Properties

 Label 225.4.h.a.91.7 Level $225$ Weight $4$ Character 225.91 Analytic conductor $13.275$ Analytic rank $0$ Dimension $28$ CM no Inner twists $2$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 225.h (of order $$5$$, degree $$4$$, minimal)

Newform invariants

 Self dual: no Analytic conductor: $$13.2754297513$$ Analytic rank: $$0$$ Dimension: $$28$$ Relative dimension: $$7$$ over $$\Q(\zeta_{5})$$ Twist minimal: no (minimal twist has level 75) Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

 Embedding label 91.7 Character $$\chi$$ $$=$$ 225.91 Dual form 225.4.h.a.136.7

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(3.76530 + 2.73565i) q^{2} +(4.22155 + 12.9926i) q^{4} +(-5.34090 + 9.82216i) q^{5} -26.0445 q^{7} +(-8.14206 + 25.0587i) q^{8} +O(q^{10})$$ $$q+(3.76530 + 2.73565i) q^{2} +(4.22155 + 12.9926i) q^{4} +(-5.34090 + 9.82216i) q^{5} -26.0445 q^{7} +(-8.14206 + 25.0587i) q^{8} +(-46.9800 + 22.3725i) q^{10} +(2.03543 + 1.47883i) q^{11} +(-32.0534 + 23.2881i) q^{13} +(-98.0653 - 71.2486i) q^{14} +(-10.7917 + 7.84062i) q^{16} +(26.2638 - 80.8316i) q^{17} +(-44.1360 + 135.837i) q^{19} +(-150.162 - 27.9275i) q^{20} +(3.61845 + 11.1365i) q^{22} +(127.177 + 92.3993i) q^{23} +(-67.9495 - 104.918i) q^{25} -184.399 q^{26} +(-109.948 - 338.386i) q^{28} +(30.9737 + 95.3273i) q^{29} +(-53.5715 + 164.876i) q^{31} +148.703 q^{32} +(320.018 - 232.506i) q^{34} +(139.101 - 255.813i) q^{35} +(48.0520 - 34.9118i) q^{37} +(-537.786 + 390.725i) q^{38} +(-202.644 - 213.809i) q^{40} +(-287.546 + 208.914i) q^{41} +109.742 q^{43} +(-10.6211 + 32.6885i) q^{44} +(226.086 + 695.821i) q^{46} +(17.9575 + 55.2674i) q^{47} +335.317 q^{49} +(31.1696 - 580.935i) q^{50} +(-437.888 - 318.144i) q^{52} +(120.787 + 371.745i) q^{53} +(-25.3963 + 12.0941i) q^{55} +(212.056 - 652.641i) q^{56} +(-144.157 + 443.669i) q^{58} +(333.759 - 242.490i) q^{59} +(-290.142 - 210.800i) q^{61} +(-652.756 + 474.255i) q^{62} +(646.244 + 469.524i) q^{64} +(-57.5458 - 439.213i) q^{65} +(108.468 - 333.831i) q^{67} +1161.09 q^{68} +(1223.57 - 582.681i) q^{70} +(-52.7887 - 162.467i) q^{71} +(754.724 + 548.339i) q^{73} +276.437 q^{74} -1951.19 q^{76} +(-53.0119 - 38.5154i) q^{77} +(-405.819 - 1248.98i) q^{79} +(-19.3744 - 147.874i) q^{80} -1654.21 q^{82} +(202.066 - 621.896i) q^{83} +(653.668 + 689.680i) q^{85} +(413.211 + 300.216i) q^{86} +(-53.6301 + 38.9646i) q^{88} +(857.273 + 622.845i) q^{89} +(834.814 - 606.528i) q^{91} +(-663.624 + 2042.42i) q^{92} +(-83.5770 + 257.224i) q^{94} +(-1098.48 - 1159.00i) q^{95} +(198.234 + 610.103i) q^{97} +(1262.57 + 917.308i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8}+O(q^{10})$$ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 $$28 q - 30 q^{4} + 15 q^{5} - 54 q^{7} + 63 q^{8} + 165 q^{10} - 19 q^{11} + 4 q^{13} + 24 q^{14} - 66 q^{16} - 208 q^{17} + 42 q^{19} - 295 q^{20} - 89 q^{22} - 32 q^{23} + 95 q^{25} - 206 q^{26} - 482 q^{28} + 716 q^{29} + 637 q^{31} + 844 q^{32} - 90 q^{34} - 430 q^{35} + 216 q^{37} - 2314 q^{38} - 500 q^{40} + 38 q^{41} - 1392 q^{43} - 603 q^{44} + 1622 q^{46} + 536 q^{47} + 162 q^{49} + 2265 q^{50} - 1922 q^{52} - 1672 q^{53} - 1000 q^{55} - 3000 q^{56} - 827 q^{58} - 973 q^{59} - 2712 q^{61} - 1057 q^{62} + 4439 q^{64} + 4360 q^{65} + 2768 q^{67} + 1370 q^{68} + 3230 q^{70} + 1074 q^{71} - 1018 q^{73} + 1414 q^{74} - 11408 q^{76} - 1607 q^{77} - 1820 q^{79} + 1290 q^{80} + 1772 q^{82} - 4045 q^{83} + 1850 q^{85} + 3986 q^{86} + 2407 q^{88} - 4542 q^{89} + 4412 q^{91} + 1089 q^{92} + 5137 q^{94} + 720 q^{95} - 5977 q^{97} + 10689 q^{98}+O(q^{100})$$ 28 * q - 30 * q^4 + 15 * q^5 - 54 * q^7 + 63 * q^8 + 165 * q^10 - 19 * q^11 + 4 * q^13 + 24 * q^14 - 66 * q^16 - 208 * q^17 + 42 * q^19 - 295 * q^20 - 89 * q^22 - 32 * q^23 + 95 * q^25 - 206 * q^26 - 482 * q^28 + 716 * q^29 + 637 * q^31 + 844 * q^32 - 90 * q^34 - 430 * q^35 + 216 * q^37 - 2314 * q^38 - 500 * q^40 + 38 * q^41 - 1392 * q^43 - 603 * q^44 + 1622 * q^46 + 536 * q^47 + 162 * q^49 + 2265 * q^50 - 1922 * q^52 - 1672 * q^53 - 1000 * q^55 - 3000 * q^56 - 827 * q^58 - 973 * q^59 - 2712 * q^61 - 1057 * q^62 + 4439 * q^64 + 4360 * q^65 + 2768 * q^67 + 1370 * q^68 + 3230 * q^70 + 1074 * q^71 - 1018 * q^73 + 1414 * q^74 - 11408 * q^76 - 1607 * q^77 - 1820 * q^79 + 1290 * q^80 + 1772 * q^82 - 4045 * q^83 + 1850 * q^85 + 3986 * q^86 + 2407 * q^88 - 4542 * q^89 + 4412 * q^91 + 1089 * q^92 + 5137 * q^94 + 720 * q^95 - 5977 * q^97 + 10689 * q^98

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 3.76530 + 2.73565i 1.33123 + 0.967198i 0.999718 + 0.0237477i $$0.00755984\pi$$
0.331515 + 0.943450i $$0.392440\pi$$
$$3$$ 0 0
$$4$$ 4.22155 + 12.9926i 0.527694 + 1.62407i
$$5$$ −5.34090 + 9.82216i −0.477705 + 0.878520i
$$6$$ 0 0
$$7$$ −26.0445 −1.40627 −0.703136 0.711056i $$-0.748217\pi$$
−0.703136 + 0.711056i $$0.748217\pi$$
$$8$$ −8.14206 + 25.0587i −0.359832 + 1.10745i
$$9$$ 0 0
$$10$$ −46.9800 + 22.3725i −1.48564 + 0.707481i
$$11$$ 2.03543 + 1.47883i 0.0557915 + 0.0405349i 0.615331 0.788268i $$-0.289022\pi$$
−0.559540 + 0.828803i $$0.689022\pi$$
