# Properties

 Label 4.7.b.a.3.2 Level $4$ Weight $7$ Character 4.3 Analytic conductor $0.920$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$4 = 2^{2}$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 4.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.920216334479$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-15})$$ Defining polynomial: $$x^{2} - x + 4$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 3.2 Root $$0.500000 + 1.93649i$$ of defining polynomial Character $$\chi$$ $$=$$ 4.3 Dual form 4.7.b.a.3.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(2.00000 + 7.74597i) q^{2} -30.9839i q^{3} +(-56.0000 + 30.9839i) q^{4} +10.0000 q^{5} +(240.000 - 61.9677i) q^{6} +309.839i q^{7} +(-352.000 - 371.806i) q^{8} -231.000 q^{9} +O(q^{10})$$ $$q+(2.00000 + 7.74597i) q^{2} -30.9839i q^{3} +(-56.0000 + 30.9839i) q^{4} +10.0000 q^{5} +(240.000 - 61.9677i) q^{6} +309.839i q^{7} +(-352.000 - 371.806i) q^{8} -231.000 q^{9} +(20.0000 + 77.4597i) q^{10} -960.500i q^{11} +(960.000 + 1735.10i) q^{12} +1466.00 q^{13} +(-2400.00 + 619.677i) q^{14} -309.839i q^{15} +(2176.00 - 3470.19i) q^{16} -4766.00 q^{17} +(-462.000 - 1789.32i) q^{18} +7529.08i q^{19} +(-560.000 + 309.839i) q^{20} +9600.00 q^{21} +(7440.00 - 1921.00i) q^{22} -10472.5i q^{23} +(-11520.0 + 10906.3i) q^{24} -15525.0 q^{25} +(2932.00 + 11355.6i) q^{26} -15430.0i q^{27} +(-9600.00 - 17351.0i) q^{28} +25498.0 q^{29} +(2400.00 - 619.677i) q^{30} +41890.2i q^{31} +(31232.0 + 9914.84i) q^{32} -29760.0 q^{33} +(-9532.00 - 36917.3i) q^{34} +3098.39i q^{35} +(12936.0 - 7157.27i) q^{36} +1994.00 q^{37} +(-58320.0 + 15058.2i) q^{38} -45422.3i q^{39} +(-3520.00 - 3718.06i) q^{40} +29362.0 q^{41} +(19200.0 + 74361.3i) q^{42} -21533.8i q^{43} +(29760.0 + 53788.0i) q^{44} -2310.00 q^{45} +(81120.0 - 20945.1i) q^{46} -7560.06i q^{47} +(-107520. - 67420.9i) q^{48} +21649.0 q^{49} +(-31050.0 - 120256. i) q^{50} +147669. i q^{51} +(-82096.0 + 45422.3i) q^{52} -192854. q^{53} +(119520. - 30859.9i) q^{54} -9605.00i q^{55} +(115200. - 109063. i) q^{56} +233280. q^{57} +(50996.0 + 197507. i) q^{58} -78420.2i q^{59} +(9600.00 + 17351.0i) q^{60} -10918.0 q^{61} +(-324480. + 83780.4i) q^{62} -71572.7i q^{63} +(-14336.0 + 261752. i) q^{64} +14660.0 q^{65} +(-59520.0 - 230520. i) q^{66} -394146. i q^{67} +(266896. - 147669. i) q^{68} -324480. q^{69} +(-24000.0 + 6196.77i) q^{70} +532241. i q^{71} +(81312.0 + 85887.3i) q^{72} +288626. q^{73} +(3988.00 + 15445.5i) q^{74} +481025. i q^{75} +(-233280. - 421628. i) q^{76} +297600. q^{77} +(351840. - 90844.7i) q^{78} -310706. i q^{79} +(21760.0 - 34701.9i) q^{80} -646479. q^{81} +(58724.0 + 227437. i) q^{82} -204153. i q^{83} +(-537600. + 297445. i) q^{84} -47660.0 q^{85} +(166800. - 43067.6i) q^{86} -790027. i q^{87} +(-357120. + 338096. i) q^{88} +310738. q^{89} +(-4620.00 - 17893.2i) q^{90} +454223. i q^{91} +(324480. + 586463. i) q^{92} +1.29792e6 q^{93} +(58560.0 - 15120.1i) q^{94} +75290.8i q^{95} +(307200. - 967688. i) q^{96} -1.45709e6 q^{97} +(43298.0 + 167692. i) q^{98} +221875. i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + 4 q^{2} - 112 q^{4} + 20 q^{5} + 480 q^{6} - 704 q^{8} - 462 q^{9} + O(q^{10})$$ $$2 q + 4 q^{2} - 112 q^{4} + 20 q^{5} + 480 q^{6} - 704 q^{8} - 462 q^{9} + 40 q^{10} + 1920 q^{12} + 2932 q^{13} - 4800 q^{14} + 4352 q^{16} - 9532 q^{17} - 924 q^{18} - 1120 q^{20} + 19200 q^{21} + 14880 q^{22} - 23040 q^{24} - 31050 q^{25} + 5864 q^{26} - 19200 q^{28} + 50996 q^{29} + 4800 q^{30} + 62464 q^{32} - 59520 q^{33} - 19064 q^{34} + 25872 q^{36} + 3988 q^{37} - 116640 q^{38} - 7040 q^{40} + 58724 q^{41} + 38400 q^{42} + 59520 q^{44} - 4620 q^{45} + 162240 q^{46} - 215040 q^{48} + 43298 q^{49} - 62100 q^{50} - 164192 q^{52} - 385708 q^{53} + 239040 q^{54} + 230400 q^{56} + 466560 q^{57} + 101992 q^{58} + 19200 q^{60} - 21836 q^{61} - 648960 q^{62} - 28672 q^{64} + 29320 q^{65} - 119040 q^{66} + 533792 q^{68} - 648960 q^{69} - 48000 q^{70} + 162624 q^{72} + 577252 q^{73} + 7976 q^{74} - 466560 q^{76} + 595200 q^{77} + 703680 q^{78} + 43520 q^{80} - 1292958 q^{81} + 117448 q^{82} - 1075200 q^{84} - 95320 q^{85} + 333600 q^{86} - 714240 q^{88} + 621476 q^{89} - 9240 q^{90} + 648960 q^{92} + 2595840 q^{93} + 117120 q^{94} + 614400 q^{96} - 2914172 q^{97} + 86596 q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.00000 + 7.74597i 0.250000 + 0.968246i
$$3$$ 30.9839i 1.14755i −0.819013 0.573775i $$-0.805478\pi$$
0.819013 0.573775i $$-0.194522\pi$$
$$4$$ −56.0000 + 30.9839i −0.875000 + 0.484123i
$$5$$ 10.0000 0.0800000 0.0400000 0.999200i $$-0.487264\pi$$
0.0400000 + 0.999200i $$0.487264\pi$$
$$6$$ 240.000 61.9677i 1.11111 0.286888i
$$7$$ 309.839i 0.903320i 0.892190 + 0.451660i $$0.149168\pi$$
−0.892190 + 0.451660i $$0.850832\pi$$
$$8$$ −352.000 371.806i −0.687500 0.726184i
$$9$$ −231.000 −0.316872
$$10$$ 20.0000 + 77.4597i 0.0200000 + 0.0774597i
$$11$$ 960.500i 0.721638i −0.932636 0.360819i $$-0.882497\pi$$
0.932636 0.360819i $$-0.117503\pi$$
$$12$$ 960.000 + 1735.10i 0.555556 + 1.00411i
$$13$$ 1466.00 0.667274 0.333637 0.942702i $$-0.391724\pi$$
0.333637 + 0.942702i $$0.391724\pi$$
$$14$$ −2400.00 + 619.677i −0.874636 + 0.225830i
$$15$$ 309.839i 0.0918040i
$$16$$ 2176.00 3470.19i 0.531250 0.847215i
$$17$$ −4766.00 −0.970079 −0.485040 0.874492i $$-0.661195\pi$$
−0.485040 + 0.874492i $$0.661195\pi$$
$$18$$ −462.000 1789.32i −0.0792181 0.306810i
$$19$$ 7529.08i 1.09769i 0.835923 + 0.548847i $$0.184933\pi$$
−0.835923 + 0.548847i $$0.815067\pi$$
$$20$$ −560.000 + 309.839i −0.0700000 + 0.0387298i
$$21$$ 9600.00 1.03661
