# Properties

 Label 441.4.e.m.361.1 Level $441$ Weight $4$ Character 441.361 Analytic conductor $26.020$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$441 = 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 441.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$26.0198423125$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 21) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 361.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 441.361 Dual form 441.4.e.m.226.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(2.00000 + 3.46410i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(-2.00000 - 3.46410i) q^{5} +O(q^{10})$$ $$q+(2.00000 + 3.46410i) q^{2} +(-4.00000 + 6.92820i) q^{4} +(-2.00000 - 3.46410i) q^{5} +(8.00000 - 13.8564i) q^{10} +(31.0000 - 53.6936i) q^{11} -62.0000 q^{13} +(32.0000 + 55.4256i) q^{16} +(42.0000 - 72.7461i) q^{17} +(-50.0000 - 86.6025i) q^{19} +32.0000 q^{20} +248.000 q^{22} +(-21.0000 - 36.3731i) q^{23} +(54.5000 - 94.3968i) q^{25} +(-124.000 - 214.774i) q^{26} +10.0000 q^{29} +(24.0000 - 41.5692i) q^{31} +(-128.000 + 221.703i) q^{32} +336.000 q^{34} +(123.000 + 213.042i) q^{37} +(200.000 - 346.410i) q^{38} +248.000 q^{41} +68.0000 q^{43} +(248.000 + 429.549i) q^{44} +(84.0000 - 145.492i) q^{46} +(162.000 + 280.592i) q^{47} +436.000 q^{50} +(248.000 - 429.549i) q^{52} +(129.000 - 223.435i) q^{53} -248.000 q^{55} +(20.0000 + 34.6410i) q^{58} +(60.0000 - 103.923i) q^{59} +(-311.000 - 538.668i) q^{61} +192.000 q^{62} -512.000 q^{64} +(124.000 + 214.774i) q^{65} +(-452.000 + 782.887i) q^{67} +(336.000 + 581.969i) q^{68} +678.000 q^{71} +(321.000 - 555.988i) q^{73} +(-492.000 + 852.169i) q^{74} +800.000 q^{76} +(-370.000 - 640.859i) q^{79} +(128.000 - 221.703i) q^{80} +(496.000 + 859.097i) q^{82} -468.000 q^{83} -336.000 q^{85} +(136.000 + 235.559i) q^{86} +(100.000 + 173.205i) q^{89} +336.000 q^{92} +(-648.000 + 1122.37i) q^{94} +(-200.000 + 346.410i) q^{95} -1266.00 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 4q^{2} - 8q^{4} - 4q^{5} + O(q^{10})$$ $$2q + 4q^{2} - 8q^{4} - 4q^{5} + 16q^{10} + 62q^{11} - 124q^{13} + 64q^{16} + 84q^{17} - 100q^{19} + 64q^{20} + 496q^{22} - 42q^{23} + 109q^{25} - 248q^{26} + 20q^{29} + 48q^{31} - 256q^{32} + 672q^{34} + 246q^{37} + 400q^{38} + 496q^{41} + 136q^{43} + 496q^{44} + 168q^{46} + 324q^{47} + 872q^{50} + 496q^{52} + 258q^{53} - 496q^{55} + 40q^{58} + 120q^{59} - 622q^{61} + 384q^{62} - 1024q^{64} + 248q^{65} - 904q^{67} + 672q^{68} + 1356q^{71} + 642q^{73} - 984q^{74} + 1600q^{76} - 740q^{79} + 256q^{80} + 992q^{82} - 936q^{83} - 672q^{85} + 272q^{86} + 200q^{89} + 672q^{92} - 1296q^{94} - 400q^{95} - 2532q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$344$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.00000 + 3.46410i 0.707107 + 1.22474i 0.965926 + 0.258819i $$0.0833333\pi$$
−0.258819 + 0.965926i $$0.583333\pi$$
$$3$$ 0 0
$$4$$ −4.00000 + 6.92820i −0.500000 + 0.866025i
$$5$$ −2.00000 3.46410i −0.178885 0.309839i 0.762614 0.646854i $$-0.223916\pi$$
−0.941499 + 0.337016i $$0.890582\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 8.00000 13.8564i 0.252982 0.438178i
$$11$$ 31.0000 53.6936i 0.849714 1.47175i −0.0317500 0.999496i $$-0.510108\pi$$
0.881464 0.472252i $$-0.156559\pi$$
$$12$$ 0 0
$$13$$ −62.0000 −1.32275 −0.661373 0.750057i $$-0.730026\pi$$
−0.661373 + 0.750057i $$0.730026\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 32.0000 + 55.4256i 0.500000 + 0.866025i
$$17$$ 42.0000 72.7461i 0.599206 1.03785i −0.393733 0.919225i $$-0.628817\pi$$
0.992939 0.118630i $$-0.0378502\pi$$
$$18$$ 0 0
$$19$$ −50.0000 86.6025i −0.603726 1.04568i −0.992251 0.124246i $$-0.960349\pi$$
0.388526 0.921438i $$-0.372984\pi$$
$$20$$ 32.0000 0.357771
$$21$$ 0 0
$$22$$ 248.000 2.40335
$$23$$ −21.0000 36.3731i −0.190383 0.329753i 0.754994 0.655731i $$-0.227640\pi$$
−0.945377 + 0.325979i $$0.894306\pi$$
$$24$$ 0 0
$$25$$ 54.5000 94.3968i 0.436000 0.755174i
$$26$$ −124.000 214.774i −0.935323 1.62003i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 10.0000 0.0640329 0.0320164 0.999487i $$-0.489807\pi$$
0.0320164 + 0.999487i $$0.489807\pi$$
$$30$$ 0 0
$$31$$ 24.0000 41.5692i 0.139049 0.240840i −0.788088 0.615563i $$-0.788929\pi$$
0.927137 + 0.374723i $$0.122262\pi$$
$$32$$ −128.000 + 221.703i −0.707107 + 1.22474i
$$33$$ 0 0
$$34$$ 336.000 1.69481
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 123.000 + 213.042i 0.546516 + 0.946593i 0.998510 + 0.0545719i $$0.0173794\pi$$
