# Properties

 Label 3150.2.d.b.3149.2 Level 3150 Weight 2 Character 3150.3149 Analytic conductor 25.153 Analytic rank 0 Dimension 8 CM no Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ = $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 3150.d (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$25.1528766367$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.40960000.1 Coefficient ring: $$\Z[a_1, \ldots, a_{17}]$$ Coefficient ring index: $$2^{6}\cdot 5^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 3149.2 Root $$1.14412 - 1.14412i$$ Character $$\chi$$ = 3150.3149 Dual form 3150.2.d.b.3149.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.00000 q^{4} +(-2.23607 - 1.41421i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q-1.00000 q^{2} +1.00000 q^{4} +(-2.23607 - 1.41421i) q^{7} -1.00000 q^{8} -1.41421i q^{11} +0.926210 q^{13} +(2.23607 + 1.41421i) q^{14} +1.00000 q^{16} -2.23607i q^{17} +7.63441i q^{19} +1.41421i q^{22} -1.00000 q^{23} -0.926210 q^{26} +(-2.23607 - 1.41421i) q^{28} +0.757359i q^{29} +4.08849i q^{31} -1.00000 q^{32} +2.23607i q^{34} +2.82843i q^{37} -7.63441i q^{38} +8.56062 q^{41} -3.58579i q^{43} -1.41421i q^{44} +1.00000 q^{46} +1.30986i q^{47} +(3.00000 + 6.32456i) q^{49} +0.926210 q^{52} -8.07107 q^{53} +(2.23607 + 1.41421i) q^{56} -0.757359i q^{58} -7.25077 q^{59} +0.926210i q^{61} -4.08849i q^{62} +1.00000 q^{64} -2.23607i q^{68} -15.6569i q^{71} +13.9590 q^{73} -2.82843i q^{74} +7.63441i q^{76} +(-2.00000 + 3.16228i) q^{77} +13.0711 q^{79} -8.56062 q^{82} -14.3426i q^{83} +3.58579i q^{86} +1.41421i q^{88} +2.61972 q^{89} +(-2.07107 - 1.30986i) q^{91} -1.00000 q^{92} -1.30986i q^{94} -0.542561 q^{97} +(-3.00000 - 6.32456i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 8q^{2} + 8q^{4} - 8q^{8} + O(q^{10})$$ $$8q - 8q^{2} + 8q^{4} - 8q^{8} + 8q^{16} - 8q^{23} - 8q^{32} + 8q^{46} + 24q^{49} - 8q^{53} + 8q^{64} - 16q^{77} + 48q^{79} + 40q^{91} - 8q^{92} - 24q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$2801$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 0 0
$$4$$ 1.00000 0.500000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −2.23607 1.41421i −0.845154 0.534522i
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.41421i 0.426401i −0.977008 0.213201i $$-0.931611\pi$$
0.977008 0.213201i $$-0.0683888\pi$$
$$12$$ 0 0
$$13$$ 0.926210 0.256884 0.128442 0.991717i $$-0.459002\pi$$
0.128442 + 0.991717i $$0.459002\pi$$
$$14$$ 2.23607 + 1.41421i 0.597614 + 0.377964i
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 2.23607i 0.542326i −0.962533 0.271163i $$-0.912592\pi$$
0.962533 0.271163i $$-0.0874083\pi$$
$$18$$ 0 0
$$19$$ 7.63441i 1.75145i 0.482806 + 0.875727i $$0.339618\pi$$
−0.482806 + 0.875727i $$0.660382\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.41421i 0.301511i
$$23$$ −1.00000 −0.208514 −0.104257 0.994550i $$-0.533247\pi$$
−0.104257 + 0.994550i $$0.533247\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ −0.926210 −0.181645
$$27$$ 0 0
$$28$$ −2.23607 1.41421i −0.422577 0.267261i
$$29$$ 0.757359i 0.140638i 0.997525 + 0.0703190i $$0.0224017\pi$$
−0.997525 + 0.0703190i $$0.977598\pi$$
$$30$$ 0 0
$$31$$ 4.08849i 0.734314i 0.930159 + 0.367157i $$0.119669\pi$$
−0.930159 + 0.367157i $$0.880331\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ 2.23607i 0.383482i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.82843i 0.464991i 0.972598 + 0.232495i $$0.0746890\pi$$
−0.972598 + 0.232495i $$0.925311\pi$$
$$38$$ 7.63441i 1.23847i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 8.56062 1.33694 0.668472 0.743737i $$-0.266948\pi$$
0.668472 + 0.743737i $$0.266948\pi$$
$$42$$ 0 0
$$43$$ 3.58579i 0.546827i −0.961897 0.273414i $$-0.911847\pi$$
0.961897 0.273414i $$-0.0881528\pi$$
$$44$$ 1.41421i 0.213201i
$$45$$ 0 0
$$46$$ 1.00000 0.147442
$$47$$ 1.30986i 0.191062i 0.995426 + 0.0955312i $$0.0304550\pi$$
