# Properties

 Label 40.6.c.a.9.4 Level $40$ Weight $6$ Character 40.9 Analytic conductor $6.415$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$40 = 2^{3} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 40.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.41535279252$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ Defining polynomial: $$x^{8} + 41 x^{6} + 460 x^{4} + 969 x^{2} + 9$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{31}\cdot 5^{3}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 9.4 Root $$3.98753i$$ of defining polynomial Character $$\chi$$ $$=$$ 40.9 Dual form 40.6.c.a.9.5

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-4.69449i q^{3} +(23.4238 + 50.7575i) q^{5} +10.2635i q^{7} +220.962 q^{9} +O(q^{10})$$ $$q-4.69449i q^{3} +(23.4238 + 50.7575i) q^{5} +10.2635i q^{7} +220.962 q^{9} +596.423 q^{11} +420.629i q^{13} +(238.281 - 109.963i) q^{15} +974.149i q^{17} +380.528 q^{19} +48.1817 q^{21} -3543.51i q^{23} +(-2027.65 + 2377.87i) q^{25} -2178.06i q^{27} -5440.89 q^{29} -3623.54 q^{31} -2799.90i q^{33} +(-520.948 + 240.409i) q^{35} +1756.01i q^{37} +1974.64 q^{39} +263.984 q^{41} -14410.5i q^{43} +(5175.76 + 11215.5i) q^{45} +23464.8i q^{47} +16701.7 q^{49} +4573.13 q^{51} -33496.0i q^{53} +(13970.5 + 30273.0i) q^{55} -1786.38i q^{57} +2906.38 q^{59} +29431.9 q^{61} +2267.83i q^{63} +(-21350.1 + 9852.72i) q^{65} +7163.34i q^{67} -16635.0 q^{69} -81353.2 q^{71} -55127.9i q^{73} +(11162.9 + 9518.80i) q^{75} +6121.36i q^{77} -16430.9 q^{79} +43468.8 q^{81} -116869. i q^{83} +(-49445.4 + 22818.2i) q^{85} +25542.2i q^{87} -99364.0 q^{89} -4317.11 q^{91} +17010.7i q^{93} +(8913.39 + 19314.6i) q^{95} +62987.8i q^{97} +131787. q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 8q^{5} - 1000q^{9} + O(q^{10})$$ $$8q + 8q^{5} - 1000q^{9} - 736q^{11} - 992q^{15} + 1376q^{19} + 1984q^{21} - 2136q^{25} + 5872q^{29} + 4224q^{31} + 19232q^{35} - 3008q^{39} + 23600q^{41} - 28328q^{45} - 45000q^{49} - 124800q^{51} + 15008q^{55} + 91680q^{59} + 123856q^{61} - 72064q^{65} - 76736q^{69} - 125632q^{71} + 222784q^{75} + 43264q^{79} + 409672q^{81} - 293760q^{85} - 41904q^{89} - 487616q^{91} + 442592q^{95} + 266848q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$$.

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

## 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
$$3$$ 4.69449i 0.301152i −0.988598 0.150576i $$-0.951887\pi$$
0.988598 0.150576i $$-0.0481128\pi$$
$$4$$ 0 0
$$5$$ 23.4238 + 50.7575i 0.419017 + 0.907978i
$$6$$ 0 0
$$7$$ 10.2635i 0.0791678i 0.999216 + 0.0395839i $$0.0126032\pi$$
−0.999216 + 0.0395839i $$0.987397\pi$$
$$8$$ 0 0
$$9$$ 220.962 0.909308
$$10$$ 0 0
$$11$$ 596.423 1.48618 0.743092 0.669189i $$-0.233358\pi$$
0.743092 + 0.669189i $$0.233358\pi$$
$$12$$ 0 0
$$13$$ 420.629i 0.690305i 0.938547 + 0.345152i $$0.112173\pi$$
−0.938547 + 0.345152i $$0.887827\pi$$
$$14$$ 0 0
$$15$$ 238.281 109.963i 0.273439 0.126188i
$$16$$ 0 0
$$17$$ 974.149i 0.817529i 0.912640 + 0.408764i $$0.134040\pi$$
−0.912640 + 0.408764i $$0.865960\pi$$
$$18$$ 0 0
$$19$$ 380.528 0.241825 0.120913 0.992663i $$-0.461418\pi$$
0.120913 + 0.992663i $$0.461418\pi$$
$$20$$ 0 0
$$21$$ 48.1817 0.0238415
$$22$$ 0 0
$$23$$ 3543.51i 1.39673i −0.715740 0.698367i $$-0.753910\pi$$
0.715740 0.698367i $$-0.246090\pi$$
$$24$$ 0 0
$$25$$ −2027.65 + 2377.87i −0.648849 + 0.760917i
$$26$$ 0 0
$$27$$ 2178.06i 0.574991i
$$28$$ 0 0
$$29$$ −5440.89 −1.20136 −0.600682 0.799488i $$-0.705104\pi$$
−0.600682 + 0.799488i $$0.705104\pi$$
$$30$$ 0 0
$$31$$ −3623.54 −0.677219 −0.338609 0.940927i $$-0.609957\pi$$
−0.338609 + 0.940927i $$0.609957\pi$$
$$32$$ 0 0
$$33$$ 2799.90i 0.447567i
$$34$$ 0 0
$$35$$ −520.948 + 240.409i −0.0718827 + 0.0331727i
$$36$$ 0 0
