# Properties

 Label 1560.2.l.d.1249.1 Level $1560$ Weight $2$ Character 1560.1249 Analytic conductor $12.457$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1560.l (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.4566627153$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.57815240704.2 Defining polynomial: $$x^{8} - 2 x^{7} + 2 x^{6} + 89 x^{4} - 170 x^{3} + 162 x^{2} - 72 x + 16$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1249.1 Root $$2.20793 - 2.20793i$$ of defining polynomial Character $$\chi$$ $$=$$ 1560.1249 Dual form 1560.2.l.d.1249.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{3} +(-2.20793 - 0.353624i) q^{5} -1.65573i q^{7} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{3} +(-2.20793 - 0.353624i) q^{5} -1.65573i q^{7} -1.00000 q^{9} -2.94848 q^{11} +1.00000i q^{13} +(-0.353624 + 2.20793i) q^{15} +1.46738i q^{17} -1.65573 q^{21} -0.532621i q^{23} +(4.74990 + 1.56155i) q^{25} +1.00000i q^{27} -5.70861 q^{29} +2.94848i q^{33} +(-0.585504 + 3.65573i) q^{35} +8.77883i q^{37} +1.00000 q^{39} +1.23987 q^{41} +1.70861i q^{43} +(2.20793 + 0.353624i) q^{45} +2.70725i q^{47} +4.25857 q^{49} +1.46738 q^{51} +8.77883i q^{53} +(6.51003 + 1.04265i) q^{55} +3.83035 q^{59} -0.241231 q^{61} +1.65573i q^{63} +(0.353624 - 2.20793i) q^{65} +2.58550i q^{67} -0.532621 q^{69} -2.55132 q^{71} -0.188347i q^{73} +(1.56155 - 4.74990i) q^{75} +4.88187i q^{77} +11.0729 q^{79} +1.00000 q^{81} +7.91566i q^{83} +(0.518900 - 3.23987i) q^{85} +5.70861i q^{87} -15.9685 q^{89} +1.65573 q^{91} +16.8641i q^{97} +2.94848 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q - 2q^{5} - 8q^{9} + O(q^{10})$$ $$8q - 2q^{5} - 8q^{9} + 2q^{11} - 2q^{15} + 14q^{21} - 16q^{29} - 8q^{35} + 8q^{39} + 14q^{41} + 2q^{45} - 18q^{49} + 6q^{51} + 10q^{55} - 4q^{59} + 22q^{61} + 2q^{65} - 10q^{69} + 30q^{71} - 4q^{75} + 2q^{79} + 8q^{81} + 24q^{85} - 18q^{89} - 14q^{91} - 2q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times$$.

 $$n$$ $$391$$ $$521$$ $$781$$ $$937$$ $$1081$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$

## 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
$$3$$ 1.00000i 0.577350i
$$4$$ 0 0
$$5$$ −2.20793 0.353624i −0.987416 0.158145i
$$6$$ 0 0
$$7$$ 1.65573i 0.625806i −0.949785 0.312903i $$-0.898699\pi$$
0.949785 0.312903i $$-0.101301\pi$$
$$8$$ 0 0
$$9$$ −1.00000 −0.333333
$$10$$ 0 0
$$11$$ −2.94848 −0.889000 −0.444500 0.895779i $$-0.646619\pi$$
−0.444500 + 0.895779i $$0.646619\pi$$
$$12$$ 0 0
$$13$$ 1.00000i 0.277350i
$$14$$ 0 0
$$15$$ −0.353624 + 2.20793i −0.0913053 + 0.570085i
$$16$$ 0 0
$$17$$ 1.46738i 0.355892i 0.984040 + 0.177946i $$0.0569452\pi$$
−0.984040 + 0.177946i $$0.943055\pi$$
$$18$$ 0 0
$$19$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$20$$ 0 0
$$21$$ −1.65573 −0.361309
$$22$$ 0 0
$$23$$ 0.532621i 0.111059i −0.998457 0.0555296i $$-0.982315\pi$$
0.998457 0.0555296i $$-0.0176847\pi$$
$$24$$ 0 0
$$25$$ 4.74990 + 1.56155i 0.949980 + 0.312311i
$$26$$ 0 0
$$27$$ 1.00000i 0.192450i
$$28$$ 0 0
$$29$$ −5.70861 −1.06006 −0.530031 0.847978i $$-0.677820\pi$$
−0.530031 + 0.847978i $$0.677820\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ 0 0
$$33$$ 2.94848i 0.513264i
$$34$$ 0 0
$$35$$ −0.585504 + 3.65573i −0.0989683 + 0.617931i
$$36$$ 0 0
$$37$$ 8.77883i 1.44323i 0.692294 + 0.721616i $$0.256600\pi$$
−0.692294 + 0.721616i $$0.743400\pi$$
$$38$$ 0 0
$$39$$ 1.00000 0.160128
$$40$$ 0 0
$$41$$ 1.23987 0.193635 0.0968175 0.995302i $$-0.469134\pi$$
0.0968175 + 0.995302i $$0.469134\pi$$
$$42$$ 0 0
$$43$$ 1.70861i 0.260561i 0.991477 + 0.130280i $$0.0415877\pi$$
−0.991477 + 0.130280i $$0.958412\pi$$
