# Properties

 Label 80.6.c.b.49.2 Level $80$ Weight $6$ Character 80.49 Analytic conductor $12.831$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$80 = 2^{4} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 80.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$12.8307055850$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-31})$$ Defining polynomial: $$x^{2} - x + 8$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 20) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 49.2 Root $$0.500000 - 2.78388i$$ of defining polynomial Character $$\chi$$ $$=$$ 80.49 Dual form 80.6.c.b.49.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+11.1355i q^{3} +(-5.00000 - 55.6776i) q^{5} +122.491i q^{7} +119.000 q^{9} +O(q^{10})$$ $$q+11.1355i q^{3} +(-5.00000 - 55.6776i) q^{5} +122.491i q^{7} +119.000 q^{9} +100.000 q^{11} +734.945i q^{13} +(620.000 - 55.6776i) q^{15} +979.927i q^{17} -2244.00 q^{19} -1364.00 q^{21} +3418.61i q^{23} +(-3075.00 + 556.776i) q^{25} +4031.06i q^{27} +7854.00 q^{29} +2144.00 q^{31} +1113.55i q^{33} +(6820.00 - 612.454i) q^{35} +10400.6i q^{37} -8184.00 q^{39} -7414.00 q^{41} -17761.2i q^{43} +(-595.000 - 6625.64i) q^{45} +9431.79i q^{47} +1803.00 q^{49} -10912.0 q^{51} -24253.2i q^{53} +(-500.000 - 5567.76i) q^{55} -24988.1i q^{57} +25972.0 q^{59} -3058.00 q^{61} +14576.4i q^{63} +(40920.0 - 3674.72i) q^{65} -58784.5i q^{67} -38068.0 q^{69} -37608.0 q^{71} +24008.2i q^{73} +(-6200.00 - 34241.8i) q^{75} +12249.1i q^{77} +79728.0 q^{79} -15971.0 q^{81} -16291.3i q^{83} +(54560.0 - 4899.63i) q^{85} +87458.4i q^{87} +826.000 q^{89} -90024.0 q^{91} +23874.6i q^{93} +(11220.0 + 124941. i) q^{95} -37593.5i q^{97} +11900.0 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - 10q^{5} + 238q^{9} + O(q^{10})$$ $$2q - 10q^{5} + 238q^{9} + 200q^{11} + 1240q^{15} - 4488q^{19} - 2728q^{21} - 6150q^{25} + 15708q^{29} + 4288q^{31} + 13640q^{35} - 16368q^{39} - 14828q^{41} - 1190q^{45} + 3606q^{49} - 21824q^{51} - 1000q^{55} + 51944q^{59} - 6116q^{61} + 81840q^{65} - 76136q^{69} - 75216q^{71} - 12400q^{75} + 159456q^{79} - 31942q^{81} + 109120q^{85} + 1652q^{89} - 180048q^{91} + 22440q^{95} + 23800q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$$.

 $$n$$ $$17$$ $$21$$ $$31$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 11.1355i 0.714345i 0.934039 + 0.357172i $$0.116259\pi$$
−0.934039 + 0.357172i $$0.883741\pi$$
$$4$$ 0 0
$$5$$ −5.00000 55.6776i −0.0894427 0.995992i
$$6$$ 0 0
$$7$$ 122.491i 0.944840i 0.881373 + 0.472420i $$0.156620\pi$$
−0.881373 + 0.472420i $$0.843380\pi$$
$$8$$ 0 0
$$9$$ 119.000 0.489712
$$10$$ 0 0
$$11$$ 100.000 0.249183 0.124591 0.992208i $$-0.460238\pi$$
0.124591 + 0.992208i $$0.460238\pi$$
$$12$$ 0 0
$$13$$ 734.945i 1.20614i 0.797690 + 0.603068i $$0.206055\pi$$
−0.797690 + 0.603068i $$0.793945\pi$$
$$14$$ 0 0
$$15$$ 620.000 55.6776i 0.711481 0.0638929i
$$16$$ 0 0
$$17$$ 979.927i 0.822377i 0.911550 + 0.411189i $$0.134886\pi$$
−0.911550 + 0.411189i $$0.865114\pi$$
$$18$$ 0 0
$$19$$ −2244.00 −1.42606 −0.713032 0.701132i $$-0.752678\pi$$
−0.713032 + 0.701132i $$0.752678\pi$$
$$20$$ 0 0
$$21$$ −1364.00 −0.674942
$$22$$ 0 0
$$23$$ 3418.61i 1.34750i 0.738958 + 0.673751i $$0.235318\pi$$
−0.738958 + 0.673751i $$0.764682\pi$$
$$24$$ 0 0
$$25$$ −3075.00 + 556.776i −0.984000 + 0.178168i
$$26$$ 0 0
$$27$$ 4031.06i 1.06417i
$$28$$ 0 0
$$29$$ 7854.00 1.73419 0.867093 0.498146i $$-0.165985\pi$$
0.867093 + 0.498146i $$0.165985\pi$$
$$30$$ 0 0
$$31$$ 2144.00 0.400701 0.200351 0.979724i $$-0.435792\pi$$
0.200351 + 0.979724i $$0.435792\pi$$
$$32$$ 0 0
$$33$$ 1113.55i 0.178002i
$$34$$ 0 0
$$35$$ 6820.00 612.454i 0.941053 0.0845091i
$$36$$ 0 0
$$37$$ 10400.6i 1.24897i 0.781035 + 0.624487i $$0.214692\pi$$
−0.781035 + 0.624487i $$0.785308\pi$$
$$38$$ 0 0