−0.995426 + 0.0955312i $$0.969545\pi$$
$$48$$ 0 0
$$49$$ 3.00000 + 6.32456i 0.428571 + 0.903508i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0.926210 0.128442
$$53$$ −8.07107 −1.10865 −0.554323 0.832301i $$-0.687023\pi$$
−0.554323 + 0.832301i $$0.687023\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 2.23607 + 1.41421i 0.298807 + 0.188982i
$$57$$ 0 0
$$58$$ 0.757359i 0.0994461i
$$59$$ −7.25077 −0.943969 −0.471985 0.881607i $$-0.656462\pi$$
−0.471985 + 0.881607i $$0.656462\pi$$
$$60$$ 0 0
$$61$$ 0.926210i 0.118589i 0.998241 + 0.0592945i $$0.0188851\pi$$
−0.998241 + 0.0592945i $$0.981115\pi$$
$$62$$ 4.08849i 0.519238i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ 2.23607i 0.271163i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 15.6569i 1.85813i −0.369921 0.929063i $$-0.620615\pi$$
0.369921 0.929063i $$-0.379385\pi$$
$$72$$ 0 0
$$73$$ 13.9590 1.63377 0.816887 0.576798i $$-0.195698\pi$$
0.816887 + 0.576798i $$0.195698\pi$$
$$74$$ 2.82843i 0.328798i
$$75$$ 0 0
$$76$$ 7.63441i 0.875727i
$$77$$ −2.00000 + 3.16228i −0.227921 + 0.360375i
$$78$$ 0 0
$$79$$ 13.0711 1.47061 0.735305 0.677736i $$-0.237039\pi$$
0.735305 + 0.677736i $$0.237039\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ −8.56062 −0.945363
$$83$$ 14.3426i 1.57431i −0.616757 0.787153i $$-0.711554\pi$$
0.616757 0.787153i $$-0.288446\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 3.58579i 0.386665i
$$87$$ 0 0
$$88$$ 1.41421i 0.150756i
$$89$$ 2.61972 0.277689 0.138845 0.990314i $$-0.455661\pi$$
0.138845 + 0.990314i $$0.455661\pi$$
$$90$$ 0 0
$$91$$ −2.07107 1.30986i −0.217107 0.137310i
$$92$$ −1.00000 −0.104257
$$93$$ 0 0
$$94$$ 1.30986i 0.135102i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −0.542561 −0.0550887 −0.0275444 0.999621i $$-0.508769\pi$$
−0.0275444 + 0.999621i $$0.508769\pi$$
$$98$$ −3.00000 6.32456i −0.303046 0.638877i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 12.1065 1.20465 0.602323 0.798252i $$-0.294242\pi$$
0.602323 + 0.798252i $$0.294242\pi$$
$$102$$ 0 0
$$103$$ 10.4130 1.02603 0.513014 0.858380i $$-0.328529\pi$$
0.513014 + 0.858380i $$0.328529\pi$$
$$104$$ −0.926210 −0.0908223
$$105$$ 0 0
$$106$$ 8.07107 0.783931
$$107$$ 2.00000 0.193347 0.0966736 0.995316i $$-0.469180\pi$$
0.0966736 + 0.995316i $$0.469180\pi$$
$$108$$ 0 0
$$109$$ 7.07107 0.677285 0.338643 0.940915i $$-0.390032\pi$$
0.338643 + 0.940915i $$0.390032\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −2.23607 1.41421i −0.211289 0.133631i
$$113$$ −1.07107 −0.100758 −0.0503788 0.998730i $$-0.516043\pi$$
−0.0503788 + 0.998730i $$0.516043\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0.757359i 0.0703190i
$$117$$ 0 0
$$118$$ 7.25077 0.667487
$$119$$ −3.16228 + 5.00000i −0.289886 + 0.458349i
$$120$$ 0 0
$$121$$ 9.00000 0.818182
$$122$$ 0.926210i 0.0838551i
$$123$$ 0 0
$$124$$ 4.08849i 0.367157i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 10.0000i 0.887357i 0.896186 + 0.443678i $$0.146327\pi$$
−0.896186 + 0.443678i $$0.853673\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 12.6491 1.10516 0.552579 0.833461i $$-0.313644\pi$$
0.552579 + 0.833461i $$0.313644\pi$$
$$132$$ 0 0
$$133$$ 10.7967 17.0711i 0.936192 1.48025i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 2.23607i 0.191741i
$$137$$ 12.1421 1.03737 0.518686 0.854965i $$-0.326421\pi$$
0.518686 + 0.854965i $$0.326421\pi$$
$$138$$ 0 0
$$139$$ 10.7967i 0.915763i 0.889013 + 0.457882i $$0.151392\pi$$
−0.889013 + 0.457882i $$0.848608\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 15.6569i 1.31389i
$$143$$ 1.30986i 0.109536i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −13.9590 −1.15525
$$147$$ 0 0
$$148$$ 2.82843i 0.232495i
$$149$$ 0.757359i 0.0620453i −0.999519 0.0310226i $$-0.990124\pi$$
0.999519 0.0310226i $$-0.00987640\pi$$
$$150$$ 0 0
$$151$$ −14.1421 −1.15087 −0.575435 0.817847i $$-0.695167\pi$$
