# Properties

 Label 880.2.b.j.529.6 Level $880$ Weight $2$ Character 880.529 Analytic conductor $7.027$ Analytic rank $0$ Dimension $8$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(529,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("880.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$880 = 2^{4} \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 880.b (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: $$7.02683537787$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.47985531136.2 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} + 19x^{6} + 91x^{4} + 45x^{2} + 4$$ x^8 + 19*x^6 + 91*x^4 + 45*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{5}$$ Twist minimal: no (minimal twist has level 440) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 529.6 Root $$0.655762i$$ of defining polynomial Character $$\chi$$ $$=$$ 880.529 Dual form 880.2.b.j.529.3

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+0.655762i q^{3} +(-2.23285 - 0.119978i) q^{5} +0.415806i q^{7} +2.56998 q^{9} +O(q^{10})$$ $$q+0.655762i q^{3} +(-2.23285 - 0.119978i) q^{5} +0.415806i q^{7} +2.56998 q^{9} -1.00000 q^{11} -4.00000i q^{13} +(0.0786769 - 1.46422i) q^{15} -6.51558i q^{17} +5.20406 q^{19} -0.272670 q^{21} +8.54830i q^{23} +(4.97121 + 0.535784i) q^{25} +3.65258i q^{27} -0.895717 q^{29} +6.73836 q^{31} -0.655762i q^{33} +(0.0498875 - 0.928432i) q^{35} +8.96410i q^{37} +2.62305 q^{39} +10.0998 q^{41} -4.78825i q^{43} +(-5.73836 - 0.308340i) q^{45} -5.61986i q^{47} +6.82711 q^{49} +4.27267 q^{51} -10.0357i q^{53} +(2.23285 + 0.119978i) q^{55} +3.41262i q^{57} -1.63408 q^{59} +7.10428 q^{61} +1.06861i q^{63} +(-0.479911 + 8.93139i) q^{65} -10.6914i q^{67} -5.60565 q^{69} +6.19302 q^{71} -3.16839i q^{73} +(-0.351347 + 3.25993i) q^{75} -0.415806i q^{77} -11.2682 q^{79} +5.31471 q^{81} +16.2429i q^{83} +(-0.781725 + 14.5483i) q^{85} -0.587377i q^{87} -9.56998 q^{89} +1.66323 q^{91} +4.41876i q^{93} +(-11.6199 - 0.624371i) q^{95} +0.591657i q^{97} -2.56998 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q - 14 q^{9}+O(q^{10})$$ 8 * q - 14 * q^9 $$8 q - 14 q^{9} - 8 q^{11} + 12 q^{15} - 18 q^{19} - 14 q^{21} - 2 q^{25} - 6 q^{29} + 30 q^{31} - 30 q^{35} + 8 q^{39} + 20 q^{41} - 22 q^{45} - 18 q^{49} + 46 q^{51} + 12 q^{59} + 58 q^{61} - 8 q^{65} + 60 q^{69} + 2 q^{71} - 26 q^{75} - 40 q^{79} + 88 q^{81} - 26 q^{85} - 42 q^{89} - 8 q^{91} - 28 q^{95} + 14 q^{99}+O(q^{100})$$ 8 * q - 14 * q^9 - 8 * q^11 + 12 * q^15 - 18 * q^19 - 14 * q^21 - 2 * q^25 - 6 * q^29 + 30 * q^31 - 30 * q^35 + 8 * q^39 + 20 * q^41 - 22 * q^45 - 18 * q^49 + 46 * q^51 + 12 * q^59 + 58 * q^61 - 8 * q^65 + 60 * q^69 + 2 * q^71 - 26 * q^75 - 40 * q^79 + 88 * q^81 - 26 * q^85 - 42 * q^89 - 8 * q^91 - 28 * q^95 + 14 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$$.

 $$n$$ $$111$$ $$177$$ $$321$$ $$661$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$1$$

## 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
$$3$$ 0.655762i 0.378604i 0.981919 + 0.189302i $$0.0606226\pi$$
−0.981919 + 0.189302i $$0.939377\pi$$
$$4$$ 0 0
$$5$$ −2.23285 0.119978i −0.998559 0.0536557i
$$6$$ 0 0
$$7$$ 0.415806i 0.157160i 0.996908 + 0.0785800i $$0.0250386\pi$$
−0.996908 + 0.0785800i $$0.974961\pi$$
$$8$$ 0 0
$$9$$ 2.56998 0.856659
$$10$$ 0 0
$$11$$ −1.00000 −0.301511
$$12$$ 0 0
$$13$$ 4.00000i 1.10940i −0.832050 0.554700i $$-0.812833\pi$$
0.832050 0.554700i $$-0.187167\pi$$
$$14$$ 0 0
$$15$$ 0.0786769 1.46422i 0.0203143 0.378059i
$$16$$ 0 0
$$17$$ 6.51558i 1.58026i −0.612939 0.790130i $$-0.710013\pi$$
0.612939 0.790130i $$-0.289987\pi$$
$$18$$ 0 0
$$19$$ 5.20406 1.19389 0.596946 0.802281i $$-0.296381\pi$$
0.596946 + 0.802281i $$0.296381\pi$$
$$20$$ 0 0
$$21$$ −0.272670 −0.0595015
$$22$$ 0 0
