Properties

 Label 560.2.bw.d.529.1 Level $560$ Weight $2$ Character 560.529 Analytic conductor $4.472$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$560 = 2^{4} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 560.bw (of order $$6$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$4.47162251319$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 70) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

 Embedding label 529.1 Root $$-0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 560.529 Dual form 560.2.bw.d.289.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.133975 + 2.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$$ $$q+(0.133975 + 2.23205i) q^{5} +(1.73205 + 2.00000i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(1.50000 - 2.59808i) q^{11} +5.00000i q^{13} +(1.73205 + 1.00000i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-6.06218 + 3.50000i) q^{23} +(-4.96410 + 0.598076i) q^{25} +4.00000 q^{29} +(-1.00000 + 1.73205i) q^{31} +(-4.23205 + 4.13397i) q^{35} +(0.866025 - 0.500000i) q^{37} +3.00000 q^{41} +2.00000i q^{43} +(5.59808 - 3.69615i) q^{45} +(6.06218 - 3.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(7.79423 + 4.50000i) q^{53} +(6.00000 + 3.00000i) q^{55} +(2.00000 - 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(2.59808 - 7.50000i) q^{63} +(-11.1603 + 0.669873i) q^{65} +(1.73205 + 1.00000i) q^{67} +6.00000 q^{71} +(-13.8564 - 8.00000i) q^{73} +(7.79423 - 1.50000i) q^{77} +(-7.00000 - 12.1244i) q^{79} +(-4.50000 + 7.79423i) q^{81} -6.00000i q^{83} +(-2.00000 + 4.00000i) q^{85} +(1.00000 + 1.73205i) q^{89} +(-10.0000 + 8.66025i) q^{91} +(-9.33013 + 6.16025i) q^{95} -12.0000i q^{97} -9.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 4 q^{5} - 6 q^{9}+O(q^{10})$$ 4 * q + 4 * q^5 - 6 * q^9 $$4 q + 4 q^{5} - 6 q^{9} + 6 q^{11} + 10 q^{19} - 6 q^{25} + 16 q^{29} - 4 q^{31} - 10 q^{35} + 12 q^{41} + 12 q^{45} - 4 q^{49} + 24 q^{55} + 8 q^{59} - 12 q^{61} - 10 q^{65} + 24 q^{71} - 28 q^{79} - 18 q^{81} - 8 q^{85} + 4 q^{89} - 40 q^{91} - 20 q^{95} - 36 q^{99}+O(q^{100})$$ 4 * q + 4 * q^5 - 6 * q^9 + 6 * q^11 + 10 * q^19 - 6 * q^25 + 16 * q^29 - 4 * q^31 - 10 * q^35 + 12 * q^41 + 12 * q^45 - 4 * q^49 + 24 * q^55 + 8 * q^59 - 12 * q^61 - 10 * q^65 + 24 * q^71 - 28 * q^79 - 18 * q^81 - 8 * q^85 + 4 * q^89 - 40 * q^91 - 20 * q^95 - 36 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$$.

 $$n$$ $$241$$ $$337$$ $$351$$ $$421$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$1$$ $$1$$

Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$4$$ 0 0
$$5$$ 0.133975 + 2.23205i 0.0599153 + 0.998203i
$$6$$ 0 0
$$7$$ 1.73205 + 2.00000i 0.654654 + 0.755929i
$$8$$ 0 0
$$9$$ −1.50000 2.59808i −0.500000 0.866025i
$$10$$ 0 0
$$11$$ 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i $$-0.683949\pi$$
0.998526 + 0.0542666i $$0.0172821\pi$$
$$12$$ 0 0
$$13$$ 5.00000i 1.38675i 0.720577 + 0.693375i $$0.243877\pi$$
−0.720577 + 0.693375i $$0.756123\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 1.73205 + 1.00000i 0.420084 + 0.242536i 0.695113 0.718900i $$-0.255354\pi$$
−0.275029 + 0.961436i $$0.588688\pi$$
$$18$$ 0 0
$$19$$ 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i $$0.0277634\pi$$
−0.422659 + 0.906289i $$0.638903\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −6.06218 + 3.50000i −1.26405 + 0.729800i −0.973856 0.227167i $$-0.927054\pi$$
−0.290196 + 0.956967i $$0.593720\pi$$
$$24$$ 0 0
$$25$$ −4.96410 + 0.598076i −0.992820 + 0.119615i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 4.00000 0.742781 0.371391 0.928477i $$-0.378881\pi$$
0.371391 + 0.928477i $$0.378881\pi$$
$$30$$ 0 0
$$31$$ −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i $$-0.890815\pi$$
0.762140 + 0.647412i $$0.224149\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −4.23205 + 4.13397i −0.715347 + 0.698769i
$$36$$ 0 0
$$37$$ 0.866025 0.500000i 0.142374 0.0821995i −0.427121 0.904194i $$-0.640472\pi$$
