# Properties

 Label 320.6.f.c.289.13 Level 320 Weight 6 Character 320.289 Analytic conductor 51.323 Analytic rank 0 Dimension 16 CM no Inner twists 8

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$320 = 2^{6} \cdot 5$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 320.f (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$51.3228223402$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 39122 x^{12} + 391243971 x^{8} + 75462898750 x^{4} + 18538406640625$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{42}\cdot 5^{6}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 289.13 Root $$-11.8760 - 0.526271i$$ of defining polynomial Character $$\chi$$ $$=$$ 320.289 Dual form 320.6.f.c.289.14

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+24.8046 q^{3} +(-53.4447 - 16.3911i) q^{5} -100.281i q^{7} +372.267 q^{9} +O(q^{10})$$ $$q+24.8046 q^{3} +(-53.4447 - 16.3911i) q^{5} -100.281i q^{7} +372.267 q^{9} -5.36667i q^{11} -506.854 q^{13} +(-1325.67 - 406.573i) q^{15} -1454.37i q^{17} +722.433i q^{19} -2487.43i q^{21} +3086.22i q^{23} +(2587.67 + 1752.03i) q^{25} +3206.40 q^{27} -7298.39i q^{29} -8609.68 q^{31} -133.118i q^{33} +(-1643.72 + 5359.50i) q^{35} -5276.52 q^{37} -12572.3 q^{39} -18175.5 q^{41} -8340.95 q^{43} +(-19895.7 - 6101.84i) q^{45} -22120.2i q^{47} +6750.67 q^{49} -36075.1i q^{51} -13363.7 q^{53} +(-87.9654 + 286.820i) q^{55} +17919.6i q^{57} +10958.8i q^{59} +10982.0i q^{61} -37331.4i q^{63} +(27088.7 + 8307.88i) q^{65} -13007.5 q^{67} +76552.4i q^{69} +36009.0 q^{71} -64286.0i q^{73} +(64186.0 + 43458.3i) q^{75} -538.177 q^{77} +48638.8 q^{79} -10927.3 q^{81} -49784.4 q^{83} +(-23838.7 + 77728.6i) q^{85} -181033. i q^{87} +7764.40 q^{89} +50828.0i q^{91} -213559. q^{93} +(11841.4 - 38610.2i) q^{95} +36848.8i q^{97} -1997.83i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q + 1904q^{9} + O(q^{10})$$ $$16q + 1904q^{9} + 880q^{25} - 100352q^{41} + 128272q^{49} + 149760q^{65} - 154576q^{81} - 459296q^{89} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$257$$ $$261$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## 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
$$3$$ 24.8046 1.59121 0.795607 0.605813i $$-0.207152\pi$$
0.795607 + 0.605813i $$0.207152\pi$$
$$4$$ 0 0
$$5$$ −53.4447 16.3911i −0.956047 0.293212i
$$6$$ 0 0
$$7$$ 100.281i 0.773526i −0.922179 0.386763i $$-0.873593\pi$$
0.922179 0.386763i $$-0.126407\pi$$
$$8$$ 0 0
$$9$$ 372.267 1.53196
$$10$$ 0 0
$$11$$ 5.36667i 0.0133728i −0.999978 0.00668641i $$-0.997872\pi$$
0.999978 0.00668641i $$-0.00212837\pi$$
$$12$$ 0 0
$$13$$ −506.854 −0.831811 −0.415906 0.909408i $$-0.636535\pi$$
−0.415906 + 0.909408i $$0.636535\pi$$
$$14$$ 0 0
$$15$$ −1325.67 406.573i −1.52128 0.466563i
$$16$$ 0 0
$$17$$ 1454.37i 1.22055i −0.792191 0.610273i $$-0.791060\pi$$
0.792191 0.610273i $$-0.208940\pi$$
$$18$$ 0 0
$$19$$ 722.433i 0.459107i 0.973296 + 0.229553i $$0.0737266\pi$$
−0.973296 + 0.229553i $$0.926273\pi$$
$$20$$ 0 0
$$21$$ 2487.43i 1.23084i
$$22$$ 0 0
$$23$$ 3086.22i 1.21649i 0.793750 + 0.608244i $$0.208126\pi$$
−0.793750 + 0.608244i $$0.791874\pi$$
$$24$$ 0 0
$$25$$ 2587.67 + 1752.03i 0.828053 + 0.560649i
$$26$$ 0 0
$$27$$ 3206.40 0.846465
$$28$$ 0 0
$$29$$ 7298.39i 1.61151i −0.592251 0.805753i $$-0.701761\pi$$
0.592251 0.805753i $$-0.298239\pi$$
$$30$$ 0 0
$$31$$ −8609.68 −1.60910 −0.804549 0.593886i $$-0.797593\pi$$
−0.804549 + 0.593886i $$0.797593\pi$$
$$32$$ 0 0
$$33$$ 133.118i 0.0212790i
$$34$$ 0 0
$$35$$ −1643.72 + 5359.50i −0.226807 + 0.739527i
$$36$$ 0 0
$$37$$ −5276.52 −0.633641 −0.316821 0.948485i $$-0.602615\pi$$
−0.316821 + 0.948485i $$0.602615\pi$$
$$38$$ 0 0
$$39$$ −12572.3 −1.32359
$$40$$ 0 0
$$41$$ −18175.5 −1.68860 −0.844301 0.535869i $$-0.819984\pi$$
