# Properties

 Label 2940.2.bb.e.949.1 Level $2940$ Weight $2$ Character 2940.949 Analytic conductor $23.476$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2940.bb (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$23.4760181943$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 60) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 949.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 2940.949 Dual form 2940.2.bb.e.1549.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 - 0.500000i) q^{3} +(2.23205 - 0.133975i) q^{5} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 - 0.500000i) q^{3} +(2.23205 - 0.133975i) q^{5} +(0.500000 + 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} +(-2.00000 - 1.00000i) q^{15} +(3.46410 + 2.00000i) q^{17} +(-3.46410 + 2.00000i) q^{23} +(4.96410 - 0.598076i) q^{25} -1.00000i q^{27} +6.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-3.46410 + 2.00000i) q^{33} +(-6.92820 + 4.00000i) q^{37} +10.0000 q^{41} -4.00000i q^{43} +(1.23205 + 1.86603i) q^{45} +(3.46410 - 2.00000i) q^{47} +(-2.00000 - 3.46410i) q^{51} +(-10.3923 - 6.00000i) q^{53} +(4.00000 - 8.00000i) q^{55} +(-2.00000 + 3.46410i) q^{59} +(1.00000 + 1.73205i) q^{61} +(3.46410 + 2.00000i) q^{67} +4.00000 q^{69} +(6.92820 + 4.00000i) q^{73} +(-4.59808 - 1.96410i) q^{75} +(-6.00000 - 10.3923i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.00000i q^{83} +(8.00000 + 4.00000i) q^{85} +(-5.19615 - 3.00000i) q^{87} +(5.00000 + 8.66025i) q^{89} +(-3.46410 + 2.00000i) q^{93} -8.00000i q^{97} +4.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{5} + 2q^{9} + O(q^{10})$$ $$4q + 2q^{5} + 2q^{9} + 8q^{11} - 8q^{15} + 6q^{25} + 24q^{29} + 8q^{31} + 40q^{41} - 2q^{45} - 8q^{51} + 16q^{55} - 8q^{59} + 4q^{61} + 16q^{69} - 8q^{75} - 24q^{79} - 2q^{81} + 32q^{85} + 20q^{89} + 16q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$$.

 $$n$$ $$1081$$ $$1177$$ $$1471$$ $$1961$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$1$$ $$1$$

## 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
$$3$$ −0.866025 0.500000i −0.500000 0.288675i
$$4$$ 0 0
$$5$$ 2.23205 0.133975i 0.998203 0.0599153i
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ 0.500000 + 0.866025i 0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ 2.00000 3.46410i 0.603023 1.04447i −0.389338 0.921095i $$-0.627296\pi$$
0.992361 0.123371i $$-0.0393705\pi$$
$$12$$ 0 0
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0 0
$$15$$ −2.00000 1.00000i −0.516398 0.258199i
$$16$$ 0 0
$$17$$ 3.46410 + 2.00000i 0.840168 + 0.485071i 0.857321 0.514782i $$-0.172127\pi$$
−0.0171533 + 0.999853i $$0.505460\pi$$
$$18$$ 0 0
$$19$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −3.46410 + 2.00000i −0.722315 + 0.417029i −0.815604 0.578610i $$-0.803595\pi$$
0.0932891 + 0.995639i $$0.470262\pi$$
$$24$$ 0 0
$$25$$ 4.96410 0.598076i 0.992820 0.119615i
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ 6.00000 1.11417 0.557086 0.830455i $$-0.311919\pi$$
0.557086 + 0.830455i $$0.311919\pi$$
$$30$$ 0 0
$$31$$ 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i $$-0.716379\pi$$
0.987829 + 0.155543i $$0.0497126\pi$$
$$32$$ 0 0
$$33$$ −3.46410 + 2.00000i −0.603023 + 0.348155i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −6.92820 + 4.00000i −1.13899 + 0.657596i −0.946180 0.323640i $$-0.895093\pi$$
−0.192809 + 0.981236i $$0.561760\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 10.0000 1.56174 0.780869 0.624695i $$-0.214777\pi$$
0.780869 + 0.624695i $$0.214777\pi$$
$$42$$ 0 0
$$43$$ 4.00000i 0.609994i −0.952353 0.304997i $$-0.901344\pi$$
0.952353 0.304997i $$-0.0986555\pi$$
$$44$$ 0 0
$$45$$ 1.23205 + 1.86603i 0.183663 + 0.278171i
$$46$$ 0 0