$$39$$ −8184.00 −0.861597
$$40$$ 0 0
$$41$$ −7414.00 −0.688800 −0.344400 0.938823i $$-0.611918\pi$$
−0.344400 + 0.938823i $$0.611918\pi$$
$$42$$ 0 0
$$43$$ 17761.2i 1.46487i −0.680835 0.732437i $$-0.738383\pi$$
0.680835 0.732437i $$-0.261617\pi$$
$$44$$ 0 0
$$45$$ −595.000 6625.64i −0.0438012 0.487749i
$$46$$ 0 0
$$47$$ 9431.79i 0.622801i 0.950279 + 0.311401i $$0.100798\pi$$
−0.950279 + 0.311401i $$0.899202\pi$$
$$48$$ 0 0
$$49$$ 1803.00 0.107277
$$50$$ 0 0
$$51$$ −10912.0 −0.587461
$$52$$ 0 0
$$53$$ 24253.2i 1.18598i −0.805208 0.592992i $$-0.797946\pi$$
0.805208 0.592992i $$-0.202054\pi$$
$$54$$ 0 0
$$55$$ −500.000 5567.76i −0.0222876 0.248184i
$$56$$ 0 0
$$57$$ 24988.1i 1.01870i
$$58$$ 0 0
$$59$$ 25972.0 0.971349 0.485675 0.874140i $$-0.338574\pi$$
0.485675 + 0.874140i $$0.338574\pi$$
$$60$$ 0 0
$$61$$ −3058.00 −0.105224 −0.0526118 0.998615i $$-0.516755\pi$$
−0.0526118 + 0.998615i $$0.516755\pi$$
$$62$$ 0 0
$$63$$ 14576.4i 0.462700i
$$64$$ 0 0
$$65$$ 40920.0 3674.72i 1.20130 0.107880i
$$66$$ 0 0
$$67$$ 58784.5i 1.59984i −0.600109 0.799918i $$-0.704876\pi$$
0.600109 0.799918i $$-0.295124\pi$$
$$68$$ 0 0
$$69$$ −38068.0 −0.962581
$$70$$ 0 0
$$71$$ −37608.0 −0.885389 −0.442695 0.896672i $$-0.645977\pi$$
−0.442695 + 0.896672i $$0.645977\pi$$
$$72$$ 0 0
$$73$$ 24008.2i 0.527294i 0.964619 + 0.263647i $$0.0849253\pi$$
−0.964619 + 0.263647i $$0.915075\pi$$
$$74$$ 0 0
$$75$$ −6200.00 34241.8i −0.127274 0.702915i
$$76$$ 0 0
$$77$$ 12249.1i 0.235438i
$$78$$ 0 0
$$79$$ 79728.0 1.43729 0.718643 0.695379i $$-0.244764\pi$$
0.718643 + 0.695379i $$0.244764\pi$$
$$80$$ 0 0
$$81$$ −15971.0 −0.270470
$$82$$ 0 0
$$83$$ 16291.3i 0.259573i −0.991542 0.129787i $$-0.958571\pi$$
0.991542 0.129787i $$-0.0414292\pi$$
$$84$$ 0 0
$$85$$ 54560.0 4899.63i 0.819081 0.0735557i
$$86$$ 0 0
$$87$$ 87458.4i 1.23881i
$$88$$ 0 0
$$89$$ 826.000 0.0110536 0.00552682 0.999985i $$-0.498241\pi$$
0.00552682 + 0.999985i $$0.498241\pi$$
$$90$$ 0 0
$$91$$ −90024.0 −1.13961
$$92$$ 0 0
$$93$$ 23874.6i 0.286239i
$$94$$ 0 0
$$95$$ 11220.0 + 124941.i 0.127551 + 1.42035i
$$96$$ 0 0
$$97$$ 37593.5i 0.405680i −0.979212 0.202840i $$-0.934983\pi$$
0.979212 0.202840i $$-0.0650172\pi$$
$$98$$ 0 0
$$99$$ 11900.0 0.122028
$$100$$ 0 0
$$101$$ −143594. −1.40066 −0.700330 0.713819i $$-0.746964\pi$$
−0.700330 + 0.713819i $$0.746964\pi$$
$$102$$ 0 0
$$103$$ 111834.i 1.03868i 0.854568 + 0.519339i $$0.173822\pi$$
−0.854568 + 0.519339i $$0.826178\pi$$
$$104$$ 0 0
$$105$$ 6820.00 + 75944.3i 0.0603686 + 0.672236i
$$106$$ 0 0
$$107$$ 92235.6i 0.778824i −0.921064 0.389412i $$-0.872678\pi$$
0.921064 0.389412i $$-0.127322\pi$$
$$108$$ 0 0
$$109$$ 106238. 0.856473 0.428236 0.903667i $$-0.359135\pi$$
0.428236 + 0.903667i $$0.359135\pi$$
$$110$$ 0 0
$$111$$ −115816. −0.892198
$$112$$ 0 0
$$113$$ 113048.i 0.832849i 0.909170 + 0.416425i $$0.136717\pi$$
−0.909170 + 0.416425i $$0.863283\pi$$
$$114$$ 0 0
$$115$$ 190340. 17093.0i 1.34210 0.120524i
$$116$$ 0 0
$$117$$ 87458.4i 0.590659i
$$118$$ 0 0
$$119$$ −120032. −0.777015
$$120$$ 0 0
$$121$$ −151051. −0.937908
$$122$$ 0 0
$$123$$ 82558.8i 0.492040i
$$124$$ 0 0
$$125$$ 46375.0 + 168425.i 0.265466 + 0.964120i
$$126$$ 0 0
$$127$$ 51568.6i 0.283711i 0.989887 + 0.141856i $$0.0453069\pi$$
−0.989887 + 0.141856i $$0.954693\pi$$
$$128$$ 0 0
$$129$$ 197780. 1.04642
$$130$$ 0 0
$$131$$ 89100.0 0.453628 0.226814 0.973938i $$-0.427169\pi$$
0.226814 + 0.973938i $$0.427169\pi$$
$$132$$ 0 0
$$133$$ 274869.i 1.34740i
$$134$$ 0 0
$$135$$ 224440. 20155.3i 1.05990 0.0951820i
$$136$$ 0 0
$$137$$ 38350.8i 0.174571i −0.996183 0.0872856i $$-0.972181\pi$$
0.996183 0.0872856i $$-0.0278193\pi$$
$$138$$ 0 0
$$139$$ −134684. −0.591261 −0.295630 0.955302i $$-0.595530\pi$$
−0.295630 + 0.955302i $$0.595530\pi$$
$$140$$ 0 0
$$141$$ −105028. −0.444895
$$142$$ 0 0
