# Properties

 Label 2240.2.g.m.449.5 Level $2240$ Weight $2$ Character 2240.449 Analytic conductor $17.886$ Analytic rank $0$ Dimension $6$ CM no Inner twists $2$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$2240 = 2^{6} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2240.g (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$17.8864900528$$ Analytic rank: $$0$$ Dimension: $$6$$ Coefficient field: 6.0.5161984.1 Defining polynomial: $$x^{6} - 4 x^{3} + 25 x^{2} - 20 x + 8$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 280) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 449.5 Root $$0.432320 + 0.432320i$$ of defining polynomial Character $$\chi$$ $$=$$ 2240.449 Dual form 2240.2.g.m.449.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.76156i q^{3} +(-0.432320 - 2.19388i) q^{5} +1.00000i q^{7} -0.103084 q^{9} +O(q^{10})$$ $$q+1.76156i q^{3} +(-0.432320 - 2.19388i) q^{5} +1.00000i q^{7} -0.103084 q^{9} -0.626198 q^{11} -5.49084i q^{13} +(3.86464 - 0.761557i) q^{15} -0.896916i q^{17} -6.38776 q^{19} -1.76156 q^{21} +3.72928i q^{23} +(-4.62620 + 1.89692i) q^{25} +5.10308i q^{27} -7.87859 q^{29} -7.52311 q^{31} -1.10308i q^{33} +(2.19388 - 0.432320i) q^{35} +6.00000i q^{37} +9.67243 q^{39} +7.72928 q^{41} +1.72928i q^{43} +(0.0445652 + 0.226153i) q^{45} +5.87859i q^{47} -1.00000 q^{49} +1.57997 q^{51} +6.77551i q^{53} +(0.270718 + 1.37380i) q^{55} -11.2524i q^{57} +0.593923 q^{59} -7.13536 q^{61} -0.103084i q^{63} +(-12.0462 + 2.37380i) q^{65} +5.79383i q^{67} -6.56934 q^{69} -5.52311 q^{71} -3.72928i q^{73} +(-3.34153 - 8.14931i) q^{75} -0.626198i q^{77} -5.67243 q^{79} -9.29862 q^{81} -17.4340i q^{83} +(-1.96772 + 0.387755i) q^{85} -13.8786i q^{87} -14.2986 q^{89} +5.49084 q^{91} -13.2524i q^{93} +(2.76156 + 14.0140i) q^{95} +10.1493i q^{97} +0.0645508 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$6q - 8q^{9} + O(q^{10})$$ $$6q - 8q^{9} + 14q^{11} + 18q^{15} - 8q^{19} + 2q^{21} - 10q^{25} + 6q^{29} - 20q^{31} - 2q^{35} - 10q^{39} + 36q^{41} + 28q^{45} - 6q^{49} + 42q^{51} + 12q^{55} - 12q^{59} - 48q^{61} - 22q^{65} + 36q^{69} - 8q^{71} - 40q^{75} + 34q^{79} + 30q^{81} - 14q^{85} + 10q^{91} + 4q^{95} - 4q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times$$.

 $$n$$ $$897$$ $$1471$$ $$1541$$ $$1921$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$ $$1$$

## 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
$$3$$ 1.76156i 1.01704i 0.861052 + 0.508518i $$0.169806\pi$$
−0.861052 + 0.508518i $$0.830194\pi$$
$$4$$ 0 0
$$5$$ −0.432320 2.19388i −0.193340 0.981132i
$$6$$ 0 0
$$7$$ 1.00000i 0.377964i
$$8$$ 0 0
$$9$$ −0.103084 −0.0343612
$$10$$ 0 0
$$11$$ −0.626198 −0.188806 −0.0944029 0.995534i $$-0.530094\pi$$
−0.0944029 + 0.995534i $$0.530094\pi$$
$$12$$ 0 0
$$13$$ 5.49084i 1.52288i −0.648233 0.761442i $$-0.724492\pi$$
0.648233 0.761442i $$-0.275508\pi$$
$$14$$ 0 0
$$15$$ 3.86464 0.761557i 0.997846 0.196633i
$$16$$ 0 0
$$17$$ 0.896916i 0.217534i −0.994067 0.108767i $$-0.965310\pi$$
0.994067 0.108767i $$-0.0346903\pi$$
$$18$$ 0 0
$$19$$ −6.38776 −1.46545 −0.732726 0.680524i $$-0.761752\pi$$
−0.732726 + 0.680524i $$0.761752\pi$$
$$20$$ 0 0
$$21$$ −1.76156 −0.384403
$$22$$ 0 0
$$23$$ 3.72928i 0.777609i 0.921320 + 0.388805i $$0.127112\pi$$
−0.921320 + 0.388805i $$0.872888\pi$$
$$24$$ 0 0
$$25$$ −4.62620 + 1.89692i −0.925240 + 0.379383i
$$26$$ 0 0
$$27$$ 5.10308i 0.982089i
$$28$$ 0 0
$$29$$ −7.87859 −1.46302 −0.731509 0.681832i $$-0.761184\pi$$
−0.731509 + 0.681832i $$0.761184\pi$$
$$30$$ 0 0
$$31$$ −7.52311 −1.35119 −0.675596 0.737272i $$-0.736113\pi$$
−0.675596 + 0.737272i $$0.736113\pi$$
$$32$$ 0 0
$$33$$ 1.10308i 0.192022i
$$34$$ 0 0
$$35$$ 2.19388 0.432320i 0.370833 0.0730755i
