# Properties

 Label 63.4.c.b.62.1 Level $63$ Weight $4$ Character 63.62 Analytic conductor $3.717$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$63 = 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 63.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.71712033036$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{111})$$ Defining polynomial: $$x^{4} + 112 x^{2} + 3025$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 62.1 Root $$8.15694i$$ of defining polynomial Character $$\chi$$ $$=$$ 63.62 Dual form 63.4.c.b.62.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-2.82843i q^{2} -21.0713 q^{5} +(-11.0000 - 14.8997i) q^{7} -22.6274i q^{8} +O(q^{10})$$ $$q-2.82843i q^{2} -21.0713 q^{5} +(-11.0000 - 14.8997i) q^{7} -22.6274i q^{8} +59.5987i q^{10} -15.5563i q^{11} +29.7993i q^{13} +(-42.1426 + 31.1127i) q^{14} -64.0000 q^{16} +63.2139 q^{17} -89.3980i q^{19} -44.0000 q^{22} +77.7817i q^{23} +319.000 q^{25} +84.2852 q^{26} -125.865i q^{29} -238.395i q^{31} -178.796i q^{34} +(231.784 + 313.955i) q^{35} -184.000 q^{37} -252.856 q^{38} +476.789i q^{40} +105.357 q^{41} -190.000 q^{43} +220.000 q^{46} -42.1426 q^{47} +(-101.000 + 327.793i) q^{49} -902.268i q^{50} +357.796i q^{53} +327.793i q^{55} +(-337.141 + 248.902i) q^{56} -356.000 q^{58} -84.2852 q^{59} -655.585i q^{61} -674.282 q^{62} -512.000 q^{64} -627.911i q^{65} +296.000 q^{67} +(888.000 - 655.585i) q^{70} -329.512i q^{71} +804.582i q^{73} +520.431i q^{74} +(-231.784 + 171.120i) q^{77} +836.000 q^{79} +1348.56 q^{80} -297.993i q^{82} +1222.14 q^{83} -1332.00 q^{85} +537.401i q^{86} -352.000 q^{88} -695.353 q^{89} +(444.000 - 327.793i) q^{91} +119.197i q^{94} +1883.73i q^{95} -566.187i q^{97} +(927.138 + 285.671i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 44q^{7} + O(q^{10})$$ $$4q - 44q^{7} - 256q^{16} - 176q^{22} + 1276q^{25} - 736q^{37} - 760q^{43} + 880q^{46} - 404q^{49} - 1424q^{58} - 2048q^{64} + 1184q^{67} + 3552q^{70} + 3344q^{79} - 5328q^{85} - 1408q^{88} + 1776q^{91} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$$.

 $$n$$ $$10$$ $$29$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 2.82843i 1.00000i −0.866025 0.500000i $$-0.833333\pi$$
0.866025 0.500000i $$-0.166667\pi$$
$$3$$ 0 0
$$4$$ 0 0
$$5$$ −21.0713 −1.88468 −0.942338 0.334664i $$-0.891377\pi$$
−0.942338 + 0.334664i $$0.891377\pi$$
$$6$$ 0 0
$$7$$ −11.0000 14.8997i −0.593944 0.804506i
$$8$$ 22.6274i 1.00000i
$$9$$ 0 0
$$10$$ 59.5987i 1.88468i
$$11$$ 15.5563i 0.426401i −0.977008 0.213201i $$-0.931611\pi$$
0.977008 0.213201i $$-0.0683888\pi$$
$$12$$ 0 0
$$13$$ 29.7993i 0.635757i 0.948131 + 0.317879i $$0.102970\pi$$
−0.948131 + 0.317879i $$0.897030\pi$$
$$14$$ −42.1426 + 31.1127i −0.804506 + 0.593944i
$$15$$ 0 0
$$16$$ −64.0000 −1.00000
$$17$$ 63.2139 0.901860 0.450930 0.892559i $$-0.351092\pi$$
0.450930 + 0.892559i $$0.351092\pi$$
$$18$$ 0 0
$$19$$ 89.3980i 1.07944i −0.841846 0.539719i $$-0.818531\pi$$
0.841846 0.539719i $$-0.181469\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −44.0000 −0.426401
$$23$$ 77.7817i 0.705157i 0.935782 + 0.352579i $$0.114695\pi$$
−0.935782 + 0.352579i $$0.885305\pi$$
$$24$$ 0 0
$$25$$ 319.000 2.55200
$$26$$ 84.2852 0.635757
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 125.865i 0.805950i −0.915211 0.402975i $$-0.867976\pi$$
0.915211 0.402975i $$-0.132024\pi$$
$$30$$ 0 0
$$31$$ 238.395i 1.38119i −0.723241 0.690596i $$-0.757348\pi$$
0.723241 0.690596i $$-0.242652\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 178.796i 0.901860i
$$35$$ 231.784 + 313.955i 1.11939 + 1.51623i
$$36$$ 0 0
$$37$$ −184.000 −0.817552 −0.408776 0.912635i $$-0.634044\pi$$
−0.408776 + 0.912635i $$0.634044\pi$$
$$38$$ −252.856 −1.07944
$$39$$ 0 0
$$40$$ 476.789i 1.88468i
$$41$$ 105.357 0.401315 0.200658 0.979661i $$-0.435692\pi$$
0.200658 + 0.979661i $$0.435692\pi$$
$$42$$ 0 0
$$43$$ −190.000 −0.673831 −0.336915 0.941535i $$-0.609384\pi$$