−0.844301 + 0.535869i $$0.819984\pi$$
$$42$$ 0 0
$$43$$ −8340.95 −0.687930 −0.343965 0.938982i $$-0.611770\pi$$
−0.343965 + 0.938982i $$0.611770\pi$$
$$44$$ 0 0
$$45$$ −19895.7 6101.84i −1.46463 0.449190i
$$46$$ 0 0
$$47$$ 22120.2i 1.46064i −0.683103 0.730322i $$-0.739370\pi$$
0.683103 0.730322i $$-0.260630\pi$$
$$48$$ 0 0
$$49$$ 6750.67 0.401658
$$50$$ 0 0
$$51$$ 36075.1i 1.94215i
$$52$$ 0 0
$$53$$ −13363.7 −0.653489 −0.326745 0.945113i $$-0.605952\pi$$
−0.326745 + 0.945113i $$0.605952\pi$$
$$54$$ 0 0
$$55$$ −87.9654 + 286.820i −0.00392108 + 0.0127851i
$$56$$ 0 0
$$57$$ 17919.6i 0.730537i
$$58$$ 0 0
$$59$$ 10958.8i 0.409859i 0.978777 + 0.204929i $$0.0656965\pi$$
−0.978777 + 0.204929i $$0.934304\pi$$
$$60$$ 0 0
$$61$$ 10982.0i 0.377883i 0.981988 + 0.188941i $$0.0605056\pi$$
−0.981988 + 0.188941i $$0.939494\pi$$
$$62$$ 0 0
$$63$$ 37331.4i 1.18501i
$$64$$ 0 0
$$65$$ 27088.7 + 8307.88i 0.795251 + 0.243897i
$$66$$ 0 0
$$67$$ −13007.5 −0.354003 −0.177002 0.984211i $$-0.556640\pi$$
−0.177002 + 0.984211i $$0.556640\pi$$
$$68$$ 0 0
$$69$$ 76552.4i 1.93569i
$$70$$ 0 0
$$71$$ 36009.0 0.847744 0.423872 0.905722i $$-0.360671\pi$$
0.423872 + 0.905722i $$0.360671\pi$$
$$72$$ 0 0
$$73$$ 64286.0i 1.41192i −0.708253 0.705959i $$-0.750516\pi$$
0.708253 0.705959i $$-0.249484\pi$$
$$74$$ 0 0
$$75$$ 64186.0 + 43458.3i 1.31761 + 0.892113i
$$76$$ 0 0
$$77$$ −538.177 −0.0103442
$$78$$ 0 0
$$79$$ 48638.8 0.876830 0.438415 0.898773i $$-0.355540\pi$$
0.438415 + 0.898773i $$0.355540\pi$$
$$80$$ 0 0
$$81$$ −10927.3 −0.185055
$$82$$ 0 0
$$83$$ −49784.4 −0.793228 −0.396614 0.917985i $$-0.629815\pi$$
−0.396614 + 0.917985i $$0.629815\pi$$
$$84$$ 0 0
$$85$$ −23838.7 + 77728.6i −0.357879 + 1.16690i
$$86$$ 0 0
$$87$$ 181033.i 2.56425i
$$88$$ 0 0
$$89$$ 7764.40 0.103904 0.0519521 0.998650i $$-0.483456\pi$$
0.0519521 + 0.998650i $$0.483456\pi$$
$$90$$ 0 0
$$91$$ 50828.0i 0.643427i
$$92$$ 0 0
$$93$$ −213559. −2.56042
$$94$$ 0 0
$$95$$ 11841.4 38610.2i 0.134616 0.438928i
$$96$$ 0 0
$$97$$ 36848.8i 0.397644i 0.980036 + 0.198822i $$0.0637116\pi$$
−0.980036 + 0.198822i $$0.936288\pi$$
$$98$$ 0 0
$$99$$ 1997.83i 0.0204867i
$$100$$ 0 0
$$101$$ 174557.i 1.70268i 0.524611 + 0.851342i $$0.324211\pi$$
−0.524611 + 0.851342i $$0.675789\pi$$
$$102$$ 0 0
$$103$$ 172505.i 1.60217i −0.598551 0.801085i $$-0.704257\pi$$
0.598551 0.801085i $$-0.295743\pi$$
$$104$$ 0 0
$$105$$ −40771.7 + 132940.i −0.360899 + 1.17675i
$$106$$ 0 0
$$107$$ 155176. 1.31028 0.655140 0.755507i $$-0.272609\pi$$
0.655140 + 0.755507i $$0.272609\pi$$
$$108$$ 0 0
$$109$$ 111055.i 0.895306i −0.894207 0.447653i $$-0.852260\pi$$
0.894207 0.447653i $$-0.147740\pi$$
$$110$$ 0 0
$$111$$ −130882. −1.00826
$$112$$ 0 0
$$113$$ 199647.i 1.47084i −0.677609 0.735422i $$-0.736984\pi$$
0.677609 0.735422i $$-0.263016\pi$$
$$114$$ 0 0
$$115$$ 50586.4 164942.i 0.356689 1.16302i
$$116$$ 0 0
$$117$$ −188685. −1.27430
$$118$$ 0 0
$$119$$ −145847. −0.944123
$$120$$ 0 0
$$121$$ 161022. 0.999821
$$122$$ 0 0
$$123$$ −450836. −2.68693
$$124$$ 0 0
$$125$$ −109579. 136051.i −0.627269 0.778803i
$$126$$ 0 0
$$127$$ 93300.5i 0.513304i 0.966504 + 0.256652i $$0.0826194\pi$$
−0.966504 + 0.256652i $$0.917381\pi$$
$$128$$ 0 0
$$129$$ −206894. −1.09464
$$130$$ 0 0
$$131$$ 174939.i 0.890655i 0.895368 + 0.445328i $$0.146913\pi$$
−0.895368 + 0.445328i $$0.853087\pi$$
$$132$$ 0 0
$$133$$ 72446.5 0.355131
$$134$$ 0 0
$$135$$ −171365. 52556.3i −0.809260 0.248194i
$$136$$ 0 0
$$137$$ 127441.i 0.580106i 0.957011 + 0.290053i $$0.0936730\pi$$
−0.957011 + 0.290053i $$0.906327\pi$$
$$138$$ 0 0
$$139$$ 393660.i 1.72816i −0.503352 0.864082i $$-0.667900\pi$$
0.503352 0.864082i $$-0.332100\pi$$
$$140$$ 0 0
$$141$$ 548682.i 2.32420i
$$142$$ 0 0