$$47$$ 3.46410 2.00000i 0.505291 0.291730i −0.225605 0.974219i $$-0.572436\pi$$
0.730896 + 0.682489i $$0.239102\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −2.00000 3.46410i −0.280056 0.485071i
$$52$$ 0 0
$$53$$ −10.3923 6.00000i −1.42749 0.824163i −0.430570 0.902557i $$-0.641688\pi$$
−0.996922 + 0.0783936i $$0.975021\pi$$
$$54$$ 0 0
$$55$$ 4.00000 8.00000i 0.539360 1.07872i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i $$-0.917180\pi$$
0.705965 + 0.708247i $$0.250514\pi$$
$$60$$ 0 0
$$61$$ 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i $$-0.125799\pi$$
−0.794879 + 0.606768i $$0.792466\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 3.46410 + 2.00000i 0.423207 + 0.244339i 0.696449 0.717607i $$-0.254762\pi$$
−0.273241 + 0.961946i $$0.588096\pi$$
$$68$$ 0 0
$$69$$ 4.00000 0.481543
$$70$$ 0 0
$$71$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$72$$ 0 0
$$73$$ 6.92820 + 4.00000i 0.810885 + 0.468165i 0.847263 0.531174i $$-0.178249\pi$$
−0.0363782 + 0.999338i $$0.511582\pi$$
$$74$$ 0 0
$$75$$ −4.59808 1.96410i −0.530940 0.226795i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −6.00000 10.3923i −0.675053 1.16923i −0.976453 0.215728i $$-0.930788\pi$$
0.301401 0.953498i $$-0.402546\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 4.00000i 0.439057i 0.975606 + 0.219529i $$0.0704519\pi$$
−0.975606 + 0.219529i $$0.929548\pi$$
$$84$$ 0 0
$$85$$ 8.00000 + 4.00000i 0.867722 + 0.433861i
$$86$$ 0 0
$$87$$ −5.19615 3.00000i −0.557086 0.321634i
$$88$$ 0 0
$$89$$ 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i $$0.0111410\pi$$
−0.469389 + 0.882992i $$0.655526\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −3.46410 + 2.00000i −0.359211 + 0.207390i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 8.00000i 0.812277i −0.913812 0.406138i $$-0.866875\pi$$
0.913812 0.406138i $$-0.133125\pi$$
$$98$$ 0 0
$$99$$ 4.00000 0.402015
$$100$$ 0 0
$$101$$ −1.00000 + 1.73205i −0.0995037 + 0.172345i −0.911479 0.411346i $$-0.865059\pi$$
0.811976 + 0.583691i $$0.198392\pi$$
$$102$$ 0 0
$$103$$ −3.46410 + 2.00000i −0.341328 + 0.197066i −0.660859 0.750510i $$-0.729808\pi$$
0.319531 + 0.947576i $$0.396475\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 10.3923 6.00000i 1.00466 0.580042i 0.0950377 0.995474i $$-0.469703\pi$$
0.909624 + 0.415432i $$0.136370\pi$$
$$108$$ 0 0
$$109$$ −1.00000 + 1.73205i −0.0957826 + 0.165900i −0.909935 0.414751i $$-0.863869\pi$$
0.814152 + 0.580651i $$0.197202\pi$$
$$110$$ 0 0
$$111$$ 8.00000 0.759326
$$112$$ 0 0
$$113$$ 12.0000i 1.12887i −0.825479 0.564433i $$-0.809095\pi$$
0.825479 0.564433i $$-0.190905\pi$$
$$114$$ 0 0
$$115$$ −7.46410 + 4.92820i −0.696031 + 0.459557i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −2.50000 4.33013i −0.227273 0.393648i
$$122$$ 0 0
$$123$$ −8.66025 5.00000i −0.780869 0.450835i
$$124$$ 0 0
$$125$$ 11.0000 2.00000i 0.983870 0.178885i
$$126$$ 0 0
$$127$$ 4.00000i 0.354943i 0.984126 + 0.177471i $$0.0567917\pi$$
−0.984126 + 0.177471i $$0.943208\pi$$
$$128$$ 0 0
$$129$$ −2.00000 + 3.46410i −0.176090 + 0.304997i
$$130$$ 0 0
$$131$$ 6.00000 + 10.3923i 0.524222 + 0.907980i 0.999602 + 0.0281993i $$0.00897729\pi$$
−0.475380 + 0.879781i $$0.657689\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −0.133975 2.23205i −0.0115307 0.192104i
$$136$$ 0 0
$$137$$ −10.3923 6.00000i −0.887875 0.512615i −0.0146279 0.999893i $$-0.504656\pi$$
−0.873247 + 0.487278i $$0.837990\pi$$
$$138$$ 0 0
$$139$$ 16.0000 1.35710 0.678551 0.734553i $$-0.262608\pi$$
0.678551 + 0.734553i $$0.262608\pi$$
$$140$$ 0 0
$$141$$ −4.00000 −0.336861
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 13.3923 0.803848i 1.11217 0.0667559i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1.00000 1.73205i −0.0819232 0.141895i 0.822153 0.569267i $$-0.192773\pi$$
