# Properties

 Label 165.6.c.b.34.12 Level $165$ Weight $6$ Character 165.34 Analytic conductor $26.463$ Analytic rank $0$ Dimension $26$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(34,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("165.34");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$165 = 3 \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 165.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

comment: select newform

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

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

 Self dual: no Analytic conductor: $$26.4633302691$$ Analytic rank: $$0$$ Dimension: $$26$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 34.12 Character $$\chi$$ $$=$$ 165.34 Dual form 165.6.c.b.34.15

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.31741i q^{2} +9.00000i q^{3} +30.2644 q^{4} +(-35.6376 - 43.0693i) q^{5} +11.8567 q^{6} +87.4786i q^{7} -82.0279i q^{8} -81.0000 q^{9} +O(q^{10})$$ $$q-1.31741i q^{2} +9.00000i q^{3} +30.2644 q^{4} +(-35.6376 - 43.0693i) q^{5} +11.8567 q^{6} +87.4786i q^{7} -82.0279i q^{8} -81.0000 q^{9} +(-56.7399 + 46.9494i) q^{10} +121.000 q^{11} +272.380i q^{12} +521.292i q^{13} +115.245 q^{14} +(387.623 - 320.739i) q^{15} +860.397 q^{16} +68.1523i q^{17} +106.710i q^{18} +1588.76 q^{19} +(-1078.55 - 1303.47i) q^{20} -787.308 q^{21} -159.407i q^{22} +191.904i q^{23} +738.251 q^{24} +(-584.921 + 3069.77i) q^{25} +686.756 q^{26} -729.000i q^{27} +2647.49i q^{28} +4252.98 q^{29} +(-422.545 - 510.659i) q^{30} -83.6771 q^{31} -3758.39i q^{32} +1089.00i q^{33} +89.7846 q^{34} +(3767.64 - 3117.53i) q^{35} -2451.42 q^{36} +14445.4i q^{37} -2093.06i q^{38} -4691.63 q^{39} +(-3532.88 + 2923.28i) q^{40} +6151.94 q^{41} +1037.21i q^{42} +1408.62i q^{43} +3662.00 q^{44} +(2886.65 + 3488.61i) q^{45} +252.816 q^{46} +14797.5i q^{47} +7743.57i q^{48} +9154.49 q^{49} +(4044.15 + 770.582i) q^{50} -613.371 q^{51} +15776.6i q^{52} +10938.4i q^{53} -960.393 q^{54} +(-4312.15 - 5211.38i) q^{55} +7175.69 q^{56} +14298.9i q^{57} -5602.92i q^{58} +16099.1 q^{59} +(11731.2 - 9706.97i) q^{60} +41095.0 q^{61} +110.237i q^{62} -7085.77i q^{63} +22581.4 q^{64} +(22451.7 - 18577.6i) q^{65} +1434.66 q^{66} +1254.02i q^{67} +2062.59i q^{68} -1727.14 q^{69} +(-4107.07 - 4963.53i) q^{70} +47638.4 q^{71} +6644.26i q^{72} -7358.01i q^{73} +19030.5 q^{74} +(-27627.9 - 5264.29i) q^{75} +48083.1 q^{76} +10584.9i q^{77} +6180.81i q^{78} -90184.5 q^{79} +(-30662.5 - 37056.7i) q^{80} +6561.00 q^{81} -8104.64i q^{82} +10857.0i q^{83} -23827.4 q^{84} +(2935.27 - 2428.79i) q^{85} +1855.73 q^{86} +38276.8i q^{87} -9925.37i q^{88} -112869. q^{89} +(4595.93 - 3802.90i) q^{90} -45601.9 q^{91} +5807.86i q^{92} -753.094i q^{93} +19494.4 q^{94} +(-56619.8 - 68426.9i) q^{95} +33825.5 q^{96} -96993.9i q^{97} -12060.2i q^{98} -9801.00 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9}+O(q^{10})$$ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 $$26 q - 418 q^{4} - 98 q^{5} + 234 q^{6} - 2106 q^{9} + 236 q^{10} + 3146 q^{11} + 1220 q^{14} + 7002 q^{16} - 540 q^{19} + 4930 q^{20} + 5472 q^{21} - 7182 q^{24} + 218 q^{25} + 5304 q^{26} - 23904 q^{29} + 12114 q^{30} + 38192 q^{31} + 2604 q^{34} - 11988 q^{35} + 33858 q^{36} - 17748 q^{39} - 41096 q^{40} + 70368 q^{41} - 50578 q^{44} + 7938 q^{45} - 8240 q^{46} - 29114 q^{49} - 133876 q^{50} + 26568 q^{51} - 18954 q^{54} - 11858 q^{55} + 119604 q^{56} + 18384 q^{59} - 14148 q^{60} + 10876 q^{61} - 213114 q^{64} - 117068 q^{65} + 28314 q^{66} - 163512 q^{69} - 58660 q^{70} + 203400 q^{71} - 27352 q^{74} - 35352 q^{75} + 279932 q^{76} - 187908 q^{79} - 256654 q^{80} + 170586 q^{81} - 196560 q^{84} + 37396 q^{85} + 741860 q^{86} + 36836 q^{89} - 19116 q^{90} + 349072 q^{91} - 129040 q^{94} - 208284 q^{95} + 209898 q^{96} - 254826 q^{99}+O(q^{100})$$ 26 * q - 418 * q^4 - 98 * q^5 + 234 * q^6 - 2106 * q^9 + 236 * q^10 + 3146 * q^11 + 1220 * q^14 + 7002 * q^16 - 540 * q^19 + 4930 * q^20 + 5472 * q^21 - 7182 * q^24 + 218 * q^25 + 5304 * q^26 - 23904 * q^29 + 12114 * q^30 + 38192 * q^31 + 2604 * q^34 - 11988 * q^35 + 33858 * q^36 - 17748 * q^39 - 41096 * q^40 + 70368 * q^41 - 50578 * q^44 + 7938 * q^45 - 8240 * q^46 - 29114 * q^49 - 133876 * q^50 + 26568 * q^51 - 18954 * q^54 - 11858 * q^55 + 119604 * q^56 + 18384 * q^59 - 14148 * q^60 + 10876 * q^61 - 213114 * q^64 - 117068 * q^65 + 28314 * q^66 - 163512 * q^69 - 58660 * q^70 + 203400 * q^71 - 27352 * q^74 - 35352 * q^75 + 279932 * q^76 - 187908 * q^79 - 256654 * q^80 + 170586 * q^81 - 196560 * q^84 + 37396 * q^85 + 741860 * q^86 + 36836 * q^89 - 19116 * q^90 + 349072 * q^91 - 129040 * q^94 - 208284 * q^95 + 209898 * q^96 - 254826 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$$.

