# Properties

 Label 108.6.e.a.37.5 Level 108 Weight 6 Character 108.37 Analytic conductor 17.321 Analytic rank 0 Dimension 10 CM no Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$108 = 2^{2} \cdot 3^{3}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 108.e (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$17.3214525398$$ Analytic rank: $$0$$ Dimension: $$10$$ Relative dimension: $$5$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ Coefficient ring: $$\Z[a_1, \ldots, a_{19}]$$ Coefficient ring index: $$2^{8}\cdot 3^{16}$$ Twist minimal: no (minimal twist has level 36) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 37.5 Root $$-1.11227i$$ of $$x^{10} + 175 x^{8} + 8800 x^{6} + 124623 x^{4} + 498609 x^{2} + 442368$$ Character $$\chi$$ $$=$$ 108.37 Dual form 108.6.e.a.73.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(55.1996 - 95.6086i) q^{5} +(-50.8724 - 88.1135i) q^{7} +O(q^{10})$$ $$q+(55.1996 - 95.6086i) q^{5} +(-50.8724 - 88.1135i) q^{7} +(-75.1560 - 130.174i) q^{11} +(-317.712 + 550.293i) q^{13} -1498.54 q^{17} +1437.69 q^{19} +(-632.053 + 1094.75i) q^{23} +(-4531.50 - 7848.79i) q^{25} +(-1388.75 - 2405.38i) q^{29} +(3484.34 - 6035.05i) q^{31} -11232.5 q^{35} -7950.71 q^{37} +(-1013.77 + 1755.90i) q^{41} +(6261.65 + 10845.5i) q^{43} +(-3241.17 - 5613.87i) q^{47} +(3227.51 - 5590.21i) q^{49} -9827.54 q^{53} -16594.3 q^{55} +(23544.0 - 40779.3i) q^{59} +(-4168.92 - 7220.78i) q^{61} +(35075.2 + 60752.0i) q^{65} +(3630.45 - 6288.12i) q^{67} -3582.33 q^{71} +58077.5 q^{73} +(-7646.73 + 13244.5i) q^{77} +(31871.4 + 55202.9i) q^{79} +(41423.3 + 71747.2i) q^{83} +(-82718.9 + 143273. i) q^{85} +3861.51 q^{89} +64651.0 q^{91} +(79359.8 - 137455. i) q^{95} +(-34638.6 - 59995.8i) q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10q + 21q^{5} + 29q^{7} + O(q^{10})$$ $$10q + 21q^{5} + 29q^{7} - 177q^{11} - 181q^{13} - 2280q^{17} - 832q^{19} - 399q^{23} - 4778q^{25} + 6033q^{29} + 2759q^{31} - 37146q^{35} - 15172q^{37} + 18435q^{41} + 1469q^{43} + 25155q^{47} - 4056q^{49} - 116844q^{53} + 14778q^{55} + 90537q^{59} + 1403q^{61} + 148407q^{65} + 13907q^{67} - 229368q^{71} + 15200q^{73} + 211983q^{77} + 29993q^{79} + 228951q^{83} - 49662q^{85} - 598332q^{89} + 124930q^{91} + 394764q^{95} + 40541q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$$.

 $$n$$ $$29$$ $$55$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$

## 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 0
$$4$$ 0 0
$$5$$ 55.1996 95.6086i 0.987441 1.71030i 0.356899 0.934143i $$-0.383834\pi$$
0.630542 0.776155i $$-0.282833\pi$$
$$6$$ 0 0
$$7$$ −50.8724 88.1135i −0.392407 0.679669i 0.600359 0.799730i $$-0.295024\pi$$
−0.992766 + 0.120061i $$0.961691\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −75.1560 130.174i −0.187276 0.324371i 0.757065 0.653339i $$-0.226633\pi$$
−0.944341 + 0.328968i $$0.893299\pi$$
$$12$$ 0 0
$$13$$ −317.712 + 550.293i −0.521405 + 0.903100i 0.478285 + 0.878205i $$0.341259\pi$$
−0.999690 + 0.0248953i $$0.992075\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1498.54 −1.25761 −0.628806 0.777562i $$-0.716456\pi$$
−0.628806 + 0.777562i $$0.716456\pi$$
$$18$$ 0 0
$$19$$ 1437.69 0.913651 0.456825 0.889556i $$-0.348986\pi$$
0.456825 + 0.889556i $$0.348986\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −632.053 + 1094.75i −0.249134 + 0.431513i −0.963286 0.268478i $$-0.913479\pi$$
0.714151 + 0.699991i $$0.246813\pi$$
$$24$$ 0 0
$$25$$ −4531.50 7848.79i −1.45008 2.51161i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −1388.75 2405.38i −0.306640 0.531116i 0.670985 0.741471i $$-0.265871\pi$$
−0.977625 + 0.210355i $$0.932538\pi$$
$$30$$ 0 0
$$31$$ 3484.34 6035.05i 0.651203 1.12792i −0.331628 0.943410i $$-0.607598\pi$$
0.982831 0.184506i $$-0.0590686\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −11232.5 −1.54992
$$36$$ 0 0
$$37$$ −7950.71 −0.954776 −0.477388 0.878693i $$-0.658416\pi$$