$$37$$ 1756.01i 0.210874i 0.994426 + 0.105437i $$0.0336241\pi$$
−0.994426 + 0.105437i $$0.966376\pi$$
$$38$$ 0 0
$$39$$ 1974.64 0.207886
$$40$$ 0 0
$$41$$ 263.984 0.0245255 0.0122628 0.999925i $$-0.496097\pi$$
0.0122628 + 0.999925i $$0.496097\pi$$
$$42$$ 0 0
$$43$$ 14410.5i 1.18853i −0.804271 0.594263i $$-0.797444\pi$$
0.804271 0.594263i $$-0.202556\pi$$
$$44$$ 0 0
$$45$$ 5175.76 + 11215.5i 0.381015 + 0.825632i
$$46$$ 0 0
$$47$$ 23464.8i 1.54943i 0.632308 + 0.774717i $$0.282108\pi$$
−0.632308 + 0.774717i $$0.717892\pi$$
$$48$$ 0 0
$$49$$ 16701.7 0.993732
$$50$$ 0 0
$$51$$ 4573.13 0.246200
$$52$$ 0 0
$$53$$ 33496.0i 1.63796i −0.573823 0.818979i $$-0.694540\pi$$
0.573823 0.818979i $$-0.305460\pi$$
$$54$$ 0 0
$$55$$ 13970.5 + 30273.0i 0.622737 + 1.34942i
$$56$$ 0 0
$$57$$ 1786.38i 0.0728261i
$$58$$ 0 0
$$59$$ 2906.38 0.108698 0.0543492 0.998522i $$-0.482692\pi$$
0.0543492 + 0.998522i $$0.482692\pi$$
$$60$$ 0 0
$$61$$ 29431.9 1.01273 0.506366 0.862319i $$-0.330989\pi$$
0.506366 + 0.862319i $$0.330989\pi$$
$$62$$ 0 0
$$63$$ 2267.83i 0.0719879i
$$64$$ 0 0
$$65$$ −21350.1 + 9852.72i −0.626782 + 0.289250i
$$66$$ 0 0
$$67$$ 7163.34i 0.194952i 0.995238 + 0.0974762i $$0.0310770\pi$$
−0.995238 + 0.0974762i $$0.968923\pi$$
$$68$$ 0 0
$$69$$ −16635.0 −0.420629
$$70$$ 0 0
$$71$$ −81353.2 −1.91527 −0.957633 0.287992i $$-0.907012\pi$$
−0.957633 + 0.287992i $$0.907012\pi$$
$$72$$ 0 0
$$73$$ 55127.9i 1.21078i −0.795930 0.605388i $$-0.793018\pi$$
0.795930 0.605388i $$-0.206982\pi$$
$$74$$ 0 0
$$75$$ 11162.9 + 9518.80i 0.229151 + 0.195402i
$$76$$ 0 0
$$77$$ 6121.36i 0.117658i
$$78$$ 0 0
$$79$$ −16430.9 −0.296205 −0.148103 0.988972i $$-0.547317\pi$$
−0.148103 + 0.988972i $$0.547317\pi$$
$$80$$ 0 0
$$81$$ 43468.8 0.736148
$$82$$ 0 0
$$83$$ 116869.i 1.86210i −0.364891 0.931050i $$-0.618894\pi$$
0.364891 0.931050i $$-0.381106\pi$$
$$84$$ 0 0
$$85$$ −49445.4 + 22818.2i −0.742299 + 0.342559i
$$86$$ 0 0
$$87$$ 25542.2i 0.361793i
$$88$$ 0 0
$$89$$ −99364.0 −1.32970 −0.664851 0.746976i $$-0.731505\pi$$
−0.664851 + 0.746976i $$0.731505\pi$$
$$90$$ 0 0
$$91$$ −4317.11 −0.0546499
$$92$$ 0 0
$$93$$ 17010.7i 0.203946i
$$94$$ 0 0
$$95$$ 8913.39 + 19314.6i 0.101329 + 0.219572i
$$96$$ 0 0
$$97$$ 62987.8i 0.679715i 0.940477 + 0.339858i $$0.110379\pi$$
−0.940477 + 0.339858i $$0.889621\pi$$
$$98$$ 0 0
$$99$$ 131787. 1.35140
$$100$$ 0 0
$$101$$ 40702.1 0.397021 0.198510 0.980099i $$-0.436390\pi$$
0.198510 + 0.980099i $$0.436390\pi$$
$$102$$ 0 0
$$103$$ 108113.i 1.00412i 0.864834 + 0.502058i $$0.167424\pi$$
−0.864834 + 0.502058i $$0.832576\pi$$
$$104$$ 0 0
$$105$$ 1128.60 + 2445.58i 0.00999000 + 0.0216476i
$$106$$ 0 0
$$107$$ 198380.i 1.67509i −0.546367 0.837546i $$-0.683990\pi$$
0.546367 0.837546i $$-0.316010\pi$$
$$108$$ 0 0
$$109$$ 89150.3 0.718715 0.359357 0.933200i $$-0.382996\pi$$
0.359357 + 0.933200i $$0.382996\pi$$
$$110$$ 0 0
$$111$$ 8243.56 0.0635049
$$112$$ 0 0
$$113$$ 165319.i 1.21795i 0.793191 + 0.608973i $$0.208418\pi$$
−0.793191 + 0.608973i $$0.791582\pi$$
$$114$$ 0 0
$$115$$ 179860. 83002.3i 1.26820 0.585255i
$$116$$ 0 0
$$117$$ 92943.0i 0.627700i
$$118$$ 0 0
$$119$$ −9998.14 −0.0647220
$$120$$ 0 0
$$121$$ 194669. 1.20874
$$122$$ 0 0
$$123$$ 1239.27i 0.00738591i
$$124$$ 0 0
$$125$$ −168190. 47220.2i −0.962775 0.270304i
$$126$$ 0 0
$$127$$ 137238.i 0.755031i 0.926003 + 0.377516i $$0.123222\pi$$
−0.926003 + 0.377516i $$0.876778\pi$$
$$128$$ 0 0
$$129$$ −67650.1 −0.357927
$$130$$ 0 0
$$131$$ −355564. −1.81026 −0.905128 0.425140i $$-0.860225\pi$$
−0.905128 + 0.425140i $$0.860225\pi$$
$$132$$ 0 0
$$133$$ 3905.53i 0.0191448i
$$134$$ 0 0
$$135$$ 110553. 51018.4i 0.522080 0.240931i
$$136$$ 0 0
$$137$$ 232937.i 1.06032i −0.847898 0.530160i $$-0.822132\pi$$
0.847898 0.530160i $$-0.177868\pi$$
$$138$$ 0 0
$$139$$ 62526.2 0.274489 0.137245 0.990537i $$-0.456175\pi$$
