# Properties

 Label 18.7.d.a.11.6 Level $18$ Weight $7$ Character 18.11 Analytic conductor $4.141$ Analytic rank $0$ Dimension $12$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,7,Mod(5,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$18 = 2 \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 18.d (of order $$6$$, 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: $$4.14097350516$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600$$ x^12 + 370*x^10 + 51793*x^8 + 3491832*x^6 + 117603792*x^4 + 1832032512*x^2 + 10453017600 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{10}\cdot 3^{10}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 11.6 Root $$3.87527i$$ of defining polynomial Character $$\chi$$ $$=$$ 18.11 Dual form 18.7.d.a.5.6

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(4.89898 + 2.82843i) q^{2} +(25.6485 + 8.43532i) q^{3} +(16.0000 + 27.7128i) q^{4} +(1.59771 - 0.922438i) q^{5} +(101.793 + 113.869i) q^{6} +(6.34411 - 10.9883i) q^{7} +181.019i q^{8} +(586.691 + 432.707i) q^{9} +O(q^{10})$$ $$q+(4.89898 + 2.82843i) q^{2} +(25.6485 + 8.43532i) q^{3} +(16.0000 + 27.7128i) q^{4} +(1.59771 - 0.922438i) q^{5} +(101.793 + 113.869i) q^{6} +(6.34411 - 10.9883i) q^{7} +181.019i q^{8} +(586.691 + 432.707i) q^{9} +10.4362 q^{10} +(-49.8080 - 28.7567i) q^{11} +(176.609 + 845.757i) q^{12} +(-1411.17 - 2444.23i) q^{13} +(62.1593 - 35.8877i) q^{14} +(48.7599 - 10.1820i) q^{15} +(-512.000 + 886.810i) q^{16} -7221.17i q^{17} +(1650.31 + 3779.23i) q^{18} -10648.3 q^{19} +(51.1267 + 29.5180i) q^{20} +(255.407 - 228.319i) q^{21} +(-162.672 - 281.757i) q^{22} +(11573.9 - 6682.21i) q^{23} +(-1526.96 + 4642.87i) q^{24} +(-7810.80 + 13528.7i) q^{25} -15965.6i q^{26} +(11397.7 + 16047.2i) q^{27} +406.023 q^{28} +(30795.1 + 17779.6i) q^{29} +(267.673 + 88.0326i) q^{30} +(8657.84 + 14995.8i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(-1034.93 - 1157.71i) q^{33} +(20424.5 - 35376.3i) q^{34} -23.4082i q^{35} +(-2604.46 + 23182.2i) q^{36} -60441.2 q^{37} +(-52166.0 - 30118.0i) q^{38} +(-15576.7 - 74594.4i) q^{39} +(166.979 + 289.216i) q^{40} +(-75436.3 + 43553.2i) q^{41} +(1897.02 - 396.132i) q^{42} +(37932.2 - 65700.4i) q^{43} -1840.43i q^{44} +(1336.51 + 150.153i) q^{45} +75600.6 q^{46} +(61896.5 + 35736.0i) q^{47} +(-20612.6 + 18426.5i) q^{48} +(58744.0 + 101748. i) q^{49} +(-76529.9 + 44184.5i) q^{50} +(60912.8 - 185212. i) q^{51} +(45157.6 - 78215.2i) q^{52} +147761. i q^{53} +(10448.9 + 110853. i) q^{54} -106.105 q^{55} +(1989.10 + 1148.41i) q^{56} +(-273114. - 89822.1i) q^{57} +(100576. + 174203. i) q^{58} +(100224. - 57864.1i) q^{59} +(1062.33 + 1188.36i) q^{60} +(20138.6 - 34881.1i) q^{61} +97952.2i q^{62} +(8476.74 - 3701.61i) q^{63} -32768.0 q^{64} +(-4509.29 - 2603.44i) q^{65} +(-1795.59 - 8598.83i) q^{66} +(90883.7 + 157415. i) q^{67} +(200119. - 115539. i) q^{68} +(353221. - 73758.9i) q^{69} +(66.2083 - 114.676i) q^{70} -301066. i q^{71} +(-78328.3 + 106202. i) q^{72} -612635. q^{73} +(-296100. - 170954. i) q^{74} +(-314454. + 281104. i) q^{75} +(-170373. - 295095. i) q^{76} +(-631.975 + 364.871i) q^{77} +(134675. - 409494. i) q^{78} +(171651. - 297308. i) q^{79} +1889.15i q^{80} +(156971. + 507730. i) q^{81} -492748. q^{82} +(-131581. - 75968.6i) q^{83} +(10413.9 + 3424.93i) q^{84} +(-6661.07 - 11537.3i) q^{85} +(371658. - 214577. i) q^{86} +(639872. + 715786. i) q^{87} +(5205.52 - 9016.22i) q^{88} -102435. i q^{89} +(6122.82 + 4515.81i) q^{90} -35810.6 q^{91} +(370366. + 213831. i) q^{92} +(95566.0 + 457652. i) q^{93} +(202153. + 350140. i) q^{94} +(-17012.9 + 9822.43i) q^{95} +(-153098. + 31969.7i) q^{96} +(247882. - 429345. i) q^{97} +664613. i q^{98} +(-16778.7 - 38423.5i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9}+O(q^{10})$$ 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9 $$12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9} + 378 q^{11} + 384 q^{12} + 1680 q^{13} - 4752 q^{14} - 10872 q^{15} - 6144 q^{16} - 2976 q^{18} - 2820 q^{19} + 13824 q^{20} + 24876 q^{21} - 3600 q^{22} - 76248 q^{23} - 6144 q^{24} + 8094 q^{25} + 127008 q^{27} + 15360 q^{28} + 97092 q^{29} + 34272 q^{30} + 21480 q^{31} - 246258 q^{33} - 27360 q^{34} + 38208 q^{36} - 25536 q^{37} + 97632 q^{38} + 42204 q^{39} - 410562 q^{41} - 222144 q^{42} + 71430 q^{43} + 13716 q^{45} - 135072 q^{46} + 347652 q^{47} + 55296 q^{48} - 135954 q^{49} + 311040 q^{50} + 336402 q^{51} - 53760 q^{52} - 173520 q^{54} + 580392 q^{55} - 152064 q^{56} - 522282 q^{57} + 159264 q^{58} + 369738 q^{59} - 170496 q^{60} + 135744 q^{61} - 103800 q^{63} - 393216 q^{64} - 753840 q^{65} + 909216 q^{66} - 289938 q^{67} + 744768 q^{68} + 2059272 q^{69} + 155952 q^{70} - 374784 q^{72} - 977700 q^{73} - 2197152 q^{74} - 2115342 q^{75} - 45120 q^{76} - 159192 q^{77} - 631488 q^{78} - 764796 q^{79} - 1428282 q^{81} + 1073088 q^{82} + 396900 q^{83} + 1441536 q^{84} + 1619568 q^{85} + 3264624 q^{86} + 3072636 q^{87} + 115200 q^{88} - 1987200 q^{90} + 355584 q^{91} - 2439936 q^{92} - 2526576 q^{93} - 736848 q^{94} - 2089260 q^{95} - 49152 q^{96} - 38874 q^{97} + 4398804 q^{99}+O(q^{100})$$ 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9 + 378 * q^11 + 384 * q^12 + 1680 * q^13 - 4752 * q^14 - 10872 * q^15 - 6144 * q^16 - 2976 * q^18 - 2820 * q^19 + 13824 * q^20 + 24876 * q^21 - 3600 * q^22 - 76248 * q^23 - 6144 * q^24 + 8094 * q^25 + 127008 * q^27 + 15360 * q^28 + 97092 * q^29 + 34272 * q^30 + 21480 * q^31 - 246258 * q^33 - 27360 * q^34 + 38208 * q^36 - 25536 * q^37 + 97632 * q^38 + 42204 * q^39 - 410562 * q^41 - 222144 * q^42 + 71430 * q^43 + 13716 * q^45 - 135072 * q^46 + 347652 * q^47 + 55296 * q^48 - 135954 * q^49 + 311040 * q^50 + 336402 * q^51 - 53760 * q^52 - 173520 * q^54 + 580392 * q^55 - 152064 * q^56 - 522282 * q^57 + 159264 * q^58 + 369738 * q^59 - 170496 * q^60 + 135744 * q^61 - 103800 * q^63 - 393216 * q^64 - 753840 * q^65 + 909216 * q^66 - 289938 * q^67 + 744768 * q^68 + 2059272 * q^69 + 155952 * q^70 - 374784 * q^72 - 977700 * q^73 - 2197152 * q^74 - 2115342 * q^75 - 45120 * q^76 - 159192 * q^77 - 631488 * q^78 - 764796 * q^79 - 1428282 * q^81 + 1073088 * q^82 + 396900 * q^83 + 1441536 * q^84 + 1619568 * q^85 + 3264624 * q^86 + 3072636 * q^87 + 115200 * q^88 - 1987200 * q^90 + 355584 * q^91 - 2439936 * q^92 - 2526576 * q^93 - 736848 * q^94 - 2089260 * q^95 - 49152 * q^96 - 38874 * q^97 + 4398804 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$$.