−0.451994 + 0.892021i $$0.649287\pi$$
$$38$$ 200.000 346.410i 0.853797 1.47882i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 248.000 0.944661 0.472330 0.881422i $$-0.343413\pi$$
0.472330 + 0.881422i $$0.343413\pi$$
$$42$$ 0 0
$$43$$ 68.0000 0.241161 0.120580 0.992704i $$-0.461524\pi$$
0.120580 + 0.992704i $$0.461524\pi$$
$$44$$ 248.000 + 429.549i 0.849714 + 1.47175i
$$45$$ 0 0
$$46$$ 84.0000 145.492i 0.269242 0.466341i
$$47$$ 162.000 + 280.592i 0.502769 + 0.870821i 0.999995 + 0.00319997i $$0.00101858\pi$$
−0.497226 + 0.867621i $$0.665648\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 436.000 1.23319
$$51$$ 0 0
$$52$$ 248.000 429.549i 0.661373 1.14553i
$$53$$ 129.000 223.435i 0.334330 0.579077i −0.649026 0.760767i $$-0.724823\pi$$
0.983356 + 0.181689i $$0.0581565\pi$$
$$54$$ 0 0
$$55$$ −248.000 −0.608006
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 20.0000 + 34.6410i 0.0452781 + 0.0784239i
$$59$$ 60.0000 103.923i 0.132396 0.229316i −0.792204 0.610256i $$-0.791066\pi$$
0.924600 + 0.380941i $$0.124400\pi$$
$$60$$ 0 0
$$61$$ −311.000 538.668i −0.652778 1.13064i −0.982446 0.186548i $$-0.940270\pi$$
0.329668 0.944097i $$-0.393063\pi$$
$$62$$ 192.000 0.393291
$$63$$ 0 0
$$64$$ −512.000 −1.00000
$$65$$ 124.000 + 214.774i 0.236620 + 0.409838i
$$66$$ 0 0
$$67$$ −452.000 + 782.887i −0.824188 + 1.42754i 0.0783505 + 0.996926i $$0.475035\pi$$
−0.902538 + 0.430609i $$0.858299\pi$$
$$68$$ 336.000 + 581.969i 0.599206 + 1.03785i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 678.000 1.13329 0.566646 0.823961i $$-0.308241\pi$$
0.566646 + 0.823961i $$0.308241\pi$$
$$72$$ 0 0
$$73$$ 321.000 555.988i 0.514660 0.891418i −0.485195 0.874406i $$-0.661251\pi$$
0.999855 0.0170119i $$-0.00541532\pi$$
$$74$$ −492.000 + 852.169i −0.772890 + 1.33868i
$$75$$ 0 0
$$76$$ 800.000 1.20745
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −370.000 640.859i −0.526940 0.912687i −0.999507 0.0313921i $$-0.990006\pi$$
0.472567 0.881295i $$-0.343327\pi$$
$$80$$ 128.000 221.703i 0.178885 0.309839i
$$81$$ 0 0
$$82$$ 496.000 + 859.097i 0.667976 + 1.15697i
$$83$$ −468.000 −0.618912 −0.309456 0.950914i $$-0.600147\pi$$
−0.309456 + 0.950914i $$0.600147\pi$$
$$84$$ 0 0
$$85$$ −336.000 −0.428757
$$86$$ 136.000 + 235.559i 0.170526 + 0.295360i
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 100.000 + 173.205i 0.119101 + 0.206289i 0.919412 0.393297i $$-0.128665\pi$$
−0.800311 + 0.599585i $$0.795332\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 336.000 0.380765
$$93$$ 0 0
$$94$$ −648.000 + 1122.37i −0.711022 + 1.23153i
$$95$$ −200.000 + 346.410i −0.215995 + 0.374115i
$$96$$ 0 0
$$97$$ −1266.00 −1.32518 −0.662592 0.748981i $$-0.730544\pi$$
−0.662592 + 0.748981i $$0.730544\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 436.000 + 755.174i 0.436000 + 0.755174i
$$101$$ 116.000 200.918i 0.114281 0.197941i −0.803211 0.595695i $$-0.796877\pi$$
0.917492 + 0.397754i $$0.130210\pi$$
$$102$$ 0 0
$$103$$ 896.000 + 1551.92i 0.857141 + 1.48461i 0.874645 + 0.484765i $$0.161095\pi$$
−0.0175038 + 0.999847i $$0.505572\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 1032.00 0.945629
$$107$$ −953.000 1650.64i −0.861028 1.49134i −0.870938 0.491393i $$-0.836488\pi$$
0.00990992 0.999951i $$-0.496846\pi$$
$$108$$ 0 0
$$109$$ 45.0000 77.9423i 0.0395433 0.0684910i −0.845576 0.533854i $$-0.820743\pi$$
0.885120 + 0.465363i $$0.154076\pi$$
$$110$$ −496.000 859.097i −0.429925 0.744652i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −458.000 −0.381283 −0.190642 0.981660i $$-0.561057\pi$$
−0.190642 + 0.981660i $$0.561057\pi$$
$$114$$ 0 0
$$115$$ −84.0000 + 145.492i −0.0681134 + 0.117976i
$$116$$ −40.0000 + 69.2820i −0.0320164 + 0.0554541i
$$117$$ 0 0
$$118$$ 480.000 0.374471
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −1256.50 2176.32i −0.944027 1.63510i
$$122$$ 1244.00 2154.67i 0.923168 1.59897i
$$123$$ 0 0
$$124$$ 192.000 + 332.554i 0.139049 + 0.240840i
$$125$$ −936.000 −0.669747
$$126$$ 0 0
$$127$$ 804.000 0.561760 0.280880 0.959743i $$-0.409374\pi$$
0.280880 + 0.959743i $$0.409374\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ −496.000 + 859.097i −0.334631 + 0.579599i
$$131$$ 406.000 + 703.213i 0.270782 + 0.469007i 0.969062 0.246817i $$-0.0793846\pi$$
−0.698281 + 0.715824i $$0.746051\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −3616.00 −2.33116
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 207.000 358.535i 0.129089 0.223589i −0.794235 0.607611i $$-0.792128\pi$$
