# Properties

 Label 1575.2.bc.a.899.2 Level $1575$ Weight $2$ Character 1575.899 Analytic conductor $12.576$ Analytic rank $0$ Dimension $8$ Inner twists $8$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1575,2,Mod(899,1575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1575, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("1575.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1575.bc (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: $$12.5764383184$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{24})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - x^{4} + 1$$ x^8 - x^4 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 63) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 899.2 Root $$-0.965926 + 0.258819i$$ of defining polynomial Character $$\chi$$ $$=$$ 1575.899 Dual form 1575.2.bc.a.1349.2

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.707107 - 1.22474i) q^{2} +(2.59808 + 0.500000i) q^{7} -2.82843 q^{8} +O(q^{10})$$ $$q+(-0.707107 - 1.22474i) q^{2} +(2.59808 + 0.500000i) q^{7} -2.82843 q^{8} +(-1.22474 - 0.707107i) q^{11} +5.19615 q^{13} +(-1.22474 - 3.53553i) q^{14} +(2.00000 + 3.46410i) q^{16} +(4.24264 + 2.44949i) q^{17} +(-1.50000 + 0.866025i) q^{19} +2.00000i q^{22} +(2.82843 + 4.89898i) q^{23} +(-3.67423 - 6.36396i) q^{26} +2.82843i q^{29} +(1.50000 + 0.866025i) q^{31} -6.92820i q^{34} +(0.866025 - 0.500000i) q^{37} +(2.12132 + 1.22474i) q^{38} -7.34847 q^{41} -1.00000i q^{43} +(4.00000 - 6.92820i) q^{46} +(10.6066 - 6.12372i) q^{47} +(6.50000 + 2.59808i) q^{49} +(-1.41421 + 2.44949i) q^{53} +(-7.34847 - 1.41421i) q^{56} +(3.46410 - 2.00000i) q^{58} +(2.44949 - 4.24264i) q^{59} +(-3.00000 + 1.73205i) q^{61} -2.44949i q^{62} +8.00000 q^{64} +(9.52628 + 5.50000i) q^{67} -7.07107i q^{71} +(-0.866025 + 1.50000i) q^{73} +(-1.22474 - 0.707107i) q^{74} +(-2.82843 - 2.44949i) q^{77} +(2.50000 + 4.33013i) q^{79} +(5.19615 + 9.00000i) q^{82} +7.34847i q^{83} +(-1.22474 + 0.707107i) q^{86} +(3.46410 + 2.00000i) q^{88} +(-2.44949 - 4.24264i) q^{89} +(13.5000 + 2.59808i) q^{91} +(-15.0000 - 8.66025i) q^{94} -10.3923 q^{97} +(-1.41421 - 9.79796i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q+O(q^{10})$$ 8 * q $$8 q + 16 q^{16} - 12 q^{19} + 12 q^{31} + 32 q^{46} + 52 q^{49} - 24 q^{61} + 64 q^{64} + 20 q^{79} + 108 q^{91} - 120 q^{94}+O(q^{100})$$ 8 * q + 16 * q^16 - 12 * q^19 + 12 * q^31 + 32 * q^46 + 52 * q^49 - 24 * q^61 + 64 * q^64 + 20 * q^79 + 108 * q^91 - 120 * q^94

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$1226$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.707107 1.22474i −0.500000 0.866025i 0.500000 0.866025i $$-0.333333\pi$$
−1.00000 $$\pi$$
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 2.59808 + 0.500000i 0.981981 + 0.188982i
$$8$$ −2.82843 −1.00000
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −1.22474 0.707107i −0.369274 0.213201i 0.303867 0.952714i $$-0.401722\pi$$
−0.673141 + 0.739514i $$0.735055\pi$$
$$12$$ 0 0
$$13$$ 5.19615 1.44115 0.720577 0.693375i $$-0.243877\pi$$
0.720577 + 0.693375i $$0.243877\pi$$
$$14$$ −1.22474 3.53553i −0.327327 0.944911i
$$15$$ 0 0
$$16$$ 2.00000 + 3.46410i 0.500000 + 0.866025i
$$17$$ 4.24264 + 2.44949i 1.02899 + 0.594089i 0.916696 0.399586i $$-0.130846\pi$$
0.112296 + 0.993675i $$0.464180\pi$$
$$18$$ 0 0
$$19$$ −1.50000 + 0.866025i −0.344124 + 0.198680i −0.662094 0.749421i $$-0.730332\pi$$
0.317970 + 0.948101i $$0.396999\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 2.00000i 0.426401i
$$23$$ 2.82843 + 4.89898i 0.589768 + 1.02151i 0.994263 + 0.106967i $$0.0341141\pi$$
−0.404495 + 0.914540i $$0.632553\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ −3.67423 6.36396i −0.720577 1.24808i
$$27$$ 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 $$-0.283621\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 6.92820i 1.18818i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0.866025 0.500000i 0.142374 0.0821995i −0.427121 0.904194i $$-0.640472\pi$$
0.569495 + 0.821995i $$0.307139\pi$$
$$38$$ 2.12132 + 1.22474i 0.344124 + 0.198680i
$$39$$ 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
$$43$$ 1.00000i 0.152499i −0.997089 0.0762493i $$-0.975706\pi$$