$$143$$ 2720.12i 0.0111237i
$$144$$ 0 0
$$145$$ −119628. + 390060.i −0.472513 + 1.54068i
$$146$$ 0 0
$$147$$ 167447. 0.639124
$$148$$ 0 0
$$149$$ 167112.i 0.616656i 0.951280 + 0.308328i $$0.0997694\pi$$
−0.951280 + 0.308328i $$0.900231\pi$$
$$150$$ 0 0
$$151$$ −184305. −0.657803 −0.328901 0.944364i $$-0.606678\pi$$
−0.328901 + 0.944364i $$0.606678\pi$$
$$152$$ 0 0
$$153$$ 541415.i 1.86983i
$$154$$ 0 0
$$155$$ 460141. + 141122.i 1.53837 + 0.471807i
$$156$$ 0 0
$$157$$ −403676. −1.30702 −0.653512 0.756916i $$-0.726705\pi$$
−0.653512 + 0.756916i $$0.726705\pi$$
$$158$$ 0 0
$$159$$ −331482. −1.03984
$$160$$ 0 0
$$161$$ 309490. 0.940984
$$162$$ 0 0
$$163$$ −357436. −1.05373 −0.526864 0.849949i $$-0.676632\pi$$
−0.526864 + 0.849949i $$0.676632\pi$$
$$164$$ 0 0
$$165$$ −2181.94 + 7114.45i −0.00623927 + 0.0203438i
$$166$$ 0 0
$$167$$ 38221.8i 0.106052i −0.998593 0.0530262i $$-0.983113\pi$$
0.998593 0.0530262i $$-0.0168867\pi$$
$$168$$ 0 0
$$169$$ −114392. −0.308090
$$170$$ 0 0
$$171$$ 268938.i 0.703334i
$$172$$ 0 0
$$173$$ 134258. 0.341056 0.170528 0.985353i $$-0.445453\pi$$
0.170528 + 0.985353i $$0.445453\pi$$
$$174$$ 0 0
$$175$$ 175696. 259494.i 0.433677 0.640520i
$$176$$ 0 0
$$177$$ 271829.i 0.652173i
$$178$$ 0 0
$$179$$ 566014.i 1.32037i 0.751105 + 0.660183i $$0.229521\pi$$
−0.751105 + 0.660183i $$0.770479\pi$$
$$180$$ 0 0
$$181$$ 572156.i 1.29813i 0.760733 + 0.649065i $$0.224840\pi$$
−0.760733 + 0.649065i $$0.775160\pi$$
$$182$$ 0 0
$$183$$ 272404.i 0.601292i
$$184$$ 0 0
$$185$$ 282002. + 86487.8i 0.605791 + 0.185791i
$$186$$ 0 0
$$187$$ −7805.15 −0.0163221
$$188$$ 0 0
$$189$$ 321542.i 0.654762i
$$190$$ 0 0
$$191$$ 685564. 1.35977 0.679883 0.733320i $$-0.262030\pi$$
0.679883 + 0.733320i $$0.262030\pi$$
$$192$$ 0 0
$$193$$ 931503.i 1.80008i −0.435810 0.900039i $$-0.643538\pi$$
0.435810 0.900039i $$-0.356462\pi$$
$$194$$ 0 0
$$195$$ 671923. + 206073.i 1.26541 + 0.388093i
$$196$$ 0 0
$$197$$ 692118. 1.27062 0.635308 0.772259i $$-0.280873\pi$$
0.635308 + 0.772259i $$0.280873\pi$$
$$198$$ 0 0
$$199$$ 969167. 1.73487 0.867433 0.497554i $$-0.165768\pi$$
0.867433 + 0.497554i $$0.165768\pi$$
$$200$$ 0 0
$$201$$ −322646. −0.563295
$$202$$ 0 0
$$203$$ −731892. −1.24654
$$204$$ 0 0
$$205$$ 971385. + 297916.i 1.61438 + 0.495119i
$$206$$ 0 0
$$207$$ 1.14890e6i 1.86361i
$$208$$ 0 0
$$209$$ 3877.06 0.00613956
$$210$$ 0 0
$$211$$ 800177.i 1.23731i −0.785661 0.618657i $$-0.787677\pi$$
0.785661 0.618657i $$-0.212323\pi$$
$$212$$ 0 0
$$213$$ 893187. 1.34894
$$214$$ 0 0
$$215$$ 445779. + 136717.i 0.657694 + 0.201709i
$$216$$ 0 0
$$217$$ 863389.i 1.24468i
$$218$$ 0 0
$$219$$ 1.59459e6i 2.24666i
$$220$$ 0 0
$$221$$ 737156.i 1.01526i
$$222$$ 0 0
$$223$$ 619923.i 0.834787i 0.908726 + 0.417394i $$0.137056\pi$$
−0.908726 + 0.417394i $$0.862944\pi$$
$$224$$ 0 0
$$225$$ 963302. + 652222.i 1.26855 + 0.858893i
$$226$$ 0 0
$$227$$ 547541. 0.705264 0.352632 0.935762i $$-0.385287\pi$$
0.352632 + 0.935762i $$0.385287\pi$$
$$228$$ 0 0
$$229$$ 368527.i 0.464387i 0.972670 + 0.232194i $$0.0745903\pi$$
−0.972670 + 0.232194i $$0.925410\pi$$
$$230$$ 0 0
$$231$$ −13349.2 −0.0164599
$$232$$ 0 0
$$233$$ 347048.i 0.418794i −0.977831 0.209397i $$-0.932850\pi$$
0.977831 0.209397i $$-0.0671500\pi$$
$$234$$ 0 0
$$235$$ −362573. + 1.18221e6i −0.428278 + 1.39644i
$$236$$ 0 0
$$237$$ 1.20646e6 1.39522
$$238$$ 0 0
$$239$$ 1.17224e6 1.32746 0.663731 0.747971i $$-0.268972\pi$$
0.663731 + 0.747971i $$0.268972\pi$$
$$240$$ 0 0
$$241$$ −1.10163e6 −1.22178 −0.610889 0.791716i $$-0.709188\pi$$
−0.610889 + 0.791716i $$0.709188\pi$$
$$242$$ 0 0
$$243$$ −1.05020e6 −1.14093
$$244$$ 0 0
$$245$$ −360787. 110651.i −0.384004 0.117771i
$$246$$ 0 0
$$247$$ 366168.i 0.381890i
$$248$$ 0 0
$$249$$ −1.23488e6 −1.26220