$$36$$ 0 0
$$37$$ 6.00000i 0.986394i 0.869918 + 0.493197i $$0.164172\pi$$
−0.869918 + 0.493197i $$0.835828\pi$$
$$38$$ 0 0
$$39$$ 9.67243 1.54883
$$40$$ 0 0
$$41$$ 7.72928 1.20711 0.603556 0.797321i $$-0.293750\pi$$
0.603556 + 0.797321i $$0.293750\pi$$
$$42$$ 0 0
$$43$$ 1.72928i 0.263713i 0.991269 + 0.131856i $$0.0420938\pi$$
−0.991269 + 0.131856i $$0.957906\pi$$
$$44$$ 0 0
$$45$$ 0.0445652 + 0.226153i 0.00664339 + 0.0337129i
$$46$$ 0 0
$$47$$ 5.87859i 0.857481i 0.903428 + 0.428741i $$0.141043\pi$$
−0.903428 + 0.428741i $$0.858957\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −0.142857
$$50$$ 0 0
$$51$$ 1.57997 0.221240
$$52$$ 0 0
$$53$$ 6.77551i 0.930688i 0.885130 + 0.465344i $$0.154069\pi$$
−0.885130 + 0.465344i $$0.845931\pi$$
$$54$$ 0 0
$$55$$ 0.270718 + 1.37380i 0.0365036 + 0.185243i
$$56$$ 0 0
$$57$$ 11.2524i 1.49042i
$$58$$ 0 0
$$59$$ 0.593923 0.0773221 0.0386611 0.999252i $$-0.487691\pi$$
0.0386611 + 0.999252i $$0.487691\pi$$
$$60$$ 0 0
$$61$$ −7.13536 −0.913589 −0.456795 0.889572i $$-0.651003\pi$$
−0.456795 + 0.889572i $$0.651003\pi$$
$$62$$ 0 0
$$63$$ 0.103084i 0.0129873i
$$64$$ 0 0
$$65$$ −12.0462 + 2.37380i −1.49415 + 0.294434i
$$66$$ 0 0
$$67$$ 5.79383i 0.707829i 0.935278 + 0.353915i $$0.115150\pi$$
−0.935278 + 0.353915i $$0.884850\pi$$
$$68$$ 0 0
$$69$$ −6.56934 −0.790856
$$70$$ 0 0
$$71$$ −5.52311 −0.655473 −0.327737 0.944769i $$-0.606286\pi$$
−0.327737 + 0.944769i $$0.606286\pi$$
$$72$$ 0 0
$$73$$ 3.72928i 0.436479i −0.975895 0.218240i $$-0.929969\pi$$
0.975895 0.218240i $$-0.0700315\pi$$
$$74$$ 0 0
$$75$$ −3.34153 8.14931i −0.385846 0.941002i
$$76$$ 0 0
$$77$$ 0.626198i 0.0713619i
$$78$$ 0 0
$$79$$ −5.67243 −0.638198 −0.319099 0.947721i $$-0.603380\pi$$
−0.319099 + 0.947721i $$0.603380\pi$$
$$80$$ 0 0
$$81$$ −9.29862 −1.03318
$$82$$ 0 0
$$83$$ 17.4340i 1.91363i −0.290700 0.956814i $$-0.593888\pi$$
0.290700 0.956814i $$-0.406112\pi$$
$$84$$ 0 0
$$85$$ −1.96772 + 0.387755i −0.213430 + 0.0420580i
$$86$$ 0 0
$$87$$ 13.8786i 1.48794i
$$88$$ 0 0
$$89$$ −14.2986 −1.51565 −0.757826 0.652457i $$-0.773738\pi$$
−0.757826 + 0.652457i $$0.773738\pi$$
$$90$$ 0 0
$$91$$ 5.49084 0.575596
$$92$$ 0 0
$$93$$ 13.2524i 1.37421i
$$94$$ 0 0
$$95$$ 2.76156 + 14.0140i 0.283330 + 1.43780i
$$96$$ 0 0
$$97$$ 10.1493i 1.03051i 0.857038 + 0.515253i $$0.172302\pi$$
−0.857038 + 0.515253i $$0.827698\pi$$
$$98$$ 0 0
$$99$$ 0.0645508 0.00648760
$$100$$ 0 0
$$101$$ −9.64015 −0.959231 −0.479615 0.877479i $$-0.659224\pi$$
−0.479615 + 0.877479i $$0.659224\pi$$
$$102$$ 0 0
$$103$$ 0.626198i 0.0617011i 0.999524 + 0.0308506i $$0.00982160\pi$$
−0.999524 + 0.0308506i $$0.990178\pi$$
$$104$$ 0 0
$$105$$ 0.761557 + 3.86464i 0.0743204 + 0.377150i
$$106$$ 0 0
$$107$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$108$$ 0 0
$$109$$ 18.9248 1.81267 0.906335 0.422561i $$-0.138869\pi$$
0.906335 + 0.422561i $$0.138869\pi$$
$$110$$ 0 0
$$111$$ −10.5693 −1.00320
$$112$$ 0 0
$$113$$ 1.04623i 0.0984209i −0.998788 0.0492105i $$-0.984329\pi$$
0.998788 0.0492105i $$-0.0156705\pi$$
$$114$$ 0 0
$$115$$ 8.18159 1.61224i 0.762937 0.150343i
$$116$$ 0 0
$$117$$ 0.566016i 0.0523282i
$$118$$ 0 0
$$119$$ 0.896916 0.0822202
$$120$$ 0 0
$$121$$ −10.6079 −0.964352
$$122$$ 0 0
$$123$$ 13.6156i 1.22767i
$$124$$ 0 0
$$125$$ 6.16160 + 9.32924i 0.551110 + 0.834432i
$$126$$ 0 0
$$127$$ 21.2803i 1.88832i −0.329485 0.944161i $$-0.606875\pi$$
0.329485 0.944161i $$-0.393125\pi$$
$$128$$ 0 0
$$129$$ −3.04623 −0.268205
$$130$$ 0 0
$$131$$ −9.91087 −0.865917 −0.432958 0.901414i $$-0.642530\pi$$
−0.432958 + 0.901414i $$0.642530\pi$$
$$132$$ 0 0
$$133$$ 6.38776i 0.553889i
$$134$$ 0 0
$$135$$ 11.1955 2.20617i 0.963559 0.189877i
$$136$$ 0 0