$$44$$ 0 0
$$45$$ 2.20793 + 0.353624i 0.329139 + 0.0527151i
$$46$$ 0 0
$$47$$ 2.70725i 0.394893i 0.980314 + 0.197446i $$0.0632648\pi$$
−0.980314 + 0.197446i $$0.936735\pi$$
$$48$$ 0 0
$$49$$ 4.25857 0.608367
$$50$$ 0 0
$$51$$ 1.46738 0.205474
$$52$$ 0 0
$$53$$ 8.77883i 1.20587i 0.797792 + 0.602933i $$0.206001\pi$$
−0.797792 + 0.602933i $$0.793999\pi$$
$$54$$ 0 0
$$55$$ 6.51003 + 1.04265i 0.877812 + 0.140591i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 3.83035 0.498670 0.249335 0.968417i $$-0.419788\pi$$
0.249335 + 0.968417i $$0.419788\pi$$
$$60$$ 0 0
$$61$$ −0.241231 −0.0308865 −0.0154432 0.999881i $$-0.504916\pi$$
−0.0154432 + 0.999881i $$0.504916\pi$$
$$62$$ 0 0
$$63$$ 1.65573i 0.208602i
$$64$$ 0 0
$$65$$ 0.353624 2.20793i 0.0438616 0.273860i
$$66$$ 0 0
$$67$$ 2.58550i 0.315870i 0.987450 + 0.157935i $$0.0504836\pi$$
−0.987450 + 0.157935i $$0.949516\pi$$
$$68$$ 0 0
$$69$$ −0.532621 −0.0641200
$$70$$ 0 0
$$71$$ −2.55132 −0.302786 −0.151393 0.988474i $$-0.548376\pi$$
−0.151393 + 0.988474i $$0.548376\pi$$
$$72$$ 0 0
$$73$$ 0.188347i 0.0220444i −0.999939 0.0110222i $$-0.996491\pi$$
0.999939 0.0110222i $$-0.00350855\pi$$
$$74$$ 0 0
$$75$$ 1.56155 4.74990i 0.180313 0.548471i
$$76$$ 0 0
$$77$$ 4.88187i 0.556341i
$$78$$ 0 0
$$79$$ 11.0729 1.24580 0.622902 0.782300i $$-0.285954\pi$$
0.622902 + 0.782300i $$0.285954\pi$$
$$80$$ 0 0
$$81$$ 1.00000 0.111111
$$82$$ 0 0
$$83$$ 7.91566i 0.868856i 0.900706 + 0.434428i $$0.143050\pi$$
−0.900706 + 0.434428i $$0.856950\pi$$
$$84$$ 0 0
$$85$$ 0.518900 3.23987i 0.0562826 0.351413i
$$86$$ 0 0
$$87$$ 5.70861i 0.612027i
$$88$$ 0 0
$$89$$ −15.9685 −1.69266 −0.846331 0.532657i $$-0.821193\pi$$
−0.846331 + 0.532657i $$0.821193\pi$$
$$90$$ 0 0
$$91$$ 1.65573 0.173567
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 16.8641i 1.71229i 0.516733 + 0.856147i $$0.327148\pi$$
−0.516733 + 0.856147i $$0.672852\pi$$
$$98$$ 0 0
$$99$$ 2.94848 0.296333
$$100$$ 0 0
$$101$$ −4.64337 −0.462032 −0.231016 0.972950i $$-0.574205\pi$$
−0.231016 + 0.972950i $$0.574205\pi$$
$$102$$ 0 0
$$103$$ 9.66071i 0.951898i −0.879473 0.475949i $$-0.842105\pi$$
0.879473 0.475949i $$-0.157895\pi$$
$$104$$ 0 0
$$105$$ 3.65573 + 0.585504i 0.356762 + 0.0571394i
$$106$$ 0 0
$$107$$ 11.9498i 1.15523i 0.816308 + 0.577617i $$0.196017\pi$$
−0.816308 + 0.577617i $$0.803983\pi$$
$$108$$ 0 0
$$109$$ −11.8970 −1.13952 −0.569761 0.821810i $$-0.692964\pi$$
−0.569761 + 0.821810i $$0.692964\pi$$
$$110$$ 0 0
$$111$$ 8.77883 0.833250
$$112$$ 0 0
$$113$$ 2.37669i 0.223581i −0.993732 0.111790i $$-0.964341\pi$$
0.993732 0.111790i $$-0.0356585\pi$$
$$114$$ 0 0
$$115$$ −0.188347 + 1.17599i −0.0175635 + 0.109662i
$$116$$ 0 0
$$117$$ 1.00000i 0.0924500i
$$118$$ 0 0
$$119$$ 2.42958 0.222719
$$120$$ 0 0
$$121$$ −2.30647 −0.209679
$$122$$ 0 0
$$123$$ 1.23987i 0.111795i
$$124$$ 0 0
$$125$$ −9.93524 5.12748i −0.888635 0.458615i
$$126$$ 0 0
$$127$$ 2.87689i 0.255283i 0.991820 + 0.127642i $$0.0407407\pi$$
−0.991820 + 0.127642i $$0.959259\pi$$
$$128$$ 0 0
$$129$$ 1.70861 0.150435
$$130$$ 0 0
$$131$$ 19.3968 1.69470 0.847351 0.531033i $$-0.178196\pi$$
0.847351 + 0.531033i $$0.178196\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0.353624 2.20793i 0.0304351 0.190028i
$$136$$ 0 0
$$137$$ 0.357994i 0.0305855i 0.999883 + 0.0152927i $$0.00486802\pi$$
−0.999883 + 0.0152927i $$0.995132\pi$$
$$138$$ 0 0
$$139$$ 4.88187 0.414075 0.207038 0.978333i $$-0.433618\pi$$
0.207038 + 0.978333i $$0.433618\pi$$
$$140$$ 0 0
$$141$$ 2.70725 0.227991
$$142$$ 0 0
$$143$$ 2.94848i 0.246564i
$$144$$ 0 0
$$145$$ 12.6042 + 2.01870i 1.04672 + 0.167644i
$$146$$ 0 0
$$147$$ 4.25857i 0.351241i