 $$n$$ $$46$$ $$56$$ $$67$$ $$\chi(n)$$ $$1$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.31741i 0.232888i −0.993197 0.116444i $$-0.962851\pi$$
0.993197 0.116444i $$-0.0371495\pi$$
$$3$$ 9.00000i 0.577350i
$$4$$ 30.2644 0.945763
$$5$$ −35.6376 43.0693i −0.637505 0.770446i
$$6$$ 11.8567 0.134458
$$7$$ 87.4786i 0.674772i 0.941366 + 0.337386i $$0.109543\pi$$
−0.941366 + 0.337386i $$0.890457\pi$$
$$8$$ 82.0279i 0.453144i
$$9$$ −81.0000 −0.333333
$$10$$ −56.7399 + 46.9494i −0.179427 + 0.148467i
$$11$$ 121.000 0.301511
$$12$$ 272.380i 0.546037i
$$13$$ 521.292i 0.855506i 0.903896 + 0.427753i $$0.140695\pi$$
−0.903896 + 0.427753i $$0.859305\pi$$
$$14$$ 115.245 0.157146
$$15$$ 387.623 320.739i 0.444817 0.368064i
$$16$$ 860.397 0.840232
$$17$$ 68.1523i 0.0571950i 0.999591 + 0.0285975i $$0.00910411\pi$$
−0.999591 + 0.0285975i $$0.990896\pi$$
$$18$$ 106.710i 0.0776292i
$$19$$ 1588.76 1.00966 0.504830 0.863219i $$-0.331555\pi$$
0.504830 + 0.863219i $$0.331555\pi$$
$$20$$ −1078.55 1303.47i −0.602929 0.728660i
$$21$$ −787.308 −0.389580
$$22$$ 159.407i 0.0702183i
$$23$$ 191.904i 0.0756422i 0.999285 + 0.0378211i $$0.0120417\pi$$
−0.999285 + 0.0378211i $$0.987958\pi$$
$$24$$ 738.251 0.261623
$$25$$ −584.921 + 3069.77i −0.187175 + 0.982327i
$$26$$ 686.756 0.199237
$$27$$ 729.000i 0.192450i
$$28$$ 2647.49i 0.638174i
$$29$$ 4252.98 0.939071 0.469535 0.882914i $$-0.344421\pi$$
0.469535 + 0.882914i $$0.344421\pi$$
$$30$$ −422.545 510.659i −0.0857175 0.103592i
$$31$$ −83.6771 −0.0156388 −0.00781938 0.999969i $$-0.502489\pi$$
−0.00781938 + 0.999969i $$0.502489\pi$$
$$32$$ 3758.39i 0.648824i
$$33$$ 1089.00i 0.174078i
$$34$$ 89.7846 0.0133200
$$35$$ 3767.64 3117.53i 0.519875 0.430170i
$$36$$ −2451.42 −0.315254
$$37$$ 14445.4i 1.73470i 0.497695 + 0.867352i $$0.334180\pi$$
−0.497695 + 0.867352i $$0.665820\pi$$
$$38$$ 2093.06i 0.235138i
$$39$$ −4691.63 −0.493926
$$40$$ −3532.88 + 2923.28i −0.349123 + 0.288882i
$$41$$ 6151.94 0.571548 0.285774 0.958297i $$-0.407749\pi$$
0.285774 + 0.958297i $$0.407749\pi$$
$$42$$ 1037.21i 0.0907283i
$$43$$ 1408.62i 0.116177i 0.998311 + 0.0580886i $$0.0185006\pi$$
−0.998311 + 0.0580886i $$0.981499\pi$$
$$44$$ 3662.00 0.285158
$$45$$ 2886.65 + 3488.61i 0.212502 + 0.256815i
$$46$$ 252.816 0.0176161
$$47$$ 14797.5i 0.977110i 0.872533 + 0.488555i $$0.162476\pi$$
−0.872533 + 0.488555i $$0.837524\pi$$
$$48$$ 7743.57i 0.485108i
$$49$$ 9154.49 0.544683
$$50$$ 4044.15 + 770.582i 0.228772 + 0.0435907i
$$51$$ −613.371 −0.0330216
$$52$$ 15776.6i 0.809106i
$$53$$ 10938.4i 0.534891i 0.963573 + 0.267445i $$0.0861795\pi$$
−0.963573 + 0.267445i $$0.913820\pi$$
$$54$$ −960.393 −0.0448192
$$55$$ −4312.15 5211.38i −0.192215 0.232298i
$$56$$ 7175.69 0.305769
$$57$$ 14298.9i 0.582928i
$$58$$ 5602.92i 0.218698i
$$59$$ 16099.1 0.602103 0.301052 0.953608i $$-0.402662\pi$$
0.301052 + 0.953608i $$0.402662\pi$$
$$60$$ 11731.2 9706.97i 0.420692 0.348101i
$$61$$ 41095.0 1.41405 0.707025 0.707189i $$-0.250037\pi$$
0.707025 + 0.707189i $$0.250037\pi$$
$$62$$ 110.237i 0.00364208i
$$63$$ 7085.77i 0.224924i
$$64$$ 22581.4 0.689129
$$65$$ 22451.7 18577.6i 0.659121 0.545389i
$$66$$ 1434.66 0.0405405
$$67$$ 1254.02i 0.0341286i 0.999854 + 0.0170643i $$0.00543199\pi$$
−0.999854 + 0.0170643i $$0.994568\pi$$
$$68$$ 2062.59i 0.0540930i
$$69$$ −1727.14 −0.0436721
$$70$$ −4107.07 4963.53i −0.100181 0.121073i
$$71$$ 47638.4 1.12153 0.560765 0.827975i $$-0.310507\pi$$
0.560765 + 0.827975i $$0.310507\pi$$
$$72$$ 6644.26i 0.151048i
$$73$$ 7358.01i 0.161604i −0.996730 0.0808022i $$-0.974252\pi$$
0.996730 0.0808022i $$-0.0257482\pi$$
$$74$$ 19030.5 0.403991
$$75$$ −27627.9 5264.29i −0.567147 0.108065i
$$76$$ 48083.1 0.954900
$$77$$ 10584.9i 0.203451i
$$78$$ 6180.81i 0.115029i
$$79$$ −90184.5 −1.62579 −0.812895 0.582411i $$-0.802110\pi$$
−0.812895 + 0.582411i $$0.802110\pi$$
$$80$$ −30662.5 37056.7i −0.535652 0.647353i
$$81$$ 6561.00 0.111111
$$82$$ 8104.64i 0.133106i
$$83$$ 10857.0i 0.172987i 0.996252 + 0.0864935i $$0.0275662\pi$$
−0.996252 + 0.0864935i $$0.972434\pi$$
$$84$$ −23827.4 −0.368450
$$85$$ 2935.27 2428.79i 0.0440657 0.0364621i
$$86$$ 1855.73 0.0270563
$$87$$ 38276.8i 0.542173i
$$88$$ 9925.37i 0.136628i
$$89$$ −112869. −1.51043 −0.755216 0.655476i $$-0.772468\pi$$
−0.755216 + 0.655476i $$0.772468\pi$$
$$90$$ 4595.93 3802.90i 0.0598091 0.0494890i
$$91$$ −45601.9 −0.577271
$$92$$ 5807.86i 0.0715396i
$$93$$ 753.094i 0.00902905i
$$94$$ 19494.4 0.227557
$$95$$ −56619.8 68426.9i −0.643664 0.777889i
$$96$$ 33825.5 0.374599
$$97$$ 96993.9i 1.04668i −0.852123 0.523341i $$-0.824685\pi$$
0.852123 0.523341i $$-0.175315\pi$$
$$98$$ 12060.2i 0.126850i
$$99$$ −9801.00 −0.100504
$$100$$ −17702.3 + 92904.9i −0.177023 + 0.929049i
$$101$$ −55750.8 −0.543810 −0.271905 0.962324i $$-0.587654\pi$$
−0.271905 + 0.962324i $$0.587654\pi$$
$$102$$ 808.062i 0.00769031i
$$103$$ 107469.i 0.998139i 0.866562 + 0.499069i $$0.166325\pi$$
−0.866562 + 0.499069i $$0.833675\pi$$
$$104$$ 42760.5 0.387667