0.923324 + 0.384022i $$0.125461\pi$$
$$138$$ 0 0
$$139$$ −1620.00 −0.988537 −0.494268 0.869309i $$-0.664564\pi$$
−0.494268 + 0.869309i $$0.664564\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 1356.00 + 2348.66i 0.801359 + 1.38799i
$$143$$ −1922.00 + 3329.00i −1.12396 + 1.94675i
$$144$$ 0 0
$$145$$ −20.0000 34.6410i −0.0114545 0.0198399i
$$146$$ 2568.00 1.45568
$$147$$ 0 0
$$148$$ −1968.00 −1.09303
$$149$$ 1185.00 + 2052.48i 0.651537 + 1.12849i 0.982750 + 0.184939i $$0.0592087\pi$$
−0.331213 + 0.943556i $$0.607458\pi$$
$$150$$ 0 0
$$151$$ 284.000 491.902i 0.153057 0.265102i −0.779293 0.626660i $$-0.784422\pi$$
0.932350 + 0.361558i $$0.117755\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −192.000 −0.0994956
$$156$$ 0 0
$$157$$ 133.000 230.363i 0.0676086 0.117102i −0.830240 0.557407i $$-0.811796\pi$$
0.897848 + 0.440305i $$0.145130\pi$$
$$158$$ 1480.00 2563.44i 0.745206 1.29073i
$$159$$ 0 0
$$160$$ 1024.00 0.505964
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 136.000 + 235.559i 0.0653518 + 0.113193i 0.896850 0.442335i $$-0.145850\pi$$
−0.831498 + 0.555527i $$0.812516\pi$$
$$164$$ −992.000 + 1718.19i −0.472330 + 0.818100i
$$165$$ 0 0
$$166$$ −936.000 1621.20i −0.437637 0.758009i
$$167$$ 1876.00 0.869277 0.434638 0.900605i $$-0.356876\pi$$
0.434638 + 0.900605i $$0.356876\pi$$
$$168$$ 0 0
$$169$$ 1647.00 0.749659
$$170$$ −672.000 1163.94i −0.303177 0.525118i
$$171$$ 0 0
$$172$$ −272.000 + 471.118i −0.120580 + 0.208851i
$$173$$ −76.0000 131.636i −0.0333998 0.0578502i 0.848842 0.528646i $$-0.177300\pi$$
−0.882242 + 0.470796i $$0.843967\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 3968.00 1.69943
$$177$$ 0 0
$$178$$ −400.000 + 692.820i −0.168434 + 0.291736i
$$179$$ 305.000 528.275i 0.127356 0.220588i −0.795295 0.606222i $$-0.792684\pi$$
0.922652 + 0.385635i $$0.126018\pi$$
$$180$$ 0 0
$$181$$ 1042.00 0.427907 0.213954 0.976844i $$-0.431366\pi$$
0.213954 + 0.976844i $$0.431366\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 492.000 852.169i 0.195527 0.338663i
$$186$$ 0 0
$$187$$ −2604.00 4510.26i −1.01831 1.76376i
$$188$$ −2592.00 −1.00554
$$189$$ 0 0
$$190$$ −1600.00 −0.610927
$$191$$ −1019.00 1764.96i −0.386033 0.668628i 0.605879 0.795557i $$-0.292821\pi$$
−0.991912 + 0.126928i $$0.959488\pi$$
$$192$$ 0 0
$$193$$ 1301.00 2253.40i 0.485223 0.840431i −0.514633 0.857411i $$-0.672072\pi$$
0.999856 + 0.0169798i $$0.00540511\pi$$
$$194$$ −2532.00 4385.55i −0.937046 1.62301i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −2354.00 −0.851348 −0.425674 0.904877i $$-0.639963\pi$$
−0.425674 + 0.904877i $$0.639963\pi$$
$$198$$ 0 0
$$199$$ −840.000 + 1454.92i −0.299226 + 0.518275i −0.975959 0.217954i $$-0.930062\pi$$
0.676733 + 0.736229i $$0.263395\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 928.000 0.323237
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −496.000 859.097i −0.168986 0.292692i
$$206$$ −3584.00 + 6207.67i −1.21218 + 2.09956i
$$207$$ 0 0
$$208$$ −1984.00 3436.39i −0.661373 1.14553i
$$209$$ −6200.00 −2.05198
$$210$$ 0 0
$$211$$ −668.000 −0.217948 −0.108974 0.994045i $$-0.534757\pi$$
−0.108974 + 0.994045i $$0.534757\pi$$
$$212$$ 1032.00 + 1787.48i 0.334330 + 0.579077i
$$213$$ 0 0
$$214$$ 3812.00 6602.58i 1.21768 2.10908i
$$215$$ −136.000 235.559i −0.0431401 0.0747209i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 360.000 0.111845
$$219$$ 0 0
$$220$$ 992.000 1718.19i 0.304003 0.526548i
$$221$$ −2604.00 + 4510.26i −0.792597 + 1.37282i
$$222$$ 0 0
$$223$$ −1832.00 −0.550134 −0.275067 0.961425i $$-0.588700\pi$$
−0.275067 + 0.961425i $$0.588700\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −916.000 1586.56i −0.269608 0.466975i
$$227$$ 2472.00 4281.63i 0.722786 1.25190i −0.237093 0.971487i $$-0.576195\pi$$
0.959879 0.280415i $$-0.0904721\pi$$
$$228$$ 0 0
$$229$$ 2735.00 + 4737.16i 0.789231 + 1.36699i 0.926439 + 0.376446i $$0.122854\pi$$
−0.137208 + 0.990542i $$0.543813\pi$$
$$230$$ −672.000 −0.192654
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −1401.00 2426.60i −0.393917 0.682284i 0.599046 0.800715i $$-0.295547\pi$$
−0.992962 + 0.118431i $$0.962213\pi$$
$$234$$ 0 0
$$235$$ 648.000 1122.37i 0.179876 0.311554i
$$236$$ 480.000 + 831.384i 0.132396 + 0.229316i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 1170.00 0.316657 0.158328 0.987386i $$-0.449390\pi$$
0.158328 + 0.987386i $$0.449390\pi$$
$$240$$ 0 0
$$241$$ 1169.00 2024.77i 0.312456 0.541190i −0.666437 0.745561i $$-0.732182\pi$$