$$250$$ 0 0
$$251$$ 97443.4i 0.0976265i −0.998808 0.0488133i $$-0.984456\pi$$
0.998808 0.0488133i $$-0.0155439\pi$$
$$252$$ 0 0
$$253$$ 16562.7 0.0162679
$$254$$ 0 0
$$255$$ −591310. + 1.92802e6i −0.569462 + 1.85679i
$$256$$ 0 0
$$257$$ 1.35298e6i 1.27779i −0.769296 0.638893i $$-0.779393\pi$$
0.769296 0.638893i $$-0.220607\pi$$
$$258$$ 0 0
$$259$$ 529136.i 0.490138i
$$260$$ 0 0
$$261$$ 2.71695e6i 2.46877i
$$262$$ 0 0
$$263$$ 892943.i 0.796039i −0.917377 0.398019i $$-0.869698\pi$$
0.917377 0.398019i $$-0.130302\pi$$
$$264$$ 0 0
$$265$$ 714221. + 219046.i 0.624766 + 0.191611i
$$266$$ 0 0
$$267$$ 192593. 0.165334
$$268$$ 0 0
$$269$$ 395573.i 0.333308i 0.986015 + 0.166654i $$0.0532963\pi$$
−0.986015 + 0.166654i $$0.946704\pi$$
$$270$$ 0 0
$$271$$ 548411. 0.453610 0.226805 0.973940i $$-0.427172\pi$$
0.226805 + 0.973940i $$0.427172\pi$$
$$272$$ 0 0
$$273$$ 1.26077e6i 1.02383i
$$274$$ 0 0
$$275$$ 9402.56 13887.2i 0.00749747 0.0110734i
$$276$$ 0 0
$$277$$ 84078.7 0.0658395 0.0329198 0.999458i $$-0.489519\pi$$
0.0329198 + 0.999458i $$0.489519\pi$$
$$278$$ 0 0
$$279$$ −3.20509e6 −2.46508
$$280$$ 0 0
$$281$$ 869957. 0.657252 0.328626 0.944460i $$-0.393414\pi$$
0.328626 + 0.944460i $$0.393414\pi$$
$$282$$ 0 0
$$283$$ 1.80499e6 1.33970 0.669852 0.742495i $$-0.266358\pi$$
0.669852 + 0.742495i $$0.266358\pi$$
$$284$$ 0 0
$$285$$ 293722. 957710.i 0.214202 0.698428i
$$286$$ 0 0
$$287$$ 1.82267e6i 1.30618i
$$288$$ 0 0
$$289$$ −695348. −0.489731
$$290$$ 0 0
$$291$$ 914020.i 0.632737i
$$292$$ 0 0
$$293$$ 734707. 0.499972 0.249986 0.968250i $$-0.419574\pi$$
0.249986 + 0.968250i $$0.419574\pi$$
$$294$$ 0 0
$$295$$ 179627. 585691.i 0.120176 0.391844i
$$296$$ 0 0
$$297$$ 17207.7i 0.0113196i
$$298$$ 0 0
$$299$$ 1.56427e6i 1.01189i
$$300$$ 0 0
$$301$$ 836441.i 0.532132i
$$302$$ 0 0
$$303$$ 4.32981e6i 2.70933i
$$304$$ 0 0
$$305$$ 180007. 586930.i 0.110800 0.361274i
$$306$$ 0 0
$$307$$ −568071. −0.343999 −0.171999 0.985097i $$-0.555023\pi$$
−0.171999 + 0.985097i $$0.555023\pi$$
$$308$$ 0 0
$$309$$ 4.27891e6i 2.54939i
$$310$$ 0 0
$$311$$ −1.69667e6 −0.994712 −0.497356 0.867547i $$-0.665696\pi$$
−0.497356 + 0.867547i $$0.665696\pi$$
$$312$$ 0 0
$$313$$ 349961.i 0.201910i −0.994891 0.100955i $$-0.967810\pi$$
0.994891 0.100955i $$-0.0321899\pi$$
$$314$$ 0 0
$$315$$ −611901. + 1.99516e6i −0.347460 + 1.13293i
$$316$$ 0 0
$$317$$ 2.16674e6 1.21104 0.605520 0.795830i $$-0.292965\pi$$
0.605520 + 0.795830i $$0.292965\pi$$
$$318$$ 0 0
$$319$$ −39168.1 −0.0215504
$$320$$ 0 0
$$321$$ 3.84907e6 2.08494
$$322$$ 0 0
$$323$$ 1.05069e6 0.560361
$$324$$ 0 0
$$325$$ −1.31157e6 888024.i −0.688784 0.466354i
$$326$$ 0 0
$$327$$ 2.75467e6i 1.42462i
$$328$$ 0 0
$$329$$ −2.21824e6 −1.12985
$$330$$ 0 0
$$331$$ 3.09909e6i 1.55476i 0.629031 + 0.777380i $$0.283452\pi$$
−0.629031 + 0.777380i $$0.716548\pi$$
$$332$$ 0 0
$$333$$ −1.96427e6 −0.970714
$$334$$ 0 0
$$335$$ 695182. + 213207.i 0.338444 + 0.103798i
$$336$$ 0 0
$$337$$ 913351.i 0.438089i −0.975715 0.219045i $$-0.929706\pi$$
0.975715 0.219045i $$-0.0702941\pi$$
$$338$$ 0 0
$$339$$ 4.95216e6i 2.34043i
$$340$$ 0 0
$$341$$ 46205.3i 0.0215182i
$$342$$ 0 0
$$343$$ 2.36239e6i 1.08422i
$$344$$ 0 0
$$345$$ 1.25478e6 4.09132e6i 0.567568 1.85061i
$$346$$ 0 0
$$347$$ −1.81927e6 −0.811100 −0.405550 0.914073i $$-0.632920\pi$$
−0.405550 + 0.914073i $$0.632920\pi$$
$$348$$ 0 0
$$349$$ 3.66132e6i 1.60907i 0.593908 + 0.804533i $$0.297584\pi$$
−0.593908 + 0.804533i $$0.702416\pi$$
$$350$$ 0 0
$$351$$ −1.62518e6 −0.704099
$$352$$ 0 0
$$353$$ 4.00606e6i 1.71112i 0.517703 + 0.855560i $$0.326787\pi$$
−0.517703 + 0.855560i $$0.673213\pi$$
$$354$$ 0 0
$$355$$ −1.92449e6 590225.i −0.810483 0.248569i
$$356$$ 0 0
$$357$$ −3.61766e6 −1.50230
$$358$$ 0 0