$$105$$ 28057.8 + 33908.8i 0.248359 + 0.300150i
$$106$$ 14410.4 0.124569
$$107$$ 25673.1i 0.216780i −0.994108 0.108390i $$-0.965430\pi$$
0.994108 0.108390i $$-0.0345696\pi$$
$$108$$ 22062.8i 0.182012i
$$109$$ −98829.6 −0.796748 −0.398374 0.917223i $$-0.630425\pi$$
−0.398374 + 0.917223i $$0.630425\pi$$
$$110$$ −6865.53 + 5680.88i −0.0540994 + 0.0447645i
$$111$$ −130009. −1.00153
$$112$$ 75266.4i 0.566965i
$$113$$ 12055.0i 0.0888120i −0.999014 0.0444060i $$-0.985860\pi$$
0.999014 0.0444060i $$-0.0141395\pi$$
$$114$$ 18837.5 0.135757
$$115$$ 8265.16 6839.00i 0.0582783 0.0482223i
$$116$$ 128714. 0.888139
$$117$$ 42224.7i 0.285169i
$$118$$ 21209.1i 0.140222i
$$119$$ −5961.87 −0.0385936
$$120$$ −26309.5 31795.9i −0.166786 0.201566i
$$121$$ 14641.0 0.0909091
$$122$$ 54139.1i 0.329315i
$$123$$ 55367.5i 0.329983i
$$124$$ −2532.44 −0.0147906
$$125$$ 153058. 84207.2i 0.876155 0.482030i
$$126$$ −9334.87 −0.0523820
$$127$$ 57953.4i 0.318838i −0.987211 0.159419i $$-0.949038\pi$$
0.987211 0.159419i $$-0.0509620\pi$$
$$128$$ 150017.i 0.809313i
$$129$$ −12677.5 −0.0670750
$$130$$ −24474.4 29578.1i −0.127014 0.153501i
$$131$$ −124350. −0.633095 −0.316548 0.948577i $$-0.602524\pi$$
−0.316548 + 0.948577i $$0.602524\pi$$
$$132$$ 32958.0i 0.164636i
$$133$$ 138983.i 0.681291i
$$134$$ 1652.06 0.00794812
$$135$$ −31397.5 + 25979.8i −0.148272 + 0.122688i
$$136$$ 5590.39 0.0259176
$$137$$ 408683.i 1.86031i −0.367170 0.930154i $$-0.619673\pi$$
0.367170 0.930154i $$-0.380327\pi$$
$$138$$ 2275.35i 0.0101707i
$$139$$ −378463. −1.66145 −0.830723 0.556686i $$-0.812073\pi$$
−0.830723 + 0.556686i $$0.812073\pi$$
$$140$$ 114025. 94350.2i 0.491679 0.406839i
$$141$$ −133177. −0.564135
$$142$$ 62759.4i 0.261191i
$$143$$ 63076.4i 0.257945i
$$144$$ −69692.2 −0.280077
$$145$$ −151566. 183173.i −0.598662 0.723503i
$$146$$ −9693.52 −0.0376357
$$147$$ 82390.4i 0.314473i
$$148$$ 437182.i 1.64062i
$$149$$ 271317. 1.00118 0.500588 0.865686i $$-0.333117\pi$$
0.500588 + 0.865686i $$0.333117\pi$$
$$150$$ −6935.24 + 36397.4i −0.0251671 + 0.132081i
$$151$$ −146748. −0.523758 −0.261879 0.965101i $$-0.584342\pi$$
−0.261879 + 0.965101i $$0.584342\pi$$
$$152$$ 130323.i 0.457522i
$$153$$ 5520.34i 0.0190650i
$$154$$ 13944.7 0.0473813
$$155$$ 2982.05 + 3603.91i 0.00996979 + 0.0120488i
$$156$$ −141990. −0.467138
$$157$$ 365562.i 1.18362i −0.806077 0.591810i $$-0.798414\pi$$
0.806077 0.591810i $$-0.201586\pi$$
$$158$$ 118810.i 0.378626i
$$159$$ −98445.8 −0.308819
$$160$$ −161871. + 133940.i −0.499884 + 0.413628i
$$161$$ −16787.5 −0.0510412
$$162$$ 8643.54i 0.0258764i
$$163$$ 16695.2i 0.0492180i −0.999697 0.0246090i $$-0.992166\pi$$
0.999697 0.0246090i $$-0.00783408\pi$$
$$164$$ 186185. 0.540549
$$165$$ 46902.4 38809.4i 0.134117 0.110975i
$$166$$ 14303.1 0.0402865
$$167$$ 568590.i 1.57764i −0.614623 0.788821i $$-0.710692\pi$$
0.614623 0.788821i $$-0.289308\pi$$
$$168$$ 64581.2i 0.176536i
$$169$$ 99547.4 0.268110
$$170$$ −3199.71 3866.96i −0.00849157 0.0102624i
$$171$$ −128690. −0.336554
$$172$$ 42630.9i 0.109876i
$$173$$ 552203.i 1.40276i −0.712788 0.701380i $$-0.752568\pi$$
0.712788 0.701380i $$-0.247432\pi$$
$$174$$ 50426.3 0.126265
$$175$$ −268539. 51168.1i −0.662846 0.126300i
$$176$$ 104108. 0.253339
$$177$$ 144892.i 0.347624i
$$178$$ 148695.i 0.351761i
$$179$$ 179962. 0.419807 0.209903 0.977722i $$-0.432685\pi$$
0.209903 + 0.977722i $$0.432685\pi$$
$$180$$ 87362.7 + 105581.i 0.200976 + 0.242887i
$$181$$ 612439. 1.38953 0.694763 0.719239i $$-0.255509\pi$$
0.694763 + 0.719239i $$0.255509\pi$$
$$182$$ 60076.5i 0.134439i
$$183$$ 369855.i 0.816402i
$$184$$ 15741.5 0.0342768
$$185$$ 622153. 514800.i 1.33650 1.10588i
$$186$$ −992.135 −0.00210275
$$187$$ 8246.43i 0.0172449i
$$188$$ 447838.i 0.924115i
$$189$$ 63771.9 0.129860
$$190$$ −90146.4 + 74591.5i −0.181161 + 0.149901i
$$191$$ 65407.8 0.129732 0.0648659 0.997894i $$-0.479338\pi$$
0.0648659 + 0.997894i $$0.479338\pi$$
$$192$$ 203232.i 0.397869i
$$193$$ 661050.i 1.27744i 0.769439 + 0.638721i $$0.220536\pi$$
−0.769439 + 0.638721i $$0.779464\pi$$
$$194$$ −127781. −0.243759
$$195$$ 167199. + 202065.i 0.314881 + 0.380544i
$$196$$ 277055. 0.515141
$$197$$ 590186.i 1.08349i 0.840544 + 0.541743i $$0.182235\pi$$
−0.840544 + 0.541743i $$0.817765\pi$$
$$198$$ 12911.9i 0.0234061i
$$199$$ 342750. 0.613543 0.306771 0.951783i $$-0.400751\pi$$
0.306771 + 0.951783i $$0.400751\pi$$
$$200$$ 251807. + 47979.8i 0.445136 + 0.0848172i
$$201$$ −11286.2 −0.0197041
$$202$$ 73446.7i 0.126647i
$$203$$ 372045.i 0.633658i
$$204$$ −18563.3 −0.0312306
$$205$$ −219240. 264959.i −0.364364 0.440347i
$$206$$ 141581. 0.232454
$$207$$ 15544.2i 0.0252141i
$$208$$ 448518.i 0.718823i
$$209$$ 192241. 0.304424
$$210$$ 44671.8 36963.6i 0.0699013 0.0578397i
$$211$$ −214655. −0.331921 −0.165960 0.986132i $$-0.553072\pi$$
−0.165960 + 0.986132i $$0.553072\pi$$
$$212$$ 331045.i 0.505880i
$$213$$ 428746.i 0.647516i
$$214$$ −33822.1 −0.0504854
$$215$$ 60668.0 50199.7i 0.0895083 0.0740636i
$$216$$ −59798.3 −0.0872076
