
$$50$$ −6991.08 −0.395475
$$51$$ 0 0
$$52$$ −1949.28 3376.26i −0.0999693 0.173152i
$$53$$ 6289.73 + 10894.1i 0.307569 + 0.532725i 0.977830 0.209400i $$-0.0671512\pi$$
−0.670261 + 0.742125i $$0.733818\pi$$
$$54$$ 0 0
$$55$$ 3015.62 0.134422
$$56$$ 24667.0 + 4898.57i 1.05111 + 0.208737i
$$57$$ 0 0
$$58$$ 1860.12 3221.83i 0.0726059 0.125757i
$$59$$ −18067.0 31292.9i −0.675702 1.17035i −0.976263 0.216588i $$-0.930507\pi$$
0.300561 0.953763i $$-0.402826\pi$$
$$60$$ 0 0
$$61$$ −2012.40 + 3485.58i −0.0692451 + 0.119936i −0.898569 0.438832i $$-0.855392\pi$$
0.829324 + 0.558768i $$0.188726\pi$$
$$62$$ 31122.6 1.02825
$$63$$ 0 0
$$64$$ 36414.2 1.11127
$$65$$ −13224.2 + 22904.9i −0.388226 + 0.672428i
$$66$$ 0 0
$$67$$ −7782.97 13480.5i −0.211816 0.366876i 0.740467 0.672093i $$-0.234604\pi$$
−0.952283 + 0.305217i $$0.901271\pi$$
$$68$$ 6091.31 10550.5i 0.159749 0.276693i
$$69$$ 0 0
$$70$$ −8867.61 26096.4i −0.216303 0.636553i
$$71$$ −12180.8 −0.286766 −0.143383 0.989667i $$-0.545798\pi$$
−0.143383 + 0.989667i $$0.545798\pi$$
$$72$$ 0 0
$$73$$ −9794.56 16964.7i −0.215119 0.372596i 0.738191 0.674592i $$-0.235680\pi$$
−0.953309 + 0.301996i $$0.902347\pi$$
$$74$$ −26304.3 45560.3i −0.558402 0.967181i
$$75$$ 0 0
$$76$$ 11498.2 0.228348
$$77$$ −3007.17 8849.75i −0.0578004 0.170100i
$$78$$ 0 0
$$79$$ −18044.9 + 31254.7i −0.325302 + 0.563439i −0.981573 0.191085i $$-0.938799\pi$$
0.656272 + 0.754525i $$0.272133\pi$$
$$80$$ −16494.5 28569.3i −0.288147 0.499085i
$$81$$ 0 0
$$82$$ −8970.66 + 15537.6i −0.147330 + 0.255182i
$$83$$ 24572.6 0.391522 0.195761 0.980652i $$-0.437282\pi$$
0.195761 + 0.980652i $$0.437282\pi$$
$$84$$ 0 0
$$85$$ −82648.2 −1.24076
$$86$$ 36888.7 63893.2i 0.537833 0.931555i
$$87$$ 0 0
$$88$$ −6992.86 12112.0i −0.0962605 0.166728i
$$89$$ −35121.7 + 60832.5i −0.470002 + 0.814068i −0.999412 0.0342986i $$-0.989080\pi$$
0.529409 + 0.848367i $$0.322414\pi$$
$$90$$ 0 0
$$91$$ 80404.6 + 15967.4i 1.01784 + 0.202130i
$$92$$ 2550.74 0.0314193
$$93$$ 0 0
$$94$$ −54444.8 94301.2i −0.635531 1.10077i
$$95$$ −39002.7 67554.7i −0.443390 0.767974i
$$96$$ 0 0
$$97$$ 105758. 1.14126 0.570630 0.821207i $$-0.306699\pi$$
0.570630 + 0.821207i $$0.306699\pi$$
$$98$$ −67740.5 + 52046.4i −0.712497 + 0.547426i
$$99$$ 0 0
$$100$$ −4240.18 + 7344.22i −0.0424018 + 0.0734422i
$$101$$ 18230.9 + 31576.8i 0.177830 + 0.308010i 0.941137 0.338025i $$-0.109759\pi$$
−0.763307 + 0.646036i $$0.776426\pi$$
$$102$$ 0 0
$$103$$ −32260.0 + 55876.0i −0.299621 + 0.518958i −0.976049 0.217550i $$-0.930193\pi$$
0.676428 + 0.736508i $$0.263527\pi$$
$$104$$ 122661. 1.11205
$$105$$ 0 0
$$106$$ −63938.4 −0.552710
$$107$$ 33022.8 57197.2i 0.278840 0.482964i −0.692257 0.721651i $$-0.743384\pi$$
0.971097 + 0.238687i $$0.0767169\pi$$
$$108$$ 0 0
$$109$$ 18969.0 + 32855.3i 0.152925 + 0.264874i 0.932302 0.361682i $$-0.117797\pi$$
−0.779377 + 0.626556i $$0.784464\pi$$
$$110$$ −7663.85 + 13274.2i −0.0603900 + 0.104599i
$$111$$ 0 0
$$112$$ −67392.2 + 76894.5i −0.507650 + 0.579229i
$$113$$ −123802. −0.912080 −0.456040 0.889959i $$-0.650733\pi$$
−0.456040 + 0.889959i $$0.650733\pi$$
$$114$$ 0 0
$$115$$ −8652.27 14986.2i −0.0610078 0.105669i
$$116$$ −2256.38 3908.16i −0.0155692 0.0269667i
$$117$$ 0 0
$$118$$ 183660. 1.21426
$$119$$ 82416.5 + 242542.i 0.533515 + 1.57007i
$$120$$ 0 0
$$121$$ 77926.6 134973.i 0.483863 0.838075i
$$122$$ −10228.5 17716.4i −0.0622177 0.107764i
$$123$$ 0 0
$$124$$ 18876.3 32694.7i 0.110246 0.190952i
$$125$$ 188243. 1.07757
$$126$$ 0 0
$$127$$ 128724. 0.708189 0.354095 0.935210i $$-0.384789\pi$$
0.354095 + 0.935210i $$0.384789\pi$$
$$128$$ −57361.0 + 99352.2i −0.309451 + 0.535985i
$$129$$ 0 0
$$130$$ −67215.3 116420.i −0.348827 0.604186i
$$131$$ −73951.1 + 128087.i −0.376501 + 0.652120i −0.990551 0.137148i $$-0.956206\pi$$
0.614049 + 0.789268i $$0.289540\pi$$
$$132$$ 0 0
$$133$$ −159355. + 181824.i −0.781153 + 0.891295i
$$134$$ 79118.0 0.380639
$$135$$ 0 0
$$136$$ 191651. + 331950.i 0.888514 + 1.53895i
$$137$$ −45578.7 78944.6i −0.207472 0.359353i 0.743445 0.668797i $$-0.233190\pi$$
−0.950918 + 0.309444i $$0.899857\pi$$
$$138$$ 0 0