$$137$$ 3.45856i 0.295485i −0.989026 0.147743i $$-0.952799\pi$$
0.989026 0.147743i $$-0.0472007\pi$$
$$138$$ 0 0
$$139$$ 20.4157 1.73163 0.865817 0.500361i $$-0.166799\pi$$
0.865817 + 0.500361i $$0.166799\pi$$
$$140$$ 0 0
$$141$$ −10.3555 −0.872089
$$142$$ 0 0
$$143$$ 3.43835i 0.287530i
$$144$$ 0 0
$$145$$ 3.40608 + 17.2847i 0.282859 + 1.43541i
$$146$$ 0 0
$$147$$ 1.76156i 0.145291i
$$148$$ 0 0
$$149$$ −17.0462 −1.39648 −0.698241 0.715863i $$-0.746033\pi$$
−0.698241 + 0.715863i $$0.746033\pi$$
$$150$$ 0 0
$$151$$ −2.89692 −0.235748 −0.117874 0.993029i $$-0.537608\pi$$
−0.117874 + 0.993029i $$0.537608\pi$$
$$152$$ 0 0
$$153$$ 0.0924575i 0.00747474i
$$154$$ 0 0
$$155$$ 3.25240 + 16.5048i 0.261239 + 1.32570i
$$156$$ 0 0
$$157$$ 10.1170i 0.807427i 0.914885 + 0.403714i $$0.132281\pi$$
−0.914885 + 0.403714i $$0.867719\pi$$
$$158$$ 0 0
$$159$$ −11.9354 −0.946543
$$160$$ 0 0
$$161$$ −3.72928 −0.293909
$$162$$ 0 0
$$163$$ 0.476886i 0.0373526i 0.999826 + 0.0186763i $$0.00594519\pi$$
−0.999826 + 0.0186763i $$0.994055\pi$$
$$164$$ 0 0
$$165$$ −2.42003 + 0.476886i −0.188399 + 0.0371255i
$$166$$ 0 0
$$167$$ 13.1676i 1.01894i −0.860488 0.509471i $$-0.829841\pi$$
0.860488 0.509471i $$-0.170159\pi$$
$$168$$ 0 0
$$169$$ −17.1493 −1.31918
$$170$$ 0 0
$$171$$ 0.658473 0.0503547
$$172$$ 0 0
$$173$$ 13.9677i 1.06195i −0.847389 0.530973i $$-0.821826\pi$$
0.847389 0.530973i $$-0.178174\pi$$
$$174$$ 0 0
$$175$$ −1.89692 4.62620i −0.143393 0.349708i
$$176$$ 0 0
$$177$$ 1.04623i 0.0786394i
$$178$$ 0 0
$$179$$ −7.45856 −0.557479 −0.278740 0.960367i $$-0.589917\pi$$
−0.278740 + 0.960367i $$0.589917\pi$$
$$180$$ 0 0
$$181$$ 14.1170 1.04931 0.524656 0.851315i $$-0.324194\pi$$
0.524656 + 0.851315i $$0.324194\pi$$
$$182$$ 0 0
$$183$$ 12.5693i 0.929153i
$$184$$ 0 0
$$185$$ 13.1633 2.59392i 0.967783 0.190709i
$$186$$ 0 0
$$187$$ 0.561647i 0.0410717i
$$188$$ 0 0
$$189$$ −5.10308 −0.371195
$$190$$ 0 0
$$191$$ 8.42003 0.609252 0.304626 0.952472i $$-0.401469\pi$$
0.304626 + 0.952472i $$0.401469\pi$$
$$192$$ 0 0
$$193$$ 22.2986i 1.60509i −0.596591 0.802545i $$-0.703479\pi$$
0.596591 0.802545i $$-0.296521\pi$$
$$194$$ 0 0
$$195$$ −4.18159 21.2201i −0.299450 1.51960i
$$196$$ 0 0
$$197$$ 26.3632i 1.87830i 0.343509 + 0.939149i $$0.388384\pi$$
−0.343509 + 0.939149i $$0.611616\pi$$
$$198$$ 0 0
$$199$$ 22.4402 1.59075 0.795373 0.606120i $$-0.207275\pi$$
0.795373 + 0.606120i $$0.207275\pi$$
$$200$$ 0 0
$$201$$ −10.2062 −0.719888
$$202$$ 0 0
$$203$$ 7.87859i 0.552969i
$$204$$ 0 0
$$205$$ −3.34153 16.9571i −0.233382 1.18434i
$$206$$ 0 0
$$207$$ 0.384428i 0.0267196i
$$208$$ 0 0
$$209$$ 4.00000 0.276686
$$210$$ 0 0
$$211$$ −15.1955 −1.04610 −0.523052 0.852301i $$-0.675207\pi$$
−0.523052 + 0.852301i $$0.675207\pi$$
$$212$$ 0 0
$$213$$ 9.72928i 0.666639i
$$214$$ 0 0
$$215$$ 3.79383 0.747604i 0.258737 0.0509862i
$$216$$ 0 0
$$217$$ 7.52311i 0.510702i
$$218$$ 0 0
$$219$$ 6.56934 0.443915
$$220$$ 0 0
$$221$$ −4.92482 −0.331279
$$222$$ 0 0
$$223$$ 6.89692i 0.461852i 0.972971 + 0.230926i $$0.0741755\pi$$
−0.972971 + 0.230926i $$0.925825\pi$$
$$224$$ 0 0
$$225$$ 0.476886 0.195541i 0.0317924 0.0130361i
$$226$$ 0 0
$$227$$ 2.77988i 0.184507i 0.995736 + 0.0922535i $$0.0294070\pi$$
−0.995736 + 0.0922535i $$0.970593\pi$$
$$228$$ 0 0
$$229$$ 18.6585 1.23299 0.616493 0.787360i $$-0.288553\pi$$
0.616493 + 0.787360i $$0.288553\pi$$
$$230$$ 0 0
$$231$$ 1.10308 0.0725776
$$232$$ 0 0
$$233$$ 11.0462i 0.723663i −0.932244 0.361831i $$-0.882152\pi$$
0.932244 0.361831i $$-0.117848\pi$$
$$234$$ 0 0
$$235$$ 12.8969 2.54144i 0.841302 0.165785i
$$236$$ 0 0
$$237$$ 9.99230i 0.649070i
$$238$$ 0 0
$$239$$ −20.1493 −1.30335 −0.651675 0.758498i $$-0.725934\pi$$
−0.651675 + 0.758498i $$0.725934\pi$$
$$240$$ 0 0