$$12$$ 0 0
$$13$$ −32.0534 + 23.2881i −0.683846 + 0.496843i −0.874632 0.484788i $$-0.838897\pi$$
0.190785 + 0.981632i $$0.438897\pi$$
$$14$$ −98.0653 71.2486i −1.87208 1.36014i
$$15$$ 0 0
$$16$$ −10.7917 + 7.84062i −0.168620 + 0.122510i
$$17$$ 26.2638 80.8316i 0.374700 1.15321i −0.568981 0.822351i $$-0.692662\pi$$
0.943681 0.330857i $$-0.107338\pi$$
$$18$$ 0 0
$$19$$ −44.1360 + 135.837i −0.532921 + 1.64016i 0.215179 + 0.976575i $$0.430967\pi$$
−0.748099 + 0.663587i $$0.769033\pi$$
$$20$$ −150.162 27.9275i −1.67886 0.312239i
$$21$$ 0 0
$$22$$ 3.61845 + 11.1365i 0.0350662 + 0.107923i
$$23$$ 127.177 + 92.3993i 1.15296 + 0.837678i 0.988872 0.148768i $$-0.0475306\pi$$
0.164092 + 0.986445i $$0.447531\pi$$
$$24$$ 0 0
$$25$$ −67.9495 104.918i −0.543596 0.839347i
$$26$$ −184.399 −1.39090
$$27$$ 0 0
$$28$$ −109.948 338.386i −0.742081 2.28389i
$$29$$ 30.9737 + 95.3273i 0.198334 + 0.610408i 0.999921 + 0.0125312i $$0.00398890\pi$$
−0.801588 + 0.597877i $$0.796011\pi$$
$$30$$ 0 0
$$31$$ −53.5715 + 164.876i −0.310378 + 0.955246i 0.667237 + 0.744846i $$0.267477\pi$$
−0.977615 + 0.210401i $$0.932523\pi$$
$$32$$ 148.703 0.821476
$$33$$ 0 0
$$34$$ 320.018 232.506i 1.61419 1.17278i
$$35$$ 139.101 255.813i 0.671783 1.23544i
$$36$$ 0 0
$$37$$ 48.0520 34.9118i 0.213506 0.155121i −0.475893 0.879503i $$-0.657875\pi$$
0.689398 + 0.724382i $$0.257875\pi$$
$$38$$ −537.786 + 390.725i −2.29580 + 1.66800i
$$39$$ 0 0
$$40$$ −202.644 213.809i −0.801022 0.845153i
$$41$$ −287.546 + 208.914i −1.09530 + 0.795779i −0.980286 0.197585i $$-0.936690\pi$$
−0.115011 + 0.993364i $$0.536690\pi$$
$$42$$ 0 0
$$43$$ 109.742 0.389198 0.194599 0.980883i $$-0.437659\pi$$
0.194599 + 0.980883i $$0.437659\pi$$
$$44$$ −10.6211 + 32.6885i −0.0363908 + 0.112000i
$$45$$ 0 0
$$46$$ 226.086 + 695.821i 0.724665 + 2.23029i
$$47$$ 17.9575 + 55.2674i 0.0557312 + 0.171523i 0.975047 0.221997i $$-0.0712574\pi$$
−0.919316 + 0.393520i $$0.871257\pi$$
$$48$$ 0 0
$$49$$ 335.317 0.977600
$$50$$ 31.1696 580.935i 0.0881610 1.64313i
$$51$$ 0 0
$$52$$ −437.888 318.144i −1.16777 0.848436i
$$53$$ 120.787 + 371.745i 0.313045 + 0.963455i 0.976552 + 0.215284i $$0.0690676\pi$$
−0.663506 + 0.748171i $$0.730932\pi$$
$$54$$ 0 0
$$55$$ −25.3963 + 12.0941i −0.0622626 + 0.0296502i
$$56$$ 212.056 652.641i 0.506021 1.55737i
$$57$$ 0 0
$$58$$ −144.157 + 443.669i −0.326357 + 1.00442i
$$59$$ 333.759 242.490i 0.736470 0.535077i −0.155134 0.987893i $$-0.549581\pi$$
0.891604 + 0.452817i $$0.149581\pi$$
$$60$$ 0 0
$$61$$ −290.142 210.800i −0.608998 0.442463i 0.240064 0.970757i $$-0.422832\pi$$
−0.849061 + 0.528294i $$0.822832\pi$$
$$62$$ −652.756 + 474.255i −1.33710 + 0.971459i
$$63$$ 0 0
$$64$$ 646.244 + 469.524i 1.26220 + 0.917039i
$$65$$ −57.5458 439.213i −0.109810 0.838118i
$$66$$ 0 0
$$67$$ 108.468 333.831i 0.197783 0.608715i −0.802149 0.597123i $$-0.796310\pi$$
0.999933 0.0115915i $$-0.00368977\pi$$
$$68$$ 1161.09 2.07062
$$69$$ 0 0
$$70$$ 1223.57 582.681i 2.08921 0.994910i
$$71$$ −52.7887 162.467i −0.0882376 0.271567i 0.897195 0.441635i $$-0.145601\pi$$
−0.985432 + 0.170068i $$0.945601\pi$$
$$72$$ 0 0
$$73$$ 754.724 + 548.339i 1.21005 + 0.879154i 0.995236 0.0975001i $$-0.0310846\pi$$
0.214817 + 0.976654i $$0.431085\pi$$
$$74$$ 276.437 0.434258
$$75$$ 0 0
$$76$$ −1951.19 −2.94496
$$77$$ −53.0119 38.5154i −0.0784580 0.0570030i
$$78$$ 0 0
$$79$$ −405.819 1248.98i −0.577952 1.77875i −0.625898 0.779905i $$-0.715267\pi$$
0.0479457 0.998850i $$-0.484733\pi$$
$$80$$ −19.3744 147.874i −0.0270766 0.206660i
$$81$$ 0 0
$$82$$ −1654.21 −2.22777
$$83$$ 202.066 621.896i 0.267225 0.822433i −0.723948 0.689855i $$-0.757674\pi$$
0.991173 0.132578i $$-0.0423255\pi$$
$$84$$ 0 0
$$85$$ 653.668 + 689.680i 0.834121 + 0.880075i
$$86$$ 413.211 + 300.216i 0.518113 + 0.376431i
$$87$$ 0 0
$$88$$ −53.6301 + 38.9646i −0.0649658 + 0.0472004i
$$89$$ 857.273 + 622.845i 1.02102 + 0.741814i 0.966492 0.256698i $$-0.0826346\pi$$
0.0545280 + 0.998512i $$0.482635\pi$$
$$90$$ 0 0
$$91$$ 834.814 606.528i 0.961674 0.698697i
$$92$$ −663.624 + 2042.42i −0.752039 + 2.31454i
$$93$$ 0 0
$$94$$ −83.5770 + 257.224i −0.0917054 + 0.282240i
$$95$$ −1098.48 1159.00i −1.18634 1.25169i
$$96$$ 0 0
$$97$$ 198.234 + 610.103i 0.207502 + 0.638624i 0.999601 + 0.0282327i $$0.00898793\pi$$
−0.792100 + 0.610392i $$0.791012\pi$$
$$98$$ 1262.57 + 917.308i 1.30141 + 0.945532i
$$99$$ 0 0
$$100$$ 1076.31 1325.76i 1.07631 1.32576i
$$101$$ −864.030 −0.851229 −0.425615 0.904904i $$-0.639942\pi$$
−0.425615 + 0.904904i $$0.639942\pi$$
$$102$$ 0 0
$$103$$ 566.152 + 1742.44i 0.541598 + 1.66687i 0.728944 + 0.684574i $$0.240012\pi$$
−0.187345 + 0.982294i $$0.559988\pi$$
$$104$$ −322.589 992.828i −0.304159 0.936104i
$$105$$ 0 0
$$106$$ −562.163 + 1730.16i −0.515115 + 1.58536i
$$107$$ 1037.99 0.937816 0.468908 0.883247i $$-0.344648\pi$$
0.468908 + 0.883247i $$0.344648\pi$$
$$108$$ 0 0
$$109$$ −1259.67 + 915.201i −1.10692 + 0.804224i −0.982176 0.187966i $$-0.939811\pi$$
−0.124743 + 0.992189i $$0.539811\pi$$
$$110$$ −128.710 23.9377i −0.111564 0.0207488i
$$111$$ 0 0
$$112$$ 281.064 204.205i 0.237126 0.172282i