$$359$$ 3.37100e6 1.38046 0.690228 0.723592i $$-0.257510\pi$$
0.690228 + 0.723592i $$0.257510\pi$$
$$360$$ 0 0
$$361$$ 1.95419e6 0.789221
$$362$$ 0 0
$$363$$ 3.99409e6 1.59093
$$364$$ 0 0
$$365$$ −1.05372e6 + 3.43574e6i −0.413991 + 1.34986i
$$366$$ 0 0
$$367$$ 3.30503e6i 1.28089i −0.768005 0.640444i $$-0.778751\pi$$
0.768005 0.640444i $$-0.221249\pi$$
$$368$$ 0 0
$$369$$ −6.76614e6 −2.58687
$$370$$ 0 0
$$371$$ 1.34013e6i 0.505491i
$$372$$ 0 0
$$373$$ −582132. −0.216646 −0.108323 0.994116i $$-0.534548\pi$$
−0.108323 + 0.994116i $$0.534548\pi$$
$$374$$ 0 0
$$375$$ −2.71807e6 3.37469e6i −0.998119 1.23924i
$$376$$ 0 0
$$377$$ 3.69922e6i 1.34047i
$$378$$ 0 0
$$379$$ 2.24404e6i 0.802478i −0.915973 0.401239i $$-0.868580\pi$$
0.915973 0.401239i $$-0.131420\pi$$
$$380$$ 0 0
$$381$$ 2.31428e6i 0.816776i
$$382$$ 0 0
$$383$$ 2.03163e6i 0.707696i −0.935303 0.353848i $$-0.884873\pi$$
0.935303 0.353848i $$-0.115127\pi$$
$$384$$ 0 0
$$385$$ 28762.7 + 8821.28i 0.00988957 + 0.00303305i
$$386$$ 0 0
$$387$$ −3.10506e6 −1.05388
$$388$$ 0 0
$$389$$ 3.29458e6i 1.10389i 0.833881 + 0.551945i $$0.186114\pi$$
−0.833881 + 0.551945i $$0.813886\pi$$
$$390$$ 0 0
$$391$$ 4.48852e6 1.48478
$$392$$ 0 0
$$393$$ 4.33930e6i 1.41722i
$$394$$ 0 0
$$395$$ −2.59949e6 797242.i −0.838291 0.257097i
$$396$$ 0 0
$$397$$ −2.66575e6 −0.848875 −0.424438 0.905457i $$-0.639528\pi$$
−0.424438 + 0.905457i $$0.639528\pi$$
$$398$$ 0 0
$$399$$ 1.79700e6 0.565089
$$400$$ 0 0
$$401$$ −1.41349e6 −0.438965 −0.219483 0.975616i $$-0.570437\pi$$
−0.219483 + 0.975616i $$0.570437\pi$$
$$402$$ 0 0
$$403$$ 4.36385e6 1.33847
$$404$$ 0 0
$$405$$ 584008. + 179111.i 0.176922 + 0.0542605i
$$406$$ 0 0
$$407$$ 28317.4i 0.00847358i
$$408$$ 0 0
$$409$$ −1.65117e6 −0.488072 −0.244036 0.969766i $$-0.578472\pi$$
−0.244036 + 0.969766i $$0.578472\pi$$
$$410$$ 0 0
$$411$$ 3.16112e6i 0.923073i
$$412$$ 0 0
$$413$$ 1.09897e6 0.317036
$$414$$ 0 0
$$415$$ 2.66071e6 + 816019.i 0.758364 + 0.232584i
$$416$$ 0 0
$$417$$ 9.76458e6i 2.74988i
$$418$$ 0 0
$$419$$ 4.58123e6i 1.27482i −0.770527 0.637408i $$-0.780007\pi$$
0.770527 0.637408i $$-0.219993\pi$$
$$420$$ 0 0
$$421$$ 3.54620e6i 0.975120i 0.873089 + 0.487560i $$0.162113\pi$$
−0.873089 + 0.487560i $$0.837887\pi$$
$$422$$ 0 0
$$423$$ 8.23461e6i 2.23765i
$$424$$ 0 0
$$425$$ 2.54811e6 3.76344e6i 0.684298 1.01068i
$$426$$ 0 0
$$427$$ 1.10129e6 0.292302
$$428$$ 0 0
$$429$$ 67471.4i 0.0177001i
$$430$$ 0 0
$$431$$ 3.24667e6 0.841871 0.420935 0.907091i $$-0.361702\pi$$
0.420935 + 0.907091i $$0.361702\pi$$
$$432$$ 0 0
$$433$$ 4.93639e6i 1.26529i 0.774443 + 0.632644i $$0.218030\pi$$
−0.774443 + 0.632644i $$0.781970\pi$$
$$434$$ 0 0
$$435$$ −2.96733e6 + 9.67527e6i −0.751870 + 2.45155i
$$436$$ 0 0
$$437$$ −2.22959e6 −0.558498
$$438$$ 0 0
$$439$$ −5.91592e6 −1.46508 −0.732539 0.680725i $$-0.761665\pi$$
−0.732539 + 0.680725i $$0.761665\pi$$
$$440$$ 0 0
$$441$$ 2.51305e6 0.615325
$$442$$ 0 0
$$443$$ 723323. 0.175115 0.0875574 0.996159i $$-0.472094\pi$$
0.0875574 + 0.996159i $$0.472094\pi$$
$$444$$ 0 0
$$445$$ −414966. 127267.i −0.0993373 0.0304660i
$$446$$ 0 0
$$447$$ 4.14515e6i 0.981231i
$$448$$ 0 0
$$449$$ −1.61902e6 −0.378999 −0.189499 0.981881i $$-0.560686\pi$$
−0.189499 + 0.981881i $$0.560686\pi$$
$$450$$ 0 0
$$451$$ 97542.1i 0.0225814i
$$452$$ 0 0
$$453$$ −4.57162e6 −1.04670
$$454$$ 0 0
$$455$$ 833125. 2.71649e6i 0.188661 0.615147i
$$456$$ 0 0
$$457$$ 419909.i 0.0940512i 0.998894 + 0.0470256i $$0.0149742\pi$$
−0.998894 + 0.0470256i $$0.985026\pi$$
$$458$$ 0 0
$$459$$ 4.66331e6i 1.03315i
$$460$$ 0 0
$$461$$ 3.17942e6i 0.696780i −0.937350 0.348390i $$-0.886728\pi$$
0.937350 0.348390i $$-0.113272\pi$$
$$462$$ 0 0
$$463$$ 620530.i 0.134527i −0.997735 0.0672636i $$-0.978573\pi$$