−0.477388 + 0.878693i $$0.658416\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −1013.77 + 1755.90i −0.0941843 + 0.163132i −0.909268 0.416211i $$-0.863358\pi$$
0.815084 + 0.579343i $$0.196691\pi$$
$$42$$ 0 0
$$43$$ 6261.65 + 10845.5i 0.516438 + 0.894496i 0.999818 + 0.0190856i $$0.00607551\pi$$
−0.483380 + 0.875410i $$0.660591\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −3241.17 5613.87i −0.214021 0.370696i 0.738948 0.673763i $$-0.235323\pi$$
−0.952969 + 0.303066i $$0.901990\pi$$
$$48$$ 0 0
$$49$$ 3227.51 5590.21i 0.192034 0.332612i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −9827.54 −0.480568 −0.240284 0.970703i $$-0.577241\pi$$
−0.240284 + 0.970703i $$0.577241\pi$$
$$54$$ 0 0
$$55$$ −16594.3 −0.739696
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 23544.0 40779.3i 0.880541 1.52514i 0.0298005 0.999556i $$-0.490513\pi$$
0.850741 0.525586i $$-0.176154\pi$$
$$60$$ 0 0
$$61$$ −4168.92 7220.78i −0.143450 0.248462i 0.785344 0.619060i $$-0.212486\pi$$
−0.928793 + 0.370598i $$0.879153\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 35075.2 + 60752.0i 1.02971 + 1.78352i
$$66$$ 0 0
$$67$$ 3630.45 6288.12i 0.0988036 0.171133i −0.812386 0.583120i $$-0.801832\pi$$
0.911190 + 0.411987i $$0.135165\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −3582.33 −0.0843372 −0.0421686 0.999111i $$-0.513427\pi$$
−0.0421686 + 0.999111i $$0.513427\pi$$
$$72$$ 0 0
$$73$$ 58077.5 1.27556 0.637780 0.770218i $$-0.279853\pi$$
0.637780 + 0.770218i $$0.279853\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −7646.73 + 13244.5i −0.146977 + 0.254571i
$$78$$ 0 0
$$79$$ 31871.4 + 55202.9i 0.574558 + 0.995163i 0.996090 + 0.0883495i $$0.0281592\pi$$
−0.421532 + 0.906814i $$0.638507\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ 41423.3 + 71747.2i 0.660008 + 1.14317i 0.980613 + 0.195954i $$0.0627804\pi$$
−0.320605 + 0.947213i $$0.603886\pi$$
$$84$$ 0 0
$$85$$ −82718.9 + 143273.i −1.24182 + 2.15089i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 3861.51 0.0516752 0.0258376 0.999666i $$-0.491775\pi$$
0.0258376 + 0.999666i $$0.491775\pi$$
$$90$$ 0 0
$$91$$ 64651.0 0.818412
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 79359.8 137455.i 0.902176 1.56262i
$$96$$ 0 0
$$97$$ −34638.6 59995.8i −0.373793 0.647428i 0.616353 0.787470i $$-0.288610\pi$$
−0.990146 + 0.140042i $$0.955276\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −12722.8 22036.6i −0.124103 0.214952i 0.797279 0.603611i $$-0.206272\pi$$
−0.921382 + 0.388659i $$0.872939\pi$$
$$102$$ 0 0
$$103$$ 31693.9 54895.4i 0.294363 0.509851i −0.680474 0.732772i $$-0.738226\pi$$
0.974836 + 0.222922i $$0.0715594\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 61158.9 0.516417 0.258208 0.966089i $$-0.416868\pi$$
0.258208 + 0.966089i $$0.416868\pi$$
$$108$$ 0 0
$$109$$ −124036. −0.999957 −0.499979 0.866038i $$-0.666659\pi$$
−0.499979 + 0.866038i $$0.666659\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 58718.5 101703.i 0.432592 0.749272i −0.564503 0.825431i $$-0.690932\pi$$
0.997096 + 0.0761589i $$0.0242656\pi$$
$$114$$ 0 0
$$115$$ 69778.2 + 120859.i 0.492011 + 0.852188i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 76234.3 + 132042.i 0.493495 + 0.854759i
$$120$$ 0 0
$$121$$ 69228.6 119908.i 0.429855 0.744531i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −655551. −3.75259
$$126$$ 0 0
$$127$$ −29838.6 −0.164161 −0.0820803 0.996626i $$-0.526156\pi$$
−0.0820803 + 0.996626i $$0.526156\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −86028.8 + 149006.i −0.437992 + 0.758624i −0.997535 0.0701777i $$-0.977643\pi$$
0.559543 + 0.828801i $$0.310977\pi$$
$$132$$ 0 0
$$133$$ −73138.5 126680.i −0.358523 0.620980i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 95180.7 + 164858.i 0.433259 + 0.750426i 0.997152 0.0754216i $$-0.0240303\pi$$
−0.563893 + 0.825848i $$0.690697\pi$$