$$23$$ 8.54830i 1.78244i 0.453568 + 0.891221i $$0.350151\pi$$
−0.453568 + 0.891221i $$0.649849\pi$$
$$24$$ 0 0
$$25$$ 4.97121 + 0.535784i 0.994242 + 0.107157i
$$26$$ 0 0
$$27$$ 3.65258i 0.702939i
$$28$$ 0 0
$$29$$ −0.895717 −0.166331 −0.0831653 0.996536i $$-0.526503\pi$$
−0.0831653 + 0.996536i $$0.526503\pi$$
$$30$$ 0 0
$$31$$ 6.73836 1.21025 0.605123 0.796132i $$-0.293124\pi$$
0.605123 + 0.796132i $$0.293124\pi$$
$$32$$ 0 0
$$33$$ 0.655762i 0.114153i
$$34$$ 0 0
$$35$$ 0.0498875 0.928432i 0.00843253 0.156934i
$$36$$ 0 0
$$37$$ 8.96410i 1.47369i 0.676062 + 0.736845i $$0.263685\pi$$
−0.676062 + 0.736845i $$0.736315\pi$$
$$38$$ 0 0
$$39$$ 2.62305 0.420024
$$40$$ 0 0
$$41$$ 10.0998 1.57732 0.788660 0.614830i $$-0.210775\pi$$
0.788660 + 0.614830i $$0.210775\pi$$
$$42$$ 0 0
$$43$$ 4.78825i 0.730201i −0.930968 0.365101i $$-0.881035\pi$$
0.930968 0.365101i $$-0.118965\pi$$
$$44$$ 0 0
$$45$$ −5.73836 0.308340i −0.855425 0.0459646i
$$46$$ 0 0
$$47$$ 5.61986i 0.819741i −0.912144 0.409871i $$-0.865574\pi$$
0.912144 0.409871i $$-0.134426\pi$$
$$48$$ 0 0
$$49$$ 6.82711 0.975301
$$50$$ 0 0
$$51$$ 4.27267 0.598293
$$52$$ 0 0
$$53$$ 10.0357i 1.37851i −0.724521 0.689253i $$-0.757939\pi$$
0.724521 0.689253i $$-0.242061\pi$$
$$54$$ 0 0
$$55$$ 2.23285 + 0.119978i 0.301077 + 0.0161778i
$$56$$ 0 0
$$57$$ 3.41262i 0.452013i
$$58$$ 0 0
$$59$$ −1.63408 −0.212739 −0.106370 0.994327i $$-0.533923\pi$$
−0.106370 + 0.994327i $$0.533923\pi$$
$$60$$ 0 0
$$61$$ 7.10428 0.909610 0.454805 0.890591i $$-0.349709\pi$$
0.454805 + 0.890591i $$0.349709\pi$$
$$62$$ 0 0
$$63$$ 1.06861i 0.134633i
$$64$$ 0 0
$$65$$ −0.479911 + 8.93139i −0.0595257 + 1.10780i
$$66$$ 0 0
$$67$$ 10.6914i 1.30617i −0.757286 0.653083i $$-0.773475\pi$$
0.757286 0.653083i $$-0.226525\pi$$
$$68$$ 0 0
$$69$$ −5.60565 −0.674841
$$70$$ 0 0
$$71$$ 6.19302 0.734977 0.367488 0.930028i $$-0.380218\pi$$
0.367488 + 0.930028i $$0.380218\pi$$
$$72$$ 0 0
$$73$$ 3.16839i 0.370832i −0.982660 0.185416i $$-0.940637\pi$$
0.982660 0.185416i $$-0.0593632\pi$$
$$74$$ 0 0
$$75$$ −0.351347 + 3.25993i −0.0405700 + 0.376424i
$$76$$ 0 0
$$77$$ 0.415806i 0.0473855i
$$78$$ 0 0
$$79$$ −11.2682 −1.26777 −0.633884 0.773428i $$-0.718540\pi$$
−0.633884 + 0.773428i $$0.718540\pi$$
$$80$$ 0 0
$$81$$ 5.31471 0.590523
$$82$$ 0 0
$$83$$ 16.2429i 1.78289i 0.453128 + 0.891446i $$0.350308\pi$$
−0.453128 + 0.891446i $$0.649692\pi$$
$$84$$ 0 0
$$85$$ −0.781725 + 14.5483i −0.0847900 + 1.57798i
$$86$$ 0 0
$$87$$ 0.587377i 0.0629735i
$$88$$ 0 0
$$89$$ −9.56998 −1.01442 −0.507208 0.861824i $$-0.669322\pi$$
−0.507208 + 0.861824i $$0.669322\pi$$
$$90$$ 0 0
$$91$$ 1.66323 0.174353
$$92$$ 0 0
$$93$$ 4.41876i 0.458204i
$$94$$ 0 0
$$95$$ −11.6199 0.624371i −1.19217 0.0640591i
$$96$$ 0 0
$$97$$ 0.591657i 0.0600737i 0.999549 + 0.0300368i $$0.00956246\pi$$
−0.999549 + 0.0300368i $$0.990438\pi$$
$$98$$ 0 0
$$99$$ −2.56998 −0.258292
$$100$$ 0 0
$$101$$ −4.62305 −0.460010 −0.230005 0.973189i $$-0.573874\pi$$
−0.230005 + 0.973189i $$0.573874\pi$$
$$102$$ 0 0
$$103$$ 8.24291i 0.812198i −0.913829 0.406099i $$-0.866889\pi$$
0.913829 0.406099i $$-0.133111\pi$$
$$104$$ 0 0
$$105$$ 0.608830 + 0.0327143i 0.0594157 + 0.00319259i
$$106$$ 0 0
$$107$$ 17.6199i 1.70338i −0.524049 0.851688i $$-0.675579\pi$$
0.524049 0.851688i $$-0.324421\pi$$
$$108$$ 0 0
$$109$$ −3.66323 −0.350873 −0.175437 0.984491i $$-0.556134\pi$$
−0.175437 + 0.984491i $$0.556134\pi$$
$$110$$ 0 0
$$111$$ −5.87832 −0.557945
$$112$$ 0 0
$$113$$ 11.4797i 1.07992i 0.841691 + 0.539959i $$0.181560\pi$$
−0.841691 + 0.539959i $$0.818440\pi$$
$$114$$ 0 0
$$115$$ 1.02561 19.0870i 0.0956382 1.77988i
$$116$$ 0 0
$$117$$ 10.2799i 0.950378i
$$118$$ 0 0
$$119$$ 2.70922 0.248354
$$120$$ 0 0
$$121$$ 1.00000 0.0909091
$$122$$ 0 0
$$123$$ 6.62305i 0.597180i
$$124$$ 0 0