$$148$$ 0 0
$$149$$ −20.6092 −1.68837 −0.844185 0.536052i $$-0.819915\pi$$
−0.844185 + 0.536052i $$0.819915\pi$$
$$150$$ 0 0
$$151$$ −3.89423 −0.316908 −0.158454 0.987366i $$-0.550651\pi$$
−0.158454 + 0.987366i $$0.550651\pi$$
$$152$$ 0 0
$$153$$ 1.46738i 0.118631i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 9.22887i 0.736544i 0.929718 + 0.368272i $$0.120051\pi$$
−0.929718 + 0.368272i $$0.879949\pi$$
$$158$$ 0 0
$$159$$ 8.77883 0.696207
$$160$$ 0 0
$$161$$ −0.881875 −0.0695015
$$162$$ 0 0
$$163$$ 16.5700i 1.29786i −0.760846 0.648932i $$-0.775216\pi$$
0.760846 0.648932i $$-0.224784\pi$$
$$164$$ 0 0
$$165$$ 1.04265 6.51003i 0.0811704 0.506805i
$$166$$ 0 0
$$167$$ 15.5390i 1.20244i 0.799083 + 0.601221i $$0.205319\pi$$
−0.799083 + 0.601221i $$0.794681\pi$$
$$168$$ 0 0
$$169$$ −1.00000 −0.0769231
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 3.17101i 0.241087i −0.992708 0.120544i $$-0.961536\pi$$
0.992708 0.120544i $$-0.0384638\pi$$
$$174$$ 0 0
$$175$$ 2.58550 7.86454i 0.195446 0.594503i
$$176$$ 0 0
$$177$$ 3.83035i 0.287907i
$$178$$ 0 0
$$179$$ −2.29411 −0.171470 −0.0857351 0.996318i $$-0.527324\pi$$
−0.0857351 + 0.996318i $$0.527324\pi$$
$$180$$ 0 0
$$181$$ −17.6105 −1.30898 −0.654491 0.756070i $$-0.727117\pi$$
−0.654491 + 0.756070i $$0.727117\pi$$
$$182$$ 0 0
$$183$$ 0.241231i 0.0178323i
$$184$$ 0 0
$$185$$ 3.10440 19.3830i 0.228240 1.42507i
$$186$$ 0 0
$$187$$ 4.32654i 0.316388i
$$188$$ 0 0
$$189$$ 1.65573 0.120436
$$190$$ 0 0
$$191$$ −0.105767 −0.00765304 −0.00382652 0.999993i $$-0.501218\pi$$
−0.00382652 + 0.999993i $$0.501218\pi$$
$$192$$ 0 0
$$193$$ 3.27903i 0.236030i 0.993012 + 0.118015i $$0.0376531\pi$$
−0.993012 + 0.118015i $$0.962347\pi$$
$$194$$ 0 0
$$195$$ −2.20793 0.353624i −0.158113 0.0253235i
$$196$$ 0 0
$$197$$ 6.01598i 0.428621i 0.976766 + 0.214310i $$0.0687504\pi$$
−0.976766 + 0.214310i $$0.931250\pi$$
$$198$$ 0 0
$$199$$ 5.33192 0.377969 0.188985 0.981980i $$-0.439480\pi$$
0.188985 + 0.981980i $$0.439480\pi$$
$$200$$ 0 0
$$201$$ 2.58550 0.182367
$$202$$ 0 0
$$203$$ 9.45190i 0.663393i
$$204$$ 0 0
$$205$$ −2.73754 0.438447i −0.191198 0.0306225i
$$206$$ 0 0
$$207$$ 0.532621i 0.0370197i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 14.5777 1.00357 0.501786 0.864992i $$-0.332676\pi$$
0.501786 + 0.864992i $$0.332676\pi$$
$$212$$ 0 0
$$213$$ 2.55132i 0.174814i
$$214$$ 0 0
$$215$$ 0.604205 3.77249i 0.0412065 0.257282i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −0.188347 −0.0127273
$$220$$ 0 0
$$221$$ −1.46738 −0.0987066
$$222$$ 0 0
$$223$$ 19.8518i 1.32937i −0.747122 0.664687i $$-0.768565\pi$$
0.747122 0.664687i $$-0.231435\pi$$
$$224$$ 0 0
$$225$$ −4.74990 1.56155i −0.316660 0.104104i
$$226$$ 0 0
$$227$$ 6.85042i 0.454678i −0.973816 0.227339i $$-0.926997\pi$$
0.973816 0.227339i $$-0.0730026\pi$$
$$228$$ 0 0
$$229$$ −18.0374 −1.19195 −0.595973 0.803005i $$-0.703233\pi$$
−0.595973 + 0.803005i $$0.703233\pi$$
$$230$$ 0 0
$$231$$ 4.88187 0.321204
$$232$$ 0 0
$$233$$ 14.4049i 0.943694i −0.881680 0.471847i $$-0.843587\pi$$
0.881680 0.471847i $$-0.156413\pi$$
$$234$$ 0 0
$$235$$ 0.957347 5.97741i 0.0624505 0.389923i
$$236$$ 0 0
$$237$$ 11.0729i 0.719265i
$$238$$ 0 0
$$239$$ −21.7350 −1.40592 −0.702961 0.711229i $$-0.748139\pi$$
−0.702961 + 0.711229i $$0.748139\pi$$
$$240$$ 0 0
$$241$$ 17.5604 1.13116 0.565582 0.824692i $$-0.308652\pi$$
0.565582 + 0.824692i $$0.308652\pi$$
$$242$$ 0 0
$$243$$ 1.00000i 0.0641500i
$$244$$ 0 0
$$245$$ −9.40262 1.50593i −0.600711 0.0962105i
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 7.91566 0.501634
$$250$$ 0 0
$$251$$ −22.7082 −1.43333 −0.716665 0.697418i $$-0.754332\pi$$
