# Properties

 Label 108.4.b.b.107.8 Level $108$ Weight $4$ Character 108.107 Analytic conductor $6.372$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 108.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.37220628062$$ Analytic rank: $$0$$ Dimension: $$12$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ Defining polynomial: $$x^{12} + 3 x^{10} - 12 x^{9} + 73 x^{8} - 12 x^{7} + 589 x^{6} + 84 x^{5} + 2452 x^{4} + 852 x^{3} + 6854 x^{2} - 888 x + 9496$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{14}\cdot 3^{12}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 107.8 Root $$-2.18604 - 2.07664i$$ of defining polynomial Character $$\chi$$ $$=$$ 108.107 Dual form 108.4.b.b.107.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.419903 + 2.79708i) q^{2} +(-7.64736 + 2.34901i) q^{4} -1.49508i q^{5} +26.1852i q^{7} +(-9.78152 - 20.4040i) q^{8} +O(q^{10})$$ $$q+(0.419903 + 2.79708i) q^{2} +(-7.64736 + 2.34901i) q^{4} -1.49508i q^{5} +26.1852i q^{7} +(-9.78152 - 20.4040i) q^{8} +(4.18188 - 0.627790i) q^{10} -56.3941 q^{11} -41.3170 q^{13} +(-73.2423 + 10.9953i) q^{14} +(52.9643 - 35.9274i) q^{16} -51.0410i q^{17} +79.0640i q^{19} +(3.51196 + 11.4335i) q^{20} +(-23.6801 - 157.739i) q^{22} -27.3688 q^{23} +122.765 q^{25} +(-17.3491 - 115.567i) q^{26} +(-61.5093 - 200.248i) q^{28} +134.567i q^{29} +187.192i q^{31} +(122.732 + 133.060i) q^{32} +(142.766 - 21.4323i) q^{34} +39.1491 q^{35} -196.585 q^{37} +(-221.149 + 33.1992i) q^{38} +(-30.5057 + 14.6242i) q^{40} -298.015i q^{41} +465.576i q^{43} +(431.267 - 132.470i) q^{44} +(-11.4922 - 76.5529i) q^{46} +373.845 q^{47} -342.667 q^{49} +(51.5492 + 343.383i) q^{50} +(315.966 - 97.0539i) q^{52} +620.093i q^{53} +84.3140i q^{55} +(534.283 - 256.131i) q^{56} +(-376.396 + 56.5052i) q^{58} +321.152 q^{59} +674.699 q^{61} +(-523.593 + 78.6026i) q^{62} +(-320.644 + 399.164i) q^{64} +61.7724i q^{65} -576.075i q^{67} +(119.896 + 390.329i) q^{68} +(16.4388 + 109.503i) q^{70} -223.813 q^{71} +70.1371 q^{73} +(-82.5465 - 549.864i) q^{74} +(-185.722 - 604.631i) q^{76} -1476.69i q^{77} -1052.32i q^{79} +(-53.7145 - 79.1862i) q^{80} +(833.574 - 125.137i) q^{82} -1219.05 q^{83} -76.3107 q^{85} +(-1302.26 + 195.497i) q^{86} +(551.621 + 1150.66i) q^{88} +1340.64i q^{89} -1081.89i q^{91} +(209.299 - 64.2895i) q^{92} +(156.979 + 1045.68i) q^{94} +118.207 q^{95} -576.059 q^{97} +(-143.887 - 958.467i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q + 6q^{4} + O(q^{10})$$ $$12q + 6q^{4} + 42q^{10} - 72q^{13} + 114q^{16} + 66q^{22} - 384q^{25} - 282q^{28} - 324q^{34} - 240q^{37} + 774q^{40} + 1752q^{46} + 288q^{49} + 924q^{52} - 948q^{58} + 144q^{61} - 3066q^{64} - 3558q^{70} + 156q^{73} + 576q^{76} + 5832q^{82} - 168q^{85} + 5022q^{88} - 3444q^{94} + 516q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$55$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.419903 + 2.79708i 0.148458 + 0.988919i
$$3$$ 0 0
$$4$$ −7.64736 + 2.34901i −0.955920 + 0.293626i
$$5$$ 1.49508i 0.133724i −0.997762 0.0668622i $$-0.978701\pi$$
0.997762 0.0668622i $$-0.0212988\pi$$
$$6$$ 0 0
$$7$$ 26.1852i 1.41387i 0.707279 + 0.706935i $$0.249923\pi$$
−0.707279 + 0.706935i $$0.750077\pi$$
$$8$$ −9.78152 20.4040i −0.432286 0.901736i
$$9$$ 0 0
$$10$$ 4.18188 0.627790i 0.132243 0.0198525i
$$11$$ −56.3941 −1.54577 −0.772885 0.634546i $$-0.781187\pi$$
−0.772885 + 0.634546i $$0.781187\pi$$
$$12$$ 0 0
$$13$$ −41.3170 −0.881482 −0.440741 0.897634i $$-0.645284\pi$$
−0.440741 + 0.897634i $$0.645284\pi$$
$$14$$ −73.2423 + 10.9953i −1.39820 + 0.209900i
$$15$$ 0 0
$$16$$ 52.9643 35.9274i 0.827568 0.561366i
$$17$$ 51.0410i 0.728192i −0.931361 0.364096i $$-0.881378\pi$$
0.931361 0.364096i $$-0.118622\pi$$
$$18$$ 0 0
$$19$$ 79.0640i 0.954659i 0.878724 + 0.477330i $$0.158395\pi$$
−0.878724 + 0.477330i $$0.841605\pi$$
$$20$$ 3.51196 + 11.4335i 0.0392650 + 0.127830i
$$21$$ 0 0
$$22$$ −23.6801 157.739i −0.229482 1.52864i
$$23$$ −27.3688 −0.248121 −0.124061 0.992275i $$-0.539592\pi$$
−0.124061 + 0.992275i $$0.539592\pi$$
$$24$$ 0 0
$$25$$ 122.765 0.982118
$$26$$ −17.3491 115.567i −0.130863 0.871714i
$$27$$ 0 0
$$28$$ −61.5093 200.248i −0.415149 1.35155i
$$29$$ 134.567i 0.861674i 0.902430 + 0.430837i $$0.141782\pi$$
−0.902430 + 0.430837i $$0.858218\pi$$
$$30$$ 0 0
$$31$$ 187.192i 1.08454i 0.840204 + 0.542270i $$0.182435\pi$$
−0.840204 + 0.542270i $$0.817565\pi$$
$$32$$ 122.732 + 133.060i 0.678004 + 0.735058i
$$33$$ 0 0