$$217$$ 7319.96i 0.0105526i
$$218$$ 130199.i 0.185553i
$$219$$ 66222.1 0.0933023
$$220$$ −130505. 157719.i −0.181790 0.219699i
$$221$$ −35527.3 −0.0489307
$$222$$ 171275.i 0.233244i
$$223$$ 118747.i 0.159904i −0.996799 0.0799521i $$-0.974523\pi$$
0.996799 0.0799521i $$-0.0254767\pi$$
$$224$$ 328779. 0.437808
$$225$$ 47378.6 248651.i 0.0623916 0.327442i
$$226$$ −15881.4 −0.0206832
$$227$$ 2183.16i 0.00281204i −0.999999 0.00140602i $$-0.999552\pi$$
0.999999 0.00140602i $$-0.000447550\pi$$
$$228$$ 432747.i 0.551312i
$$229$$ −123704. −0.155881 −0.0779407 0.996958i $$-0.524834\pi$$
−0.0779407 + 0.996958i $$0.524834\pi$$
$$230$$ −9009.77 10888.6i −0.0112304 0.0135723i
$$231$$ −95264.2 −0.117463
$$232$$ 348863.i 0.425534i
$$233$$ 1.16587e6i 1.40689i 0.710748 + 0.703446i $$0.248356\pi$$
−0.710748 + 0.703446i $$0.751644\pi$$
$$234$$ −55627.3 −0.0664122
$$235$$ 637317. 527347.i 0.752811 0.622912i
$$236$$ 487229. 0.569447
$$237$$ 811661.i 0.938650i
$$238$$ 7854.24i 0.00898797i
$$239$$ −770619. −0.872659 −0.436330 0.899787i $$-0.643722\pi$$
−0.436330 + 0.899787i $$0.643722\pi$$
$$240$$ 333510. 275963.i 0.373750 0.309259i
$$241$$ −1.42541e6 −1.58087 −0.790434 0.612547i $$-0.790145\pi$$
−0.790434 + 0.612547i $$0.790145\pi$$
$$242$$ 19288.2i 0.0211716i
$$243$$ 59049.0i 0.0641500i
$$244$$ 1.24372e6 1.33736
$$245$$ −326244. 394277.i −0.347238 0.419649i
$$246$$ 72941.7 0.0768490
$$247$$ 828211.i 0.863771i
$$248$$ 6863.86i 0.00708662i
$$249$$ −97712.7 −0.0998741
$$250$$ −110935. 201640.i −0.112259 0.204046i
$$251$$ −668745. −0.670002 −0.335001 0.942218i $$-0.608737\pi$$
−0.335001 + 0.942218i $$0.608737\pi$$
$$252$$ 214447.i 0.212725i
$$253$$ 23220.4i 0.0228070i
$$254$$ −76348.5 −0.0742534
$$255$$ 21859.1 + 26417.4i 0.0210514 + 0.0254413i
$$256$$ 524969. 0.500650
$$257$$ 1.08696e6i 1.02655i −0.858223 0.513276i $$-0.828432\pi$$
0.858223 0.513276i $$-0.171568\pi$$
$$258$$ 16701.5i 0.0156209i
$$259$$ −1.26366e6 −1.17053
$$260$$ 679487. 562241.i 0.623373 0.515809i
$$261$$ −344491. −0.313024
$$262$$ 163821.i 0.147440i
$$263$$ 865881.i 0.771914i 0.922517 + 0.385957i $$0.126129\pi$$
−0.922517 + 0.385957i $$0.873871\pi$$
$$264$$ 89328.3 0.0788823
$$265$$ 471110. 389819.i 0.412105 0.340996i
$$266$$ 183098. 0.158664
$$267$$ 1.01582e6i 0.872049i
$$268$$ 37952.2i 0.0322775i
$$269$$ −455847. −0.384094 −0.192047 0.981386i $$-0.561513\pi$$
−0.192047 + 0.981386i $$0.561513\pi$$
$$270$$ 34226.1 + 41363.4i 0.0285725 + 0.0345308i
$$271$$ 1.93670e6 1.60191 0.800955 0.598725i $$-0.204326\pi$$
0.800955 + 0.598725i $$0.204326\pi$$
$$272$$ 58638.1i 0.0480571i
$$273$$ 410417.i 0.333288i
$$274$$ −538403. −0.433243
$$275$$ −70775.5 + 371442.i −0.0564353 + 0.296183i
$$276$$ −52270.8 −0.0413034
$$277$$ 1.67891e6i 1.31470i 0.753584 + 0.657352i $$0.228323\pi$$
−0.753584 + 0.657352i $$0.771677\pi$$
$$278$$ 498591.i 0.386930i
$$279$$ 6777.85 0.00521292
$$280$$ −255724. 309051.i −0.194929 0.235578i
$$281$$ −1.66433e6 −1.25740 −0.628700 0.777648i $$-0.716413\pi$$
−0.628700 + 0.777648i $$0.716413\pi$$
$$282$$ 175449.i 0.131380i
$$283$$ 529051.i 0.392673i 0.980537 + 0.196337i $$0.0629045\pi$$
−0.980537 + 0.196337i $$0.937095\pi$$
$$284$$ 1.44175e6 1.06070
$$285$$ 615842. 509578.i 0.449115 0.371620i
$$286$$ 83097.5 0.0600721
$$287$$ 538163.i 0.385664i
$$288$$ 304430.i 0.216275i
$$289$$ 1.41521e6 0.996729
$$290$$ −241314. + 199675.i −0.168495 + 0.139421i
$$291$$ 872945. 0.604302
$$292$$ 222686.i 0.152839i
$$293$$ 1.17586e6i 0.800178i −0.916476 0.400089i $$-0.868979\pi$$
0.916476 0.400089i $$-0.131021\pi$$
$$294$$ 108542. 0.0732369
$$295$$ −573733. 693375.i −0.383844 0.463888i
$$296$$ 1.18493e6 0.786071
$$297$$ 88209.0i 0.0580259i
$$298$$ 357436.i 0.233162i
$$299$$ −100038. −0.0647123
$$300$$ −836144. 159321.i −0.536386 0.102204i
$$301$$ −123224. −0.0783931
$$302$$ 193328.i 0.121977i
$$303$$ 501757.i 0.313969i
$$304$$ 1.36697e6 0.848349
$$305$$ −1.46453e6 1.76993e6i −0.901464 1.08945i
$$306$$ −7272.55 −0.00444000
$$307$$ 1.53089e6i 0.927037i −0.886087 0.463518i $$-0.846587\pi$$
0.886087 0.463518i $$-0.153413\pi$$
$$308$$ 320346.i 0.192417i
$$309$$ −967223. −0.576276
$$310$$ 4747.83 3928.59i 0.00280602 0.00232184i
$$311$$ −1.11621e6 −0.654400 −0.327200 0.944955i $$-0.606105\pi$$
−0.327200 + 0.944955i $$0.606105\pi$$
$$312$$ 384844.i 0.223820i
$$313$$ 864587.i 0.498824i 0.968397 + 0.249412i $$0.0802374\pi$$
−0.968397 + 0.249412i $$0.919763\pi$$
$$314$$ −481596. −0.275651
$$315$$ −305179. + 252520.i −0.173292 + 0.143390i
$$316$$ −2.72938e6 −1.53761
$$317$$ 1.80604e6i 1.00943i 0.863285 + 0.504717i $$0.168403\pi$$
−0.863285 + 0.504717i $$0.831597\pi$$
$$318$$ 129694.i 0.0719202i
$$319$$ 514611. 0.283140
$$320$$ −804746. 972563.i −0.439323 0.530937i
$$321$$ 231058. 0.125158
$$322$$ 22116.0i 0.0118869i
$$323$$ 108278.i 0.0577476i
$$324$$ 198565. 0.105085
$$325$$ −1.60025e6 304915.i −0.840386 0.160129i
$$326$$ −21994.5 −0.0114623
$$327$$ 889466.i 0.460003i
$$328$$ 504630.i 0.258994i
$$329$$ −1.29446e6 −0.659326