0.997089 0.0762493i $$-0.0242945\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 4.00000 6.92820i 0.589768 1.02151i
$$47$$ 10.6066 6.12372i 1.54713 0.893237i 0.548773 0.835971i $$-0.315095\pi$$
0.998359 0.0572655i $$-0.0182382\pi$$
$$48$$ 0 0
$$49$$ 6.50000 + 2.59808i 0.928571 + 0.371154i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −1.41421 + 2.44949i −0.194257 + 0.336463i −0.946657 0.322244i $$-0.895563\pi$$
0.752400 + 0.658707i $$0.228896\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −7.34847 1.41421i −0.981981 0.188982i
$$57$$ 0 0
$$58$$ 3.46410 2.00000i 0.454859 0.262613i
$$59$$ 2.44949 4.24264i 0.318896 0.552345i −0.661362 0.750067i $$-0.730021\pi$$
0.980258 + 0.197722i $$0.0633545\pi$$
$$60$$ 0 0
$$61$$ −3.00000 + 1.73205i −0.384111 + 0.221766i −0.679605 0.733578i $$-0.737849\pi$$
0.295495 + 0.955344i $$0.404516\pi$$
$$62$$ 2.44949i 0.311086i
$$63$$ 0 0
$$64$$ 8.00000 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 9.52628 + 5.50000i 1.16382 + 0.671932i 0.952217 0.305424i $$-0.0987981\pi$$
0.211604 + 0.977356i $$0.432131\pi$$
$$68$$ 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
$$73$$ −0.866025 + 1.50000i −0.101361 + 0.175562i −0.912245 0.409644i $$-0.865653\pi$$
0.810885 + 0.585206i $$0.198986\pi$$
$$74$$ −1.22474 0.707107i −0.142374 0.0821995i
$$75$$ 0 0
$$76$$ 0 0
$$77$$ −2.82843 2.44949i −0.322329 0.279145i
$$78$$ 0 0
$$79$$ 2.50000 + 4.33013i 0.281272 + 0.487177i 0.971698 0.236225i $$-0.0759104\pi$$
−0.690426 + 0.723403i $$0.742577\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 5.19615 + 9.00000i 0.573819 + 0.993884i
$$83$$ 7.34847i 0.806599i 0.915068 + 0.403300i $$0.132137\pi$$
−0.915068 + 0.403300i $$0.867863\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −1.22474 + 0.707107i −0.132068 + 0.0762493i
$$87$$ 0 0
$$88$$ 3.46410 + 2.00000i 0.369274 + 0.213201i
$$89$$ −2.44949 4.24264i −0.259645 0.449719i 0.706502 0.707712i $$-0.250272\pi$$
−0.966147 + 0.257993i $$0.916939\pi$$
$$90$$ 0 0
$$91$$ 13.5000 + 2.59808i 1.41518 + 0.272352i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ −15.0000 8.66025i −1.54713 0.893237i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −10.3923 −1.05518 −0.527589 0.849500i $$-0.676904\pi$$
−0.527589 + 0.849500i $$0.676904\pi$$
$$98$$ −1.41421 9.79796i −0.142857 0.989743i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 8.57321 14.8492i 0.853067 1.47755i −0.0253604 0.999678i $$-0.508073\pi$$
0.878427 0.477876i $$-0.158593\pi$$
$$102$$ 0 0
$$103$$ −4.33013 7.50000i −0.426660 0.738997i 0.569914 0.821705i $$-0.306977\pi$$
−0.996574 + 0.0827075i $$0.973643\pi$$
$$104$$ −14.6969 −1.44115
$$105$$ 0 0
$$106$$ 4.00000 0.388514
$$107$$ 1.41421 + 2.44949i 0.136717 + 0.236801i 0.926252 0.376905i $$-0.123012\pi$$
−0.789535 + 0.613706i $$0.789678\pi$$
$$108$$ 0 0
$$109$$ −0.500000 + 0.866025i −0.0478913 + 0.0829502i −0.888977 0.457951i $$-0.848583\pi$$
0.841086 + 0.540901i $$0.181917\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 3.46410 + 10.0000i 0.327327 + 0.944911i
$$113$$ −1.41421 −0.133038 −0.0665190 0.997785i $$-0.521189\pi$$
−0.0665190 + 0.997785i $$0.521189\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ −6.92820 −0.637793
$$119$$ 9.79796 + 8.48528i 0.898177 + 0.777844i
$$120$$ 0 0
$$121$$ −4.50000 7.79423i −0.409091 0.708566i
$$122$$ 4.24264 + 2.44949i 0.384111 + 0.221766i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 11.0000i 0.976092i −0.872818 0.488046i $$-0.837710\pi$$
0.872818 0.488046i $$-0.162290\pi$$
$$128$$ −5.65685 9.79796i −0.500000 0.866025i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ −1.22474 2.12132i −0.107006 0.185341i 0.807550 0.589799i $$-0.200793\pi$$
−0.914556 + 0.404459i $$0.867460\pi$$
$$132$$ 0 0
$$133$$ −4.33013 + 1.50000i −0.375470 + 0.130066i
$$134$$ 15.5563i 1.34386i
$$135$$ 0 0
$$136$$ −12.0000 6.92820i −1.02899 0.594089i
$$137$$ 5.65685 9.79796i 0.483298 0.837096i −0.516518 0.856276i $$-0.672772\pi$$
0.999816 + 0.0191800i $$0.00610555\pi$$
$$138$$ 0 0
$$139$$ 5.19615i 0.440732i 0.975417 + 0.220366i $$0.0707252\pi$$
−0.975417 + 0.220366i $$0.929275\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ −8.66025 + 5.00000i −0.726752 + 0.419591i