$$241$$ 3.72928 0.240224 0.120112 0.992760i $$-0.461675\pi$$
0.120112 + 0.992760i $$0.461675\pi$$
$$242$$ 0 0
$$243$$ 1.07081i 0.0686924i
$$244$$ 0 0
$$245$$ 0.432320 + 2.19388i 0.0276199 + 0.140162i
$$246$$ 0 0
$$247$$ 35.0741i 2.23171i
$$248$$ 0 0
$$249$$ 30.7110 1.94623
$$250$$ 0 0
$$251$$ −21.4985 −1.35698 −0.678488 0.734612i $$-0.737364\pi$$
−0.678488 + 0.734612i $$0.737364\pi$$
$$252$$ 0 0
$$253$$ 2.33527i 0.146817i
$$254$$ 0 0
$$255$$ −0.683053 3.46626i −0.0427744 0.217066i
$$256$$ 0 0
$$257$$ 4.27072i 0.266400i −0.991089 0.133200i $$-0.957475\pi$$
0.991089 0.133200i $$-0.0425253\pi$$
$$258$$ 0 0
$$259$$ −6.00000 −0.372822
$$260$$ 0 0
$$261$$ 0.812155 0.0502711
$$262$$ 0 0
$$263$$ 11.4586i 0.706565i 0.935517 + 0.353283i $$0.114935\pi$$
−0.935517 + 0.353283i $$0.885065\pi$$
$$264$$ 0 0
$$265$$ 14.8646 2.92919i 0.913128 0.179939i
$$266$$ 0 0
$$267$$ 25.1878i 1.54147i
$$268$$ 0 0
$$269$$ −7.07081 −0.431115 −0.215557 0.976491i $$-0.569157\pi$$
−0.215557 + 0.976491i $$0.569157\pi$$
$$270$$ 0 0
$$271$$ −17.0096 −1.03326 −0.516629 0.856209i $$-0.672813\pi$$
−0.516629 + 0.856209i $$0.672813\pi$$
$$272$$ 0 0
$$273$$ 9.67243i 0.585402i
$$274$$ 0 0
$$275$$ 2.89692 1.18785i 0.174691 0.0716298i
$$276$$ 0 0
$$277$$ 18.7755i 1.12811i −0.825737 0.564056i $$-0.809240\pi$$
0.825737 0.564056i $$-0.190760\pi$$
$$278$$ 0 0
$$279$$ 0.775511 0.0464286
$$280$$ 0 0
$$281$$ −4.59829 −0.274311 −0.137156 0.990550i $$-0.543796\pi$$
−0.137156 + 0.990550i $$0.543796\pi$$
$$282$$ 0 0
$$283$$ 13.5833i 0.807443i −0.914882 0.403722i $$-0.867716\pi$$
0.914882 0.403722i $$-0.132284\pi$$
$$284$$ 0 0
$$285$$ −24.6864 + 4.86464i −1.46229 + 0.288156i
$$286$$ 0 0
$$287$$ 7.72928i 0.456245i
$$288$$ 0 0
$$289$$ 16.1955 0.952679
$$290$$ 0 0
$$291$$ −17.8786 −1.04806
$$292$$ 0 0
$$293$$ 11.8261i 0.690889i −0.938439 0.345444i $$-0.887728\pi$$
0.938439 0.345444i $$-0.112272\pi$$
$$294$$ 0 0
$$295$$ −0.256765 1.30299i −0.0149494 0.0758632i
$$296$$ 0 0
$$297$$ 3.19554i 0.185424i
$$298$$ 0 0
$$299$$ 20.4769 1.18421
$$300$$ 0 0
$$301$$ −1.72928 −0.0996741
$$302$$ 0 0
$$303$$ 16.9817i 0.975572i
$$304$$ 0 0
$$305$$ 3.08476 + 15.6541i 0.176633 + 0.896351i
$$306$$ 0 0
$$307$$ 20.9860i 1.19774i 0.800847 + 0.598868i $$0.204383\pi$$
−0.800847 + 0.598868i $$0.795617\pi$$
$$308$$ 0 0
$$309$$ −1.10308 −0.0627522
$$310$$ 0 0
$$311$$ 22.5048 1.27613 0.638065 0.769983i $$-0.279735\pi$$
0.638065 + 0.769983i $$0.279735\pi$$
$$312$$ 0 0
$$313$$ 12.4846i 0.705670i −0.935686 0.352835i $$-0.885218\pi$$
0.935686 0.352835i $$-0.114782\pi$$
$$314$$ 0 0
$$315$$ −0.226153 + 0.0445652i −0.0127423 + 0.00251096i
$$316$$ 0 0
$$317$$ 25.5231i 1.43352i 0.697319 + 0.716760i $$0.254376\pi$$
−0.697319 + 0.716760i $$0.745624\pi$$
$$318$$ 0 0
$$319$$ 4.93356 0.276226
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 5.72928i 0.318786i
$$324$$ 0 0
$$325$$ 10.4157 + 25.4017i 0.577757 + 1.40903i
$$326$$ 0 0
$$327$$ 33.3372i 1.84355i
$$328$$ 0 0
$$329$$ −5.87859 −0.324097
$$330$$ 0 0
$$331$$ −2.68305 −0.147474 −0.0737370 0.997278i $$-0.523493\pi$$
−0.0737370 + 0.997278i $$0.523493\pi$$
$$332$$ 0 0
$$333$$ 0.618502i 0.0338937i
$$334$$ 0 0
$$335$$ 12.7110 2.50479i 0.694474 0.136851i
$$336$$ 0 0
$$337$$ 12.5048i 0.681179i −0.940212 0.340590i $$-0.889373\pi$$
0.940212 0.340590i $$-0.110627\pi$$
$$338$$ 0 0
$$339$$ 1.84299 0.100098
$$340$$ 0 0
$$341$$ 4.71096 0.255113
$$342$$ 0 0
$$343$$ 1.00000i 0.0539949i
$$344$$ 0 0
$$345$$ 2.84006 + 14.4123i 0.152904 + 0.775934i
$$346$$ 0 0
$$347$$ 28.9450i 1.55385i 0.629593 + 0.776925i $$0.283222\pi$$
−0.629593 + 0.776925i $$0.716778\pi$$
$$348$$ 0 0
$$349$$ 32.1449 1.72068 0.860340 0.509721i $$-0.170251\pi$$
0.860340 + 0.509721i $$0.170251\pi$$
$$350$$ 0 0
$$351$$ 28.0202 1.49561
