# Properties

 Label 225.4.k.c.49.1 Level $225$ Weight $4$ Character 225.49 Analytic conductor $13.275$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 225.k (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$13.2754297513$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - 23 x^{10} + 198 x^{8} - 719 x^{6} + 886 x^{4} + 585 x^{2} + 81$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{6}\cdot 3^{2}$$ Twist minimal: no (minimal twist has level 45) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 49.1 Root $$-2.88506 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 225.49 Dual form 225.4.k.c.124.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-3.96084 + 2.28679i) q^{2} +(-3.96084 - 3.36330i) q^{3} +(6.45882 - 11.1870i) q^{4} +(23.3794 + 4.26387i) q^{6} +(-17.4197 + 10.0573i) q^{7} +22.4912i q^{8} +(4.37646 + 26.6429i) q^{9} +O(q^{10})$$ $$q+(-3.96084 + 2.28679i) q^{2} +(-3.96084 - 3.36330i) q^{3} +(6.45882 - 11.1870i) q^{4} +(23.3794 + 4.26387i) q^{6} +(-17.4197 + 10.0573i) q^{7} +22.4912i q^{8} +(4.37646 + 26.6429i) q^{9} +(-33.1708 - 57.4535i) q^{11} +(-63.2076 + 22.5870i) q^{12} +(-40.5305 - 23.4003i) q^{13} +(45.9977 - 79.6704i) q^{14} +(0.237854 + 0.411975i) q^{16} -47.6233i q^{17} +(-78.2613 - 95.5203i) q^{18} +9.95276 q^{19} +(102.822 + 18.7524i) q^{21} +(262.768 + 151.709i) q^{22} +(8.30695 + 4.79602i) q^{23} +(75.6447 - 89.0841i) q^{24} +214.046 q^{26} +(72.2737 - 120.248i) q^{27} +259.832i q^{28} +(-89.3675 - 154.789i) q^{29} +(-77.0186 + 133.400i) q^{31} +(-157.708 - 91.0527i) q^{32} +(-61.8491 + 339.127i) q^{33} +(108.905 + 188.628i) q^{34} +(326.322 + 123.123i) q^{36} +248.864i q^{37} +(-39.4213 + 22.7599i) q^{38} +(81.8326 + 229.001i) q^{39} +(-124.832 + 216.216i) q^{41} +(-450.145 + 160.857i) q^{42} +(183.809 - 106.122i) q^{43} -856.976 q^{44} -43.8700 q^{46} +(411.963 - 237.847i) q^{47} +(0.443494 - 2.43174i) q^{48} +(30.7973 - 53.3425i) q^{49} +(-160.171 + 188.628i) q^{51} +(-523.559 + 302.277i) q^{52} +546.314i q^{53} +(-11.2831 + 641.556i) q^{54} +(-226.200 - 391.790i) q^{56} +(-39.4213 - 33.4741i) q^{57} +(707.940 + 408.729i) q^{58} +(-209.648 + 363.121i) q^{59} +(272.605 + 472.165i) q^{61} -704.502i q^{62} +(-344.192 - 420.097i) q^{63} +829.068 q^{64} +(-530.538 - 1484.66i) q^{66} +(387.872 + 223.938i) q^{67} +(-532.762 - 307.590i) q^{68} +(-16.7720 - 46.9350i) q^{69} +409.542 q^{71} +(-599.232 + 98.4319i) q^{72} +358.548i q^{73} +(-569.100 - 985.710i) q^{74} +(64.2831 - 111.342i) q^{76} +(1155.65 + 667.215i) q^{77} +(-847.803 - 719.902i) q^{78} +(-325.776 - 564.260i) q^{79} +(-690.693 + 233.204i) q^{81} -1141.86i q^{82} +(704.202 - 406.571i) q^{83} +(873.893 - 1029.15i) q^{84} +(-485.359 + 840.667i) q^{86} +(-166.631 + 913.663i) q^{87} +(1292.20 - 746.051i) q^{88} +201.000 q^{89} +941.373 q^{91} +(107.306 - 61.9532i) q^{92} +(753.723 - 269.340i) q^{93} +(-1087.81 + 1884.14i) q^{94} +(318.418 + 891.064i) q^{96} +(218.367 - 126.074i) q^{97} +281.708i q^{98} +(1385.56 - 1135.21i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} + O(q^{10})$$ $$12 q + 22 q^{4} + 168 q^{6} - 114 q^{9} - 28 q^{11} - 54 q^{14} + 26 q^{16} + 656 q^{19} - 288 q^{21} + 126 q^{24} + 1736 q^{26} - 670 q^{29} + 704 q^{31} - 104 q^{34} + 2172 q^{36} + 780 q^{39} - 374 q^{41} - 3928 q^{44} - 804 q^{46} + 860 q^{49} - 360 q^{51} - 1278 q^{54} - 1410 q^{56} - 596 q^{59} + 2878 q^{61} + 6276 q^{64} - 1932 q^{66} + 1746 q^{69} + 280 q^{71} - 640 q^{74} - 408 q^{76} - 764 q^{79} - 2502 q^{81} + 1818 q^{84} - 3160 q^{86} - 6876 q^{89} - 2840 q^{91} - 4154 q^{94} + 2310 q^{96} + 1524 q^{99} + O(q^{100})$$

## Character values

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

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −3.96084 + 2.28679i −1.40037 + 0.808502i −0.994430 0.105398i $$-0.966388\pi$$
−0.405937 + 0.913901i $$0.633055\pi$$
$$3$$ −3.96084 3.36330i −0.762263 0.647267i
$$4$$ 6.45882 11.1870i 0.807352 1.39838i
$$5$$ 0 0
$$6$$ 23.3794 + 4.26387i 1.59077 + 0.290120i
$$7$$ −17.4197 + 10.0573i −0.940575 + 0.543041i −0.890141 0.455686i $$-0.849394\pi$$
−0.0504348 + 0.998727i $$0.516061\pi$$
$$8$$ 22.4912i 0.993981i
$$9$$ 4.37646 + 26.6429i 0.162091 + 0.986776i
$$10$$ 0 0
$$11$$ −33.1708 57.4535i −0.909215 1.57481i −0.815157 0.579240i $$-0.803349\pi$$
−0.0940582 0.995567i $$-0.529984\pi$$
$$12$$ −63.2076 + 22.5870i −1.52054 + 0.543358i
$$13$$ −40.5305 23.4003i −0.864703 0.499237i 0.000881222 1.00000i $$-0.499719\pi$$
−0.865584 + 0.500763i $$0.833053\pi$$
$$14$$ 45.9977 79.6704i 0.878101 1.52092i
$$15$$ 0 0
$$16$$ 0.237854 + 0.411975i 0.00371647 + 0.00643711i
$$17$$ 47.6233i 0.679432i −0.940528 0.339716i $$-0.889669\pi$$
0.940528 0.339716i $$-0.110331\pi$$
$$18$$ −78.2613 95.5203i −1.02480 1.25080i
$$19$$ 9.95276 0.120175 0.0600874 0.998193i $$-0.480862\pi$$
0.0600874 + 0.998193i $$0.480862\pi$$
$$20$$ 0 0
$$21$$ 102.822 + 18.7524i 1.06846 + 0.194863i
$$22$$ 262.768 + 151.709i 2.54647 + 1.47021i
$$23$$ 8.30695 + 4.79602i 0.0753095 + 0.0434800i 0.537182 0.843466i $$-0.319489\pi$$
−0.461872 + 0.886946i $$0.652822\pi$$
$$24$$ 75.6447 89.0841i 0.643371 0.757675i
$$25$$ 0 0
$$26$$ 214.046 1.61454
$$27$$ 72.2737 120.248i 0.515151 0.857099i
$$28$$ 259.832i 1.75370i
$$29$$ −89.3675 154.789i −0.572246 0.991158i −0.996335 0.0855380i $$-0.972739\pi$$
