# Properties

 Label 920.2.e.c.369.11 Level $920$ Weight $2$ Character 920.369 Analytic conductor $7.346$ Analytic rank $0$ Dimension $16$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$920 = 2^{3} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 920.e (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$7.34623698596$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 2 x^{15} + 2 x^{14} + 6 x^{13} + 100 x^{12} - 196 x^{11} + 210 x^{10} + 702 x^{9} + 1572 x^{8} - 1594 x^{7} + 2464 x^{6} + 9568 x^{5} + 15457 x^{4} + 4336 x^{3} + \cdots + 1024$$ x^16 - 2*x^15 + 2*x^14 + 6*x^13 + 100*x^12 - 196*x^11 + 210*x^10 + 702*x^9 + 1572*x^8 - 1594*x^7 + 2464*x^6 + 9568*x^5 + 15457*x^4 + 4336*x^3 + 128*x^2 - 512*x + 1024 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 369.11 Root $$0.303680 - 0.303680i$$ of defining polynomial Character $$\chi$$ $$=$$ 920.369 Dual form 920.2.e.c.369.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+0.540724i q^{3} +(2.21535 - 0.303680i) q^{5} +1.15693i q^{7} +2.70762 q^{9} +O(q^{10})$$ $$q+0.540724i q^{3} +(2.21535 - 0.303680i) q^{5} +1.15693i q^{7} +2.70762 q^{9} +2.10688 q^{11} -5.59296i q^{13} +(0.164207 + 1.19789i) q^{15} +0.244199i q^{17} -1.45043 q^{19} -0.625580 q^{21} +1.00000i q^{23} +(4.81556 - 1.34552i) q^{25} +3.08625i q^{27} -4.29653 q^{29} +3.19717 q^{31} +1.13924i q^{33} +(0.351337 + 2.56301i) q^{35} -0.807940i q^{37} +3.02425 q^{39} -1.59546 q^{41} +5.98219i q^{43} +(5.99832 - 0.822250i) q^{45} -0.624940i q^{47} +5.66151 q^{49} -0.132044 q^{51} +0.536087i q^{53} +(4.66747 - 0.639817i) q^{55} -0.784283i q^{57} +1.03806 q^{59} +3.77846 q^{61} +3.13253i q^{63} +(-1.69847 - 12.3904i) q^{65} -4.61571i q^{67} -0.540724 q^{69} +6.77489 q^{71} +8.87290i q^{73} +(0.727553 + 2.60389i) q^{75} +2.43751i q^{77} -14.8521 q^{79} +6.45405 q^{81} -6.11896i q^{83} +(0.0741583 + 0.540985i) q^{85} -2.32323i q^{87} -5.79942 q^{89} +6.47066 q^{91} +1.72879i q^{93} +(-3.21321 + 0.440467i) q^{95} -2.38582i q^{97} +5.70462 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q - 2 q^{5} - 22 q^{9}+O(q^{10})$$ 16 * q - 2 * q^5 - 22 * q^9 $$16 q - 2 q^{5} - 22 q^{9} + 14 q^{11} + 6 q^{15} - 22 q^{19} + 12 q^{25} - 44 q^{29} + 18 q^{31} + 20 q^{35} + 14 q^{41} + 14 q^{45} - 78 q^{49} - 38 q^{51} + 30 q^{55} - 64 q^{59} + 34 q^{61} + 6 q^{65} + 6 q^{69} + 30 q^{71} + 56 q^{75} + 4 q^{79} + 48 q^{81} + 52 q^{85} - 92 q^{89} - 70 q^{91} + 38 q^{95} - 122 q^{99}+O(q^{100})$$ 16 * q - 2 * q^5 - 22 * q^9 + 14 * q^11 + 6 * q^15 - 22 * q^19 + 12 * q^25 - 44 * q^29 + 18 * q^31 + 20 * q^35 + 14 * q^41 + 14 * q^45 - 78 * q^49 - 38 * q^51 + 30 * q^55 - 64 * q^59 + 34 * q^61 + 6 * q^65 + 6 * q^69 + 30 * q^71 + 56 * q^75 + 4 * q^79 + 48 * q^81 + 52 * q^85 - 92 * q^89 - 70 * q^91 + 38 * q^95 - 122 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$$.

 $$n$$ $$231$$ $$281$$ $$461$$ $$737$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$-1$$

## 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
$$3$$ 0.540724i 0.312187i 0.987742 + 0.156094i $$0.0498901\pi$$
−0.987742 + 0.156094i $$0.950110\pi$$
$$4$$ 0 0
$$5$$ 2.21535 0.303680i 0.990735 0.135810i
$$6$$ 0 0
$$7$$ 1.15693i 0.437279i 0.975806 + 0.218639i $$0.0701618\pi$$
−0.975806 + 0.218639i $$0.929838\pi$$
$$8$$ 0 0
$$9$$ 2.70762 0.902539
$$10$$ 0 0
$$11$$ 2.10688 0.635247 0.317624 0.948217i $$-0.397115\pi$$
0.317624 + 0.948217i $$0.397115\pi$$
$$12$$ 0 0
$$13$$ 5.59296i 1.55121i −0.631220 0.775604i $$-0.717446\pi$$
0.631220 0.775604i $$-0.282554\pi$$
$$14$$ 0 0
$$15$$ 0.164207 + 1.19789i 0.0423981 + 0.309295i
$$16$$ 0 0
$$17$$ 0.244199i 0.0592268i 0.999561 + 0.0296134i $$0.00942762\pi$$
−0.999561 + 0.0296134i $$0.990572\pi$$
$$18$$ 0 0
$$19$$ −1.45043 −0.332752 −0.166376 0.986062i $$-0.553206\pi$$
−0.166376 + 0.986062i $$0.553206\pi$$
