# Properties

 Label 1456.2.r.g.417.1 Level $1456$ Weight $2$ Character 1456.417 Analytic conductor $11.626$ Analytic rank $0$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,2,Mod(417,1456)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1456.417");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1456 = 2^{4} \cdot 7 \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1456.r (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

 Self dual: no Analytic conductor: $$11.6262185343$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{17}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 417.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1456.417 Dual form 1456.2.r.g.625.1

## $q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$$ $$q+(-0.500000 + 2.59808i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-1.50000 + 2.59808i) q^{11} -1.00000 q^{13} +(-3.50000 + 6.06218i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(-3.00000 - 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} -5.00000 q^{29} +(-4.00000 - 6.92820i) q^{37} -2.00000 q^{43} +(3.50000 + 6.06218i) q^{47} +(-6.50000 - 2.59808i) q^{49} +(1.50000 - 2.59808i) q^{53} +(-3.50000 + 6.06218i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-7.50000 + 2.59808i) q^{63} +(-1.50000 + 2.59808i) q^{67} +5.00000 q^{71} +(-7.00000 + 12.1244i) q^{73} +(-6.00000 - 5.19615i) q^{77} +(-3.00000 - 5.19615i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(0.500000 - 2.59808i) q^{91} -14.0000 q^{97} -9.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - q^{7} + 3 q^{9}+O(q^{10})$$ 2 * q - q^7 + 3 * q^9 $$2 q - q^{7} + 3 q^{9} - 3 q^{11} - 2 q^{13} - 7 q^{17} - 7 q^{19} - 6 q^{23} + 5 q^{25} - 10 q^{29} - 8 q^{37} - 4 q^{43} + 7 q^{47} - 13 q^{49} + 3 q^{53} - 7 q^{59} + 7 q^{61} - 15 q^{63} - 3 q^{67} + 10 q^{71} - 14 q^{73} - 12 q^{77} - 6 q^{79} - 9 q^{81} + q^{91} - 28 q^{97} - 18 q^{99}+O(q^{100})$$ 2 * q - q^7 + 3 * q^9 - 3 * q^11 - 2 * q^13 - 7 * q^17 - 7 * q^19 - 6 * q^23 + 5 * q^25 - 10 * q^29 - 8 * q^37 - 4 * q^43 + 7 * q^47 - 13 * q^49 + 3 * q^53 - 7 * q^59 + 7 * q^61 - 15 * q^63 - 3 * q^67 + 10 * q^71 - 14 * q^73 - 12 * q^77 - 6 * q^79 - 9 * q^81 + q^91 - 28 * q^97 - 18 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$$.

 $$n$$ $$561$$ $$911$$ $$1093$$ $$1249$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## 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 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$4$$ 0 0
$$5$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$6$$ 0 0
$$7$$ −0.500000 + 2.59808i −0.188982 + 0.981981i
$$8$$ 0 0
$$9$$ 1.50000 + 2.59808i 0.500000 + 0.866025i
$$10$$ 0 0
$$11$$ −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i $$-0.982718\pi$$
0.546259 + 0.837616i $$0.316051\pi$$
$$12$$ 0 0
$$13$$ −1.00000 −0.277350
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −3.50000 + 6.06218i −0.848875 + 1.47029i 0.0333386 + 0.999444i $$0.489386\pi$$
−0.882213 + 0.470850i $$0.843947\pi$$
$$18$$ 0 0
$$19$$ −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i $$-0.869927\pi$$
0.114708 0.993399i $$-0.463407\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i $$-0.951544\pi$$
0.362892 0.931831i $$-0.381789\pi$$
$$24$$ 0 0
$$25$$ 2.50000 4.33013i 0.500000 0.866025i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −5.00000 −0.928477 −0.464238 0.885710i $$-0.653672\pi$$