$$34$$ 142.766 21.4323i 0.720123 0.108106i
$$35$$ 39.1491 0.189069
$$36$$ 0 0
$$37$$ −196.585 −0.873469 −0.436734 0.899590i $$-0.643865\pi$$
−0.436734 + 0.899590i $$0.643865\pi$$
$$38$$ −221.149 + 33.1992i −0.944081 + 0.141727i
$$39$$ 0 0
$$40$$ −30.5057 + 14.6242i −0.120584 + 0.0578072i
$$41$$ 298.015i 1.13517i −0.823313 0.567587i $$-0.807877\pi$$
0.823313 0.567587i $$-0.192123\pi$$
$$42$$ 0 0
$$43$$ 465.576i 1.65115i 0.564289 + 0.825577i $$0.309150\pi$$
−0.564289 + 0.825577i $$0.690850\pi$$
$$44$$ 431.267 132.470i 1.47763 0.453878i
$$45$$ 0 0
$$46$$ −11.4922 76.5529i −0.0368356 0.245372i
$$47$$ 373.845 1.16023 0.580116 0.814534i $$-0.303007\pi$$
0.580116 + 0.814534i $$0.303007\pi$$
$$48$$ 0 0
$$49$$ −342.667 −0.999028
$$50$$ 51.5492 + 343.383i 0.145803 + 0.971235i
$$51$$ 0 0
$$52$$ 315.966 97.0539i 0.842627 0.258826i
$$53$$ 620.093i 1.60710i 0.595237 + 0.803550i $$0.297058\pi$$
−0.595237 + 0.803550i $$0.702942\pi$$
$$54$$ 0 0
$$55$$ 84.3140i 0.206707i
$$56$$ 534.283 256.131i 1.27494 0.611196i
$$57$$ 0 0
$$58$$ −376.396 + 56.5052i −0.852125 + 0.127922i
$$59$$ 321.152 0.708652 0.354326 0.935122i $$-0.384710\pi$$
0.354326 + 0.935122i $$0.384710\pi$$
$$60$$ 0 0
$$61$$ 674.699 1.41617 0.708085 0.706127i $$-0.249559\pi$$
0.708085 + 0.706127i $$0.249559\pi$$
$$62$$ −523.593 + 78.6026i −1.07252 + 0.161009i
$$63$$ 0 0
$$64$$ −320.644 + 399.164i −0.626257 + 0.779616i
$$65$$ 61.7724i 0.117876i
$$66$$ 0 0
$$67$$ 576.075i 1.05043i −0.850970 0.525215i $$-0.823985\pi$$
0.850970 0.525215i $$-0.176015\pi$$
$$68$$ 119.896 + 390.329i 0.213816 + 0.696094i
$$69$$ 0 0
$$70$$ 16.4388 + 109.503i 0.0280688 + 0.186974i
$$71$$ −223.813 −0.374110 −0.187055 0.982349i $$-0.559894\pi$$
−0.187055 + 0.982349i $$0.559894\pi$$
$$72$$ 0 0
$$73$$ 70.1371 0.112451 0.0562255 0.998418i $$-0.482093\pi$$
0.0562255 + 0.998418i $$0.482093\pi$$
$$74$$ −82.5465 549.864i −0.129673 0.863790i
$$75$$ 0 0
$$76$$ −185.722 604.631i −0.280313 0.912578i
$$77$$ 1476.69i 2.18552i
$$78$$ 0 0
$$79$$ 1052.32i 1.49868i −0.662187 0.749338i $$-0.730372\pi$$
0.662187 0.749338i $$-0.269628\pi$$
$$80$$ −53.7145 79.1862i −0.0750684 0.110666i
$$81$$ 0 0
$$82$$ 833.574 125.137i 1.12260 0.168526i
$$83$$ −1219.05 −1.61214 −0.806070 0.591820i $$-0.798409\pi$$
−0.806070 + 0.591820i $$0.798409\pi$$
$$84$$ 0 0
$$85$$ −76.3107 −0.0973771
$$86$$ −1302.26 + 195.497i −1.63286 + 0.245127i
$$87$$ 0 0
$$88$$ 551.621 + 1150.66i 0.668215 + 1.39388i
$$89$$ 1340.64i 1.59672i 0.602183 + 0.798358i $$0.294298\pi$$
−0.602183 + 0.798358i $$0.705702\pi$$
$$90$$ 0 0
$$91$$ 1081.89i 1.24630i
$$92$$ 209.299 64.2895i 0.237184 0.0728548i
$$93$$ 0 0
$$94$$ 156.979 + 1045.68i 0.172246 + 1.14737i
$$95$$ 118.207 0.127661
$$96$$ 0 0
$$97$$ −576.059 −0.602989 −0.301494 0.953468i $$-0.597485\pi$$
−0.301494 + 0.953468i $$0.597485\pi$$
$$98$$ −143.887 958.467i −0.148314 0.987957i
$$99$$ 0 0
$$100$$ −938.826 + 288.375i −0.938826 + 0.288375i
$$101$$ 116.079i 0.114359i 0.998364 + 0.0571797i $$0.0182108\pi$$
−0.998364 + 0.0571797i $$0.981789\pi$$
$$102$$ 0 0
$$103$$ 165.074i 0.157915i −0.996878 0.0789573i $$-0.974841\pi$$
0.996878 0.0789573i $$-0.0251591\pi$$
$$104$$ 404.143 + 843.030i 0.381052 + 0.794864i
$$105$$ 0 0
$$106$$ −1734.45 + 260.379i −1.58929 + 0.238587i
$$107$$ −936.718 −0.846318 −0.423159 0.906056i $$-0.639079\pi$$
−0.423159 + 0.906056i $$0.639079\pi$$
$$108$$ 0 0
$$109$$ 346.957 0.304885 0.152443 0.988312i $$-0.451286\pi$$
0.152443 + 0.988312i $$0.451286\pi$$
$$110$$ −235.833 + 35.4037i −0.204417 + 0.0306874i
$$111$$ 0 0
$$112$$ 940.768 + 1386.88i 0.793698 + 1.17007i
$$113$$ 1462.22i 1.21729i −0.793443 0.608645i $$-0.791713\pi$$
0.793443 0.608645i $$-0.208287\pi$$
$$114$$ 0 0
$$115$$ 40.9187i 0.0331799i
$$116$$ −316.100 1029.09i −0.253010 0.823691i
$$117$$ 0 0
$$118$$ 134.853 + 898.290i 0.105205 + 0.700799i
$$119$$ 1336.52 1.02957
$$120$$ 0 0
$$121$$ 1849.30 1.38941
$$122$$ 283.308 + 1887.19i 0.210242 + 1.40048i
$$123$$ 0 0
$$124$$ −439.716 1431.53i −0.318449 1.03673i
$$125$$ 370.429i 0.265058i
$$126$$ 0 0
$$127$$ 265.004i 0.185160i 0.995705 + 0.0925800i $$0.0295114\pi$$
−0.995705 + 0.0925800i $$0.970489\pi$$
$$128$$ −1251.13 729.258i −0.863950 0.503577i
$$129$$ 0 0
$$130$$ −172.783 + 25.9384i −0.116569 + 0.0174996i
$$131$$ −1151.86 −0.768231 −0.384115 0.923285i $$-0.625493\pi$$
−0.384115 + 0.923285i $$0.625493\pi$$
$$132$$ 0 0
$$133$$ −2070.31 −1.34976
$$134$$ 1611.33 241.896i 1.03879 0.155945i
$$135$$ 0 0
$$136$$ −1041.44 + 499.259i −0.656637 + 0.314787i