−0.716665 + 0.697418i $$0.754332\pi$$
$$252$$ 0 0
$$253$$ 1.57042i 0.0987316i
$$254$$ 0 0
$$255$$ −3.23987 0.518900i −0.202888 0.0324948i
$$256$$ 0 0
$$257$$ 6.58278i 0.410623i 0.978697 + 0.205311i $$0.0658207\pi$$
−0.978697 + 0.205311i $$0.934179\pi$$
$$258$$ 0 0
$$259$$ 14.5353 0.903182
$$260$$ 0 0
$$261$$ 5.70861 0.353354
$$262$$ 0 0
$$263$$ 4.24349i 0.261665i −0.991405 0.130832i $$-0.958235\pi$$
0.991405 0.130832i $$-0.0417649\pi$$
$$264$$ 0 0
$$265$$ 3.10440 19.3830i 0.190702 1.19069i
$$266$$ 0 0
$$267$$ 15.9685i 0.977259i
$$268$$ 0 0
$$269$$ −12.6434 −0.770880 −0.385440 0.922733i $$-0.625950\pi$$
−0.385440 + 0.922733i $$0.625950\pi$$
$$270$$ 0 0
$$271$$ −23.7665 −1.44371 −0.721855 0.692044i $$-0.756710\pi$$
−0.721855 + 0.692044i $$0.756710\pi$$
$$272$$ 0 0
$$273$$ 1.65573i 0.100209i
$$274$$ 0 0
$$275$$ −14.0050 4.60421i −0.844532 0.277644i
$$276$$ 0 0
$$277$$ 17.8765i 1.07409i 0.843552 + 0.537047i $$0.180460\pi$$
−0.843552 + 0.537047i $$0.819540\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 8.39540 0.500827 0.250414 0.968139i $$-0.419433\pi$$
0.250414 + 0.968139i $$0.419433\pi$$
$$282$$ 0 0
$$283$$ 13.9344i 0.828312i 0.910206 + 0.414156i $$0.135923\pi$$
−0.910206 + 0.414156i $$0.864077\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 2.05288i 0.121178i
$$288$$ 0 0
$$289$$ 14.8468 0.873341
$$290$$ 0 0
$$291$$ 16.8641 0.988593
$$292$$ 0 0
$$293$$ 11.4085i 0.666491i −0.942840 0.333245i $$-0.891856\pi$$
0.942840 0.333245i $$-0.108144\pi$$
$$294$$ 0 0
$$295$$ −8.45715 1.35450i −0.492394 0.0788623i
$$296$$ 0 0
$$297$$ 2.94848i 0.171088i
$$298$$ 0 0
$$299$$ 0.532621 0.0308023
$$300$$ 0 0
$$301$$ 2.82899 0.163060
$$302$$ 0 0
$$303$$ 4.64337i 0.266755i
$$304$$ 0 0
$$305$$ 0.532621 + 0.0853050i 0.0304978 + 0.00488455i
$$306$$ 0 0
$$307$$ 2.50790i 0.143134i −0.997436 0.0715668i $$-0.977200\pi$$
0.997436 0.0715668i $$-0.0227999\pi$$
$$308$$ 0 0
$$309$$ −9.66071 −0.549578
$$310$$ 0 0
$$311$$ −6.96220 −0.394790 −0.197395 0.980324i $$-0.563248\pi$$
−0.197395 + 0.980324i $$0.563248\pi$$
$$312$$ 0 0
$$313$$ 16.0880i 0.909349i 0.890658 + 0.454675i $$0.150244\pi$$
−0.890658 + 0.454675i $$0.849756\pi$$
$$314$$ 0 0
$$315$$ 0.585504 3.65573i 0.0329894 0.205977i
$$316$$ 0 0
$$317$$ 1.25263i 0.0703545i 0.999381 + 0.0351772i $$0.0111996\pi$$
−0.999381 + 0.0351772i $$0.988800\pi$$
$$318$$ 0 0
$$319$$ 16.8317 0.942395
$$320$$ 0 0
$$321$$ 11.9498 0.666975
$$322$$ 0 0
$$323$$ 0 0
$$324$$ 0 0
$$325$$ −1.56155 + 4.74990i −0.0866194 + 0.263477i
$$326$$ 0 0
$$327$$ 11.8970i 0.657903i
$$328$$ 0 0
$$329$$ 4.48246 0.247126
$$330$$ 0 0
$$331$$ −8.24349 −0.453103 −0.226552 0.973999i $$-0.572745\pi$$
−0.226552 + 0.973999i $$0.572745\pi$$
$$332$$ 0 0
$$333$$ 8.77883i 0.481077i
$$334$$ 0 0
$$335$$ 0.914296 5.70861i 0.0499533 0.311895i
$$336$$ 0 0
$$337$$ 22.1227i 1.20510i −0.798081 0.602550i $$-0.794151\pi$$
0.798081 0.602550i $$-0.205849\pi$$
$$338$$ 0 0
$$339$$ −2.37669 −0.129084
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 18.6411i 1.00653i
$$344$$ 0 0
$$345$$ 1.17599 + 0.188347i 0.0633131 + 0.0101403i
$$346$$ 0 0
$$347$$ 18.4395i 0.989886i 0.868925 + 0.494943i $$0.164811\pi$$
−0.868925 + 0.494943i $$0.835189\pi$$
$$348$$ 0 0
$$349$$ −19.6634 −1.05256 −0.526280 0.850312i $$-0.676414\pi$$
−0.526280 + 0.850312i $$0.676414\pi$$
$$350$$ 0 0
$$351$$ −1.00000 −0.0533761
$$352$$ 0 0
$$353$$ 1.18971i 0.0633219i 0.999499 + 0.0316609i $$0.0100797\pi$$
−0.999499 + 0.0316609i $$0.989920\pi$$
$$354$$ 0 0
$$355$$ 5.63314 + 0.902208i 0.298976 + 0.0478842i
$$356$$ 0 0
$$357$$ 2.42958i 0.128587i
$$358$$ 0 0
$$359$$ −4.98090 −0.262882 −0.131441 0.991324i $$-0.541960\pi$$