$$330$$ −51127.9 61789.8i −0.0258448 0.0312343i
$$331$$ 1.85701e6 0.931634 0.465817 0.884881i $$-0.345761\pi$$
0.465817 + 0.884881i $$0.345761\pi$$
$$332$$ 328580.i 0.163605i
$$333$$ 1.17008e6i 0.578235i
$$334$$ −749068. −0.367413
$$335$$ 54009.8 44690.3i 0.0262942 0.0217571i
$$336$$ −677397. −0.327337
$$337$$ 2.18068e6i 1.04597i −0.852343 0.522983i $$-0.824819\pi$$
0.852343 0.522983i $$-0.175181\pi$$
$$338$$ 131145.i 0.0624395i
$$339$$ 108495. 0.0512757
$$340$$ 88834.2 73505.8i 0.0416757 0.0344845i
$$341$$ −10124.9 −0.00471527
$$342$$ 169538.i 0.0783792i
$$343$$ 2.27108e6i 1.04231i
$$344$$ 115546. 0.0526451
$$345$$ 61551.0 + 74386.4i 0.0278411 + 0.0336470i
$$346$$ −727478. −0.326685
$$347$$ 2.59930e6i 1.15886i −0.815021 0.579432i $$-0.803274\pi$$
0.815021 0.579432i $$-0.196726\pi$$
$$348$$ 1.15843e6i 0.512767i
$$349$$ −1.17216e6 −0.515138 −0.257569 0.966260i $$-0.582921\pi$$
−0.257569 + 0.966260i $$0.582921\pi$$
$$350$$ −67409.5 + 353777.i −0.0294138 + 0.154369i
$$351$$ 380022. 0.164642
$$352$$ 454765.i 0.195628i
$$353$$ 1.57881e6i 0.674364i 0.941440 + 0.337182i $$0.109474\pi$$
−0.941440 + 0.337182i $$0.890526\pi$$
$$354$$ 190882. 0.0809574
$$355$$ −1.69772e6 2.05175e6i −0.714982 0.864079i
$$356$$ −3.41593e6 −1.42851
$$357$$ 53656.8i 0.0222820i
$$358$$ 237085.i 0.0977678i
$$359$$ −3.19520e6 −1.30847 −0.654233 0.756293i $$-0.727008\pi$$
−0.654233 + 0.756293i $$0.727008\pi$$
$$360$$ 286163. 236785.i 0.116374 0.0962939i
$$361$$ 48073.9 0.0194152
$$362$$ 806834.i 0.323603i
$$363$$ 131769.i 0.0524864i
$$364$$ −1.38012e6 −0.545962
$$365$$ −316904. + 262222.i −0.124507 + 0.103024i
$$366$$ 487252. 0.190130
$$367$$ 2.52046e6i 0.976819i −0.872615 0.488409i $$-0.837577\pi$$
0.872615 0.488409i $$-0.162423\pi$$
$$368$$ 165114.i 0.0635570i
$$369$$ −498307. −0.190516
$$370$$ −678203. 819631.i −0.257546 0.311253i
$$371$$ −956879. −0.360929
$$372$$ 22792.0i 0.00853934i
$$373$$ 1.66879e6i 0.621053i 0.950565 + 0.310527i $$0.100505\pi$$
−0.950565 + 0.310527i $$0.899495\pi$$
$$374$$ 10863.9 0.00401614
$$375$$ 757865. + 1.37752e6i 0.278300 + 0.505848i
$$376$$ 1.21381e6 0.442772
$$377$$ 2.21705e6i 0.803380i
$$378$$ 84013.9i 0.0302428i
$$379$$ 3.13030e6 1.11941 0.559704 0.828692i $$-0.310915\pi$$
0.559704 + 0.828692i $$0.310915\pi$$
$$380$$ −1.71357e6 2.07090e6i −0.608754 0.735699i
$$381$$ 521581. 0.184081
$$382$$ 86169.0i 0.0302129i
$$383$$ 4.30969e6i 1.50124i 0.660737 + 0.750618i $$0.270244\pi$$
−0.660737 + 0.750618i $$0.729756\pi$$
$$384$$ 1.35016e6 0.467257
$$385$$ 455884. 377221.i 0.156748 0.129701i
$$386$$ 870875. 0.297500
$$387$$ 114098.i 0.0387258i
$$388$$ 2.93546e6i 0.989914i
$$389$$ 2.45755e6 0.823432 0.411716 0.911312i $$-0.364929\pi$$
0.411716 + 0.911312i $$0.364929\pi$$
$$390$$ 266203. 220269.i 0.0886239 0.0733318i
$$391$$ −13078.7 −0.00432636
$$392$$ 750923.i 0.246820i
$$393$$ 1.11915e6i 0.365518i
$$394$$ 777518. 0.252330
$$395$$ 3.21396e6 + 3.88418e6i 1.03645 + 1.25258i
$$396$$ −296622. −0.0950528
$$397$$ 5.93203e6i 1.88898i −0.328544 0.944489i $$-0.606558\pi$$
0.328544 0.944489i $$-0.393442\pi$$
$$398$$ 451543.i 0.142887i
$$399$$ −1.25085e6 −0.393343
$$400$$ −503265. + 2.64122e6i −0.157270 + 0.825382i
$$401$$ 4.56758e6 1.41849 0.709243 0.704964i $$-0.249037\pi$$
0.709243 + 0.704964i $$0.249037\pi$$
$$402$$ 14868.6i 0.00458885i
$$403$$ 43620.2i 0.0133791i
$$404$$ −1.68727e6 −0.514316
$$405$$ −233818. 282577.i −0.0708339 0.0856051i
$$406$$ 490136. 0.147571
$$407$$ 1.74789e6i 0.523033i
$$408$$ 50313.5i 0.0149635i
$$409$$ 5.87934e6 1.73788 0.868941 0.494915i $$-0.164801\pi$$
0.868941 + 0.494915i $$0.164801\pi$$
$$410$$ −349061. + 288830.i −0.102551 + 0.0848560i
$$411$$ 3.67814e6 1.07405
$$412$$ 3.25249e6i 0.944003i
$$413$$ 1.40833e6i 0.406282i
$$414$$ −20478.1 −0.00587205
$$415$$ 467601. 386916.i 0.133277 0.110280i
$$416$$ 1.95922e6 0.555072
$$417$$ 3.40616e6i 0.959236i
$$418$$ 253260.i 0.0708966i
$$419$$ −6.12464e6 −1.70430 −0.852149 0.523299i $$-0.824701\pi$$
−0.852149 + 0.523299i $$0.824701\pi$$
$$420$$ 849152. + 1.02623e6i 0.234889 + 0.283871i
$$421$$ −2.83114e6 −0.778495 −0.389248 0.921133i $$-0.627265\pi$$
−0.389248 + 0.921133i $$0.627265\pi$$
$$422$$ 282789.i 0.0773003i
$$423$$ 1.19860e6i 0.325703i
$$424$$ 897256. 0.242383
$$425$$ −209212. 39863.7i −0.0561842 0.0107055i
$$426$$ 564834. 0.150799
$$427$$ 3.59494e6i 0.954161i
$$428$$ 776983.i 0.205023i
$$429$$ −567687. −0.148924
$$430$$ −66133.6 79924.7i −0.0172485 0.0208454i
$$431$$ 6.20538e6 1.60907 0.804536 0.593904i $$-0.202414\pi$$
0.804536 + 0.593904i $$0.202414\pi$$
$$432$$ 627230.i 0.161703i
$$433$$ 422736.i 0.108355i 0.998531 + 0.0541775i $$0.0172537\pi$$
−0.998531 + 0.0541775i $$0.982746\pi$$
$$434$$ −9643.40 −0.00245757
$$435$$ 1.64855e6 1.36409e6i 0.417715 0.345638i
$$436$$ −2.99102e6 −0.753535
$$437$$ 304890.i 0.0763730i
$$438$$ 87241.7i 0.0217290i
$$439$$ 4.07012e6 1.00797 0.503983 0.863713i $$-0.331867\pi$$
0.503983 + 0.863713i $$0.331867\pi$$
$$440$$ −427478. + 353717.i −0.105265 + 0.0871011i