$$113$$ −788.953 + 573.208i −0.656800 + 0.477193i −0.865581 0.500769i $$-0.833051\pi$$
0.208781 + 0.977963i $$0.433051\pi$$
$$114$$ 0 0
$$115$$ −1586.80 + 755.654i −1.28669 + 0.612740i
$$116$$ −1107.79 + 804.858i −0.886689 + 0.644217i
$$117$$ 0 0
$$118$$ 1920.07 1.49794
$$119$$ −684.027 + 2105.22i −0.526930 + 1.62172i
$$120$$ 0 0
$$121$$ −409.346 1259.84i −0.307547 0.946534i
$$122$$ −515.794 1587.45i −0.382769 1.17804i
$$123$$ 0 0
$$124$$ −2368.33 −1.71518
$$125$$ 1393.44 107.052i 0.997062 0.0766002i
$$126$$ 0 0
$$127$$ 832.392 + 604.768i 0.581597 + 0.422555i 0.839300 0.543669i $$-0.182965\pi$$
−0.257702 + 0.966224i $$0.582965\pi$$
$$128$$ 781.235 + 2404.39i 0.539469 + 1.66032i
$$129$$ 0 0
$$130$$ 984.855 1811.19i 0.664442 1.22194i
$$131$$ 825.045 2539.23i 0.550264 1.69354i −0.157870 0.987460i $$-0.550463\pi$$
0.708134 0.706078i $$-0.249537\pi$$
$$132$$ 0 0
$$133$$ 1149.50 3537.80i 0.749431 2.30651i
$$134$$ 1321.66 960.241i 0.852044 0.619046i
$$135$$ 0 0
$$136$$ 1811.69 + 1316.27i 1.14229 + 0.829921i
$$137$$ −986.533 + 716.758i −0.615221 + 0.446984i −0.851249 0.524762i $$-0.824154\pi$$
0.236028 + 0.971746i $$0.424154\pi$$
$$138$$ 0 0
$$139$$ −708.126 514.484i −0.432104 0.313942i 0.350386 0.936606i $$-0.386051\pi$$
−0.782490 + 0.622664i $$0.786051\pi$$
$$140$$ 3910.90 + 727.357i 2.36094 + 0.439092i
$$141$$ 0 0
$$142$$ 245.687 756.148i 0.145194 0.446863i
$$143$$ −99.6816 −0.0582923
$$144$$ 0 0
$$145$$ −1101.75 204.905i −0.631001 0.117355i
$$146$$ 1341.70 + 4129.32i 0.760546 + 2.34072i
$$147$$ 0 0
$$148$$ 656.449 + 476.938i 0.364593 + 0.264893i
$$149$$ 819.633 0.450650 0.225325 0.974284i $$-0.427656\pi$$
0.225325 + 0.974284i $$0.427656\pi$$
$$150$$ 0 0
$$151$$ 567.457 0.305821 0.152911 0.988240i $$-0.451135\pi$$
0.152911 + 0.988240i $$0.451135\pi$$
$$152$$ −3044.53 2211.98i −1.62463 1.18036i
$$153$$ 0 0
$$154$$ −94.2409 290.044i −0.0493126 0.151769i
$$155$$ −1333.32 1406.78i −0.690934 0.729000i
$$156$$ 0 0
$$157$$ −1643.63 −0.835516 −0.417758 0.908558i $$-0.637184\pi$$
−0.417758 + 0.908558i $$0.637184\pi$$
$$158$$ 1888.75 5812.97i 0.951018 2.92693i
$$159$$ 0 0
$$160$$ −794.208 + 1460.58i −0.392423 + 0.721683i
$$161$$ −3312.26 2406.49i −1.62138 1.17800i
$$162$$ 0 0
$$163$$ 1035.78 752.538i 0.497721 0.361615i −0.310425 0.950598i $$-0.600471\pi$$
0.808146 + 0.588982i $$0.200471\pi$$
$$164$$ −3928.23 2854.03i −1.87039 1.35892i
$$165$$ 0 0
$$166$$ 2462.13 1788.84i 1.15119 0.836391i
$$167$$ 487.198 1499.44i 0.225752 0.694792i −0.772463 0.635060i $$-0.780975\pi$$
0.998214 0.0597320i $$-0.0190246\pi$$
$$168$$ 0 0
$$169$$ −193.829 + 596.545i −0.0882246 + 0.271527i
$$170$$ 574.531 + 4385.06i 0.259203 + 1.97834i
$$171$$ 0 0
$$172$$ 463.282 + 1425.83i 0.205377 + 0.632086i
$$173$$ 1797.33 + 1305.83i 0.789874 + 0.573877i 0.907926 0.419131i $$-0.137665\pi$$
−0.118052 + 0.993007i $$0.537665\pi$$
$$174$$ 0 0
$$175$$ 1769.71 + 2732.55i 0.764444 + 1.18035i
$$176$$ −33.5607 −0.0143735
$$177$$ 0 0
$$178$$ 1524.00 + 4690.39i 0.641734 + 1.97506i
$$179$$ −931.708 2867.50i −0.389045 1.19736i −0.933503 0.358570i $$-0.883264\pi$$
0.544458 0.838788i $$-0.316736\pi$$
$$180$$ 0 0
$$181$$ 764.093 2351.64i 0.313782 0.965722i −0.662471 0.749088i $$-0.730492\pi$$
0.976253 0.216634i $$-0.0695079\pi$$
$$182$$ 4802.57 1.95599
$$183$$ 0 0
$$184$$ −3350.88 + 2434.56i −1.34256 + 0.975425i
$$185$$ 86.2684 + 658.435i 0.0342842 + 0.261671i
$$186$$ 0 0
$$187$$ 172.994 125.688i 0.0676502 0.0491508i
$$188$$ −642.259 + 466.628i −0.249157 + 0.181023i
$$189$$ 0 0
$$190$$ −965.494 7369.04i −0.368654 2.81372i
$$191$$ −518.536 + 376.738i −0.196439 + 0.142722i −0.681657 0.731672i $$-0.738740\pi$$
0.485218 + 0.874393i $$0.338740\pi$$
$$192$$ 0 0
$$193$$ −658.953 −0.245764 −0.122882 0.992421i $$-0.539214\pi$$
−0.122882 + 0.992421i $$0.539214\pi$$
$$194$$ −922.615 + 2839.52i −0.341443 + 1.05085i
$$195$$ 0 0
$$196$$ 1415.56 + 4356.63i 0.515873 + 1.58769i
$$197$$ −865.948 2665.12i −0.313179 0.963866i −0.976498 0.215529i $$-0.930853\pi$$
0.663318 0.748337i $$-0.269147\pi$$
$$198$$ 0 0
$$199$$ −2715.89 −0.967459 −0.483729 0.875218i $$-0.660718\pi$$
−0.483729 + 0.875218i $$0.660718\pi$$
$$200$$ 3182.36 848.474i 1.12514 0.299981i
$$201$$ 0 0
$$202$$ −3253.33 2363.68i −1.13318 0.823307i
$$203$$ −806.696 2482.75i −0.278911 0.858400i
$$204$$ 0 0
$$205$$ −516.235 3940.11i −0.175880 1.34239i
$$206$$ −2634.96 + 8109.58i −0.891197 + 2.74282i
$$207$$ 0 0
$$208$$ 163.317 502.637i 0.0544421 0.167556i
$$209$$ −290.715 + 211.217i −0.0962162 + 0.0699051i
$$210$$ 0 0
$$211$$ 1402.23 + 1018.78i 0.457505 + 0.332397i 0.792552 0.609805i $$-0.208752\pi$$
−0.335047 + 0.942201i $$0.608752\pi$$
$$212$$ −4320.02 + 3138.68i −1.39953 + 1.01682i
$$213$$ 0 0
$$214$$ 3908.34 + 2839.58i 1.24845 + 0.907053i
$$215$$ −586.122 + 1077.90i −0.185922 + 0.341918i
$$216$$ 0 0
$$217$$ 1395.24 4294.12i 0.436476 1.34334i
$$218$$ −7246.68 −2.25141
$$219$$ 0 0
$$220$$ −264.345 278.909i −0.0810098 0.0854728i
$$221$$ 1040.57 + 3202.56i 0.316727 + 0.974784i
$$222$$ 0 0
$$223$$ −3541.18 2572.82i −1.06338 0.772594i −0.0886732 0.996061i $$-0.528263\pi$$
