# Properties

 Label 1152.2.k.f.865.4 Level $1152$ Weight $2$ Character 1152.865 Analytic conductor $9.199$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Learn more

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(289,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1152.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1152 = 2^{7} \cdot 3^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1152.k (of order $$4$$, 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: $$9.19876631285$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(i)$$ Coefficient field: 8.0.18939904.2 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2$$ x^8 - 4*x^7 + 14*x^6 - 28*x^5 + 43*x^4 - 44*x^3 + 30*x^2 - 12*x + 2 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{6}$$ Twist minimal: no (minimal twist has level 48) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 865.4 Root $$0.500000 + 0.0297061i$$ of defining polynomial Character $$\chi$$ $$=$$ 1152.865 Dual form 1152.2.k.f.289.4

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(1.74912 + 1.74912i) q^{5} +2.55765i q^{7} +O(q^{10})$$ $$q+(1.74912 + 1.74912i) q^{5} +2.55765i q^{7} +(-0.473626 - 0.473626i) q^{11} +(-2.88784 + 2.88784i) q^{13} +6.44549 q^{17} +(-4.55765 + 4.55765i) q^{19} -2.82843i q^{23} +1.11882i q^{25} +(-3.07931 + 3.07931i) q^{29} -6.55765 q^{31} +(-4.47363 + 4.47363i) q^{35} +(2.72922 + 2.72922i) q^{37} +0.788632i q^{41} +(-0.389604 - 0.389604i) q^{43} +2.82843 q^{47} +0.458440 q^{49} +(-2.57754 - 2.57754i) q^{53} -1.65685i q^{55} +(-4.00000 - 4.00000i) q^{59} +(4.38607 - 4.38607i) q^{61} -10.1023 q^{65} +(-2.11882 + 2.11882i) q^{67} +5.11529i q^{71} +14.7721i q^{73} +(1.21137 - 1.21137i) q^{77} +6.32000 q^{79} +(-0.641669 + 0.641669i) q^{83} +(11.2739 + 11.2739i) q^{85} +6.31724i q^{89} +(-7.38607 - 7.38607i) q^{91} -15.9437 q^{95} +12.6533 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q+O(q^{10})$$ 8 * q $$8 q + 8 q^{11} - 8 q^{19} - 16 q^{29} - 24 q^{31} - 24 q^{35} + 16 q^{37} - 8 q^{43} - 8 q^{49} + 16 q^{53} - 32 q^{59} - 16 q^{61} + 16 q^{65} - 16 q^{67} + 16 q^{77} + 24 q^{79} + 40 q^{83} + 16 q^{85} - 8 q^{91} - 48 q^{95}+O(q^{100})$$ 8 * q + 8 * q^11 - 8 * q^19 - 16 * q^29 - 24 * q^31 - 24 * q^35 + 16 * q^37 - 8 * q^43 - 8 * q^49 + 16 * q^53 - 32 * q^59 - 16 * q^61 + 16 * q^65 - 16 * q^67 + 16 * q^77 + 24 * q^79 + 40 * q^83 + 16 * q^85 - 8 * q^91 - 48 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$641$$ $$901$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{4}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0 0
$$4$$ 0 0
$$5$$ 1.74912 + 1.74912i 0.782229 + 0.782229i 0.980207 0.197977i $$-0.0634373\pi$$
−0.197977 + 0.980207i $$0.563437\pi$$
$$6$$ 0 0
$$7$$ 2.55765i 0.966700i 0.875427 + 0.483350i $$0.160580\pi$$
−0.875427 + 0.483350i $$0.839420\pi$$
$$8$$ 0 0
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −0.473626 0.473626i −0.142804 0.142804i 0.632091 0.774894i $$-0.282197\pi$$
−0.774894 + 0.632091i $$0.782197\pi$$
$$12$$ 0 0
$$13$$ −2.88784 + 2.88784i −0.800943 + 0.800943i −0.983243 0.182300i $$-0.941646\pi$$
0.182300 + 0.983243i $$0.441646\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 6.44549 1.56326 0.781630 0.623742i $$-0.214389\pi$$
0.781630 + 0.623742i $$0.214389\pi$$
$$18$$ 0 0
$$19$$ −4.55765 + 4.55765i −1.04560 + 1.04560i −0.0466864 + 0.998910i $$0.514866\pi$$
−0.998910 + 0.0466864i $$0.985134\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 2.82843i 0.589768i −0.955533 0.294884i $$-0.904719\pi$$
0.955533 0.294884i $$-0.0952810\pi$$
$$24$$ 0 0
$$25$$ 1.11882i 0.223765i
$$26$$ 0 0
