# Properties

 Label 33.6.f.a.2.1 Level $33$ Weight $6$ Character 33.2 Analytic conductor $5.293$ Analytic rank $0$ Dimension $72$ CM no Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,6,Mod(2,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("33.2");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$33 = 3 \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 33.f (of order $$10$$, degree $$4$$, minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$5.29266605383$$ Analytic rank: $$0$$ Dimension: $$72$$ Relative dimension: $$18$$ over $$\Q(\zeta_{10})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

## Embedding invariants

 Embedding label 2.1 Character $$\chi$$ $$=$$ 33.2 Dual form 33.6.f.a.17.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-3.08173 + 9.48458i) q^{2} +(-12.5347 + 9.26724i) q^{3} +(-54.5716 - 39.6486i) q^{4} +(16.3931 - 5.32643i) q^{5} +(-49.2674 - 147.445i) q^{6} +(-74.1699 + 102.086i) q^{7} +(286.047 - 207.825i) q^{8} +(71.2363 - 232.324i) q^{9} +O(q^{10})$$ $$q+(-3.08173 + 9.48458i) q^{2} +(-12.5347 + 9.26724i) q^{3} +(-54.5716 - 39.6486i) q^{4} +(16.3931 - 5.32643i) q^{5} +(-49.2674 - 147.445i) q^{6} +(-74.1699 + 102.086i) q^{7} +(286.047 - 207.825i) q^{8} +(71.2363 - 232.324i) q^{9} +171.896i q^{10} +(293.152 + 274.067i) q^{11} +(1051.47 - 8.74606i) q^{12} +(-289.976 - 94.2191i) q^{13} +(-739.673 - 1018.07i) q^{14} +(-156.121 + 218.684i) q^{15} +(422.592 + 1300.60i) q^{16} +(-415.883 - 1279.96i) q^{17} +(1983.96 + 1391.60i) q^{18} +(-1592.36 - 2191.69i) q^{19} +(-1105.78 - 359.290i) q^{20} +(-16.3611 - 1966.97i) q^{21} +(-3502.83 + 1935.82i) q^{22} +3564.43i q^{23} +(-1659.54 + 5255.89i) q^{24} +(-2287.82 + 1662.20i) q^{25} +(1787.26 - 2459.95i) q^{26} +(1260.08 + 3572.27i) q^{27} +(8095.14 - 2630.27i) q^{28} +(-3069.44 - 2230.08i) q^{29} +(-1593.00 - 2154.66i) q^{30} +(848.134 - 2610.29i) q^{31} -2323.64 q^{32} +(-6214.41 - 718.637i) q^{33} +13421.5 q^{34} +(-672.118 + 2068.57i) q^{35} +(-13098.8 + 9853.86i) q^{36} +(-159.754 - 116.068i) q^{37} +(25694.5 - 8348.65i) q^{38} +(4507.91 - 1506.28i) q^{39} +(3582.22 - 4930.50i) q^{40} +(-13619.3 + 9894.99i) q^{41} +(18706.3 + 5906.48i) q^{42} +6557.27i q^{43} +(-5131.38 - 26579.4i) q^{44} +(-69.6748 - 4187.94i) q^{45} +(-33807.1 - 10984.6i) q^{46} +(-6782.17 - 9334.86i) q^{47} +(-17350.1 - 12386.4i) q^{48} +(273.244 + 840.959i) q^{49} +(-8714.80 - 26821.4i) q^{50} +(17074.6 + 12189.8i) q^{51} +(12088.8 + 16638.8i) q^{52} +(12489.0 + 4057.92i) q^{53} +(-37764.7 + 942.546i) q^{54} +(6265.46 + 2931.36i) q^{55} +44615.8i q^{56} +(40270.7 + 12715.4i) q^{57} +(30610.5 - 22239.9i) q^{58} +(-15685.5 + 21589.2i) q^{59} +(17190.3 - 5743.96i) q^{60} +(-27166.3 + 8826.87i) q^{61} +(22143.7 + 16088.4i) q^{62} +(18433.5 + 24503.7i) q^{63} +(-6362.11 + 19580.6i) q^{64} -5255.46 q^{65} +(25967.1 - 56726.4i) q^{66} -28557.0 q^{67} +(-28053.1 + 86338.5i) q^{68} +(-33032.4 - 44678.9i) q^{69} +(-17548.2 - 12749.5i) q^{70} +(65896.0 - 21410.9i) q^{71} +(-27905.8 - 81260.2i) q^{72} +(18393.0 - 25315.8i) q^{73} +(1593.17 - 1157.51i) q^{74} +(13273.1 - 42036.8i) q^{75} +182739. i q^{76} +(-49721.6 + 9599.18i) q^{77} +(394.250 + 47397.6i) q^{78} +(-80830.9 - 26263.6i) q^{79} +(13855.2 + 19070.0i) q^{80} +(-48899.8 - 33099.8i) q^{81} +(-51878.9 - 159667. i) q^{82} +(22963.6 + 70674.6i) q^{83} +(-77094.7 + 107989. i) q^{84} +(-13635.2 - 18767.3i) q^{85} +(-62192.9 - 20207.7i) q^{86} +(59141.2 - 491.932i) q^{87} +(140813. + 17471.8i) q^{88} -49217.1i q^{89} +(39935.5 + 12245.2i) q^{90} +(31126.0 - 22614.4i) q^{91} +(141324. - 194516. i) q^{92} +(13559.1 + 40579.0i) q^{93} +(109438. - 35558.6i) q^{94} +(-37777.6 - 27447.0i) q^{95} +(29126.1 - 21533.7i) q^{96} +(-7336.07 + 22578.1i) q^{97} -8818.20 q^{98} +(84555.5 - 48582.6i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$72 q + 18 q^{3} - 262 q^{4} + 15 q^{6} - 10 q^{7} + 292 q^{9}+O(q^{10})$$ 72 * q + 18 * q^3 - 262 * q^4 + 15 * q^6 - 10 * q^7 + 292 * q^9 $$72 q + 18 q^{3} - 262 q^{4} + 15 q^{6} - 10 q^{7} + 292 q^{9} + 1854 q^{12} - 10 q^{13} - 762 q^{15} - 10122 q^{16} + 4815 q^{18} + 4460 q^{19} + 4628 q^{22} - 805 q^{24} + 13708 q^{25} + 6108 q^{27} - 28130 q^{28} - 15470 q^{30} + 4340 q^{31} - 508 q^{33} + 18732 q^{34} - 56461 q^{36} + 978 q^{37} + 23360 q^{39} + 69750 q^{40} + 60788 q^{42} - 31356 q^{45} - 52090 q^{46} + 4238 q^{48} - 58448 q^{49} - 178950 q^{51} - 14190 q^{52} + 86600 q^{55} + 266190 q^{57} + 137102 q^{58} + 284090 q^{60} - 77890 q^{61} - 120330 q^{63} - 379114 q^{64} - 323304 q^{66} + 42668 q^{67} - 271816 q^{69} + 87176 q^{70} + 343960 q^{72} + 116440 q^{73} + 326202 q^{75} + 155512 q^{78} - 350590 q^{79} - 208088 q^{81} - 606424 q^{82} - 220680 q^{84} + 665610 q^{85} + 1152974 q^{88} + 293440 q^{90} + 621014 q^{91} + 478456 q^{93} - 521270 q^{94} - 1246430 q^{96} - 1030446 q^{97} - 590000 q^{99}+O(q^{100})$$ 72 * q + 18 * q^3 - 262 * q^4 + 15 * q^6 - 10 * q^7 + 292 * q^9 + 1854 * q^12 - 10 * q^13 - 762 * q^15 - 10122 * q^16 + 4815 * q^18 + 4460 * q^19 + 4628 * q^22 - 805 * q^24 + 13708 * q^25 + 6108 * q^27 - 28130 * q^28 - 15470 * q^30 + 4340 * q^31 - 508 * q^33 + 18732 * q^34 - 56461 * q^36 + 978 * q^37 + 23360 * q^39 + 69750 * q^40 + 60788 * q^42 - 31356 * q^45 - 52090 * q^46 + 4238 * q^48 - 58448 * q^49 - 178950 * q^51 - 14190 * q^52 + 86600 * q^55 + 266190 * q^57 + 137102 * q^58 + 284090 * q^60 - 77890 * q^61 - 120330 * q^63 - 379114 * q^64 - 323304 * q^66 + 42668 * q^67 - 271816 * q^69 + 87176 * q^70 + 343960 * q^72 + 116440 * q^73 + 326202 * q^75 + 155512 * q^78 - 350590 * q^79 - 208088 * q^81 - 606424 * q^82 - 220680 * q^84 + 665610 * q^85 + 1152974 * q^88 + 293440 * q^90 + 621014 * q^91 + 478456 * q^93 - 521270 * q^94 - 1246430 * q^96 - 1030446 * q^97 - 590000 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$$.

