# Properties

 Label 2240.2.k.a.1791.2 Level $2240$ Weight $2$ Character 2240.1791 Analytic conductor $17.886$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,2,Mod(1791,2240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2240, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))

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

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

chi := DirichletCharacter("2240.1791");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2240 = 2^{6} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2240.k (of order $$2$$, degree $$1$$, 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: $$17.8864900528$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{12})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 140) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1791.2 Root $$0.866025 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 2240.1791 Dual form 2240.2.k.a.1791.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.73205 q^{3} +1.00000i q^{5} +(1.73205 - 2.00000i) q^{7} +O(q^{10})$$ $$q-1.73205 q^{3} +1.00000i q^{5} +(1.73205 - 2.00000i) q^{7} +3.73205i q^{11} -6.46410i q^{13} -1.73205i q^{15} +0.464102i q^{17} -6.00000 q^{19} +(-3.00000 + 3.46410i) q^{21} +5.46410i q^{23} -1.00000 q^{25} +5.19615 q^{27} +5.92820 q^{29} -6.00000 q^{31} -6.46410i q^{33} +(2.00000 + 1.73205i) q^{35} +2.53590 q^{37} +11.1962i q^{39} +3.46410i q^{41} +2.00000i q^{43} -1.73205 q^{47} +(-1.00000 - 6.92820i) q^{49} -0.803848i q^{51} -2.00000 q^{53} -3.73205 q^{55} +10.3923 q^{57} -3.46410 q^{59} -2.53590i q^{61} +6.46410 q^{65} +3.46410i q^{67} -9.46410i q^{69} -0.535898i q^{71} -0.928203i q^{73} +1.73205 q^{75} +(7.46410 + 6.46410i) q^{77} +2.66025i q^{79} -9.00000 q^{81} -8.53590 q^{83} -0.464102 q^{85} -10.2679 q^{87} +9.46410i q^{89} +(-12.9282 - 11.1962i) q^{91} +10.3923 q^{93} -6.00000i q^{95} +7.39230i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q+O(q^{10})$$ 4 * q $$4 q - 24 q^{19} - 12 q^{21} - 4 q^{25} - 4 q^{29} - 24 q^{31} + 8 q^{35} + 24 q^{37} - 4 q^{49} - 8 q^{53} - 8 q^{55} + 12 q^{65} + 16 q^{77} - 36 q^{81} - 48 q^{83} + 12 q^{85} - 48 q^{87} - 24 q^{91}+O(q^{100})$$ 4 * q - 24 * q^19 - 12 * q^21 - 4 * q^25 - 4 * q^29 - 24 * q^31 + 8 * q^35 + 24 * q^37 - 4 * q^49 - 8 * q^53 - 8 * q^55 + 12 * q^65 + 16 * q^77 - 36 * q^81 - 48 * q^83 + 12 * q^85 - 48 * q^87 - 24 * q^91

## Character values

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

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

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.73205 −1.00000 −0.500000 0.866025i $$-0.666667\pi$$
−0.500000 + 0.866025i $$0.666667\pi$$
$$4$$ 0 0
$$5$$ 1.00000i 0.447214i
$$6$$ 0 0
$$7$$ 1.73205 2.00000i 0.654654 0.755929i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 3.73205i 1.12526i 0.826710 + 0.562628i $$0.190210\pi$$
−0.826710 + 0.562628i $$0.809790\pi$$
$$12$$ 0 0
$$13$$ 6.46410i 1.79282i −0.443227 0.896410i $$-0.646166\pi$$
0.443227 0.896410i $$-0.353834\pi$$
$$14$$ 0 0
$$15$$ 1.73205i 0.447214i
$$16$$ 0 0
$$17$$ 0.464102i 0.112561i 0.998415 + 0.0562806i $$0.0179241\pi$$
−0.998415 + 0.0562806i $$0.982076\pi$$
$$18$$ 0 0
$$19$$ −6.00000 −1.37649 −0.688247 0.725476i $$-0.741620\pi$$
−0.688247 + 0.725476i $$0.741620\pi$$
$$20$$ 0 0
$$21$$ −3.00000 + 3.46410i −0.654654 + 0.755929i
$$22$$ 0 0
$$23$$ 5.46410i 1.13934i 0.821872 + 0.569672i $$0.192930\pi$$
−0.821872 + 0.569672i $$0.807070\pi$$
$$24$$ 0 0
$$25$$ −1.00000 −0.200000
$$26$$ 0 0
$$27$$ 5.19615 1.00000
$$28$$ 0 0
$$29$$ 5.92820 1.10084 0.550420 0.834888i $$-0.314468\pi$$