$$139$$ −334657. −1.46914 −0.734570 0.678533i $$-0.762616\pi$$
−0.734570 + 0.678533i $$0.762616\pi$$
$$140$$ −32792.9 6512.26i −0.141403 0.0280809i
$$141$$ 0 0
$$142$$ 30955.9 53617.3i 0.128832 0.223143i
$$143$$ −22793.9 39480.2i −0.0932135 0.161451i
$$144$$ 0 0
$$145$$ −15307.5 + 26513.4i −0.0604623 + 0.104724i
$$146$$ 99566.9 0.386574
$$147$$ 0 0
$$148$$ −63815.5 −0.239482
$$149$$ 69135.7 119746.i 0.255115 0.441873i −0.709812 0.704392i $$-0.751220\pi$$
0.964927 + 0.262519i $$0.0845532\pi$$
$$150$$ 0 0
$$151$$ −55584.6 96275.4i −0.198386 0.343615i 0.749619 0.661870i $$-0.230237\pi$$
−0.948005 + 0.318254i $$0.896903\pi$$
$$152$$ −180885. + 313302.i −0.635029 + 1.09990i
$$153$$ 0 0
$$154$$ 46597.2 + 9253.63i 0.158328 + 0.0314420i
$$155$$ −256118. −0.856270
$$156$$ 0 0
$$157$$ 19074.3 + 33037.6i 0.0617587 + 0.106969i 0.895252 0.445561i $$-0.146996\pi$$
−0.833493 + 0.552530i $$0.813662\pi$$
$$158$$ −91717.9 158860.i −0.292288 0.506258i
$$159$$ 0 0
$$160$$ −91972.3 −0.284025
$$161$$ −35350.9 + 40335.4i −0.107482 + 0.122637i
$$162$$ 0 0
$$163$$ 106452. 184381.i 0.313824 0.543559i −0.665363 0.746520i $$-0.731723\pi$$
0.979187 + 0.202961i $$0.0650565\pi$$
$$164$$ 10881.7 + 18847.6i 0.0315926 + 0.0547200i
$$165$$ 0 0
$$166$$ −62448.3 + 108164.i −0.175894 + 0.304657i
$$167$$ 120396. 0.334057 0.167028 0.985952i $$-0.446583\pi$$
0.167028 + 0.985952i $$0.446583\pi$$
$$168$$ 0 0
$$169$$ 28532.2 0.0768456
$$170$$ 210041. 363801.i 0.557418 0.965477i
$$171$$ 0 0
$$172$$ −44747.0 77504.1i −0.115330 0.199758i
$$173$$ 356457. 617402.i 0.905507 1.56838i 0.0852723 0.996358i $$-0.472824\pi$$
0.820235 0.572027i $$-0.193843\pi$$
$$174$$ 0 0
$$175$$ −57370.5 168835.i −0.141610 0.416741i
$$176$$ 56861.7 0.138369
$$177$$ 0 0
$$178$$ −178515. 309197.i −0.422304 0.731451i
$$179$$ −374869. 649292.i −0.874474 1.51463i −0.857322 0.514780i $$-0.827873\pi$$
−0.0171519 0.999853i $$-0.505460\pi$$
$$180$$ 0 0
$$181$$ 623718. 1.41511 0.707557 0.706656i $$-0.249797\pi$$
0.707557 + 0.706656i $$0.249797\pi$$
$$182$$ −274624. + 313346.i −0.614554 + 0.701206i
$$183$$ 0 0
$$184$$ −40127.1 + 69502.2i −0.0873762 + 0.151340i
$$185$$ 216466. + 374930.i 0.465008 + 0.805417i
$$186$$ 0 0
$$187$$ 71228.6 123372.i 0.148953 0.257995i
$$188$$ −132086. −0.272560
$$189$$ 0 0
$$190$$ 396483. 0.796784
$$191$$ 208863. 361761.i 0.414265 0.717528i −0.581086 0.813842i $$-0.697372\pi$$
0.995351 + 0.0963141i $$0.0307053\pi$$
$$192$$ 0 0
$$193$$ −385350. 667446.i −0.744667 1.28980i −0.950350 0.311183i $$-0.899275\pi$$
0.205683 0.978619i $$-0.434058\pi$$
$$194$$ −268772. + 465527.i −0.512719 + 0.888056i
$$195$$ 0 0
$$196$$ 13589.8 + 102729.i 0.0252681 + 0.191009i
$$197$$ 479193. 0.879721 0.439861 0.898066i $$-0.355028\pi$$
0.439861 + 0.898066i $$0.355028\pi$$
$$198$$ 0 0
$$199$$ 214343. + 371253.i 0.383687 + 0.664565i 0.991586 0.129449i $$-0.0413210\pi$$
−0.607899 + 0.794014i $$0.707988\pi$$
$$200$$ −133409. 231072.i −0.235836 0.408481i
$$201$$ 0 0
$$202$$ −185327. −0.319565
$$203$$ 93071.7 + 18482.9i 0.158518 + 0.0314797i
$$204$$ 0 0
$$205$$ 73822.4 127864.i 0.122688 0.212502i
$$206$$ −163970. 284005.i −0.269213 0.466291i
$$207$$ 0 0
$$208$$ −249351. + 431889.i −0.399625 + 0.692171i
$$209$$ 134455. 0.212917
$$210$$ 0 0
$$211$$ −588544. −0.910066 −0.455033 0.890475i $$-0.650373\pi$$
−0.455033 + 0.890475i $$0.650373\pi$$
$$212$$ −38779.5 + 67168.1i −0.0592601 + 0.102642i
$$213$$ 0 0
$$214$$ 167847. + 290720.i 0.250541 + 0.433950i
$$215$$ −303569. + 525797.i −0.447879 + 0.775750i
$$216$$ 0 0
$$217$$ 255400. + 751612.i 0.368189 + 1.08354i
$$218$$ −192830. −0.274811
$$219$$ 0 0
$$220$$ 9296.45 + 16101.9i 0.0129497 + 0.0224296i
$$221$$ 624706. + 1.08202e6i 0.860389 + 1.49024i
$$222$$ 0 0
$$223$$ −363249. −0.489151 −0.244575 0.969630i $$-0.578649\pi$$
−0.244575 + 0.969630i $$0.578649\pi$$
$$224$$ 91714.4 + 269905.i 0.122129 + 0.359410i
$$225$$ 0 0
$$226$$ 314629. 544954.i 0.409758 0.709722i
$$227$$ −421521. 730095.i −0.542943 0.940405i −0.998733 0.0503177i $$-0.983977\pi$$
0.455790 0.890087i $$-0.349357\pi$$
$$228$$ 0 0
$$229$$ 284333. 492479.i 0.358293 0.620582i −0.629382 0.777096i $$-0.716692\pi$$