$$137$$ 2348.67i 1.46467i 0.680943 + 0.732337i $$0.261570\pi$$
−0.680943 + 0.732337i $$0.738430\pi$$
$$138$$ 0 0
$$139$$ 215.240i 0.131341i −0.997841 0.0656706i $$-0.979081\pi$$
0.997841 0.0656706i $$-0.0209187\pi$$
$$140$$ −299.388 + 91.9616i −0.180735 + 0.0555155i
$$141$$ 0 0
$$142$$ −93.9799 626.025i −0.0555396 0.369964i
$$143$$ 2330.04 1.36257
$$144$$ 0 0
$$145$$ 201.190 0.115227
$$146$$ 29.4508 + 196.179i 0.0166943 + 0.111205i
$$147$$ 0 0
$$148$$ 1503.36 461.779i 0.834967 0.256473i
$$149$$ 219.954i 0.120935i 0.998170 + 0.0604674i $$0.0192591\pi$$
−0.998170 + 0.0604674i $$0.980741\pi$$
$$150$$ 0 0
$$151$$ 1148.02i 0.618703i −0.950948 0.309351i $$-0.899888\pi$$
0.950948 0.309351i $$-0.100112\pi$$
$$152$$ 1613.22 773.366i 0.860851 0.412686i
$$153$$ 0 0
$$154$$ 4130.44 620.068i 2.16130 0.324458i
$$155$$ 279.869 0.145030
$$156$$ 0 0
$$157$$ −276.320 −0.140463 −0.0702316 0.997531i $$-0.522374\pi$$
−0.0702316 + 0.997531i $$0.522374\pi$$
$$158$$ 2943.43 441.873i 1.48207 0.222491i
$$159$$ 0 0
$$160$$ 198.936 183.495i 0.0982952 0.0906658i
$$161$$ 716.659i 0.350811i
$$162$$ 0 0
$$163$$ 1419.15i 0.681941i 0.940074 + 0.340971i $$0.110756\pi$$
−0.940074 + 0.340971i $$0.889244\pi$$
$$164$$ 700.040 + 2279.03i 0.333317 + 1.08514i
$$165$$ 0 0
$$166$$ −511.880 3409.77i −0.239335 1.59428i
$$167$$ 3508.69 1.62581 0.812906 0.582394i $$-0.197884\pi$$
0.812906 + 0.582394i $$0.197884\pi$$
$$168$$ 0 0
$$169$$ −489.908 −0.222990
$$170$$ −32.0431 213.447i −0.0144564 0.0962980i
$$171$$ 0 0
$$172$$ −1093.64 3560.43i −0.484822 1.57837i
$$173$$ 330.965i 0.145450i −0.997352 0.0727248i $$-0.976831\pi$$
0.997352 0.0727248i $$-0.0231695\pi$$
$$174$$ 0 0
$$175$$ 3214.62i 1.38859i
$$176$$ −2986.88 + 2026.10i −1.27923 + 0.867743i
$$177$$ 0 0
$$178$$ −3749.89 + 562.939i −1.57902 + 0.237045i
$$179$$ −1136.75 −0.474662 −0.237331 0.971429i $$-0.576273\pi$$
−0.237331 + 0.971429i $$0.576273\pi$$
$$180$$ 0 0
$$181$$ 2056.92 0.844692 0.422346 0.906435i $$-0.361207\pi$$
0.422346 + 0.906435i $$0.361207\pi$$
$$182$$ 3026.15 454.291i 1.23249 0.185023i
$$183$$ 0 0
$$184$$ 267.709 + 558.432i 0.107259 + 0.223740i
$$185$$ 293.911i 0.116804i
$$186$$ 0 0
$$187$$ 2878.42i 1.12562i
$$188$$ −2858.93 + 878.164i −1.10909 + 0.340674i
$$189$$ 0 0
$$190$$ 49.6356 + 330.636i 0.0189523 + 0.126247i
$$191$$ −1983.23 −0.751316 −0.375658 0.926758i $$-0.622583\pi$$
−0.375658 + 0.926758i $$0.622583\pi$$
$$192$$ 0 0
$$193$$ −189.908 −0.0708283 −0.0354141 0.999373i $$-0.511275\pi$$
−0.0354141 + 0.999373i $$0.511275\pi$$
$$194$$ −241.889 1611.29i −0.0895185 0.596307i
$$195$$ 0 0
$$196$$ 2620.50 804.926i 0.954991 0.293340i
$$197$$ 2160.42i 0.781337i 0.920531 + 0.390669i $$0.127756\pi$$
−0.920531 + 0.390669i $$0.872244\pi$$
$$198$$ 0 0
$$199$$ 2656.23i 0.946205i 0.881007 + 0.473103i $$0.156866\pi$$
−0.881007 + 0.473103i $$0.843134\pi$$
$$200$$ −1200.83 2504.89i −0.424556 0.885611i
$$201$$ 0 0
$$202$$ −324.683 + 48.7419i −0.113092 + 0.0169776i
$$203$$ −3523.68 −1.21829
$$204$$ 0 0
$$205$$ −445.558 −0.151801
$$206$$ 461.725 69.3149i 0.156165 0.0234437i
$$207$$ 0 0
$$208$$ −2188.33 + 1484.41i −0.729486 + 0.494834i
$$209$$ 4458.75i 1.47568i
$$210$$ 0 0
$$211$$ 1001.20i 0.326662i 0.986571 + 0.163331i $$0.0522239\pi$$
−0.986571 + 0.163331i $$0.947776\pi$$
$$212$$ −1456.60 4742.07i −0.471886 1.53626i
$$213$$ 0 0
$$214$$ −393.331 2620.08i −0.125643 0.836939i
$$215$$ 696.075 0.220800
$$216$$ 0 0
$$217$$ −4901.68 −1.53340
$$218$$ 145.688 + 970.469i 0.0452626 + 0.301507i
$$219$$ 0 0
$$220$$ −198.054 644.780i −0.0606946 0.197596i
$$221$$ 2108.86i 0.641888i
$$222$$ 0 0
$$223$$ 3193.62i 0.959015i 0.877538 + 0.479507i $$0.159185\pi$$
−0.877538 + 0.479507i $$0.840815\pi$$
$$224$$ −3484.20 + 3213.76i −1.03928 + 0.958610i
$$225$$ 0 0
$$226$$ 4089.94 613.989i 1.20380 0.180717i
$$227$$ −1714.72 −0.501366 −0.250683 0.968069i $$-0.580655\pi$$
−0.250683 + 0.968069i $$0.580655\pi$$
$$228$$ 0 0
$$229$$ −407.497 −0.117590 −0.0587951 0.998270i $$-0.518726\pi$$
−0.0587951 + 0.998270i $$0.518726\pi$$
$$230$$ −114.453 + 17.1819i −0.0328122 + 0.00492582i
$$231$$ 0 0
$$232$$ 2745.71 1316.27i 0.777003 0.372490i
$$233$$ 3210.54i 0.902702i −0.892346 0.451351i $$-0.850942\pi$$
0.892346 0.451351i $$-0.149058\pi$$
$$234$$ 0 0
$$235$$ 558.930i 0.155151i
$$236$$ −2455.97 + 754.389i −0.677415 + 0.208079i
$$237$$ 0 0
$$238$$ 561.209 + 3738.36i 0.152848 + 1.01816i
$$239$$ 1561.19 0.422532 0.211266 0.977429i $$-0.432241\pi$$