0.550420 + 0.834888i $$0.314468\pi$$
$$30$$ 0 0
$$31$$ −6.00000 −1.07763 −0.538816 0.842424i $$-0.681128\pi$$
−0.538816 + 0.842424i $$0.681128\pi$$
$$32$$ 0 0
$$33$$ 6.46410i 1.12526i
$$34$$ 0 0
$$35$$ 2.00000 + 1.73205i 0.338062 + 0.292770i
$$36$$ 0 0
$$37$$ 2.53590 0.416899 0.208450 0.978033i $$-0.433158\pi$$
0.208450 + 0.978033i $$0.433158\pi$$
$$38$$ 0 0
$$39$$ 11.1962i 1.79282i
$$40$$ 0 0
$$41$$ 3.46410i 0.541002i 0.962720 + 0.270501i $$0.0871893\pi$$
−0.962720 + 0.270501i $$0.912811\pi$$
$$42$$ 0 0
$$43$$ 2.00000i 0.304997i 0.988304 + 0.152499i $$0.0487319\pi$$
−0.988304 + 0.152499i $$0.951268\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −1.73205 −0.252646 −0.126323 0.991989i $$-0.540318\pi$$
−0.126323 + 0.991989i $$0.540318\pi$$
$$48$$ 0 0
$$49$$ −1.00000 6.92820i −0.142857 0.989743i
$$50$$ 0 0
$$51$$ 0.803848i 0.112561i
$$52$$ 0 0
$$53$$ −2.00000 −0.274721 −0.137361 0.990521i $$-0.543862\pi$$
−0.137361 + 0.990521i $$0.543862\pi$$
$$54$$ 0 0
$$55$$ −3.73205 −0.503230
$$56$$ 0 0
$$57$$ 10.3923 1.37649
$$58$$ 0 0
$$59$$ −3.46410 −0.450988 −0.225494 0.974245i $$-0.572400\pi$$
−0.225494 + 0.974245i $$0.572400\pi$$
$$60$$ 0 0
$$61$$ 2.53590i 0.324689i −0.986734 0.162344i $$-0.948094\pi$$
0.986734 0.162344i $$-0.0519055\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 6.46410 0.801773
$$66$$ 0 0
$$67$$ 3.46410i 0.423207i 0.977356 + 0.211604i $$0.0678686\pi$$
−0.977356 + 0.211604i $$0.932131\pi$$
$$68$$ 0 0
$$69$$ 9.46410i 1.13934i
$$70$$ 0 0
$$71$$ 0.535898i 0.0635994i −0.999494 0.0317997i $$-0.989876\pi$$
0.999494 0.0317997i $$-0.0101239\pi$$
$$72$$ 0 0
$$73$$ 0.928203i 0.108638i −0.998524 0.0543190i $$-0.982701\pi$$
0.998524 0.0543190i $$-0.0172988\pi$$
$$74$$ 0 0
$$75$$ 1.73205 0.200000
$$76$$ 0 0
$$77$$ 7.46410 + 6.46410i 0.850613 + 0.736653i
$$78$$ 0 0
$$79$$ 2.66025i 0.299302i 0.988739 + 0.149651i $$0.0478150\pi$$
−0.988739 + 0.149651i $$0.952185\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −1.00000
$$82$$ 0 0
$$83$$ −8.53590 −0.936937 −0.468468 0.883480i $$-0.655194\pi$$
−0.468468 + 0.883480i $$0.655194\pi$$
$$84$$ 0 0
$$85$$ −0.464102 −0.0503389
$$86$$ 0 0
$$87$$ −10.2679 −1.10084
$$88$$ 0 0
$$89$$ 9.46410i 1.00319i 0.865102 + 0.501596i $$0.167254\pi$$
−0.865102 + 0.501596i $$0.832746\pi$$
$$90$$ 0 0
$$91$$ −12.9282 11.1962i −1.35524 1.17368i
$$92$$ 0 0
$$93$$ 10.3923 1.07763
$$94$$ 0 0
$$95$$ 6.00000i 0.615587i
$$96$$ 0 0
$$97$$ 7.39230i 0.750575i 0.926908 + 0.375287i $$0.122456\pi$$
−0.926908 + 0.375287i $$0.877544\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 8.53590i 0.849354i 0.905345 + 0.424677i $$0.139612\pi$$
−0.905345 + 0.424677i $$0.860388\pi$$
$$102$$ 0 0
$$103$$ −17.1962 −1.69439 −0.847194 0.531284i $$-0.821710\pi$$
−0.847194 + 0.531284i $$0.821710\pi$$
$$104$$ 0 0
$$105$$ −3.46410 3.00000i −0.338062 0.292770i
$$106$$ 0 0
$$107$$ 18.3923i 1.77805i 0.457857 + 0.889026i $$0.348617\pi$$
−0.457857 + 0.889026i $$0.651383\pi$$
$$108$$ 0 0
$$109$$ −15.9282 −1.52565 −0.762823 0.646608i $$-0.776187\pi$$
−0.762823 + 0.646608i $$0.776187\pi$$
$$110$$ 0 0
$$111$$ −4.39230 −0.416899
$$112$$ 0 0
$$113$$ −1.46410 −0.137731 −0.0688655 0.997626i $$-0.521938\pi$$
−0.0688655 + 0.997626i $$0.521938\pi$$
$$114$$ 0 0
$$115$$ −5.46410 −0.509530
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0.928203 + 0.803848i 0.0850883 + 0.0736886i
$$120$$ 0 0
$$121$$ −2.92820 −0.266200
$$122$$ 0 0
$$123$$ 6.00000i 0.541002i
$$124$$ 0 0
$$125$$ 1.00000i 0.0894427i
$$126$$ 0 0
$$127$$ 8.53590i 0.757438i 0.925512 + 0.378719i $$0.123635\pi$$
−0.925512 + 0.378719i $$0.876365\pi$$
$$128$$ 0 0
$$129$$ 3.46410i 0.304997i