$$20$$ 0 0
$$21$$ −0.625580 −0.136513
$$22$$ 0 0
$$23$$ 1.00000i 0.208514i
$$24$$ 0 0
$$25$$ 4.81556 1.34552i 0.963111 0.269103i
$$26$$ 0 0
$$27$$ 3.08625i 0.593948i
$$28$$ 0 0
$$29$$ −4.29653 −0.797845 −0.398922 0.916985i $$-0.630616\pi$$
−0.398922 + 0.916985i $$0.630616\pi$$
$$30$$ 0 0
$$31$$ 3.19717 0.574229 0.287114 0.957896i $$-0.407304\pi$$
0.287114 + 0.957896i $$0.407304\pi$$
$$32$$ 0 0
$$33$$ 1.13924i 0.198316i
$$34$$ 0 0
$$35$$ 0.351337 + 2.56301i 0.0593868 + 0.433227i
$$36$$ 0 0
$$37$$ 0.807940i 0.132824i −0.997792 0.0664122i $$-0.978845\pi$$
0.997792 0.0664122i $$-0.0211552\pi$$
$$38$$ 0 0
$$39$$ 3.02425 0.484267
$$40$$ 0 0
$$41$$ −1.59546 −0.249169 −0.124585 0.992209i $$-0.539760\pi$$
−0.124585 + 0.992209i $$0.539760\pi$$
$$42$$ 0 0
$$43$$ 5.98219i 0.912275i 0.889909 + 0.456138i $$0.150768\pi$$
−0.889909 + 0.456138i $$0.849232\pi$$
$$44$$ 0 0
$$45$$ 5.99832 0.822250i 0.894177 0.122574i
$$46$$ 0 0
$$47$$ 0.624940i 0.0911569i −0.998961 0.0455784i $$-0.985487\pi$$
0.998961 0.0455784i $$-0.0145131\pi$$
$$48$$ 0 0
$$49$$ 5.66151 0.808787
$$50$$ 0 0
$$51$$ −0.132044 −0.0184899
$$52$$ 0 0
$$53$$ 0.536087i 0.0736372i 0.999322 + 0.0368186i $$0.0117224\pi$$
−0.999322 + 0.0368186i $$0.988278\pi$$
$$54$$ 0 0
$$55$$ 4.66747 0.639817i 0.629362 0.0862729i
$$56$$ 0 0
$$57$$ 0.784283i 0.103881i
$$58$$ 0 0
$$59$$ 1.03806 0.135144 0.0675721 0.997714i $$-0.478475\pi$$
0.0675721 + 0.997714i $$0.478475\pi$$
$$60$$ 0 0
$$61$$ 3.77846 0.483783 0.241891 0.970303i $$-0.422232\pi$$
0.241891 + 0.970303i $$0.422232\pi$$
$$62$$ 0 0
$$63$$ 3.13253i 0.394661i
$$64$$ 0 0
$$65$$ −1.69847 12.3904i −0.210669 1.53684i
$$66$$ 0 0
$$67$$ 4.61571i 0.563899i −0.959429 0.281949i $$-0.909019\pi$$
0.959429 0.281949i $$-0.0909811\pi$$
$$68$$ 0 0
$$69$$ −0.540724 −0.0650955
$$70$$ 0 0
$$71$$ 6.77489 0.804032 0.402016 0.915633i $$-0.368310\pi$$
0.402016 + 0.915633i $$0.368310\pi$$
$$72$$ 0 0
$$73$$ 8.87290i 1.03849i 0.854624 + 0.519247i $$0.173788\pi$$
−0.854624 + 0.519247i $$0.826212\pi$$
$$74$$ 0 0
$$75$$ 0.727553 + 2.60389i 0.0840106 + 0.300671i
$$76$$ 0 0
$$77$$ 2.43751i 0.277780i
$$78$$ 0 0
$$79$$ −14.8521 −1.67099 −0.835494 0.549500i $$-0.814818\pi$$
−0.835494 + 0.549500i $$0.814818\pi$$
$$80$$ 0 0
$$81$$ 6.45405 0.717116
$$82$$ 0 0
$$83$$ 6.11896i 0.671644i −0.941926 0.335822i $$-0.890986\pi$$
0.941926 0.335822i $$-0.109014\pi$$
$$84$$ 0 0
$$85$$ 0.0741583 + 0.540985i 0.00804360 + 0.0586781i
$$86$$ 0 0
$$87$$ 2.32323i 0.249077i
$$88$$ 0 0
$$89$$ −5.79942 −0.614737 −0.307369 0.951591i $$-0.599448\pi$$
−0.307369 + 0.951591i $$0.599448\pi$$
$$90$$ 0 0
$$91$$ 6.47066 0.678310
$$92$$ 0 0
$$93$$ 1.72879i 0.179267i
$$94$$ 0 0
$$95$$ −3.21321 + 0.440467i −0.329669 + 0.0451910i
$$96$$ 0 0
$$97$$ 2.38582i 0.242244i −0.992638 0.121122i $$-0.961351\pi$$
0.992638 0.121122i $$-0.0386492\pi$$
$$98$$ 0 0
$$99$$ 5.70462 0.573336
$$100$$ 0 0
$$101$$ 8.33379 0.829243 0.414621 0.909994i $$-0.363914\pi$$
0.414621 + 0.909994i $$0.363914\pi$$
$$102$$ 0 0
$$103$$ 12.4250i 1.22427i 0.790754 + 0.612135i $$0.209689\pi$$
−0.790754 + 0.612135i $$0.790311\pi$$
$$104$$ 0 0
$$105$$ −1.38588 + 0.189976i −0.135248 + 0.0185398i
$$106$$ 0 0
$$107$$ 15.5804i 1.50621i 0.657899 + 0.753106i $$0.271445\pi$$
−0.657899 + 0.753106i $$0.728555\pi$$
$$108$$ 0 0
$$109$$ −9.71396 −0.930428 −0.465214 0.885198i $$-0.654023\pi$$
−0.465214 + 0.885198i $$0.654023\pi$$
$$110$$ 0 0
$$111$$ 0.436872 0.0414661
$$112$$ 0 0
$$113$$ 2.69724i 0.253735i 0.991920 + 0.126867i $$0.0404922\pi$$
−0.991920 + 0.126867i $$0.959508\pi$$
$$114$$ 0 0
$$115$$ 0.303680 + 2.21535i 0.0283183 + 0.206583i
$$116$$ 0 0
$$117$$ 15.1436i 1.40003i
$$118$$ 0 0
$$119$$ −0.282521 −0.0258986
$$120$$ 0 0
$$121$$ −6.56107 −0.596461
$$122$$ 0 0
$$123$$ 0.862705i 0.0777875i
$$124$$ 0 0
$$125$$ 10.2595 4.44318i 0.917641 0.397410i