$$143$$ −6.36396 3.67423i −0.532181 0.307255i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 2.44949 0.202721
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −4.89898 + 2.82843i −0.401340 + 0.231714i −0.687062 0.726599i $$-0.741100\pi$$
0.285722 + 0.958313i $$0.407767\pi$$
$$150$$ 0 0
$$151$$ 11.0000 19.0526i 0.895167 1.55048i 0.0615699 0.998103i $$-0.480389\pi$$
0.833597 0.552372i $$-0.186277\pi$$
$$152$$ 4.24264 2.44949i 0.344124 0.198680i
$$153$$ 0 0
$$154$$ −1.00000 + 5.19615i −0.0805823 + 0.418718i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 8.66025 15.0000i 0.691164 1.19713i −0.280293 0.959914i $$-0.590432\pi$$
0.971457 0.237216i $$-0.0762349\pi$$
$$158$$ 3.53553 6.12372i 0.281272 0.487177i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 4.89898 + 14.1421i 0.386094 + 1.11456i
$$162$$ 0 0
$$163$$ −8.66025 + 5.00000i −0.678323 + 0.391630i −0.799223 0.601035i $$-0.794755\pi$$
0.120900 + 0.992665i $$0.461422\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 9.00000 5.19615i 0.698535 0.403300i
$$167$$ 7.34847i 0.568642i 0.958729 + 0.284321i $$0.0917681\pi$$
−0.958729 + 0.284321i $$0.908232\pi$$
$$168$$ 0 0
$$169$$ 14.0000 1.07692
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 8.48528 4.89898i 0.645124 0.372463i −0.141462 0.989944i $$-0.545180\pi$$
0.786586 + 0.617481i $$0.211847\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 5.65685i 0.426401i
$$177$$ 0 0
$$178$$ −3.46410 + 6.00000i −0.259645 + 0.449719i
$$179$$ 8.57321 + 4.94975i 0.640792 + 0.369961i 0.784920 0.619598i $$-0.212704\pi$$
−0.144127 + 0.989559i $$0.546038\pi$$
$$180$$ 0 0
$$181$$ 15.5885i 1.15868i 0.815086 + 0.579340i $$0.196690\pi$$
−0.815086 + 0.579340i $$0.803310\pi$$
$$182$$ −6.36396 18.3712i −0.471728 1.36176i
$$183$$ 0 0
$$184$$ −8.00000 13.8564i −0.589768 1.02151i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −3.46410 6.00000i −0.253320 0.438763i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 1.22474 0.707107i 0.0886194 0.0511645i −0.455035 0.890473i $$-0.650373\pi$$
0.543655 + 0.839309i $$0.317040\pi$$
$$192$$ 0 0
$$193$$ −9.52628 5.50000i −0.685717 0.395899i 0.116289 0.993215i $$-0.462900\pi$$
−0.802005 + 0.597317i $$0.796234\pi$$
$$194$$ 7.34847 + 12.7279i 0.527589 + 0.913812i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ −19.7990 −1.41062 −0.705310 0.708899i $$-0.749192\pi$$
−0.705310 + 0.708899i $$0.749192\pi$$
$$198$$ 0 0
$$199$$ 12.0000 + 6.92820i 0.850657 + 0.491127i 0.860873 0.508821i $$-0.169918\pi$$
−0.0102152 + 0.999948i $$0.503252\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ −24.2487 −1.70613
$$203$$ −1.41421 + 7.34847i −0.0992583 + 0.515761i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −6.12372 + 10.6066i −0.426660 + 0.738997i
$$207$$ 0 0
$$208$$ 10.3923 + 18.0000i 0.720577 + 1.24808i
$$209$$ 2.44949 0.169435
$$210$$ 0 0
$$211$$ −22.0000 −1.51454 −0.757271 0.653101i $$-0.773468\pi$$
−0.757271 + 0.653101i $$0.773468\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 2.00000 3.46410i 0.136717 0.236801i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 3.46410 + 3.00000i 0.235159 + 0.203653i
$$218$$ 1.41421 0.0957826
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 22.0454 + 12.7279i 1.48293 + 0.856173i
$$222$$ 0 0
$$223$$ −20.7846 −1.39184 −0.695920 0.718119i $$-0.745003\pi$$
−0.695920 + 0.718119i $$0.745003\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 1.00000 + 1.73205i 0.0665190 + 0.115214i
$$227$$ 23.3345 + 13.4722i 1.54877 + 0.894181i 0.998236 + 0.0593658i $$0.0189078\pi$$
0.550530 + 0.834815i $$0.314425\pi$$
$$228$$ 0 0
$$229$$ −19.5000 + 11.2583i −1.28860 + 0.743971i −0.978404 0.206702i $$-0.933727\pi$$
−0.310192 + 0.950674i $$0.600393\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 8.00000i 0.525226i
$$233$$ 4.94975 + 8.57321i 0.324269 + 0.561650i 0.981364 0.192158i $$-0.0615485\pi$$
−0.657095 + 0.753807i $$0.728215\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 3.46410 18.0000i 0.224544 1.16677i
$$239$$ 26.8701i 1.73808i −0.494742 0.869040i $$-0.664738\pi$$
0.494742 0.869040i $$-0.335262\pi$$
$$240$$ 0 0