$$130$$ 0 0
$$131$$ −9.46410 −0.826882 −0.413441 0.910531i $$-0.635673\pi$$
−0.413441 + 0.910531i $$0.635673\pi$$
$$132$$ 0 0
$$133$$ −10.3923 + 12.0000i −0.901127 + 1.04053i
$$134$$ 0 0
$$135$$ 5.19615i 0.447214i
$$136$$ 0 0
$$137$$ −0.392305 −0.0335169 −0.0167584 0.999860i $$-0.505335\pi$$
−0.0167584 + 0.999860i $$0.505335\pi$$
$$138$$ 0 0
$$139$$ 6.92820 0.587643 0.293821 0.955860i $$-0.405073\pi$$
0.293821 + 0.955860i $$0.405073\pi$$
$$140$$ 0 0
$$141$$ 3.00000 0.252646
$$142$$ 0 0
$$143$$ 24.1244 2.01738
$$144$$ 0 0
$$145$$ 5.92820i 0.492310i
$$146$$ 0 0
$$147$$ 1.73205 + 12.0000i 0.142857 + 0.989743i
$$148$$ 0 0
$$149$$ −16.9282 −1.38681 −0.693406 0.720547i $$-0.743891\pi$$
−0.693406 + 0.720547i $$0.743891\pi$$
$$150$$ 0 0
$$151$$ 4.80385i 0.390932i −0.980711 0.195466i $$-0.937378\pi$$
0.980711 0.195466i $$-0.0626219\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 6.00000i 0.481932i
$$156$$ 0 0
$$157$$ 19.8564i 1.58471i 0.610058 + 0.792357i $$0.291146\pi$$
−0.610058 + 0.792357i $$0.708854\pi$$
$$158$$ 0 0
$$159$$ 3.46410 0.274721
$$160$$ 0 0
$$161$$ 10.9282 + 9.46410i 0.861263 + 0.745876i
$$162$$ 0 0
$$163$$ 20.7846i 1.62798i 0.580881 + 0.813988i $$0.302708\pi$$
−0.580881 + 0.813988i $$0.697292\pi$$
$$164$$ 0 0
$$165$$ 6.46410 0.503230
$$166$$ 0 0
$$167$$ 5.19615 0.402090 0.201045 0.979582i $$-0.435566\pi$$
0.201045 + 0.979582i $$0.435566\pi$$
$$168$$ 0 0
$$169$$ −28.7846 −2.21420
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 20.3205i 1.54494i −0.635051 0.772470i $$-0.719021\pi$$
0.635051 0.772470i $$-0.280979\pi$$
$$174$$ 0 0
$$175$$ −1.73205 + 2.00000i −0.130931 + 0.151186i
$$176$$ 0 0
$$177$$ 6.00000 0.450988
$$178$$ 0 0
$$179$$ 14.3923i 1.07573i 0.843031 + 0.537866i $$0.180769\pi$$
−0.843031 + 0.537866i $$0.819231\pi$$
$$180$$ 0 0
$$181$$ 12.9282i 0.960946i −0.877010 0.480473i $$-0.840465\pi$$
0.877010 0.480473i $$-0.159535\pi$$
$$182$$ 0 0
$$183$$ 4.39230i 0.324689i
$$184$$ 0 0
$$185$$ 2.53590i 0.186443i
$$186$$ 0 0
$$187$$ −1.73205 −0.126660
$$188$$ 0 0
$$189$$ 9.00000 10.3923i 0.654654 0.755929i
$$190$$ 0 0
$$191$$ 3.19615i 0.231265i 0.993292 + 0.115633i $$0.0368896\pi$$
−0.993292 + 0.115633i $$0.963110\pi$$
$$192$$ 0 0
$$193$$ −2.53590 −0.182538 −0.0912690 0.995826i $$-0.529092\pi$$
−0.0912690 + 0.995826i $$0.529092\pi$$
$$194$$ 0 0
$$195$$ −11.1962 −0.801773
$$196$$ 0 0
$$197$$ −21.3205 −1.51902 −0.759512 0.650494i $$-0.774562\pi$$
−0.759512 + 0.650494i $$0.774562\pi$$
$$198$$ 0 0
$$199$$ −3.46410 −0.245564 −0.122782 0.992434i $$-0.539182\pi$$
−0.122782 + 0.992434i $$0.539182\pi$$
$$200$$ 0 0
$$201$$ 6.00000i 0.423207i
$$202$$ 0 0
$$203$$ 10.2679 11.8564i 0.720669 0.832157i
$$204$$ 0 0
$$205$$ −3.46410 −0.241943
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 22.3923i 1.54891i
$$210$$ 0 0
$$211$$ 7.19615i 0.495404i −0.968836 0.247702i $$-0.920325\pi$$
0.968836 0.247702i $$-0.0796753\pi$$
$$212$$ 0 0
$$213$$ 0.928203i 0.0635994i
$$214$$ 0 0
$$215$$ −2.00000 −0.136399
$$216$$ 0 0
$$217$$ −10.3923 + 12.0000i −0.705476 + 0.814613i
$$218$$ 0 0
$$219$$ 1.60770i 0.108638i
$$220$$ 0 0
$$221$$ 3.00000 0.201802
$$222$$ 0 0
$$223$$ −10.2679 −0.687593 −0.343796 0.939044i $$-0.611713\pi$$
−0.343796 + 0.939044i $$0.611713\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −3.33975 −0.221667 −0.110833 0.993839i $$-0.535352\pi$$
−0.110833 + 0.993839i $$0.535352\pi$$
$$228$$ 0 0
$$229$$ 15.4641i 1.02190i 0.859611 + 0.510948i $$0.170706\pi$$
−0.859611 + 0.510948i $$0.829294\pi$$
$$230$$ 0 0
$$231$$ −12.9282 11.1962i −0.850613 0.736653i
$$232$$ 0 0
$$233$$ −22.9282 −1.50208 −0.751038 0.660259i $$-0.770447\pi$$