0.424089 0.905620i $$-0.360594\pi$$
$$30$$ 0 0
$$31$$ −77.0186 + 133.400i −0.446224 + 0.772883i −0.998137 0.0610190i $$-0.980565\pi$$
0.551912 + 0.833902i $$0.313898\pi$$
$$32$$ −157.708 91.0527i −0.871222 0.503000i
$$33$$ −61.8491 + 339.127i −0.326259 + 1.78892i
$$34$$ 108.905 + 188.628i 0.549323 + 0.951455i
$$35$$ 0 0
$$36$$ 326.322 + 123.123i 1.51075 + 0.570012i
$$37$$ 248.864i 1.10576i 0.833262 + 0.552878i $$0.186471\pi$$
−0.833262 + 0.552878i $$0.813529\pi$$
$$38$$ −39.4213 + 22.7599i −0.168289 + 0.0971616i
$$39$$ 81.8326 + 229.001i 0.335992 + 0.940244i
$$40$$ 0 0
$$41$$ −124.832 + 216.216i −0.475500 + 0.823590i −0.999606 0.0280628i $$-0.991066\pi$$
0.524106 + 0.851653i $$0.324400\pi$$
$$42$$ −450.145 + 160.857i −1.65378 + 0.590972i
$$43$$ 183.809 106.122i 0.651876 0.376361i −0.137299 0.990530i $$-0.543842\pi$$
0.789175 + 0.614169i $$0.210509\pi$$
$$44$$ −856.976 −2.93623
$$45$$ 0 0
$$46$$ −43.8700 −0.140615
$$47$$ 411.963 237.847i 1.27853 0.738160i 0.301953 0.953323i $$-0.402362\pi$$
0.976578 + 0.215163i $$0.0690282\pi$$
$$48$$ 0.443494 2.43174i 0.00133360 0.00731232i
$$49$$ 30.7973 53.3425i 0.0897880 0.155517i
$$50$$ 0 0
$$51$$ −160.171 + 188.628i −0.439774 + 0.517906i
$$52$$ −523.559 + 302.277i −1.39624 + 0.806120i
$$53$$ 546.314i 1.41589i 0.706269 + 0.707944i $$0.250377\pi$$
−0.706269 + 0.707944i $$0.749623\pi$$
$$54$$ −11.2831 + 641.556i −0.0284341 + 1.61675i
$$55$$ 0 0
$$56$$ −226.200 391.790i −0.539773 0.934914i
$$57$$ −39.4213 33.4741i −0.0916048 0.0777851i
$$58$$ 707.940 + 408.729i 1.60271 + 0.925324i
$$59$$ −209.648 + 363.121i −0.462608 + 0.801261i −0.999090 0.0426512i $$-0.986420\pi$$
0.536482 + 0.843912i $$0.319753\pi$$
$$60$$ 0 0
$$61$$ 272.605 + 472.165i 0.572188 + 0.991059i 0.996341 + 0.0854682i $$0.0272386\pi$$
−0.424153 + 0.905591i $$0.639428\pi$$
$$62$$ 704.502i 1.44309i
$$63$$ −344.192 420.097i −0.688319 0.840115i
$$64$$ 829.068 1.61927
$$65$$ 0 0
$$66$$ −530.538 1484.66i −0.989466 2.76893i
$$67$$ 387.872 + 223.938i 0.707256 + 0.408335i 0.810044 0.586369i $$-0.199443\pi$$
−0.102788 + 0.994703i $$0.532776\pi$$
$$68$$ −532.762 307.590i −0.950102 0.548541i
$$69$$ −16.7720 46.9350i −0.0292625 0.0818885i
$$70$$ 0 0
$$71$$ 409.542 0.684559 0.342279 0.939598i $$-0.388801\pi$$
0.342279 + 0.939598i $$0.388801\pi$$
$$72$$ −599.232 + 98.4319i −0.980836 + 0.161115i
$$73$$ 358.548i 0.574861i 0.957801 + 0.287431i $$0.0928011\pi$$
−0.957801 + 0.287431i $$0.907199\pi$$
$$74$$ −569.100 985.710i −0.894007 1.54847i
$$75$$ 0 0
$$76$$ 64.2831 111.342i 0.0970234 0.168049i
$$77$$ 1155.65 + 667.215i 1.71037 + 0.987483i
$$78$$ −847.803 719.902i −1.23070 1.04504i
$$79$$ −325.776 564.260i −0.463958 0.803598i 0.535196 0.844728i $$-0.320238\pi$$
−0.999154 + 0.0411297i $$0.986904\pi$$
$$80$$ 0 0
$$81$$ −690.693 + 233.204i −0.947453 + 0.319895i
$$82$$ 1141.86i 1.53777i
$$83$$ 704.202 406.571i 0.931280 0.537675i 0.0440636 0.999029i $$-0.485970\pi$$
0.887216 + 0.461354i $$0.152636\pi$$
$$84$$ 873.893 1029.15i 1.13511 1.33678i
$$85$$ 0 0
$$86$$ −485.359 + 840.667i −0.608577 + 1.05409i
$$87$$ −166.631 + 913.663i −0.205342 + 1.12592i
$$88$$ 1292.20 746.051i 1.56533 0.903743i
$$89$$ 201.000 0.239393 0.119696 0.992811i $$-0.461808\pi$$
0.119696 + 0.992811i $$0.461808\pi$$
$$90$$ 0 0
$$91$$ 941.373 1.08442
$$92$$ 107.306 61.9532i 0.121603 0.0702073i
$$93$$ 753.723 269.340i 0.840402 0.300314i
$$94$$ −1087.81 + 1884.14i −1.19361 + 2.06739i
$$95$$ 0 0
$$96$$ 318.418 + 891.064i 0.338525 + 0.947331i
$$97$$ 218.367 126.074i 0.228576 0.131968i −0.381339 0.924435i $$-0.624537\pi$$
0.609915 + 0.792467i $$0.291204\pi$$
$$98$$ 281.708i 0.290375i
$$99$$ 1385.56 1135.21i 1.40661 1.15245i
$$100$$ 0 0
$$101$$ −21.8013 37.7610i −0.0214783 0.0372016i 0.855086 0.518485i $$-0.173504\pi$$
−0.876565 + 0.481284i $$0.840171\pi$$
$$102$$ 203.060 1113.40i 0.197117 1.08082i
$$103$$ −1247.38 720.176i −1.19328 0.688942i −0.234233 0.972180i $$-0.575258\pi$$
−0.959050 + 0.283238i $$0.908591\pi$$
$$104$$ 526.301 911.581i 0.496232 0.859498i
$$105$$ 0 0
$$106$$ −1249.31 2163.86i −1.14475 1.98276i
$$107$$ 355.755i 0.321422i 0.987002 + 0.160711i $$0.0513786\pi$$
−0.987002 + 0.160711i $$0.948621\pi$$
$$108$$ −878.409 1585.18i −0.782638 1.41236i
$$109$$ 1522.51 1.33789 0.668946 0.743311i $$-0.266746\pi$$
0.668946 + 0.743311i $$0.266746\pi$$
$$110$$ 0 0
$$111$$ 837.004 985.710i 0.715720 0.842878i
$$112$$ −8.28669 4.78432i −0.00699124 0.00403639i
$$113$$ −704.077 406.499i −0.586142 0.338409i 0.177429 0.984134i $$-0.443222\pi$$
−0.763570 + 0.645725i $$0.776555\pi$$
$$114$$ 232.689 + 42.4373i 0.191170 + 0.0348650i
$$115$$ 0 0
$$116$$ −2308.83 −1.84802
$$117$$ 446.073 1182.26i 0.352474 0.934190i
$$118$$ 1917.69i 1.49608i
$$119$$ 478.960 + 829.584i 0.368960 + 0.639057i
$$120$$ 0 0
$$121$$ −1535.10 + 2658.87i −1.15334 + 1.99765i
$$122$$ −2159.49 1246.78i −1.60255 0.925231i
$$123$$ 1221.64 436.547i 0.895539 0.320017i
$$124$$ 994.899 + 1723.22i 0.720521 + 1.24798i
$$125$$ 0 0
$$126$$ 2323.96 + 876.841i 1.64313 + 0.619962i
$$127$$ 864.662i 0.604144i −0.953285 0.302072i $$-0.902322\pi$$
0.953285 0.302072i $$-0.0976784\pi$$
$$128$$ −2022.14 + 1167.48i −1.39636 + 0.806187i
$$129$$ −1084.96 197.872i −0.740507 0.135052i
$$130$$ 0 0