0.569495 + 0.821995i $$0.307139\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 3.00000 0.468521 0.234261 0.972174i $$-0.424733\pi$$
0.234261 + 0.972174i $$0.424733\pi$$
$$42$$ 0 0
$$43$$ 2.00000i 0.304997i 0.988304 + 0.152499i $$0.0487319\pi$$
−0.988304 + 0.152499i $$0.951268\pi$$
$$44$$ 0 0
$$45$$ 5.59808 3.69615i 0.834512 0.550990i
$$46$$ 0 0
$$47$$ 6.06218 3.50000i 0.884260 0.510527i 0.0121990 0.999926i $$-0.496117\pi$$
0.872060 + 0.489398i $$0.162783\pi$$
$$48$$ 0 0
$$49$$ −1.00000 + 6.92820i −0.142857 + 0.989743i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 7.79423 + 4.50000i 1.07062 + 0.618123i 0.928351 0.371706i $$-0.121227\pi$$
0.142269 + 0.989828i $$0.454560\pi$$
$$54$$ 0 0
$$55$$ 6.00000 + 3.00000i 0.809040 + 0.404520i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i $$-0.749486\pi$$
0.966342 + 0.257260i $$0.0828195\pi$$
$$60$$ 0 0
$$61$$ −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i $$-0.292159\pi$$
−0.991645 + 0.128994i $$0.958825\pi$$
$$62$$ 0 0
$$63$$ 2.59808 7.50000i 0.327327 0.944911i
$$64$$ 0 0
$$65$$ −11.1603 + 0.669873i −1.38426 + 0.0830875i
$$66$$ 0 0
$$67$$ 1.73205 + 1.00000i 0.211604 + 0.122169i 0.602056 0.798454i $$-0.294348\pi$$
−0.390453 + 0.920623i $$0.627682\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 0 0
$$73$$ −13.8564 8.00000i −1.62177 0.936329i −0.986447 0.164083i $$-0.947534\pi$$
−0.635323 0.772246i $$-0.719133\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 7.79423 1.50000i 0.888235 0.170941i
$$78$$ 0 0
$$79$$ −7.00000 12.1244i −0.787562 1.36410i −0.927457 0.373930i $$-0.878010\pi$$
0.139895 0.990166i $$-0.455323\pi$$
$$80$$ 0 0
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 6.00000i 0.658586i −0.944228 0.329293i $$-0.893190\pi$$
0.944228 0.329293i $$-0.106810\pi$$
$$84$$ 0 0
$$85$$ −2.00000 + 4.00000i −0.216930 + 0.433861i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 1.00000 + 1.73205i 0.106000 + 0.183597i 0.914146 0.405385i $$-0.132862\pi$$
−0.808146 + 0.588982i $$0.799529\pi$$
$$90$$ 0 0
$$91$$ −10.0000 + 8.66025i −1.04828 + 0.907841i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −9.33013 + 6.16025i −0.957251 + 0.632029i
$$96$$ 0 0
$$97$$ 12.0000i 1.21842i −0.793011 0.609208i $$-0.791488\pi$$
0.793011 0.609208i $$-0.208512\pi$$
$$98$$ 0 0
$$99$$ −9.00000 −0.904534
$$100$$ 0 0
$$101$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$102$$ 0 0
$$103$$ −6.92820 + 4.00000i −0.682656 + 0.394132i −0.800855 0.598858i $$-0.795621\pi$$
0.118199 + 0.992990i $$0.462288\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 13.8564 8.00000i 1.33955 0.773389i 0.352809 0.935695i $$-0.385227\pi$$
0.986740 + 0.162306i $$0.0518932\pi$$
$$108$$ 0 0
$$109$$ 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i $$-0.802798\pi$$
0.909935 + 0.414751i $$0.136131\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 14.0000i 1.31701i −0.752577 0.658505i $$-0.771189\pi$$
0.752577 0.658505i $$-0.228811\pi$$
$$114$$ 0 0
$$115$$ −8.62436 13.0622i −0.804225 1.21805i
$$116$$ 0 0
$$117$$ 12.9904 7.50000i 1.20096 0.693375i
$$118$$ 0 0
$$119$$ 1.00000 + 5.19615i 0.0916698 + 0.476331i
$$120$$ 0 0
$$121$$ 1.00000 + 1.73205i 0.0909091 + 0.157459i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −2.00000 11.0000i −0.178885 0.983870i
$$126$$ 0 0
$$127$$ 7.00000i 0.621150i −0.950549 0.310575i $$-0.899478\pi$$
0.950549 0.310575i $$-0.100522\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −0.500000 0.866025i −0.0436852 0.0756650i 0.843356 0.537355i $$-0.180577\pi$$
−0.887041 + 0.461690i $$0.847243\pi$$
$$132$$ 0 0
$$133$$ −4.33013 + 12.5000i −0.375470 + 1.08389i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 6.92820 + 4.00000i 0.591916 + 0.341743i 0.765855 0.643013i $$-0.222316\pi$$
−0.173939 + 0.984757i $$0.555649\pi$$
$$138$$ 0 0
$$139$$ 16.0000 1.35710 0.678551 0.734553i $$-0.262608\pi$$