$$352$$ 0 0
$$353$$ 8.17722i 0.435229i 0.976035 + 0.217615i $$0.0698276\pi$$
−0.976035 + 0.217615i $$0.930172\pi$$
$$354$$ 0 0
$$355$$ 2.38776 + 12.1170i 0.126729 + 0.643106i
$$356$$ 0 0
$$357$$ 1.57997i 0.0836208i
$$358$$ 0 0
$$359$$ 18.5048 0.976646 0.488323 0.872663i $$-0.337609\pi$$
0.488323 + 0.872663i $$0.337609\pi$$
$$360$$ 0 0
$$361$$ 21.8034 1.14755
$$362$$ 0 0
$$363$$ 18.6864i 0.980781i
$$364$$ 0 0
$$365$$ −8.18159 + 1.61224i −0.428244 + 0.0843887i
$$366$$ 0 0
$$367$$ 27.4942i 1.43518i −0.696464 0.717592i $$-0.745244\pi$$
0.696464 0.717592i $$-0.254756\pi$$
$$368$$ 0 0
$$369$$ −0.796763 −0.0414778
$$370$$ 0 0
$$371$$ −6.77551 −0.351767
$$372$$ 0 0
$$373$$ 6.06455i 0.314011i −0.987598 0.157005i $$-0.949816\pi$$
0.987598 0.157005i $$-0.0501840\pi$$
$$374$$ 0 0
$$375$$ −16.4340 + 10.8540i −0.848647 + 0.560499i
$$376$$ 0 0
$$377$$ 43.2601i 2.22801i
$$378$$ 0 0
$$379$$ 5.72928 0.294293 0.147147 0.989115i $$-0.452991\pi$$
0.147147 + 0.989115i $$0.452991\pi$$
$$380$$ 0 0
$$381$$ 37.4865 1.92049
$$382$$ 0 0
$$383$$ 1.72928i 0.0883622i 0.999024 + 0.0441811i $$0.0140679\pi$$
−0.999024 + 0.0441811i $$0.985932\pi$$
$$384$$ 0 0
$$385$$ −1.37380 + 0.270718i −0.0700154 + 0.0137971i
$$386$$ 0 0
$$387$$ 0.178261i 0.00906150i
$$388$$ 0 0
$$389$$ −36.7187 −1.86171 −0.930855 0.365389i $$-0.880936\pi$$
−0.930855 + 0.365389i $$0.880936\pi$$
$$390$$ 0 0
$$391$$ 3.34485 0.169157
$$392$$ 0 0
$$393$$ 17.4586i 0.880668i
$$394$$ 0 0
$$395$$ 2.45231 + 12.4446i 0.123389 + 0.626156i
$$396$$ 0 0
$$397$$ 2.03228i 0.101997i −0.998699 0.0509985i $$-0.983760\pi$$
0.998699 0.0509985i $$-0.0162404\pi$$
$$398$$ 0 0
$$399$$ 11.2524 0.563324
$$400$$ 0 0
$$401$$ −1.64452 −0.0821234 −0.0410617 0.999157i $$-0.513074\pi$$
−0.0410617 + 0.999157i $$0.513074\pi$$
$$402$$ 0 0
$$403$$ 41.3082i 2.05771i
$$404$$ 0 0
$$405$$ 4.01999 + 20.4000i 0.199755 + 1.01369i
$$406$$ 0 0
$$407$$ 3.75719i 0.186237i
$$408$$ 0 0
$$409$$ 4.98168 0.246328 0.123164 0.992386i $$-0.460696\pi$$
0.123164 + 0.992386i $$0.460696\pi$$
$$410$$ 0 0
$$411$$ 6.09246 0.300519
$$412$$ 0 0
$$413$$ 0.593923i 0.0292250i
$$414$$ 0 0
$$415$$ −38.2480 + 7.53707i −1.87752 + 0.369980i
$$416$$ 0 0
$$417$$ 35.9634i 1.76113i
$$418$$ 0 0
$$419$$ −22.9205 −1.11974 −0.559869 0.828581i $$-0.689148\pi$$
−0.559869 + 0.828581i $$0.689148\pi$$
$$420$$ 0 0
$$421$$ 20.9527 1.02117 0.510587 0.859826i $$-0.329428\pi$$
0.510587 + 0.859826i $$0.329428\pi$$
$$422$$ 0 0
$$423$$ 0.605987i 0.0294641i
$$424$$ 0 0
$$425$$ 1.70138 + 4.14931i 0.0825288 + 0.201271i
$$426$$ 0 0
$$427$$ 7.13536i 0.345304i
$$428$$ 0 0
$$429$$ −6.05685 −0.292428
$$430$$ 0 0
$$431$$ −33.1589 −1.59721 −0.798604 0.601857i $$-0.794428\pi$$
−0.798604 + 0.601857i $$0.794428\pi$$
$$432$$ 0 0
$$433$$ 18.5414i 0.891045i −0.895271 0.445522i $$-0.853018\pi$$
0.895271 0.445522i $$-0.146982\pi$$
$$434$$ 0 0
$$435$$ −30.4479 + 6.00000i −1.45987 + 0.287678i
$$436$$ 0 0
$$437$$ 23.8217i 1.13955i
$$438$$ 0 0
$$439$$ −20.8401 −0.994642 −0.497321 0.867567i $$-0.665683\pi$$
−0.497321 + 0.867567i $$0.665683\pi$$
$$440$$ 0 0
$$441$$ 0.103084 0.00490875
$$442$$ 0 0
$$443$$ 17.5510i 0.833874i 0.908935 + 0.416937i $$0.136896\pi$$
−0.908935 + 0.416937i $$0.863104\pi$$
$$444$$ 0 0
$$445$$ 6.18159 + 31.3694i 0.293035 + 1.48705i
$$446$$ 0 0
$$447$$ 30.0279i 1.42027i
$$448$$ 0 0
$$449$$ 13.1955 0.622736 0.311368 0.950289i $$-0.399213\pi$$
0.311368 + 0.950289i $$0.399213\pi$$
$$450$$ 0 0
$$451$$ −4.84006 −0.227910
$$452$$ 0 0
$$453$$ 5.10308i 0.239764i
$$454$$ 0 0
$$455$$ −2.37380 12.0462i −0.111286 0.564736i
$$456$$ 0 0
$$457$$ 29.1020i 1.36134i 0.732592 + 0.680668i $$0.238310\pi$$
−0.732592 + 0.680668i $$0.761690\pi$$
$$458$$ 0 0
$$459$$ 4.57704 0.213638
$$460$$ 0 0