−0.575435 + 0.817847i $$0.695167\pi$$
$$152$$ 7.63441i 0.619233i
$$153$$ 0 0
$$154$$ 2.00000 3.16228i 0.161165 0.254824i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −10.7967 −0.861670 −0.430835 0.902431i $$-0.641781\pi$$
−0.430835 + 0.902431i $$0.641781\pi$$
$$158$$ −13.0711 −1.03988
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 2.23607 + 1.41421i 0.176227 + 0.111456i
$$162$$ 0 0
$$163$$ 7.92893i 0.621042i −0.950567 0.310521i $$-0.899497\pi$$
0.950567 0.310521i $$-0.100503\pi$$
$$164$$ 8.56062 0.668472
$$165$$ 0 0
$$166$$ 14.3426i 1.11320i
$$167$$ 12.1065i 0.936833i 0.883508 + 0.468416i $$0.155175\pi$$
−0.883508 + 0.468416i $$0.844825\pi$$
$$168$$ 0 0
$$169$$ −12.1421 −0.934010
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 3.58579i 0.273414i
$$173$$ 10.2541i 0.779607i −0.920898 0.389804i $$-0.872543\pi$$
0.920898 0.389804i $$-0.127457\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 1.41421i 0.106600i
$$177$$ 0 0
$$178$$ −2.61972 −0.196356
$$179$$ 11.3137i 0.845626i −0.906217 0.422813i $$-0.861043\pi$$
0.906217 0.422813i $$-0.138957\pi$$
$$180$$ 0 0
$$181$$ 2.61972i 0.194722i −0.995249 0.0973610i $$-0.968960\pi$$
0.995249 0.0973610i $$-0.0310401\pi$$
$$182$$ 2.07107 + 1.30986i 0.153518 + 0.0970932i
$$183$$ 0 0
$$184$$ 1.00000 0.0737210
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −3.16228 −0.231249
$$188$$ 1.30986i 0.0955312i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0.656854i 0.0475283i 0.999718 + 0.0237642i $$0.00756508\pi$$
−0.999718 + 0.0237642i $$0.992435\pi$$
$$192$$ 0 0
$$193$$ 8.48528i 0.610784i −0.952227 0.305392i $$-0.901213\pi$$
0.952227 0.305392i $$-0.0987875\pi$$
$$194$$ 0.542561 0.0389536
$$195$$ 0 0
$$196$$ 3.00000 + 6.32456i 0.214286 + 0.451754i
$$197$$ 5.92893 0.422419 0.211209 0.977441i $$-0.432260\pi$$
0.211209 + 0.977441i $$0.432260\pi$$
$$198$$ 0 0
$$199$$ 21.5934i 1.53071i 0.643606 + 0.765357i $$0.277438\pi$$
−0.643606 + 0.765357i $$0.722562\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −12.1065 −0.851814
$$203$$ 1.07107 1.69351i 0.0751742 0.118861i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −10.4130 −0.725511
$$207$$ 0 0
$$208$$ 0.926210 0.0642211
$$209$$ 10.7967 0.746823
$$210$$ 0 0
$$211$$ 16.2132 1.11616 0.558081 0.829786i $$-0.311538\pi$$
0.558081 + 0.829786i $$0.311538\pi$$
$$212$$ −8.07107 −0.554323
$$213$$ 0 0
$$214$$ −2.00000 −0.136717
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 5.78199 9.14214i 0.392507 0.620609i
$$218$$ −7.07107 −0.478913
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 2.07107i 0.139315i
$$222$$ 0 0
$$223$$ 13.0328 0.872738 0.436369 0.899768i $$-0.356264\pi$$
0.436369 + 0.899768i $$0.356264\pi$$
$$224$$ 2.23607 + 1.41421i 0.149404 + 0.0944911i
$$225$$ 0 0
$$226$$ 1.07107 0.0712464
$$227$$ 25.1393i 1.66855i 0.551345 + 0.834277i $$0.314115\pi$$
−0.551345 + 0.834277i $$0.685885\pi$$
$$228$$ 0 0
$$229$$ 10.7967i 0.713465i −0.934206 0.356733i $$-0.883891\pi$$
0.934206 0.356733i $$-0.116109\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0.757359i 0.0497231i
$$233$$ 23.0711 1.51144 0.755718 0.654897i $$-0.227288\pi$$
0.755718 + 0.654897i $$0.227288\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −7.25077 −0.471985
$$237$$ 0 0
$$238$$ 3.16228 5.00000i 0.204980 0.324102i
$$239$$ 7.17157i 0.463890i 0.972729 + 0.231945i $$0.0745090\pi$$
−0.972729 + 0.231945i $$0.925491\pi$$
$$240$$ 0 0
$$241$$ 4.47214i 0.288076i −0.989572 0.144038i $$-0.953991\pi$$
0.989572 0.144038i $$-0.0460087\pi$$
$$242$$ −9.00000 −0.578542
$$243$$ 0 0
$$244$$ 0.926210i 0.0592945i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 7.07107i 0.449921i
$$248$$ 4.08849i 0.259619i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 18.8148 1.18758 0.593788 0.804621i $$-0.297632\pi$$
0.593788 + 0.804621i $$0.297632\pi$$
$$252$$ 0 0
$$253$$ 1.41421i 0.0889108i