$$126$$ 0 0
$$127$$ 4.40424i 0.390813i 0.980722 + 0.195406i $$0.0626026\pi$$
−0.980722 + 0.195406i $$0.937397\pi$$
$$128$$ 0 0
$$129$$ −3.23471 −0.284801
$$130$$ 0 0
$$131$$ 1.65815 0.144873 0.0724367 0.997373i $$-0.476922\pi$$
0.0724367 + 0.997373i $$0.476922\pi$$
$$132$$ 0 0
$$133$$ 1.67805i 0.145505i
$$134$$ 0 0
$$135$$ 0.937232 + 6.83712i 0.0806641 + 0.588445i
$$136$$ 0 0
$$137$$ 2.70894i 0.231440i −0.993282 0.115720i $$-0.963082\pi$$
0.993282 0.115720i $$-0.0369176\pi$$
$$138$$ 0 0
$$139$$ −8.99503 −0.762949 −0.381474 0.924379i $$-0.624584\pi$$
−0.381474 + 0.924379i $$0.624584\pi$$
$$140$$ 0 0
$$141$$ 0.337920 0.0284580
$$142$$ 0 0
$$143$$ 11.7837i 0.985400i
$$144$$ 0 0
$$145$$ −9.51831 + 1.30477i −0.790453 + 0.108355i
$$146$$ 0 0
$$147$$ 3.06132i 0.252493i
$$148$$ 0 0
$$149$$ −9.54172 −0.781688 −0.390844 0.920457i $$-0.627817\pi$$
−0.390844 + 0.920457i $$0.627817\pi$$
$$150$$ 0 0
$$151$$ −12.1471 −0.988514 −0.494257 0.869316i $$-0.664560\pi$$
−0.494257 + 0.869316i $$0.664560\pi$$
$$152$$ 0 0
$$153$$ 0.661196i 0.0534545i
$$154$$ 0 0
$$155$$ 7.08285 0.970918i 0.568909 0.0779860i
$$156$$ 0 0
$$157$$ 19.1756i 1.53038i −0.643806 0.765189i $$-0.722646\pi$$
0.643806 0.765189i $$-0.277354\pi$$
$$158$$ 0 0
$$159$$ −0.289875 −0.0229886
$$160$$ 0 0
$$161$$ −1.15693 −0.0911789
$$162$$ 0 0
$$163$$ 17.3397i 1.35815i −0.734071 0.679073i $$-0.762382\pi$$
0.734071 0.679073i $$-0.237618\pi$$
$$164$$ 0 0
$$165$$ 0.345965 + 2.52381i 0.0269333 + 0.196479i
$$166$$ 0 0
$$167$$ 0.582642i 0.0450862i −0.999746 0.0225431i $$-0.992824\pi$$
0.999746 0.0225431i $$-0.00717629\pi$$
$$168$$ 0 0
$$169$$ −18.2812 −1.40624
$$170$$ 0 0
$$171$$ −3.92721 −0.300321
$$172$$ 0 0
$$173$$ 12.0591i 0.916840i −0.888736 0.458420i $$-0.848416\pi$$
0.888736 0.458420i $$-0.151584\pi$$
$$174$$ 0 0
$$175$$ 1.55667 + 5.57126i 0.117673 + 0.421148i
$$176$$ 0 0
$$177$$ 0.561305i 0.0421903i
$$178$$ 0 0
$$179$$ −18.0142 −1.34645 −0.673223 0.739439i $$-0.735091\pi$$
−0.673223 + 0.739439i $$0.735091\pi$$
$$180$$ 0 0
$$181$$ 3.33577 0.247946 0.123973 0.992286i $$-0.460436\pi$$
0.123973 + 0.992286i $$0.460436\pi$$
$$182$$ 0 0
$$183$$ 2.04311i 0.151031i
$$184$$ 0 0
$$185$$ −0.245355 1.78987i −0.0180389 0.131594i
$$186$$ 0 0
$$187$$ 0.514496i 0.0376237i
$$188$$ 0 0
$$189$$ −3.57057 −0.259721
$$190$$ 0 0
$$191$$ −2.90013 −0.209846 −0.104923 0.994480i $$-0.533460\pi$$
−0.104923 + 0.994480i $$0.533460\pi$$
$$192$$ 0 0
$$193$$ 11.6127i 0.835898i 0.908470 + 0.417949i $$0.137251\pi$$
−0.908470 + 0.417949i $$0.862749\pi$$
$$194$$ 0 0
$$195$$ 6.69977 0.918404i 0.479780 0.0657683i
$$196$$ 0 0
$$197$$ 0.156603i 0.0111575i 0.999984 + 0.00557876i $$0.00177579\pi$$
−0.999984 + 0.00557876i $$0.998224\pi$$
$$198$$ 0 0
$$199$$ −23.3474 −1.65506 −0.827528 0.561425i $$-0.810253\pi$$
−0.827528 + 0.561425i $$0.810253\pi$$
$$200$$ 0 0
$$201$$ 2.49583 0.176042
$$202$$ 0 0
$$203$$ 4.97078i 0.348880i
$$204$$ 0 0
$$205$$ −3.53451 + 0.484511i −0.246861 + 0.0338397i
$$206$$ 0 0
$$207$$ 2.70762i 0.188192i
$$208$$ 0 0
$$209$$ −3.05588 −0.211380
$$210$$ 0 0
$$211$$ −21.2620 −1.46374 −0.731870 0.681445i $$-0.761352\pi$$
−0.731870 + 0.681445i $$0.761352\pi$$
$$212$$ 0 0
$$213$$ 3.66335i 0.251008i
$$214$$ 0 0
$$215$$ 1.81667 + 13.2526i 0.123896 + 0.903823i
$$216$$ 0 0
$$217$$ 3.69890i 0.251098i
$$218$$ 0 0
$$219$$ −4.79779 −0.324205
$$220$$ 0 0
$$221$$ 1.36579 0.0918731
$$222$$ 0 0
$$223$$ 28.7628i 1.92610i −0.269328 0.963049i $$-0.586801\pi$$
0.269328 0.963049i $$-0.413199\pi$$
$$224$$ 0 0
$$225$$ 13.0387 3.64315i 0.869246 0.242876i
$$226$$ 0 0
$$227$$ 6.08990i 0.404201i 0.979365 + 0.202100i $$0.0647768\pi$$
−0.979365 + 0.202100i $$0.935223\pi$$
$$228$$ 0 0
$$229$$ −19.9294 −1.31697 −0.658486 0.752593i $$-0.728803\pi$$
−0.658486 + 0.752593i $$0.728803\pi$$
$$230$$ 0 0