$$241$$ −12.0000 6.92820i −0.772988 0.446285i 0.0609515 0.998141i $$-0.480586\pi$$
−0.833939 + 0.551856i $$0.813920\pi$$
$$242$$ −6.36396 + 11.0227i −0.409091 + 0.708566i
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −7.79423 + 4.50000i −0.495935 + 0.286328i
$$248$$ −4.24264 2.44949i −0.269408 0.155543i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$252$$ 0 0
$$253$$ 8.00000i 0.502956i
$$254$$ −13.4722 + 7.77817i −0.845321 + 0.488046i
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −2.12132 + 1.22474i −0.132324 + 0.0763975i −0.564701 0.825296i $$-0.691008\pi$$
0.432377 + 0.901693i $$0.357675\pi$$
$$258$$ 0 0
$$259$$ 2.50000 0.866025i 0.155342 0.0538122i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −1.73205 + 3.00000i −0.107006 + 0.185341i
$$263$$ 7.07107 12.2474i 0.436021 0.755210i −0.561358 0.827573i $$-0.689721\pi$$
0.997378 + 0.0723633i $$0.0230541\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 4.89898 + 4.24264i 0.300376 + 0.260133i
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −8.57321 + 14.8492i −0.522718 + 0.905374i 0.476932 + 0.878940i $$0.341749\pi$$
−0.999651 + 0.0264343i $$0.991585\pi$$
$$270$$ 0 0
$$271$$ −12.0000 + 6.92820i −0.728948 + 0.420858i −0.818037 0.575165i $$-0.804938\pi$$
0.0890891 + 0.996024i $$0.471604\pi$$
$$272$$ 19.5959i 1.18818i
$$273$$ 0 0
$$274$$ −16.0000 −0.966595
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 19.9186 + 11.5000i 1.19679 + 0.690968i 0.959839 0.280553i $$-0.0905179\pi$$
0.236953 + 0.971521i $$0.423851\pi$$
$$278$$ 6.36396 3.67423i 0.381685 0.220366i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 22.6274i 1.34984i 0.737892 + 0.674919i $$0.235822\pi$$
−0.737892 + 0.674919i $$0.764178\pi$$
$$282$$ 0 0
$$283$$ −0.866025 + 1.50000i −0.0514799 + 0.0891657i −0.890617 0.454754i $$-0.849727\pi$$
0.839137 + 0.543920i $$0.183060\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 10.3923i 0.614510i
$$287$$ −19.0919 3.67423i −1.12696 0.216883i
$$288$$ 0 0
$$289$$ 3.50000 + 6.06218i 0.205882 + 0.356599i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 14.6969i 0.858604i 0.903161 + 0.429302i $$0.141240\pi$$
−0.903161 + 0.429302i $$0.858760\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −2.44949 + 1.41421i −0.142374 + 0.0821995i
$$297$$ 0 0
$$298$$ 6.92820 + 4.00000i 0.401340 + 0.231714i
$$299$$ 14.6969 + 25.4558i 0.849946 + 1.47215i
$$300$$ 0 0
$$301$$ 0.500000 2.59808i 0.0288195 0.149751i
$$302$$ −31.1127 −1.79033
$$303$$ 0 0
$$304$$ −6.00000 3.46410i −0.344124 0.198680i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −15.5885 −0.889680 −0.444840 0.895610i $$-0.646740\pi$$
−0.444840 + 0.895610i $$0.646740\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 8.57321 14.8492i 0.486142 0.842023i −0.513731 0.857951i $$-0.671737\pi$$
0.999873 + 0.0159282i $$0.00507031\pi$$
$$312$$ 0 0
$$313$$ 6.06218 + 10.5000i 0.342655 + 0.593495i 0.984925 0.172983i $$-0.0553406\pi$$
−0.642270 + 0.766478i $$0.722007\pi$$
$$314$$ −24.4949 −1.38233
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −7.07107 12.2474i −0.397151 0.687885i 0.596222 0.802819i $$-0.296668\pi$$
−0.993373 + 0.114934i $$0.963334\pi$$
$$318$$ 0 0
$$319$$ 2.00000 3.46410i 0.111979 0.193952i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 13.8564 16.0000i 0.772187 0.891645i
$$323$$ −8.48528 −0.472134
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 12.2474 + 7.07107i 0.678323 + 0.391630i
$$327$$ 0 0
$$328$$ 20.7846 1.14764
$$329$$ 30.6186 10.6066i 1.68806 0.584761i
$$330$$ 0 0
$$331$$ 15.5000 + 26.8468i 0.851957 + 1.47563i 0.879440 + 0.476011i $$0.157918\pi$$
−0.0274825 + 0.999622i $$0.508749\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 9.00000 5.19615i 0.492458 0.284321i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 23.0000i 1.25289i −0.779466 0.626445i $$-0.784509\pi$$
0.779466 0.626445i $$-0.215491\pi$$
$$338$$ −9.89949 17.1464i −0.538462 0.932643i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −1.22474 2.12132i −0.0663237 0.114876i
$$342$$ 0 0
$$343$$ 15.5885 + 10.0000i 0.841698 + 0.539949i
$$344$$ 2.82843i 0.152499i
$$345$$ 0 0
$$346$$ −12.0000 6.92820i −0.645124 0.372463i
$$347$$ −15.5563 + 26.9444i −0.835109 + 1.44645i 0.0588334 + 0.998268i $$0.481262\pi$$