 $$n$$ $$11$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 4.89898 + 2.82843i 0.612372 + 0.353553i
$$3$$ 25.6485 + 8.43532i 0.949944 + 0.312419i
$$4$$ 16.0000 + 27.7128i 0.250000 + 0.433013i
$$5$$ 1.59771 0.922438i 0.0127817 0.00737950i −0.493596 0.869692i $$-0.664318\pi$$
0.506377 + 0.862312i $$0.330984\pi$$
$$6$$ 101.793 + 113.869i 0.471263 + 0.527173i
$$7$$ 6.34411 10.9883i 0.0184959 0.0320359i −0.856629 0.515932i $$-0.827446\pi$$
0.875125 + 0.483897i $$0.160779\pi$$
$$8$$ 181.019i 0.353553i
$$9$$ 586.691 + 432.707i 0.804788 + 0.593562i
$$10$$ 10.4362 0.0104362
$$11$$ −49.8080 28.7567i −0.0374215 0.0216053i 0.481173 0.876626i $$-0.340211\pi$$
−0.518594 + 0.855021i $$0.673544\pi$$
$$12$$ 176.609 + 845.757i 0.102205 + 0.489443i
$$13$$ −1411.17 2444.23i −0.642319 1.11253i −0.984914 0.173046i $$-0.944639\pi$$
0.342595 0.939483i $$-0.388694\pi$$
$$14$$ 62.1593 35.8877i 0.0226528 0.0130786i
$$15$$ 48.7599 10.1820i 0.0144474 0.00301687i
$$16$$ −512.000 + 886.810i −0.125000 + 0.216506i
$$17$$ 7221.17i 1.46981i −0.678171 0.734904i $$-0.737227\pi$$
0.678171 0.734904i $$-0.262773\pi$$
$$18$$ 1650.31 + 3779.23i 0.282974 + 0.648017i
$$19$$ −10648.3 −1.55246 −0.776231 0.630449i $$-0.782871\pi$$
−0.776231 + 0.630449i $$0.782871\pi$$
$$20$$ 51.1267 + 29.5180i 0.00639084 + 0.00368975i
$$21$$ 255.407 228.319i 0.0275787 0.0246538i
$$22$$ −162.672 281.757i −0.0152773 0.0264610i
$$23$$ 11573.9 6682.21i 0.951256 0.549208i 0.0577851 0.998329i $$-0.481596\pi$$
0.893471 + 0.449121i $$0.148263\pi$$
$$24$$ −1526.96 + 4642.87i −0.110457 + 0.335856i
$$25$$ −7810.80 + 13528.7i −0.499891 + 0.865837i
$$26$$ 15965.6i 0.908376i
$$27$$ 11397.7 + 16047.2i 0.579064 + 0.815282i
$$28$$ 406.023 0.0184959
$$29$$ 30795.1 + 17779.6i 1.26266 + 0.729000i 0.973589 0.228307i $$-0.0733190\pi$$
0.289075 + 0.957306i $$0.406652\pi$$
$$30$$ 267.673 + 88.0326i 0.00991380 + 0.00326047i
$$31$$ 8657.84 + 14995.8i 0.290619 + 0.503367i 0.973956 0.226736i $$-0.0728054\pi$$
−0.683337 + 0.730103i $$0.739472\pi$$
$$32$$ −5016.55 + 2896.31i −0.153093 + 0.0883883i
$$33$$ −1034.93 1157.71i −0.0287984 0.0322151i
$$34$$ 20424.5 35376.3i 0.519656 0.900070i
$$35$$ 23.4082i 0.000545963i
$$36$$ −2604.46 + 23182.2i −0.0558227 + 0.496874i
$$37$$ −60441.2 −1.19324 −0.596620 0.802524i $$-0.703490\pi$$
−0.596620 + 0.802524i $$0.703490\pi$$
$$38$$ −52166.0 30118.0i −0.950685 0.548878i
$$39$$ −15576.7 74594.4i −0.262592 1.25751i
$$40$$ 166.979 + 289.216i 0.00260905 + 0.00451900i
$$41$$ −75436.3 + 43553.2i −1.09453 + 0.631929i −0.934780 0.355228i $$-0.884403\pi$$
−0.159754 + 0.987157i $$0.551070\pi$$
$$42$$ 1897.02 396.132i 0.0256049 0.00534677i
$$43$$ 37932.2 65700.4i 0.477092 0.826348i −0.522563 0.852601i $$-0.675024\pi$$
0.999655 + 0.0262527i $$0.00835745\pi$$
$$44$$ 1840.43i 0.0216053i
$$45$$ 1336.51 + 150.153i 0.0146667 + 0.00164777i
$$46$$ 75600.6 0.776697
$$47$$ 61896.5 + 35736.0i 0.596174 + 0.344201i 0.767535 0.641007i $$-0.221483\pi$$
−0.171361 + 0.985208i $$0.554817\pi$$
$$48$$ −20612.6 + 18426.5i −0.186384 + 0.166617i
$$49$$ 58744.0 + 101748.i 0.499316 + 0.864840i
$$50$$ −76529.9 + 44184.5i −0.612239 + 0.353476i
$$51$$ 60912.8 185212.i 0.459196 1.39624i
$$52$$ 45157.6 78215.2i 0.321159 0.556265i
$$53$$ 147761.i 0.992505i 0.868178 + 0.496252i $$0.165291\pi$$
−0.868178 + 0.496252i $$0.834709\pi$$
$$54$$ 10448.9 + 110853.i 0.0663571 + 0.703986i
$$55$$ −106.105 −0.000637746
$$56$$ 1989.10 + 1148.41i 0.0113264 + 0.00653930i
$$57$$ −273114. 89822.1i −1.47475 0.485019i
$$58$$ 100576. + 174203.i 0.515481 + 0.892838i
$$59$$ 100224. 57864.1i 0.487993 0.281743i −0.235748 0.971814i $$-0.575754\pi$$
0.723742 + 0.690071i $$0.242421\pi$$
$$60$$ 1062.33 + 1188.36i 0.00491819 + 0.00550168i
$$61$$ 20138.6 34881.1i 0.0887239 0.153674i −0.818248 0.574865i $$-0.805054\pi$$
0.906972 + 0.421191i $$0.138388\pi$$
$$62$$ 97952.2i 0.410998i
$$63$$ 8476.74 3701.61i 0.0339006 0.0148036i
$$64$$ −32768.0 −0.125000
$$65$$ −4509.29 2603.44i −0.0164198 0.00947999i
$$66$$ −1795.59 8598.83i −0.00624563 0.0299094i
$$67$$ 90883.7 + 157415.i 0.302177 + 0.523386i 0.976629 0.214933i $$-0.0689533\pi$$
−0.674452 + 0.738319i $$0.735620\pi$$
$$68$$ 200119. 115539.i 0.636445 0.367452i
$$69$$ 353221. 73758.9i 1.07522 0.224526i
$$70$$ 66.2083 114.676i 0.000193027 0.000334333i
$$71$$ 301066.i 0.841175i −0.907252 0.420588i $$-0.861824\pi$$
0.907252 0.420588i $$-0.138176\pi$$
$$72$$ −78328.3 + 106202.i −0.209856 + 0.284536i
$$73$$ −612635. −1.57483 −0.787415 0.616424i $$-0.788581\pi$$
−0.787415 + 0.616424i $$0.788581\pi$$
$$74$$ −296100. 170954.i −0.730707 0.421874i
$$75$$ −314454. + 281104.i −0.745373 + 0.666321i
$$76$$ −170373. 295095.i −0.388116 0.672236i
$$77$$ −631.975 + 364.871i −0.00138429 + 0.000799221i
$$78$$ 134675. 409494.i 0.283794 0.862907i
$$79$$ 171651. 297308.i 0.348149 0.603012i −0.637772 0.770225i $$-0.720144\pi$$
0.985921 + 0.167214i $$0.0534770\pi$$
$$80$$ 1889.15i 0.00368975i
$$81$$ 156971. + 507730.i 0.295369 + 0.955383i
$$82$$ −492748. −0.893683
$$83$$ −131581. 75968.6i −0.230123 0.132862i 0.380506 0.924779i $$-0.375750\pi$$
−0.610629 + 0.791917i $$0.709083\pi$$
$$84$$ 10413.9 + 3424.93i 0.0175701 + 0.00577849i
$$85$$ −6661.07 11537.3i −0.0108464 0.0187866i
$$86$$ 371658. 214577.i 0.584316 0.337355i
$$87$$ 639872. + 715786.i 0.971707 + 1.08699i
$$88$$ 5205.52 9016.22i 0.00763864 0.0132305i
$$89$$ 102435.i 0.145304i −0.997357 0.0726520i $$-0.976854\pi$$
0.997357 0.0726520i $$-0.0231462\pi$$
$$90$$ 6122.82 + 4515.81i 0.00839893 + 0.00619452i
$$91$$ −35810.6 −0.0475212
$$92$$ 370366. + 213831.i 0.475628 + 0.274604i
$$93$$ 95566.0 + 457652.i 0.118810 + 0.568966i
$$94$$ 202153. + 350140.i 0.243387 + 0.421558i
$$95$$ −17012.9 + 9822.43i −0.0198431 + 0.0114564i
$$96$$ −153098. + 31969.7i −0.173044 + 0.0361348i
$$97$$ 247882. 429345.i 0.271600 0.470425i −0.697672 0.716418i $$-0.745780\pi$$
0.969272 + 0.245992i $$0.0791138\pi$$
$$98$$ 664613.i 0.706139i
$$99$$ −16778.7 38423.5i −0.0172923 0.0395997i
$$100$$ −499891. −0.499891
$$101$$ 68156.2 + 39350.0i 0.0661517 + 0.0381927i 0.532711 0.846297i $$-0.321173\pi$$
−0.466559 + 0.884490i $$0.654507\pi$$
$$102$$ 822270. 735062.i 0.774843 0.692666i
$$103$$ 326814. + 566059.i 0.299081 + 0.518024i 0.975926 0.218102i $$-0.0699865\pi$$
−0.676845 + 0.736126i $$0.736653\pi$$
$$104$$ 442452. 255450.i 0.393338 0.227094i
$$105$$ 197.455 600.384i 0.000170569 0.000518634i