 $$n$$ $$13$$ $$23$$ $$\chi(n)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −3.08173 + 9.48458i −0.544777 + 1.67665i 0.176742 + 0.984257i $$0.443444\pi$$
−0.721519 + 0.692395i $$0.756556\pi$$
$$3$$ −12.5347 + 9.26724i −0.804100 + 0.594494i
$$4$$ −54.5716 39.6486i −1.70536 1.23902i
$$5$$ 16.3931 5.32643i 0.293248 0.0952821i −0.158698 0.987327i $$-0.550730\pi$$
0.451947 + 0.892045i $$0.350730\pi$$
$$6$$ −49.2674 147.445i −0.558704 1.67206i
$$7$$ −74.1699 + 102.086i −0.572114 + 0.787448i −0.992803 0.119757i $$-0.961788\pi$$
0.420689 + 0.907205i $$0.361788\pi$$
$$8$$ 286.047 207.825i 1.58020 1.14808i
$$9$$ 71.2363 232.324i 0.293154 0.956065i
$$10$$ 171.896i 0.543583i
$$11$$ 293.152 + 274.067i 0.730484 + 0.682929i
$$12$$ 1051.47 8.74606i 2.10787 0.0175331i
$$13$$ −289.976 94.2191i −0.475888 0.154625i 0.0612456 0.998123i $$-0.480493\pi$$
−0.537133 + 0.843498i $$0.680493\pi$$
$$14$$ −739.673 1018.07i −1.00860 1.38822i
$$15$$ −156.121 + 218.684i −0.179156 + 0.250951i
$$16$$ 422.592 + 1300.60i 0.412687 + 1.27012i
$$17$$ −415.883 1279.96i −0.349019 1.07417i −0.959397 0.282060i $$-0.908982\pi$$
0.610378 0.792110i $$-0.291018\pi$$
$$18$$ 1983.96 + 1391.60i 1.44329 + 1.01236i
$$19$$ −1592.36 2191.69i −1.01195 1.39282i −0.917700 0.397274i $$-0.869956\pi$$
−0.0942452 0.995549i $$-0.530044\pi$$
$$20$$ −1105.78 359.290i −0.618151 0.200849i
$$21$$ −16.3611 1966.97i −0.00809589 0.973305i
$$22$$ −3502.83 + 1935.82i −1.54299 + 0.852724i
$$23$$ 3564.43i 1.40498i 0.711694 + 0.702490i $$0.247928\pi$$
−0.711694 + 0.702490i $$0.752072\pi$$
$$24$$ −1659.54 + 5255.89i −0.588111 + 1.86259i
$$25$$ −2287.82 + 1662.20i −0.732101 + 0.531903i
$$26$$ 1787.26 2459.95i 0.518505 0.713661i
$$27$$ 1260.08 + 3572.27i 0.332650 + 0.943050i
$$28$$ 8095.14 2630.27i 1.95132 0.634024i
$$29$$ −3069.44 2230.08i −0.677742 0.492408i 0.194866 0.980830i $$-0.437573\pi$$
−0.872608 + 0.488422i $$0.837573\pi$$
$$30$$ −1593.00 2154.66i −0.323157 0.437095i
$$31$$ 848.134 2610.29i 0.158511 0.487847i −0.839989 0.542604i $$-0.817438\pi$$
0.998500 + 0.0547568i $$0.0174384\pi$$
$$32$$ −2323.64 −0.401138
$$33$$ −6214.41 718.637i −0.993380 0.114875i
$$34$$ 13421.5 1.99115
$$35$$ −672.118 + 2068.57i −0.0927418 + 0.285430i
$$36$$ −13098.8 + 9853.86i −1.68452 + 1.26722i
$$37$$ −159.754 116.068i −0.0191843 0.0139382i 0.578152 0.815929i $$-0.303774\pi$$
−0.597336 + 0.801991i $$0.703774\pi$$
$$38$$ 25694.5 8348.65i 2.88656 0.937902i
$$39$$ 4507.91 1506.28i 0.474585 0.158578i
$$40$$ 3582.22 4930.50i 0.353999 0.487238i
$$41$$ −13619.3 + 9894.99i −1.26530 + 0.919297i −0.999005 0.0445934i $$-0.985801\pi$$
−0.266299 + 0.963891i $$0.585801\pi$$
$$42$$ 18706.3 + 5906.48i 1.63630 + 0.516661i
$$43$$ 6557.27i 0.540819i 0.962745 + 0.270410i $$0.0871591\pi$$
−0.962745 + 0.270410i $$0.912841\pi$$
$$44$$ −5131.38 26579.4i −0.399579 2.06973i
$$45$$ −69.6748 4187.94i −0.00512914 0.308297i
$$46$$ −33807.1 10984.6i −2.35566 0.765401i
$$47$$ −6782.17 9334.86i −0.447841 0.616401i 0.524091 0.851663i $$-0.324405\pi$$
−0.971932 + 0.235262i $$0.924405\pi$$
$$48$$ −17350.1 12386.4i −1.08692 0.775964i
$$49$$ 273.244 + 840.959i 0.0162578 + 0.0500362i
$$50$$ −8714.80 26821.4i −0.492983 1.51725i
$$51$$ 17074.6 + 12189.8i 0.919234 + 0.656250i
$$52$$ 12088.8 + 16638.8i 0.619977 + 0.853325i
$$53$$ 12489.0 + 4057.92i 0.610714 + 0.198433i 0.598013 0.801486i $$-0.295957\pi$$
0.0127007 + 0.999919i $$0.495957\pi$$
$$54$$ −37764.7 + 942.546i −1.76239 + 0.0439864i
$$55$$ 6265.46 + 2931.36i 0.279284 + 0.130666i
$$56$$ 44615.8i 1.90116i
$$57$$ 40270.7 + 12715.4i 1.64173 + 0.518374i
$$58$$ 30610.5 22239.9i 1.19482 0.868084i
$$59$$ −15685.5 + 21589.2i −0.586635 + 0.807434i −0.994403 0.105651i $$-0.966307\pi$$
0.407768 + 0.913086i $$0.366307\pi$$
$$60$$ 17190.3 5743.96i 0.616459 0.205984i
$$61$$ −27166.3 + 8826.87i −0.934773 + 0.303726i −0.736513 0.676424i $$-0.763529\pi$$
−0.198260 + 0.980150i $$0.563529\pi$$
$$62$$ 22143.7 + 16088.4i 0.731597 + 0.531536i
$$63$$ 18433.5 + 24503.7i 0.585134 + 0.777822i
$$64$$ −6362.11 + 19580.6i −0.194156 + 0.597552i
$$65$$ −5255.46 −0.154286
$$66$$ 25967.1 56726.4i 0.733776 1.60297i
$$67$$ −28557.0 −0.777186 −0.388593 0.921409i $$-0.627039\pi$$
−0.388593 + 0.921409i $$0.627039\pi$$
$$68$$ −28053.1 + 86338.5i −0.735712 + 2.26429i
$$69$$ −33032.4 44678.9i −0.835252 1.12974i
$$70$$ −17548.2 12749.5i −0.428043 0.310992i
$$71$$ 65896.0 21410.9i 1.55136 0.504068i 0.596879 0.802331i $$-0.296407\pi$$
0.954484 + 0.298263i $$0.0964073\pi$$
$$72$$ −27905.8 81260.2i −0.634400 1.84734i
$$73$$ 18393.0 25315.8i 0.403966 0.556012i −0.557768 0.829997i $$-0.688342\pi$$
0.961734 + 0.273985i $$0.0883419\pi$$
$$74$$ 1593.17 1157.51i 0.0338207 0.0245722i
$$75$$ 13273.1 42036.8i 0.272470 0.862933i
$$76$$ 182739.i 3.62909i
$$77$$ −49721.6 + 9599.18i −0.955692 + 0.184505i
$$78$$ 394.250 + 47397.6i 0.00733728 + 0.882103i
$$79$$ −80830.9 26263.6i −1.45717 0.473463i −0.529964 0.848020i $$-0.677795\pi$$
−0.927204 + 0.374557i $$0.877795\pi$$
$$80$$ 13855.2 + 19070.0i 0.242040 + 0.333139i
$$81$$ −48899.8 33099.8i −0.828122 0.560548i
$$82$$ −51878.9 159667.i −0.852033 2.62229i
$$83$$ 22963.6 + 70674.6i 0.365885 + 1.12608i 0.949425 + 0.313993i $$0.101667\pi$$
−0.583541 + 0.812084i $$0.698333\pi$$
$$84$$ −77094.7 + 107989.i −1.19214 + 1.66987i
$$85$$ −13635.2 18767.3i −0.204698 0.281743i
$$86$$ −62192.9 20207.7i −0.906765 0.294626i
$$87$$ 59141.2 491.932i 0.837706 0.00696798i
$$88$$ 140813. + 17471.8i 1.93837 + 0.240509i
$$89$$ 49217.1i 0.658629i −0.944220 0.329315i $$-0.893182\pi$$
0.944220 0.329315i $$-0.106818\pi$$
$$90$$ 39935.5 + 12245.2i 0.519701 + 0.159353i
$$91$$ 31126.0 22614.4i 0.394021 0.286273i
$$92$$ 141324. 194516.i 1.74080 2.39600i
$$93$$ 13559.1 + 40579.0i 0.162563 + 0.486512i
$$94$$ 109438. 35558.6i 1.27746 0.415073i
$$95$$ −37777.6 27447.0i −0.429462 0.312023i
$$96$$ 29126.1 21533.7i 0.322555 0.238474i
$$97$$ −7336.07 + 22578.1i −0.0791651 + 0.243645i −0.982805 0.184649i $$-0.940885\pi$$
0.903639 + 0.428294i $$0.140885\pi$$
$$98$$ −8818.20 −0.0927502
$$99$$ 84555.5 48582.6i 0.867069 0.498188i
$$100$$ 190753. 1.90753
$$101$$ 13737.8 42280.6i 0.134003 0.412418i −0.861431 0.507875i $$-0.830431\pi$$
0.995434 + 0.0954569i $$0.0304312\pi$$
$$102$$ −168234. + 124380.i −1.60108 + 1.18372i
$$103$$ 43715.1 + 31760.9i 0.406012 + 0.294985i 0.771985 0.635640i $$-0.219264\pi$$
−0.365973 + 0.930625i $$0.619264\pi$$
$$104$$ −102528. + 33313.3i −0.929520 + 0.302019i
$$105$$ −10745.1 32157.5i −0.0951127 0.284649i