−0.336915 + 0.941535i $$0.609384\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 220.000 0.705157
$$47$$ −42.1426 −0.130790 −0.0653950 0.997859i $$-0.520831\pi$$
−0.0653950 + 0.997859i $$0.520831\pi$$
$$48$$ 0 0
$$49$$ −101.000 + 327.793i −0.294461 + 0.955664i
$$50$$ 902.268i 2.55200i
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 357.796i 0.927303i 0.886018 + 0.463652i $$0.153461\pi$$
−0.886018 + 0.463652i $$0.846539\pi$$
$$54$$ 0 0
$$55$$ 327.793i 0.803628i
$$56$$ −337.141 + 248.902i −0.804506 + 0.593944i
$$57$$ 0 0
$$58$$ −356.000 −0.805950
$$59$$ −84.2852 −0.185983 −0.0929915 0.995667i $$-0.529643\pi$$
−0.0929915 + 0.995667i $$0.529643\pi$$
$$60$$ 0 0
$$61$$ 655.585i 1.37605i −0.725687 0.688025i $$-0.758478\pi$$
0.725687 0.688025i $$-0.241522\pi$$
$$62$$ −674.282 −1.38119
$$63$$ 0 0
$$64$$ −512.000 −1.00000
$$65$$ 627.911i 1.19820i
$$66$$ 0 0
$$67$$ 296.000 0.539734 0.269867 0.962898i $$-0.413020\pi$$
0.269867 + 0.962898i $$0.413020\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 888.000 655.585i 1.51623 1.11939i
$$71$$ 329.512i 0.550787i −0.961332 0.275393i $$-0.911192\pi$$
0.961332 0.275393i $$-0.0888081\pi$$
$$72$$ 0 0
$$73$$ 804.582i 1.28999i 0.764187 + 0.644994i $$0.223140\pi$$
−0.764187 + 0.644994i $$0.776860\pi$$
$$74$$ 520.431i 0.817552i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −231.784 + 171.120i −0.343043 + 0.253259i
$$78$$ 0 0
$$79$$ 836.000 1.19060 0.595300 0.803504i $$-0.297033\pi$$
0.595300 + 0.803504i $$0.297033\pi$$
$$80$$ 1348.56 1.88468
$$81$$ 0 0
$$82$$ 297.993i 0.401315i
$$83$$ 1222.14 1.61623 0.808113 0.589027i $$-0.200489\pi$$
0.808113 + 0.589027i $$0.200489\pi$$
$$84$$ 0 0
$$85$$ −1332.00 −1.69971
$$86$$ 537.401i 0.673831i
$$87$$ 0 0
$$88$$ −352.000 −0.426401
$$89$$ −695.353 −0.828172 −0.414086 0.910238i $$-0.635899\pi$$
−0.414086 + 0.910238i $$0.635899\pi$$
$$90$$ 0 0
$$91$$ 444.000 327.793i 0.511471 0.377604i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 119.197i 0.130790i
$$95$$ 1883.73i 2.03439i
$$96$$ 0 0
$$97$$ 566.187i 0.592656i −0.955086 0.296328i $$-0.904238\pi$$
0.955086 0.296328i $$-0.0957621\pi$$
$$98$$ 927.138 + 285.671i 0.955664 + 0.294461i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −737.496 −0.726570 −0.363285 0.931678i $$-0.618345\pi$$
−0.363285 + 0.931678i $$0.618345\pi$$
$$102$$ 0 0
$$103$$ 655.585i 0.627153i 0.949563 + 0.313576i $$0.101527\pi$$
−0.949563 + 0.313576i $$0.898473\pi$$
$$104$$ 674.282 0.635757
$$105$$ 0 0
$$106$$ 1012.00 0.927303
$$107$$ 1984.14i 1.79266i −0.443391 0.896328i $$-0.646225\pi$$
0.443391 0.896328i $$-0.353775\pi$$
$$108$$ 0 0
$$109$$ −844.000 −0.741656 −0.370828 0.928702i $$-0.620926\pi$$
−0.370828 + 0.928702i $$0.620926\pi$$
$$110$$ 927.138 0.803628
$$111$$ 0 0
$$112$$ 704.000 + 953.579i 0.593944 + 0.804506i
$$113$$ 575.585i 0.479172i −0.970875 0.239586i $$-0.922988\pi$$
0.970875 0.239586i $$-0.0770118\pi$$
$$114$$ 0 0
$$115$$ 1638.96i 1.32899i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 238.395i 0.185983i
$$119$$ −695.353 941.866i −0.535655 0.725552i
$$120$$ 0 0
$$121$$ 1089.00 0.818182
$$122$$ −1854.28 −1.37605
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −4087.83 −2.92502
$$126$$ 0 0
$$127$$ −220.000 −0.153715 −0.0768577 0.997042i $$-0.524489\pi$$
−0.0768577 + 0.997042i $$0.524489\pi$$
$$128$$ 1448.15i 1.00000i
$$129$$ 0 0
$$130$$ −1776.00 −1.19820
$$131$$ 1306.42 0.871317 0.435659 0.900112i $$-0.356516\pi$$
0.435659 + 0.900112i $$0.356516\pi$$
$$132$$ 0 0
$$133$$ −1332.00 + 983.378i −0.868414 + 0.641125i
$$134$$ 837.214i 0.539734i
$$135$$ 0 0
$$136$$ 1430.37i 0.901860i
$$137$$ 1568.36i 0.978060i −0.872267 0.489030i $$-0.837351\pi$$
0.872267 0.489030i $$-0.162649\pi$$
$$138$$ 0 0
$$139$$ 655.585i 0.400043i 0.979791 + 0.200022i $$0.0641012\pi$$
−0.979791 + 0.200022i $$0.935899\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −932.000 −0.550787