$$22$$ 7440.00 1921.00i 0.698723 0.180409i
$$23$$ 10472.5i 0.860734i −0.902654 0.430367i $$-0.858384\pi$$
0.902654 0.430367i $$-0.141616\pi$$
$$24$$ −11520.0 + 10906.3i −0.833333 + 0.788941i
$$25$$ −15525.0 −0.993600
$$26$$ 2932.00 + 11355.6i 0.166818 + 0.646085i
$$27$$ 15430.0i 0.783923i
$$28$$ −9600.00 17351.0i −0.437318 0.790405i
$$29$$ 25498.0 1.04547 0.522736 0.852495i $$-0.324911\pi$$
0.522736 + 0.852495i $$0.324911\pi$$
$$30$$ 2400.00 619.677i 0.0888889 0.0229510i
$$31$$ 41890.2i 1.40614i 0.711123 + 0.703068i $$0.248187\pi$$
−0.711123 + 0.703068i $$0.751813\pi$$
$$32$$ 31232.0 + 9914.84i 0.953125 + 0.302577i
$$33$$ −29760.0 −0.828116
$$34$$ −9532.00 36917.3i −0.242520 0.939275i
$$35$$ 3098.39i 0.0722656i
$$36$$ 12936.0 7157.27i 0.277263 0.153405i
$$37$$ 1994.00 0.0393659 0.0196829 0.999806i $$-0.493734\pi$$
0.0196829 + 0.999806i $$0.493734\pi$$
$$38$$ −58320.0 + 15058.2i −1.06284 + 0.274423i
$$39$$ 45422.3i 0.765730i
$$40$$ −3520.00 3718.06i −0.0550000 0.0580948i
$$41$$ 29362.0 0.426024 0.213012 0.977050i $$-0.431673\pi$$
0.213012 + 0.977050i $$0.431673\pi$$
$$42$$ 19200.0 + 74361.3i 0.259151 + 1.00369i
$$43$$ 21533.8i 0.270841i −0.990788 0.135421i $$-0.956761\pi$$
0.990788 0.135421i $$-0.0432386\pi$$
$$44$$ 29760.0 + 53788.0i 0.349361 + 0.631433i
$$45$$ −2310.00 −0.0253498
$$46$$ 81120.0 20945.1i 0.833402 0.215183i
$$47$$ 7560.06i 0.0728168i −0.999337 0.0364084i $$-0.988408\pi$$
0.999337 0.0364084i $$-0.0115917\pi$$
$$48$$ −107520. 67420.9i −0.972222 0.609636i
$$49$$ 21649.0 0.184013
$$50$$ −31050.0 120256.i −0.248400 0.962049i
$$51$$ 147669.i 1.11322i
$$52$$ −82096.0 + 45422.3i −0.583864 + 0.323042i
$$53$$ −192854. −1.29539 −0.647696 0.761899i $$-0.724267\pi$$
−0.647696 + 0.761899i $$0.724267\pi$$
$$54$$ 119520. 30859.9i 0.759031 0.195981i
$$55$$ 9605.00i 0.0577310i
$$56$$ 115200. 109063.i 0.655977 0.621032i
$$57$$ 233280. 1.25966
$$58$$ 50996.0 + 197507.i 0.261368 + 1.01227i
$$59$$ 78420.2i 0.381831i −0.981606 0.190916i $$-0.938854\pi$$
0.981606 0.190916i $$-0.0611457\pi$$
$$60$$ 9600.00 + 17351.0i 0.0444444 + 0.0803285i
$$61$$ −10918.0 −0.0481009 −0.0240505 0.999711i $$-0.507656\pi$$
−0.0240505 + 0.999711i $$0.507656\pi$$
$$62$$ −324480. + 83780.4i −1.36149 + 0.351534i
$$63$$ 71572.7i 0.286237i
$$64$$ −14336.0 + 261752.i −0.0546875 + 0.998504i
$$65$$ 14660.0 0.0533819
$$66$$ −59520.0 230520.i −0.207029 0.801820i
$$67$$ 394146.i 1.31049i −0.755418 0.655243i $$-0.772566\pi$$
0.755418 0.655243i $$-0.227434\pi$$
$$68$$ 266896. 147669.i 0.848819 0.469638i
$$69$$ −324480. −0.987735
$$70$$ −24000.0 + 6196.77i −0.0699708 + 0.0180664i
$$71$$ 532241.i 1.48708i 0.668694 + 0.743538i $$0.266854\pi$$
−0.668694 + 0.743538i $$0.733146\pi$$
$$72$$ 81312.0 + 85887.3i 0.217850 + 0.230108i
$$73$$ 288626. 0.741937 0.370968 0.928646i $$-0.379026\pi$$
0.370968 + 0.928646i $$0.379026\pi$$
$$74$$ 3988.00 + 15445.5i 0.00984147 + 0.0381159i
$$75$$ 481025.i 1.14021i
$$76$$ −233280. 421628.i −0.531419 0.960482i
$$77$$ 297600. 0.651870
$$78$$ 351840. 90844.7i 0.741415 0.191433i
$$79$$ 310706.i 0.630186i −0.949061 0.315093i $$-0.897964\pi$$
0.949061 0.315093i $$-0.102036\pi$$
$$80$$ 21760.0 34701.9i 0.0425000 0.0677772i
$$81$$ −646479. −1.21646
$$82$$ 58724.0 + 227437.i 0.106506 + 0.412496i
$$83$$ 204153.i 0.357043i −0.983936 0.178522i $$-0.942869\pi$$
0.983936 0.178522i $$-0.0571314\pi$$
$$84$$ −537600. + 297445.i −0.907029 + 0.501844i
$$85$$ −47660.0 −0.0776064
$$86$$ 166800. 43067.6i 0.262241 0.0677104i
$$87$$ 790027.i 1.19973i
$$88$$ −357120. + 338096.i −0.524042 + 0.496126i
$$89$$ 310738. 0.440783 0.220391 0.975412i $$-0.429267\pi$$
0.220391 + 0.975412i $$0.429267\pi$$
$$90$$ −4620.00 17893.2i −0.00633745 0.0245448i
$$91$$ 454223.i 0.602761i
$$92$$ 324480. + 586463.i 0.416701 + 0.753142i
$$93$$ 1.29792e6 1.61361
$$94$$ 58560.0 15120.1i 0.0705046 0.0182042i
$$95$$ 75290.8i 0.0878155i
$$96$$ 307200. 967688.i 0.347222 1.09376i
$$97$$ −1.45709e6 −1.59650 −0.798252 0.602324i $$-0.794242\pi$$
−0.798252 + 0.602324i $$0.794242\pi$$
$$98$$ 43298.0 + 167692.i 0.0460034 + 0.178170i
$$99$$ 221875.i 0.228667i
$$100$$ 869400. 481025.i 0.869400 0.481025i
$$101$$ −639158. −0.620360 −0.310180 0.950678i $$-0.600389\pi$$
−0.310180 + 0.950678i $$0.600389\pi$$
$$102$$ −1.14384e6 + 295338.i −1.07787 + 0.278304i
$$103$$ 1.38913e6i 1.27125i 0.771997 + 0.635626i $$0.219258\pi$$
−0.771997 + 0.635626i $$0.780742\pi$$
$$104$$ −516032. 545068.i −0.458751 0.484564i
$$105$$ 96000.0 0.0829284
$$106$$ −385708. 1.49384e6i −0.323848 1.25426i
$$107$$ 1.14935e6i 0.938209i −0.883143 0.469105i $$-0.844577\pi$$
0.883143 0.469105i $$-0.155423\pi$$
$$108$$ 478080. + 864078.i 0.379515 + 0.685933i
$$109$$ 1.53574e6 1.18587 0.592936 0.805250i $$-0.297969\pi$$
0.592936 + 0.805250i $$0.297969\pi$$
$$110$$ 74400.0 19210.0i 0.0558978 0.0144328i
$$111$$ 61781.8i 0.0451743i
$$112$$ 1.07520e6 + 674209.i 0.765306 + 0.479889i
$$113$$ −601694. −0.417004 −0.208502 0.978022i $$-0.566859\pi$$
−0.208502 + 0.978022i $$0.566859\pi$$
$$114$$ 466560. + 1.80698e6i 0.314915 + 1.21966i
$$115$$ 104725.i 0.0688587i
$$116$$ −1.42789e6 + 790027.i −0.914787 + 0.506137i
$$117$$ −338646. −0.211441
$$118$$ 607440. 156840.i 0.369707 0.0954579i
$$119$$ 1.47669e6i 0.876292i
$$120$$ −115200. + 109063.i −0.0666667 + 0.0631153i
$$121$$ 849001. 0.479239
$$122$$ −21836.0 84570.5i −0.0120252 0.0465735i
$$123$$ 909748.i 0.488884i
$$124$$ −1.29792e6 2.34585e6i −0.680743 1.23037i
$$125$$ −311500. −0.159488
$$126$$ 554400. 143145.i 0.277148 0.0715593i
$$127$$ 1.67462e6i 0.817531i 0.912640 + 0.408765i $$0.134041\pi$$
−0.912640 + 0.408765i $$0.865959\pi$$