−0.464238 + 0.885710i $$0.653672\pi$$
$$30$$ 0 0
$$31$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −4.00000 6.92820i −0.657596 1.13899i −0.981236 0.192809i $$-0.938240\pi$$
0.323640 0.946180i $$-0.395093\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$42$$ 0 0
$$43$$ −2.00000 −0.304997 −0.152499 0.988304i $$-0.548732\pi$$
−0.152499 + 0.988304i $$0.548732\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 3.50000 + 6.06218i 0.510527 + 0.884260i 0.999926 + 0.0121990i $$0.00388317\pi$$
−0.489398 + 0.872060i $$0.662783\pi$$
$$48$$ 0 0
$$49$$ −6.50000 2.59808i −0.928571 0.371154i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i $$-0.767275\pi$$
0.950464 + 0.310835i $$0.100609\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −3.50000 + 6.06218i −0.455661 + 0.789228i −0.998726 0.0504625i $$-0.983930\pi$$
0.543065 + 0.839691i $$0.317264\pi$$
$$60$$ 0 0
$$61$$ 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i $$-0.0187572\pi$$
−0.550135 + 0.835076i $$0.685424\pi$$
$$62$$ 0 0
$$63$$ −7.50000 + 2.59808i −0.944911 + 0.327327i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −1.50000 + 2.59808i −0.183254 + 0.317406i −0.942987 0.332830i $$-0.891996\pi$$
0.759733 + 0.650236i $$0.225330\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 5.00000 0.593391 0.296695 0.954972i $$-0.404115\pi$$
0.296695 + 0.954972i $$0.404115\pi$$
$$72$$ 0 0
$$73$$ −7.00000 + 12.1244i −0.819288 + 1.41905i 0.0869195 + 0.996215i $$0.472298\pi$$
−0.906208 + 0.422833i $$0.861036\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −6.00000 5.19615i −0.683763 0.592157i
$$78$$ 0 0
$$79$$ −3.00000 5.19615i −0.337526 0.584613i 0.646440 0.762964i $$-0.276257\pi$$
−0.983967 + 0.178352i $$0.942924\pi$$
$$80$$ 0 0
$$81$$ −4.50000 + 7.79423i −0.500000 + 0.866025i
$$82$$ 0 0
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$90$$ 0 0
$$91$$ 0.500000 2.59808i 0.0524142 0.272352i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ 0 0
$$99$$ −9.00000 −0.904534
$$100$$ 0 0
$$101$$ 7.00000 12.1244i 0.696526 1.20642i −0.273138 0.961975i $$-0.588061\pi$$
0.969664 0.244443i $$-0.0786053\pi$$
$$102$$ 0 0
$$103$$ 7.00000 + 12.1244i 0.689730 + 1.19465i 0.971925 + 0.235291i $$0.0756043\pi$$
−0.282194 + 0.959357i $$0.591062\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 4.00000 + 6.92820i 0.386695 + 0.669775i 0.992003 0.126217i $$-0.0402834\pi$$
−0.605308 + 0.795991i $$0.706950\pi$$
$$108$$ 0 0
$$109$$ −2.00000 + 3.46410i −0.191565 + 0.331801i −0.945769 0.324840i $$-0.894690\pi$$
0.754204 + 0.656640i $$0.228023\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 9.00000 0.846649 0.423324 0.905978i $$-0.360863\pi$$
0.423324 + 0.905978i $$0.360863\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.50000 2.59808i −0.138675 0.240192i
$$118$$ 0 0
$$119$$ −14.0000 12.1244i −1.28338 1.11144i
$$120$$ 0 0
$$121$$ 1.00000 + 1.73205i 0.0909091 + 0.157459i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −2.00000 −0.177471 −0.0887357 0.996055i $$-0.528283\pi$$
−0.0887357 + 0.996055i $$0.528283\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 7.00000 + 12.1244i 0.611593 + 1.05931i 0.990972 + 0.134069i $$0.0428042\pi$$
−0.379379 + 0.925241i $$0.623862\pi$$
$$132$$ 0 0
$$133$$ 17.5000 6.06218i 1.51744 0.525657i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −2.00000 + 3.46410i −0.170872 + 0.295958i −0.938725 0.344668i $$-0.887992\pi$$