−0.974712 + 0.223467i $$0.928263\pi$$
$$224$$ −3872.90 −1.15522
$$225$$ 0 0
$$226$$ −4538.74 −1.33589
$$227$$ −1819.26 1321.77i −0.531931 0.386471i 0.289148 0.957284i $$-0.406628\pi$$
−0.821080 + 0.570814i $$0.806628\pi$$
$$228$$ 0 0
$$229$$ 693.843 + 2135.43i 0.200220 + 0.616215i 0.999876 + 0.0157557i $$0.00501539\pi$$
−0.799656 + 0.600459i $$0.794985\pi$$
$$230$$ −8041.97 1495.66i −2.30553 0.428787i
$$231$$ 0 0
$$232$$ −2640.97 −0.747362
$$233$$ −218.901 + 673.707i −0.0615479 + 0.189425i −0.977103 0.212768i $$-0.931752\pi$$
0.915555 + 0.402193i $$0.131752\pi$$
$$234$$ 0 0
$$235$$ −638.754 118.797i −0.177310 0.0329764i
$$236$$ 4559.56 + 3312.71i 1.25763 + 0.913725i
$$237$$ 0 0
$$238$$ −8334.70 + 6055.52i −2.26999 + 1.64925i
$$239$$ 4411.37 + 3205.04i 1.19392 + 0.867435i 0.993673 0.112309i $$-0.0358248\pi$$
0.200249 + 0.979745i $$0.435825\pi$$
$$240$$ 0 0
$$241$$ −4628.17 + 3362.56i −1.23704 + 0.898762i −0.997397 0.0720995i $$-0.977030\pi$$
−0.239642 + 0.970861i $$0.577030\pi$$
$$242$$ 1905.16 5863.48i 0.506068 1.55752i
$$243$$ 0 0
$$244$$ 1514.00 4659.60i 0.397228 1.22254i
$$245$$ −1790.89 + 3293.53i −0.467004 + 0.858841i
$$246$$ 0 0
$$247$$ −1748.67 5381.87i −0.450468 1.38640i
$$248$$ −3695.40 2684.86i −0.946202 0.687456i
$$249$$ 0 0
$$250$$ 5539.56 + 3408.87i 1.40141 + 0.862383i
$$251$$ −2045.23 −0.514319 −0.257159 0.966369i $$-0.582787\pi$$
−0.257159 + 0.966369i $$0.582787\pi$$
$$252$$ 0 0
$$253$$ 122.217 + 376.145i 0.0303704 + 0.0934705i
$$254$$ 1479.77 + 4554.26i 0.365547 + 1.12504i
$$255$$ 0 0
$$256$$ −1661.25 + 5112.79i −0.405578 + 1.24824i
$$257$$ −407.547 −0.0989186 −0.0494593 0.998776i $$-0.515750\pi$$
−0.0494593 + 0.998776i $$0.515750\pi$$
$$258$$ 0 0
$$259$$ −1251.49 + 909.262i −0.300247 + 0.218142i
$$260$$ 5463.58 2601.83i 1.30322 0.620610i
$$261$$ 0 0
$$262$$ 10053.0 7303.91i 2.37052 1.72228i
$$263$$ −717.991 + 521.651i −0.168339 + 0.122306i −0.668765 0.743474i $$-0.733177\pi$$
0.500426 + 0.865779i $$0.333177\pi$$
$$264$$ 0 0
$$265$$ −4296.45 799.062i −0.995958 0.185230i
$$266$$ 14006.4 10176.2i 3.22852 2.34566i
$$267$$ 0 0
$$268$$ 4795.23 1.09297
$$269$$ −1864.45 + 5738.18i −0.422592 + 1.30061i 0.482688 + 0.875792i $$0.339660\pi$$
−0.905281 + 0.424814i $$0.860340\pi$$
$$270$$ 0 0
$$271$$ 2019.40 + 6215.08i 0.452656 + 1.39313i 0.873865 + 0.486169i $$0.161606\pi$$
−0.421209 + 0.906964i $$0.638394\pi$$
$$272$$ 350.339 + 1078.23i 0.0780972 + 0.240358i
$$273$$ 0 0
$$274$$ −5675.39 −1.25132
$$275$$ 16.8496 314.040i 0.00369480 0.0688630i
$$276$$ 0 0
$$277$$ 4454.88 + 3236.66i 0.966309 + 0.702064i 0.954607 0.297867i $$-0.0962753\pi$$
0.0117014 + 0.999932i $$0.496275\pi$$
$$278$$ −1258.86 3874.37i −0.271587 0.835860i
$$279$$ 0 0
$$280$$ 5277.77 + 5568.54i 1.12645 + 1.18851i
$$281$$ 2323.54 7151.11i 0.493276 1.51815i −0.326350 0.945249i $$-0.605819\pi$$
0.819626 0.572898i $$-0.194181\pi$$
$$282$$ 0 0
$$283$$ 1384.45 4260.88i 0.290801 0.894994i −0.693798 0.720169i $$-0.744064\pi$$
0.984600 0.174825i $$-0.0559359\pi$$
$$284$$ 1888.02 1371.73i 0.394483 0.286609i
$$285$$ 0 0
$$286$$ −375.331 272.694i −0.0776006 0.0563802i
$$287$$ 7489.00 5441.08i 1.54028 1.11908i
$$288$$ 0 0
$$289$$ −1869.26 1358.09i −0.380471 0.276429i
$$290$$ −3587.86 3785.52i −0.726504 0.766529i
$$291$$ 0 0
$$292$$ −3938.24 + 12120.7i −0.789275 + 2.42914i
$$293$$ 6672.17 1.33035 0.665174 0.746688i $$-0.268357\pi$$
0.665174 + 0.746688i $$0.268357\pi$$
$$294$$ 0 0
$$295$$ 599.201 + 4573.35i 0.118261 + 0.902612i
$$296$$ 483.602 + 1488.37i 0.0949622 + 0.292264i
$$297$$ 0 0
$$298$$ 3086.16 + 2242.23i 0.599921 + 0.435868i
$$299$$ −6228.25 −1.20464
$$300$$ 0 0
$$301$$ −2858.18 −0.547318
$$302$$ 2136.65 + 1552.36i 0.407120 + 0.295790i
$$303$$ 0 0
$$304$$ −588.742 1811.96i −0.111075 0.341852i
$$305$$ 3620.13 1723.95i 0.679634 0.323650i
$$306$$ 0 0
$$307$$ 5433.28 1.01008 0.505039 0.863097i $$-0.331478\pi$$
0.505039 + 0.863097i $$0.331478\pi$$
$$308$$ 276.622 851.356i 0.0511754 0.157502i
$$309$$ 0 0
$$310$$ −1171.90 8944.42i −0.214708 1.63874i
$$311$$ 415.035 + 301.541i 0.0756736 + 0.0549801i 0.624979 0.780642i $$-0.285108\pi$$
−0.549305 + 0.835622i $$0.685108\pi$$
$$312$$ 0 0
$$313$$ 806.159 585.709i 0.145581 0.105771i −0.512611 0.858621i $$-0.671322\pi$$
0.658192 + 0.752850i $$0.271322\pi$$
$$314$$ −6188.75 4496.39i −1.11227 0.808109i
$$315$$ 0 0
$$316$$ 14514.4 10545.3i 2.58385 1.87728i
$$317$$ −1322.77 + 4071.07i −0.234366 + 0.721305i 0.762838 + 0.646589i $$0.223805\pi$$
−0.997205 + 0.0747164i $$0.976195\pi$$
$$318$$ 0 0
$$319$$ −77.9278 + 239.837i −0.0136775 + 0.0420950i
$$320$$ −8063.27 + 3839.83i −1.40859 + 0.670791i
$$321$$ 0 0
$$322$$ −5888.30 18122.3i −1.01908 3.13639i
$$323$$ 9820.71 + 7135.17i 1.69176 + 1.22914i
$$324$$ 0 0
$$325$$ 4621.36 + 1780.57i 0.788760 + 0.303902i
$$326$$ 5958.70 1.01234
$$327$$ 0 0
$$328$$ −2893.90 8906.52i −0.487162 1.49933i
$$329$$ −467.694 1439.41i −0.0783732 0.241208i
$$330$$ 0 0
$$331$$ −918.630 + 2827.25i −0.152545 + 0.469486i −0.997904 0.0647132i $$-0.979387\pi$$
0.845359 + 0.534199i $$0.179387\pi$$
$$332$$ 8933.07 1.47670
$$333$$ 0 0