0.978893 + 0.204371i $$0.0655150\pi$$
$$242$$ 5026.00 8705.29i 1.33506 2.31238i
$$243$$ 0 0
$$244$$ 4976.00 1.30556
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 3100.00 + 5369.36i 0.798576 + 1.38317i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ −1872.00 3242.40i −0.473583 0.820269i
$$251$$ −2792.00 −0.702109 −0.351055 0.936355i $$-0.614177\pi$$
−0.351055 + 0.936355i $$0.614177\pi$$
$$252$$ 0 0
$$253$$ −2604.00 −0.647083
$$254$$ 1608.00 + 2785.14i 0.397224 + 0.688012i
$$255$$ 0 0
$$256$$ −2048.00 + 3547.24i −0.500000 + 0.866025i
$$257$$ 3512.00 + 6082.96i 0.852422 + 1.47644i 0.879016 + 0.476792i $$0.158201\pi$$
−0.0265936 + 0.999646i $$0.508466\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −1984.00 −0.473240
$$261$$ 0 0
$$262$$ −1624.00 + 2812.85i −0.382943 + 0.663277i
$$263$$ 1219.00 2111.37i 0.285805 0.495029i −0.686999 0.726658i $$-0.741072\pi$$
0.972804 + 0.231629i $$0.0744056\pi$$
$$264$$ 0 0
$$265$$ −1032.00 −0.239227
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −3616.00 6263.10i −0.824188 1.42754i
$$269$$ −3390.00 + 5871.65i −0.768372 + 1.33086i 0.170074 + 0.985431i $$0.445599\pi$$
−0.938446 + 0.345427i $$0.887734\pi$$
$$270$$ 0 0
$$271$$ 964.000 + 1669.70i 0.216084 + 0.374269i 0.953607 0.301053i $$-0.0973381\pi$$
−0.737523 + 0.675322i $$0.764005\pi$$
$$272$$ 5376.00 1.19841
$$273$$ 0 0
$$274$$ 1656.00 0.365119
$$275$$ −3379.00 5852.60i −0.740950 1.28336i
$$276$$ 0 0
$$277$$ −2777.00 + 4809.91i −0.602360 + 1.04332i 0.390103 + 0.920771i $$0.372440\pi$$
−0.992463 + 0.122547i $$0.960894\pi$$
$$278$$ −3240.00 5611.84i −0.699001 1.21071i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1942.00 −0.412278 −0.206139 0.978523i $$-0.566090\pi$$
−0.206139 + 0.978523i $$0.566090\pi$$
$$282$$ 0 0
$$283$$ −2414.00 + 4181.17i −0.507058 + 0.878250i 0.492909 + 0.870081i $$0.335934\pi$$
−0.999967 + 0.00816911i $$0.997400\pi$$
$$284$$ −2712.00 + 4697.32i −0.566646 + 0.981460i
$$285$$ 0 0
$$286$$ −15376.0 −3.17903
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −1071.50 1855.89i −0.218095 0.377751i
$$290$$ 80.0000 138.564i 0.0161992 0.0280578i
$$291$$ 0 0
$$292$$ 2568.00 + 4447.91i 0.514660 + 0.891418i
$$293$$ 6152.00 1.22663 0.613317 0.789837i $$-0.289835\pi$$
0.613317 + 0.789837i $$0.289835\pi$$
$$294$$ 0 0
$$295$$ −480.000 −0.0947345
$$296$$ 0 0
$$297$$ 0 0
$$298$$ −4740.00 + 8209.92i −0.921412 + 1.59593i
$$299$$ 1302.00 + 2255.13i 0.251828 + 0.436179i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 2272.00 0.432910
$$303$$ 0 0
$$304$$ 3200.00 5542.56i 0.603726 1.04568i
$$305$$ −1244.00 + 2154.67i −0.233545 + 0.404512i
$$306$$ 0 0
$$307$$ 5884.00 1.09387 0.546934 0.837176i $$-0.315795\pi$$
0.546934 + 0.837176i $$0.315795\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ −384.000 665.108i −0.0703540 0.121857i
$$311$$ 4566.00 7908.54i 0.832521 1.44197i −0.0635115 0.997981i $$-0.520230\pi$$
0.896033 0.443988i $$-0.146437\pi$$
$$312$$ 0 0
$$313$$ 4691.00 + 8125.05i 0.847128 + 1.46727i 0.883760 + 0.467940i $$0.155004\pi$$
−0.0366327 + 0.999329i $$0.511663\pi$$
$$314$$ 1064.00 0.191226
$$315$$ 0 0
$$316$$ 5920.00 1.05388
$$317$$ 1557.00 + 2696.80i 0.275867 + 0.477816i 0.970353 0.241690i $$-0.0777017\pi$$
−0.694487 + 0.719506i $$0.744368\pi$$
$$318$$ 0 0
$$319$$ 310.000 536.936i 0.0544096 0.0942402i
$$320$$ 1024.00 + 1773.62i 0.178885 + 0.309839i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −8400.00 −1.44702
$$324$$ 0 0
$$325$$ −3379.00 + 5852.60i −0.576718 + 0.998904i
$$326$$ −544.000 + 942.236i −0.0924214 + 0.160079i
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −766.000 1326.75i −0.127200 0.220317i 0.795391 0.606097i $$-0.207266\pi$$
−0.922591 + 0.385780i $$0.873932\pi$$
$$332$$ 1872.00 3242.40i 0.309456 0.535993i
$$333$$ 0 0
$$334$$ 3752.00 + 6498.65i 0.614672 + 1.06464i
$$335$$ 3616.00 0.589741
$$336$$ 0 0
$$337$$ −4166.00 −0.673402 −0.336701 0.941612i $$-0.609311\pi$$
−0.336701 + 0.941612i $$0.609311\pi$$
$$338$$ 3294.00 + 5705.38i 0.530089 + 0.918141i
$$339$$ 0 0
$$340$$ 1344.00 2327.88i 0.214378 0.371314i
$$341$$ −1488.00 2577.29i −0.236304 0.409291i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 304.000 526.543i 0.0472345 0.0818126i
$$347$$ −5683.00 + 9843.24i −0.879191 + 1.52280i −0.0269617 + 0.999636i $$0.508583\pi$$
−0.852230 + 0.523168i $$0.824750\pi$$
$$348$$ 0 0
$$349$$ 9310.00 1.42795 0.713973 0.700174i $$-0.246894\pi$$
0.713973 + 0.700174i $$0.246894\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 7936.00 + 13745.6i 1.20168 + 2.08137i
