# Properties

 Label 74.5.d.a.43.5 Level $74$ Weight $5$ Character 74.43 Analytic conductor $7.649$ Analytic rank $0$ Dimension $14$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$74 = 2 \cdot 37$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 74.d (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.64937726820$$ Analytic rank: $$0$$ Dimension: $$14$$ Relative dimension: $$7$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ Defining polynomial: $$x^{14} + 727 x^{12} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + 220261242916 x^{2} + 446074380544$$ x^14 + 727*x^12 + 198453*x^10 + 24875201*x^8 + 1392846203*x^6 + 29089700589*x^4 + 220261242916*x^2 + 446074380544 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 43.5 Root $$4.34447i$$ of defining polynomial Character $$\chi$$ $$=$$ 74.43 Dual form 74.5.d.a.31.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-2.00000 + 2.00000i) q^{2} +5.34447i q^{3} -8.00000i q^{4} +(10.1818 + 10.1818i) q^{5} +(-10.6889 - 10.6889i) q^{6} -94.0964 q^{7} +(16.0000 + 16.0000i) q^{8} +52.4367 q^{9} +O(q^{10})$$ $$q+(-2.00000 + 2.00000i) q^{2} +5.34447i q^{3} -8.00000i q^{4} +(10.1818 + 10.1818i) q^{5} +(-10.6889 - 10.6889i) q^{6} -94.0964 q^{7} +(16.0000 + 16.0000i) q^{8} +52.4367 q^{9} -40.7273 q^{10} +104.701i q^{11} +42.7557 q^{12} +(-156.979 - 156.979i) q^{13} +(188.193 - 188.193i) q^{14} +(-54.4165 + 54.4165i) q^{15} -64.0000 q^{16} +(-288.653 - 288.653i) q^{17} +(-104.873 + 104.873i) q^{18} +(-257.997 - 257.997i) q^{19} +(81.4547 - 81.4547i) q^{20} -502.895i q^{21} +(-209.402 - 209.402i) q^{22} +(226.710 + 226.710i) q^{23} +(-85.5115 + 85.5115i) q^{24} -417.660i q^{25} +627.917 q^{26} +713.148i q^{27} +752.771i q^{28} +(-59.2294 + 59.2294i) q^{29} -217.666i q^{30} +(-608.888 + 608.888i) q^{31} +(128.000 - 128.000i) q^{32} -559.571 q^{33} +1154.61 q^{34} +(-958.074 - 958.074i) q^{35} -419.493i q^{36} +(-913.654 + 1019.51i) q^{37} +1031.99 q^{38} +(838.970 - 838.970i) q^{39} +325.819i q^{40} +1818.47i q^{41} +(1005.79 + 1005.79i) q^{42} +(1889.70 + 1889.70i) q^{43} +837.608 q^{44} +(533.902 + 533.902i) q^{45} -906.840 q^{46} -2515.46 q^{47} -342.046i q^{48} +6453.12 q^{49} +(835.321 + 835.321i) q^{50} +(1542.70 - 1542.70i) q^{51} +(-1255.83 + 1255.83i) q^{52} -185.050 q^{53} +(-1426.30 - 1426.30i) q^{54} +(-1066.05 + 1066.05i) q^{55} +(-1505.54 - 1505.54i) q^{56} +(1378.85 - 1378.85i) q^{57} -236.918i q^{58} +(-1987.36 - 1987.36i) q^{59} +(435.332 + 435.332i) q^{60} +(-4805.67 + 4805.67i) q^{61} -2435.55i q^{62} -4934.10 q^{63} +512.000i q^{64} -3196.67i q^{65} +(1119.14 - 1119.14i) q^{66} +2627.87i q^{67} +(-2309.23 + 2309.23i) q^{68} +(-1211.64 + 1211.64i) q^{69} +3832.29 q^{70} +5726.26 q^{71} +(838.987 + 838.987i) q^{72} -7873.75i q^{73} +(-211.711 - 3866.32i) q^{74} +2232.17 q^{75} +(-2063.97 + 2063.97i) q^{76} -9851.98i q^{77} +3355.88i q^{78} +(3214.81 + 3214.81i) q^{79} +(-651.637 - 651.637i) q^{80} +435.978 q^{81} +(-3636.95 - 3636.95i) q^{82} -9870.10 q^{83} -4023.16 q^{84} -5878.04i q^{85} -7558.78 q^{86} +(-316.550 - 316.550i) q^{87} +(-1675.22 + 1675.22i) q^{88} +(3659.89 - 3659.89i) q^{89} -2135.61 q^{90} +(14771.2 + 14771.2i) q^{91} +(1813.68 - 1813.68i) q^{92} +(-3254.18 - 3254.18i) q^{93} +(5030.93 - 5030.93i) q^{94} -5253.76i q^{95} +(684.092 + 684.092i) q^{96} +(945.694 + 945.694i) q^{97} +(-12906.2 + 12906.2i) q^{98} +5490.17i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9}+O(q^{10})$$ 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 $$14 q - 28 q^{2} - 12 q^{5} - 40 q^{6} + 48 q^{7} + 224 q^{8} - 346 q^{9} + 48 q^{10} + 160 q^{12} - 56 q^{13} - 96 q^{14} - 378 q^{15} - 896 q^{16} - 348 q^{17} + 692 q^{18} - 184 q^{19} - 96 q^{20} - 320 q^{22} - 502 q^{23} - 320 q^{24} + 224 q^{26} - 474 q^{29} - 630 q^{31} + 1792 q^{32} + 632 q^{33} + 1392 q^{34} + 1826 q^{35} - 2544 q^{37} + 736 q^{38} - 798 q^{39} - 224 q^{42} + 1936 q^{43} + 1280 q^{44} + 6162 q^{45} + 2008 q^{46} + 5716 q^{47} + 7862 q^{49} - 1372 q^{50} - 2422 q^{51} - 448 q^{52} - 20228 q^{53} - 656 q^{54} + 14006 q^{55} + 768 q^{56} - 2270 q^{57} - 4502 q^{59} + 3024 q^{60} - 11906 q^{61} - 2588 q^{63} - 1264 q^{66} - 2784 q^{68} + 21440 q^{69} - 7304 q^{70} - 11224 q^{71} - 5536 q^{72} + 4924 q^{74} - 18652 q^{75} - 1472 q^{76} + 20488 q^{79} + 768 q^{80} - 1706 q^{81} + 9808 q^{82} - 20224 q^{83} + 896 q^{84} - 7744 q^{86} + 19636 q^{87} - 2560 q^{88} + 13864 q^{89} - 24648 q^{90} - 6070 q^{91} - 4016 q^{92} - 13800 q^{93} - 11432 q^{94} + 2560 q^{96} + 16622 q^{97} - 15724 q^{98}+O(q^{100})$$ 14 * q - 28 * q^2 - 12 * q^5 - 40 * q^6 + 48 * q^7 + 224 * q^8 - 346 * q^9 + 48 * q^10 + 160 * q^12 - 56 * q^13 - 96 * q^14 - 378 * q^15 - 896 * q^16 - 348 * q^17 + 692 * q^18 - 184 * q^19 - 96 * q^20 - 320 * q^22 - 502 * q^23 - 320 * q^24 + 224 * q^26 - 474 * q^29 - 630 * q^31 + 1792 * q^32 + 632 * q^33 + 1392 * q^34 + 1826 * q^35 - 2544 * q^37 + 736 * q^38 - 798 * q^39 - 224 * q^42 + 1936 * q^43 + 1280 * q^44 + 6162 * q^45 + 2008 * q^46 + 5716 * q^47 + 7862 * q^49 - 1372 * q^50 - 2422 * q^51 - 448 * q^52 - 20228 * q^53 - 656 * q^54 + 14006 * q^55 + 768 * q^56 - 2270 * q^57 - 4502 * q^59 + 3024 * q^60 - 11906 * q^61 - 2588 * q^63 - 1264 * q^66 - 2784 * q^68 + 21440 * q^69 - 7304 * q^70 - 11224 * q^71 - 5536 * q^72 + 4924 * q^74 - 18652 * q^75 - 1472 * q^76 + 20488 * q^79 + 768 * q^80 - 1706 * q^81 + 9808 * q^82 - 20224 * q^83 + 896 * q^84 - 7744 * q^86 + 19636 * q^87 - 2560 * q^88 + 13864 * q^89 - 24648 * q^90 - 6070 * q^91 - 4016 * q^92 - 13800 * q^93 - 11432 * q^94 + 2560 * q^96 + 16622 * q^97 - 15724 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$$.