$$441$$ −741514. −0.181561
$$442$$ 46804.0i 0.0113953i
$$443$$ 4.95245e6i 1.19898i 0.800384 + 0.599488i $$0.204629\pi$$
−0.800384 + 0.599488i $$0.795371\pi$$
$$444$$ −3.93464e6 −0.947212
$$445$$ 4.02240e6 + 4.86120e6i 0.962908 + 1.16371i
$$446$$ −156438. −0.0372397
$$447$$ 2.44185e6i 0.578029i
$$448$$ 1.97539e6i 0.465004i
$$449$$ −7.34037e6 −1.71831 −0.859157 0.511713i $$-0.829011\pi$$
−0.859157 + 0.511713i $$0.829011\pi$$
$$450$$ −327576. 62417.1i −0.0762572 0.0145302i
$$451$$ 744385. 0.172328
$$452$$ 364838.i 0.0839952i
$$453$$ 1.32073e6i 0.302392i
$$454$$ −2876.12 −0.000654888
$$455$$ 1.62514e6 + 1.96404e6i 0.368013 + 0.444756i
$$456$$ 1.17291e6 0.264150
$$457$$ 2.07655e6i 0.465106i −0.972584 0.232553i $$-0.925292\pi$$
0.972584 0.232553i $$-0.0747080\pi$$
$$458$$ 162969.i 0.0363029i
$$459$$ 49683.0 0.0110072
$$460$$ 250140. 206978.i 0.0551174 0.0456069i
$$461$$ −1.68917e6 −0.370186 −0.185093 0.982721i $$-0.559259\pi$$
−0.185093 + 0.982721i $$0.559259\pi$$
$$462$$ 125502.i 0.0273556i
$$463$$ 1.35953e6i 0.294739i −0.989082 0.147369i $$-0.952919\pi$$
0.989082 0.147369i $$-0.0470806\pi$$
$$464$$ 3.65925e6 0.789037
$$465$$ −32435.2 + 26838.5i −0.00695639 + 0.00575606i
$$466$$ 1.53593e6 0.327648
$$467$$ 8.47580e6i 1.79841i 0.437528 + 0.899205i $$0.355854\pi$$
−0.437528 + 0.899205i $$0.644146\pi$$
$$468$$ 1.27791e6i 0.269702i
$$469$$ −109700. −0.0230290
$$470$$ −694733. 839608.i −0.145069 0.175320i
$$471$$ 3.29006e6 0.683363
$$472$$ 1.32057e6i 0.272840i
$$473$$ 170442.i 0.0350288i
$$474$$ −1.06929e6 −0.218600
$$475$$ −929302. + 4.87714e6i −0.188983 + 0.991817i
$$476$$ −180433. −0.0365004
$$477$$ 886013.i 0.178297i
$$478$$ 1.01522e6i 0.203232i
$$479$$ 3.52896e6 0.702762 0.351381 0.936233i $$-0.385712\pi$$
0.351381 + 0.936233i $$0.385712\pi$$
$$480$$ −1.20546e6 1.45684e6i −0.238808 0.288608i
$$481$$ −7.53028e6 −1.48405
$$482$$ 1.87784e6i 0.368165i
$$483$$ 151087.i 0.0294687i
$$484$$ 443101. 0.0859785
$$485$$ −4.17745e6 + 3.45663e6i −0.806413 + 0.667265i
$$486$$ 77791.8 0.0149397
$$487$$ 4.66713e6i 0.891719i −0.895103 0.445859i $$-0.852898\pi$$
0.895103 0.445859i $$-0.147102\pi$$
$$488$$ 3.37094e6i 0.640768i
$$489$$ 150257. 0.0284160
$$490$$ −519425. + 429798.i −0.0977311 + 0.0808675i
$$491$$ −7.22516e6 −1.35252 −0.676260 0.736663i $$-0.736400\pi$$
−0.676260 + 0.736663i $$0.736400\pi$$
$$492$$ 1.67566e6i 0.312086i
$$493$$ 289850.i 0.0537102i
$$494$$ 1.09109e6 0.201162
$$495$$ 349284. + 422122.i 0.0640717 + 0.0774328i
$$496$$ −71995.6 −0.0131402
$$497$$ 4.16734e6i 0.756777i
$$498$$ 128728.i 0.0232594i
$$499$$ 1.04815e7 1.88440 0.942202 0.335046i $$-0.108752\pi$$
0.942202 + 0.335046i $$0.108752\pi$$
$$500$$ 4.63221e6 2.54848e6i 0.828635 0.455886i
$$501$$ 5.11731e6 0.910852
$$502$$ 881012.i 0.156035i
$$503$$ 8.37701e6i 1.47628i −0.674647 0.738140i $$-0.735704\pi$$
0.674647 0.738140i $$-0.264296\pi$$
$$504$$ −581230. −0.101923
$$505$$ 1.98682e6 + 2.40114e6i 0.346682 + 0.418977i
$$506$$ 30590.8 0.00531146
$$507$$ 895926.i 0.154793i
$$508$$ 1.75393e6i 0.301545i
$$509$$ −3.17550e6 −0.543272 −0.271636 0.962400i $$-0.587565\pi$$
−0.271636 + 0.962400i $$0.587565\pi$$
$$510$$ 34802.6 28797.4i 0.00592497 0.00490261i
$$511$$ 643668. 0.109046
$$512$$ 5.49216e6i 0.925908i
$$513$$ 1.15821e6i 0.194309i
$$514$$ −1.43198e6 −0.239071
$$515$$ 4.62862e6 3.82995e6i 0.769012 0.636318i
$$516$$ −383678. −0.0634371
$$517$$ 1.79050e6i 0.294610i
$$518$$ 1.66477e6i 0.272602i
$$519$$ 4.96982e6 0.809884
$$520$$ −1.52388e6 1.84166e6i −0.247140 0.298677i
$$521$$ 3.72507e6 0.601230 0.300615 0.953746i $$-0.402808\pi$$
0.300615 + 0.953746i $$0.402808\pi$$
$$522$$ 453837.i 0.0728993i
$$523$$ 3.77963e6i 0.604219i −0.953273 0.302110i $$-0.902309\pi$$
0.953273 0.302110i $$-0.0976909\pi$$
$$524$$ −3.76339e6 −0.598758
$$525$$ 460513. 2.41685e6i 0.0729195 0.382694i
$$526$$ 1.14072e6 0.179769
$$527$$ 5702.79i 0.000894460i
$$528$$ 936973.i 0.146266i
$$529$$ 6.39952e6 0.994278
$$530$$ −513553. 620646.i −0.0794137 0.0959741i
$$531$$ −1.30403e6 −0.200701
$$532$$ 4.20624e6i 0.644340i
$$533$$ 3.20696e6i 0.488962i
$$534$$ −1.33826e6 −0.203089
$$535$$ −1.10572e6 + 914929.i −0.167017 + 0.138198i
$$536$$ 102865. 0.0154652
$$537$$ 1.61966e6i 0.242375i
$$538$$ 600538.i 0.0894509i
$$539$$ 1.10769e6 0.164228
$$540$$ −950227. + 786264.i −0.140231 + 0.116034i
$$541$$ −6.08511e6 −0.893871 −0.446936 0.894566i $$-0.647485\pi$$
−0.446936 + 0.894566i $$0.647485\pi$$
$$542$$ 2.55142e6i 0.373065i
$$543$$ 5.51195e6i 0.802243i
$$544$$ 256143. 0.0371095
$$545$$ 3.52205e6 + 4.25652e6i 0.507931 + 0.613851i
$$546$$ −540689. −0.0776186
$$547$$ 2.49034e6i 0.355870i 0.984042 + 0.177935i $$0.0569416\pi$$
−0.984042 + 0.177935i $$0.943058\pi$$
$$548$$ 1.23685e7i 1.75941i
$$549$$ −3.32870e6 −0.471350
$$550$$ 489342. + 93240.4i 0.0689773 + 0.0131431i
$$551$$ 6.75698e6 0.948143
$$552$$ 141673.i 0.0197897i
$$553$$ 7.88922e6i 1.09704i
$$554$$ 2.21181e6 0.306178
$$555$$ 4.63320e6 + 5.59937e6i 0.638481 + 0.771626i