0.987676 + 0.156513i $$0.0500254\pi$$
$$230$$ 87954.8 0.109633
$$231$$ 0 0
$$232$$ 141985. 0.173190
$$233$$ −528255. + 914965.i −0.637461 + 1.10412i 0.348526 + 0.937299i $$0.386682\pi$$
−0.985988 + 0.166817i $$0.946651\pi$$
$$234$$ 0 0
$$235$$ 448043. + 776034.i 0.529237 + 0.916666i
$$236$$ 111392. 192937.i 0.130189 0.225495i
$$237$$ 0 0
$$238$$ −1.27707e6 253611.i −1.46142 0.290219i
$$239$$ −853715. −0.966759 −0.483379 0.875411i $$-0.660591\pi$$
−0.483379 + 0.875411i $$0.660591\pi$$
$$240$$ 0 0
$$241$$ 194444. + 336787.i 0.215651 + 0.373519i 0.953474 0.301476i $$-0.0974792\pi$$
−0.737823 + 0.674995i $$0.764146\pi$$
$$242$$ 396082. + 686034.i 0.434757 + 0.753022i
$$243$$ 0 0
$$244$$ −24815.0 −0.0266833
$$245$$ 557458. 428306.i 0.593330 0.455867i
$$246$$ 0 0
$$247$$ −589612. + 1.02124e6i −0.614928 + 1.06509i
$$248$$ 593906. + 1.02868e6i 0.613181 + 1.06206i
$$249$$ 0 0
$$250$$ −478398. + 828609.i −0.484104 + 0.838493i
$$251$$ 839328. 0.840906 0.420453 0.907314i $$-0.361871\pi$$
0.420453 + 0.907314i $$0.361871\pi$$
$$252$$ 0 0
$$253$$ 29827.1 0.0292961
$$254$$ −327136. + 566616.i −0.318159 + 0.551067i
$$255$$ 0 0
$$256$$ 291075. + 504157.i 0.277591 + 0.480802i
$$257$$ 145993. 252867.i 0.137879 0.238814i −0.788814 0.614632i $$-0.789305\pi$$
0.926694 + 0.375817i $$0.122638\pi$$
$$258$$ 0 0
$$259$$ 884423. 1.00913e6i 0.819239 0.934752i
$$260$$ −163068. −0.149601
$$261$$ 0 0
$$262$$ −375876. 651037.i −0.338292 0.585939i
$$263$$ −144248. 249844.i −0.128594 0.222731i 0.794538 0.607214i $$-0.207713\pi$$
−0.923132 + 0.384483i $$0.874380\pi$$
$$264$$ 0 0
$$265$$ 526169. 0.460268
$$266$$ −395371. 1.16353e6i −0.342611 1.00826i
$$267$$ 0 0
$$268$$ 47986.1 83114.4i 0.0408111 0.0706869i
$$269$$ −129685. 224621.i −0.109272 0.189265i 0.806204 0.591638i $$-0.201519\pi$$
−0.915476 + 0.402374i $$0.868185\pi$$
$$270$$ 0 0
$$271$$ 1.09776e6 1.90137e6i 0.907994 1.57269i 0.0911464 0.995838i $$-0.470947\pi$$
0.816847 0.576854i $$-0.195720\pi$$
$$272$$ −1.55839e6 −1.27719
$$273$$ 0 0
$$274$$ 463331. 0.372834
$$275$$ −49582.5 + 85879.5i −0.0395364 + 0.0684790i
$$276$$ 0 0
$$277$$ −63495.3 109977.i −0.0497213 0.0861198i 0.840094 0.542441i $$-0.182500\pi$$
−0.889815 + 0.456322i $$0.849167\pi$$
$$278$$ 850491. 1.47309e6i 0.660021 1.14319i
$$279$$ 0 0
$$280$$ 693327. 791086.i 0.528497 0.603016i
$$281$$ 2.22759e6 1.68294 0.841472 0.540301i $$-0.181690\pi$$
0.841472 + 0.540301i $$0.181690\pi$$
$$282$$ 0 0
$$283$$ −594473. 1.02966e6i −0.441231 0.764235i 0.556550 0.830814i $$-0.312125\pi$$
−0.997781 + 0.0665792i $$0.978792\pi$$
$$284$$ −37550.4 65039.1i −0.0276260 0.0478497i
$$285$$ 0 0
$$286$$ 231712. 0.167507
$$287$$ −448850. 89136.0i −0.321659 0.0638776i
$$288$$ 0 0
$$289$$ −1.24221e6 + 2.15157e6i −0.874884 + 1.51534i
$$290$$ −77804.5 134761.i −0.0543263 0.0940958i
$$291$$ 0 0
$$292$$ 60388.6 104596.i 0.0414475 0.0717891i
$$293$$ −1.83223e6 −1.24684 −0.623421 0.781886i $$-0.714258\pi$$
−0.623421 + 0.781886i $$0.714258\pi$$
$$294$$ 0 0
$$295$$ −1.51140e6 −1.01117
$$296$$ 1.00392e6 1.73883e6i 0.665991 1.15353i
$$297$$ 0 0
$$298$$ 351400. + 608643.i 0.229225 + 0.397029i
$$299$$ −130798. + 226549.i −0.0846104 + 0.146550i
$$300$$ 0 0
$$301$$ 1.84574e6 + 366541.i 1.17423 + 0.233188i
$$302$$ 565047. 0.356506
$$303$$ 0 0
$$304$$ −735423. 1.27379e6i −0.456408 0.790522i
$$305$$ 84173.8 + 145793.i 0.0518117 + 0.0897404i
$$306$$ 0 0
$$307$$ −717638. −0.434569 −0.217285 0.976108i $$-0.569720\pi$$
−0.217285 + 0.976108i $$0.569720\pi$$
$$308$$ 37982.9 43338.4i 0.0228145 0.0260313i
$$309$$ 0 0
$$310$$ 650893. 1.12738e6i 0.384685 0.666294i
$$311$$ −428446. 742090.i −0.251186 0.435067i 0.712667 0.701503i $$-0.247487\pi$$
−0.963853 + 0.266436i $$0.914154\pi$$
$$312$$ 0 0
$$313$$ −808495. + 1.40035e6i −0.466462 + 0.807936i −0.999266 0.0383025i $$-0.987805\pi$$
0.532804 + 0.846239i $$0.321138\pi$$
$$314$$ −193900. −0.110982
$$315$$ 0 0
$$316$$ −222512. −0.125354
$$317$$ −1.13280e6 + 1.96206e6i −0.633145 + 1.09664i 0.353760 + 0.935336i $$0.384903\pi$$
−0.986905 + 0.161303i $$0.948430\pi$$
$$318$$ 0 0
$$319$$ −26384.9 45700.0i −0.0145171 0.0251443i