$$231$$ −1.31802 −0.0867194
$$232$$ 0 0
$$233$$ 9.63207i 0.631018i 0.948923 + 0.315509i $$0.102175\pi$$
−0.948923 + 0.315509i $$0.897825\pi$$
$$234$$ 0 0
$$235$$ −0.189782 1.38446i −0.0123800 0.0903123i
$$236$$ 0 0
$$237$$ 8.03087i 0.521661i
$$238$$ 0 0
$$239$$ −13.2583 −0.857607 −0.428803 0.903398i $$-0.641065\pi$$
−0.428803 + 0.903398i $$0.641065\pi$$
$$240$$ 0 0
$$241$$ −14.4250 −0.929195 −0.464597 0.885522i $$-0.653801\pi$$
−0.464597 + 0.885522i $$0.653801\pi$$
$$242$$ 0 0
$$243$$ 12.7486i 0.817823i
$$244$$ 0 0
$$245$$ 12.5422 1.71929i 0.801294 0.109841i
$$246$$ 0 0
$$247$$ 8.11220i 0.516167i
$$248$$ 0 0
$$249$$ 3.30867 0.209678
$$250$$ 0 0
$$251$$ 18.6789 1.17900 0.589500 0.807768i $$-0.299325\pi$$
0.589500 + 0.807768i $$0.299325\pi$$
$$252$$ 0 0
$$253$$ 2.10688i 0.132458i
$$254$$ 0 0
$$255$$ −0.292524 + 0.0400992i −0.0183185 + 0.00251111i
$$256$$ 0 0
$$257$$ 25.5035i 1.59087i 0.606042 + 0.795433i $$0.292756\pi$$
−0.606042 + 0.795433i $$0.707244\pi$$
$$258$$ 0 0
$$259$$ 0.934730 0.0580813
$$260$$ 0 0
$$261$$ −11.6333 −0.720086
$$262$$ 0 0
$$263$$ 18.4521i 1.13780i −0.822405 0.568902i $$-0.807368\pi$$
0.822405 0.568902i $$-0.192632\pi$$
$$264$$ 0 0
$$265$$ 0.162799 + 1.18762i 0.0100007 + 0.0729549i
$$266$$ 0 0
$$267$$ 3.13589i 0.191913i
$$268$$ 0 0
$$269$$ −2.02723 −0.123602 −0.0618012 0.998088i $$-0.519684\pi$$
−0.0618012 + 0.998088i $$0.519684\pi$$
$$270$$ 0 0
$$271$$ 26.7402 1.62435 0.812175 0.583414i $$-0.198284\pi$$
0.812175 + 0.583414i $$0.198284\pi$$
$$272$$ 0 0
$$273$$ 3.49884i 0.211760i
$$274$$ 0 0
$$275$$ 10.1458 2.83484i 0.611814 0.170947i
$$276$$ 0 0
$$277$$ 18.8601i 1.13320i −0.823995 0.566598i $$-0.808259\pi$$
0.823995 0.566598i $$-0.191741\pi$$
$$278$$ 0 0
$$279$$ 8.65672 0.518264
$$280$$ 0 0
$$281$$ 6.09240 0.363442 0.181721 0.983350i $$-0.441833\pi$$
0.181721 + 0.983350i $$0.441833\pi$$
$$282$$ 0 0
$$283$$ 15.6971i 0.933095i −0.884496 0.466548i $$-0.845498\pi$$
0.884496 0.466548i $$-0.154502\pi$$
$$284$$ 0 0
$$285$$ −0.238171 1.73746i −0.0141080 0.102918i
$$286$$ 0 0
$$287$$ 1.84584i 0.108956i
$$288$$ 0 0
$$289$$ 16.9404 0.996492
$$290$$ 0 0
$$291$$ 1.29007 0.0756254
$$292$$ 0 0
$$293$$ 20.3629i 1.18962i 0.803868 + 0.594808i $$0.202772\pi$$
−0.803868 + 0.594808i $$0.797228\pi$$
$$294$$ 0 0
$$295$$ 2.29967 0.315239i 0.133892 0.0183539i
$$296$$ 0 0
$$297$$ 6.50234i 0.377304i
$$298$$ 0 0
$$299$$ 5.59296 0.323449
$$300$$ 0 0
$$301$$ −6.92098 −0.398918
$$302$$ 0 0
$$303$$ 4.50628i 0.258879i
$$304$$ 0 0
$$305$$ 8.37062 1.14744i 0.479300 0.0657025i
$$306$$ 0 0
$$307$$ 6.31386i 0.360351i 0.983634 + 0.180176i $$0.0576666\pi$$
−0.983634 + 0.180176i $$0.942333\pi$$
$$308$$ 0 0
$$309$$ −6.71848 −0.382201
$$310$$ 0 0
$$311$$ −2.26901 −0.128664 −0.0643318 0.997929i $$-0.520492\pi$$
−0.0643318 + 0.997929i $$0.520492\pi$$
$$312$$ 0 0
$$313$$ 25.8886i 1.46331i 0.681676 + 0.731654i $$0.261251\pi$$
−0.681676 + 0.731654i $$0.738749\pi$$
$$314$$ 0 0
$$315$$ 0.951286 + 6.93964i 0.0535989 + 0.391004i
$$316$$ 0 0
$$317$$ 0.952783i 0.0535136i 0.999642 + 0.0267568i $$0.00851798\pi$$
−0.999642 + 0.0267568i $$0.991482\pi$$
$$318$$ 0 0
$$319$$ −9.05225 −0.506829
$$320$$ 0 0
$$321$$ −8.42468 −0.470220
$$322$$ 0 0
$$323$$ 0.354193i 0.0197078i
$$324$$ 0 0
$$325$$ −7.52542 26.9332i −0.417435 1.49399i
$$326$$ 0 0
$$327$$ 5.25257i 0.290468i
$$328$$ 0 0
$$329$$ 0.723012 0.0398609
$$330$$ 0 0
$$331$$ −14.7188 −0.809017 −0.404509 0.914534i $$-0.632557\pi$$
−0.404509 + 0.914534i $$0.632557\pi$$
$$332$$ 0 0
$$333$$ 2.18759i 0.119879i
$$334$$ 0 0
$$335$$ −1.40170 10.2254i −0.0765831 0.558674i
$$336$$ 0 0
$$337$$ 23.7550i 1.29402i 0.762482 + 0.647010i $$0.223981\pi$$
−0.762482 + 0.647010i $$0.776019\pi$$
$$338$$ 0 0
$$339$$ −1.45846 −0.0792127
$$340$$ 0 0
$$341$$ 6.73605 0.364777
$$342$$ 0 0
$$343$$ 14.6485i 0.790944i
$$344$$ 0 0