 $$n$$ $$39$$ $$\chi(n)$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −2.00000 + 2.00000i −0.500000 + 0.500000i
$$3$$ 5.34447i 0.593830i 0.954904 + 0.296915i $$0.0959577\pi$$
−0.954904 + 0.296915i $$0.904042\pi$$
$$4$$ 8.00000i 0.500000i
$$5$$ 10.1818 + 10.1818i 0.407273 + 0.407273i 0.880787 0.473513i $$-0.157014\pi$$
−0.473513 + 0.880787i $$0.657014\pi$$
$$6$$ −10.6889 10.6889i −0.296915 0.296915i
$$7$$ −94.0964 −1.92033 −0.960167 0.279427i $$-0.909855\pi$$
−0.960167 + 0.279427i $$0.909855\pi$$
$$8$$ 16.0000 + 16.0000i 0.250000 + 0.250000i
$$9$$ 52.4367 0.647366
$$10$$ −40.7273 −0.407273
$$11$$ 104.701i 0.865297i 0.901563 + 0.432649i $$0.142421\pi$$
−0.901563 + 0.432649i $$0.857579\pi$$
$$12$$ 42.7557 0.296915
$$13$$ −156.979 156.979i −0.928871 0.928871i 0.0687618 0.997633i $$-0.478095\pi$$
−0.997633 + 0.0687618i $$0.978095\pi$$
$$14$$ 188.193 188.193i 0.960167 0.960167i
$$15$$ −54.4165 + 54.4165i −0.241851 + 0.241851i
$$16$$ −64.0000 −0.250000
$$17$$ −288.653 288.653i −0.998801 0.998801i 0.00119826 0.999999i $$-0.499619\pi$$
−0.999999 + 0.00119826i $$0.999619\pi$$
$$18$$ −104.873 + 104.873i −0.323683 + 0.323683i
$$19$$ −257.997 257.997i −0.714672 0.714672i 0.252837 0.967509i $$-0.418636\pi$$
−0.967509 + 0.252837i $$0.918636\pi$$
$$20$$ 81.4547 81.4547i 0.203637 0.203637i
$$21$$ 502.895i 1.14035i
$$22$$ −209.402 209.402i −0.432649 0.432649i
$$23$$ 226.710 + 226.710i 0.428563 + 0.428563i 0.888139 0.459575i $$-0.151998\pi$$
−0.459575 + 0.888139i $$0.651998\pi$$
$$24$$ −85.5115 + 85.5115i −0.148457 + 0.148457i
$$25$$ 417.660i 0.668257i
$$26$$ 627.917 0.928871
$$27$$ 713.148i 0.978255i
$$28$$ 752.771i 0.960167i
$$29$$ −59.2294 + 59.2294i −0.0704274 + 0.0704274i −0.741443 0.671016i $$-0.765858\pi$$
0.671016 + 0.741443i $$0.265858\pi$$
$$30$$ 217.666i 0.241851i
$$31$$ −608.888 + 608.888i −0.633598 + 0.633598i −0.948969 0.315371i $$-0.897871\pi$$
0.315371 + 0.948969i $$0.397871\pi$$
$$32$$ 128.000 128.000i 0.125000 0.125000i
$$33$$ −559.571 −0.513839
$$34$$ 1154.61 0.998801
$$35$$ −958.074 958.074i −0.782101 0.782101i
$$36$$ 419.493i 0.323683i
$$37$$ −913.654 + 1019.51i −0.667388 + 0.744711i
$$38$$ 1031.99 0.714672
$$39$$ 838.970 838.970i 0.551591 0.551591i
$$40$$ 325.819i 0.203637i
$$41$$ 1818.47i 1.08178i 0.841093 + 0.540891i $$0.181913\pi$$
−0.841093 + 0.540891i $$0.818087\pi$$
$$42$$ 1005.79 + 1005.79i 0.570175 + 0.570175i
$$43$$ 1889.70 + 1889.70i 1.02201 + 1.02201i 0.999752 + 0.0222575i $$0.00708538\pi$$
0.0222575 + 0.999752i $$0.492915\pi$$
$$44$$ 837.608 0.432649
$$45$$ 533.902 + 533.902i 0.263655 + 0.263655i
$$46$$ −906.840 −0.428563
$$47$$ −2515.46 −1.13873 −0.569367 0.822084i $$-0.692812\pi$$
−0.569367 + 0.822084i $$0.692812\pi$$
$$48$$ 342.046i 0.148457i
$$49$$ 6453.12 2.68768
$$50$$ 835.321 + 835.321i 0.334128 + 0.334128i
$$51$$ 1542.70 1542.70i 0.593118 0.593118i
$$52$$ −1255.83 + 1255.83i −0.464436 + 0.464436i
$$53$$ −185.050 −0.0658777 −0.0329388 0.999457i $$-0.510487\pi$$
−0.0329388 + 0.999457i $$0.510487\pi$$
$$54$$ −1426.30 1426.30i −0.489127 0.489127i
$$55$$ −1066.05 + 1066.05i −0.352413 + 0.352413i
$$56$$ −1505.54 1505.54i −0.480083 0.480083i
$$57$$ 1378.85 1378.85i 0.424393 0.424393i
$$58$$ 236.918i 0.0704274i
$$59$$ −1987.36 1987.36i −0.570916 0.570916i 0.361468 0.932384i $$-0.382276\pi$$
−0.932384 + 0.361468i $$0.882276\pi$$
$$60$$ 435.332 + 435.332i 0.120925 + 0.120925i
$$61$$ −4805.67 + 4805.67i −1.29150 + 1.29150i −0.357642 + 0.933859i $$0.616419\pi$$
−0.933859 + 0.357642i $$0.883581\pi$$
$$62$$ 2435.55i 0.633598i
$$63$$ −4934.10 −1.24316
$$64$$ 512.000i 0.125000i
$$65$$ 3196.67i 0.756609i
$$66$$ 1119.14 1119.14i 0.256920 0.256920i
$$67$$ 2627.87i 0.585402i 0.956204 + 0.292701i $$0.0945540\pi$$
−0.956204 + 0.292701i $$0.905446\pi$$
$$68$$ −2309.23 + 2309.23i −0.499401 + 0.499401i
$$69$$ −1211.64 + 1211.64i −0.254494 + 0.254494i
$$70$$ 3832.29 0.782101
$$71$$ 5726.26 1.13594 0.567968 0.823050i $$-0.307730\pi$$
0.567968 + 0.823050i $$0.307730\pi$$
$$72$$ 838.987 + 838.987i 0.161842 + 0.161842i
$$73$$ 7873.75i 1.47753i −0.673964 0.738764i $$-0.735410\pi$$
0.673964 0.738764i $$-0.264590\pi$$
$$74$$ −211.711 3866.32i −0.0386615 0.706049i
$$75$$ 2232.17 0.396831
$$76$$ −2063.97 + 2063.97i −0.357336 + 0.357336i
$$77$$ 9851.98i 1.66166i
$$78$$ 3355.88i 0.551591i
$$79$$ 3214.81 + 3214.81i 0.515112 + 0.515112i 0.916088 0.400977i $$-0.131329\pi$$
−0.400977 + 0.916088i $$0.631329\pi$$
$$80$$ −651.637 651.637i −0.101818 0.101818i
$$81$$ 435.978 0.0664499
$$82$$ −3636.95 3636.95i −0.540891 0.540891i
$$83$$ −9870.10 −1.43273 −0.716367 0.697724i $$-0.754196\pi$$
−0.716367 + 0.697724i $$0.754196\pi$$
$$84$$ −4023.16 −0.570175
$$85$$ 5878.04i 0.813570i
$$86$$ −7558.78 −1.02201
$$87$$ −316.550 316.550i −0.0418218 0.0418218i
$$88$$ −1675.22 + 1675.22i −0.216324 + 0.216324i
$$89$$ 3659.89 3659.89i 0.462049 0.462049i −0.437278 0.899327i $$-0.644057\pi$$
0.899327 + 0.437278i $$0.144057\pi$$
$$90$$ −2135.61 −0.263655
$$91$$ 14771.2 + 14771.2i 1.78374 + 1.78374i
$$92$$ 1813.68 1813.68i 0.214282 0.214282i
$$93$$ −3254.18 3254.18i −0.376249 0.376249i
$$94$$ 5030.93 5030.93i 0.569367 0.569367i
$$95$$ 5253.76i 0.582134i
$$96$$ 684.092 + 684.092i 0.0742287 + 0.0742287i
$$97$$ 945.694 + 945.694i 0.100510 + 0.100510i 0.755573 0.655064i $$-0.227358\pi$$
−0.655064 + 0.755573i $$0.727358\pi$$
$$98$$ −12906.2 + 12906.2i −1.34384 + 1.34384i
$$99$$ 5490.17i 0.560164i
$$100$$ −3341.28 −0.334128
$$101$$ 18425.6i 1.80625i 0.429378 + 0.903125i $$0.358733\pi$$
−0.429378 + 0.903125i $$0.641267\pi$$
$$102$$ 6170.79i 0.593118i