0.137245 + 0.990537i $$0.456175\pi$$
$$140$$ 0 0
$$141$$ 110155. 0.466614
$$142$$ 0 0
$$143$$ 250873.i 1.02592i
$$144$$ 0 0
$$145$$ −127446. 276166.i −0.503392 1.09081i
$$146$$ 0 0
$$147$$ 78405.8i 0.299264i
$$148$$ 0 0
$$149$$ −267151. −0.985804 −0.492902 0.870085i $$-0.664064\pi$$
−0.492902 + 0.870085i $$0.664064\pi$$
$$150$$ 0 0
$$151$$ −329630. −1.17648 −0.588240 0.808686i $$-0.700179\pi$$
−0.588240 + 0.808686i $$0.700179\pi$$
$$152$$ 0 0
$$153$$ 215250.i 0.743385i
$$154$$ 0 0
$$155$$ −84877.0 183922.i −0.283766 0.614900i
$$156$$ 0 0
$$157$$ 400955.i 1.29822i −0.760696 0.649108i $$-0.775142\pi$$
0.760696 0.649108i $$-0.224858\pi$$
$$158$$ 0 0
$$159$$ −157246. −0.493274
$$160$$ 0 0
$$161$$ 36368.6 0.110576
$$162$$ 0 0
$$163$$ 511411.i 1.50765i 0.657074 + 0.753826i $$0.271794\pi$$
−0.657074 + 0.753826i $$0.728206\pi$$
$$164$$ 0 0
$$165$$ 142116. 65584.2i 0.406381 0.187538i
$$166$$ 0 0
$$167$$ 63650.1i 0.176607i −0.996094 0.0883035i $$-0.971855\pi$$
0.996094 0.0883035i $$-0.0281445\pi$$
$$168$$ 0 0
$$169$$ 194364. 0.523479
$$170$$ 0 0
$$171$$ 84082.0 0.219894
$$172$$ 0 0
$$173$$ 33351.0i 0.0847214i 0.999102 + 0.0423607i $$0.0134879\pi$$
−0.999102 + 0.0423607i $$0.986512\pi$$
$$174$$ 0 0
$$175$$ −24405.1 20810.7i −0.0602401 0.0513680i
$$176$$ 0 0
$$177$$ 13644.0i 0.0327347i
$$178$$ 0 0
$$179$$ 314739. 0.734207 0.367103 0.930180i $$-0.380350\pi$$
0.367103 + 0.930180i $$0.380350\pi$$
$$180$$ 0 0
$$181$$ 415818. 0.943425 0.471712 0.881753i $$-0.343636\pi$$
0.471712 + 0.881753i $$0.343636\pi$$
$$182$$ 0 0
$$183$$ 138168.i 0.304986i
$$184$$ 0 0
$$185$$ −89130.7 + 41132.3i −0.191469 + 0.0883596i
$$186$$ 0 0
$$187$$ 581005.i 1.21500i
$$188$$ 0 0
$$189$$ 22354.5 0.0455208
$$190$$ 0 0
$$191$$ 494250. 0.980310 0.490155 0.871635i $$-0.336940\pi$$
0.490155 + 0.871635i $$0.336940\pi$$
$$192$$ 0 0
$$193$$ 62426.1i 0.120635i 0.998179 + 0.0603175i $$0.0192113\pi$$
−0.998179 + 0.0603175i $$0.980789\pi$$
$$194$$ 0 0
$$195$$ 46253.5 + 100228.i 0.0871080 + 0.188756i
$$196$$ 0 0
$$197$$ 513844.i 0.943334i 0.881777 + 0.471667i $$0.156348\pi$$
−0.881777 + 0.471667i $$0.843652\pi$$
$$198$$ 0 0
$$199$$ 29132.1 0.0521481 0.0260741 0.999660i $$-0.491699\pi$$
0.0260741 + 0.999660i $$0.491699\pi$$
$$200$$ 0 0
$$201$$ 33628.2 0.0587102
$$202$$ 0 0
$$203$$ 55842.3i 0.0951094i
$$204$$ 0 0
$$205$$ 6183.51 + 13399.2i 0.0102766 + 0.0222687i
$$206$$ 0 0
$$207$$ 782980.i 1.27006i
$$208$$ 0 0
$$209$$ 226955. 0.359397
$$210$$ 0 0
$$211$$ −330044. −0.510347 −0.255173 0.966895i $$-0.582133\pi$$
−0.255173 + 0.966895i $$0.582133\pi$$
$$212$$ 0 0
$$213$$ 381912.i 0.576785i
$$214$$ 0 0
$$215$$ 731443. 337549.i 1.07916 0.498013i
$$216$$ 0 0
$$217$$ 37190.1i 0.0536139i
$$218$$ 0 0
$$219$$ −258797. −0.364627
$$220$$ 0 0
$$221$$ −409756. −0.564344
$$222$$ 0 0
$$223$$ 930113.i 1.25249i −0.779627 0.626244i $$-0.784591\pi$$
0.779627 0.626244i $$-0.215409\pi$$
$$224$$ 0 0
$$225$$ −448034. + 525417.i −0.590004 + 0.691908i
$$226$$ 0 0
$$227$$ 37009.2i 0.0476699i −0.999716 0.0238350i $$-0.992412\pi$$
0.999716 0.0238350i $$-0.00758762\pi$$
$$228$$ 0 0
$$229$$ −506969. −0.638841 −0.319421 0.947613i $$-0.603488\pi$$
−0.319421 + 0.947613i $$0.603488\pi$$
$$230$$ 0 0
$$231$$ 28736.7 0.0354329
$$232$$ 0 0
$$233$$ 378560.i 0.456819i −0.973565 0.228410i $$-0.926647\pi$$
0.973565 0.228410i $$-0.0733526\pi$$
$$234$$ 0 0
$$235$$ −1.19102e6 + 549635.i −1.40685 + 0.649239i
$$236$$ 0 0
$$237$$ 77134.5i 0.0892026i
$$238$$ 0 0
$$239$$ −105854. −0.119870 −0.0599351 0.998202i $$-0.519089\pi$$
−0.0599351 + 0.998202i $$0.519089\pi$$
$$240$$ 0 0
$$241$$ −1.14897e6 −1.27429 −0.637144 0.770745i $$-0.719884\pi$$
−0.637144 + 0.770745i $$0.719884\pi$$
$$242$$ 0 0
$$243$$ 733333.i 0.796683i
$$244$$ 0 0
$$245$$ 391216. + 847735.i 0.416391 + 0.902288i