−0.904076 + 0.427372i $$0.859440\pi$$
$$150$$ 0 0
$$151$$ 10.0000 17.3205i 0.813788 1.40952i −0.0964061 0.995342i $$-0.530735\pi$$
0.910195 0.414181i $$-0.135932\pi$$
$$152$$ 0 0
$$153$$ 4.00000i 0.323381i
$$154$$ 0 0
$$155$$ 4.00000 8.00000i 0.321288 0.642575i
$$156$$ 0 0
$$157$$ 6.92820 + 4.00000i 0.552931 + 0.319235i 0.750303 0.661094i $$-0.229907\pi$$
−0.197372 + 0.980329i $$0.563241\pi$$
$$158$$ 0 0
$$159$$ 6.00000 + 10.3923i 0.475831 + 0.824163i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −17.3205 + 10.0000i −1.35665 + 0.783260i −0.989170 0.146772i $$-0.953112\pi$$
−0.367477 + 0.930033i $$0.619778\pi$$
$$164$$ 0 0
$$165$$ −7.46410 + 4.92820i −0.581080 + 0.383660i
$$166$$ 0 0
$$167$$ 12.0000i 0.928588i −0.885681 0.464294i $$-0.846308\pi$$
0.885681 0.464294i $$-0.153692\pi$$
$$168$$ 0 0
$$169$$ 13.0000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −3.46410 + 2.00000i −0.263371 + 0.152057i −0.625871 0.779926i $$-0.715256\pi$$
0.362500 + 0.931984i $$0.381923\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 3.46410 2.00000i 0.260378 0.150329i
$$178$$ 0 0
$$179$$ 2.00000 3.46410i 0.149487 0.258919i −0.781551 0.623841i $$-0.785571\pi$$
0.931038 + 0.364922i $$0.118904\pi$$
$$180$$ 0 0
$$181$$ 10.0000 0.743294 0.371647 0.928374i $$-0.378793\pi$$
0.371647 + 0.928374i $$0.378793\pi$$
$$182$$ 0 0
$$183$$ 2.00000i 0.147844i
$$184$$ 0 0
$$185$$ −14.9282 + 9.85641i −1.09754 + 0.724657i
$$186$$ 0 0
$$187$$ 13.8564 8.00000i 1.01328 0.585018i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i $$-0.831886\pi$$
−0.00454614 0.999990i $$-0.501447\pi$$
$$192$$ 0 0
$$193$$ 13.8564 + 8.00000i 0.997406 + 0.575853i 0.907480 0.420096i $$-0.138004\pi$$
0.0899262 + 0.995948i $$0.471337\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 4.00000i 0.284988i −0.989796 0.142494i $$-0.954488\pi$$
0.989796 0.142494i $$-0.0455122\pi$$
$$198$$ 0 0
$$199$$ 6.00000 10.3923i 0.425329 0.736691i −0.571122 0.820865i $$-0.693492\pi$$
0.996451 + 0.0841740i $$0.0268252\pi$$
$$200$$ 0 0
$$201$$ −2.00000 3.46410i −0.141069 0.244339i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 22.3205 1.33975i 1.55893 0.0935719i
$$206$$ 0 0
$$207$$ −3.46410 2.00000i −0.240772 0.139010i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −0.535898 8.92820i −0.0365480 0.608898i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −4.00000 6.92820i −0.270295 0.468165i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 20.0000i 1.33930i −0.742677 0.669650i $$-0.766444\pi$$
0.742677 0.669650i $$-0.233556\pi$$
$$224$$ 0 0
$$225$$ 3.00000 + 4.00000i 0.200000 + 0.266667i
$$226$$ 0 0
$$227$$ −17.3205 10.0000i −1.14960 0.663723i −0.200812 0.979630i $$-0.564358\pi$$
−0.948790 + 0.315906i $$0.897691\pi$$
$$228$$ 0 0
$$229$$ −13.0000 22.5167i −0.859064 1.48794i −0.872823 0.488037i $$-0.837713\pi$$
0.0137585 0.999905i $$-0.495620\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −17.3205 + 10.0000i −1.13470 + 0.655122i −0.945114 0.326741i $$-0.894049\pi$$
−0.189590 + 0.981863i $$0.560716\pi$$
$$234$$ 0 0
$$235$$ 7.46410 4.92820i 0.486904 0.321481i
$$236$$ 0 0
$$237$$ 12.0000i 0.779484i
$$238$$ 0 0
$$239$$ −8.00000 −0.517477 −0.258738 0.965947i $$-0.583307\pi$$
−0.258738 + 0.965947i $$0.583307\pi$$
$$240$$ 0 0
$$241$$ −1.00000 + 1.73205i −0.0644157 + 0.111571i −0.896435 0.443176i $$-0.853852\pi$$
0.832019 + 0.554747i $$0.187185\pi$$
$$242$$ 0 0
$$243$$ 0.866025 0.500000i 0.0555556 0.0320750i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 2.00000 3.46410i 0.126745 0.219529i
$$250$$ 0 0
$$251$$ 12.0000 0.757433 0.378717 0.925513i $$-0.376365\pi$$
0.378717 + 0.925513i $$0.376365\pi$$
$$252$$ 0 0
$$253$$ 16.0000i 1.00591i
$$254$$ 0 0
$$255$$ −4.92820 7.46410i −0.308616 0.467420i
