# Properties

 Label 162.7.d.d.107.2 Level $162$ Weight $7$ Character 162.107 Analytic conductor $37.269$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$162 = 2 \cdot 3^{4}$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 162.d (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$37.2687615464$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} - 2x^{2} + 4$$ x^4 - 2*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 18) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 107.2 Root $$-1.22474 + 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 162.107 Dual form 162.7.d.d.53.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-150.644 + 86.9741i) q^{5} +(242.000 - 419.156i) q^{7} +181.019i q^{8} +O(q^{10})$$ $$q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(-150.644 + 86.9741i) q^{5} +(242.000 - 419.156i) q^{7} +181.019i q^{8} -984.000 q^{10} +(1161.06 + 670.337i) q^{11} +(-1684.00 - 2916.77i) q^{13} +(2371.11 - 1368.96i) q^{14} +(-512.000 + 886.810i) q^{16} -12.7279i q^{17} +5744.00 q^{19} +(-4820.60 - 2783.17i) q^{20} +(3792.00 + 6567.94i) q^{22} +(2924.69 - 1688.57i) q^{23} +(7316.50 - 12672.5i) q^{25} -19052.3i q^{26} +15488.0 q^{28} +(25422.0 + 14677.4i) q^{29} +(19898.0 + 34464.3i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(36.0000 - 62.3538i) q^{34} +84191.0i q^{35} +52526.0 q^{37} +(28139.7 + 16246.5i) q^{38} +(-15744.0 - 27269.4i) q^{40} +(32079.7 - 18521.2i) q^{41} +(-1900.00 + 3290.90i) q^{43} +42901.6i q^{44} +19104.0 q^{46} +(66503.6 + 38395.9i) q^{47} +(-58303.5 - 100985. i) q^{49} +(71686.8 - 41388.4i) q^{50} +(53888.0 - 93336.8i) q^{52} -238738. i q^{53} -233208. q^{55} +(75875.4 + 43806.7i) q^{56} +(83028.0 + 143809. i) q^{58} +(216368. - 124920. i) q^{59} +(-6625.00 + 11474.8i) q^{61} +225120. i q^{62} -32768.0 q^{64} +(507368. + 292929. i) q^{65} +(-84484.0 - 146331. i) q^{67} +(352.727 - 203.647i) q^{68} +(-238128. + 412450. i) q^{70} +531467. i q^{71} +236144. q^{73} +(257324. + 148566. i) q^{74} +(91904.0 + 159182. i) q^{76} +(561952. - 324443. i) q^{77} +(17558.0 - 30411.3i) q^{79} -178123. i q^{80} +209544. q^{82} +(-9508.92 - 5489.98i) q^{83} +(1107.00 + 1917.38i) q^{85} +(-18616.1 + 10748.0i) q^{86} +(-121344. + 210174. i) q^{88} +129328. i q^{89} -1.63011e6 q^{91} +(93590.1 + 54034.3i) q^{92} +(217200. + 376201. i) q^{94} +(-865297. + 499579. i) q^{95} +(160712. - 278361. i) q^{97} -659629. i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 64 q^{4} + 968 q^{7}+O(q^{10})$$ 4 * q + 64 * q^4 + 968 * q^7 $$4 q + 64 q^{4} + 968 q^{7} - 3936 q^{10} - 6736 q^{13} - 2048 q^{16} + 22976 q^{19} + 15168 q^{22} + 29266 q^{25} + 61952 q^{28} + 79592 q^{31} + 144 q^{34} + 210104 q^{37} - 62976 q^{40} - 7600 q^{43} + 76416 q^{46} - 233214 q^{49} + 215552 q^{52} - 932832 q^{55} + 332112 q^{58} - 26500 q^{61} - 131072 q^{64} - 337936 q^{67} - 952512 q^{70} + 944576 q^{73} + 367616 q^{76} + 70232 q^{79} + 838176 q^{82} + 4428 q^{85} - 485376 q^{88} - 6520448 q^{91} + 868800 q^{94} + 642848 q^{97}+O(q^{100})$$ 4 * q + 64 * q^4 + 968 * q^7 - 3936 * q^10 - 6736 * q^13 - 2048 * q^16 + 22976 * q^19 + 15168 * q^22 + 29266 * q^25 + 61952 * q^28 + 79592 * q^31 + 144 * q^34 + 210104 * q^37 - 62976 * q^40 - 7600 * q^43 + 76416 * q^46 - 233214 * q^49 + 215552 * q^52 - 932832 * q^55 + 332112 * q^58 - 26500 * q^61 - 131072 * q^64 - 337936 * q^67 - 952512 * q^70 + 944576 * q^73 + 367616 * q^76 + 70232 * q^79 + 838176 * q^82 + 4428 * q^85 - 485376 * q^88 - 6520448 * q^91 + 868800 * q^94 + 642848 * q^97

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$$.

 $$n$$ $$83$$ $$\chi(n)$$ $$e\left(\frac{1}{6}\right)$$

## 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
$$3$$ 0 0
$$4$$ 16.0000 + 27.7128i 0.250000 + 0.433013i
$$5$$ −150.644 + 86.9741i −1.20515 + 0.695793i −0.961696 0.274120i $$-0.911614\pi$$
−0.243453 + 0.969913i $$0.578280\pi$$
$$6$$ 0 0
$$7$$ 242.000 419.156i 0.705539 1.22203i −0.260957 0.965350i $$-0.584038\pi$$
0.966497 0.256680i $$-0.0826285\pi$$
$$8$$ 181.019i 0.353553i
$$9$$ 0 0
$$10$$ −984.000 −0.984000
$$11$$ 1161.06 + 670.337i 0.872320 + 0.503634i 0.868119 0.496357i $$-0.165329\pi$$
0.00420160 + 0.999991i $$0.498663\pi$$
$$12$$ 0 0
$$13$$ −1684.00 2916.77i −0.766500 1.32762i −0.939450 0.342686i $$-0.888663\pi$$
0.172950 0.984931i $$-0.444670\pi$$
$$14$$ 2371.11 1368.96i 0.864106 0.498892i
$$15$$ 0 0
$$16$$ −512.000 + 886.810i −0.125000 + 0.216506i
$$17$$ 12.7279i 0.00259066i −0.999999 0.00129533i $$-0.999588\pi$$
0.999999 0.00129533i $$-0.000412317\pi$$
$$18$$ 0 0
$$19$$ 5744.00 0.837440 0.418720 0.908115i $$-0.362479\pi$$
0.418720 + 0.908115i $$0.362479\pi$$
$$20$$ −4820.60 2783.17i −0.602574 0.347897i
$$21$$ 0 0
$$22$$ 3792.00 + 6567.94i 0.356123 + 0.616824i
$$23$$ 2924.69 1688.57i 0.240379 0.138783i −0.374972 0.927036i $$-0.622348\pi$$
0.615351 + 0.788253i $$0.289014\pi$$
$$24$$ 0 0
$$25$$ 7316.50 12672.5i 0.468256 0.811043i