$$106$$ −76975.3 + 105947.i −0.665406 + 0.915853i
$$107$$ −50478.6 + 36674.9i −0.426234 + 0.309677i −0.780141 0.625603i $$-0.784853\pi$$
0.353907 + 0.935281i $$0.384853\pi$$
$$108$$ 72871.0 244905.i 0.601167 2.02040i
$$109$$ 91208.5i 0.735307i −0.929963 0.367654i $$-0.880161\pi$$
0.929963 0.367654i $$-0.119839\pi$$
$$110$$ −47111.1 + 50391.6i −0.371229 + 0.397079i
$$111$$ 3078.09 25.6033i 0.0237123 0.000197237i
$$112$$ −164117. 53324.9i −1.23626 0.401685i
$$113$$ 60501.1 + 83272.6i 0.445725 + 0.613488i 0.971472 0.237153i $$-0.0762142\pi$$
−0.525747 + 0.850641i $$0.676214\pi$$
$$114$$ −244703. + 342765.i −1.76351 + 2.47021i
$$115$$ 18985.7 + 58431.9i 0.133870 + 0.412008i
$$116$$ 79084.8 + 243398.i 0.545693 + 1.67947i
$$117$$ −42546.2 + 60656.6i −0.287340 + 0.409651i
$$118$$ −156426. 215302.i −1.03420 1.42346i
$$119$$ 161512. + 52478.4i 1.04553 + 0.339714i
$$120$$ 790.200 + 94999.6i 0.00500938 + 0.602238i
$$121$$ 10825.1 + 160687.i 0.0672150 + 0.997739i
$$122$$ 284863.i 1.73275i
$$123$$ 79014.1 250244.i 0.470914 1.49142i
$$124$$ −149778. + 108820.i −0.874771 + 0.635558i
$$125$$ −60311.6 + 83011.9i −0.345244 + 0.475188i
$$126$$ −289214. + 99319.9i −1.62290 + 0.557327i
$$127$$ −24025.4 + 7806.32i −0.132179 + 0.0429474i −0.374359 0.927284i $$-0.622137\pi$$
0.242181 + 0.970231i $$0.422137\pi$$
$$128$$ −226263. 164390.i −1.22064 0.886848i
$$129$$ −60767.8 82193.3i −0.321514 0.434873i
$$130$$ 16195.9 49845.8i 0.0840516 0.258684i
$$131$$ 71268.0 0.362841 0.181420 0.983406i $$-0.441931\pi$$
0.181420 + 0.983406i $$0.441931\pi$$
$$132$$ 310638. + 285610.i 1.55174 + 1.42672i
$$133$$ 341847. 1.67572
$$134$$ 88004.8 270851.i 0.423394 1.30307i
$$135$$ 39684.0 + 51848.8i 0.187405 + 0.244852i
$$136$$ −384969. 279696.i −1.78476 1.29670i
$$137$$ −235626. + 76559.5i −1.07256 + 0.348496i −0.791484 0.611190i $$-0.790691\pi$$
−0.281076 + 0.959686i $$0.590691\pi$$
$$138$$ 525558. 175610.i 2.34921 0.784968i
$$139$$ 28178.0 38783.7i 0.123701 0.170260i −0.742675 0.669652i $$-0.766443\pi$$
0.866376 + 0.499392i $$0.166443\pi$$
$$140$$ 118694. 86236.5i 0.511811 0.371853i
$$141$$ 171521. + 54157.4i 0.726556 + 0.229409i
$$142$$ 690978.i 2.87570i
$$143$$ −59184.8 107094.i −0.242030 0.437949i
$$144$$ 332265. 5527.90i 1.33530 0.0222154i
$$145$$ −62196.0 20208.7i −0.245664 0.0798212i
$$146$$ 183427. + 252466.i 0.712167 + 0.980214i
$$147$$ −11218.4 8008.93i −0.0428191 0.0305690i
$$148$$ 4116.09 + 12668.0i 0.0154465 + 0.0475395i
$$149$$ 59646.3 + 183572.i 0.220099 + 0.677395i 0.998752 + 0.0499404i $$0.0159031\pi$$
−0.778653 + 0.627454i $$0.784097\pi$$
$$150$$ 357798. + 255435.i 1.29840 + 0.926943i
$$151$$ 247390. + 340504.i 0.882959 + 1.21529i 0.975593 + 0.219589i $$0.0704715\pi$$
−0.0926334 + 0.995700i $$0.529528\pi$$
$$152$$ −910978. 295995.i −3.19815 1.03914i
$$153$$ −326990. + 5440.15i −1.12929 + 0.0187881i
$$154$$ 62184.0 501170.i 0.211289 1.70288i
$$155$$ 47308.2i 0.158164i
$$156$$ −305726. 96532.4i −1.00582 0.317586i
$$157$$ −1878.51 + 1364.82i −0.00608225 + 0.00441902i −0.590822 0.806802i $$-0.701197\pi$$
0.584740 + 0.811221i $$0.301197\pi$$
$$158$$ 498197. 685710.i 1.58766 2.18523i
$$159$$ −194151. + 64873.8i −0.609042 + 0.203506i
$$160$$ −38091.6 + 12376.7i −0.117633 + 0.0382213i
$$161$$ −363879. 264373.i −1.10635 0.803809i
$$162$$ 464633. 361789.i 1.39099 1.08310i
$$163$$ 16782.3 51650.6i 0.0494746 0.152267i −0.923267 0.384159i $$-0.874492\pi$$
0.972742 + 0.231892i $$0.0744915\pi$$
$$164$$ 1.13555e6 3.29683
$$165$$ −105701. + 21320.0i −0.302252 + 0.0609645i
$$166$$ −741086. −2.08737
$$167$$ −27781.1 + 85501.4i −0.0770829 + 0.237237i −0.982172 0.187986i $$-0.939804\pi$$
0.905089 + 0.425222i $$0.139804\pi$$
$$168$$ −413465. 559245.i −1.13023 1.52872i
$$169$$ −225173. 163598.i −0.606457 0.440617i
$$170$$ 220019. 71488.6i 0.583900 0.189721i
$$171$$ −622617. + 213815.i −1.62829 + 0.559175i
$$172$$ 259987. 357841.i 0.670085 0.922293i
$$173$$ −374003. + 271729.i −0.950080 + 0.690274i −0.950826 0.309726i $$-0.899763\pi$$
0.000745610 1.00000i $$0.499763\pi$$
$$174$$ −177591. + 562445.i −0.444680 + 1.40834i
$$175$$ 356839.i 0.880801i
$$176$$ −232570. + 497093.i −0.565941 + 1.20964i
$$177$$ −3460.06 415976.i −0.00830137 0.998009i
$$178$$ 466803. + 151674.i 1.10429 + 0.358806i
$$179$$ 416368. + 573081.i 0.971280 + 1.33685i 0.941398 + 0.337299i $$0.109513\pi$$
0.0298823 + 0.999553i $$0.490487\pi$$
$$180$$ −162244. + 231305.i −0.373238 + 0.532113i
$$181$$ 21713.4 + 66826.9i 0.0492641 + 0.151619i 0.972662 0.232224i $$-0.0746002\pi$$
−0.923398 + 0.383843i $$0.874600\pi$$
$$182$$ 118566. + 364908.i 0.265327 + 0.816592i
$$183$$ 258720. 362399.i 0.571087 0.799943i
$$184$$ 740777. + 1.01959e6i 1.61303 + 2.22015i
$$185$$ −3237.08 1051.79i −0.00695384 0.00225944i
$$186$$ −426660. + 3548.93i −0.904272 + 0.00752168i
$$187$$ 228878. 489202.i 0.478629 1.02302i
$$188$$ 778322.i 1.60607i
$$189$$ −458139. 136319.i −0.932917 0.277588i
$$190$$ 376743. 273720.i 0.757115 0.550076i
$$191$$ −34495.7 + 47479.3i −0.0684198 + 0.0941718i −0.841856 0.539703i $$-0.818537\pi$$
0.773436 + 0.633875i $$0.218537\pi$$
$$192$$ −101711. 304395.i −0.199120 0.595916i
$$193$$ 27977.4 9090.41i 0.0540648 0.0175667i −0.281860 0.959456i $$-0.590951\pi$$
0.335925 + 0.941889i $$0.390951\pi$$
$$194$$ −191536. 139159.i −0.365381 0.265465i
$$195$$ 65875.5 48703.6i 0.124062 0.0917222i
$$196$$ 18431.5 56726.2i 0.0342704 0.105474i
$$197$$ −722159. −1.32577 −0.662884 0.748722i $$-0.730668\pi$$
−0.662884 + 0.748722i $$0.730668\pi$$
$$198$$ 200209. + 951691.i 0.362928 + 1.72517i
$$199$$ −398686. −0.713671 −0.356835 0.934167i $$-0.616144\pi$$
−0.356835 + 0.934167i $$0.616144\pi$$
$$200$$ −308976. + 950931.i −0.546198 + 1.68102i
$$201$$ 357953. 264645.i 0.624936 0.462033i
$$202$$ 358677. + 260594.i 0.618480 + 0.449352i
$$203$$ 455321. 147943.i 0.775492 0.251973i
$$204$$ −448483. 1.34220e6i −0.754520 2.25809i
$$205$$ −170557. + 234752.i −0.283456 + 0.390143i
$$206$$ −435957. + 316741.i −0.715773 + 0.520040i
$$207$$ 828101. + 253917.i 1.34325 + 0.411875i
$$208$$ 416960.i 0.668246i
$$209$$ 133869. 1.07891e6i 0.211990 1.70852i
$$210$$ 338114. 2812.41i 0.529072 0.00440079i
$$211$$ 295619. + 96052.5i 0.457116 + 0.148526i 0.528519 0.848922i $$-0.322748\pi$$
−0.0714029 + 0.997448i $$0.522748\pi$$
$$212$$ −520653. 716618.i −0.795626 1.09509i
$$213$$ −627565. + 879053.i −0.947785 + 1.32760i
$$214$$ −192284. 591790.i −0.287018 0.883351i
$$215$$ 34926.9 + 107494.i 0.0515304 + 0.158594i