0.211266 + 0.977429i $$0.432241\pi$$
$$240$$ 0 0
$$241$$ 1460.89 0.390475 0.195238 0.980756i $$-0.437452\pi$$
0.195238 + 0.980756i $$0.437452\pi$$
$$242$$ 776.526 + 5172.65i 0.206269 + 1.37401i
$$243$$ 0 0
$$244$$ −5159.67 + 1584.87i −1.35375 + 0.415824i
$$245$$ 512.316i 0.133594i
$$246$$ 0 0
$$247$$ 3266.69i 0.841515i
$$248$$ 3819.47 1831.03i 0.977970 0.468832i
$$249$$ 0 0
$$250$$ 1036.12 155.544i 0.262120 0.0393499i
$$251$$ −6868.44 −1.72722 −0.863609 0.504162i $$-0.831802\pi$$
−0.863609 + 0.504162i $$0.831802\pi$$
$$252$$ 0 0
$$253$$ 1543.44 0.383539
$$254$$ −741.239 + 111.276i −0.183108 + 0.0274885i
$$255$$ 0 0
$$256$$ 1514.44 3805.74i 0.369737 0.929137i
$$257$$ 4450.84i 1.08029i 0.841570 + 0.540147i $$0.181632\pi$$
−0.841570 + 0.540147i $$0.818368\pi$$
$$258$$ 0 0
$$259$$ 5147.62i 1.23497i
$$260$$ −145.104 472.396i −0.0346114 0.112680i
$$261$$ 0 0
$$262$$ −483.668 3221.84i −0.114050 0.759718i
$$263$$ 6525.31 1.52991 0.764957 0.644081i $$-0.222760\pi$$
0.764957 + 0.644081i $$0.222760\pi$$
$$264$$ 0 0
$$265$$ 927.091 0.214909
$$266$$ −869.329 5790.83i −0.200383 1.33481i
$$267$$ 0 0
$$268$$ 1353.20 + 4405.46i 0.308433 + 1.00413i
$$269$$ 3222.22i 0.730343i −0.930940 0.365171i $$-0.881010\pi$$
0.930940 0.365171i $$-0.118990\pi$$
$$270$$ 0 0
$$271$$ 7368.93i 1.65177i −0.563837 0.825886i $$-0.690675\pi$$
0.563837 0.825886i $$-0.309325\pi$$
$$272$$ −1833.77 2703.35i −0.408782 0.602628i
$$273$$ 0 0
$$274$$ −6569.42 + 986.212i −1.44844 + 0.217443i
$$275$$ −6923.21 −1.51813
$$276$$ 0 0
$$277$$ 9078.61 1.96924 0.984622 0.174699i $$-0.0558952\pi$$
0.984622 + 0.174699i $$0.0558952\pi$$
$$278$$ 602.045 90.3800i 0.129886 0.0194987i
$$279$$ 0 0
$$280$$ −382.938 798.798i −0.0817319 0.170490i
$$281$$ 2613.34i 0.554801i −0.960754 0.277400i $$-0.910527\pi$$
0.960754 0.277400i $$-0.0894729\pi$$
$$282$$ 0 0
$$283$$ 927.970i 0.194919i −0.995239 0.0974596i $$-0.968928\pi$$
0.995239 0.0974596i $$-0.0310717\pi$$
$$284$$ 1711.58 525.739i 0.357619 0.109848i
$$285$$ 0 0
$$286$$ 978.388 + 6517.31i 0.202284 + 1.34747i
$$287$$ 7803.60 1.60499
$$288$$ 0 0
$$289$$ 2307.81 0.469736
$$290$$ 84.4801 + 562.745i 0.0171064 + 0.113950i
$$291$$ 0 0
$$292$$ −536.364 + 164.753i −0.107494 + 0.0330185i
$$293$$ 5351.73i 1.06707i 0.845778 + 0.533535i $$0.179137\pi$$
−0.845778 + 0.533535i $$0.820863\pi$$
$$294$$ 0 0
$$295$$ 480.150i 0.0947641i
$$296$$ 1922.90 + 4011.11i 0.377589 + 0.787639i
$$297$$ 0 0
$$298$$ −615.229 + 92.3591i −0.119595 + 0.0179538i
$$299$$ 1130.80 0.218714
$$300$$ 0 0
$$301$$ −12191.2 −2.33452
$$302$$ 3211.10 482.055i 0.611847 0.0918514i
$$303$$ 0 0
$$304$$ 2840.57 + 4187.57i 0.535913 + 0.790045i
$$305$$ 1008.73i 0.189377i
$$306$$ 0 0
$$307$$ 1892.38i 0.351804i 0.984408 + 0.175902i $$0.0562842\pi$$
−0.984408 + 0.175902i $$0.943716\pi$$
$$308$$ 3468.76 + 11292.8i 0.641725 + 2.08918i
$$309$$ 0 0
$$310$$ 117.518 + 782.816i 0.0215308 + 0.143422i
$$311$$ 5645.22 1.02930 0.514648 0.857402i $$-0.327923\pi$$
0.514648 + 0.857402i $$0.327923\pi$$
$$312$$ 0 0
$$313$$ −818.001 −0.147719 −0.0738597 0.997269i $$-0.523532\pi$$
−0.0738597 + 0.997269i $$0.523532\pi$$
$$314$$ −116.027 772.890i −0.0208529 0.138907i
$$315$$ 0 0
$$316$$ 2471.91 + 8047.49i 0.440050 + 1.43262i
$$317$$ 1946.72i 0.344917i −0.985017 0.172458i $$-0.944829\pi$$
0.985017 0.172458i $$-0.0551710\pi$$
$$318$$ 0 0
$$319$$ 7588.81i 1.33195i
$$320$$ 596.784 + 479.390i 0.104254 + 0.0837459i
$$321$$ 0 0
$$322$$ 2004.55 300.927i 0.346924 0.0520807i
$$323$$ 4035.51 0.695176
$$324$$ 0 0
$$325$$ −5072.27 −0.865719
$$326$$ −3969.48 + 595.905i −0.674385 + 0.101240i
$$327$$ 0 0
$$328$$ −6080.69 + 2915.04i −1.02363 + 0.490720i
$$329$$ 9789.22i 1.64042i
$$330$$ 0 0
$$331$$ 3404.83i 0.565396i −0.959209 0.282698i $$-0.908771\pi$$
0.959209 0.282698i $$-0.0912295\pi$$
$$332$$ 9322.48 2863.55i 1.54108 0.473366i
$$333$$ 0 0
$$334$$ 1473.31 + 9814.11i 0.241365 + 1.60780i
$$335$$ −861.281 −0.140468
$$336$$ 0 0
$$337$$ 7072.15 1.14316 0.571579 0.820547i $$-0.306331\pi$$
0.571579 + 0.820547i $$0.306331\pi$$
$$338$$ −205.714 1370.31i −0.0331046 0.220519i
$$339$$ 0 0
$$340$$ 583.575 179.254i 0.0930848 0.0285924i
$$341$$ 10556.6i 1.67645i
$$342$$ 0 0
$$343$$ 8.73194i 0.00137458i
$$344$$ 9499.60 4554.04i 1.48891 0.713771i
$$345$$ 0 0
$$346$$ 925.736 138.973i 0.143838 0.0215932i
$$347$$ 5783.02 0.894665 0.447332 0.894368i $$-0.352374\pi$$
0.447332 + 0.894368i $$0.352374\pi$$
$$348$$ 0 0
$$349$$ 1748.60 0.268196 0.134098 0.990968i $$-0.457186\pi$$