$$320$$ 761561. 1.31906e6i 0.415747 0.720096i
$$321$$ 0 0
$$322$$ −87708.2 258115.i −0.0471412 0.138731i
$$323$$ −3.68495e6 −1.96528
$$324$$ 0 0
$$325$$ −434860. 753200.i −0.228371 0.395551i
$$326$$ 541072. + 937163.i 0.281975 + 0.488395i
$$327$$ 0 0
$$328$$ −684740. −0.351432
$$329$$ 1.83059e6 2.08870e6i 0.932396 1.06386i
$$330$$ 0 0
$$331$$ −354825. + 614575.i −0.178010 + 0.308322i −0.941199 0.337853i $$-0.890299\pi$$
0.763189 + 0.646175i $$0.223633\pi$$
$$332$$ 75751.5 + 131205.i 0.0377178 + 0.0653291i
$$333$$ 0 0
$$334$$ −305972. + 529958.i −0.150077 + 0.259941i
$$335$$ −651086. −0.316976
$$336$$ 0 0
$$337$$ 603572. 0.289504 0.144752 0.989468i $$-0.453762\pi$$
0.144752 + 0.989468i $$0.453762\pi$$
$$338$$ −72511.3 + 125593.i −0.0345234 + 0.0597963i
$$339$$ 0 0
$$340$$ −254785. 441300.i −0.119530 0.207032i
$$341$$ 220730. 382315.i 0.102796 0.178047i
$$342$$ 0 0
$$343$$ −1.81281e6 1.20883e6i −0.831990 0.554791i
$$344$$ 2.81576e6 1.28292
$$345$$ 0 0
$$346$$ 1.81179e6 + 3.13811e6i 0.813611 + 1.40922i
$$347$$ 878655. + 1.52188e6i 0.391737 + 0.678509i 0.992679 0.120784i $$-0.0385409\pi$$
−0.600942 + 0.799293i $$0.705208\pi$$
$$348$$ 0 0
$$349$$ 391875. 0.172220 0.0861102 0.996286i $$-0.472556\pi$$
0.0861102 + 0.996286i $$0.472556\pi$$
$$350$$ 888977. + 176540.i 0.387901 + 0.0770323i
$$351$$ 0 0
$$352$$ 79264.3 137290.i 0.0340974 0.0590584i
$$353$$ 246204. + 426437.i 0.105162 + 0.182145i 0.913804 0.406155i $$-0.133131\pi$$
−0.808643 + 0.588300i $$0.799797\pi$$
$$354$$ 0 0
$$355$$ −254746. + 441233.i −0.107284 + 0.185822i
$$356$$ −433087. −0.181113
$$357$$ 0 0
$$358$$ 3.81074e6 1.57145
$$359$$ −1.88516e6 + 3.26519e6i −0.771991 + 1.33713i 0.164480 + 0.986380i $$0.447406\pi$$
−0.936470 + 0.350747i $$0.885928\pi$$
$$360$$ 0 0
$$361$$ −500924. 867625.i −0.202304 0.350400i
$$362$$ −1.58510e6 + 2.74548e6i −0.635750 + 1.10115i
$$363$$ 0 0
$$364$$ 162611. + 478544.i 0.0643273 + 0.189308i
$$365$$ −819367. −0.321919
$$366$$ 0 0
$$367$$ 1.09884e6 + 1.90325e6i 0.425863 + 0.737617i 0.996501 0.0835854i $$-0.0266371\pi$$
−0.570637 + 0.821202i $$0.693304\pi$$
$$368$$ −163145. 282575.i −0.0627991 0.108771i
$$369$$ 0 0
$$370$$ −2.20049e6 −0.835632
$$371$$ −524694. 1.54411e6i −0.197911 0.582431i
$$372$$ 0 0
$$373$$ 828178. 1.43445e6i 0.308213 0.533841i −0.669758 0.742579i $$-0.733602\pi$$
0.977972 + 0.208738i $$0.0669356\pi$$
$$374$$ 362038. + 627068.i 0.133837 + 0.231812i
$$375$$ 0 0
$$376$$ 2.07791e6 3.59905e6i 0.757981 1.31286i
$$377$$ 462814. 0.167708
$$378$$ 0 0
$$379$$ −2.82050e6 −1.00862 −0.504310 0.863523i $$-0.668253\pi$$
−0.504310 + 0.863523i $$0.668253\pi$$
$$380$$ 240472. 416510.i 0.0854291 0.147968i
$$381$$ 0 0
$$382$$ 1.06160e6 + 1.83875e6i 0.372223 + 0.644709i
$$383$$ 1.62422e6 2.81324e6i 0.565781 0.979962i −0.431195 0.902259i $$-0.641908\pi$$
0.996977 0.0777034i $$-0.0247587\pi$$
$$384$$ 0 0
$$385$$ −383463. 76151.0i −0.131847 0.0261833i
$$386$$ 3.91729e6 1.33819
$$387$$ 0 0
$$388$$ 326027. + 564696.i 0.109945 + 0.190430i
$$389$$ 2.32674e6 + 4.03003e6i 0.779604 + 1.35031i 0.932170 + 0.362021i $$0.117913\pi$$
−0.152566 + 0.988293i $$0.548754\pi$$
$$390$$ 0 0
$$391$$ −817461. −0.270411
$$392$$ −3.01293e6 1.24579e6i −0.990316 0.409478i
$$393$$ 0 0
$$394$$ −1.21781e6 + 2.10931e6i −0.395221 + 0.684543i
$$395$$ 754775. + 1.30731e6i 0.243402 + 0.421585i
$$396$$ 0 0
$$397$$ 581804. 1.00771e6i 0.185268 0.320894i −0.758399 0.651791i $$-0.774018\pi$$
0.943667 + 0.330897i $$0.107351\pi$$
$$398$$ −2.17891e6 −0.689495
$$399$$ 0 0
$$400$$ 1.08480e6 0.339001
$$401$$ 161190. 279189.i 0.0500584 0.0867037i −0.839910 0.542725i $$-0.817393\pi$$
0.889969 + 0.456021i $$0.150726\pi$$
$$402$$ 0 0
$$403$$ 1.93589e6 + 3.35307e6i 0.593771 + 1.02844i
$$404$$ −112403. + 194688.i −0.0342630 + 0.0593452i
$$405$$ 0 0
$$406$$ −317889. + 362711.i −0.0957106 + 0.109206i
$$407$$ −746226. −0.223298
$$408$$ 0 0
$$409$$ −693451. 1.20109e6i −0.204978 0.355033i 0.745148 0.666900i $$-0.232379\pi$$
−0.950126 + 0.311867i $$0.899046\pi$$
$$410$$ 375222. + 649903.i 0.110237 + 0.190936i
$$411$$ 0 0
$$412$$ −397800. −0.115457