$$345$$ −1.19789 + 0.164207i −0.0644924 + 0.00884062i
$$346$$ 0 0
$$347$$ 20.8557i 1.11959i −0.828630 0.559797i $$-0.810879\pi$$
0.828630 0.559797i $$-0.189121\pi$$
$$348$$ 0 0
$$349$$ 12.8328 0.686922 0.343461 0.939167i $$-0.388401\pi$$
0.343461 + 0.939167i $$0.388401\pi$$
$$350$$ 0 0
$$351$$ 17.2612 0.921337
$$352$$ 0 0
$$353$$ 30.4888i 1.62275i 0.584523 + 0.811377i $$0.301282\pi$$
−0.584523 + 0.811377i $$0.698718\pi$$
$$354$$ 0 0
$$355$$ 15.0088 2.05740i 0.796583 0.109196i
$$356$$ 0 0
$$357$$ 0.152766i 0.00808522i
$$358$$ 0 0
$$359$$ −11.0247 −0.581864 −0.290932 0.956744i $$-0.593965\pi$$
−0.290932 + 0.956744i $$0.593965\pi$$
$$360$$ 0 0
$$361$$ −16.8963 −0.889276
$$362$$ 0 0
$$363$$ 3.54773i 0.186207i
$$364$$ 0 0
$$365$$ 2.69453 + 19.6566i 0.141038 + 1.02887i
$$366$$ 0 0
$$367$$ 18.5124i 0.966340i −0.875527 0.483170i $$-0.839485\pi$$
0.875527 0.483170i $$-0.160515\pi$$
$$368$$ 0 0
$$369$$ −4.31990 −0.224885
$$370$$ 0 0
$$371$$ −0.620215 −0.0322000
$$372$$ 0 0
$$373$$ 26.4707i 1.37060i −0.728260 0.685301i $$-0.759670\pi$$
0.728260 0.685301i $$-0.240330\pi$$
$$374$$ 0 0
$$375$$ 2.40254 + 5.54758i 0.124066 + 0.286476i
$$376$$ 0 0
$$377$$ 24.0303i 1.23762i
$$378$$ 0 0
$$379$$ −10.8785 −0.558791 −0.279395 0.960176i $$-0.590134\pi$$
−0.279395 + 0.960176i $$0.590134\pi$$
$$380$$ 0 0
$$381$$ −2.38148 −0.122007
$$382$$ 0 0
$$383$$ 21.6026i 1.10384i −0.833897 0.551920i $$-0.813895\pi$$
0.833897 0.551920i $$-0.186105\pi$$
$$384$$ 0 0
$$385$$ 0.740224 + 5.39994i 0.0377253 + 0.275206i
$$386$$ 0 0
$$387$$ 16.1975i 0.823364i
$$388$$ 0 0
$$389$$ 29.4117 1.49123 0.745617 0.666374i $$-0.232155\pi$$
0.745617 + 0.666374i $$0.232155\pi$$
$$390$$ 0 0
$$391$$ −0.244199 −0.0123497
$$392$$ 0 0
$$393$$ 0.896603i 0.0452276i
$$394$$ 0 0
$$395$$ −32.9025 + 4.51028i −1.65551 + 0.226937i
$$396$$ 0 0
$$397$$ 33.2753i 1.67004i −0.550219 0.835021i $$-0.685456\pi$$
0.550219 0.835021i $$-0.314544\pi$$
$$398$$ 0 0
$$399$$ 0.907360 0.0454248
$$400$$ 0 0
$$401$$ 33.7280 1.68429 0.842147 0.539248i $$-0.181292\pi$$
0.842147 + 0.539248i $$0.181292\pi$$
$$402$$ 0 0
$$403$$ 17.8816i 0.890748i
$$404$$ 0 0
$$405$$ 14.2980 1.95997i 0.710472 0.0973915i
$$406$$ 0 0
$$407$$ 1.70223i 0.0843764i
$$408$$ 0 0
$$409$$ −22.6282 −1.11889 −0.559445 0.828867i $$-0.688986\pi$$
−0.559445 + 0.828867i $$0.688986\pi$$
$$410$$ 0 0
$$411$$ 1.46479 0.0722527
$$412$$ 0 0
$$413$$ 1.20097i 0.0590956i
$$414$$ 0 0
$$415$$ −1.85821 13.5556i −0.0912159 0.665421i
$$416$$ 0 0
$$417$$ 4.86383i 0.238183i
$$418$$ 0 0
$$419$$ 34.6846 1.69446 0.847228 0.531230i $$-0.178270\pi$$
0.847228 + 0.531230i $$0.178270\pi$$
$$420$$ 0 0
$$421$$ −0.348044 −0.0169626 −0.00848131 0.999964i $$-0.502700\pi$$
−0.00848131 + 0.999964i $$0.502700\pi$$
$$422$$ 0 0
$$423$$ 1.69210i 0.0822726i
$$424$$ 0 0
$$425$$ 0.328573 + 1.17595i 0.0159381 + 0.0570420i
$$426$$ 0 0
$$427$$ 4.37142i 0.211548i
$$428$$ 0 0
$$429$$ 6.37172 0.307629
$$430$$ 0 0
$$431$$ 21.2559 1.02386 0.511930 0.859027i $$-0.328931\pi$$
0.511930 + 0.859027i $$0.328931\pi$$
$$432$$ 0 0
$$433$$ 29.3363i 1.40981i 0.709301 + 0.704906i $$0.249011\pi$$
−0.709301 + 0.704906i $$0.750989\pi$$
$$434$$ 0 0
$$435$$ −0.705521 5.14678i −0.0338271 0.246769i
$$436$$ 0 0
$$437$$ 1.45043i 0.0693835i
$$438$$ 0 0
$$439$$ −20.2210 −0.965096 −0.482548 0.875870i $$-0.660289\pi$$
−0.482548 + 0.875870i $$0.660289\pi$$
$$440$$ 0 0
$$441$$ 15.3292 0.729962
$$442$$ 0 0
$$443$$ 33.8124i 1.60648i −0.595657 0.803239i $$-0.703108\pi$$
0.595657 0.803239i $$-0.296892\pi$$
$$444$$ 0 0
$$445$$ −12.8478 + 1.76117i −0.609042 + 0.0834875i
$$446$$ 0 0
$$447$$ 5.15944i 0.244033i
$$448$$ 0 0
$$449$$ −17.7383 −0.837120 −0.418560 0.908189i $$-0.637465\pi$$
−0.418560 + 0.908189i $$0.637465\pi$$
$$450$$ 0 0
$$451$$ −3.36144 −0.158284
$$452$$ 0 0
$$453$$ 6.56821i 0.308601i
$$454$$ 0 0