0.767853 + 0.640626i $$0.221325\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 1.50000 2.59808i 0.125436 0.217262i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i $$-0.0876260\pi$$
−0.716578 + 0.697507i $$0.754293\pi$$
$$150$$ 0 0
$$151$$ −1.50000 + 2.59808i −0.122068 + 0.211428i −0.920583 0.390547i $$-0.872286\pi$$
0.798515 + 0.601975i $$0.205619\pi$$
$$152$$ 0 0
$$153$$ −21.0000 −1.69775
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −3.50000 + 6.06218i −0.279330 + 0.483814i −0.971219 0.238190i $$-0.923446\pi$$
0.691888 + 0.722005i $$0.256779\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 15.0000 5.19615i 1.18217 0.409514i
$$162$$ 0 0
$$163$$ −6.50000 11.2583i −0.509119 0.881820i −0.999944 0.0105623i $$-0.996638\pi$$
0.490825 0.871258i $$-0.336695\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 7.00000 0.541676 0.270838 0.962625i $$-0.412699\pi$$
0.270838 + 0.962625i $$0.412699\pi$$
$$168$$ 0 0
$$169$$ 1.00000 0.0769231
$$170$$ 0 0
$$171$$ 10.5000 18.1865i 0.802955 1.39076i
$$172$$ 0 0
$$173$$ −3.50000 6.06218i −0.266100 0.460899i 0.701751 0.712422i $$-0.252402\pi$$
−0.967851 + 0.251523i $$0.919068\pi$$
$$174$$ 0 0
$$175$$ 10.0000 + 8.66025i 0.755929 + 0.654654i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −5.00000 + 8.66025i −0.373718 + 0.647298i −0.990134 0.140122i $$-0.955250\pi$$
0.616417 + 0.787420i $$0.288584\pi$$
$$180$$ 0 0
$$181$$ −7.00000 −0.520306 −0.260153 0.965567i $$-0.583773\pi$$
−0.260153 + 0.965567i $$0.583773\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −10.5000 18.1865i −0.767836 1.32993i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −10.0000 17.3205i −0.723575 1.25327i −0.959558 0.281511i $$-0.909164\pi$$
0.235983 0.971757i $$-0.424169\pi$$
$$192$$ 0 0
$$193$$ −2.00000 + 3.46410i −0.143963 + 0.249351i −0.928986 0.370116i $$-0.879318\pi$$
0.785022 + 0.619467i $$0.212651\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 2.00000 0.142494 0.0712470 0.997459i $$-0.477302\pi$$
0.0712470 + 0.997459i $$0.477302\pi$$
$$198$$ 0 0
$$199$$ −7.00000 + 12.1244i −0.496217 + 0.859473i −0.999990 0.00436292i $$-0.998611\pi$$
0.503774 + 0.863836i $$0.331945\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 2.50000 12.9904i 0.175466 0.911746i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 9.00000 15.5885i 0.625543 1.08347i
$$208$$ 0 0
$$209$$ 21.0000 1.45260
$$210$$ 0 0
$$211$$ 26.0000 1.78991 0.894957 0.446153i $$-0.147206\pi$$
0.894957 + 0.446153i $$0.147206\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 3.50000 6.06218i 0.235435 0.407786i
$$222$$ 0 0
$$223$$ −21.0000 −1.40626 −0.703132 0.711059i $$-0.748216\pi$$
−0.703132 + 0.711059i $$0.748216\pi$$
$$224$$ 0 0
$$225$$ 15.0000 1.00000
$$226$$ 0 0
$$227$$ −14.0000 + 24.2487i −0.929213 + 1.60944i −0.144571 + 0.989494i $$0.546180\pi$$
−0.784642 + 0.619949i $$0.787153\pi$$
$$228$$ 0 0
$$229$$ −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i $$-0.319740\pi$$
−0.999088 + 0.0426906i $$0.986407\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 13.5000 + 23.3827i 0.884414 + 1.53185i 0.846383 + 0.532574i $$0.178775\pi$$
0.0380310 + 0.999277i $$0.487891\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 19.0000 1.22901 0.614504 0.788914i $$-0.289356\pi$$