$$556$$ −1.14540e7 −1.57133
$$557$$ 5.36235e6i 0.732347i −0.930547 0.366173i $$-0.880668\pi$$
0.930547 0.366173i $$-0.119332\pi$$
$$558$$ 8929.21i 0.00121403i
$$559$$ −734300. −0.0993903
$$560$$ 3.24167e6 2.68231e6i 0.436816 0.361443i
$$561$$ −74217.9 −0.00995638
$$562$$ 2.19261e6i 0.292833i
$$563$$ 479316.i 0.0637310i −0.999492 0.0318655i $$-0.989855\pi$$
0.999492 0.0318655i $$-0.0101448\pi$$
$$564$$ −4.03054e6 −0.533538
$$565$$ −519201. + 429612.i −0.0684249 + 0.0566181i
$$566$$ 696978. 0.0914488
$$567$$ 573947.i 0.0749746i
$$568$$ 3.90768e6i 0.508215i
$$569$$ −3.08333e6 −0.399245 −0.199623 0.979873i $$-0.563972\pi$$
−0.199623 + 0.979873i $$0.563972\pi$$
$$570$$ −671324. 811317.i −0.0865456 0.104593i
$$571$$ −5.85646e6 −0.751701 −0.375850 0.926680i $$-0.622649\pi$$
−0.375850 + 0.926680i $$0.622649\pi$$
$$572$$ 1.90897e6i 0.243955i
$$573$$ 588670.i 0.0749007i
$$574$$ 708982. 0.0898164
$$575$$ −589101. 112249.i −0.0743054 0.0141583i
$$576$$ −1.82909e6 −0.229710
$$577$$ 5.66144e6i 0.707925i 0.935260 + 0.353963i $$0.115166\pi$$
−0.935260 + 0.353963i $$0.884834\pi$$
$$578$$ 1.86442e6i 0.232126i
$$579$$ −5.94945e6 −0.737531
$$580$$ −4.58706e6 5.54362e6i −0.566193 0.684263i
$$581$$ −949753. −0.116727
$$582$$ 1.15003e6i 0.140735i
$$583$$ 1.32355e6i 0.161276i
$$584$$ −603562. −0.0732301
$$585$$ −1.81859e6 + 1.50479e6i −0.219707 + 0.181796i
$$586$$ −1.54909e6 −0.186352
$$587$$ 1.39978e7i 1.67674i 0.545104 + 0.838368i $$0.316490\pi$$
−0.545104 + 0.838368i $$0.683510\pi$$
$$588$$ 2.49350e6i 0.297417i
$$589$$ −132943. −0.0157899
$$590$$ −913460. + 755842.i −0.108034 + 0.0893925i
$$591$$ −5.31167e6 −0.625551
$$592$$ 1.24288e7i 1.45755i
$$593$$ 1.27936e7i 1.49402i −0.664810 0.747012i $$-0.731488\pi$$
0.664810 0.747012i $$-0.268512\pi$$
$$594$$ −116208. −0.0135135
$$595$$ 212467. + 256773.i 0.0246036 + 0.0297343i
$$596$$ 8.21124e6 0.946876
$$597$$ 3.08475e6i 0.354229i
$$598$$ 131791.i 0.0150707i
$$599$$ 1.21733e7 1.38625 0.693125 0.720818i $$-0.256234\pi$$
0.693125 + 0.720818i $$0.256234\pi$$
$$600$$ −431819. + 2.26626e6i −0.0489692 + 0.256999i
$$601$$ −6.74801e6 −0.762060 −0.381030 0.924563i $$-0.624431\pi$$
−0.381030 + 0.924563i $$0.624431\pi$$
$$602$$ 162336.i 0.0182568i
$$603$$ 101576.i 0.0113762i
$$604$$ −4.44125e6 −0.495351
$$605$$ −521770. 630577.i −0.0579550 0.0700406i
$$606$$ −661020. −0.0731195
$$607$$ 1.16658e7i 1.28512i −0.766234 0.642561i $$-0.777872\pi$$
0.766234 0.642561i $$-0.222128\pi$$
$$608$$ 5.97120e6i 0.655092i
$$609$$ −3.34840e6 −0.365843
$$610$$ −2.33173e6 + 1.92939e6i −0.253719 + 0.209940i
$$611$$ −7.71382e6 −0.835923
$$612$$ 167070.i 0.0180310i
$$613$$ 1.36615e7i 1.46841i −0.678928 0.734204i $$-0.737555\pi$$
0.678928 0.734204i $$-0.262445\pi$$
$$614$$ −2.01681e6 −0.215895
$$615$$ 2.38464e6 1.97316e6i 0.254234 0.210366i
$$616$$ 868258. 0.0921928
$$617$$ 1.15742e7i 1.22399i −0.790862 0.611995i $$-0.790367\pi$$
0.790862 0.611995i $$-0.209633\pi$$
$$618$$ 1.27423e6i 0.134207i
$$619$$ −9.22658e6 −0.967863 −0.483932 0.875106i $$-0.660792\pi$$
−0.483932 + 0.875106i $$0.660792\pi$$
$$620$$ 90250.1 + 109070.i 0.00942906 + 0.0113953i
$$621$$ 139898. 0.0145574
$$622$$ 1.47050e6i 0.152402i
$$623$$ 9.87366e6i 1.01920i
$$624$$ −4.03667e6 −0.415013
$$625$$ −9.08136e6 3.59115e6i −0.929931 0.367734i
$$626$$ 1.13902e6 0.116170
$$627$$ 1.73016e6i 0.175759i
$$628$$ 1.10635e7i 1.11942i
$$629$$ −984487. −0.0992164
$$630$$ 332673. + 402046.i 0.0333938 + 0.0403575i
$$631$$ 1.03002e7 1.02985 0.514923 0.857237i $$-0.327821\pi$$
0.514923 + 0.857237i $$0.327821\pi$$
$$632$$ 7.39764e6i 0.736717i
$$633$$ 1.93189e6i 0.191635i
$$634$$ 2.37929e6 0.235085
$$635$$ −2.49601e6 + 2.06532e6i −0.245647 + 0.203261i
$$636$$ −2.97941e6 −0.292070
$$637$$ 4.77217e6i 0.465980i
$$638$$ 677954.i 0.0659399i
$$639$$ −3.85871e6 −0.373844
$$640$$ −6.46114e6 + 5.34626e6i −0.623532 + 0.515941i
$$641$$ −3.06165e6 −0.294313 −0.147157 0.989113i $$-0.547012\pi$$
−0.147157 + 0.989113i $$0.547012\pi$$
$$642$$ 304399.i 0.0291478i
$$643$$ 1.62044e6i 0.154563i −0.997009 0.0772813i $$-0.975376\pi$$
0.997009 0.0772813i $$-0.0246240\pi$$
$$644$$ −508064. −0.0482729
$$645$$ 451797. + 546012.i 0.0427606 + 0.0516777i
$$646$$ 142647. 0.0134487
$$647$$ 1.57992e6i 0.148380i −0.997244 0.0741900i $$-0.976363\pi$$
0.997244 0.0741900i $$-0.0236371\pi$$
$$648$$ 538185.i 0.0503494i
$$649$$ 1.94799e6 0.181541
$$650$$ −401698. + 2.10818e6i −0.0372921 + 0.195716i
$$651$$ 65879.6 0.00609254
$$652$$ 505272.i 0.0465486i
$$653$$ 1.29080e6i 0.118462i 0.998244 + 0.0592308i $$0.0188648\pi$$
−0.998244 + 0.0592308i $$0.981135\pi$$
$$654$$ −1.17179e6 −0.107129
$$655$$ 4.43155e6 + 5.35568e6i 0.403601 + 0.487766i
$$656$$ 5.29311e6 0.480232
$$657$$ 595999.i 0.0538681i
$$658$$ 1.70534e6i 0.153549i
$$659$$ −1.44401e7 −1.29525 −0.647627 0.761957i $$-0.724239\pi$$
−0.647627 + 0.761957i $$0.724239\pi$$
$$660$$ 1.41947e6 1.17454e6i 0.126843 0.104956i
$$661$$ 8.80403e6 0.783751 0.391875 0.920018i $$-0.371826\pi$$
0.391875 + 0.920018i $$0.371826\pi$$