$$106$$ −417932. + 723879.i −0.350903 + 0.607783i
$$107$$ 1.53176e6i 1.25037i −0.780476 0.625186i $$-0.785023\pi$$
0.780476 0.625186i $$-0.214977\pi$$
$$108$$ −262349. + 572618.i −0.208261 + 0.454563i
$$109$$ 863246. 0.666584 0.333292 0.942824i $$-0.391840\pi$$
0.333292 + 0.942824i $$0.391840\pi$$
$$110$$ −519.806 300.110i −0.000390538 0.000225477i
$$111$$ −1.55023e6 509841.i −1.13351 0.372791i
$$112$$ 6496.36 + 11252.0i 0.00462398 + 0.00800897i
$$113$$ −1.51141e6 + 872613.i −1.04748 + 0.604765i −0.921944 0.387324i $$-0.873400\pi$$
−0.125540 + 0.992089i $$0.540066\pi$$
$$114$$ −1.08392e6 1.21252e6i −0.731618 0.818416i
$$115$$ 12327.8 21352.5i 0.00810576 0.0140396i
$$116$$ 1.13789e6i 0.729000i
$$117$$ 229710. 2.04463e6i 0.143424 1.27661i
$$118$$ 654658. 0.398445
$$119$$ −79348.4 45811.8i −0.0470866 0.0271855i
$$120$$ 1843.13 + 8826.48i 0.00106663 + 0.00510792i
$$121$$ −884127. 1.53135e6i −0.499066 0.864408i
$$122$$ 197318. 113921.i 0.108664 0.0627373i
$$123$$ −2.30221e6 + 480744.i −1.23717 + 0.258344i
$$124$$ −277051. + 479866.i −0.145310 + 0.251684i
$$125$$ 57646.1i 0.0295148i
$$126$$ 51997.1 + 5841.76i 0.0259937 + 0.00292033i
$$127$$ 3.20463e6 1.56447 0.782234 0.622985i $$-0.214080\pi$$
0.782234 + 0.622985i $$0.214080\pi$$
$$128$$ −160530. 92681.9i −0.0765466 0.0441942i
$$129$$ 1.52711e6 1.36515e6i 0.711378 0.635932i
$$130$$ −14727.3 25508.4i −0.00670336 0.0116106i
$$131$$ −2.63987e6 + 1.52413e6i −1.17427 + 0.677967i −0.954683 0.297625i $$-0.903805\pi$$
−0.219590 + 0.975592i $$0.570472\pi$$
$$132$$ 15524.6 47204.2i 0.00674992 0.0205239i
$$133$$ −67554.2 + 117007.i −0.0287142 + 0.0497345i
$$134$$ 1.02823e6i 0.427343i
$$135$$ 33012.8 + 15125.1i 0.0134178 + 0.00614746i
$$136$$ 1.30717e6 0.519656
$$137$$ 3.54873e6 + 2.04886e6i 1.38010 + 0.796802i 0.992171 0.124887i $$-0.0398567\pi$$
0.387931 + 0.921689i $$0.373190\pi$$
$$138$$ 1.93904e6 + 637715.i 0.737819 + 0.242655i
$$139$$ 556460. + 963816.i 0.207200 + 0.358881i 0.950831 0.309709i $$-0.100232\pi$$
−0.743632 + 0.668590i $$0.766898\pi$$
$$140$$ 648.706 374.531i 0.000236409 0.000136491i
$$141$$ 1.28611e6 + 1.43869e6i 0.458797 + 0.513228i
$$142$$ 851543. 1.47492e6i 0.297400 0.515112i
$$143$$ 162323.i 0.0555100i
$$144$$ −684114. + 298737.i −0.229108 + 0.100047i
$$145$$ 65602.2 0.0215186
$$146$$ −3.00129e6 1.73279e6i −0.964382 0.556786i
$$147$$ 648422. + 3.10520e6i 0.204129 + 0.977546i
$$148$$ −967059. 1.67500e6i −0.298310 0.516688i
$$149$$ −440188. + 254142.i −0.133070 + 0.0768278i −0.565057 0.825052i $$-0.691146\pi$$
0.431987 + 0.901880i $$0.357812\pi$$
$$150$$ −2.33559e6 + 487713.i −0.692026 + 0.144508i
$$151$$ −2.81751e6 + 4.88007e6i −0.818341 + 1.41741i 0.0885624 + 0.996071i $$0.471773\pi$$
−0.906904 + 0.421338i $$0.861561\pi$$
$$152$$ 1.92756e6i 0.548878i
$$153$$ 3.12465e6 4.23659e6i 0.872422 1.18288i
$$154$$ −4128.04 −0.00113027
$$155$$ 27665.4 + 15972.6i 0.00742920 + 0.00428925i
$$156$$ 1.81799e6 1.62518e6i 0.478871 0.428084i
$$157$$ −2.68126e6 4.64408e6i −0.692852 1.20005i −0.970900 0.239487i $$-0.923021\pi$$
0.278048 0.960567i $$-0.410313\pi$$
$$158$$ 1.68183e6 971005.i 0.426394 0.246179i
$$159$$ −1.24641e6 + 3.78985e6i −0.310078 + 0.942824i
$$160$$ −5343.33 + 9254.92i −0.00130452 + 0.00225950i
$$161$$ 169571.i 0.0406324i
$$162$$ −667079. + 2.93134e6i −0.156903 + 0.689479i
$$163$$ −2.42021e6 −0.558844 −0.279422 0.960168i $$-0.590143\pi$$
−0.279422 + 0.960168i $$0.590143\pi$$
$$164$$ −2.41396e6 1.39370e6i −0.547267 0.315965i
$$165$$ −2721.43 895.030i −0.000605823 0.000199244i
$$166$$ −429743. 744337.i −0.0939474 0.162722i
$$167$$ 7.16092e6 4.13436e6i 1.53751 0.887685i 0.538532 0.842605i $$-0.318979\pi$$
0.998983 0.0450793i $$-0.0143541\pi$$
$$168$$ 41330.2 + 46233.5i 0.00871645 + 0.00975056i
$$169$$ −1.56942e6 + 2.71832e6i −0.325147 + 0.563171i
$$170$$ 75361.5i 0.0153392i
$$171$$ −6.24728e6 4.60761e6i −1.24940 0.921482i
$$172$$ 2.42766e6 0.477092
$$173$$ 2.27322e6 + 1.31244e6i 0.439039 + 0.253479i 0.703190 0.711002i $$-0.251758\pi$$
−0.264151 + 0.964481i $$0.585092\pi$$
$$174$$ 1.11017e6 + 5.31645e6i 0.210738 + 1.00919i
$$175$$ 99105.0 + 171655.i 0.0184919 + 0.0320289i
$$176$$ 51003.4 29446.8i 0.00935538 0.00540133i
$$177$$ 3.05869e6 638709.i 0.551588 0.115182i
$$178$$ 289729. 501826.i 0.0513727 0.0889802i
$$179$$ 7.60442e6i 1.32589i −0.748669 0.662944i $$-0.769307\pi$$
0.748669 0.662944i $$-0.230693\pi$$
$$180$$ 17222.9 + 39440.8i 0.00295318 + 0.00676282i
$$181$$ −9.89440e6 −1.66861 −0.834303 0.551306i $$-0.814130\pi$$
−0.834303 + 0.551306i $$0.814130\pi$$
$$182$$ −175435. 101288.i −0.0291006 0.0168013i
$$183$$ 810759. 724773.i 0.132294 0.118263i
$$184$$ 1.20961e6 + 2.09511e6i 0.194174 + 0.336320i
$$185$$ −96567.4 + 55753.2i −0.0152516 + 0.00880552i
$$186$$ −826258. + 2.51233e6i −0.128404 + 0.390425i
$$187$$ −207657. + 359672.i −0.0317557 + 0.0550024i
$$188$$ 2.28710e6i 0.344201i
$$189$$ 248640. 23436.6i 0.0368286 0.00347143i
$$190$$ −111128. −0.0162018
$$191$$ −1.09559e6 632537.i −0.157234 0.0907791i 0.419319 0.907839i $$-0.362269\pi$$
−0.576553 + 0.817060i $$0.695602\pi$$
$$192$$ −840450. 276409.i −0.118743 0.0390524i
$$193$$ −654987. 1.13447e6i −0.0911089 0.157805i 0.816869 0.576823i $$-0.195708\pi$$
−0.907978 + 0.419018i $$0.862374\pi$$
$$194$$ 2.42874e6 1.40223e6i 0.332641 0.192050i
$$195$$ −93695.7 104812.i −0.0126362 0.0141353i
$$196$$ −1.87981e6 + 3.25592e6i −0.249658 + 0.432420i
$$197$$ 9.83234e6i 1.28605i 0.765845 + 0.643025i $$0.222321\pi$$
−0.765845 + 0.643025i $$0.777679\pi$$
$$198$$ 26479.6 235694.i 0.00341127 0.0303635i
$$199$$ 1.36283e7 1.72934 0.864672 0.502336i $$-0.167526\pi$$
0.864672 + 0.502336i $$0.167526\pi$$
$$200$$ −2.44896e6 1.41391e6i −0.306120 0.176738i
$$201$$ 1.00318e6 + 4.80410e6i 0.123536 + 0.591594i
$$202$$ 222597. + 385549.i 0.0270063 + 0.0467763i
$$203$$ 390735. 225591.i 0.0467083 0.0269671i
$$204$$ 6.10735e6 1.27533e6i 0.719387 0.150221i
$$205$$ −80350.2 + 139171.i −0.00932664 + 0.0161542i
$$206$$ 3.69748e6i 0.422965i
$$207$$ 9.68176e6 + 1.08772e6i 1.09155 + 0.122633i
$$208$$ 2.89009e6 0.321159
$$209$$ 530373. + 306211.i 0.0580955 + 0.0335414i
$$210$$ 2665.47 2382.78i 0.000287817 0.000257292i
$$211$$ 1.55640e6 + 2.69577e6i 0.165682 + 0.286969i 0.936897 0.349605i $$-0.113684\pi$$
−0.771216 + 0.636574i $$0.780351\pi$$
$$212$$ −4.09488e6 + 2.36418e6i −0.429767 + 0.248126i