0.614504 + 0.788914i $$0.289356\pi$$
$$240$$ 0 0
$$241$$ −14.0000 + 24.2487i −0.901819 + 1.56200i −0.0766885 + 0.997055i $$0.524435\pi$$
−0.825131 + 0.564942i $$0.808899\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 3.50000 + 6.06218i 0.222700 + 0.385727i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 14.0000 0.883672 0.441836 0.897096i $$-0.354327\pi$$
0.441836 + 0.897096i $$0.354327\pi$$
$$252$$ 0 0
$$253$$ 18.0000 1.13165
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 7.00000 + 12.1244i 0.436648 + 0.756297i 0.997429 0.0716680i $$-0.0228322\pi$$
−0.560781 + 0.827964i $$0.689499\pi$$
$$258$$ 0 0
$$259$$ 20.0000 6.92820i 1.24274 0.430498i
$$260$$ 0 0
$$261$$ −7.50000 12.9904i −0.464238 0.804084i
$$262$$ 0 0
$$263$$ −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i $$0.431818\pi$$
−0.952517 + 0.304487i $$0.901515\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 10.5000 18.1865i 0.640196 1.10885i −0.345192 0.938532i $$-0.612186\pi$$
0.985389 0.170321i $$-0.0544803\pi$$
$$270$$ 0 0
$$271$$ −3.50000 6.06218i −0.212610 0.368251i 0.739921 0.672694i $$-0.234863\pi$$
−0.952531 + 0.304443i $$0.901530\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 7.50000 + 12.9904i 0.452267 + 0.783349i
$$276$$ 0 0
$$277$$ 8.50000 14.7224i 0.510716 0.884585i −0.489207 0.872167i $$-0.662714\pi$$
0.999923 0.0124177i $$-0.00395278\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −12.0000 −0.715860 −0.357930 0.933748i $$-0.616517\pi$$
−0.357930 + 0.933748i $$0.616517\pi$$
$$282$$ 0 0
$$283$$ −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i $$-0.969939\pi$$
0.579437 + 0.815017i $$0.303272\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −16.0000 27.7128i −0.941176 1.63017i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 14.0000 0.817889 0.408944 0.912559i $$-0.365897\pi$$
0.408944 + 0.912559i $$0.365897\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 3.00000 + 5.19615i 0.173494 + 0.300501i
$$300$$ 0 0
$$301$$ 1.00000 5.19615i 0.0576390 0.299501i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −21.0000 −1.19853 −0.599267 0.800549i $$-0.704541\pi$$
−0.599267 + 0.800549i $$0.704541\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$312$$ 0 0
$$313$$ 7.00000 + 12.1244i 0.395663 + 0.685309i 0.993186 0.116543i $$-0.0371814\pi$$
−0.597522 + 0.801852i $$0.703848\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i $$-0.112775\pi$$
−0.769395 + 0.638774i $$0.779442\pi$$
$$318$$ 0 0
$$319$$ 7.50000 12.9904i 0.419919 0.727322i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 49.0000 2.72643
$$324$$ 0 0
$$325$$ −2.50000 + 4.33013i −0.138675 + 0.240192i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −17.5000 + 6.06218i −0.964806 + 0.334219i
$$330$$ 0 0
$$331$$ −10.0000 17.3205i −0.549650 0.952021i −0.998298 0.0583130i $$-0.981428\pi$$
0.448649 0.893708i $$-0.351905\pi$$
$$332$$ 0 0
$$333$$ 12.0000 20.7846i 0.657596 1.13899i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 23.0000 1.25289 0.626445 0.779466i $$-0.284509\pi$$
0.626445 + 0.779466i $$0.284509\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 10.0000 15.5885i 0.539949 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 2.00000 3.46410i 0.107366 0.185963i −0.807337 0.590091i $$-0.799092\pi$$
0.914702 + 0.404128i $$0.132425\pi$$
$$348$$ 0 0
$$349$$ 14.0000 0.749403 0.374701 0.927146i $$-0.377745\pi$$