0.134098 + 0.990968i $$0.457186\pi$$
$$350$$ −8991.57 + 1349.83i −1.37320 + 0.206147i
$$351$$ 0 0
$$352$$ −6921.36 7503.79i −1.04804 1.13623i
$$353$$ 9552.31i 1.44028i 0.693830 + 0.720139i $$0.255922\pi$$
−0.693830 + 0.720139i $$0.744078\pi$$
$$354$$ 0 0
$$355$$ 334.620i 0.0500276i
$$356$$ −3149.18 10252.4i −0.468837 1.52633i
$$357$$ 0 0
$$358$$ −477.323 3179.58i −0.0704673 0.469402i
$$359$$ 921.392 0.135457 0.0677287 0.997704i $$-0.478425\pi$$
0.0677287 + 0.997704i $$0.478425\pi$$
$$360$$ 0 0
$$361$$ 607.881 0.0886254
$$362$$ 863.704 + 5753.37i 0.125401 + 0.835332i
$$363$$ 0 0
$$364$$ 2541.38 + 8273.64i 0.365946 + 1.19136i
$$365$$ 104.861i 0.0150375i
$$366$$ 0 0
$$367$$ 8490.66i 1.20765i 0.797115 + 0.603827i $$0.206358\pi$$
−0.797115 + 0.603827i $$0.793642\pi$$
$$368$$ −1449.57 + 983.291i −0.205337 + 0.139287i
$$369$$ 0 0
$$370$$ −822.094 + 123.414i −0.115510 + 0.0173405i
$$371$$ −16237.3 −2.27223
$$372$$ 0 0
$$373$$ 2824.92 0.392142 0.196071 0.980590i $$-0.437182\pi$$
0.196071 + 0.980590i $$0.437182\pi$$
$$374$$ −8051.17 + 1208.65i −1.11314 + 0.167107i
$$375$$ 0 0
$$376$$ −3656.77 7627.92i −0.501552 1.04622i
$$377$$ 5559.92i 0.759550i
$$378$$ 0 0
$$379$$ 5322.35i 0.721348i −0.932692 0.360674i $$-0.882547\pi$$
0.932692 0.360674i $$-0.117453\pi$$
$$380$$ −903.975 + 277.670i −0.122034 + 0.0374847i
$$381$$ 0 0
$$382$$ −832.763 5547.26i −0.111539 0.742990i
$$383$$ −8320.49 −1.11007 −0.555035 0.831827i $$-0.687295\pi$$
−0.555035 + 0.831827i $$0.687295\pi$$
$$384$$ 0 0
$$385$$ −2207.78 −0.292257
$$386$$ −79.7428 531.188i −0.0105150 0.0700434i
$$387$$ 0 0
$$388$$ 4405.33 1353.17i 0.576409 0.177053i
$$389$$ 8358.52i 1.08944i −0.838617 0.544722i $$-0.816635\pi$$
0.838617 0.544722i $$-0.183365\pi$$
$$390$$ 0 0
$$391$$ 1396.93i 0.180680i
$$392$$ 3351.80 + 6991.76i 0.431866 + 0.900860i
$$393$$ 0 0
$$394$$ −6042.87 + 907.166i −0.772679 + 0.115996i
$$395$$ −1573.31 −0.200410
$$396$$ 0 0
$$397$$ 7283.17 0.920735 0.460367 0.887728i $$-0.347718\pi$$
0.460367 + 0.887728i $$0.347718\pi$$
$$398$$ −7429.69 + 1115.36i −0.935720 + 0.140472i
$$399$$ 0 0
$$400$$ 6502.15 4410.62i 0.812769 0.551327i
$$401$$ 1549.41i 0.192952i −0.995335 0.0964759i $$-0.969243\pi$$
0.995335 0.0964759i $$-0.0307571\pi$$
$$402$$ 0 0
$$403$$ 7734.22i 0.956003i
$$404$$ −272.671 887.699i −0.0335789 0.109318i
$$405$$ 0 0
$$406$$ −1479.60 9856.03i −0.180866 1.20479i
$$407$$ 11086.2 1.35018
$$408$$ 0 0
$$409$$ 3291.67 0.397952 0.198976 0.980004i $$-0.436238\pi$$
0.198976 + 0.980004i $$0.436238\pi$$
$$410$$ −187.091 1246.26i −0.0225360 0.150118i
$$411$$ 0 0
$$412$$ 387.759 + 1262.38i 0.0463678 + 0.150954i
$$413$$ 8409.45i 1.00194i
$$414$$ 0 0
$$415$$ 1822.58i 0.215583i
$$416$$ −5070.91 5497.62i −0.597649 0.647940i
$$417$$ 0 0
$$418$$ 12471.5 1872.24i 1.45933 0.219077i
$$419$$ −5299.78 −0.617927 −0.308964 0.951074i $$-0.599982\pi$$
−0.308964 + 0.951074i $$0.599982\pi$$
$$420$$ 0 0
$$421$$ −10681.4 −1.23653 −0.618265 0.785970i $$-0.712164\pi$$
−0.618265 + 0.785970i $$0.712164\pi$$
$$422$$ −2800.45 + 420.408i −0.323042 + 0.0484956i
$$423$$ 0 0
$$424$$ 12652.4 6065.45i 1.44918 0.694727i
$$425$$ 6266.04i 0.715170i
$$426$$ 0 0
$$427$$ 17667.2i 2.00228i
$$428$$ 7163.43 2200.36i 0.809012 0.248501i
$$429$$ 0 0
$$430$$ 292.284 + 1946.98i 0.0327795 + 0.218353i
$$431$$ −9866.13 −1.10263 −0.551316 0.834296i $$-0.685874\pi$$
−0.551316 + 0.834296i $$0.685874\pi$$
$$432$$ 0 0
$$433$$ −12560.2 −1.39400 −0.697002 0.717069i $$-0.745483\pi$$
−0.697002 + 0.717069i $$0.745483\pi$$
$$434$$ −2058.23 13710.4i −0.227645 1.51641i
$$435$$ 0 0
$$436$$ −2653.31 + 815.005i −0.291446 + 0.0895221i
$$437$$ 2163.89i 0.236871i
$$438$$ 0 0
$$439$$ 929.228i 0.101024i 0.998723 + 0.0505121i $$0.0160854\pi$$
−0.998723 + 0.0505121i $$0.983915\pi$$
$$440$$ 1720.34 824.719i 0.186396 0.0893567i
$$441$$ 0 0
$$442$$ −5898.66 + 885.516i −0.634775 + 0.0952935i
$$443$$ 4373.85 0.469092 0.234546 0.972105i $$-0.424640\pi$$
0.234546 + 0.972105i $$0.424640\pi$$
$$444$$ 0 0
$$445$$ 2004.37 0.213520
$$446$$ −8932.81 + 1341.01i −0.948388 + 0.142373i
$$447$$ 0 0
$$448$$ −10452.2 8396.13i −1.10228 0.885446i
$$449$$ 14149.5i 1.48721i 0.668618 + 0.743606i $$0.266886\pi$$
−0.668618 + 0.743606i $$0.733114\pi$$
$$450$$ 0 0
$$451$$ 16806.3i 1.75472i
$$452$$ 3434.76 + 11182.1i 0.357428 + 1.16363i
$$453$$ 0 0
$$454$$ −720.017 4796.22i −0.0744319 0.495810i
$$455$$ −1617.52 −0.166661
$$456$$ 0 0
$$457$$ −12582.4 −1.28792 −0.643960 0.765059i $$-0.722710\pi$$