$$334$$ 5936.39 4313.04i 0.972529 0.706584i
$$335$$ 2699.62 + 2848.35i 0.440286 + 0.464543i
$$336$$ 0 0
$$337$$ −1248.14 + 906.825i −0.201752 + 0.146581i −0.684074 0.729413i $$-0.739794\pi$$
0.482322 + 0.875994i $$0.339794\pi$$
$$338$$ −2361.76 + 1715.92i −0.380068 + 0.276136i
$$339$$ 0 0
$$340$$ −6201.25 + 11404.4i −0.989146 + 1.81908i
$$341$$ −352.865 + 256.371i −0.0560373 + 0.0407135i
$$342$$ 0 0
$$343$$ 200.108 0.0315009
$$344$$ −893.526 + 2749.99i −0.140046 + 0.431016i
$$345$$ 0 0
$$346$$ 3195.16 + 9833.70i 0.496454 + 1.52793i
$$347$$ 1738.01 + 5349.05i 0.268880 + 0.827527i 0.990774 + 0.135524i $$0.0432717\pi$$
−0.721894 + 0.692003i $$0.756728\pi$$
$$348$$ 0 0
$$349$$ 3546.44 0.543945 0.271972 0.962305i $$-0.412324\pi$$
0.271972 + 0.962305i $$0.412324\pi$$
$$350$$ −811.798 + 15130.2i −0.123978 + 2.31069i
$$351$$ 0 0
$$352$$ 302.675 + 219.906i 0.0458313 + 0.0332984i
$$353$$ 592.091 + 1822.27i 0.0892742 + 0.274758i 0.985719 0.168397i $$-0.0538591\pi$$
−0.896445 + 0.443155i $$0.853859\pi$$
$$354$$ 0 0
$$355$$ 1877.72 + 349.221i 0.280729 + 0.0522105i
$$356$$ −4473.36 + 13767.6i −0.665976 + 2.04966i
$$357$$ 0 0
$$358$$ 4336.32 13345.8i 0.640172 1.97025i
$$359$$ 2130.22 1547.69i 0.313171 0.227532i −0.420085 0.907485i $$-0.638000\pi$$
0.733256 + 0.679953i $$0.238000\pi$$
$$360$$ 0 0
$$361$$ −10954.6 7958.96i −1.59711 1.16037i
$$362$$ 9310.28 6764.32i 1.35176 0.982112i
$$363$$ 0 0
$$364$$ 11404.6 + 8285.92i 1.64221 + 1.19313i
$$365$$ −9416.78 + 4484.39i −1.35040 + 0.643079i
$$366$$ 0 0
$$367$$ −2102.12 + 6469.65i −0.298991 + 0.920199i 0.682861 + 0.730548i $$0.260735\pi$$
−0.981852 + 0.189650i $$0.939265\pi$$
$$368$$ −2096.92 −0.297037
$$369$$ 0 0
$$370$$ −1476.42 + 2715.20i −0.207447 + 0.381505i
$$371$$ −3145.85 9681.92i −0.440227 1.35488i
$$372$$ 0 0
$$373$$ 5424.55 + 3941.17i 0.753010 + 0.547094i 0.896758 0.442520i $$-0.145916\pi$$
−0.143748 + 0.989614i $$0.545916\pi$$
$$374$$ 995.212 0.137597
$$375$$ 0 0
$$376$$ −1531.14 −0.210007
$$377$$ −3212.81 2334.24i −0.438907 0.318885i
$$378$$ 0 0
$$379$$ 1202.29 + 3700.27i 0.162948 + 0.501504i 0.998879 0.0473310i $$-0.0150716\pi$$
−0.835931 + 0.548835i $$0.815072\pi$$
$$380$$ 10421.1 19164.9i 1.40682 2.58721i
$$381$$ 0 0
$$382$$ −2983.06 −0.399547
$$383$$ 1743.53 5366.04i 0.232612 0.715906i −0.764817 0.644247i $$-0.777171\pi$$
0.997429 0.0716588i $$-0.0228293\pi$$
$$384$$ 0 0
$$385$$ 661.435 314.984i 0.0875581 0.0416963i
$$386$$ −2481.15 1802.66i −0.327169 0.237702i
$$387$$ 0 0
$$388$$ −7089.96 + 5151.16i −0.927676 + 0.673996i
$$389$$ −3785.35 2750.22i −0.493380 0.358462i 0.313102 0.949719i $$-0.398632\pi$$
−0.806483 + 0.591257i $$0.798632\pi$$
$$390$$ 0 0
$$391$$ 10808.9 7853.14i 1.39803 1.01573i
$$392$$ −2730.17 + 8402.59i −0.351771 + 1.08264i
$$393$$ 0 0
$$394$$ 4030.26 12403.9i 0.515334 1.58604i
$$395$$ 14435.2 + 2684.68i 1.83876 + 0.341977i
$$396$$ 0 0
$$397$$ 2589.33 + 7969.14i 0.327342 + 1.00746i 0.970372 + 0.241614i $$0.0776769\pi$$
−0.643030 + 0.765841i $$0.722323\pi$$
$$398$$ −10226.1 7429.72i −1.28791 0.935724i
$$399$$ 0 0
$$400$$ 1555.92 + 599.480i 0.194489 + 0.0749350i
$$401$$ −6042.30 −0.752464 −0.376232 0.926525i $$-0.622780\pi$$
−0.376232 + 0.926525i $$0.622780\pi$$
$$402$$ 0 0
$$403$$ −2122.51 6532.42i −0.262357 0.807451i
$$404$$ −3647.55 11226.0i −0.449189 1.38246i
$$405$$ 0 0
$$406$$ 3754.49 11555.1i 0.458947 1.41249i
$$407$$ 149.435 0.0181996
$$408$$ 0 0
$$409$$ −5290.72 + 3843.93i −0.639631 + 0.464719i −0.859723 0.510760i $$-0.829364\pi$$
0.220092 + 0.975479i $$0.429364\pi$$
$$410$$ 8834.99 16247.9i 1.06422 1.95714i
$$411$$ 0 0
$$412$$ −20248.7 + 14711.6i −2.42132 + 1.75919i
$$413$$ −8692.59 + 6315.54i −1.03568 + 0.752463i
$$414$$ 0 0
$$415$$ 5029.14 + 5306.21i 0.594869 + 0.627642i
$$416$$ −4766.43 + 3463.01i −0.561763 + 0.408145i
$$417$$ 0 0
$$418$$ −1672.44 −0.195698
$$419$$ −4050.94 + 12467.5i −0.472319 + 1.45365i 0.377221 + 0.926123i $$0.376880\pi$$
−0.849540 + 0.527525i $$0.823120\pi$$
$$420$$ 0 0
$$421$$ 1054.72 + 3246.11i 0.122100 + 0.375785i 0.993362 0.115034i $$-0.0366977\pi$$
−0.871262 + 0.490819i $$0.836698\pi$$
$$422$$ 2492.79 + 7672.01i 0.287552 + 0.884995i
$$423$$ 0 0
$$424$$ −10298.9 −1.17962
$$425$$ −10265.3 + 2736.91i −1.17163 + 0.312376i
$$426$$ 0 0
$$427$$ 7556.60 + 5490.19i 0.856416 + 0.622223i
$$428$$ 4381.93 + 13486.2i 0.494880 + 1.52308i
$$429$$ 0 0
$$430$$ −5155.69 + 2455.20i −0.578208 + 0.275350i
$$431$$ 467.178 1437.83i 0.0522116 0.160691i −0.921551 0.388258i $$-0.873077\pi$$
0.973762 + 0.227567i $$0.0730771\pi$$
$$432$$ 0 0
$$433$$ −2665.17 + 8202.55i −0.295797 + 0.910368i 0.687156 + 0.726510i $$0.258859\pi$$
−0.982953 + 0.183858i $$0.941141\pi$$
$$434$$ 17000.7 12351.7i 1.88032 1.36613i
$$435$$ 0 0
$$436$$ −17208.6 12502.8i −1.89023 1.37333i
$$437$$ −18164.3 + 13197.1i −1.98836 + 1.44463i
$$438$$ 0 0
$$439$$ 2854.86 + 2074.17i 0.310375 + 0.225501i 0.732058 0.681243i $$-0.238560\pi$$
−0.421682 + 0.906744i $$0.638560\pi$$
$$440$$ −96.2828 734.869i −0.0104320 0.0796216i
$$441$$ 0 0
$$442$$ −4843.00 + 14905.2i −0.521172 + 1.60400i