$$128$$ −2.05619e6 + 412457.i −0.980469 + 0.196675i
$$129$$ −667200. −0.310804
$$130$$ 29320.0 + 113556.i 0.0133455 + 0.0516868i
$$131$$ 2.84454e6i 1.26531i 0.774433 + 0.632656i $$0.218035\pi$$
−0.774433 + 0.632656i $$0.781965\pi$$
$$132$$ 1.66656e6 922080.i 0.724601 0.400910i
$$133$$ −2.33280e6 −0.991568
$$134$$ 3.05304e6 788292.i 1.26887 0.327622i
$$135$$ 154300.i 0.0627139i
$$136$$ 1.67763e6 + 1.77203e6i 0.666930 + 0.704456i
$$137$$ 3.81003e6 1.48172 0.740862 0.671658i $$-0.234417\pi$$
0.740862 + 0.671658i $$0.234417\pi$$
$$138$$ −648960. 2.51341e6i −0.246934 0.956371i
$$139$$ 138839.i 0.0516971i 0.999666 + 0.0258485i $$0.00822877\pi$$
−0.999666 + 0.0258485i $$0.991771\pi$$
$$140$$ −96000.0 173510.i −0.0349854 0.0632324i
$$141$$ −234240. −0.0835610
$$142$$ −4.12272e6 + 1.06448e6i −1.43986 + 0.371769i
$$143$$ 1.40809e6i 0.481530i
$$144$$ −502656. + 801615.i −0.168338 + 0.268459i
$$145$$ 254980. 0.0836377
$$146$$ 577252. + 2.23569e6i 0.185484 + 0.718377i
$$147$$ 670770.i 0.211165i
$$148$$ −111664. + 61781.8i −0.0344451 + 0.0190579i
$$149$$ −3.27426e6 −0.989816 −0.494908 0.868945i $$-0.664798\pi$$
−0.494908 + 0.868945i $$0.664798\pi$$
$$150$$ −3.72600e6 + 962049.i −1.10400 + 0.285052i
$$151$$ 5.59352e6i 1.62463i −0.583220 0.812314i $$-0.698207\pi$$
0.583220 0.812314i $$-0.301793\pi$$
$$152$$ 2.79936e6 2.65024e6i 0.797128 0.754664i
$$153$$ 1.10095e6 0.307391
$$154$$ 595200. + 2.30520e6i 0.162967 + 0.631170i
$$155$$ 418902.i 0.112491i
$$156$$ 1.40736e6 + 2.54365e6i 0.370708 + 0.670014i
$$157$$ 816794. 0.211064 0.105532 0.994416i $$-0.466345\pi$$
0.105532 + 0.994416i $$0.466345\pi$$
$$158$$ 2.40672e6 621412.i 0.610175 0.157546i
$$159$$ 5.97536e6i 1.48653i
$$160$$ 312320. + 99148.4i 0.0762500 + 0.0242061i
$$161$$ 3.24480e6 0.777518
$$162$$ −1.29296e6 5.00760e6i −0.304116 1.17784i
$$163$$ 1.84593e6i 0.426237i −0.977026 0.213119i $$-0.931638\pi$$
0.977026 0.213119i $$-0.0683621\pi$$
$$164$$ −1.64427e6 + 909748.i −0.372771 + 0.206248i
$$165$$ −297600. −0.0662493
$$166$$ 1.58136e6 408305.i 0.345706 0.0892608i
$$167$$ 7.96515e6i 1.71019i 0.518471 + 0.855095i $$0.326501\pi$$
−0.518471 + 0.855095i $$0.673499\pi$$
$$168$$ −3.37920e6 3.56934e6i −0.712666 0.752766i
$$169$$ −2.67765e6 −0.554746
$$170$$ −95320.0 369173.i −0.0194016 0.0751420i
$$171$$ 1.73922e6i 0.347829i
$$172$$ 667200. + 1.20589e6i 0.131121 + 0.236986i
$$173$$ −5.12653e6 −0.990115 −0.495057 0.868860i $$-0.664853\pi$$
−0.495057 + 0.868860i $$0.664853\pi$$
$$174$$ 6.11952e6 1.58005e6i 1.16163 0.299933i
$$175$$ 4.81025e6i 0.897538i
$$176$$ −3.33312e6 2.09005e6i −0.611382 0.383370i
$$177$$ −2.42976e6 −0.438171
$$178$$ 621476. + 2.40697e6i 0.110196 + 0.426786i
$$179$$ 2.33411e6i 0.406969i −0.979078 0.203485i $$-0.934773\pi$$
0.979078 0.203485i $$-0.0652267\pi$$
$$180$$ 129360. 71572.7i 0.0221811 0.0122724i
$$181$$ 9.69156e6 1.63440 0.817199 0.576355i $$-0.195525\pi$$
0.817199 + 0.576355i $$0.195525\pi$$
$$182$$ −3.51840e6 + 908447.i −0.583621 + 0.150690i
$$183$$ 338282.i 0.0551983i
$$184$$ −3.89376e6 + 3.68634e6i −0.625051 + 0.591754i
$$185$$ 19940.0 0.00314927
$$186$$ 2.59584e6 + 1.00536e7i 0.403403 + 1.56237i
$$187$$ 4.57774e6i 0.700046i
$$188$$ 234240. + 423364.i 0.0352523 + 0.0637147i
$$189$$ 4.78080e6 0.708134
$$190$$ −583200. + 150582.i −0.0850270 + 0.0219539i
$$191$$ 1.14164e7i 1.63844i −0.573479 0.819220i $$-0.694407\pi$$
0.573479 0.819220i $$-0.305593\pi$$
$$192$$ 8.11008e6 + 444185.i 1.14583 + 0.0627567i
$$193$$ −2.43033e6 −0.338060 −0.169030 0.985611i $$-0.554064\pi$$
−0.169030 + 0.985611i $$0.554064\pi$$
$$194$$ −2.91417e6 1.12865e7i −0.399126 1.54581i
$$195$$ 454223.i 0.0612584i
$$196$$ −1.21234e6 + 670770.i −0.161012 + 0.0890851i
$$197$$ −2.23065e6 −0.291764 −0.145882 0.989302i $$-0.546602\pi$$
−0.145882 + 0.989302i $$0.546602\pi$$
$$198$$ −1.71864e6 + 443751.i −0.221406 + 0.0571668i
$$199$$ 4.89576e6i 0.621242i 0.950534 + 0.310621i $$0.100537\pi$$
−0.950534 + 0.310621i $$0.899463\pi$$
$$200$$ 5.46480e6 + 5.77229e6i 0.683100 + 0.721537i
$$201$$ −1.22122e7 −1.50385
$$202$$ −1.27832e6 4.95090e6i −0.155090 0.600661i
$$203$$ 7.90027e6i 0.944395i
$$204$$ −4.57536e6 8.26947e6i −0.538933 0.974063i
$$205$$ 293620. 0.0340819
$$206$$ −1.07602e7 + 2.77826e6i −1.23088 + 0.317813i
$$207$$ 2.41916e6i 0.272743i
$$208$$ 3.19002e6 5.08730e6i 0.354489 0.565324i
$$209$$ 7.23168e6 0.792137
$$210$$ 192000. + 743613.i 0.0207321 + 0.0802951i
$$211$$ 3.90951e6i 0.416174i 0.978110 + 0.208087i $$0.0667238\pi$$
−0.978110 + 0.208087i $$0.933276\pi$$
$$212$$ 1.07998e7 5.97536e6i 1.13347 0.627129i
$$213$$ 1.64909e7 1.70650
$$214$$ 8.90280e6 2.29869e6i 0.908417 0.234552i
$$215$$ 215338.i 0.0216673i
$$216$$ −5.73696e6 + 5.43135e6i −0.569273 + 0.538947i
$$217$$ −1.29792e7 −1.27019
$$218$$ 3.07148e6 + 1.18958e7i 0.296468 + 1.14822i
$$219$$ 8.94275e6i 0.851410i
$$220$$ 297600. + 537880.i 0.0279489 + 0.0505146i
$$221$$ −6.98696e6 −0.647308
$$222$$ 478560. 123564.i 0.0437399 0.0112936i
$$223$$ 3.33114e6i 0.300385i 0.988657 + 0.150192i $$0.0479893\pi$$
−0.988657 + 0.150192i $$0.952011\pi$$
$$224$$ −3.07200e6 + 9.67688e6i −0.273324 + 0.860977i
$$225$$ 3.58628e6 0.314844
$$226$$ −1.20339e6 4.66070e6i −0.104251 0.403763i
$$227$$ 1.35033e7i 1.15442i −0.816597 0.577208i $$-0.804142\pi$$
0.816597 0.577208i $$-0.195858\pi$$
$$228$$ −1.30637e7 + 7.22792e6i −1.10220 + 0.609830i
$$229$$ 1.59598e6 0.132899 0.0664493 0.997790i $$-0.478833\pi$$
0.0664493 + 0.997790i $$0.478833\pi$$
$$230$$ 811200. 209451.i 0.0666721 0.0172147i
$$231$$ 9.22080e6i 0.748053i
$$232$$ −8.97530e6 9.48032e6i −0.718762 0.759205i