$$143$$ 463.569 0.271088
$$144$$ 0 0
$$145$$ 2652.14i 1.51895i
$$146$$ 2275.70 1.28999
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 1466.54i 0.806333i −0.915127 0.403166i $$-0.867910\pi$$
0.915127 0.403166i $$-0.132090\pi$$
$$150$$ 0 0
$$151$$ 1970.00 1.06170 0.530849 0.847467i $$-0.321873\pi$$
0.530849 + 0.847467i $$0.321873\pi$$
$$152$$ −2022.85 −1.07944
$$153$$ 0 0
$$154$$ 484.000 + 655.585i 0.253259 + 0.343043i
$$155$$ 5023.29i 2.60310i
$$156$$ 0 0
$$157$$ 2622.34i 1.33303i 0.745492 + 0.666515i $$0.232215\pi$$
−0.745492 + 0.666515i $$0.767785\pi$$
$$158$$ 2364.57i 1.19060i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 1158.92 855.599i 0.567303 0.418824i
$$162$$ 0 0
$$163$$ −1336.00 −0.641985 −0.320993 0.947082i $$-0.604016\pi$$
−0.320993 + 0.947082i $$0.604016\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 3456.72i 1.61623i
$$167$$ 2317.84 1.07401 0.537006 0.843578i $$-0.319555\pi$$
0.537006 + 0.843578i $$0.319555\pi$$
$$168$$ 0 0
$$169$$ 1309.00 0.595812
$$170$$ 3767.46i 1.69971i
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −231.784 −0.101863 −0.0509313 0.998702i $$-0.516219\pi$$
−0.0509313 + 0.998702i $$0.516219\pi$$
$$174$$ 0 0
$$175$$ −3509.00 4752.99i −1.51575 2.05310i
$$176$$ 995.606i 0.426401i
$$177$$ 0 0
$$178$$ 1966.76i 0.828172i
$$179$$ 108.894i 0.0454701i −0.999742 0.0227351i $$-0.992763\pi$$
0.999742 0.0227351i $$-0.00723742\pi$$
$$180$$ 0 0
$$181$$ 2592.54i 1.06465i −0.846539 0.532326i $$-0.821318\pi$$
0.846539 0.532326i $$-0.178682\pi$$
$$182$$ −927.138 1255.82i −0.377604 0.511471i
$$183$$ 0 0
$$184$$ 1760.00 0.705157
$$185$$ 3877.12 1.54082
$$186$$ 0 0
$$187$$ 983.378i 0.384555i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 5328.00 2.03439
$$191$$ 2224.56i 0.842740i 0.906889 + 0.421370i $$0.138451\pi$$
−0.906889 + 0.421370i $$0.861549\pi$$
$$192$$ 0 0
$$193$$ 3740.00 1.39488 0.697438 0.716645i $$-0.254323\pi$$
0.697438 + 0.716645i $$0.254323\pi$$
$$194$$ −1601.42 −0.592656
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1197.84i 0.433211i 0.976259 + 0.216605i $$0.0694985\pi$$
−0.976259 + 0.216605i $$0.930502\pi$$
$$198$$ 0 0
$$199$$ 804.582i 0.286610i −0.989679 0.143305i $$-0.954227\pi$$
0.989679 0.143305i $$-0.0457729\pi$$
$$200$$ 7218.15i 2.55200i
$$201$$ 0 0
$$202$$ 2085.95i 0.726570i
$$203$$ −1875.35 + 1384.52i −0.648392 + 0.478689i
$$204$$ 0 0
$$205$$ −2220.00 −0.756349
$$206$$ 1854.28 0.627153
$$207$$ 0 0
$$208$$ 1907.16i 0.635757i
$$209$$ −1390.71 −0.460274
$$210$$ 0 0
$$211$$ 3590.00 1.17131 0.585654 0.810561i $$-0.300838\pi$$
0.585654 + 0.810561i $$0.300838\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ −5612.00 −1.79266
$$215$$ 4003.55 1.26995
$$216$$ 0 0
$$217$$ −3552.00 + 2622.34i −1.11118 + 0.820351i
$$218$$ 2387.19i 0.741656i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 1883.73i 0.573365i
$$222$$ 0 0
$$223$$ 3009.73i 0.903796i 0.892070 + 0.451898i $$0.149253\pi$$
−0.892070 + 0.451898i $$0.850747\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −1628.00 −0.479172
$$227$$ −3708.55 −1.08434 −0.542170 0.840269i $$-0.682397\pi$$
−0.542170 + 0.840269i $$0.682397\pi$$
$$228$$ 0 0
$$229$$ 327.793i 0.0945902i −0.998881 0.0472951i $$-0.984940\pi$$
0.998881 0.0472951i $$-0.0150601\pi$$
$$230$$ −4635.69 −1.32899
$$231$$ 0 0
$$232$$ −2848.00 −0.805950
$$233$$ 643.467i 0.180922i −0.995900 0.0904612i $$-0.971166\pi$$
0.995900 0.0904612i $$-0.0288341\pi$$
$$234$$ 0 0
$$235$$ 888.000 0.246497
$$236$$ 0 0
$$237$$ 0 0
$$238$$ −2664.00 + 1966.76i −0.725552 + 0.535655i
$$239$$ 646.296i 0.174918i 0.996168 + 0.0874590i $$0.0278747\pi$$
−0.996168 + 0.0874590i $$0.972125\pi$$
$$240$$ 0 0
$$241$$ 387.391i 0.103544i −0.998659 0.0517719i $$-0.983513\pi$$
0.998659 0.0517719i $$-0.0164869\pi$$
$$242$$ 3080.16i 0.818182i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 2128.20 6907.02i 0.554963 1.80112i
$$246$$ 0 0
$$247$$ 2664.00 0.686260