−0.643960 + 0.765059i $$0.722710\pi$$
$$458$$ −171.109 1139.80i −0.0174572 0.116287i
$$459$$ 0 0
$$460$$ −96.1183 312.920i −0.00974247 0.0317173i
$$461$$ 10602.2i 1.07114i 0.844492 + 0.535568i $$0.179902\pi$$
−0.844492 + 0.535568i $$0.820098\pi$$
$$462$$ 0 0
$$463$$ 5080.88i 0.509997i 0.966941 + 0.254999i $$0.0820750\pi$$
−0.966941 + 0.254999i $$0.917925\pi$$
$$464$$ 4834.66 + 7127.27i 0.483714 + 0.713093i
$$465$$ 0 0
$$466$$ 8980.16 1348.12i 0.892699 0.134013i
$$467$$ −6903.92 −0.684102 −0.342051 0.939681i $$-0.611121\pi$$
−0.342051 + 0.939681i $$0.611121\pi$$
$$468$$ 0 0
$$469$$ 15084.7 1.48517
$$470$$ 1563.37 234.696i 0.153432 0.0230335i
$$471$$ 0 0
$$472$$ −3141.36 6552.78i −0.306341 0.639017i
$$473$$ 26255.8i 2.55231i
$$474$$ 0 0
$$475$$ 9706.27i 0.937588i
$$476$$ −10220.9 + 3139.50i −0.984186 + 0.302308i
$$477$$ 0 0
$$478$$ 655.548 + 4366.78i 0.0627282 + 0.417849i
$$479$$ 5114.56 0.487871 0.243936 0.969791i $$-0.421561\pi$$
0.243936 + 0.969791i $$0.421561\pi$$
$$480$$ 0 0
$$481$$ 8122.29 0.769947
$$482$$ 613.434 + 4086.25i 0.0579692 + 0.386148i
$$483$$ 0 0
$$484$$ −14142.3 + 4344.02i −1.32816 + 0.407966i
$$485$$ 861.257i 0.0806344i
$$486$$ 0 0
$$487$$ 15594.2i 1.45101i 0.688218 + 0.725504i $$0.258393\pi$$
−0.688218 + 0.725504i $$0.741607\pi$$
$$488$$ −6599.58 13766.5i −0.612191 1.27701i
$$489$$ 0 0
$$490$$ −1432.99 + 215.123i −0.132114 + 0.0198332i
$$491$$ 10521.0 0.967023 0.483511 0.875338i $$-0.339361\pi$$
0.483511 + 0.875338i $$0.339361\pi$$
$$492$$ 0 0
$$493$$ 6868.46 0.627464
$$494$$ 9137.20 1371.69i 0.832190 0.124930i
$$495$$ 0 0
$$496$$ 6725.34 + 9914.52i 0.608824 + 0.897531i
$$497$$ 5860.61i 0.528942i
$$498$$ 0 0
$$499$$ 8984.43i 0.806009i −0.915198 0.403004i $$-0.867966\pi$$
0.915198 0.403004i $$-0.132034\pi$$
$$500$$ 870.141 + 2832.81i 0.0778278 + 0.253374i
$$501$$ 0 0
$$502$$ −2884.08 19211.6i −0.256420 1.70808i
$$503$$ 4299.12 0.381090 0.190545 0.981678i $$-0.438974\pi$$
0.190545 + 0.981678i $$0.438974\pi$$
$$504$$ 0 0
$$505$$ 173.548 0.0152926
$$506$$ 648.095 + 4317.13i 0.0569394 + 0.379288i
$$507$$ 0 0
$$508$$ −622.497 2026.58i −0.0543678 0.176998i
$$509$$ 2984.83i 0.259922i 0.991519 + 0.129961i $$0.0414853\pi$$
−0.991519 + 0.129961i $$0.958515\pi$$
$$510$$ 0 0
$$511$$ 1836.56i 0.158991i
$$512$$ 11280.9 + 2637.98i 0.973731 + 0.227702i
$$513$$ 0 0
$$514$$ −12449.4 + 1868.92i −1.06832 + 0.160378i
$$515$$ −246.799 −0.0211170
$$516$$ 0 0
$$517$$ −21082.7 −1.79345
$$518$$ 14398.3 2161.50i 1.22129 0.183341i
$$519$$ 0 0
$$520$$ 1260.40 604.228i 0.106293 0.0509560i
$$521$$ 12255.7i 1.03058i 0.857016 + 0.515290i $$0.172316\pi$$
−0.857016 + 0.515290i $$0.827684\pi$$
$$522$$ 0 0
$$523$$ 15148.5i 1.26654i −0.773932 0.633269i $$-0.781713\pi$$
0.773932 0.633269i $$-0.218287\pi$$
$$524$$ 8808.67 2705.72i 0.734367 0.225572i
$$525$$ 0 0
$$526$$ 2739.99 + 18251.8i 0.227128 + 1.51296i
$$527$$ 9554.49 0.789754
$$528$$ 0 0
$$529$$ −11417.9 −0.938436
$$530$$ 389.288 + 2593.15i 0.0319049 + 0.212527i
$$531$$ 0 0
$$532$$ 15832.4 4863.17i 1.29027 0.396326i
$$533$$ 12313.1i 1.00064i
$$534$$ 0 0
$$535$$ 1400.47i 0.113173i
$$536$$ −11754.2 + 5634.89i −0.947211 + 0.454086i
$$537$$ 0 0
$$538$$ 9012.82 1353.02i 0.722250 0.108425i
$$539$$ 19324.4 1.54427
$$540$$ 0 0
$$541$$ 5723.84 0.454875 0.227437 0.973793i $$-0.426965\pi$$
0.227437 + 0.973793i $$0.426965\pi$$
$$542$$ 20611.5 3094.23i 1.63347 0.245219i
$$543$$ 0 0
$$544$$ 6791.50 6264.36i 0.535263 0.493717i
$$545$$ 518.730i 0.0407706i
$$546$$ 0 0
$$547$$ 8367.43i 0.654051i 0.945016 + 0.327025i $$0.106046\pi$$
−0.945016 + 0.327025i $$0.893954\pi$$
$$548$$ −5517.04 17961.1i −0.430066 1.40011i
$$549$$ 0 0
$$550$$ −2907.08 19364.8i −0.225378 1.50131i
$$551$$ −10639.4 −0.822605
$$552$$ 0 0
$$553$$ 27555.3 2.11893
$$554$$ 3812.13 + 25393.6i 0.292350 + 1.94742i
$$555$$ 0 0
$$556$$ 505.601 + 1646.02i 0.0385652 + 0.125552i
$$557$$ 15824.2i 1.20375i 0.798589 + 0.601877i $$0.205580\pi$$
−0.798589 + 0.601877i $$0.794420\pi$$
$$558$$ 0 0
$$559$$ 19236.2i 1.45546i
$$560$$ 2073.51 1406.53i 0.156467 0.106137i
$$561$$ 0 0
$$562$$ 7309.74 1097.35i 0.548653 0.0823647i
$$563$$ 2781.72 0.208233 0.104117 0.994565i $$-0.466798\pi$$
0.104117 + 0.994565i $$0.466798\pi$$
$$564$$ 0 0
$$565$$ −2186.14 −0.162781
$$566$$ 2595.61 389.657i 0.192759 0.0289373i
$$567$$ 0 0
$$568$$ 2189.24 + 4566.68i 0.161722 + 0.337348i
$$569$$ 4687.63i 0.345370i 0.984977 + 0.172685i $$0.0552443\pi$$
−0.984977 + 0.172685i $$0.944756\pi$$
$$570$$ 0 0