$$125$$ −11.0357 1.79276i −0.987060 0.160349i
$$126$$ 0 0
$$127$$ 9.13995i 0.811040i 0.914086 + 0.405520i $$0.132909\pi$$
−0.914086 + 0.405520i $$0.867091\pi$$
$$128$$ 0 0
$$129$$ 3.13995 0.276457
$$130$$ 0 0
$$131$$ 2.48123 0.216787 0.108393 0.994108i $$-0.465429\pi$$
0.108393 + 0.994108i $$0.465429\pi$$
$$132$$ 0 0
$$133$$ 2.16388i 0.187632i
$$134$$ 0 0
$$135$$ 0.438228 8.15565i 0.0377167 0.701926i
$$136$$ 0 0
$$137$$ 7.40834i 0.632937i 0.948603 + 0.316469i $$0.102497\pi$$
−0.948603 + 0.316469i $$0.897503\pi$$
$$138$$ 0 0
$$139$$ −1.69166 −0.143485 −0.0717424 0.997423i $$-0.522856\pi$$
−0.0717424 + 0.997423i $$0.522856\pi$$
$$140$$ 0 0
$$141$$ 3.68529 0.310358
$$142$$ 0 0
$$143$$ 4.00000i 0.334497i
$$144$$ 0 0
$$145$$ 2.00000 + 0.107466i 0.166091 + 0.00892458i
$$146$$ 0 0
$$147$$ 4.47696i 0.369253i
$$148$$ 0 0
$$149$$ −3.74940 −0.307163 −0.153581 0.988136i $$-0.549081\pi$$
−0.153581 + 0.988136i $$0.549081\pi$$
$$150$$ 0 0
$$151$$ 15.1400 1.23207 0.616036 0.787718i $$-0.288738\pi$$
0.616036 + 0.787718i $$0.288738\pi$$
$$152$$ 0 0
$$153$$ 16.7449i 1.35374i
$$154$$ 0 0
$$155$$ −15.0457 0.808454i −1.20850 0.0649366i
$$156$$ 0 0
$$157$$ 11.5871i 0.924755i 0.886683 + 0.462378i $$0.153004\pi$$
−0.886683 + 0.462378i $$0.846996\pi$$
$$158$$ 0 0
$$159$$ 6.58101 0.521908
$$160$$ 0 0
$$161$$ −3.55444 −0.280129
$$162$$ 0 0
$$163$$ 6.82392i 0.534491i 0.963629 + 0.267245i $$0.0861134\pi$$
−0.963629 + 0.267245i $$0.913887\pi$$
$$164$$ 0 0
$$165$$ −0.0786769 + 1.46422i −0.00612499 + 0.113989i
$$166$$ 0 0
$$167$$ 7.10428i 0.549746i −0.961481 0.274873i $$-0.911364\pi$$
0.961481 0.274873i $$-0.0886358\pi$$
$$168$$ 0 0
$$169$$ −3.00000 −0.230769
$$170$$ 0 0
$$171$$ 13.3743 1.02276
$$172$$ 0 0
$$173$$ 9.31152i 0.707942i −0.935256 0.353971i $$-0.884831\pi$$
0.935256 0.353971i $$-0.115169\pi$$
$$174$$ 0 0
$$175$$ −0.222782 + 2.06706i −0.0168408 + 0.156255i
$$176$$ 0 0
$$177$$ 1.07157i 0.0805440i
$$178$$ 0 0
$$179$$ −26.6368 −1.99093 −0.995464 0.0951359i $$-0.969671\pi$$
−0.995464 + 0.0951359i $$0.969671\pi$$
$$180$$ 0 0
$$181$$ 1.01103 0.0751495 0.0375748 0.999294i $$-0.488037\pi$$
0.0375748 + 0.999294i $$0.488037\pi$$
$$182$$ 0 0
$$183$$ 4.65872i 0.344382i
$$184$$ 0 0
$$185$$ 1.07549 20.0155i 0.0790718 1.47157i
$$186$$ 0 0
$$187$$ 6.51558i 0.476466i
$$188$$ 0 0
$$189$$ −1.51877 −0.110474
$$190$$ 0 0
$$191$$ −10.5655 −0.764490 −0.382245 0.924061i $$-0.624849\pi$$
−0.382245 + 0.924061i $$0.624849\pi$$
$$192$$ 0 0
$$193$$ 11.8271i 0.851334i −0.904880 0.425667i $$-0.860040\pi$$
0.904880 0.425667i $$-0.139960\pi$$
$$194$$ 0 0
$$195$$ −5.85686 0.314707i −0.419419 0.0225367i
$$196$$ 0 0
$$197$$ 1.31152i 0.0934422i −0.998908 0.0467211i $$-0.985123\pi$$
0.998908 0.0467211i $$-0.0148772\pi$$
$$198$$ 0 0
$$199$$ −11.8271 −0.838401 −0.419201 0.907894i $$-0.637690\pi$$
−0.419201 + 0.907894i $$0.637690\pi$$
$$200$$ 0 0
$$201$$ 7.01103 0.494520
$$202$$ 0 0
$$203$$ 0.372445i 0.0261405i
$$204$$ 0 0
$$205$$ −22.5513 1.21175i −1.57505 0.0846322i
$$206$$ 0 0
$$207$$ 21.9689i 1.52695i
$$208$$ 0 0
$$209$$ −5.20406 −0.359972
$$210$$ 0 0
$$211$$ 8.37244 0.576383 0.288191 0.957573i $$-0.406946\pi$$
0.288191 + 0.957573i $$0.406946\pi$$
$$212$$ 0 0
$$213$$ 4.06115i 0.278265i
$$214$$ 0 0
$$215$$ −0.574484 + 10.6914i −0.0391795 + 0.729150i
$$216$$ 0 0
$$217$$ 2.80185i 0.190202i
$$218$$ 0 0
$$219$$ 2.07771 0.140398
$$220$$ 0 0
$$221$$ −26.0623 −1.75314
$$222$$ 0 0
$$223$$ 22.1461i 1.48301i −0.670946 0.741506i $$-0.734112\pi$$
0.670946 0.741506i $$-0.265888\pi$$
$$224$$ 0 0
$$225$$ 12.7759 + 1.37695i 0.851726 + 0.0917968i
$$226$$ 0 0
$$227$$ 21.8194i 1.44821i 0.689692 + 0.724103i $$0.257746\pi$$
−0.689692 + 0.724103i $$0.742254\pi$$
$$228$$ 0 0
$$229$$ −2.80247 −0.185192 −0.0925962 0.995704i $$-0.529517\pi$$