$$246$$ 0 0
$$247$$ 160061.i 0.166933i
$$248$$ 0 0
$$249$$ −548639. −0.560775
$$250$$ 0 0
$$251$$ 655956. 0.657189 0.328595 0.944471i $$-0.393425\pi$$
0.328595 + 0.944471i $$0.393425\pi$$
$$252$$ 0 0
$$253$$ 2.11343e6i 2.07580i
$$254$$ 0 0
$$255$$ 107120. + 232121.i 0.103162 + 0.223544i
$$256$$ 0 0
$$257$$ 986720.i 0.931883i 0.884816 + 0.465941i $$0.154284\pi$$
−0.884816 + 0.465941i $$0.845716\pi$$
$$258$$ 0 0
$$259$$ −18022.7 −0.0166944
$$260$$ 0 0
$$261$$ −1.20223e6 −1.09241
$$262$$ 0 0
$$263$$ 865331.i 0.771424i −0.922619 0.385712i $$-0.873956\pi$$
0.922619 0.385712i $$-0.126044\pi$$
$$264$$ 0 0
$$265$$ 1.70017e6 784602.i 1.48723 0.686333i
$$266$$ 0 0
$$267$$ 466463.i 0.400442i
$$268$$ 0 0
$$269$$ 1.75595e6 1.47956 0.739780 0.672849i $$-0.234930\pi$$
0.739780 + 0.672849i $$0.234930\pi$$
$$270$$ 0 0
$$271$$ 1.07635e6 0.890287 0.445143 0.895459i $$-0.353153\pi$$
0.445143 + 0.895459i $$0.353153\pi$$
$$272$$ 0 0
$$273$$ 20266.6i 0.0164579i
$$274$$ 0 0
$$275$$ −1.20934e6 + 1.41821e6i −0.964310 + 1.13086i
$$276$$ 0 0
$$277$$ 620129.i 0.485605i 0.970076 + 0.242802i $$0.0780666\pi$$
−0.970076 + 0.242802i $$0.921933\pi$$
$$278$$ 0 0
$$279$$ −800664. −0.615800
$$280$$ 0 0
$$281$$ 884924. 0.668560 0.334280 0.942474i $$-0.391507\pi$$
0.334280 + 0.942474i $$0.391507\pi$$
$$282$$ 0 0
$$283$$ 1.06088e6i 0.787408i 0.919237 + 0.393704i $$0.128806\pi$$
−0.919237 + 0.393704i $$0.871194\pi$$
$$284$$ 0 0
$$285$$ 90672.4 41843.8i 0.0661246 0.0305154i
$$286$$ 0 0
$$287$$ 2709.39i 0.00194163i
$$288$$ 0 0
$$289$$ 470891. 0.331646
$$290$$ 0 0
$$291$$ 295696. 0.204697
$$292$$ 0 0
$$293$$ 585847.i 0.398672i 0.979931 + 0.199336i $$0.0638784\pi$$
−0.979931 + 0.199336i $$0.936122\pi$$
$$294$$ 0 0
$$295$$ 68078.5 + 147521.i 0.0455465 + 0.0986958i
$$296$$ 0 0
$$297$$ 1.29905e6i 0.854543i
$$298$$ 0 0
$$299$$ 1.49050e6 0.964172
$$300$$ 0 0
$$301$$ 147902. 0.0940931
$$302$$ 0 0
$$303$$ 191076.i 0.119563i
$$304$$ 0 0
$$305$$ 689407. + 1.49389e6i 0.424352 + 0.919539i
$$306$$ 0 0
$$307$$ 2.33467e6i 1.41377i 0.707328 + 0.706886i $$0.249901\pi$$
−0.707328 + 0.706886i $$0.750099\pi$$
$$308$$ 0 0
$$309$$ 507534. 0.302391
$$310$$ 0 0
$$311$$ 2.18712e6 1.28225 0.641123 0.767438i $$-0.278469\pi$$
0.641123 + 0.767438i $$0.278469\pi$$
$$312$$ 0 0
$$313$$ 2.76800e6i 1.59700i −0.601993 0.798501i $$-0.705626\pi$$
0.601993 0.798501i $$-0.294374\pi$$
$$314$$ 0 0
$$315$$ −115110. + 53121.2i −0.0653635 + 0.0301642i
$$316$$ 0 0
$$317$$ 1.71952e6i 0.961077i −0.876974 0.480538i $$-0.840441\pi$$
0.876974 0.480538i $$-0.159559\pi$$
$$318$$ 0 0
$$319$$ −3.24507e6 −1.78545
$$320$$ 0 0
$$321$$ −931293. −0.504457
$$322$$ 0 0
$$323$$ 370691.i 0.197699i
$$324$$ 0 0
$$325$$ −1.00020e6 852891.i −0.525265 0.447904i
$$326$$ 0 0
$$327$$ 418515.i 0.216442i
$$328$$ 0 0
$$329$$ −240830. −0.122665
$$330$$ 0 0
$$331$$ −1.24759e6 −0.625895 −0.312948 0.949770i $$-0.601316\pi$$
−0.312948 + 0.949770i $$0.601316\pi$$
$$332$$ 0 0
$$333$$ 388011.i 0.191749i
$$334$$ 0 0
$$335$$ −363593. + 167792.i −0.177013 + 0.0816884i
$$336$$ 0 0
$$337$$ 1.96509e6i 0.942556i 0.881985 + 0.471278i $$0.156207\pi$$
−0.881985 + 0.471278i $$0.843793\pi$$
$$338$$ 0 0
$$339$$ 776090. 0.366786
$$340$$ 0 0
$$341$$ −2.16116e6 −1.00647
$$342$$ 0 0
$$343$$ 343915.i 0.157839i
$$344$$ 0 0
$$345$$ −389653. 844349.i −0.176251 0.381922i
$$346$$ 0 0
$$347$$ 3.27623e6i 1.46067i −0.683091 0.730333i $$-0.739365\pi$$
0.683091 0.730333i $$-0.260635\pi$$
$$348$$ 0 0
$$349$$ −101966. −0.0448117 −0.0224058 0.999749i $$-0.507133\pi$$
−0.0224058 + 0.999749i $$0.507133\pi$$
$$350$$ 0 0
$$351$$ 916157. 0.396919
$$352$$ 0 0
$$353$$ 3.03342e6i 1.29567i 0.761779 + 0.647837i $$0.224326\pi$$
−0.761779 + 0.647837i $$0.775674\pi$$
$$354$$ 0 0
$$355$$ −1.90560e6 4.12929e6i −0.802529 1.73902i
$$356$$ 0 0