$$256$$ 0 0
$$257$$ −10.3923 + 6.00000i −0.648254 + 0.374270i −0.787787 0.615948i $$-0.788773\pi$$
0.139533 + 0.990217i $$0.455440\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 3.00000 + 5.19615i 0.185695 + 0.321634i
$$262$$ 0 0
$$263$$ 3.46410 + 2.00000i 0.213606 + 0.123325i 0.602986 0.797752i $$-0.293977\pi$$
−0.389380 + 0.921077i $$0.627311\pi$$
$$264$$ 0 0
$$265$$ −24.0000 12.0000i −1.47431 0.737154i
$$266$$ 0 0
$$267$$ 10.0000i 0.611990i
$$268$$ 0 0
$$269$$ −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i $$-0.891886\pi$$
0.759958 + 0.649972i $$0.225219\pi$$
$$270$$ 0 0
$$271$$ 2.00000 + 3.46410i 0.121491 + 0.210429i 0.920356 0.391082i $$-0.127899\pi$$
−0.798865 + 0.601511i $$0.794566\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 7.85641 18.3923i 0.473759 1.10910i
$$276$$ 0 0
$$277$$ 27.7128 + 16.0000i 1.66510 + 0.961347i 0.970221 + 0.242222i $$0.0778761\pi$$
0.694881 + 0.719125i $$0.255457\pi$$
$$278$$ 0 0
$$279$$ 4.00000 0.239474
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ 24.2487 + 14.0000i 1.44144 + 0.832214i 0.997946 0.0640654i $$-0.0204066\pi$$
0.443491 + 0.896279i $$0.353740\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −0.500000 0.866025i −0.0294118 0.0509427i
$$290$$ 0 0
$$291$$ −4.00000 + 6.92820i −0.234484 + 0.406138i
$$292$$ 0 0
$$293$$ 12.0000i 0.701047i 0.936554 + 0.350524i $$0.113996\pi$$
−0.936554 + 0.350524i $$0.886004\pi$$
$$294$$ 0 0
$$295$$ −4.00000 + 8.00000i −0.232889 + 0.465778i
$$296$$ 0 0
$$297$$ −3.46410 2.00000i −0.201008 0.116052i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 1.73205 1.00000i 0.0995037 0.0574485i
$$304$$ 0 0
$$305$$ 2.46410 + 3.73205i 0.141094 + 0.213697i
$$306$$ 0 0
$$307$$ 12.0000i 0.684876i −0.939540 0.342438i $$-0.888747\pi$$
0.939540 0.342438i $$-0.111253\pi$$
$$308$$ 0 0
$$309$$ 4.00000 0.227552
$$310$$ 0 0
$$311$$ 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i $$-0.595114\pi$$
0.974841 0.222900i $$-0.0715523\pi$$
$$312$$ 0 0
$$313$$ 13.8564 8.00000i 0.783210 0.452187i −0.0543564 0.998522i $$-0.517311\pi$$
0.837567 + 0.546335i $$0.183977\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 3.46410 2.00000i 0.194563 0.112331i −0.399554 0.916710i $$-0.630835\pi$$
0.594117 + 0.804379i $$0.297502\pi$$
$$318$$ 0 0
$$319$$ 12.0000 20.7846i 0.671871 1.16371i
$$320$$ 0 0
$$321$$ −12.0000 −0.669775
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 1.73205 1.00000i 0.0957826 0.0553001i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i $$-0.0961066\pi$$
−0.734905 + 0.678170i $$0.762773\pi$$
$$332$$ 0 0
$$333$$ −6.92820 4.00000i −0.379663 0.219199i
$$334$$ 0 0
$$335$$ 8.00000 + 4.00000i 0.437087 + 0.218543i
$$336$$ 0 0
$$337$$ 8.00000i 0.435788i −0.975972 0.217894i $$-0.930081\pi$$
0.975972 0.217894i $$-0.0699187\pi$$
$$338$$ 0 0
$$339$$ −6.00000 + 10.3923i −0.325875 + 0.564433i
$$340$$ 0 0
$$341$$ −8.00000 13.8564i −0.433224 0.750366i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 8.92820 0.535898i 0.480678 0.0288518i
$$346$$ 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
$$349$$ −14.0000 −0.749403 −0.374701 0.927146i $$-0.622255\pi$$
−0.374701 + 0.927146i $$0.622255\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 24.2487 + 14.0000i 1.29063 + 0.745145i 0.978766 0.204982i $$-0.0657137\pi$$
0.311863 + 0.950127i $$0.399047\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 12.0000 + 20.7846i 0.633336 + 1.09697i 0.986865 + 0.161546i $$0.0516481\pi$$
−0.353529 + 0.935423i $$0.615019\pi$$
$$360$$ 0 0
$$361$$ 9.50000 16.4545i 0.500000 0.866025i
$$362$$ 0 0
$$363$$ 5.00000i 0.262432i
$$364$$ 0 0
$$365$$ 16.0000 + 8.00000i 0.837478 + 0.418739i
$$366$$ 0 0
$$367$$ 3.46410 + 2.00000i 0.180825 + 0.104399i 0.587680 0.809093i $$-0.300041\pi$$