$$254$$ 10.0000i 0.627456i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 21.2097i 1.32303i 0.749933 + 0.661513i $$0.230086\pi$$
−0.749933 + 0.661513i $$0.769914\pi$$
$$258$$ 0 0
$$259$$ 4.00000 6.32456i 0.248548 0.392989i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −12.6491 −0.781465
$$263$$ −29.2843 −1.80575 −0.902873 0.429908i $$-0.858546\pi$$
−0.902873 + 0.429908i $$0.858546\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −10.7967 + 17.0711i −0.661988 + 1.04669i
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 27.9179 1.70219 0.851093 0.525014i $$-0.175940\pi$$
0.851093 + 0.525014i $$0.175940\pi$$
$$270$$ 0 0
$$271$$ 7.09185i 0.430799i −0.976526 0.215400i $$-0.930895\pi$$
0.976526 0.215400i $$-0.0691054\pi$$
$$272$$ 2.23607i 0.135582i
$$273$$ 0 0
$$274$$ −12.1421 −0.733533
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 21.2132i 1.27458i −0.770625 0.637289i $$-0.780056\pi$$
0.770625 0.637289i $$-0.219944\pi$$
$$278$$ 10.7967i 0.647543i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 28.4853i 1.69929i −0.527356 0.849645i $$-0.676816\pi$$
0.527356 0.849645i $$-0.323184\pi$$
$$282$$ 0 0
$$283$$ −7.63441 −0.453819 −0.226909 0.973916i $$-0.572862\pi$$
−0.226909 + 0.973916i $$0.572862\pi$$
$$284$$ 15.6569i 0.929063i
$$285$$ 0 0
$$286$$ 1.30986i 0.0774535i
$$287$$ −19.1421 12.1065i −1.12992 0.714627i
$$288$$ 0 0
$$289$$ 12.0000 0.705882
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 13.9590 0.816887
$$293$$ 25.2982i 1.47794i 0.673740 + 0.738969i $$0.264687\pi$$
−0.673740 + 0.738969i $$0.735313\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 2.82843i 0.164399i
$$297$$ 0 0
$$298$$ 0.757359i 0.0438726i
$$299$$ −0.926210 −0.0535641
$$300$$ 0 0
$$301$$ −5.07107 + 8.01806i −0.292291 + 0.462153i
$$302$$ 14.1421 0.813788
$$303$$ 0 0
$$304$$ 7.63441i 0.437864i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 3.70484 0.211446 0.105723 0.994396i $$-0.466284\pi$$
0.105723 + 0.994396i $$0.466284\pi$$
$$308$$ −2.00000 + 3.16228i −0.113961 + 0.180187i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −5.23943 −0.297101 −0.148550 0.988905i $$-0.547461\pi$$
−0.148550 + 0.988905i $$0.547461\pi$$
$$312$$ 0 0
$$313$$ 16.5787 0.937083 0.468541 0.883442i $$-0.344780\pi$$
0.468541 + 0.883442i $$0.344780\pi$$
$$314$$ 10.7967 0.609293
$$315$$ 0 0
$$316$$ 13.0711 0.735305
$$317$$ 30.0711 1.68896 0.844480 0.535588i $$-0.179910\pi$$
0.844480 + 0.535588i $$0.179910\pi$$
$$318$$ 0 0
$$319$$ 1.07107 0.0599683
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −2.23607 1.41421i −0.124611 0.0788110i
$$323$$ 17.0711 0.949860
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 7.92893i 0.439143i
$$327$$ 0 0
$$328$$ −8.56062 −0.472681
$$329$$ 1.85242 2.92893i 0.102127 0.161477i
$$330$$ 0 0
$$331$$ 7.92893 0.435814 0.217907 0.975970i $$-0.430077\pi$$
0.217907 + 0.975970i $$0.430077\pi$$
$$332$$ 14.3426i 0.787153i
$$333$$ 0 0
$$334$$ 12.1065i 0.662441i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 11.9706i 0.652078i 0.945356 + 0.326039i $$0.105714\pi$$
−0.945356 + 0.326039i $$0.894286\pi$$
$$338$$ 12.1421 0.660445
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 5.78199 0.313113
$$342$$ 0 0
$$343$$ 2.23607 18.3848i 0.120736 0.992685i
$$344$$ 3.58579i 0.193333i
$$345$$ 0 0
$$346$$ 10.2541i 0.551265i
$$347$$ 9.07107 0.486960 0.243480 0.969906i $$-0.421711\pi$$
0.243480 + 0.969906i $$0.421711\pi$$
$$348$$ 0 0
$$349$$ 6.16564i 0.330039i −0.986290 0.165020i $$-0.947231\pi$$
0.986290 0.165020i $$-0.0527688\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 1.41421i 0.0753778i
$$353$$ 18.9737i 1.00987i 0.863158 + 0.504933i $$0.168483\pi$$
−0.863158 + 0.504933i $$0.831517\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 2.61972 0.138845
$$357$$ 0 0
$$358$$ 11.3137i 0.597948i
$$359$$ 16.3137i 0.861005i 0.902589 + 0.430502i $$0.141664\pi$$
−0.902589 + 0.430502i $$0.858336\pi$$
$$360$$ 0 0
$$361$$ −39.2843 −2.06759