$$357$$ 46936.2i 0.0194911i
$$358$$ 0 0
$$359$$ −2.68388e6 −1.09908 −0.549538 0.835469i $$-0.685196\pi$$
−0.549538 + 0.835469i $$0.685196\pi$$
$$360$$ 0 0
$$361$$ −2.33130e6 −0.941520
$$362$$ 0 0
$$363$$ 913874.i 0.364015i
$$364$$ 0 0
$$365$$ 2.79815e6 1.29130e6i 1.09936 0.507336i
$$366$$ 0 0
$$367$$ 1.17487e6i 0.455329i 0.973740 + 0.227664i $$0.0731089\pi$$
−0.973740 + 0.227664i $$0.926891\pi$$
$$368$$ 0 0
$$369$$ 58330.5 0.0223013
$$370$$ 0 0
$$371$$ 343784. 0.129674
$$372$$ 0 0
$$373$$ 4.13661e6i 1.53947i 0.638361 + 0.769737i $$0.279613\pi$$
−0.638361 + 0.769737i $$0.720387\pi$$
$$374$$ 0 0
$$375$$ −221675. + 789566.i −0.0814025 + 0.289941i
$$376$$ 0 0
$$377$$ 2.28860e6i 0.829308i
$$378$$ 0 0
$$379$$ 4.02996e6 1.44113 0.720565 0.693387i $$-0.243883\pi$$
0.720565 + 0.693387i $$0.243883\pi$$
$$380$$ 0 0
$$381$$ 644262. 0.227379
$$382$$ 0 0
$$383$$ 3.29187e6i 1.14669i 0.819314 + 0.573345i $$0.194355\pi$$
−0.819314 + 0.573345i $$0.805645\pi$$
$$384$$ 0 0
$$385$$ −310705. + 143385.i −0.106831 + 0.0493007i
$$386$$ 0 0
$$387$$ 3.18418e6i 1.08074i
$$388$$ 0 0
$$389$$ −3.23387e6 −1.08355 −0.541774 0.840524i $$-0.682247\pi$$
−0.541774 + 0.840524i $$0.682247\pi$$
$$390$$ 0 0
$$391$$ 3.45190e6 1.14187
$$392$$ 0 0
$$393$$ 1.66919e6i 0.545161i
$$394$$ 0 0
$$395$$ −384872. 833990.i −0.124115 0.268948i
$$396$$ 0 0
$$397$$ 1.50766e6i 0.480095i 0.970761 + 0.240047i $$0.0771630\pi$$
−0.970761 + 0.240047i $$0.922837\pi$$
$$398$$ 0 0
$$399$$ 18334.5 0.00576549
$$400$$ 0 0
$$401$$ −132613. −0.0411837 −0.0205918 0.999788i $$-0.506555\pi$$
−0.0205918 + 0.999788i $$0.506555\pi$$
$$402$$ 0 0
$$403$$ 1.52417e6i 0.467487i
$$404$$ 0 0
$$405$$ 1.01820e6 + 2.20637e6i 0.308459 + 0.668407i
$$406$$ 0 0
$$407$$ 1.04732e6i 0.313397i
$$408$$ 0 0
$$409$$ 4.30354e6 1.27209 0.636044 0.771653i $$-0.280570\pi$$
0.636044 + 0.771653i $$0.280570\pi$$
$$410$$ 0 0
$$411$$ −1.09352e6 −0.319317
$$412$$ 0 0
$$413$$ 29829.6i 0.00860541i
$$414$$ 0 0
$$415$$ 5.93197e6 2.73751e6i 1.69075 0.780252i
$$416$$ 0 0
$$417$$ 293529.i 0.0826628i
$$418$$ 0 0
$$419$$ 5.35654e6 1.49056 0.745280 0.666752i $$-0.232316\pi$$
0.745280 + 0.666752i $$0.232316\pi$$
$$420$$ 0 0
$$421$$ 2.95420e6 0.812335 0.406167 0.913799i $$-0.366865\pi$$
0.406167 + 0.913799i $$0.366865\pi$$
$$422$$ 0 0
$$423$$ 5.18483e6i 1.40891i
$$424$$ 0 0
$$425$$ −2.31640e6 1.97524e6i −0.622071 0.530453i
$$426$$ 0 0
$$427$$ 302074.i 0.0801758i
$$428$$ 0 0
$$429$$ 1.17772e6 0.308958
$$430$$ 0 0
$$431$$ −5.93581e6 −1.53917 −0.769586 0.638543i $$-0.779537\pi$$
−0.769586 + 0.638543i $$0.779537\pi$$
$$432$$ 0 0
$$433$$ 2.72633e6i 0.698810i 0.936972 + 0.349405i $$0.113616\pi$$
−0.936972 + 0.349405i $$0.886384\pi$$
$$434$$ 0 0
$$435$$ −1.29646e6 + 598294.i −0.328500 + 0.151597i
$$436$$ 0 0
$$437$$ 1.34840e6i 0.337766i
$$438$$ 0 0
$$439$$ −6.39220e6 −1.58303 −0.791515 0.611150i $$-0.790707\pi$$
−0.791515 + 0.611150i $$0.790707\pi$$
$$440$$ 0 0
$$441$$ 3.69043e6 0.903609
$$442$$ 0 0
$$443$$ 990808.i 0.239872i 0.992782 + 0.119936i $$0.0382690\pi$$
−0.992782 + 0.119936i $$0.961731\pi$$
$$444$$ 0 0
$$445$$ −2.32748e6 5.04347e6i −0.557168 1.20734i
$$446$$ 0 0
$$447$$ 1.25414e6i 0.296877i
$$448$$ 0 0
$$449$$ −4.79185e6 −1.12173 −0.560864 0.827908i $$-0.689531\pi$$
−0.560864 + 0.827908i $$0.689531\pi$$
$$450$$ 0 0
$$451$$ 157446. 0.0364495
$$452$$ 0 0
$$453$$ 1.54745e6i 0.354299i
$$454$$ 0 0
$$455$$ −101123. 219126.i −0.0228993 0.0496210i
$$456$$ 0 0
$$457$$ 1.50517e6i 0.337128i 0.985691 + 0.168564i $$0.0539130\pi$$
−0.985691 + 0.168564i $$0.946087\pi$$
$$458$$ 0 0
$$459$$ 2.12176e6 0.470072
$$460$$ 0 0
$$461$$ 1.28168e6 0.280883 0.140442 0.990089i $$-0.455148\pi$$
0.140442 + 0.990089i $$0.455148\pi$$
$$462$$ 0 0
$$463$$ 700105.i 0.151779i −0.997116 0.0758893i $$-0.975820\pi$$
0.997116 0.0758893i $$-0.0241796\pi$$