−0.751038 + 0.660259i $$0.770447\pi$$
$$234$$ 0 0
$$235$$ 1.73205i 0.112987i
$$236$$ 0 0
$$237$$ 4.60770i 0.299302i
$$238$$ 0 0
$$239$$ 27.9808i 1.80993i −0.425491 0.904963i $$-0.639899\pi$$
0.425491 0.904963i $$-0.360101\pi$$
$$240$$ 0 0
$$241$$ 4.39230i 0.282933i −0.989943 0.141467i $$-0.954818\pi$$
0.989943 0.141467i $$-0.0451818\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 6.92820 1.00000i 0.442627 0.0638877i
$$246$$ 0 0
$$247$$ 38.7846i 2.46781i
$$248$$ 0 0
$$249$$ 14.7846 0.936937
$$250$$ 0 0
$$251$$ −1.85641 −0.117175 −0.0585877 0.998282i $$-0.518660\pi$$
−0.0585877 + 0.998282i $$0.518660\pi$$
$$252$$ 0 0
$$253$$ −20.3923 −1.28205
$$254$$ 0 0
$$255$$ 0.803848 0.0503389
$$256$$ 0 0
$$257$$ 6.00000i 0.374270i 0.982334 + 0.187135i $$0.0599201\pi$$
−0.982334 + 0.187135i $$0.940080\pi$$
$$258$$ 0 0
$$259$$ 4.39230 5.07180i 0.272925 0.315146i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 4.53590i 0.279695i 0.990173 + 0.139848i $$0.0446613\pi$$
−0.990173 + 0.139848i $$0.955339\pi$$
$$264$$ 0 0
$$265$$ 2.00000i 0.122859i
$$266$$ 0 0
$$267$$ 16.3923i 1.00319i
$$268$$ 0 0
$$269$$ 12.0000i 0.731653i 0.930683 + 0.365826i $$0.119214\pi$$
−0.930683 + 0.365826i $$0.880786\pi$$
$$270$$ 0 0
$$271$$ 2.53590 0.154045 0.0770224 0.997029i $$-0.475459\pi$$
0.0770224 + 0.997029i $$0.475459\pi$$
$$272$$ 0 0
$$273$$ 22.3923 + 19.3923i 1.35524 + 1.17368i
$$274$$ 0 0
$$275$$ 3.73205i 0.225051i
$$276$$ 0 0
$$277$$ 24.7846 1.48916 0.744581 0.667532i $$-0.232649\pi$$
0.744581 + 0.667532i $$0.232649\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 5.92820 0.353647 0.176823 0.984243i $$-0.443418\pi$$
0.176823 + 0.984243i $$0.443418\pi$$
$$282$$ 0 0
$$283$$ 12.1244 0.720718 0.360359 0.932814i $$-0.382654\pi$$
0.360359 + 0.932814i $$0.382654\pi$$
$$284$$ 0 0
$$285$$ 10.3923i 0.615587i
$$286$$ 0 0
$$287$$ 6.92820 + 6.00000i 0.408959 + 0.354169i
$$288$$ 0 0
$$289$$ 16.7846 0.987330
$$290$$ 0 0
$$291$$ 12.8038i 0.750575i
$$292$$ 0 0
$$293$$ 14.3205i 0.836613i 0.908306 + 0.418307i $$0.137376\pi$$
−0.908306 + 0.418307i $$0.862624\pi$$
$$294$$ 0 0
$$295$$ 3.46410i 0.201688i
$$296$$ 0 0
$$297$$ 19.3923i 1.12526i
$$298$$ 0 0
$$299$$ 35.3205 2.04264
$$300$$ 0 0
$$301$$ 4.00000 + 3.46410i 0.230556 + 0.199667i
$$302$$ 0 0
$$303$$ 14.7846i 0.849354i
$$304$$ 0 0
$$305$$ 2.53590 0.145205
$$306$$ 0 0
$$307$$ 1.73205 0.0988534 0.0494267 0.998778i $$-0.484261\pi$$
0.0494267 + 0.998778i $$0.484261\pi$$
$$308$$ 0 0
$$309$$ 29.7846 1.69439
$$310$$ 0 0
$$311$$ −19.8564 −1.12595 −0.562977 0.826473i $$-0.690344\pi$$
−0.562977 + 0.826473i $$0.690344\pi$$
$$312$$ 0 0
$$313$$ 24.4641i 1.38279i −0.722476 0.691396i $$-0.756996\pi$$
0.722476 0.691396i $$-0.243004\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 16.9282 0.950783 0.475391 0.879774i $$-0.342306\pi$$
0.475391 + 0.879774i $$0.342306\pi$$
$$318$$ 0 0
$$319$$ 22.1244i 1.23873i
$$320$$ 0 0
$$321$$ 31.8564i 1.77805i
$$322$$ 0 0
$$323$$ 2.78461i 0.154940i
$$324$$ 0 0
$$325$$ 6.46410i 0.358564i
$$326$$ 0 0
$$327$$ 27.5885 1.52565
$$328$$ 0 0
$$329$$ −3.00000 + 3.46410i −0.165395 + 0.190982i
$$330$$ 0 0
$$331$$ 5.60770i 0.308227i −0.988053 0.154113i $$-0.950748\pi$$
0.988053 0.154113i $$-0.0492521\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −3.46410 −0.189264
$$336$$ 0 0
$$337$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$338$$ 0 0
$$339$$ 2.53590 0.137731
$$340$$ 0 0
$$341$$ 22.3923i 1.21261i
$$342$$ 0 0
$$343$$ −15.5885 10.0000i −0.841698 0.539949i
$$344$$ 0 0
$$345$$ 9.46410 0.509530
$$346$$ 0 0
$$347$$ 14.2487i 0.764911i −0.923974 0.382455i $$-0.875079\pi$$
0.923974 0.382455i $$-0.124921\pi$$