$$362$$ 2.61972i 0.137689i
$$363$$ 0 0
$$364$$ −2.07107 1.30986i −0.108553 0.0686552i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 24.5967 1.28394 0.641970 0.766730i $$-0.278117\pi$$
0.641970 + 0.766730i $$0.278117\pi$$
$$368$$ −1.00000 −0.0521286
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 18.0475 + 11.4142i 0.936977 + 0.592596i
$$372$$ 0 0
$$373$$ 7.07107i 0.366126i 0.983101 + 0.183063i $$0.0586012\pi$$
−0.983101 + 0.183063i $$0.941399\pi$$
$$374$$ 3.16228 0.163517
$$375$$ 0 0
$$376$$ 1.30986i 0.0675508i
$$377$$ 0.701474i 0.0361277i
$$378$$ 0 0
$$379$$ −22.0711 −1.13371 −0.566857 0.823816i $$-0.691841\pi$$
−0.566857 + 0.823816i $$0.691841\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0.656854i 0.0336076i
$$383$$ 16.0361i 0.819408i 0.912219 + 0.409704i $$0.134368\pi$$
−0.912219 + 0.409704i $$0.865632\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 8.48528i 0.431889i
$$387$$ 0 0
$$388$$ −0.542561 −0.0275444
$$389$$ 22.8284i 1.15745i −0.815524 0.578724i $$-0.803551\pi$$
0.815524 0.578724i $$-0.196449\pi$$
$$390$$ 0 0
$$391$$ 2.23607i 0.113083i
$$392$$ −3.00000 6.32456i −0.151523 0.319438i
$$393$$ 0 0
$$394$$ −5.92893 −0.298695
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 29.6114 1.48616 0.743078 0.669205i $$-0.233365\pi$$
0.743078 + 0.669205i $$0.233365\pi$$
$$398$$ 21.5934i 1.08238i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 9.79899i 0.489338i 0.969607 + 0.244669i $$0.0786793\pi$$
−0.969607 + 0.244669i $$0.921321\pi$$
$$402$$ 0 0
$$403$$ 3.78680i 0.188634i
$$404$$ 12.1065 0.602323
$$405$$ 0 0
$$406$$ −1.07107 + 1.69351i −0.0531562 + 0.0840473i
$$407$$ 4.00000 0.198273
$$408$$ 0 0
$$409$$ 22.9032i 1.13249i −0.824236 0.566246i $$-0.808395\pi$$
0.824236 0.566246i $$-0.191605\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 10.4130 0.513014
$$413$$ 16.2132 + 10.2541i 0.797800 + 0.504573i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −0.926210 −0.0454112
$$417$$ 0 0
$$418$$ −10.7967 −0.528083
$$419$$ −28.8441 −1.40913 −0.704564 0.709640i $$-0.748858\pi$$
−0.704564 + 0.709640i $$0.748858\pi$$
$$420$$ 0 0
$$421$$ 33.3553 1.62564 0.812820 0.582515i $$-0.197931\pi$$
0.812820 + 0.582515i $$0.197931\pi$$
$$422$$ −16.2132 −0.789246
$$423$$ 0 0
$$424$$ 8.07107 0.391966
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 1.30986 2.07107i 0.0633885 0.100226i
$$428$$ 2.00000 0.0966736
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 4.79899i 0.231159i −0.993298 0.115580i $$-0.963127\pi$$
0.993298 0.115580i $$-0.0368725\pi$$
$$432$$ 0 0
$$433$$ 9.71157 0.466708 0.233354 0.972392i $$-0.425030\pi$$
0.233354 + 0.972392i $$0.425030\pi$$
$$434$$ −5.78199 + 9.14214i −0.277545 + 0.438837i
$$435$$ 0 0
$$436$$ 7.07107 0.338643
$$437$$ 7.63441i 0.365204i
$$438$$ 0 0
$$439$$ 4.08849i 0.195133i 0.995229 + 0.0975664i $$0.0311058\pi$$
−0.995229 + 0.0975664i $$0.968894\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 2.07107i 0.0985106i
$$443$$ 23.0711 1.09614 0.548070 0.836433i $$-0.315363\pi$$
0.548070 + 0.836433i $$0.315363\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −13.0328 −0.617119
$$447$$ 0 0
$$448$$ −2.23607 1.41421i −0.105644 0.0668153i
$$449$$ 18.3848i 0.867631i −0.901002 0.433816i $$-0.857167\pi$$
0.901002 0.433816i $$-0.142833\pi$$
$$450$$ 0 0
$$451$$ 12.1065i 0.570075i
$$452$$ −1.07107 −0.0503788
$$453$$ 0 0
$$454$$ 25.1393i 1.17985i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 17.8284i 0.833979i −0.908911 0.416989i $$-0.863085\pi$$
0.908911 0.416989i $$-0.136915\pi$$
$$458$$ 10.7967i 0.504496i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −38.9394 −1.81359 −0.906794 0.421575i $$-0.861477\pi$$
−0.906794 + 0.421575i $$0.861477\pi$$
$$462$$ 0 0
$$463$$ 38.2843i 1.77922i 0.456720 + 0.889610i $$0.349024\pi$$
−0.456720 + 0.889610i $$0.650976\pi$$
$$464$$ 0.757359i 0.0351595i
$$465$$ 0 0
$$466$$ −23.0711 −1.06875