$$662$$ 2.44645e6i 0.216966i
$$663$$ 319745.i 0.0282501i
$$664$$ 890574. 0.0783880
$$665$$ 5.98589e6 4.95302e6i 0.524898 0.434326i
$$666$$ −1.54147e6 −0.134664
$$667$$ 816163.i 0.0710334i
$$668$$ 1.72081e7i 1.49208i
$$669$$ 1.06872e6 0.0923207
$$670$$ −58875.5 71153.1i −0.00506697 0.00612360i
$$671$$ 4.97250e6 0.426352
$$672$$ 2.95901e6i 0.252769i
$$673$$ 1.43891e7i 1.22461i 0.790623 + 0.612303i $$0.209757\pi$$
−0.790623 + 0.612303i $$0.790243\pi$$
$$674$$ −2.87286e6 −0.243593
$$675$$ 2.23786e6 + 426408.i 0.189049 + 0.0360218i
$$676$$ 3.01274e6 0.253569
$$677$$ 1.21710e7i 1.02060i −0.859997 0.510299i $$-0.829535\pi$$
0.859997 0.510299i $$-0.170465\pi$$
$$678$$ 142933.i 0.0119415i
$$679$$ 8.48489e6 0.706272
$$680$$ −199228. 240774.i −0.0165226 0.0199681i
$$681$$ 19648.4 0.00162353
$$682$$ 13338.7i 0.00109813i
$$683$$ 5.96383e6i 0.489186i −0.969626 0.244593i $$-0.921346\pi$$
0.969626 0.244593i $$-0.0786543\pi$$
$$684$$ −3.89473e6 −0.318300
$$685$$ −1.76017e7 + 1.45645e7i −1.43327 + 1.18596i
$$686$$ 2.99194e6 0.242741
$$687$$ 1.11333e6i 0.0899982i
$$688$$ 1.21197e6i 0.0976158i
$$689$$ −5.70212e6 −0.457602
$$690$$ 97997.5 81088.0i 0.00783596 0.00648386i
$$691$$ −1.10524e7 −0.880565 −0.440283 0.897859i $$-0.645122\pi$$
−0.440283 + 0.897859i $$0.645122\pi$$
$$692$$ 1.67121e7i 1.32668i
$$693$$ 857378.i 0.0678171i
$$694$$ −3.42434e6 −0.269885
$$695$$ 1.34875e7 + 1.63001e7i 1.05918 + 1.28005i
$$696$$ 3.13977e6 0.245682
$$697$$ 419269.i 0.0326897i
$$698$$ 1.54422e6i 0.119969i
$$699$$ −1.04928e7 −0.812270
$$700$$ −8.12719e6 1.54857e6i −0.626896 0.119450i
$$701$$ −9.86637e6 −0.758337 −0.379168 0.925328i $$-0.623790\pi$$
−0.379168 + 0.925328i $$0.623790\pi$$
$$702$$ 500645.i 0.0383431i
$$703$$ 2.29503e7i 1.75146i
$$704$$ 2.73235e6 0.207780
$$705$$ 4.74612e6 + 5.73585e6i 0.359639 + 0.434635i
$$706$$ 2.07995e6 0.157051
$$707$$ 4.87700e6i 0.366948i
$$708$$ 4.38506e6i 0.328770i
$$709$$ 1.65852e7 1.23910 0.619550 0.784957i $$-0.287315\pi$$
0.619550 + 0.784957i $$0.287315\pi$$
$$710$$ −2.70300e6 + 2.23659e6i −0.201233 + 0.166510i
$$711$$ 7.30495e6 0.541930
$$712$$ 9.25844e6i 0.684444i
$$713$$ 16058.0i 0.00118295i
$$714$$ −70688.1 −0.00518921
$$715$$ 2.71665e6 2.24789e6i 0.198733 0.164441i
$$716$$ 5.44646e6 0.397038
$$717$$ 6.93557e6i 0.503830i
$$718$$ 4.20940e6i 0.304725i
$$719$$ 1.70621e6 0.123086 0.0615430 0.998104i $$-0.480398\pi$$
0.0615430 + 0.998104i $$0.480398\pi$$
$$720$$ 2.48366e6 + 3.00159e6i 0.178551 + 0.215784i
$$721$$ −9.40126e6 −0.673516
$$722$$ 63333.1i 0.00452156i
$$723$$ 1.28286e7i 0.912715i
$$724$$ 1.85351e7 1.31416
$$725$$ −2.48766e6 + 1.30557e7i −0.175770 + 0.922474i
$$726$$ 173594. 0.0122234
$$727$$ 4.79877e6i 0.336739i −0.985724 0.168370i $$-0.946150\pi$$
0.985724 0.168370i $$-0.0538502\pi$$
$$728$$ 3.74063e6i 0.261587i
$$729$$ −531441. −0.0370370
$$730$$ 345454. + 417493.i 0.0239929 + 0.0289962i
$$731$$ −96000.4 −0.00664476
$$732$$ 1.11935e7i 0.772123i
$$733$$ 2.10050e7i 1.44398i −0.691902 0.721991i $$-0.743227\pi$$
0.691902 0.721991i $$-0.256773\pi$$
$$734$$ −3.32048e6 −0.227489
$$735$$ 3.54849e6 2.93620e6i 0.242285 0.200478i
$$736$$ 721250. 0.0490785
$$737$$ 151737.i 0.0102901i
$$738$$ 656475.i 0.0443688i
$$739$$ 1.45144e7 0.977660 0.488830 0.872379i $$-0.337424\pi$$
0.488830 + 0.872379i $$0.337424\pi$$
$$740$$ 1.88291e7 1.55801e7i 1.26401 1.04590i
$$741$$ −7.45390e6 −0.498698
$$742$$ 1.26060e6i 0.0840560i
$$743$$ 1.33510e7i 0.887245i 0.896214 + 0.443622i $$0.146307\pi$$
−0.896214 + 0.443622i $$0.853693\pi$$
$$744$$ −61774.7 −0.00409146
$$745$$ −9.66907e6 1.16854e7i −0.638255 0.771353i
$$746$$ 2.19848e6 0.144636
$$747$$ 879414.i 0.0576623i
$$748$$ 249573.i 0.0163096i
$$749$$ 2.24585e6 0.146277
$$750$$ 1.81476e6 998419.i 0.117806 0.0648127i
$$751$$ 1.03902e7 0.672242 0.336121 0.941819i $$-0.390885\pi$$
0.336121 + 0.941819i $$0.390885\pi$$
$$752$$ 1.27317e7i 0.820999i
$$753$$ 6.01870e6i 0.386826i
$$754$$ 2.92076e6 0.187097
$$755$$ 5.22976e6 + 6.32034e6i 0.333898 + 0.403527i
$$756$$ 1.93002e6 0.122817
$$757$$ 1.09141e7i 0.692227i 0.938193 + 0.346113i $$0.112499\pi$$
−0.938193 + 0.346113i $$0.887501\pi$$
$$758$$ 4.12390e6i 0.260696i
$$759$$ −208983. −0.0131676
$$760$$ −5.61291e6 + 4.64440e6i −0.352496 + 0.291673i
$$761$$ 1.04145e7 0.651894 0.325947 0.945388i $$-0.394317\pi$$
0.325947 + 0.945388i $$0.394317\pi$$
$$762$$ 687136.i 0.0428702i
$$763$$ 8.64548e6i 0.537623i
$$764$$ 1.97953e6 0.122696
$$765$$ −237757. + 196732.i −0.0146886 + 0.0121540i
$$766$$ 5.67763e6 0.349619
$$767$$ 8.39232e6i 0.515103i
$$768$$ 4.72472e6i 0.289050i
$$769$$ 9.42825e6 0.574930 0.287465 0.957791i $$-0.407187\pi$$
0.287465 + 0.957791i $$0.407187\pi$$
$$770$$ −496955. 600587.i −0.0302058 0.0365047i
$$771$$ 9.78265e6 0.592681
$$772$$ 2.00063e7i 1.20816i
$$773$$ 1.18529e7i 0.713469i −0.934206 0.356734i $$-0.883890\pi$$
0.934206 0.356734i $$-0.116110\pi$$
$$774$$ −150314. −0.00901875
$$775$$ 48944.5 256870.i 0.00292718 0.0153624i
$$776$$ −7.95620e6 −0.474298