0.678551 + 0.734553i $$0.262608\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 12.9904 + 7.50000i 1.08631 + 0.627182i
$$144$$ 0 0
$$145$$ 0.535898 + 8.92820i 0.0445039 + 0.741447i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i $$-0.902763\pi$$
0.216394 0.976306i $$-0.430570\pi$$
$$150$$ 0 0
$$151$$ −3.00000 + 5.19615i −0.244137 + 0.422857i −0.961888 0.273442i $$-0.911838\pi$$
0.717752 + 0.696299i $$0.245171\pi$$
$$152$$ 0 0
$$153$$ 6.00000i 0.485071i
$$154$$ 0 0
$$155$$ −4.00000 2.00000i −0.321288 0.160644i
$$156$$ 0 0
$$157$$ 7.79423 + 4.50000i 0.622047 + 0.359139i 0.777666 0.628678i $$-0.216404\pi$$
−0.155618 + 0.987817i $$0.549737\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −17.5000 6.06218i −1.37919 0.477767i
$$162$$ 0 0
$$163$$ −10.3923 + 6.00000i −0.813988 + 0.469956i −0.848339 0.529454i $$-0.822397\pi$$
0.0343508 + 0.999410i $$0.489064\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 15.0000i 1.16073i −0.814355 0.580367i $$-0.802909\pi$$
0.814355 0.580367i $$-0.197091\pi$$
$$168$$ 0 0
$$169$$ −12.0000 −0.923077
$$170$$ 0 0
$$171$$ 7.50000 12.9904i 0.573539 0.993399i
$$172$$ 0 0
$$173$$ −7.79423 + 4.50000i −0.592584 + 0.342129i −0.766119 0.642699i $$-0.777815\pi$$
0.173534 + 0.984828i $$0.444481\pi$$
$$174$$ 0 0
$$175$$ −9.79423 8.89230i −0.740374 0.672195i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −6.50000 + 11.2583i −0.485833 + 0.841487i −0.999867 0.0162823i $$-0.994817\pi$$
0.514035 + 0.857769i $$0.328150\pi$$
$$180$$ 0 0
$$181$$ 26.0000 1.93256 0.966282 0.257485i $$-0.0828937\pi$$
0.966282 + 0.257485i $$0.0828937\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1.23205 + 1.86603i 0.0905822 + 0.137193i
$$186$$ 0 0
$$187$$ 5.19615 3.00000i 0.379980 0.219382i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −10.0000 17.3205i −0.723575 1.25327i −0.959558 0.281511i $$-0.909164\pi$$
0.235983 0.971757i $$-0.424169\pi$$
$$192$$ 0 0
$$193$$ −8.66025 5.00000i −0.623379 0.359908i 0.154805 0.987945i $$-0.450525\pi$$
−0.778183 + 0.628037i $$0.783859\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 5.00000i 0.356235i −0.984009 0.178118i $$-0.942999\pi$$
0.984009 0.178118i $$-0.0570008\pi$$
$$198$$ 0 0
$$199$$ −9.00000 + 15.5885i −0.637993 + 1.10504i 0.347879 + 0.937539i $$0.386902\pi$$
−0.985873 + 0.167497i $$0.946431\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 6.92820 + 8.00000i 0.486265 + 0.561490i
$$204$$ 0 0
$$205$$ 0.401924 + 6.69615i 0.0280716 + 0.467680i
$$206$$ 0 0
$$207$$ 18.1865 + 10.5000i 1.26405 + 0.729800i
$$208$$ 0 0
$$209$$ 15.0000 1.03757
$$210$$ 0 0
$$211$$ 9.00000 0.619586 0.309793 0.950804i $$-0.399740\pi$$
0.309793 + 0.950804i $$0.399740\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −4.46410 + 0.267949i −0.304449 + 0.0182740i
$$216$$ 0 0
$$217$$ −5.19615 + 1.00000i −0.352738 + 0.0678844i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −5.00000 + 8.66025i −0.336336 + 0.582552i
$$222$$ 0 0
$$223$$ 8.00000i 0.535720i −0.963458 0.267860i $$-0.913684\pi$$
0.963458 0.267860i $$-0.0863164\pi$$
$$224$$ 0 0
$$225$$ 9.00000 + 12.0000i 0.600000 + 0.800000i
$$226$$ 0 0
$$227$$ −5.19615 3.00000i −0.344881 0.199117i 0.317547 0.948242i $$-0.397141\pi$$
−0.662428 + 0.749125i $$0.730474\pi$$
$$228$$ 0 0
$$229$$ 8.00000 + 13.8564i 0.528655 + 0.915657i 0.999442 + 0.0334101i $$0.0106368\pi$$
−0.470787 + 0.882247i $$0.656030\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 6.92820 4.00000i 0.453882 0.262049i −0.255586 0.966786i $$-0.582269\pi$$
0.709468 + 0.704737i $$0.248935\pi$$
$$234$$ 0 0
$$235$$ 8.62436 + 13.0622i 0.562591 + 0.852083i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 20.0000 1.29369 0.646846 0.762620i $$-0.276088\pi$$
0.646846 + 0.762620i $$0.276088\pi$$
$$240$$ 0 0
$$241$$ 4.50000 7.79423i 0.289870 0.502070i −0.683908 0.729568i $$-0.739721\pi$$
0.973779 + 0.227498i $$0.0730544\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −15.5981 1.30385i −0.996525 0.0832998i
$$246$$ 0 0