$$143$$ 73494.5i 0.300549i
$$144$$ 0 0
$$145$$ −39270.0 437292.i −0.155110 1.72724i
$$146$$ 0 0
$$147$$ 20077.4i 0.0766325i
$$148$$ 0 0
$$149$$ 248006. 0.915159 0.457579 0.889169i $$-0.348717\pi$$
0.457579 + 0.889169i $$0.348717\pi$$
$$150$$ 0 0
$$151$$ −313720. −1.11970 −0.559848 0.828596i $$-0.689140\pi$$
−0.559848 + 0.828596i $$0.689140\pi$$
$$152$$ 0 0
$$153$$ 116611.i 0.402728i
$$154$$ 0 0
$$155$$ −10720.0 119373.i −0.0358398 0.399095i
$$156$$ 0 0
$$157$$ 245583.i 0.795150i −0.917570 0.397575i $$-0.869852\pi$$
0.917570 0.397575i $$-0.130148\pi$$
$$158$$ 0 0
$$159$$ 270072. 0.847202
$$160$$ 0 0
$$161$$ −418748. −1.27317
$$162$$ 0 0
$$163$$ 397483.i 1.17179i −0.810388 0.585894i $$-0.800743\pi$$
0.810388 0.585894i $$-0.199257\pi$$
$$164$$ 0 0
$$165$$ 62000.0 5567.76i 0.177289 0.0159210i
$$166$$ 0 0
$$167$$ 189983.i 0.527138i −0.964641 0.263569i $$-0.915100\pi$$
0.964641 0.263569i $$-0.0848996\pi$$
$$168$$ 0 0
$$169$$ −168851. −0.454765
$$170$$ 0 0
$$171$$ −267036. −0.698360
$$172$$ 0 0
$$173$$ 81088.9i 0.205990i 0.994682 + 0.102995i $$0.0328426\pi$$
−0.994682 + 0.102995i $$0.967157\pi$$
$$174$$ 0 0
$$175$$ −68200.0 376659.i −0.168341 0.929723i
$$176$$ 0 0
$$177$$ 289212.i 0.693878i
$$178$$ 0 0
$$179$$ 142108. 0.331502 0.165751 0.986168i $$-0.446995\pi$$
0.165751 + 0.986168i $$0.446995\pi$$
$$180$$ 0 0
$$181$$ 250790. 0.569002 0.284501 0.958676i $$-0.408172\pi$$
0.284501 + 0.958676i $$0.408172\pi$$
$$182$$ 0 0
$$183$$ 34052.4i 0.0751659i
$$184$$ 0 0
$$185$$ 579080. 52002.9i 1.24397 0.111712i
$$186$$ 0 0
$$187$$ 97992.7i 0.204922i
$$188$$ 0 0
$$189$$ −493768. −1.00547
$$190$$ 0 0
$$191$$ 209472. 0.415473 0.207736 0.978185i $$-0.433390\pi$$
0.207736 + 0.978185i $$0.433390\pi$$
$$192$$ 0 0
$$193$$ 356693.i 0.689289i −0.938733 0.344645i $$-0.887999\pi$$
0.938733 0.344645i $$-0.112001\pi$$
$$194$$ 0 0
$$195$$ 40920.0 + 455666.i 0.0770636 + 0.858144i
$$196$$ 0 0
$$197$$ 86478.5i 0.158761i 0.996844 + 0.0793803i $$0.0252941\pi$$
−0.996844 + 0.0793803i $$0.974706\pi$$
$$198$$ 0 0
$$199$$ 749208. 1.34113 0.670563 0.741852i $$-0.266053\pi$$
0.670563 + 0.741852i $$0.266053\pi$$
$$200$$ 0 0
$$201$$ 654596. 1.14283
$$202$$ 0 0
$$203$$ 962043.i 1.63853i
$$204$$ 0 0
$$205$$ 37070.0 + 412794.i 0.0616081 + 0.686039i
$$206$$ 0 0
$$207$$ 406814.i 0.659888i
$$208$$ 0 0
$$209$$ −224400. −0.355351
$$210$$ 0 0
$$211$$ −287364. −0.444351 −0.222176 0.975007i $$-0.571316\pi$$
−0.222176 + 0.975007i $$0.571316\pi$$
$$212$$ 0 0
$$213$$ 418785.i 0.632473i
$$214$$ 0 0
$$215$$ −988900. + 88805.8i −1.45900 + 0.131022i
$$216$$ 0 0
$$217$$ 262620.i 0.378599i
$$218$$ 0 0
$$219$$ −267344. −0.376669
$$220$$ 0 0
$$221$$ −720192. −0.991899
$$222$$ 0 0
$$223$$ 1.18866e6i 1.60065i −0.599567 0.800325i $$-0.704660\pi$$
0.599567 0.800325i $$-0.295340\pi$$
$$224$$ 0 0
$$225$$ −365925. + 66256.4i −0.481877 + 0.0872512i
$$226$$ 0 0
$$227$$ 978334.i 1.26015i 0.776534 + 0.630075i $$0.216976\pi$$
−0.776534 + 0.630075i $$0.783024\pi$$
$$228$$ 0 0
$$229$$ −506474. −0.638217 −0.319109 0.947718i $$-0.603383\pi$$
−0.319109 + 0.947718i $$0.603383\pi$$
$$230$$ 0 0
$$231$$ −136400. −0.168184
$$232$$ 0 0
$$233$$ 1.55465e6i 1.87605i 0.346571 + 0.938024i $$0.387346\pi$$
−0.346571 + 0.938024i $$0.612654\pi$$
$$234$$ 0 0
$$235$$ 525140. 47159.0i 0.620305 0.0557051i
$$236$$ 0 0
$$237$$ 887813.i 1.02672i
$$238$$ 0 0
$$239$$ −374704. −0.424320 −0.212160 0.977235i $$-0.568050\pi$$
−0.212160 + 0.977235i $$0.568050\pi$$
$$240$$ 0 0
$$241$$ 843634. 0.935646 0.467823 0.883822i $$-0.345039\pi$$
0.467823 + 0.883822i $$0.345039\pi$$
$$242$$ 0 0
$$243$$ 801702.i 0.870959i
$$244$$ 0 0
$$245$$ −9015.00 100387.i −0.00959512 0.106847i
$$246$$ 0 0
$$247$$ 1.64922e6i 1.72003i
$$248$$ 0 0
$$249$$ 181412. 0.185425
$$250$$ 0 0
$$251$$ 1.72050e6 1.72373 0.861867 0.507134i $$-0.169295\pi$$