$$233$$ 8.04383e6 0.635909 0.317954 0.948106i $$-0.397004\pi$$
0.317954 + 0.948106i $$0.397004\pi$$
$$234$$ −677292. 2.62314e6i −0.0528601 0.204726i
$$235$$ 75600.6i 0.00582535i
$$236$$ 2.42976e6 + 4.39153e6i 0.184853 + 0.334103i
$$237$$ −9.62688e6 −0.723170
$$238$$ 1.14384e7 2.95338e6i 0.848466 0.219073i
$$239$$ 1.12532e7i 0.824296i 0.911117 + 0.412148i $$0.135221\pi$$
−0.911117 + 0.412148i $$0.864779\pi$$
$$240$$ −1.07520e6 674209.i −0.0777778 0.0487709i
$$241$$ 5.05104e6 0.360853 0.180426 0.983589i $$-0.442252\pi$$
0.180426 + 0.983589i $$0.442252\pi$$
$$242$$ 1.69800e6 + 6.57633e6i 0.119810 + 0.464021i
$$243$$ 8.78197e6i 0.612031i
$$244$$ 611408. 338282.i 0.0420883 0.0232868i
$$245$$ 216490. 0.0147211
$$246$$ 7.04688e6 1.81950e6i 0.473360 0.122221i
$$247$$ 1.10376e7i 0.732462i
$$248$$ 1.55750e7 1.47453e7i 1.02111 0.966718i
$$249$$ −6.32544e6 −0.409725
$$250$$ −623000. 2.41287e6i −0.0398720 0.154424i
$$251$$ 4.71590e6i 0.298225i 0.988820 + 0.149112i $$0.0476416\pi$$
−0.988820 + 0.149112i $$0.952358\pi$$
$$252$$ 2.21760e6 + 4.00807e6i 0.138574 + 0.250457i
$$253$$ −1.00589e7 −0.621138
$$254$$ −1.29715e7 + 3.34923e6i −0.791571 + 0.204383i
$$255$$ 1.47669e6i 0.0890572i
$$256$$ −7.30726e6 1.51023e7i −0.435547 0.900166i
$$257$$ 2.34552e7 1.38178 0.690892 0.722958i $$-0.257218\pi$$
0.690892 + 0.722958i $$0.257218\pi$$
$$258$$ −1.33440e6 5.16811e6i −0.0777011 0.300935i
$$259$$ 617818.i 0.0355600i
$$260$$ −820960. + 454223.i −0.0467091 + 0.0258434i
$$261$$ −5.89004e6 −0.331281
$$262$$ −2.20337e7 + 5.68907e6i −1.22513 + 0.316328i
$$263$$ 2.16993e7i 1.19283i −0.802676 0.596415i $$-0.796591\pi$$
0.802676 0.596415i $$-0.203409\pi$$
$$264$$ 1.04755e7 + 1.10650e7i 0.569330 + 0.601365i
$$265$$ −1.92854e6 −0.103631
$$266$$ −4.66560e6 1.80698e7i −0.247892 0.960082i
$$267$$ 9.62786e6i 0.505820i
$$268$$ 1.22122e7 + 2.20722e7i 0.634436 + 1.14668i
$$269$$ −2.94278e7 −1.51182 −0.755911 0.654674i $$-0.772806\pi$$
−0.755911 + 0.654674i $$0.772806\pi$$
$$270$$ 1.19520e6 308599.i 0.0607225 0.0156785i
$$271$$ 8.51474e6i 0.427822i −0.976853 0.213911i $$-0.931380\pi$$
0.976853 0.213911i $$-0.0686203\pi$$
$$272$$ −1.03708e7 + 1.65389e7i −0.515355 + 0.821866i
$$273$$ 1.40736e7 0.691699
$$274$$ 7.62007e6 + 2.95124e7i 0.370431 + 1.43467i
$$275$$ 1.49118e7i 0.717019i
$$276$$ 1.81709e7 1.00536e7i 0.864269 0.478185i
$$277$$ 2.76226e7 1.29965 0.649824 0.760085i $$-0.274843\pi$$
0.649824 + 0.760085i $$0.274843\pi$$
$$278$$ −1.07544e6 + 277677.i −0.0500555 + 0.0129243i
$$279$$ 9.67663e6i 0.445566i
$$280$$ 1.15200e6 1.09063e6i 0.0524781 0.0496826i
$$281$$ 8.64008e6 0.389403 0.194701 0.980863i $$-0.437626\pi$$
0.194701 + 0.980863i $$0.437626\pi$$
$$282$$ −468480. 1.81442e6i −0.0208903 0.0809076i
$$283$$ 1.27350e7i 0.561873i −0.959726 0.280937i $$-0.909355\pi$$
0.959726 0.280937i $$-0.0906450\pi$$
$$284$$ −1.64909e7 2.98055e7i −0.719928 1.30119i
$$285$$ 2.33280e6 0.100773
$$286$$ 1.09070e7 2.81619e6i 0.466239 0.120382i
$$287$$ 9.09748e6i 0.384836i
$$288$$ −7.21459e6 2.29033e6i −0.302019 0.0958783i
$$289$$ −1.42281e6 −0.0589460
$$290$$ 509960. + 1.97507e6i 0.0209094 + 0.0809819i
$$291$$ 4.51462e7i 1.83207i
$$292$$ −1.61631e7 + 8.94275e6i −0.649195 + 0.359189i
$$293$$ −4.45415e7 −1.77077 −0.885385 0.464859i $$-0.846105\pi$$
−0.885385 + 0.464859i $$0.846105\pi$$
$$294$$ 5.19576e6 1.34154e6i 0.204459 0.0527912i
$$295$$ 784202.i 0.0305465i
$$296$$ −701888. 741382.i −0.0270640 0.0285869i
$$297$$ −1.48205e7 −0.565709
$$298$$ −6.54852e6 2.53623e7i −0.247454 0.958386i
$$299$$ 1.53528e7i 0.574345i
$$300$$ −1.49040e7 2.69374e7i −0.552000 0.997681i
$$301$$ 6.67200e6 0.244656
$$302$$ 4.33272e7 1.11870e7i 1.57304 0.406157i
$$303$$ 1.98036e7i 0.711895i
$$304$$ 2.61274e7 + 1.63833e7i 0.929983 + 0.583150i
$$305$$ −109180. −0.00384808
$$306$$ 2.20189e6 + 8.52789e6i 0.0768479 + 0.297630i
$$307$$ 4.89051e7i 1.69020i −0.534606 0.845102i $$-0.679540\pi$$
0.534606 0.845102i $$-0.320460\pi$$
$$308$$ −1.66656e7 + 9.22080e6i −0.570386 + 0.315585i
$$309$$ 4.30406e7 1.45883
$$310$$ −3.24480e6 + 837804.i −0.108919 + 0.0281227i
$$311$$ 5.00220e7i 1.66295i 0.555559 + 0.831477i $$0.312504\pi$$
−0.555559 + 0.831477i $$0.687496\pi$$
$$312$$ −1.68883e7 + 1.59887e7i −0.556061 + 0.526440i
$$313$$ 1.12719e6 0.0367589 0.0183795 0.999831i $$-0.494149\pi$$
0.0183795 + 0.999831i $$0.494149\pi$$
$$314$$ 1.63359e6 + 6.32686e6i 0.0527659 + 0.204362i
$$315$$ 715727.i 0.0228990i
$$316$$ 9.62688e6 + 1.73995e7i 0.305087 + 0.551413i
$$317$$ 3.44882e7 1.08266 0.541330 0.840810i $$-0.317921\pi$$
0.541330 + 0.840810i $$0.317921\pi$$
$$318$$ −4.62850e7 + 1.19507e7i −1.43932 + 0.371632i
$$319$$ 2.44908e7i 0.754452i
$$320$$ −143360. + 2.61752e6i −0.00437500 + 0.0798803i
$$321$$ −3.56112e7 −1.07664
$$322$$ 6.48960e6 + 2.51341e7i 0.194379 + 0.752828i
$$323$$ 3.58836e7i 1.06485i
$$324$$ 3.62028e7 2.00304e7i 1.06441 0.588918i
$$325$$ −2.27596e7 −0.663003
$$326$$ 1.42985e7 3.69185e6i 0.412702 0.106559i
$$327$$ 4.75831e7i 1.36085i
$$328$$ −1.03354e7 1.09170e7i −0.292891 0.309372i
$$329$$ 2.34240e6 0.0657769
$$330$$ −595200. 2.30520e6i −0.0165623 0.0641456i
$$331$$ 4.02696e7i 1.11044i 0.831705 + 0.555218i $$0.187365\pi$$
−0.831705 + 0.555218i $$0.812635\pi$$
$$332$$ 6.32544e6 + 1.14326e7i 0.172853 + 0.312413i
$$333$$ −460614. −0.0124740
$$334$$ −6.16978e7 + 1.59303e7i −1.65588 + 0.427547i
$$335$$ 3.94146e6i 0.104839i
$$336$$ 2.08896e7 3.33139e7i 0.550696 0.878228i
$$337$$ −3.42531e7 −0.894973 −0.447487 0.894291i $$-0.647681\pi$$
−0.447487 + 0.894291i $$0.647681\pi$$
$$338$$ −5.35531e6 2.07410e7i −0.138687 0.537131i
$$339$$ 1.86428e7i 0.478533i