$$247$$ −21.6506 + 12.5000i −1.37760 + 0.795356i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −5.00000 −0.315597 −0.157799 0.987471i $$-0.550440\pi$$
−0.157799 + 0.987471i $$0.550440\pi$$
$$252$$ 0 0
$$253$$ 21.0000i 1.32026i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −5.19615 + 3.00000i −0.324127 + 0.187135i −0.653231 0.757159i $$-0.726587\pi$$
0.329104 + 0.944294i $$0.393253\pi$$
$$258$$ 0 0
$$259$$ 2.50000 + 0.866025i 0.155342 + 0.0538122i
$$260$$ 0 0
$$261$$ −6.00000 10.3923i −0.371391 0.643268i
$$262$$ 0 0
$$263$$ 0 0 0.500000 0.866025i $$-0.333333\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$264$$ 0 0
$$265$$ −9.00000 + 18.0000i −0.552866 + 1.10573i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −5.00000 + 8.66025i −0.304855 + 0.528025i −0.977229 0.212187i $$-0.931941\pi$$
0.672374 + 0.740212i $$0.265275\pi$$
$$270$$ 0 0
$$271$$ 12.0000 + 20.7846i 0.728948 + 1.26258i 0.957328 + 0.289003i $$0.0933238\pi$$
−0.228380 + 0.973572i $$0.573343\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −5.89230 + 13.7942i −0.355319 + 0.831823i
$$276$$ 0 0
$$277$$ 1.73205 + 1.00000i 0.104069 + 0.0600842i 0.551131 0.834419i $$-0.314196\pi$$
−0.447062 + 0.894503i $$0.647530\pi$$
$$278$$ 0 0
$$279$$ 6.00000 0.359211
$$280$$ 0 0
$$281$$ 9.00000 0.536895 0.268447 0.963294i $$-0.413489\pi$$
0.268447 + 0.963294i $$0.413489\pi$$
$$282$$ 0 0
$$283$$ −12.1244 7.00000i −0.720718 0.416107i 0.0942988 0.995544i $$-0.469939\pi$$
−0.815017 + 0.579437i $$0.803272\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 5.19615 + 6.00000i 0.306719 + 0.354169i
$$288$$ 0 0
$$289$$ −6.50000 11.2583i −0.382353 0.662255i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 9.00000i 0.525786i 0.964825 + 0.262893i $$0.0846766\pi$$
−0.964825 + 0.262893i $$0.915323\pi$$
$$294$$ 0 0
$$295$$ 8.00000 + 4.00000i 0.465778 + 0.232889i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −17.5000 30.3109i −1.01205 1.75292i
$$300$$ 0 0
$$301$$ −4.00000 + 3.46410i −0.230556 + 0.199667i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 11.1962 7.39230i 0.641090 0.423282i
$$306$$ 0 0
$$307$$ 22.0000i 1.25561i 0.778372 + 0.627803i $$0.216046\pi$$
−0.778372 + 0.627803i $$0.783954\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 3.00000 5.19615i 0.170114 0.294647i −0.768345 0.640036i $$-0.778920\pi$$
0.938460 + 0.345389i $$0.112253\pi$$
$$312$$ 0 0
$$313$$ 19.0526 11.0000i 1.07691 0.621757i 0.146852 0.989158i $$-0.453086\pi$$
0.930062 + 0.367402i $$0.119753\pi$$
$$314$$ 0 0
$$315$$ 17.0885 + 4.79423i 0.962825 + 0.270124i
$$316$$ 0 0
$$317$$ −1.73205 + 1.00000i −0.0972817 + 0.0561656i −0.547852 0.836576i $$-0.684554\pi$$
0.450570 + 0.892741i $$0.351221\pi$$
$$318$$ 0 0
$$319$$ 6.00000 10.3923i 0.335936 0.581857i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 10.0000i 0.556415i
$$324$$ 0 0
$$325$$ −2.99038 24.8205i −0.165876 1.37679i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 17.5000 + 6.06218i 0.964806 + 0.334219i
$$330$$ 0 0
$$331$$ 2.50000 + 4.33013i 0.137412 + 0.238005i 0.926516 0.376254i $$-0.122788\pi$$
−0.789104 + 0.614260i $$0.789455\pi$$
$$332$$ 0 0
$$333$$ −2.59808 1.50000i −0.142374 0.0821995i
$$334$$ 0 0
$$335$$ −2.00000 + 4.00000i −0.109272 + 0.218543i
$$336$$ 0 0
$$337$$ 10.0000i 0.544735i 0.962193 + 0.272367i $$0.0878066\pi$$
−0.962193 + 0.272367i $$0.912193\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 3.00000 + 5.19615i 0.162459 + 0.281387i
$$342$$ 0 0
$$343$$ −15.5885 + 10.0000i −0.841698 + 0.539949i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −10.3923 6.00000i −0.557888 0.322097i 0.194409 0.980921i $$-0.437721\pi$$
−0.752297 + 0.658824i $$0.771054\pi$$
$$348$$ 0 0
$$349$$ 12.0000 0.642345 0.321173 0.947021i $$-0.395923\pi$$
0.321173 + 0.947021i $$0.395923\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 20.7846 + 12.0000i 1.10625 + 0.638696i 0.937856 0.347024i $$-0.112808\pi$$
0.168397 + 0.985719i $$0.446141\pi$$
$$354$$ 0 0