−0.131441 + 0.991324i $$0.541960\pi$$
$$360$$ 0 0
$$361$$ −19.0000 −1.00000
$$362$$ 0 0
$$363$$ 2.30647i 0.121058i
$$364$$ 0 0
$$365$$ −0.0666042 + 0.415858i −0.00348622 + 0.0217670i
$$366$$ 0 0
$$367$$ 10.7160i 0.559370i 0.960092 + 0.279685i $$0.0902300\pi$$
−0.960092 + 0.279685i $$0.909770\pi$$
$$368$$ 0 0
$$369$$ −1.23987 −0.0645450
$$370$$ 0 0
$$371$$ 14.5353 0.754638
$$372$$ 0 0
$$373$$ 22.8691i 1.18412i −0.805895 0.592059i $$-0.798315\pi$$
0.805895 0.592059i $$-0.201685\pi$$
$$374$$ 0 0
$$375$$ −5.12748 + 9.93524i −0.264782 + 0.513054i
$$376$$ 0 0
$$377$$ 5.70861i 0.294008i
$$378$$ 0 0
$$379$$ −26.5325 −1.36289 −0.681443 0.731871i $$-0.738647\pi$$
−0.681443 + 0.731871i $$0.738647\pi$$
$$380$$ 0 0
$$381$$ 2.87689 0.147388
$$382$$ 0 0
$$383$$ 38.3325i 1.95870i −0.202176 0.979349i $$-0.564801\pi$$
0.202176 0.979349i $$-0.435199\pi$$
$$384$$ 0 0
$$385$$ 1.72635 10.7788i 0.0879828 0.549340i
$$386$$ 0 0
$$387$$ 1.70861i 0.0868535i
$$388$$ 0 0
$$389$$ 7.87650 0.399354 0.199677 0.979862i $$-0.436011\pi$$
0.199677 + 0.979862i $$0.436011\pi$$
$$390$$ 0 0
$$391$$ 0.781557 0.0395250
$$392$$ 0 0
$$393$$ 19.3968i 0.978437i
$$394$$ 0 0
$$395$$ −24.4483 3.91566i −1.23013 0.197018i
$$396$$ 0 0
$$397$$ 0.673065i 0.0337802i −0.999857 0.0168901i $$-0.994623\pi$$
0.999857 0.0168901i $$-0.00537654\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −26.3981 −1.31826 −0.659130 0.752029i $$-0.729075\pi$$
−0.659130 + 0.752029i $$0.729075\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ −2.20793 0.353624i −0.109713 0.0175717i
$$406$$ 0 0
$$407$$ 25.8842i 1.28303i
$$408$$ 0 0
$$409$$ 33.4646 1.65472 0.827359 0.561674i $$-0.189843\pi$$
0.827359 + 0.561674i $$0.189843\pi$$
$$410$$ 0 0
$$411$$ 0.357994 0.0176585
$$412$$ 0 0
$$413$$ 6.34202i 0.312070i
$$414$$ 0 0
$$415$$ 2.79917 17.4772i 0.137406 0.857923i
$$416$$ 0 0
$$417$$ 4.88187i 0.239066i
$$418$$ 0 0
$$419$$ 32.3068 1.57829 0.789145 0.614207i $$-0.210524\pi$$
0.789145 + 0.614207i $$0.210524\pi$$
$$420$$ 0 0
$$421$$ 2.33929 0.114010 0.0570051 0.998374i $$-0.481845\pi$$
0.0570051 + 0.998374i $$0.481845\pi$$
$$422$$ 0 0
$$423$$ 2.70725i 0.131631i
$$424$$ 0 0
$$425$$ −2.29139 + 6.96990i −0.111149 + 0.338090i
$$426$$ 0 0
$$427$$ 0.399413i 0.0193289i
$$428$$ 0 0
$$429$$ −2.94848 −0.142354
$$430$$ 0 0
$$431$$ −20.5138 −0.988117 −0.494059 0.869429i $$-0.664487\pi$$
−0.494059 + 0.869429i $$0.664487\pi$$
$$432$$ 0 0
$$433$$ 24.8514i 1.19428i 0.802137 + 0.597141i $$0.203697\pi$$
−0.802137 + 0.597141i $$0.796303\pi$$
$$434$$ 0 0
$$435$$ 2.01870 12.6042i 0.0967893 0.604325i
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 8.18337 0.390571 0.195285 0.980746i $$-0.437437\pi$$
0.195285 + 0.980746i $$0.437437\pi$$
$$440$$ 0 0
$$441$$ −4.25857 −0.202789
$$442$$ 0 0
$$443$$ 26.1961i 1.24461i −0.782774 0.622306i $$-0.786196\pi$$
0.782774 0.622306i $$-0.213804\pi$$
$$444$$ 0 0
$$445$$ 35.2574 + 5.64686i 1.67136 + 0.267687i
$$446$$ 0 0
$$447$$ 20.6092i 0.974781i
$$448$$ 0 0
$$449$$ 11.8034 0.557036 0.278518 0.960431i $$-0.410157\pi$$
0.278518 + 0.960431i $$0.410157\pi$$
$$450$$ 0 0
$$451$$ −3.65573 −0.172141
$$452$$ 0 0
$$453$$ 3.89423i 0.182967i
$$454$$ 0 0
$$455$$ −3.65573 0.585504i −0.171383 0.0274489i
$$456$$ 0 0
$$457$$ 1.86454i 0.0872193i 0.999049 + 0.0436097i $$0.0138858\pi$$
−0.999049 + 0.0436097i $$0.986114\pi$$
$$458$$ 0 0
$$459$$ −1.46738 −0.0684914
$$460$$ 0 0
$$461$$ 7.42822 0.345967 0.172983 0.984925i $$-0.444659\pi$$
0.172983 + 0.984925i $$0.444659\pi$$
$$462$$ 0 0
$$463$$ 29.0829i 1.35160i −0.737086 0.675799i $$-0.763799\pi$$