$$340$$ 2.66896e6 1.47669e6i 0.0679056 0.0375710i
$$341$$ 4.02355e7 1.01472
$$342$$ 1.34719e7 3.47843e6i 0.336784 0.0869572i
$$343$$ 4.31599e7i 1.06954i
$$344$$ −8.00640e6 + 7.57989e6i −0.196681 + 0.186203i
$$345$$ −3.24480e6 −0.0790188
$$346$$ −1.02531e7 3.97100e7i −0.247529 0.958674i
$$347$$ 5.45496e7i 1.30558i 0.757539 + 0.652790i $$0.226401\pi$$
−0.757539 + 0.652790i $$0.773599\pi$$
$$348$$ 2.44781e7 + 4.42415e7i 0.580817 + 1.04976i
$$349$$ 4.70009e7 1.10568 0.552840 0.833287i $$-0.313544\pi$$
0.552840 + 0.833287i $$0.313544\pi$$
$$350$$ 3.72600e7 9.62049e6i 0.869038 0.224385i
$$351$$ 2.26203e7i 0.523091i
$$352$$ 9.52320e6 2.99983e7i 0.218351 0.687811i
$$353$$ −1.27231e7 −0.289248 −0.144624 0.989487i $$-0.546197\pi$$
−0.144624 + 0.989487i $$0.546197\pi$$
$$354$$ −4.85952e6 1.88208e7i −0.109543 0.424257i
$$355$$ 5.32241e6i 0.118966i
$$356$$ −1.74013e7 + 9.62786e6i −0.385685 + 0.213393i
$$357$$ −4.57536e7 −1.00559
$$358$$ 1.80799e7 4.66822e6i 0.394046 0.101742i
$$359$$ 2.02153e7i 0.436915i −0.975846 0.218457i $$-0.929898\pi$$
0.975846 0.218457i $$-0.0701025\pi$$
$$360$$ 813120. + 858873.i 0.0174280 + 0.0184086i
$$361$$ −9.64116e6 −0.204931
$$362$$ 1.93831e7 + 7.50705e7i 0.408600 + 1.58250i
$$363$$ 2.63053e7i 0.549951i
$$364$$ −1.40736e7 2.54365e7i −0.291811 0.527416i
$$365$$ 2.88626e6 0.0593549
$$366$$ −2.62032e6 + 676564.i −0.0534455 + 0.0137996i
$$367$$ 1.11057e7i 0.224672i −0.993670 0.112336i $$-0.964167\pi$$
0.993670 0.112336i $$-0.0358333\pi$$
$$368$$ −3.63418e7 2.27883e7i −0.729227 0.457265i
$$369$$ −6.78262e6 −0.134995
$$370$$ 39880.0 + 154455.i 0.000787318 + 0.00304927i
$$371$$ 5.97536e7i 1.17015i
$$372$$ −7.26835e7 + 4.02146e7i −1.41191 + 0.781186i
$$373$$ 687146. 0.0132411 0.00662053 0.999978i $$-0.497893\pi$$
0.00662053 + 0.999978i $$0.497893\pi$$
$$374$$ −3.54590e7 + 9.15548e6i −0.677817 + 0.175011i
$$375$$ 9.65147e6i 0.183021i
$$376$$ −2.81088e6 + 2.66114e6i −0.0528785 + 0.0500616i
$$377$$ 3.73801e7 0.697615
$$378$$ 9.56160e6 + 3.70319e7i 0.177033 + 0.685647i
$$379$$ 1.48499e7i 0.272775i 0.990656 + 0.136388i $$0.0435492\pi$$
−0.990656 + 0.136388i $$0.956451\pi$$
$$380$$ −2.33280e6 4.21628e6i −0.0425135 0.0768385i
$$381$$ 5.18861e7 0.938158
$$382$$ 8.84314e7 2.28329e7i 1.58641 0.409610i
$$383$$ 3.35885e7i 0.597853i −0.954276 0.298926i $$-0.903372\pi$$
0.954276 0.298926i $$-0.0966285\pi$$
$$384$$ 1.27795e7 + 6.37088e7i 0.225694 + 1.12514i
$$385$$ 2.97600e6 0.0521496
$$386$$ −4.86067e6 1.88253e7i −0.0845150 0.327325i
$$387$$ 4.97430e6i 0.0858222i
$$388$$ 8.15968e7 4.51462e7i 1.39694 0.772904i
$$389$$ −1.01122e8 −1.71789 −0.858946 0.512066i $$-0.828880\pi$$
−0.858946 + 0.512066i $$0.828880\pi$$
$$390$$ 3.51840e6 908447.i 0.0593132 0.0153146i
$$391$$ 4.99122e7i 0.834980i
$$392$$ −7.62045e6 8.04924e6i −0.126509 0.133628i
$$393$$ 8.81347e7 1.45201
$$394$$ −4.46129e6 1.72785e7i −0.0729410 0.282499i
$$395$$ 3.10706e6i 0.0504149i
$$396$$ −6.87456e6 1.24250e7i −0.110703 0.200084i
$$397$$ −3.48266e7 −0.556595 −0.278297 0.960495i $$-0.589770\pi$$
−0.278297 + 0.960495i $$0.589770\pi$$
$$398$$ −3.79224e7 + 9.79152e6i −0.601515 + 0.155311i
$$399$$ 7.22792e7i 1.13787i
$$400$$ −3.37824e7 + 5.38747e7i −0.527850 + 0.841793i
$$401$$ −6.88398e7 −1.06760 −0.533798 0.845612i $$-0.679236\pi$$
−0.533798 + 0.845612i $$0.679236\pi$$
$$402$$ −2.44243e7 9.45950e7i −0.375962 1.45610i
$$403$$ 6.14110e7i 0.938277i
$$404$$ 3.57928e7 1.98036e7i 0.542815 0.300331i
$$405$$ −6.46479e6 −0.0973171
$$406$$ −6.11952e7 + 1.58005e7i −0.914406 + 0.236099i
$$407$$ 1.91524e6i 0.0284079i
$$408$$ 5.49043e7 5.19795e7i 0.808399 0.765335i
$$409$$ 4.59959e7 0.672278 0.336139 0.941812i $$-0.390879\pi$$
0.336139 + 0.941812i $$0.390879\pi$$
$$410$$ 587240. + 2.27437e6i 0.00852048 + 0.0329997i
$$411$$ 1.18050e8i 1.70035i
$$412$$ −4.30406e7 7.77913e7i −0.615442 1.11234i
$$413$$ 2.42976e7 0.344916
$$414$$ −1.87387e7 + 4.83832e6i −0.264082 + 0.0681857i
$$415$$ 2.04153e6i 0.0285635i
$$416$$ 4.57861e7 + 1.45352e7i 0.635995 + 0.201902i
$$417$$ 4.30176e6 0.0593250
$$418$$ 1.44634e7 + 5.60164e7i 0.198034 + 0.766983i
$$419$$ 2.71153e7i 0.368615i 0.982869 + 0.184307i $$0.0590042\pi$$
−0.982869 + 0.184307i $$0.940996\pi$$
$$420$$ −5.37600e6 + 2.97445e6i −0.0725624 + 0.0401475i
$$421$$ −9.42078e7 −1.26253 −0.631263 0.775569i $$-0.717463\pi$$
−0.631263 + 0.775569i $$0.717463\pi$$
$$422$$ −3.02830e7 + 7.81903e6i −0.402959 + 0.104044i
$$423$$ 1.74637e6i 0.0230737i
$$424$$ 6.78846e7 + 7.17044e7i 0.890582 + 0.940693i
$$425$$ 7.39922e7 0.963871
$$426$$ 3.29818e7 + 1.27738e8i 0.426624 + 1.65231i
$$427$$ 3.38282e6i 0.0434505i
$$428$$ 3.56112e7 + 6.43634e7i 0.454209 + 0.820933i
$$429$$ −4.36282e7 −0.552580
$$430$$ 1.66800e6 430676.i 0.0209793 0.00541683i
$$431$$ 5.19187e7i 0.648473i −0.945976 0.324236i $$-0.894893\pi$$
0.945976 0.324236i $$-0.105107\pi$$
$$432$$ −5.35450e7 3.35756e7i −0.664152 0.416459i
$$433$$ 8.40210e7 1.03496 0.517481 0.855695i $$-0.326870\pi$$
0.517481 + 0.855695i $$0.326870\pi$$
$$434$$ −2.59584e7 1.00536e8i −0.317548 1.22986i
$$435$$ 7.90027e6i 0.0959785i
$$436$$ −8.60013e7 + 4.75831e7i −1.03764 + 0.574108i
$$437$$ 7.88486e7 0.944822
$$438$$ 6.92702e7 1.78855e7i 0.824374 0.212852i
$$439$$ 1.48115e8i 1.75068i −0.483512 0.875338i $$-0.660639\pi$$
0.483512 0.875338i $$-0.339361\pi$$
$$440$$ −3.57120e6 + 3.38096e6i −0.0419234 + 0.0396901i
$$441$$ −5.00092e6 −0.0583088
$$442$$ −1.39739e7 5.41207e7i −0.161827 0.626754i
$$443$$ 8.03735e7i 0.924489i 0.886752 + 0.462245i $$0.152956\pi$$
−0.886752 + 0.462245i $$0.847044\pi$$
$$444$$ 1.91424e6 + 3.45978e6i 0.0218699 + 0.0395275i
$$445$$ 3.10738e6 0.0352626