$$138$$ 0 0
$$139$$ 168532. 291905.i 0.739852 1.28146i −0.212710 0.977115i $$-0.568229\pi$$
0.952562 0.304345i $$-0.0984376\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 95511.9 0.390586
$$144$$ 0 0
$$145$$ −306634. −1.21115
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −27549.4 + 47716.9i −0.101659 + 0.176079i −0.912368 0.409370i $$-0.865748\pi$$
0.810709 + 0.585449i $$0.199082\pi$$
$$150$$ 0 0
$$151$$ −167032. 289308.i −0.596152 1.03257i −0.993383 0.114847i $$-0.963362\pi$$
0.397231 0.917719i $$-0.369971\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −384669. 666266.i −1.28605 2.22750i
$$156$$ 0 0
$$157$$ 60053.4 104015.i 0.194441 0.336782i −0.752276 0.658848i $$-0.771044\pi$$
0.946717 + 0.322066i $$0.104377\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 128616. 0.391048
$$162$$ 0 0
$$163$$ 367083. 1.08217 0.541085 0.840968i $$-0.318014\pi$$
0.541085 + 0.840968i $$0.318014\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 294724. 510477.i 0.817758 1.41640i −0.0895730 0.995980i $$-0.528550\pi$$
0.907331 0.420418i $$-0.138116\pi$$
$$168$$ 0 0
$$169$$ −16235.3 28120.4i −0.0437264 0.0757363i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 218229. + 377983.i 0.554366 + 0.960190i 0.997953 + 0.0639583i $$0.0203725\pi$$
−0.443587 + 0.896231i $$0.646294\pi$$
$$174$$ 0 0
$$175$$ −461056. + 798572.i −1.13804 + 1.97115i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −241064. −0.562341 −0.281171 0.959658i $$-0.590723\pi$$
−0.281171 + 0.959658i $$0.590723\pi$$
$$180$$ 0 0
$$181$$ 27128.8 0.0615510 0.0307755 0.999526i $$-0.490202\pi$$
0.0307755 + 0.999526i $$0.490202\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ −438876. + 760156.i −0.942785 + 1.63295i
$$186$$ 0 0
$$187$$ 112624. + 195071.i 0.235520 + 0.407933i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −28036.3 48560.2i −0.0556079 0.0963157i 0.836881 0.547384i $$-0.184376\pi$$
−0.892489 + 0.451068i $$0.851043\pi$$
$$192$$ 0 0
$$193$$ −177242. + 306992.i −0.342510 + 0.593244i −0.984898 0.173135i $$-0.944610\pi$$
0.642388 + 0.766379i $$0.277944\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 816895. 1.49969 0.749844 0.661615i $$-0.230129\pi$$
0.749844 + 0.661615i $$0.230129\pi$$
$$198$$ 0 0
$$199$$ 860396. 1.54016 0.770079 0.637948i $$-0.220217\pi$$
0.770079 + 0.637948i $$0.220217\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −141298. + 244735.i −0.240655 + 0.416827i
$$204$$ 0 0
$$205$$ 111919. + 193850.i 0.186003 + 0.322166i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −108051. 187149.i −0.171105 0.296362i
$$210$$ 0 0
$$211$$ 193586. 335300.i 0.299341 0.518475i −0.676644 0.736310i $$-0.736566\pi$$
0.975985 + 0.217836i $$0.0698997\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 1.38256e6 2.03981
$$216$$ 0 0
$$217$$ −709026. −1.02215
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 476105. 824637.i 0.655725 1.13575i
$$222$$ 0 0
$$223$$ 147497. + 255472.i 0.198619 + 0.344018i 0.948081 0.318029i $$-0.103021\pi$$
−0.749462 + 0.662047i $$0.769688\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 343990. + 595808.i 0.443079 + 0.767435i 0.997916 0.0645238i $$-0.0205529\pi$$
−0.554837 + 0.831959i $$0.687220\pi$$
$$228$$ 0 0
$$229$$ 543233. 940908.i 0.684538 1.18565i −0.289044 0.957316i $$-0.593337\pi$$
0.973582 0.228339i $$-0.0733294\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ −168058. −0.202801 −0.101400 0.994846i $$-0.532332\pi$$
−0.101400 + 0.994846i $$0.532332\pi$$
$$234$$ 0 0
$$235$$ −715646. −0.845334
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −773138. + 1.33911e6i −0.875512 + 1.51643i −0.0192952 + 0.999814i $$0.506142\pi$$
−0.856217 + 0.516617i $$0.827191\pi$$
$$240$$ 0 0
$$241$$ 576865. + 999160.i 0.639782 + 1.10813i 0.985480 + 0.169789i $$0.0543086\pi$$
−0.345699 + 0.938346i $$0.612358\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ −356314. 617155.i −0.379244 0.656869i