$$26$$ 19052.3i 1.08399i
$$27$$ 0 0
$$28$$ 15488.0 0.705539
$$29$$ 25422.0 + 14677.4i 1.04236 + 0.601805i 0.920500 0.390743i $$-0.127782\pi$$
0.121857 + 0.992548i $$0.461115\pi$$
$$30$$ 0 0
$$31$$ 19898.0 + 34464.3i 0.667920 + 1.15687i 0.978485 + 0.206319i $$0.0661484\pi$$
−0.310565 + 0.950552i $$0.600518\pi$$
$$32$$ −5016.55 + 2896.31i −0.153093 + 0.0883883i
$$33$$ 0 0
$$34$$ 36.0000 62.3538i 0.000915937 0.00158645i
$$35$$ 84191.0i 1.96364i
$$36$$ 0 0
$$37$$ 52526.0 1.03698 0.518489 0.855085i $$-0.326495\pi$$
0.518489 + 0.855085i $$0.326495\pi$$
$$38$$ 28139.7 + 16246.5i 0.512825 + 0.296080i
$$39$$ 0 0
$$40$$ −15744.0 27269.4i −0.246000 0.426084i
$$41$$ 32079.7 18521.2i 0.465457 0.268732i −0.248879 0.968535i $$-0.580062\pi$$
0.714336 + 0.699803i $$0.246729\pi$$
$$42$$ 0 0
$$43$$ −1900.00 + 3290.90i −0.0238973 + 0.0413913i −0.877727 0.479162i $$-0.840941\pi$$
0.853829 + 0.520553i $$0.174274\pi$$
$$44$$ 42901.6i 0.503634i
$$45$$ 0 0
$$46$$ 19104.0 0.196269
$$47$$ 66503.6 + 38395.9i 0.640548 + 0.369821i 0.784826 0.619717i $$-0.212752\pi$$
−0.144277 + 0.989537i $$0.546086\pi$$
$$48$$ 0 0
$$49$$ −58303.5 100985.i −0.495572 0.858355i
$$50$$ 71686.8 41388.4i 0.573494 0.331107i
$$51$$ 0 0
$$52$$ 53888.0 93336.8i 0.383250 0.663808i
$$53$$ 238738.i 1.60359i −0.597599 0.801795i $$-0.703879\pi$$
0.597599 0.801795i $$-0.296121\pi$$
$$54$$ 0 0
$$55$$ −233208. −1.40170
$$56$$ 75875.4 + 43806.7i 0.432053 + 0.249446i
$$57$$ 0 0
$$58$$ 83028.0 + 143809.i 0.425540 + 0.737057i
$$59$$ 216368. 124920.i 1.05351 0.608243i 0.129878 0.991530i $$-0.458541\pi$$
0.923629 + 0.383287i $$0.125208\pi$$
$$60$$ 0 0
$$61$$ −6625.00 + 11474.8i −0.0291875 + 0.0505542i −0.880250 0.474510i $$-0.842625\pi$$
0.851063 + 0.525064i $$0.175959\pi$$
$$62$$ 225120.i 0.944581i
$$63$$ 0 0
$$64$$ −32768.0 −0.125000
$$65$$ 507368. + 292929.i 1.84749 + 1.06665i
$$66$$ 0 0
$$67$$ −84484.0 146331.i −0.280899 0.486531i 0.690707 0.723134i $$-0.257299\pi$$
−0.971606 + 0.236603i $$0.923966\pi$$
$$68$$ 352.727 203.647i 0.00112179 0.000647665i
$$69$$ 0 0
$$70$$ −238128. + 412450.i −0.694251 + 1.20248i
$$71$$ 531467.i 1.48491i 0.669894 + 0.742457i $$0.266340\pi$$
−0.669894 + 0.742457i $$0.733660\pi$$
$$72$$ 0 0
$$73$$ 236144. 0.607027 0.303514 0.952827i $$-0.401840\pi$$
0.303514 + 0.952827i $$0.401840\pi$$
$$74$$ 257324. + 148566.i 0.635016 + 0.366627i
$$75$$ 0 0
$$76$$ 91904.0 + 159182.i 0.209360 + 0.362622i
$$77$$ 561952. 324443.i 1.23091 0.710668i
$$78$$ 0 0
$$79$$ 17558.0 30411.3i 0.0356118 0.0616814i −0.847670 0.530524i $$-0.821995\pi$$
0.883282 + 0.468842i $$0.155329\pi$$
$$80$$ 178123.i 0.347897i
$$81$$ 0 0
$$82$$ 209544. 0.380044
$$83$$ −9508.92 5489.98i −0.0166302 0.00960144i 0.491662 0.870786i $$-0.336390\pi$$
−0.508292 + 0.861185i $$0.669723\pi$$
$$84$$ 0 0
$$85$$ 1107.00 + 1917.38i 0.00180256 + 0.00312213i
$$86$$ −18616.1 + 10748.0i −0.0292681 + 0.0168979i
$$87$$ 0 0
$$88$$ −121344. + 210174.i −0.178062 + 0.308412i
$$89$$ 129328.i 0.183453i 0.995784 + 0.0917263i $$0.0292385\pi$$
−0.995784 + 0.0917263i $$0.970762\pi$$
$$90$$ 0 0
$$91$$ −1.63011e6 −2.16318
$$92$$ 93590.1 + 54034.3i 0.120189 + 0.0693914i
$$93$$ 0 0
$$94$$ 217200. + 376201.i 0.261503 + 0.452936i
$$95$$ −865297. + 499579.i −1.00924 + 0.582685i
$$96$$ 0 0
$$97$$ 160712. 278361.i 0.176089 0.304996i −0.764448 0.644685i $$-0.776989\pi$$
0.940538 + 0.339689i $$0.110322\pi$$
$$98$$ 659629.i 0.700844i
$$99$$ 0 0
$$100$$ 468256. 0.468256
$$101$$ 579181. + 334390.i 0.562147 + 0.324556i 0.754007 0.656867i $$-0.228119\pi$$
−0.191860 + 0.981422i $$0.561452\pi$$
$$102$$ 0 0
$$103$$ −996706. 1.72635e6i −0.912127 1.57985i −0.811054 0.584972i $$-0.801106\pi$$
−0.101073 0.994879i $$-0.532228\pi$$
$$104$$ 527992. 304837.i 0.469383 0.270999i
$$105$$ 0 0
$$106$$ 675252. 1.16957e6i 0.566955 0.981994i
$$107$$ 260668.i 0.212783i 0.994324 + 0.106391i $$0.0339296\pi$$
−0.994324 + 0.106391i $$0.966070\pi$$
$$108$$ 0 0
$$109$$ 194456. 0.150156 0.0750779 0.997178i $$-0.476079\pi$$
0.0750779 + 0.997178i $$0.476079\pi$$
$$110$$ −1.14248e6 659612.i −0.858363 0.495576i
$$111$$ 0 0
$$112$$ 247808. + 429216.i 0.176385 + 0.305508i
$$113$$ 711784. 410949.i 0.493302 0.284808i −0.232641 0.972563i $$-0.574737\pi$$
0.725943 + 0.687755i $$0.241404\pi$$
$$114$$ 0 0
$$115$$ −293724. + 508745.i −0.193128 + 0.334508i
$$116$$ 939355.i 0.601805i
$$117$$ 0 0
$$118$$ 1.41331e6 0.860185
$$119$$ −5334.99 3080.16i −0.00316587 0.00182781i
$$120$$ 0 0
$$121$$ 12923.5 + 22384.2i 0.00729498 + 0.0126353i
$$122$$ −64911.5 + 37476.7i −0.0357472 + 0.0206387i
$$123$$ 0 0
$$124$$ −636736. + 1.10286e6i −0.333960 + 0.578436i
$$125$$ 172557.i 0.0883490i
$$126$$ 0 0
$$127$$ 3.05721e6 1.49250 0.746250 0.665666i $$-0.231852\pi$$
0.746250 + 0.665666i $$0.231852\pi$$
$$128$$ −160530. 92681.9i −0.0765466 0.0441942i
$$129$$ 0 0
$$130$$ 1.65706e6 + 2.87011e6i 0.754236 + 1.30637i