$$355$$ 0.803848 + 13.3923i 0.0426638 + 0.710790i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −8.00000 13.8564i −0.422224 0.731313i 0.573933 0.818902i $$-0.305417\pi$$
−0.996157 + 0.0875892i $$0.972084\pi$$
$$360$$ 0 0
$$361$$ −3.00000 + 5.19615i −0.157895 + 0.273482i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 16.0000 32.0000i 0.837478 1.67496i
$$366$$ 0 0
$$367$$ 11.2583 + 6.50000i 0.587680 + 0.339297i 0.764180 0.645003i $$-0.223144\pi$$
−0.176500 + 0.984301i $$0.556477\pi$$
$$368$$ 0 0
$$369$$ −4.50000 7.79423i −0.234261 0.405751i
$$370$$ 0 0
$$371$$ 4.50000 + 23.3827i 0.233628 + 1.21397i
$$372$$ 0 0
$$373$$ −22.5167 + 13.0000i −1.16587 + 0.673114i −0.952703 0.303902i $$-0.901711\pi$$
−0.213165 + 0.977016i $$0.568377\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 20.0000i 1.03005i
$$378$$ 0 0
$$379$$ −29.0000 −1.48963 −0.744815 0.667271i $$-0.767462\pi$$
−0.744815 + 0.667271i $$0.767462\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 18.1865 10.5000i 0.929288 0.536525i 0.0427020 0.999088i $$-0.486403\pi$$
0.886586 + 0.462563i $$0.153070\pi$$
$$384$$ 0 0
$$385$$ 4.39230 + 17.1962i 0.223853 + 0.876397i
$$386$$ 0 0
$$387$$ 5.19615 3.00000i 0.264135 0.152499i
$$388$$ 0 0
$$389$$ −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i $$-0.881939\pi$$
0.779895 + 0.625910i $$0.215272\pi$$
$$390$$ 0 0
$$391$$ −14.0000 −0.708010
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 26.1244 17.2487i 1.31446 0.867877i
$$396$$ 0 0
$$397$$ −12.1244 + 7.00000i −0.608504 + 0.351320i −0.772380 0.635161i $$-0.780934\pi$$
0.163876 + 0.986481i $$0.447600\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 7.50000 + 12.9904i 0.374532 + 0.648709i 0.990257 0.139253i $$-0.0444700\pi$$
−0.615725 + 0.787961i $$0.711137\pi$$
$$402$$ 0 0
$$403$$ −8.66025 5.00000i −0.431398 0.249068i
$$404$$ 0 0
$$405$$ −18.0000 9.00000i −0.894427 0.447214i
$$406$$ 0 0
$$407$$ 3.00000i 0.148704i
$$408$$ 0 0
$$409$$ −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i $$-0.945837\pi$$
0.639430 + 0.768849i $$0.279170\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 10.3923 2.00000i 0.511372 0.0984136i
$$414$$ 0 0
$$415$$ 13.3923 0.803848i 0.657402 0.0394593i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 35.0000 1.70986 0.854931 0.518742i $$-0.173599\pi$$
0.854931 + 0.518742i $$0.173599\pi$$
$$420$$ 0 0
$$421$$ −20.0000 −0.974740 −0.487370 0.873195i $$-0.662044\pi$$
−0.487370 + 0.873195i $$0.662044\pi$$
$$422$$ 0 0
$$423$$ −18.1865 10.5000i −0.884260 0.510527i
$$424$$ 0 0
$$425$$ −9.19615 3.92820i −0.446079 0.190546i
$$426$$ 0 0
$$427$$ 5.19615 15.0000i 0.251459 0.725901i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 1.00000 1.73205i 0.0481683 0.0834300i −0.840936 0.541135i $$-0.817995\pi$$
0.889104 + 0.457705i $$0.151328\pi$$
$$432$$ 0 0
$$433$$ 28.0000i 1.34559i −0.739827 0.672797i $$-0.765093\pi$$
0.739827 0.672797i $$-0.234907\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −30.3109 17.5000i −1.44997 0.837139i
$$438$$ 0 0
$$439$$ 14.0000 + 24.2487i 0.668184 + 1.15733i 0.978412 + 0.206666i $$0.0662612\pi$$
−0.310228 + 0.950662i $$0.600405\pi$$
$$440$$ 0 0
$$441$$ 19.5000 7.79423i 0.928571 0.371154i
$$442$$ 0 0
$$443$$ 25.9808 15.0000i 1.23438 0.712672i 0.266443 0.963851i $$-0.414152\pi$$
0.967941 + 0.251179i $$0.0808184\pi$$
$$444$$ 0 0
$$445$$ −3.73205 + 2.46410i −0.176916 + 0.116810i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −5.00000 −0.235965 −0.117982 0.993016i $$-0.537643\pi$$
−0.117982 + 0.993016i $$0.537643\pi$$
$$450$$ 0 0
$$451$$ 4.50000 7.79423i 0.211897 0.367016i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ −20.6699 21.1603i −0.969019 0.992008i
$$456$$ 0 0
$$457$$ −8.66025 + 5.00000i −0.405110 + 0.233890i −0.688686 0.725059i $$-0.741812\pi$$
0.283577 + 0.958950i $$0.408479\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −32.0000 −1.49039 −0.745194 0.666847i $$-0.767643\pi$$