−0.893942 + 0.448183i $$0.852071\pi$$
$$348$$ 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
$$353$$ 14.8492 + 8.57321i 0.790345 + 0.456306i 0.840084 0.542456i $$-0.182506\pi$$
−0.0497387 + 0.998762i $$0.515839\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 14.0000i 0.739923i
$$359$$ 24.4949 14.1421i 1.29279 0.746393i 0.313643 0.949541i $$-0.398450\pi$$
0.979148 + 0.203148i $$0.0651171\pi$$
$$360$$ 0 0
$$361$$ −8.00000 + 13.8564i −0.421053 + 0.729285i
$$362$$ 19.0919 11.0227i 1.00345 0.579340i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0.866025 1.50000i 0.0452062 0.0782994i −0.842537 0.538639i $$-0.818939\pi$$
0.887743 + 0.460339i $$0.152272\pi$$
$$368$$ −11.3137 + 19.5959i −0.589768 + 1.02151i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −4.89898 + 5.65685i −0.254342 + 0.293689i
$$372$$ 0 0
$$373$$ 25.1147 14.5000i 1.30039 0.750782i 0.319921 0.947444i $$-0.396344\pi$$
0.980471 + 0.196663i $$0.0630104\pi$$
$$374$$ −4.89898 + 8.48528i −0.253320 + 0.438763i
$$375$$ 0 0
$$376$$ −30.0000 + 17.3205i −1.54713 + 0.893237i
$$377$$ 14.6969i 0.756931i
$$378$$ 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
$$382$$ −1.73205 1.00000i −0.0886194 0.0511645i
$$383$$ −16.9706 + 9.79796i −0.867155 + 0.500652i −0.866402 0.499347i $$-0.833573\pi$$
−0.000753393 1.00000i $$0.500240\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 15.5563i 0.791797i
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 23.2702 + 13.4350i 1.17984 + 0.681183i 0.955978 0.293437i $$-0.0947991\pi$$
0.223865 + 0.974620i $$0.428132\pi$$
$$390$$ 0 0
$$391$$ 27.7128i 1.40150i
$$392$$ −18.3848 7.34847i −0.928571 0.371154i
$$393$$ 0 0
$$394$$ 14.0000 + 24.2487i 0.705310 + 1.22163i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −0.866025 1.50000i −0.0434646 0.0752828i 0.843475 0.537169i $$-0.180506\pi$$
−0.886939 + 0.461886i $$0.847173\pi$$
$$398$$ 19.5959i 0.982255i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −17.1464 + 9.89949i −0.856252 + 0.494357i −0.862755 0.505622i $$-0.831263\pi$$
0.00650355 + 0.999979i $$0.497930\pi$$
$$402$$ 0 0
$$403$$ 7.79423 + 4.50000i 0.388258 + 0.224161i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 10.0000 3.46410i 0.496292 0.171920i
$$407$$ −1.41421 −0.0701000
$$408$$ 0 0
$$409$$ −28.5000 16.4545i −1.40923 0.813622i −0.413920 0.910313i $$-0.635841\pi$$
−0.995314 + 0.0966915i $$0.969174\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 8.48528 9.79796i 0.417533 0.482126i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ −1.73205 3.00000i −0.0847174 0.146735i
$$419$$ −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 $$0.507758\pi$$
$$422$$ 15.5563 + 26.9444i 0.757271 + 1.31163i
$$423$$ 0 0
$$424$$ 4.00000 6.92820i 0.194257 0.336463i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −8.66025 + 3.00000i −0.419099 + 0.145180i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 13.4722 + 7.77817i 0.648933 + 0.374661i 0.788047 0.615615i $$-0.211092\pi$$
−0.139114 + 0.990276i $$0.544426\pi$$
$$432$$ 0 0
$$433$$ −15.5885 −0.749133 −0.374567 0.927200i $$-0.622209\pi$$
−0.374567 + 0.927200i $$0.622209\pi$$
$$434$$ 1.22474 6.36396i 0.0587896 0.305480i
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −8.48528 4.89898i −0.405906 0.234350i
$$438$$ 0 0
$$439$$ −24.0000 + 13.8564i −1.14546 + 0.661330i −0.947776 0.318936i $$-0.896674\pi$$
−0.197681 + 0.980266i $$0.563341\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 36.0000i 1.71235i
$$443$$ 19.7990 + 34.2929i 0.940678 + 1.62930i 0.764181 + 0.645002i $$0.223143\pi$$
0.176497 + 0.984301i $$0.443523\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 14.6969 + 25.4558i 0.695920 + 1.20537i
$$447$$ 0 0
$$448$$ 20.7846 + 4.00000i 0.981981 + 0.188982i
$$449$$ 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
$$454$$ 38.1051i 1.78836i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −4.33013 + 2.50000i −0.202555 + 0.116945i −0.597847 0.801611i $$-0.703977\pi$$
0.395292 + 0.918556i $$0.370643\pi$$
$$458$$ 27.5772 + 15.9217i 1.28860 + 0.743971i
$$459$$ 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
$$463$$ 13.0000i 0.604161i −0.953282 0.302081i $$-0.902319\pi$$