−0.406855 + 0.913493i $$0.633375\pi$$
$$368$$ 0 0
$$369$$ 5.00000 + 8.66025i 0.260290 + 0.450835i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −20.7846 + 12.0000i −1.07619 + 0.621336i −0.929865 0.367901i $$-0.880077\pi$$
−0.146321 + 0.989237i $$0.546743\pi$$
$$374$$ 0 0
$$375$$ −10.5263 3.76795i −0.543575 0.194576i
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ −8.00000 −0.410932 −0.205466 0.978664i $$-0.565871\pi$$
−0.205466 + 0.978664i $$0.565871\pi$$
$$380$$ 0 0
$$381$$ 2.00000 3.46410i 0.102463 0.177471i
$$382$$ 0 0
$$383$$ −24.2487 + 14.0000i −1.23905 + 0.715367i −0.968900 0.247451i $$-0.920407\pi$$
−0.270151 + 0.962818i $$0.587074\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 3.46410 2.00000i 0.176090 0.101666i
$$388$$ 0 0
$$389$$ −17.0000 + 29.4449i −0.861934 + 1.49291i 0.00812520 + 0.999967i $$0.497414\pi$$
−0.870059 + 0.492947i $$0.835920\pi$$
$$390$$ 0 0
$$391$$ −16.0000 −0.809155
$$392$$ 0 0
$$393$$ 12.0000i 0.605320i
$$394$$ 0 0
$$395$$ −14.7846 22.3923i −0.743894 1.12668i
$$396$$ 0 0
$$397$$ 6.92820 4.00000i 0.347717 0.200754i −0.315963 0.948772i $$-0.602327\pi$$
0.663679 + 0.748017i $$0.268994\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 7.00000 + 12.1244i 0.349563 + 0.605461i 0.986172 0.165726i $$-0.0529966\pi$$
−0.636609 + 0.771187i $$0.719663\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −1.00000 + 2.00000i −0.0496904 + 0.0993808i
$$406$$ 0 0
$$407$$ 32.0000i 1.58618i
$$408$$ 0 0
$$409$$ −13.0000 + 22.5167i −0.642809 + 1.11338i 0.341994 + 0.939702i $$0.388898\pi$$
−0.984803 + 0.173675i $$0.944436\pi$$
$$410$$ 0 0
$$411$$ 6.00000 + 10.3923i 0.295958 + 0.512615i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0.535898 + 8.92820i 0.0263062 + 0.438268i
$$416$$ 0 0
$$417$$ −13.8564 8.00000i −0.678551 0.391762i
$$418$$ 0 0
$$419$$ −28.0000 −1.36789 −0.683945 0.729534i $$-0.739737\pi$$
−0.683945 + 0.729534i $$0.739737\pi$$
$$420$$ 0 0
$$421$$ 10.0000 0.487370 0.243685 0.969854i $$-0.421644\pi$$
0.243685 + 0.969854i $$0.421644\pi$$
$$422$$ 0 0
$$423$$ 3.46410 + 2.00000i 0.168430 + 0.0972433i
$$424$$ 0 0
$$425$$ 18.3923 + 7.85641i 0.892158 + 0.381092i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −4.00000 + 6.92820i −0.192673 + 0.333720i −0.946135 0.323772i $$-0.895049\pi$$
0.753462 + 0.657491i $$0.228382\pi$$
$$432$$ 0 0
$$433$$ 16.0000i 0.768911i 0.923144 + 0.384455i $$0.125611\pi$$
−0.923144 + 0.384455i $$0.874389\pi$$
$$434$$ 0 0
$$435$$ −12.0000 6.00000i −0.575356 0.287678i
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 6.00000 + 10.3923i 0.286364 + 0.495998i 0.972939 0.231062i $$-0.0742199\pi$$
−0.686575 + 0.727059i $$0.740887\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −31.1769 + 18.0000i −1.48126 + 0.855206i −0.999774 0.0212481i $$-0.993236\pi$$
−0.481486 + 0.876454i $$0.659903\pi$$
$$444$$ 0 0
$$445$$ 12.3205 + 18.6603i 0.584048 + 0.884581i
$$446$$ 0 0
$$447$$ 2.00000i 0.0945968i
$$448$$ 0 0
$$449$$ −18.0000 −0.849473 −0.424736 0.905317i $$-0.639633\pi$$
−0.424736 + 0.905317i $$0.639633\pi$$
$$450$$ 0 0
$$451$$ 20.0000 34.6410i 0.941763 1.63118i
$$452$$ 0 0
$$453$$ −17.3205 + 10.0000i −0.813788 + 0.469841i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 34.6410 20.0000i 1.62044 0.935561i 0.633636 0.773631i $$-0.281562\pi$$
0.986802 0.161929i $$-0.0517716\pi$$
$$458$$ 0 0
$$459$$ 2.00000 3.46410i 0.0933520 0.161690i
$$460$$ 0 0
$$461$$ −6.00000 −0.279448 −0.139724 0.990190i $$-0.544622\pi$$
−0.139724 + 0.990190i $$0.544622\pi$$
$$462$$ 0 0
$$463$$ 12.0000i 0.557687i −0.960337 0.278844i $$-0.910049\pi$$
0.960337 0.278844i $$-0.0899511\pi$$
$$464$$ 0 0
$$465$$ −7.46410 + 4.92820i −0.346139 + 0.228540i
$$466$$ 0 0
