# Properties

 Label 1008.2.bt.b.593.1 Level $1008$ Weight $2$ Character 1008.593 Analytic conductor $8.049$ Analytic rank $0$ Dimension $4$ Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(17,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("1008.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1008 = 2^{4} \cdot 3^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1008.bt (of order $$6$$, 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: $$8.04892052375$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\sqrt{-2}, \sqrt{-3})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - 2x^{2} + 4$$ x^4 - 2*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 63) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 593.1 Root $$1.22474 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 1008.593 Dual form 1008.2.bt.b.17.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-1.22474 + 2.12132i) q^{5} +(0.500000 + 2.59808i) q^{7} +O(q^{10})$$ $$q+(-1.22474 + 2.12132i) q^{5} +(0.500000 + 2.59808i) q^{7} +(1.22474 - 0.707107i) q^{11} +5.19615i q^{13} +(-2.44949 - 4.24264i) q^{17} +(-1.50000 - 0.866025i) q^{19} +(-4.89898 - 2.82843i) q^{23} +(-0.500000 - 0.866025i) q^{25} +2.82843i q^{29} +(-1.50000 + 0.866025i) q^{31} +(-6.12372 - 2.12132i) q^{35} +(0.500000 - 0.866025i) q^{37} -7.34847 q^{41} +1.00000 q^{43} +(-6.12372 + 10.6066i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(2.44949 - 1.41421i) q^{53} +3.46410i q^{55} +(2.44949 + 4.24264i) q^{59} +(-3.00000 - 1.73205i) q^{61} +(-11.0227 - 6.36396i) q^{65} +(5.50000 + 9.52628i) q^{67} -7.07107i q^{71} +(1.50000 - 0.866025i) q^{73} +(2.44949 + 2.82843i) q^{77} +(2.50000 - 4.33013i) q^{79} -7.34847 q^{83} +12.0000 q^{85} +(2.44949 - 4.24264i) q^{89} +(-13.5000 + 2.59808i) q^{91} +(3.67423 - 2.12132i) q^{95} +10.3923i q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 2 q^{7}+O(q^{10})$$ 4 * q + 2 * q^7 $$4 q + 2 q^{7} - 6 q^{19} - 2 q^{25} - 6 q^{31} + 2 q^{37} + 4 q^{43} - 26 q^{49} - 12 q^{61} + 22 q^{67} + 6 q^{73} + 10 q^{79} + 48 q^{85} - 54 q^{91}+O(q^{100})$$ 4 * q + 2 * q^7 - 6 * q^19 - 2 * q^25 - 6 * q^31 + 2 * q^37 + 4 * q^43 - 26 * q^49 - 12 * q^61 + 22 * q^67 + 6 * q^73 + 10 * q^79 + 48 * q^85 - 54 * q^91

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$577$$ $$757$$ $$785$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-1$$

## 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 0
$$4$$ 0 0
$$5$$ −1.22474 + 2.12132i −0.547723 + 0.948683i 0.450708 + 0.892672i $$0.351172\pi$$
−0.998430 + 0.0560116i $$0.982162\pi$$
$$6$$ 0 0
$$7$$ 0.500000 + 2.59808i 0.188982 + 0.981981i
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.22474 0.707107i 0.369274 0.213201i −0.303867 0.952714i $$-0.598278\pi$$
0.673141 + 0.739514i $$0.264945\pi$$
$$12$$ 0 0
$$13$$ 5.19615i 1.44115i 0.693375 + 0.720577i $$0.256123\pi$$
−0.693375 + 0.720577i $$0.743877\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −2.44949 4.24264i −0.594089 1.02899i −0.993675 0.112296i $$-0.964180\pi$$
0.399586 0.916696i $$-0.369154\pi$$
$$18$$ 0 0
$$19$$ −1.50000 0.866025i −0.344124 0.198680i 0.317970 0.948101i $$-0.396999\pi$$
−0.662094 + 0.749421i $$0.730332\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −4.89898 2.82843i −1.02151 0.589768i −0.106967 0.994263i $$-0.534114\pi$$
−0.914540 + 0.404495i $$0.867447\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 2.82843i 0.525226i 0.964901 + 0.262613i $$0.0845842\pi$$
−0.964901 + 0.262613i $$0.915416\pi$$
$$30$$ 0 0
$$31$$ −1.50000 + 0.866025i −0.269408 + 0.155543i −0.628619 0.777714i $$-0.716379\pi$$
0.359211 + 0.933257i $$0.383046\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −6.12372 2.12132i −1.03510 0.358569i
$$36$$ 0 0
$$37$$ 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i $$-0.807139\pi$$