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −3.07931 + 3.07931i −0.571813 + 0.571813i −0.932635 0.360821i $$-0.882496\pi$$
0.360821 + 0.932635i $$0.382496\pi$$
$$30$$ 0 0
$$31$$ −6.55765 −1.17779 −0.588894 0.808210i $$-0.700437\pi$$
−0.588894 + 0.808210i $$0.700437\pi$$
$$32$$ 0 0
$$33$$ 0 0
$$34$$ 0 0
$$35$$ −4.47363 + 4.47363i −0.756181 + 0.756181i
$$36$$ 0 0
$$37$$ 2.72922 + 2.72922i 0.448681 + 0.448681i 0.894916 0.446235i $$-0.147235\pi$$
−0.446235 + 0.894916i $$0.647235\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0.788632i 0.123164i 0.998102 + 0.0615818i $$0.0196145\pi$$
−0.998102 + 0.0615818i $$0.980385\pi$$
$$42$$ 0 0
$$43$$ −0.389604 0.389604i −0.0594141 0.0594141i 0.676775 0.736190i $$-0.263377\pi$$
−0.736190 + 0.676775i $$0.763377\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 2.82843 0.412568 0.206284 0.978492i $$-0.433863\pi$$
0.206284 + 0.978492i $$0.433863\pi$$
$$48$$ 0 0
$$49$$ 0.458440 0.0654915
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ −2.57754 2.57754i −0.354053 0.354053i 0.507562 0.861615i $$-0.330547\pi$$
−0.861615 + 0.507562i $$0.830547\pi$$
$$54$$ 0 0
$$55$$ 1.65685i 0.223410i
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ −4.00000 4.00000i −0.520756 0.520756i 0.397044 0.917800i $$-0.370036\pi$$
−0.917800 + 0.397044i $$0.870036\pi$$
$$60$$ 0 0
$$61$$ 4.38607 4.38607i 0.561579 0.561579i −0.368177 0.929756i $$-0.620018\pi$$
0.929756 + 0.368177i $$0.120018\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −10.1023 −1.25304
$$66$$ 0 0
$$67$$ −2.11882 + 2.11882i −0.258856 + 0.258856i −0.824589 0.565733i $$-0.808593\pi$$
0.565733 + 0.824589i $$0.308593\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 5.11529i 0.607074i 0.952820 + 0.303537i $$0.0981676\pi$$
−0.952820 + 0.303537i $$0.901832\pi$$
$$72$$ 0 0
$$73$$ 14.7721i 1.72895i 0.502676 + 0.864475i $$0.332349\pi$$
−0.502676 + 0.864475i $$0.667651\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 1.21137 1.21137i 0.138048 0.138048i
$$78$$ 0 0
$$79$$ 6.32000 0.711055 0.355528 0.934666i $$-0.384301\pi$$
0.355528 + 0.934666i $$0.384301\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 0 0
$$83$$ −0.641669 + 0.641669i −0.0704323 + 0.0704323i −0.741445 0.671013i $$-0.765859\pi$$
0.671013 + 0.741445i $$0.265859\pi$$
$$84$$ 0 0
$$85$$ 11.2739 + 11.2739i 1.22283 + 1.22283i
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 6.31724i 0.669626i 0.942285 + 0.334813i $$0.108673\pi$$
−0.942285 + 0.334813i $$0.891327\pi$$
$$90$$ 0 0
$$91$$ −7.38607 7.38607i −0.774271 0.774271i
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ −15.9437 −1.63579
$$96$$ 0 0
$$97$$ 12.6533 1.28475 0.642375 0.766390i $$-0.277949\pi$$
0.642375 + 0.766390i $$0.277949\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 7.52480 + 7.52480i 0.748745 + 0.748745i 0.974244 0.225498i $$-0.0724010\pi$$
−0.225498 + 0.974244i $$0.572401\pi$$
$$102$$ 0 0
$$103$$ 3.33686i 0.328790i −0.986395 0.164395i $$-0.947433\pi$$
0.986395 0.164395i $$-0.0525672\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 14.0625 + 14.0625i 1.35948 + 1.35948i 0.874560 + 0.484918i $$0.161151\pi$$
0.484918 + 0.874560i $$0.338849\pi$$
$$108$$ 0 0
$$109$$ −2.76901 + 2.76901i −0.265224 + 0.265224i −0.827172 0.561949i $$-0.810052\pi$$
0.561949 + 0.827172i $$0.310052\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −2.23765 −0.210500 −0.105250 0.994446i $$-0.533564\pi$$
−0.105250 + 0.994446i $$0.533564\pi$$
$$114$$ 0 0
$$115$$ 4.94725 4.94725i 0.461334 0.461334i
$$116$$ 0 0
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 16.4853i 1.51120i
$$120$$ 0 0
$$121$$ 10.5514i 0.959214i
$$122$$ 0 0