$$467$$ −10.3923 + 6.00000i −0.480899 + 0.277647i −0.720791 0.693153i $$-0.756221\pi$$
0.239892 + 0.970799i $$0.422888\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −4.00000 6.92820i −0.184310 0.319235i
$$472$$ 0 0
$$473$$ −13.8564 8.00000i −0.637118 0.367840i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 12.0000i 0.549442i
$$478$$ 0 0
$$479$$ 8.00000 13.8564i 0.365529 0.633115i −0.623332 0.781958i $$-0.714221\pi$$
0.988861 + 0.148842i $$0.0475547\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −1.07180 17.8564i −0.0486678 0.810818i
$$486$$ 0 0
$$487$$ 10.3923 + 6.00000i 0.470920 + 0.271886i 0.716625 0.697459i $$-0.245686\pi$$
−0.245705 + 0.969345i $$0.579019\pi$$
$$488$$ 0 0
$$489$$ 20.0000 0.904431
$$490$$ 0 0
$$491$$ −36.0000 −1.62466 −0.812329 0.583200i $$-0.801800\pi$$
−0.812329 + 0.583200i $$0.801800\pi$$
$$492$$ 0 0
$$493$$ 20.7846 + 12.0000i 0.936092 + 0.540453i
$$494$$ 0 0
$$495$$ 8.92820 0.535898i 0.401293 0.0240868i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 12.0000 + 20.7846i 0.537194 + 0.930447i 0.999054 + 0.0434940i $$0.0138489\pi$$
−0.461860 + 0.886953i $$0.652818\pi$$
$$500$$ 0 0
$$501$$ −6.00000 + 10.3923i −0.268060 + 0.464294i
$$502$$ 0 0
$$503$$ 36.0000i 1.60516i 0.596544 + 0.802580i $$0.296540\pi$$
−0.596544 + 0.802580i $$0.703460\pi$$
$$504$$ 0 0
$$505$$ −2.00000 + 4.00000i −0.0889988 + 0.177998i
$$506$$ 0 0
$$507$$ −11.2583 6.50000i −0.500000 0.288675i
$$508$$ 0 0
$$509$$ −21.0000 36.3731i −0.930809 1.61221i −0.781943 0.623350i $$-0.785771\pi$$
−0.148866 0.988857i $$-0.547562\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −7.46410 + 4.92820i −0.328908 + 0.217163i
$$516$$ 0 0
$$517$$ 16.0000i 0.703679i
$$518$$ 0 0
$$519$$ 4.00000 0.175581
$$520$$ 0 0
$$521$$ −19.0000 + 32.9090i −0.832405 + 1.44177i 0.0637207 + 0.997968i $$0.479703\pi$$
−0.896126 + 0.443800i $$0.853630\pi$$
$$522$$ 0 0
$$523$$ −24.2487 + 14.0000i −1.06032 + 0.612177i −0.925521 0.378695i $$-0.876373\pi$$
−0.134801 + 0.990873i $$0.543039\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 13.8564 8.00000i 0.603595 0.348485i
$$528$$ 0 0
$$529$$ −3.50000 + 6.06218i −0.152174 + 0.263573i
$$530$$ 0 0
$$531$$ −4.00000 −0.173585
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 22.3923 14.7846i 0.968104 0.639194i
$$536$$ 0 0
$$537$$ −3.46410 + 2.00000i −0.149487 + 0.0863064i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 1.00000 + 1.73205i 0.0429934 + 0.0744667i 0.886721 0.462304i $$-0.152977\pi$$
−0.843728 + 0.536771i $$0.819644\pi$$
$$542$$ 0 0
$$543$$ −8.66025 5.00000i −0.371647 0.214571i
$$544$$ 0 0
$$545$$ −2.00000 + 4.00000i −0.0856706 + 0.171341i
$$546$$ 0 0
$$547$$ 28.0000i 1.19719i 0.801050 + 0.598597i $$0.204275\pi$$
−0.801050 + 0.598597i $$0.795725\pi$$
$$548$$ 0 0
$$549$$ −1.00000 + 1.73205i −0.0426790 + 0.0739221i
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 17.8564 1.07180i 0.757962 0.0454952i
$$556$$ 0 0
$$557$$ 10.3923 + 6.00000i 0.440336 + 0.254228i 0.703740 0.710457i $$-0.251512\pi$$
−0.263404 + 0.964686i $$0.584845\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −16.0000 −0.675521
$$562$$ 0 0
$$563$$ −17.3205 10.0000i −0.729972 0.421450i 0.0884397 0.996082i $$-0.471812\pi$$
−0.818412 + 0.574632i $$0.805145\pi$$
$$564$$ 0 0
$$565$$ −1.60770 26.7846i −0.0676362 1.12684i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 13.0000 + 22.5167i 0.544988 + 0.943948i 0.998608 + 0.0527519i $$0.0167993\pi$$
−0.453619 + 0.891196i $$0.649867\pi$$
$$570$$ 0 0
$$571$$ −20.0000 + 34.6410i −0.836974 + 1.44968i 0.0554391 + 0.998462i $$0.482344\pi$$
−0.892413 + 0.451219i $$0.850989\pi$$
$$572$$ 0 0
$$573$$ 24.0000i 1.00261i
$$574$$ 0 0
$$575$$ −16.0000 + 12.0000i −0.667246 + 0.500435i
$$576$$ 0 0