$$248$$ −5394.25 −1.38119
$$249$$ 0 0
$$250$$ 11562.1i 2.92502i
$$251$$ 6194.96 1.55786 0.778930 0.627111i $$-0.215763\pi$$
0.778930 + 0.627111i $$0.215763\pi$$
$$252$$ 0 0
$$253$$ 1210.00 0.300680
$$254$$ 622.254i 0.153715i
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −3561.05 −0.864328 −0.432164 0.901795i $$-0.642250\pi$$
−0.432164 + 0.901795i $$0.642250\pi$$
$$258$$ 0 0
$$259$$ 2024.00 + 2741.54i 0.485580 + 0.657725i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 3695.12i 0.871317i
$$263$$ 601.041i 0.140919i −0.997515 0.0704596i $$-0.977553\pi$$
0.997515 0.0704596i $$-0.0224466\pi$$
$$264$$ 0 0
$$265$$ 7539.23i 1.74767i
$$266$$ 2781.41 + 3767.46i 0.641125 + 0.868414i
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −4867.47 −1.10325 −0.551626 0.834091i $$-0.685993\pi$$
−0.551626 + 0.834091i $$0.685993\pi$$
$$270$$ 0 0
$$271$$ 1787.96i 0.400778i −0.979716 0.200389i $$-0.935779\pi$$
0.979716 0.200389i $$-0.0642206\pi$$
$$272$$ −4045.69 −0.901860
$$273$$ 0 0
$$274$$ −4436.00 −0.978060
$$275$$ 4962.48i 1.08818i
$$276$$ 0 0
$$277$$ −1126.00 −0.244241 −0.122121 0.992515i $$-0.538969\pi$$
−0.122121 + 0.992515i $$0.538969\pi$$
$$278$$ 1854.28 0.400043
$$279$$ 0 0
$$280$$ 7104.00 5244.68i 1.51623 1.11939i
$$281$$ 5075.61i 1.07753i 0.842456 + 0.538765i $$0.181109\pi$$
−0.842456 + 0.538765i $$0.818891\pi$$
$$282$$ 0 0
$$283$$ 7122.04i 1.49598i −0.663712 0.747988i $$-0.731020\pi$$
0.663712 0.747988i $$-0.268980\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 1311.17i 0.271088i
$$287$$ −1158.92 1569.78i −0.238359 0.322861i
$$288$$ 0 0
$$289$$ −917.000 −0.186648
$$290$$ 7501.39 1.51895
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 231.784 0.0462150 0.0231075 0.999733i $$-0.492644\pi$$
0.0231075 + 0.999733i $$0.492644\pi$$
$$294$$ 0 0
$$295$$ 1776.00 0.350518
$$296$$ 4163.44i 0.817552i
$$297$$ 0 0
$$298$$ −4148.00 −0.806333
$$299$$ −2317.84 −0.448309
$$300$$ 0 0
$$301$$ 2090.00 + 2830.94i 0.400218 + 0.542101i
$$302$$ 5572.00i 1.06170i
$$303$$ 0 0
$$304$$ 5721.47i 1.07944i
$$305$$ 13814.0i 2.59341i
$$306$$ 0 0
$$307$$ 8850.40i 1.64534i 0.568520 + 0.822669i $$0.307516\pi$$
−0.568520 + 0.822669i $$0.692484\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 14208.0 2.60310
$$311$$ 6489.96 1.18332 0.591659 0.806188i $$-0.298473\pi$$
0.591659 + 0.806188i $$0.298473\pi$$
$$312$$ 0 0
$$313$$ 10847.0i 1.95881i −0.201916 0.979403i $$-0.564717\pi$$
0.201916 0.979403i $$-0.435283\pi$$
$$314$$ 7417.10 1.33303
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 1780.49i 0.315465i −0.987482 0.157733i $$-0.949582\pi$$
0.987482 0.157733i $$-0.0504184\pi$$
$$318$$ 0 0
$$319$$ −1958.00 −0.343658
$$320$$ 10788.5 1.88468
$$321$$ 0 0
$$322$$ −2420.00 3277.93i −0.418824 0.567303i
$$323$$ 5651.20i 0.973502i
$$324$$ 0 0
$$325$$ 9505.99i 1.62245i
$$326$$ 3778.78i 0.641985i
$$327$$ 0 0
$$328$$ 2383.95i 0.401315i
$$329$$ 463.569 + 627.911i 0.0776820 + 0.105221i
$$330$$ 0 0
$$331$$ −9526.00 −1.58186 −0.790931 0.611905i $$-0.790403\pi$$
−0.790931 + 0.611905i $$0.790403\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 6555.85i 1.07401i
$$335$$ −6237.11 −1.01722
$$336$$ 0 0
$$337$$ −8272.00 −1.33711 −0.668553 0.743665i $$-0.733086\pi$$
−0.668553 + 0.743665i $$0.733086\pi$$
$$338$$ 3702.41i 0.595812i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −3708.55 −0.588942
$$342$$ 0 0
$$343$$ 5995.00 2100.85i 0.943731 0.330715i
$$344$$ 4299.21i 0.673831i
$$345$$ 0 0
$$346$$ 655.585i 0.101863i
$$347$$ 9784.94i 1.51378i 0.653540 + 0.756892i $$0.273283\pi$$
−0.653540 + 0.756892i $$0.726717\pi$$
$$348$$ 0 0
$$349$$ 6317.46i 0.968956i 0.874803 + 0.484478i $$0.160990\pi$$
−0.874803 + 0.484478i $$0.839010\pi$$
$$350$$ −13443.5 + 9924.95i −2.05310 + 1.51575i
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 5457.47 0.822866 0.411433 0.911440i $$-0.365028\pi$$
0.411433 + 0.911440i $$0.365028\pi$$
$$354$$ 0 0