0.374701 + 0.927146i $$0.377745\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ −7.00000 + 12.1244i −0.372572 + 0.645314i −0.989960 0.141344i $$-0.954858\pi$$
0.617388 + 0.786659i $$0.288191\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 4.00000 + 6.92820i 0.211112 + 0.365657i 0.952063 0.305903i $$-0.0989582\pi$$
−0.740951 + 0.671559i $$0.765625\pi$$
$$360$$ 0 0
$$361$$ −15.0000 + 25.9808i −0.789474 + 1.36741i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 7.00000 12.1244i 0.365397 0.632886i −0.623443 0.781869i $$-0.714267\pi$$
0.988840 + 0.148983i $$0.0475999\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 6.00000 + 5.19615i 0.311504 + 0.269771i
$$372$$ 0 0
$$373$$ −7.50000 12.9904i −0.388335 0.672616i 0.603890 0.797067i $$-0.293616\pi$$
−0.992226 + 0.124451i $$0.960283\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 5.00000 0.257513
$$378$$ 0 0
$$379$$ 12.0000 0.616399 0.308199 0.951322i $$-0.400274\pi$$
0.308199 + 0.951322i $$0.400274\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −3.00000 5.19615i −0.152499 0.264135i
$$388$$ 0 0
$$389$$ 1.50000 2.59808i 0.0760530 0.131728i −0.825491 0.564416i $$-0.809102\pi$$
0.901544 + 0.432688i $$0.142435\pi$$
$$390$$ 0 0
$$391$$ 42.0000 2.12403
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −7.00000 12.1244i −0.351320 0.608504i 0.635161 0.772380i $$-0.280934\pi$$
−0.986481 + 0.163876i $$0.947600\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −11.0000 19.0526i −0.549314 0.951439i −0.998322 0.0579116i $$-0.981556\pi$$
0.449008 0.893528i $$-0.351777\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 24.0000 1.18964
$$408$$ 0 0
$$409$$ 14.0000 24.2487i 0.692255 1.19902i −0.278842 0.960337i $$-0.589950\pi$$
0.971097 0.238685i $$-0.0767162\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −14.0000 12.1244i −0.688895 0.596601i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −14.0000 −0.683945 −0.341972 0.939710i $$-0.611095\pi$$
−0.341972 + 0.939710i $$0.611095\pi$$
$$420$$ 0 0
$$421$$ 30.0000 1.46211 0.731055 0.682318i $$-0.239028\pi$$
0.731055 + 0.682318i $$0.239028\pi$$
$$422$$ 0 0
$$423$$ −10.5000 + 18.1865i −0.510527 + 0.884260i
$$424$$ 0 0
$$425$$ 17.5000 + 30.3109i 0.848875 + 1.47029i
$$426$$ 0 0
$$427$$ −17.5000 + 6.06218i −0.846884 + 0.293369i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −12.0000 + 20.7846i −0.578020 + 1.00116i 0.417687 + 0.908591i $$0.362841\pi$$
−0.995706 + 0.0925683i $$0.970492\pi$$
$$432$$ 0 0
$$433$$ 21.0000 1.00920 0.504598 0.863355i $$-0.331641\pi$$
0.504598 + 0.863355i $$0.331641\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −21.0000 + 36.3731i −1.00457 + 1.73996i
$$438$$ 0 0
$$439$$ 7.00000 + 12.1244i 0.334092 + 0.578664i 0.983310 0.181938i $$-0.0582371\pi$$
−0.649218 + 0.760602i $$0.724904\pi$$
$$440$$ 0 0
$$441$$ −3.00000 20.7846i −0.142857 0.989743i
$$442$$ 0 0
$$443$$ −10.0000 17.3205i −0.475114 0.822922i 0.524479 0.851423i $$-0.324260\pi$$
−0.999594 + 0.0285009i $$0.990927\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −12.0000 −0.566315 −0.283158 0.959073i $$-0.591382\pi$$
−0.283158 + 0.959073i $$0.591382\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 3.00000 + 5.19615i 0.140334 + 0.243066i 0.927622 0.373519i $$-0.121849\pi$$
−0.787288 + 0.616585i $$0.788516\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −28.0000 −1.30409 −0.652045 0.758180i $$-0.726089\pi$$