0.953282 0.302081i $$-0.0976812\pi$$
$$464$$ −9.79796 + 5.65685i −0.454859 + 0.262613i
$$465$$ 0 0
$$466$$ 7.00000 12.1244i 0.324269 0.561650i
$$467$$ 23.3345 13.4722i 1.07979 0.623419i 0.148952 0.988844i $$-0.452410\pi$$
0.930841 + 0.365426i $$0.119077\pi$$
$$468$$ 0 0
$$469$$ 22.0000 + 19.0526i 1.01587 + 0.879765i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −6.92820 + 12.0000i −0.318896 + 0.552345i
$$473$$ −0.707107 + 1.22474i −0.0325128 + 0.0563138i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −32.9090 + 19.0000i −1.50522 + 0.869040i
$$479$$ 2.44949 4.24264i 0.111920 0.193851i −0.804624 0.593784i $$-0.797633\pi$$
0.916544 + 0.399933i $$0.130967\pi$$
$$480$$ 0 0
$$481$$ 4.50000 2.59808i 0.205182 0.118462i
$$482$$ 19.5959i 0.892570i
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 14.7224 + 8.50000i 0.667137 + 0.385172i 0.794991 0.606621i $$-0.207476\pi$$
−0.127854 + 0.991793i $$0.540809\pi$$
$$488$$ 8.48528 4.89898i 0.384111 0.221766i
$$489$$ 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
$$493$$ −6.92820 + 12.0000i −0.312031 + 0.540453i
$$494$$ 11.0227 + 6.36396i 0.495935 + 0.286328i
$$495$$ 0 0
$$496$$ 6.92820i 0.311086i
$$497$$ 3.53553 18.3712i 0.158590 0.824060i
$$498$$ 0 0
$$499$$ −12.5000 21.6506i −0.559577 0.969216i −0.997532 0.0702185i $$-0.977630\pi$$
0.437955 0.898997i $$-0.355703\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 22.0454i 0.982956i 0.870890 + 0.491478i $$0.163543\pi$$
−0.870890 + 0.491478i $$0.836457\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −9.79796 + 5.65685i −0.435572 + 0.251478i
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 1.22474 + 2.12132i 0.0542859 + 0.0940259i 0.891891 0.452250i $$-0.149378\pi$$
−0.837605 + 0.546276i $$0.816045\pi$$
$$510$$ 0 0
$$511$$ −3.00000 + 3.46410i −0.132712 + 0.153243i
$$512$$ −22.6274 −1.00000
$$513$$ 0 0
$$514$$ 3.00000 + 1.73205i 0.132324 + 0.0763975i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −17.3205 −0.761755
$$518$$ −2.82843 2.44949i −0.124274 0.107624i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −2.44949 + 4.24264i −0.107314 + 0.185873i −0.914681 0.404176i $$-0.867558\pi$$
0.807367 + 0.590049i $$0.200892\pi$$
$$522$$ 0 0
$$523$$ 0.866025 + 1.50000i 0.0378686 + 0.0655904i 0.884339 0.466846i $$-0.154610\pi$$
−0.846470 + 0.532437i $$0.821276\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −20.0000 −0.872041
$$527$$ 4.24264 + 7.34847i 0.184812 + 0.320104i
$$528$$ 0 0
$$529$$ −4.50000 + 7.79423i −0.195652 + 0.338880i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −38.1838 −1.65392
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −26.9444 15.5563i −1.16382 0.671932i
$$537$$ 0 0
$$538$$ 24.2487 1.04544
$$539$$ −6.12372 7.77817i −0.263767 0.335030i
$$540$$ 0 0
$$541$$ −8.50000 14.7224i −0.365444 0.632967i 0.623404 0.781900i $$-0.285749\pi$$
−0.988847 + 0.148933i $$0.952416\pi$$
$$542$$ 16.9706 + 9.79796i 0.728948 + 0.420858i
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 10.0000i 0.427569i 0.976881 + 0.213785i $$0.0685791\pi$$
−0.976881 + 0.213785i $$0.931421\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −2.44949 4.24264i −0.104352 0.180743i
$$552$$ 0 0
$$553$$ 4.33013 + 12.5000i 0.184136 + 0.531554i
$$554$$ 32.5269i 1.38194i
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 7.77817 13.4722i 0.329572 0.570835i −0.652855 0.757483i $$-0.726429\pi$$
0.982427 + 0.186648i $$0.0597623\pi$$
$$558$$ 0 0
$$559$$ 5.19615i 0.219774i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 27.7128 16.0000i 1.16899 0.674919i
$$563$$ −23.3345 13.4722i −0.983433 0.567785i −0.0801281 0.996785i $$-0.525533\pi$$
−0.903305 + 0.428999i $$0.858866\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 2.44949 0.102960
$$567$$ 0 0
$$568$$ 20.0000i 0.839181i
$$569$$ −1.22474 + 0.707107i −0.0513440 + 0.0296435i −0.525452 0.850823i $$-0.676104\pi$$
0.474108 + 0.880467i $$0.342771\pi$$
$$570$$ 0 0
$$571$$ −5.50000 + 9.52628i −0.230168 + 0.398662i −0.957857 0.287244i $$-0.907261\pi$$
0.727690 + 0.685907i $$0.240594\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 9.00000 + 25.9808i 0.375653 + 1.08442i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 0.866025 1.50000i 0.0360531 0.0624458i −0.847436 0.530898i $$-0.821855\pi$$