$$455$$ 14.3348 1.96501i 0.672025 0.0921212i
$$456$$ 0 0
$$457$$ 31.7861i 1.48689i 0.668797 + 0.743445i $$0.266810\pi$$
−0.668797 + 0.743445i $$0.733190\pi$$
$$458$$ 0 0
$$459$$ −0.753657 −0.0351777
$$460$$ 0 0
$$461$$ 17.2206 0.802044 0.401022 0.916068i $$-0.368655\pi$$
0.401022 + 0.916068i $$0.368655\pi$$
$$462$$ 0 0
$$463$$ 40.0085i 1.85935i −0.368376 0.929677i $$-0.620086\pi$$
0.368376 0.929677i $$-0.379914\pi$$
$$464$$ 0 0
$$465$$ 0.524999 + 3.82987i 0.0243462 + 0.177606i
$$466$$ 0 0
$$467$$ 11.9947i 0.555049i −0.960719 0.277524i $$-0.910486\pi$$
0.960719 0.277524i $$-0.0895140\pi$$
$$468$$ 0 0
$$469$$ 5.34006 0.246581
$$470$$ 0 0
$$471$$ 10.3687 0.477764
$$472$$ 0 0
$$473$$ 12.6037i 0.579520i
$$474$$ 0 0
$$475$$ −6.98463 + 1.95158i −0.320477 + 0.0895446i
$$476$$ 0 0
$$477$$ 1.45152i 0.0664604i
$$478$$ 0 0
$$479$$ 20.8249 0.951514 0.475757 0.879577i $$-0.342174\pi$$
0.475757 + 0.879577i $$0.342174\pi$$
$$480$$ 0 0
$$481$$ −4.51877 −0.206038
$$482$$ 0 0
$$483$$ 0.625580i 0.0284649i
$$484$$ 0 0
$$485$$ −0.724528 5.28544i −0.0328991 0.239999i
$$486$$ 0 0
$$487$$ 16.5640i 0.750584i 0.926907 + 0.375292i $$0.122458\pi$$
−0.926907 + 0.375292i $$0.877542\pi$$
$$488$$ 0 0
$$489$$ 9.37597 0.423996
$$490$$ 0 0
$$491$$ 28.8494 1.30196 0.650978 0.759097i $$-0.274359\pi$$
0.650978 + 0.759097i $$0.274359\pi$$
$$492$$ 0 0
$$493$$ 1.04921i 0.0472538i
$$494$$ 0 0
$$495$$ 12.6377 1.73238i 0.568024 0.0778647i
$$496$$ 0 0
$$497$$ 7.83808i 0.351586i
$$498$$ 0 0
$$499$$ 14.0289 0.628021 0.314011 0.949419i $$-0.398327\pi$$
0.314011 + 0.949419i $$0.398327\pi$$
$$500$$ 0 0
$$501$$ 0.315048 0.0140753
$$502$$ 0 0
$$503$$ 23.2157i 1.03514i 0.855642 + 0.517568i $$0.173162\pi$$
−0.855642 + 0.517568i $$0.826838\pi$$
$$504$$ 0 0
$$505$$ 18.4623 2.53081i 0.821560 0.112619i
$$506$$ 0 0
$$507$$ 9.88507i 0.439011i
$$508$$ 0 0
$$509$$ 17.6290 0.781394 0.390697 0.920519i $$-0.372234\pi$$
0.390697 + 0.920519i $$0.372234\pi$$
$$510$$ 0 0
$$511$$ −10.2653 −0.454111
$$512$$ 0 0
$$513$$ 4.47638i 0.197637i
$$514$$ 0 0
$$515$$ 3.77322 + 27.5257i 0.166268 + 1.21293i
$$516$$ 0 0
$$517$$ 1.31667i 0.0579072i
$$518$$ 0 0
$$519$$ 6.52067 0.286226
$$520$$ 0 0
$$521$$ −1.64734 −0.0721711 −0.0360855 0.999349i $$-0.511489\pi$$
−0.0360855 + 0.999349i $$0.511489\pi$$
$$522$$ 0 0
$$523$$ 40.1998i 1.75781i 0.476994 + 0.878907i $$0.341726\pi$$
−0.476994 + 0.878907i $$0.658274\pi$$
$$524$$ 0 0
$$525$$ −3.01252 + 0.841729i −0.131477 + 0.0367360i
$$526$$ 0 0
$$527$$ 0.780744i 0.0340098i
$$528$$ 0 0
$$529$$ −1.00000 −0.0434783
$$530$$ 0 0
$$531$$ 2.81067 0.121973
$$532$$ 0 0
$$533$$ 8.92336i 0.386513i
$$534$$ 0 0
$$535$$ 4.73145 + 34.5160i 0.204559 + 1.49226i
$$536$$ 0 0
$$537$$ 9.74072i 0.420343i
$$538$$ 0 0
$$539$$ 11.9281 0.513780
$$540$$ 0 0
$$541$$ 26.8419 1.15403 0.577013 0.816735i $$-0.304218\pi$$
0.577013 + 0.816735i $$0.304218\pi$$
$$542$$ 0 0
$$543$$ 1.80373i 0.0774055i
$$544$$ 0 0
$$545$$ −21.5198 + 2.94994i −0.921808 + 0.126361i
$$546$$ 0 0
$$547$$ 20.7472i 0.887087i 0.896253 + 0.443544i $$0.146279\pi$$
−0.896253 + 0.443544i $$0.853721\pi$$
$$548$$ 0 0
$$549$$ 10.2306 0.436633
$$550$$ 0 0
$$551$$ 6.23181 0.265484
$$552$$ 0 0
$$553$$ 17.1828i 0.730687i
$$554$$ 0 0
$$555$$ 0.967826 0.132670i 0.0410819 0.00563151i
$$556$$ 0 0
$$557$$ 18.1711i 0.769933i 0.922931 + 0.384966i $$0.125787\pi$$
−0.922931 + 0.384966i $$0.874213\pi$$
$$558$$ 0 0
$$559$$ 33.4581 1.41513
$$560$$ 0 0
$$561$$ −0.278201 −0.0117456
$$562$$ 0 0
$$563$$ 22.9947i 0.969110i −0.874761 0.484555i $$-0.838982\pi$$
0.874761 0.484555i $$-0.161018\pi$$
$$564$$ 0 0
$$565$$ 0.819098 + 5.97532i 0.0344597 + 0.251384i
$$566$$ 0 0
$$567$$ 7.46688i 0.313580i
$$568$$ 0 0
$$569$$ −27.0829 −1.13537 −0.567687 0.823245i $$-0.692162\pi$$
−0.567687 + 0.823245i $$0.692162\pi$$
$$570$$ 0 0