$$461$$ 18.8280 0.876907 0.438454 0.898754i $$-0.355526\pi$$
0.438454 + 0.898754i $$0.355526\pi$$
$$462$$ 0 0
$$463$$ 14.0925i 0.654932i 0.944863 + 0.327466i $$0.106195\pi$$
−0.944863 + 0.327466i $$0.893805\pi$$
$$464$$ 0 0
$$465$$ −29.0741 + 5.72928i −1.34828 + 0.265689i
$$466$$ 0 0
$$467$$ 12.2663i 0.567619i 0.958881 + 0.283809i $$0.0915983\pi$$
−0.958881 + 0.283809i $$0.908402\pi$$
$$468$$ 0 0
$$469$$ −5.79383 −0.267534
$$470$$ 0 0
$$471$$ −17.8217 −0.821182
$$472$$ 0 0
$$473$$ 1.08287i 0.0497905i
$$474$$ 0 0
$$475$$ 29.5510 12.1170i 1.35589 0.555968i
$$476$$ 0 0
$$477$$ 0.698445i 0.0319796i
$$478$$ 0 0
$$479$$ −14.1570 −0.646850 −0.323425 0.946254i $$-0.604834\pi$$
−0.323425 + 0.946254i $$0.604834\pi$$
$$480$$ 0 0
$$481$$ 32.9450 1.50216
$$482$$ 0 0
$$483$$ 6.56934i 0.298915i
$$484$$ 0 0
$$485$$ 22.2663 4.38776i 1.01106 0.199238i
$$486$$ 0 0
$$487$$ 30.2341i 1.37004i 0.728526 + 0.685018i $$0.240206\pi$$
−0.728526 + 0.685018i $$0.759794\pi$$
$$488$$ 0 0
$$489$$ −0.840061 −0.0379889
$$490$$ 0 0
$$491$$ 39.9065 1.80096 0.900478 0.434902i $$-0.143217\pi$$
0.900478 + 0.434902i $$0.143217\pi$$
$$492$$ 0 0
$$493$$ 7.06644i 0.318256i
$$494$$ 0 0
$$495$$ −0.0279066 0.141617i −0.00125431 0.00636519i
$$496$$ 0 0
$$497$$ 5.52311i 0.247746i
$$498$$ 0 0
$$499$$ −27.3246 −1.22322 −0.611610 0.791160i $$-0.709478\pi$$
−0.611610 + 0.791160i $$0.709478\pi$$
$$500$$ 0 0
$$501$$ 23.1955 1.03630
$$502$$ 0 0
$$503$$ 1.40171i 0.0624991i −0.999512 0.0312495i $$-0.990051\pi$$
0.999512 0.0312495i $$-0.00994866\pi$$
$$504$$ 0 0
$$505$$ 4.16763 + 21.1493i 0.185457 + 0.941132i
$$506$$ 0 0
$$507$$ 30.2095i 1.34165i
$$508$$ 0 0
$$509$$ 18.6585 0.827022 0.413511 0.910499i $$-0.364302\pi$$
0.413511 + 0.910499i $$0.364302\pi$$
$$510$$ 0 0
$$511$$ 3.72928 0.164974
$$512$$ 0 0
$$513$$ 32.5972i 1.43920i
$$514$$ 0 0
$$515$$ 1.37380 0.270718i 0.0605369 0.0119293i
$$516$$ 0 0
$$517$$ 3.68116i 0.161897i
$$518$$ 0 0
$$519$$ 24.6049 1.08004
$$520$$ 0 0
$$521$$ −4.02791 −0.176466 −0.0882329 0.996100i $$-0.528122\pi$$
−0.0882329 + 0.996100i $$0.528122\pi$$
$$522$$ 0 0
$$523$$ 38.4436i 1.68102i 0.541796 + 0.840510i $$0.317744\pi$$
−0.541796 + 0.840510i $$0.682256\pi$$
$$524$$ 0 0
$$525$$ 8.14931 3.34153i 0.355665 0.145836i
$$526$$ 0 0
$$527$$ 6.74760i 0.293930i
$$528$$ 0 0
$$529$$ 9.09246 0.395324
$$530$$ 0 0
$$531$$ −0.0612237 −0.00265688
$$532$$ 0 0
$$533$$ 42.4402i 1.83829i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 13.1387i 0.566976i
$$538$$ 0 0
$$539$$ 0.626198 0.0269723
$$540$$ 0 0
$$541$$ −12.4846 −0.536754 −0.268377 0.963314i $$-0.586487\pi$$
−0.268377 + 0.963314i $$0.586487\pi$$
$$542$$ 0 0
$$543$$ 24.8680i 1.06719i
$$544$$ 0 0
$$545$$ −8.18159 41.5187i −0.350461 1.77847i
$$546$$ 0 0
$$547$$ 37.7851i 1.61557i −0.589474 0.807787i $$-0.700665\pi$$
0.589474 0.807787i $$-0.299335\pi$$
$$548$$ 0 0
$$549$$ 0.735539 0.0313921
$$550$$ 0 0
$$551$$ 50.3265 2.14398
$$552$$ 0 0
$$553$$ 5.67243i 0.241216i
$$554$$ 0 0
$$555$$ 4.56934 + 23.1878i 0.193958 + 0.984269i
$$556$$ 0 0
$$557$$ 1.93545i 0.0820076i 0.999159 + 0.0410038i $$0.0130556\pi$$
−0.999159 + 0.0410038i $$0.986944\pi$$
$$558$$ 0 0
$$559$$ 9.49521 0.401604
$$560$$ 0 0
$$561$$ −0.989374 −0.0417714
$$562$$ 0 0
$$563$$ 29.8463i 1.25787i −0.777457 0.628936i $$-0.783491\pi$$
0.777457 0.628936i $$-0.216509\pi$$
$$564$$ 0 0
$$565$$ −2.29530 + 0.452306i −0.0965639 + 0.0190287i
$$566$$ 0 0
$$567$$ 9.29862i 0.390506i
$$568$$ 0 0
$$569$$ −15.3449 −0.643290 −0.321645 0.946860i $$-0.604236\pi$$
−0.321645 + 0.946860i $$0.604236\pi$$
$$570$$ 0 0
$$571$$ 35.8217 1.49909 0.749547 0.661952i $$-0.230272\pi$$
0.749547 + 0.661952i $$0.230272\pi$$
$$572$$ 0 0
$$573$$ 14.8324i 0.619631i
$$574$$ 0 0