0.861867 + 0.507134i $$0.169295\pi$$
$$252$$ 0 0
$$253$$ 341861.i 0.335775i
$$254$$ 0 0
$$255$$ 54560.0 + 607554.i 0.0525441 + 0.585106i
$$256$$ 0 0
$$257$$ 1.55220e6i 1.46594i −0.680262 0.732969i $$-0.738134\pi$$
0.680262 0.732969i $$-0.261866\pi$$
$$258$$ 0 0
$$259$$ −1.27398e6 −1.18008
$$260$$ 0 0
$$261$$ 934626. 0.849252
$$262$$ 0 0
$$263$$ 407772.i 0.363520i 0.983343 + 0.181760i $$0.0581793\pi$$
−0.983343 + 0.181760i $$0.941821\pi$$
$$264$$ 0 0
$$265$$ −1.35036e6 + 121266.i −1.18123 + 0.106078i
$$266$$ 0 0
$$267$$ 9197.95i 0.00789610i
$$268$$ 0 0
$$269$$ 1.82710e6 1.53951 0.769754 0.638340i $$-0.220379\pi$$
0.769754 + 0.638340i $$0.220379\pi$$
$$270$$ 0 0
$$271$$ 616880. 0.510243 0.255122 0.966909i $$-0.417884\pi$$
0.255122 + 0.966909i $$0.417884\pi$$
$$272$$ 0 0
$$273$$ 1.00246e6i 0.814071i
$$274$$ 0 0
$$275$$ −307500. + 55677.6i −0.245196 + 0.0443965i
$$276$$ 0 0
$$277$$ 1.83712e6i 1.43859i −0.694704 0.719296i $$-0.744465\pi$$
0.694704 0.719296i $$-0.255535\pi$$
$$278$$ 0 0
$$279$$ 255136. 0.196228
$$280$$ 0 0
$$281$$ −1.22093e6 −0.922415 −0.461208 0.887292i $$-0.652584\pi$$
−0.461208 + 0.887292i $$0.652584\pi$$
$$282$$ 0 0
$$283$$ 688766.i 0.511217i 0.966780 + 0.255609i $$0.0822758\pi$$
−0.966780 + 0.255609i $$0.917724\pi$$
$$284$$ 0 0
$$285$$ −1.39128e6 + 124941.i −1.01462 + 0.0911154i
$$286$$ 0 0
$$287$$ 908147.i 0.650806i
$$288$$ 0 0
$$289$$ 459601. 0.323695
$$290$$ 0 0
$$291$$ 418624. 0.289796
$$292$$ 0 0
$$293$$ 856211.i 0.582655i −0.956623 0.291328i $$-0.905903\pi$$
0.956623 0.291328i $$-0.0940970\pi$$
$$294$$ 0 0
$$295$$ −129860. 1.44606e6i −0.0868801 0.967456i
$$296$$ 0 0
$$297$$ 403106.i 0.265172i
$$298$$ 0 0
$$299$$ −2.51249e6 −1.62527
$$300$$ 0 0
$$301$$ 2.17558e6 1.38407
$$302$$ 0 0
$$303$$ 1.59900e6i 1.00055i
$$304$$ 0 0
$$305$$ 15290.0 + 170262.i 0.00941148 + 0.104802i
$$306$$ 0 0
$$307$$ 1.09617e6i 0.663792i −0.943316 0.331896i $$-0.892312\pi$$
0.943316 0.331896i $$-0.107688\pi$$
$$308$$ 0 0
$$309$$ −1.24533e6 −0.741974
$$310$$ 0 0
$$311$$ 2.12465e6 1.24562 0.622811 0.782373i $$-0.285991\pi$$
0.622811 + 0.782373i $$0.285991\pi$$
$$312$$ 0 0
$$313$$ 294824.i 0.170099i −0.996377 0.0850496i $$-0.972895\pi$$
0.996377 0.0850496i $$-0.0271049\pi$$
$$314$$ 0 0
$$315$$ 811580. 72882.0i 0.460845 0.0413851i
$$316$$ 0 0
$$317$$ 2.53153e6i 1.41493i 0.706749 + 0.707465i $$0.250161\pi$$
−0.706749 + 0.707465i $$0.749839\pi$$
$$318$$ 0 0
$$319$$ 785400. 0.432130
$$320$$ 0 0
$$321$$ 1.02709e6 0.556348
$$322$$ 0 0
$$323$$ 2.19896e6i 1.17276i
$$324$$ 0 0
$$325$$ −409200. 2.25996e6i −0.214895 1.18684i
$$326$$ 0 0
$$327$$ 1.18302e6i 0.611817i
$$328$$ 0 0
$$329$$ −1.15531e6 −0.588448
$$330$$ 0 0
$$331$$ 1.17021e6 0.587076 0.293538 0.955947i $$-0.405167\pi$$
0.293538 + 0.955947i $$0.405167\pi$$
$$332$$ 0 0
$$333$$ 1.23767e6i 0.611637i
$$334$$ 0 0
$$335$$ −3.27298e6 + 293922.i −1.59342 + 0.143094i
$$336$$ 0 0
$$337$$ 1.86872e6i 0.896333i −0.893950 0.448167i $$-0.852077\pi$$
0.893950 0.448167i $$-0.147923\pi$$
$$338$$ 0 0
$$339$$ −1.25885e6 −0.594941
$$340$$ 0 0
$$341$$ 214400. 0.0998479
$$342$$ 0 0
$$343$$ 2.27955e6i 1.04620i
$$344$$ 0 0
$$345$$ 190340. + 2.11954e6i 0.0860959 + 0.958723i
$$346$$ 0 0
$$347$$ 1.63342e6i 0.728237i 0.931353 + 0.364119i $$0.118630\pi$$
−0.931353 + 0.364119i $$0.881370\pi$$
$$348$$ 0 0
$$349$$ −2.00629e6 −0.881719 −0.440859 0.897576i $$-0.645326\pi$$
−0.440859 + 0.897576i $$0.645326\pi$$
$$350$$ 0 0
$$351$$ −2.96261e6 −1.28353
$$352$$ 0 0
$$353$$ 1.80859e6i 0.772508i −0.922392 0.386254i $$-0.873769\pi$$
0.922392 0.386254i $$-0.126231\pi$$
$$354$$ 0 0
$$355$$ 188040. + 2.09392e6i 0.0791916 + 0.881841i
$$356$$ 0 0
$$357$$ 1.33662e6i 0.555057i
$$358$$ 0 0
$$359$$ 4.50674e6 1.84555 0.922777 0.385334i $$-0.125914\pi$$
0.922777 + 0.385334i $$0.125914\pi$$
$$360$$ 0 0