$$103$$ −663.465 + 663.465i −0.0625379 + 0.0625379i −0.737684 0.675146i $$-0.764081\pi$$
0.675146 + 0.737684i $$0.264081\pi$$
$$104$$ 5023.34i 0.464436i
$$105$$ 5120.39 5120.39i 0.464435 0.464435i
$$106$$ 370.101 370.101i 0.0329388 0.0329388i
$$107$$ −1562.94 −0.136513 −0.0682565 0.997668i $$-0.521744\pi$$
−0.0682565 + 0.997668i $$0.521744\pi$$
$$108$$ 5705.18 0.489127
$$109$$ −10571.0 10571.0i −0.889738 0.889738i 0.104759 0.994498i $$-0.466593\pi$$
−0.994498 + 0.104759i $$0.966593\pi$$
$$110$$ 4264.19i 0.352413i
$$111$$ −5448.73 4882.99i −0.442231 0.396314i
$$112$$ 6022.17 0.480083
$$113$$ 4684.76 4684.76i 0.366886 0.366886i −0.499455 0.866340i $$-0.666466\pi$$
0.866340 + 0.499455i $$0.166466\pi$$
$$114$$ 5515.42i 0.424393i
$$115$$ 4616.65i 0.349085i
$$116$$ 473.835 + 473.835i 0.0352137 + 0.0352137i
$$117$$ −8231.47 8231.47i −0.601320 0.601320i
$$118$$ 7949.43 0.570916
$$119$$ 27161.2 + 27161.2i 1.91803 + 1.91803i
$$120$$ −1741.33 −0.120925
$$121$$ 3678.71 0.251261
$$122$$ 19222.7i 1.29150i
$$123$$ −9718.77 −0.642394
$$124$$ 4871.10 + 4871.10i 0.316799 + 0.316799i
$$125$$ 10616.2 10616.2i 0.679437 0.679437i
$$126$$ 9868.20 9868.20i 0.621580 0.621580i
$$127$$ 860.617 0.0533584 0.0266792 0.999644i $$-0.491507\pi$$
0.0266792 + 0.999644i $$0.491507\pi$$
$$128$$ −1024.00 1024.00i −0.0625000 0.0625000i
$$129$$ −10099.4 + 10099.4i −0.606900 + 0.606900i
$$130$$ 6393.35 + 6393.35i 0.378305 + 0.378305i
$$131$$ 9264.84 9264.84i 0.539878 0.539878i −0.383615 0.923493i $$-0.625321\pi$$
0.923493 + 0.383615i $$0.125321\pi$$
$$132$$ 4476.57i 0.256920i
$$133$$ 24276.5 + 24276.5i 1.37241 + 1.37241i
$$134$$ −5255.74 5255.74i −0.292701 0.292701i
$$135$$ −7261.15 + 7261.15i −0.398417 + 0.398417i
$$136$$ 9236.91i 0.499401i
$$137$$ −12740.7 −0.678817 −0.339409 0.940639i $$-0.610227\pi$$
−0.339409 + 0.940639i $$0.610227\pi$$
$$138$$ 4846.58i 0.254494i
$$139$$ 2561.90i 0.132597i −0.997800 0.0662984i $$-0.978881\pi$$
0.997800 0.0662984i $$-0.0211189\pi$$
$$140$$ −7664.59 + 7664.59i −0.391050 + 0.391050i
$$141$$ 13443.8i 0.676214i
$$142$$ −11452.5 + 11452.5i −0.567968 + 0.567968i
$$143$$ 16435.9 16435.9i 0.803750 0.803750i
$$144$$ −3355.95 −0.161842
$$145$$ −1206.13 −0.0573664
$$146$$ 15747.5 + 15747.5i 0.738764 + 0.738764i
$$147$$ 34488.5i 1.59602i
$$148$$ 8156.07 + 7309.23i 0.372355 + 0.333694i
$$149$$ −16513.4 −0.743814 −0.371907 0.928270i $$-0.621296\pi$$
−0.371907 + 0.928270i $$0.621296\pi$$
$$150$$ −4464.34 + 4464.34i −0.198415 + 0.198415i
$$151$$ 3594.24i 0.157635i −0.996889 0.0788176i $$-0.974886\pi$$
0.996889 0.0788176i $$-0.0251145\pi$$
$$152$$ 8255.89i 0.357336i
$$153$$ −15136.0 15136.0i −0.646590 0.646590i
$$154$$ 19704.0 + 19704.0i 0.830830 + 0.830830i
$$155$$ −12399.2 −0.516095
$$156$$ −6711.76 6711.76i −0.275796 0.275796i
$$157$$ 1308.30 0.0530772 0.0265386 0.999648i $$-0.491552\pi$$
0.0265386 + 0.999648i $$0.491552\pi$$
$$158$$ −12859.3 −0.515112
$$159$$ 988.995i 0.0391201i
$$160$$ 2606.55 0.101818
$$161$$ −21332.6 21332.6i −0.822985 0.822985i
$$162$$ −871.955 + 871.955i −0.0332249 + 0.0332249i
$$163$$ −19856.3 + 19856.3i −0.747347 + 0.747347i −0.973980 0.226633i $$-0.927228\pi$$
0.226633 + 0.973980i $$0.427228\pi$$
$$164$$ 14547.8 0.540891
$$165$$ −5697.46 5697.46i −0.209273 0.209273i
$$166$$ 19740.2 19740.2i 0.716367 0.716367i
$$167$$ −16420.6 16420.6i −0.588786 0.588786i 0.348517 0.937303i $$-0.386685\pi$$
−0.937303 + 0.348517i $$0.886685\pi$$
$$168$$ 8046.32 8046.32i 0.285088 0.285088i
$$169$$ 20724.0i 0.725604i
$$170$$ 11756.1 + 11756.1i 0.406785 + 0.406785i
$$171$$ −13528.5 13528.5i −0.462655 0.462655i
$$172$$ 15117.6 15117.6i 0.511005 0.511005i
$$173$$ 1380.88i 0.0461384i 0.999734 + 0.0230692i $$0.00734381\pi$$
−0.999734 + 0.0230692i $$0.992656\pi$$
$$174$$ 1266.20 0.0418218
$$175$$ 39300.3i 1.28328i
$$176$$ 6700.86i 0.216324i
$$177$$ 10621.4 10621.4i 0.339027 0.339027i
$$178$$ 14639.6i 0.462049i
$$179$$ −11082.5 + 11082.5i −0.345886 + 0.345886i −0.858575 0.512688i $$-0.828650\pi$$
0.512688 + 0.858575i $$0.328650\pi$$
$$180$$ 4271.21 4271.21i 0.131828 0.131828i
$$181$$ 17811.1 0.543667 0.271833 0.962344i $$-0.412370\pi$$
0.271833 + 0.962344i $$0.412370\pi$$
$$182$$ −59084.7 −1.78374
$$183$$ −25683.8 25683.8i −0.766931 0.766931i
$$184$$ 7254.72i 0.214282i
$$185$$ −19683.1 + 1077.80i −0.575110 + 0.0314916i
$$186$$ 13016.7 0.376249
$$187$$ 30222.3 30222.3i 0.864260 0.864260i
$$188$$ 20123.7i 0.569367i
$$189$$ 67104.6i 1.87858i
$$190$$ 10507.5 + 10507.5i 0.291067 + 0.291067i
$$191$$ −14170.9 14170.9i −0.388446 0.388446i 0.485687 0.874133i $$-0.338569\pi$$
−0.874133 + 0.485687i $$0.838569\pi$$
$$192$$ −2736.37 −0.0742287
$$193$$ −31829.7 31829.7i −0.854511 0.854511i 0.136174 0.990685i $$-0.456519\pi$$
−0.990685 + 0.136174i $$0.956519\pi$$
$$194$$ −3782.78 −0.100510
$$195$$ 17084.5 0.449297
$$196$$ 51625.0i 1.34384i
$$197$$ 38635.1 0.995520 0.497760 0.867315i $$-0.334156\pi$$
0.497760 + 0.867315i $$0.334156\pi$$
$$198$$ −10980.3 10980.3i −0.280082 0.280082i
$$199$$ −42102.2 + 42102.2i −1.06316 + 1.06316i −0.0652938 + 0.997866i $$0.520798\pi$$
−0.997866 + 0.0652938i $$0.979202\pi$$
$$200$$ 6682.57 6682.57i 0.167064 0.167064i
$$201$$ −14044.6 −0.347629
$$202$$ −36851.1 36851.1i −0.903125 0.903125i
$$203$$ 5573.27 5573.27i 0.135244 0.135244i
$$204$$ −12341.6 12341.6i −0.296559 0.296559i
$$205$$ −18515.4 + 18515.4i −0.440581 + 0.440581i
$$206$$ 2653.86i 0.0625379i
$$207$$ 11887.9 + 11887.9i 0.277438 + 0.277438i
$$208$$ 10046.7 + 10046.7i 0.232218 + 0.232218i
$$209$$ 27012.5 27012.5i 0.618404 0.618404i
$$210$$ 20481.6i 0.464435i