$$216$$ 1.10285e6 + 759960.i 1.60835 + 1.10830i
$$217$$ 203568. + 280187.i 0.293468 + 0.403924i
$$218$$ 865074. + 281080.i 1.23285 + 0.400579i
$$219$$ 4057.30 + 487778.i 0.00571646 + 0.687245i
$$220$$ −225692. 408386.i −0.314384 0.568871i
$$221$$ 410341.i 0.565151i
$$222$$ −9242.99 + 29273.3i −0.0125872 + 0.0398647i
$$223$$ −856628. + 622377.i −1.15353 + 0.838091i −0.988947 0.148271i $$-0.952629\pi$$
−0.164587 + 0.986363i $$0.552629\pi$$
$$224$$ 172344. 237211.i 0.229497 0.315875i
$$225$$ 223192. + 649923.i 0.293915 + 0.855866i
$$226$$ −976253. + 317204.i −1.27143 + 0.413112i
$$227$$ 242231. + 175991.i 0.312008 + 0.226687i 0.732758 0.680490i $$-0.238233\pi$$
−0.420750 + 0.907177i $$0.638233\pi$$
$$228$$ −1.69349e6 2.29058e6i −2.15747 2.91815i
$$229$$ 151421. 466026.i 0.190808 0.587248i −0.809192 0.587545i $$-0.800095\pi$$
1.00000 0.000297029i $$9.45474e-5\pi$$
$$230$$ −612711. −0.763723
$$231$$ 534286. 581104.i 0.658785 0.716513i
$$232$$ −1.34147e6 −1.63629
$$233$$ 273321. 841197.i 0.329825 1.01510i −0.639390 0.768883i $$-0.720813\pi$$
0.969215 0.246215i $$-0.0791869\pi$$
$$234$$ −444187. 590460.i −0.530305 0.704937i
$$235$$ −160902. 116902.i −0.190061 0.138087i
$$236$$ 1.71197e6 556251.i 2.00085 0.650116i
$$237$$ 1.25658e6 419875.i 1.45318 0.485566i
$$238$$ −995471. + 1.37015e6i −1.13916 + 1.56792i
$$239$$ −609646. + 442934.i −0.690372 + 0.501585i −0.876782 0.480887i $$-0.840315\pi$$
0.186410 + 0.982472i $$0.440315\pi$$
$$240$$ −350396. 110637.i −0.392673 0.123986i
$$241$$ 507817.i 0.563202i −0.959532 0.281601i $$-0.909135\pi$$
0.959532 0.281601i $$-0.0908655\pi$$
$$242$$ −1.55741e6 392522.i −1.70948 0.430849i
$$243$$ 919687. 38270.7i 0.999135 0.0415767i
$$244$$ 1.83248e6 + 595409.i 1.97045 + 0.640237i
$$245$$ 8958.62 + 12330.5i 0.00953512 + 0.0131240i
$$246$$ 2.12996e6 + 1.52060e6i 2.24405 + 1.60205i
$$247$$ 255247. + 785570.i 0.266206 + 0.819299i
$$248$$ −299877. 922927.i −0.309610 0.952880i
$$249$$ −942800. 673074.i −0.963654 0.687963i
$$250$$ −601468. 827850.i −0.608643 0.837725i
$$251$$ 1.43568e6 + 466480.i 1.43838 + 0.467357i 0.921391 0.388638i $$-0.127054\pi$$
0.516985 + 0.855994i $$0.327054\pi$$
$$252$$ −34406.5 2.06807e6i −0.0341302 2.05146i
$$253$$ −976893. + 1.04492e6i −0.959502 + 1.02632i
$$254$$ 251927.i 0.245014i
$$255$$ 344834. + 108881.i 0.332093 + 0.104858i
$$256$$ 1.72345e6 1.25216e6i 1.64361 1.19415i
$$257$$ 622580. 856908.i 0.587980 0.809285i −0.406562 0.913623i $$-0.633272\pi$$
0.994542 + 0.104338i $$0.0332724\pi$$
$$258$$ 966838. 323060.i 0.904283 0.302158i
$$259$$ 23697.8 7699.90i 0.0219513 0.00713240i
$$260$$ 286799. + 208371.i 0.263114 + 0.191163i
$$261$$ −736756. + 554242.i −0.669457 + 0.503614i
$$262$$ −219628. + 675947.i −0.197667 + 0.608358i
$$263$$ −295852. −0.263745 −0.131873 0.991267i $$-0.542099\pi$$
−0.131873 + 0.991267i $$0.542099\pi$$
$$264$$ −1.92696e6 + 1.08595e6i −1.70162 + 0.958957i
$$265$$ 226347. 0.197998
$$266$$ −1.05348e6 + 3.24227e6i −0.912896 + 2.80961i
$$267$$ 456107. + 616921.i 0.391551 + 0.529604i
$$268$$ 1.55840e6 + 1.13224e6i 1.32538 + 0.962948i
$$269$$ 1.15363e6 374838.i 0.972046 0.315837i 0.220404 0.975409i $$-0.429262\pi$$
0.751642 + 0.659572i $$0.229262\pi$$
$$270$$ −614059. + 216602.i −0.512626 + 0.180823i
$$271$$ 901471. 1.24077e6i 0.745639 1.02628i −0.252635 0.967562i $$-0.581297\pi$$
0.998274 0.0587225i $$-0.0187027\pi$$
$$272$$ 1.48897e6 1.08180e6i 1.22029 0.886592i
$$273$$ −180582. + 571916.i −0.146645 + 0.464436i
$$274$$ 2.47075e6i 1.98816i
$$275$$ −1.12623e6 139740.i −0.898040 0.111427i
$$276$$ 31174.7 + 3.74789e6i 0.0246337 + 2.96152i
$$277$$ −438937. 142619.i −0.343719 0.111681i 0.132070 0.991240i $$-0.457837\pi$$
−0.475789 + 0.879559i $$0.657837\pi$$
$$278$$ 281010. + 386777.i 0.218077 + 0.300157i
$$279$$ −546014. 382989.i −0.419946 0.294561i
$$280$$ 237643. + 731390.i 0.181147 + 0.557512i
$$281$$ 3223.82 + 9921.89i 0.00243559 + 0.00749598i 0.952267 0.305267i $$-0.0987456\pi$$
−0.949831 + 0.312763i $$0.898746\pi$$
$$282$$ −1.04224e6 + 1.45990e6i −0.780450 + 1.09320i
$$283$$ −470286. 647293.i −0.349056 0.480435i 0.598003 0.801494i $$-0.295961\pi$$
−0.947059 + 0.321059i $$0.895961\pi$$
$$284$$ −4.44496e6 1.44426e6i −3.27018 1.06255i
$$285$$ 727888. 6054.52i 0.530826 0.00441538i
$$286$$ 1.19813e6 231309.i 0.866140 0.167216i
$$287$$ 2.12425e6i 1.52230i
$$288$$ −165528. + 539837.i −0.117595 + 0.383514i
$$289$$ −316642. + 230054.i −0.223010 + 0.162026i
$$290$$ 383342. 527625.i 0.267665 0.368409i
$$291$$ −117281. 350994.i −0.0811890 0.242978i
$$292$$ −2.00747e6 + 652267.i −1.37782 + 0.447680i
$$293$$ 910633. + 661613.i 0.619690 + 0.450231i 0.852813 0.522216i $$-0.174895\pi$$
−0.233124 + 0.972447i $$0.574895\pi$$
$$294$$ 110533. 81720.4i 0.0745804 0.0551394i
$$295$$ −142140. + 437462.i −0.0950958 + 0.292675i
$$296$$ −69818.8 −0.0463173
$$297$$ −609649. + 1.39256e6i −0.401041 + 0.916060i
$$298$$ −1.92492e6 −1.25566
$$299$$ 335837. 1.03360e6i 0.217245 0.668612i
$$300$$ −2.39103e6 + 1.76776e6i −1.53385 + 1.13402i
$$301$$ −669407. 486352.i −0.425867 0.309410i
$$302$$ −3.99192e6 + 1.29705e6i −2.51863 + 0.818353i
$$303$$ 219626. + 657285.i 0.137428 + 0.411289i
$$304$$ 2.17761e6 2.99722e6i 1.35144 1.86009i
$$305$$ −398324. + 289399.i −0.245181 + 0.178134i
$$306$$ 956097. 3.11813e6i 0.583712 1.90367i
$$307$$ 1.91538e6i 1.15987i 0.814663 + 0.579935i $$0.196922\pi$$
−0.814663 + 0.579935i $$0.803078\pi$$
$$308$$ 3.09398e6 + 1.44755e6i 1.85841 + 0.869472i
$$309$$ −842291. + 7006.12i −0.501841 + 0.00417428i
$$310$$ 448698. + 145791.i 0.265185 + 0.0861640i
$$311$$ −1.41391e6 1.94608e6i −0.828934 1.14093i −0.988121 0.153681i $$-0.950887\pi$$
0.159187 0.987248i $$-0.449113\pi$$
$$312$$ 976431. 1.36772e6i 0.567878 0.795448i
$$313$$ −427646. 1.31616e6i −0.246731 0.759360i −0.995347 0.0963562i $$-0.969281\pi$$
0.748616 0.663004i $$-0.230719\pi$$
$$314$$ −7155.67 22022.9i −0.00409568 0.0126052i
$$315$$ 432698. + 303506.i 0.245702 + 0.172342i
$$316$$ 3.36976e6 + 4.63808e6i 1.89837 + 2.61288i
$$317$$ 2.74938e6 + 893329.i 1.53669 + 0.499302i 0.950462 0.310841i $$-0.100611\pi$$
0.586232 + 0.810143i $$0.300611\pi$$
$$318$$ −16979.9 2.04137e6i −0.00941604 1.13202i
$$319$$ −288620. 1.49499e6i −0.158800 0.822546i
$$320$$ 354873.i 0.193731i
$$321$$ 292858. 927505.i 0.158634 0.502405i
$$322$$ 3.62884e6 2.63651e6i 1.95042 1.41706i
$$323$$ −2.14304e6 + 2.94964e6i −1.14294 + 1.57312i
$$324$$ 1.35618e6 + 3.74512e6i 0.717718 + 1.98200i
$$325$$ 820023. 266442.i 0.430643 0.139925i