0.997735 0.0672636i $$-0.0214269\pi$$
$$464$$ 0 0
$$465$$ 1.14136e7 + 3.50046e6i 2.44788 + 0.750746i
$$466$$ 0 0
$$467$$ 1.96565e6 0.417075 0.208538 0.978014i $$-0.433130\pi$$
0.208538 + 0.978014i $$0.433130\pi$$
$$468$$ 0 0
$$469$$ 1.30441e6i 0.273831i
$$470$$ 0 0
$$471$$ −1.00130e7 −2.07975
$$472$$ 0 0
$$473$$ 44763.1i 0.00919957i
$$474$$ 0 0
$$475$$ −1.26572e6 + 1.86942e6i −0.257398 + 0.380165i
$$476$$ 0 0
$$477$$ −4.97487e6 −1.00112
$$478$$ 0 0
$$479$$ −4.57977e6 −0.912022 −0.456011 0.889974i $$-0.650722\pi$$
−0.456011 + 0.889974i $$0.650722\pi$$
$$480$$ 0 0
$$481$$ 2.67443e6 0.527070
$$482$$ 0 0
$$483$$ 7.67677e6 1.49731
$$484$$ 0 0
$$485$$ 603991. 1.96937e6i 0.116594 0.380167i
$$486$$ 0 0
$$487$$ 9.22794e6i 1.76312i −0.472070 0.881561i $$-0.656493\pi$$
0.472070 0.881561i $$-0.343507\pi$$
$$488$$ 0 0
$$489$$ −8.86603e6 −1.67671
$$490$$ 0 0
$$491$$ 6.77438e6i 1.26814i −0.773277 0.634068i $$-0.781384\pi$$
0.773277 0.634068i $$-0.218616\pi$$
$$492$$ 0 0
$$493$$ −1.06146e7 −1.96692
$$494$$ 0 0
$$495$$ −32746.6 + 106774.i −0.00600694 + 0.0195862i
$$496$$ 0 0
$$497$$ 3.61102e6i 0.655752i
$$498$$ 0 0
$$499$$ 3.54380e6i 0.637115i −0.947903 0.318558i $$-0.896802\pi$$
0.947903 0.318558i $$-0.103198\pi$$
$$500$$ 0 0
$$501$$ 948077.i 0.168752i
$$502$$ 0 0
$$503$$ 582992.i 0.102741i −0.998680 0.0513704i $$-0.983641\pi$$
0.998680 0.0513704i $$-0.0163589\pi$$
$$504$$ 0 0
$$505$$ 2.86118e6 9.32915e6i 0.499248 1.62785i
$$506$$ 0 0
$$507$$ −2.83744e6 −0.490237
$$508$$ 0 0
$$509$$ 1.00694e7i 1.72270i −0.508013 0.861349i $$-0.669620\pi$$
0.508013 0.861349i $$-0.330380\pi$$
$$510$$ 0 0
$$511$$ −6.44668e6 −1.09215
$$512$$ 0 0
$$513$$ 2.31641e6i 0.388618i
$$514$$ 0 0
$$515$$ −2.82754e6 + 9.21947e6i −0.469775 + 1.53175i
$$516$$ 0 0
$$517$$ −118712. −0.0195329
$$518$$ 0 0
$$519$$ 3.33022e6 0.542693
$$520$$ 0 0
$$521$$ −6.76200e6 −1.09139 −0.545696 0.837983i $$-0.683735\pi$$
−0.545696 + 0.837983i $$0.683735\pi$$
$$522$$ 0 0
$$523$$ −6.39905e6 −1.02297 −0.511483 0.859293i $$-0.670904\pi$$
−0.511483 + 0.859293i $$0.670904\pi$$
$$524$$ 0 0
$$525$$ 4.35806e6 6.43665e6i 0.690072 1.01921i
$$526$$ 0 0
$$527$$ 1.25217e7i 1.96398i
$$528$$ 0 0
$$529$$ −3.08843e6 −0.479842
$$530$$ 0 0
$$531$$ 4.07961e6i 0.627888i
$$532$$ 0 0
$$533$$ 9.21235e6 1.40460
$$534$$ 0 0
$$535$$ −8.29332e6 2.54349e6i −1.25269 0.384190i
$$536$$ 0 0
$$537$$ 1.40397e7i 2.10098i
$$538$$ 0 0
$$539$$ 36228.6i 0.00537130i
$$540$$ 0 0
$$541$$ 9.42388e6i 1.38432i −0.721744 0.692160i $$-0.756659\pi$$
0.721744 0.692160i $$-0.243341\pi$$
$$542$$ 0 0
$$543$$ 1.41921e7i 2.06560i
$$544$$ 0 0
$$545$$ −1.82031e6 + 5.93529e6i −0.262514 + 0.855955i
$$546$$ 0 0
$$547$$ −1.39418e6 −0.199228 −0.0996138 0.995026i $$-0.531761\pi$$
−0.0996138 + 0.995026i $$0.531761\pi$$
$$548$$ 0 0
$$549$$ 4.08824e6i 0.578902i
$$550$$ 0 0
$$551$$ 5.27260e6 0.739854
$$552$$ 0 0
$$553$$ 4.87756e6i 0.678250i
$$554$$ 0 0
$$555$$ 6.99494e6 + 2.14529e6i 0.963943 + 0.295634i
$$556$$ 0 0
$$557$$ 1.27617e6 0.174289 0.0871445 0.996196i $$-0.472226\pi$$
0.0871445 + 0.996196i $$0.472226\pi$$
$$558$$ 0 0
$$559$$ 4.22765e6 0.572228
$$560$$ 0 0
$$561$$ −193603. −0.0259720
$$562$$ 0 0
$$563$$ −1.87381e6 −0.249146 −0.124573 0.992210i $$-0.539756\pi$$
−0.124573 + 0.992210i $$0.539756\pi$$
$$564$$ 0 0
$$565$$ −3.27243e6 + 1.06701e7i −0.431269 + 1.40620i
$$566$$ 0 0
$$567$$ 1.09581e6i 0.143145i
$$568$$ 0 0
$$569$$ −6.96458e6 −0.901808 −0.450904 0.892572i $$-0.648898\pi$$
−0.450904 + 0.892572i $$0.648898\pi$$
$$570$$ 0 0
$$571$$ 344717.i 0.0442458i −0.999755 0.0221229i $$-0.992957\pi$$
0.999755 0.0221229i $$-0.00704251\pi$$
$$572$$ 0 0
$$573$$ 1.70051e7 2.16368
$$574$$ 0 0
$$575$$ −5.40715e6 + 7.98612e6i −0.682023 + 1.00732i
$$576$$ 0 0