$$211$$ 3844.31 0.0863483 0.0431742 0.999068i $$-0.486253\pi$$
0.0431742 + 0.999068i $$0.486253\pi$$
$$212$$ 1480.40i 0.0329388i
$$213$$ 30603.8i 0.674553i
$$214$$ 3125.87 3125.87i 0.0682565 0.0682565i
$$215$$ 38481.1i 0.832475i
$$216$$ −11410.4 + 11410.4i −0.244564 + 0.244564i
$$217$$ 57294.1 57294.1i 1.21672 1.21672i
$$218$$ 42283.9 0.889738
$$219$$ 42081.0 0.877400
$$220$$ 8528.38 + 8528.38i 0.176206 + 0.176206i
$$221$$ 90625.2i 1.85552i
$$222$$ 20663.4 1131.48i 0.419273 0.0229584i
$$223$$ −61406.0 −1.23481 −0.617406 0.786644i $$-0.711817\pi$$
−0.617406 + 0.786644i $$0.711817\pi$$
$$224$$ −12044.3 + 12044.3i −0.240042 + 0.240042i
$$225$$ 21900.7i 0.432607i
$$226$$ 18739.0i 0.366886i
$$227$$ 27233.3 + 27233.3i 0.528504 + 0.528504i 0.920126 0.391622i $$-0.128086\pi$$
−0.391622 + 0.920126i $$0.628086\pi$$
$$228$$ −11030.8 11030.8i −0.212197 0.212197i
$$229$$ 65938.4 1.25738 0.628691 0.777655i $$-0.283591\pi$$
0.628691 + 0.777655i $$0.283591\pi$$
$$230$$ −9233.30 9233.30i −0.174542 0.174542i
$$231$$ 52653.6 0.986742
$$232$$ −1895.34 −0.0352137
$$233$$ 56189.5i 1.03501i 0.855681 + 0.517504i $$0.173139\pi$$
−0.855681 + 0.517504i $$0.826861\pi$$
$$234$$ 32925.9 0.601320
$$235$$ −25612.0 25612.0i −0.463776 0.463776i
$$236$$ −15898.9 + 15898.9i −0.285458 + 0.285458i
$$237$$ −17181.5 + 17181.5i −0.305889 + 0.305889i
$$238$$ −108645. −1.91803
$$239$$ −79431.0 79431.0i −1.39057 1.39057i −0.824036 0.566538i $$-0.808282\pi$$
−0.566538 0.824036i $$-0.691718\pi$$
$$240$$ 3482.65 3482.65i 0.0604627 0.0604627i
$$241$$ 21019.1 + 21019.1i 0.361893 + 0.361893i 0.864509 0.502617i $$-0.167629\pi$$
−0.502617 + 0.864509i $$0.667629\pi$$
$$242$$ −7357.42 + 7357.42i −0.125630 + 0.125630i
$$243$$ 60095.0i 1.01771i
$$244$$ 38445.4 + 38445.4i 0.645750 + 0.645750i
$$245$$ 65704.6 + 65704.6i 1.09462 + 1.09462i
$$246$$ 19437.5 19437.5i 0.321197 0.321197i
$$247$$ 81000.2i 1.32768i
$$248$$ −19484.4 −0.316799
$$249$$ 52750.4i 0.850800i
$$250$$ 42464.8i 0.679437i
$$251$$ 57975.7 57975.7i 0.920235 0.920235i −0.0768107 0.997046i $$-0.524474\pi$$
0.997046 + 0.0768107i $$0.0244737\pi$$
$$252$$ 39472.8i 0.621580i
$$253$$ −23736.8 + 23736.8i −0.370835 + 0.370835i
$$254$$ −1721.23 + 1721.23i −0.0266792 + 0.0266792i
$$255$$ 31415.0 0.483122
$$256$$ 4096.00 0.0625000
$$257$$ −47329.8 47329.8i −0.716586 0.716586i 0.251318 0.967904i $$-0.419136\pi$$
−0.967904 + 0.251318i $$0.919136\pi$$
$$258$$ 40397.7i 0.606900i
$$259$$ 85971.5 95932.1i 1.28161 1.43009i
$$260$$ −25573.4 −0.378305
$$261$$ −3105.79 + 3105.79i −0.0455923 + 0.0455923i
$$262$$ 37059.4i 0.539878i
$$263$$ 75854.7i 1.09666i 0.836263 + 0.548329i $$0.184736\pi$$
−0.836263 + 0.548329i $$0.815264\pi$$
$$264$$ −8953.13 8953.13i −0.128460 0.128460i
$$265$$ −1884.15 1884.15i −0.0268302 0.0268302i
$$266$$ −97106.2 −1.37241
$$267$$ 19560.2 + 19560.2i 0.274378 + 0.274378i
$$268$$ 21023.0 0.292701
$$269$$ 92814.4 1.28266 0.641329 0.767266i $$-0.278384\pi$$
0.641329 + 0.767266i $$0.278384\pi$$
$$270$$ 29044.6i 0.398417i
$$271$$ 3154.18 0.0429485 0.0214743 0.999769i $$-0.493164\pi$$
0.0214743 + 0.999769i $$0.493164\pi$$
$$272$$ 18473.8 + 18473.8i 0.249700 + 0.249700i
$$273$$ −78944.0 + 78944.0i −1.05924 + 1.05924i
$$274$$ 25481.4 25481.4i 0.339409 0.339409i
$$275$$ 43729.5 0.578241
$$276$$ 9693.15 + 9693.15i 0.127247 + 0.127247i
$$277$$ 64846.9 64846.9i 0.845142 0.845142i −0.144380 0.989522i $$-0.546119\pi$$
0.989522 + 0.144380i $$0.0461188\pi$$
$$278$$ 5123.81 + 5123.81i 0.0662984 + 0.0662984i
$$279$$ −31928.1 + 31928.1i −0.410170 + 0.410170i
$$280$$ 30658.4i 0.391050i
$$281$$ 65861.6 + 65861.6i 0.834103 + 0.834103i 0.988075 0.153972i $$-0.0492066\pi$$
−0.153972 + 0.988075i $$0.549207\pi$$
$$282$$ 26887.6 + 26887.6i 0.338107 + 0.338107i
$$283$$ 19240.4 19240.4i 0.240238 0.240238i −0.576711 0.816948i $$-0.695664\pi$$
0.816948 + 0.576711i $$0.195664\pi$$
$$284$$ 45810.0i 0.567968i
$$285$$ 28078.5 0.345688
$$286$$ 65743.5i 0.803750i
$$287$$ 171112.i 2.07738i
$$288$$ 6711.90 6711.90i 0.0809208 0.0809208i
$$289$$ 83120.7i 0.995207i
$$290$$ 2412.26 2412.26i 0.0286832 0.0286832i
$$291$$ −5054.23 + 5054.23i −0.0596855 + 0.0596855i
$$292$$ −62990.0 −0.738764
$$293$$ −79617.5 −0.927413 −0.463706 0.885989i $$-0.653481\pi$$
−0.463706 + 0.885989i $$0.653481\pi$$
$$294$$ −68977.0 68977.0i −0.798012 0.798012i
$$295$$ 40469.9i 0.465038i
$$296$$ −30930.6 + 1693.69i −0.353025 + 0.0193308i
$$297$$ −74667.3 −0.846481
$$298$$ 33026.8 33026.8i 0.371907 0.371907i
$$299$$ 71177.5i 0.796160i
$$300$$ 17857.4i 0.198415i
$$301$$ −177814. 177814.i −1.96260 1.96260i
$$302$$ 7188.48 + 7188.48i 0.0788176 + 0.0788176i
$$303$$ −98474.7 −1.07260
$$304$$ 16511.8 + 16511.8i 0.178668 + 0.178668i
$$305$$ −97861.2 −1.05199
$$306$$ 60544.1 0.646590
$$307$$ 65571.3i 0.695725i −0.937546 0.347862i $$-0.886908\pi$$
0.937546 0.347862i $$-0.113092\pi$$
$$308$$ −78815.8 −0.830830
$$309$$ −3545.86 3545.86i −0.0371369 0.0371369i
$$310$$ 24798.4 24798.4i 0.258048 0.258048i
$$311$$ 48552.1 48552.1i 0.501981 0.501981i −0.410072 0.912053i $$-0.634497\pi$$
0.912053 + 0.410072i $$0.134497\pi$$
$$312$$ 26847.0 0.275796
$$313$$ 16168.1 + 16168.1i 0.165033 + 0.165033i 0.784792 0.619759i $$-0.212770\pi$$
−0.619759 + 0.784792i $$0.712770\pi$$
$$314$$ −2616.60 + 2616.60i −0.0265386 + 0.0265386i
$$315$$ −50238.2 50238.2i −0.506306 0.506306i
$$316$$ 25718.5 25718.5i 0.257556 0.257556i
$$317$$ 93230.4i 0.927767i 0.885896 + 0.463884i $$0.153544\pi$$
−0.885896 + 0.463884i $$0.846456\pi$$
$$318$$ 1977.99 + 1977.99i 0.0195601 + 0.0195601i