0.904194 + 0.427121i $$0.140472\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −7.34847 −1.14764 −0.573819 0.818982i $$-0.694539\pi$$
−0.573819 + 0.818982i $$0.694539\pi$$
$$42$$ 0 0
$$43$$ 1.00000 0.152499 0.0762493 0.997089i $$-0.475706\pi$$
0.0762493 + 0.997089i $$0.475706\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ −6.12372 + 10.6066i −0.893237 + 1.54713i −0.0572655 + 0.998359i $$0.518238\pi$$
−0.835971 + 0.548773i $$0.815095\pi$$
$$48$$ 0 0
$$49$$ −6.50000 + 2.59808i −0.928571 + 0.371154i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 2.44949 1.41421i 0.336463 0.194257i −0.322244 0.946657i $$-0.604437\pi$$
0.658707 + 0.752400i $$0.271104\pi$$
$$54$$ 0 0
$$55$$ 3.46410i 0.467099i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 2.44949 + 4.24264i 0.318896 + 0.552345i 0.980258 0.197722i $$-0.0633545\pi$$
−0.661362 + 0.750067i $$0.730021\pi$$
$$60$$ 0 0
$$61$$ −3.00000 1.73205i −0.384111 0.221766i 0.295495 0.955344i $$-0.404516\pi$$
−0.679605 + 0.733578i $$0.737849\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −11.0227 6.36396i −1.36720 0.789352i
$$66$$ 0 0
$$67$$ 5.50000 + 9.52628i 0.671932 + 1.16382i 0.977356 + 0.211604i $$0.0678686\pi$$
−0.305424 + 0.952217i $$0.598798\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 7.07107i 0.839181i −0.907713 0.419591i $$-0.862174\pi$$
0.907713 0.419591i $$-0.137826\pi$$
$$72$$ 0 0
$$73$$ 1.50000 0.866025i 0.175562 0.101361i −0.409644 0.912245i $$-0.634347\pi$$
0.585206 + 0.810885i $$0.301014\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 2.44949 + 2.82843i 0.279145 + 0.322329i
$$78$$ 0 0
$$79$$ 2.50000 4.33013i 0.281272 0.487177i −0.690426 0.723403i $$-0.742577\pi$$
0.971698 + 0.236225i $$0.0759104\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −7.34847 −0.806599 −0.403300 0.915068i $$-0.632137\pi$$
−0.403300 + 0.915068i $$0.632137\pi$$
$$84$$ 0 0
$$85$$ 12.0000 1.30158
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 2.44949 4.24264i 0.259645 0.449719i −0.706502 0.707712i $$-0.749728\pi$$
0.966147 + 0.257993i $$0.0830610\pi$$
$$90$$ 0 0
$$91$$ −13.5000 + 2.59808i −1.41518 + 0.272352i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 3.67423 2.12132i 0.376969 0.217643i
$$96$$ 0 0
$$97$$ 10.3923i 1.05518i 0.849500 + 0.527589i $$0.176904\pi$$
−0.849500 + 0.527589i $$0.823096\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 8.57321 + 14.8492i 0.853067 + 1.47755i 0.878427 + 0.477876i $$0.158593\pi$$
−0.0253604 + 0.999678i $$0.508073\pi$$
$$102$$ 0 0
$$103$$ 7.50000 + 4.33013i 0.738997 + 0.426660i 0.821705 0.569914i $$-0.193023\pi$$
−0.0827075 + 0.996574i $$0.526357\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 2.44949 + 1.41421i 0.236801 + 0.136717i 0.613706 0.789535i $$-0.289678\pi$$
−0.376905 + 0.926252i $$0.623012\pi$$
$$108$$ 0 0
$$109$$ 0.500000 + 0.866025i 0.0478913 + 0.0829502i 0.888977 0.457951i $$-0.151417\pi$$
−0.841086 + 0.540901i $$0.818083\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1.41421i 0.133038i −0.997785 0.0665190i $$-0.978811\pi$$
0.997785 0.0665190i $$-0.0211893\pi$$
$$114$$ 0 0
$$115$$ 12.0000 6.92820i 1.11901 0.646058i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 9.79796 8.48528i 0.898177 0.777844i
$$120$$ 0 0
$$121$$ −4.50000 + 7.79423i −0.409091 + 0.708566i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ −9.79796 −0.876356
$$126$$ 0 0
$$127$$ −11.0000 −0.976092 −0.488046 0.872818i $$-0.662290\pi$$
−0.488046 + 0.872818i $$0.662290\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 1.22474 2.12132i 0.107006 0.185341i −0.807550 0.589799i $$-0.799207\pi$$
0.914556 + 0.404459i $$0.132540\pi$$
$$132$$ 0 0
$$133$$ 1.50000 4.33013i 0.130066 0.375470i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 9.79796 5.65685i 0.837096 0.483298i −0.0191800 0.999816i $$-0.506106\pi$$