0.737086 0.675799i $$-0.236201\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 10.5727i 0.489248i 0.969618 + 0.244624i $$0.0786646\pi$$
−0.969618 + 0.244624i $$0.921335\pi$$
$$468$$ 0 0
$$469$$ 4.28089 0.197673
$$470$$ 0 0
$$471$$ 9.22887 0.425244
$$472$$ 0 0
$$473$$ 5.03780i 0.231638i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 8.77883i 0.401955i
$$478$$ 0 0
$$479$$ 19.6166 0.896304 0.448152 0.893957i $$-0.352082\pi$$
0.448152 + 0.893957i $$0.352082\pi$$
$$480$$ 0 0
$$481$$ −8.77883 −0.400280
$$482$$ 0 0
$$483$$ 0.881875i 0.0401267i
$$484$$ 0 0
$$485$$ 5.96356 37.2348i 0.270791 1.69075i
$$486$$ 0 0
$$487$$ 0.235782i 0.0106843i 0.999986 + 0.00534215i $$0.00170047\pi$$
−0.999986 + 0.00534215i $$0.998300\pi$$
$$488$$ 0 0
$$489$$ −16.5700 −0.749322
$$490$$ 0 0
$$491$$ −23.6183 −1.06588 −0.532938 0.846154i $$-0.678912\pi$$
−0.532938 + 0.846154i $$0.678912\pi$$
$$492$$ 0 0
$$493$$ 8.37669i 0.377267i
$$494$$ 0 0
$$495$$ −6.51003 1.04265i −0.292604 0.0468637i
$$496$$ 0 0
$$497$$ 4.22429i 0.189485i
$$498$$ 0 0
$$499$$ 18.2737 0.818041 0.409021 0.912525i $$-0.365870\pi$$
0.409021 + 0.912525i $$0.365870\pi$$
$$500$$ 0 0
$$501$$ 15.5390 0.694230
$$502$$ 0 0
$$503$$ 27.8722i 1.24276i 0.783509 + 0.621381i $$0.213428\pi$$
−0.783509 + 0.621381i $$0.786572\pi$$
$$504$$ 0 0
$$505$$ 10.2522 + 1.64201i 0.456218 + 0.0730683i
$$506$$ 0 0
$$507$$ 1.00000i 0.0444116i
$$508$$ 0 0
$$509$$ −17.2878 −0.766267 −0.383134 0.923693i $$-0.625155\pi$$
−0.383134 + 0.923693i $$0.625155\pi$$
$$510$$ 0 0
$$511$$ −0.311852 −0.0137955
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −3.41626 + 21.3302i −0.150538 + 0.939919i
$$516$$ 0 0
$$517$$ 7.98226i 0.351060i
$$518$$ 0 0
$$519$$ −3.17101 −0.139192
$$520$$ 0 0
$$521$$ 26.9474 1.18059 0.590294 0.807188i $$-0.299012\pi$$
0.590294 + 0.807188i $$0.299012\pi$$
$$522$$ 0 0
$$523$$ 0.150946i 0.00660040i −0.999995 0.00330020i $$-0.998950\pi$$
0.999995 0.00330020i $$-0.00105049\pi$$
$$524$$ 0 0
$$525$$ −7.86454 2.58550i −0.343236 0.112841i
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 22.7163 0.987666
$$530$$ 0 0
$$531$$ −3.83035 −0.166223
$$532$$ 0 0
$$533$$ 1.23987i 0.0537047i
$$534$$ 0 0
$$535$$ 4.22575 26.3844i 0.182695 1.14070i
$$536$$ 0 0
$$537$$ 2.29411i 0.0989983i
$$538$$ 0 0
$$539$$ −12.5563 −0.540838
$$540$$ 0 0
$$541$$ −1.97256 −0.0848069 −0.0424035 0.999101i $$-0.513501\pi$$
−0.0424035 + 0.999101i $$0.513501\pi$$
$$542$$ 0 0
$$543$$ 17.6105i 0.755741i
$$544$$ 0 0
$$545$$ 26.2676 + 4.20705i 1.12518 + 0.180210i
$$546$$ 0 0
$$547$$ 21.6128i 0.924097i −0.886855 0.462048i $$-0.847115\pi$$
0.886855 0.462048i $$-0.152885\pi$$
$$548$$ 0 0
$$549$$ 0.241231 0.0102955
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 18.3338i 0.779631i
$$554$$ 0 0
$$555$$ −19.3830 3.10440i −0.822764 0.131775i
$$556$$ 0 0
$$557$$ 36.1619i 1.53223i 0.642705 + 0.766114i $$0.277812\pi$$
−0.642705 + 0.766114i $$0.722188\pi$$
$$558$$ 0 0
$$559$$ −1.70861 −0.0722665
$$560$$ 0 0
$$561$$ −4.32654 −0.182666
$$562$$ 0 0
$$563$$ 9.05248i 0.381517i 0.981637 + 0.190758i $$0.0610947\pi$$
−0.981637 + 0.190758i $$0.938905\pi$$
$$564$$ 0 0
$$565$$ −0.840456 + 5.24757i −0.0353583 + 0.220767i
$$566$$ 0 0
$$567$$ 1.65573i 0.0695340i
$$568$$ 0 0
$$569$$ −17.7255 −0.743094 −0.371547 0.928414i $$-0.621172\pi$$
−0.371547 + 0.928414i $$0.621172\pi$$
$$570$$ 0 0
$$571$$ −17.4095 −0.728566 −0.364283 0.931288i $$-0.618686\pi$$
−0.364283 + 0.931288i $$0.618686\pi$$
$$572$$ 0 0
$$573$$ 0.105767i 0.00441848i
$$574$$ 0 0
$$575$$ 0.831716 2.52990i 0.0346849 0.105504i
$$576$$ 0 0
$$577$$ 27.0729i 1.12706i 0.826095 + 0.563531i $$0.190557\pi$$
−0.826095 + 0.563531i $$0.809443\pi$$
$$578$$ 0 0
$$579$$ 3.27903 0.136272