$$319$$ −6201.38 6201.38i −0.0609406 0.0609406i
$$320$$ −5213.10 + 5213.10i −0.0509092 + 0.0509092i
$$321$$ 8353.07i 0.0810655i
$$322$$ 85330.3 0.822985
$$323$$ 148943.i 1.42763i
$$324$$ 3487.82i 0.0332249i
$$325$$ −65564.0 + 65564.0i −0.620725 + 0.620725i
$$326$$ 79425.1i 0.747347i
$$327$$ 56496.2 56496.2i 0.528353 0.528353i
$$328$$ −29095.6 + 29095.6i −0.270445 + 0.270445i
$$329$$ 236696. 2.18675
$$330$$ 22789.8 0.209273
$$331$$ −16551.9 16551.9i −0.151075 0.151075i 0.627523 0.778598i $$-0.284069\pi$$
−0.778598 + 0.627523i $$0.784069\pi$$
$$332$$ 78960.8i 0.716367i
$$333$$ −47909.0 + 53459.7i −0.432044 + 0.482101i
$$334$$ 65682.6 0.588786
$$335$$ −26756.5 + 26756.5i −0.238419 + 0.238419i
$$336$$ 32185.3i 0.285088i
$$337$$ 154951.i 1.36437i 0.731177 + 0.682187i $$0.238971\pi$$
−0.731177 + 0.682187i $$0.761029\pi$$
$$338$$ −41447.9 41447.9i −0.362802 0.362802i
$$339$$ 25037.6 + 25037.6i 0.217868 + 0.217868i
$$340$$ −47024.4 −0.406785
$$341$$ −63751.1 63751.1i −0.548251 0.548251i
$$342$$ 54114.0 0.462655
$$343$$ −381290. −3.24091
$$344$$ 60470.3i 0.511005i
$$345$$ −24673.5 −0.207297
$$346$$ −2761.75 2761.75i −0.0230692 0.0230692i
$$347$$ 78775.8 78775.8i 0.654235 0.654235i −0.299775 0.954010i $$-0.596912\pi$$
0.954010 + 0.299775i $$0.0969116\pi$$
$$348$$ −2532.40 + 2532.40i −0.0209109 + 0.0209109i
$$349$$ −85580.9 −0.702629 −0.351314 0.936258i $$-0.614265\pi$$
−0.351314 + 0.936258i $$0.614265\pi$$
$$350$$ −78600.7 78600.7i −0.641638 0.641638i
$$351$$ 111949. 111949.i 0.908673 0.908673i
$$352$$ 13401.7 + 13401.7i 0.108162 + 0.108162i
$$353$$ 142011. 142011.i 1.13965 1.13965i 0.151136 0.988513i $$-0.451707\pi$$
0.988513 0.151136i $$-0.0482933\pi$$
$$354$$ 42485.5i 0.339027i
$$355$$ 58303.8 + 58303.8i 0.462637 + 0.462637i
$$356$$ −29279.1 29279.1i −0.231025 0.231025i
$$357$$ −145162. + 145162.i −1.13898 + 1.13898i
$$358$$ 44330.2i 0.345886i
$$359$$ 8356.70 0.0648404 0.0324202 0.999474i $$-0.489679\pi$$
0.0324202 + 0.999474i $$0.489679\pi$$
$$360$$ 17084.9i 0.131828i
$$361$$ 2803.52i 0.0215124i
$$362$$ −35622.1 + 35622.1i −0.271833 + 0.271833i
$$363$$ 19660.7i 0.149206i
$$364$$ 118169. 118169.i 0.891872 0.891872i
$$365$$ 80169.2 80169.2i 0.601758 0.601758i
$$366$$ 102735. 0.766931
$$367$$ 18123.6 0.134559 0.0672795 0.997734i $$-0.478568\pi$$
0.0672795 + 0.997734i $$0.478568\pi$$
$$368$$ −14509.4 14509.4i −0.107141 0.107141i
$$369$$ 95354.8i 0.700309i
$$370$$ 37210.7 41521.9i 0.271809 0.303301i
$$371$$ 17412.6 0.126507
$$372$$ −26033.4 + 26033.4i −0.188125 + 0.188125i
$$373$$ 54554.8i 0.392117i 0.980592 + 0.196058i $$0.0628142\pi$$
−0.980592 + 0.196058i $$0.937186\pi$$
$$374$$ 120889.i 0.864260i
$$375$$ 56737.9 + 56737.9i 0.403470 + 0.403470i
$$376$$ −40247.4 40247.4i −0.284683 0.284683i
$$377$$ 18595.6 0.130836
$$378$$ 134209. + 134209.i 0.939288 + 0.939288i
$$379$$ −217488. −1.51411 −0.757053 0.653354i $$-0.773361\pi$$
−0.757053 + 0.653354i $$0.773361\pi$$
$$380$$ −42030.1 −0.291067
$$381$$ 4599.54i 0.0316858i
$$382$$ 56683.5 0.388446
$$383$$ 114457. + 114457.i 0.780269 + 0.780269i 0.979876 0.199607i $$-0.0639666\pi$$
−0.199607 + 0.979876i $$0.563967\pi$$
$$384$$ 5472.73 5472.73i 0.0371143 0.0371143i
$$385$$ 100311. 100311.i 0.676750 0.676750i
$$386$$ 127319. 0.854511
$$387$$ 99089.4 + 99089.4i 0.661615 + 0.661615i
$$388$$ 7565.56 7565.56i 0.0502548 0.0502548i
$$389$$ −129419. 129419.i −0.855260 0.855260i 0.135515 0.990775i $$-0.456731\pi$$
−0.990775 + 0.135515i $$0.956731\pi$$
$$390$$ −34169.0 + 34169.0i −0.224648 + 0.224648i
$$391$$ 130881.i 0.856099i
$$392$$ 103250. + 103250.i 0.671920 + 0.671920i
$$393$$ 49515.6 + 49515.6i 0.320595 + 0.320595i
$$394$$ −77270.2 + 77270.2i −0.497760 + 0.497760i
$$395$$ 65465.4i 0.419583i
$$396$$ 43921.4 0.280082
$$397$$ 89391.0i 0.567170i −0.958947 0.283585i $$-0.908476\pi$$
0.958947 0.283585i $$-0.0915237\pi$$
$$398$$ 168409.i 1.06316i
$$399$$ −129745. + 129745.i −0.814977 + 0.814977i
$$400$$ 26730.3i 0.167064i
$$401$$ −11590.6 + 11590.6i −0.0720807 + 0.0720807i −0.742228 0.670147i $$-0.766231\pi$$
0.670147 + 0.742228i $$0.266231\pi$$
$$402$$ 28089.1 28089.1i 0.173814 0.173814i
$$403$$ 191165. 1.17706
$$404$$ 147404. 0.903125
$$405$$ 4439.05 + 4439.05i 0.0270633 + 0.0270633i
$$406$$ 22293.1i 0.135244i
$$407$$ −106744. 95660.4i −0.644396 0.577489i
$$408$$ 49366.4 0.296559
$$409$$ −158731. + 158731.i −0.948890 + 0.948890i −0.998756 0.0498664i $$-0.984120\pi$$
0.0498664 + 0.998756i $$0.484120\pi$$
$$410$$ 74061.6i 0.440581i
$$411$$ 68092.3i 0.403102i
$$412$$ 5307.72 + 5307.72i 0.0312690 + 0.0312690i
$$413$$ 187003. + 187003.i 1.09635 + 1.09635i
$$414$$ −47551.7 −0.277438
$$415$$ −100496. 100496.i −0.583514 0.583514i
$$416$$ −40186.7 −0.232218
$$417$$ 13692.0 0.0787399
$$418$$ 108050.i 0.618404i
$$419$$ −53640.6 −0.305538 −0.152769 0.988262i $$-0.548819\pi$$
−0.152769 + 0.988262i $$0.548819\pi$$
$$420$$ −40963.1 40963.1i −0.232217 0.232217i
$$421$$ −113029. + 113029.i −0.637716 + 0.637716i −0.949992 0.312276i $$-0.898909\pi$$
0.312276 + 0.949992i $$0.398909\pi$$
$$422$$ −7688.63 + 7688.63i −0.0431742 + 0.0431742i
$$423$$ −131903. −0.737178
$$424$$ −2960.81 2960.81i −0.0164694 0.0164694i
$$425$$ −120559. + 120559.i −0.667456 + 0.667456i
$$426$$ −61207.6 61207.6i −0.337276 0.337276i
$$427$$ 452196. 452196.i 2.48011 2.48011i
$$428$$ 12503.5i 0.0682565i
$$429$$ 87841.0 + 87841.0i 0.477290 + 0.477290i
$$430$$ −76962.3 76962.3i −0.416237 0.416237i
$$431$$ 208728. 208728.i 1.12364 1.12364i 0.132448 0.991190i $$-0.457716\pi$$
0.991190 0.132448i $$-0.0422839\pi$$
$$432$$ 45641.5i 0.244564i