0.856276 + 0.516518i $$0.172772\pi$$
$$138$$ 0 0
$$139$$ 5.19615i 0.440732i −0.975417 0.220366i $$-0.929275\pi$$
0.975417 0.220366i $$-0.0707252\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 3.67423 + 6.36396i 0.307255 + 0.532181i
$$144$$ 0 0
$$145$$ −6.00000 3.46410i −0.498273 0.287678i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ 4.89898 + 2.82843i 0.401340 + 0.231714i 0.687062 0.726599i $$-0.258900\pi$$
−0.285722 + 0.958313i $$0.592233\pi$$
$$150$$ 0 0
$$151$$ −11.0000 19.0526i −0.895167 1.55048i −0.833597 0.552372i $$-0.813723\pi$$
−0.0615699 0.998103i $$-0.519611\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 4.24264i 0.340777i
$$156$$ 0 0
$$157$$ 15.0000 8.66025i 1.19713 0.691164i 0.237216 0.971457i $$-0.423765\pi$$
0.959914 + 0.280293i $$0.0904318\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 4.89898 14.1421i 0.386094 1.11456i
$$162$$ 0 0
$$163$$ −5.00000 + 8.66025i −0.391630 + 0.678323i −0.992665 0.120900i $$-0.961422\pi$$
0.601035 + 0.799223i $$0.294755\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 7.34847 0.568642 0.284321 0.958729i $$-0.408232\pi$$
0.284321 + 0.958729i $$0.408232\pi$$
$$168$$ 0 0
$$169$$ −14.0000 −1.07692
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ −4.89898 + 8.48528i −0.372463 + 0.645124i −0.989944 0.141462i $$-0.954820\pi$$
0.617481 + 0.786586i $$0.288153\pi$$
$$174$$ 0 0
$$175$$ 2.00000 1.73205i 0.151186 0.130931i
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 8.57321 4.94975i 0.640792 0.369961i −0.144127 0.989559i $$-0.546038\pi$$
0.784920 + 0.619598i $$0.212704\pi$$
$$180$$ 0 0
$$181$$ 15.5885i 1.15868i −0.815086 0.579340i $$-0.803310\pi$$
0.815086 0.579340i $$-0.196690\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 1.22474 + 2.12132i 0.0900450 + 0.155963i
$$186$$ 0 0
$$187$$ −6.00000 3.46410i −0.438763 0.253320i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −1.22474 0.707107i −0.0886194 0.0511645i 0.455035 0.890473i $$-0.349627\pi$$
−0.543655 + 0.839309i $$0.682960\pi$$
$$192$$ 0 0
$$193$$ −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i $$-0.296234\pi$$
−0.993215 + 0.116289i $$0.962900\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 19.7990i 1.41062i 0.708899 + 0.705310i $$0.249192\pi$$
−0.708899 + 0.705310i $$0.750808\pi$$
$$198$$ 0 0
$$199$$ 12.0000 6.92820i 0.850657 0.491127i −0.0102152 0.999948i $$-0.503252\pi$$
0.860873 + 0.508821i $$0.169918\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −7.34847 + 1.41421i −0.515761 + 0.0992583i
$$204$$ 0 0
$$205$$ 9.00000 15.5885i 0.628587 1.08875i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −2.44949 −0.169435
$$210$$ 0 0
$$211$$ 22.0000 1.51454 0.757271 0.653101i $$-0.226532\pi$$
0.757271 + 0.653101i $$0.226532\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ −1.22474 + 2.12132i −0.0835269 + 0.144673i
$$216$$ 0 0
$$217$$ −3.00000 3.46410i −0.203653 0.235159i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 22.0454 12.7279i 1.48293 0.856173i
$$222$$ 0 0
$$223$$ 20.7846i 1.39184i 0.718119 + 0.695920i $$0.245003\pi$$
−0.718119 + 0.695920i $$0.754997\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 13.4722 + 23.3345i 0.894181 + 1.54877i 0.834815 + 0.550530i $$0.185575\pi$$
0.0593658 + 0.998236i $$0.481092\pi$$
$$228$$ 0 0
$$229$$ 19.5000 + 11.2583i 1.28860 + 0.743971i 0.978404 0.206702i $$-0.0662732\pi$$
0.310192 + 0.950674i $$0.399607\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 8.57321 + 4.94975i 0.561650 + 0.324269i 0.753807 0.657095i $$-0.228215\pi$$
−0.192158 + 0.981364i $$0.561548\pi$$
$$234$$ 0 0
$$235$$ −15.0000 25.9808i −0.978492 1.69480i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 26.8701i 1.73808i 0.494742 + 0.869040i $$0.335262\pi$$
−0.494742 + 0.869040i $$0.664738\pi$$
$$240$$ 0 0
$$241$$ −12.0000 + 6.92820i −0.772988 + 0.446285i −0.833939 0.551856i $$-0.813920\pi$$