−0.0925962 + 0.995704i $$0.529517\pi$$
$$230$$ 0 0
$$231$$ 0.272670 0.0179404
$$232$$ 0 0
$$233$$ 8.24424i 0.540098i −0.962847 0.270049i $$-0.912960\pi$$
0.962847 0.270049i $$-0.0870399\pi$$
$$234$$ 0 0
$$235$$ −0.674259 + 12.5483i −0.0439838 + 0.818561i
$$236$$ 0 0
$$237$$ 7.38923i 0.479982i
$$238$$ 0 0
$$239$$ −11.2682 −0.728877 −0.364438 0.931227i $$-0.618739\pi$$
−0.364438 + 0.931227i $$0.618739\pi$$
$$240$$ 0 0
$$241$$ 22.3860 1.44201 0.721006 0.692929i $$-0.243680\pi$$
0.721006 + 0.692929i $$0.243680\pi$$
$$242$$ 0 0
$$243$$ 14.4429i 0.926514i
$$244$$ 0 0
$$245$$ −15.2439 0.819101i −0.973896 0.0523304i
$$246$$ 0 0
$$247$$ 20.8162i 1.32451i
$$248$$ 0 0
$$249$$ −10.6515 −0.675010
$$250$$ 0 0
$$251$$ −3.84265 −0.242546 −0.121273 0.992619i $$-0.538698\pi$$
−0.121273 + 0.992619i $$0.538698\pi$$
$$252$$ 0 0
$$253$$ 8.54830i 0.537427i
$$254$$ 0 0
$$255$$ −9.54022 0.512626i −0.597432 0.0321019i
$$256$$ 0 0
$$257$$ 10.6230i 0.662648i 0.943517 + 0.331324i $$0.107495\pi$$
−0.943517 + 0.331324i $$0.892505\pi$$
$$258$$ 0 0
$$259$$ −3.72733 −0.231605
$$260$$ 0 0
$$261$$ −2.30197 −0.142489
$$262$$ 0 0
$$263$$ 5.79276i 0.357197i 0.983922 + 0.178598i $$0.0571563\pi$$
−0.983922 + 0.178598i $$0.942844\pi$$
$$264$$ 0 0
$$265$$ −1.20406 + 22.4081i −0.0739647 + 1.37652i
$$266$$ 0 0
$$267$$ 6.27563i 0.384062i
$$268$$ 0 0
$$269$$ 8.20857 0.500485 0.250243 0.968183i $$-0.419490\pi$$
0.250243 + 0.968183i $$0.419490\pi$$
$$270$$ 0 0
$$271$$ −27.3111 −1.65903 −0.829515 0.558485i $$-0.811383\pi$$
−0.829515 + 0.558485i $$0.811383\pi$$
$$272$$ 0 0
$$273$$ 1.09068i 0.0660109i
$$274$$ 0 0
$$275$$ −4.97121 0.535784i −0.299775 0.0323090i
$$276$$ 0 0
$$277$$ 14.4735i 0.869631i −0.900520 0.434815i $$-0.856814\pi$$
0.900520 0.434815i $$-0.143186\pi$$
$$278$$ 0 0
$$279$$ 17.3174 1.03677
$$280$$ 0 0
$$281$$ 16.2799 0.971178 0.485589 0.874187i $$-0.338605\pi$$
0.485589 + 0.874187i $$0.338605\pi$$
$$282$$ 0 0
$$283$$ 10.5169i 0.625165i 0.949891 + 0.312583i $$0.101194\pi$$
−0.949891 + 0.312583i $$0.898806\pi$$
$$284$$ 0 0
$$285$$ 0.409439 7.61986i 0.0242531 0.451362i
$$286$$ 0 0
$$287$$ 4.19955i 0.247892i
$$288$$ 0 0
$$289$$ −25.4528 −1.49722
$$290$$ 0 0
$$291$$ −0.387986 −0.0227441
$$292$$ 0 0
$$293$$ 9.37695i 0.547807i 0.961757 + 0.273904i $$0.0883150\pi$$
−0.961757 + 0.273904i $$0.911685\pi$$
$$294$$ 0 0
$$295$$ 3.64865 + 0.196053i 0.212433 + 0.0114147i
$$296$$ 0 0
$$297$$ 3.65258i 0.211944i
$$298$$ 0 0
$$299$$ 34.1932 1.97744
$$300$$ 0 0
$$301$$ 1.99099 0.114758
$$302$$ 0 0
$$303$$ 3.03162i 0.174162i
$$304$$ 0 0
$$305$$ −15.8628 0.852356i −0.908300 0.0488058i
$$306$$ 0 0
$$307$$ 2.09978i 0.119840i −0.998203 0.0599202i $$-0.980915\pi$$
0.998203 0.0599202i $$-0.0190846\pi$$
$$308$$ 0 0
$$309$$ 5.40539 0.307502
$$310$$ 0 0
$$311$$ 20.3724 1.15522 0.577608 0.816314i $$-0.303986\pi$$
0.577608 + 0.816314i $$0.303986\pi$$
$$312$$ 0 0
$$313$$ 23.8968i 1.35073i 0.737485 + 0.675364i $$0.236013\pi$$
−0.737485 + 0.675364i $$0.763987\pi$$
$$314$$ 0 0
$$315$$ 0.128210 2.38605i 0.00722380 0.134439i
$$316$$ 0 0
$$317$$ 5.86114i 0.329195i −0.986361 0.164597i $$-0.947368\pi$$
0.986361 0.164597i $$-0.0526325\pi$$
$$318$$ 0 0
$$319$$ 0.895717 0.0501506
$$320$$ 0 0
$$321$$ 11.5544 0.644906
$$322$$ 0 0
$$323$$ 33.9075i 1.88666i
$$324$$ 0 0
$$325$$ 2.14314 19.8848i 0.118880 1.10301i
$$326$$ 0 0
$$327$$ 2.40220i 0.132842i
$$328$$ 0 0
$$329$$ 2.33677 0.128831
$$330$$ 0 0
$$331$$ 0.574484 0.0315765 0.0157882 0.999875i $$-0.494974\pi$$
0.0157882 + 0.999875i $$0.494974\pi$$
$$332$$ 0 0
$$333$$ 23.0375i 1.26245i
$$334$$ 0 0
$$335$$ −1.28273 + 23.8723i −0.0700833 + 1.30428i
$$336$$ 0 0
$$337$$ 4.10747i 0.223748i −0.993722 0.111874i $$-0.964315\pi$$
0.993722 0.111874i $$-0.0356853\pi$$
$$338$$ 0 0
$$339$$ −7.52794 −0.408862
$$340$$ 0 0
$$341$$ −6.73836 −0.364903