$$433$$ −75452.6 −0.402437 −0.201219 0.979546i $$-0.564490\pi$$
−0.201219 + 0.979546i $$0.564490\pi$$
$$434$$ 229176.i 1.21672i
$$435$$ 6446.11i 0.0340658i
$$436$$ −84567.9 + 84567.9i −0.444869 + 0.444869i
$$437$$ 116981.i 0.612565i
$$438$$ −84162.0 + 84162.0i −0.438700 + 0.438700i
$$439$$ −246708. + 246708.i −1.28013 + 1.28013i −0.339535 + 0.940593i $$0.610270\pi$$
−0.940593 + 0.339535i $$0.889730\pi$$
$$440$$ −34113.5 −0.176206
$$441$$ 338380. 1.73992
$$442$$ −181250. 181250.i −0.927758 0.927758i
$$443$$ 68941.1i 0.351294i 0.984453 + 0.175647i $$0.0562017\pi$$
−0.984453 + 0.175647i $$0.943798\pi$$
$$444$$ −39063.9 + 43589.8i −0.198157 + 0.221116i
$$445$$ 74528.8 0.376361
$$446$$ 122812. 122812.i 0.617406 0.617406i
$$447$$ 88255.4i 0.441699i
$$448$$ 48177.3i 0.240042i
$$449$$ 143056. + 143056.i 0.709600 + 0.709600i 0.966451 0.256851i $$-0.0826849\pi$$
−0.256851 + 0.966451i $$0.582685\pi$$
$$450$$ 43801.5 + 43801.5i 0.216304 + 0.216304i
$$451$$ −190396. −0.936062
$$452$$ −37478.1 37478.1i −0.183443 0.183443i
$$453$$ 19209.3 0.0936085
$$454$$ −108933. −0.528504
$$455$$ 300795.i 1.45294i
$$456$$ 44123.3 0.212197
$$457$$ 133820. + 133820.i 0.640752 + 0.640752i 0.950740 0.309988i $$-0.100325\pi$$
−0.309988 + 0.950740i $$0.600325\pi$$
$$458$$ −131877. + 131877.i −0.628691 + 0.628691i
$$459$$ 205853. 205853.i 0.977082 0.977082i
$$460$$ 36933.2 0.174542
$$461$$ 40084.3 + 40084.3i 0.188613 + 0.188613i 0.795096 0.606483i $$-0.207420\pi$$
−0.606483 + 0.795096i $$0.707420\pi$$
$$462$$ −105307. + 105307.i −0.493371 + 0.493371i
$$463$$ −230400. 230400.i −1.07478 1.07478i −0.996968 0.0778161i $$-0.975205\pi$$
−0.0778161 0.996968i $$-0.524795\pi$$
$$464$$ 3790.68 3790.68i 0.0176068 0.0176068i
$$465$$ 66267.0i 0.306473i
$$466$$ −112379. 112379.i −0.517504 0.517504i
$$467$$ 106600. + 106600.i 0.488790 + 0.488790i 0.907924 0.419134i $$-0.137666\pi$$
−0.419134 + 0.907924i $$0.637666\pi$$
$$468$$ −65851.8 + 65851.8i −0.300660 + 0.300660i
$$469$$ 247273.i 1.12417i
$$470$$ 102448. 0.463776
$$471$$ 6992.16i 0.0315188i
$$472$$ 63595.5i 0.285458i
$$473$$ −197853. + 197853.i −0.884342 + 0.884342i
$$474$$ 68725.8i 0.305889i
$$475$$ −107755. + 107755.i −0.477584 + 0.477584i
$$476$$ 217290. 217290.i 0.959016 0.959016i
$$477$$ −9703.43 −0.0426470
$$478$$ 317724. 1.39057
$$479$$ −142463. 142463.i −0.620913 0.620913i 0.324852 0.945765i $$-0.394685\pi$$
−0.945765 + 0.324852i $$0.894685\pi$$
$$480$$ 13930.6i 0.0604627i
$$481$$ 303466. 16617.1i 1.31166 0.0718232i
$$482$$ −84076.4 −0.361893
$$483$$ 114011. 114011.i 0.488713 0.488713i
$$484$$ 29429.7i 0.125630i
$$485$$ 19257.8i 0.0818697i
$$486$$ −120190. 120190.i −0.508857 0.508857i
$$487$$ 22476.6 + 22476.6i 0.0947706 + 0.0947706i 0.752903 0.658132i $$-0.228653\pi$$
−0.658132 + 0.752903i $$0.728653\pi$$
$$488$$ −153782. −0.645750
$$489$$ −106121. 106121.i −0.443797 0.443797i
$$490$$ −262819. −1.09462
$$491$$ −132795. −0.550831 −0.275416 0.961325i $$-0.588815\pi$$
−0.275416 + 0.961325i $$0.588815\pi$$
$$492$$ 77750.2i 0.321197i
$$493$$ 34193.6 0.140686
$$494$$ −162000. 162000.i −0.663838 0.663838i
$$495$$ −55900.0 + 55900.0i −0.228140 + 0.228140i
$$496$$ 38968.8 38968.8i 0.158399 0.158399i
$$497$$ −538820. −2.18138
$$498$$ 105501. + 105501.i 0.425400 + 0.425400i
$$499$$ 206696. 206696.i 0.830101 0.830101i −0.157430 0.987530i $$-0.550321\pi$$
0.987530 + 0.157430i $$0.0503207\pi$$
$$500$$ −84929.6 84929.6i −0.339718 0.339718i
$$501$$ 87759.6 87759.6i 0.349638 0.349638i
$$502$$ 231903.i 0.920235i
$$503$$ −119635. 119635.i −0.472849 0.472849i 0.429987 0.902835i $$-0.358518\pi$$
−0.902835 + 0.429987i $$0.858518\pi$$
$$504$$ −78945.6 78945.6i −0.310790 0.310790i
$$505$$ −187606. + 187606.i −0.735637 + 0.735637i
$$506$$ 94947.0i 0.370835i
$$507$$ −110759. −0.430885
$$508$$ 6884.94i 0.0266792i
$$509$$ 78749.6i 0.303957i −0.988384 0.151979i $$-0.951435\pi$$
0.988384 0.151979i $$-0.0485645\pi$$
$$510$$ −62830.0 + 62830.0i −0.241561 + 0.241561i
$$511$$ 740891.i 2.83735i
$$512$$ −8192.00 + 8192.00i −0.0312500 + 0.0312500i
$$513$$ 183990. 183990.i 0.699131 0.699131i
$$514$$ 189319. 0.716586
$$515$$ −13510.6 −0.0509401
$$516$$ 80795.3 + 80795.3i 0.303450 + 0.303450i
$$517$$ 263371.i 0.985343i
$$518$$ 19921.2 + 363807.i 0.0742431 + 1.35585i
$$519$$ −7380.05 −0.0273984
$$520$$ 51146.8 51146.8i 0.189152 0.189152i
$$521$$ 283986.i 1.04622i −0.852266 0.523109i $$-0.824772\pi$$
0.852266 0.523109i $$-0.175228\pi$$
$$522$$ 12423.2i 0.0455923i
$$523$$ 173621. + 173621.i 0.634746 + 0.634746i 0.949255 0.314508i $$-0.101840\pi$$
−0.314508 + 0.949255i $$0.601840\pi$$
$$524$$ −74118.7 74118.7i −0.269939 0.269939i
$$525$$ −210039. −0.762047
$$526$$ −151709. 151709.i −0.548329 0.548329i
$$527$$ 351515. 1.26568
$$528$$ 35812.5 0.128460
$$529$$ 177046.i 0.632667i
$$530$$ 7536.61 0.0268302
$$531$$ −104210. 104210.i −0.369592 0.369592i
$$532$$ 194212. 194212.i 0.686204 0.686204i
$$533$$ 285463. 285463.i 1.00484 1.00484i
$$534$$ −78240.6 −0.274378
$$535$$ −15913.6 15913.6i −0.0555981 0.0555981i
$$536$$ −42045.9 + 42045.9i −0.146350 + 0.146350i
$$537$$ −59230.3 59230.3i −0.205398 0.205398i
$$538$$ −185629. + 185629.i −0.641329 + 0.641329i
$$539$$ 675648.i 2.32564i
$$540$$ 58089.2 + 58089.2i 0.199209 + 0.199209i
$$541$$ 207308. + 207308.i 0.708308 + 0.708308i 0.966179 0.257871i $$-0.0830210\pi$$
−0.257871 + 0.966179i $$0.583021\pi$$
$$542$$ −6308.37 + 6308.37i −0.0214743 + 0.0214743i
$$543$$ 95190.7i 0.322845i
$$544$$ −73895.3 −0.249700
$$545$$ 215264.i 0.724734i
$$546$$ 315776.i 1.05924i
$$547$$ 150439. 150439.i 0.502790 0.502790i −0.409514 0.912304i $$-0.634302\pi$$