−0.652045 + 0.758180i $$0.726089\pi$$
$$462$$ 0 0
$$463$$ −16.0000 −0.743583 −0.371792 0.928316i $$-0.621256\pi$$
−0.371792 + 0.928316i $$0.621256\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 7.00000 + 12.1244i 0.323921 + 0.561048i 0.981293 0.192518i $$-0.0616653\pi$$
−0.657372 + 0.753566i $$0.728332\pi$$
$$468$$ 0 0
$$469$$ −6.00000 5.19615i −0.277054 0.239936i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 3.00000 5.19615i 0.137940 0.238919i
$$474$$ 0 0
$$475$$ −35.0000 −1.60591
$$476$$ 0 0
$$477$$ 9.00000 0.412082
$$478$$ 0 0
$$479$$ 3.50000 6.06218i 0.159919 0.276988i −0.774920 0.632059i $$-0.782210\pi$$
0.934839 + 0.355071i $$0.115543\pi$$
$$480$$ 0 0
$$481$$ 4.00000 + 6.92820i 0.182384 + 0.315899i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 12.5000 21.6506i 0.566429 0.981084i −0.430486 0.902597i $$-0.641658\pi$$
0.996915 0.0784867i $$-0.0250088\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −30.0000 −1.35388 −0.676941 0.736038i $$-0.736695\pi$$
−0.676941 + 0.736038i $$0.736695\pi$$
$$492$$ 0 0
$$493$$ 17.5000 30.3109i 0.788160 1.36513i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −2.50000 + 12.9904i −0.112140 + 0.582698i
$$498$$ 0 0
$$499$$ 4.00000 + 6.92820i 0.179065 + 0.310149i 0.941560 0.336844i $$-0.109360\pi$$
−0.762496 + 0.646993i $$0.776026\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 28.0000 1.24846 0.624229 0.781241i $$-0.285413\pi$$
0.624229 + 0.781241i $$0.285413\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 14.0000 + 24.2487i 0.620539 + 1.07481i 0.989385 + 0.145315i $$0.0464195\pi$$
−0.368846 + 0.929490i $$0.620247\pi$$
$$510$$ 0 0
$$511$$ −28.0000 24.2487i −1.23865 1.07270i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −21.0000 −0.923579
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 7.00000 12.1244i 0.306676 0.531178i −0.670957 0.741496i $$-0.734117\pi$$
0.977633 + 0.210318i $$0.0674500\pi$$
$$522$$ 0 0
$$523$$ −7.00000 12.1244i −0.306089 0.530161i 0.671414 0.741082i $$-0.265687\pi$$
−0.977503 + 0.210921i $$0.932354\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −6.50000 + 11.2583i −0.282609 + 0.489493i
$$530$$ 0 0
$$531$$ −21.0000 −0.911322
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ 16.5000 12.9904i 0.710705 0.559535i
$$540$$ 0 0
$$541$$ −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i $$-0.221681\pi$$
−0.939110 + 0.343617i $$0.888348\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −2.00000 −0.0855138 −0.0427569 0.999086i $$-0.513614\pi$$
−0.0427569 + 0.999086i $$0.513614\pi$$
$$548$$ 0 0
$$549$$ −10.5000 + 18.1865i −0.448129 + 0.776182i
$$550$$ 0 0
$$551$$ 17.5000 + 30.3109i 0.745525 + 1.29129i
$$552$$ 0 0
$$553$$ 15.0000 5.19615i 0.637865 0.220963i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −9.00000 + 15.5885i −0.381342 + 0.660504i −0.991254 0.131965i $$-0.957871\pi$$
0.609912 + 0.792469i $$0.291205\pi$$
$$558$$ 0 0
$$559$$ 2.00000 0.0845910
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 14.0000 24.2487i 0.590030 1.02196i −0.404198 0.914671i $$-0.632449\pi$$
0.994228 0.107290i $$-0.0342173\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ −18.0000 15.5885i −0.755929 0.654654i
$$568$$ 0 0
$$569$$ −0.500000 0.866025i −0.0209611 0.0363057i 0.855355 0.518043i $$-0.173339\pi$$