$$131$$ 1089.26 1886.65i 0.726482 1.25830i −0.231879 0.972745i $$-0.574487\pi$$
0.958361 0.285559i $$-0.0921792\pi$$
$$132$$ 3394.34 + 2882.27i 2.23818 + 1.90052i
$$133$$ −173.374 + 100.098i −0.113033 + 0.0652599i
$$134$$ −2048.40 −1.32056
$$135$$ 0 0
$$136$$ 1071.11 0.675343
$$137$$ −1991.13 + 1149.58i −1.24171 + 0.716900i −0.969442 0.245322i $$-0.921106\pi$$
−0.272266 + 0.962222i $$0.587773\pi$$
$$138$$ 173.762 + 147.548i 0.107185 + 0.0910152i
$$139$$ −1066.98 + 1848.06i −0.651077 + 1.12770i 0.331785 + 0.943355i $$0.392349\pi$$
−0.982862 + 0.184343i $$0.940984\pi$$
$$140$$ 0 0
$$141$$ −2431.67 443.481i −1.45236 0.264878i
$$142$$ −1622.13 + 936.536i −0.958634 + 0.553467i
$$143$$ 3104.83i 1.81565i
$$144$$ −9.93528 + 8.14012i −0.00574958 + 0.00471072i
$$145$$ 0 0
$$146$$ −819.924 1420.15i −0.464777 0.805017i
$$147$$ −301.390 + 107.700i −0.169103 + 0.0604284i
$$148$$ 2784.04 + 1607.37i 1.54626 + 0.892735i
$$149$$ 875.309 1516.08i 0.481263 0.833572i −0.518506 0.855074i $$-0.673512\pi$$
0.999769 + 0.0215024i $$0.00684497\pi$$
$$150$$ 0 0
$$151$$ −437.977 758.598i −0.236040 0.408833i 0.723534 0.690288i $$-0.242516\pi$$
−0.959574 + 0.281455i $$0.909183\pi$$
$$152$$ 223.850i 0.119451i
$$153$$ 1268.83 208.421i 0.670447 0.110130i
$$154$$ −6103.12 −3.19353
$$155$$ 0 0
$$156$$ 3090.38 + 563.615i 1.58608 + 0.289265i
$$157$$ 224.642 + 129.697i 0.114194 + 0.0659298i 0.556009 0.831176i $$-0.312332\pi$$
−0.441815 + 0.897106i $$0.645665\pi$$
$$158$$ 2580.69 + 1489.96i 1.29942 + 0.750222i
$$159$$ 1837.42 2163.86i 0.916457 1.07928i
$$160$$ 0 0
$$161$$ −192.939 −0.0944457
$$162$$ 2202.44 2503.15i 1.06815 1.21399i
$$163$$ 1201.80i 0.577498i 0.957405 + 0.288749i $$0.0932393\pi$$
−0.957405 + 0.288749i $$0.906761\pi$$
$$164$$ 1612.54 + 2792.99i 0.767792 + 1.32986i
$$165$$ 0 0
$$166$$ −1859.49 + 3220.72i −0.869422 + 1.50588i
$$167$$ 1453.97 + 839.452i 0.673724 + 0.388975i 0.797486 0.603337i $$-0.206163\pi$$
−0.123762 + 0.992312i $$0.539496\pi$$
$$168$$ −421.765 + 2312.60i −0.193690 + 1.06203i
$$169$$ −3.35162 5.80518i −0.00152554 0.00264232i
$$170$$ 0 0
$$171$$ 43.5578 + 265.171i 0.0194792 + 0.118586i
$$172$$ 2741.70i 1.21542i
$$173$$ −806.961 + 465.899i −0.354636 + 0.204749i −0.666725 0.745303i $$-0.732305\pi$$
0.312089 + 0.950053i $$0.398971\pi$$
$$174$$ −1429.36 3999.92i −0.622754 1.74272i
$$175$$ 0 0
$$176$$ 15.7796 27.3311i 0.00675814 0.0117054i
$$177$$ 2051.67 733.155i 0.871259 0.311341i
$$178$$ −796.127 + 459.644i −0.335237 + 0.193549i
$$179$$ −1023.40 −0.427333 −0.213667 0.976907i $$-0.568541\pi$$
−0.213667 + 0.976907i $$0.568541\pi$$
$$180$$ 0 0
$$181$$ 2639.93 1.08411 0.542056 0.840342i $$-0.317646\pi$$
0.542056 + 0.840342i $$0.317646\pi$$
$$182$$ −3728.62 + 2152.72i −1.51859 + 0.876760i
$$183$$ 508.289 2787.02i 0.205322 1.12581i
$$184$$ −107.868 + 186.833i −0.0432182 + 0.0748562i
$$185$$ 0 0
$$186$$ −2369.45 + 2790.42i −0.934067 + 1.10002i
$$187$$ −2736.13 + 1579.70i −1.06997 + 0.617750i
$$188$$ 6144.84i 2.38382i
$$189$$ −49.6230 + 2821.56i −0.0190981 + 1.08591i
$$190$$ 0 0
$$191$$ 406.640 + 704.322i 0.154050 + 0.266822i 0.932713 0.360621i $$-0.117435\pi$$
−0.778663 + 0.627442i $$0.784102\pi$$
$$192$$ −3283.80 2788.40i −1.23431 1.04810i
$$193$$ −705.154 407.121i −0.262995 0.151840i 0.362705 0.931904i $$-0.381853\pi$$
−0.625700 + 0.780064i $$0.715187\pi$$
$$194$$ −576.612 + 998.720i −0.213393 + 0.369608i
$$195$$ 0 0
$$196$$ −397.828 689.059i −0.144981 0.251115i
$$197$$ 4078.41i 1.47500i 0.675348 + 0.737499i $$0.263994\pi$$
−0.675348 + 0.737499i $$0.736006\pi$$
$$198$$ −2891.99 + 7664.87i −1.03800 + 2.75110i
$$199$$ 1342.49 0.478224 0.239112 0.970992i $$-0.423144\pi$$
0.239112 + 0.970992i $$0.423144\pi$$
$$200$$ 0 0
$$201$$ −783.129 2191.51i −0.274814 0.769042i
$$202$$ 172.703 + 99.7101i 0.0601551 + 0.0347306i
$$203$$ 3113.51 + 1797.58i 1.07648 + 0.621506i
$$204$$ 1075.67 + 3010.15i 0.369175 + 1.03310i
$$205$$ 0 0
$$206$$ 6587.56 2.22805
$$207$$ −91.4250 + 242.311i −0.0306980 + 0.0813613i
$$208$$ 22.2634i 0.00742159i
$$209$$ −330.141 571.821i −0.109265 0.189252i
$$210$$ 0 0
$$211$$ 1477.49 2559.08i 0.482059 0.834950i −0.517729 0.855545i $$-0.673222\pi$$
0.999788 + 0.0205943i $$0.00655583\pi$$
$$212$$ 6111.62 + 3528.55i 1.97994 + 1.14312i
$$213$$ −1622.13 1377.41i −0.521814 0.443092i
$$214$$ −813.536 1409.09i −0.259870 0.450108i
$$215$$ 0 0
$$216$$ 2704.52 + 1625.52i 0.851940 + 0.512050i
$$217$$ 3098.39i 0.969273i
$$218$$ −6030.42 + 3481.66i −1.87354 + 1.08169i
$$219$$ 1205.90 1420.15i 0.372089 0.438196i
$$220$$ 0 0
$$221$$ −1114.40 + 1930.20i −0.339198 + 0.587507i
$$222$$ −1061.12 + 5818.29i −0.320802 + 1.75900i
$$223$$ −3037.03 + 1753.43i −0.911993 + 0.526539i −0.881072 0.472982i $$-0.843177\pi$$
−0.0309212 + 0.999522i $$0.509844\pi$$
$$224$$ 3662.97 1.09260
$$225$$ 0 0
$$226$$ 3718.31 1.09442
$$227$$ 565.364 326.413i 0.165306 0.0954396i −0.415064 0.909792i $$-0.636241\pi$$
0.580371 + 0.814352i $$0.302908\pi$$
$$228$$ −629.090 + 224.803i −0.182730 + 0.0652979i
$$229$$ 2291.78 3969.47i 0.661331 1.14546i −0.318935 0.947776i $$-0.603325\pi$$
0.980266 0.197682i $$-0.0633414\pi$$
$$230$$ 0 0
$$231$$ −2333.30 6529.52i −0.664588 1.85979i
$$232$$ 3481.39 2009.98i 0.985192 0.568801i
$$233$$ 317.527i 0.0892785i −0.999003 0.0446392i $$-0.985786\pi$$
0.999003 0.0446392i $$-0.0142138\pi$$