$$575$$ −7.07414 17.2524i −0.295012 0.719475i
$$576$$ 0 0
$$577$$ 2.92482i 0.121762i −0.998145 0.0608810i $$-0.980609\pi$$
0.998145 0.0608810i $$-0.0193910\pi$$
$$578$$ 0 0
$$579$$ 39.2803 1.63243
$$580$$ 0 0
$$581$$ 17.4340 0.723284
$$582$$ 0 0
$$583$$ 4.24281i 0.175719i
$$584$$ 0 0
$$585$$ 1.24177 0.244700i 0.0513409 0.0101171i
$$586$$ 0 0
$$587$$ 19.5756i 0.807972i −0.914765 0.403986i $$-0.867625\pi$$
0.914765 0.403986i $$-0.132375\pi$$
$$588$$ 0 0
$$589$$ 48.0558 1.98011
$$590$$ 0 0
$$591$$ −46.4402 −1.91030
$$592$$ 0 0
$$593$$ 8.00770i 0.328837i 0.986391 + 0.164418i $$0.0525747\pi$$
−0.986391 + 0.164418i $$0.947425\pi$$
$$594$$ 0 0
$$595$$ −0.387755 1.96772i −0.0158964 0.0806688i
$$596$$ 0 0
$$597$$ 39.5298i 1.61785i
$$598$$ 0 0
$$599$$ −29.3005 −1.19719 −0.598593 0.801053i $$-0.704273\pi$$
−0.598593 + 0.801053i $$0.704273\pi$$
$$600$$ 0 0
$$601$$ 21.3449 0.870675 0.435337 0.900267i $$-0.356629\pi$$
0.435337 + 0.900267i $$0.356629\pi$$
$$602$$ 0 0
$$603$$ 0.597250i 0.0243219i
$$604$$ 0 0
$$605$$ 4.58600 + 23.2724i 0.186447 + 0.946157i
$$606$$ 0 0
$$607$$ 9.53081i 0.386844i 0.981116 + 0.193422i $$0.0619586\pi$$
−0.981116 + 0.193422i $$0.938041\pi$$
$$608$$ 0 0
$$609$$ 13.8786 0.562389
$$610$$ 0 0
$$611$$ 32.2784 1.30584
$$612$$ 0 0
$$613$$ 9.75719i 0.394089i 0.980395 + 0.197045i $$0.0631344\pi$$
−0.980395 + 0.197045i $$0.936866\pi$$
$$614$$ 0 0
$$615$$ 29.8709 5.88629i 1.20451 0.237358i
$$616$$ 0 0
$$617$$ 37.9267i 1.52687i 0.645884 + 0.763436i $$0.276489\pi$$
−0.645884 + 0.763436i $$0.723511\pi$$
$$618$$ 0 0
$$619$$ −41.9109 −1.68454 −0.842270 0.539056i $$-0.818781\pi$$
−0.842270 + 0.539056i $$0.818781\pi$$
$$620$$ 0 0
$$621$$ −19.0308 −0.763681
$$622$$ 0 0
$$623$$ 14.2986i 0.572862i
$$624$$ 0 0
$$625$$ 17.8034 17.5510i 0.712137 0.702041i
$$626$$ 0 0
$$627$$ 7.04623i 0.281399i
$$628$$ 0 0
$$629$$ 5.38150 0.214574
$$630$$ 0 0
$$631$$ 8.42003 0.335196 0.167598 0.985855i $$-0.446399\pi$$
0.167598 + 0.985855i $$0.446399\pi$$
$$632$$ 0 0
$$633$$ 26.7678i 1.06393i
$$634$$ 0 0
$$635$$ −46.6864 + 9.19991i −1.85269 + 0.365087i
$$636$$ 0 0
$$637$$ 5.49084i 0.217555i
$$638$$ 0 0
$$639$$ 0.569343 0.0225229
$$640$$ 0 0
$$641$$ −2.07707 −0.0820392 −0.0410196 0.999158i $$-0.513061\pi$$
−0.0410196 + 0.999158i $$0.513061\pi$$
$$642$$ 0 0
$$643$$ 27.2480i 1.07456i −0.843405 0.537279i $$-0.819452\pi$$
0.843405 0.537279i $$-0.180548\pi$$
$$644$$ 0 0
$$645$$ 1.31695 + 6.68305i 0.0518547 + 0.263145i
$$646$$ 0 0
$$647$$ 12.3632i 0.486047i 0.970020 + 0.243023i $$0.0781391\pi$$
−0.970020 + 0.243023i $$0.921861\pi$$
$$648$$ 0 0
$$649$$ −0.371913 −0.0145989
$$650$$ 0 0
$$651$$ 13.2524 0.519402
$$652$$ 0 0
$$653$$ 37.3449i 1.46142i −0.682690 0.730709i $$-0.739190\pi$$
0.682690 0.730709i $$-0.260810\pi$$
$$654$$ 0 0
$$655$$ 4.28467 + 21.7432i 0.167416 + 0.849578i
$$656$$ 0 0
$$657$$ 0.384428i 0.0149980i
$$658$$ 0 0
$$659$$ 14.1772 0.552266 0.276133 0.961119i $$-0.410947\pi$$
0.276133 + 0.961119i $$0.410947\pi$$
$$660$$ 0 0
$$661$$ 1.76925 0.0688160 0.0344080 0.999408i $$-0.489045\pi$$
0.0344080 + 0.999408i $$0.489045\pi$$
$$662$$ 0 0
$$663$$ 8.67536i 0.336923i
$$664$$ 0 0
$$665$$ −14.0140 + 2.76156i −0.543438 + 0.107089i
$$666$$ 0 0
$$667$$ 29.3815i 1.13766i
$$668$$ 0 0
$$669$$ −12.1493 −0.469720
$$670$$ 0 0
$$671$$ 4.46815 0.172491
$$672$$ 0 0
$$673$$ 4.05581i 0.156340i 0.996940 + 0.0781701i $$0.0249077\pi$$
−0.996940 + 0.0781701i $$0.975092\pi$$
$$674$$ 0 0
$$675$$ −9.68012 23.6079i −0.372588 0.908668i
$$676$$ 0 0
$$677$$ 9.37713i 0.360392i −0.983631 0.180196i $$-0.942327\pi$$
0.983631 0.180196i $$-0.0576733\pi$$
$$678$$ 0 0
$$679$$ −10.1493 −0.389495
$$680$$ 0 0
$$681$$ −4.89692 −0.187650
$$682$$ 0 0
$$683$$ 5.49521i 0.210268i −0.994458 0.105134i $$-0.966473\pi$$