−0.876316 + 0.481737i $$0.840006\pi$$
$$570$$ 0 0
$$571$$ 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i $$-0.806660\pi$$
0.904835 + 0.425762i $$0.139994\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ −30.0000 −1.25109
$$576$$ 0 0
$$577$$ −7.00000 + 12.1244i −0.291414 + 0.504744i −0.974144 0.225927i $$-0.927459\pi$$
0.682730 + 0.730670i $$0.260792\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 4.50000 + 7.79423i 0.186371 + 0.322804i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −21.0000 −0.866763 −0.433381 0.901211i $$-0.642680\pi$$
−0.433381 + 0.901211i $$0.642680\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 16.0000 27.7128i 0.653742 1.13231i −0.328465 0.944516i $$-0.606531\pi$$
0.982208 0.187799i $$-0.0601353\pi$$
$$600$$ 0 0
$$601$$ −7.00000 −0.285536 −0.142768 0.989756i $$-0.545600\pi$$
−0.142768 + 0.989756i $$0.545600\pi$$
$$602$$ 0 0
$$603$$ −9.00000 −0.366508
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 7.00000 + 12.1244i 0.284121 + 0.492112i 0.972396 0.233338i $$-0.0749648\pi$$
−0.688274 + 0.725450i $$0.741632\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −3.50000 6.06218i −0.141595 0.245249i
$$612$$ 0 0
$$613$$ −16.0000 + 27.7128i −0.646234 + 1.11931i 0.337781 + 0.941225i $$0.390324\pi$$
−0.984015 + 0.178085i $$0.943010\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 30.0000 1.20775 0.603877 0.797077i $$-0.293622\pi$$
0.603877 + 0.797077i $$0.293622\pi$$
$$618$$ 0 0
$$619$$ −14.0000 + 24.2487i −0.562708 + 0.974638i 0.434551 + 0.900647i $$0.356907\pi$$
−0.997259 + 0.0739910i $$0.976426\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ −12.5000 21.6506i −0.500000 0.866025i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 56.0000 2.23287
$$630$$ 0 0
$$631$$ −16.0000 −0.636950 −0.318475 0.947931i $$-0.603171\pi$$
−0.318475 + 0.947931i $$0.603171\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 6.50000 + 2.59808i 0.257539 + 0.102940i
$$638$$ 0 0
$$639$$ 7.50000 + 12.9904i 0.296695 + 0.513892i
$$640$$ 0 0
$$641$$ −9.00000 + 15.5885i −0.355479 + 0.615707i −0.987200 0.159489i $$-0.949015\pi$$
0.631721 + 0.775196i $$0.282349\pi$$
$$642$$ 0 0
$$643$$ 7.00000 0.276053 0.138027 0.990429i $$-0.455924\pi$$
0.138027 + 0.990429i $$0.455924\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −21.0000 + 36.3731i −0.825595 + 1.42997i 0.0758684 + 0.997118i $$0.475827\pi$$
−0.901464 + 0.432855i $$0.857506\pi$$
$$648$$ 0 0
$$649$$ −10.5000 18.1865i −0.412161 0.713884i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 3.00000 + 5.19615i 0.117399 + 0.203341i 0.918736 0.394872i $$-0.129211\pi$$
−0.801337 + 0.598213i $$0.795878\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −42.0000 −1.63858
$$658$$ 0 0
$$659$$ 40.0000 1.55818 0.779089 0.626913i $$-0.215682\pi$$
0.779089 + 0.626913i $$0.215682\pi$$
$$660$$ 0 0
$$661$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 15.0000 + 25.9808i 0.580802 + 1.00598i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −21.0000 −0.810696
$$672$$ 0 0
$$673$$ −26.0000 −1.00223 −0.501113 0.865382i $$-0.667076\pi$$
−0.501113 + 0.865382i $$0.667076\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 17.5000 + 30.3109i 0.672580 + 1.16494i 0.977170 + 0.212459i $$0.0681471\pi$$
−0.304590 + 0.952483i $$0.598520\pi$$
$$678$$ 0 0