$$246$$ 0 0
$$247$$ −456770. + 791149.i −0.476382 + 0.825118i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 586711. 0.587814 0.293907 0.955834i $$-0.405044\pi$$
0.293907 + 0.955834i $$0.405044\pi$$
$$252$$ 0 0
$$253$$ 190010. 0.186628
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 54171.0 93826.9i 0.0511604 0.0886124i −0.839311 0.543651i $$-0.817041\pi$$
0.890471 + 0.455039i $$0.150375\pi$$
$$258$$ 0 0
$$259$$ 404471. + 700565.i 0.374661 + 0.648931i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ −868353. 1.50403e6i −0.774117 1.34081i −0.935289 0.353884i $$-0.884861\pi$$
0.161172 0.986926i $$-0.448473\pi$$
$$264$$ 0 0
$$265$$ −542476. + 939597.i −0.474533 + 0.821915i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −18297.3 −0.0154172 −0.00770860 0.999970i $$-0.502454\pi$$
−0.00770860 + 0.999970i $$0.502454\pi$$
$$270$$ 0 0
$$271$$ 7105.09 0.00587688 0.00293844 0.999996i $$-0.499065\pi$$
0.00293844 + 0.999996i $$0.499065\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −681139. + 1.17977e6i −0.543130 + 0.940729i
$$276$$ 0 0
$$277$$ −355202. 615227.i −0.278148 0.481766i 0.692777 0.721152i $$-0.256387\pi$$
−0.970924 + 0.239386i $$0.923054\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −514224. 890661.i −0.388496 0.672894i 0.603752 0.797172i $$-0.293672\pi$$
−0.992247 + 0.124278i $$0.960338\pi$$
$$282$$ 0 0
$$283$$ 922317. 1.59750e6i 0.684564 1.18570i −0.289010 0.957326i $$-0.593326\pi$$
0.973574 0.228374i $$-0.0733407\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 206291. 0.147834
$$288$$ 0 0
$$289$$ 825769. 0.581586
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 470486. 814906.i 0.320168 0.554547i −0.660355 0.750954i $$-0.729594\pi$$
0.980522 + 0.196407i $$0.0629274\pi$$
$$294$$ 0 0
$$295$$ −2.59924e6 4.50201e6i −1.73896 3.01198i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ −401621. 695629.i −0.259800 0.449987i
$$300$$ 0 0
$$301$$ 637090. 1.10347e6i 0.405307 0.702013i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ −920492. −0.566592
$$306$$ 0 0
$$307$$ −2.93094e6 −1.77485 −0.887425 0.460952i $$-0.847508\pi$$
−0.887425 + 0.460952i $$0.847508\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.14126e6 + 1.97671e6i −0.669086 + 1.15889i 0.309074 + 0.951038i $$0.399981\pi$$
−0.978160 + 0.207853i $$0.933352\pi$$
$$312$$ 0 0
$$313$$ −401324. 695114.i −0.231544 0.401047i 0.726718 0.686936i $$-0.241045\pi$$
−0.958263 + 0.285889i $$0.907711\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 555982. + 962990.i 0.310751 + 0.538237i 0.978525 0.206127i $$-0.0660861\pi$$
−0.667774 + 0.744364i $$0.732753\pi$$
$$318$$ 0 0
$$319$$ −208746. + 361558.i −0.114853 + 0.198930i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −2.15443e6 −1.14902
$$324$$ 0 0
$$325$$ 5.75885e6 3.02432
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −329772. + 571182.i −0.167967 + 0.290927i
$$330$$ 0 0
$$331$$ 613290. + 1.06225e6i 0.307678 + 0.532913i 0.977854 0.209289i $$-0.0671149\pi$$
−0.670176 + 0.742202i $$0.733782\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −400799. 694203.i −0.195126 0.337967i
$$336$$ 0 0
$$337$$ −1.15064e6 + 1.99297e6i −0.551907 + 0.955930i 0.446230 + 0.894918i $$0.352766\pi$$
−0.998137 + 0.0610122i $$0.980567\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −1.04748e6 −0.487818
$$342$$ 0 0
$$343$$ −2.36679e6 −1.08624
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 809651. 1.40236e6i 0.360973 0.625223i −0.627149 0.778900i $$-0.715778\pi$$
0.988121 + 0.153677i $$0.0491115\pi$$
$$348$$ 0 0
$$349$$ 139307. + 241287.i 0.0612223 + 0.106040i 0.895012 0.446042i $$-0.147167\pi$$
−0.833790 + 0.552082i $$0.813833\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 1.68496e6 + 2.91844e6i 0.719704 + 1.24656i 0.961117 + 0.276142i $$0.0890559\pi$$
−0.241413 + 0.970422i $$0.577611\pi$$
$$354$$ 0 0