$$413$$ 1.50716e6 + 4.43540e6i 0.434794 + 1.27955i
$$414$$ 0 0
$$415$$ 513907. 890112.i 0.146475 0.253702i
$$416$$ 695182. + 1.20409e6i 0.196954 + 0.341135i
$$417$$ 0 0
$$418$$ −341700. + 591842.i −0.0956543 + 0.165678i
$$419$$ −4.90871e6 −1.36594 −0.682971 0.730446i $$-0.739312\pi$$
−0.682971 + 0.730446i $$0.739312\pi$$
$$420$$ 0 0
$$421$$ 2.43924e6 0.670733 0.335367 0.942088i $$-0.391140\pi$$
0.335367 + 0.942088i $$0.391140\pi$$
$$422$$ 1.49572e6 2.59065e6i 0.408854 0.708155i
$$423$$ 0 0
$$424$$ −1.22012e6 2.11331e6i −0.329601 0.570886i
$$425$$ 1.35889e6 2.35367e6i 0.364933 0.632082i
$$426$$ 0 0
$$427$$ 343912. 392404.i 0.0912805 0.104151i
$$428$$ 407206. 0.107450
$$429$$ 0 0
$$430$$ −1.54297e6 2.67250e6i −0.402426 0.697022i
$$431$$ −2.61376e6 4.52717e6i −0.677755 1.17391i −0.975655 0.219309i $$-0.929620\pi$$
0.297900 0.954597i $$-0.403714\pi$$
$$432$$ 0 0
$$433$$ −2.63022e6 −0.674174 −0.337087 0.941473i $$-0.609442\pi$$
−0.337087 + 0.941473i $$0.609442\pi$$
$$434$$ −3.95751e6 785914.i −1.00855 0.200286i
$$435$$ 0 0
$$436$$ −116954. + 202570.i −0.0294645 + 0.0510340i
$$437$$ −385770. 668173.i −0.0966328 0.167373i
$$438$$ 0 0
$$439$$ −1.27706e6 + 2.21193e6i −0.316264 + 0.547785i −0.979705 0.200443i $$-0.935762\pi$$
0.663442 + 0.748228i $$0.269095\pi$$
$$440$$ −584990. −0.144051
$$441$$ 0 0
$$442$$ −6.35046e6 −1.54614
$$443$$ 1.91950e6 3.32467e6i 0.464707 0.804896i −0.534481 0.845180i $$-0.679493\pi$$
0.999188 + 0.0402844i $$0.0128264\pi$$
$$444$$ 0 0
$$445$$ 1.46906e6 + 2.54448e6i 0.351672 + 0.609114i
$$446$$ 923155. 1.59895e6i 0.219754 0.380626i
$$447$$ 0 0
$$448$$ −4.63039e6 919538.i −1.08999 0.216459i
$$449$$ −1.49369e6 −0.349658 −0.174829 0.984599i $$-0.555937\pi$$
−0.174829 + 0.984599i $$0.555937\pi$$
$$450$$ 0 0
$$451$$ 127244. + 220394.i 0.0294576 + 0.0510221i
$$452$$ −381653. 661043.i −0.0878664 0.152189i
$$453$$ 0 0
$$454$$ 4.28498e6 0.975684
$$455$$ 2.25997e6 2.57862e6i 0.511768 0.583928i
$$456$$ 0 0
$$457$$ 1.08111e6 1.87253e6i 0.242146 0.419410i −0.719179 0.694825i $$-0.755482\pi$$
0.961325 + 0.275415i $$0.0888153\pi$$
$$458$$ 1.44520e6 + 2.50316e6i 0.321932 + 0.557602i
$$459$$ 0 0
$$460$$ 53345.8 92397.6i 0.0117545 0.0203594i
$$461$$ 6.11949e6 1.34111 0.670553 0.741862i $$-0.266057\pi$$
0.670553 + 0.741862i $$0.266057\pi$$
$$462$$ 0 0
$$463$$ 3.93615e6 0.853335 0.426667 0.904409i $$-0.359687\pi$$
0.426667 + 0.904409i $$0.359687\pi$$
$$464$$ −288634. + 499929.i −0.0622376 + 0.107799i
$$465$$ 0 0
$$466$$ −2.68500e6 4.65055e6i −0.572768 0.992063i
$$467$$ −2.73522e6 + 4.73754e6i −0.580363 + 1.00522i 0.415073 + 0.909788i $$0.363756\pi$$
−0.995436 + 0.0954306i $$0.969577\pi$$
$$468$$ 0 0
$$469$$ 649261. + 1.91070e6i 0.136297 + 0.401107i
$$470$$ −4.55459e6 −0.951054
$$471$$ 0 0
$$472$$ 3.50475e6 + 6.07040e6i 0.724105 + 1.25419i
$$473$$ −523248. 906293.i −0.107536 0.186258i
$$474$$ 0 0
$$475$$ 2.56511e6 0.521641
$$476$$ −1.04098e6 + 1.18776e6i −0.210585 + 0.240277i
$$477$$ 0 0
$$478$$ 2.16962e6 3.75788e6i 0.434323 0.752270i
$$479$$ −3.33145e6 5.77023e6i −0.663428 1.14909i −0.979709 0.200426i $$-0.935767\pi$$
0.316280 0.948666i $$-0.397566\pi$$
$$480$$ 0 0
$$481$$ 3.27236e6 5.66790e6i 0.644910 1.11702i
$$482$$ −1.97663e6 −0.387531
$$483$$ 0 0
$$484$$ 960916. 0.186454
$$485$$ 2.21181e6 3.83096e6i 0.426966 0.739526i
$$486$$ 0 0
$$487$$ −4.76846e6 8.25922e6i −0.911079 1.57804i −0.812543 0.582902i $$-0.801917\pi$$
−0.0985363 0.995133i $$-0.531416\pi$$
$$488$$ 390378. 676154.i 0.0742054 0.128527i
$$489$$ 0 0
$$490$$ 468604. + 3.54231e6i 0.0881690 + 0.666493i
$$491$$ 8.19294e6 1.53369 0.766843 0.641835i $$-0.221827\pi$$
0.766843 + 0.641835i $$0.221827\pi$$
$$492$$ 0 0
$$493$$ 723123. + 1.25249e6i 0.133997 + 0.232090i
$$494$$ −2.99686e6 5.19071e6i −0.552521 0.956995i
$$495$$ 0 0
$$496$$ −4.82928e6 −0.881411
$$497$$ 1.54889e6 + 307590.i 0.281274 + 0.0558575i
$$498$$ 0 0
$$499$$ 2.15718e6 3.73635e6i 0.387825 0.671733i −0.604332 0.796733i $$-0.706560\pi$$
0.992157 + 0.125000i $$0.0398931\pi$$
$$500$$ 580309. + 1.00512e6i 0.103809 + 0.179802i
$$501$$ 0 0
$$502$$ −2.13305e6 + 3.69455e6i −0.377783 + 0.654339i