$$213$$ 2.53959e6 7.72189e6i 0.262799 0.799070i
$$214$$ 4.33247e6 7.50405e6i 0.442073 0.765693i
$$215$$ 139960.i 0.0140828i
$$216$$ −2.90485e6 + 2.06321e6i −0.288246 + 0.204730i
$$217$$ 219705. 0.0215011
$$218$$ 4.22902e6 + 2.44163e6i 0.408198 + 0.235673i
$$219$$ −1.57132e7 5.16778e6i −1.49600 0.492007i
$$220$$ −1697.68 2940.47i −0.000159437 0.000276152i
$$221$$ −1.76502e7 + 1.01903e7i −1.63520 + 0.944085i
$$222$$ −6.15248e6 6.88240e6i −0.562330 0.629044i
$$223$$ 1.00499e7 1.74069e7i 0.906248 1.56967i 0.0870139 0.996207i $$-0.472268\pi$$
0.819234 0.573460i $$-0.194399\pi$$
$$224$$ 73498.0i 0.00653930i
$$225$$ −1.04365e7 + 4.55738e6i −0.916234 + 0.400099i
$$226$$ −9.87249e6 −0.855267
$$227$$ −1.03090e7 5.95188e6i −0.881328 0.508835i −0.0102317 0.999948i $$-0.503257\pi$$
−0.871096 + 0.491113i $$0.836590\pi$$
$$228$$ −1.88060e6 9.00591e6i −0.158669 0.759841i
$$229$$ 1.55174e6 + 2.68769e6i 0.129215 + 0.223807i 0.923373 0.383905i $$-0.125421\pi$$
−0.794158 + 0.607712i $$0.792088\pi$$
$$230$$ 120788. 69736.8i 0.00992749 0.00573164i
$$231$$ −19287.0 + 4027.48i −0.00156469 + 0.000326736i
$$232$$ −3.21845e6 + 5.57451e6i −0.257740 + 0.446419i
$$233$$ 9.36024e6i 0.739979i 0.929036 + 0.369989i $$0.120639\pi$$
−0.929036 + 0.369989i $$0.879361\pi$$
$$234$$ 6.90843e6 9.36688e6i 0.539177 0.731051i
$$235$$ 131857. 0.0101601
$$236$$ 3.20715e6 + 1.85165e6i 0.243997 + 0.140872i
$$237$$ 6.91048e6 6.17758e6i 0.519115 0.464059i
$$238$$ −259151. 448862.i −0.0192230 0.0332953i
$$239$$ 6.05702e6 3.49702e6i 0.443676 0.256156i −0.261480 0.965209i $$-0.584211\pi$$
0.705156 + 0.709053i $$0.250877\pi$$
$$240$$ −15935.6 + 48453.9i −0.00115275 + 0.00350506i
$$241$$ 2.06773e6 3.58141e6i 0.147721 0.255860i −0.782664 0.622445i $$-0.786140\pi$$
0.930385 + 0.366585i $$0.119473\pi$$
$$242$$ 1.00028e7i 0.705786i
$$243$$ −256792. + 1.43466e7i −0.0178963 + 0.999840i
$$244$$ 1.28887e6 0.0887239
$$245$$ 187712. + 108375.i 0.0127642 + 0.00736940i
$$246$$ −1.26382e7 4.15649e6i −0.848949 0.279204i
$$247$$ 1.50267e7 + 2.60269e7i 0.997176 + 1.72716i
$$248$$ −2.71453e6 + 1.56724e6i −0.177967 + 0.102749i
$$249$$ −2.73405e6 3.05841e6i −0.177096 0.198106i
$$250$$ −163048. + 282407.i −0.0104351 + 0.0180740i
$$251$$ 6.15130e6i 0.388997i −0.980903 0.194498i $$-0.937692\pi$$
0.980903 0.194498i $$-0.0623079\pi$$
$$252$$ 238210. + 175689.i 0.0148853 + 0.0109785i
$$253$$ −768633. −0.0474633
$$254$$ 1.56994e7 + 9.06406e6i 0.958037 + 0.553123i
$$255$$ −73525.6 352103.i −0.00443423 0.0212349i
$$256$$ −524288. 908093.i −0.0312500 0.0541266i
$$257$$ 6.62383e6 3.82427e6i 0.390220 0.225294i −0.292035 0.956408i $$-0.594332\pi$$
0.682256 + 0.731114i $$0.260999\pi$$
$$258$$ 1.13425e7 2.36852e6i 0.660464 0.137917i
$$259$$ −383445. + 664147.i −0.0220701 + 0.0382265i
$$260$$ 166620.i 0.00947999i
$$261$$ 1.03739e7 + 2.37564e7i 0.583471 + 1.33616i
$$262$$ −1.72436e7 −0.958790
$$263$$ 7.24714e6 + 4.18414e6i 0.398382 + 0.230006i 0.685786 0.727804i $$-0.259459\pi$$
−0.287404 + 0.957810i $$0.592792\pi$$
$$264$$ 209568. 187342.i 0.0113897 0.0101818i
$$265$$ 136300. + 236079.i 0.00732419 + 0.0126859i
$$266$$ −661893. + 382144.i −0.0351676 + 0.0203040i
$$267$$ 864071. 2.62730e6i 0.0453958 0.138031i
$$268$$ −2.90828e6 + 5.03729e6i −0.151089 + 0.261693i
$$269$$ 2.26505e7i 1.16364i −0.813316 0.581822i $$-0.802340\pi$$
0.813316 0.581822i $$-0.197660\pi$$
$$270$$ 118949. + 167472.i 0.00604322 + 0.00850844i
$$271$$ −1.56983e7 −0.788758 −0.394379 0.918948i $$-0.629040\pi$$
−0.394379 + 0.918948i $$0.629040\pi$$
$$272$$ 6.40380e6 + 3.69724e6i 0.318223 + 0.183726i
$$273$$ −918487. 302074.i −0.0451424 0.0148465i
$$274$$ 1.15901e7 + 2.00746e7i 0.563424 + 0.975879i
$$275$$ 778081. 449225.i 0.0374134 0.0216006i
$$276$$ 7.69559e6 + 8.60859e6i 0.366029 + 0.409454i
$$277$$ 9.51658e6 1.64832e7i 0.447756 0.775537i −0.550483 0.834846i $$-0.685557\pi$$
0.998240 + 0.0593095i $$0.0188899\pi$$
$$278$$ 6.29562e6i 0.293025i
$$279$$ −1.40931e6 + 1.25442e7i −0.0648926 + 0.577605i
$$280$$ 4237.33 0.000193027
$$281$$ −1.12171e7 6.47622e6i −0.505549 0.291879i 0.225453 0.974254i $$-0.427614\pi$$
−0.731002 + 0.682375i $$0.760947\pi$$
$$282$$ 2.23139e6 + 1.06858e7i 0.0995010 + 0.476496i
$$283$$ −1.67469e7 2.90065e7i −0.738883 1.27978i −0.952999 0.302974i $$-0.902020\pi$$
0.214116 0.976808i $$-0.431313\pi$$
$$284$$ 8.34338e6 4.81705e6i 0.364240 0.210294i
$$285$$ −519212. + 108421.i −0.0224290 + 0.00468358i
$$286$$ −459118. + 795216.i −0.0196258 + 0.0339928i
$$287$$ 1.10522e6i 0.0467525i
$$288$$ −4.19642e6 471458.i −0.175672 0.0197363i
$$289$$ −2.80077e7 −1.16033
$$290$$ 321384. + 185551.i 0.0131774 + 0.00760798i
$$291$$ 9.97946e6 8.92108e6i 0.404975 0.362025i
$$292$$ −9.80217e6 1.69779e7i −0.393707 0.681921i
$$293$$ 1.31069e7 7.56728e6i 0.521072 0.300841i −0.216301 0.976327i $$-0.569399\pi$$
0.737373 + 0.675486i $$0.236066\pi$$
$$294$$ −5.60622e6 + 1.70463e7i −0.220611 + 0.670793i
$$295$$ 106752. 184900.i 0.00415825 0.00720229i
$$296$$ 1.09410e7i 0.421874i
$$297$$ −106234. 1.12704e6i −0.00405502 0.0430200i
$$298$$ −2.87529e6 −0.108651
$$299$$ −3.26657e7 1.88595e7i −1.22202 0.705533i
$$300$$ −1.28215e7 4.21674e6i −0.474869 0.156176i
$$301$$ −481291. 833621.i −0.0176485 0.0305682i
$$302$$ −2.76058e7 + 1.59382e7i −1.00226 + 0.578655i
$$303$$ 1.41617e6 + 1.58419e6i 0.0509083 + 0.0569480i
$$304$$ 5.45195e6 9.44305e6i 0.194058 0.336118i
$$305$$ 74306.5i 0.00261895i
$$306$$ 2.72905e7 1.19171e7i 0.952460 0.415918i
$$307$$ −5.41823e6 −0.187259 −0.0936294 0.995607i $$-0.529847\pi$$
−0.0936294 + 0.995607i $$0.529847\pi$$
$$308$$ −20223.2 11675.9i −0.000692146 0.000399611i
$$309$$ 3.60741e6 + 1.72753e7i 0.122270 + 0.585533i
$$310$$ 90354.8 + 156499.i 0.00303296 + 0.00525324i
$$311$$ 2.36986e7 1.36824e7i 0.787848 0.454864i −0.0513567 0.998680i $$-0.516355\pi$$
0.839204 + 0.543816i $$0.183021\pi$$
$$312$$ 1.35030e7 2.81968e6i 0.444598 0.0928402i
$$313$$ −1.13895e7 + 1.97272e7i −0.371426 + 0.643328i −0.989785 0.142567i $$-0.954464\pi$$
0.618360 + 0.785895i $$0.287798\pi$$
$$314$$ 3.03350e7i 0.979840i
$$315$$ 10128.9 13733.4i 0.000324063 0.000439385i
$$316$$ 1.09857e7 0.348149
$$317$$ 2.29031e7 + 1.32231e7i 0.718979 + 0.415103i 0.814377 0.580337i $$-0.197079\pi$$
−0.0953979 + 0.995439i $$0.530412\pi$$
$$318$$ −1.68255e7 + 1.50410e7i −0.523222 + 0.467731i
$$319$$ −1.02256e6 1.77113e6i −0.0315005 0.0545605i
$$320$$ −52353.7 + 30226.4i −0.00159771 + 0.000922438i