$$131$$ −2.66206e6 + 1.53694e6i −1.18414 + 0.683664i −0.956969 0.290191i $$-0.906281\pi$$
−0.227172 + 0.973855i $$0.572948\pi$$
$$132$$ 0 0
$$133$$ 1.39005e6 2.40763e6i 0.590847 1.02338i
$$134$$ 955827.i 0.397251i
$$135$$ 0 0
$$136$$ 2304.00 0.000915937
$$137$$ −3.88336e6 2.24206e6i −1.51024 0.871938i −0.999929 0.0119482i $$-0.996197\pi$$
−0.510312 0.859990i $$-0.670470\pi$$
$$138$$ 0 0
$$139$$ 546164. + 945984.i 0.203366 + 0.352241i 0.949611 0.313431i $$-0.101478\pi$$
−0.746245 + 0.665672i $$0.768145\pi$$
$$140$$ −2.33317e6 + 1.34706e6i −0.850280 + 0.490909i
$$141$$ 0 0
$$142$$ −1.50322e6 + 2.60365e6i −0.524996 + 0.909321i
$$143$$ 4.51539e6i 1.54414i
$$144$$ 0 0
$$145$$ −5.10622e6 −1.67493
$$146$$ 1.15686e6 + 667916.i 0.371727 + 0.214617i
$$147$$ 0 0
$$148$$ 840416. + 1.45564e6i 0.259244 + 0.449024i
$$149$$ 1.92333e6 1.11044e6i 0.581428 0.335687i −0.180273 0.983617i $$-0.557698\pi$$
0.761701 + 0.647929i $$0.224365\pi$$
$$150$$ 0 0
$$151$$ 2.03935e6 3.53226e6i 0.592327 1.02594i −0.401591 0.915819i $$-0.631543\pi$$
0.993918 0.110122i $$-0.0351241\pi$$
$$152$$ 1.03978e6i 0.296080i
$$153$$ 0 0
$$154$$ 3.67066e6 1.00504
$$155$$ −5.99501e6 3.46122e6i −1.60989 0.929468i
$$156$$ 0 0
$$157$$ −3.07784e6 5.33097e6i −0.795329 1.37755i −0.922630 0.385686i $$-0.873965\pi$$
0.127301 0.991864i $$-0.459369\pi$$
$$158$$ 172033. 99323.0i 0.0436154 0.0251813i
$$159$$ 0 0
$$160$$ 503808. 872621.i 0.123000 0.213042i
$$161$$ 1.63454e6i 0.391667i
$$162$$ 0 0
$$163$$ 800696. 0.184886 0.0924432 0.995718i $$-0.470532\pi$$
0.0924432 + 0.995718i $$0.470532\pi$$
$$164$$ 1.02655e6 + 592680.i 0.232728 + 0.134366i
$$165$$ 0 0
$$166$$ −31056.0 53790.6i −0.00678924 0.0117593i
$$167$$ −4.16097e6 + 2.40234e6i −0.893398 + 0.515804i −0.875052 0.484028i $$-0.839173\pi$$
−0.0183455 + 0.999832i $$0.505840\pi$$
$$168$$ 0 0
$$169$$ −3.25831e6 + 5.64355e6i −0.675044 + 1.16921i
$$170$$ 12524.3i 0.00254921i
$$171$$ 0 0
$$172$$ −121600. −0.0238973
$$173$$ −3.09164e6 1.78496e6i −0.597106 0.344739i 0.170796 0.985306i $$-0.445366\pi$$
−0.767902 + 0.640567i $$0.778699\pi$$
$$174$$ 0 0
$$175$$ −3.54119e6 6.13351e6i −0.660746 1.14445i
$$176$$ −1.18892e6 + 686425.i −0.218080 + 0.125909i
$$177$$ 0 0
$$178$$ −365796. + 633577.i −0.0648603 + 0.112341i
$$179$$ 7.43698e6i 1.29669i 0.761345 + 0.648347i $$0.224539\pi$$
−0.761345 + 0.648347i $$0.775461\pi$$
$$180$$ 0 0
$$181$$ −1.03812e7 −1.75070 −0.875350 0.483491i $$-0.839369\pi$$
−0.875350 + 0.483491i $$0.839369\pi$$
$$182$$ −7.98589e6 4.61065e6i −1.32467 0.764801i
$$183$$ 0 0
$$184$$ 305664. + 529426.i 0.0490671 + 0.0849868i
$$185$$ −7.91271e6 + 4.56840e6i −1.24971 + 0.721521i
$$186$$ 0 0
$$187$$ 8532.00 14777.9i 0.00130475 0.00225989i
$$188$$ 2.45734e6i 0.369821i
$$189$$ 0 0
$$190$$ −5.65210e6 −0.824041
$$191$$ 1.12532e7 + 6.49703e6i 1.61501 + 0.932426i 0.988185 + 0.153266i $$0.0489793\pi$$
0.626825 + 0.779160i $$0.284354\pi$$
$$192$$ 0 0
$$193$$ 1.96598e6 + 3.40517e6i 0.273468 + 0.473660i 0.969747 0.244110i $$-0.0784959\pi$$
−0.696279 + 0.717771i $$0.745163\pi$$
$$194$$ 1.57465e6 909124.i 0.215665 0.124514i
$$195$$ 0 0
$$196$$ 1.86571e6 3.23151e6i 0.247786 0.429178i
$$197$$ 5.37967e6i 0.703651i −0.936066 0.351825i $$-0.885561\pi$$
0.936066 0.351825i $$-0.114439\pi$$
$$198$$ 0 0
$$199$$ −565900. −0.0718093 −0.0359046 0.999355i $$-0.511431\pi$$
−0.0359046 + 0.999355i $$0.511431\pi$$
$$200$$ 2.29398e6 + 1.32443e6i 0.286747 + 0.165553i
$$201$$ 0 0
$$202$$ 1.89160e6 + 3.27634e6i 0.229496 + 0.397498i
$$203$$ 1.23043e7 7.10387e6i 1.47085 0.849194i
$$204$$ 0 0
$$205$$ −3.22174e6 + 5.58022e6i −0.373963 + 0.647723i
$$206$$ 1.12764e7i 1.28994i
$$207$$ 0 0
$$208$$ 3.44883e6 0.383250
$$209$$ 6.66912e6 + 3.85042e6i 0.730516 + 0.421763i
$$210$$ 0 0
$$211$$ 6.75825e6 + 1.17056e7i 0.719427 + 1.24608i 0.961227 + 0.275759i $$0.0889291\pi$$
−0.241799 + 0.970326i $$0.577738\pi$$
$$212$$ 6.61609e6 3.81980e6i 0.694375 0.400897i
$$213$$ 0 0
$$214$$ −737280. + 1.27701e6i −0.0752300 + 0.130302i
$$215$$ 661003.i 0.0665102i
$$216$$ 0 0
$$217$$ 1.92613e7 1.88497
$$218$$ 952636. + 550005.i 0.0919512 + 0.0530881i
$$219$$ 0 0
$$220$$ −3.73133e6 6.46285e6i −0.350425 0.606954i
$$221$$ −37124.5 + 21433.8i −0.00343941 + 0.00198574i
$$222$$ 0 0
$$223$$ 2.67742e6 4.63742e6i 0.241436 0.418179i −0.719688 0.694298i $$-0.755715\pi$$
0.961123 + 0.276119i $$0.0890484\pi$$
$$224$$ 2.80363e6i 0.249446i
$$225$$ 0 0
$$226$$ 4.64935e6 0.402779
$$227$$ −1.17834e7 6.80317e6i −1.00738 0.581612i −0.0969580 0.995288i $$-0.530911\pi$$
−0.910424 + 0.413676i $$0.864245\pi$$
$$228$$ 0 0
$$229$$ −2.17320e6 3.76410e6i −0.180965 0.313440i 0.761245 0.648465i $$-0.224589\pi$$
−0.942209 + 0.335025i $$0.891255\pi$$
$$230$$ −2.87790e6 + 1.66155e6i −0.236533 + 0.136562i
$$231$$ 0 0
$$232$$ −2.65690e6 + 4.60188e6i −0.212770 + 0.368529i
$$233$$ 2.02333e7i 1.59956i 0.600297 + 0.799778i $$0.295049\pi$$
−0.600297 + 0.799778i $$0.704951\pi$$
$$234$$ 0 0
$$235$$ −1.33578e7 −1.02927