$$503$$ 1.04015e7 1.83306 0.916529 0.399968i $$-0.130979\pi$$
0.916529 + 0.399968i $$0.130979\pi$$
$$504$$ 0 0
$$505$$ 1.52511e6 0.266117
$$506$$ −75802.0 + 131293.i −0.0131615 + 0.0227963i
$$507$$ 0 0
$$508$$ 396825. + 687320.i 0.0682243 + 0.118168i
$$509$$ −1.54698e6 + 2.67945e6i −0.264661 + 0.458406i −0.967475 0.252968i $$-0.918593\pi$$
0.702814 + 0.711374i $$0.251927\pi$$
$$510$$ 0 0
$$511$$ 817069. + 2.40454e6i 0.138422 + 0.407361i
$$512$$ −6.63004e6 −1.11774
$$513$$ 0 0
$$514$$ 742048. + 1.28527e6i 0.123887 + 0.214578i
$$515$$ 1.34936e6 + 2.33716e6i 0.224187 + 0.388303i
$$516$$ 0 0
$$517$$ −1.54455e6 −0.254141
$$518$$ 2.19432e6 + 6.45763e6i 0.359315 + 1.05742i
$$519$$ 0 0
$$520$$ 2.56531e6 4.44324e6i 0.416036 0.720596i
$$521$$ −3.80087e6 6.58331e6i −0.613464 1.06255i −0.990652 0.136414i $$-0.956442\pi$$
0.377188 0.926137i $$-0.376891\pi$$
$$522$$ 0 0
$$523$$ −2.37835e6 + 4.11942e6i −0.380208 + 0.658539i −0.991092 0.133181i $$-0.957481\pi$$
0.610884 + 0.791720i $$0.290814\pi$$
$$524$$ −911895. −0.145083
$$525$$ 0 0
$$526$$ 1.46635e6 0.231086
$$527$$ −6.04947e6 + 1.04780e7i −0.948835 + 1.64343i
$$528$$ 0 0
$$529$$ 3.13259e6 + 5.42581e6i 0.486704 + 0.842996i
$$530$$ −1.33720e6 + 2.31609e6i −0.206779 + 0.358151i
$$531$$ 0 0
$$532$$ −1.46210e6 290355.i −0.223974 0.0444786i
$$533$$ −2.23198e6 −0.340308
$$534$$ 0 0
$$535$$ −1.38127e6 2.39242e6i −0.208638 0.361371i
$$536$$ 1.50979e6 + 2.61503e6i 0.226989 + 0.393156i
$$537$$ 0 0
$$538$$ 1.31832e6 0.196365
$$539$$ 158912. + 1.20126e6i 0.0235605 + 0.178100i
$$540$$ 0 0
$$541$$ −5.50261e6 + 9.53079e6i −0.808305 + 1.40003i 0.105732 + 0.994395i $$0.466281\pi$$
−0.914037 + 0.405631i $$0.867052\pi$$
$$542$$ 5.57964e6 + 9.66421e6i 0.815845 + 1.41309i
$$543$$ 0 0
$$544$$ −2.17237e6 + 3.76266e6i −0.314729 + 0.545127i
$$545$$ 1.58686e6 0.228848
$$546$$ 0 0
$$547$$ −4.46311e6 −0.637778 −0.318889 0.947792i $$-0.603310\pi$$
−0.318889 + 0.947792i $$0.603310\pi$$
$$548$$ 281017. 486735.i 0.0399743 0.0692375i
$$549$$ 0 0
$$550$$ −252016. 436505.i −0.0355240 0.0615294i
$$551$$ −682501. + 1.18213e6i −0.0957688 + 0.165876i
$$552$$ 0 0
$$553$$ 3.08381e6 3.51863e6i 0.428820 0.489284i
$$554$$ 645463. 0.0893505
$$555$$ 0 0
$$556$$ −1.03167e6 1.78690e6i −0.141532 0.245140i
$$557$$ −3.22611e6 5.58779e6i −0.440597 0.763136i 0.557137 0.830421i $$-0.311900\pi$$
−0.997734 + 0.0672845i $$0.978566\pi$$
$$558$$ 0 0
$$559$$ 9.17823e6 1.24231
$$560$$ 1.37598e6 + 4.04936e6i 0.185414 + 0.545653i
$$561$$ 0 0
$$562$$ −5.66116e6 + 9.80541e6i −0.756074 + 1.30956i
$$563$$ 873740. + 1.51336e6i 0.116175 + 0.201220i 0.918249 0.396004i $$-0.129603\pi$$
−0.802074 + 0.597225i $$0.796270\pi$$
$$564$$ 0 0
$$565$$ −2.58918e6 + 4.48459e6i −0.341225 + 0.591019i
$$566$$ 6.04313e6 0.792905
$$567$$ 0 0
$$568$$ 2.36290e6 0.307308
$$569$$ 256394. 444088.i 0.0331992 0.0575027i −0.848948 0.528476i $$-0.822764\pi$$
0.882148 + 0.470973i $$0.156097\pi$$
$$570$$ 0 0
$$571$$ −2.61182e6 4.52380e6i −0.335238 0.580649i 0.648293 0.761391i $$-0.275483\pi$$
−0.983530 + 0.180742i $$0.942150\pi$$
$$572$$ 140536. 243416.i 0.0179597 0.0311071i
$$573$$ 0 0
$$574$$ 1.53306e6 1.74922e6i 0.194213 0.221597i
$$575$$ 569038. 0.0717748
$$576$$ 0 0
$$577$$ −3.31987e6 5.75018e6i −0.415127 0.719021i 0.580315 0.814392i $$-0.302930\pi$$
−0.995442 + 0.0953713i $$0.969596\pi$$
$$578$$ −6.31386e6 1.09359e7i −0.786096 1.36156i
$$579$$ 0 0
$$580$$ −188758. −0.0232989
$$581$$ −3.12462e6 620511.i −0.384022 0.0762621i
$$582$$ 0 0
$$583$$ −453467. + 785429.i −0.0552554 + 0.0957051i
$$584$$ 1.90001e6 + 3.29092e6i 0.230528 + 0.399286i
$$585$$ 0 0
$$586$$ 4.65640e6 8.06512e6i 0.560152 0.970212i
$$587$$ −774096. −0.0927256 −0.0463628 0.998925i $$-0.514763\pi$$
−0.0463628 + 0.998925i $$0.514763\pi$$
$$588$$ 0 0
$$589$$ −1.14193e7 −1.35628
$$590$$ 3.84104e6 6.65287e6i 0.454275 0.786827i
$$591$$ 0 0
$$592$$ 4.08162e6 + 7.06957e6i 0.478661 + 0.829065i
$$593$$ −7.18778e6 + 1.24496e7i −0.839379 + 1.45385i 0.0510354 + 0.998697i $$0.483748\pi$$
−0.890415 + 0.455150i $$0.849585\pi$$
$$594$$ 0 0
$$595$$ 1.05094e7 + 2.08705e6i 1.21699 + 0.241679i
$$596$$ 852515. 0.0983075