0.0609515 + 0.998141i $$0.480586\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 2.44949 16.9706i 0.156492 1.08421i
$$246$$ 0 0
$$247$$ 4.50000 7.79423i 0.286328 0.495935i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ −8.00000 −0.502956
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −1.22474 + 2.12132i −0.0763975 + 0.132324i −0.901693 0.432377i $$-0.857675\pi$$
0.825296 + 0.564701i $$0.191008\pi$$
$$258$$ 0 0
$$259$$ 2.50000 + 0.866025i 0.155342 + 0.0538122i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 12.2474 7.07107i 0.755210 0.436021i −0.0723633 0.997378i $$-0.523054\pi$$
0.827573 + 0.561358i $$0.189721\pi$$
$$264$$ 0 0
$$265$$ 6.92820i 0.425596i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 8.57321 + 14.8492i 0.522718 + 0.905374i 0.999651 + 0.0264343i $$0.00841529\pi$$
−0.476932 + 0.878940i $$0.658251\pi$$
$$270$$ 0 0
$$271$$ 12.0000 + 6.92820i 0.728948 + 0.420858i 0.818037 0.575165i $$-0.195062\pi$$
−0.0890891 + 0.996024i $$0.528396\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −1.22474 0.707107i −0.0738549 0.0426401i
$$276$$ 0 0
$$277$$ −11.5000 19.9186i −0.690968 1.19679i −0.971521 0.236953i $$-0.923851\pi$$
0.280553 0.959839i $$-0.409482\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 22.6274i 1.34984i −0.737892 0.674919i $$-0.764178\pi$$
0.737892 0.674919i $$-0.235822\pi$$
$$282$$ 0 0
$$283$$ −1.50000 + 0.866025i −0.0891657 + 0.0514799i −0.543920 0.839137i $$-0.683060\pi$$
0.454754 + 0.890617i $$0.349727\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −3.67423 19.0919i −0.216883 1.12696i
$$288$$ 0 0
$$289$$ −3.50000 + 6.06218i −0.205882 + 0.356599i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 14.6969 0.858604 0.429302 0.903161i $$-0.358760\pi$$
0.429302 + 0.903161i $$0.358760\pi$$
$$294$$ 0 0
$$295$$ −12.0000 −0.698667
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 14.6969 25.4558i 0.849946 1.47215i
$$300$$ 0 0
$$301$$ 0.500000 + 2.59808i 0.0288195 + 0.149751i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 7.34847 4.24264i 0.420772 0.242933i
$$306$$ 0 0
$$307$$ 15.5885i 0.889680i −0.895610 0.444840i $$-0.853260\pi$$
0.895610 0.444840i $$-0.146740\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −8.57321 14.8492i −0.486142 0.842023i 0.513731 0.857951i $$-0.328263\pi$$
−0.999873 + 0.0159282i $$0.994930\pi$$
$$312$$ 0 0
$$313$$ 10.5000 + 6.06218i 0.593495 + 0.342655i 0.766478 0.642270i $$-0.222007\pi$$
−0.172983 + 0.984925i $$0.555341\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 12.2474 + 7.07107i 0.687885 + 0.397151i 0.802819 0.596222i $$-0.203332\pi$$
−0.114934 + 0.993373i $$0.536666\pi$$
$$318$$ 0 0
$$319$$ 2.00000 + 3.46410i 0.111979 + 0.193952i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 8.48528i 0.472134i
$$324$$ 0 0
$$325$$ 4.50000 2.59808i 0.249615 0.144115i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ −30.6186 10.6066i −1.68806 0.584761i
$$330$$ 0 0
$$331$$ −15.5000 + 26.8468i −0.851957 + 1.47563i 0.0274825 + 0.999622i $$0.491251\pi$$
−0.879440 + 0.476011i $$0.842082\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −26.9444 −1.47213
$$336$$ 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
$$341$$ −1.22474 + 2.12132i −0.0663237 + 0.114876i
$$342$$ 0 0
$$343$$ −10.0000 15.5885i −0.539949 0.841698i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 26.9444 15.5563i 1.44645 0.835109i 0.448183 0.893942i $$-0.352071\pi$$
0.998268 + 0.0588334i $$0.0187381\pi$$
$$348$$ 0 0
$$349$$ 10.3923i 0.556287i 0.960539 + 0.278144i $$0.0897191\pi$$
−0.960539 + 0.278144i $$0.910281\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 8.57321 + 14.8492i 0.456306 + 0.790345i 0.998762 0.0497387i $$-0.0158389\pi$$
−0.542456 + 0.840084i $$0.682506\pi$$
$$354$$ 0 0