$$326$$ 438165. + 318346.i 0.228346 + 0.165903i
$$327$$ 845251. + 1.14327e6i 0.437136 + 0.591261i
$$328$$ −1.83933e6 + 5.66086e6i −0.944004 + 2.90535i
$$329$$ 1.45599e6 0.741600
$$330$$ 123531. 1.06823e6i 0.0624440 0.539984i
$$331$$ −1.08115e6 −0.542394 −0.271197 0.962524i $$-0.587419\pi$$
−0.271197 + 0.962524i $$0.587419\pi$$
$$332$$ 1.54899e6 4.76730e6i 0.771264 2.37371i
$$333$$ −38345.6 + 28846.3i −0.0189498 + 0.0142554i
$$334$$ −725331. 526984.i −0.355771 0.258482i
$$335$$ −468137. + 152107.i −0.227909 + 0.0740520i
$$336$$ 2.55133e6 852504.i 1.23287 0.411953i
$$337$$ 2.12194e6 2.92060e6i 1.01779 1.40087i 0.104048 0.994572i $$-0.466820\pi$$
0.913742 0.406295i $$-0.133180\pi$$
$$338$$ 2.24558e6 1.63151e6i 1.06915 0.776779i
$$339$$ −1.53007e6 483117.i −0.723123 0.228325i
$$340$$ 1.56478e6i 0.734099i
$$341$$ 964027. 532765.i 0.448955 0.248113i
$$342$$ −109208. 6.56417e6i −0.0504882 3.03469i
$$343$$ −2.12312e6 689842.i −0.974403 0.316603i
$$344$$ 1.36277e6 + 1.87569e6i 0.620905 + 0.854602i
$$345$$ −779482. 556480.i −0.352581 0.251711i
$$346$$ −1.42466e6 4.38466e6i −0.639767 1.96900i
$$347$$ 120889. + 372057.i 0.0538967 + 0.165877i 0.974382 0.224901i $$-0.0722059\pi$$
−0.920485 + 0.390778i $$0.872206\pi$$
$$348$$ −3.24693e6 2.31802e6i −1.43723 1.02605i
$$349$$ 432812. + 595714.i 0.190211 + 0.261803i 0.893462 0.449139i $$-0.148269\pi$$
−0.703251 + 0.710942i $$0.748269\pi$$
$$350$$ 3.38447e6 + 1.09968e6i 1.47680 + 0.479840i
$$351$$ −28816.9 1.15460e6i −0.0124847 0.500222i
$$352$$ −681179. 636834.i −0.293025 0.273949i
$$353$$ 456511.i 0.194991i 0.995236 + 0.0974956i $$0.0310832\pi$$
−0.995236 + 0.0974956i $$0.968917\pi$$
$$354$$ 3.95601e6 + 1.24911e6i 1.67784 + 0.529774i
$$355$$ 966195. 701981.i 0.406906 0.295634i
$$356$$ −1.95139e6 + 2.68586e6i −0.816054 + 1.12320i
$$357$$ −2.51083e6 + 838970.i −1.04267 + 0.348398i
$$358$$ −6.71856e6 + 2.18299e6i −2.77057 + 0.900212i
$$359$$ −2.72419e6 1.97924e6i −1.11558 0.810517i −0.132047 0.991243i $$-0.542155\pi$$
−0.983533 + 0.180727i $$0.942155\pi$$
$$360$$ −890289. 1.18347e6i −0.362055 0.481282i
$$361$$ −1.50276e6 + 4.62502e6i −0.606906 + 1.86786i
$$362$$ −700739. −0.281051
$$363$$ −1.62481e6 1.91384e6i −0.647197 0.762323i
$$364$$ −2.59522e6 −1.02665
$$365$$ 166675. 512973.i 0.0654844 0.201540i
$$366$$ 2.63989e6 + 3.57066e6i 1.03011 + 1.39331i
$$367$$ 1.27740e6 + 928086.i 0.495065 + 0.359686i 0.807129 0.590375i $$-0.201020\pi$$
−0.312064 + 0.950061i $$0.601020\pi$$
$$368$$ −4.63591e6 + 1.50630e6i −1.78449 + 0.579817i
$$369$$ 1.32865e6 + 3.86897e6i 0.507980 + 1.47921i
$$370$$ 19951.6 27461.0i 0.00757658 0.0104283i
$$371$$ −1.34057e6 + 973977.i −0.505654 + 0.367379i
$$372$$ 868958. 2.75206e6i 0.325568 1.03110i
$$373$$ 1.28174e6i 0.477012i 0.971141 + 0.238506i $$0.0766577\pi$$
−0.971141 + 0.238506i $$0.923342\pi$$
$$374$$ 3.93453e6 + 3.67839e6i 1.45450 + 1.35981i
$$375$$ −13304.1 1.59945e6i −0.00488549 0.587344i
$$376$$ −3.88004e6 1.26070e6i −1.41536 0.459878i
$$377$$ 679950. + 935870.i 0.246390 + 0.339127i
$$378$$ 2.70478e6 3.92516e6i 0.973650 1.41295i
$$379$$ 1.30191e6 + 4.00687e6i 0.465568 + 1.43287i 0.858267 + 0.513204i $$0.171542\pi$$
−0.392699 + 0.919667i $$0.628458\pi$$
$$380$$ 973347. + 2.99566e6i 0.345787 + 1.06422i
$$381$$ 228807. 320499.i 0.0807528 0.113113i
$$382$$ −344015. 473496.i −0.120620 0.166019i
$$383$$ −4.85737e6 1.57825e6i −1.69201 0.549769i −0.704834 0.709373i $$-0.748978\pi$$
−0.987181 + 0.159604i $$0.948978\pi$$
$$384$$ 4.35957e6 36262.6i 1.50874 0.0125496i
$$385$$ −763960. + 422199.i −0.262675 + 0.145166i
$$386$$ 293368.i 0.100218i
$$387$$ 1.52341e6 + 467116.i 0.517058 + 0.158543i
$$388$$ 1.29553e6 941258.i 0.436886 0.317416i
$$389$$ −319117. + 439227.i −0.106924 + 0.147169i −0.859126 0.511765i $$-0.828992\pi$$
0.752201 + 0.658933i $$0.228992\pi$$
$$390$$ 258923. + 774892.i 0.0862004 + 0.257976i
$$391$$ 4.56231e6 1.48239e6i 1.50919 0.490365i
$$392$$ 252933. + 183766.i 0.0831362 + 0.0604020i
$$393$$ −893321. + 660458.i −0.291760 + 0.215707i
$$394$$ 2.22550e6 6.84938e6i 0.722248 2.22285i
$$395$$ −1.46496e6 −0.472425
$$396$$ −6.54056e6 701274.i −2.09593 0.224724i
$$397$$ 5.45539e6 1.73720 0.868600 0.495514i $$-0.165020\pi$$
0.868600 + 0.495514i $$0.165020\pi$$
$$398$$ 1.22864e6 3.78136e6i 0.388792 1.19658i
$$399$$ −4.28494e6 + 3.16798e6i −1.34745 + 0.996208i
$$400$$ −3.12867e6 2.27311e6i −0.977709 0.710347i
$$401$$ 2.81417e6 914381.i 0.873957 0.283966i 0.162511 0.986707i $$-0.448041\pi$$
0.711446 + 0.702741i $$0.248041\pi$$
$$402$$ 1.40693e6 + 4.21059e6i 0.434217 + 1.29950i
$$403$$ −491877. + 677011.i −0.150867 + 0.207651i
$$404$$ −2.42606e6 + 1.76264e6i −0.739517 + 0.537290i
$$405$$ −977922. 282146.i −0.296256 0.0854746i
$$406$$ 4.77444e6i 1.43750i
$$407$$ −15021.7 77808.8i −0.00449503 0.0232832i
$$408$$ 7.41748e6 61698.1i 2.20600 0.0183494i
$$409$$ −181361. 58927.9i −0.0536088 0.0174186i 0.282090 0.959388i $$-0.408972\pi$$
−0.335699 + 0.941969i $$0.608972\pi$$
$$410$$ −1.70091e6 2.34110e6i −0.499714 0.687798i
$$411$$ 2.24400e6 3.14325e6i 0.655267 0.917856i
$$412$$ −1.12633e6 3.46649e6i −0.326906 1.00611i
$$413$$ −1.04057e6 3.20254e6i −0.300190 0.923890i
$$414$$ −4.96027e6 + 7.07169e6i −1.42234 + 2.02779i
$$415$$ 752887. + 1.03626e6i 0.214590 + 0.295358i
$$416$$ 673801. + 218931.i 0.190897 + 0.0620261i
$$417$$ 6215.77 + 747274.i 0.00175047 + 0.210446i
$$418$$ 9.82049e6 + 4.59460e6i 2.74911 + 1.28620i
$$419$$ 5.26693e6i 1.46562i 0.680432 + 0.732811i $$0.261792\pi$$
−0.680432 + 0.732811i $$0.738208\pi$$
$$420$$ −688621. + 2.18092e6i −0.190483 + 0.603276i
$$421$$ 170205. 123661.i 0.0468024 0.0340039i −0.564138 0.825680i $$-0.690791\pi$$
0.610940 + 0.791677i $$0.290791\pi$$
$$422$$ −1.82203e6 + 2.50781e6i −0.498053 + 0.685511i
$$423$$ −2.65185e6 + 910680.i −0.720606 + 0.247466i
$$424$$ 4.41577e6 1.43477e6i 1.19287 0.387586i
$$425$$ 3.07900e6 + 2.23703e6i 0.826871 + 0.600757i
$$426$$ −6.40346e6 8.66119e6i −1.70959 2.31235i
$$427$$ 1.11382e6 3.42799e6i 0.295628 0.909851i
$$428$$ 4.20881e6 1.11058
$$429$$ 1.73432e6 + 793904.i 0.454975 + 0.208269i
$$430$$ −1.12717e6 −0.293980
$$431$$ −1.66690e6 + 5.13019e6i −0.432231 + 1.33027i 0.463666 + 0.886010i $$0.346534\pi$$
−0.895897 + 0.444261i $$0.853466\pi$$
$$432$$ −4.11361e6 + 3.14847e6i −1.06051 + 0.811691i
$$433$$ −588032. 427230.i −0.150723 0.109507i 0.509868 0.860253i $$-0.329694\pi$$
−0.660591 + 0.750746i $$0.729694\pi$$
$$434$$ −3.28480e6 + 1.06730e6i −0.837114 + 0.271995i
$$435$$ 966885. 323076.i 0.244992 0.0818618i