$$321$$ 1.29209e7 3.92873e7i 0.390640 1.18778i
$$322$$ 479618. 830723.i 0.0143657 0.0248822i
$$323$$ 7.68934e7i 2.28182i
$$324$$ −1.15591e7 + 1.24738e7i −0.339851 + 0.366744i
$$325$$ 4.40896e7 1.28436
$$326$$ −1.18566e7 6.84539e6i −0.342221 0.197581i
$$327$$ 2.21410e7 + 7.28176e6i 0.633218 + 0.208254i
$$328$$ −7.88397e6 1.36554e7i −0.223421 0.386976i
$$329$$ 785356. 453426.i 0.0220536 0.0127326i
$$330$$ −10800.7 12082.1i −0.000300546 0.000336203i
$$331$$ −2.25635e7 + 3.90812e7i −0.622190 + 1.07766i 0.366887 + 0.930265i $$0.380424\pi$$
−0.989077 + 0.147399i $$0.952910\pi$$
$$332$$ 4.86199e6i 0.132862i
$$333$$ −3.54603e7 2.61533e7i −0.960306 0.708262i
$$334$$ 4.67749e7 1.25538
$$335$$ 290411. + 167669.i 0.00772466 + 0.00445983i
$$336$$ 71707.5 + 343397.i 0.00189037 + 0.00905270i
$$337$$ 1.56916e7 + 2.71787e7i 0.409994 + 0.710131i 0.994889 0.100978i $$-0.0321973\pi$$
−0.584894 + 0.811110i $$0.698864\pi$$
$$338$$ −1.53771e7 + 8.87800e6i −0.398222 + 0.229914i
$$339$$ −4.61262e7 + 9.63199e6i −1.18399 + 0.247239i
$$340$$ 213154. 369194.i 0.00542322 0.00939330i
$$341$$ 995883.i 0.0251157i
$$342$$ −1.75730e7 4.02425e7i −0.439307 1.00602i
$$343$$ 2.98347e6 0.0739331
$$344$$ 1.18931e7 + 6.86646e6i 0.292158 + 0.168678i
$$345$$ 496306. 443669.i 0.0120863 0.0108044i
$$346$$ 7.42430e6 + 1.28593e7i 0.179237 + 0.310447i
$$347$$ 9.52685e6 5.50033e6i 0.228014 0.131644i −0.381642 0.924310i $$-0.624641\pi$$
0.609655 + 0.792667i $$0.291308\pi$$
$$348$$ −9.59849e6 + 2.91852e7i −0.227753 + 0.692509i
$$349$$ 1.73905e6 3.01213e6i 0.0409107 0.0708594i −0.844845 0.535011i $$-0.820307\pi$$
0.885756 + 0.464152i $$0.153641\pi$$
$$350$$ 1.12125e6i 0.0261515i
$$351$$ 2.31388e7 5.05040e7i 0.535081 1.16790i
$$352$$ 333153. 0.00763864
$$353$$ 2.33541e7 + 1.34835e7i 0.530932 + 0.306534i 0.741396 0.671068i $$-0.234164\pi$$
−0.210464 + 0.977602i $$0.567497\pi$$
$$354$$ 1.67910e7 + 5.52225e6i 0.378500 + 0.124482i
$$355$$ −277714. 481016.i −0.00620745 0.0107516i
$$356$$ 2.83876e6 1.63896e6i 0.0629185 0.0363260i
$$357$$ −1.64873e6 1.84433e6i −0.0362364 0.0405354i
$$358$$ 2.15086e7 3.72539e7i 0.468773 0.811938i
$$359$$ 8.82517e7i 1.90739i 0.300775 + 0.953695i $$0.402755\pi$$
−0.300775 + 0.953695i $$0.597245\pi$$
$$360$$ −27180.7 + 241933.i −0.000582576 + 0.00518547i
$$361$$ 6.63412e7 1.41014
$$362$$ −4.84725e7 2.79856e7i −1.02181 0.589941i
$$363$$ −9.75907e6 4.67348e7i −0.204027 0.977058i
$$364$$ −572969. 992411.i −0.0118803 0.0205773i
$$365$$ −978813. + 565118.i −0.0201290 + 0.0116215i
$$366$$ 6.02186e6 1.25747e6i 0.122825 0.0256481i
$$367$$ −1.50282e7 + 2.60296e7i −0.304024 + 0.526585i −0.977044 0.213040i $$-0.931664\pi$$
0.673019 + 0.739625i $$0.264997\pi$$
$$368$$ 1.36852e7i 0.274604i
$$369$$ −6.31036e7 7.08954e6i −1.25596 0.141104i
$$370$$ −630776. −0.0124529
$$371$$ 1.62365e6 + 937412.i 0.0317958 + 0.0183573i
$$372$$ −1.11538e7 + 9.97083e6i −0.216667 + 0.193688i
$$373$$ −1.95923e7 3.39349e7i −0.377537 0.653913i 0.613166 0.789954i $$-0.289896\pi$$
−0.990703 + 0.136041i $$0.956562\pi$$
$$374$$ −2.03461e6 + 1.17468e6i −0.0388926 + 0.0224547i
$$375$$ −486263. + 1.47854e6i −0.00922099 + 0.0280374i
$$376$$ −6.46890e6 + 1.12045e7i −0.121693 + 0.210779i
$$377$$ 1.00360e8i 1.87300i
$$378$$ 1.28437e6 + 588445.i 0.0237802 + 0.0108951i
$$379$$ −3.94927e7 −0.725436 −0.362718 0.931899i $$-0.618151\pi$$
−0.362718 + 0.931899i $$0.618151\pi$$
$$380$$ −544414. 314318.i −0.00992153 0.00572820i
$$381$$ 8.21939e7 + 2.70321e7i 1.48616 + 0.488770i
$$382$$ −3.57817e6 6.19757e6i −0.0641905 0.111181i
$$383$$ −5.89496e7 + 3.40346e7i −1.04926 + 0.605793i −0.922443 0.386133i $$-0.873811\pi$$
−0.126821 + 0.991926i $$0.540477\pi$$
$$384$$ −3.33555e6 3.73127e6i −0.0589079 0.0658966i
$$385$$ −673.141 + 1165.91i −1.17957e−5 + 2.04308e-5i
$$386$$ 7.41034e6i 0.128847i
$$387$$ 5.06835e7 2.21323e7i 0.874447 0.381852i
$$388$$ 1.58645e7 0.271600
$$389$$ −6.88443e7 3.97473e7i −1.16955 0.675241i −0.215977 0.976398i $$-0.569294\pi$$
−0.953574 + 0.301157i $$0.902627\pi$$
$$390$$ −162561. 778482.i −0.00274046 0.0131236i
$$391$$ −4.82534e7 8.35773e7i −0.807230 1.39816i
$$392$$ −1.84183e7 + 1.06338e7i −0.305767 + 0.176535i
$$393$$ −8.05653e7 + 1.68235e7i −1.32730 + 0.277165i
$$394$$ −2.78101e7 + 4.81684e7i −0.454688 + 0.787542i
$$395$$ 633349.i 0.0102767i
$$396$$ 796365. 1.07976e6i 0.0128241 0.0173877i
$$397$$ −4.50639e6 −0.0720206 −0.0360103 0.999351i $$-0.511465\pi$$
−0.0360103 + 0.999351i $$0.511465\pi$$
$$398$$ 6.67646e7 + 3.85466e7i 1.05900 + 0.611416i
$$399$$ −2.71966e6 + 2.43122e6i −0.0428149 + 0.0382741i
$$400$$ −7.99826e6 1.38534e7i −0.124973 0.216459i
$$401$$ 3.46331e7 1.99954e7i 0.537104 0.310097i −0.206801 0.978383i $$-0.566305\pi$$
0.743904 + 0.668286i $$0.232972\pi$$
$$402$$ −8.67346e6 + 2.63726e7i −0.133510 + 0.405952i
$$403$$ 2.44354e7 4.23234e7i 0.373340 0.646645i
$$404$$ 2.51840e6i 0.0381927i
$$405$$ 719143. + 666409.i 0.0108256 + 0.0100317i
$$406$$ 2.55227e6 0.0381372
$$407$$ 3.01046e6 + 1.73809e6i 0.0446529 + 0.0257803i
$$408$$ 3.35270e7 + 1.10264e7i 0.493644 + 0.162350i
$$409$$ 2.00563e7 + 3.47385e7i 0.293144 + 0.507740i 0.974551 0.224164i $$-0.0719653\pi$$
−0.681408 + 0.731904i $$0.738632\pi$$
$$410$$ −787268. + 454529.i −0.0114228 + 0.00659493i
$$411$$ 7.37368e7 + 8.24848e7i 1.06208 + 1.18809i
$$412$$ −1.04581e7 + 1.81139e7i −0.149541 + 0.259012i
$$413$$ 1.46838e6i 0.0208444i
$$414$$ 4.43542e7 + 3.27129e7i 0.625077 + 0.461018i
$$415$$ −280305. −0.00392181
$$416$$ 1.41585e7 + 8.17440e6i 0.196669 + 0.113547i
$$417$$ 6.14225e6 + 2.94144e7i 0.0847071 + 0.405650i
$$418$$ 1.73219e6 + 3.00024e6i 0.0237174 + 0.0410797i
$$419$$ 7.70293e7 4.44729e7i 1.04716 0.604579i 0.125309 0.992118i $$-0.460008\pi$$
0.921854 + 0.387538i $$0.126675\pi$$
$$420$$ 19797.6 4134.10i 0.000267218 5.57999e-5i
$$421$$ −2.31687e7 + 4.01293e7i −0.310495 + 0.537793i −0.978470 0.206391i $$-0.933828\pi$$
0.667975 + 0.744184i $$0.267161\pi$$
$$422$$ 1.76087e7i 0.234309i
$$423$$ 2.08509e7 + 4.77490e7i 0.275489 + 0.630875i
$$424$$ −2.67476e7 −0.350903
$$425$$ 9.76930e7 + 5.64031e7i 1.27261 + 0.734744i
$$426$$ 3.42822e7 3.06463e7i 0.443445 0.396415i
$$427$$ −255523. 442579.i −0.00328206 0.00568470i
$$428$$ 4.24493e7 2.45081e7i 0.541427 0.312593i
$$429$$ −1.36925e6 + 4.16334e6i −0.0173424 + 0.0527314i
$$430$$ 395867. 685662.i 0.00497902 0.00862392i