−0.745194 + 0.666847i $$0.767643\pi$$
$$462$$ 0 0
$$463$$ 17.0000i 0.790057i −0.918669 0.395029i $$-0.870735\pi$$
0.918669 0.395029i $$-0.129265\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −29.4449 + 17.0000i −1.36255 + 0.786666i −0.989962 0.141332i $$-0.954861\pi$$
−0.372584 + 0.927999i $$0.621528\pi$$
$$468$$ 0 0
$$469$$ 1.00000 + 5.19615i 0.0461757 + 0.239936i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 5.19615 + 3.00000i 0.238919 + 0.137940i
$$474$$ 0 0
$$475$$ −15.0000 20.0000i −0.688247 0.917663i
$$476$$ 0 0
$$477$$ 27.0000i 1.23625i
$$478$$ 0 0
$$479$$ −18.0000 + 31.1769i −0.822441 + 1.42451i 0.0814184 + 0.996680i $$0.474055\pi$$
−0.903859 + 0.427830i $$0.859278\pi$$
$$480$$ 0 0
$$481$$ 2.50000 + 4.33013i 0.113990 + 0.197437i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 26.7846 1.60770i 1.21623 0.0730017i
$$486$$ 0 0
$$487$$ −27.7128 16.0000i −1.25579 0.725029i −0.283535 0.958962i $$-0.591507\pi$$
−0.972253 + 0.233933i $$0.924840\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −24.0000 −1.08310 −0.541552 0.840667i $$-0.682163\pi$$
−0.541552 + 0.840667i $$0.682163\pi$$
$$492$$ 0 0
$$493$$ 6.92820 + 4.00000i 0.312031 + 0.180151i
$$494$$ 0 0
$$495$$ −1.20577 20.0885i −0.0541954 0.902909i
$$496$$ 0 0
$$497$$ 10.3923 + 12.0000i 0.466159 + 0.538274i
$$498$$ 0 0
$$499$$ −2.00000 3.46410i −0.0895323 0.155074i 0.817781 0.575529i $$-0.195204\pi$$
−0.907314 + 0.420455i $$0.861871\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 40.0000i 1.78351i 0.452517 + 0.891756i $$0.350526\pi$$
−0.452517 + 0.891756i $$0.649474\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −17.0000 29.4449i −0.753512 1.30512i −0.946111 0.323843i $$-0.895025\pi$$
0.192599 0.981278i $$-0.438308\pi$$
$$510$$ 0 0
$$511$$ −8.00000 41.5692i −0.353899 1.83891i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −9.85641 14.9282i −0.434325 0.657815i
$$516$$ 0 0
$$517$$ 21.0000i 0.923579i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 13.5000 23.3827i 0.591446 1.02441i −0.402592 0.915379i $$-0.631891\pi$$
0.994038 0.109035i $$-0.0347759\pi$$
$$522$$ 0 0
$$523$$ 13.8564 8.00000i 0.605898 0.349816i −0.165460 0.986216i $$-0.552911\pi$$
0.771358 + 0.636401i $$0.219578\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −3.46410 + 2.00000i −0.150899 + 0.0871214i
$$528$$ 0 0
$$529$$ 13.0000 22.5167i 0.565217 0.978985i
$$530$$ 0 0
$$531$$ −12.0000 −0.520756
$$532$$ 0 0
$$533$$ 15.0000i 0.649722i
$$534$$ 0 0
$$535$$ 19.7128 + 29.8564i 0.852259 + 1.29081i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 16.5000 + 12.9904i 0.710705 + 0.559535i
$$540$$ 0 0
$$541$$ 8.00000 + 13.8564i 0.343947 + 0.595733i 0.985162 0.171628i $$-0.0549027\pi$$
−0.641215 + 0.767361i $$0.721569\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 4.00000 + 2.00000i 0.171341 + 0.0856706i
$$546$$ 0 0
$$547$$ 26.0000i 1.11168i 0.831289 + 0.555840i $$0.187603\pi$$
−0.831289 + 0.555840i $$0.812397\pi$$
$$548$$ 0 0
$$549$$ −9.00000 + 15.5885i −0.384111 + 0.665299i
$$550$$ 0 0
$$551$$ 10.0000 + 17.3205i 0.426014 + 0.737878i
$$552$$ 0 0
$$553$$ 12.1244 35.0000i 0.515580 1.48835i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −19.9186 11.5000i −0.843978 0.487271i 0.0146368 0.999893i $$-0.495341\pi$$
−0.858614 + 0.512622i $$0.828674\pi$$
$$558$$ 0 0
$$559$$ −10.0000 −0.422955
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ −1.73205 1.00000i −0.0729972 0.0421450i 0.463057 0.886328i $$-0.346752\pi$$
−0.536054 + 0.844183i $$0.680086\pi$$
$$564$$ 0 0
$$565$$ 31.2487 1.87564i 1.31464 0.0789090i
$$566$$ 0 0
$$567$$ −23.3827 + 4.50000i −0.981981 + 0.188982i
$$568$$ 0 0
$$569$$ −7.50000 12.9904i −0.314416 0.544585i 0.664897 0.746935i $$-0.268475\pi$$
−0.979313 + 0.202350i $$0.935142\pi$$
$$570$$ 0 0
$$571$$ 16.0000 27.7128i 0.669579 1.15975i −0.308443 0.951243i $$-0.599808\pi$$
0.978022 0.208502i $$-0.0668588\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 28.0000 21.0000i 1.16768 0.875761i