$$446$$ −2.58029e7 + 6.66227e6i −0.290846 + 0.0750962i
$$447$$ 1.01449e8i 1.13586i
$$448$$ −8.11008e7 4.44185e6i −0.901968 0.0494003i
$$449$$ −8.80925e7 −0.973196 −0.486598 0.873626i $$-0.661762\pi$$
−0.486598 + 0.873626i $$0.661762\pi$$
$$450$$ 7.17255e6 + 2.77792e7i 0.0787111 + 0.304847i
$$451$$ 2.82022e7i 0.307435i
$$452$$ 3.36949e7 1.86428e7i 0.364879 0.201881i
$$453$$ −1.73309e8 −1.86434
$$454$$ 1.04596e8 2.70066e7i 1.11776 0.288604i
$$455$$ 4.54223e6i 0.0482209i
$$456$$ −8.21146e7 8.67350e7i −0.866015 0.914745i
$$457$$ −3.75423e7 −0.393344 −0.196672 0.980469i $$-0.563013\pi$$
−0.196672 + 0.980469i $$0.563013\pi$$
$$458$$ 3.19196e6 + 1.23624e7i 0.0332247 + 0.128679i
$$459$$ 7.35392e7i 0.760468i
$$460$$ 3.24480e6 + 5.86463e6i 0.0333361 + 0.0602514i
$$461$$ 1.15260e8 1.17646 0.588228 0.808695i $$-0.299826\pi$$
0.588228 + 0.808695i $$0.299826\pi$$
$$462$$ 7.14240e7 1.84416e7i 0.724300 0.187013i
$$463$$ 1.03415e7i 0.104194i −0.998642 0.0520970i $$-0.983410\pi$$
0.998642 0.0520970i $$-0.0165905\pi$$
$$464$$ 5.54836e7 8.84830e7i 0.555407 0.885739i
$$465$$ 1.29792e7 0.129089
$$466$$ 1.60877e7 + 6.23072e7i 0.158977 + 0.615716i
$$467$$ 1.64223e8i 1.61243i 0.591620 + 0.806217i $$0.298489\pi$$
−0.591620 + 0.806217i $$0.701511\pi$$
$$468$$ 1.89642e7 1.04926e7i 0.185011 0.102363i
$$469$$ 1.22122e8 1.18379
$$470$$ 585600. 151201.i 0.00564037 0.00145634i
$$471$$ 2.53074e7i 0.242206i
$$472$$ −2.91571e7 + 2.76039e7i −0.277280 + 0.262509i
$$473$$ −2.06832e7 −0.195449
$$474$$ −1.92538e7 7.45695e7i −0.180793 0.700207i
$$475$$ 1.16889e8i 1.09067i
$$476$$ 4.57536e7 + 8.26947e7i 0.424233 + 0.766755i
$$477$$ 4.45493e7 0.410474
$$478$$ −8.71670e7 + 2.25064e7i −0.798121 + 0.206074i
$$479$$ 7.76230e7i 0.706291i 0.935568 + 0.353146i $$0.114888\pi$$
−0.935568 + 0.353146i $$0.885112\pi$$
$$480$$ 3.07200e6 9.67688e6i 0.0277778 0.0875007i
$$481$$ 2.92320e6 0.0262678
$$482$$ 1.01021e7 + 3.91252e7i 0.0902132 + 0.349394i
$$483$$ 1.00536e8i 0.892241i
$$484$$ −4.75441e7 + 2.63053e7i −0.419334 + 0.232011i
$$485$$ −1.45709e7 −0.127720
$$486$$ −6.80249e7 + 1.75639e7i −0.592596 + 0.153008i
$$487$$ 1.08071e7i 0.0935670i −0.998905 0.0467835i $$-0.985103\pi$$
0.998905 0.0467835i $$-0.0148971\pi$$
$$488$$ 3.84314e6 + 4.05938e6i 0.0330694 + 0.0349302i
$$489$$ −5.71939e7 −0.489129
$$490$$ 432980. + 1.67692e6i 0.00368027 + 0.0142536i
$$491$$ 1.85067e8i 1.56345i −0.623624 0.781724i $$-0.714340\pi$$
0.623624 0.781724i $$-0.285660\pi$$
$$492$$ 2.81875e7 + 5.09459e7i 0.236680 + 0.427774i
$$493$$ −1.21523e8 −1.01419
$$494$$ −8.54971e7 + 2.20753e7i −0.709203 + 0.183115i
$$495$$ 2.21875e6i 0.0182934i
$$496$$ 1.45367e8 + 9.11530e7i 1.19130 + 0.747010i
$$497$$ −1.64909e8 −1.34331
$$498$$ −1.26509e7 4.89966e7i −0.102431 0.396715i
$$499$$ 6.83704e7i 0.550258i −0.961407 0.275129i $$-0.911279\pi$$
0.961407 0.275129i $$-0.0887206\pi$$
$$500$$ 1.74440e7 9.65147e6i 0.139552 0.0772118i
$$501$$ 2.46791e8 1.96253
$$502$$ −3.65292e7 + 9.43180e6i −0.288755 + 0.0745561i
$$503$$ 1.31562e7i 0.103377i 0.998663 + 0.0516887i $$0.0164604\pi$$
−0.998663 + 0.0516887i $$0.983540\pi$$
$$504$$ −2.66112e7 + 2.51936e7i −0.207861 + 0.196788i
$$505$$ −6.39158e6 −0.0496288
$$506$$ −2.01178e7 7.79157e7i −0.155284 0.601414i
$$507$$ 8.29640e7i 0.636599i
$$508$$ −5.18861e7 9.37785e7i −0.395785 0.715339i
$$509$$ 1.34186e8 1.01755 0.508775 0.860900i $$-0.330099\pi$$
0.508775 + 0.860900i $$0.330099\pi$$
$$510$$ −1.14384e7 + 2.95338e6i −0.0862293 + 0.0222643i
$$511$$ 8.94275e7i 0.670206i
$$512$$ 1.02367e8 8.68064e7i 0.762695 0.646758i
$$513$$ 1.16173e8 0.860508
$$514$$ 4.69105e7 + 1.81683e8i 0.345446 + 1.33791i
$$515$$ 1.38913e7i 0.101700i
$$516$$ 3.73632e7 2.06724e7i 0.271954 0.150467i
$$517$$ −7.26144e6 −0.0525474
$$518$$ −4.78560e6 + 1.23564e6i −0.0344308 + 0.00888999i
$$519$$ 1.58840e8i 1.13621i
$$520$$ −5.16032e6 5.45068e6i −0.0367000 0.0387651i
$$521$$ −1.98565e8 −1.40407 −0.702036 0.712142i $$-0.747725\pi$$
−0.702036 + 0.712142i $$0.747725\pi$$
$$522$$ −1.17801e7 4.56240e7i −0.0828203 0.320761i
$$523$$ 2.15512e8i 1.50649i 0.657740 + 0.753245i $$0.271513\pi$$
−0.657740 + 0.753245i $$0.728487\pi$$
$$524$$ −8.81347e7 1.59294e8i −0.612566 1.10715i
$$525$$ −1.49040e8 −1.02997
$$526$$ 1.68082e8 4.33986e7i 1.15495 0.298207i
$$527$$ 1.99649e8i 1.36406i
$$528$$ −6.47578e7 + 1.03273e8i −0.439937 + 0.701592i
$$529$$ 3.83616e7 0.259137
$$530$$ −3.85708e6 1.49384e7i −0.0259078 0.100341i
$$531$$ 1.81151e7i 0.120992i
$$532$$ 1.30637e8 7.22792e7i 0.867622 0.480041i
$$533$$ 4.30447e7 0.284275
$$534$$ 7.45771e7 1.92557e7i 0.489758 0.126455i
$$535$$ 1.14935e7i 0.0750567i
$$536$$ −1.46546e8 + 1.38739e8i −0.951655 + 0.900959i
$$537$$ −7.23197e7 −0.467018
$$538$$ −5.88556e7 2.27947e8i −0.377956 1.46382i
$$539$$ 2.07939e7i 0.132791i
$$540$$ 4.78080e6 + 8.64078e6i 0.0303612 + 0.0548746i
$$541$$ 1.44188e7 0.0910623 0.0455311 0.998963i $$-0.485502\pi$$
0.0455311 + 0.998963i $$0.485502\pi$$
$$542$$ 6.59549e7 1.70295e7i 0.414237 0.106956i
$$543$$ 3.00282e8i 1.87556i
$$544$$ −1.48852e8 4.72541e7i −0.924607 0.293524i
$$545$$ 1.53574e7 0.0948697
$$546$$ 2.81472e7 + 1.09014e8i 0.172925 + 0.669735i
$$547$$ 4.24129e7i 0.259141i 0.991570 + 0.129571i $$0.0413599\pi$$
−0.991570 + 0.129571i $$0.958640\pi$$
$$548$$ −2.13362e8 + 1.18050e8i −1.29651 + 0.717336i
$$549$$ 2.52206e6 0.0152419
$$550$$ −1.15506e8 + 2.98235e7i −0.694251 + 0.179255i
$$551$$ 1.91976e8i 1.14761i
$$552$$ 1.14217e8 + 1.20644e8i 0.679068 + 0.717278i
$$553$$ 9.62688e7 0.569259
$$554$$ 5.52453e7 + 2.13964e8i 0.324912 + 1.25838i
$$555$$ 617818.i 0.00361395i
$$556$$ −4.30176e6 7.77497e6i −0.0250277 0.0452350i