$$348$$ 0 0
$$349$$ 29.3205i 1.56949i −0.619818 0.784745i $$-0.712794\pi$$
0.619818 0.784745i $$-0.287206\pi$$
$$350$$ 0 0
$$351$$ 33.5885i 1.79282i
$$352$$ 0 0
$$353$$ 13.3923i 0.712800i 0.934333 + 0.356400i $$0.115996\pi$$
−0.934333 + 0.356400i $$0.884004\pi$$
$$354$$ 0 0
$$355$$ 0.535898 0.0284425
$$356$$ 0 0
$$357$$ −1.60770 1.39230i −0.0850883 0.0736886i
$$358$$ 0 0
$$359$$ 9.32051i 0.491918i 0.969280 + 0.245959i $$0.0791028\pi$$
−0.969280 + 0.245959i $$0.920897\pi$$
$$360$$ 0 0
$$361$$ 17.0000 0.894737
$$362$$ 0 0
$$363$$ 5.07180 0.266200
$$364$$ 0 0
$$365$$ 0.928203 0.0485844
$$366$$ 0 0
$$367$$ 36.1244 1.88568 0.942838 0.333251i $$-0.108146\pi$$
0.942838 + 0.333251i $$0.108146\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −3.46410 + 4.00000i −0.179847 + 0.207670i
$$372$$ 0 0
$$373$$ 24.3923 1.26299 0.631493 0.775382i $$-0.282443\pi$$
0.631493 + 0.775382i $$0.282443\pi$$
$$374$$ 0 0
$$375$$ 1.73205i 0.0894427i
$$376$$ 0 0
$$377$$ 38.3205i 1.97361i
$$378$$ 0 0
$$379$$ 26.3923i 1.35568i 0.735209 + 0.677841i $$0.237084\pi$$
−0.735209 + 0.677841i $$0.762916\pi$$
$$380$$ 0 0
$$381$$ 14.7846i 0.757438i
$$382$$ 0 0
$$383$$ 20.5359 1.04934 0.524668 0.851307i $$-0.324190\pi$$
0.524668 + 0.851307i $$0.324190\pi$$
$$384$$ 0 0
$$385$$ −6.46410 + 7.46410i −0.329441 + 0.380406i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −6.85641 −0.347634 −0.173817 0.984778i $$-0.555610\pi$$
−0.173817 + 0.984778i $$0.555610\pi$$
$$390$$ 0 0
$$391$$ −2.53590 −0.128246
$$392$$ 0 0
$$393$$ 16.3923 0.826882
$$394$$ 0 0
$$395$$ −2.66025 −0.133852
$$396$$ 0 0
$$397$$ 5.53590i 0.277839i −0.990304 0.138919i $$-0.955637\pi$$
0.990304 0.138919i $$-0.0443629\pi$$
$$398$$ 0 0
$$399$$ 18.0000 20.7846i 0.901127 1.04053i
$$400$$ 0 0
$$401$$ −23.9282 −1.19492 −0.597459 0.801900i $$-0.703823\pi$$
−0.597459 + 0.801900i $$0.703823\pi$$
$$402$$ 0 0
$$403$$ 38.7846i 1.93200i
$$404$$ 0 0
$$405$$ 9.00000i 0.447214i
$$406$$ 0 0
$$407$$ 9.46410i 0.469118i
$$408$$ 0 0
$$409$$ 31.8564i 1.57520i 0.616188 + 0.787599i $$0.288676\pi$$
−0.616188 + 0.787599i $$0.711324\pi$$
$$410$$ 0 0
$$411$$ 0.679492 0.0335169
$$412$$ 0 0
$$413$$ −6.00000 + 6.92820i −0.295241 + 0.340915i
$$414$$ 0 0
$$415$$ 8.53590i 0.419011i
$$416$$ 0 0
$$417$$ −12.0000 −0.587643
$$418$$ 0 0
$$419$$ −24.2487 −1.18463 −0.592314 0.805708i $$-0.701785\pi$$
−0.592314 + 0.805708i $$0.701785\pi$$
$$420$$ 0 0
$$421$$ −19.0000 −0.926003 −0.463002 0.886357i $$-0.653228\pi$$
−0.463002 + 0.886357i $$0.653228\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0.464102i 0.0225122i
$$426$$ 0 0
$$427$$ −5.07180 4.39230i −0.245441 0.212559i
$$428$$ 0 0
$$429$$ −41.7846 −2.01738
$$430$$ 0 0
$$431$$ 17.5885i 0.847206i −0.905848 0.423603i $$-0.860765\pi$$
0.905848 0.423603i $$-0.139235\pi$$
$$432$$ 0 0
$$433$$ 4.14359i 0.199128i −0.995031 0.0995642i $$-0.968255\pi$$
0.995031 0.0995642i $$-0.0317449\pi$$
$$434$$ 0 0
$$435$$ 10.2679i 0.492310i
$$436$$ 0 0
$$437$$ 32.7846i 1.56830i
$$438$$ 0 0
$$439$$ 15.7128 0.749932 0.374966 0.927039i $$-0.377654\pi$$
0.374966 + 0.927039i $$0.377654\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 26.0000i 1.23530i −0.786454 0.617649i $$-0.788085\pi$$
0.786454 0.617649i $$-0.211915\pi$$
$$444$$ 0 0
$$445$$ −9.46410 −0.448641
$$446$$ 0 0
$$447$$ 29.3205 1.38681
$$448$$ 0 0
$$449$$ −1.92820 −0.0909975 −0.0454988 0.998964i $$-0.514488\pi$$
−0.0454988 + 0.998964i $$0.514488\pi$$
$$450$$ 0 0
$$451$$ −12.9282 −0.608765
$$452$$ 0 0
$$453$$ 8.32051i 0.390932i
$$454$$ 0 0
$$455$$ 11.1962 12.9282i 0.524884 0.606084i
$$456$$ 0 0
$$457$$ 27.4641 1.28472 0.642358 0.766405i $$-0.277956\pi$$