$$576$$ 0 0
$$577$$ 3.46410 + 2.00000i 0.144212 + 0.0832611i 0.570370 0.821388i $$-0.306800\pi$$
−0.426158 + 0.904649i $$0.640133\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 12.0000 10.3923i 0.497844 0.431145i
$$582$$ 0 0
$$583$$ 23.3827 13.5000i 0.968412 0.559113i
$$584$$ 0 0
$$585$$ 18.4808 + 27.9904i 0.764085 + 1.15726i
$$586$$ 0 0
$$587$$ 34.0000i 1.40333i −0.712507 0.701665i $$-0.752440\pi$$
0.712507 0.701665i $$-0.247560\pi$$
$$588$$ 0 0
$$589$$ −10.0000 −0.412043
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 5.19615 3.00000i 0.213380 0.123195i −0.389501 0.921026i $$-0.627353\pi$$
0.602881 + 0.797831i $$0.294019\pi$$
$$594$$ 0 0
$$595$$ −11.4641 + 2.92820i −0.469982 + 0.120045i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 6.00000 10.3923i 0.245153 0.424618i −0.717021 0.697051i $$-0.754495\pi$$
0.962175 + 0.272433i $$0.0878284\pi$$
$$600$$ 0 0
$$601$$ −22.0000 −0.897399 −0.448699 0.893683i $$-0.648113\pi$$
−0.448699 + 0.893683i $$0.648113\pi$$
$$602$$ 0 0
$$603$$ 6.00000i 0.244339i
$$604$$ 0 0
$$605$$ −3.73205 + 2.46410i −0.151729 + 0.100180i
$$606$$ 0 0
$$607$$ 11.2583 6.50000i 0.456962 0.263827i −0.253804 0.967256i $$-0.581682\pi$$
0.710766 + 0.703429i $$0.248349\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 17.5000 + 30.3109i 0.707974 + 1.22625i
$$612$$ 0 0
$$613$$ −12.9904 7.50000i −0.524677 0.302922i 0.214169 0.976797i $$-0.431296\pi$$
−0.738846 + 0.673874i $$0.764629\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 14.0000i 0.563619i 0.959470 + 0.281809i $$0.0909346\pi$$
−0.959470 + 0.281809i $$0.909065\pi$$
$$618$$ 0 0
$$619$$ −9.50000 + 16.4545i −0.381837 + 0.661361i −0.991325 0.131434i $$-0.958042\pi$$
0.609488 + 0.792796i $$0.291375\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −1.73205 + 5.00000i −0.0693932 + 0.200321i
$$624$$ 0 0
$$625$$ 24.2846 5.93782i 0.971384 0.237513i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 2.00000 0.0797452
$$630$$ 0 0
$$631$$ 18.0000 0.716569 0.358284 0.933613i $$-0.383362\pi$$
0.358284 + 0.933613i $$0.383362\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 15.6244 0.937822i 0.620034 0.0372163i
$$636$$ 0 0
$$637$$ −34.6410 5.00000i −1.37253 0.198107i
$$638$$ 0 0
$$639$$ −9.00000 15.5885i −0.356034 0.616670i
$$640$$ 0 0
$$641$$ 2.50000 4.33013i 0.0987441 0.171030i −0.812421 0.583071i $$-0.801851\pi$$
0.911165 + 0.412042i $$0.135184\pi$$
$$642$$ 0 0
$$643$$ 14.0000i 0.552106i −0.961142 0.276053i $$-0.910973\pi$$
0.961142 0.276053i $$-0.0890266\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −23.3827 13.5000i −0.919268 0.530740i −0.0358667 0.999357i $$-0.511419\pi$$
−0.883402 + 0.468617i $$0.844753\pi$$
$$648$$ 0 0
$$649$$ −6.00000 10.3923i −0.235521 0.407934i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −2.59808 + 1.50000i −0.101671 + 0.0586995i −0.549973 0.835182i $$-0.685362\pi$$
0.448303 + 0.893882i $$0.352029\pi$$
$$654$$ 0 0
$$655$$ 1.86603 1.23205i 0.0729116 0.0481402i
$$656$$ 0 0
$$657$$ 48.0000i 1.87266i
$$658$$ 0 0
$$659$$ −36.0000 −1.40236 −0.701180 0.712984i $$-0.747343\pi$$
−0.701180 + 0.712984i $$0.747343\pi$$
$$660$$ 0 0
$$661$$ −8.00000 + 13.8564i −0.311164 + 0.538952i −0.978615 0.205702i $$-0.934052\pi$$
0.667451 + 0.744654i $$0.267385\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −28.4808 7.99038i −1.10444 0.309854i
$$666$$ 0 0
$$667$$ −24.2487 + 14.0000i −0.938914 + 0.542082i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −18.0000 −0.694882
$$672$$ 0 0
$$673$$ 32.0000i 1.23351i −0.787155 0.616755i $$-0.788447\pi$$
0.787155 0.616755i $$-0.211553\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −14.7224 + 8.50000i −0.565829 + 0.326682i −0.755482 0.655170i $$-0.772597\pi$$
0.189653 + 0.981851i $$0.439264\pi$$
$$678$$ 0 0
$$679$$ 24.0000 20.7846i 0.921035 0.797640i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 38.1051 + 22.0000i 1.45805 + 0.841807i 0.998916 0.0465592i $$-0.0148256\pi$$