$$436$$ −3.61629e6 + 4.97739e6i −0.911059 + 1.25397i
$$437$$ 7.81213e6 5.67585e6i 1.95689 1.42176i
$$438$$ −4.63887e6 1.46471e6i −1.15538 0.364811i
$$439$$ 3.86167e6i 0.956344i −0.878266 0.478172i $$-0.841300\pi$$
0.878266 0.478172i $$-0.158700\pi$$
$$440$$ 2.40142e6 463616.i 0.591340 0.114163i
$$441$$ 214840. 3574.29i 0.0526039 0.000875172i
$$442$$ −3.89191e6 1.26456e6i −0.947562 0.307881i
$$443$$ 3855.69 + 5306.90i 0.000933454 + 0.00128479i 0.809483 0.587143i $$-0.199747\pi$$
−0.808550 + 0.588427i $$0.799747\pi$$
$$444$$ −168991. 120645.i −0.0406825 0.0290436i
$$445$$ −262152. 806820.i −0.0627556 0.193142i
$$446$$ −3.26309e6 1.00428e7i −0.776769 2.39065i
$$447$$ −2.44886e6 1.74827e6i −0.579689 0.413846i
$$448$$ −1.52703e6 2.10177e6i −0.359461 0.494756i
$$449$$ 2.40360e6 + 780977.i 0.562660 + 0.182819i 0.576518 0.817085i $$-0.304411\pi$$
−0.0138576 + 0.999904i $$0.504411\pi$$
$$450$$ −6.85206e6 + 113998.i −1.59511 + 0.0265378i
$$451$$ −6.70442e6 831868.i −1.55210 0.192581i
$$452$$ 6.94310e6i 1.59848i
$$453$$ −6.25649e6 1.97548e6i −1.43247 0.452300i
$$454$$ −2.41570e6 + 1.75511e6i −0.550050 + 0.399635i
$$455$$ 389797. 536509.i 0.0882694 0.121492i
$$456$$ 1.41619e7 4.73206e6i 3.18940 1.06571i
$$457$$ −1.74901e6 + 568288.i −0.391744 + 0.127285i −0.498264 0.867025i $$-0.666029\pi$$
0.106520 + 0.994311i $$0.466029\pi$$
$$458$$ 3.95342e6 + 2.87233e6i 0.880662 + 0.639839i
$$459$$ 4.04831e6 3.09849e6i 0.896895 0.686465i
$$460$$ 1.28066e6 3.94148e6i 0.282189 0.868490i
$$461$$ −4.02082e6 −0.881176 −0.440588 0.897709i $$-0.645230\pi$$
−0.440588 + 0.897709i $$0.645230\pi$$
$$462$$ 3.86501e6 + 6.85828e6i 0.842452 + 1.49489i
$$463$$ −1.13351e6 −0.245739 −0.122869 0.992423i $$-0.539210\pi$$
−0.122869 + 0.992423i $$0.539210\pi$$
$$464$$ 1.60333e6 4.93454e6i 0.345722 1.06402i
$$465$$ 438416. + 592993.i 0.0940274 + 0.127179i
$$466$$ 7.13609e6 + 5.18467e6i 1.52228 + 1.10600i
$$467$$ −166459. + 54085.8i −0.0353196 + 0.0114760i −0.326623 0.945155i $$-0.605911\pi$$
0.291304 + 0.956631i $$0.405911\pi$$
$$468$$ 4.72676e6 1.62323e6i 0.997583 0.342583i
$$469$$ 2.11807e6 2.91527e6i 0.444640 0.611994i
$$470$$ 1.60463e6 1.16583e6i 0.335065 0.243439i
$$471$$ 10898.4 34516.2i 0.00226366 0.00716920i
$$472$$ 9.43537e6i 1.94941i
$$473$$ −1.79713e6 + 1.92228e6i −0.369341 + 0.395060i
$$474$$ 109897. + 1.32121e7i 0.0224668 + 2.70100i
$$475$$ 7.28605e6 + 2.36738e6i 1.48169 + 0.481431i
$$476$$ −6.73327e6 9.26755e6i −1.36210 1.87477i
$$477$$ 1.83242e6 2.61242e6i 0.368748 0.525711i
$$478$$ −2.32228e6 7.14724e6i −0.464884 1.43077i
$$479$$ −2.90160e6 8.93020e6i −0.577828 1.77837i −0.626342 0.779549i $$-0.715448\pi$$
0.0485138 0.998823i $$-0.484552\pi$$
$$480$$ 362768. 508142.i 0.0718664 0.100666i
$$481$$ 35389.0 + 48708.8i 0.00697438 + 0.00959941i
$$482$$ 4.81643e6 + 1.56495e6i 0.944294 + 0.306820i
$$483$$ 7.01111e6 58318.0i 1.36747 0.0113746i
$$484$$ 5.78026e6 9.19813e6i 1.12159 1.78479i
$$485$$ 409200.i 0.0789916i
$$486$$ −2.47124e6 + 8.84078e6i −0.474596 + 1.69785i
$$487$$ −4.70612e6 + 3.41920e6i −0.899168 + 0.653284i −0.938252 0.345952i $$-0.887556\pi$$
0.0390839 + 0.999236i $$0.487556\pi$$
$$488$$ −5.93639e6 + 8.17074e6i −1.12842 + 1.55314i
$$489$$ 268298. + 802949.i 0.0507394 + 0.151850i
$$490$$ −144557. + 46969.6i −0.0271988 + 0.00883743i
$$491$$ 6.61631e6 + 4.80703e6i 1.23855 + 0.899857i 0.997501 0.0706573i $$-0.0225097\pi$$
0.241046 + 0.970514i $$0.422510\pi$$
$$492$$ −1.42337e7 + 1.05234e7i −2.65098 + 1.95994i
$$493$$ −1.57788e6 + 4.85620e6i −0.292385 + 0.899870i
$$494$$ −8.23740e6 −1.51870
$$495$$ 1.12735e6 1.24680e6i 0.206798 0.228709i
$$496$$ 3.75336e6 0.685040
$$497$$ −2.70175e6 + 8.31512e6i −0.490629 + 1.51000i
$$498$$ 9.28928e6 6.86783e6i 1.67845 1.24093i
$$499$$ −7.35641e6 5.34475e6i −1.32256 0.960894i −0.999897 0.0143798i $$-0.995423\pi$$
−0.322661 0.946515i $$-0.604577\pi$$
$$500$$ 6.58261e6 2.13882e6i 1.17753 0.382603i
$$501$$ −444135. 1.32919e6i −0.0790535 0.236587i
$$502$$ −8.84872e6 + 1.21792e7i −1.56719 + 2.15705i
$$503$$ −3.47085e6 + 2.52172e6i −0.611668 + 0.444403i −0.850001 0.526781i $$-0.823399\pi$$
0.238333 + 0.971183i $$0.423399\pi$$
$$504$$ 1.03653e7 + 3.17827e6i 1.81763 + 0.557332i
$$505$$ 766283.i 0.133709i
$$506$$ −6.90009e6 1.24856e7i −1.19806 2.16786i
$$507$$ 4.33858e6 36088.0i 0.749596 0.00623509i
$$508$$ 1.62061e6 + 526569.i 0.278625 + 0.0905307i
$$509$$ −2.13272e6 2.93544e6i −0.364871 0.502202i 0.586627 0.809858i $$-0.300456\pi$$
−0.951498 + 0.307655i $$0.900456\pi$$
$$510$$ −2.09537e6 + 2.93506e6i −0.356726 + 0.499680i
$$511$$ 1.22018e6 + 3.75534e6i 0.206715 + 0.636205i
$$512$$ 3.79940e6 + 1.16933e7i 0.640530 + 1.97135i
$$513$$ 5.82283e6 8.45004e6i 0.976878 1.41764i
$$514$$ 6.20879e6 + 8.54567e6i 1.03657 + 1.42672i
$$515$$ 885798. + 287813.i 0.147169 + 0.0478181i
$$516$$ 57350.3 + 6.89478e6i 0.00948225 + 1.13998i
$$517$$ 570175. 4.59531e6i 0.0938170 0.756115i
$$518$$ 248493.i 0.0406902i
$$519$$ 2.16983e6 6.87202e6i 0.353596 1.11987i
$$520$$ −1.50331e6 + 1.09222e6i −0.243803 + 0.177133i
$$521$$ 5.54908e6 7.63765e6i 0.895626 1.23272i −0.0762168 0.997091i $$-0.524284\pi$$
0.971842 0.235632i $$-0.0757159\pi$$
$$522$$ −2.98627e6 8.69584e6i −0.479681 1.39680i
$$523$$ −470165. + 152766.i −0.0751616 + 0.0244215i −0.346356 0.938103i $$-0.612581\pi$$
0.271195 + 0.962524i $$0.412581\pi$$
$$524$$ −3.88921e6 2.82567e6i −0.618775 0.449567i
$$525$$ 3.30692e6 + 4.47287e6i 0.523631 + 0.708252i
$$526$$ 911733. 2.80603e6i 0.143682 0.442209i
$$527$$ −3.69378e6 −0.579354
$$528$$ −1.69150e6 8.38618e6i −0.264050 1.30912i
$$529$$ −6.26880e6 −0.973969
$$530$$ −697540. + 2.14681e6i −0.107865 + 0.331973i
$$531$$ 3.89832e6 + 5.18205e6i 0.599986 + 0.797564i
$$532$$ −1.86551e7 1.35537e7i −2.85772 2.07625i
$$533$$ 4.88157e6 1.58612e6i 0.744289 0.241834i
$$534$$ −7.25683e6 + 2.42480e6i −1.10127 + 0.367979i
$$535$$ −632154. + 870085.i −0.0954857 + 0.131425i
$$536$$ −8.16863e6 + 5.93486e6i −1.22811 + 0.892274i
$$537$$ −1.05299e7 3.32480e6i −1.57576 0.497543i
$$538$$ 1.20969e7i 1.80184i
$$539$$ −150377. + 321416.i −0.0222952 + 0.0476536i
$$540$$ −109889. 4.40289e6i −0.0162170 0.649760i
$$541$$ −1.01079e7 3.28427e6i −1.48481 0.482442i −0.549261 0.835651i $$-0.685091\pi$$
−0.935545 + 0.353209i $$0.885091\pi$$
$$542$$ 8.99008e6 + 1.23738e7i 1.31451 + 1.80927i
$$543$$ −891471. 636431.i −0.129750 0.0926300i
$$544$$ 966363. + 2.97416e6i 0.140005 + 0.430890i
$$545$$ −485816. 1.49519e6i −0.0700617 0.215628i
$$546$$ −4.86788e6 3.47523e6i −0.698808 0.498886i