$$355$$ 6943.24i 1.03805i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ −308.000 −0.0454701
$$359$$ 10842.8i 1.59404i −0.603954 0.797019i $$-0.706409\pi$$
0.603954 0.797019i $$-0.293591\pi$$
$$360$$ 0 0
$$361$$ −1133.00 −0.165184
$$362$$ −7332.82 −1.06465
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 16953.6i 2.43121i
$$366$$ 0 0
$$367$$ 3724.92i 0.529807i 0.964275 + 0.264903i $$0.0853400\pi$$
−0.964275 + 0.264903i $$0.914660\pi$$
$$368$$ 4978.03i 0.705157i
$$369$$ 0 0
$$370$$ 10966.2i 1.54082i
$$371$$ 5331.04 3935.76i 0.746021 0.550766i
$$372$$ 0 0
$$373$$ 4202.00 0.583301 0.291651 0.956525i $$-0.405796\pi$$
0.291651 + 0.956525i $$0.405796\pi$$
$$374$$ −2781.41 −0.384555
$$375$$ 0 0
$$376$$ 953.579i 0.130790i
$$377$$ 3750.69 0.512389
$$378$$ 0 0
$$379$$ −2506.00 −0.339643 −0.169821 0.985475i $$-0.554319\pi$$
−0.169821 + 0.985475i $$0.554319\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 6292.00 0.842740
$$383$$ −13106.4 −1.74857 −0.874286 0.485410i $$-0.838670\pi$$
−0.874286 + 0.485410i $$0.838670\pi$$
$$384$$ 0 0
$$385$$ 4884.00 3605.72i 0.646524 0.477310i
$$386$$ 10578.3i 1.39488i
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 4631.55i 0.603673i −0.953360 0.301837i $$-0.902400\pi$$
0.953360 0.301837i $$-0.0975997\pi$$
$$390$$ 0 0
$$391$$ 4916.89i 0.635953i
$$392$$ 7417.10 + 2285.37i 0.955664 + 0.294461i
$$393$$ 0 0
$$394$$ 3388.00 0.433211
$$395$$ −17615.6 −2.24389
$$396$$ 0 0
$$397$$ 8045.82i 1.01715i 0.861018 + 0.508574i $$0.169827\pi$$
−0.861018 + 0.508574i $$0.830173\pi$$
$$398$$ −2275.70 −0.286610
$$399$$ 0 0
$$400$$ −20416.0 −2.55200
$$401$$ 13552.4i 1.68772i 0.536565 + 0.843859i $$0.319722\pi$$
−0.536565 + 0.843859i $$0.680278\pi$$
$$402$$ 0 0
$$403$$ 7104.00 0.878103
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 3916.00 + 5304.28i 0.478689 + 0.648392i
$$407$$ 2862.37i 0.348605i
$$408$$ 0 0
$$409$$ 10161.6i 1.22850i −0.789111 0.614251i $$-0.789458\pi$$
0.789111 0.614251i $$-0.210542\pi$$
$$410$$ 6279.11i 0.756349i
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 927.138 + 1255.82i 0.110464 + 0.149625i
$$414$$ 0 0
$$415$$ −25752.0 −3.04606
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 3933.51i 0.460274i
$$419$$ −8934.23 −1.04168 −0.520842 0.853653i $$-0.674382\pi$$
−0.520842 + 0.853653i $$0.674382\pi$$
$$420$$ 0 0
$$421$$ 5606.00 0.648978 0.324489 0.945889i $$-0.394808\pi$$
0.324489 + 0.945889i $$0.394808\pi$$
$$422$$ 10154.1i 1.17131i
$$423$$ 0 0
$$424$$ 8096.00 0.927303
$$425$$ 20165.2 2.30155
$$426$$ 0 0
$$427$$ −9768.00 + 7211.44i −1.10704 + 0.817297i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 11323.7i 1.26995i
$$431$$ 883.883i 0.0987823i 0.998780 + 0.0493911i $$0.0157281\pi$$
−0.998780 + 0.0493911i $$0.984272\pi$$
$$432$$ 0 0
$$433$$ 1966.76i 0.218282i −0.994026 0.109141i $$-0.965190\pi$$
0.994026 0.109141i $$-0.0348101\pi$$
$$434$$ 7417.10 + 10046.6i 0.820351 + 1.11118i
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 6953.53 0.761173
$$438$$ 0 0
$$439$$ 387.391i 0.0421166i −0.999778 0.0210583i $$-0.993296\pi$$
0.999778 0.0210583i $$-0.00670356\pi$$
$$440$$ 7417.10 0.803628
$$441$$ 0 0
$$442$$ 5328.00 0.573365
$$443$$ 2623.37i 0.281354i 0.990056 + 0.140677i $$0.0449279\pi$$
−0.990056 + 0.140677i $$0.955072\pi$$
$$444$$ 0 0
$$445$$ 14652.0 1.56083
$$446$$ 8512.81 0.903796
$$447$$ 0 0
$$448$$ 5632.00 + 7628.63i 0.593944 + 0.804506i
$$449$$ 5140.67i 0.540319i −0.962816 0.270159i $$-0.912924\pi$$
0.962816 0.270159i $$-0.0870764\pi$$
$$450$$ 0 0
$$451$$ 1638.96i 0.171121i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 10489.4i 1.08434i
$$455$$ −9355.66 + 6907.02i −0.963956 + 0.711662i
$$456$$ 0 0
$$457$$ 3608.00 0.369311 0.184655 0.982803i $$-0.440883\pi$$
0.184655 + 0.982803i $$0.440883\pi$$
$$458$$ −927.138 −0.0945902
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 1538.21 0.155404 0.0777021 0.996977i $$-0.475242\pi$$