0.883489 + 0.468452i $$0.155188\pi$$
$$578$$ 4.94975 8.57321i 0.205882 0.356599i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −3.67423 + 19.0919i −0.152433 + 0.792065i
$$582$$ 0 0
$$583$$ 3.46410 2.00000i 0.143468 0.0828315i
$$584$$ 2.44949 4.24264i 0.101361 0.175562i
$$585$$ 0 0
$$586$$ 18.0000 10.3923i 0.743573 0.429302i
$$587$$ 14.6969i 0.606608i 0.952894 + 0.303304i $$0.0980897\pi$$
−0.952894 + 0.303304i $$0.901910\pi$$
$$588$$ 0 0
$$589$$ −3.00000 −0.123613
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 3.46410 + 2.00000i 0.142374 + 0.0821995i
$$593$$ 14.8492 8.57321i 0.609785 0.352060i −0.163096 0.986610i $$-0.552148\pi$$
0.772881 + 0.634550i $$0.218815\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 20.7846 36.0000i 0.849946 1.47215i
$$599$$ 4.89898 + 2.82843i 0.200167 + 0.115566i 0.596733 0.802440i $$-0.296465\pi$$
−0.396566 + 0.918006i $$0.629798\pi$$
$$600$$ 0 0
$$601$$ 25.9808i 1.05978i −0.848067 0.529889i $$-0.822234\pi$$
0.848067 0.529889i $$-0.177766\pi$$
$$602$$ −3.53553 + 1.22474i −0.144098 + 0.0499169i
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 19.9186 + 34.5000i 0.808470 + 1.40031i 0.913923 + 0.405887i $$0.133038\pi$$
−0.105453 + 0.994424i $$0.533629\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 55.1135 31.8198i 2.22965 1.28729i
$$612$$ 0 0
$$613$$ −6.92820 4.00000i −0.279827 0.161558i 0.353518 0.935428i $$-0.384985\pi$$
−0.633345 + 0.773869i $$0.718319\pi$$
$$614$$ 11.0227 + 19.0919i 0.444840 + 0.770486i
$$615$$ 0 0
$$616$$ 8.00000 + 6.92820i 0.322329 + 0.279145i
$$617$$ −24.0416 −0.967880 −0.483940 0.875101i $$-0.660795\pi$$
−0.483940 + 0.875101i $$0.660795\pi$$
$$618$$ 0 0
$$619$$ 25.5000 + 14.7224i 1.02493 + 0.591744i 0.915529 0.402253i $$-0.131773\pi$$
0.109403 + 0.993997i $$0.465106\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −24.2487 −0.972285
$$623$$ −4.24264 12.2474i −0.169978 0.490684i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 8.57321 14.8492i 0.342655 0.593495i
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 4.89898 0.195335
$$630$$ 0 0
$$631$$ 38.0000 1.51276 0.756378 0.654135i $$-0.226967\pi$$
0.756378 + 0.654135i $$0.226967\pi$$
$$632$$ −7.07107 12.2474i −0.281272 0.487177i
$$633$$ 0 0
$$634$$ −10.0000 + 17.3205i −0.397151 + 0.687885i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 33.7750 + 13.5000i 1.33821 + 0.534889i
$$638$$ −5.65685 −0.223957
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −12.2474 7.07107i −0.483745 0.279290i 0.238231 0.971209i $$-0.423433\pi$$
−0.721976 + 0.691918i $$0.756766\pi$$
$$642$$ 0 0
$$643$$ −25.9808 −1.02458 −0.512291 0.858812i $$-0.671203\pi$$
−0.512291 + 0.858812i $$0.671203\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 6.00000 + 10.3923i 0.236067 + 0.408880i
$$647$$ −14.8492 8.57321i −0.583784 0.337048i 0.178852 0.983876i $$-0.442762\pi$$
−0.762636 + 0.646828i $$0.776095\pi$$
$$648$$ 0 0
$$649$$ −6.00000 + 3.46410i −0.235521 + 0.135978i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −3.53553 6.12372i −0.138356 0.239640i 0.788518 0.615011i $$-0.210849\pi$$
−0.926875 + 0.375371i $$0.877515\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −14.6969 25.4558i −0.573819 0.993884i
$$657$$ 0 0
$$658$$ −34.6410 30.0000i −1.35045 1.16952i
$$659$$ 22.6274i 0.881439i −0.897645 0.440720i $$-0.854723\pi$$
0.897645 0.440720i $$-0.145277\pi$$
$$660$$ 0 0
$$661$$ −25.5000 14.7224i −0.991835 0.572636i −0.0860127 0.996294i $$-0.527413\pi$$
−0.905822 + 0.423658i $$0.860746\pi$$
$$662$$ 21.9203 37.9671i 0.851957 1.47563i
$$663$$ 0 0
$$664$$ 20.7846i 0.806599i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −13.8564 + 8.00000i −0.536522 + 0.309761i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 4.89898 0.189123
$$672$$ 0 0
$$673$$ 35.0000i 1.34915i 0.738206 + 0.674575i $$0.235673\pi$$
−0.738206 + 0.674575i $$0.764327\pi$$
$$674$$ −28.1691 + 16.2635i −1.08503 + 0.626445i
$$675$$ 0 0
$$676$$ 0 0
$$677$$ −8.48528 + 4.89898i −0.326116 + 0.188283i −0.654115 0.756395i $$-0.726959\pi$$
0.327999 + 0.944678i $$0.393626\pi$$
$$678$$ 0 0