0.912304 + 0.409514i $$0.134302\pi$$
$$548$$ 101926.i 0.339409i
$$549$$ −251994. + 251994.i −0.836074 + 0.836074i
$$550$$ −87458.9 + 87458.9i −0.289120 + 0.289120i
$$551$$ 30562.0 0.100665
$$552$$ −38772.6 −0.127247
$$553$$ −302502. 302502.i −0.989187 0.989187i
$$554$$ 259388.i 0.845142i
$$555$$ −5760.27 105196.i −0.0187007 0.341517i
$$556$$ −20495.2 −0.0662984
$$557$$ −38740.6 + 38740.6i −0.124869 + 0.124869i −0.766780 0.641910i $$-0.778142\pi$$
0.641910 + 0.766780i $$0.278142\pi$$
$$558$$ 127712.i 0.410170i
$$559$$ 593286.i 1.89863i
$$560$$ 61316.7 + 61316.7i 0.195525 + 0.195525i
$$561$$ 161522. + 161522.i 0.513223 + 0.513223i
$$562$$ −263446. −0.834103
$$563$$ 124572. + 124572.i 0.393011 + 0.393011i 0.875759 0.482748i $$-0.160361\pi$$
−0.482748 + 0.875759i $$0.660361\pi$$
$$564$$ −107550. −0.338107
$$565$$ 95399.0 0.298845
$$566$$ 76961.6i 0.240238i
$$567$$ −41023.9 −0.127606
$$568$$ 91620.1 + 91620.1i 0.283984 + 0.283984i
$$569$$ 101858. 101858.i 0.314609 0.314609i −0.532083 0.846692i $$-0.678591\pi$$
0.846692 + 0.532083i $$0.178591\pi$$
$$570$$ −56157.1 + 56157.1i −0.172844 + 0.172844i
$$571$$ −110278. −0.338234 −0.169117 0.985596i $$-0.554092\pi$$
−0.169117 + 0.985596i $$0.554092\pi$$
$$572$$ −131487. 131487.i −0.401875 0.401875i
$$573$$ 75735.8 75735.8i 0.230670 0.230670i
$$574$$ 342224. + 342224.i 1.03869 + 1.03869i
$$575$$ 94687.8 94687.8i 0.286390 0.286390i
$$576$$ 26847.6i 0.0809208i
$$577$$ 196203. + 196203.i 0.589324 + 0.589324i 0.937448 0.348124i $$-0.113181\pi$$
−0.348124 + 0.937448i $$0.613181\pi$$
$$578$$ −166241. 166241.i −0.497603 0.497603i
$$579$$ 170113. 170113.i 0.507434 0.507434i
$$580$$ 9649.02i 0.0286832i
$$581$$ 928741. 2.75133
$$582$$ 20216.9i 0.0596855i
$$583$$ 19375.0i 0.0570038i
$$584$$ 125980. 125980.i 0.369382 0.369382i
$$585$$ 167623.i 0.489803i
$$586$$ 159235. 159235.i 0.463706 0.463706i
$$587$$ −189138. + 189138.i −0.548913 + 0.548913i −0.926126 0.377213i $$-0.876882\pi$$
0.377213 + 0.926126i $$0.376882\pi$$
$$588$$ 275908. 0.798012
$$589$$ 314182. 0.905630
$$590$$ 80939.8 + 80939.8i 0.232519 + 0.232519i
$$591$$ 206484.i 0.591169i
$$592$$ 58473.8 65248.6i 0.166847 0.186178i
$$593$$ −477286. −1.35728 −0.678640 0.734471i $$-0.737430\pi$$
−0.678640 + 0.734471i $$0.737430\pi$$
$$594$$ 149335. 149335.i 0.423241 0.423241i
$$595$$ 553103.i 1.56233i
$$596$$ 132107.i 0.371907i
$$597$$ −225014. 225014.i −0.631336 0.631336i
$$598$$ 142355. + 142355.i 0.398080 + 0.398080i
$$599$$ −693204. −1.93200 −0.966000 0.258540i $$-0.916758\pi$$
−0.966000 + 0.258540i $$0.916758\pi$$
$$600$$ 35714.8 + 35714.8i 0.0992077 + 0.0992077i
$$601$$ −450318. −1.24672 −0.623362 0.781933i $$-0.714234\pi$$
−0.623362 + 0.781933i $$0.714234\pi$$
$$602$$ 711254. 1.96260
$$603$$ 137797.i 0.378970i
$$604$$ −28753.9 −0.0788176
$$605$$ 37456.0 + 37456.0i 0.102332 + 0.102332i
$$606$$ 196949. 196949.i 0.536302 0.536302i
$$607$$ −80454.7 + 80454.7i −0.218360 + 0.218360i −0.807807 0.589447i $$-0.799346\pi$$
0.589447 + 0.807807i $$0.299346\pi$$
$$608$$ −66047.1 −0.178668
$$609$$ 29786.2 + 29786.2i 0.0803119 + 0.0803119i
$$610$$ 195722. 195722.i 0.525994 0.525994i
$$611$$ 394875. + 394875.i 1.05774 + 1.05774i
$$612$$ −121088. + 121088.i −0.323295 + 0.323295i
$$613$$ 427684.i 1.13816i 0.822283 + 0.569078i $$0.192700\pi$$
−0.822283 + 0.569078i $$0.807300\pi$$
$$614$$ 131143. + 131143.i 0.347862 + 0.347862i
$$615$$ −98955.0 98955.0i −0.261630 0.261630i
$$616$$ 157632. 157632.i 0.415415 0.415415i
$$617$$ 423563.i 1.11262i 0.830974 + 0.556311i $$0.187784\pi$$
−0.830974 + 0.556311i $$0.812216\pi$$
$$618$$ 14183.5 0.0371369
$$619$$ 704207.i 1.83789i 0.394389 + 0.918944i $$0.370956\pi$$
−0.394389 + 0.918944i $$0.629044\pi$$
$$620$$ 99193.5i 0.258048i
$$621$$ −161678. + 161678.i −0.419244 + 0.419244i
$$622$$ 194208.i 0.501981i
$$623$$ −344382. + 344382.i −0.887288 + 0.887288i
$$624$$ −53694.1 + 53694.1i −0.137898 + 0.137898i
$$625$$ −44853.1 −0.114824
$$626$$ −64672.5 −0.165033
$$627$$ 144367. + 144367.i 0.367226 + 0.367226i
$$628$$ 10466.4i 0.0265386i
$$629$$ 558014. 30555.5i 1.41041 0.0772304i
$$630$$ 200953. 0.506306
$$631$$ 187320. 187320.i 0.470462 0.470462i −0.431602 0.902064i $$-0.642051\pi$$
0.902064 + 0.431602i $$0.142051\pi$$
$$632$$ 102874.i 0.257556i
$$633$$ 20545.8i 0.0512762i
$$634$$ −186461. 186461.i −0.463884 0.463884i
$$635$$ 8762.66 + 8762.66i 0.0217315 + 0.0217315i
$$636$$ −7911.96 −0.0195601
$$637$$ −1.01301e6 1.01301e6i −2.49651 2.49651i
$$638$$ 24805.5 0.0609406
$$639$$ 300266. 0.735367
$$640$$ 20852.4i 0.0509092i
$$641$$ −709193. −1.72603 −0.863015 0.505178i $$-0.831427\pi$$
−0.863015 + 0.505178i $$0.831427\pi$$
$$642$$ 16706.1 + 16706.1i 0.0405327 + 0.0405327i
$$643$$ 217277. 217277.i 0.525522 0.525522i −0.393712 0.919234i $$-0.628809\pi$$
0.919234 + 0.393712i $$0.128809\pi$$
$$644$$ −170661. + 170661.i −0.411492 + 0.411492i
$$645$$ −205661. −0.494348
$$646$$ −297887. 297887.i −0.713815 0.713815i
$$647$$ 110695. 110695.i 0.264435 0.264435i −0.562418 0.826853i $$-0.690129\pi$$
0.826853 + 0.562418i $$0.190129\pi$$
$$648$$ 6975.64 + 6975.64i 0.0166125 + 0.0166125i
$$649$$ 208078. 208078.i 0.494012 0.494012i
$$650$$ 262256.i 0.620725i
$$651$$ 306206. + 306206.i 0.722524 + 0.722524i
$$652$$ 158850. + 158850.i 0.373674 + 0.373674i
$$653$$ −239393. + 239393.i −0.561417 + 0.561417i −0.929710 0.368292i $$-0.879943\pi$$
0.368292 + 0.929710i $$0.379943\pi$$
$$654$$ 225985.i 0.528353i
$$655$$ 188666. 0.439756
$$656$$ 116382.i 0.270445i
$$657$$ 412873.i 0.956502i
$$658$$ −473392. + 473392.i −1.09337 + 1.09337i