$$236$$ 6.92379e6 + 3.99745e6i 0.526754 + 0.304121i
$$237$$ 0 0
$$238$$ −17424.0 30179.3i −0.00129246 0.00223861i
$$239$$ 1.76623e7 1.01973e7i 1.29376 0.746953i 0.314442 0.949277i $$-0.398183\pi$$
0.979319 + 0.202324i $$0.0648494\pi$$
$$240$$ 0 0
$$241$$ 1.56046e6 2.70280e6i 0.111481 0.193092i −0.804886 0.593429i $$-0.797774\pi$$
0.916368 + 0.400337i $$0.131107\pi$$
$$242$$ 146213.i 0.0103167i
$$243$$ 0 0
$$244$$ −424000. −0.0291875
$$245$$ 1.75661e7 + 1.01418e7i 1.19448 + 0.689631i
$$246$$ 0 0
$$247$$ −9.67290e6 1.67539e7i −0.641897 1.11180i
$$248$$ −6.23871e6 + 3.60192e6i −0.409016 + 0.236145i
$$249$$ 0 0
$$250$$ 488064. 845352.i 0.0312361 0.0541025i
$$251$$ 5.09519e6i 0.322210i −0.986937 0.161105i $$-0.948494\pi$$
0.986937 0.161105i $$-0.0515058\pi$$
$$252$$ 0 0
$$253$$ 4.52765e6 0.279583
$$254$$ 1.49772e7 + 8.64710e6i 0.913966 + 0.527678i
$$255$$ 0 0
$$256$$ −524288. 908093.i −0.0312500 0.0541266i
$$257$$ −1.25031e7 + 7.21869e6i −0.736580 + 0.425264i −0.820824 0.571181i $$-0.806486\pi$$
0.0842448 + 0.996445i $$0.473152\pi$$
$$258$$ 0 0
$$259$$ 1.27113e7 2.20166e7i 0.731628 1.26722i
$$260$$ 1.87474e7i 1.06665i
$$261$$ 0 0
$$262$$ −1.73885e7 −0.966847
$$263$$ 2.70691e7 + 1.56283e7i 1.48801 + 0.859104i 0.999906 0.0136808i $$-0.00435487\pi$$
0.488105 + 0.872785i $$0.337688\pi$$
$$264$$ 0 0
$$265$$ 2.07640e7 + 3.59643e7i 1.11577 + 1.93256i
$$266$$ 1.36196e7 7.86330e6i 0.723637 0.417792i
$$267$$ 0 0
$$268$$ 2.70349e6 4.68258e6i 0.140449 0.243266i
$$269$$ 251338.i 0.0129122i −0.999979 0.00645612i $$-0.997945\pi$$
0.999979 0.00645612i $$-0.00205506\pi$$
$$270$$ 0 0
$$271$$ 2.96399e7 1.48925 0.744627 0.667481i $$-0.232627\pi$$
0.744627 + 0.667481i $$0.232627\pi$$
$$272$$ 11287.2 + 6516.70i 0.000560895 + 0.000323833i
$$273$$ 0 0
$$274$$ −1.26830e7 2.19676e7i −0.616553 1.06790i
$$275$$ 1.69898e7 9.80904e6i 0.816938 0.471660i
$$276$$ 0 0
$$277$$ −6.61064e6 + 1.14500e7i −0.311031 + 0.538722i −0.978586 0.205839i $$-0.934008\pi$$
0.667555 + 0.744561i $$0.267341\pi$$
$$278$$ 6.17914e6i 0.287603i
$$279$$ 0 0
$$280$$ −1.52402e7 −0.694251
$$281$$ −5.30320e6 3.06180e6i −0.239011 0.137993i 0.375711 0.926737i $$-0.377399\pi$$
−0.614722 + 0.788744i $$0.710732\pi$$
$$282$$ 0 0
$$283$$ 3.37162e6 + 5.83982e6i 0.148758 + 0.257656i 0.930769 0.365609i $$-0.119139\pi$$
−0.782011 + 0.623265i $$0.785806\pi$$
$$284$$ −1.47284e7 + 8.50347e6i −0.642987 + 0.371229i
$$285$$ 0 0
$$286$$ 1.27715e7 2.21208e7i 0.545937 0.945590i
$$287$$ 1.79286e7i 0.758403i
$$288$$ 0 0
$$289$$ 2.41374e7 0.999993
$$290$$ −2.50153e7 1.44426e7i −1.02568 0.592176i
$$291$$ 0 0
$$292$$ 3.77830e6 + 6.54421e6i 0.151757 + 0.262851i
$$293$$ 8.68096e6 5.01195e6i 0.345116 0.199253i −0.317416 0.948286i $$-0.602815\pi$$
0.662532 + 0.749034i $$0.269482\pi$$
$$294$$ 0 0
$$295$$ −2.17297e7 + 3.76369e7i −0.846422 + 1.46605i
$$296$$ 9.50822e6i 0.366627i
$$297$$ 0 0
$$298$$ 1.25632e7 0.474734
$$299$$ −9.85036e6 5.68711e6i −0.368501 0.212754i
$$300$$ 0 0
$$301$$ 919600. + 1.59279e6i 0.0337209 + 0.0584064i
$$302$$ 1.99815e7 1.15363e7i 0.725450 0.418839i
$$303$$ 0 0
$$304$$ −2.94093e6 + 5.09384e6i −0.104680 + 0.181311i
$$305$$ 2.30481e6i 0.0812337i
$$306$$ 0 0
$$307$$ −5.23060e6 −0.180774 −0.0903871 0.995907i $$-0.528810\pi$$
−0.0903871 + 0.995907i $$0.528810\pi$$
$$308$$ 1.79825e7 + 1.03822e7i 0.615456 + 0.355334i
$$309$$ 0 0
$$310$$ −1.95796e7 3.39129e7i −0.657233 1.13836i
$$311$$ −2.70392e7 + 1.56111e7i −0.898901 + 0.518981i −0.876844 0.480776i $$-0.840355\pi$$
−0.0220578 + 0.999757i $$0.507022\pi$$
$$312$$ 0 0
$$313$$ −1.12389e7 + 1.94664e7i −0.366515 + 0.634822i −0.989018 0.147795i $$-0.952782\pi$$
0.622503 + 0.782617i $$0.286116\pi$$
$$314$$ 3.48218e7i 1.12477i
$$315$$ 0 0
$$316$$ 1.12371e6 0.0356118
$$317$$ −2.39206e7 1.38106e7i −0.750921 0.433544i 0.0751058 0.997176i $$-0.476071\pi$$
−0.826026 + 0.563631i $$0.809404\pi$$
$$318$$ 0 0
$$319$$ 1.96776e7 + 3.40827e7i 0.606179 + 1.04993i
$$320$$ 4.93629e6 2.84997e6i 0.150644 0.0869741i
$$321$$ 0 0
$$322$$ 4.62317e6 8.00756e6i 0.138475 0.239846i
$$323$$ 73109.2i 0.00216952i
$$324$$ 0 0
$$325$$ −4.92839e7 −1.43567
$$326$$ 3.92259e6 + 2.26471e6i 0.113219 + 0.0653672i
$$327$$ 0 0
$$328$$ 3.35270e6 + 5.80705e6i 0.0950110 + 0.164564i
$$329$$ 3.21878e7 1.85836e7i 0.903864 0.521846i
$$330$$ 0 0
$$331$$ 2.88069e6 4.98950e6i 0.0794352 0.137586i −0.823571 0.567213i $$-0.808022\pi$$
0.903006 + 0.429627i $$0.141355\pi$$
$$332$$ 351359.i 0.00960144i
$$333$$ 0 0
$$334$$ −2.71793e7 −0.729456
$$335$$ 2.54540e7 + 1.46958e7i 0.677050 + 0.390895i
$$336$$ 0 0
$$337$$ 2.00526e7 + 3.47321e7i 0.523939 + 0.907489i 0.999612 + 0.0278665i $$0.00887132\pi$$
−0.475673 + 0.879622i $$0.657795\pi$$
$$338$$ −3.19248e7 + 1.84318e7i −0.826756 + 0.477328i
$$339$$ 0 0
$$340$$ −35424.0 + 61356.2i −0.000901282 + 0.00156107i
$$341$$ 5.33535e7i 1.34555i
$$342$$ 0 0
$$343$$ 504328. 0.0124977
$$344$$ −595716. 343937.i −0.0146340 0.00844896i
$$345$$ 0 0