$$355$$ 15.0000 + 8.66025i 0.796117 + 0.459639i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 24.4949 + 14.1421i 1.29279 + 0.746393i 0.979148 0.203148i $$-0.0651171\pi$$
0.313643 + 0.949541i $$0.398450\pi$$
$$360$$ 0 0
$$361$$ −8.00000 13.8564i −0.421053 0.729285i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 4.24264i 0.222070i
$$366$$ 0 0
$$367$$ −1.50000 + 0.866025i −0.0782994 + 0.0452062i −0.538639 0.842537i $$-0.681061\pi$$
0.460339 + 0.887743i $$0.347728\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 4.89898 + 5.65685i 0.254342 + 0.293689i
$$372$$ 0 0
$$373$$ −14.5000 + 25.1147i −0.750782 + 1.30039i 0.196663 + 0.980471i $$0.436990\pi$$
−0.947444 + 0.319921i $$0.896344\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −14.6969 −0.756931
$$378$$ 0 0
$$379$$ 7.00000 0.359566 0.179783 0.983706i $$-0.442460\pi$$
0.179783 + 0.983706i $$0.442460\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −9.79796 + 16.9706i −0.500652 + 0.867155i 0.499347 + 0.866402i $$0.333573\pi$$
−1.00000 0.000753393i $$0.999760\pi$$
$$384$$ 0 0
$$385$$ −9.00000 + 1.73205i −0.458682 + 0.0882735i
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −23.2702 + 13.4350i −1.17984 + 0.681183i −0.955978 0.293437i $$-0.905201\pi$$
−0.223865 + 0.974620i $$0.571868\pi$$
$$390$$ 0 0
$$391$$ 27.7128i 1.40150i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 6.12372 + 10.6066i 0.308118 + 0.533676i
$$396$$ 0 0
$$397$$ 1.50000 + 0.866025i 0.0752828 + 0.0434646i 0.537169 0.843475i $$-0.319494\pi$$
−0.461886 + 0.886939i $$0.652827\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −17.1464 9.89949i −0.856252 0.494357i 0.00650355 0.999979i $$-0.497930\pi$$
−0.862755 + 0.505622i $$0.831263\pi$$
$$402$$ 0 0
$$403$$ −4.50000 7.79423i −0.224161 0.388258i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 1.41421i 0.0701000i
$$408$$ 0 0
$$409$$ 28.5000 16.4545i 1.40923 0.813622i 0.413920 0.910313i $$-0.364159\pi$$
0.995314 + 0.0966915i $$0.0308260\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ −9.79796 + 8.48528i −0.482126 + 0.417533i
$$414$$ 0 0
$$415$$ 9.00000 15.5885i 0.441793 0.765207i
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −36.7423 −1.79498 −0.897491 0.441034i $$-0.854612\pi$$
−0.897491 + 0.441034i $$0.854612\pi$$
$$420$$ 0 0
$$421$$ −1.00000 −0.0487370 −0.0243685 0.999703i $$-0.507758\pi$$
−0.0243685 + 0.999703i $$0.507758\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −2.44949 + 4.24264i −0.118818 + 0.205798i
$$426$$ 0 0
$$427$$ 3.00000 8.66025i 0.145180 0.419099i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −13.4722 + 7.77817i −0.648933 + 0.374661i −0.788047 0.615615i $$-0.788908\pi$$
0.139114 + 0.990276i $$0.455574\pi$$
$$432$$ 0 0
$$433$$ 15.5885i 0.749133i −0.927200 0.374567i $$-0.877791\pi$$
0.927200 0.374567i $$-0.122209\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 4.89898 + 8.48528i 0.234350 + 0.405906i
$$438$$ 0 0
$$439$$ −24.0000 13.8564i −1.14546 0.661330i −0.197681 0.980266i $$-0.563341\pi$$
−0.947776 + 0.318936i $$0.896674\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −34.2929 19.7990i −1.62930 0.940678i −0.984301 0.176497i $$-0.943523\pi$$
−0.645002 0.764181i $$-0.723143\pi$$
$$444$$ 0 0
$$445$$ 6.00000 + 10.3923i 0.284427 + 0.492642i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 7.07107i 0.333704i 0.985982 + 0.166852i $$0.0533603\pi$$
−0.985982 + 0.166852i $$0.946640\pi$$
$$450$$ 0 0
$$451$$ −9.00000 + 5.19615i −0.423793 + 0.244677i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 11.0227 31.8198i 0.516752 1.49174i
$$456$$ 0 0
$$457$$ −2.50000 + 4.33013i −0.116945 + 0.202555i −0.918556 0.395292i $$-0.870643\pi$$
0.801611 + 0.597847i $$0.203977\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −14.6969 −0.684505 −0.342252 0.939608i $$-0.611190\pi$$
−0.342252 + 0.939608i $$0.611190\pi$$