$$443$$ 9589.40 1.02846 0.514228 0.857653i $$-0.328078\pi$$
0.514228 + 0.857653i $$0.328078\pi$$
$$444$$ 0 0
$$445$$ −10696.3 + 5093.71i −1.13944 + 0.542618i
$$446$$ −6295.26 19374.8i −0.668362 2.05701i
$$447$$ 0 0
$$448$$ −16831.1 12228.5i −1.77499 1.28961i
$$449$$ 9820.81 1.03223 0.516117 0.856518i $$-0.327377\pi$$
0.516117 + 0.856518i $$0.327377\pi$$
$$450$$ 0 0
$$451$$ −894.230 −0.0933650
$$452$$ −10778.1 7830.72i −1.12159 0.814881i
$$453$$ 0 0
$$454$$ −3234.15 9953.70i −0.334331 1.02897i
$$455$$ 1498.75 + 11439.1i 0.154423 + 1.17862i
$$456$$ 0 0
$$457$$ 1597.23 0.163491 0.0817455 0.996653i $$-0.473951\pi$$
0.0817455 + 0.996653i $$0.473951\pi$$
$$458$$ −3229.26 + 9938.63i −0.329461 + 1.01398i
$$459$$ 0 0
$$460$$ −16516.7 17426.6i −1.67412 1.76635i
$$461$$ −3157.65 2294.17i −0.319016 0.231779i 0.416740 0.909026i $$-0.363173\pi$$
−0.735755 + 0.677247i $$0.763173\pi$$
$$462$$ 0 0
$$463$$ 12670.8 9205.86i 1.27184 0.924044i 0.272563 0.962138i $$-0.412129\pi$$
0.999274 + 0.0380937i $$0.0121285\pi$$
$$464$$ −1081.68 785.890i −0.108224 0.0786293i
$$465$$ 0 0
$$466$$ −2667.25 + 1937.87i −0.265146 + 0.192640i
$$467$$ 1976.88 6084.21i 0.195887 0.602878i −0.804078 0.594523i $$-0.797341\pi$$
0.999965 0.00835414i $$-0.00265924\pi$$
$$468$$ 0 0
$$469$$ −2825.00 + 8694.46i −0.278137 + 0.856019i
$$470$$ −2080.11 2194.71i −0.204146 0.215393i
$$471$$ 0 0
$$472$$ 3359.00 + 10337.9i 0.327564 + 1.00814i
$$473$$ 223.373 + 162.290i 0.0217139 + 0.0157761i
$$474$$ 0 0
$$475$$ 17250.8 4599.36i 1.66636 0.444280i
$$476$$ −30239.9 −2.91186
$$477$$ 0 0
$$478$$ 7842.22 + 24135.9i 0.750408 + 2.30952i
$$479$$ 3178.50 + 9782.42i 0.303193 + 0.933132i 0.980345 + 0.197289i $$0.0632137\pi$$
−0.677153 + 0.735843i $$0.736786\pi$$
$$480$$ 0 0
$$481$$ −727.197 + 2238.08i −0.0689342 + 0.212158i
$$482$$ −26625.2 −2.51607
$$483$$ 0 0
$$484$$ 14640.5 10636.9i 1.37495 0.998960i
$$485$$ −7051.28 1311.41i −0.660169 0.122780i
$$486$$ 0 0
$$487$$ −1685.55 + 1224.62i −0.156837 + 0.113949i −0.663436 0.748233i $$-0.730902\pi$$
0.506599 + 0.862182i $$0.330902\pi$$
$$488$$ 7644.73 5554.22i 0.709141 0.515221i
$$489$$ 0 0
$$490$$ −15753.2 + 7501.87i −1.45236 + 0.691633i
$$491$$ 14323.2 10406.4i 1.31649 0.956487i 0.316522 0.948585i $$-0.397485\pi$$
0.999969 0.00790172i $$-0.00251522\pi$$
$$492$$ 0 0
$$493$$ 8518.94 0.778243
$$494$$ 8138.61 25048.1i 0.741242 2.28131i
$$495$$ 0 0
$$496$$ −714.605 2199.33i −0.0646909 0.199098i
$$497$$ 1374.86 + 4231.37i 0.124086 + 0.381897i
$$498$$ 0 0
$$499$$ 5018.92 0.450256 0.225128 0.974329i $$-0.427720\pi$$
0.225128 + 0.974329i $$0.427720\pi$$
$$500$$ 7273.35 + 17652.4i 0.650548 + 1.57888i
$$501$$ 0 0
$$502$$ −7700.91 5595.04i −0.684678 0.497448i
$$503$$ 3109.30 + 9569.44i 0.275620 + 0.848270i 0.989055 + 0.147549i $$0.0471384\pi$$
−0.713435 + 0.700721i $$0.752862\pi$$
$$504$$ 0 0
$$505$$ 4614.70 8486.64i 0.406636 0.747822i
$$506$$ −568.818 + 1750.64i −0.0499744 + 0.153805i
$$507$$ 0 0
$$508$$ −4343.53 + 13368.0i −0.379356 + 1.16754i
$$509$$ −4301.55 + 3125.26i −0.374584 + 0.272151i −0.759109 0.650963i $$-0.774365\pi$$
0.384525 + 0.923114i $$0.374365\pi$$
$$510$$ 0 0
$$511$$ −19656.4 14281.2i −1.70166 1.23633i
$$512$$ −3879.49 + 2818.62i −0.334865 + 0.243294i
$$513$$ 0 0
$$514$$ −1534.53 1114.90i −0.131684 0.0956738i
$$515$$ −20138.3 3745.35i −1.72310 0.320466i
$$516$$ 0 0
$$517$$ −45.1798 + 139.049i −0.00384334 + 0.0118286i
$$518$$ −7199.66 −0.610685
$$519$$ 0 0
$$520$$ 11474.6 + 2134.08i 0.967685 + 0.179972i
$$521$$ 1938.78 + 5966.95i 0.163032 + 0.501760i 0.998886 0.0471916i $$-0.0150271\pi$$
−0.835854 + 0.548952i $$0.815027\pi$$
$$522$$ 0 0
$$523$$ −11374.4 8264.02i −0.950994 0.690937i 4.79448e−5 1.00000i $$-0.499985\pi$$
−0.951042 + 0.309063i $$0.899985\pi$$
$$524$$ 36474.1 3.04080
$$525$$ 0 0
$$526$$ −4130.50 −0.342392
$$527$$ 11920.2 + 8660.54i 0.985299 + 0.715862i
$$528$$ 0 0
$$529$$ 3876.48 + 11930.6i 0.318606 + 0.980568i
$$530$$ −13991.5 14762.3i −1.14670 1.20987i
$$531$$ 0 0
$$532$$ 50817.9 4.14142
$$533$$ 4351.59 13392.8i 0.353637 1.08838i
$$534$$ 0 0
$$535$$ −5543.80 + 10195.3i −0.447999 + 0.823890i
$$536$$ 7482.20 + 5436.14i 0.602951 + 0.438070i
$$537$$ 0 0
$$538$$ −22717.8 + 16505.5i −1.82051 + 1.32268i
$$539$$ 682.515 + 495.876i 0.0545417 + 0.0396269i
$$540$$ 0 0
$$541$$ 16286.0 11832.5i 1.29425 0.940328i 0.294369 0.955692i $$-0.404890\pi$$
0.999882 + 0.0153633i $$0.00489048\pi$$
$$542$$ −9398.62 + 28926.0i −0.744844 + 2.29239i
$$543$$ 0 0
$$544$$ 3905.50 12019.9i 0.307807 0.947332i
$$545$$ −2261.49 17260.6i −0.177746 1.35663i
$$546$$ 0 0
$$547$$ −4085.46 12573.8i −0.319345 0.982843i −0.973929 0.226854i $$-0.927156\pi$$
0.654584 0.755989i $$-0.272844\pi$$
$$548$$ −13477.3 9791.80i −1.05058 0.763293i
$$549$$ 0 0
$$550$$ 922.547 1136.36i 0.0715228 0.0880991i
$$551$$ −14316.0 −1.10686
$$552$$ 0 0
$$553$$ 10569.4 + 32529.2i 0.812758 + 2.50141i
$$554$$ 7919.57 + 24373.9i 0.607347 + 1.86922i
$$555$$ 0 0
$$556$$ 3695.09 11372.3i 0.281846 0.867434i
$$557$$ 14165.4 1.07757 0.538786 0.842442i $$-0.318883\pi$$
0.538786 + 0.842442i $$0.318883\pi$$
$$558$$ 0 0