0.0777021 + 0.996977i $$0.475242\pi$$
$$462$$ 0 0
$$463$$ 1772.00 0.177866 0.0889329 0.996038i $$-0.471654\pi$$
0.0889329 + 0.996038i $$0.471654\pi$$
$$464$$ 8055.36i 0.805950i
$$465$$ 0 0
$$466$$ −1820.00 −0.180922
$$467$$ 12769.2 1.26529 0.632643 0.774443i $$-0.281970\pi$$
0.632643 + 0.774443i $$0.281970\pi$$
$$468$$ 0 0
$$469$$ −3256.00 4410.30i −0.320572 0.434219i
$$470$$ 2511.64i 0.246497i
$$471$$ 0 0
$$472$$ 1907.16i 0.185983i
$$473$$ 2955.71i 0.287322i
$$474$$ 0 0
$$475$$ 28518.0i 2.75472i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 1828.00 0.174918
$$479$$ 4635.69 0.442192 0.221096 0.975252i $$-0.429037\pi$$
0.221096 + 0.975252i $$0.429037\pi$$
$$480$$ 0 0
$$481$$ 5483.08i 0.519765i
$$482$$ −1095.71 −0.103544
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 11930.3i 1.11696i
$$486$$ 0 0
$$487$$ 1958.00 0.182188 0.0910939 0.995842i $$-0.470964\pi$$
0.0910939 + 0.995842i $$0.470964\pi$$
$$488$$ −14834.2 −1.37605
$$489$$ 0 0
$$490$$ −19536.0 6019.46i −1.80112 0.554963i
$$491$$ 7126.22i 0.654994i −0.944852 0.327497i $$-0.893795\pi$$
0.944852 0.327497i $$-0.106205\pi$$
$$492$$ 0 0
$$493$$ 7956.42i 0.726854i
$$494$$ 7534.93i 0.686260i
$$495$$ 0 0
$$496$$ 15257.3i 1.38119i
$$497$$ −4909.61 + 3624.63i −0.443111 + 0.327137i
$$498$$ 0 0
$$499$$ 10310.0 0.924928 0.462464 0.886638i $$-0.346965\pi$$
0.462464 + 0.886638i $$0.346965\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 17522.0i 1.55786i
$$503$$ 126.428 0.0112070 0.00560352 0.999984i $$-0.498216\pi$$
0.00560352 + 0.999984i $$0.498216\pi$$
$$504$$ 0 0
$$505$$ 15540.0 1.36935
$$506$$ 3422.40i 0.300680i
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −7101.03 −0.618365 −0.309182 0.951003i $$-0.600055\pi$$
−0.309182 + 0.951003i $$0.600055\pi$$
$$510$$ 0 0
$$511$$ 11988.0 8850.40i 1.03780 0.766181i
$$512$$ 11585.2i 1.00000i
$$513$$ 0 0
$$514$$ 10072.2i 0.864328i
$$515$$ 13814.0i 1.18198i
$$516$$ 0 0
$$517$$ 655.585i 0.0557691i
$$518$$ 7754.24 5724.74i 0.657725 0.485580i
$$519$$ 0 0
$$520$$ −14208.0 −1.19820
$$521$$ 4488.19 0.377411 0.188705 0.982034i $$-0.439571\pi$$
0.188705 + 0.982034i $$0.439571\pi$$
$$522$$ 0 0
$$523$$ 9297.39i 0.777336i 0.921378 + 0.388668i $$0.127065\pi$$
−0.921378 + 0.388668i $$0.872935\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −1700.00 −0.140919
$$527$$ 15069.9i 1.24564i
$$528$$ 0 0
$$529$$ 6117.00 0.502753
$$530$$ −21324.2 −1.74767
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 3139.55i 0.255139i
$$534$$ 0 0
$$535$$ 41808.5i 3.37857i
$$536$$ 6697.72i 0.539734i
$$537$$ 0 0
$$538$$ 13767.3i 1.10325i
$$539$$ 5099.26 + 1571.19i 0.407496 + 0.125558i
$$540$$ 0 0
$$541$$ −15646.0 −1.24339 −0.621695 0.783259i $$-0.713556\pi$$
−0.621695 + 0.783259i $$0.713556\pi$$
$$542$$ −5057.11 −0.400778
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 17784.2 1.39778
$$546$$ 0 0
$$547$$ 1880.00 0.146952 0.0734762 0.997297i $$-0.476591\pi$$
0.0734762 + 0.997297i $$0.476591\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ −14036.0 −1.08818
$$551$$ −11252.1 −0.869972
$$552$$ 0 0
$$553$$ −9196.00 12456.1i −0.707150 0.957845i
$$554$$ 3184.81i 0.244241i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 7001.77i 0.532629i 0.963886 + 0.266315i $$0.0858060\pi$$
−0.963886 + 0.266315i $$0.914194\pi$$
$$558$$ 0 0
$$559$$ 5661.87i 0.428393i
$$560$$ −14834.2 20093.1i −1.11939 1.51623i
$$561$$ 0 0
$$562$$ 14356.0 1.07753
$$563$$ 8386.38 0.627786 0.313893 0.949458i $$-0.398367\pi$$
0.313893 + 0.949458i $$0.398367\pi$$
$$564$$ 0 0
$$565$$ 12128.3i 0.903084i
$$566$$ −20144.2 −1.49598
$$567$$ 0 0
$$568$$ −7456.00 −0.550787
$$569$$ 17905.4i 1.31921i 0.751612 + 0.659606i $$0.229277\pi$$
−0.751612 + 0.659606i $$0.770723\pi$$
$$570$$ 0 0
$$571$$ −24736.0 −1.81291 −0.906453 0.422307i $$-0.861221\pi$$
−0.906453 + 0.422307i $$0.861221\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −4440.00 + 3277.93i −0.322861 + 0.238359i