$$346$$ −1.00973e7 1.74890e7i −0.243767 0.422217i
$$347$$ −5.87275e7 + 3.39064e7i −1.40557 + 0.811508i −0.994957 0.100301i $$-0.968020\pi$$
−0.410616 + 0.911808i $$0.634686\pi$$
$$348$$ 0 0
$$349$$ 2.10319e7 3.64284e7i 0.494769 0.856965i −0.505213 0.862995i $$-0.668586\pi$$
0.999982 + 0.00602956i $$0.00191928\pi$$
$$350$$ 4.00639e7i 0.934436i
$$351$$ 0 0
$$352$$ −7.76602e6 −0.178062
$$353$$ −1.52399e7 8.79878e6i −0.346465 0.200032i 0.316662 0.948538i $$-0.397438\pi$$
−0.663127 + 0.748507i $$0.730771\pi$$
$$354$$ 0 0
$$355$$ −4.62239e7 8.00621e7i −1.03319 1.78954i
$$356$$ −3.58405e6 + 2.06925e6i −0.0794373 + 0.0458632i
$$357$$ 0 0
$$358$$ −2.10349e7 + 3.64336e7i −0.458450 + 0.794059i
$$359$$ 1.39920e7i 0.302410i 0.988502 + 0.151205i $$0.0483154\pi$$
−0.988502 + 0.151205i $$0.951685\pi$$
$$360$$ 0 0
$$361$$ −1.40523e7 −0.298694
$$362$$ −5.08572e7 2.93624e7i −1.07208 0.618966i
$$363$$ 0 0
$$364$$ −2.60818e7 4.51750e7i −0.540796 0.936686i
$$365$$ −3.55736e7 + 2.05384e7i −0.731559 + 0.422365i
$$366$$ 0 0
$$367$$ 1.32927e7 2.30237e7i 0.268916 0.465776i −0.699666 0.714470i $$-0.746668\pi$$
0.968582 + 0.248694i $$0.0800013\pi$$
$$368$$ 3.45819e6i 0.0693914i
$$369$$ 0 0
$$370$$ −5.16856e7 −1.02039
$$371$$ −1.00068e8 5.77745e7i −1.95963 1.13140i
$$372$$ 0 0
$$373$$ −8.94146e6 1.54871e7i −0.172299 0.298430i 0.766924 0.641737i $$-0.221786\pi$$
−0.939223 + 0.343307i $$0.888453\pi$$
$$374$$ 83596.2 48264.3i 0.00159798 0.000922595i
$$375$$ 0 0
$$376$$ −6.95040e6 + 1.20384e7i −0.130751 + 0.226468i
$$377$$ 9.88671e7i 1.84513i
$$378$$ 0 0
$$379$$ 7.20978e7 1.32435 0.662177 0.749347i $$-0.269633\pi$$
0.662177 + 0.749347i $$0.269633\pi$$
$$380$$ −2.76895e7 1.59865e7i −0.504620 0.291342i
$$381$$ 0 0
$$382$$ 3.67527e7 + 6.36576e7i 0.659325 + 1.14198i
$$383$$ −7.52272e6 + 4.34324e6i −0.133899 + 0.0773068i −0.565453 0.824780i $$-0.691299\pi$$
0.431554 + 0.902087i $$0.357965\pi$$
$$384$$ 0 0
$$385$$ −5.64363e7 + 9.77506e7i −0.988955 + 1.71292i
$$386$$ 2.22425e7i 0.386742i
$$387$$ 0 0
$$388$$ 1.02856e7 0.176089
$$389$$ −4.28173e7 2.47206e7i −0.727395 0.419962i 0.0900736 0.995935i $$-0.471290\pi$$
−0.817468 + 0.575974i $$0.804623\pi$$
$$390$$ 0 0
$$391$$ −21492.0 37225.2i −0.000359539 0.000622741i
$$392$$ 1.82802e7 1.05541e7i 0.303474 0.175211i
$$393$$ 0 0
$$394$$ 1.52160e7 2.63549e7i 0.248778 0.430896i
$$395$$ 6.10837e6i 0.0991137i
$$396$$ 0 0
$$397$$ 1.56911e7 0.250774 0.125387 0.992108i $$-0.459983\pi$$
0.125387 + 0.992108i $$0.459983\pi$$
$$398$$ −2.77233e6 1.60061e6i −0.0439740 0.0253884i
$$399$$ 0 0
$$400$$ 7.49210e6 + 1.29767e7i 0.117064 + 0.202761i
$$401$$ 4.10941e7 2.37257e7i 0.637304 0.367947i −0.146272 0.989244i $$-0.546727\pi$$
0.783575 + 0.621297i $$0.213394\pi$$
$$402$$ 0 0
$$403$$ 6.70165e7 1.16076e8i 1.02392 1.77348i
$$404$$ 2.14010e7i 0.324556i
$$405$$ 0 0
$$406$$ 8.03711e7 1.20094
$$407$$ 6.09857e7 + 3.52101e7i 0.904576 + 0.522257i
$$408$$ 0 0
$$409$$ 5.77558e7 + 1.00036e8i 0.844162 + 1.46213i 0.886347 + 0.463022i $$0.153235\pi$$
−0.0421850 + 0.999110i $$0.513432\pi$$
$$410$$ −3.15665e7 + 1.82249e7i −0.458009 + 0.264432i
$$411$$ 0 0
$$412$$ 3.18946e7 5.52431e7i 0.456064 0.789925i
$$413$$ 1.20923e8i 1.71656i
$$414$$ 0 0
$$415$$ 1.90994e6 0.0267225
$$416$$ 1.68958e7 + 9.75477e6i 0.234692 + 0.135499i
$$417$$ 0 0
$$418$$ 2.17812e7 + 3.77262e7i 0.298232 + 0.516553i
$$419$$ −1.27040e8 + 7.33466e7i −1.72702 + 0.997098i −0.825447 + 0.564480i $$0.809077\pi$$
−0.901577 + 0.432618i $$0.857590\pi$$
$$420$$ 0 0
$$421$$ −6.96194e7 + 1.20584e8i −0.933005 + 1.61601i −0.154852 + 0.987938i $$0.549490\pi$$
−0.778153 + 0.628075i $$0.783843\pi$$
$$422$$ 7.64609e7i 1.01742i
$$423$$ 0 0
$$424$$ 4.32161e7 0.566955
$$425$$ −161295. 93123.8i −0.00210114 0.00121309i
$$426$$ 0 0
$$427$$ 3.20650e6 + 5.55382e6i 0.0411858 + 0.0713359i
$$428$$ −7.22384e6 + 4.17069e6i −0.0921376 + 0.0531957i
$$429$$ 0 0
$$430$$ 1.86960e6 3.23824e6i 0.0235149 0.0407290i
$$431$$ 1.00392e8i 1.25391i 0.779056 + 0.626954i $$0.215699\pi$$
−0.779056 + 0.626954i $$0.784301\pi$$
$$432$$ 0 0
$$433$$ −4.00631e7 −0.493493 −0.246747 0.969080i $$-0.579362\pi$$
−0.246747 + 0.969080i $$0.579362\pi$$
$$434$$ 9.43605e7 + 5.44791e7i 1.15431 + 0.666439i
$$435$$ 0 0
$$436$$ 3.11130e6 + 5.38892e6i 0.0375389 + 0.0650193i
$$437$$ 1.67994e7 9.69915e6i 0.201303 0.116222i
$$438$$ 0 0
$$439$$ 6.92959e7 1.20024e8i 0.819057 1.41865i −0.0873208 0.996180i $$-0.527831\pi$$
0.906378 0.422468i $$-0.138836\pi$$
$$440$$ 4.22152e7i 0.495576i
$$441$$ 0 0
$$442$$ −242496. −0.00280826
$$443$$ −9.65121e7 5.57213e7i −1.11012 0.640929i −0.171261 0.985226i $$-0.554784\pi$$
−0.938861 + 0.344296i $$0.888117\pi$$
$$444$$ 0 0
$$445$$ −1.12482e7 1.94825e7i −0.127645 0.221088i
$$446$$ 2.62332e7 1.51458e7i 0.295697 0.170721i
$$447$$ 0 0
$$448$$ −7.92986e6 + 1.37349e7i −0.0881924 + 0.152754i
$$449$$ 6.11166e7i 0.675181i 0.941293 + 0.337591i $$0.109612\pi$$
−0.941293 + 0.337591i $$0.890388\pi$$