$$467$$ 29.6114i 1.37025i −0.728424 0.685127i $$-0.759747\pi$$
0.728424 0.685127i $$-0.240253\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 7.25077 0.333744
$$473$$ −5.07107 −0.233168
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −3.16228 + 5.00000i −0.144943 + 0.229175i
$$477$$ 0 0
$$478$$ 7.17157i 0.328020i
$$479$$ −33.6999 −1.53979 −0.769895 0.638171i $$-0.779691\pi$$
−0.769895 + 0.638171i $$0.779691\pi$$
$$480$$ 0 0
$$481$$ 2.61972i 0.119449i
$$482$$ 4.47214i 0.203700i
$$483$$ 0 0
$$484$$ 9.00000 0.409091
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 29.8995i 1.35488i −0.735580 0.677438i $$-0.763090\pi$$
0.735580 0.677438i $$-0.236910\pi$$
$$488$$ 0.926210i 0.0419275i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 21.5147i 0.970946i −0.874252 0.485473i $$-0.838647\pi$$
0.874252 0.485473i $$-0.161353\pi$$
$$492$$ 0 0
$$493$$ 1.69351 0.0762717
$$494$$ 7.07107i 0.318142i
$$495$$ 0 0
$$496$$ 4.08849i 0.183579i
$$497$$ −22.1421 + 35.0098i −0.993211 + 1.57040i
$$498$$ 0 0
$$499$$ 22.0711 0.988037 0.494018 0.869451i $$-0.335528\pi$$
0.494018 + 0.869451i $$0.335528\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −18.8148 −0.839744
$$503$$ 21.8181i 0.972822i 0.873730 + 0.486411i $$0.161694\pi$$
−0.873730 + 0.486411i $$0.838306\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 1.41421i 0.0628695i
$$507$$ 0 0
$$508$$ 10.0000i 0.443678i
$$509$$ −0.224736 −0.00996125 −0.00498063 0.999988i $$-0.501585\pi$$
−0.00498063 + 0.999988i $$0.501585\pi$$
$$510$$ 0 0
$$511$$ −31.2132 19.7410i −1.38079 0.873289i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ 21.2097i 0.935521i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 1.85242 0.0814693
$$518$$ −4.00000 + 6.32456i −0.175750 + 0.277885i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 17.5049 0.766903 0.383452 0.923561i $$-0.374735\pi$$
0.383452 + 0.923561i $$0.374735\pi$$
$$522$$ 0 0
$$523$$ −28.4605 −1.24449 −0.622245 0.782822i $$-0.713779\pi$$
−0.622245 + 0.782822i $$0.713779\pi$$
$$524$$ 12.6491 0.552579
$$525$$ 0 0
$$526$$ 29.2843 1.27685
$$527$$ 9.14214 0.398238
$$528$$ 0 0
$$529$$ −22.0000 −0.956522
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 10.7967 17.0711i 0.468096 0.740125i
$$533$$ 7.92893 0.343440
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ −27.9179 −1.20363
$$539$$ 8.94427 4.24264i 0.385257 0.182743i
$$540$$ 0 0
$$541$$ 5.07107 0.218022 0.109011 0.994041i $$-0.465232\pi$$
0.109011 + 0.994041i $$0.465232\pi$$
$$542$$ 7.09185i 0.304621i
$$543$$ 0 0
$$544$$ 2.23607i 0.0958706i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 16.2132i 0.693227i 0.938008 + 0.346613i $$0.112668\pi$$
−0.938008 + 0.346613i $$0.887332\pi$$
$$548$$ 12.1421 0.518686
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −5.78199 −0.246321
$$552$$ 0 0
$$553$$ −29.2278 18.4853i −1.24289 0.786074i
$$554$$ 21.2132i 0.901263i
$$555$$ 0 0
$$556$$ 10.7967i 0.457882i
$$557$$ −26.1421 −1.10768 −0.553839 0.832624i $$-0.686838\pi$$
−0.553839 + 0.832624i $$0.686838\pi$$
$$558$$ 0 0
$$559$$ 3.32119i 0.140471i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 28.4853i 1.20158i
$$563$$ 24.3720i 1.02716i −0.858042 0.513579i $$-0.828319\pi$$
0.858042 0.513579i $$-0.171681\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 7.63441 0.320898
$$567$$ 0 0
$$568$$ 15.6569i 0.656947i
$$569$$ 22.5269i 0.944377i 0.881498 + 0.472189i $$0.156536\pi$$
−0.881498 + 0.472189i $$0.843464\pi$$
$$570$$ 0 0
$$571$$ −38.2132 −1.59917 −0.799586 0.600551i $$-0.794948\pi$$
−0.799586 + 0.600551i $$0.794948\pi$$
$$572$$ 1.30986i 0.0547679i
$$573$$ 0 0
$$574$$ 19.1421 + 12.1065i 0.798977 + 0.505318i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 23.4458 0.976062 0.488031 0.872826i $$-0.337715\pi$$
0.488031 + 0.872826i $$0.337715\pi$$
$$578$$ −12.0000 −0.499134
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −20.2835 + 32.0711i −0.841502 + 1.33053i