$$577$$ −27.7128 16.0000i −1.15370 0.666089i −0.203913 0.978989i $$-0.565366\pi$$
−0.949786 + 0.312900i $$0.898699\pi$$
$$578$$ 0 0
$$579$$ −8.00000 13.8564i −0.332469 0.575853i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −41.5692 + 24.0000i −1.72162 + 0.993978i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 36.0000i 1.48588i 0.669359 + 0.742940i $$0.266569\pi$$
−0.669359 + 0.742940i $$0.733431\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −2.00000 + 3.46410i −0.0822690 + 0.142494i
$$592$$ 0 0
$$593$$ −31.1769 + 18.0000i −1.28028 + 0.739171i −0.976900 0.213697i $$-0.931449\pi$$
−0.303383 + 0.952869i $$0.598116\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −10.3923 + 6.00000i −0.425329 + 0.245564i
$$598$$ 0 0
$$599$$ −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i $$-0.996449\pi$$
0.509631 + 0.860393i $$0.329782\pi$$
$$600$$ 0 0
$$601$$ −38.0000 −1.55005 −0.775026 0.631929i $$-0.782263\pi$$
−0.775026 + 0.631929i $$0.782263\pi$$
$$602$$ 0 0
$$603$$ 4.00000i 0.162893i
$$604$$ 0 0
$$605$$ −6.16025 9.33013i −0.250450 0.379324i
$$606$$ 0 0
$$607$$ 24.2487 14.0000i 0.984225 0.568242i 0.0806818 0.996740i $$-0.474290\pi$$
0.903543 + 0.428497i $$0.140957\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −6.92820 4.00000i −0.279827 0.161558i 0.353518 0.935428i $$-0.384985\pi$$
−0.633345 + 0.773869i $$0.718319\pi$$
$$614$$ 0 0
$$615$$ −20.0000 10.0000i −0.806478 0.403239i
$$616$$ 0 0
$$617$$ 44.0000i 1.77137i −0.464283 0.885687i $$-0.653688\pi$$
0.464283 0.885687i $$-0.346312\pi$$
$$618$$ 0 0
$$619$$ 8.00000 13.8564i 0.321547 0.556936i −0.659260 0.751915i $$-0.729130\pi$$
0.980807 + 0.194979i $$0.0624638\pi$$
$$620$$ 0 0
$$621$$ 2.00000 + 3.46410i 0.0802572 + 0.139010i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 24.2846 5.93782i 0.971384 0.237513i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −32.0000 −1.27592
$$630$$ 0 0
$$631$$ −28.0000 −1.11466 −0.557331 0.830290i $$-0.688175\pi$$
−0.557331 + 0.830290i $$0.688175\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0.535898 + 8.92820i 0.0212665 + 0.354305i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −7.00000 + 12.1244i −0.276483 + 0.478883i −0.970508 0.241068i $$-0.922502\pi$$
0.694025 + 0.719951i $$0.255836\pi$$
$$642$$ 0 0
$$643$$ 36.0000i 1.41970i 0.704352 + 0.709851i $$0.251238\pi$$
−0.704352 + 0.709851i $$0.748762\pi$$
$$644$$ 0 0
$$645$$ −4.00000 + 8.00000i −0.157500 + 0.315000i
$$646$$ 0 0
$$647$$ 10.3923 + 6.00000i 0.408564 + 0.235884i 0.690172 0.723645i $$-0.257535\pi$$
−0.281609 + 0.959529i $$0.590868\pi$$
$$648$$ 0 0
$$649$$ 8.00000 + 13.8564i 0.314027 + 0.543912i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −3.46410 + 2.00000i −0.135561 + 0.0782660i −0.566247 0.824236i $$-0.691605\pi$$
0.430686 + 0.902502i $$0.358272\pi$$
$$654$$ 0 0
$$655$$ 14.7846 + 22.3923i 0.577683 + 0.874940i
$$656$$ 0 0
$$657$$ 8.00000i 0.312110i
$$658$$ 0 0
$$659$$ −28.0000 −1.09073 −0.545363 0.838200i $$-0.683608\pi$$
−0.545363 + 0.838200i $$0.683608\pi$$
$$660$$ 0 0
$$661$$ −11.0000 + 19.0526i −0.427850 + 0.741059i −0.996682 0.0813955i $$-0.974062\pi$$
0.568831 + 0.822454i $$0.307396\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −20.7846 + 12.0000i −0.804783 + 0.464642i
$$668$$ 0 0
$$669$$ −10.0000 + 17.3205i −0.386622 + 0.669650i
$$670$$ 0 0
$$671$$ 8.00000 0.308837
$$672$$ 0 0
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ −0.598076 4.96410i −0.0230200 0.191068i
$$676$$ 0 0
$$677$$ −3.46410 + 2.00000i −0.133136 + 0.0768662i −0.565089 0.825030i $$-0.691158\pi$$
0.431953 + 0.901896i $$0.357825\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 10.0000 + 17.3205i 0.383201 + 0.663723i
$$682$$ 0 0
$$683$$ −38.1051 22.0000i −1.45805 0.841807i −0.459136 0.888366i $$-0.651841\pi$$