$$450$$ 0 0
$$451$$ 4.96619e7 0.541370
$$452$$ 2.27771e7 + 1.31504e7i 0.246651 + 0.142404i
$$453$$ 0 0
$$454$$ −3.84845e7 6.66572e7i −0.411262 0.712327i
$$455$$ 2.45566e8 1.41778e8i 2.60696 1.50513i
$$456$$ 0 0
$$457$$ −1.78332e7 + 3.08881e7i −0.186845 + 0.323625i −0.944197 0.329382i $$-0.893160\pi$$
0.757352 + 0.653007i $$0.226493\pi$$
$$458$$ 2.45870e7i 0.255923i
$$459$$ 0 0
$$460$$ −1.87983e7 −0.193128
$$461$$ 1.31621e8 + 7.59914e7i 1.34345 + 0.775642i 0.987312 0.158791i $$-0.0507595\pi$$
0.356139 + 0.934433i $$0.384093\pi$$
$$462$$ 0 0
$$463$$ −5.74891e7 9.95740e7i −0.579218 1.00324i −0.995569 0.0940314i $$-0.970025\pi$$
0.416351 0.909204i $$-0.363309\pi$$
$$464$$ −2.60322e7 + 1.50297e7i −0.260589 + 0.150451i
$$465$$ 0 0
$$466$$ −5.72284e7 + 9.91226e7i −0.565528 + 0.979523i
$$467$$ 8.81705e7i 0.865711i −0.901463 0.432855i $$-0.857506\pi$$
0.901463 0.432855i $$-0.142494\pi$$
$$468$$ 0 0
$$469$$ −8.17805e7 −0.792741
$$470$$ −6.54396e7 3.77816e7i −0.630300 0.363904i
$$471$$ 0 0
$$472$$ 2.26130e7 + 3.91669e7i 0.215046 + 0.372471i
$$473$$ −4.41202e6 + 2.54728e6i −0.0416921 + 0.0240710i
$$474$$ 0 0
$$475$$ 4.20260e7 7.27911e7i 0.392136 0.679200i
$$476$$ 197130.i 0.00182781i
$$477$$ 0 0
$$478$$ 1.15370e8 1.05635
$$479$$ −7.74563e7 4.47194e7i −0.704774 0.406902i 0.104349 0.994541i $$-0.466724\pi$$
−0.809123 + 0.587639i $$0.800057\pi$$
$$480$$ 0 0
$$481$$ −8.84538e7 1.53206e8i −0.794843 1.37671i
$$482$$ 1.52894e7 8.82732e6i 0.136536 0.0788293i
$$483$$ 0 0
$$484$$ −413552. + 716293.i −0.00364749 + 0.00631764i
$$485$$ 5.59111e7i 0.490087i
$$486$$ 0 0
$$487$$ −7.51688e7 −0.650805 −0.325403 0.945576i $$-0.605500\pi$$
−0.325403 + 0.945576i $$0.605500\pi$$
$$488$$ −2.07717e6 1.19925e6i −0.0178736 0.0103193i
$$489$$ 0 0
$$490$$ 5.73706e7 + 9.93689e7i 0.487642 + 0.844621i
$$491$$ −3.90424e7 + 2.25411e7i −0.329831 + 0.190428i −0.655766 0.754964i $$-0.727654\pi$$
0.325935 + 0.945392i $$0.394321\pi$$
$$492$$ 0 0
$$493$$ 186813. 323570.i 0.00155907 0.00270039i
$$494$$ 1.09436e8i 0.907780i
$$495$$ 0 0
$$496$$ −4.07511e7 −0.333960
$$497$$ 2.22768e8 + 1.28615e8i 1.81461 + 1.04767i
$$498$$ 0 0
$$499$$ −4.57729e7 7.92810e7i −0.368389 0.638069i 0.620925 0.783870i $$-0.286757\pi$$
−0.989314 + 0.145801i $$0.953424\pi$$
$$500$$ 4.78203e6 2.76091e6i 0.0382562 0.0220873i
$$501$$ 0 0
$$502$$ 1.44114e7 2.49612e7i 0.113919 0.197313i
$$503$$ 1.61043e8i 1.26543i 0.774386 + 0.632713i $$0.218059\pi$$
−0.774386 + 0.632713i $$0.781941\pi$$
$$504$$ 0 0
$$505$$ −1.16333e8 −0.903295
$$506$$ 2.21809e7 + 1.28061e7i 0.171209 + 0.0988476i
$$507$$ 0 0
$$508$$ 4.89154e7 + 8.47239e7i 0.373125 + 0.646272i
$$509$$ −2.07841e7 + 1.19997e7i −0.157608 + 0.0909951i −0.576730 0.816935i $$-0.695671\pi$$
0.419122 + 0.907930i $$0.362338\pi$$
$$510$$ 0 0
$$511$$ 5.71468e7 9.89812e7i 0.428282 0.741806i
$$512$$ 5.93164e6i 0.0441942i
$$513$$ 0 0
$$514$$ −8.16702e7 −0.601415
$$515$$ 3.00295e8 + 1.73375e8i 2.19850 + 1.26930i
$$516$$ 0 0
$$517$$ 5.14764e7 + 8.91597e7i 0.372509 + 0.645204i
$$518$$ 1.24545e8 7.19059e7i 0.896058 0.517339i
$$519$$ 0 0
$$520$$ −5.30258e7 + 9.18434e7i −0.377118 + 0.653187i
$$521$$ 9.00897e7i 0.637033i 0.947917 + 0.318517i $$0.103185\pi$$
−0.947917 + 0.318517i $$0.896815\pi$$
$$522$$ 0 0
$$523$$ −3.77691e7 −0.264016 −0.132008 0.991249i $$-0.542143\pi$$
−0.132008 + 0.991249i $$0.542143\pi$$
$$524$$ −8.51858e7 4.91820e7i −0.592070 0.341832i
$$525$$ 0 0
$$526$$ 8.84073e7 + 1.53126e8i 0.607478 + 1.05218i
$$527$$ 438660. 253260.i 0.00299706 0.00173035i
$$528$$ 0 0
$$529$$ −6.83154e7 + 1.18326e8i −0.461479 + 0.799304i
$$530$$ 2.34918e8i 1.57793i
$$531$$ 0 0
$$532$$ 8.89631e7 0.590847
$$533$$ −1.08045e8 6.23796e7i −0.713545 0.411965i
$$534$$ 0 0
$$535$$ −2.26714e7 3.92679e7i −0.148053 0.256435i
$$536$$ 2.64887e7 1.52932e7i 0.172015 0.0993128i
$$537$$ 0 0
$$538$$ 710892. 1.23130e6i 0.00456517 0.00790710i
$$539$$ 1.56332e8i 0.998347i
$$540$$ 0 0
$$541$$ 2.54800e7 0.160919 0.0804595 0.996758i $$-0.474361\pi$$
0.0804595 + 0.996758i $$0.474361\pi$$
$$542$$ 1.45205e8 + 8.38343e7i 0.911978 + 0.526531i
$$543$$ 0 0
$$544$$ 36864.0 + 63850.3i 0.000228984 + 0.000396612i
$$545$$ −2.92936e7 + 1.69126e7i −0.180960 + 0.104477i
$$546$$ 0 0
$$547$$ −1.02608e8 + 1.77722e8i −0.626930 + 1.08587i 0.361234 + 0.932475i $$0.382355\pi$$
−0.988164 + 0.153399i $$0.950978\pi$$
$$548$$ 1.43492e8i 0.871938i
$$549$$ 0 0
$$550$$ 1.10977e8 0.667027
$$551$$ 1.46024e8 + 8.43071e7i 0.872911 + 0.503975i
$$552$$ 0 0
$$553$$ −8.49807e6 1.47191e7i −0.0502510 0.0870373i
$$554$$ −6.47707e7 + 3.73954e7i −0.380934 + 0.219932i
$$555$$ 0 0
$$556$$ −1.74772e7 + 3.02715e7i −0.101683 + 0.176120i
$$557$$ 2.41143e8i 1.39543i 0.716375 + 0.697715i $$0.245800\pi$$
−0.716375 + 0.697715i $$0.754200\pi$$
$$558$$ 0 0
$$559$$ 1.27984e7 0.0732690
$$560$$ −7.46614e7 4.31058e7i −0.425140 0.245455i
$$561$$ 0 0
$$562$$ −1.73202e7 2.99994e7i −0.0975760 0.169007i