$$582$$ 0 0
$$583$$ 11.4142i 0.472728i
$$584$$ −13.9590 −0.577626
$$585$$ 0 0
$$586$$ 25.2982i 1.04506i
$$587$$ 15.4277i 0.636771i −0.947961 0.318385i $$-0.896859\pi$$
0.947961 0.318385i $$-0.103141\pi$$
$$588$$ 0 0
$$589$$ −31.2132 −1.28612
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 2.82843i 0.116248i
$$593$$ 46.8916i 1.92561i 0.270202 + 0.962804i $$0.412910\pi$$
−0.270202 + 0.962804i $$0.587090\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0.757359i 0.0310226i
$$597$$ 0 0
$$598$$ 0.926210 0.0378755
$$599$$ 3.68629i 0.150618i 0.997160 + 0.0753089i $$0.0239943\pi$$
−0.997160 + 0.0753089i $$0.976006\pi$$
$$600$$ 0 0
$$601$$ 12.1065i 0.493836i −0.969036 0.246918i $$-0.920582\pi$$
0.969036 0.246918i $$-0.0794179\pi$$
$$602$$ 5.07107 8.01806i 0.206681 0.326792i
$$603$$ 0 0
$$604$$ −14.1421 −0.575435
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −43.9541 −1.78404 −0.892020 0.451996i $$-0.850712\pi$$
−0.892020 + 0.451996i $$0.850712\pi$$
$$608$$ 7.63441i 0.309616i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 1.21320i 0.0490810i
$$612$$ 0 0
$$613$$ 15.8579i 0.640493i 0.947334 + 0.320247i $$0.103766\pi$$
−0.947334 + 0.320247i $$0.896234\pi$$
$$614$$ −3.70484 −0.149515
$$615$$ 0 0
$$616$$ 2.00000 3.16228i 0.0805823 0.127412i
$$617$$ 32.0000 1.28827 0.644136 0.764911i $$-0.277217\pi$$
0.644136 + 0.764911i $$0.277217\pi$$
$$618$$ 0 0
$$619$$ 18.2064i 0.731776i −0.930659 0.365888i $$-0.880765\pi$$
0.930659 0.365888i $$-0.119235\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 5.23943 0.210082
$$623$$ −5.85786 3.70484i −0.234690 0.148431i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ −16.5787 −0.662618
$$627$$ 0 0
$$628$$ −10.7967 −0.430835
$$629$$ 6.32456 0.252177
$$630$$ 0 0
$$631$$ 10.2843 0.409410 0.204705 0.978824i $$-0.434376\pi$$
0.204705 + 0.978824i $$0.434376\pi$$
$$632$$ −13.0711 −0.519939
$$633$$ 0 0
$$634$$ −30.0711 −1.19427
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 2.77863 + 5.85786i 0.110093 + 0.232097i
$$638$$ −1.07107 −0.0424040
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 28.4853i 1.12510i 0.826763 + 0.562550i $$0.190180\pi$$
−0.826763 + 0.562550i $$0.809820\pi$$
$$642$$ 0 0
$$643$$ −29.9951 −1.18289 −0.591446 0.806345i $$-0.701443\pi$$
−0.591446 + 0.806345i $$0.701443\pi$$
$$644$$ 2.23607 + 1.41421i 0.0881134 + 0.0557278i
$$645$$ 0 0
$$646$$ −17.0711 −0.671652
$$647$$ 37.0869i 1.45804i −0.684493 0.729019i $$-0.739977\pi$$
0.684493 0.729019i $$-0.260023\pi$$
$$648$$ 0 0
$$649$$ 10.2541i 0.402510i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 7.92893i 0.310521i
$$653$$ 8.14214 0.318626 0.159313 0.987228i $$-0.449072\pi$$
0.159313 + 0.987228i $$0.449072\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 8.56062 0.334236
$$657$$ 0 0
$$658$$ −1.85242 + 2.92893i −0.0722148 + 0.114182i
$$659$$ 48.3848i 1.88480i 0.334483 + 0.942402i $$0.391438\pi$$
−0.334483 + 0.942402i $$0.608562\pi$$
$$660$$ 0 0
$$661$$ 18.2064i 0.708146i −0.935218 0.354073i $$-0.884796\pi$$
0.935218 0.354073i $$-0.115204\pi$$
$$662$$ −7.92893 −0.308167
$$663$$ 0 0
$$664$$ 14.3426i 0.556602i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0.757359i 0.0293251i
$$668$$ 12.1065i 0.468416i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 1.30986 0.0505665
$$672$$ 0 0
$$673$$ 34.7990i 1.34140i 0.741728 + 0.670701i $$0.234007\pi$$
−0.741728 + 0.670701i $$0.765993\pi$$
$$674$$ 11.9706i 0.461089i
$$675$$ 0 0
$$676$$ −12.1421 −0.467005
$$677$$ 22.9032i 0.880243i 0.897938 + 0.440122i $$0.145065\pi$$
−0.897938 + 0.440122i $$0.854935\pi$$
$$678$$ 0 0
$$679$$ 1.21320 + 0.767297i 0.0465585 + 0.0294462i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −5.78199 −0.221404
$$683$$ −36.0000 −1.37750 −0.688751 0.724998i $$-0.741841\pi$$
−0.688751 + 0.724998i $$0.741841\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −2.23607 + 18.3848i −0.0853735 + 0.701934i