$$580$$ 0 0
$$581$$ 13.1062 0.543735
$$582$$ 0 0
$$583$$ 25.8842i 1.07201i
$$584$$ 0 0
$$585$$ −0.353624 + 2.20793i −0.0146205 + 0.0912866i
$$586$$ 0 0
$$587$$ 21.5417i 0.889121i −0.895749 0.444560i $$-0.853360\pi$$
0.895749 0.444560i $$-0.146640\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 6.01598 0.247464
$$592$$ 0 0
$$593$$ 0.542087i 0.0222608i 0.999938 + 0.0111304i $$0.00354300\pi$$
−0.999938 + 0.0111304i $$0.996457\pi$$
$$594$$ 0 0
$$595$$ −5.36434 0.859157i −0.219916 0.0352220i
$$596$$ 0 0
$$597$$ 5.33192i 0.218221i
$$598$$ 0 0
$$599$$ 4.72595 0.193097 0.0965485 0.995328i $$-0.469220\pi$$
0.0965485 + 0.995328i $$0.469220\pi$$
$$600$$ 0 0
$$601$$ −2.47203 −0.100836 −0.0504182 0.998728i $$-0.516055\pi$$
−0.0504182 + 0.998728i $$0.516055\pi$$
$$602$$ 0 0
$$603$$ 2.58550i 0.105290i
$$604$$ 0 0
$$605$$ 5.09253 + 0.815624i 0.207041 + 0.0331598i
$$606$$ 0 0
$$607$$ 42.8966i 1.74112i 0.492064 + 0.870559i $$0.336242\pi$$
−0.492064 + 0.870559i $$0.663758\pi$$
$$608$$ 0 0
$$609$$ 9.45190 0.383010
$$610$$ 0 0
$$611$$ −2.70725 −0.109524
$$612$$ 0 0
$$613$$ 39.5175i 1.59610i 0.602594 + 0.798048i $$0.294134\pi$$
−0.602594 + 0.798048i $$0.705866\pi$$
$$614$$ 0 0
$$615$$ −0.438447 + 2.73754i −0.0176799 + 0.110388i
$$616$$ 0 0
$$617$$ 32.2951i 1.30015i 0.759870 + 0.650075i $$0.225263\pi$$
−0.759870 + 0.650075i $$0.774737\pi$$
$$618$$ 0 0
$$619$$ 17.4793 0.702554 0.351277 0.936272i $$-0.385748\pi$$
0.351277 + 0.936272i $$0.385748\pi$$
$$620$$ 0 0
$$621$$ 0.532621 0.0213733
$$622$$ 0 0
$$623$$ 26.4395i 1.05928i
$$624$$ 0 0
$$625$$ 20.1231 + 14.8344i 0.804924 + 0.593378i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −12.8819 −0.513634
$$630$$ 0 0
$$631$$ −0.376695 −0.0149960 −0.00749799 0.999972i $$-0.502387\pi$$
−0.00749799 + 0.999972i $$0.502387\pi$$
$$632$$ 0 0
$$633$$ 14.5777i 0.579413i
$$634$$ 0 0
$$635$$ 1.01734 6.35198i 0.0403718 0.252071i
$$636$$ 0 0
$$637$$ 4.25857i 0.168731i
$$638$$ 0 0
$$639$$ 2.55132 0.100929
$$640$$ 0 0
$$641$$ 30.3921 1.20042 0.600208 0.799844i $$-0.295084\pi$$
0.600208 + 0.799844i $$0.295084\pi$$
$$642$$ 0 0
$$643$$ 17.3918i 0.685865i 0.939360 + 0.342932i $$0.111420\pi$$
−0.939360 + 0.342932i $$0.888580\pi$$
$$644$$ 0 0
$$645$$ −3.77249 0.604205i −0.148542 0.0237906i
$$646$$ 0 0
$$647$$ 34.1331i 1.34191i 0.741497 + 0.670956i $$0.234116\pi$$
−0.741497 + 0.670956i $$0.765884\pi$$
$$648$$ 0 0
$$649$$ −11.2937 −0.443317
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 20.6284i 0.807250i 0.914925 + 0.403625i $$0.132250\pi$$
−0.914925 + 0.403625i $$0.867750\pi$$
$$654$$ 0 0
$$655$$ −42.8267 6.85916i −1.67338 0.268009i
$$656$$ 0 0
$$657$$ 0.188347i 0.00734814i
$$658$$ 0 0
$$659$$ 17.3940 0.677575 0.338788 0.940863i $$-0.389983\pi$$
0.338788 + 0.940863i $$0.389983\pi$$
$$660$$ 0 0
$$661$$ −9.04053 −0.351636 −0.175818 0.984423i $$-0.556257\pi$$
−0.175818 + 0.984423i $$0.556257\pi$$
$$662$$ 0 0
$$663$$ 1.46738i 0.0569883i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 3.04053i 0.117730i
$$668$$ 0 0
$$669$$ −19.8518 −0.767514
$$670$$ 0 0
$$671$$ 0.711265 0.0274581
$$672$$ 0 0
$$673$$ 12.7634i 0.491991i 0.969271 + 0.245996i $$0.0791148\pi$$
−0.969271 + 0.245996i $$0.920885\pi$$
$$674$$ 0 0
$$675$$ −1.56155 + 4.74990i −0.0601042 + 0.182824i
$$676$$ 0 0
$$677$$ 15.9251i 0.612052i 0.952023 + 0.306026i $$0.0989995\pi$$
−0.952023 + 0.306026i $$0.901001\pi$$
$$678$$ 0 0
$$679$$ 27.9224 1.07156
$$680$$ 0 0
$$681$$ −6.85042 −0.262509
$$682$$ 0 0
$$683$$ 9.04927i 0.346261i 0.984899 + 0.173130i $$0.0553882\pi$$
−0.984899 + 0.173130i $$0.944612\pi$$
$$684$$ 0 0
$$685$$ 0.126595 0.790425i 0.00483696 0.0302006i