$$355$$ −197743. + 342501.i −0.0832781 + 0.144242i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −272571. −0.111621 −0.0558103 0.998441i $$-0.517774\pi$$
−0.0558103 + 0.998441i $$0.517774\pi$$
$$360$$ 0 0
$$361$$ −409156. −0.165242
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 3.20586e6 5.55271e6i 1.25954 2.18159i
$$366$$ 0 0
$$367$$ 1.97882e6 + 3.42743e6i 0.766906 + 1.32832i 0.939233 + 0.343281i $$0.111538\pi$$
−0.172327 + 0.985040i $$0.555129\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 499950. + 865939.i 0.188578 + 0.326627i
$$372$$ 0 0
$$373$$ 961939. 1.66613e6i 0.357994 0.620063i −0.629632 0.776894i $$-0.716794\pi$$
0.987626 + 0.156830i $$0.0501276\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 1.76489e6 0.639534
$$378$$ 0 0
$$379$$ −3.11015e6 −1.11220 −0.556101 0.831115i $$-0.687703\pi$$
−0.556101 + 0.831115i $$0.687703\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −1.41711e6 + 2.45450e6i −0.493634 + 0.855000i −0.999973 0.00733479i $$-0.997665\pi$$
0.506339 + 0.862335i $$0.330999\pi$$
$$384$$ 0 0
$$385$$ 844193. + 1.46218e6i 0.290262 + 0.502748i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −1.02692e6 1.77867e6i −0.344081 0.595966i 0.641105 0.767453i $$-0.278476\pi$$
−0.985186 + 0.171487i $$0.945143\pi$$
$$390$$ 0 0
$$391$$ 947157. 1.64052e6i 0.313314 0.542676i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 7.03716e6 2.26937
$$396$$ 0 0
$$397$$ −3.82167e6 −1.21696 −0.608480 0.793569i $$-0.708220\pi$$
−0.608480 + 0.793569i $$0.708220\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 2.65864e6 4.60491e6i 0.825656 1.43008i −0.0757604 0.997126i $$-0.524138\pi$$
0.901417 0.432953i $$-0.142528\pi$$
$$402$$ 0 0
$$403$$ 2.21403e6 + 3.83482e6i 0.679081 + 1.17620i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 597543. + 1.03498e6i 0.178807 + 0.309702i
$$408$$ 0 0
$$409$$ −1.57922e6 + 2.73528e6i −0.466803 + 0.808526i −0.999281 0.0379179i $$-0.987927\pi$$
0.532478 + 0.846444i $$0.321261\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −4.79095e6 −1.38212
$$414$$ 0 0
$$415$$ 9.14620e6 2.60688
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −1.80782e6 + 3.13124e6i −0.503060 + 0.871326i 0.496933 + 0.867789i $$0.334459\pi$$
−0.999994 + 0.00353739i $$0.998874\pi$$
$$420$$ 0 0
$$421$$ −514445. 891044.i −0.141460 0.245016i 0.786587 0.617480i $$-0.211846\pi$$
−0.928047 + 0.372464i $$0.878513\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 6.79064e6 + 1.17617e7i 1.82364 + 3.15863i
$$426$$ 0 0
$$427$$ −424166. + 734677.i −0.112581 + 0.194996i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −6.21668e6 −1.61200 −0.806001 0.591914i $$-0.798372\pi$$
−0.806001 + 0.591914i $$0.798372\pi$$
$$432$$ 0 0
$$433$$ −598070. −0.153297 −0.0766483 0.997058i $$-0.524422\pi$$
−0.0766483 + 0.997058i $$0.524422\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −908694. + 1.57390e6i −0.227622 + 0.394253i
$$438$$ 0 0
$$439$$ 246548. + 427034.i 0.0610577 + 0.105755i 0.894938 0.446190i $$-0.147219\pi$$
−0.833881 + 0.551945i $$0.813886\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −97755.8 169318.i −0.0236665 0.0409915i 0.853950 0.520356i $$-0.174201\pi$$
−0.877616 + 0.479364i $$0.840867\pi$$
$$444$$ 0 0
$$445$$ 213154. 369194.i 0.0510263 0.0883801i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 1.51225e6 0.354004 0.177002 0.984210i $$-0.443360\pi$$
0.177002 + 0.984210i $$0.443360\pi$$
$$450$$ 0 0
$$451$$ 304763. 0.0705538
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 3.56871e6 6.18119e6i 0.808133 1.39973i
$$456$$ 0 0
$$457$$ −1.28236e6 2.22111e6i −0.287223 0.497484i 0.685923 0.727674i $$-0.259399\pi$$
−0.973146 + 0.230190i $$0.926065\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −2.68336e6 4.64772e6i −0.588067 1.01856i −0.994485 0.104875i $$-0.966556\pi$$
0.406418 0.913687i $$-0.366778\pi$$
$$462$$ 0 0