$$353$$ −4286.00 + 7423.57i −0.646234 + 1.11931i 0.337780 + 0.941225i $$0.390324\pi$$
−0.984015 + 0.178086i $$0.943009\pi$$
$$354$$ 0 0
$$355$$ −1356.00 2348.66i −0.202730 0.351138i
$$356$$ −1600.00 −0.238202
$$357$$ 0 0
$$358$$ 2440.00 0.360218
$$359$$ −2395.00 4148.26i −0.352098 0.609852i 0.634519 0.772908i $$-0.281198\pi$$
−0.986617 + 0.163056i $$0.947865\pi$$
$$360$$ 0 0
$$361$$ −1570.50 + 2720.19i −0.228969 + 0.396586i
$$362$$ 2084.00 + 3609.59i 0.302576 + 0.524077i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −2568.00 −0.368261
$$366$$ 0 0
$$367$$ −2712.00 + 4697.32i −0.385736 + 0.668115i −0.991871 0.127247i $$-0.959386\pi$$
0.606135 + 0.795362i $$0.292719\pi$$
$$368$$ 1344.00 2327.88i 0.190383 0.329753i
$$369$$ 0 0
$$370$$ 3936.00 0.553035
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −919.000 1591.75i −0.127571 0.220960i 0.795164 0.606395i $$-0.207385\pi$$
−0.922735 + 0.385435i $$0.874051\pi$$
$$374$$ 10416.0 18041.0i 1.44010 2.49433i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −620.000 −0.0846993
$$378$$ 0 0
$$379$$ −4260.00 −0.577365 −0.288683 0.957425i $$-0.593217\pi$$
−0.288683 + 0.957425i $$0.593217\pi$$
$$380$$ −1600.00 2771.28i −0.215995 0.374115i
$$381$$ 0 0
$$382$$ 4076.00 7059.84i 0.545933 0.945583i
$$383$$ 4524.00 + 7835.80i 0.603566 + 1.04541i 0.992276 + 0.124046i $$0.0395872\pi$$
−0.388711 + 0.921360i $$0.627080\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 10408.0 1.37242
$$387$$ 0 0
$$388$$ 5064.00 8771.11i 0.662592 1.14764i
$$389$$ −5745.00 + 9950.63i −0.748800 + 1.29696i 0.199599 + 0.979878i $$0.436036\pi$$
−0.948398 + 0.317081i $$0.897297\pi$$
$$390$$ 0 0
$$391$$ −3528.00 −0.456314
$$392$$ 0 0
$$393$$ 0 0
$$394$$ −4708.00 8154.50i −0.601994 1.04268i
$$395$$ −1480.00 + 2563.44i −0.188524 + 0.326533i
$$396$$ 0 0
$$397$$ 933.000 + 1616.00i 0.117949 + 0.204294i 0.918955 0.394363i $$-0.129035\pi$$
−0.801005 + 0.598657i $$0.795701\pi$$
$$398$$ −6720.00 −0.846340
$$399$$ 0 0
$$400$$ 6976.00 0.872000
$$401$$ 6831.00 + 11831.6i 0.850683 + 1.47343i 0.880593 + 0.473873i $$0.157145\pi$$
−0.0299100 + 0.999553i $$0.509522\pi$$
$$402$$ 0 0
$$403$$ −1488.00 + 2577.29i −0.183927 + 0.318571i
$$404$$ 928.000 + 1607.34i 0.114281 + 0.197941i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 15252.0 1.85753
$$408$$ 0 0
$$409$$ 6605.00 11440.2i 0.798524 1.38308i −0.122054 0.992524i $$-0.538948\pi$$
0.920577 0.390560i $$-0.127719\pi$$
$$410$$ 1984.00 3436.39i 0.238982 0.413930i
$$411$$ 0 0
$$412$$ −14336.0 −1.71428
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 936.000 + 1621.20i 0.110714 + 0.191763i
$$416$$ 7936.00 13745.6i 0.935323 1.62003i
$$417$$ 0 0
$$418$$ −12400.0 21477.4i −1.45097 2.51315i
$$419$$ −6960.00 −0.811499 −0.405750 0.913984i $$-0.632990\pi$$
−0.405750 + 0.913984i $$0.632990\pi$$
$$420$$ 0 0
$$421$$ 8162.00 0.944873 0.472437 0.881365i $$-0.343375\pi$$
0.472437 + 0.881365i $$0.343375\pi$$
$$422$$ −1336.00 2314.02i −0.154112 0.266931i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −4578.00 7929.33i −0.522507 0.905009i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 15248.0 1.72206
$$429$$ 0 0
$$430$$ 544.000 942.236i 0.0610093 0.105671i
$$431$$ 8301.00 14377.8i 0.927715 1.60685i 0.140579 0.990069i $$-0.455104\pi$$
0.787136 0.616780i $$-0.211563\pi$$
$$432$$ 0 0
$$433$$ 7738.00 0.858810 0.429405 0.903112i $$-0.358723\pi$$
0.429405 + 0.903112i $$0.358723\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 360.000 + 623.538i 0.0395433 + 0.0684910i
$$437$$ −2100.00 + 3637.31i −0.229878 + 0.398160i
$$438$$ 0 0
$$439$$ 420.000 + 727.461i 0.0456617 + 0.0790885i 0.887953 0.459934i $$-0.152127\pi$$
−0.842291 + 0.539023i $$0.818794\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ −20832.0 −2.24180
$$443$$ 3309.00 + 5731.36i 0.354888 + 0.614684i 0.987099 0.160113i $$-0.0511857\pi$$
−0.632211 + 0.774796i $$0.717852\pi$$
$$444$$ 0 0
$$445$$ 400.000 692.820i 0.0426108 0.0738041i
$$446$$ −3664.00 6346.23i −0.389003 0.673773i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −3090.00 −0.324780 −0.162390 0.986727i $$-0.551920\pi$$
−0.162390 + 0.986727i $$0.551920\pi$$
$$450$$ 0 0
$$451$$ 7688.00 13316.0i 0.802691 1.39030i
$$452$$ 1832.00 3173.12i 0.190642 0.330201i
$$453$$ 0 0
$$454$$ 19776.0 2.04435
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −2957.00 5121.67i −0.302675 0.524249i 0.674066 0.738671i $$-0.264546\pi$$
−0.976741 + 0.214422i $$0.931213\pi$$