$$361$$ 2.55944e6 1.03366
$$362$$ 0 0
$$363$$ 1.68203e6i 0.669989i
$$364$$ 0 0
$$365$$ 1.33672e6 120041.i 0.525180 0.0471626i
$$366$$ 0 0
$$367$$ 3.02796e6i 1.17351i 0.809766 + 0.586753i $$0.199594\pi$$
−0.809766 + 0.586753i $$0.800406\pi$$
$$368$$ 0 0
$$369$$ −882266. −0.337313
$$370$$ 0 0
$$371$$ 2.97079e6 1.12057
$$372$$ 0 0
$$373$$ 1.16342e6i 0.432976i 0.976285 + 0.216488i $$0.0694602\pi$$
−0.976285 + 0.216488i $$0.930540\pi$$
$$374$$ 0 0
$$375$$ −1.87550e6 + 516410.i −0.688714 + 0.189634i
$$376$$ 0 0
$$377$$ 5.77226e6i 2.09167i
$$378$$ 0 0
$$379$$ 832052. 0.297545 0.148772 0.988871i $$-0.452468\pi$$
0.148772 + 0.988871i $$0.452468\pi$$
$$380$$ 0 0
$$381$$ −574244. −0.202667
$$382$$ 0 0
$$383$$ 2.86948e6i 0.999554i 0.866154 + 0.499777i $$0.166585\pi$$
−0.866154 + 0.499777i $$0.833415\pi$$
$$384$$ 0 0
$$385$$ 682000. 61245.4i 0.234494 0.0210582i
$$386$$ 0 0
$$387$$ 2.11358e6i 0.717366i
$$388$$ 0 0
$$389$$ 311926. 0.104515 0.0522574 0.998634i $$-0.483358\pi$$
0.0522574 + 0.998634i $$0.483358\pi$$
$$390$$ 0 0
$$391$$ −3.34998e6 −1.10816
$$392$$ 0 0
$$393$$ 992176.i 0.324046i
$$394$$ 0 0
$$395$$ −398640. 4.43907e6i −0.128555 1.43153i
$$396$$ 0 0
$$397$$ 2.95619e6i 0.941362i 0.882304 + 0.470681i $$0.155992\pi$$
−0.882304 + 0.470681i $$0.844008\pi$$
$$398$$ 0 0
$$399$$ 3.06082e6 0.962509
$$400$$ 0 0
$$401$$ 2770.00 0.000860238 0.000430119 1.00000i $$-0.499863\pi$$
0.000430119 1.00000i $$0.499863\pi$$
$$402$$ 0 0
$$403$$ 1.57572e6i 0.483300i
$$404$$ 0 0
$$405$$ 79855.0 + 889228.i 0.0241916 + 0.269386i
$$406$$ 0 0
$$407$$ 1.04006e6i 0.311223i
$$408$$ 0 0
$$409$$ −1.97985e6 −0.585225 −0.292613 0.956231i $$-0.594525\pi$$
−0.292613 + 0.956231i $$0.594525\pi$$
$$410$$ 0 0
$$411$$ 427056. 0.124704
$$412$$ 0 0
$$413$$ 3.18133e6i 0.917770i
$$414$$ 0 0
$$415$$ −907060. + 81456.4i −0.258533 + 0.0232169i
$$416$$ 0 0
$$417$$ 1.49978e6i 0.422364i
$$418$$ 0 0
$$419$$ −5.10120e6 −1.41951 −0.709754 0.704450i $$-0.751194\pi$$
−0.709754 + 0.704450i $$0.751194\pi$$
$$420$$ 0 0
$$421$$ −2.43223e6 −0.668806 −0.334403 0.942430i $$-0.608535\pi$$
−0.334403 + 0.942430i $$0.608535\pi$$
$$422$$ 0 0
$$423$$ 1.12238e6i 0.304993i
$$424$$ 0 0
$$425$$ −545600. 3.01327e6i −0.146522 0.809219i
$$426$$ 0 0
$$427$$ 374577.i 0.0994194i
$$428$$ 0 0
$$429$$ −818400. −0.214695
$$430$$ 0 0
$$431$$ −918896. −0.238272 −0.119136 0.992878i $$-0.538012\pi$$
−0.119136 + 0.992878i $$0.538012\pi$$
$$432$$ 0 0
$$433$$ 2.05455e6i 0.526619i −0.964711 0.263310i $$-0.915186\pi$$
0.964711 0.263310i $$-0.0848141\pi$$
$$434$$ 0 0
$$435$$ 4.86948e6 437292.i 1.23384 0.110802i
$$436$$ 0 0
$$437$$ 7.67135e6i 1.92162i
$$438$$ 0 0
$$439$$ −676632. −0.167568 −0.0837840 0.996484i $$-0.526701\pi$$
−0.0837840 + 0.996484i $$0.526701\pi$$
$$440$$ 0 0
$$441$$ 214557. 0.0525347
$$442$$ 0 0
$$443$$ 2.53092e6i 0.612729i −0.951914 0.306365i $$-0.900887\pi$$
0.951914 0.306365i $$-0.0991126\pi$$
$$444$$ 0 0
$$445$$ −4130.00 45989.7i −0.000988667 0.0110093i
$$446$$ 0 0
$$447$$ 2.76168e6i 0.653739i
$$448$$ 0 0
$$449$$ 5.17619e6 1.21170 0.605849 0.795579i $$-0.292833\pi$$
0.605849 + 0.795579i $$0.292833\pi$$
$$450$$ 0 0
$$451$$ −741400. −0.171637
$$452$$ 0 0
$$453$$ 3.49344e6i 0.799848i
$$454$$ 0 0
$$455$$ 450120. + 5.01232e6i 0.101929 + 1.13504i
$$456$$ 0 0
$$457$$ 3.11274e6i 0.697191i 0.937273 + 0.348596i $$0.113341\pi$$
−0.937273 + 0.348596i $$0.886659\pi$$
$$458$$ 0 0
$$459$$ −3.95014e6 −0.875147
$$460$$ 0 0
$$461$$ −2.64957e6 −0.580662 −0.290331 0.956926i $$-0.593765\pi$$
−0.290331 + 0.956926i $$0.593765\pi$$
$$462$$ 0 0
$$463$$ 2.59165e6i 0.561854i −0.959729 0.280927i $$-0.909358\pi$$
0.959729 0.280927i $$-0.0906420\pi$$
$$464$$ 0 0
$$465$$ 1.32928e6 119373.i 0.285091 0.0256020i
$$466$$ 0 0
$$467$$ 6.62135e6i 1.40493i −0.711719 0.702465i $$-0.752083\pi$$
0.711719 0.702465i $$-0.247917\pi$$