$$571$$ −10.5631 −0.442053 −0.221027 0.975268i $$-0.570941\pi$$
−0.221027 + 0.975268i $$0.570941\pi$$
$$572$$ 0 0
$$573$$ 1.56817i 0.0655112i
$$574$$ 0 0
$$575$$ 1.34552 + 4.81556i 0.0561119 + 0.200823i
$$576$$ 0 0
$$577$$ 2.51016i 0.104499i −0.998634 0.0522496i $$-0.983361\pi$$
0.998634 0.0522496i $$-0.0166392\pi$$
$$578$$ 0 0
$$579$$ −6.27925 −0.260957
$$580$$ 0 0
$$581$$ 7.07922 0.293695
$$582$$ 0 0
$$583$$ 1.12947i 0.0467778i
$$584$$ 0 0
$$585$$ −4.59881 33.5484i −0.190137 1.38705i
$$586$$ 0 0
$$587$$ 43.0923i 1.77861i −0.457315 0.889305i $$-0.651189\pi$$
0.457315 0.889305i $$-0.348811\pi$$
$$588$$ 0 0
$$589$$ −4.63727 −0.191076
$$590$$ 0 0
$$591$$ −0.0846792 −0.00348324
$$592$$ 0 0
$$593$$ 29.7306i 1.22089i −0.792059 0.610444i $$-0.790991\pi$$
0.792059 0.610444i $$-0.209009\pi$$
$$594$$ 0 0
$$595$$ −0.625882 + 0.0857960i −0.0256587 + 0.00351729i
$$596$$ 0 0
$$597$$ 12.6245i 0.516687i
$$598$$ 0 0
$$599$$ 22.9491 0.937674 0.468837 0.883285i $$-0.344673\pi$$
0.468837 + 0.883285i $$0.344673\pi$$
$$600$$ 0 0
$$601$$ 3.49920 0.142735 0.0713677 0.997450i $$-0.477264\pi$$
0.0713677 + 0.997450i $$0.477264\pi$$
$$602$$ 0 0
$$603$$ 12.4976i 0.508941i
$$604$$ 0 0
$$605$$ −14.5351 + 1.99247i −0.590934 + 0.0810053i
$$606$$ 0 0
$$607$$ 42.5670i 1.72774i 0.503714 + 0.863871i $$0.331967\pi$$
−0.503714 + 0.863871i $$0.668033\pi$$
$$608$$ 0 0
$$609$$ 2.68782 0.108916
$$610$$ 0 0
$$611$$ −3.49526 −0.141403
$$612$$ 0 0
$$613$$ 28.0072i 1.13120i 0.824679 + 0.565600i $$0.191356\pi$$
−0.824679 + 0.565600i $$0.808644\pi$$
$$614$$ 0 0
$$615$$ −0.261987 1.91119i −0.0105643 0.0770668i
$$616$$ 0 0
$$617$$ 3.14856i 0.126756i 0.997990 + 0.0633781i $$0.0201874\pi$$
−0.997990 + 0.0633781i $$0.979813\pi$$
$$618$$ 0 0
$$619$$ −13.1433 −0.528275 −0.264137 0.964485i $$-0.585087\pi$$
−0.264137 + 0.964485i $$0.585087\pi$$
$$620$$ 0 0
$$621$$ −3.08625 −0.123847
$$622$$ 0 0
$$623$$ 6.70953i 0.268812i
$$624$$ 0 0
$$625$$ 21.3792 12.9588i 0.855167 0.518353i
$$626$$ 0 0
$$627$$ 1.65239i 0.0659900i
$$628$$ 0 0
$$629$$ 0.197298 0.00786677
$$630$$ 0 0
$$631$$ −35.4545 −1.41142 −0.705711 0.708500i $$-0.749372\pi$$
−0.705711 + 0.708500i $$0.749372\pi$$
$$632$$ 0 0
$$633$$ 11.4969i 0.456961i
$$634$$ 0 0
$$635$$ 1.33748 + 9.75693i 0.0530763 + 0.387192i
$$636$$ 0 0
$$637$$ 31.6646i 1.25460i
$$638$$ 0 0
$$639$$ 18.3438 0.725670
$$640$$ 0 0
$$641$$ 9.79611 0.386923 0.193462 0.981108i $$-0.438029\pi$$
0.193462 + 0.981108i $$0.438029\pi$$
$$642$$ 0 0
$$643$$ 15.6613i 0.617621i 0.951124 + 0.308810i $$0.0999308\pi$$
−0.951124 + 0.308810i $$0.900069\pi$$
$$644$$ 0 0
$$645$$ −7.16602 + 0.982319i −0.282162 + 0.0386788i
$$646$$ 0 0
$$647$$ 38.6953i 1.52127i −0.649180 0.760634i $$-0.724888\pi$$
0.649180 0.760634i $$-0.275112\pi$$
$$648$$ 0 0
$$649$$ 2.18707 0.0858500
$$650$$ 0 0
$$651$$ −2.00009 −0.0783896
$$652$$ 0 0
$$653$$ 37.8261i 1.48025i 0.672469 + 0.740125i $$0.265234\pi$$
−0.672469 + 0.740125i $$0.734766\pi$$
$$654$$ 0 0
$$655$$ 3.67339 0.503548i 0.143531 0.0196753i
$$656$$ 0 0
$$657$$ 24.0244i 0.937282i
$$658$$ 0 0
$$659$$ −9.00852 −0.350922 −0.175461 0.984486i $$-0.556142\pi$$
−0.175461 + 0.984486i $$0.556142\pi$$
$$660$$ 0 0
$$661$$ −26.0490 −1.01319 −0.506594 0.862185i $$-0.669096\pi$$
−0.506594 + 0.862185i $$0.669096\pi$$
$$662$$ 0 0
$$663$$ 0.738517i 0.0286816i
$$664$$ 0 0
$$665$$ −0.509590 3.71746i −0.0197611 0.144157i
$$666$$ 0 0
$$667$$ 4.29653i 0.166362i
$$668$$ 0 0
$$669$$ 15.5527 0.601303
$$670$$ 0 0
$$671$$ 7.96076 0.307322
$$672$$ 0 0
$$673$$ 4.68835i 0.180722i −0.995909 0.0903612i $$-0.971198\pi$$
0.995909 0.0903612i $$-0.0288022\pi$$
$$674$$ 0 0
$$675$$ 4.15260 + 14.8620i 0.159834 + 0.572038i
$$676$$ 0 0
$$677$$ 31.1370i 1.19669i −0.801238 0.598346i $$-0.795825\pi$$
0.801238 0.598346i $$-0.204175\pi$$
$$678$$ 0 0
$$679$$ 2.76023 0.105928
$$680$$ 0 0