$$458$$ −10940.0 + 18948.6i −1.11614 + 1.93321i
$$459$$ 0 0
$$460$$ −672.000 1163.94i −0.0681134 0.117976i
$$461$$ 15968.0 1.61324 0.806620 0.591070i $$-0.201294\pi$$
0.806620 + 0.591070i $$0.201294\pi$$
$$462$$ 0 0
$$463$$ −1172.00 −0.117640 −0.0588202 0.998269i $$-0.518734\pi$$
−0.0588202 + 0.998269i $$0.518734\pi$$
$$464$$ 320.000 + 554.256i 0.0320164 + 0.0554541i
$$465$$ 0 0
$$466$$ 5604.00 9706.41i 0.557082 0.964895i
$$467$$ 2652.00 + 4593.40i 0.262784 + 0.455154i 0.966981 0.254850i $$-0.0820261\pi$$
−0.704197 + 0.710005i $$0.748693\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 5184.00 0.508766
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 2108.00 3651.16i 0.204917 0.354927i
$$474$$ 0 0
$$475$$ −10900.0 −1.05290
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 2340.00 + 4053.00i 0.223910 + 0.387824i
$$479$$ 2870.00 4970.99i 0.273765 0.474176i −0.696057 0.717986i $$-0.745064\pi$$
0.969823 + 0.243810i $$0.0783975\pi$$
$$480$$ 0 0
$$481$$ −7626.00 13208.6i −0.722902 1.25210i
$$482$$ 9352.00 0.883759
$$483$$ 0 0
$$484$$ 20104.0 1.88805
$$485$$ 2532.00 + 4385.55i 0.237056 + 0.410593i
$$486$$ 0 0
$$487$$ −4472.00 + 7745.73i −0.416110 + 0.720724i −0.995544 0.0942951i $$-0.969940\pi$$
0.579434 + 0.815019i $$0.303274\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 5558.00 0.510853 0.255427 0.966828i $$-0.417784\pi$$
0.255427 + 0.966828i $$0.417784\pi$$
$$492$$ 0 0
$$493$$ 420.000 727.461i 0.0383689 0.0664568i
$$494$$ −12400.0 + 21477.4i −1.12936 + 1.95610i
$$495$$ 0 0
$$496$$ 3072.00 0.278099
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 9910.00 + 17164.6i 0.889043 + 1.53987i 0.841008 + 0.541022i $$0.181963\pi$$
0.0480349 + 0.998846i $$0.484704\pi$$
$$500$$ 3744.00 6484.80i 0.334874 0.580018i
$$501$$ 0 0
$$502$$ −5584.00 9671.77i −0.496466 0.859905i
$$503$$ −1848.00 −0.163814 −0.0819068 0.996640i $$-0.526101\pi$$
−0.0819068 + 0.996640i $$0.526101\pi$$
$$504$$ 0 0
$$505$$ −928.000 −0.0817732
$$506$$ −5208.00 9020.52i −0.457557 0.792512i
$$507$$ 0 0
$$508$$ −3216.00 + 5570.28i −0.280880 + 0.486498i
$$509$$ 170.000 + 294.449i 0.0148038 + 0.0256409i 0.873332 0.487125i $$-0.161954\pi$$
−0.858529 + 0.512766i $$0.828621\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −16384.0 −1.41421
$$513$$ 0 0
$$514$$ −14048.0 + 24331.8i −1.20551 + 2.08800i
$$515$$ 3584.00 6207.67i 0.306660 0.531151i
$$516$$ 0 0
$$517$$ 20088.0 1.70884
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 5106.00 8843.85i 0.429363 0.743678i −0.567454 0.823405i $$-0.692072\pi$$
0.996817 + 0.0797272i $$0.0254049\pi$$
$$522$$ 0 0
$$523$$ 4666.00 + 8081.75i 0.390115 + 0.675698i 0.992464 0.122534i $$-0.0391021\pi$$
−0.602350 + 0.798232i $$0.705769\pi$$
$$524$$ −6496.00 −0.541563
$$525$$ 0 0
$$526$$ 9752.00 0.808379
$$527$$ −2016.00 3491.81i −0.166638 0.288626i
$$528$$ 0 0
$$529$$ 5201.50 9009.26i 0.427509 0.740467i
$$530$$ −2064.00 3574.95i −0.169159 0.292993i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −15376.0 −1.24955
$$534$$ 0 0
$$535$$ −3812.00 + 6602.58i −0.308051 + 0.533559i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −27120.0 −2.17328
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 4499.00 + 7792.50i 0.357536 + 0.619271i 0.987549 0.157314i $$-0.0502835\pi$$
−0.630012 + 0.776585i $$0.716950\pi$$
$$542$$ −3856.00 + 6678.79i −0.305589 + 0.529296i
$$543$$ 0 0
$$544$$ 10752.0 + 18623.0i 0.847405 + 1.46775i
$$545$$ −360.000 −0.0282949
$$546$$ 0 0
$$547$$ −3416.00 −0.267016 −0.133508 0.991048i $$-0.542624\pi$$
−0.133508 + 0.991048i $$0.542624\pi$$
$$548$$ 1656.00 + 2868.28i 0.129089 + 0.223589i
$$549$$ 0 0
$$550$$ 13516.0 23410.4i 1.04786 1.81495i
$$551$$ −500.000 866.025i −0.0386583 0.0669581i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −22216.0 −1.70373
$$555$$ 0 0
$$556$$ 6480.00 11223.7i 0.494268 0.856098i
$$557$$ −263.000 + 455.529i −0.0200066 + 0.0346524i −0.875855 0.482574i $$-0.839702\pi$$
0.855849 + 0.517226i $$0.173035\pi$$
$$558$$ 0 0
$$559$$ −4216.00 −0.318994
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −3884.00 6727.29i −0.291524 0.504935i
$$563$$ −3356.00 + 5812.76i −0.251223 + 0.435131i −0.963863 0.266399i $$-0.914166\pi$$
0.712640 + 0.701530i $$0.247499\pi$$
$$564$$ 0 0
$$565$$ 916.000 + 1586.56i 0.0682060 + 0.118136i
$$566$$ −19312.0 −1.43418
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 2095.00 + 3628.65i 0.154353 + 0.267348i 0.932823 0.360334i $$-0.117337\pi$$
−0.778470 + 0.627682i $$0.784004\pi$$
$$570$$ 0 0