−0.998916 + 0.0465592i $$0.985174\pi$$
$$684$$ 0 0
$$685$$ −24.0000 12.0000i −0.916993 0.458496i
$$686$$ 0 0
$$687$$ 26.0000i 0.991962i
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ −16.0000 27.7128i −0.608669 1.05425i −0.991460 0.130410i $$-0.958371\pi$$
0.382791 0.923835i $$-0.374963\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 35.7128 2.14359i 1.35466 0.0813111i
$$696$$ 0 0
$$697$$ 34.6410 + 20.0000i 1.31212 + 0.757554i
$$698$$ 0 0
$$699$$ 20.0000 0.756469
$$700$$ 0 0
$$701$$ 26.0000 0.982006 0.491003 0.871158i $$-0.336630\pi$$
0.491003 + 0.871158i $$0.336630\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ −8.92820 + 0.535898i −0.336256 + 0.0201831i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −3.00000 5.19615i −0.112667 0.195146i 0.804178 0.594389i $$-0.202606\pi$$
−0.916845 + 0.399244i $$0.869273\pi$$
$$710$$ 0 0
$$711$$ 6.00000 10.3923i 0.225018 0.389742i
$$712$$ 0 0
$$713$$ 16.0000i 0.599205i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 6.92820 + 4.00000i 0.258738 + 0.149383i
$$718$$ 0 0
$$719$$ −4.00000 6.92820i −0.149175 0.258378i 0.781748 0.623595i $$-0.214328\pi$$
−0.930923 + 0.365216i $$0.880995\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 1.73205 1.00000i 0.0644157 0.0371904i
$$724$$ 0 0
$$725$$ 29.7846 3.58846i 1.10617 0.133272i
$$726$$ 0 0
$$727$$ 12.0000i 0.445055i 0.974926 + 0.222528i $$0.0714308\pi$$
−0.974926 + 0.222528i $$0.928569\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ 8.00000 13.8564i 0.295891 0.512498i
$$732$$ 0 0
$$733$$ −13.8564 + 8.00000i −0.511798 + 0.295487i −0.733572 0.679611i $$-0.762148\pi$$
0.221774 + 0.975098i $$0.428815\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 13.8564 8.00000i 0.510407 0.294684i
$$738$$ 0 0
$$739$$ 20.0000 34.6410i 0.735712 1.27429i −0.218698 0.975793i $$-0.570181\pi$$
0.954410 0.298498i $$-0.0964856\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 36.0000i 1.32071i −0.750953 0.660356i $$-0.770405\pi$$
0.750953 0.660356i $$-0.229595\pi$$
$$744$$ 0 0
$$745$$ −2.46410 3.73205i −0.0902777 0.136732i
$$746$$ 0 0
$$747$$ −3.46410 + 2.00000i −0.126745 + 0.0731762i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 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
$$753$$ −10.3923 6.00000i −0.378717 0.218652i
$$754$$ 0 0
$$755$$ 20.0000 40.0000i 0.727875 1.45575i
$$756$$ 0 0
$$757$$ 16.0000i 0.581530i 0.956795 + 0.290765i $$0.0939098\pi$$
−0.956795 + 0.290765i $$0.906090\pi$$
$$758$$ 0 0
$$759$$ 8.00000 13.8564i 0.290382 0.502956i
$$760$$ 0 0
$$761$$ 21.0000 + 36.3731i 0.761249 + 1.31852i 0.942207 + 0.335032i $$0.108747\pi$$
−0.180957 + 0.983491i $$0.557920\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0.535898 + 8.92820i 0.0193754 + 0.322800i
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −18.0000 −0.649097 −0.324548 0.945869i $$-0.605212\pi$$
−0.324548 + 0.945869i $$0.605212\pi$$
$$770$$ 0 0
$$771$$ 12.0000 0.432169
$$772$$ 0 0
$$773$$ 10.3923 + 6.00000i 0.373785 + 0.215805i 0.675111 0.737716i $$-0.264096\pi$$
−0.301326 + 0.953521i $$0.597429\pi$$
$$774$$ 0 0
$$775$$ 7.85641 18.3923i 0.282210 0.660671i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 6.00000i 0.214423i
$$784$$ 0 0
$$785$$ 16.0000 + 8.00000i 0.571064 + 0.285532i
$$786$$ 0 0
$$787$$ 24.2487 + 14.0000i 0.864373 + 0.499046i 0.865474 0.500953i $$-0.167017\pi$$
−0.00110111 + 0.999999i $$0.500350\pi$$
$$788$$ 0 0
$$789$$ −2.00000 3.46410i −0.0712019 0.123325i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 14.7846 + 22.3923i 0.524356 + 0.794173i
$$796$$ 0 0
$$797$$ 28.0000i 0.991811i −0.868377 0.495905i $$-0.834836\pi$$
0.868377 0.495905i $$-0.165164\pi$$
$$798$$ 0 0
$$799$$ 16.0000 0.566039
$$800$$ 0 0
$$801$$ −5.00000 + 8.66025i −0.176666 +