$$462$$ 0 0
$$463$$ 13.0000 0.604161 0.302081 0.953282i $$-0.402319\pi$$
0.302081 + 0.953282i $$0.402319\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −13.4722 + 23.3345i −0.623419 + 1.07979i 0.365426 + 0.930841i $$0.380923\pi$$
−0.988844 + 0.148952i $$0.952410\pi$$
$$468$$ 0 0
$$469$$ −22.0000 + 19.0526i −1.01587 + 0.879765i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 1.22474 0.707107i 0.0563138 0.0325128i
$$474$$ 0 0
$$475$$ 1.73205i 0.0794719i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 2.44949 + 4.24264i 0.111920 + 0.193851i 0.916544 0.399933i $$-0.130967\pi$$
−0.804624 + 0.593784i $$0.797633\pi$$
$$480$$ 0 0
$$481$$ 4.50000 + 2.59808i 0.205182 + 0.118462i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −22.0454 12.7279i −1.00103 0.577945i
$$486$$ 0 0
$$487$$ 8.50000 + 14.7224i 0.385172 + 0.667137i 0.991793 0.127854i $$-0.0408089\pi$$
−0.606621 + 0.794991i $$0.707476\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 11.3137i 0.510581i −0.966864 0.255290i $$-0.917829\pi$$
0.966864 0.255290i $$-0.0821710\pi$$
$$492$$ 0 0
$$493$$ 12.0000 6.92820i 0.540453 0.312031i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 18.3712 3.53553i 0.824060 0.158590i
$$498$$ 0 0
$$499$$ −12.5000 + 21.6506i −0.559577 + 0.969216i 0.437955 + 0.898997i $$0.355703\pi$$
−0.997532 + 0.0702185i $$0.977630\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ −22.0454 −0.982956 −0.491478 0.870890i $$-0.663543\pi$$
−0.491478 + 0.870890i $$0.663543\pi$$
$$504$$ 0 0
$$505$$ −42.0000 −1.86898
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −1.22474 + 2.12132i −0.0542859 + 0.0940259i −0.891891 0.452250i $$-0.850622\pi$$
0.837605 + 0.546276i $$0.183955\pi$$
$$510$$ 0 0
$$511$$ 3.00000 + 3.46410i 0.132712 + 0.153243i
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ −18.3712 + 10.6066i −0.809531 + 0.467383i
$$516$$ 0 0
$$517$$ 17.3205i 0.761755i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −2.44949 4.24264i −0.107314 0.185873i 0.807367 0.590049i $$-0.200892\pi$$
−0.914681 + 0.404176i $$0.867558\pi$$
$$522$$ 0 0
$$523$$ −1.50000 0.866025i −0.0655904 0.0378686i 0.466846 0.884339i $$-0.345390\pi$$
−0.532437 + 0.846470i $$0.678724\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 7.34847 + 4.24264i 0.320104 + 0.184812i
$$528$$ 0 0
$$529$$ 4.50000 + 7.79423i 0.195652 + 0.338880i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 38.1838i 1.65392i
$$534$$ 0 0
$$535$$ −6.00000 + 3.46410i −0.259403 + 0.149766i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −6.12372 + 7.77817i −0.263767 + 0.335030i
$$540$$ 0 0
$$541$$ −8.50000 + 14.7224i −0.365444 + 0.632967i −0.988847 0.148933i $$-0.952416\pi$$
0.623404 + 0.781900i $$0.285749\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −2.44949 −0.104925
$$546$$ 0 0
$$547$$ 10.0000 0.427569 0.213785 0.976881i $$-0.431421\pi$$
0.213785 + 0.976881i $$0.431421\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 2.44949 4.24264i 0.104352 0.180743i
$$552$$ 0 0
$$553$$ 12.5000 + 4.33013i 0.531554 + 0.184136i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 13.4722 7.77817i 0.570835 0.329572i −0.186648 0.982427i $$-0.559762\pi$$
0.757483 + 0.652855i $$0.226429\pi$$
$$558$$ 0 0
$$559$$ 5.19615i 0.219774i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 13.4722 + 23.3345i 0.567785 + 0.983433i 0.996785 + 0.0801281i $$0.0255329\pi$$
−0.428999 + 0.903305i $$0.641134\pi$$
$$564$$ 0 0
$$565$$ 3.00000 + 1.73205i 0.126211 + 0.0728679i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 1.22474 + 0.707107i 0.0513440 + 0.0296435i 0.525452 0.850823i $$-0.323896\pi$$
−0.474108 + 0.880467i $$0.657229\pi$$
$$570$$ 0 0
$$571$$ 5.50000 + 9.52628i 0.230168 + 0.398662i 0.957857 0.287244i $$-0.0927391\pi$$
−0.727690 + 0.685907i $$0.759406\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 5.65685i 0.235907i