$$571$$ −1516.00 + 2625.79i −0.111108 + 0.192445i −0.916217 0.400682i $$-0.868773\pi$$
0.805109 + 0.593126i $$0.202107\pi$$
$$572$$ −15376.0 26632.0i −1.12396 1.94675i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −4578.00 −0.332027
$$576$$ 0 0
$$577$$ −2717.00 + 4705.98i −0.196032 + 0.339537i −0.947238 0.320531i $$-0.896139\pi$$
0.751207 + 0.660067i $$0.229472\pi$$
$$578$$ 4286.00 7423.57i 0.308433 0.534221i
$$579$$ 0 0
$$580$$ 320.000 0.0229091
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −7998.00 13852.9i −0.568170 0.984100i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 12304.0 + 21311.2i 0.867361 + 1.50231i
$$587$$ −464.000 −0.0326258 −0.0163129 0.999867i $$-0.505193\pi$$
−0.0163129 + 0.999867i $$0.505193\pi$$
$$588$$ 0 0
$$589$$ −4800.00 −0.335790
$$590$$ −960.000 1662.77i −0.0669874 0.116026i
$$591$$ 0 0
$$592$$ −7872.00 + 13634.7i −0.546516 + 0.946593i
$$593$$ 5874.00 + 10174.1i 0.406773 + 0.704551i 0.994526 0.104489i $$-0.0333207\pi$$
−0.587753 + 0.809040i $$0.699987\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −18960.0 −1.30307
$$597$$ 0 0
$$598$$ −5208.00 + 9020.52i −0.356139 + 0.616850i
$$599$$ 3825.00 6625.09i 0.260910 0.451910i −0.705574 0.708636i $$-0.749311\pi$$
0.966484 + 0.256727i $$0.0826440\pi$$
$$600$$ 0 0
$$601$$ −22878.0 −1.55277 −0.776384 0.630261i $$-0.782948\pi$$
−0.776384 + 0.630261i $$0.782948\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 2272.00 + 3935.22i 0.153057 + 0.265102i
$$605$$ −5026.00 + 8705.29i −0.337745 + 0.584992i
$$606$$ 0 0
$$607$$ −352.000 609.682i −0.0235375 0.0407681i 0.854017 0.520246i $$-0.174160\pi$$
−0.877554 + 0.479477i $$0.840826\pi$$
$$608$$ 25600.0 1.70759
$$609$$ 0 0
$$610$$ −9952.00 −0.660565
$$611$$ −10044.0 17396.7i −0.665036 1.15188i
$$612$$ 0 0
$$613$$ −12479.0 + 21614.3i −0.822222 + 1.42413i 0.0818021 + 0.996649i $$0.473932\pi$$
−0.904024 + 0.427482i $$0.859401\pi$$
$$614$$ 11768.0 + 20382.8i 0.773482 + 1.33971i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 8826.00 0.575886 0.287943 0.957648i $$-0.407029\pi$$
0.287943 + 0.957648i $$0.407029\pi$$
$$618$$ 0 0
$$619$$ −10610.0 + 18377.1i −0.688937 + 1.19327i 0.283245 + 0.959047i $$0.408589\pi$$
−0.972182 + 0.234226i $$0.924744\pi$$
$$620$$ 768.000 1330.22i 0.0497478 0.0861657i
$$621$$ 0 0
$$622$$ 36528.0 2.35473
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −4940.50 8557.20i −0.316192 0.547661i
$$626$$ −18764.0 + 32500.2i −1.19802 + 2.07503i
$$627$$ 0 0
$$628$$ 1064.00 + 1842.90i 0.0676086 + 0.117102i
$$629$$ 20664.0 1.30990
$$630$$ 0 0
$$631$$ −3268.00 −0.206176 −0.103088 0.994672i $$-0.532872\pi$$
−0.103088 + 0.994672i $$0.532872\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ −6228.00 + 10787.2i −0.390135 + 0.675733i
$$635$$ −1608.00 2785.14i −0.100491 0.174055i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 2480.00 0.153894
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 6531.00 11312.0i 0.402432 0.697033i −0.591587 0.806241i $$-0.701498\pi$$
0.994019 + 0.109208i $$0.0348316\pi$$
$$642$$ 0 0
$$643$$ −28012.0 −1.71802 −0.859009 0.511961i $$-0.828919\pi$$
−0.859009 + 0.511961i $$0.828919\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −16800.0 29098.5i −1.02320 1.77223i
$$647$$ 1922.00 3329.00i 0.116788 0.202282i −0.801705 0.597720i $$-0.796074\pi$$
0.918493 + 0.395437i $$0.129407\pi$$
$$648$$ 0 0
$$649$$ −3720.00 6443.23i −0.224997 0.389705i
$$650$$ −27032.0 −1.63120
$$651$$ 0 0
$$652$$ −2176.00 −0.130704
$$653$$ −14241.0 24666.1i −0.853436 1.47819i −0.878089 0.478498i $$-0.841182\pi$$
0.0246533 0.999696i $$-0.492152\pi$$
$$654$$ 0 0
$$655$$ 1624.00 2812.85i 0.0968778 0.167797i
$$656$$ 7936.00 + 13745.6i 0.472330 + 0.818100i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 9330.00 0.551510 0.275755 0.961228i $$-0.411072\pi$$
0.275755 + 0.961228i $$0.411072\pi$$
$$660$$ 0 0
$$661$$ −4391.00 + 7605.44i −0.258381 + 0.447530i −0.965808 0.259257i $$-0.916522\pi$$
0.707427 + 0.706786i $$0.249856\pi$$
$$662$$ 3064.00 5307.00i 0.179888 0.311575i
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −210.000 363.731i −0.0121908 0.0211150i
$$668$$ −7504.00 + 12997.3i −0.434638 + 0.752816i
$$669$$ 0 0
$$670$$ 7232.00 + 12526.2i 0.417010 + 0.722282i
$$671$$ −38564.0 −2.21870
$$672$$ 0 0
$$673$$ −10562.0 −0.604956 −0.302478 0.953156i $$-0.597814\pi$$
−0.302478 + 0.953156i $$0.597814\pi$$
$$674$$ −8332.00 14431.4i −0.476167 0.824746i
$$675$$ 0 0
$$676$$ −6588.00 + 11410.8i −0.374829 + 0.649223i