$$681$$ −3.29296 −0.126186
$$682$$ 0 0
$$683$$ 15.2671i 0.584180i 0.956391 + 0.292090i $$0.0943507\pi$$
−0.956391 + 0.292090i $$0.905649\pi$$
$$684$$ 0 0
$$685$$ −0.822652 6.00125i −0.0314319 0.229296i
$$686$$ 0 0
$$687$$ 10.7763i 0.411142i
$$688$$ 0 0
$$689$$ 2.99831 0.114227
$$690$$ 0 0
$$691$$ −30.3229 −1.15354 −0.576768 0.816908i $$-0.695686\pi$$
−0.576768 + 0.816908i $$0.695686\pi$$
$$692$$ 0 0
$$693$$ 6.59985i 0.250707i
$$694$$ 0 0
$$695$$ −19.9271 + 2.73161i −0.755880 + 0.103616i
$$696$$ 0 0
$$697$$ 0.389610i 0.0147575i
$$698$$ 0 0
$$699$$ −5.20829 −0.196996
$$700$$ 0 0
$$701$$ −19.7545 −0.746118 −0.373059 0.927808i $$-0.621691\pi$$
−0.373059 + 0.927808i $$0.621691\pi$$
$$702$$ 0 0
$$703$$ 1.17186i 0.0441975i
$$704$$ 0 0
$$705$$ 0.748611 0.102620i 0.0281943 0.00386488i
$$706$$ 0 0
$$707$$ 9.64161i 0.362610i
$$708$$ 0 0
$$709$$ −7.45728 −0.280064 −0.140032 0.990147i $$-0.544721\pi$$
−0.140032 + 0.990147i $$0.544721\pi$$
$$710$$ 0 0
$$711$$ −40.2137 −1.50813
$$712$$ 0 0
$$713$$ 3.19717i 0.119735i
$$714$$ 0 0
$$715$$ −3.57847 26.1050i −0.133827 0.976271i
$$716$$ 0 0
$$717$$ 7.16907i 0.267734i
$$718$$ 0 0
$$719$$ −48.4683 −1.80756 −0.903781 0.427995i $$-0.859220\pi$$
−0.903781 + 0.427995i $$0.859220\pi$$
$$720$$ 0 0
$$721$$ −14.3748 −0.535347
$$722$$ 0 0
$$723$$ 7.79993i 0.290083i
$$724$$ 0 0
$$725$$ −20.6902 + 5.78105i −0.768413 + 0.214703i
$$726$$ 0 0
$$727$$ 49.7498i 1.84512i 0.385856 + 0.922559i $$0.373906\pi$$
−0.385856 + 0.922559i $$0.626094\pi$$
$$728$$ 0 0
$$729$$ 12.4687 0.461802
$$730$$ 0 0
$$731$$ −1.46084 −0.0540312
$$732$$ 0 0
$$733$$ 12.1579i 0.449063i 0.974467 + 0.224531i $$0.0720851\pi$$
−0.974467 + 0.224531i $$0.927915\pi$$
$$734$$ 0 0
$$735$$ 0.929661 + 6.78189i 0.0342911 + 0.250154i
$$736$$ 0 0
$$737$$ 9.72474i 0.358215i
$$738$$ 0 0
$$739$$ 20.5807 0.757075 0.378537 0.925586i $$-0.376427\pi$$
0.378537 + 0.925586i $$0.376427\pi$$
$$740$$ 0 0
$$741$$ −4.38646 −0.161141
$$742$$ 0 0
$$743$$ 22.7862i 0.835944i 0.908460 + 0.417972i $$0.137259\pi$$
−0.908460 + 0.417972i $$0.862741\pi$$
$$744$$ 0 0
$$745$$ −21.1383 + 2.89763i −0.774446 + 0.106161i
$$746$$ 0 0
$$747$$ 16.5678i 0.606185i
$$748$$ 0 0
$$749$$ −18.0254 −0.658634
$$750$$ 0 0
$$751$$ 1.69147 0.0617226 0.0308613 0.999524i $$-0.490175\pi$$
0.0308613 + 0.999524i $$0.490175\pi$$
$$752$$ 0 0
$$753$$ 10.1001i 0.368069i
$$754$$ 0 0
$$755$$ −26.9100 + 3.68883i −0.979355 + 0.134250i
$$756$$ 0 0
$$757$$ 25.7514i 0.935952i −0.883741 0.467976i $$-0.844983\pi$$
0.883741 0.467976i $$-0.155017\pi$$
$$758$$ 0 0
$$759$$ −1.13924 −0.0413518
$$760$$ 0 0
$$761$$ 41.5286 1.50541 0.752706 0.658357i $$-0.228748\pi$$
0.752706 + 0.658357i $$0.228748\pi$$
$$762$$ 0 0
$$763$$ 11.2384i 0.406856i
$$764$$ 0 0
$$765$$ 0.200792 + 1.46478i 0.00725966 + 0.0529593i
$$766$$ 0 0
$$767$$ 5.80584i 0.209637i
$$768$$ 0 0
$$769$$ −0.962676 −0.0347150 −0.0173575 0.999849i $$-0.505525\pi$$
−0.0173575 + 0.999849i $$0.505525\pi$$
$$770$$ 0 0
$$771$$ −13.7904 −0.496648
$$772$$ 0 0
$$773$$ 42.5570i 1.53067i 0.643633 + 0.765334i $$0.277426\pi$$
−0.643633 + 0.765334i $$0.722574\pi$$
$$774$$ 0 0
$$775$$ 15.3962 4.30185i 0.553046 0.154527i
$$776$$ 0 0
$$777$$ 0.505431i 0.0181322i
$$778$$ 0 0
$$779$$ 2.31411 0.0829115
$$780$$ 0 0
$$781$$ 14.2739 0.510759
$$782$$ 0 0
$$783$$ 13.2601i 0.473879i
$$784$$ 0 0
$$785$$ −5.82325 42.4806i −0.207841 1.51620i
$$786$$ 0 0
$$787$$ 32.0542i 1.14261i 0.820738 + 0.571304i $$0.193562\pi$$
−0.820738 + 0.571304i $$0.806438\pi$$
$$788$$ 0 0
$$789$$ 9.97749 0.355208
$$790$$ 0 0
$$791$$ −3.12051 −0.110953
$$792$$ 0 0
$$793$$ 21.1328i 0.750447i
$$794$$ 0 0
$$795$$ −0.642175 + 0.0880293i −0.0227756 + 0.00312208i
$$796$$ 0 0
$$797$$ 42.6339i 1.51017i 0.655628 + 0.755084i $$0.272404\pi$$
−0.655628 + 0.755084i $$0.727596\pi$$
$$798$$ 0 0
$$799$$ 0.152609 0.00539893