$$342$$ 0 0
$$343$$ 5.74940i 0.310438i
$$344$$ 0 0
$$345$$ 12.5166 + 0.672553i 0.673868 + 0.0362090i
$$346$$ 0 0
$$347$$ 8.30834i 0.446015i 0.974817 + 0.223008i $$0.0715875\pi$$
−0.974817 + 0.223008i $$0.928413\pi$$
$$348$$ 0 0
$$349$$ 18.4858 0.989523 0.494762 0.869029i $$-0.335255\pi$$
0.494762 + 0.869029i $$0.335255\pi$$
$$350$$ 0 0
$$351$$ 14.6103 0.779841
$$352$$ 0 0
$$353$$ 26.5199i 1.41151i −0.708456 0.705755i $$-0.750608\pi$$
0.708456 0.705755i $$-0.249392\pi$$
$$354$$ 0 0
$$355$$ −13.8281 0.743025i −0.733918 0.0394357i
$$356$$ 0 0
$$357$$ 1.77660i 0.0940278i
$$358$$ 0 0
$$359$$ −18.8226 −0.993419 −0.496709 0.867917i $$-0.665459\pi$$
−0.496709 + 0.867917i $$0.665459\pi$$
$$360$$ 0 0
$$361$$ 8.08222 0.425380
$$362$$ 0 0
$$363$$ 0.655762i 0.0344186i
$$364$$ 0 0
$$365$$ −0.380136 + 7.07452i −0.0198972 + 0.370298i
$$366$$ 0 0
$$367$$ 10.2115i 0.533037i 0.963830 + 0.266519i $$0.0858734\pi$$
−0.963830 + 0.266519i $$0.914127\pi$$
$$368$$ 0 0
$$369$$ 25.9562 1.35122
$$370$$ 0 0
$$371$$ 4.17289 0.216646
$$372$$ 0 0
$$373$$ 32.3363i 1.67431i 0.546965 + 0.837156i $$0.315783\pi$$
−0.546965 + 0.837156i $$0.684217\pi$$
$$374$$ 0 0
$$375$$ 1.17562 7.23677i 0.0607089 0.373705i
$$376$$ 0 0
$$377$$ 3.58287i 0.184527i
$$378$$ 0 0
$$379$$ 15.3686 0.789434 0.394717 0.918803i $$-0.370843\pi$$
0.394717 + 0.918803i $$0.370843\pi$$
$$380$$ 0 0
$$381$$ −5.99363 −0.307063
$$382$$ 0 0
$$383$$ 13.6662i 0.698309i −0.937065 0.349155i $$-0.886469\pi$$
0.937065 0.349155i $$-0.113531\pi$$
$$384$$ 0 0
$$385$$ −0.0498875 + 0.928432i −0.00254250 + 0.0473173i
$$386$$ 0 0
$$387$$ 12.3057i 0.625534i
$$388$$ 0 0
$$389$$ 9.01103 0.456878 0.228439 0.973558i $$-0.426638\pi$$
0.228439 + 0.973558i $$0.426638\pi$$
$$390$$ 0 0
$$391$$ 55.6971 2.81672
$$392$$ 0 0
$$393$$ 1.62710i 0.0820763i
$$394$$ 0 0
$$395$$ 25.1601 + 1.35193i 1.26594 + 0.0680229i
$$396$$ 0 0
$$397$$ 3.45466i 0.173384i −0.996235 0.0866922i $$-0.972370\pi$$
0.996235 0.0866922i $$-0.0276297\pi$$
$$398$$ 0 0
$$399$$ −1.41899 −0.0710384
$$400$$ 0 0
$$401$$ −1.62756 −0.0812762 −0.0406381 0.999174i $$-0.512939\pi$$
−0.0406381 + 0.999174i $$0.512939\pi$$
$$402$$ 0 0
$$403$$ 26.9535i 1.34265i
$$404$$ 0 0
$$405$$ −11.8669 0.637647i −0.589672 0.0316849i
$$406$$ 0 0
$$407$$ 8.96410i 0.444334i
$$408$$ 0 0
$$409$$ −6.54534 −0.323646 −0.161823 0.986820i $$-0.551737\pi$$
−0.161823 + 0.986820i $$0.551737\pi$$
$$410$$ 0 0
$$411$$ −4.85811 −0.239633
$$412$$ 0 0
$$413$$ 0.679461i 0.0334341i
$$414$$ 0 0
$$415$$ 1.94879 36.2679i 0.0956623 1.78032i
$$416$$ 0 0
$$417$$ 1.10933i 0.0543239i
$$418$$ 0 0
$$419$$ −34.4795 −1.68443 −0.842216 0.539141i $$-0.818749\pi$$
−0.842216 + 0.539141i $$0.818749\pi$$
$$420$$ 0 0
$$421$$ 6.54534 0.319000 0.159500 0.987198i $$-0.449012\pi$$
0.159500 + 0.987198i $$0.449012\pi$$
$$422$$ 0 0
$$423$$ 14.4429i 0.702239i
$$424$$ 0 0
$$425$$ 3.49094 32.3903i 0.169336 1.57116i
$$426$$ 0 0
$$427$$ 2.95401i 0.142954i
$$428$$ 0 0
$$429$$ −2.62305 −0.126642
$$430$$ 0 0
$$431$$ −36.1711 −1.74230 −0.871151 0.491016i $$-0.836626\pi$$
−0.871151 + 0.491016i $$0.836626\pi$$
$$432$$ 0 0
$$433$$ 38.1027i 1.83110i 0.402204 + 0.915550i $$0.368244\pi$$
−0.402204 + 0.915550i $$0.631756\pi$$
$$434$$ 0 0
$$435$$ −0.0704722 + 1.31152i −0.00337889 + 0.0628828i
$$436$$ 0 0
$$437$$ 44.4858i 2.12805i
$$438$$ 0 0
$$439$$ 12.1282 0.578848 0.289424 0.957201i $$-0.406536\pi$$
0.289424 + 0.957201i $$0.406536\pi$$
$$440$$ 0 0
$$441$$ 17.5455 0.835500
$$442$$ 0 0
$$443$$ 16.5483i 0.786233i −0.919489 0.393117i $$-0.871397\pi$$
0.919489 0.393117i $$-0.128603\pi$$
$$444$$ 0 0
$$445$$ 21.3683 + 1.14818i 1.01295 + 0.0544292i
$$446$$ 0 0
$$447$$ 2.45871i 0.116293i
$$448$$ 0 0
$$449$$ −15.6056 −0.736476 −0.368238 0.929732i $$-0.620039\pi$$
−0.368238 + 0.929732i $$0.620039\pi$$