$$577$$ 5.35769e6i 0.669944i −0.942228 0.334972i $$-0.891273\pi$$
0.942228 0.334972i $$-0.108727\pi$$
$$578$$ 0 0
$$579$$ 2.31055e7i 2.86431i
$$580$$ 0 0
$$581$$ 4.99245e6i 0.613583i
$$582$$ 0 0
$$583$$ 71718.8i 0.00873900i
$$584$$ 0 0
$$585$$ 1.00842e7 + 3.09275e6i 1.21829 + 0.373641i
$$586$$ 0 0
$$587$$ −1.33004e6 −0.159320 −0.0796599 0.996822i $$-0.525383\pi$$
−0.0796599 + 0.996822i $$0.525383\pi$$
$$588$$ 0 0
$$589$$ 6.21992e6i 0.738748i
$$590$$ 0 0
$$591$$ 1.71677e7 2.02182
$$592$$ 0 0
$$593$$ 4.87875e6i 0.569734i −0.958567 0.284867i $$-0.908051\pi$$
0.958567 0.284867i $$-0.0919494\pi$$
$$594$$ 0 0
$$595$$ 7.79472e6 + 2.39058e6i 0.902627 + 0.276828i
$$596$$ 0 0
$$597$$ 2.40398e7 2.76054
$$598$$ 0 0
$$599$$ −2.71017e6 −0.308624 −0.154312 0.988022i $$-0.549316\pi$$
−0.154312 + 0.988022i $$0.549316\pi$$
$$600$$ 0 0
$$601$$ 1.02295e7 1.15523 0.577615 0.816309i $$-0.303983\pi$$
0.577615 + 0.816309i $$0.303983\pi$$
$$602$$ 0 0
$$603$$ −4.84226e6 −0.542319
$$604$$ 0 0
$$605$$ −8.60578e6 2.63932e6i −0.955876 0.293160i
$$606$$ 0 0
$$607$$ 6.63212e6i 0.730602i −0.930890 0.365301i $$-0.880966\pi$$
0.930890 0.365301i $$-0.119034\pi$$
$$608$$ 0 0
$$609$$ −1.81543e7 −1.98351
$$610$$ 0 0
$$611$$ 1.12117e7i 1.21498i
$$612$$ 0 0
$$613$$ −7.17868e6 −0.771602 −0.385801 0.922582i $$-0.626075\pi$$
−0.385801 + 0.922582i $$0.626075\pi$$
$$614$$ 0 0
$$615$$ 2.40948e7 + 7.38968e6i 2.56883 + 0.787840i
$$616$$ 0 0
$$617$$ 1.22481e7i 1.29526i 0.761956 + 0.647629i $$0.224239\pi$$
−0.761956 + 0.647629i $$0.775761\pi$$
$$618$$ 0 0
$$619$$ 2.10012e6i 0.220302i −0.993915 0.110151i $$-0.964867\pi$$
0.993915 0.110151i $$-0.0351334\pi$$
$$620$$ 0 0
$$621$$ 9.89568e6i 1.02971i
$$622$$ 0 0
$$623$$ 778624.i 0.0803725i
$$624$$ 0 0
$$625$$ 3.62641e6 + 9.06734e6i 0.371345 + 0.928495i
$$626$$ 0 0
$$627$$ 96168.9 0.00976935
$$628$$ 0 0
$$629$$ 7.67404e6i 0.773388i
$$630$$ 0 0
$$631$$ −5.94323e6 −0.594223 −0.297111 0.954843i $$-0.596023\pi$$
−0.297111 + 0.954843i $$0.596023\pi$$
$$632$$ 0 0
$$633$$ 1.98481e7i 1.96883i
$$634$$ 0 0
$$635$$ 1.52929e6 4.98641e6i 0.150507 0.490743i
$$636$$ 0 0
$$637$$ −3.42160e6 −0.334104
$$638$$ 0 0
$$639$$ 1.34049e7 1.29871
$$640$$ 0 0
$$641$$ 1.73665e7 1.66943 0.834713 0.550686i $$-0.185634\pi$$
0.834713 + 0.550686i $$0.185634\pi$$
$$642$$ 0 0
$$643$$ −1.88563e7 −1.79858 −0.899290 0.437353i $$-0.855916\pi$$
−0.899290 + 0.437353i $$0.855916\pi$$
$$644$$ 0 0
$$645$$ 1.10574e7 + 3.39121e6i 1.04653 + 0.320963i
$$646$$ 0 0
$$647$$ 2.16987e6i 0.203785i 0.994795 + 0.101893i $$0.0324898\pi$$
−0.994795 + 0.101893i $$0.967510\pi$$
$$648$$ 0 0
$$649$$ 58812.5 0.00548097
$$650$$ 0 0
$$651$$ 2.14160e7i 1.98055i
$$652$$ 0 0
$$653$$ 1.97704e7 1.81440 0.907198 0.420703i $$-0.138217\pi$$
0.907198 + 0.420703i $$0.138217\pi$$
$$654$$ 0 0
$$655$$ 2.86744e6 9.34958e6i 0.261151 0.851509i
$$656$$ 0 0
$$657$$ 2.39315e7i 2.16300i
$$658$$ 0 0
$$659$$ 3.61872e6i 0.324595i −0.986742 0.162297i $$-0.948110\pi$$
0.986742 0.162297i $$-0.0518904\pi$$
$$660$$ 0 0
$$661$$ 3.75269e6i 0.334071i 0.985951 + 0.167036i $$0.0534195\pi$$
−0.985951 + 0.167036i $$0.946580\pi$$
$$662$$ 0 0
$$663$$ 1.82848e7i 1.61550i
$$664$$ 0 0
$$665$$ −3.87188e6 1.18748e6i −0.339522 0.104129i
$$666$$ 0 0
$$667$$ 2.25245e7 1.96038
$$668$$ 0 0
$$669$$ 1.53769e7i 1.32833i
$$670$$ 0 0
$$671$$ 58936.8 0.00505336
$$672$$ 0 0
$$673$$ 1.93077e6i 0.164321i 0.996619 + 0.0821606i $$0.0261820\pi$$
−0.996619 + 0.0821606i $$0.973818\pi$$
$$674$$ 0 0
$$675$$ 8.29710e6 + 5.61771e6i 0.700918 + 0.474570i
$$676$$ 0 0
$$677$$ 7.53721e6 0.632032 0.316016 0.948754i $$-0.397655\pi$$
0.316016 + 0.948754i $$0.397655\pi$$
$$678$$ 0 0
$$679$$ 3.69525e6 0.307588
$$680$$ 0 0
$$681$$ 1.35815e7 1.12223
$$682$$ 0 0
$$683$$ −2.28279e6 −0.187247 −0.0936234 0.995608i $$-0.529845\pi$$