$$563$$ 1.46252e8 8.44386e7i 0.819552 0.473168i −0.0307102 0.999528i $$-0.509777\pi$$
0.850262 + 0.526360i $$0.176444\pi$$
$$564$$ 0 0
$$565$$ −7.14838e7 + 1.23814e8i −0.396335 + 0.686472i
$$566$$ 3.81456e7i 0.210375i
$$567$$ 0 0
$$568$$ −9.62058e7 −0.524996
$$569$$ −2.11306e8 1.21998e8i −1.14703 0.662238i −0.198869 0.980026i $$-0.563727\pi$$
−0.948162 + 0.317788i $$0.897060\pi$$
$$570$$ 0 0
$$571$$ −1.20751e8 2.09147e8i −0.648608 1.12342i −0.983456 0.181149i $$-0.942018\pi$$
0.334848 0.942272i $$-0.391315\pi$$
$$572$$ 1.25134e8 7.22463e7i 0.668633 0.386036i
$$573$$ 0 0
$$574$$ 5.07096e7 8.78317e7i 0.268136 0.464425i
$$575$$ 4.94177e7i 0.259944i
$$576$$ 0 0
$$577$$ −4.93979e7 −0.257147 −0.128573 0.991700i $$-0.541040\pi$$
−0.128573 + 0.991700i $$0.541040\pi$$
$$578$$ 1.18249e8 + 6.82709e7i 0.612368 + 0.353551i
$$579$$ 0 0
$$580$$ −8.16996e7 1.41508e8i −0.418732 0.725264i
$$581$$ −4.60232e6 + 2.65715e6i −0.0234665 + 0.0135484i
$$582$$ 0 0
$$583$$ 1.60035e8 2.77188e8i 0.807623 1.39884i
$$584$$ 4.27466e7i 0.214617i
$$585$$ 0 0
$$586$$ 5.67038e7 0.281786
$$587$$ −1.49001e8 8.60260e7i −0.736675 0.425320i 0.0841840 0.996450i $$-0.473172\pi$$
−0.820859 + 0.571131i $$0.806505\pi$$
$$588$$ 0 0
$$589$$ 1.14294e8 + 1.97963e8i 0.559343 + 0.968810i
$$590$$ −2.12906e8 + 1.22922e8i −1.03665 + 0.598511i
$$591$$ 0 0
$$592$$ −2.68933e7 + 4.65806e7i −0.129622 + 0.224512i
$$593$$ 2.70643e8i 1.29788i −0.760841 0.648938i $$-0.775213\pi$$
0.760841 0.648938i $$-0.224787\pi$$
$$594$$ 0 0
$$595$$ 1.07158e6 0.00508712
$$596$$ 6.15467e7 + 3.55340e7i 0.290714 + 0.167844i
$$597$$ 0 0
$$598$$ −3.21711e7 5.57220e7i −0.150440 0.260569i
$$599$$ 1.50082e8 8.66497e7i 0.698308 0.403169i −0.108409 0.994106i $$-0.534575\pi$$
0.806717 + 0.590938i $$0.201242\pi$$
$$600$$ 0 0
$$601$$ 2.15545e8 3.73335e8i 0.992921 1.71979i 0.393598 0.919282i $$-0.371230\pi$$
0.599323 0.800507i $$-0.295437\pi$$
$$602$$ 1.04041e7i 0.0476886i
$$603$$ 0 0
$$604$$ 1.30519e8 0.592327
$$605$$ −3.89369e6 2.24802e6i −0.0175831 0.0101516i
$$606$$ 0 0
$$607$$ −8.34953e6 1.44618e7i −0.0373332 0.0646631i 0.846755 0.531983i $$-0.178553\pi$$
−0.884088 + 0.467320i $$0.845220\pi$$
$$608$$ −2.88151e7 + 1.66364e7i −0.128206 + 0.0740199i
$$609$$ 0 0
$$610$$ 6.51900e6 1.12912e7i 0.0287205 0.0497453i
$$611$$ 2.58635e8i 1.13387i
$$612$$ 0 0
$$613$$ −1.92321e8 −0.834920 −0.417460 0.908695i $$-0.637080\pi$$
−0.417460 + 0.908695i $$0.637080\pi$$
$$614$$ −2.56246e7 1.47944e7i −0.110701 0.0639133i
$$615$$ 0 0
$$616$$ 5.87305e7 + 1.01724e8i 0.251259 + 0.435193i
$$617$$ 1.61967e8 9.35117e7i 0.689558 0.398117i −0.113888 0.993494i $$-0.536331\pi$$
0.803447 + 0.595377i $$0.202997\pi$$
$$618$$ 0 0
$$619$$ −1.27437e8 + 2.20727e8i −0.537307 + 0.930643i 0.461741 + 0.887015i $$0.347225\pi$$
−0.999048 + 0.0436278i $$0.986108\pi$$
$$620$$ 2.21518e8i 0.929468i
$$621$$ 0 0
$$622$$ −1.76619e8 −0.733950
$$623$$ 5.42088e7 + 3.12975e7i 0.224185 + 0.129433i
$$624$$ 0 0
$$625$$ 1.29328e8 + 2.24003e8i 0.529729 + 0.917517i
$$626$$ −1.10118e8 + 6.35769e7i −0.448887 + 0.259165i
$$627$$ 0 0
$$628$$ 9.84908e7 1.70591e8i 0.397665 0.688775i
$$629$$ 668547.i 0.00268646i
$$630$$ 0 0
$$631$$ 9.23602e7 0.367618 0.183809 0.982962i $$-0.441157\pi$$
0.183809 + 0.982962i $$0.441157\pi$$
$$632$$ 5.50504e6 + 3.17834e6i 0.0218077 + 0.0125907i
$$633$$ 0 0
$$634$$ −7.81243e7 1.35315e8i −0.306562 0.530981i
$$635$$ −4.60549e8 + 2.65898e8i −1.79869 + 1.03847i
$$636$$ 0 0
$$637$$ −1.96366e8 + 3.40116e8i −0.759711 + 1.31586i
$$638$$ 2.22627e8i 0.857267i
$$639$$ 0 0
$$640$$ 3.22437e7 0.123000
$$641$$ −3.67771e8 2.12333e8i −1.39638 0.806200i −0.402368 0.915478i $$-0.631813\pi$$
−0.994011 + 0.109278i $$0.965146\pi$$
$$642$$ 0 0
$$643$$ −1.87973e8 3.25579e8i −0.707071 1.22468i −0.965939 0.258770i $$-0.916683\pi$$
0.258868 0.965913i $$-0.416650\pi$$
$$644$$ 4.52976e7 2.61526e7i 0.169597 0.0979168i
$$645$$ 0 0
$$646$$ 206784. 358160.i 0.000767042 0.00132856i
$$647$$ 2.63747e7i 0.0973813i −0.998814 0.0486906i $$-0.984495\pi$$
0.998814 0.0486906i $$-0.0155048\pi$$
$$648$$ 0 0
$$649$$ 3.34955e8 1.22533
$$650$$ −2.41441e8 1.39396e8i −0.879166 0.507587i
$$651$$ 0 0
$$652$$ 1.28111e7 + 2.21895e7i 0.0462216 + 0.0800581i
$$653$$ −2.24090e8 + 1.29378e8i −0.804790 + 0.464645i −0.845143 0.534540i $$-0.820485\pi$$
0.0403536 + 0.999185i $$0.487152\pi$$
$$654$$ 0 0
$$655$$ 2.67348e8 4.63060e8i 0.951377 1.64783i
$$656$$ 3.79315e7i 0.134366i
$$657$$ 0 0
$$658$$ 2.10250e8 0.738002
$$659$$ −1.20676e8 6.96725e7i −0.421663 0.243447i 0.274126 0.961694i $$-0.411612\pi$$
−0.695789 + 0.718247i $$0.744945\pi$$
$$660$$ 0 0
$$661$$ 2.36272e8 + 4.09236e8i 0.818104 + 1.41700i 0.907077 + 0.420964i $$0.138308\pi$$
−0.0889731 + 0.996034i $$0.528359\pi$$
$$662$$ 2.82249e7 1.62957e7i 0.0972878 0.0561691i
$$663$$ 0 0
$$664$$ 993792. 1.72130e6i 0.00339462 0.00587966i
$$665$$ 4.83593e8i 1.64443i
$$666$$ 0 0
$$667$$ 9.91354e7 0.334081