$$431$$ 1.17075e8i 1.46228i −0.682227 0.731140i $$-0.738988\pi$$
0.682227 0.731140i $$-0.261012\pi$$
$$432$$ −2.00664e7 + 1.89144e6i −0.248897 + 0.0234608i
$$433$$ 1.81236e7 0.223244 0.111622 0.993751i $$-0.464395\pi$$
0.111622 + 0.993751i $$0.464395\pi$$
$$434$$ 1.07633e6 + 621419.i 0.0131667 + 0.00760178i
$$435$$ 1.68260e6 + 553375.i 0.0204415 + 0.00672283i
$$436$$ 1.38119e7 + 2.39230e7i 0.166646 + 0.288639i
$$437$$ −1.23243e8 + 7.11545e7i −1.47679 + 0.852624i
$$438$$ −6.23619e7 6.97604e7i −0.742159 0.830208i
$$439$$ −3.02641e6 + 5.24189e6i −0.0357712 + 0.0619576i −0.883357 0.468701i $$-0.844722\pi$$
0.847586 + 0.530659i $$0.178055\pi$$
$$440$$ 19207.1i 0.000225477i
$$441$$ −9.56229e6 + 8.51133e7i −0.111493 + 0.992388i
$$442$$ −1.15290e8 −1.33514
$$443$$ 4.21347e6 + 2.43265e6i 0.0484651 + 0.0279813i 0.524037 0.851696i $$-0.324425\pi$$
−0.475572 + 0.879677i $$0.657759\pi$$
$$444$$ −1.06745e7 5.11186e7i −0.121955 0.584023i
$$445$$ −94489.7 163661.i −0.00107227 0.00185723i
$$446$$ 9.84684e7 5.68508e7i 1.10992 0.640814i
$$447$$ −1.34339e7 + 2.80525e6i −0.150411 + 0.0314086i
$$448$$ −207884. + 360065.i −0.00231199 + 0.00400449i
$$449$$ 1.43332e8i 1.58345i −0.610877 0.791725i $$-0.709183\pi$$
0.610877 0.791725i $$-0.290817\pi$$
$$450$$ −6.40183e7 7.19232e6i −0.702533 0.0789280i
$$451$$ 5.00978e6 0.0546121
$$452$$ −4.83651e7 2.79236e7i −0.523742 0.302382i
$$453$$ −1.13430e8 + 1.01400e8i −1.22020 + 1.09079i
$$454$$ −3.36689e7 5.83163e7i −0.359800 0.623193i
$$455$$ −57214.9 + 33033.0i −0.000607400 + 0.000350682i
$$456$$ 1.62595e7 4.94389e7i 0.171480 0.521404i
$$457$$ −4.87353e7 + 8.44121e7i −0.510617 + 0.884415i 0.489307 + 0.872111i $$0.337250\pi$$
−0.999924 + 0.0123031i $$0.996084\pi$$
$$458$$ 1.75559e7i 0.182738i
$$459$$ 1.15879e8 8.23048e7i 1.19831 0.851113i
$$460$$ 788982. 0.00810576
$$461$$ −4.63065e7 2.67351e7i −0.472650 0.272884i 0.244699 0.969599i $$-0.421311\pi$$
−0.717348 + 0.696715i $$0.754644\pi$$
$$462$$ −105878. 34821.4i −0.00107369 0.000353118i
$$463$$ −1.53890e7 2.66545e7i −0.155048 0.268552i 0.778028 0.628229i $$-0.216220\pi$$
−0.933077 + 0.359678i $$0.882887\pi$$
$$464$$ −3.15342e7 + 1.82063e7i −0.315666 + 0.182250i
$$465$$ 574842. + 643040.i 0.00571728 + 0.00639557i
$$466$$ −2.64748e7 + 4.58556e7i −0.261622 + 0.453142i
$$467$$ 1.10305e8i 1.08304i 0.840688 + 0.541519i $$0.182151\pi$$
−0.840688 + 0.541519i $$0.817849\pi$$
$$468$$ 6.03378e7 2.63482e7i 0.588643 0.257047i
$$469$$ 2.30630e6 0.0223562
$$470$$ 645964. + 372947.i 0.00622178 + 0.00359215i
$$471$$ −2.95960e7 1.41731e8i −0.283250 1.35644i
$$472$$ 1.04745e7 + 1.81424e7i 0.0996112 + 0.172532i
$$473$$ −3.77865e6 + 2.18161e6i −0.0357070 + 0.0206155i
$$474$$ 5.13271e7 1.07180e7i 0.481961 0.100642i
$$475$$ 8.31720e7 1.44058e8i 0.776062 1.34418i
$$476$$ 2.93196e6i 0.0271855i
$$477$$ −6.39372e7 + 8.66901e7i −0.589113 + 0.798756i
$$478$$ 3.95643e7 0.362260
$$479$$ −7.31282e6 4.22206e6i −0.0665393 0.0384165i 0.466361 0.884594i $$-0.345565\pi$$
−0.532901 + 0.846178i $$0.678898\pi$$
$$480$$ −215117. + 192302.i −0.00194514 + 0.00173884i
$$481$$ 8.52931e7 + 1.47732e8i 0.766441 + 1.32751i
$$482$$ 2.02595e7 1.16968e7i 0.180920 0.104454i
$$483$$ 1.43038e6 4.34923e6i 0.0126944 0.0385986i
$$484$$ 2.82921e7 4.90033e7i 0.249533 0.432204i
$$485$$ 914623.i 0.00801710i
$$486$$ −4.18364e7 + 6.95574e7i −0.364456 + 0.605947i
$$487$$ −3.58999e7 −0.310818 −0.155409 0.987850i $$-0.549669\pi$$
−0.155409 + 0.987850i $$0.549669\pi$$
$$488$$ 6.31416e6 + 3.64548e6i 0.0543321 + 0.0313686i
$$489$$ −6.20748e7 2.04153e7i −0.530871 0.174594i
$$490$$ 613064. + 1.06186e6i 0.00521095 + 0.00902564i
$$491$$ −6.98926e7 + 4.03525e7i −0.590455 + 0.340899i −0.765277 0.643701i $$-0.777398\pi$$
0.174823 + 0.984600i $$0.444065\pi$$
$$492$$ −5.01582e7 5.61089e7i −0.421159 0.471125i
$$493$$ 1.28389e8 2.22377e8i 1.07149 1.85587i
$$494$$ 1.70007e8i 1.41022i
$$495$$ −62250.8 45912.3i −0.000513251 0.000378542i
$$496$$ −1.77312e7 −0.145310
$$497$$ −3.30821e6 1.90999e6i −0.0269478 0.0155583i
$$498$$ −4.74355e6 2.27162e7i −0.0384074 0.183928i
$$499$$ 4.86033e7 + 8.41833e7i 0.391169 + 0.677524i 0.992604 0.121398i $$-0.0387376\pi$$
−0.601435 + 0.798921i $$0.705404\pi$$
$$500$$ −1.59753e6 + 922337.i −0.0127803 + 0.00737870i
$$501$$ 2.18541e8 4.56354e7i 1.73788 0.362902i
$$502$$ 1.73985e7 3.01351e7i 0.137531 0.238211i
$$503$$ 1.31021e8i 1.02952i 0.857333 + 0.514762i $$0.172120\pi$$
−0.857333 + 0.514762i $$0.827880\pi$$
$$504$$ 670062. + 1.53445e6i 0.00523388 + 0.0119857i
$$505$$ 145192. 0.00112737
$$506$$ −3.76552e6 2.17402e6i −0.0290652 0.0167808i
$$507$$ −6.31833e7 + 5.64823e7i −0.484817 + 0.433399i
$$508$$ 5.12741e7 + 8.88093e7i 0.391117 + 0.677435i
$$509$$ −1.64280e8 + 9.48472e7i −1.24575 + 0.719236i −0.970260 0.242067i $$-0.922175\pi$$
−0.275493 + 0.961303i $$0.588841\pi$$
$$510$$ 635698. 1.93291e6i 0.00479226 0.0145714i
$$511$$ −3.88662e6 + 6.73183e6i −0.0291279 + 0.0504511i
$$512$$ 5.93164e6i 0.0441942i
$$513$$ −1.21367e8 1.70876e8i −0.898975 1.26569i
$$514$$ 4.32667e7 0.318614
$$515$$ 1.04431e6 + 602931.i 0.00764552 + 0.00441414i
$$516$$ 6.22658e7 + 2.04781e7i 0.453211 + 0.149053i
$$517$$ −2.05530e6 3.55988e6i −0.0148731 0.0257610i
$$518$$ −3.75698e6 + 2.16909e6i −0.0270302 + 0.0156059i
$$519$$ 4.72337e7 + 5.28375e7i 0.337871 + 0.377955i
$$520$$ 471273. 816269.i 0.00335168 0.00580528i
$$521$$ 3.24426e7i 0.229405i 0.993400 + 0.114702i $$0.0365914\pi$$
−0.993400 + 0.114702i $$0.963409\pi$$
$$522$$ −1.63717e7 + 1.45724e8i −0.115102 + 1.02452i
$$523$$ 8.16094e7 0.570473 0.285237 0.958457i $$-0.407928\pi$$
0.285237 + 0.958457i $$0.407928\pi$$
$$524$$ −8.44759e7 4.87722e7i −0.587137 0.338983i
$$525$$ 1.09393e6 + 5.23868e6i 0.00755983 + 0.0362029i
$$526$$ 2.36691e7 + 4.09960e7i 0.162639 + 0.281699i
$$527$$ 1.08287e8 6.25197e7i 0.739853 0.427154i
$$528$$ 1.55656e6 325037.i 0.0105746 0.00220816i
$$529$$ 1.52860e7 2.64761e7i 0.103259 0.178849i
$$530$$ 1.54206e6i 0.0103580i
$$531$$ 8.38384e7 + 9.41906e6i 0.559963 + 0.0629106i
$$532$$ −4.32347e6 −0.0287142
$$533$$ 2.12908e8 + 1.22922e8i 1.40608 + 0.811800i
$$534$$ 1.16642e7 1.04271e7i 0.0766004 0.0684764i
$$535$$ −1.41295e6 2.44730e6i −0.00922712 0.0159818i
$$536$$ −2.84952e7 + 1.64517e7i −0.185045 + 0.106836i
$$537$$ 6.41457e7 1.95042e8i 0.414233 1.25952i
$$538$$ 6.40652e7 1.10964e8i 0.411410 0.712584i
$$539$$ 6.75713e6i 0.0431515i
$$540$$ 109046. + 1.15688e6i 0.000692515 + 0.00734694i