$$464$$ 0 0
$$465$$ −863420. + 398454.i −0.185178 + 0.0854567i
$$466$$ 0 0
$$467$$ 1.89776e6i 0.402669i −0.979523 0.201334i $$-0.935472\pi$$
0.979523 0.201334i $$-0.0645278\pi$$
$$468$$ 0 0
$$469$$ −73520.6 −0.0154340
$$470$$ 0 0
$$471$$ −1.88228e6 −0.390960
$$472$$ 0 0
$$473$$ 8.59478e6i 1.76637i
$$474$$ 0 0
$$475$$ −771578. + 904843.i −0.156908 + 0.184009i
$$476$$ 0 0
$$477$$ 7.40133e6i 1.48941i
$$478$$ 0 0
$$479$$ −6.88878e6 −1.37184 −0.685920 0.727677i $$-0.740600\pi$$
−0.685920 + 0.727677i $$0.740600\pi$$
$$480$$ 0 0
$$481$$ −738628. −0.145567
$$482$$ 0 0
$$483$$ 170732.i 0.0333003i
$$484$$ 0 0
$$485$$ −3.19710e6 + 1.47541e6i −0.617167 + 0.284812i
$$486$$ 0 0
$$487$$ 3.31559e6i 0.633488i 0.948511 + 0.316744i $$0.102590\pi$$
−0.948511 + 0.316744i $$0.897410\pi$$
$$488$$ 0 0
$$489$$ 2.40081e6 0.454032
$$490$$ 0 0
$$491$$ −6.55075e6 −1.22627 −0.613137 0.789977i $$-0.710092\pi$$
−0.613137 + 0.789977i $$0.710092\pi$$
$$492$$ 0 0
$$493$$ 5.30024e6i 0.982150i
$$494$$ 0 0
$$495$$ 3.08694e6 + 6.68917e6i 0.566259 + 1.22704i
$$496$$ 0 0
$$497$$ 834966.i 0.151627i
$$498$$ 0 0
$$499$$ 4.14654e6 0.745477 0.372738 0.927936i $$-0.378419\pi$$
0.372738 + 0.927936i $$0.378419\pi$$
$$500$$ 0 0
$$501$$ −298805. −0.0531855
$$502$$ 0 0
$$503$$ 386446.i 0.0681035i −0.999420 0.0340517i $$-0.989159\pi$$
0.999420 0.0340517i $$-0.0108411\pi$$
$$504$$ 0 0
$$505$$ 953396. + 2.06594e6i 0.166358 + 0.360486i
$$506$$ 0 0
$$507$$ 912440.i 0.157647i
$$508$$ 0 0
$$509$$ −3.04725e6 −0.521331 −0.260665 0.965429i $$-0.583942\pi$$
−0.260665 + 0.965429i $$0.583942\pi$$
$$510$$ 0 0
$$511$$ 565802. 0.0958545
$$512$$ 0 0
$$513$$ 828813.i 0.139048i
$$514$$ 0 0
$$515$$ −5.48753e6 + 2.53241e6i −0.911715 + 0.420742i
$$516$$ 0 0
$$517$$ 1.39950e7i 2.30274i
$$518$$ 0 0
$$519$$ 156566. 0.0255140
$$520$$ 0 0
$$521$$ 8.88552e6 1.43413 0.717065 0.697007i $$-0.245485\pi$$
0.717065 + 0.697007i $$0.245485\pi$$
$$522$$ 0 0
$$523$$ 4.92458e6i 0.787254i −0.919270 0.393627i $$-0.871220\pi$$
0.919270 0.393627i $$-0.128780\pi$$
$$524$$ 0 0
$$525$$ −97695.8 + 114570.i −0.0154696 + 0.0181414i
$$526$$ 0 0
$$527$$ 3.52987e6i 0.553646i
$$528$$ 0 0
$$529$$ −6.12010e6 −0.950866
$$530$$ 0 0
$$531$$ 642200. 0.0988403
$$532$$ 0 0
$$533$$ 111040.i 0.0169301i
$$534$$ 0 0
$$535$$ 1.00693e7 4.64681e6i 1.52095 0.701892i
$$536$$ 0 0
$$537$$ 1.47754e6i 0.221108i
$$538$$ 0 0
$$539$$ 9.96126e6 1.47687
$$540$$ 0 0
$$541$$ 5.45948e6 0.801970 0.400985 0.916085i $$-0.368668\pi$$
0.400985 + 0.916085i $$0.368668\pi$$
$$542$$ 0 0
$$543$$ 1.95205e6i 0.284114i
$$544$$ 0 0
$$545$$ 2.08824e6 + 4.52505e6i 0.301154 + 0.652577i
$$546$$ 0 0
$$547$$ 9.70824e6i 1.38731i 0.720309 + 0.693653i $$0.244000\pi$$
−0.720309 + 0.693653i $$0.756000\pi$$
$$548$$ 0 0
$$549$$ 6.50334e6 0.920885
$$550$$ 0 0
$$551$$ −2.07041e6 −0.290521
$$552$$ 0 0
$$553$$ 168637.i 0.0234499i
$$554$$ 0 0
$$555$$ 193095. + 418423.i 0.0266097 + 0.0576611i
$$556$$ 0 0
$$557$$ 4.77260e6i 0.651804i −0.945404 0.325902i $$-0.894332\pi$$
0.945404 0.325902i $$-0.105668\pi$$
$$558$$ 0 0
$$559$$ 6.06149e6 0.820446
$$560$$ 0 0
$$561$$ 2.72752e6 0.365899
$$562$$ 0 0
$$563$$ 2.16768e6i 0.288220i −0.989562 0.144110i $$-0.953968\pi$$
0.989562 0.144110i $$-0.0460319\pi$$
$$564$$ 0 0
$$565$$ −8.39121e6 + 3.87240e6i −1.10587 + 0.510340i
$$566$$ 0 0
$$567$$ 446140.i 0.0582792i
$$568$$ 0 0
$$569$$ −4.17864e6 −0.541070 −0.270535 0.962710i $$-0.587201\pi$$
−0.270535 + 0.962710i $$0.587201\pi$$
$$570$$ 0 0
$$571$$ −7.89574e6 −1.01345 −0.506725 0.862108i $$-0.669144\pi$$
−0.506725 + 0.862108i $$0.669144\pi$$
$$572$$ 0 0
$$573$$ 2.32025e6i 0.295222i
$$574$$ 0 0
$$575$$ 8.42598e6 + 7.18501e6i 1.06280 + 0.906270i
$$576$$ 0 0
$$577$$ 1.34605e7i 1.68315i 0.540141 + 0.841575i $$0.318371\pi$$
−0.540141 + 0.841575i $$0.681629\pi$$