$$547$$ 2.86887e6 + 3.94866e6i 0.409961 + 0.564263i 0.963209 0.268754i $$-0.0866118\pi$$
−0.553248 + 0.833017i $$0.686612\pi$$
$$548$$ 1.58940e7 + 5.16426e6i 2.26090 + 0.734610i
$$549$$ 115464. + 6.94017e6i 0.0163499 + 0.982742i
$$550$$ 4.79611e6 1.02512e7i 0.676056 1.44500i
$$551$$ 1.02784e7i 1.44226i
$$552$$ −1.87342e7 5.91530e6i −2.61691 0.826284i
$$553$$ 8.67637e6 6.30375e6i 1.20649 0.876569i
$$554$$ 2.70537e6 3.72362e6i 0.374500 0.515455i
$$555$$ 50323.0 16815.0i 0.00693480 0.00231720i
$$556$$ −3.07544e6 + 999271.i −0.421910 + 0.137087i
$$557$$ −17976.1 13060.4i −0.00245503 0.00178369i 0.586557 0.809908i $$-0.300483\pi$$
−0.589012 + 0.808124i $$0.700483\pi$$
$$558$$ 5.31515e6 3.99844e6i 0.722654 0.543633i
$$559$$ 617820. 1.90145e6i 0.0836243 0.257369i
$$560$$ −2.97442e6 −0.400804
$$561$$ 1.66465e6 + 8.25305e6i 0.223313 + 1.10715i
$$562$$ −104040. −0.0138950
$$563$$ −3.41570e6 + 1.05124e7i −0.454159 + 1.39776i 0.417960 + 0.908465i $$0.362745\pi$$
−0.872119 + 0.489293i $$0.837255\pi$$
$$564$$ −7.21290e6 9.75602e6i −0.954799 1.29144i
$$565$$ 1.43535e6 + 1.04284e6i 0.189163 + 0.137435i
$$566$$ 7.58859e6 2.46568e6i 0.995680 0.323516i
$$567$$ 7.00592e6 2.53698e6i 0.915183 0.331405i
$$568$$ 1.43996e7 1.98194e7i 1.87275 2.57762i
$$569$$ 293279. 213080.i 0.0379752 0.0275906i −0.568636 0.822589i $$-0.692529\pi$$
0.606611 + 0.794999i $$0.292529\pi$$
$$570$$ −2.18573e6 + 6.92237e6i −0.281779 + 0.892416i
$$571$$ 3.49015e6i 0.447975i −0.974592 0.223987i $$-0.928093\pi$$
0.974592 0.223987i $$-0.0719074\pi$$
$$572$$ −1.01630e6 + 8.19086e6i −0.129877 + 1.04674i
$$573$$ −7609.40 914818.i −0.000968197 0.116399i
$$574$$ 2.01476e7 + 6.54636e6i 2.55237 + 0.829316i
$$575$$ −5.92478e6 8.15475e6i −0.747313 1.02859i
$$576$$ 4.09582e6 + 2.87292e6i 0.514381 + 0.360801i
$$577$$ 4.06324e6 + 1.25054e7i 0.508081 + 1.56371i 0.795528 + 0.605916i $$0.207193\pi$$
−0.287447 + 0.957796i $$0.592807\pi$$
$$578$$ −1.20616e6 3.71218e6i −0.150171 0.462178i
$$579$$ −266445. + 373219.i −0.0330302 + 0.0462666i
$$580$$ 2.59289e6 + 3.56880e6i 0.320047 + 0.440507i
$$581$$ −8.91811e6 2.89767e6i −1.09605 0.356130i
$$582$$ 3.69046e6 30697.0i 0.451620 0.00375655i
$$583$$ 2.54903e6 + 4.61241e6i 0.310601 + 0.562026i
$$584$$ 1.10640e7i 1.34240i
$$585$$ −374380. + 1.22097e6i −0.0452296 + 0.147508i
$$586$$ −9.08144e6 + 6.59805e6i −1.09247 + 0.793728i
$$587$$ 1.68134e6 2.31417e6i 0.201401 0.277204i −0.696355 0.717697i $$-0.745196\pi$$
0.897756 + 0.440493i $$0.145196\pi$$
$$588$$ 294663. + 881854.i 0.0351465 + 0.105185i
$$589$$ −7.07148e6 + 2.29766e6i −0.839890 + 0.272897i
$$590$$ −3.71110e6 2.69627e6i −0.438908 0.318885i
$$591$$ 9.05204e6 6.69243e6i 1.06605 0.788161i
$$592$$ 83447.7 256825.i 0.00978611 0.0301185i
$$593$$ 5.67693e6 0.662944 0.331472 0.943465i $$-0.392455\pi$$
0.331472 + 0.943465i $$0.392455\pi$$
$$594$$ −1.13291e7 1.00738e7i −1.31744 1.17145i
$$595$$ 2.92720e6 0.338969
$$596$$ 4.02339e6 1.23827e7i 0.463956 1.42791i
$$597$$ 4.99740e6 3.69472e6i 0.573863 0.424273i
$$598$$ 8.76830e6 + 6.37054e6i 1.00268 + 0.728490i
$$599$$ 2.59919e6 844527.i 0.295985 0.0961715i −0.157260 0.987557i $$-0.550266\pi$$
0.453245 + 0.891386i $$0.350266\pi$$
$$600$$ −4.93959e6 1.47830e7i −0.560161 1.67642i
$$601$$ 2.23979e6 3.08280e6i 0.252942 0.348144i −0.663597 0.748090i $$-0.730971\pi$$
0.916539 + 0.399946i $$0.130971\pi$$
$$602$$ 6.67577e6 4.85023e6i 0.750776 0.545471i
$$603$$ −2.03429e6 + 6.63447e6i −0.227835 + 0.743041i
$$604$$ 2.83905e7i 3.16651i
$$605$$ 1.03334e6 + 2.57649e6i 0.114777 + 0.286181i
$$606$$ −6.91090e6 + 57484.4i −0.764457 + 0.00635870i
$$607$$ 6.88566e6 + 2.23729e6i 0.758532 + 0.246462i 0.662648 0.748931i $$-0.269432\pi$$
0.0958835 + 0.995393i $$0.469432\pi$$
$$608$$ 3.70007e6 + 5.09271e6i 0.405930 + 0.558714i
$$609$$ −4.33628e6 + 6.07398e6i −0.473777 + 0.663636i
$$610$$ −1.51730e6 4.66978e6i −0.165100 0.508126i
$$611$$ 1.08715e6 + 3.34590e6i 0.117811 + 0.362585i
$$612$$ 1.80601e7 + 1.26678e7i 1.94913 + 1.36717i
$$613$$ 974039. + 1.34065e6i 0.104695 + 0.144100i 0.858150 0.513400i $$-0.171614\pi$$
−0.753455 + 0.657500i $$0.771614\pi$$
$$614$$ −1.81666e7 5.90268e6i −1.94470 0.631871i
$$615$$ −37623.1 4.52313e6i −0.00401113 0.482227i
$$616$$ −1.22277e7 + 1.30792e7i −1.29836 + 1.38877i
$$617$$ 9.19781e6i 0.972684i 0.873769 + 0.486342i $$0.161669\pi$$
−0.873769 + 0.486342i $$0.838331\pi$$
$$618$$ 2.52926e6 8.01037e6i 0.266393 0.843687i
$$619$$ −1.08437e7 + 7.87838e6i −1.13749 + 0.826438i −0.986768 0.162137i $$-0.948161\pi$$
−0.150727 + 0.988575i $$0.548161\pi$$
$$620$$ −1.87570e6 + 2.58168e6i −0.195968 + 0.269726i
$$621$$ −1.27331e7 + 4.49145e6i −1.32497 + 0.467367i
$$622$$ 2.28150e7 7.41303e6i 2.36453 0.768281i
$$623$$ 5.02438e6 + 3.65043e6i 0.518636 + 0.376811i
$$624$$ 3.86407e6 + 5.22647e6i 0.397268 + 0.537337i
$$625$$ 2.18430e6 6.72259e6i 0.223672 0.688393i
$$626$$ 1.38011e7 1.40760
$$627$$ 8.32055e6 + 1.47644e7i 0.845246 + 1.49985i
$$628$$ 156626. 0.0158477
$$629$$ −82123.0 + 252748.i −0.00827633 + 0.0254719i
$$630$$ −4.21209e6 + 3.16864e6i −0.422811 + 0.318069i
$$631$$ −7.64910e6 5.55740e6i −0.764781 0.555646i 0.135592 0.990765i $$-0.456706\pi$$
−0.900373 + 0.435119i $$0.856706\pi$$
$$632$$ −2.85796e7 + 9.28609e6i −2.84619 + 0.924784i
$$633$$ −4.59563e6 + 1.53559e6i −0.455865 + 0.152323i
$$634$$ −1.69457e7 + 2.33237e7i −1.67431 + 2.30449i
$$635$$ −352270. + 255939.i −0.0346690 + 0.0251885i
$$636$$ 1.31673e7 + 4.15755e6i 1.29078 + 0.407563i
$$637$$ 269603.i 0.0263255i
$$638$$ 1.50688e7 + 1.86970e6i 1.46563 + 0.181853i
$$639$$ −280075. 1.68345e7i −0.0271345 1.63097i
$$640$$ −4.58475e6 1.48968e6i −0.442452 0.143761i
$$641$$ −2.12492e6 2.92471e6i −0.204267 0.281149i 0.694577 0.719419i $$-0.255592\pi$$
−0.898844 + 0.438269i $$0.855592\pi$$
$$642$$ 7.89449e6 + 5.63595e6i 0.755938 + 0.539672i
$$643$$ −1.80649e6 5.55980e6i −0.172309 0.530313i 0.827191 0.561920i $$-0.189937\pi$$
−0.999500 + 0.0316078i $$0.989937\pi$$
$$644$$ 9.37541e6 + 2.88546e7i 0.890791 + 2.74157i
$$645$$ −1.43397e6 1.02373e6i −0.135719 0.0968911i
$$646$$ −2.13718e7 2.94158e7i −2.01493 2.77331i
$$647$$ −1.62291e7 5.27315e6i −1.52417 0.495232i −0.577212 0.816594i $$-0.695859\pi$$
−0.946957 + 0.321362i $$0.895859\pi$$
$$648$$ −2.08666e7 + 694508.i −1.95215 + 0.0649740i
$$649$$ −1.05151e7 + 2.03004e6i −0.979949 + 0.189188i
$$650$$ 8.59867e6i 0.798267i
$$651$$ −5.14823e6 1.62554e6i −0.476108 0.150330i
$$652$$ −2.96371e6 + 2.15326e6i −0.273034 + 0.198371i