$$541$$ −1.52147e8 −0.960884 −0.480442 0.877027i $$-0.659524\pi$$
−0.480442 + 0.877027i $$0.659524\pi$$
$$542$$ −7.69055e7 4.44014e7i −0.483014 0.278868i
$$543$$ −2.53777e8 8.34625e7i −1.58508 0.521305i
$$544$$ 2.09147e7 + 3.62254e7i 0.129914 + 0.225017i
$$545$$ 1.37922e6 796291.i 0.00852006 0.00491906i
$$546$$ −3.64526e6 4.07773e6i −0.0223950 0.0250519i
$$547$$ −8.56437e7 + 1.48339e8i −0.523279 + 0.906346i 0.476354 + 0.879254i $$0.341958\pi$$
−0.999633 + 0.0270921i $$0.991375\pi$$
$$548$$ 1.31127e8i 0.796802i
$$549$$ 2.69084e7 1.17503e7i 0.162619 0.0710122i
$$550$$ 5.08240e6 0.0305479
$$551$$ −3.27917e8 1.89323e8i −1.96024 1.13174i
$$552$$ 1.33518e7 + 6.39397e7i 0.0793820 + 0.380149i
$$553$$ −2.17794e6 3.77231e6i −0.0128787 0.0223065i
$$554$$ 9.32431e7 5.38339e7i 0.548387 0.316612i
$$555$$ −2.94711e6 + 615409.i −0.0172392 + 0.00359986i
$$556$$ −1.78067e7 + 3.08421e7i −0.103600 + 0.179440i
$$557$$ 2.71640e8i 1.57191i −0.618283 0.785956i $$-0.712171\pi$$
0.618283 0.785956i $$-0.287829\pi$$
$$558$$ −4.23846e7 + 5.74677e7i −0.243952 + 0.330766i
$$559$$ −2.14116e8 −1.22578
$$560$$ 20758.6 + 11985.0i 0.000118204 + 6.82454e-5i
$$561$$ −8.36003e6 + 7.47340e6i −0.0473499 + 0.0423282i
$$562$$ −3.66351e7 6.34538e7i −0.206390 0.357477i
$$563$$ 2.27013e8 1.31066e8i 1.27211 0.734454i 0.296727 0.954962i $$-0.404105\pi$$
0.975385 + 0.220508i $$0.0707715\pi$$
$$564$$ −1.92924e7 + 5.86607e7i −0.107535 + 0.326972i
$$565$$ −1.60986e6 + 2.78836e6i −0.00892573 + 0.0154598i
$$566$$ 1.89470e8i 1.04494i
$$567$$ 6.57494e6 + 1.49624e6i 0.0360697 + 0.00820830i
$$568$$ 5.44987e7 0.297400
$$569$$ 2.40050e8 + 1.38593e8i 1.30306 + 0.752324i 0.980928 0.194370i $$-0.0622662\pi$$
0.322135 + 0.946694i $$0.395600\pi$$
$$570$$ −2.85027e6 937401.i −0.0153908 0.00506175i
$$571$$ 3.53749e7 + 6.12712e7i 0.190015 + 0.329115i 0.945255 0.326333i $$-0.105813\pi$$
−0.755240 + 0.655448i $$0.772480\pi$$
$$572$$ −4.49842e6 + 2.59717e6i −0.0240366 + 0.0138775i
$$573$$ −2.27645e7 2.54652e7i −0.121002 0.135358i
$$574$$ −3.12605e6 + 5.41447e6i −0.0165295 + 0.0286299i
$$575$$ 2.08774e8i 1.09818i
$$576$$ −1.92247e7 1.41789e7i −0.100599 0.0741952i
$$577$$ −1.69497e8 −0.882336 −0.441168 0.897425i $$-0.645436\pi$$
−0.441168 + 0.897425i $$0.645436\pi$$
$$578$$ −1.37209e8 7.92176e7i −0.710557 0.410240i
$$579$$ −7.22981e6 3.46225e7i −0.0372470 0.178370i
$$580$$ 1.04963e6 + 1.81802e6i 0.00537965 + 0.00931783i
$$581$$ −1.66953e6 + 963906.i −0.00851269 + 0.00491480i
$$582$$ 7.41218e7 1.54780e7i 0.375991 0.0785137i
$$583$$ 4.24912e6 7.35969e6i 0.0214434 0.0371410i
$$584$$ 1.10899e8i 0.556786i
$$585$$ −1.51903e6 3.47862e6i −0.00758752 0.0173756i
$$586$$ 8.56140e7 0.425453
$$587$$ 2.49955e8 + 1.44312e8i 1.23580 + 0.713489i 0.968233 0.250051i $$-0.0804474\pi$$
0.267566 + 0.963540i $$0.413781\pi$$
$$588$$ −7.56790e7 + 6.76528e7i −0.372257 + 0.332777i
$$589$$ −9.21916e7 1.59680e8i −0.451175 0.781458i
$$590$$ 1.04595e6 603881.i 0.00509279 0.00294032i
$$591$$ −8.29389e7 + 2.52185e8i −0.401787 + 1.22168i
$$592$$ 3.09459e7 5.35999e7i 0.149155 0.258344i
$$593$$ 1.14093e8i 0.547135i −0.961853 0.273567i $$-0.911796\pi$$
0.961853 0.273567i $$-0.0882037\pi$$
$$594$$ 2.66731e6 5.82182e6i 0.0127267 0.0277779i
$$595$$ −169034. −0.000802461
$$596$$ −1.40860e7 8.13256e6i −0.0665348 0.0384139i
$$597$$ 3.49545e8 + 1.14959e8i 1.64278 + 0.540281i
$$598$$ −1.06686e8 1.84785e8i −0.498887 0.864098i
$$599$$ −8.39663e7 + 4.84780e7i −0.390683 + 0.225561i −0.682456 0.730927i $$-0.739088\pi$$
0.291773 + 0.956488i $$0.405755\pi$$
$$600$$ −5.08853e7 5.69223e7i −0.235580 0.263529i
$$601$$ −2.05589e8 + 3.56090e8i −0.947056 + 1.64035i −0.195475 + 0.980709i $$0.562625\pi$$
−0.751581 + 0.659640i $$0.770709\pi$$
$$602$$ 5.44519e6i 0.0249588i
$$603$$ −1.47940e7 + 1.31680e8i −0.0674734 + 0.600576i
$$604$$ −1.80321e8 −0.818341
$$605$$ −2.82515e6 1.63110e6i −0.0127578 0.00736572i
$$606$$ 2.45705e6 + 1.17664e7i 0.0110407 + 0.0528722i
$$607$$ 5.43359e7 + 9.41126e7i 0.242952 + 0.420806i 0.961554 0.274616i $$-0.0885508\pi$$
−0.718602 + 0.695422i $$0.755217\pi$$
$$608$$ 5.34180e7 3.08409e7i 0.237671 0.137220i
$$609$$ 1.19247e7 2.49009e6i 0.0527953 0.0110246i
$$610$$ 210171. 364026.i 0.000925939 0.00160377i
$$611$$ 2.01719e8i 0.884347i
$$612$$ 1.67402e8 + 1.88073e7i 0.730309 + 0.0820486i
$$613$$ 2.58460e8 1.12205 0.561025 0.827799i $$-0.310407\pi$$
0.561025 + 0.827799i $$0.310407\pi$$
$$614$$ −2.65438e7 1.53251e7i −0.114672 0.0662060i
$$615$$ −3.23481e6 + 2.89174e6i −0.0139067 + 0.0124318i
$$616$$ −66048.7 114400.i −0.000282567 0.000489421i
$$617$$ 1.05483e8 6.09007e7i 0.449084 0.259278i −0.258360 0.966049i $$-0.583182\pi$$
0.707443 + 0.706770i $$0.249849\pi$$
$$618$$ −3.11894e7 + 9.48348e7i −0.132142 + 0.401793i
$$619$$ −6.31246e7 + 1.09335e8i −0.266150 + 0.460985i −0.967864 0.251473i $$-0.919085\pi$$
0.701714 + 0.712459i $$0.252418\pi$$
$$620$$ 1.02225e6i 0.00428925i
$$621$$ 2.39147e8 + 1.09567e8i 0.998597 + 0.457515i
$$622$$ 1.54799e8 0.643275
$$623$$ −1.12559e6 649857.i −0.00465494 0.00268753i
$$624$$ 7.41264e7 + 2.43788e7i 0.305084 + 0.100336i
$$625$$ −1.21991e8 2.11294e8i −0.499673 0.865460i
$$626$$ −1.11594e8 + 6.44288e7i −0.454902 + 0.262638i
$$627$$ 1.10203e7 + 1.23277e7i 0.0447085 + 0.0500127i
$$628$$ 8.58004e7 1.48611e8i 0.346426 0.600027i
$$629$$ 4.36456e8i 1.75383i
$$630$$ 88464.9 38630.7i 0.000353793 0.000154494i
$$631$$ 1.13561e6 0.00452003 0.00226002 0.999997i $$-0.499281\pi$$
0.00226002 + 0.999997i $$0.499281\pi$$
$$632$$ 5.38186e7 + 3.10722e7i 0.213197 + 0.123089i
$$633$$ 1.71797e7 + 8.22711e7i 0.0677337 + 0.324367i
$$634$$ 7.48011e7 + 1.29559e8i 0.293522 + 0.508395i
$$635$$ 5.12007e6 2.95607e6i 0.0199965 0.0115450i
$$636$$ −1.24970e8 + 2.60960e7i −0.485774 + 0.101439i
$$637$$ 1.65796e8 2.87167e8i 0.641440 1.11101i
$$638$$ 1.15690e7i 0.0445485i
$$639$$ 1.30273e8 1.76633e8i 0.499289 0.676968i
$$640$$ −341973. −0.00130452
$$641$$ −9.76272e6 5.63651e6i −0.0370678 0.0214011i 0.481352 0.876528i $$-0.340146\pi$$
−0.518419 + 0.855127i $$0.673479\pi$$
$$642$$ 1.74420e8 1.55922e8i 0.659162 0.589253i
$$643$$ 1.61344e7 + 2.79457e7i 0.0606905 + 0.105119i 0.894774 0.446519i $$-0.147336\pi$$
−0.834084 + 0.551638i $$0.814003\pi$$
$$644$$ 4.69928e6 2.71313e6i 0.0175944 0.0101581i
$$645$$ 1.18061e6 3.58977e6i 0.00439974 0.0133779i
$$646$$ −2.17487e8 + 3.76699e8i −0.806745 + 1.39732i