$$578$$ 0 0
$$579$$ 293059. 0.0363294
$$580$$ 0 0
$$581$$ 1.19948e6 0.147418
$$582$$ 0 0
$$583$$ 1.99778e7i 2.43431i
$$584$$ 0 0
$$585$$ −4.71756e6 + 2.17707e6i −0.569938 + 0.263017i
$$586$$ 0 0
$$587$$ 1.43350e6i 0.171713i −0.996308 0.0858564i $$-0.972637\pi$$
0.996308 0.0858564i $$-0.0273626\pi$$
$$588$$ 0 0
$$589$$ −1.37886e6 −0.163769
$$590$$ 0 0
$$591$$ 2.41223e6 0.284087
$$592$$ 0 0
$$593$$ 1.38150e6i 0.161330i 0.996741 + 0.0806649i $$0.0257044\pi$$
−0.996741 + 0.0806649i $$0.974296\pi$$
$$594$$ 0 0
$$595$$ −234194. 507481.i −0.0271196 0.0587661i
$$596$$ 0 0
$$597$$ 136760.i 0.0157045i
$$598$$ 0 0
$$599$$ −6.53001e6 −0.743612 −0.371806 0.928310i $$-0.621261\pi$$
−0.371806 + 0.928310i $$0.621261\pi$$
$$600$$ 0 0
$$601$$ −3.81467e6 −0.430795 −0.215398 0.976526i $$-0.569105\pi$$
−0.215398 + 0.976526i $$0.569105\pi$$
$$602$$ 0 0
$$603$$ 1.58282e6i 0.177272i
$$604$$ 0 0
$$605$$ 4.55989e6 + 9.88094e6i 0.506484 + 1.09751i
$$606$$ 0 0
$$607$$ 1.06018e7i 1.16791i −0.811787 0.583954i $$-0.801505\pi$$
0.811787 0.583954i $$-0.198495\pi$$
$$608$$ 0 0
$$609$$ −262151. −0.0286424
$$610$$ 0 0
$$611$$ −9.87000e6 −1.06958
$$612$$ 0 0
$$613$$ 5.80630e6i 0.624091i −0.950067 0.312046i $$-0.898986\pi$$
0.950067 0.312046i $$-0.101014\pi$$
$$614$$ 0 0
$$615$$ 62902.4 29028.4i 0.00670624 0.00309482i
$$616$$ 0 0
$$617$$ 6.80508e6i 0.719648i −0.933020 0.359824i $$-0.882837\pi$$
0.933020 0.359824i $$-0.117163\pi$$
$$618$$ 0 0
$$619$$ −852530. −0.0894299 −0.0447150 0.999000i $$-0.514238\pi$$
−0.0447150 + 0.999000i $$0.514238\pi$$
$$620$$ 0 0
$$621$$ −7.71798e6 −0.803110
$$622$$ 0 0
$$623$$ 1.01982e6i 0.105270i
$$624$$ 0 0
$$625$$ −1.54286e6 9.64298e6i −0.157989 0.987441i
$$626$$ 0 0
$$627$$ 1.06544e6i 0.108233i
$$628$$ 0 0
$$629$$ −1.71061e6 −0.172395
$$630$$ 0 0
$$631$$ 8.01341e6 0.801205 0.400603 0.916252i $$-0.368801\pi$$
0.400603 + 0.916252i $$0.368801\pi$$
$$632$$ 0 0
$$633$$ 1.54939e6i 0.153692i
$$634$$ 0 0
$$635$$ −6.96586e6 + 3.21463e6i −0.685552 + 0.316371i
$$636$$ 0 0
$$637$$ 7.02521e6i 0.685978i
$$638$$ 0 0
$$639$$ −1.79760e7 −1.74157
$$640$$ 0 0
$$641$$ −3.68737e6 −0.354464 −0.177232 0.984169i $$-0.556714\pi$$
−0.177232 + 0.984169i $$0.556714\pi$$
$$642$$ 0 0
$$643$$ 9.97031e6i 0.951001i 0.879715 + 0.475501i $$0.157733\pi$$
−0.879715 + 0.475501i $$0.842267\pi$$
$$644$$ 0 0
$$645$$ −1.58462e6 3.43375e6i −0.149977 0.324990i
$$646$$ 0 0
$$647$$ 1.73097e6i 0.162566i 0.996691 + 0.0812830i $$0.0259018\pi$$
−0.996691 + 0.0812830i $$0.974098\pi$$
$$648$$ 0 0
$$649$$ 1.73343e6 0.161546
$$650$$ 0 0
$$651$$ −174588. −0.0161459
$$652$$ 0 0
$$653$$ 1.15248e6i 0.105767i 0.998601 + 0.0528836i $$0.0168412\pi$$
−0.998601 + 0.0528836i $$0.983159\pi$$
$$654$$ 0 0
$$655$$ −8.32865e6 1.80476e7i −0.758528 1.64367i
$$656$$ 0 0
$$657$$ 1.21811e7i 1.10097i
$$658$$ 0 0
$$659$$ 1.53161e7 1.37384 0.686919 0.726734i $$-0.258963\pi$$
0.686919 + 0.726734i $$0.258963\pi$$
$$660$$ 0 0
$$661$$ 1.69450e6 0.150848 0.0754238 0.997152i $$-0.475969\pi$$
0.0754238 + 0.997152i $$0.475969\pi$$
$$662$$ 0 0
$$663$$ 1.92359e6i 0.169953i
$$664$$ 0 0
$$665$$ −198235. + 91482.2i −0.0173831 + 0.00802199i
$$666$$ 0 0
$$667$$ 1.92798e7i 1.67799i
$$668$$ 0 0
$$669$$ −4.36641e6 −0.377189
$$670$$ 0 0
$$671$$ 1.75539e7 1.50511
$$672$$ 0 0
$$673$$ 1.53955e6i 0.131026i −0.997852 0.0655129i $$-0.979132\pi$$
0.997852 0.0655129i $$-0.0208683\pi$$
$$674$$ 0 0
$$675$$ 5.17914e6 + 4.41636e6i 0.437520 + 0.373083i
$$676$$ 0 0
$$677$$ 1.16833e7i 0.979702i −0.871806 0.489851i $$-0.837051\pi$$
0.871806 0.489851i $$-0.162949\pi$$
$$678$$ 0 0
$$679$$ −646473. −0.0538116
$$680$$ 0 0
$$681$$ −173739. −0.0143559
$$682$$ 0 0
$$683$$ 1.49762e7i 1.22843i 0.789139 + 0.614215i $$0.210527\pi$$
−0.789139 + 0.614215i $$0.789473\pi$$
$$684$$ 0 0