$$468$$ 0 0
$$469$$ 7.20056e6 1.51159
$$470$$ 0 0
$$471$$ 2.73470e6 0.568011
$$472$$ 0 0
$$473$$ 1.77612e6i 0.365022i
$$474$$ 0 0
$$475$$ 6.90030e6 1.24941e6i 1.40325 0.254080i
$$476$$ 0 0
$$477$$ 2.88613e6i 0.580791i
$$478$$ 0 0
$$479$$ 6.89322e6 1.37272 0.686362 0.727260i $$-0.259207\pi$$
0.686362 + 0.727260i $$0.259207\pi$$
$$480$$ 0 0
$$481$$ −7.64386e6 −1.50643
$$482$$ 0 0
$$483$$ 4.66298e6i 0.909485i
$$484$$ 0 0
$$485$$ −2.09312e6 + 187968.i −0.404054 + 0.0362852i
$$486$$ 0 0
$$487$$ 5.65370e6i 1.08021i −0.841596 0.540107i $$-0.818384\pi$$
0.841596 0.540107i $$-0.181616\pi$$
$$488$$ 0 0
$$489$$ 4.42618e6 0.837061
$$490$$ 0 0
$$491$$ −5.88390e6 −1.10144 −0.550721 0.834689i $$-0.685647\pi$$
−0.550721 + 0.834689i $$0.685647\pi$$
$$492$$ 0 0
$$493$$ 7.69634e6i 1.42616i
$$494$$ 0 0
$$495$$ −59500.0 662564.i −0.0109145 0.121539i
$$496$$ 0 0
$$497$$ 4.60663e6i 0.836552i
$$498$$ 0 0
$$499$$ −6.72080e6 −1.20829 −0.604143 0.796876i $$-0.706485\pi$$
−0.604143 + 0.796876i $$0.706485\pi$$
$$500$$ 0 0
$$501$$ 2.11556e6 0.376558
$$502$$ 0 0
$$503$$ 469262.i 0.0826981i −0.999145 0.0413491i $$-0.986834\pi$$
0.999145 0.0413491i $$-0.0131656\pi$$
$$504$$ 0 0
$$505$$ 717970. + 7.99498e6i 0.125279 + 1.39505i
$$506$$ 0 0
$$507$$ 1.88025e6i 0.324859i
$$508$$ 0 0
$$509$$ 294414. 0.0503691 0.0251845 0.999683i $$-0.491983\pi$$
0.0251845 + 0.999683i $$0.491983\pi$$
$$510$$ 0 0
$$511$$ −2.94078e6 −0.498208
$$512$$ 0 0
$$513$$ 9.04570e6i 1.51757i
$$514$$ 0 0
$$515$$ 6.22666e6 559171.i 1.03452 0.0929023i
$$516$$ 0 0
$$517$$ 943179.i 0.155191i
$$518$$ 0 0
$$519$$ −902968. −0.147148
$$520$$ 0 0
$$521$$ −7.10025e6 −1.14599 −0.572993 0.819560i $$-0.694218\pi$$
−0.572993 + 0.819560i $$0.694218\pi$$
$$522$$ 0 0
$$523$$ 5.96567e6i 0.953685i 0.878989 + 0.476843i $$0.158219\pi$$
−0.878989 + 0.476843i $$0.841781\pi$$
$$524$$ 0 0
$$525$$ 4.19430e6 759443.i 0.664142 0.120253i
$$526$$ 0 0
$$527$$ 2.10096e6i 0.329528i
$$528$$ 0 0
$$529$$ −5.25053e6 −0.815763
$$530$$ 0 0
$$531$$ 3.09067e6 0.475681
$$532$$ 0 0
$$533$$ 5.44888e6i 0.830786i
$$534$$ 0 0
$$535$$ −5.13546e6 + 461178.i −0.775702 + 0.0696601i
$$536$$ 0 0
$$537$$ 1.58245e6i 0.236807i
$$538$$ 0 0
$$539$$ 180300. 0.0267315
$$540$$ 0 0
$$541$$ −2.72367e6 −0.400093 −0.200046 0.979786i $$-0.564109\pi$$
−0.200046 + 0.979786i $$0.564109\pi$$
$$542$$ 0 0
$$543$$ 2.79268e6i 0.406463i
$$544$$ 0 0
$$545$$ −531190. 5.91508e6i −0.0766053 0.853040i
$$546$$ 0 0
$$547$$ 9.22148e6i 1.31775i 0.752254 + 0.658874i $$0.228967\pi$$
−0.752254 + 0.658874i $$0.771033\pi$$
$$548$$ 0 0
$$549$$ −363902. −0.0515292
$$550$$ 0 0
$$551$$ −1.76244e7 −2.47306
$$552$$ 0 0
$$553$$ 9.76595e6i 1.35801i
$$554$$ 0 0
$$555$$ 579080. + 6.44836e6i 0.0798006 + 0.888622i
$$556$$ 0 0
$$557$$ 3.42852e6i 0.468240i 0.972208 + 0.234120i $$0.0752209\pi$$
−0.972208 + 0.234120i $$0.924779\pi$$
$$558$$ 0 0
$$559$$ 1.30535e7 1.76684
$$560$$ 0 0
$$561$$ −1.09120e6 −0.146385
$$562$$ 0 0
$$563$$ 5.77899e6i 0.768389i 0.923252 + 0.384195i $$0.125521\pi$$
−0.923252 + 0.384195i $$0.874479\pi$$
$$564$$ 0 0
$$565$$ 6.29424e6 565239.i 0.829511 0.0744923i
$$566$$ 0 0
$$567$$ 1.95630e6i 0.255551i
$$568$$ 0 0
$$569$$ 3.89257e6 0.504029 0.252015 0.967723i $$-0.418907\pi$$
0.252015 + 0.967723i $$0.418907\pi$$
$$570$$ 0 0
$$571$$ 5.06277e6 0.649828 0.324914 0.945744i $$-0.394665\pi$$
0.324914 + 0.945744i $$0.394665\pi$$
$$572$$ 0 0
$$573$$ 2.33258e6i 0.296791i
$$574$$ 0 0
$$575$$ −1.90340e6 1.05122e7i −0.240082 1.32594i
$$576$$ 0 0
$$577$$ 3.30075e6i 0.412737i 0.978474 + 0.206368i $$0.0661645\pi$$
−0.978474 + 0.206368i $$0.933836\pi$$
$$578$$ 0 0
$$579$$ 3.97197e6 0.492390
$$580$$ 0 0
$$581$$ 1.99553e6 0.245255
$$582$$ 0 0
$$583$$ 2.42532e6i 0.295527i
$$584$$ 0 0
$$585$$ 4.86948e6 437292.i 0.588292 0.0528302i
$$586$$ 0 0