$$677$$ −13008.0 22530.5i −0.738461 1.27905i −0.953188 0.302378i $$-0.902220\pi$$
0.214727 0.976674i $$-0.431114\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 5952.00 10309.2i 0.334185 0.578825i
$$683$$ 4449.00 7705.89i 0.249248 0.431710i −0.714070 0.700075i $$-0.753150\pi$$
0.963317 + 0.268365i $$0.0864833\pi$$
$$684$$ 0 0
$$685$$ −1656.00 −0.0923686
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 2176.00 + 3768.94i 0.120580 + 0.208851i
$$689$$ −7998.00 + 13852.9i −0.442234 + 0.765973i
$$690$$ 0 0
$$691$$ −15286.0 26476.1i −0.841544 1.45760i −0.888589 0.458704i $$-0.848314\pi$$
0.0470452 0.998893i $$-0.485020\pi$$
$$692$$ 1216.00 0.0667997
$$693$$ 0 0
$$694$$ −45464.0 −2.48673
$$695$$ 3240.00 + 5611.84i 0.176835 + 0.306287i
$$696$$ 0 0
$$697$$ 10416.0 18041.0i 0.566046 0.980421i
$$698$$ 18620.0 + 32250.8i 1.00971 + 1.74887i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 30618.0 1.64968 0.824840 0.565366i $$-0.191265\pi$$
0.824840 + 0.565366i $$0.191265\pi$$
$$702$$ 0 0
$$703$$ 12300.0 21304.2i 0.659891 1.14296i
$$704$$ −15872.0 + 27491.1i −0.849714 + 1.47175i
$$705$$ 0 0
$$706$$ −34288.0 −1.82783
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 4065.00 + 7040.79i 0.215323 + 0.372951i 0.953373 0.301796i $$-0.0975861\pi$$
−0.738049 + 0.674747i $$0.764253\pi$$
$$710$$ 5424.00 9394.64i 0.286703 0.496584i
$$711$$ 0 0
$$712$$ 0 0
$$713$$ −2016.00 −0.105890
$$714$$ 0 0
$$715$$ 15376.0 0.804237
$$716$$ 2440.00 + 4226.20i 0.127356 + 0.220588i
$$717$$ 0 0
$$718$$ 9580.00 16593.0i 0.497942 0.862461i
$$719$$ −13920.0 24110.1i −0.722014 1.25057i −0.960191 0.279344i $$-0.909883\pi$$
0.238177 0.971222i $$-0.423450\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −12564.0 −0.647623
$$723$$ 0 0
$$724$$ −4168.00 + 7219.19i −0.213954 + 0.370579i
$$725$$ 545.000 943.968i 0.0279183 0.0483560i
$$726$$ 0 0
$$727$$ 14624.0 0.746044 0.373022 0.927822i $$-0.378322\pi$$
0.373022 + 0.927822i $$0.378322\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ −5136.00 8895.81i −0.260400 0.451026i
$$731$$ 2856.00 4946.74i 0.144505 0.250290i
$$732$$ 0 0
$$733$$ 10431.0 + 18067.0i 0.525618 + 0.910397i 0.999555 + 0.0298378i $$0.00949909\pi$$
−0.473937 + 0.880559i $$0.657168\pi$$
$$734$$ −21696.0 −1.09103
$$735$$ 0 0
$$736$$ 10752.0 0.538484
$$737$$ 28024.0 + 48539.0i 1.40065 + 2.42599i
$$738$$ 0 0
$$739$$ 6960.00 12055.1i 0.346452 0.600072i −0.639165 0.769070i $$-0.720720\pi$$
0.985616 + 0.168998i $$0.0540532\pi$$
$$740$$ 3936.00 + 6817.35i 0.195527 + 0.338663i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −25578.0 −1.26294 −0.631471 0.775400i $$-0.717548\pi$$
−0.631471 + 0.775400i $$0.717548\pi$$
$$744$$ 0 0
$$745$$ 4740.00 8209.92i 0.233101 0.403743i
$$746$$ 3676.00 6367.02i 0.180413 0.312484i
$$747$$ 0 0
$$748$$ 41664.0 2.03661
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −16736.0 28987.6i −0.813189 1.40849i −0.910621 0.413243i $$-0.864396\pi$$
0.0974312 0.995242i $$-0.468937\pi$$
$$752$$ −10368.0 + 17957.9i −0.502769 + 0.870821i
$$753$$ 0 0
$$754$$ −1240.00 2147.74i −0.0598914 0.103735i
$$755$$ −2272.00 −0.109519
$$756$$ 0 0
$$757$$ 25934.0 1.24516 0.622581 0.782556i $$-0.286084\pi$$
0.622581 + 0.782556i $$0.286084\pi$$
$$758$$ −8520.00 14757.1i −0.408259 0.707125i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 13476.0 + 23341.1i 0.641925 + 1.11185i 0.985003 + 0.172539i $$0.0551971\pi$$
−0.343078 + 0.939307i $$0.611470\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 16304.0 0.772065
$$765$$ 0 0
$$766$$ −18096.0 + 31343.2i −0.853571 + 1.47843i
$$767$$ −3720.00 + 6443.23i −0.175126 + 0.303327i
$$768$$ 0 0
$$769$$ 23450.0 1.09965 0.549824 0.835281i $$-0.314695\pi$$
0.549824 + 0.835281i $$0.314695\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 10408.0 + 18027.2i 0.485223 + 0.840431i
$$773$$ 19784.0 34266.9i 0.920545 1.59443i 0.121970 0.992534i $$-0.461079\pi$$
0.798574 0.601896i $$-0.205588\pi$$
$$774$$ 0 0
$$775$$ −2616.00 4531.04i −0.121251 0.210013i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −45960.0 −2.11793
$$779$$ −12400.0 21477.4i −0.570316 0.987816i
$$780$$ 0 0
$$781$$ 21018.0 36404.2i 0.962975 1.66792i
$$782$$ −7056.00 12221.4i −0.322662 0.558868i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −1064.00 −0.0483768
$$786$$ 0 0
$$787$$ 6178.00 10700.6i 0.279825 0.484670i −0.691516 0.722361i $$-0.743057\pi$$
0.971341 + 0.237690i $$0.0763904\pi$$
$$788$$ 9416.00 16309.0i 0.425674 0.737289i
$$789$$ 0 0
$$790$$ −11840.0 −0.533226
$$791$$