$$463$$ −2.75107e6 + 4.76500e6i −0.596417 + 1.03302i 0.396928 + 0.917850i $$0.370076\pi$$
−0.993345 + 0.115175i $$0.963257\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −964114. −0.204567 −0.102284 0.994755i $$-0.532615\pi$$
−0.102284 + 0.994755i $$0.532615\pi$$
$$468$$ 0 0
$$469$$ −738757. −0.155085
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 941202. 1.63021e6i 0.193433 0.335035i
$$474$$ 0 0
$$475$$ −6.51488e6 1.12841e7i −1.32487 2.29474i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −281267. 487168.i −0.0560118 0.0970153i 0.836660 0.547723i $$-0.184505\pi$$
−0.892672 + 0.450707i $$0.851172\pi$$
$$480$$ 0 0
$$481$$ 2.52603e6 4.37522e6i 0.497825 0.862258i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −7.64815e6 −1.47639
$$486$$ 0 0
$$487$$ 3.14185e6 0.600292 0.300146 0.953893i $$-0.402965\pi$$
0.300146 + 0.953893i $$0.402965\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 2.86681e6 4.96545e6i 0.536654 0.929512i −0.462427 0.886657i $$-0.653021\pi$$
0.999081 0.0428549i $$-0.0136453\pi$$
$$492$$ 0 0
$$493$$ 2.08110e6 + 3.60457e6i 0.385634 + 0.667937i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 182241. + 315651.i 0.0330945 + 0.0573214i
$$498$$ 0 0
$$499$$ −857810. + 1.48577e6i −0.154220 + 0.267116i −0.932775 0.360460i $$-0.882620\pi$$
0.778555 + 0.627576i $$0.215953\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 5.15229e6 0.907989 0.453995 0.891004i $$-0.349999\pi$$
0.453995 + 0.891004i $$0.349999\pi$$
$$504$$ 0 0
$$505$$ −2.80919e6 −0.490176
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −521280. + 902884.i −0.0891819 + 0.154468i −0.907166 0.420774i $$-0.861759\pi$$
0.817984 + 0.575242i $$0.195092\pi$$
$$510$$ 0 0
$$511$$ −2.95454e6 5.11742e6i −0.500539 0.866959i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −3.49898e6 6.06041e6i −0.581331 1.00690i
$$516$$ 0 0
$$517$$ −487187. + 843833.i −0.0801621 + 0.138845i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −9.52239e6 −1.53692 −0.768461 0.639897i $$-0.778977\pi$$
−0.768461 + 0.639897i $$0.778977\pi$$
$$522$$ 0 0
$$523$$ −2.97573e6 −0.475706 −0.237853 0.971301i $$-0.576444\pi$$
−0.237853 + 0.971301i $$0.576444\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −5.22143e6 + 9.04378e6i −0.818960 + 1.41848i
$$528$$ 0 0
$$529$$ 2.41919e6 + 4.19016e6i 0.375864 + 0.651016i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −644172. 1.11574e6i −0.0982163 0.170116i
$$534$$ 0 0
$$535$$ 3.37595e6 5.84731e6i 0.509931 0.883226i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −970266. −0.143853
$$540$$ 0 0
$$541$$ 1.80579e6 0.265261 0.132631 0.991166i $$-0.457658\pi$$
0.132631 + 0.991166i $$0.457658\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −6.84674e6 + 1.18589e7i −0.987399 + 1.71023i
$$546$$ 0 0
$$547$$ 4.68486e6 + 8.11442e6i 0.669466 + 1.15955i 0.978054 + 0.208353i $$0.0668104\pi$$
−0.308587 + 0.951196i $$0.599856\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −1.99658e6 3.45819e6i −0.280162 0.485254i
$$552$$ 0 0
$$553$$ 3.24275e6 5.61660e6i 0.450921 0.781018i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −3.53733e6 −0.483101 −0.241550 0.970388i $$-0.577656\pi$$
−0.241550 + 0.970388i $$0.577656\pi$$
$$558$$ 0 0
$$559$$ −7.95761e6 −1.07709
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 1.39030e6 2.40807e6i 0.184858 0.320183i −0.758671 0.651474i $$-0.774151\pi$$
0.943529 + 0.331291i $$0.107484\pi$$
$$564$$ 0 0
$$565$$ −6.48248e6 1.12280e7i −0.854319 1.47972i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 3.67647e6 + 6.36782e6i 0.476047 + 0.824537i 0.999623 0.0274412i $$-0.00873590\pi$$
−0.523576 + 0.851979i $$0.675403\pi$$
$$570$$ 0 0
$$571$$ 2.87585e6 4.98112e6i 0.369128 0.639348i −0.620302 0.784363i $$-0.712990\pi$$
0.989429 + 0.145016i $$0.0463232\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1.14566e7 1.44506
$$576$$ 0 0
$$577$$ −1.30488e7 −1.63167 −0.815835 0.578285i $$-0.803722\pi$$