$$587$$ 5.16997e6i 0.619288i 0.950853 + 0.309644i $$0.100210\pi$$
−0.950853 + 0.309644i $$0.899790\pi$$
$$588$$ 0 0
$$589$$ −4.81114e6 −0.571425
$$590$$ 0 0
$$591$$ −962984. −0.113410
$$592$$ 0 0
$$593$$ 1.58484e7i 1.85075i 0.379055 + 0.925374i $$0.376249\pi$$
−0.379055 + 0.925374i $$0.623751\pi$$
$$594$$ 0 0
$$595$$ 600160. + 6.68310e6i 0.0694984 + 0.773901i
$$596$$ 0 0
$$597$$ 8.34283e6i 0.958026i
$$598$$ 0 0
$$599$$ 1.66146e7 1.89201 0.946004 0.324156i $$-0.105080\pi$$
0.946004 + 0.324156i $$0.105080\pi$$
$$600$$ 0 0
$$601$$ 7.88249e6 0.890179 0.445089 0.895486i $$-0.353172\pi$$
0.445089 + 0.895486i $$0.353172\pi$$
$$602$$ 0 0
$$603$$ 6.99535e6i 0.783459i
$$604$$ 0 0
$$605$$ 755255. + 8.41016e6i 0.0838890 + 0.934149i
$$606$$ 0 0
$$607$$ 782594.i 0.0862114i 0.999071 + 0.0431057i $$0.0137252\pi$$
−0.999071 + 0.0431057i $$0.986275\pi$$
$$608$$ 0 0
$$609$$ −1.07129e7 −1.17047
$$610$$ 0 0
$$611$$ −6.93185e6 −0.751183
$$612$$ 0 0
$$613$$ 2.41233e6i 0.259290i −0.991560 0.129645i $$-0.958616\pi$$
0.991560 0.129645i $$-0.0413838\pi$$
$$614$$ 0 0
$$615$$ −4.59668e6 + 412794.i −0.490068 + 0.0440094i
$$616$$ 0 0
$$617$$ 9.66355e6i 1.02194i −0.859600 0.510968i $$-0.829287\pi$$
0.859600 0.510968i $$-0.170713\pi$$
$$618$$ 0 0
$$619$$ −1.80036e7 −1.88857 −0.944283 0.329134i $$-0.893243\pi$$
−0.944283 + 0.329134i $$0.893243\pi$$
$$620$$ 0 0
$$621$$ −1.37806e7 −1.43397
$$622$$ 0 0
$$623$$ 101177.i 0.0104439i
$$624$$ 0 0
$$625$$ 9.14562e6 3.42418e6i 0.936512 0.350636i
$$626$$ 0 0
$$627$$ 2.49881e6i 0.253843i
$$628$$ 0 0
$$629$$ −1.01918e7 −1.02713
$$630$$ 0 0
$$631$$ 4.80081e6 0.480000 0.240000 0.970773i $$-0.422853\pi$$
0.240000 + 0.970773i $$0.422853\pi$$
$$632$$ 0 0
$$633$$ 3.19995e6i 0.317420i
$$634$$ 0 0
$$635$$ 2.87122e6 257843.i 0.282574 0.0253759i
$$636$$ 0 0
$$637$$ 1.32511e6i 0.129390i
$$638$$ 0 0
$$639$$ −4.47535e6 −0.433586
$$640$$ 0 0
$$641$$ 1.44950e7 1.39340 0.696698 0.717365i $$-0.254652\pi$$
0.696698 + 0.717365i $$0.254652\pi$$
$$642$$ 0 0
$$643$$ 1.82430e7i 1.74008i 0.492979 + 0.870041i $$0.335908\pi$$
−0.492979 + 0.870041i $$0.664092\pi$$
$$644$$ 0 0
$$645$$ −988900. 1.10119e7i −0.0935951 1.04223i
$$646$$ 0 0
$$647$$ 9.64592e6i 0.905905i −0.891535 0.452953i $$-0.850371\pi$$
0.891535 0.452953i $$-0.149629\pi$$
$$648$$ 0 0
$$649$$ 2.59720e6 0.242044
$$650$$ 0 0
$$651$$ −2.92442e6 −0.270450
$$652$$ 0 0
$$653$$ 1.92807e7i 1.76945i −0.466111 0.884726i $$-0.654345\pi$$
0.466111 0.884726i $$-0.345655\pi$$
$$654$$ 0 0
$$655$$ −445500. 4.96088e6i −0.0405737 0.451809i
$$656$$ 0 0
$$657$$ 2.85698e6i 0.258222i
$$658$$ 0 0
$$659$$ 9.70592e6 0.870609 0.435304 0.900283i $$-0.356641\pi$$
0.435304 + 0.900283i $$0.356641\pi$$
$$660$$ 0 0
$$661$$ −4.28396e6 −0.381366 −0.190683 0.981652i $$-0.561070\pi$$
−0.190683 + 0.981652i $$0.561070\pi$$
$$662$$ 0 0
$$663$$ 8.01972e6i 0.708558i
$$664$$ 0 0
$$665$$ −1.53041e7 + 1.37435e6i −1.34200 + 0.120515i
$$666$$ 0 0
$$667$$ 2.68497e7i 2.33682i
$$668$$ 0 0
$$669$$ 1.32364e7 1.14342
$$670$$ 0 0
$$671$$ −305800. −0.0262199
$$672$$ 0 0
$$673$$ 1.30585e7i 1.11136i −0.831395 0.555681i $$-0.812458\pi$$
0.831395 0.555681i $$-0.187542\pi$$
$$674$$ 0 0
$$675$$ −2.24440e6 1.23955e7i −0.189601 1.04714i
$$676$$ 0 0
$$677$$ 8.42565e6i 0.706532i 0.935523 + 0.353266i $$0.114929\pi$$
−0.935523 + 0.353266i $$0.885071\pi$$
$$678$$ 0 0
$$679$$ 4.60486e6 0.383303
$$680$$ 0 0
$$681$$ −1.08943e7 −0.900182
$$682$$ 0 0
$$683$$ 1.64100e7i 1.34603i −0.739627 0.673017i $$-0.764998\pi$$
0.739627 0.673017i $$-0.235002\pi$$
$$684$$ 0 0
$$685$$ −2.13528e6 + 191754.i −0.173872 + 0.0156141i
$$686$$ 0 0
$$687$$ 5.63986e6i 0.455907i
$$688$$ 0 0
$$689$$ 1.78248e7 1.43046
$$690$$ 0 0
$$691$$ 1.12139e7 0.893428 0.446714 0.894677i $$-0.352594\pi$$
0.446714 + 0.894677i $$0.352594\pi$$
$$692$$ 0 0
$$693$$ 1.45764e6i 0.115297i