$$597$$ 0 0
$$598$$ −664816. 1.15150e6i −0.0760236 0.131677i
$$599$$ 6.04174e6 + 1.04646e7i 0.688010 + 1.19167i 0.972481 + 0.232984i $$0.0748489\pi$$
−0.284471 + 0.958685i $$0.591818\pi$$
$$600$$ 0 0
$$601$$ 5.75607e6 0.650040 0.325020 0.945707i $$-0.394629\pi$$
0.325020 + 0.945707i $$0.394629\pi$$
$$602$$ −6.30416e6 + 7.19305e6i −0.708984 + 0.808950i
$$603$$ 0 0
$$604$$ 342708. 593588.i 0.0382237 0.0662053i
$$605$$ −3.25948e6 5.64559e6i −0.362043 0.627077i
$$606$$ 0 0
$$607$$ −2.10060e6 + 3.63835e6i −0.231405 + 0.400805i −0.958222 0.286026i $$-0.907666\pi$$
0.726817 + 0.686831i $$0.240999\pi$$
$$608$$ −4.10067e6 −0.449879
$$609$$ 0 0
$$610$$ −855671. −0.0931070
$$611$$ 6.77317e6 1.17315e7i 0.733988 1.27130i
$$612$$ 0 0
$$613$$ 1.32271e6 + 2.29101e6i 0.142172 + 0.246249i 0.928314 0.371796i $$-0.121258\pi$$
−0.786142 + 0.618046i $$0.787925\pi$$
$$614$$ 1.82379e6 3.15890e6i 0.195233 0.338154i
$$615$$ 0 0
$$616$$ 583349. + 1.71673e6i 0.0619408 + 0.182285i
$$617$$ −6.43533e6 −0.680546 −0.340273 0.940327i $$-0.610520\pi$$
−0.340273 + 0.940327i $$0.610520\pi$$
$$618$$ 0 0
$$619$$ −7.05885e6 1.22263e7i −0.740469 1.28253i −0.952282 0.305220i $$-0.901270\pi$$
0.211812 0.977310i $$-0.432063\pi$$
$$620$$ −789551. 1.36754e6i −0.0824899 0.142877i
$$621$$ 0 0
$$622$$ 4.35538e6 0.451388
$$623$$ 6.00218e6 6.84848e6i 0.619567 0.706927i
$$624$$ 0 0
$$625$$ 1.78774e6 3.09646e6i 0.183065 0.317077i
$$626$$ −4.10939e6 7.11767e6i −0.419123 0.725942i
$$627$$ 0 0
$$628$$ −117603. + 203694.i −0.0118992 + 0.0206101i
$$629$$ 2.04516e7 2.06111
$$630$$ 0 0
$$631$$ −4.70856e6 −0.470777 −0.235388 0.971901i $$-0.575636\pi$$
−0.235388 + 0.971901i $$0.575636\pi$$
$$632$$ 3.50046e6 6.06298e6i 0.348604 0.603800i
$$633$$ 0 0
$$634$$ −5.75773e6 9.97268e6i −0.568890 0.985346i
$$635$$ 2.69210e6 4.66286e6i 0.264946 0.458900i
$$636$$ 0 0
$$637$$ −9.82094e6 4.06078e6i −0.958968 0.396516i
$$638$$ 268217. 0.0260876
$$639$$ 0 0
$$640$$ 2.39928e6 + 4.15567e6i 0.231542 + 0.401043i
$$641$$ −5.20870e6 9.02173e6i −0.500707 0.867251i −1.00000 0.000816994i $$-0.999740\pi$$
0.499292 0.866434i $$-0.333593\pi$$
$$642$$ 0 0
$$643$$ 1.27284e7 1.21407 0.607037 0.794674i $$-0.292358\pi$$
0.607037 + 0.794674i $$0.292358\pi$$
$$644$$ −324349. 64411.8i −0.0308175 0.00611999i
$$645$$ 0 0
$$646$$ 9.36487e6 1.62204e7i 0.882918 1.52926i
$$647$$ −8.06740e6 1.39731e7i −0.757657 1.31230i −0.944042 0.329824i $$-0.893011\pi$$
0.186385 0.982477i $$-0.440323\pi$$
$$648$$ 0 0
$$649$$ 1.30256e6 2.25611e6i 0.121391 0.210256i
$$650$$ 4.42058e6 0.410390
$$651$$ 0 0
$$652$$ 1.31267e6 0.120931
$$653$$ −7.51475e6 + 1.30159e7i −0.689654 + 1.19452i 0.282296 + 0.959327i $$0.408904\pi$$
−0.971950 + 0.235189i $$0.924429\pi$$
$$654$$ 0 0
$$655$$ 3.09320e6 + 5.35758e6i 0.281712 + 0.487939i
$$656$$ 1.39197e6 2.41097e6i 0.126291 0.218742i
$$657$$ 0 0
$$658$$ 4.54182e6 + 1.33661e7i 0.408945 + 1.20348i
$$659$$ −1.67927e7 −1.50628 −0.753140 0.657860i $$-0.771462\pi$$
−0.753140 + 0.657860i $$0.771462\pi$$
$$660$$ 0 0
$$661$$ −5.42702e6 9.39987e6i −0.483123 0.836794i 0.516689 0.856173i $$-0.327164\pi$$
−0.999812 + 0.0193794i $$0.993831\pi$$
$$662$$ −1.80349e6 3.12374e6i −0.159944 0.277032i
$$663$$ 0 0
$$664$$ −4.76675e6 −0.419567
$$665$$ 3.25363e6 + 9.57506e6i 0.285308 + 0.839629i
$$666$$ 0 0
$$667$$ −151404. + 262240.i −0.0131772 + 0.0228236i
$$668$$ 371152. + 642853.i 0.0321818 + 0.0557405i
$$669$$ 0 0
$$670$$ 1.65466e6 2.86595e6i 0.142404 0.246651i
$$671$$ −290174. −0.0248801
$$672$$ 0 0
$$673$$ 1.23697e7 1.05274 0.526371 0.850255i $$-0.323552\pi$$
0.526371 + 0.850255i $$0.323552\pi$$
$$674$$ −1.53391e6 + 2.65680e6i −0.130062 + 0.225273i
$$675$$ 0 0
$$676$$ 87958.1 + 152348.i 0.00740302 + 0.0128224i
$$677$$ −502503. + 870361.i −0.0421373 + 0.0729840i −0.886325 0.463064i $$-0.846750\pi$$
0.844188 + 0.536048i $$0.180083\pi$$
$$678$$ 0 0
$$679$$ −1.34481e7 2.67062e6i −1.11940 0.222299i
$$680$$ 1.60326e7 1.32963
$$681$$ 0 0
$$682$$ 1.12192e6 + 1.94322e6i 0.0923633 + 0.159978i
$$683$$ 935093. + 1.61963e6i 0.0767014 + 0.132851i 0.901825 0.432102i $$-0.142228\pi$$
−0.825123 + 0.564952i $$0.808895\pi$$