$$559$$ −3517.60 + 2555.69i −0.266152 + 0.193370i
$$560$$ 504.598 + 3851.30i 0.0380771 + 0.290620i
$$561$$ 0 0
$$562$$ 28311.7 20569.7i 2.12501 1.54391i
$$563$$ 9115.09 6622.50i 0.682336 0.495746i −0.191796 0.981435i $$-0.561431\pi$$
0.874132 + 0.485689i $$0.161431\pi$$
$$564$$ 0 0
$$565$$ −1416.42 10810.7i −0.105467 0.804970i
$$566$$ 16869.1 12256.1i 1.25276 0.910183i
$$567$$ 0 0
$$568$$ 4501.02 0.332497
$$569$$ 2287.20 7039.27i 0.168514 0.518632i −0.830764 0.556624i $$-0.812096\pi$$
0.999278 + 0.0379926i $$0.0120963\pi$$
$$570$$ 0 0
$$571$$ −4038.92 12430.5i −0.296013 0.911035i −0.982879 0.184251i $$-0.941014\pi$$
0.686866 0.726784i $$-0.258986\pi$$
$$572$$ −420.811 1295.12i −0.0307605 0.0946710i
$$573$$ 0 0
$$574$$ 43083.2 3.13285
$$575$$ 1052.79 19621.7i 0.0763552 1.42310i
$$576$$ 0 0
$$577$$ −6647.54 4829.72i −0.479620 0.348464i 0.321559 0.946890i $$-0.395793\pi$$
−0.801179 + 0.598425i $$0.795793\pi$$
$$578$$ −3323.04 10227.3i −0.239135 0.735982i
$$579$$ 0 0
$$580$$ −1988.83 15179.6i −0.142382 1.08672i
$$581$$ −5262.71 + 16197.0i −0.375790 + 1.15656i
$$582$$ 0 0
$$583$$ −303.893 + 935.286i −0.0215883 + 0.0664418i
$$584$$ −19885.7 + 14447.8i −1.40903 + 1.02372i
$$585$$ 0 0
$$586$$ 25122.7 + 18252.7i 1.77100 + 1.28671i
$$587$$ 16152.0 11735.1i 1.13572 0.825145i 0.149199 0.988807i $$-0.452331\pi$$
0.986517 + 0.163662i $$0.0523306\pi$$
$$588$$ 0 0
$$589$$ −20031.8 14554.0i −1.40135 1.01814i
$$590$$ −10254.9 + 18859.2i −0.715572 + 1.31597i
$$591$$ 0 0
$$592$$ −244.832 + 753.515i −0.0169975 + 0.0523130i
$$593$$ 14429.9 0.999267 0.499634 0.866237i $$-0.333468\pi$$
0.499634 + 0.866237i $$0.333468\pi$$
$$594$$ 0 0
$$595$$ −17024.5 17962.4i −1.17300 1.23762i
$$596$$ 3460.12 + 10649.2i 0.237805 + 0.731890i
$$597$$ 0 0
$$598$$ −23451.2 17038.3i −1.60366 1.16513i
$$599$$ 7838.61 0.534686 0.267343 0.963601i $$-0.413854\pi$$
0.267343 + 0.963601i $$0.413854\pi$$
$$600$$ 0 0
$$601$$ −25163.3 −1.70787 −0.853937 0.520376i $$-0.825792\pi$$
−0.853937 + 0.520376i $$0.825792\pi$$
$$602$$ −10761.9 7818.97i −0.728608 0.529365i
$$603$$ 0 0
$$604$$ 2395.55 + 7372.74i 0.161380 + 0.496677i
$$605$$ 14560.6 + 2708.01i 0.978466 + 0.181977i
$$606$$ 0 0
$$607$$ −563.698 −0.0376932 −0.0188466 0.999822i $$-0.505999\pi$$
−0.0188466 + 0.999822i $$0.505999\pi$$
$$608$$ −6563.16 + 20199.3i −0.437781 + 1.34735i
$$609$$ 0 0
$$610$$ 18347.0 + 3412.21i 1.21778 + 0.226486i
$$611$$ −1862.67 1353.31i −0.123332 0.0896057i
$$612$$ 0 0
$$613$$ 5449.70 3959.44i 0.359072 0.260881i −0.393593 0.919285i $$-0.628768\pi$$
0.752665 + 0.658404i $$0.228768\pi$$
$$614$$ 20457.9 + 14863.6i 1.34465 + 0.976945i
$$615$$ 0 0
$$616$$ 1396.77 1014.81i 0.0913595 0.0663766i
$$617$$ 3151.55 9699.47i 0.205635 0.632878i −0.794052 0.607850i $$-0.792032\pi$$
0.999687 0.0250287i $$-0.00796772\pi$$
$$618$$ 0 0
$$619$$ 2342.12 7208.30i 0.152080 0.468055i −0.845773 0.533543i $$-0.820860\pi$$
0.997853 + 0.0654878i $$0.0208604\pi$$
$$620$$ 12649.0 23262.1i 0.819348 1.50682i
$$621$$ 0 0
$$622$$ 737.821 + 2270.78i 0.0475626 + 0.146383i
$$623$$ −22327.3 16221.7i −1.43583 1.04319i
$$624$$ 0 0
$$625$$ −6390.73 + 14258.3i −0.409006 + 0.912531i
$$626$$ 4637.72 0.296103
$$627$$ 0 0
$$628$$ −6938.67 21355.0i −0.440896 1.35694i
$$629$$ −1559.95 4801.04i −0.0988861 0.304340i
$$630$$ 0 0
$$631$$ 1413.93 4351.64i 0.0892042 0.274542i −0.896496 0.443052i $$-0.853896\pi$$
0.985700 + 0.168510i $$0.0538956\pi$$
$$632$$ 34602.1 2.17784
$$633$$ 0 0
$$634$$ −16117.6 + 11710.1i −1.00964 + 0.733547i
$$635$$ −10385.9 + 4945.88i −0.649055 + 0.309088i
$$636$$ 0 0
$$637$$ −10748.0 + 7808.90i −0.668528 + 0.485714i
$$638$$ −949.532 + 689.875i −0.0589221 + 0.0428094i
$$639$$ 0 0
$$640$$ −27788.8 5168.22i −1.71633 0.319206i
$$641$$ −14330.6 + 10411.8i −0.883034 + 0.641562i −0.934052 0.357136i $$-0.883753\pi$$
0.0510186 + 0.998698i $$0.483753\pi$$
$$642$$ 0 0
$$643$$ −13212.2 −0.810323 −0.405162 0.914245i $$-0.632785\pi$$
−0.405162 + 0.914245i $$0.632785\pi$$
$$644$$ 17283.8 53193.9i 1.05757 3.25487i
$$645$$ 0 0
$$646$$ 17458.6 + 53732.0i 1.06331 + 3.27254i
$$647$$ −1302.73 4009.39i −0.0791586 0.243625i 0.903644 0.428284i $$-0.140882\pi$$
−0.982803 + 0.184659i $$0.940882\pi$$
$$648$$ 0 0
$$649$$ 1037.95 0.0627780
$$650$$ 12529.8 + 19346.8i 0.756091 + 1.16745i
$$651$$ 0 0
$$652$$ 14150.0 + 10280.6i 0.849935 + 0.617514i
$$653$$ −8093.51 24909.3i −0.485028 1.49276i −0.831940 0.554866i $$-0.812770\pi$$
0.346911 0.937898i $$-0.387230\pi$$
$$654$$ 0 0
$$655$$ 20534.2 + 21665.5i 1.22494 + 1.29243i
$$656$$ 1465.09 4509.08i 0.0871983 0.268369i
$$657$$ 0 0
$$658$$ 2176.72 6699.26i 0.128963 0.396906i
$$659$$ −10410.7 + 7563.80i −0.615391 + 0.447107i −0.851308 0.524666i $$-0.824190\pi$$
0.235918 + 0.971773i $$0.424190\pi$$
$$660$$ 0 0
$$661$$ 17474.6 + 12696.0i 1.02827 + 0.747078i 0.967961 0.251102i $$-0.0807929\pi$$
0.0603043 + 0.998180i $$0.480793\pi$$
$$662$$ −11193.3 + 8132.40i −0.657159 + 0.477454i
$$663$$ 0 0
$$664$$ 13938.6 + 10127.0i 0.814645 + 0.591874i
$$665$$ 28609.5 + 30185.6i 1.66831 + 1.76022i
$$666$$ 0 0
$$667$$ −4869.04 + 14985.4i −0.282654 + 0.869918i