$$694$$ 0 0
$$695$$ 673420. + 7.49889e6i 0.0528840 + 0.588891i
$$696$$ 0 0
$$697$$ 7.26518e6i 0.566453i
$$698$$ 0 0
$$699$$ −1.73119e7 −1.34014
$$700$$ 0 0
$$701$$ 2.04707e7 1.57339 0.786696 0.617340i $$-0.211790\pi$$
0.786696 + 0.617340i $$0.211790\pi$$
$$702$$ 0 0
$$703$$ 2.33389e7i 1.78112i
$$704$$ 0 0
$$705$$ 525140. + 5.84771e6i 0.0397926 + 0.443112i
$$706$$ 0 0
$$707$$ 1.75889e7i 1.32340i
$$708$$ 0 0
$$709$$ 81654.0 0.00610045 0.00305023 0.999995i $$-0.499029\pi$$
0.00305023 + 0.999995i $$0.499029\pi$$
$$710$$ 0 0
$$711$$ 9.48763e6 0.703856
$$712$$ 0 0
$$713$$ 7.32949e6i 0.539946i
$$714$$ 0 0
$$715$$ 4.09200e6 367472.i 0.299344 0.0268819i
$$716$$ 0 0
$$717$$ 4.17253e6i 0.303111i
$$718$$ 0 0
$$719$$ −8.61006e6 −0.621132 −0.310566 0.950552i $$-0.600519\pi$$
−0.310566 + 0.950552i $$0.600519\pi$$
$$720$$ 0 0
$$721$$ −1.36987e7 −0.981386
$$722$$ 0 0
$$723$$ 9.39431e6i 0.668373i
$$724$$ 0 0
$$725$$ −2.41510e7 + 4.37292e6i −1.70644 + 0.308977i
$$726$$ 0 0
$$727$$ 1.17682e7i 0.825796i −0.910777 0.412898i $$-0.864517\pi$$
0.910777 0.412898i $$-0.135483\pi$$
$$728$$ 0 0
$$729$$ −1.28083e7 −0.892635
$$730$$ 0 0
$$731$$ 1.74046e7 1.20468
$$732$$ 0 0
$$733$$ 3.93759e6i 0.270689i −0.990799 0.135344i $$-0.956786\pi$$
0.990799 0.135344i $$-0.0432141\pi$$
$$734$$ 0 0
$$735$$ 1.11786e6 100387.i 0.0763254 0.00685422i
$$736$$ 0 0
$$737$$ 5.87845e6i 0.398652i
$$738$$ 0 0
$$739$$ −2.30602e7 −1.55329 −0.776643 0.629941i $$-0.783079\pi$$
−0.776643 + 0.629941i $$0.783079\pi$$
$$740$$ 0 0
$$741$$ 1.83649e7 1.22869
$$742$$ 0 0
$$743$$ 1.72675e6i 0.114751i 0.998353 + 0.0573757i $$0.0182733\pi$$
−0.998353 + 0.0573757i $$0.981727\pi$$
$$744$$ 0 0
$$745$$ −1.24003e6 1.38084e7i −0.0818543 0.911491i
$$746$$ 0 0
$$747$$ 1.93866e6i 0.127116i
$$748$$ 0 0
$$749$$ 1.12980e7 0.735864
$$750$$ 0 0
$$751$$ 2.58030e6 0.166944 0.0834720 0.996510i $$-0.473399\pi$$
0.0834720 + 0.996510i $$0.473399\pi$$
$$752$$ 0 0
$$753$$ 1.91587e7i 1.23134i
$$754$$ 0 0
$$755$$ 1.56860e6 + 1.74672e7i 0.100149 + 1.11521i
$$756$$ 0 0
$$757$$ 5.75878e6i 0.365251i −0.983183 0.182625i $$-0.941540\pi$$
0.983183 0.182625i $$-0.0584595\pi$$
$$758$$ 0 0
$$759$$ −3.80680e6 −0.239859
$$760$$ 0 0
$$761$$ 1.40499e7 0.879450 0.439725 0.898133i $$-0.355076\pi$$
0.439725 + 0.898133i $$0.355076\pi$$
$$762$$ 0 0
$$763$$ 1.30132e7i 0.809230i
$$764$$ 0 0
$$765$$ 6.49264e6 583056.i 0.401114 0.0360211i
$$766$$ 0 0
$$767$$ 1.90880e7i 1.17158i
$$768$$ 0 0
$$769$$ 5.59898e6 0.341423 0.170712 0.985321i $$-0.445393\pi$$
0.170712 + 0.985321i $$0.445393\pi$$
$$770$$ 0 0
$$771$$ 1.72846e7 1.04719
$$772$$ 0 0
$$773$$ 6.34625e6i 0.382004i 0.981590 + 0.191002i $$0.0611738\pi$$
−0.981590 + 0.191002i $$0.938826\pi$$
$$774$$ 0 0
$$775$$ −6.59280e6 + 1.19373e6i −0.394290 + 0.0713923i
$$776$$ 0 0
$$777$$ 1.41864e7i 0.842984i
$$778$$ 0 0
$$779$$ 1.66370e7 0.982272
$$780$$ 0 0
$$781$$ −3.76080e6 −0.220624
$$782$$ 0 0
$$783$$ 3.16600e7i 1.84547i
$$784$$ 0 0
$$785$$ −1.36735e7 + 1.22791e6i −0.791963 + 0.0711204i
$$786$$ 0 0
$$787$$ 1.73688e7i 0.999617i −0.866136 0.499809i $$-0.833404\pi$$
0.866136 0.499809i $$-0.166596\pi$$
$$788$$ 0 0
$$789$$ −4.54076e6 −0.259678
$$790$$ 0 0
$$791$$ −1.38473e7 −0.786909
$$792$$ 0 0
$$793$$ 2.24746e6i 0.126914i
$$794$$ 0 0
$$795$$ −1.35036e6 1.50370e7i −0.0757760 0.843806i
$$796$$ 0 0
$$797$$ 8.06932e6i 0.449978i −0.974361 0.224989i $$-0.927765\pi$$
0.974361 0.224989i $$-0.0722346\pi$$
$$798$$ 0 0
$$799$$ −9.24246e6 −0.512178
$$800$$ 0 0
$$801$$ 98294.0 0.00541310
$$802$$ 0 0
$$803$$ 2.40082e6i 0.131393i
$$804$$ 0 0
$$805$$ 2.09374e6 + 2.33149e7i 0.113876 + 1.26807i
$$806$$ 0 0
$$807$$ 2.03457e7i 1.09974i
$$808$$ 0 0
$$809$$ −1.94554e7 −1.04513 −0.522564 0.852600i $$-0.675024\pi$$
−0.522564 + 0.852600i $$0.675024\pi$$
$$810$$ 0 0
$$811$$ 2.85204e6 0.152266 0.0761330