$$653$$ −4.36095e6 + 6.00233e6i −0.400219 + 0.550854i −0.960799 0.277246i $$-0.910578\pi$$
0.560580 + 0.828100i $$0.310578\pi$$
$$654$$ −1.34483e7 + 4.49361e6i −1.22948 + 0.410819i
$$655$$ 1.16830e6 379604.i 0.106402 0.0345723i
$$656$$ −1.86249e7 1.35318e7i −1.68979 1.22771i
$$657$$ −4.57121e6 6.07653e6i −0.413160 0.549215i
$$658$$ −4.48697e6 + 1.38095e7i −0.404007 + 1.24341i
$$659$$ 3.07316e6 0.275659 0.137829 0.990456i $$-0.455987\pi$$
0.137829 + 0.990456i $$0.455987\pi$$
$$660$$ 6.61359e6 + 3.02744e6i 0.590986 + 0.270530i
$$661$$ 1.62900e7 1.45017 0.725084 0.688660i $$-0.241801\pi$$
0.725084 + 0.688660i $$0.241801\pi$$
$$662$$ 3.33180e6 1.02542e7i 0.295484 0.909406i
$$663$$ −3.80273e6 5.14350e6i −0.335979 0.454438i
$$664$$ 2.12566e7 + 1.54438e7i 1.87100 + 1.35936i
$$665$$ 5.60392e6 1.82082e6i 0.491403 0.159667i
$$666$$ −155425. 452588.i −0.0135780 0.0395383i
$$667$$ 7.94896e6 1.09408e7i 0.691824 0.952214i
$$668$$ 4.90607e6 3.56447e6i 0.425395 0.309068i
$$669$$ 4.96984e6 1.57399e7i 0.429316 1.35968i
$$670$$ 4.90883e6i 0.422465i
$$671$$ −1.03830e7 4.85779e6i −0.890260 0.416516i
$$672$$ 38017.3 + 4.57053e6i 0.00324757 + 0.390430i
$$673$$ −1.72302e7 5.59843e6i −1.46640 0.476462i −0.536382 0.843976i $$-0.680209\pi$$
−0.930018 + 0.367513i $$0.880209\pi$$
$$674$$ 2.11614e7 + 2.91262e7i 1.79430 + 2.46964i
$$675$$ −8.82064e6 6.07820e6i −0.745145 0.513471i
$$676$$ 5.80164e6 + 1.78556e7i 0.488297 + 1.50282i
$$677$$ −913131. 2.81033e6i −0.0765704 0.235660i 0.905444 0.424466i $$-0.139538\pi$$
−0.982014 + 0.188806i $$0.939538\pi$$
$$678$$ 9.29742e6 1.30232e7i 0.776762 1.08804i
$$679$$ −1.76080e6 2.42353e6i −0.146566 0.201731i
$$680$$ −7.80061e6 2.53457e6i −0.646929 0.210200i
$$681$$ −4.66725e6 + 38821.9i −0.385650 + 0.00320781i
$$682$$ 2.08218e6 + 1.07852e7i 0.171418 + 0.887908i
$$683$$ 6.38682e6i 0.523881i −0.965084 0.261940i $$-0.915638\pi$$
0.965084 0.261940i $$-0.0843624\pi$$
$$684$$ 4.24546e7 + 1.30177e7i 3.46964 + 1.06388i
$$685$$ −3.45484e6 + 2.51009e6i −0.281321 + 0.204392i
$$686$$ 1.30857e7 1.80110e7i 1.06166 1.46126i
$$687$$ 2.42076e6 + 7.24474e6i 0.195686 + 0.585641i
$$688$$ −8.52841e6 + 2.77105e6i −0.686905 + 0.223189i
$$689$$ −3.23918e6 2.35340e6i −0.259948 0.188863i
$$690$$ 7.68013e6 5.67814e6i 0.614110 0.454029i
$$691$$ 789562. 2.43002e6i 0.0629059 0.193604i −0.914664 0.404214i $$-0.867545\pi$$
0.977570 + 0.210610i $$0.0675450\pi$$
$$692$$ 3.11836e7 2.47549
$$693$$ −1.31186e6 + 1.22353e7i −0.103766 + 0.967792i
$$694$$ −3.90135e6 −0.307480
$$695$$ 255346. 785873.i 0.0200524 0.0617149i
$$696$$ 1.68149e7 1.24317e7i 1.31574 0.972766i
$$697$$ 1.83292e7 + 1.33169e7i 1.42910 + 1.03830i
$$698$$ −6.98391e6 + 2.26921e6i −0.542575 + 0.176293i
$$699$$ 4.36958e6 + 1.30771e7i 0.338257 + 1.01232i
$$700$$ −1.41482e7 + 1.94733e7i −1.09133 + 1.50208i
$$701$$ −1.37433e7 + 9.98508e6i −1.05632 + 0.767462i −0.973404 0.229095i $$-0.926423\pi$$
−0.0829161 + 0.996557i $$0.526423\pi$$
$$702$$ 1.10397e7 + 3.28484e6i 0.845500 + 0.251577i
$$703$$ 534953.i 0.0408251i
$$704$$ −7.23146e6 + 3.99643e6i −0.549914 + 0.303907i
$$705$$ 3.10022e6 25787.4i 0.234920 0.00195405i
$$706$$ −4.32982e6 1.40684e6i −0.326932 0.106227i
$$707$$ 3.29733e6 + 4.53839e6i 0.248093 + 0.341470i
$$708$$ −1.63040e7 + 2.28376e7i −1.22240 + 1.71225i
$$709$$ −843988. 2.59753e6i −0.0630552 0.194064i 0.914566 0.404436i $$-0.132532\pi$$
−0.977621 + 0.210373i $$0.932532\pi$$
$$710$$ 3.68045e6 + 1.13273e7i 0.274003 + 0.843294i
$$711$$ −1.18597e7 + 1.69080e7i −0.879835 + 1.25435i
$$712$$ −1.02285e7 1.40784e7i −0.756161 1.04077i
$$713$$ 9.30418e6 + 3.02311e6i 0.685416 + 0.222705i
$$714$$ −219590. 2.63996e7i −0.0161201 1.93799i
$$715$$ −1.54065e6 1.44035e6i −0.112704 0.105367i
$$716$$ 4.77823e7i 3.48325i
$$717$$ 3.53694e6 1.12018e7i 0.256939 0.813746i
$$718$$ 2.71674e7 1.97383e7i 1.96670 1.42889i
$$719$$ 9.12920e6 1.25653e7i 0.658583 0.906462i −0.340851 0.940117i $$-0.610715\pi$$
0.999433 + 0.0336559i $$0.0107150\pi$$
$$720$$ 5.41740e6 1.86041e6i 0.389457 0.133745i
$$721$$ −6.48470e6 + 2.10701e6i −0.464570 + 0.150948i
$$722$$ −3.92352e7 2.85061e7i −2.80113 2.03514i
$$723$$ 4.70606e6 + 6.36532e6i 0.334820 + 0.452871i
$$724$$ 1.46466e6 4.50776e6i 0.103846 0.319605i
$$725$$ 1.07291e7 0.758089
$$726$$ 2.31592e7 9.51273e6i 1.63073 0.669828i
$$727$$ −1.42022e7 −0.996594 −0.498297 0.867006i $$-0.666041\pi$$
−0.498297 + 0.867006i $$0.666041\pi$$
$$728$$ 4.20366e6 1.29375e7i 0.293967 0.904738i
$$729$$ −1.11733e7 + 9.00267e6i −0.778688 + 0.627412i
$$730$$ 4.35168e6 + 3.16168e6i 0.302239 + 0.219589i
$$731$$ 8.39302e6 2.72706e6i 0.580932 0.188756i
$$732$$ −2.84874e7 + 9.51879e6i −1.96505 + 0.656605i
$$733$$ 3.15560e6 4.34331e6i 0.216931 0.298580i −0.686658 0.726981i $$-0.740923\pi$$
0.903589 + 0.428401i $$0.140923\pi$$
$$734$$ −1.27391e7 + 9.25550e6i −0.872768 + 0.634103i
$$735$$ −226563. 71536.9i −0.0154693 0.00488441i
$$736$$ 8.28244e6i 0.563591i
$$737$$ −8.37153e6 7.82654e6i −0.567723 0.530763i
$$738$$ −4.07901e7 + 678625.i −2.75685 + 0.0458658i
$$739$$ 2.07203e7 + 6.73245e6i 1.39568 + 0.453484i 0.907791 0.419422i $$-0.137767\pi$$
0.487888 + 0.872906i $$0.337767\pi$$
$$740$$ 134951. + 185744.i 0.00905933 + 0.0124691i
$$741$$ −1.04795e7 7.48143e6i −0.701125 0.500540i
$$742$$ −5.10651e6 1.57162e7i −0.340498 1.04794i
$$743$$ 1.30647e6 + 4.02089e6i 0.0868213 + 0.267208i 0.985036 0.172348i $$-0.0551355\pi$$
−0.898215 + 0.439557i $$0.855135\pi$$
$$744$$ 1.23119e7 + 8.78956e6i 0.815439 + 0.582150i
$$745$$ 1.95557e6 + 2.69162e6i 0.129087 + 0.177673i
$$746$$ −1.21568e7 3.94998e6i −0.799783 0.259865i
$$747$$ 1.80552e7 300385.i 1.18386 0.0196960i
$$748$$ −3.18864e7 + 1.76218e7i −2.08378 + 1.15159i
$$749$$ 7.87334e6i 0.512808i
$$750$$ 1.52111e7 + 4.80288e6i 0.987433 + 0.311780i
$$751$$ 1.82426e7 1.32540e7i 1.18028 0.857526i 0.188079 0.982154i $$-0.439774\pi$$
0.992204 + 0.124628i $$0.0397737\pi$$
$$752$$ 9.27486e6 1.27658e7i 0.598085 0.823193i
$$753$$ −2.23187e7 + 7.45760e6i −1.43444 + 0.479304i
$$754$$ −1.09718e7 + 3.56494e6i −0.702826 + 0.228362i
$$755$$ 5.86916e6 + 4.26420e6i 0.374722 + 0.272251i
$$756$$ 1.95965e7 + 2.56037e7i 1.24702 + 1.62929i
$$757$$ −6.22088e6 + 1.91459e7i −0.394559 + 1.21433i 0.534746 + 0.845013i $$0.320407\pi$$
−0.929305 + 0.369314i $$0.879593\pi$$
$$758$$ −4.20156e7 −2.65606
$$759$$ 2.56153e6 2.21508e7i 0.161397 1.39568i
$$760$$ −1.65103e7 −1.03686
$$761$$ 1.90484e6 5.86249e6i 0.119233 0.366962i −0.873573 0.486693i $$-0.838203\pi$$
0.992806 + 0.119731i $$0.0382032\pi$$