0.994458 0.105134i $$-0.0335272\pi$$
$$684$$ 0 0
$$685$$ −7.58767 + 1.49521i −0.289910 + 0.0571290i
$$686$$ 0 0
$$687$$ 32.8680i 1.25399i
$$688$$ 0 0
$$689$$ 37.2032 1.41733
$$690$$ 0 0
$$691$$ −3.03416 −0.115425 −0.0577125 0.998333i $$-0.518381\pi$$
−0.0577125 + 0.998333i $$0.518381\pi$$
$$692$$ 0 0
$$693$$ 0.0645508i 0.00245208i
$$694$$ 0 0
$$695$$ −8.82611 44.7895i −0.334793 1.69896i
$$696$$ 0 0
$$697$$ 6.93252i 0.262588i
$$698$$ 0 0
$$699$$ 19.4586 0.735990
$$700$$ 0 0
$$701$$ −35.2234 −1.33037 −0.665186 0.746678i $$-0.731648\pi$$
−0.665186 + 0.746678i $$0.731648\pi$$
$$702$$ 0 0
$$703$$ 38.3265i 1.44551i
$$704$$ 0 0
$$705$$ 4.47689 + 22.7187i 0.168609 + 0.855634i
$$706$$ 0 0
$$707$$ 9.64015i 0.362555i
$$708$$ 0 0
$$709$$ 28.7187 1.07855 0.539276 0.842129i $$-0.318698\pi$$
0.539276 + 0.842129i $$0.318698\pi$$
$$710$$ 0 0
$$711$$ 0.584735 0.0219293
$$712$$ 0 0
$$713$$ 28.0558i 1.05070i
$$714$$ 0 0
$$715$$ 7.54333 1.48647i 0.282104 0.0555908i
$$716$$ 0 0
$$717$$ 35.4942i 1.32555i
$$718$$ 0 0
$$719$$ −8.60599 −0.320949 −0.160475 0.987040i $$-0.551302\pi$$
−0.160475 + 0.987040i $$0.551302\pi$$
$$720$$ 0 0
$$721$$ −0.626198 −0.0233208
$$722$$ 0 0
$$723$$ 6.56934i 0.244316i
$$724$$ 0 0
$$725$$ 36.4479 14.9450i 1.35364 0.555045i
$$726$$ 0 0
$$727$$ 15.2803i 0.566715i −0.959014 0.283358i $$-0.908552\pi$$
0.959014 0.283358i $$-0.0914483\pi$$
$$728$$ 0 0
$$729$$ −26.0096 −0.963318
$$730$$ 0 0
$$731$$ 1.55102 0.0573666
$$732$$ 0 0
$$733$$ 46.0235i 1.69992i 0.526849 + 0.849959i $$0.323373\pi$$
−0.526849 + 0.849959i $$0.676627\pi$$
$$734$$ 0 0
$$735$$ −3.86464 + 0.761557i −0.142549 + 0.0280905i
$$736$$ 0 0
$$737$$ 3.62809i 0.133642i
$$738$$ 0 0
$$739$$ −46.3467 −1.70489 −0.852446 0.522815i $$-0.824882\pi$$
−0.852446 + 0.522815i $$0.824882\pi$$
$$740$$ 0 0
$$741$$ −61.7851 −2.26973
$$742$$ 0 0
$$743$$ 10.7755i 0.395315i −0.980271 0.197658i $$-0.936667\pi$$
0.980271 0.197658i $$-0.0633334\pi$$
$$744$$ 0 0
$$745$$ 7.36943 + 37.3973i 0.269995 + 1.37013i
$$746$$ 0 0
$$747$$ 1.79716i 0.0657546i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −2.76781 −0.100999 −0.0504995 0.998724i $$-0.516081\pi$$
−0.0504995 + 0.998724i $$0.516081\pi$$
$$752$$ 0 0
$$753$$ 37.8709i 1.38009i
$$754$$ 0 0
$$755$$ 1.25240 + 6.35548i 0.0455794 + 0.231300i
$$756$$ 0 0
$$757$$ 14.8401i 0.539371i 0.962948 + 0.269686i $$0.0869198\pi$$
−0.962948 + 0.269686i $$0.913080\pi$$
$$758$$ 0 0
$$759$$ 4.11371 0.149318
$$760$$ 0 0
$$761$$ 31.3169 1.13524 0.567619 0.823291i $$-0.307865\pi$$
0.567619 + 0.823291i $$0.307865\pi$$
$$762$$ 0 0
$$763$$ 18.9248i 0.685125i
$$764$$ 0 0
$$765$$ 0.202840 0.0399712i 0.00733371 0.00144516i
$$766$$ 0 0
$$767$$ 3.26113i 0.117753i
$$768$$ 0 0
$$769$$ −8.92586 −0.321875 −0.160937 0.986965i $$-0.551452\pi$$
−0.160937 + 0.986965i $$0.551452\pi$$
$$770$$ 0 0
$$771$$ 7.52311 0.270938
$$772$$ 0 0
$$773$$ 36.7711i 1.32257i −0.750136 0.661283i $$-0.770012\pi$$
0.750136 0.661283i $$-0.229988\pi$$
$$774$$ 0 0
$$775$$ 34.8034 14.2707i 1.25018 0.512619i
$$776$$ 0 0
$$777$$ 10.5693i 0.379173i
$$778$$ 0 0
$$779$$ −49.3728 −1.76896
$$780$$ 0 0
$$781$$ 3.45856 0.123757
$$782$$ 0 0
$$783$$ 40.2051i 1.43681i
$$784$$ 0 0
$$785$$ 22.1955 4.37380i 0.792193 0.156108i
$$786$$ 0 0
$$787$$ 6.53707i 0.233021i −0.993189 0.116511i $$-0.962829\pi$$
0.993189 0.116511i $$-0.0371709\pi$$
$$788$$ 0 0
$$789$$ −20.1849 −0.718602
$$790$$ 0 0
$$791$$ 1.04623 0.0371996
$$792$$ 0 0
$$793$$ 39.1791i 1.39129i
$$794$$ 0 0
$$795$$ 5.15994 + 26.1849i 0.183004 + 0.928683i
$$796$$ 0 0
$$797$$ 7.82611i 0.277215i 0.990347 + 0.138607i $$0.0442626\pi$$
−0.990347 + 0.138607i $$0.955737\pi$$
$$798$$ 0 0
$$799$$ 5.27261 0.186531
$$800$$ 0 0
$$801$$ 1.47396 0.0520796
$$802$$ 0 0