−0.0936234 + 0.995608i $$0.529845\pi$$
$$684$$ 0 0
$$685$$ 2.08889e6 6.81104e6i 0.170094 0.554609i
$$686$$ 0 0
$$687$$ 9.14114e6i 0.738939i
$$688$$ 0 0
$$689$$ 6.77347e6 0.543580
$$690$$ 0 0
$$691$$ 4.89825e6i 0.390252i −0.980778 0.195126i $$-0.937488\pi$$
0.980778 0.195126i $$-0.0625116\pi$$
$$692$$ 0 0
$$693$$ −200345. −0.0158470
$$694$$ 0 0
$$695$$ −6.45251e6 + 2.10391e7i −0.506718 + 1.65221i
$$696$$ 0 0
$$697$$ 2.64340e7i 2.06102i
$$698$$ 0 0
$$699$$ 8.60838e6i 0.666390i
$$700$$ 0 0
$$701$$ 1.36266e7i 1.04735i −0.851917 0.523676i $$-0.824560\pi$$
0.851917 0.523676i $$-0.175440\pi$$
$$702$$ 0 0
$$703$$ 3.81194e6i 0.290909i
$$704$$ 0 0
$$705$$ −8.99347e6 + 2.93241e7i −0.681483 + 2.22204i
$$706$$ 0 0
$$707$$ 1.75048e7 1.31707
$$708$$ 0 0
$$709$$ 1.03111e7i 0.770350i −0.922843 0.385175i $$-0.874141\pi$$
0.922843 0.385175i $$-0.125859\pi$$
$$710$$ 0 0
$$711$$ 1.81066e7 1.34327
$$712$$ 0 0
$$713$$ 2.65714e7i 1.95745i
$$714$$ 0 0
$$715$$ 44585.6 145376.i 0.00326159 0.0106348i
$$716$$ 0 0
$$717$$ 2.90769e7 2.11228
$$718$$ 0 0
$$719$$ −9.38661e6 −0.677153 −0.338576 0.940939i $$-0.609945\pi$$
−0.338576 + 0.940939i $$0.609945\pi$$
$$720$$ 0 0
$$721$$ −1.72990e7 −1.23932
$$722$$ 0 0
$$723$$ −2.73254e7 −1.94411
$$724$$ 0 0
$$725$$ 1.27870e7 1.88858e7i 0.903490 1.33441i
$$726$$ 0 0
$$727$$ 4.62442e6i 0.324505i 0.986749 + 0.162252i $$0.0518759\pi$$
−0.986749 + 0.162252i $$0.948124\pi$$
$$728$$ 0 0
$$729$$ −2.33945e7 −1.63040
$$730$$ 0 0
$$731$$ 1.21309e7i 0.839650i
$$732$$ 0 0
$$733$$ −2.68859e7 −1.84827 −0.924134 0.382068i $$-0.875212\pi$$
−0.924134 + 0.382068i $$0.875212\pi$$
$$734$$ 0 0
$$735$$ −8.94917e6 2.74464e6i −0.611033 0.187399i
$$736$$ 0 0
$$737$$ 69807.0i 0.00473403i
$$738$$ 0 0
$$739$$ 686127.i 0.0462161i 0.999733 + 0.0231081i $$0.00735618\pi$$
−0.999733 + 0.0231081i $$0.992644\pi$$
$$740$$ 0 0
$$741$$ 9.08265e6i 0.607669i
$$742$$ 0 0
$$743$$ 1.09400e7i 0.727017i 0.931591 + 0.363508i $$0.118421\pi$$
−0.931591 + 0.363508i $$0.881579\pi$$
$$744$$ 0 0
$$745$$ 2.73915e6 8.93126e6i 0.180811 0.589552i
$$746$$ 0 0
$$747$$ −1.85331e7 −1.21520
$$748$$ 0 0
$$749$$ 1.55612e7i 1.01354i
$$750$$ 0 0
$$751$$ −2.37534e7 −1.53683 −0.768416 0.639951i $$-0.778955\pi$$
−0.768416 + 0.639951i $$0.778955\pi$$
$$752$$ 0 0
$$753$$ 2.41704e6i 0.155345i
$$754$$ 0 0
$$755$$ 9.85014e6 + 3.02096e6i 0.628891 + 0.192876i
$$756$$ 0 0
$$757$$ −2.95506e7 −1.87424 −0.937122 0.349003i $$-0.886520\pi$$
−0.937122 + 0.349003i $$0.886520\pi$$
$$758$$ 0 0
$$759$$ 410832. 0.0258857
$$760$$ 0 0
$$761$$ 2.38225e6 0.149116 0.0745582 0.997217i $$-0.476245\pi$$
0.0745582 + 0.997217i $$0.476245\pi$$
$$762$$ 0 0
$$763$$ −1.11367e7 −0.692542
$$764$$ 0 0
$$765$$ −8.87437e6 + 2.89358e7i −0.548256 + 1.78764i
$$766$$ 0 0
$$767$$ 5.55453e6i 0.340925i
$$768$$ 0 0
$$769$$ −1.58003e7 −0.963495 −0.481747 0.876310i $$-0.659998\pi$$
−0.481747 + 0.876310i $$0.659998\pi$$
$$770$$ 0 0
$$771$$ 3.35600e7i 2.03323i
$$772$$ 0 0
$$773$$ −8.84834e6 −0.532615 −0.266307 0.963888i $$-0.585804\pi$$
−0.266307 + 0.963888i $$0.585804\pi$$
$$774$$ 0 0
$$775$$ −2.22790e7 1.50844e7i −1.33242 0.902140i
$$776$$ 0 0
$$777$$ 1.31250e7i 0.779914i
$$778$$ 0 0
$$779$$ 1.31306e7i 0.775249i
$$780$$ 0 0
$$781$$ 193248.i 0.0113367i
$$782$$ 0 0
$$783$$ 2.34016e7i 1.36408i
$$784$$ 0 0
$$785$$ 2.15743e7 + 6.61667e6i 1.24958 + 0.383235i
$$786$$ 0 0
$$787$$ −5.30753e6 −0.305461 −0.152730 0.988268i $$-0.548807\pi$$
−0.152730 + 0.988268i $$0.548807\pi$$
$$788$$ 0 0
$$789$$ 2.21491e7i 1.26667i
$$790$$ 0 0
$$791$$ −2.00209e7 −1.13774
$$792$$ 0 0
$$793$$ 5.56628e6i 0.314327i
$$794$$ 0 0
$$795$$ 1.77159e7 + 5.43334e6i 0.994137 + 0.304894i
$$796$$ 0 0
$$797$$ −1.99099e7 −1.11026 −0.555128 0.831765i $$-0.687331\pi$$