$$679$$ −27.0000 5.19615i −1.03616 0.199410i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ −1.73205 + 3.00000i −0.0663237 + 0.114876i
$$683$$ 24.0416 41.6413i 0.919927 1.59336i 0.120405 0.992725i $$-0.461581\pi$$
0.799522 0.600636i $$-0.205086\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 1.22474 26.1630i 0.0467610 0.998906i
$$687$$ 0 0
$$688$$ 3.46410 2.00000i 0.132068 0.0762493i
$$689$$ −7.34847 + 12.7279i −0.279954 + 0.484895i
$$690$$ 0 0
$$691$$ 37.5000 21.6506i 1.42657 0.823629i 0.429719 0.902963i $$-0.358613\pi$$
0.996848 + 0.0793336i $$0.0252792\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 44.0000 1.67022
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −31.1769 18.0000i −1.18091 0.681799i
$$698$$ 12.7279 7.34847i 0.481759 0.278144i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 5.65685i 0.213656i 0.994277 + 0.106828i $$0.0340695\pi$$
−0.994277 + 0.106828i $$0.965931\pi$$
$$702$$ 0 0
$$703$$ −0.866025 + 1.50000i −0.0326628 + 0.0565736i
$$704$$ −9.79796 5.65685i −0.369274 0.213201i
$$705$$ 0 0
$$706$$ 24.2487i 0.912612i
$$707$$ 29.6985 34.2929i 1.11693 1.28972i
$$708$$ 0 0
$$709$$ −20.0000 34.6410i −0.751116 1.30097i −0.947282 0.320400i $$-0.896183\pi$$
0.196167 0.980571i $$-0.437151\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 6.92820 + 12.0000i 0.259645 + 0.449719i
$$713$$ 9.79796i 0.366936i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ −34.6410 20.0000i −1.29279 0.746393i
$$719$$ −13.4722 23.3345i −0.502428 0.870231i −0.999996 0.00280593i $$-0.999107\pi$$
0.497568 0.867425i $$-0.334226\pi$$
$$720$$ 0 0
$$721$$ −7.50000 21.6506i −0.279315 0.806312i
$$722$$ 22.6274 0.842105
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ −25.9808 −0.963573 −0.481787 0.876289i $$-0.660012\pi$$
−0.481787 + 0.876289i $$0.660012\pi$$
$$728$$ −38.1838 7.34847i −1.41518 0.272352i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 2.44949 4.24264i 0.0905977 0.156920i
$$732$$ 0 0
$$733$$ −19.9186 34.5000i −0.735710 1.27429i −0.954411 0.298495i $$-0.903515\pi$$
0.218702 0.975792i $$-0.429818\pi$$
$$734$$ −2.44949 −0.0904123
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −7.77817 13.4722i −0.286513 0.496255i
$$738$$ 0 0
$$739$$ −0.500000 + 0.866025i −0.0183928 + 0.0318573i −0.875075 0.483987i $$-0.839188\pi$$
0.856683 + 0.515844i $$0.172522\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 10.3923 + 2.00000i 0.381514 + 0.0734223i
$$743$$ 24.0416 0.882002 0.441001 0.897507i $$-0.354624\pi$$
0.441001 + 0.897507i $$0.354624\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −35.5176 20.5061i −1.30039 0.750782i
$$747$$ 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 −0.999424 0.0339490i $$-0.989192\pi$$
0.470311 0.882501i $$-0.344142\pi$$
$$752$$ 42.4264 + 24.4949i 1.54713 + 0.893237i
$$753$$ 0 0
$$754$$ 18.0000 10.3923i 0.655521 0.378465i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 2.00000i 0.0726912i −0.999339 0.0363456i $$-0.988428\pi$$
0.999339 0.0363456i $$-0.0115717\pi$$
$$758$$ −4.94975 8.57321i −0.179783 0.311393i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −12.2474 21.2132i −0.443970 0.768978i 0.554010 0.832510i $$-0.313097\pi$$
−0.997980 + 0.0635319i $$0.979764\pi$$
$$762$$ 0 0
$$763$$ −1.73205 + 2.00000i −0.0627044 + 0.0724049i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 24.0000 + 13.8564i 0.867155 + 0.500652i
$$767$$ 12.7279 22.0454i 0.459579 0.796014i
$$768$$ 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
$$773$$ −23.3345 13.4722i −0.839284 0.484561i 0.0177365 0.999843i $$-0.494354\pi$$
−0.857021 + 0.515282i $$0.827687\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 29.3939 1.05518
$$777$$ 0 0
$$778$$ 38.0000i 1.36237i
$$779$$ 11.0227 6.36396i 0.394929 0.228013i
$$780$$ 0 0
$$781$$ −5.00000 + 8.66025i −0.178914 + 0.309888i
$$782$$ 33.9411 19.5959i 1.21373 0.700749i
$$783$$ 0 0
$$784$$ 4.00000 + 27.7128i 0.142857 + 0.989743i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −22.5167 + 39.0000i −0.802632 + 1.39020i 0.115246 + 0.993337i $$0.463234\pi$$
−0.917878 + 0.396863i $$0.870099\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −3.67423 0.707107i −0.130641 0.0251418i
$$792$$ 0 0