$$234$$ 936.765 + 5702.83i 0.261702 + 1.59319i
$$235$$ 0 0
$$236$$ 2708.16 + 4690.67i 0.746975 + 1.29380i
$$237$$ −607.430 + 3330.62i −0.166485 + 0.912858i
$$238$$ −3794.17 2190.56i −1.03336 0.596610i
$$239$$ 928.835 1608.79i 0.251386 0.435414i −0.712521 0.701650i $$-0.752447\pi$$
0.963908 + 0.266236i $$0.0857802\pi$$
$$240$$ 0 0
$$241$$ 1633.47 + 2829.25i 0.436602 + 0.756217i 0.997425 0.0717190i $$-0.0228485\pi$$
−0.560823 + 0.827936i $$0.689515\pi$$
$$242$$ 14041.8i 3.72993i
$$243$$ 3520.06 + 1399.33i 0.929266 + 0.369411i
$$244$$ 7042.82 1.84783
$$245$$ 0 0
$$246$$ −3840.41 + 4522.72i −0.995349 + 1.17219i
$$247$$ −403.390 232.898i −0.103915 0.0599956i
$$248$$ −3000.33 1732.24i −0.768231 0.443538i
$$249$$ −4156.65 758.079i −1.05790 0.192937i
$$250$$ 0 0
$$251$$ −5641.37 −1.41865 −0.709323 0.704884i $$-0.750999\pi$$
−0.709323 + 0.704884i $$0.750999\pi$$
$$252$$ −6922.70 + 1137.15i −1.73051 + 0.284260i
$$253$$ 636.351i 0.158131i
$$254$$ 1977.30 + 3424.78i 0.488452 + 0.846024i
$$255$$ 0 0
$$256$$ 2023.31 3504.47i 0.493971 0.855584i
$$257$$ 1016.25 + 586.731i 0.246661 + 0.142410i 0.618234 0.785994i $$-0.287848\pi$$
−0.371574 + 0.928404i $$0.621182\pi$$
$$258$$ 4749.84 1697.34i 1.14617 0.409580i
$$259$$ −2502.89 4335.14i −0.600472 1.04005i
$$260$$ 0 0
$$261$$ 3732.92 3058.44i 0.885295 0.725336i
$$262$$ 9963.64i 2.34945i
$$263$$ 2509.71 1448.98i 0.588423 0.339726i −0.176051 0.984381i $$-0.556332\pi$$
0.764474 + 0.644655i $$0.222999\pi$$
$$264$$ −7627.38 1391.06i −1.77815 0.324295i
$$265$$ 0 0
$$266$$ 457.804 792.940i 0.105526 0.182776i
$$267$$ −796.127 676.022i −0.182480 0.154951i
$$268$$ 5010.40 2892.75i 1.14201 0.659340i
$$269$$ −2930.13 −0.664138 −0.332069 0.943255i $$-0.607747\pi$$
−0.332069 + 0.943255i $$0.607747\pi$$
$$270$$ 0 0
$$271$$ −668.881 −0.149932 −0.0749661 0.997186i $$-0.523885\pi$$
−0.0749661 + 0.997186i $$0.523885\pi$$
$$272$$ 19.6196 11.3274i 0.00437358 0.00252509i
$$273$$ −3728.62 3166.12i −0.826617 0.701912i
$$274$$ 5257.70 9106.60i 1.15923 2.00785i
$$275$$ 0 0
$$276$$ −633.389 115.516i −0.138136 0.0251929i
$$277$$ −547.874 + 316.315i −0.118840 + 0.0686121i −0.558241 0.829679i $$-0.688524\pi$$
0.439402 + 0.898291i $$0.355190\pi$$
$$278$$ 9759.80i 2.10559i
$$279$$ −3891.24 1468.18i −0.834991 0.315046i
$$280$$ 0 0
$$281$$ 1797.65 + 3113.62i 0.381633 + 0.661007i 0.991296 0.131653i $$-0.0420286\pi$$
−0.609663 + 0.792661i $$0.708695\pi$$
$$282$$ 10645.6 3804.16i 2.24800 0.803313i
$$283$$ 436.796 + 252.184i 0.0917485 + 0.0529710i 0.545172 0.838324i $$-0.316464\pi$$
−0.453424 + 0.891295i $$0.649798\pi$$
$$284$$ 2645.16 4581.55i 0.552680 0.957270i
$$285$$ 0 0
$$286$$ −7100.08 12297.7i −1.46796 2.54258i
$$287$$ 5021.88i 1.03286i
$$288$$ 1735.71 4600.29i 0.355131 0.941232i
$$289$$ 2645.02 0.538372
$$290$$ 0 0
$$291$$ −1288.94 235.074i −0.259654 0.0473549i
$$292$$ 4011.08 + 2315.80i 0.803872 + 0.464116i
$$293$$ 5368.06 + 3099.25i 1.07033 + 0.617953i 0.928270 0.371906i $$-0.121296\pi$$
0.142055 + 0.989859i $$0.454629\pi$$
$$294$$ 947.467 1115.80i 0.187950 0.221343i
$$295$$ 0 0
$$296$$ −5597.26 −1.09910
$$297$$ −9306.02 163.666i −1.81815 0.0319760i
$$298$$ 8006.60i 1.55641i
$$299$$ −224.457 388.770i −0.0434136 0.0751945i
$$300$$ 0 0
$$301$$ −2134.60 + 3697.24i −0.408759 + 0.707991i
$$302$$ 3469.51 + 2003.12i 0.661086 + 0.381678i
$$303$$ −40.6500 + 222.889i −0.00770719 + 0.0422596i
$$304$$ 2.36730 + 4.10029i 0.000446626 + 0.000773578i
$$305$$ 0 0
$$306$$ −4548.99 + 3727.06i −0.849832 + 0.696281i
$$307$$ 1966.79i 0.365636i −0.983147 0.182818i $$-0.941478\pi$$
0.983147 0.182818i $$-0.0585220\pi$$
$$308$$ 14928.3 8618.84i 2.76174 1.59449i
$$309$$ 2518.51 + 7047.81i 0.463666 + 1.29753i
$$310$$ 0 0
$$311$$ 1153.05 1997.15i 0.210237 0.364141i −0.741552 0.670896i $$-0.765910\pi$$
0.951789 + 0.306755i $$0.0992431\pi$$
$$312$$ −5150.51 + 1840.51i −0.934584 + 0.333970i
$$313$$ −8922.14 + 5151.20i −1.61121 + 0.930234i −0.622122 + 0.782920i $$0.713729\pi$$
−0.989090 + 0.147314i $$0.952937\pi$$
$$314$$ −1186.36 −0.213218
$$315$$ 0 0
$$316$$ −8416.51 −1.49831
$$317$$ −1473.83 + 850.916i −0.261131 + 0.150764i −0.624850 0.780745i $$-0.714840\pi$$
0.363719 + 0.931509i $$0.381507\pi$$
$$318$$ −2329.41 + 12772.5i −0.410777 + 2.25235i
$$319$$ −5928.78 + 10268.9i −1.04059 + 1.80235i
$$320$$ 0 0
$$321$$ 1196.51 1409.09i 0.208046 0.245008i
$$322$$ 764.201 441.212i 0.132259 0.0763596i
$$323$$ 473.983i 0.0816506i
$$324$$ −1852.21 + 9233.01i −0.317595 + 1.58316i
$$325$$ 0 0
$$326$$ −2748.26 4760.13i −0.466908 0.808709i
$$327$$ −6030.42 5120.66i −1.01983 0.865973i
$$328$$ −4862.95 2807.63i −0.818633 0.472638i
$$329$$ −4784.18 + 8286.44i −0.801703 + 1.38859i
$$330$$ 0 0
$$331$$ 4175.74 + 7232.60i 0.693413 + 1.20103i 0.970713 + 0.240243i $$0.0772271\pi$$
−0.277300 + 0.960783i $$0.589440\pi$$
$$332$$ 10503.9i 1.73637i
$$333$$ −6630.47 + 1089.14i −1.09113 + 0.179233i
$$334$$ −7678.61 −1.25795
$$335$$ 0 0
$$336$$ 16.7311 + 46.8205i 0.00271654 + 0.00760199i
$$337$$ 6804.73 + 3928.71i 1.09993 + 0.635046i 0.936203 0.351459i $$-0.114314\pi$$
0.163729 + 0.986505i $$0.447648\pi$$
$$338$$ 26.5504 + 15.3289i 0.00427264 + 0.00246681i
$$339$$ 1421.56 + 3978.10i 0.227753 + 0.637347i
$$340$$ 0 0
$$341$$ 10219.1 1.62286
$$342$$ −778.916 950.691i −0.123155 0.150314i
$$343$$ 5660.34i 0.891048i