0.459136 + 0.888366i $$0.348159\pi$$
$$684$$ 0 0
$$685$$ −8.00000 + 16.0000i −0.305664 + 0.611329i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −22.5000 + 38.9711i −0.857182 + 1.48468i
$$690$$ 0 0
$$691$$ −22.0000 38.1051i −0.836919 1.44959i −0.892458 0.451130i $$-0.851021\pi$$
0.0555386 0.998457i $$-0.482312\pi$$
$$692$$ 0 0
$$693$$ −15.5885 18.0000i −0.592157 0.683763i
$$694$$ 0 0
$$695$$ 2.14359 + 35.7128i 0.0813111 + 1.35466i
$$696$$ 0 0
$$697$$ 5.19615 + 3.00000i 0.196818 + 0.113633i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 26.0000 0.982006 0.491003 0.871158i $$-0.336630\pi$$
0.491003 + 0.871158i $$0.336630\pi$$
$$702$$ 0 0
$$703$$ 4.33013 + 2.50000i 0.163314 + 0.0942893i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 6.00000 + 10.3923i 0.225335 + 0.390291i 0.956420 0.291995i $$-0.0943191\pi$$
−0.731085 + 0.682286i $$0.760986\pi$$
$$710$$ 0 0
$$711$$ −21.0000 + 36.3731i −0.787562 + 1.36410i
$$712$$ 0 0
$$713$$ 14.0000i 0.524304i
$$714$$ 0 0
$$715$$ −15.0000 + 30.0000i −0.560968 + 1.12194i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −13.0000 22.5167i −0.484818 0.839730i 0.515030 0.857172i $$-0.327781\pi$$
−0.999848 + 0.0174426i $$0.994448\pi$$
$$720$$ 0 0
$$721$$ −20.0000 6.92820i −0.744839 0.258020i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −19.8564 + 2.39230i −0.737448 + 0.0888480i
$$726$$ 0 0
$$727$$ 29.0000i 1.07555i 0.843088 + 0.537775i $$0.180735\pi$$
−0.843088 + 0.537775i $$0.819265\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ −2.00000 + 3.46410i −0.0739727 + 0.128124i
$$732$$ 0 0
$$733$$ −35.5070 + 20.5000i −1.31148 + 0.757185i −0.982342 0.187096i $$-0.940092\pi$$
−0.329141 + 0.944281i $$0.606759\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 5.19615 3.00000i 0.191403 0.110506i
$$738$$ 0 0
$$739$$ 14.5000 25.1147i 0.533391 0.923861i −0.465848 0.884865i $$-0.654251\pi$$
0.999239 0.0389959i $$-0.0124159\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 21.0000i 0.770415i −0.922830 0.385208i $$-0.874130\pi$$
0.922830 0.385208i $$-0.125870\pi$$
$$744$$ 0 0
$$745$$ 33.5885 22.1769i 1.23059 0.812499i
$$746$$ 0 0
$$747$$ −15.5885 + 9.00000i −0.570352 + 0.329293i
$$748$$ 0 0
$$749$$ 40.0000 + 13.8564i 1.46157 + 0.506302i
$$750$$ 0 0
$$751$$ 14.0000 + 24.2487i 0.510867 + 0.884848i 0.999921 + 0.0125942i $$0.00400897\pi$$
−0.489053 + 0.872254i $$0.662658\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −12.0000 6.00000i −0.436725 0.218362i
$$756$$ 0 0
$$757$$ 42.0000i 1.52652i 0.646094 + 0.763258i $$0.276401\pi$$
−0.646094 + 0.763258i $$0.723599\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −0.500000 0.866025i −0.0181250 0.0313934i 0.856821 0.515615i $$-0.172436\pi$$
−0.874946 + 0.484221i $$0.839103\pi$$
$$762$$ 0 0
$$763$$ 5.19615 1.00000i 0.188113 0.0362024i
$$764$$ 0 0
$$765$$ 13.3923 0.803848i 0.484200 0.0290632i
$$766$$ 0 0
$$767$$ 17.3205 + 10.0000i 0.625407 + 0.361079i
$$768$$ 0 0
$$769$$ 29.0000 1.04577 0.522883 0.852404i $$-0.324856\pi$$
0.522883 + 0.852404i $$0.324856\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 38.9711 + 22.5000i 1.40169 + 0.809269i 0.994567 0.104102i $$-0.0331970\pi$$
0.407128 + 0.913371i $$0.366530\pi$$
$$774$$ 0 0
$$775$$ 3.92820 9.19615i 0.141105 0.330336i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 7.50000 + 12.9904i 0.268715 + 0.465429i
$$780$$ 0 0
$$781$$ 9.00000 15.5885i 0.322045 0.557799i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −9.00000 + 18.0000i −0.321224 + 0.642448i
$$786$$ 0 0
$$787$$ 15.5885 + 9.00000i 0.555668 + 0.320815i 0.751405 0.659841i $$-0.229376\pi$$
−0.195737 + 0.980656i $$0.562710\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 28.0000 24.2487i 0.995565 0.862185i
$$792$$ 0 0
$$793$$ 25.9808 15.0000i 0.922604 0.532666i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 2.00000i 0.0708436i −0.999372 0.0354218i $$-0.988723\pi$$
0.999372 0.0354218i $$-0.0112775\pi$$
$$798$$ 0 0