$$450$$ 0 0
$$451$$ −10.0998 −0.475580
$$452$$ 0 0
$$453$$ 9.92820i 0.466468i
$$454$$ 0 0
$$455$$ −3.71373 0.199550i −0.174102 0.00935505i
$$456$$ 0 0
$$457$$ 5.87761i 0.274943i −0.990506 0.137471i $$-0.956102\pi$$
0.990506 0.137471i $$-0.0438975\pi$$
$$458$$ 0 0
$$459$$ 23.7987 1.11083
$$460$$ 0 0
$$461$$ 36.7495 1.71159 0.855797 0.517312i $$-0.173067\pi$$
0.855797 + 0.517312i $$0.173067\pi$$
$$462$$ 0 0
$$463$$ 19.3081i 0.897324i −0.893702 0.448662i $$-0.851901\pi$$
0.893702 0.448662i $$-0.148099\pi$$
$$464$$ 0 0
$$465$$ 0.530153 9.86642i 0.0245853 0.457544i
$$466$$ 0 0
$$467$$ 11.4129i 0.528127i 0.964505 + 0.264064i $$0.0850629\pi$$
−0.964505 + 0.264064i $$0.914937\pi$$
$$468$$ 0 0
$$469$$ 4.44556 0.205277
$$470$$ 0 0
$$471$$ −7.59841 −0.350116
$$472$$ 0 0
$$473$$ 4.78825i 0.220164i
$$474$$ 0 0
$$475$$ 25.8705 + 2.78825i 1.18702 + 0.127934i
$$476$$ 0 0
$$477$$ 25.7914i 1.18091i
$$478$$ 0 0
$$479$$ 29.2307 1.33559 0.667793 0.744347i $$-0.267239\pi$$
0.667793 + 0.744347i $$0.267239\pi$$
$$480$$ 0 0
$$481$$ 35.8564 1.63491
$$482$$ 0 0
$$483$$ 2.33086i 0.106058i
$$484$$ 0 0
$$485$$ 0.0709857 1.32108i 0.00322329 0.0599871i
$$486$$ 0 0
$$487$$ 33.2932i 1.50866i 0.656496 + 0.754329i $$0.272038\pi$$
−0.656496 + 0.754329i $$0.727962\pi$$
$$488$$ 0 0
$$489$$ −4.47487 −0.202361
$$490$$ 0 0
$$491$$ 24.5151 1.10635 0.553176 0.833064i $$-0.313416\pi$$
0.553176 + 0.833064i $$0.313416\pi$$
$$492$$ 0 0
$$493$$ 5.83612i 0.262846i
$$494$$ 0 0
$$495$$ 5.73836 + 0.308340i 0.257920 + 0.0138589i
$$496$$ 0 0
$$497$$ 2.57510i 0.115509i
$$498$$ 0 0
$$499$$ −18.9093 −0.846497 −0.423249 0.906014i $$-0.639110\pi$$
−0.423249 + 0.906014i $$0.639110\pi$$
$$500$$ 0 0
$$501$$ 4.65872 0.208136
$$502$$ 0 0
$$503$$ 9.42031i 0.420031i 0.977698 + 0.210016i $$0.0673515\pi$$
−0.977698 + 0.210016i $$0.932649\pi$$
$$504$$ 0 0
$$505$$ 10.3226 + 0.554663i 0.459348 + 0.0246822i
$$506$$ 0 0
$$507$$ 1.96729i 0.0873702i
$$508$$ 0 0
$$509$$ 16.7804 0.743778 0.371889 0.928277i $$-0.378710\pi$$
0.371889 + 0.928277i $$0.378710\pi$$
$$510$$ 0 0
$$511$$ 1.31744 0.0582799
$$512$$ 0 0
$$513$$ 19.0082i 0.839234i
$$514$$ 0 0
$$515$$ −0.988966 + 18.4052i −0.0435791 + 0.811028i
$$516$$ 0 0
$$517$$ 5.61986i 0.247161i
$$518$$ 0 0
$$519$$ 6.10614 0.268030
$$520$$ 0 0
$$521$$ −37.8273 −1.65724 −0.828621 0.559810i $$-0.810874\pi$$
−0.828621 + 0.559810i $$0.810874\pi$$
$$522$$ 0 0
$$523$$ 10.0998i 0.441632i −0.975315 0.220816i $$-0.929128\pi$$
0.975315 0.220816i $$-0.0708721\pi$$
$$524$$ 0 0
$$525$$ −1.35550 0.146092i −0.0591589 0.00637599i
$$526$$ 0 0
$$527$$ 43.9044i 1.91250i
$$528$$ 0 0
$$529$$ −50.0734 −2.17710
$$530$$ 0 0
$$531$$ −4.19955 −0.182245
$$532$$ 0 0
$$533$$ 40.3991i 1.74988i
$$534$$ 0 0
$$535$$ −2.11399 + 39.3425i −0.0913959 + 1.70092i
$$536$$ 0 0
$$537$$ 17.4674i 0.753774i
$$538$$ 0 0
$$539$$ −6.82711 −0.294064
$$540$$ 0 0
$$541$$ −29.9269 −1.28666 −0.643329 0.765590i $$-0.722447\pi$$
−0.643329 + 0.765590i $$0.722447\pi$$
$$542$$ 0 0
$$543$$ 0.662997i 0.0284519i
$$544$$ 0 0
$$545$$ 8.17942 + 0.439506i 0.350368 + 0.0188264i
$$546$$ 0 0
$$547$$ 23.7630i 1.01603i 0.861347 + 0.508016i $$0.169621\pi$$
−0.861347 + 0.508016i $$0.830379\pi$$
$$548$$ 0 0
$$549$$ 18.2578 0.779226
$$550$$ 0 0
$$551$$ −4.66137 −0.198581
$$552$$ 0 0
$$553$$ 4.68537i 0.199242i
$$554$$ 0 0
$$555$$ 13.1254 + 0.705267i 0.557141 + 0.0299369i
$$556$$ 0 0
$$557$$ 24.3363i 1.03116i 0.856841 + 0.515581i $$0.172424\pi$$
−0.856841 + 0.515581i $$0.827576\pi$$
$$558$$ 0 0
$$559$$ −19.1530 −0.810086
$$560$$ 0 0
$$561$$ −4.27267 −0.180392
$$562$$ 0 0
$$563$$ 8.85368i 0.373138i 0.982442 + 0.186569i $$0.0597368\pi$$
−0.982442 + 0.186569i $$0.940263\pi$$
$$564$$ 0 0
$$565$$ 1.37731 25.6324i 0.0579437 1.07836i
$$566$$ 0 0
$$567$$ 2.20989i 0.0928066i
$$568$$ 0 0