$$557$$ 8.90848e7 0.515511 0.257756 0.966210i $$-0.417017\pi$$
0.257756 + 0.966210i $$0.417017\pi$$
$$558$$ 7.49549e7 1.93533e7i 0.431417 0.111391i
$$559$$ 3.15685e7i 0.180725i
$$560$$ 1.07520e7 + 6.74209e6i 0.0612245 + 0.0383911i
$$561$$ 1.41836e8 0.803338
$$562$$ 1.72802e7 + 6.69258e7i 0.0973507 + 0.377037i
$$563$$ 2.41576e8i 1.35372i −0.736112 0.676860i $$-0.763340\pi$$
0.736112 0.676860i $$-0.236660\pi$$
$$564$$ 1.31174e7 7.25766e6i 0.0731159 0.0404538i
$$565$$ −6.01694e6 −0.0333603
$$566$$ 9.86446e7 2.54699e7i 0.544031 0.140468i
$$567$$ 2.00304e8i 1.09886i
$$568$$ 1.97891e8 1.87349e8i 1.07989 1.02236i
$$569$$ −2.56141e7 −0.139041 −0.0695203 0.997581i $$-0.522147\pi$$
−0.0695203 + 0.997581i $$0.522147\pi$$
$$570$$ 4.66560e6 + 1.80698e7i 0.0251932 + 0.0975728i
$$571$$ 1.10781e8i 0.595057i 0.954713 + 0.297528i $$0.0961623\pi$$
−0.954713 + 0.297528i $$0.903838\pi$$
$$572$$ 4.36282e7 + 7.88532e7i 0.233120 + 0.421339i
$$573$$ −3.53725e8 −1.88019
$$574$$ −7.04688e7 + 1.81950e7i −0.372616 + 0.0962090i
$$575$$ 1.62586e8i 0.855225i
$$576$$ 3.31162e6 6.04646e7i 0.0173290 0.316398i
$$577$$ 1.07272e8 0.558415 0.279208 0.960231i $$-0.409928\pi$$
0.279208 + 0.960231i $$0.409928\pi$$
$$578$$ −2.84563e6 1.10211e7i −0.0147365 0.0570742i
$$579$$ 7.53011e7i 0.387941i
$$580$$ −1.42789e7 + 7.90027e6i −0.0731830 + 0.0404909i
$$581$$ 6.32544e7 0.322524
$$582$$ −3.49701e8 + 9.02923e7i −1.77389 + 0.458017i
$$583$$ 1.85236e8i 0.934803i
$$584$$ −1.01596e8 1.07313e8i −0.510082 0.538783i
$$585$$ −3.38646e6 −0.0169152
$$586$$ −8.90830e7 3.45017e8i −0.442692 1.71454i
$$587$$ 2.16397e7i 0.106988i 0.998568 + 0.0534941i $$0.0170358\pi$$
−0.998568 + 0.0534941i $$0.982964\pi$$
$$588$$ 2.07830e7 + 3.75631e7i 0.102230 + 0.184769i
$$589$$ −3.15395e8 −1.54351
$$590$$ 6.07440e6 1.56840e6i 0.0295765 0.00763663i
$$591$$ 6.91140e7i 0.334814i
$$592$$ 4.33894e6 6.91956e6i 0.0209131 0.0333514i
$$593$$ 2.00341e8 0.960738 0.480369 0.877066i $$-0.340503\pi$$
0.480369 + 0.877066i $$0.340503\pi$$
$$594$$ −2.96410e7 1.14799e8i −0.141427 0.547745i
$$595$$ 1.47669e7i 0.0701033i
$$596$$ 1.83359e8 1.01449e8i 0.866089 0.479193i
$$597$$ 1.51690e8 0.712907
$$598$$ 1.18922e8 3.07055e7i 0.556107 0.143586i
$$599$$ 1.37592e8i 0.640197i −0.947384 0.320098i $$-0.896284\pi$$
0.947384 0.320098i $$-0.103716\pi$$
$$600$$ 1.78848e8 1.69321e8i 0.828000 0.783892i
$$601$$ −1.90306e8 −0.876655 −0.438327 0.898815i $$-0.644429\pi$$
−0.438327 + 0.898815i $$0.644429\pi$$
$$602$$ 1.33440e7 + 5.16811e7i 0.0611641 + 0.236888i
$$603$$ 9.10477e7i 0.415257i
$$604$$ 1.73309e8 + 3.13237e8i 0.786520 + 1.42155i
$$605$$ 8.49001e6 0.0383391
$$606$$ −1.53398e8 + 3.96072e7i −0.689289 + 0.177974i
$$607$$ 1.25461e8i 0.560974i 0.959858 + 0.280487i $$0.0904960\pi$$
−0.959858 + 0.280487i $$0.909504\pi$$
$$608$$ −7.46496e7 + 2.35148e8i −0.332137 + 1.04624i
$$609$$ 2.44781e8 1.08374
$$610$$ −218360. 845705.i −0.000962019 0.00372588i
$$611$$ 1.10831e7i 0.0485888i
$$612$$ −6.16530e7 + 3.41116e7i −0.268967 + 0.148815i
$$613$$ −9.91111e7 −0.430270 −0.215135 0.976584i $$-0.569019\pi$$
−0.215135 + 0.976584i $$0.569019\pi$$
$$614$$ 3.78817e8 9.78102e7i 1.63653 0.422551i
$$615$$ 9.09748e6i 0.0391107i
$$616$$ −1.04755e8 1.10650e8i −0.448160 0.473378i
$$617$$ 3.70827e7 0.157876 0.0789379 0.996880i $$-0.474847\pi$$
0.0789379 + 0.996880i $$0.474847\pi$$
$$618$$ 8.60813e7 + 3.33391e8i 0.364706 + 1.41250i
$$619$$ 4.05274e8i 1.70874i −0.519662 0.854372i $$-0.673942\pi$$
0.519662 0.854372i $$-0.326058\pi$$
$$620$$ −1.29792e7 2.34585e7i −0.0544594 0.0984295i
$$621$$ −1.61591e8 −0.674749
$$622$$ −3.87469e8 + 1.00044e8i −1.61015 + 0.415738i
$$623$$ 9.62786e7i 0.398168i
$$624$$ −1.57624e8 9.88390e7i −0.648738 0.406794i
$$625$$ 2.39463e8 0.980841
$$626$$ 2.25437e6 + 8.73115e6i 0.00918973 + 0.0355917i
$$627$$ 2.24065e8i 0.909017i
$$628$$ −4.57405e7 + 2.53074e7i −0.184681 + 0.102181i
$$629$$ −9.50340e6 −0.0381880
$$630$$ 5.54400e6 1.43145e6i 0.0221718 0.00572474i
$$631$$ 2.52648e7i 0.100561i −0.998735 0.0502803i $$-0.983989\pi$$
0.998735 0.0502803i $$-0.0160115\pi$$
$$632$$ −1.15523e8 + 1.09369e8i −0.457631 + 0.433253i
$$633$$ 1.21132e8 0.477581
$$634$$ 6.89763e7 + 2.67144e8i 0.270665 + 1.04828i
$$635$$ 1.67462e7i 0.0654025i
$$636$$ −1.85140e8 3.34620e8i −0.719662 1.30071i
$$637$$ 3.17374e7 0.122787
$$638$$ 1.89705e8 4.89817e7i 0.730495 0.188613i
$$639$$ 1.22948e8i 0.471213i
$$640$$ −2.05619e7 + 4.12457e6i −0.0784375 + 0.0157340i
$$641$$ −4.21293e8 −1.59959 −0.799797 0.600270i $$-0.795060\pi$$
−0.799797 + 0.600270i $$0.795060\pi$$
$$642$$ −7.12224e7 2.75843e8i −0.269161 1.04245i
$$643$$ 8.17706e7i 0.307584i 0.988103 + 0.153792i $$0.0491486\pi$$
−0.988103 + 0.153792i $$0.950851\pi$$
$$644$$ −1.81709e8 + 1.00536e8i −0.680328 + 0.376414i
$$645$$ −6.67200e6 −0.0248643
$$646$$ 2.77953e8 7.17672e7i 1.03104 0.266212i
$$647$$ 1.84284e8i 0.680416i −0.940350 0.340208i $$-0.889503\pi$$
0.940350 0.340208i $$-0.110497\pi$$
$$648$$ 2.27561e8 + 2.40365e8i 0.836319 + 0.883377i
$$649$$ −7.53226e7 −0.275544
$$650$$ −4.55193e7 1.76295e8i −0.165751 0.641950i
$$651$$ 4.02146e8i 1.45761i
$$652$$ 5.71939e7 + 1.03372e8i 0.206351 + 0.372958i
$$653$$ 6.43842e7 0.231228 0.115614 0.993294i $$-0.463117\pi$$
0.115614 + 0.993294i $$0.463117\pi$$
$$654$$ 3.68577e8 9.51662e7i 1.31764 0.340212i
$$655$$ 2.84454e7i 0.101225i
$$656$$ 6.38917e7 1.01892e8i 0.226325 0.360934i
$$657$$ −6.66726e7 −0.235099
$$658$$ 4.68480e6 + 1.81442e7i 0.0164442 + 0.0636882i
$$659$$ 5.38099e8i 1.88021i 0.340889 + 0.940103i $$0.389272\pi$$
−0.340889 + 0.940103i $$0.610728\pi$$
$$660$$ 1.66656e7 9.22080e6i 0.0579681 0.0320728i