$$575$$ 24812.4i 1.79956i
$$576$$ 0 0
$$577$$ 17343.2i 1.25131i −0.780099 0.625656i $$-0.784831\pi$$
0.780099 0.625656i $$-0.215169\pi$$
$$578$$ 2593.67i 0.186648i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −13443.5 18209.4i −0.959949 1.30026i
$$582$$ 0 0
$$583$$ 5566.00 0.395403
$$584$$ 18205.6 1.28999
$$585$$ 0 0
$$586$$ 655.585i 0.0462150i
$$587$$ −3329.27 −0.234095 −0.117047 0.993126i $$-0.537343\pi$$
−0.117047 + 0.993126i $$0.537343\pi$$
$$588$$ 0 0
$$589$$ −21312.0 −1.49091
$$590$$ 5023.29i 0.350518i
$$591$$ 0 0
$$592$$ 11776.0 0.817552
$$593$$ 22567.4 1.56278 0.781392 0.624041i $$-0.214510\pi$$
0.781392 + 0.624041i $$0.214510\pi$$
$$594$$ 0 0
$$595$$ 14652.0 + 19846.4i 1.00954 + 1.36743i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 6555.85i 0.448309i
$$599$$ 25216.8i 1.72009i −0.510221 0.860044i $$-0.670436\pi$$
0.510221 0.860044i $$-0.329564\pi$$
$$600$$ 0 0
$$601$$ 13290.5i 0.902048i 0.892512 + 0.451024i $$0.148941\pi$$
−0.892512 + 0.451024i $$0.851059\pi$$
$$602$$ 8007.10 5911.41i 0.542101 0.400218i
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −22946.7 −1.54201
$$606$$ 0 0
$$607$$ 18386.2i 1.22944i −0.788744 0.614722i $$-0.789268\pi$$
0.788744 0.614722i $$-0.210732\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 39072.0 2.59341
$$611$$ 1255.82i 0.0831507i
$$612$$ 0 0
$$613$$ −26554.0 −1.74960 −0.874801 0.484483i $$-0.839008\pi$$
−0.874801 + 0.484483i $$0.839008\pi$$
$$614$$ 25032.7 1.64534
$$615$$ 0 0
$$616$$ 3872.00 + 5244.68i 0.253259 + 0.343043i
$$617$$ 26475.5i 1.72749i 0.503927 + 0.863746i $$0.331888\pi$$
−0.503927 + 0.863746i $$0.668112\pi$$
$$618$$ 0 0
$$619$$ 16389.6i 1.06422i −0.846674 0.532112i $$-0.821398\pi$$
0.846674 0.532112i $$-0.178602\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 18356.4i 1.18332i
$$623$$ 7648.88 + 10360.5i 0.491888 + 0.666269i
$$624$$ 0 0
$$625$$ 46261.0 2.96070
$$626$$ −30679.8 −1.95881
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −11631.4 −0.737318
$$630$$ 0 0
$$631$$ 24860.0 1.56840 0.784200 0.620508i $$-0.213073\pi$$
0.784200 + 0.620508i $$0.213073\pi$$
$$632$$ 18916.5i 1.19060i
$$633$$ 0 0
$$634$$ −5036.00 −0.315465
$$635$$ 4635.69 0.289703
$$636$$ 0 0
$$637$$ −9768.00 3009.73i −0.607570 0.187206i
$$638$$ 5538.06i 0.343658i
$$639$$ 0 0
$$640$$ 30514.5i 1.88468i
$$641$$ 5279.26i 0.325301i 0.986684 + 0.162651i $$0.0520044\pi$$
−0.986684 + 0.162651i $$0.947996\pi$$
$$642$$ 0 0
$$643$$ 2652.14i 0.162660i −0.996687 0.0813299i $$-0.974083\pi$$
0.996687 0.0813299i $$-0.0259167\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −15984.0 −0.973502
$$647$$ 23009.9 1.39816 0.699081 0.715042i $$-0.253593\pi$$
0.699081 + 0.715042i $$0.253593\pi$$
$$648$$ 0 0
$$649$$ 1311.17i 0.0793035i
$$650$$ 26887.0 1.62245
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 5864.74i 0.351463i 0.984438 + 0.175731i $$0.0562290\pi$$
−0.984438 + 0.175731i $$0.943771\pi$$
$$654$$ 0 0
$$655$$ −27528.0 −1.64215
$$656$$ −6742.82 −0.401315
$$657$$ 0 0
$$658$$ 1776.00 1311.17i 0.105221 0.0776820i
$$659$$ 2759.13i 0.163096i 0.996669 + 0.0815482i $$0.0259864\pi$$
−0.996669 + 0.0815482i $$0.974014\pi$$
$$660$$ 0 0
$$661$$ 20978.7i 1.23446i −0.786783 0.617230i $$-0.788255\pi$$
0.786783 0.617230i $$-0.211745\pi$$
$$662$$ 26943.6i 1.58186i
$$663$$ 0 0
$$664$$ 27653.8i 1.61623i
$$665$$ 28067.0 20721.1i 1.63668 1.20831i
$$666$$ 0 0
$$667$$ 9790.00 0.568321
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 17641.2i 1.01722i
$$671$$ −10198.5 −0.586750
$$672$$ 0 0
$$673$$ −13636.0 −0.781024 −0.390512 0.920598i $$-0.627702\pi$$
−0.390512 + 0.920598i $$0.627702\pi$$
$$674$$ 23396.7i 1.33711i
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −9966.73 −0.565809 −0.282904 0.959148i $$-0.591298\pi$$
−0.282904 + 0.959148i $$0.591298\pi$$
$$678$$ 0 0
$$679$$ −8436.00 + 6228.06i −0.476795 + 0.352004i
$$680$$ 30139.7i 1.69971i
$$681$$ 0 0
$$682$$ 10489.4i 0.588942i