$$659$$ 597265.i 1.37530i −0.726044 0.687648i $$-0.758643\pi$$
0.726044 0.687648i $$-0.241357\pi$$
$$660$$ −45579.7 + 45579.7i −0.104636 + 0.104636i
$$661$$ −38924.4 + 38924.4i −0.0890881 + 0.0890881i −0.750246 0.661158i $$-0.770065\pi$$
0.661158 + 0.750246i $$0.270065\pi$$
$$662$$ 66207.6 0.151075
$$663$$ −484343. −1.10186
$$664$$ −157922. 157922.i −0.358183 0.358183i
$$665$$ 494359.i 1.11789i
$$666$$ −11101.4 202737.i −0.0250282 0.457073i
$$667$$ −26855.8 −0.0603652
$$668$$ −131365. + 131365.i −0.294393 + 0.294393i
$$669$$ 328182.i 0.733268i
$$670$$ 107026.i 0.238419i
$$671$$ −503159. 503159.i −1.11753 1.11753i
$$672$$ −64370.5 64370.5i −0.142544 0.142544i
$$673$$ 528423. 1.16668 0.583340 0.812228i $$-0.301745\pi$$
0.583340 + 0.812228i $$0.301745\pi$$
$$674$$ −309901. 309901.i −0.682187 0.682187i
$$675$$ 297854. 0.653725
$$676$$ 165792. 0.362802
$$677$$ 504764.i 1.10131i 0.834732 + 0.550657i $$0.185623\pi$$
−0.834732 + 0.550657i $$0.814377\pi$$
$$678$$ −100150. −0.217868
$$679$$ −88986.4 88986.4i −0.193012 0.193012i
$$680$$ 94048.7 94048.7i 0.203393 0.203393i
$$681$$ −145547. + 145547.i −0.313841 + 0.313841i
$$682$$ 255004. 0.548251
$$683$$ −360139. 360139.i −0.772020 0.772020i 0.206440 0.978459i $$-0.433812\pi$$
−0.978459 + 0.206440i $$0.933812\pi$$
$$684$$ −108228. + 108228.i −0.231327 + 0.231327i
$$685$$ −129724. 129724.i −0.276464 0.276464i
$$686$$ 762580. 762580.i 1.62046 1.62046i
$$687$$ 352406.i 0.746671i
$$688$$ −120941. 120941.i −0.255502 0.255502i
$$689$$ 29049.1 + 29049.1i 0.0611919 + 0.0611919i
$$690$$ 49347.0 49347.0i 0.103648 0.103648i
$$691$$ 850032.i 1.78024i 0.455723 + 0.890122i $$0.349381\pi$$
−0.455723 + 0.890122i $$0.650619\pi$$
$$692$$ 11047.0 0.0230692
$$693$$ 516605.i 1.07570i
$$694$$ 315103.i 0.654235i
$$695$$ 26084.9 26084.9i 0.0540032 0.0540032i
$$696$$ 10129.6i 0.0209109i
$$697$$ 524909. 524909.i 1.08048 1.08048i
$$698$$ 171162. 171162.i 0.351314 0.351314i
$$699$$ −300303. −0.614618
$$700$$ 314403. 0.641638
$$701$$ −67567.6 67567.6i −0.137500 0.137500i 0.635007 0.772507i $$-0.280997\pi$$
−0.772507 + 0.635007i $$0.780997\pi$$
$$702$$ 447798.i 0.908673i
$$703$$ 498749. 27310.3i 1.00919 0.0552607i
$$704$$ −53606.9 −0.108162
$$705$$ 136883. 136883.i 0.275404 0.275404i
$$706$$ 568042.i 1.13965i
$$707$$ 1.73378e6i 3.46860i
$$708$$ −84971.0 84971.0i −0.169513 0.169513i
$$709$$ −223391. 223391.i −0.444399 0.444399i 0.449089 0.893487i $$-0.351749\pi$$
−0.893487 + 0.449089i $$0.851749\pi$$
$$710$$ −233215. −0.462637
$$711$$ 168574. + 168574.i 0.333466 + 0.333466i
$$712$$ 117117. 0.231025
$$713$$ −276082. −0.543074
$$714$$ 580649.i 1.13898i
$$715$$ 334695. 0.654692
$$716$$ 88660.4 + 88660.4i 0.172943 + 0.172943i
$$717$$ 424516. 424516.i 0.825764 0.825764i
$$718$$ −16713.4 + 16713.4i −0.0324202 + 0.0324202i
$$719$$ −964220. −1.86517 −0.932585 0.360950i $$-0.882452\pi$$
−0.932585 + 0.360950i $$0.882452\pi$$
$$720$$ −34169.7 34169.7i −0.0659138 0.0659138i
$$721$$ 62429.6 62429.6i 0.120094 0.120094i
$$722$$ −5607.04 5607.04i −0.0107562 0.0107562i
$$723$$ −112336. + 112336.i −0.214903 + 0.214903i
$$724$$ 142489.i 0.271833i
$$725$$ 24737.8 + 24737.8i 0.0470636 + 0.0470636i
$$726$$ −39321.5 39321.5i −0.0746030 0.0746030i
$$727$$ −223895. + 223895.i −0.423620 + 0.423620i −0.886448 0.462828i $$-0.846835\pi$$
0.462828 + 0.886448i $$0.346835\pi$$
$$728$$ 472678.i 0.891872i
$$729$$ −285862. −0.537899
$$730$$ 320677.i 0.601758i
$$731$$ 1.09093e6i 2.04157i
$$732$$ −205470. + 205470.i −0.383466 + 0.383466i
$$733$$ 551842.i 1.02709i 0.858064 + 0.513543i $$0.171667\pi$$
−0.858064 + 0.513543i $$0.828333\pi$$
$$734$$ −36247.2 + 36247.2i −0.0672795 + 0.0672795i
$$735$$ −351156. + 351156.i −0.650018 + 0.650018i
$$736$$ 58037.8 0.107141
$$737$$ −275140. −0.506547
$$738$$ −190710. 190710.i −0.350155 0.350155i
$$739$$ 137775.i 0.252278i −0.992013 0.126139i $$-0.959741\pi$$
0.992013 0.126139i $$-0.0402586\pi$$
$$740$$ 8622.41 + 157465.i 0.0157458 + 0.287555i
$$741$$ −432903. −0.788414
$$742$$ −34825.1 + 34825.1i −0.0632536 + 0.0632536i
$$743$$ 352194.i 0.637977i −0.947759 0.318988i $$-0.896657\pi$$
0.947759 0.318988i $$-0.103343\pi$$
$$744$$ 104134.i 0.188125i
$$745$$ −168137. 168137.i −0.302936 0.302936i
$$746$$ −109110. 109110.i −0.196058 0.196058i
$$747$$ −517555. −0.927504
$$748$$ −241778. 241778.i −0.432130 0.432130i
$$749$$ 147067. 0.262151
$$750$$ −226952. −0.403470
$$751$$ 1.08959e6i 1.93190i 0.258737 + 0.965948i $$0.416694\pi$$
−0.258737 + 0.965948i $$0.583306\pi$$
$$752$$ 160990. 0.284683
$$753$$ 309849. + 309849.i 0.546463 + 0.546463i
$$754$$ −37191.2 + 37191.2i −0.0654180 + 0.0654180i
$$755$$ 36596.0 36596.0i 0.0642006 0.0642006i
$$756$$ −536837. −0.939288
$$757$$ 103856. + 103856.i 0.181233 + 0.181233i 0.791893 0.610660i $$-0.209096\pi$$
−0.610660 + 0.791893i $$0.709096\pi$$
$$758$$ 434975. 434975.i 0.757053 0.757053i
$$759$$ −126860. 126860.i −0.220213 0.220213i
$$760$$ 84060.1 84060.1i 0.145533 0.145533i
$$761$$ 357264.i 0.616908i 0.951239 + 0.308454i $$0.0998116\pi$$
−0.951239 + 0.308454i $$0.900188\pi$$
$$762$$ −9199.08 9199.08i −0.0158429 0.0158429i
$$763$$ 994691. + 994691.i 1.70859 + 1.70859i
$$764$$ −113367. + 113367.i −0.194223 + 0.194223i
$$765$$ 308225.i 0.526678i
$$766$$ −457827. −0.780269
$$767$$ 623948.i 1.06061i
$$768$$ 21890.9i 0.0371143i
$$769$$ 305401. 305401.i 0.516438 0.516438i −0.400054 0.916492i $$-0.631009\pi$$
0.916492 + 0.400054i $$0.131009\pi$$
$$770$$ 401245.i 0.676750i
$$771$$ 252952. 252952.i 0.425530 0.425530i
$$772$$ −254637. + 254637.i −0.427255 + 0.427255i