0.642358 + 0.766405i $$0.277956\pi$$
$$458$$ 0 0
$$459$$ 2.41154i 0.112561i
$$460$$ 0 0
$$461$$ 27.7128i 1.29071i 0.763881 + 0.645357i $$0.223291\pi$$
−0.763881 + 0.645357i $$0.776709\pi$$
$$462$$ 0 0
$$463$$ 4.39230i 0.204128i −0.994778 0.102064i $$-0.967455\pi$$
0.994778 0.102064i $$-0.0325446\pi$$
$$464$$ 0 0
$$465$$ 10.3923i 0.481932i
$$466$$ 0 0
$$467$$ 22.5167 1.04195 0.520973 0.853573i $$-0.325569\pi$$
0.520973 + 0.853573i $$0.325569\pi$$
$$468$$ 0 0
$$469$$ 6.92820 + 6.00000i 0.319915 + 0.277054i
$$470$$ 0 0
$$471$$ 34.3923i 1.58471i
$$472$$ 0 0
$$473$$ −7.46410 −0.343200
$$474$$ 0 0
$$475$$ 6.00000 0.275299
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −37.1769 −1.69866 −0.849328 0.527865i $$-0.822993\pi$$
−0.849328 + 0.527865i $$0.822993\pi$$
$$480$$ 0 0
$$481$$ 16.3923i 0.747425i
$$482$$ 0 0
$$483$$ −18.9282 16.3923i −0.861263 0.745876i
$$484$$ 0 0
$$485$$ −7.39230 −0.335667
$$486$$ 0 0
$$487$$ 28.7846i 1.30436i −0.758066 0.652178i $$-0.773856\pi$$
0.758066 0.652178i $$-0.226144\pi$$
$$488$$ 0 0
$$489$$ 36.0000i 1.62798i
$$490$$ 0 0
$$491$$ 34.1244i 1.54001i −0.638037 0.770005i $$-0.720254\pi$$
0.638037 0.770005i $$-0.279746\pi$$
$$492$$ 0 0
$$493$$ 2.75129i 0.123912i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −1.07180 0.928203i −0.0480767 0.0416356i
$$498$$ 0 0
$$499$$ 5.58846i 0.250174i −0.992146 0.125087i $$-0.960079\pi$$
0.992146 0.125087i $$-0.0399210\pi$$
$$500$$ 0 0
$$501$$ −9.00000 −0.402090
$$502$$ 0 0
$$503$$ 15.5885 0.695055 0.347527 0.937670i $$-0.387021\pi$$
0.347527 + 0.937670i $$0.387021\pi$$
$$504$$ 0 0
$$505$$ −8.53590 −0.379842
$$506$$ 0 0
$$507$$ 49.8564 2.21420
$$508$$ 0 0
$$509$$ 1.85641i 0.0822838i 0.999153 + 0.0411419i $$0.0130996\pi$$
−0.999153 + 0.0411419i $$0.986900\pi$$
$$510$$ 0 0
$$511$$ −1.85641 1.60770i −0.0821226 0.0711202i
$$512$$ 0 0
$$513$$ −31.1769 −1.37649
$$514$$ 0 0
$$515$$ 17.1962i 0.757753i
$$516$$ 0 0
$$517$$ 6.46410i 0.284291i
$$518$$ 0 0
$$519$$ 35.1962i 1.54494i
$$520$$ 0 0
$$521$$ 34.3923i 1.50675i 0.657589 + 0.753377i $$0.271576\pi$$
−0.657589 + 0.753377i $$0.728424\pi$$
$$522$$ 0 0
$$523$$ −24.2487 −1.06032 −0.530161 0.847897i $$-0.677869\pi$$
−0.530161 + 0.847897i $$0.677869\pi$$
$$524$$ 0 0
$$525$$ 3.00000 3.46410i 0.130931 0.151186i
$$526$$ 0 0
$$527$$ 2.78461i 0.121300i
$$528$$ 0 0
$$529$$ −6.85641 −0.298105
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 22.3923 0.969918
$$534$$ 0 0
$$535$$ −18.3923 −0.795169
$$536$$ 0 0
$$537$$ 24.9282i 1.07573i
$$538$$ 0 0
$$539$$ 25.8564 3.73205i 1.11371 0.160751i
$$540$$ 0 0
$$541$$ 33.7846 1.45251 0.726257 0.687423i $$-0.241258\pi$$
0.726257 + 0.687423i $$0.241258\pi$$
$$542$$ 0 0
$$543$$ 22.3923i 0.960946i
$$544$$ 0 0
$$545$$ 15.9282i 0.682289i
$$546$$ 0 0
$$547$$ 14.5359i 0.621510i 0.950490 + 0.310755i $$0.100582\pi$$
−0.950490 + 0.310755i $$0.899418\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −35.5692 −1.51530
$$552$$ 0 0
$$553$$ 5.32051 + 4.60770i 0.226251 + 0.195939i
$$554$$ 0 0
$$555$$ 4.39230i 0.186443i
$$556$$ 0 0
$$557$$ −5.85641 −0.248144 −0.124072 0.992273i $$-0.539595\pi$$
−0.124072 + 0.992273i $$0.539595\pi$$
$$558$$ 0 0
$$559$$ 12.9282 0.546805
$$560$$ 0 0
$$561$$ 3.00000 0.126660
$$562$$ 0 0
$$563$$ 43.1769 1.81969 0.909845 0.414948i $$-0.136200\pi$$
0.909845 + 0.414948i $$0.136200\pi$$
$$564$$ 0 0
$$565$$ 1.46410i 0.0615952i
$$566$$ 0 0
$$567$$ −15.5885 + 18.0000i −0.654654 + 0.755929i
$$568$$ 0 0
$$569$$ 20.9282 0.877356 0.438678 0.898644i $$-0.355447\pi$$
0.438678 + 0.898644i $$0.355447\pi$$
$$570$$ 0 0
$$571$$ 41.3205i 1.72921i −0.502453 0.864605i $$-0.667569\pi$$