$$683$$ 202.233i 0.0113297i −0.999984 0.00566487i $$-0.998197\pi$$
0.999984 0.00566487i $$-0.00180319\pi$$
$$684$$ 0 0
$$685$$ 33047.5i 1.84333i
$$686$$ −5942.11 16956.4i −0.330715 0.943731i
$$687$$ 0 0
$$688$$ 12160.0 0.673831
$$689$$ −10662.1 −0.589540
$$690$$ 0 0
$$691$$ 20084.7i 1.10573i 0.833271 + 0.552865i $$0.186466\pi$$
−0.833271 + 0.552865i $$0.813534\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 27676.0 1.51378
$$695$$ 13814.0i 0.753952i
$$696$$ 0 0
$$697$$ 6660.00 0.361930
$$698$$ 17868.5 0.968956
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 22883.4i 1.23294i −0.787377 0.616472i $$-0.788561\pi$$
0.787377 0.616472i $$-0.211439\pi$$
$$702$$ 0 0
$$703$$ 16449.2i 0.882496i
$$704$$ 7964.85i 0.426401i
$$705$$ 0 0
$$706$$ 15436.1i 0.822866i
$$707$$ 8112.45 + 10988.4i 0.431542 + 0.584530i
$$708$$ 0 0
$$709$$ 12212.0 0.646871 0.323435 0.946250i $$-0.395162\pi$$
0.323435 + 0.946250i $$0.395162\pi$$
$$710$$ 19638.5 1.03805
$$711$$ 0 0
$$712$$ 15734.0i 0.828172i
$$713$$ 18542.8 0.973957
$$714$$ 0 0
$$715$$ −9768.00 −0.510913
$$716$$ 0 0
$$717$$ 0 0
$$718$$ −30668.0 −1.59404
$$719$$ −28825.5 −1.49515 −0.747574 0.664178i $$-0.768782\pi$$
−0.747574 + 0.664178i $$0.768782\pi$$
$$720$$ 0 0
$$721$$ 9768.00 7211.44i 0.504548 0.372494i
$$722$$ 3204.61i 0.165184i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 40150.9i 2.05678i
$$726$$ 0 0
$$727$$ 3277.93i 0.167224i 0.996498 + 0.0836118i $$0.0266456\pi$$
−0.996498 + 0.0836118i $$0.973354\pi$$
$$728$$ −7417.10 10046.6i −0.377604 0.511471i
$$729$$ 0 0
$$730$$ −47952.0 −2.43121
$$731$$ −12010.6 −0.607701
$$732$$ 0 0
$$733$$ 12128.3i 0.611146i −0.952169 0.305573i $$-0.901152\pi$$
0.952169 0.305573i $$-0.0988480\pi$$
$$734$$ 10535.7 0.529807
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 4604.68i 0.230143i
$$738$$ 0 0
$$739$$ 1760.00 0.0876085 0.0438042 0.999040i $$-0.486052\pi$$
0.0438042 + 0.999040i $$0.486052\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ −11132.0 15078.5i −0.550766 0.746021i
$$743$$ 22436.5i 1.10783i 0.832574 + 0.553913i $$0.186866\pi$$
−0.832574 + 0.553913i $$0.813134\pi$$
$$744$$ 0 0
$$745$$ 30901.9i 1.51968i
$$746$$ 11885.1i 0.583301i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −29563.0 + 21825.6i −1.44220 + 1.06474i
$$750$$ 0 0
$$751$$ −5122.00 −0.248874 −0.124437 0.992228i $$-0.539712\pi$$
−0.124437 + 0.992228i $$0.539712\pi$$
$$752$$ 2697.13 0.130790
$$753$$ 0 0
$$754$$ 10608.6i 0.512389i
$$755$$ −41510.5 −2.00095
$$756$$ 0 0
$$757$$ −18772.0 −0.901295 −0.450647 0.892702i $$-0.648807\pi$$
−0.450647 + 0.892702i $$0.648807\pi$$
$$758$$ 7088.04i 0.339643i
$$759$$ 0 0
$$760$$ 42624.0 2.03439
$$761$$ −28973.0 −1.38012 −0.690061 0.723752i $$-0.742416\pi$$
−0.690061 + 0.723752i $$0.742416\pi$$
$$762$$ 0 0
$$763$$ 9284.00 + 12575.3i 0.440502 + 0.596667i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 37070.4i 1.74857i
$$767$$ 2511.64i 0.118240i
$$768$$ 0 0
$$769$$ 11740.9i 0.550571i 0.961363 + 0.275285i $$0.0887724\pi$$
−0.961363 + 0.275285i $$0.911228\pi$$
$$770$$ −10198.5 13814.0i −0.477310 0.646524i
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −12706.0 −0.591207 −0.295603 0.955311i $$-0.595521\pi$$
−0.295603 + 0.955311i $$0.595521\pi$$
$$774$$ 0 0
$$775$$ 76047.9i 3.52480i
$$776$$ −12811.4 −0.592656
$$777$$ 0 0
$$778$$ −13100.0 −0.603673
$$779$$ 9418.66i 0.433195i
$$780$$ 0 0
$$781$$ −5126.00 −0.234856
$$782$$ 13907.1 0.635953
$$783$$ 0 0
$$784$$ 6464.00 20978.7i 0.294461 0.955664i
$$785$$ 55256.2i 2.51233i
$$786$$ 0 0
$$787$$ 26342.6i 1.19315i −0.802556 0.596577i $$-0.796527\pi$$
0.802556 0.596577i $$-0.203473\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 49824.5i 2.24389i
$$791$$ −8576.02 + 6331.43i −0.385497 + 0.284602i
$$792$$ 0 0
$$793$$ 19536.0 0.874834
$$794$$ 22757.0 1.01715
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 19448.8 0.864382 0.432191 0.901782i $$-0.357741\pi$$
0