−0.815835 + 0.578285i $$0.803722\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 4.21460e6 7.29990e6i 0.517983 0.897173i
$$582$$ 0 0
$$583$$ 738598. + 1.27929e6i 0.0899989 + 0.155883i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 623618. + 1.08014e6i 0.0747005 + 0.129385i 0.900956 0.433910i $$-0.142867\pi$$
−0.826255 + 0.563296i $$0.809533\pi$$
$$588$$ 0 0
$$589$$ 5.00939e6 8.67652e6i 0.594972 1.03052i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 1.32769e7 1.55045 0.775226 0.631684i $$-0.217636\pi$$
0.775226 + 0.631684i $$0.217636\pi$$
$$594$$ 0 0
$$595$$ 1.68324e7 1.94919
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 2.02457e6 3.50666e6i 0.230551 0.399325i −0.727420 0.686193i $$-0.759281\pi$$
0.957970 + 0.286868i $$0.0926140\pi$$
$$600$$ 0 0
$$601$$ 3.41857e6 + 5.92113e6i 0.386063 + 0.668681i 0.991916 0.126896i $$-0.0405014\pi$$
−0.605853 + 0.795577i $$0.707168\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −7.64279e6 1.32377e7i −0.848914 1.47036i
$$606$$ 0 0
$$607$$ −348100. + 602927.i −0.0383471 + 0.0664191i −0.884562 0.466423i $$-0.845543\pi$$
0.846215 + 0.532842i $$0.178876\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 4.11904e6 0.446367
$$612$$ 0 0
$$613$$ −1.42785e6 −0.153473 −0.0767363 0.997051i $$-0.524450\pi$$
−0.0767363 + 0.997051i $$0.524450\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −7.51675e6 + 1.30194e7i −0.794908 + 1.37682i 0.127989 + 0.991776i $$0.459148\pi$$
−0.922897 + 0.385046i $$0.874186\pi$$
$$618$$ 0 0
$$619$$ 3.58151e6 + 6.20336e6i 0.375699 + 0.650730i 0.990431 0.138006i $$-0.0440693\pi$$
−0.614732 + 0.788736i $$0.710736\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −196444. 340251.i −0.0202777 0.0351221i
$$624$$ 0 0
$$625$$ −2.20252e7 + 3.81488e7i −2.25538 + 3.90644i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 1.19145e7 1.20074
$$630$$ 0 0
$$631$$ 1.38021e7 1.37998 0.689989 0.723820i $$-0.257615\pi$$
0.689989 + 0.723820i $$0.257615\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −1.64708e6 + 2.85283e6i −0.162099 + 0.280764i
$$636$$ 0 0
$$637$$ 2.05084e6 + 3.55215e6i 0.200254 + 0.346851i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −2.02329e6 3.50445e6i −0.194497 0.336879i 0.752238 0.658891i $$-0.228974\pi$$
−0.946736 + 0.322012i $$0.895641\pi$$
$$642$$ 0 0
$$643$$ −5.44381e6 + 9.42896e6i −0.519249 + 0.899366i 0.480501 + 0.876994i $$0.340455\pi$$
−0.999750 + 0.0223713i $$0.992878\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 8.45797e6 0.794339 0.397169 0.917745i $$-0.369993\pi$$
0.397169 + 0.917745i $$0.369993\pi$$
$$648$$ 0 0
$$649$$ −7.07788e6 −0.659617
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 2.47774e6 4.29157e6i 0.227391 0.393853i −0.729643 0.683828i $$-0.760314\pi$$
0.957034 + 0.289975i $$0.0936472\pi$$
$$654$$ 0 0
$$655$$ 9.49752e6 + 1.64502e7i 0.864982 + 1.49819i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 8.37152e6 + 1.44999e7i 0.750915 + 1.30062i 0.947380 + 0.320113i $$0.103721\pi$$
−0.196464 + 0.980511i $$0.562946\pi$$
$$660$$ 0 0
$$661$$ 7.53992e6 1.30595e7i 0.671217 1.16258i −0.306342 0.951922i $$-0.599105\pi$$
0.977559 0.210661i $$-0.0675617\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ −1.61489e7 −1.41608
$$666$$ 0 0
$$667$$ 3.51105e6 0.305578
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −626639. + 1.08537e6i −0.0537293 + 0.0930619i
$$672$$ 0 0
$$673$$ −7.07096e6 1.22473e7i −0.601784 1.04232i −0.992551 0.121831i $$-0.961123\pi$$
0.390767 0.920490i $$-0.372210\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 7.29397e6 + 1.26335e7i 0.611635 + 1.05938i 0.990965 + 0.134122i $$0.0428213\pi$$
−0.379330 + 0.925262i $$0.623845\pi$$
$$678$$ 0 0
$$679$$ −3.52429e6 + 6.10425e6i −0.293358 + 0.508110i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 1.10096e7 0.903065 0.451532 0.892255i $$-0.350878\pi$$
0.451532 + 0.892255i $$0.350878\pi$$