$$685$$ 1.18233e7 5.45626e6i 0.962747 0.444292i
$$686$$ 0 0
$$687$$ 2.37996e6i 0.192388i
$$688$$ 0 0
$$689$$ 1.40894e7 1.13069
$$690$$ 0 0
$$691$$ −9.90115e6 −0.788843 −0.394422 0.918930i $$-0.629055\pi$$
−0.394422 + 0.918930i $$0.629055\pi$$
$$692$$ 0 0
$$693$$ 1.35259e6i 0.106987i
$$694$$ 0 0
$$695$$ 1.46460e6 + 3.17368e6i 0.115016 + 0.249230i
$$696$$ 0 0
$$697$$ 257160.i 0.0200503i
$$698$$ 0 0
$$699$$ −1.77714e6 −0.137572
$$700$$ 0 0
$$701$$ 1.48933e7 1.14471 0.572357 0.820005i $$-0.306029\pi$$
0.572357 + 0.820005i $$0.306029\pi$$
$$702$$ 0 0
$$703$$ 668209.i 0.0509946i
$$704$$ 0 0
$$705$$ 2.58026e6 + 5.59122e6i 0.195519 + 0.423676i
$$706$$ 0 0
$$707$$ 417744.i 0.0314313i
$$708$$ 0 0
$$709$$ −3.63694e6 −0.271719 −0.135860 0.990728i $$-0.543380\pi$$
−0.135860 + 0.990728i $$0.543380\pi$$
$$710$$ 0 0
$$711$$ −3.63059e6 −0.269342
$$712$$ 0 0
$$713$$ 1.28400e7i 0.945894i
$$714$$ 0 0
$$715$$ −1.27337e7 + 5.87639e6i −0.931514 + 0.429878i
$$716$$ 0 0
$$717$$ 496929.i 0.0360991i
$$718$$ 0 0
$$719$$ 1.17971e7 0.851044 0.425522 0.904948i $$-0.360091\pi$$
0.425522 + 0.904948i $$0.360091\pi$$
$$720$$ 0 0
$$721$$ −1.10961e6 −0.0794936
$$722$$ 0 0
$$723$$ 5.39384e6i 0.383754i
$$724$$ 0 0
$$725$$ 1.10322e7 1.29377e7i 0.779505 0.914139i
$$726$$ 0 0
$$727$$ 7.53381e6i 0.528663i −0.964432 0.264331i $$-0.914849\pi$$
0.964432 0.264331i $$-0.0851513\pi$$
$$728$$ 0 0
$$729$$ 7.12030e6 0.496226
$$730$$ 0 0
$$731$$ 1.40380e7 0.971655
$$732$$ 0 0
$$733$$ 1.36302e7i 0.937003i 0.883463 + 0.468501i $$0.155206\pi$$
−0.883463 + 0.468501i $$0.844794\pi$$
$$734$$ 0 0
$$735$$ 3.97968e6 1.83656e6i 0.271725 0.125397i
$$736$$ 0 0
$$737$$ 4.27238e6i 0.289735i
$$738$$ 0 0
$$739$$ −1.07655e7 −0.725141 −0.362571 0.931956i $$-0.618101\pi$$
−0.362571 + 0.931956i $$0.618101\pi$$
$$740$$ 0 0
$$741$$ 751405. 0.0502722
$$742$$ 0 0
$$743$$ 2.53921e7i 1.68743i 0.536788 + 0.843717i $$0.319637\pi$$
−0.536788 + 0.843717i $$0.680363\pi$$
$$744$$ 0 0
$$745$$ −6.25768e6 1.35599e7i −0.413069 0.895089i
$$746$$ 0 0
$$747$$ 2.58235e7i 1.69322i
$$748$$ 0 0
$$749$$ 2.03607e6 0.132613
$$750$$ 0 0
$$751$$ 8.06289e6 0.521664 0.260832 0.965384i $$-0.416003\pi$$
0.260832 + 0.965384i $$0.416003\pi$$
$$752$$ 0 0
$$753$$ 3.07938e6i 0.197914i
$$754$$ 0 0
$$755$$ −7.72118e6 1.67312e7i −0.492965 1.06822i
$$756$$ 0 0
$$757$$ 1.08891e7i 0.690639i −0.938485 0.345319i $$-0.887771\pi$$
0.938485 0.345319i $$-0.112229\pi$$
$$758$$ 0 0
$$759$$ −9.92147e6 −0.625132
$$760$$ 0 0
$$761$$ −1.07800e7 −0.674773 −0.337387 0.941366i $$-0.609543\pi$$
−0.337387 + 0.941366i $$0.609543\pi$$
$$762$$ 0 0
$$763$$ 914990.i 0.0568991i
$$764$$ 0 0
$$765$$ −1.09255e7 + 5.04196e6i −0.674978 + 0.311491i
$$766$$ 0 0
$$767$$ 1.22251e6i 0.0750350i
$$768$$ 0 0
$$769$$ 8.24398e6 0.502714 0.251357 0.967894i $$-0.419123\pi$$
0.251357 + 0.967894i $$0.419123\pi$$
$$770$$ 0 0
$$771$$ 4.63215e6 0.280638
$$772$$ 0 0
$$773$$ 3.76264e6i 0.226487i 0.993567 + 0.113244i $$0.0361240\pi$$
−0.993567 + 0.113244i $$0.963876\pi$$
$$774$$ 0 0
$$775$$ 7.34729e6 8.61629e6i 0.439413 0.515307i
$$776$$ 0 0
$$777$$ 84607.5i 0.00502755i
$$778$$ 0 0
$$779$$ 100453. 0.00593090
$$780$$ 0 0
$$781$$ −4.85209e7 −2.84644
$$782$$ 0 0
$$783$$ 1.18506e7i 0.690774i
$$784$$ 0 0
$$785$$ 2.03515e7 9.39189e6i 1.17875 0.543975i
$$786$$ 0 0
$$787$$ 1.14314e7i 0.657906i 0.944346 + 0.328953i $$0.106696\pi$$
−0.944346 + 0.328953i $$0.893304\pi$$
$$788$$ 0 0
$$789$$ −4.06229e6 −0.232315
$$790$$ 0 0
$$791$$ −1.69675e6 −0.0964221
$$792$$ 0 0
$$793$$ 1.23799e7i 0.699094i
$$794$$ 0 0
$$795$$ −3.68330e6 7.98144e6i −0.206690 0.447882i
$$796$$ 0 0
$$797$$ 1.82556e7i 1.01801i 0.860765 + 0.509003i $$0.169986\pi$$
−0.860765 + 0.509003i $$0.830014\pi$$
$$798$$ 0 0
$$799$$ −2.28583e7 −1.26671
$$800$$ 0 0
$$801$$ −2.19557e7 −1.20911
$$802$$ 0 0
$$803$$ 3.28795e7i