$$569$$ −26.3860 −1.10616 −0.553080 0.833128i $$-0.686548\pi$$
−0.553080 + 0.833128i $$0.686548\pi$$
$$570$$ 0 0
$$571$$ −6.45280 −0.270041 −0.135021 0.990843i $$-0.543110\pi$$
−0.135021 + 0.990843i $$0.543110\pi$$
$$572$$ 0 0
$$573$$ 6.92843i 0.289439i
$$574$$ 0 0
$$575$$ −4.58004 + 42.4954i −0.191001 + 1.77218i
$$576$$ 0 0
$$577$$ 12.1745i 0.506832i −0.967357 0.253416i $$-0.918446\pi$$
0.967357 0.253416i $$-0.0815542\pi$$
$$578$$ 0 0
$$579$$ 7.75576 0.322319
$$580$$ 0 0
$$581$$ −6.75390 −0.280199
$$582$$ 0 0
$$583$$ 10.0357i 0.415635i
$$584$$ 0 0
$$585$$ −1.23336 + 22.9535i −0.0509932 + 0.949009i
$$586$$ 0 0
$$587$$ 22.9521i 0.947336i −0.880704 0.473668i $$-0.842930\pi$$
0.880704 0.473668i $$-0.157070\pi$$
$$588$$ 0 0
$$589$$ 35.0668 1.44490
$$590$$ 0 0
$$591$$ 0.860047 0.0353776
$$592$$ 0 0
$$593$$ 10.4081i 0.427410i 0.976898 + 0.213705i $$0.0685531\pi$$
−0.976898 + 0.213705i $$0.931447\pi$$
$$594$$ 0 0
$$595$$ −6.04927 0.325046i −0.247996 0.0133256i
$$596$$ 0 0
$$597$$ 7.75576i 0.317422i
$$598$$ 0 0
$$599$$ −8.98913 −0.367286 −0.183643 0.982993i $$-0.558789\pi$$
−0.183643 + 0.982993i $$0.558789\pi$$
$$600$$ 0 0
$$601$$ −3.57650 −0.145889 −0.0729443 0.997336i $$-0.523240\pi$$
−0.0729443 + 0.997336i $$0.523240\pi$$
$$602$$ 0 0
$$603$$ 27.4767i 1.11894i
$$604$$ 0 0
$$605$$ −2.23285 0.119978i −0.0907781 0.00487779i
$$606$$ 0 0
$$607$$ 27.0235i 1.09685i 0.836200 + 0.548424i $$0.184772\pi$$
−0.836200 + 0.548424i $$0.815228\pi$$
$$608$$ 0 0
$$609$$ 0.244235 0.00989691
$$610$$ 0 0
$$611$$ −22.4795 −0.909421
$$612$$ 0 0
$$613$$ 44.5572i 1.79965i −0.436254 0.899823i $$-0.643695\pi$$
0.436254 0.899823i $$-0.356305\pi$$
$$614$$ 0 0
$$615$$ 0.794619 14.7883i 0.0320421 0.596320i
$$616$$ 0 0
$$617$$ 15.2966i 0.615818i 0.951416 + 0.307909i $$0.0996292\pi$$
−0.951416 + 0.307909i $$0.900371\pi$$
$$618$$ 0 0
$$619$$ 14.5655 0.585436 0.292718 0.956199i $$-0.405440\pi$$
0.292718 + 0.956199i $$0.405440\pi$$
$$620$$ 0 0
$$621$$ −31.2233 −1.25295
$$622$$ 0 0
$$623$$ 3.97926i 0.159426i
$$624$$ 0 0
$$625$$ 24.4259 + 5.32699i 0.977035 + 0.213080i
$$626$$ 0 0
$$627$$ 3.41262i 0.136287i
$$628$$ 0 0
$$629$$ 58.4063 2.32881
$$630$$ 0 0
$$631$$ 22.0779 0.878906 0.439453 0.898266i $$-0.355172\pi$$
0.439453 + 0.898266i $$0.355172\pi$$
$$632$$ 0 0
$$633$$ 5.49033i 0.218221i
$$634$$ 0 0
$$635$$ 1.09659 20.4081i 0.0435169 0.809871i
$$636$$ 0 0
$$637$$ 27.3084i 1.08200i
$$638$$ 0 0
$$639$$ 15.9159 0.629624
$$640$$ 0 0
$$641$$ −31.2152 −1.23293 −0.616463 0.787384i $$-0.711435\pi$$
−0.616463 + 0.787384i $$0.711435\pi$$
$$642$$ 0 0
$$643$$ 10.4498i 0.412102i 0.978541 + 0.206051i $$0.0660612\pi$$
−0.978541 + 0.206051i $$0.933939\pi$$
$$644$$ 0 0
$$645$$ −7.01103 0.376725i −0.276059 0.0148335i
$$646$$ 0 0
$$647$$ 26.1307i 1.02730i 0.857999 + 0.513652i $$0.171708\pi$$
−0.857999 + 0.513652i $$0.828292\pi$$
$$648$$ 0 0
$$649$$ 1.63408 0.0641433
$$650$$ 0 0
$$651$$ −1.83735 −0.0720114
$$652$$ 0 0
$$653$$ 44.2097i 1.73006i 0.501719 + 0.865030i $$0.332701\pi$$
−0.501719 + 0.865030i $$0.667299\pi$$
$$654$$ 0 0
$$655$$ −5.54022 0.297693i −0.216474 0.0116318i
$$656$$ 0 0
$$657$$ 8.14268i 0.317676i
$$658$$ 0 0
$$659$$ 6.96706 0.271398 0.135699 0.990750i $$-0.456672\pi$$
0.135699 + 0.990750i $$0.456672\pi$$
$$660$$ 0 0
$$661$$ −9.19753 −0.357743 −0.178871 0.983872i $$-0.557245\pi$$
−0.178871 + 0.983872i $$0.557245\pi$$
$$662$$ 0 0
$$663$$ 17.0907i 0.663747i
$$664$$ 0 0
$$665$$ 0.259618 4.83161i 0.0100675 0.187362i
$$666$$ 0 0
$$667$$ 7.65686i 0.296475i
$$668$$ 0 0
$$669$$ 14.5226 0.561475
$$670$$ 0 0
$$671$$ −7.10428 −0.274258
$$672$$ 0 0
$$673$$ 8.72415i 0.336291i −0.985762 0.168146i $$-0.946222\pi$$
0.985762 0.168146i $$-0.0537779\pi$$
$$674$$ 0 0
$$675$$ −1.95699 + 18.1577i −0.0753247 + 0.698892i
$$676$$ 0 0