$$686$$ 0 0
$$687$$ 18.0374i 0.688170i
$$688$$ 0 0
$$689$$ −8.77883 −0.334447
$$690$$ 0 0
$$691$$ −41.4848 −1.57816 −0.789078 0.614293i $$-0.789441\pi$$
−0.789078 + 0.614293i $$0.789441\pi$$
$$692$$ 0 0
$$693$$ 4.88187i 0.185447i
$$694$$ 0 0
$$695$$ −10.7788 1.72635i −0.408864 0.0654841i
$$696$$ 0 0
$$697$$ 1.81936i 0.0689131i
$$698$$ 0 0
$$699$$ −14.4049 −0.544842
$$700$$ 0 0
$$701$$ 1.08298 0.0409036 0.0204518 0.999791i $$-0.493490\pi$$
0.0204518 + 0.999791i $$0.493490\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ −5.97741 0.957347i −0.225122 0.0360558i
$$706$$ 0 0
$$707$$ 7.68815i 0.289143i
$$708$$ 0 0
$$709$$ 29.9371 1.12431 0.562155 0.827032i $$-0.309972\pi$$
0.562155 + 0.827032i $$0.309972\pi$$
$$710$$ 0 0
$$711$$ −11.0729 −0.415268
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ −1.04265 + 6.51003i −0.0389930 + 0.243461i
$$716$$ 0 0
$$717$$ 21.7350i 0.811709i
$$718$$ 0 0
$$719$$ 29.4793 1.09939 0.549697 0.835364i $$-0.314743\pi$$
0.549697 + 0.835364i $$0.314743\pi$$
$$720$$ 0 0
$$721$$ −15.9955 −0.595703
$$722$$ 0 0
$$723$$ 17.5604i 0.653078i
$$724$$ 0 0
$$725$$ −27.1153 8.91430i −1.00704 0.331069i
$$726$$ 0 0
$$727$$ 8.43456i 0.312820i −0.987692 0.156410i $$-0.950008\pi$$
0.987692 0.156410i $$-0.0499922\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −0.0370370
$$730$$ 0 0
$$731$$ −2.50718 −0.0927314
$$732$$ 0 0
$$733$$ 11.5449i 0.426421i 0.977006 + 0.213210i $$0.0683920\pi$$
−0.977006 + 0.213210i $$0.931608\pi$$
$$734$$ 0 0
$$735$$ −1.50593 + 9.40262i −0.0555471 + 0.346821i
$$736$$ 0 0
$$737$$ 7.62331i 0.280808i
$$738$$ 0 0
$$739$$ −14.2891 −0.525632 −0.262816 0.964846i $$-0.584651\pi$$
−0.262816 + 0.964846i $$0.584651\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 2.60693i 0.0956390i −0.998856 0.0478195i $$-0.984773\pi$$
0.998856 0.0478195i $$-0.0152272\pi$$
$$744$$ 0 0
$$745$$ 45.5036 + 7.28790i 1.66712 + 0.267008i
$$746$$ 0 0
$$747$$ 7.91566i 0.289619i
$$748$$ 0 0
$$749$$ 19.7857 0.722953
$$750$$ 0 0
$$751$$ −46.1277 −1.68322 −0.841612 0.540083i $$-0.818393\pi$$
−0.841612 + 0.540083i $$0.818393\pi$$
$$752$$ 0 0
$$753$$ 22.7082i 0.827533i
$$754$$ 0 0
$$755$$ 8.59819 + 1.37709i 0.312920 + 0.0501176i
$$756$$ 0 0
$$757$$ 20.6229i 0.749552i 0.927115 + 0.374776i $$0.122280\pi$$
−0.927115 + 0.374776i $$0.877720\pi$$
$$758$$ 0 0
$$759$$ 1.57042 0.0570027
$$760$$ 0 0
$$761$$ 52.6872 1.90991 0.954954 0.296752i $$-0.0959036\pi$$
0.954954 + 0.296752i $$0.0959036\pi$$
$$762$$ 0 0
$$763$$ 19.6981i 0.713119i
$$764$$ 0 0
$$765$$ −0.518900 + 3.23987i −0.0187609 + 0.117138i
$$766$$ 0 0
$$767$$ 3.83035i 0.138306i
$$768$$ 0 0
$$769$$ −31.2458 −1.12675 −0.563376 0.826200i $$-0.690498\pi$$
−0.563376 + 0.826200i $$0.690498\pi$$
$$770$$ 0 0
$$771$$ 6.58278 0.237073
$$772$$ 0 0
$$773$$ 41.0584i 1.47677i −0.674380 0.738385i $$-0.735589\pi$$
0.674380 0.738385i $$-0.264411\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 14.5353i 0.521453i
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 7.52252 0.269177
$$782$$ 0 0
$$783$$ 5.70861i 0.204009i
$$784$$ 0 0
$$785$$ 3.26355 20.3767i 0.116481 0.727275i
$$786$$ 0 0
$$787$$ 26.7067i 0.951990i 0.879448 + 0.475995i $$0.157912\pi$$
−0.879448 + 0.475995i $$0.842088\pi$$
$$788$$ 0 0
$$789$$ −4.24349 −0.151072
$$790$$ 0 0
$$791$$ −3.93516 −0.139918
$$792$$ 0 0
$$793$$ 0.241231i 0.00856636i
$$794$$ 0 0
$$795$$ −19.3830 3.10440i −0.687445 0.110102i
$$796$$ 0 0
$$797$$ 15.8293i 0.560703i −0.959897 0.280352i $$-0.909549\pi$$
0.959897 0.280352i $$-0.0904511\pi$$
$$798$$ 0 0
$$799$$ −3.97256 −0.140539
$$800$$ 0 0
$$801$$ 15.9685 0.564221
$$802$$ 0 0
$$803$$ 0.555339i 0.0195975i
$$804$$ 0 0