0.502453 0.864605i $$-0.332431\pi$$
$$572$$ 0 0
$$573$$ 5.53590i 0.231265i
$$574$$ 0 0
$$575$$ 5.46410i 0.227869i
$$576$$ 0 0
$$577$$ 1.39230i 0.0579624i −0.999580 0.0289812i $$-0.990774\pi$$
0.999580 0.0289812i $$-0.00922630\pi$$
$$578$$ 0 0
$$579$$ 4.39230 0.182538
$$580$$ 0 0
$$581$$ −14.7846 + 17.0718i −0.613369 + 0.708257i
$$582$$ 0 0
$$583$$ 7.46410i 0.309132i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 27.4641 1.13356 0.566782 0.823868i $$-0.308188\pi$$
0.566782 + 0.823868i $$0.308188\pi$$
$$588$$ 0 0
$$589$$ 36.0000 1.48335
$$590$$ 0 0
$$591$$ 36.9282 1.51902
$$592$$ 0 0
$$593$$ 23.5359i 0.966504i 0.875481 + 0.483252i $$0.160544\pi$$
−0.875481 + 0.483252i $$0.839456\pi$$
$$594$$ 0 0
$$595$$ −0.803848 + 0.928203i −0.0329545 + 0.0380526i
$$596$$ 0 0
$$597$$ 6.00000 0.245564
$$598$$ 0 0
$$599$$ 14.1244i 0.577106i −0.957464 0.288553i $$-0.906826\pi$$
0.957464 0.288553i $$-0.0931741\pi$$
$$600$$ 0 0
$$601$$ 26.7846i 1.09257i 0.837600 + 0.546284i $$0.183958\pi$$
−0.837600 + 0.546284i $$0.816042\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 2.92820i 0.119048i
$$606$$ 0 0
$$607$$ −18.8038 −0.763225 −0.381612 0.924322i $$-0.624631\pi$$
−0.381612 + 0.924322i $$0.624631\pi$$
$$608$$ 0 0
$$609$$ −17.7846 + 20.5359i −0.720669 + 0.832157i
$$610$$ 0 0
$$611$$ 11.1962i 0.452948i
$$612$$ 0 0
$$613$$ 10.0000 0.403896 0.201948 0.979396i $$-0.435273\pi$$
0.201948 + 0.979396i $$0.435273\pi$$
$$614$$ 0 0
$$615$$ 6.00000 0.241943
$$616$$ 0 0
$$617$$ −9.07180 −0.365217 −0.182608 0.983186i $$-0.558454\pi$$
−0.182608 + 0.983186i $$0.558454\pi$$
$$618$$ 0 0
$$619$$ −35.3205 −1.41965 −0.709826 0.704378i $$-0.751226\pi$$
−0.709826 + 0.704378i $$0.751226\pi$$
$$620$$ 0 0
$$621$$ 28.3923i 1.13934i
$$622$$ 0 0
$$623$$ 18.9282 + 16.3923i 0.758342 + 0.656744i
$$624$$ 0 0
$$625$$ 1.00000 0.0400000
$$626$$ 0 0
$$627$$ 38.7846i 1.54891i
$$628$$ 0 0
$$629$$ 1.17691i 0.0469267i
$$630$$ 0 0
$$631$$ 26.9090i 1.07123i 0.844463 + 0.535614i $$0.179920\pi$$
−0.844463 + 0.535614i $$0.820080\pi$$
$$632$$ 0 0
$$633$$ 12.4641i 0.495404i
$$634$$ 0 0
$$635$$ −8.53590 −0.338737
$$636$$ 0 0
$$637$$ −44.7846 + 6.46410i −1.77443 + 0.256117i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −4.92820 −0.194652 −0.0973262 0.995253i $$-0.531029\pi$$
−0.0973262 + 0.995253i $$0.531029\pi$$
$$642$$ 0 0
$$643$$ 31.0526 1.22459 0.612297 0.790628i $$-0.290246\pi$$
0.612297 + 0.790628i $$0.290246\pi$$
$$644$$ 0 0
$$645$$ 3.46410 0.136399
$$646$$ 0 0
$$647$$ 10.3923 0.408564 0.204282 0.978912i $$-0.434514\pi$$
0.204282 + 0.978912i $$0.434514\pi$$
$$648$$ 0 0
$$649$$ 12.9282i 0.507476i
$$650$$ 0 0
$$651$$ 18.0000 20.7846i 0.705476 0.814613i
$$652$$ 0 0
$$653$$ −38.3923 −1.50241 −0.751203 0.660071i $$-0.770526\pi$$
−0.751203 + 0.660071i $$0.770526\pi$$
$$654$$ 0 0
$$655$$ 9.46410i 0.369793i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 20.8038i 0.810403i −0.914227 0.405201i $$-0.867201\pi$$
0.914227 0.405201i $$-0.132799\pi$$
$$660$$ 0 0
$$661$$ 15.7128i 0.611158i 0.952167 + 0.305579i $$0.0988499\pi$$
−0.952167 + 0.305579i $$0.901150\pi$$
$$662$$ 0 0
$$663$$ −5.19615 −0.201802
$$664$$ 0 0
$$665$$ −12.0000 10.3923i −0.465340 0.402996i
$$666$$ 0 0
$$667$$ 32.3923i 1.25424i
$$668$$ 0 0
$$669$$ 17.7846 0.687593
$$670$$ 0 0
$$671$$ 9.46410 0.365358
$$672$$ 0 0
$$673$$ 49.1769 1.89563 0.947815 0.318820i $$-0.103286\pi$$
0.947815 + 0.318820i $$0.103286\pi$$
$$674$$ 0 0
$$675$$ −5.19615 −0.200000
$$676$$ 0 0
$$677$$ 4.60770i 0.177088i 0.996072 + 0.0885441i $$0.0282214\pi$$
−0.996072 + 0.0885441i $$0.971779\pi$$
$$678$$ 0 0
$$679$$ 14.7846 + 12.8038i 0.567381 + 0.491367i