$$668$$ 21538.4 1.24752
$$669$$ 0 0
$$670$$ 2372.79 + 18110.1i 0.136819 + 1.04426i
$$671$$ −278.827 858.140i −0.0160417 0.0493713i
$$672$$ 0 0
$$673$$ −8553.18 6214.25i −0.489897 0.355931i 0.315248 0.949009i $$-0.397912\pi$$
−0.805145 + 0.593078i $$0.797912\pi$$
$$674$$ −7180.37 −0.410352
$$675$$ 0 0
$$676$$ −8568.93 −0.487536
$$677$$ −12670.0 9205.29i −0.719272 0.522582i 0.166879 0.985977i $$-0.446631\pi$$
−0.886152 + 0.463395i $$0.846631\pi$$
$$678$$ 0 0
$$679$$ −5162.92 15889.8i −0.291804 0.898079i
$$680$$ −22604.7 + 10764.6i −1.27478 + 0.607066i
$$681$$ 0 0
$$682$$ −2029.98 −0.113977
$$683$$ −7323.05 + 22538.0i −0.410261 + 1.26265i 0.506160 + 0.862440i $$0.331065\pi$$
−0.916421 + 0.400215i $$0.868935\pi$$
$$684$$ 0 0
$$685$$ −1771.13 13518.0i −0.0987906 0.754010i
$$686$$ 753.466 + 547.425i 0.0419351 + 0.0304676i
$$687$$ 0 0
$$688$$ −1184.30 + 860.446i −0.0656266 + 0.0476805i
$$689$$ −12528.9 9102.77i −0.692761 0.503320i
$$690$$ 0 0
$$691$$ −3580.95 + 2601.71i −0.197143 + 0.143233i −0.681978 0.731373i $$-0.738880\pi$$
0.484835 + 0.874606i $$0.338880\pi$$
$$692$$ −9378.67 + 28864.6i −0.515207 + 1.58564i
$$693$$ 0 0
$$694$$ −8088.99 + 24895.3i −0.442441 + 1.36169i
$$695$$ 8835.37 4207.52i 0.482223 0.229641i
$$696$$ 0 0
$$697$$ 9334.84 + 28729.7i 0.507292 + 1.56128i
$$698$$ 13353.4 + 9701.82i 0.724118 + 0.526102i
$$699$$ 0 0
$$700$$ −28032.0 + 34528.7i −1.51358 + 1.86438i
$$701$$ −5192.49 −0.279768 −0.139884 0.990168i $$-0.544673\pi$$
−0.139884 + 0.990168i $$0.544673\pi$$
$$702$$ 0 0
$$703$$ 2621.48 + 8068.10i 0.140642 + 0.432851i
$$704$$ 621.041 + 1911.37i 0.0332477 + 0.102326i
$$705$$ 0 0
$$706$$ −2755.69 + 8481.13i −0.146900 + 0.452113i
$$707$$ 22503.2 1.19706
$$708$$ 0 0
$$709$$ 906.237 658.420i 0.0480035 0.0348766i −0.563525 0.826099i $$-0.690555\pi$$
0.611528 + 0.791223i $$0.290555\pi$$
$$710$$ 6114.81 + 6451.69i 0.323218 + 0.341025i
$$711$$ 0 0
$$712$$ −22587.6 + 16410.9i −1.18892 + 0.863798i
$$713$$ −22047.5 + 16018.4i −1.15804 + 0.841368i
$$714$$ 0 0
$$715$$ 532.390 979.089i 0.0278465 0.0512110i
$$716$$ 33323.0 24210.6i 1.73930 1.26368i
$$717$$ 0 0
$$718$$ 12254.8 0.636973
$$719$$ −7041.08 + 21670.2i −0.365213 + 1.12401i 0.584635 + 0.811297i $$0.301238\pi$$
−0.949848 + 0.312713i $$0.898762\pi$$
$$720$$ 0 0
$$721$$ −14745.2 45380.9i −0.761634 2.34407i
$$722$$ −19474.3 59935.7i −1.00382 3.08944i
$$723$$ 0 0
$$724$$ 33779.5 1.73399
$$725$$ 7896.94 9727.16i 0.404531 0.498286i
$$726$$ 0 0
$$727$$ −25911.7 18825.9i −1.32188 0.960406i −0.999907 0.0136585i $$-0.995652\pi$$
−0.321978 0.946747i $$-0.604348\pi$$
$$728$$ 8401.69 + 25857.7i 0.427730 + 1.31642i
$$729$$ 0 0
$$730$$ −47724.7 8875.93i −2.41969 0.450018i
$$731$$ 2882.24 8870.62i 0.145832 0.448826i
$$732$$ 0 0
$$733$$ 6712.80 20659.9i 0.338258 1.04105i −0.626837 0.779151i $$-0.715651\pi$$
0.965095 0.261901i $$-0.0843492\pi$$
$$734$$ −25613.8 + 18609.5i −1.28804 + 0.935816i
$$735$$ 0 0
$$736$$ 18911.6 + 13740.0i 0.947132 + 0.688132i
$$737$$ 714.458 519.084i 0.0357088 0.0259440i
$$738$$ 0 0
$$739$$ −24270.5 17633.5i −1.20812 0.877754i −0.213066 0.977038i $$-0.568345\pi$$
−0.995059 + 0.0992837i $$0.968345\pi$$
$$740$$ −8190.60 + 3900.47i −0.406882 + 0.193762i
$$741$$ 0 0
$$742$$ 14641.3 45061.2i 0.724391 2.22945i
$$743$$ 5551.03 0.274088 0.137044 0.990565i $$-0.456240\pi$$
0.137044 + 0.990565i $$0.456240\pi$$
$$744$$ 0 0
$$745$$ −4377.58 + 8050.56i −0.215278 + 0.395906i
$$746$$ 9643.40 + 29679.3i 0.473284 + 1.45662i
$$747$$ 0 0
$$748$$ 2363.31 + 1717.05i 0.115523 + 0.0839324i
$$749$$ −27033.9 −1.31882
$$750$$ 0 0
$$751$$ 5337.87 0.259363 0.129682 0.991556i $$-0.458604\pi$$
0.129682 + 0.991556i $$0.458604\pi$$
$$752$$ −627.122 455.631i −0.0304106 0.0220946i
$$753$$ 0 0
$$754$$ −5711.51 17578.2i −0.275863 0.849020i
$$755$$ −3030.73 + 5573.66i −0.146092 + 0.268670i
$$756$$ 0 0
$$757$$ −17462.2 −0.838409 −0.419205 0.907892i $$-0.637691\pi$$
−0.419205 + 0.907892i $$0.637691\pi$$
$$758$$ −5595.65 + 17221.6i −0.268131 + 0.825222i
$$759$$ 0 0
$$760$$ 37987.0 18089.9i 1.81307 0.863406i
$$761$$ 11011.7 + 8000.49i 0.524540 + 0.381100i 0.818311 0.574775i $$-0.194911\pi$$
−0.293772 + 0.955876i $$0.594911\pi$$
$$762$$ 0 0
$$763$$ 32807.4 23836.0i 1.55663 1.13096i
$$764$$ −7083.83 5146.71i −0.335450 0.243719i
$$765$$ 0 0
$$766$$ 21244.5 15435.1i 1.00208 0.728056i
$$767$$ −5050.96 + 15545.2i −0.237783 + 0.731820i
$$768$$ 0 0
$$769$$ −7403.09 + 22784.4i −0.347155 + 1.06843i 0.613265 + 0.789877i $$0.289856\pi$$
−0.960420 + 0.278556i $$0.910144\pi$$
$$770$$ 3352.19 + 623.446i 0.156889 + 0.0291785i
$$771$$ 0 0
$$772$$ −2781.80 8561.50i −0.129688 0.399139i
$$773$$ −28541.9 20736.9i −1.32805 0.964883i −0.999794 0.0202938i $$-0.993540\pi$$
−0.328254 0.944590i $$-0.606460\pi$$
$$774$$ 0 0
$$775$$ 20938.7 5582.62i 0.970504 0.258753i
$$776$$ −16902.4 −0.781909
$$777$$ 0 0
$$778$$ −6729.34 20710.8i −0.310101 0.954393i
$$779$$ −15687.1 48280.0i −0.721501 2.22055i
$$780$$ 0 0
$$781$$ 132.813 408.756i 0.00608505 0.0187278i
$$782$$ 62182.2 2.84352
$$783$$ 0 0
$$784$$ −3618.63 + 2629.09i −0.164843 + 0.119765i
$$785$$ 8778.47