$$344$$ 2386.82 + 4134.10i 0.374095 + 0.647952i
$$345$$ 0 0
$$346$$ 2130.83 3690.70i 0.331081 0.573449i
$$347$$ −1049.78 606.088i −0.162406 0.0937652i 0.416594 0.909093i $$-0.363224\pi$$
−0.579000 + 0.815327i $$0.696557\pi$$
$$348$$ 9144.91 + 7765.29i 1.40867 + 1.19616i
$$349$$ 699.332 + 1211.28i 0.107262 + 0.185783i 0.914660 0.404224i $$-0.132458\pi$$
−0.807398 + 0.590007i $$0.799125\pi$$
$$350$$ 0 0
$$351$$ −5743.12 + 3182.47i −0.873348 + 0.483954i
$$352$$ 12081.2i 1.82934i
$$353$$ −2276.28 + 1314.21i −0.343214 + 0.198154i −0.661692 0.749776i $$-0.730161\pi$$
0.318479 + 0.947930i $$0.396828\pi$$
$$354$$ −6449.75 + 7595.64i −0.968362 + 1.14041i
$$355$$ 0 0
$$356$$ 1298.22 2248.59i 0.193274 0.334761i
$$357$$ 893.053 4896.73i 0.132396 0.725946i
$$358$$ 4053.53 2340.31i 0.598424 0.345500i
$$359$$ −3677.48 −0.540640 −0.270320 0.962770i $$-0.587130\pi$$
−0.270320 + 0.962770i $$0.587130\pi$$
$$360$$ 0 0
$$361$$ −6759.94 −0.985558
$$362$$ −10456.3 + 6036.96i −1.51815 + 0.876507i
$$363$$ 15022.9 5368.36i 2.17217 0.776215i
$$364$$ 6080.16 10531.1i 0.875513 1.51643i
$$365$$ 0 0
$$366$$ 4360.08 + 12201.3i 0.622692 + 1.74255i
$$367$$ 9898.47 5714.88i 1.40789 0.812846i 0.412706 0.910864i $$-0.364584\pi$$
0.995185 + 0.0980185i $$0.0312504\pi$$
$$368$$ 4.56301i 0.000646368i
$$369$$ −6306.94 2379.64i −0.889773 0.335715i
$$370$$ 0 0
$$371$$ −5494.43 9516.63i −0.768886 1.33175i
$$372$$ 1855.05 10171.5i 0.258549 1.41766i
$$373$$ 1957.13 + 1129.95i 0.271679 + 0.156854i 0.629650 0.776879i $$-0.283198\pi$$
−0.357971 + 0.933733i $$0.616531\pi$$
$$374$$ 7224.90 12513.9i 0.998905 1.73015i
$$375$$ 0 0
$$376$$ 5349.47 + 9265.55i 0.733717 + 1.27084i
$$377$$ 8364.90i 1.14274i
$$378$$ −6255.76 11289.2i −0.851221 1.53612i
$$379$$ 11815.8 1.60142 0.800709 0.599053i $$-0.204456\pi$$
0.800709 + 0.599053i $$0.204456\pi$$
$$380$$ 0 0
$$381$$ −2908.12 + 3424.78i −0.391043 + 0.460517i
$$382$$ −3221.27 1859.80i −0.431452 0.249099i
$$383$$ −6997.68 4040.11i −0.933589 0.539008i −0.0456440 0.998958i $$-0.514534\pi$$
−0.887945 + 0.459950i $$0.847867\pi$$
$$384$$ 11936.0 + 2176.85i 1.58621 + 0.289289i
$$385$$ 0 0
$$386$$ 3724.00 0.491054
$$387$$ 3631.85 + 4432.78i 0.477047 + 0.582251i
$$388$$ 3257.17i 0.426180i
$$389$$ 1550.22 + 2685.05i 0.202054 + 0.349968i 0.949190 0.314703i $$-0.101905\pi$$
−0.747136 + 0.664671i $$0.768572\pi$$
$$390$$ 0 0
$$391$$ 228.402 395.604i 0.0295417 0.0511677i
$$392$$ 1199.74 + 692.669i 0.154581 + 0.0892476i
$$393$$ −10659.8 + 3809.22i −1.36823 + 0.488931i
$$394$$ −9326.47 16153.9i −1.19254 2.06554i
$$395$$ 0 0
$$396$$ −3750.52 22832.4i −0.475936 2.89740i
$$397$$ 11990.1i 1.51578i −0.652382 0.757890i $$-0.726230\pi$$
0.652382 0.757890i $$-0.273770\pi$$
$$398$$ −5317.38 + 3069.99i −0.669689 + 0.386645i
$$399$$ 1023.36 + 186.638i 0.128402 + 0.0234176i
$$400$$ 0 0
$$401$$ −6426.63 + 11131.3i −0.800326 + 1.38620i 0.119076 + 0.992885i $$0.462007\pi$$
−0.919402 + 0.393320i $$0.871327\pi$$
$$402$$ 8113.38 + 6889.38i 1.00661 + 0.854753i
$$403$$ 6243.21 3604.52i 0.771703 0.445543i
$$404$$ −563.243 −0.0693623
$$405$$ 0 0
$$406$$ −16442.8 −2.00996
$$407$$ 14298.1 8255.02i 1.74135 1.00537i
$$408$$ −4242.48 3602.45i −0.514789 0.437127i
$$409$$ 1112.54 1926.98i 0.134503 0.232966i −0.790904 0.611940i $$-0.790390\pi$$
0.925408 + 0.378974i $$0.123723\pi$$
$$410$$ 0 0
$$411$$ 11752.9 + 2143.47i 1.41053 + 0.257249i
$$412$$ −16113.2 + 9302.97i −1.92680 + 1.11244i
$$413$$ 8433.95i 1.00486i
$$414$$ −191.995 1168.82i −0.0227924 0.138755i
$$415$$ 0 0
$$416$$ 4261.32 + 7380.83i 0.502232 + 0.869891i
$$417$$ 10441.7 3731.29i 1.22621 0.438183i
$$418$$ 2615.27 + 1509.93i 0.306021 + 0.176682i
$$419$$ 4838.33 8380.23i 0.564123 0.977090i −0.433007 0.901390i $$-0.642548\pi$$
0.997131 0.0756998i $$-0.0241191\pi$$
$$420$$ 0 0
$$421$$ 4981.30 + 8627.87i 0.576660 + 0.998804i 0.995859 + 0.0909098i $$0.0289775\pi$$
−0.419199 + 0.907894i $$0.637689\pi$$
$$422$$ 13514.8i 1.55898i
$$423$$ 8139.88 + 9934.98i 0.935637 + 1.14197i
$$424$$ −12287.3 −1.40737
$$425$$ 0 0
$$426$$ 9574.84 + 1746.23i 1.08897 + 0.198604i
$$427$$ −9497.39 5483.32i −1.07637 0.621444i
$$428$$ 3979.83 + 2297.76i 0.449468 + 0.259500i
$$429$$ 10442.5 12297.7i 1.17521 1.38401i
$$430$$ 0 0
$$431$$ −2461.47 −0.275092 −0.137546 0.990495i $$-0.543922\pi$$
−0.137546 + 0.990495i $$0.543922\pi$$
$$432$$ 66.7297 + 1.17358i 0.00743179 + 0.000130704i
$$433$$ 7818.49i 0.867743i −0.900975 0.433871i $$-0.857147\pi$$
0.900975 0.433871i $$-0.142853\pi$$
$$434$$ 7085.36 + 12272.2i 0.783660 + 1.35734i
$$435$$ 0 0
$$436$$ 9833.63 17032.3i 1.08015 1.87087i
$$437$$ 82.6770 + 47.7336i 0.00905030 + 0.00522519i
$$438$$ −1528.80 + 8382.64i −0.166779 + 0.914470i
$$439$$ 3105.91 + 5379.60i 0.337670 + 0.584862i 0.983994 0.178201i $$-0.0570278\pi$$
−0.646324 + 0.763063i $$0.723694\pi$$
$$440$$ 0 0
$$441$$ 1555.98 + 587.080i 0.168015 + 0.0633927i
$$442$$ 10193.6i 1.09697i
$$443$$ −2584.52 + 1492.17i −0.277188 + 0.160034i −0.632150 0.774846i $$-0.717827\pi$$
0.354962 + 0.934881i $$0.384494\pi$$
$$444$$ −5621.08 15730.1i −0.600822 1.68134i
$$445$$ 0 0
$$446$$ 8019.45 13890.1i 0.851417 1.47470i
$$447$$ −8565.99 + 3061.02i −0.906392 + 0.323896i
$$448$$ −14442.1 + 8338.16i −1.52305 + 0.879333i
$$449$$ 810.476 0.0851865 0.0425932 0.999092i $$-0.486438\pi$$