$$576$$ 0 0
$$577$$ 1.50000 0.866025i 0.0624458 0.0360531i −0.468452 0.883489i $$-0.655188\pi$$
0.530898 + 0.847436i $$0.321855\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −3.67423 19.0919i −0.152433 0.792065i
$$582$$ 0 0
$$583$$ 2.00000 3.46410i 0.0828315 0.143468i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 14.6969 0.606608 0.303304 0.952894i $$-0.401910\pi$$
0.303304 + 0.952894i $$0.401910\pi$$
$$588$$ 0 0
$$589$$ 3.00000 0.123613
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −8.57321 + 14.8492i −0.352060 + 0.609785i −0.986610 0.163096i $$-0.947852\pi$$
0.634550 + 0.772881i $$0.281185\pi$$
$$594$$ 0 0
$$595$$ 6.00000 + 31.1769i 0.245976 + 1.27813i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 4.89898 2.82843i 0.200167 0.115566i −0.396566 0.918006i $$-0.629798\pi$$
0.596733 + 0.802440i $$0.296465\pi$$
$$600$$ 0 0
$$601$$ 25.9808i 1.05978i 0.848067 + 0.529889i $$0.177766\pi$$
−0.848067 + 0.529889i $$0.822234\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ −11.0227 19.0919i −0.448137 0.776195i
$$606$$ 0 0
$$607$$ 34.5000 + 19.9186i 1.40031 + 0.808470i 0.994424 0.105453i $$-0.0336291\pi$$
0.405887 + 0.913923i $$0.366962\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −55.1135 31.8198i −2.22965 1.28729i
$$612$$ 0 0
$$613$$ −4.00000 6.92820i −0.161558 0.279827i 0.773869 0.633345i $$-0.218319\pi$$
−0.935428 + 0.353518i $$0.884985\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 24.0416i 0.967880i 0.875101 + 0.483940i $$0.160795\pi$$
−0.875101 + 0.483940i $$0.839205\pi$$
$$618$$ 0 0
$$619$$ 25.5000 14.7224i 1.02493 0.591744i 0.109403 0.993997i $$-0.465106\pi$$
0.915529 + 0.402253i $$0.131773\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 12.2474 + 4.24264i 0.490684 + 0.169978i
$$624$$ 0 0
$$625$$ 14.5000 25.1147i 0.580000 1.00459i
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ −4.89898 −0.195335
$$630$$ 0 0
$$631$$ −38.0000 −1.51276 −0.756378 0.654135i $$-0.773033\pi$$
−0.756378 + 0.654135i $$0.773033\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 13.4722 23.3345i 0.534628 0.926002i
$$636$$ 0 0
$$637$$ −13.5000 33.7750i −0.534889 1.33821i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −12.2474 + 7.07107i −0.483745 + 0.279290i −0.721976 0.691918i $$-0.756766\pi$$
0.238231 + 0.971209i $$0.423433\pi$$
$$642$$ 0 0
$$643$$ 25.9808i 1.02458i 0.858812 + 0.512291i $$0.171203\pi$$
−0.858812 + 0.512291i $$0.828797\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −8.57321 14.8492i −0.337048 0.583784i 0.646828 0.762636i $$-0.276095\pi$$
−0.983876 + 0.178852i $$0.942762\pi$$
$$648$$ 0 0
$$649$$ 6.00000 + 3.46410i 0.235521 + 0.135978i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −6.12372 3.53553i −0.239640 0.138356i 0.375371 0.926875i $$-0.377515\pi$$
−0.615011 + 0.788518i $$0.710849\pi$$
$$654$$ 0 0
$$655$$ 3.00000 + 5.19615i 0.117220 + 0.203030i
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ 22.6274i 0.881439i 0.897645 + 0.440720i $$0.145277\pi$$
−0.897645 + 0.440720i $$0.854723\pi$$
$$660$$ 0 0
$$661$$ −25.5000 + 14.7224i −0.991835 + 0.572636i −0.905822 0.423658i $$-0.860746\pi$$
−0.0860127 + 0.996294i $$0.527413\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 7.34847 + 8.48528i 0.284961 + 0.329045i
$$666$$ 0 0
$$667$$ 8.00000 13.8564i 0.309761 0.536522i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −4.89898 −0.189123
$$672$$ 0 0
$$673$$ 35.0000 1.34915 0.674575 0.738206i $$-0.264327\pi$$
0.674575 + 0.738206i $$0.264327\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −4.89898 + 8.48528i −0.188283 + 0.326116i −0.944678 0.327999i $$-0.893626\pi$$
0.756395 + 0.654115i $$0.226959\pi$$
$$678$$ 0 0
$$679$$ −27.0000 + 5.19615i −1.03616 + 0.199410i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 41.6413 24.0416i 1.59336 0.919927i 0.600636 0.799522i $$-0.294914\pi$$