$$680$$ 0 0
$$681$$ 5.78461 0.221667
$$682$$ 0 0
$$683$$ 27.3205i 1.04539i −0.852520 0.522695i $$-0.824927\pi$$
0.852520 0.522695i $$-0.175073\pi$$
$$684$$ 0 0
$$685$$ 0.392305i 0.0149892i
$$686$$ 0 0
$$687$$ 26.7846i 1.02190i
$$688$$ 0 0
$$689$$ 12.9282i 0.492525i
$$690$$ 0 0
$$691$$ −46.6410 −1.77431 −0.887154 0.461474i $$-0.847321\pi$$
−0.887154 + 0.461474i $$0.847321\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 6.92820i 0.262802i
$$696$$ 0 0
$$697$$ −1.60770 −0.0608958
$$698$$ 0 0
$$699$$ 39.7128 1.50208
$$700$$ 0 0
$$701$$ −3.78461 −0.142943 −0.0714714 0.997443i $$-0.522769\pi$$
−0.0714714 + 0.997443i $$0.522769\pi$$
$$702$$ 0 0
$$703$$ −15.2154 −0.573859
$$704$$ 0 0
$$705$$ 3.00000i 0.112987i
$$706$$ 0 0
$$707$$ 17.0718 + 14.7846i 0.642051 + 0.556032i
$$708$$ 0 0
$$709$$ −21.0000 −0.788672 −0.394336 0.918966i $$-0.629025\pi$$
−0.394336 + 0.918966i $$0.629025\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 32.7846i 1.22779i
$$714$$ 0 0
$$715$$ 24.1244i 0.902200i
$$716$$ 0 0
$$717$$ 48.4641i 1.80993i
$$718$$ 0 0
$$719$$ 45.4641 1.69552 0.847762 0.530376i $$-0.177949\pi$$
0.847762 + 0.530376i $$0.177949\pi$$
$$720$$ 0 0
$$721$$ −29.7846 + 34.3923i −1.10924 + 1.28084i
$$722$$ 0 0
$$723$$ 7.60770i 0.282933i
$$724$$ 0 0
$$725$$ −5.92820 −0.220168
$$726$$ 0 0
$$727$$ −34.3923 −1.27554 −0.637770 0.770227i $$-0.720143\pi$$
−0.637770 + 0.770227i $$0.720143\pi$$
$$728$$ 0 0
$$729$$ 27.0000 1.00000
$$730$$ 0 0
$$731$$ −0.928203 −0.0343308
$$732$$ 0 0
$$733$$ 18.4641i 0.681987i −0.940066 0.340994i $$-0.889237\pi$$
0.940066 0.340994i $$-0.110763\pi$$
$$734$$ 0 0
$$735$$ −12.0000 + 1.73205i −0.442627 + 0.0638877i
$$736$$ 0 0
$$737$$ −12.9282 −0.476216
$$738$$ 0 0
$$739$$ 7.73205i 0.284428i −0.989836 0.142214i $$-0.954578\pi$$
0.989836 0.142214i $$-0.0454221\pi$$
$$740$$ 0 0
$$741$$ 67.1769i 2.46781i
$$742$$ 0 0
$$743$$ 9.60770i 0.352472i −0.984348 0.176236i $$-0.943608\pi$$
0.984348 0.176236i $$-0.0563922\pi$$
$$744$$ 0 0
$$745$$ 16.9282i 0.620201i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 36.7846 + 31.8564i 1.34408 + 1.16401i
$$750$$ 0 0
$$751$$ 5.58846i 0.203926i −0.994788 0.101963i $$-0.967488\pi$$
0.994788 0.101963i $$-0.0325123\pi$$
$$752$$ 0 0
$$753$$ 3.21539 0.117175
$$754$$ 0 0
$$755$$ 4.80385 0.174830
$$756$$ 0 0
$$757$$ −10.1436 −0.368675 −0.184338 0.982863i $$-0.559014\pi$$
−0.184338 + 0.982863i $$0.559014\pi$$
$$758$$ 0 0
$$759$$ 35.3205 1.28205
$$760$$ 0 0
$$761$$ 6.24871i 0.226516i 0.993566 + 0.113258i $$0.0361286\pi$$
−0.993566 + 0.113258i $$0.963871\pi$$
$$762$$ 0 0
$$763$$ −27.5885 + 31.8564i −0.998769 + 1.15328i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 22.3923i 0.808539i
$$768$$ 0 0
$$769$$ 18.0000i 0.649097i 0.945869 + 0.324548i $$0.105212\pi$$
−0.945869 + 0.324548i $$0.894788\pi$$
$$770$$ 0 0
$$771$$ 10.3923i 0.374270i
$$772$$ 0 0
$$773$$ 12.4641i 0.448303i 0.974554 + 0.224151i $$0.0719610\pi$$
−0.974554 + 0.224151i $$0.928039\pi$$
$$774$$ 0 0
$$775$$ 6.00000 0.215526
$$776$$ 0 0
$$777$$ −7.60770 + 8.78461i −0.272925 + 0.315146i
$$778$$ 0 0
$$779$$ 20.7846i 0.744686i
$$780$$ 0 0
$$781$$ 2.00000 0.0715656
$$782$$ 0 0
$$783$$ 30.8038 1.10084
$$784$$ 0 0
$$785$$ −19.8564 −0.708706
$$786$$ 0 0
$$787$$ −15.3397 −0.546803 −0.273401 0.961900i $$-0.588149\pi$$
−0.273401 + 0.961900i $$0.588149\pi$$
$$788$$ 0 0
$$789$$ 7.85641i 0.279695i
$$790$$ 0 0
$$791$$ −2.53590 + 2.92820i −0.0901662 + 0.104115i
$$792$$ 0 0
$$793$$ −16.3923 −0.582108
$$794$$ 0 0
$$795$$ 3.46410i 0.122859i
$$796$$ 0 0
$$797$$ 40.1769i 1.42314i −0.702616 0.711570i $$-0.747985\pi$$
0.702616 0.711570i $$-0.252015\pi$$