0.0425932 + 0.999092i $$0.486438\pi$$
$$450$$ 0 0
$$451$$ 16563.1 1.72933
$$452$$ −9095.01 + 5251.01i −0.946446 + 0.546431i
$$453$$ −816.637 + 4477.73i −0.0846996 + 0.464420i
$$454$$ −1492.88 + 2585.74i −0.154326 + 0.267301i
$$455$$ 0 0
$$456$$ 752.873 886.632i 0.0773169 0.0910534i
$$457$$ 1361.20 785.887i 0.139331 0.0804425i −0.428714 0.903440i $$-0.641033\pi$$
0.568045 + 0.822998i $$0.307700\pi$$
$$458$$ 20963.2i 2.13875i
$$459$$ −5726.59 3441.91i −0.582341 0.350010i
$$460$$ 0 0
$$461$$ −1031.35 1786.34i −0.104196 0.180474i 0.809213 0.587515i $$-0.199894\pi$$
−0.913410 + 0.407042i $$0.866560\pi$$
$$462$$ 24173.5 + 20526.6i 2.43431 + 2.06707i
$$463$$ 2410.35 + 1391.62i 0.241940 + 0.139684i 0.616068 0.787693i $$-0.288725\pi$$
−0.374128 + 0.927377i $$0.622058\pi$$
$$464$$ 42.5128 73.6344i 0.00425347 0.00736722i
$$465$$ 0 0
$$466$$ 726.118 + 1257.67i 0.0721819 + 0.125023i
$$467$$ 10939.7i 1.08400i 0.840379 + 0.541999i $$0.182332\pi$$
−0.840379 + 0.541999i $$0.817668\pi$$
$$468$$ −10344.9 12626.2i −1.02178 1.24711i
$$469$$ −9008.83 −0.886970
$$470$$ 0 0
$$471$$ −453.561 1269.25i −0.0443716 0.124170i
$$472$$ −8167.04 4715.24i −0.796438 0.459823i
$$473$$ −12194.2 7040.33i −1.18539 0.684386i
$$474$$ −5210.51 14581.1i −0.504908 1.41294i
$$475$$ 0 0
$$476$$ 12374.1 1.19152
$$477$$ −14555.4 + 2390.92i −1.39716 + 0.229503i
$$478$$ 8496.21i 0.812986i
$$479$$ 7311.85 + 12664.5i 0.697467 + 1.20805i 0.969342 + 0.245716i $$0.0790230\pi$$
−0.271875 + 0.962333i $$0.587644\pi$$
$$480$$ 0 0
$$481$$ 5823.49 10086.6i 0.552034 0.956151i
$$482$$ −12939.8 7470.81i −1.22281 0.705987i
$$483$$ 764.201 + 648.913i 0.0719925 + 0.0611316i
$$484$$ 19829.9 + 34346.4i 1.86231 + 3.22562i
$$485$$ 0 0
$$486$$ −17142.3 + 2507.13i −1.59998 + 0.234003i
$$487$$ 16473.6i 1.53284i 0.642341 + 0.766419i $$0.277963\pi$$
−0.642341 + 0.766419i $$0.722037\pi$$
$$488$$ −10619.6 + 6131.22i −0.985093 + 0.568744i
$$489$$ 4042.01 4760.13i 0.373795 0.440206i
$$490$$ 0 0
$$491$$ −10264.6 + 17778.8i −0.943450 + 1.63410i −0.184626 + 0.982809i $$0.559107\pi$$
−0.758825 + 0.651295i $$0.774226\pi$$
$$492$$ 3006.68 16486.0i 0.275511 1.51067i
$$493$$ −7371.56 + 4255.97i −0.673425 + 0.388802i
$$494$$ 2130.35 0.194026
$$495$$ 0 0
$$496$$ −73.2768 −0.00663352
$$497$$ −7134.10 + 4118.87i −0.643879 + 0.371744i
$$498$$ 18197.4 6502.76i 1.63744 0.585132i
$$499$$ −7202.31 + 12474.8i −0.646131 + 1.11913i 0.337908 + 0.941179i $$0.390281\pi$$
−0.984039 + 0.177953i $$0.943053\pi$$
$$500$$ 0 0
$$501$$ −2935.63 8215.08i −0.261785 0.732580i
$$502$$ 22344.5 12900.6i 1.98663 1.14698i
$$503$$ 2953.63i 0.261821i 0.991394 + 0.130910i $$0.0417901\pi$$
−0.991394 + 0.130910i $$0.958210\pi$$
$$504$$ 9448.49 7741.30i 0.835058 0.684176i
$$505$$ 0 0
$$506$$ 1455.20 + 2520.48i 0.127849 + 0.221441i
$$507$$ −6.24932 + 34.2659i −0.000547420 + 0.00300158i
$$508$$ −9672.98 5584.69i −0.844821 0.487757i
$$509$$ −8684.44 + 15041.9i −0.756250 + 1.30986i 0.188500 + 0.982073i $$0.439637\pi$$
−0.944750 + 0.327790i $$0.893696\pi$$
$$510$$ 0 0
$$511$$ −3606.02 6245.80i −0.312174 0.540701i
$$512$$ 172.223i 0.0148657i
$$513$$ 719.323 1196.80i 0.0619082 0.103002i
$$514$$ −5366.92 −0.460554
$$515$$ 0 0
$$516$$ −9221.16 + 10859.4i −0.786703 + 0.926473i
$$517$$ −27330.3 15779.1i −2.32492 1.34229i
$$518$$ 19827.1 + 11447.2i 1.68176 + 0.970966i
$$519$$ 4763.20 + 868.699i 0.402854 + 0.0734714i
$$520$$ 0 0
$$521$$ −6146.30 −0.516841 −0.258421 0.966033i $$-0.583202\pi$$
−0.258421 + 0.966033i $$0.583202\pi$$
$$522$$ −7791.48 + 20650.4i −0.653303 + 1.73150i
$$523$$ 4554.68i 0.380807i 0.981706 + 0.190404i $$0.0609797\pi$$
−0.981706 + 0.190404i $$0.939020\pi$$
$$524$$ −14070.7 24371.1i −1.17305 2.03179i
$$525$$ 0 0
$$526$$ −6627.03 + 11478.4i −0.549339 + 0.951483i
$$527$$ 6352.96 + 3667.88i 0.525122 + 0.303179i
$$528$$ −154.423 + 55.1824i −0.0127280 + 0.00454831i
$$529$$ −6037.50 10457.3i −0.496219 0.859476i
$$530$$ 0 0
$$531$$ −10592.1 3996.46i −0.865649 0.326613i
$$532$$ 2586.05i 0.210751i
$$533$$ 10119.0 5842.22i 0.822333 0.474774i
$$534$$ 4699.25 + 857.037i 0.380817 + 0.0694525i
$$535$$ 0 0
$$536$$ −5036.64 + 8723.72i −0.405877 + 0.702999i
$$537$$ 4053.53 + 3442.01i 0.325741 + 0.276599i
$$538$$ 11605.8 6700.59i 0.930037 0.536957i
$$539$$ −4086.28 −0.326547
$$540$$ 0 0
$$541$$ 18091.8 1.43776 0.718879 0.695135i $$-0.244655\pi$$
0.718879 + 0.695135i $$0.244655\pi$$
$$542$$ 2649.33 1529.59i 0.209960 0.121221i
$$543$$ −10456.3 8878.86i −0.826379 0.701710i
$$544$$ −4336.23 + 7510.58i −0.341754 + 0.591936i
$$545$$ 0 0
$$546$$ 22008.7 + 4013.89i 1.72507 + 0.314613i
$$547$$ 13667.1 7890.69i 1.06830 0.616786i 0.140586 0.990068i $$-0.455101\pi$$
0.927718 + 0.373283i $$0.121768\pi$$
$$548$$ 29699.7i 2.31516i
$$549$$ −11386.8 + 9329.41i −0.885206 + 0.725263i
$$550$$ 0 0
$$551$$ −889.453 1540.58i −0.0687694 0.119112i
$$552$$ 1055.62 377.223i 0.0813956 0.0290864i
$$553$$ 11349.8 + 6552.83i 0.872774 + 0.503896i
$$554$$ 1446.69 2505.75i 0.110946 0.192164i
$$555$$ 0 0
$$556$$ 13782.8 + 23872.5i 1.05130 + 1.82090i
$$557$$ 13954.5i 1.06153i −0.847519 0.530766i $$-0.821904\pi$$
0.847519 0.530766i $$-0.178096\pi$$
$$558$$ 18770.0 3083.22i 1.42401 0.233913i
$$559$$ −9933.18 −0.751572
$$560$$ 0 0
$$561$$ 16150.4 + 2945.46i 1.21545 + 0.221671i