$$571$$ 15169.4i 1.11177i −0.831259 0.555885i $$-0.812379\pi$$
0.831259 0.555885i $$-0.187621\pi$$
$$572$$ −17818.6 + 5473.27i −1.30251 + 0.400085i
$$573$$ 0 0
$$574$$ 3276.75 + 21827.3i 0.238274 + 1.58720i
$$575$$ −3359.92 −0.243684
$$576$$ 0 0
$$577$$ −14452.3 −1.04273 −0.521367 0.853332i $$-0.674578\pi$$
−0.521367 + 0.853332i $$0.674578\pi$$
$$578$$ 969.057 + 6455.15i 0.0697361 + 0.464531i
$$579$$ 0 0
$$580$$ −1538.57 + 472.596i −0.110148 + 0.0338336i
$$581$$ 31921.0i 2.27936i
$$582$$ 0 0
$$583$$ 34969.6i 2.48421i
$$584$$ −686.047 1431.07i −0.0486110 0.101401i
$$585$$ 0 0
$$586$$ −14969.3 + 2247.21i −1.05525 + 0.158415i
$$587$$ 7405.55 0.520715 0.260358 0.965512i $$-0.416160\pi$$
0.260358 + 0.965512i $$0.416160\pi$$
$$588$$ 0 0
$$589$$ −14800.2 −1.03537
$$590$$ 1343.02 201.616i 0.0937140 0.0140685i
$$591$$ 0 0
$$592$$ −10412.0 + 7062.79i −0.722855 + 0.490336i
$$593$$ 19888.1i 1.37725i −0.725120 0.688623i $$-0.758216\pi$$
0.725120 0.688623i $$-0.241784\pi$$
$$594$$ 0 0
$$595$$ 1998.21i 0.137679i
$$596$$ −516.672 1682.06i −0.0355096 0.115604i
$$597$$ 0 0
$$598$$ 474.824 + 3162.93i 0.0324699 + 0.216291i
$$599$$ 2335.49 0.159308 0.0796539 0.996823i $$-0.474618\pi$$
0.0796539 + 0.996823i $$0.474618\pi$$
$$600$$ 0 0
$$601$$ 24547.9 1.66611 0.833054 0.553192i $$-0.186590\pi$$
0.833054 + 0.553192i $$0.186590\pi$$
$$602$$ −5119.12 34099.9i −0.346578 2.30865i
$$603$$ 0 0
$$604$$ 2696.70 + 8779.29i 0.181667 + 0.591431i
$$605$$ 2764.86i 0.185798i
$$606$$ 0 0
$$607$$ 18328.9i 1.22561i 0.790233 + 0.612806i $$0.209959\pi$$
−0.790233 + 0.612806i $$0.790041\pi$$
$$608$$ −10520.2 + 9703.68i −0.701730 + 0.647263i
$$609$$ 0 0
$$610$$ 2821.51 423.570i 0.187278 0.0281145i
$$611$$ −15446.1 −1.02272
$$612$$ 0 0
$$613$$ 6450.01 0.424981 0.212491 0.977163i $$-0.431843\pi$$
0.212491 + 0.977163i $$0.431843\pi$$
$$614$$ −5293.15 + 794.616i −0.347906 + 0.0522282i
$$615$$ 0 0
$$616$$ −30130.4 + 14444.3i −1.97076 + 0.944769i
$$617$$ 6724.96i 0.438795i 0.975636 + 0.219398i $$0.0704092\pi$$
−0.975636 + 0.219398i $$0.929591\pi$$
$$618$$ 0 0
$$619$$ 3136.55i 0.203665i −0.994802 0.101832i $$-0.967529\pi$$
0.994802 0.101832i $$-0.0324705\pi$$
$$620$$ −2140.26 + 657.413i −0.138637 + 0.0425844i
$$621$$ 0 0
$$622$$ 2370.44 + 15790.2i 0.152807 + 1.01789i
$$623$$ −35105.0 −2.25755
$$624$$ 0 0
$$625$$ 14791.8 0.946673
$$626$$ −343.481 2288.02i −0.0219301 0.146082i
$$627$$ 0 0
$$628$$ 2113.12 649.077i 0.134272 0.0412436i
$$629$$ 10033.9i 0.636053i
$$630$$ 0 0
$$631$$ 6061.57i 0.382420i 0.981549 + 0.191210i $$0.0612412\pi$$
−0.981549 + 0.191210i $$0.938759\pi$$
$$632$$ −21471.5 + 10293.3i −1.35141 + 0.647857i
$$633$$ 0 0
$$634$$ 5445.14 817.433i 0.341095 0.0512057i
$$635$$ 396.204 0.0247604
$$636$$ 0 0
$$637$$ 14157.9 0.880625
$$638$$ 21226.6 3186.56i 1.31719 0.197739i
$$639$$ 0 0
$$640$$ −1090.30 + 1870.55i −0.0673406 + 0.115531i
$$641$$ 18603.3i 1.14631i 0.819446 + 0.573157i $$0.194281\pi$$
−0.819446 + 0.573157i $$0.805719\pi$$
$$642$$ 0 0
$$643$$ 21602.4i 1.32491i −0.749103 0.662453i $$-0.769515\pi$$
0.749103 0.662453i $$-0.230485\pi$$
$$644$$ 1683.44 + 5480.55i 0.103007 + 0.335348i
$$645$$ 0 0
$$646$$ 1694.52 + 11287.7i 0.103204 + 0.687472i
$$647$$ −672.754 −0.0408790 −0.0204395 0.999791i $$-0.506507\pi$$
−0.0204395 + 0.999791i $$0.506507\pi$$
$$648$$ 0 0
$$649$$ −18111.1 −1.09541
$$650$$ −2129.86 14187.6i −0.128523 0.856126i
$$651$$ 0 0
$$652$$ −3333.59 10852.8i −0.200236 0.651882i
$$653$$ 3322.88i 0.199134i −0.995031 0.0995668i $$-0.968254\pi$$
0.995031 0.0995668i $$-0.0317457\pi$$
$$654$$ 0 0
$$655$$ 1722.12i 0.102731i
$$656$$ −10706.9 15784.2i −0.637248 0.939434i
$$657$$ 0 0
$$658$$ −27381.3 + 4110.52i −1.62224 + 0.243533i
$$659$$ 25093.7 1.48332 0.741662 0.670773i $$-0.234038\pi$$
0.741662 + 0.670773i $$0.234038\pi$$
$$660$$ 0 0
$$661$$ −28966.3 −1.70447 −0.852237 0.523157i $$-0.824754\pi$$
−0.852237 + 0.523157i $$0.824754\pi$$
$$662$$ 9523.59 1429.70i 0.559131 0.0839376i
$$663$$ 0 0
$$664$$ 11924.1 + 24873.4i 0.696906 + 1.45373i
$$665$$ 3095.29i 0.180496i
$$666$$ 0 0
$$667$$ 3682.95i 0.213800i
$$668$$ −26832.2 + 8241.94i −1.55415 + 0.477381i
$$669$$ 0 0
$$670$$ −361.654 2409.08i −0.0208536 0.138912i
$$671$$ −38049.1 −2.18907
$$672$$ 0 0
$$673$$ −4710.36 −0.269793 −0.134897 0.990860i $$-0.543070\pi$$
−0.134897 + 0.990860i $$0.543070\pi$$
$$674$$ 2969.62 + 19781.4i 0.169711 + 1.13049i
$$675$$ 0 0
$$676$$ 3746.51 1150.80i 0.213160 0.0654755i
$$677$$ 4784.53i 0.271617i 0.990735 + 0.135808i $$0.0433631\pi$$