$$677$$ 8.76618i 0.336912i −0.985709 0.168456i $$-0.946122\pi$$
0.985709 0.168456i $$-0.0538781\pi$$
$$678$$ 0 0
$$679$$ −0.246015 −0.00944118
$$680$$ 0 0
$$681$$ −14.3083 −0.548297
$$682$$ 0 0
$$683$$ 49.2320i 1.88381i 0.335877 + 0.941906i $$0.390967\pi$$
−0.335877 + 0.941906i $$0.609033\pi$$
$$684$$ 0 0
$$685$$ 0.888837 16.5417i 0.0339607 0.632026i
$$686$$ 0 0
$$687$$ 1.83775i 0.0701146i
$$688$$ 0 0
$$689$$ −40.1427 −1.52931
$$690$$ 0 0
$$691$$ 18.1483 0.690395 0.345198 0.938530i $$-0.387812\pi$$
0.345198 + 0.938530i $$0.387812\pi$$
$$692$$ 0 0
$$693$$ 1.06861i 0.0405932i
$$694$$ 0 0
$$695$$ 3.77722 + 0.202962i 0.143278 + 0.00769877i
$$696$$ 0 0
$$697$$ 65.8059i 2.49258i
$$698$$ 0 0
$$699$$ 5.40626 0.204483
$$700$$ 0 0
$$701$$ 22.6587 0.855808 0.427904 0.903824i $$-0.359252\pi$$
0.427904 + 0.903824i $$0.359252\pi$$
$$702$$ 0 0
$$703$$ 46.6497i 1.75943i
$$704$$ 0 0
$$705$$ −8.22869 0.442153i −0.309911 0.0166525i
$$706$$ 0 0
$$707$$ 1.92229i 0.0722952i
$$708$$ 0 0
$$709$$ 36.7366 1.37967 0.689836 0.723966i $$-0.257683\pi$$
0.689836 + 0.723966i $$0.257683\pi$$
$$710$$ 0 0
$$711$$ −28.9589 −1.08604
$$712$$ 0 0
$$713$$ 57.6015i 2.15719i
$$714$$ 0 0
$$715$$ 0.479911 8.93139i 0.0179477 0.334015i
$$716$$ 0 0
$$717$$ 7.38923i 0.275956i
$$718$$ 0 0
$$719$$ 8.74738 0.326222 0.163111 0.986608i $$-0.447847\pi$$
0.163111 + 0.986608i $$0.447847\pi$$
$$720$$ 0 0
$$721$$ 3.42745 0.127645
$$722$$ 0 0
$$723$$ 14.6799i 0.545952i
$$724$$ 0 0
$$725$$ −4.45280 0.479911i −0.165373 0.0178235i
$$726$$ 0 0
$$727$$ 2.20887i 0.0819226i −0.999161 0.0409613i $$-0.986958\pi$$
0.999161 0.0409613i $$-0.0130420\pi$$
$$728$$ 0 0
$$729$$ 6.47301 0.239741
$$730$$ 0 0
$$731$$ −31.1982 −1.15391
$$732$$ 0 0
$$733$$ 3.58552i 0.132434i 0.997805 + 0.0662171i $$0.0210930\pi$$
−0.997805 + 0.0662171i $$0.978907\pi$$
$$734$$ 0 0
$$735$$ 0.537135 9.99636i 0.0198125 0.368721i
$$736$$ 0 0
$$737$$ 10.6914i 0.393824i
$$738$$ 0 0
$$739$$ −24.9314 −0.917116 −0.458558 0.888665i $$-0.651634\pi$$
−0.458558 + 0.888665i $$0.651634\pi$$
$$740$$ 0 0
$$741$$ 13.6505 0.501463
$$742$$ 0 0
$$743$$ 21.4257i 0.786032i −0.919532 0.393016i $$-0.871432\pi$$
0.919532 0.393016i $$-0.128568\pi$$
$$744$$ 0 0
$$745$$ 8.37183 + 0.449844i 0.306720 + 0.0164810i
$$746$$ 0 0
$$747$$ 41.7439i 1.52733i
$$748$$ 0 0
$$749$$ 7.32645 0.267703
$$750$$ 0 0
$$751$$ −28.1582 −1.02751 −0.513754 0.857938i $$-0.671746\pi$$
−0.513754 + 0.857938i $$0.671746\pi$$
$$752$$ 0 0
$$753$$ 2.51986i 0.0918288i
$$754$$ 0 0
$$755$$ −33.8052 1.81646i −1.23030 0.0661077i
$$756$$ 0 0
$$757$$ 10.7513i 0.390761i 0.980728 + 0.195381i $$0.0625942\pi$$
−0.980728 + 0.195381i $$0.937406\pi$$
$$758$$ 0 0
$$759$$ 5.60565 0.203472
$$760$$ 0 0
$$761$$ −38.0429 −1.37905 −0.689527 0.724260i $$-0.742182\pi$$
−0.689527 + 0.724260i $$0.742182\pi$$
$$762$$ 0 0
$$763$$ 1.52319i 0.0551433i
$$764$$ 0 0
$$765$$ −2.00901 + 37.3888i −0.0726361 + 1.35179i
$$766$$ 0 0
$$767$$ 6.53632i 0.236013i
$$768$$ 0 0
$$769$$ −26.2280 −0.945805 −0.472903 0.881115i $$-0.656794\pi$$
−0.472903 + 0.881115i $$0.656794\pi$$
$$770$$ 0 0
$$771$$ −6.96619 −0.250881
$$772$$ 0 0
$$773$$ 8.94499i 0.321729i −0.986977 0.160864i $$-0.948572\pi$$
0.986977 0.160864i $$-0.0514282\pi$$
$$774$$ 0 0
$$775$$ 33.4978 + 3.61031i 1.20328 + 0.129686i
$$776$$ 0 0
$$777$$ 2.44424i 0.0876867i
$$778$$ 0 0
$$779$$ 52.5598 1.88315
$$780$$ 0 0
$$781$$ −6.19302 −0.221604
$$782$$ 0 0
$$783$$ 3.27168i 0.116920i
$$784$$ 0 0
$$785$$ 1.39020 25.8723i 0.0496184 0.923423i
$$786$$ 0 0
$$787$$ 29.9716i 1.06837i −0.845367 0.534185i $$-0.820618\pi$$
0.845367 0.534185i $$-0.179382\pi$$
$$788$$ 0 0
$$789$$ −3.79867 −0.135236
$$790$$ 0 0
$$791$$ −4.77332 −0.169720
$$792$$ 0 0
$$793$$ 28.4171i 1.00912i
$$794$$ 0 0
$$795$$ −14.6944 0.789575i −0.521156 0.0280033i
$$796$$