$$562$$ −14240.4 8221.69i −1.06885 0.617102i
$$563$$ −11781.4 6801.97i −0.881927 0.509181i −0.0106339 0.999943i $$-0.503385\pi$$
−0.871293 + 0.490762i $$0.836718\pi$$
$$564$$ −20666.9 + 24338.7i −1.54297 + 1.81710i
$$565$$ 0 0
$$566$$ −2306.77 −0.171309
$$567$$ 9686.28 11008.8i 0.717435 0.815392i
$$568$$ 9211.10i 0.680438i
$$569$$ −6229.30 10789.5i −0.458956 0.794935i 0.539950 0.841697i $$-0.318443\pi$$
−0.998906 + 0.0467619i $$0.985110\pi$$
$$570$$ 0 0
$$571$$ 6728.56 11654.2i 0.493137 0.854139i −0.506831 0.862045i $$-0.669183\pi$$
0.999969 + 0.00790629i $$0.00251668\pi$$
$$572$$ 34733.7 + 20053.5i 2.53897 + 1.46587i
$$573$$ 758.207 4157.36i 0.0552785 0.303100i
$$574$$ 11484.0 + 19890.8i 0.835074 + 1.44639i
$$575$$ 0 0
$$576$$ 3628.38 + 22088.8i 0.262470 + 1.59786i
$$577$$ 3722.70i 0.268592i 0.990941 + 0.134296i $$0.0428774\pi$$
−0.990941 + 0.134296i $$0.957123\pi$$
$$578$$ −10476.5 + 6048.61i −0.753918 + 0.435275i
$$579$$ 1423.73 + 3984.18i 0.102190 + 0.285971i
$$580$$ 0 0
$$581$$ −8177.99 + 14164.7i −0.583959 + 1.01145i
$$582$$ 5642.86 2016.45i 0.401897 0.143616i
$$583$$ 31387.7 18121.7i 2.22975 1.28735i
$$584$$ −8064.19 −0.571401
$$585$$ 0 0
$$586$$ −28349.3 −1.99847
$$587$$ −15190.4 + 8770.16i −1.06810 + 0.616667i −0.927661 0.373423i $$-0.878184\pi$$
−0.140437 + 0.990090i $$0.544851\pi$$
$$588$$ −741.777 + 4067.27i −0.0520244 + 0.285257i
$$589$$ −766.548 + 1327.70i −0.0536249 + 0.0928810i
$$590$$ 0 0
$$591$$ 13716.9 16153.9i 0.954718 1.12434i
$$592$$ −102.526 + 59.1933i −0.00711788 + 0.00410951i
$$593$$ 22350.6i 1.54777i 0.633325 + 0.773886i $$0.281690\pi$$
−0.633325 + 0.773886i $$0.718310\pi$$
$$594$$ 37233.9 20632.7i 2.57193 1.42520i
$$595$$ 0 0
$$596$$ −11306.9 19584.2i −0.777097 1.34597i
$$597$$ −5317.38 4515.19i −0.364533 0.309539i
$$598$$ 1778.07 + 1026.57i 0.121590 + 0.0702000i
$$599$$ −1280.81 + 2218.43i −0.0873665 + 0.151323i −0.906397 0.422427i $$-0.861178\pi$$
0.819031 + 0.573750i $$0.194512\pi$$
$$600$$ 0 0
$$601$$ −6692.51 11591.8i −0.454232 0.786752i 0.544412 0.838818i $$-0.316753\pi$$
−0.998644 + 0.0520656i $$0.983420\pi$$
$$602$$ 19525.6i 1.32193i
$$603$$ −4268.87 + 11314.1i −0.288295 + 0.764091i
$$604$$ −11315.3 −0.762270
$$605$$ 0 0
$$606$$ −348.693 975.786i −0.0233741 0.0654103i
$$607$$ 24793.1 + 14314.3i 1.65786 + 0.957166i 0.973700 + 0.227835i $$0.0731646\pi$$
0.684161 + 0.729331i $$0.260169\pi$$
$$608$$ −1569.63 906.226i −0.104699 0.0604479i
$$609$$ −6286.29 17591.6i −0.418281 1.17052i
$$610$$ 0 0
$$611$$ −22262.8 −1.47407
$$612$$ 5863.50 15540.5i 0.387284 1.02645i
$$613$$ 7188.12i 0.473614i −0.971557 0.236807i $$-0.923899\pi$$
0.971557 0.236807i $$-0.0761010\pi$$
$$614$$ 4497.63 + 7790.12i 0.295618 + 0.512025i
$$615$$ 0 0
$$616$$ −15006.5 + 25992.0i −0.981539 + 1.70008i
$$617$$ −13452.6 7766.88i −0.877767 0.506779i −0.00784559 0.999969i $$-0.502497\pi$$
−0.869922 + 0.493190i $$0.835831\pi$$
$$618$$ −26092.3 22155.9i −1.69836 1.44214i
$$619$$ −11079.9 19191.0i −0.719450 1.24612i −0.961218 0.275789i $$-0.911061\pi$$
0.241769 0.970334i $$-0.422272\pi$$
$$620$$ 0 0
$$621$$ 1177.08 652.265i 0.0760624 0.0421490i
$$622$$ 10547.2i 0.679908i
$$623$$ −3501.36 + 2021.51i −0.225167 + 0.130000i
$$624$$ −74.8785 + 88.1818i −0.00480375 + 0.00565721i
$$625$$ 0 0
$$626$$ 23559.4 40806.1i 1.50419 2.60534i
$$627$$ −615.569 + 3375.25i −0.0392081 + 0.214983i
$$628$$ 2901.85 1675.38i 0.184389 0.106457i
$$629$$ 11851.7 0.751287
$$630$$ 0 0
$$631$$ −25582.8 −1.61400 −0.807002 0.590549i $$-0.798911\pi$$
−0.807002 + 0.590549i $$0.798911\pi$$
$$632$$ 12690.9 7327.10i 0.798761 0.461165i
$$633$$ −14459.0 + 5166.88i −0.907891 + 0.324431i
$$634$$ 3891.73 6740.68i 0.243786 0.422250i
$$635$$ 0 0
$$636$$ −12339.6 34531.2i −0.769334 2.15291i
$$637$$ −2496.46 + 1441.33i −0.155280 + 0.0896510i
$$638$$ 54231.5i 3.36527i
$$639$$ 1792.34 + 10911.4i 0.110961 + 0.675506i
$$640$$ 0 0
$$641$$ −1905.34 3300.14i −0.117405 0.203351i 0.801334 0.598217i $$-0.204124\pi$$
−0.918738 + 0.394867i $$0.870791\pi$$
$$642$$ −1516.89 + 8317.33i −0.0932507 + 0.511306i
$$643$$ 23140.3 + 13360.0i 1.41923 + 0.819391i 0.996231 0.0867402i $$-0.0276450\pi$$
0.422996 + 0.906131i $$0.360978\pi$$
$$644$$ −1246.16 + 2158.41i −0.0762509 + 0.132071i
$$645$$ 0 0
$$646$$ 1083.90 + 1877.37i 0.0660147 + 0.114341i
$$647$$ 5114.23i 0.310759i 0.987855 + 0.155380i $$0.0496601\pi$$
−0.987855 + 0.155380i $$0.950340\pi$$
$$648$$ −5245.03 15534.5i −0.317970 0.941750i
$$649$$ 27816.8 1.68244
$$650$$ 0 0
$$651$$ −10420.8 + 12272.2i −0.627378 + 0.738842i
$$652$$ 13444.5 + 7762.20i 0.807559 + 0.466244i
$$653$$ −7682.56 4435.53i −0.460401 0.265813i 0.251812 0.967776i $$-0.418974\pi$$
−0.712213 + 0.701964i $$0.752307\pi$$
$$654$$ 35595.4 + 6491.79i 2.12827 + 0.388148i
$$655$$ 0 0
$$656$$ −118.767 −0.00706872
$$657$$ −9552.78 + 1569.17i −0.567259 + 0.0931799i
$$658$$ 43761.7i 2.59272i
$$659$$ −12102.2 20961.7i −0.715382 1.23908i −0.962812 0.270172i $$-0.912920\pi$$
0.247430 0.968906i $$-0.420414\pi$$
$$660$$ 0 0
$$661$$ −10689.8 + 18515.2i −0.629023 + 1.08950i 0.358726 + 0.933443i $$0.383211\pi$$
−0.987748 + 0.156056i $$0.950122\pi$$
$$662$$ −33078.9 19098.1i −1.94207 1.12125i
$$663$$ 10905.8 3897.14i 0.638832 0.228284i
$$664$$ 9144.28 + 15838.4i 0.534438 + 0.925674i
$$665$$ 0 0
$$666$$ 23771.6 19476.4i 1.38308 1.13318i