$$668$$ −1.33151e8 7.68747e7i −0.446699 0.257902i
$$669$$ 0 0
$$670$$ 8.31323e7 + 1.43989e8i 0.276405 + 0.478747i
$$671$$ −1.53840e7 + 8.88197e6i −0.0509216 + 0.0293996i
$$672$$ 0 0
$$673$$ −2.74417e8 + 4.75304e8i −0.900254 + 1.55929i −0.0730906 + 0.997325i $$0.523286\pi$$
−0.827164 + 0.561961i $$0.810047\pi$$
$$674$$ 2.26869e8i 0.740961i
$$675$$ 0 0
$$676$$ −2.08532e8 −0.675044
$$677$$ −8.72609e7 5.03801e7i −0.281225 0.162365i 0.352753 0.935717i $$-0.385246\pi$$
−0.633978 + 0.773351i $$0.718579\pi$$
$$678$$ 0 0
$$679$$ −7.77846e7 1.34727e8i −0.248476 0.430373i
$$680$$ −347083. + 200388.i −0.00110384 + 0.000637303i
$$681$$ 0 0
$$682$$ −1.50906e8 + 2.61378e8i −0.475724 + 0.823977i
$$683$$ 313056.i 0.000982562i 1.00000 0.000491281i $$0.000156380\pi$$
−1.00000 0.000491281i $$0.999844\pi$$
$$684$$ 0 0
$$685$$ 7.80005e8 2.42675
$$686$$ 2.47069e6 + 1.42645e6i 0.00765326 + 0.00441861i
$$687$$ 0 0
$$688$$ −1.94560e6 3.36988e6i −0.00597432 0.0103478i
$$689$$ −6.96344e8 + 4.02034e8i −2.12895 + 1.22915i
$$690$$ 0 0
$$691$$ 1.86406e8 3.22865e8i 0.564971 0.978558i −0.432082 0.901834i $$-0.642221\pi$$
0.997052 0.0767236i $$-0.0244459\pi$$
$$692$$ 1.14238e8i 0.344739i
$$693$$ 0 0
$$694$$ −3.83607e8 −1.14765
$$695$$ −1.64552e8 9.50043e7i −0.490173 0.283002i
$$696$$ 0 0
$$697$$ −235737. 408308.i −0.000696193 0.00120584i
$$698$$ 2.06070e8 1.18975e8i 0.605966 0.349855i
$$699$$ 0 0
$$700$$ 1.13318e8 1.96272e8i 0.330373 0.572223i
$$701$$ 6.21170e8i 1.80325i −0.432517 0.901626i $$-0.642374\pi$$
0.432517 0.901626i $$-0.357626\pi$$
$$702$$ 0 0
$$703$$ 3.01709e8 0.868406
$$704$$ −3.80456e7 2.19656e7i −0.109040 0.0629543i
$$705$$ 0 0
$$706$$ −4.97734e7 8.62101e7i −0.141444 0.244988i
$$707$$ 2.80323e8 1.61845e8i 0.793234 0.457974i
$$708$$ 0 0
$$709$$ 1.23255e8 2.13484e8i 0.345833 0.599000i −0.639672 0.768648i $$-0.720930\pi$$
0.985505 + 0.169648i $$0.0542631\pi$$
$$710$$ 5.22964e8i 1.46116i
$$711$$ 0 0
$$712$$ −2.34109e7 −0.0648603
$$713$$ 1.16391e8 + 6.71984e7i 0.321108 + 0.185392i
$$714$$ 0 0
$$715$$ 3.92722e8 + 6.80215e8i 1.07440 + 1.86092i
$$716$$ −2.06100e8 + 1.18992e8i −0.561485 + 0.324173i
$$717$$ 0 0
$$718$$ −3.95754e7 + 6.85466e7i −0.106918 + 0.185188i
$$719$$ 9.60389e7i 0.258381i 0.991620 + 0.129191i $$0.0412379\pi$$
−0.991620 + 0.129191i $$0.958762\pi$$
$$720$$ 0 0
$$721$$ −9.64811e8 −2.57417
$$722$$ −6.88421e7 3.97460e7i −0.182912 0.105604i
$$723$$ 0 0
$$724$$ −1.66099e8 2.87692e8i −0.437675 0.758075i
$$725$$ 3.72001e8 2.14775e8i 0.976179 0.563597i
$$726$$ 0 0
$$727$$ −1.95685e8 + 3.38937e8i −0.509278 + 0.882096i 0.490664 + 0.871349i $$0.336754\pi$$
−0.999942 + 0.0107471i $$0.996579\pi$$
$$728$$ 2.95082e8i 0.764801i
$$729$$ 0 0
$$730$$ −2.32366e8 −0.597315
$$731$$ 41886.3 + 24183.1i 0.000107231 + 6.19097e-5i
$$732$$ 0 0
$$733$$ −1.74539e7 3.02311e7i −0.0443181 0.0767611i 0.843015 0.537889i $$-0.180778\pi$$
−0.887334 + 0.461128i $$0.847445\pi$$
$$734$$ 1.30242e8 7.51951e7i 0.329353 0.190152i
$$735$$ 0 0
$$736$$ −9.78125e6 + 1.69416e7i −0.0245336 + 0.0424934i
$$737$$ 2.26531e8i 0.565881i
$$738$$ 0 0
$$739$$ −3.02999e8 −0.750773 −0.375386 0.926868i $$-0.622490\pi$$
−0.375386 + 0.926868i $$0.622490\pi$$
$$740$$ −2.53207e8 1.46189e8i −0.624856 0.360761i
$$741$$ 0 0
$$742$$ −3.26822e8 5.66072e8i −0.800018 1.38567i
$$743$$ −2.12720e8 + 1.22814e8i −0.518612 + 0.299421i −0.736367 0.676583i $$-0.763460\pi$$
0.217754 + 0.976004i $$0.430127\pi$$
$$744$$ 0 0
$$745$$ −1.93159e8 + 3.34560e8i −0.467138 + 0.809107i
$$746$$ 1.01161e8i 0.243667i
$$747$$ 0 0
$$748$$ 546048. 0.00130475
$$749$$ 1.09261e8 + 6.30816e7i 0.260027 + 0.150127i
$$750$$ 0 0
$$751$$ 4.11635e7 + 7.12973e7i 0.0971835 + 0.168327i 0.910518 0.413470i $$-0.135683\pi$$
−0.813334 + 0.581797i $$0.802350\pi$$
$$752$$ −6.80997e7 + 3.93174e7i −0.160137 + 0.0924552i
$$753$$ 0 0
$$754$$ 2.79638e8 4.84348e8i 0.652353 1.12991i
$$755$$ 7.09484e8i 1.64855i
$$756$$ 0 0
$$757$$ −6.03579e8 −1.39138 −0.695691 0.718341i $$-0.744902\pi$$
−0.695691 + 0.718341i $$0.744902\pi$$
$$758$$ 3.53205e8 + 2.03923e8i 0.810998 + 0.468230i
$$759$$ 0 0
$$760$$ −9.04335e7 1.56635e8i −0.206010 0.356820i
$$761$$ 2.01769e8 1.16491e8i 0.457825 0.264325i −0.253304 0.967387i $$-0.581517\pi$$
0.711129 + 0.703061i $$0.248184\pi$$
$$762$$ 0 0
$$763$$ 4.70584e7 8.15075e7i 0.105941 0.183495i
$$764$$ 4.15810e8i 0.932426i
$$765$$ 0 0
$$766$$ −4.91382e7 −0.109328
$$767$$ −7.28729e8 4.20732e8i −1.61503 0.932436i
$$768$$ 0 0
$$769$$ −4.07898e8 7.06500e8i −0.896958 1.55358i −0.831362 0.555731i $$-0.812438\pi$$
−0.0655965 0.997846i $$-0.520895\pi$$
$$770$$ −5.52961e8 + 3.19252e8i −1.21122 + 0.699297i
$$771$$ 0 0
$$772$$ −6.29113e7 + 1.08966e8i −0.136734 + 0.236830i
$$773$$ 3.66587e8i 0.793667i 0.917891 + 0.396833i $$0.129891\pi$$
−0.917891 + 0.396833i $$0.870109\pi$$
$$774$$ 0 0
$$775$$ 5.82335e8 1.25103
$$776$$ 5.03888e7 + 2.90920e7i 0.107832 + 0.0622570i
$$777$$ 0 0
$$778$$ −1.39841e8 2.42211e8i −0.296958 0.514346i