$$679$$ 7.00000 36.3731i 0.268635 1.39587i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −12.0000 + 20.7846i −0.459167 + 0.795301i −0.998917 0.0465244i $$-0.985185\pi$$
0.539750 + 0.841825i $$0.318519\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −1.50000 + 2.59808i −0.0571454 + 0.0989788i
$$690$$ 0 0
$$691$$ 17.5000 + 30.3109i 0.665731 + 1.15308i 0.979086 + 0.203445i $$0.0652137\pi$$
−0.313355 + 0.949636i $$0.601453\pi$$
$$692$$ 0 0
$$693$$ 4.50000 23.3827i 0.170941 0.888235i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 30.0000 1.13308 0.566542 0.824033i $$-0.308281\pi$$
0.566542 + 0.824033i $$0.308281\pi$$
$$702$$ 0 0
$$703$$ −28.0000 + 48.4974i −1.05604 + 1.82911i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 28.0000 + 24.2487i 1.05305 + 0.911967i
$$708$$ 0 0
$$709$$ −25.0000 43.3013i −0.938895 1.62621i −0.767537 0.641004i $$-0.778518\pi$$
−0.171358 0.985209i $$-0.554815\pi$$
$$710$$ 0 0
$$711$$ 9.00000 15.5885i 0.337526 0.584613i
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −21.0000 36.3731i −0.783168 1.35649i −0.930087 0.367338i $$-0.880269\pi$$
0.146920 0.989148i $$-0.453064\pi$$
$$720$$ 0 0
$$721$$ −35.0000 + 12.1244i −1.30347 + 0.451535i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −12.5000 + 21.6506i −0.464238 + 0.804084i
$$726$$ 0 0
$$727$$ −28.0000 −1.03846 −0.519231 0.854634i $$-0.673782\pi$$
−0.519231 + 0.854634i $$0.673782\pi$$
$$728$$ 0 0
$$729$$ −27.0000 −1.00000
$$730$$ 0 0
$$731$$ 7.00000 12.1244i 0.258904 0.448435i
$$732$$ 0 0
$$733$$ −21.0000 36.3731i −0.775653 1.34347i −0.934427 0.356155i $$-0.884088\pi$$
0.158774 0.987315i $$-0.449246\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −4.50000 7.79423i −0.165760 0.287104i
$$738$$ 0 0
$$739$$ 2.00000 3.46410i 0.0735712 0.127429i −0.826893 0.562360i $$-0.809894\pi$$
0.900464 + 0.434930i $$0.143227\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −9.00000 −0.330178 −0.165089 0.986279i $$-0.552791\pi$$
−0.165089 + 0.986279i $$0.552791\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −20.0000 + 6.92820i −0.730784 + 0.253151i
$$750$$ 0 0
$$751$$ −10.0000 17.3205i −0.364905 0.632034i 0.623856 0.781540i $$-0.285565\pi$$
−0.988761 + 0.149505i $$0.952232\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 9.00000 0.327111 0.163555 0.986534i $$-0.447704\pi$$
0.163555 + 0.986534i $$0.447704\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$762$$ 0 0
$$763$$ −8.00000 6.92820i −0.289619 0.250818i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 3.50000 6.06218i 0.126378 0.218893i
$$768$$ 0 0
$$769$$ −14.0000 −0.504853 −0.252426 0.967616i $$-0.581229\pi$$
−0.252426 + 0.967616i $$0.581229\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −21.0000 + 36.3731i −0.755318 + 1.30825i 0.189899 + 0.981804i $$0.439184\pi$$
−0.945216 + 0.326445i $$0.894149\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 0 0
$$780$$ 0 0
$$781$$ −7.50000 + 12.9904i −0.268371 + 0.464832i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 3.50000 6.06218i 0.124762 0.216093i −0.796878 0.604140i $$-0.793517\pi$$
0.921640 + 0.388047i $$0.126850\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −4.50000 + 23.3827i −0.160002 + 0.831393i
$$792$$ 0 0
$$793$$ −3.50000 6.06218i −0.124289 0.215274i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −42.0000 −1.48772 −0.743858 0.668338i $$-0.767006\pi$$
−0.743858 + 0.668338i $$0.767006\pi$$
$$798$$ 0 0