$$684$$ 0 0
$$685$$ −3.81290e6 −0.310476
$$686$$ 9.92808e6 4.90755e6i 0.805480 0.398157i
$$687$$ 0 0
$$688$$ −5.72401e6 + 9.91427e6i −0.461030 + 0.798527i
$$689$$ −3.97711e6 6.88855e6i −0.319168 0.552815i
$$690$$ 0 0
$$691$$ −9.69333e6 + 1.67893e7i −0.772286 + 1.33764i 0.164022 + 0.986457i $$0.447553\pi$$
−0.936307 + 0.351181i $$0.885780\pi$$
$$692$$ 4.39549e6 0.348933
$$693$$ 0 0
$$694$$ −8.93199e6 −0.703963
$$695$$ −6.99896e6 + 1.21226e7i −0.549631 + 0.951989i
$$696$$ 0 0
$$697$$ −3.48735e6 6.04026e6i −0.271902 0.470949i
$$698$$ −995905. + 1.72496e6i −0.0773712 + 0.134011i
$$699$$ 0 0
$$700$$ 724634. 826807.i 0.0558951 0.0637763i
$$701$$ −1.17488e7 −0.903024 −0.451512 0.892265i $$-0.649115\pi$$
−0.451512 + 0.892265i $$0.649115\pi$$
$$702$$ 0 0
$$703$$ 9.65134e6 + 1.67166e7i 0.736545 + 1.27573i
$$704$$ 1.31267e6 + 2.27361e6i 0.0998214 + 0.172896i
$$705$$ 0 0
$$706$$ −2.50279e6 −0.188978
$$707$$ −1.52083e6 4.47564e6i −0.114428 0.336749i
$$708$$ 0 0
$$709$$ −8.39738e6 + 1.45447e7i −0.627377 + 1.08665i 0.360699 + 0.932682i $$0.382538\pi$$
−0.988076 + 0.153966i $$0.950795\pi$$
$$710$$ −1.29481e6 2.24268e6i −0.0963965 0.166964i
$$711$$ 0 0
$$712$$ 6.81312e6 1.18007e7i 0.503670 0.872382i
$$713$$ −2.53322e6 −0.186616
$$714$$ 0 0
$$715$$ −1.90683e6 −0.139491
$$716$$ 2.31126e6 4.00323e6i 0.168487 0.291828i
$$717$$ 0 0
$$718$$ −9.58182e6 1.65962e7i −0.693644 1.20143i
$$719$$ −8.25652e6 + 1.43007e7i −0.595628 + 1.03166i 0.397830 + 0.917459i $$0.369763\pi$$
−0.993458 + 0.114199i $$0.963570\pi$$
$$720$$ 0 0
$$721$$ 5.51314e6 6.29049e6i 0.394967 0.450657i
$$722$$ 5.09215e6 0.363545
$$723$$ 0 0
$$724$$ 1.92277e6 + 3.33034e6i 0.136327 + 0.236125i
$$725$$ −503369. 871861.i −0.0355665 0.0616030i
$$726$$ 0 0
$$727$$ −1.25756e6 −0.0882453 −0.0441227 0.999026i $$-0.514049\pi$$
−0.0441227 + 0.999026i $$0.514049\pi$$
$$728$$ −1.55974e7 3.09745e6i −1.09075 0.216609i
$$729$$ 0 0
$$730$$ 2.08232e6 3.60669e6i 0.144624 0.250496i
$$731$$ 1.43405e7 + 2.48385e7i 0.992592 + 1.71922i
$$732$$ 0 0
$$733$$ 991661. 1.71761e6i 0.0681716 0.118077i −0.829925 0.557875i $$-0.811617\pi$$
0.898096 + 0.439798i $$0.144950\pi$$
$$734$$ −1.11703e7 −0.765288
$$735$$ 0 0
$$736$$ −909684. −0.0619007
$$737$$ 561125. 971896.i 0.0380532 0.0659100i
$$738$$ 0 0
$$739$$ 1.19404e7 + 2.06813e7i 0.804278 + 1.39305i 0.916777 + 0.399399i $$0.130781\pi$$
−0.112499 + 0.993652i $$0.535885\pi$$
$$740$$ −1.33463e6 + 2.31164e6i −0.0895943 + 0.155182i
$$741$$ 0 0
$$742$$ 8.13032e6 + 1.61458e6i 0.542123 + 0.107659i
$$743$$ 1.90819e7 1.26809 0.634043 0.773298i $$-0.281394\pi$$
0.634043 + 0.773298i $$0.281394\pi$$
$$744$$ 0 0
$$745$$ −2.89178e6 5.00871e6i −0.190886 0.330625i
$$746$$ 4.20943e6 + 7.29095e6i 0.276934 + 0.479664i
$$747$$ 0 0
$$748$$ 878323. 0.0573985
$$749$$ −5.64349e6 + 6.43922e6i −0.367573 + 0.419400i
$$750$$ 0 0
$$751$$ 1.87903e6 3.25457e6i 0.121572 0.210569i −0.798816 0.601576i $$-0.794540\pi$$
0.920388 + 0.391007i $$0.127873\pi$$
$$752$$ 8.44817e6 + 1.46327e7i 0.544776 + 0.943580i
$$753$$ 0 0
$$754$$ −1.17619e6 + 2.03722e6i −0.0753439 + 0.130500i
$$755$$ −4.64994e6 −0.296880
$$756$$ 0 0
$$757$$ 1.69904e7 1.07761 0.538807 0.842429i $$-0.318875\pi$$
0.538807 + 0.842429i $$0.318875\pi$$
$$758$$ 7.16795e6 1.24153e7i 0.453129 0.784843i
$$759$$ 0 0
$$760$$ 7.56599e6 + 1.31047e7i 0.475151 + 0.822986i
$$761$$ 1.11999e7 1.93988e7i 0.701056 1.21426i −0.267040 0.963685i $$-0.586046\pi$$
0.968096 0.250579i $$-0.0806211\pi$$
$$762$$ 0 0
$$763$$ −1.58241e6 4.65685e6i −0.0984027 0.289588i
$$764$$ 2.57550e6 0.159635
$$765$$ 0 0
$$766$$ 8.25554e6 + 1.42990e7i 0.508362 + 0.880510i
$$767$$ 1.14241e7 + 1.97871e7i 0.701184 + 1.21449i
$$768$$ 0 0
$$769$$ −1.87866e7 −1.14560 −0.572799 0.819696i $$-0.694142\pi$$
−0.572799 + 0.819696i $$0.694142\pi$$
$$770$$ 1.30973e6 1.49440e6i 0.0796075 0.0908321i
$$771$$ 0 0
$$772$$ 2.37589e6 4.11516e6i 0.143477 0.248509i
$$773$$ 4.65419e6 + 8.06129e6i 0.280153 + 0.485239i 0.971422 0.237358i $$-0.0762815\pi$$
−0.691269 + 0.722597i $$0.742948\pi$$
$$774$$ 0 0
$$775$$ 4.21106e6 7.29377e6i 0.251847 0.436212i
$$776$$ −2.05156e7 </