$$667$$ 1714.43i 0.0995248i
$$668$$ 18781.9 10843.7i 1.08787 0.628079i
$$669$$ 17926.5 + 3269.38i 1.03599 + 0.188941i
$$670$$ 0 0
$$671$$ 18085.0 31324.2i 1.04048 1.80217i
$$672$$ −14508.4 12319.6i −0.832849 0.707203i
$$673$$ −25722.1 + 14850.7i −1.47328 + 0.850597i −0.999548 0.0300732i $$-0.990426\pi$$
−0.473730 + 0.880670i $$0.657093\pi$$
$$674$$ −35936.6 −2.05375
$$675$$ 0 0
$$676$$ −86.5900 −0.00492661
$$677$$ 2304.91 1330.74i 0.130849 0.0755459i −0.433147 0.901324i $$-0.642597\pi$$
0.563996 + 0.825778i $$0.309263\pi$$
$$678$$ −14727.6 12505.8i −0.834235 0.708381i
$$679$$ −2535.93 + 4392.36i −0.143328 + 0.248252i
$$680$$ 0 0
$$681$$ −3337.14 608.618i −0.187782 0.0342471i
$$682$$ −40476.1 + 23368.9i −2.27259 + 1.31208i
$$683$$ 28698.1i 1.60776i −0.594789 0.803882i $$-0.702765\pi$$
0.594789 0.803882i $$-0.297235\pi$$
$$684$$ 3247.80 + 1225.41i 0.181554 + 0.0685010i
$$685$$ 0 0
$$686$$ 12944.0 + 22419.7i 0.720415 + 1.24780i
$$687$$ −22427.9 + 8014.51i −1.24553 + 0.445084i
$$688$$ 87.4396 + 50.4833i 0.00484535 + 0.00279747i
$$689$$ 12783.9 22142.4i 0.706863 1.22432i
$$690$$ 0 0
$$691$$ −8412.62 14571.1i −0.463142 0.802186i 0.535973 0.844235i $$-0.319945\pi$$
−0.999116 + 0.0420492i $$0.986611\pi$$
$$692$$ 12036.6i 0.661220i
$$693$$ −12718.9 + 33710.0i −0.697189 + 1.84781i
$$694$$ 5543.99 0.303238
$$695$$ 0 0
$$696$$ −20549.4 3747.74i −1.11914 0.204106i
$$697$$ 10296.9 + 5944.92i 0.559574 + 0.323070i
$$698$$ −5539.88 3198.45i −0.300412 0.173443i
$$699$$ −1067.94 + 1257.67i −0.0577870 + 0.0680537i
$$700$$ 0 0
$$701$$ −998.795 −0.0538145 −0.0269073 0.999638i $$-0.508566\pi$$
−0.0269073 + 0.999638i $$0.508566\pi$$
$$702$$ 15469.9 25738.6i 0.831730 1.38382i
$$703$$ 2476.88i 0.132884i
$$704$$ −27500.8 47632.9i −1.47227 2.55004i
$$705$$ 0 0
$$706$$ 6010.66 10410.8i 0.320417 0.554978i
$$707$$ 759.545 + 438.523i 0.0404040 + 0.0233272i
$$708$$ 5049.54 27687.3i 0.268041 1.46971i
$$709$$ 16626.9 + 28798.6i 0.880727 + 1.52546i 0.850534 + 0.525921i $$0.176279\pi$$
0.0301937 + 0.999544i $$0.490388\pi$$
$$710$$ 0 0
$$711$$ 13607.8 11149.1i 0.717768 0.588078i
$$712$$ 4520.73i 0.237952i
$$713$$ −1279.58 + 738.765i −0.0672099 + 0.0388036i
$$714$$ 7660.56 + 21437.4i 0.401526 + 1.12363i
$$715$$ 0 0
$$716$$ −6609.97 + 11448.8i −0.345009 + 0.597573i
$$717$$ −9089.81 + 3248.21i −0.473452 + 0.169186i
$$718$$ 14565.9 8409.62i 0.757095 0.437109i
$$719$$ −1178.94 −0.0611503 −0.0305752 0.999532i $$-0.509734\pi$$
−0.0305752 + 0.999532i $$0.509734\pi$$
$$720$$ 0 0
$$721$$ 28972.0 1.49650
$$722$$ 26775.0 15458.6i 1.38014 0.796826i
$$723$$ 3045.71 16700.1i 0.156668 0.859034i
$$724$$ 17050.8 29532.9i 0.875260 1.51600i
$$725$$ 0 0
$$726$$ −47226.8 + 55617.4i −2.41426 + 2.84319i
$$727$$ 10978.3 6338.35i 0.560061 0.323351i −0.193109 0.981177i $$-0.561857\pi$$
0.753170 + 0.657826i $$0.228524\pi$$
$$728$$ 21172.6i 1.07790i
$$729$$ −9236.02 17381.5i −0.469238 0.883072i
$$730$$ 0 0
$$731$$ −5053.90 8753.61i −0.255712 0.442906i
$$732$$ −27895.5 23687.1i −1.40853 1.19604i
$$733$$ 8492.98 + 4903.42i 0.427961 + 0.247083i 0.698478 0.715632i $$-0.253861\pi$$
−0.270517 + 0.962715i $$0.587195\pi$$
$$734$$ −26137.5 + 45271.4i −1.31438 + 2.27657i
$$735$$ 0 0
$$736$$ −873.381 1512.74i −0.0437408 0.0757613i
$$737$$ 29712.8i 1.48506i
$$738$$ 30422.5 4997.30i 1.51744 0.249259i
$$739$$ 29970.4 1.49185 0.745927 0.666028i $$-0.232007\pi$$
0.745927 + 0.666028i $$0.232007\pi$$
$$740$$ 0 0
$$741$$ 814.460 + 2279.19i 0.0403778 + 0.112994i
$$742$$ 43525.1 + 25129.2i 2.15345 + 1.24329i
$$743$$ 18790.6 + 10848.8i 0.927808 + 0.535670i 0.886118 0.463460i $$-0.153392\pi$$
0.0416904 + 0.999131i $$0.486726\pi$$
$$744$$ 6057.78 + 16952.1i 0.298507 + 0.835344i
$$745$$ 0 0
$$746$$ −10335.8 −0.507267
$$747$$ 13914.2 + 16982.7i 0.681516 + 0.831812i
$$748$$ 40812.1i 1.99497i
$$749$$ −3577.92 6197.14i −0.174545 0.302321i
$$750$$ 0 0
$$751$$ −8512.10 + 14743.4i −0.413596 + 0.716370i −0.995280 0.0970452i $$-0.969061\pi$$
0.581684 + 0.813415i $$0.302394\pi$$
$$752$$ 195.974 + 113.146i 0.00950324 + 0.00548670i
$$753$$ 22344.5 + 18973.6i 1.08138 + 0.918243i
$$754$$ −19128.8 33132.0i −0.923911 1.60026i
$$755$$ 0 0
$$756$$ 31244.2 + 18779.0i 1.50310 + 0.903422i
$$757$$ 30745.2i 1.47616i 0.674714 + 0.738080i $$0.264267\pi$$
−0.674714 + 0.738080i $$0.735733\pi$$
$$758$$ −46800.5 + 27020.3i −2.24257 + 1.29475i
$$759$$ −2140.24 + 2520.48i −0.102353 + 0.120537i
$$760$$ 0 0
$$761$$ −10748.3 + 18616.6i −0.511992 + 0.886797i 0.487911 + 0.872893i $$0.337759\pi$$
−0.999903 + 0.0139035i $$0.995574\pi$$
$$762$$ 3686.81 20215.3i 0.175274 0.961052i
$$763$$ −26521.7 + 15312.3i −1.25839 + 0.726530i
$$764$$ 10505.7 0.497489
$$765$$ 0 0
$$766$$ 36955.5 1.74316
$$767$$ 16994.3 9811.66i 0.800037 0.461902i
$$768$$ −19800.6 + 7075.65i −0.930327 + 0.332449i
$$769$$ 11028.7 19102.4i 0.517174 0.895772i −0.482627 0.875826i $$-0.660317\pi$$
0.999801 0.0199457i $$-0.00634935\pi$$
$$770$$ 0 0
$$771$$ −2051.84 5741.89i −0.0958434 0.268209i
$$772$$ −9108.93 + 5259.04i −0.424660 + 0.245178i
$$773$$ 30155.8i 1.40314i −0.712601 0.701570i $$-0.752483\pi$$
0.712601 0.701570i $$-0.247517\pi$$
$$774$$ −24522.0 9252.26i −1.13879 0.429671i
$$775$$ 0 0
$$776$$ 2835.57 + 4911.35i 0.131174 + 0.227200i
$$777$$ −4666.81 + 25588.7i −0.215471 + 1.18146i
$$778$$