$$687$$ 0 0
$$688$$ 3.58579i 0.136707i
$$689$$ −7.47550 −0.284794
$$690$$ 0 0
$$691$$ 23.9884i 0.912560i −0.889836 0.456280i $$-0.849181\pi$$
0.889836 0.456280i $$-0.150819\pi$$
$$692$$ 10.2541i 0.389804i
$$693$$ 0 0
$$694$$ −9.07107 −0.344333
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 19.1421i 0.725060i
$$698$$ 6.16564i 0.233373i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 41.8701i 1.58141i −0.612197 0.790705i $$-0.709714\pi$$
0.612197 0.790705i $$-0.290286\pi$$
$$702$$ 0 0
$$703$$ −21.5934 −0.814410
$$704$$ 1.41421i 0.0533002i
$$705$$ 0 0
$$706$$ 18.9737i 0.714083i
$$707$$ −27.0711 17.1212i −1.01811 0.643911i
$$708$$ 0 0
$$709$$ −24.1421 −0.906677 −0.453338 0.891338i $$-0.649767\pi$$
−0.453338 + 0.891338i $$0.649767\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −2.61972 −0.0981780
$$713$$ 4.08849i 0.153115i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 11.3137i 0.422813i
$$717$$ 0 0
$$718$$ 16.3137i 0.608822i
$$719$$ −23.9884 −0.894615 −0.447307 0.894380i $$-0.647617\pi$$
−0.447307 + 0.894380i $$0.647617\pi$$
$$720$$ 0 0
$$721$$ −23.2843 14.7263i −0.867152 0.548435i
$$722$$ 39.2843 1.46201
$$723$$ 0 0
$$724$$ 2.61972i 0.0973610i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 6.70820 0.248794 0.124397 0.992233i $$-0.460300\pi$$
0.124397 + 0.992233i $$0.460300\pi$$
$$728$$ 2.07107 + 1.30986i 0.0767589 + 0.0485466i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −8.01806 −0.296559
$$732$$ 0 0
$$733$$ −39.6408 −1.46417 −0.732084 0.681214i $$-0.761452\pi$$
−0.732084 + 0.681214i $$0.761452\pi$$
$$734$$ −24.5967 −0.907883
$$735$$ 0 0
$$736$$ 1.00000 0.0368605
$$737$$ 0 0
$$738$$ 0 0
$$739$$ 26.3553 0.969497 0.484748 0.874654i $$-0.338911\pi$$
0.484748 + 0.874654i $$0.338911\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −18.0475 11.4142i −0.662543 0.419029i
$$743$$ 35.1421 1.28924 0.644620 0.764503i $$-0.277016\pi$$
0.644620 + 0.764503i $$0.277016\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 7.07107i 0.258890i
$$747$$ 0 0
$$748$$ −3.16228 −0.115624
$$749$$ −4.47214 2.82843i −0.163408 0.103348i
$$750$$ 0 0
$$751$$ 31.2132 1.13899 0.569493 0.821996i $$-0.307140\pi$$
0.569493 + 0.821996i $$0.307140\pi$$
$$752$$ 1.30986i 0.0477656i
$$753$$ 0 0
$$754$$ 0.701474i 0.0255462i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 44.0416i 1.60072i 0.599520 + 0.800360i $$0.295358\pi$$
−0.599520 + 0.800360i $$0.704642\pi$$
$$758$$ 22.0711 0.801657
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −31.3050 −1.13480 −0.567402 0.823441i $$-0.692051\pi$$
−0.567402 + 0.823441i $$0.692051\pi$$
$$762$$ 0 0
$$763$$ −15.8114 10.0000i −0.572411 0.362024i
$$764$$ 0.656854i 0.0237642i
$$765$$ 0 0
$$766$$ 16.0361i 0.579409i
$$767$$ −6.71573 −0.242491
$$768$$ 0 0
$$769$$ 15.0441i 0.542504i −0.962508 0.271252i $$-0.912562\pi$$
0.962508 0.271252i $$-0.0874376\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 8.48528i 0.305392i
$$773$$ 17.3460i 0.623892i 0.950100 + 0.311946i $$0.100981\pi$$
−0.950100 + 0.311946i $$0.899019\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0.542561 0.0194768
$$777$$ 0 0
$$778$$ 22.8284i 0.818439i
$$779$$ 65.3553i 2.34160i
$$780$$ 0 0
$$781$$ −22.1421 −0.792308
$$782$$ 2.23607i 0.0799616i
$$783$$ 0 0
$$784$$ 3.00000 + 6.32456i 0.107143 + 0.225877i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −33.9247 −1.20928 −0.604642 0.796497i $$-0.706684\pi$$
−0.604642 + 0.796497i $$0.706684\pi$$
$$788$$ 5.92893 0.211209
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 2.39498 + 1.51472i 0.0851557 + 0.0538572i
$$792$$ 0 0
$$793$$ 0.857864i 0.0304637i
$$794$$ −29.6114 −1.05087
$$795$$ 0 0
$$796$$ 21.5934i 0.765357i
$$797$$ 11.0214i 0.390399i 0.980764 + 0.195199i $$0.0625354\pi$$
−0.980764 + 0.195199i $$0.937465\pi$$
$$798$$ 0 0
$$799$$ 2.92893 0.103618
$$800$$ 0 0
$$801$$ 0 0
$$802$$ 9.79899i 0.346014i