0.992725 0.120405i $$-0.0384193\pi$$
$$684$$ 0 0
$$685$$ 27.7128i 1.05885i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 7.34847 + 12.7279i 0.279954 + 0.484895i
$$690$$ 0 0
$$691$$ −37.5000 21.6506i −1.42657 0.823629i −0.429719 0.902963i $$-0.641387\pi$$
−0.996848 + 0.0793336i $$0.974721\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 11.0227 + 6.36396i 0.418115 + 0.241399i
$$696$$ 0 0
$$697$$ 18.0000 + 31.1769i 0.681799 + 1.18091i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 5.65685i 0.213656i −0.994277 0.106828i $$-0.965931\pi$$
0.994277 0.106828i $$-0.0340695\pi$$
$$702$$ 0 0
$$703$$ −1.50000 + 0.866025i −0.0565736 + 0.0326628i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −34.2929 + 29.6985i −1.28972 + 1.11693i
$$708$$ 0 0
$$709$$ 20.0000 34.6410i 0.751116 1.30097i −0.196167 0.980571i $$-0.562849\pi$$
0.947282 0.320400i $$-0.103817\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 9.79796 0.366936
$$714$$ 0 0
$$715$$ −18.0000 −0.673162
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −13.4722 + 23.3345i −0.502428 + 0.870231i 0.497568 + 0.867425i $$0.334226\pi$$
−0.999996 + 0.00280593i $$0.999107\pi$$
$$720$$ 0 0
$$721$$ −7.50000 + 21.6506i −0.279315 + 0.806312i
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 2.44949 1.41421i 0.0909718 0.0525226i
$$726$$ 0 0
$$727$$ 25.9808i 0.963573i −0.876289 0.481787i $$-0.839988\pi$$
0.876289 0.481787i $$-0.160012\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −2.44949 4.24264i −0.0905977 0.156920i
$$732$$ 0 0
$$733$$ −34.5000 19.9186i −1.27429 0.735710i −0.298495 0.954411i $$-0.596485\pi$$
−0.975792 + 0.218702i $$0.929818\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 13.4722 + 7.77817i 0.496255 + 0.286513i
$$738$$ 0 0
$$739$$ −0.500000 0.866025i −0.0183928 0.0318573i 0.856683 0.515844i $$-0.172522\pi$$
−0.875075 + 0.483987i $$0.839188\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 24.0416i 0.882002i −0.897507 0.441001i $$-0.854624\pi$$
0.897507 0.441001i $$-0.145376\pi$$
$$744$$ 0 0
$$745$$ −12.0000 + 6.92820i −0.439646 + 0.253830i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −2.44949 + 7.07107i −0.0895024 + 0.258371i
$$750$$ 0 0
$$751$$ 14.5000 25.1147i 0.529113 0.916450i −0.470311 0.882501i $$-0.655858\pi$$
0.999424 0.0339490i $$-0.0108084\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 53.8888 1.96121
$$756$$ 0 0
$$757$$ 2.00000 0.0726912 0.0363456 0.999339i $$-0.488428\pi$$
0.0363456 + 0.999339i $$0.488428\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −12.2474 + 21.2132i −0.443970 + 0.768978i −0.997980 0.0635319i $$-0.979764\pi$$
0.554010 + 0.832510i $$0.313097\pi$$
$$762$$ 0 0
$$763$$ −2.00000 + 1.73205i −0.0724049 + 0.0627044i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −22.0454 + 12.7279i −0.796014 + 0.459579i
$$768$$ 0 0
$$769$$ 25.9808i 0.936890i −0.883493 0.468445i $$-0.844814\pi$$
0.883493 0.468445i $$-0.155186\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −13.4722 23.3345i −0.484561 0.839284i 0.515282 0.857021i $$-0.327687\pi$$
−0.999843 + 0.0177365i $$0.994354\pi$$
$$774$$ 0 0
$$775$$ 1.50000 + 0.866025i 0.0538816 + 0.0311086i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 11.0227 + 6.36396i 0.394929 + 0.228013i
$$780$$ 0 0
$$781$$ −5.00000 8.66025i −0.178914 0.309888i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 42.4264i 1.51426i
$$786$$ 0 0
$$787$$ 39.0000 22.5167i 1.39020 0.802632i 0.396863 0.917878i $$-0.370099\pi$$
0.993337 + 0.115246i $$0.0367655\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 3.67423 0.707107i 0.130641 0.0251418i
$$792$$ 0 0
$$793$$ 9.00000 15.5885i 0.319599 0.553562i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −29.3939 −1.04118 −0.520592 0.853805i $$-0.674289\pi$$
−0.520592