−0.990735 + 0.135808i $$0.956637\pi$$
$$678$$ 0 0
$$679$$ 15084.2i 0.852548i
$$680$$ 746.434 + 1557.04i 0.0420948 + 0.0878085i
$$681$$ 0 0
$$682$$ 29527.6 4432.73i 1.65787 0.248883i
$$683$$ 18019.8 1.00953 0.504764 0.863258i $$-0.331580\pi$$
0.504764 + 0.863258i $$0.331580\pi$$
$$684$$ 0 0
$$685$$ 3511.46 0.195863
$$686$$ −24.4240 + 3.66657i −0.00135935 + 0.000204067i
$$687$$ 0 0
$$688$$ 16726.9 + 24658.9i 0.926902 + 1.36644i
$$689$$ 25620.4i 1.41663i
$$690$$ 0 0
$$691$$ 16956.5i 0.933511i 0.884386 + 0.466756i $$0.154577\pi$$
−0.884386 + 0.466756i $$0.845423\pi$$
$$692$$ 777.439 + 2531.01i 0.0427078 + 0.139038i
$$693$$ 0 0
$$694$$ 2428.31 + 16175.6i 0.132820 + 0.884751i
$$695$$ −321.802 −0.0175635
$$696$$ 0 0
$$697$$ −15211.0 −0.826625
$$698$$ 734.243 + 4890.99i 0.0398159 + 0.265225i
$$699$$ 0 0
$$700$$ −7551.17 24583.4i −0.407725 1.32738i
$$701$$ 30620.5i 1.64982i −0.565266 0.824909i $$-0.691226\pi$$
0.565266 0.824909i $$-0.308774\pi$$
$$702$$ 0 0
$$703$$ 15542.8i 0.833865i
$$704$$ 18082.4 22510.5i 0.968050 1.20511i
$$705$$ 0 0
$$706$$ −26718.6 + 4011.04i −1.42432 + 0.213821i
$$707$$ −3039.56 −0.161689
$$708$$ 0 0
$$709$$ 24192.8 1.28149 0.640747 0.767752i $$-0.278625\pi$$
0.640747 + 0.767752i $$0.278625\pi$$
$$710$$ −935.961 + 140.508i −0.0494732 + 0.00742700i
$$711$$ 0 0
$$712$$ 27354.4 13113.5i 1.43982 0.690238i
$$713$$ 5123.23i 0.269098i
$$714$$ 0 0
$$715$$ 3483.60i 0.182209i
$$716$$ 8693.11 2670.23i 0.453739 0.139373i
$$717$$ 0 0
$$718$$ 386.895 + 2577.21i 0.0201098 + 0.133956i
$$719$$ −37146.6 −1.92675 −0.963377 0.268151i $$-0.913588\pi$$
−0.963377 + 0.268151i $$0.913588\pi$$
$$720$$ 0 0
$$721$$ 4322.49 0.223271
$$722$$ 255.251 + 1700.30i 0.0131571 + 0.0876433i
$$723$$ 0 0
$$724$$ −15730.0 + 4831.71i −0.807459 + 0.248024i
$$725$$ 16520.1i 0.846265i
$$726$$ 0 0
$$727$$ 14614.3i 0.745551i 0.927922 + 0.372775i $$0.121594\pi$$
−0.927922 + 0.372775i $$0.878406\pi$$
$$728$$ −22074.9 + 10582.6i −1.12383 + 0.538759i
$$729$$ 0 0
$$730$$ 293.305 44.0314i 0.0148708 0.00223243i
$$731$$ 23763.5 1.20236
$$732$$ 0 0
$$733$$ −8044.73 −0.405374 −0.202687 0.979244i $$-0.564967\pi$$
−0.202687 + 0.979244i $$0.564967\pi$$
$$734$$ −23749.1 + 3565.25i −1.19427 + 0.179286i
$$735$$ 0 0
$$736$$ −3359.03 3641.68i −0.168227 0.182384i
$$737$$ 32487.3i 1.62372i
$$738$$ 0 0
$$739$$ 7025.01i 0.349688i −0.984596 0.174844i $$-0.944058\pi$$
0.984596 0.174844i $$-0.0559420\pi$$
$$740$$ −690.399 2247.64i −0.0342967 0.111655i
$$741$$ 0 0
$$742$$ −6818.08 45417.0i −0.337331 2.24705i
$$743$$ 27063.4 1.33629 0.668143 0.744033i $$-0.267089\pi$$
0.668143 + 0.744033i $$0.267089\pi$$
$$744$$ 0 0
$$745$$ 328.849 0.0161719
$$746$$ 1186.19 + 7901.54i 0.0582166 + 0.387796i
$$747$$ 0 0
$$748$$ −6761.42 22012.3i −0.330511 1.07600i
$$749$$ 24528.2i 1.19658i
$$750$$ 0 0
$$751$$ 11434.2i 0.555579i −0.960642 0.277789i $$-0.910398\pi$$
0.960642 0.277789i $$-0.0896017\pi$$
$$752$$ 19800.4 13431.3i 0.960170 0.651315i
$$753$$ 0 0
$$754$$ 15551.6 2334.62i 0.751133 0.112761i
$$755$$ −1716.38 −0.0827357
$$756$$ 0 0
$$757$$ 22087.2 1.06046 0.530232 0.847853i $$-0.322105\pi$$
0.530232 + 0.847853i $$0.322105\pi$$
$$758$$ 14887.1 2234.87i 0.713354 0.107090i
$$759$$ 0 0
$$760$$ −1156.25 2411.90i −0.0551862 0.115117i
$$761$$ 35524.0i 1.69218i 0.533043 + 0.846088i $$0.321048\pi$$
−0.533043 + 0.846088i $$0.678952\pi$$
$$762$$ 0 0
$$763$$ 9085.16i 0.431068i
$$764$$ 15166.5 4658.62i 0.718198 0.220606i
$$765$$ 0 0
$$766$$ −3493.79 23273.1i −0.164799 1.09777i
$$767$$ −13269.0 −0.624664
$$768$$ 0 0
$$769$$ 21213.0 0.994745 0.497372 0.867537i $$-0.334298\pi$$
0.497372 + 0.867537i $$0.334298\pi$$
$$770$$ −927.054 6175.36i −0.0433879 0.289019i
$$771$$ 0 0
$$772$$ 1452.29 446.095i 0.0677062 0.0207970i
$$773$$ 14370.7i 0.668663i 0.942456 + 0.334332i $$0.108511\pi$$
−0.942456 + 0.334332i $$0.891489\pi$$
$$774$$ 0 0
$$775$$ 22980.6i 1.06515i
$$776$$ 5634.73 + 11753.9i 0.260664 + 0.543737i
$$777$$ 0 0
$$778$$ 23379.5 3509.77i 1.07737 0.161737i
$$779$$ 23562.3 1.08371
$$780$$ 0 0
$$781$$ 12621.8 0.578287
$$782$$ −3907.34 + 586.575i −0.178678 + 0.0268234i
$$783$$ 0 0
$$784$$ −18149.1 + 12311.1i −0.826763 + 0.560820i
$$785$$ 413.122i 0.0187834i
$$786$$ 0 0
$$787$$ 41642.9i 1.88616i 0.332564 + 0.943081i $$0.392086\pi$$
−0.332564 + 0.943081i $$0.607914\pi$$
$$788$$ −5074.84 16521.5i −0.229421 0.746896i
$$789$$ 0 0
$$790$$ −660.637 4400.68i −0.0297524 0.198189i
$$791$$ 38288.5 1.72109 </