$$661$$ 2.83897e8 0.983008 0.491504 0.870875i $$-0.336447\pi$$
0.491504 + 0.870875i $$0.336447\pi$$
$$662$$ −3.11927e8 + 8.05393e7i −1.07518 + 0.277609i
$$663$$ 2.16483e8i 0.742819i
$$664$$ −7.59053e7 + 7.18617e7i −0.259279 + 0.245467i
$$665$$ −2.33280e7 −0.0793255
$$666$$ −921228. 3.56790e6i −0.00311849 0.0120779i
$$667$$ 2.67029e8i 0.899872i
$$668$$ −2.46791e8 4.46048e8i −0.827942 1.49642i
$$669$$ 1.03212e8 0.344707
$$670$$ 3.05304e7 7.88292e6i 0.101510 0.0262097i
$$671$$ 1.04867e7i 0.0347115i
$$672$$ 2.99827e8 + 9.51824e7i 0.988014 + 0.313653i
$$673$$ 2.77693e8 0.911002 0.455501 0.890235i $$-0.349460\pi$$
0.455501 + 0.890235i $$0.349460\pi$$
$$674$$ −6.85062e7 2.65323e8i −0.223743 0.866554i
$$675$$ 2.39550e8i 0.778906i
$$676$$ 1.49949e8 8.29640e7i 0.485403 0.268565i
$$677$$ −9.23026e7 −0.297473 −0.148737 0.988877i $$-0.547521\pi$$
−0.148737 + 0.988877i $$0.547521\pi$$
$$678$$ −1.44407e8 + 3.72856e7i −0.463338 + 0.119633i
$$679$$ 4.51462e8i 1.44215i
$$680$$ 1.67763e7 + 1.77203e7i 0.0533544 + 0.0563565i
$$681$$ −4.18384e8 −1.32475
$$682$$ 8.04710e7 + 3.11663e8i 0.253680 + 0.982499i
$$683$$ 2.70862e8i 0.850132i −0.905162 0.425066i $$-0.860251\pi$$
0.905162 0.425066i $$-0.139749\pi$$
$$684$$ 5.38877e7 + 9.73962e7i 0.168392 + 0.304350i
$$685$$ 3.81003e7 0.118538
$$686$$ −3.34315e8 + 8.63198e7i −1.03558 + 0.267386i
$$687$$ 4.94496e7i 0.152508i
$$688$$ −7.47264e7 4.68575e7i −0.229461 0.143884i
$$689$$ −2.82724e8 −0.864380
$$690$$ −6.48960e6 2.51341e7i −0.0197547 0.0765097i
$$691$$ 1.92568e7i 0.0583645i −0.999574 0.0291823i $$-0.990710\pi$$
0.999574 0.0291823i $$-0.00929032\pi$$
$$692$$ 2.87086e8 1.58840e8i 0.866350 0.479337i
$$693$$ −6.87456e7 −0.206560
$$694$$ −4.22539e8 + 1.09099e8i −1.26412 + 0.326395i
$$695$$ 1.38839e6i 0.00413577i
$$696$$ −2.93737e8 + 2.78089e8i −0.871226 + 0.824815i
$$697$$ −1.39939e8 −0.413277
$$698$$ 9.40017e7 + 3.64067e8i 0.276420 + 1.07057i
$$699$$ 2.49229e8i 0.729738i
$$700$$ 1.49040e8 + 2.69374e8i 0.434519 + 0.785346i
$$701$$ 3.52234e8 1.02253 0.511266 0.859423i $$-0.329177\pi$$
0.511266 + 0.859423i $$0.329177\pi$$
$$702$$ 1.75216e8 4.52407e7i 0.506481 0.130773i
$$703$$ 1.50130e7i 0.0432117i
$$704$$ 2.51412e8 + 1.37697e7i 0.720558 + 0.0394646i
$$705$$ −2.34240e6 −0.00668488
$$706$$ −2.54463e7 9.85530e7i −0.0723119 0.280063i
$$707$$ 1.98036e8i 0.560384i
$$708$$ 1.36067e8 7.52834e7i 0.383400 0.212129i
$$709$$ 4.62733e8 1.29835 0.649175 0.760639i $$-0.275114\pi$$
0.649175 + 0.760639i $$0.275114\pi$$
$$710$$ −4.12272e7 + 1.06448e7i −0.115188 + 0.0297415i
$$711$$ 7.17731e7i 0.199689i
$$712$$ −1.09380e8 1.15534e8i −0.303038 0.320089i
$$713$$ 4.38697e8 1.21031
$$714$$ −9.15072e7 3.54406e8i −0.251397 0.973658i
$$715$$ 1.40809e7i 0.0385224i
$$716$$ 7.23197e7 + 1.30710e8i 0.197023 + 0.356098i
$$717$$ 3.48668e8 0.945921
$$718$$ 1.56587e8 4.04306e7i 0.423041 0.109229i
$$719$$ 4.60385e8i 1.23861i 0.785150 + 0.619305i $$0.212586\pi$$
−0.785150 + 0.619305i $$0.787414\pi$$
$$720$$ −5.02656e6 + 8.01615e6i −0.0134671 + 0.0214767i
$$721$$ −4.30406e8 −1.14835
$$722$$ −1.92823e7 7.46801e7i −0.0512327 0.198424i
$$723$$ 1.56501e8i 0.414097i
$$724$$ −5.42727e8 + 3.00282e8i −1.43010 + 0.791250i
$$725$$ −3.95856e8 −1.03878
$$726$$ 2.03760e8 5.26107e7i 0.532488 0.137488i
$$727$$ 4.82173e8i 1.25487i 0.778668 + 0.627437i $$0.215896\pi$$
−0.778668 + 0.627437i $$0.784104\pi$$
$$728$$ 1.68883e8 1.59887e8i 0.437716 0.414398i
$$729$$ −1.99184e8 −0.514128
$$730$$ 5.77252e6 + 2.23569e7i 0.0148387 + 0.0574702i
$$731$$ 1.02630e8i 0.262738i
$$732$$ −1.04813e7 1.89438e7i −0.0267227 0.0482985i
$$733$$ −5.08270e8 −1.29057 −0.645287 0.763941i $$-0.723262\pi$$
−0.645287 + 0.763941i $$0.723262\pi$$
$$734$$ 8.60246e7 2.22115e7i 0.217538 0.0561680i
$$735$$ 6.70770e6i 0.0168932i
$$736$$ 1.03834e8 3.27079e8i 0.260438 0.820387i
$$737$$ −3.78577e8 −0.945696
$$738$$ −1.35652e7 5.25380e7i −0.0337488 0.130709i
$$739$$ 1.27767e8i 0.316582i 0.987392 + 0.158291i $$0.0505984\pi$$
−0.987392 + 0.158291i $$0.949402\pi$$
$$740$$ −1.11664e6 + 617818.i −0.00275561 + 0.00152463i
$$741$$ 3.41988e8 0.840537
$$742$$ 4.62850e8 1.19507e8i 1.13300 0.292538i
$$743$$ 2.83312e8i 0.690716i −0.938471 0.345358i $$-0.887758\pi$$
0.938471 0.345358i $$-0.112242\pi$$
$$744$$ −4.56868e8 4.82575e8i −1.10936 1.17178i
$$745$$ −3.27426e7 −0.0791853
$$746$$ 1.37429e6 + 5.32261e6i 0.00331026 + 0.0128206i
$$747$$ 4.71593e7i 0.113137i
$$748$$ −1.41836e8 2.56354e8i −0.338908 0.612540i
$$749$$ 3.56112e8 0.847503
$$750$$ −7.47600e7 + 1.93029e7i −0.177209 + 0.0457551i
$$751$$ 2.15309e8i 0.508325i −0.967161 0.254163i $$-0.918200\pi$$
0.967161 0.254163i $$-0.0817999\pi$$
$$752$$ −2.62349e7 1.64507e7i −0.0616915 0.0386839i
$$753$$ 1.46117e8 0.342228
$$754$$ 7.47601e7 + 2.89545e8i 0.174404 + 0.675463i
$$755$$ 5.59352e7i 0.129970i
$$756$$ −2.67725e8 + 1.48128e8i −0.619617 + 0.342824i
$$757$$ −3.03985e8 −0.700753 −0.350377 0.936609i $$-0.613946\pi$$
−0.350377 + 0.936609i $$0.613946\pi$$
$$758$$ −1.15026e8 + 2.96997e7i −0.264113 + 0.0681938i
$$759$$ 3.11663e8i 0.712787i
$$760$$ 2.79936e7 2.65024e7i 0.0637702 0.0603731i
$$761$$ 8.63611e8 1.95959 0.979793 0.200014i $$-0.0640988\pi$$
0.979793 + 0.200014i $$0.0640988\pi$$
$$762$$ 1.03772e8 + 4.01908e8i 0.234539 + 0.908367i
$$763$$ 4.75831e8i 1.07122i
$$764$$ 3.53725e8 + 6.39321e8i 0.793206 + 1.43364i
$$765$$ 1.10095e7 0.0245913
$$766$$ 2.60175e8 6.71770e7i 0.578868 0.149463i
$$767$$ 1.14964e8i 0.254786i
$$768$$ −4.67927e8 + 2.26407e8i −1.03299 + 0.499812i
$$769$$ −1.97898e7 −0.0435174 −0.0217587 0.999763i $$-0.506927\pi$$
−0.0217587 + 0.999763i $$0.506927\pi$$