$$684$$ 0 0
$$685$$ 2.10158e7 1.71127
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 3.12233e6 5.40803e6i 0.250571 0.434001i
$$690$$ 0 0
$$691$$ −5.51793e6 9.55733e6i −0.439623 0.761450i 0.558037 0.829816i $$-0.311555\pi$$
−0.997660 + 0.0683661i $$0.978221\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −1.86058e7 3.22261e7i −1.46112 2.53073i
$$696$$ 0 0
$$697$$ 1.51917e6 2.63128e6i 0.118447 0.205157i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 2.51294e7 1.93146 0.965732 0.259542i $$-0.0835717\pi$$
0.965732 + 0.259542i $$0.0835717\pi$$
$$702$$ 0 0
$$703$$ −1.14306e7 −0.872332
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −1.29448e6 + 2.24211e6i −0.0973974 + 0.168697i
$$708$$ 0 0
$$709$$ −6.26506e6 1.08514e7i −0.468068 0.810718i 0.531266 0.847205i $$-0.321717\pi$$
−0.999334 + 0.0364869i $$0.988383\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 4.40457e6 + 7.62894e6i 0.324474 + 0.562006i
$$714$$ 0 0
$$715$$ 5.27222e6 9.13175e6i 0.385681 0.668019i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 1.72246e6 0.124258 0.0621292 0.998068i $$-0.480211\pi$$
0.0621292 + 0.998068i $$0.480211\pi$$
$$720$$ 0 0
$$721$$ −6.44937e6 −0.462040
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −1.25862e7 + 2.18000e7i −0.889304 + 1.54032i
$$726$$ 0 0
$$727$$ −3.49425e6 6.05221e6i −0.245198 0.424696i 0.716989 0.697084i $$-0.245520\pi$$
−0.962187 + 0.272389i $$0.912186\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −9.38335e6 1.62524e7i −0.649478 1.12493i
$$732$$ 0 0
$$733$$ 2.96305e6 5.13214e6i 0.203694 0.352808i −0.746022 0.665922i $$-0.768039\pi$$
0.949716 + 0.313113i $$0.101372\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −1.09140e6 −0.0740142
$$738$$ 0 0
$$739$$ −1.06632e7 −0.718254 −0.359127 0.933289i $$-0.616925\pi$$
−0.359127 + 0.933289i $$0.616925\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −9.24932e6 + 1.60203e7i −0.614664 + 1.06463i 0.375779 + 0.926709i $$0.377375\pi$$
−0.990443 + 0.137920i $$0.955958\pi$$
$$744$$ 0 0
$$745$$ 3.04143e6 + 5.26791e6i 0.200765 + 0.347734i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −3.11130e6 5.38892e6i −0.202645 0.350992i
$$750$$ 0 0
$$751$$ 1.30624e7 2.26247e7i 0.845127 1.46380i −0.0403845 0.999184i $$-0.512858\pi$$
0.885511 0.464618i $$-0.153808\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −3.68804e7 −2.35466
$$756$$ 0 0
$$757$$ 2.49174e7 1.58039 0.790193 0.612858i $$-0.209980\pi$$
0.790193 + 0.612858i $$0.209980\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 5.62194e6 9.73748e6i 0.351904 0.609516i −0.634679 0.772776i $$-0.718868\pi$$
0.986583 + 0.163260i $$0.0522010\pi$$
$$762$$ 0 0
$$763$$ 6.31000e6 + 1.09292e7i 0.392390 + 0.679640i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 1.49604e7 + 2.59122e7i 0.918237 + 1.59043i
$$768$$ 0 0
$$769$$ −4.33731e6 + 7.51244e6i −0.264487 + 0.458105i −0.967429 0.253142i $$-0.918536\pi$$
0.702942 + 0.711247i $$0.251869\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −2.17066e7 −1.30660 −0.653300 0.757099i $$-0.726616\pi$$
−0.653300 + 0.757099i $$0.726616\pi$$
$$774$$ 0 0
$$775$$ −6.31571e7 −3.77718
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −1.45748e6 + 2.52443e6i −0.0860516 + 0.149046i
$$780$$ 0 0
$$781$$ 269233. + 466326.i 0.0157943 + 0.0273566i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −6.62985e6 1.14832e7i −0.383998 0.665105i
$$786$$ 0 0
$$787$$ −3.93215e6 + 6.81068e6i −0.226304 + 0.391971i −0.956710 0.291043i $$-0.905998\pi$$
0.730406 + 0.683014i $$0.239331\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −1.19486e7 −0.679009
$$792$$ 0 0
$$793$$ 5.29807e6 0.299181
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 9.48089e6 1.64214e7i 0.528693 0.915723i −0.470747 0.882268i $$-0.656016\pi$$
0.999440 0.0334547i $$-0.0106509\pi$$
$$798$$ 0 0
$$799$$ 4.85703e6 + 8.41262e6i 0.269156 + 0.466192i
$$800$$ 0 0
$$801$$ 0 0