$$647$$ 4.30138e8i 1.58816i −0.607812 0.794081i $$-0.707952\pi$$
0.607812 0.794081i $$-0.292048\pi$$
$$648$$ −9.19089e7 + 2.84148e7i −0.337779 + 0.104429i
$$649$$ −6.65592e6 −0.0243486
$$650$$ 2.15994e8 + 1.24704e8i 0.786505 + 0.454089i
$$651$$ 5.63510e6 + 1.85328e6i 0.0204248 + 0.00671736i
$$652$$ −3.87234e7 6.70709e7i −0.139711 0.241986i
$$653$$ −4.50239e8 + 2.59945e8i −1.61697 + 0.933561i −0.629277 + 0.777181i $$0.716649\pi$$
−0.987697 + 0.156380i $$0.950018\pi$$
$$654$$ 8.78722e7 + 9.82973e7i 0.314136 + 0.351405i
$$655$$ −2.81183e6 + 4.87024e6i −0.0100061 + 0.0173311i
$$656$$ 8.91969e7i 0.315965i
$$657$$ −3.59428e8 2.65091e8i −1.26740 0.934759i
$$658$$ 5.12993e6 0.0180067
$$659$$ −3.59541e8 2.07581e8i −1.25630 0.725322i −0.283943 0.958841i $$-0.591643\pi$$
−0.972352 + 0.233519i $$0.924976\pi$$
$$660$$ −18739.2 89739.1i −6.51806e−5 0.000312140i
$$661$$ −2.11607e8 3.66515e8i −0.732700 1.26907i −0.955725 0.294261i $$-0.904926\pi$$
0.223025 0.974813i $$-0.428407\pi$$
$$662$$ −2.21077e8 + 1.27639e8i −0.762024 + 0.439955i
$$663$$ −5.38659e8 + 1.12482e8i −1.84830 + 0.385959i
$$664$$ 1.37518e7 2.38188e7i 0.0469737 0.0813609i
$$665$$ 249258.i 0.000847587i
$$666$$ −9.97465e7 2.28421e8i −0.337657 0.773239i
$$667$$ 4.75227e8 1.60149
$$668$$ 2.29149e8 + 1.32299e8i 0.768757 + 0.443842i
$$669$$ 4.04598e8 3.61687e8i 1.35128 1.20797i
$$670$$ 948480. + 1.64281e6i 0.00315358 + 0.00546216i
$$671$$ −2.00613e6 + 1.15824e6i −0.00664036 + 0.00383382i
$$672$$ −619979. + 1.88511e6i −0.00204300 + 0.00621197i
$$673$$ 862893. 1.49457e6i 0.00283082 0.00490312i −0.864607 0.502450i $$-0.832432\pi$$
0.867437 + 0.497546i $$0.165766\pi$$
$$674$$ 1.77530e8i 0.579820i
$$675$$ −3.06123e8 + 2.88549e7i −0.995370 + 0.0938227i
$$676$$ −1.00443e8 −0.325147
$$677$$ −1.62390e8 9.37561e7i −0.523352 0.302158i 0.214953 0.976624i $$-0.431040\pi$$
−0.738305 + 0.674467i $$0.764374\pi$$
$$678$$ −2.53215e8 8.32776e7i −0.812456 0.267202i
$$679$$ −3.14518e6 5.44761e6i −0.0100470 0.0174019i
$$680$$ 2.08848e6 1.20578e6i 0.00664207 0.00383480i
$$681$$ −2.14203e8 2.39616e8i −0.678242 0.758708i
$$682$$ 2.81678e6 4.87881e6i 0.00887974 0.0153802i
$$683$$ 3.29781e8i 1.03506i 0.855666 + 0.517528i $$0.173148\pi$$
−0.855666 + 0.517528i $$0.826852\pi$$
$$684$$ 2.77332e7 2.46851e8i 0.0866626 0.771378i
$$685$$ 7.55978e6 0.0235200
$$686$$ 1.46159e7 + 8.43852e6i 0.0452746 + 0.0261393i
$$687$$ 1.71283e7 + 8.20248e7i 0.0528254 + 0.252973i
$$688$$ 3.88425e7 + 6.72773e7i 0.119273 + 0.206587i
$$689$$ 3.61162e8 2.08517e8i 1.10419 0.637505i
$$690$$ 3.68628e6 769762.i 0.0112212 0.00234320i
$$691$$ 7.94682e7 1.37643e8i 0.240857 0.417177i −0.720102 0.693869i $$-0.755905\pi$$
0.960959 + 0.276692i $$0.0892381\pi$$
$$692$$ 8.39964e7i 0.253479i
$$693$$ −528656. 59393.3i −0.00158845 0.000178459i
$$694$$ 6.22291e7 0.186172
$$695$$ 1.77812e6 + 1.02660e6i 0.00529672 + 0.00305806i
$$696$$ −1.29571e8 + 1.15829e8i −0.384309 + 0.343550i
$$697$$ 3.14505e8 + 5.44738e8i 0.928814 + 1.60875i
$$698$$ 1.70392e7 9.83758e6i 0.0501052 0.0289282i
$$699$$ −7.89566e7 + 2.40076e8i −0.231184 + 0.702938i
$$700$$ −3.17136e6 + 5.49296e6i −0.00924595 + 0.0160145i
$$701$$ 1.13256e8i 0.328780i 0.986395 + 0.164390i $$0.0525656\pi$$
−0.986395 + 0.164390i $$0.947434\pi$$
$$702$$ 2.56203e8 1.81972e8i 0.740583 0.526008i
$$703$$ 6.43598e8 1.85246
$$704$$ 1.63211e6 + 942299.i 0.00467769 + 0.00270067i
$$705$$ 3.38193e6 + 1.11225e6i 0.00965155 + 0.00317422i
$$706$$ 7.62742e7 + 1.32111e8i 0.216752 + 0.375426i
$$707$$ 864780. 499281.i 0.00244707 0.00141282i
$$708$$ 6.66394e7 + 7.45455e7i 0.187772 + 0.210049i
$$709$$ −2.95239e7 + 5.11369e7i −0.0828390 + 0.143481i −0.904468 0.426541i $$-0.859732\pi$$
0.821629 + 0.570022i $$0.193065\pi$$
$$710$$ 3.14198e6i 0.00877866i
$$711$$ 2.29353e8 1.00154e8i 0.638111 0.278649i
$$712$$ 1.85427e7 0.0513727
$$713$$ 2.00410e8 + 1.15707e8i 0.552906 + 0.319221i
$$714$$ −2.86053e6 1.36987e7i −0.00785872 0.0376343i
$$715$$ 149733. + 259345.i 0.000409636 + 0.000709511i
$$716$$ 2.10740e8 1.21671e8i 0.574127 0.331472i
$$717$$ 1.84852e8 3.86005e7i 0.501495 0.104721i
$$718$$ −2.49613e8 + 4.32343e8i −0.674364 + 1.16803i
$$719$$ 1.17775e8i 0.316860i 0.987370 + 0.158430i $$0.0506433\pi$$
−0.987370 + 0.158430i $$0.949357\pi$$
$$720$$ −817449. + 1.10835e6i −0.00219010 + 0.00296947i
$$721$$ 8.29337e6 0.0221272
$$722$$ 3.25004e8 + 1.87641e8i 0.863530 + 0.498559i
$$723$$ 8.32444e7 7.44157e7i 0.220262 0.196902i
$$724$$ −1.58310e8 2.74202e8i −0.417152 0.722528i
$$725$$ −4.81069e8 + 2.77745e8i −1.26239 + 0.728841i
$$726$$ 8.43764e7 2.56556e8i 0.220501 0.670458i
$$727$$ −1.08321e8 + 1.87617e8i −0.281909 + 0.488281i −0.971855 0.235580i $$-0.924301\pi$$
0.689946 + 0.723861i $$0.257634\pi$$
$$728$$ 6.48240e6i 0.0168013i
$$729$$ −1.27605e8 + 3.65803e8i −0.329370 + 0.944201i
$$730$$ −6.39358e6 −0.0164352
$$731$$ −4.74434e8 2.73914e8i −1.21457 0.701234i
$$732$$ 3.30576e7 + 1.08721e7i 0.0842827 + 0.0277190i
$$733$$ −2.54830e8 4.41379e8i −0.647052 1.12073i −0.983824 0.179140i $$-0.942668\pi$$
0.336772 0.941586i $$-0.390665\pi$$
$$734$$ −1.47245e8 + 8.50122e7i −0.372352 + 0.214978i
$$735$$ 3.90034e6 + 4.36307e6i 0.00982292 + 0.0109883i
$$736$$ −3.87075e7 + 6.70434e7i −0.0970872 + 0.168160i
$$737$$ 1.04541e7i 0.0261145i
$$738$$ −2.89091e8 2.13215e8i −0.719226 0.530456i
$$739$$ 1.66066e8 0.411479 0.205740 0.978607i $$-0.434040\pi$$
0.205740 + 0.978607i $$0.434040\pi$$
$$740$$ −3.09016e6 1.78410e6i −0.00762580 0.00440276i
$$741$$ 1.65866e8 + 7.94307e8i 0.407664 + 1.95224i
$$742$$ 5.30280e6 + 9.18473e6i 0.0129806 + 0.0224830i
$$743$$ 6.45800e8 3.72853e8i 1.57446 0.909016i 0.578849 0.815434i $$-0.303502\pi$$
0.995612 0.0935810i $$-0.0298314\pi$$
$$744$$ −8.28438e7 + 1.72993e7i −0.201160 + 0.0420058i
$$745$$ −468861. + 812091.i −0.00113390 + 0.00196397i
$$746$$ 2.21662e8i 0.533918i
$$747$$ −4.43255e7 1.01506e8i −0.106339 0.243518i
$$748$$ −1.32900e7 −0.0317557
$$749$$ −1.68314e7 9.71764e6i −0.0400568 0.0231268i
$$750$$ −6.56412e6 + 5.86795e6i −0.0155594 + 0.0139092i
$$751$$ 5.23107e7 + 9.06048e7i 0.123501 + 0.213910i 0.921146 0.389217i $$-0.127254\pi$$
−0.797645 + 0.603127i $$0.793921\pi$$
$$752$$ −6.33820e7 + 3.65936e7i −0.149043 + 0.0860502i
$$753$$ 5.18882e7 1.57772e8i 0.121530 0.369525i
$$754$$ 2.83862e8 4.91663e8i 0.662206 1.14697i
$$755$$ 1.03959e7i 0.0241558i
$$756$$ 4.62773e6 + 6.51553e6i 0.0107103 + 0.0150794i