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 6.78863 6.78863i 0.607194 0.607194i
$$126$$ 0 0
$$127$$ −12.2145 −1.08386 −0.541931 0.840423i $$-0.682307\pi$$
−0.541931 + 0.840423i $$0.682307\pi$$
$$128$$ 0 0
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 3.77568 3.77568i 0.329883 0.329883i −0.522659 0.852542i $$-0.675060\pi$$
0.852542 + 0.522659i $$0.175060\pi$$
$$132$$ 0 0
$$133$$ −11.6569 11.6569i −1.01078 1.01078i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 5.10587i 0.436224i −0.975924 0.218112i $$-0.930010\pi$$
0.975924 0.218112i $$-0.0699898\pi$$
$$138$$ 0 0
$$139$$ 11.7757 + 11.7757i 0.998800 + 0.998800i 0.999999 0.00119925i $$-0.000381735\pi$$
−0.00119925 + 0.999999i $$0.500382\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 2.73551 0.228755
$$144$$ 0 0
$$145$$ −10.7721 −0.894578
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −7.90774 7.90774i −0.647827 0.647827i 0.304640 0.952467i $$-0.401464\pi$$
−0.952467 + 0.304640i $$0.901464\pi$$
$$150$$ 0 0
$$151$$ 14.6506i 1.19225i 0.802893 + 0.596123i $$0.203293\pi$$
−0.802893 + 0.596123i $$0.796707\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ −11.4701 11.4701i −0.921300 0.921300i
$$156$$ 0 0
$$157$$ 3.15196 3.15196i 0.251553 0.251553i −0.570054 0.821607i $$-0.693078\pi$$
0.821607 + 0.570054i $$0.193078\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 7.23412 0.570128
$$162$$ 0 0
$$163$$ 5.50490 5.50490i 0.431177 0.431177i −0.457852 0.889029i $$-0.651381\pi$$
0.889029 + 0.457852i $$0.151381\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 20.1814i 1.56168i −0.624730 0.780841i $$-0.714791\pi$$
0.624730 0.780841i $$-0.285209\pi$$
$$168$$ 0 0
$$169$$ 3.67923i 0.283018i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 4.35322 4.35322i 0.330969 0.330969i −0.521985 0.852955i $$-0.674808\pi$$
0.852955 + 0.521985i $$0.174808\pi$$
$$174$$ 0 0
$$175$$ −2.86156 −0.216313
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 13.2833 13.2833i 0.992843 0.992843i −0.00713130 0.999975i $$-0.502270\pi$$
0.999975 + 0.00713130i $$0.00226998\pi$$
$$180$$ 0 0
$$181$$ −6.34628 6.34628i −0.471715 0.471715i 0.430754 0.902469i $$-0.358248\pi$$
−0.902469 + 0.430754i $$0.858248\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 9.54745i 0.701943i
$$186$$ 0 0
$$187$$ −3.05275 3.05275i −0.223239 0.223239i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 5.60058 0.405243 0.202622 0.979257i $$-0.435054\pi$$
0.202622 + 0.979257i $$0.435054\pi$$
$$192$$ 0 0
$$193$$ −19.4514 −1.40014 −0.700071 0.714074i $$-0.746848\pi$$
−0.700071 + 0.714074i $$0.746848\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 1.23793 + 1.23793i 0.0881988 + 0.0881988i 0.749830 0.661631i $$-0.230135\pi$$
−0.661631 + 0.749830i $$0.730135\pi$$
$$198$$ 0 0
$$199$$ 0.993710i 0.0704422i 0.999380 + 0.0352211i $$0.0112135\pi$$
−0.999380 + 0.0352211i $$0.988786\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ −7.87579 7.87579i −0.552772 0.552772i
$$204$$ 0 0
$$205$$ −1.37941 + 1.37941i −0.0963422 + 0.0963422i
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ 4.31724 0.298630
$$210$$ 0 0
$$211$$ 4.22432 4.22432i 0.290814 0.290814i −0.546588 0.837402i $$-0.684073\pi$$
0.837402 + 0.546588i $$0.184073\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 1.36293i 0.0929509i
$$216$$ 0 0
$$217$$ 16.7721i 1.13857i
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −18.6135 + 18.6135i −1.25208 + 1.25208i
$$222$$ 0 0
$$223$$ 23.7659 1.59148 0.795740 0.605639i $$-0.207082\pi$$
0.795740 + 0.605639i $$0.207082\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0.641669 0.641669i 0.0425891 0.0425891i −0.685492 0.728081i $$-0.740413\pi$$
0.728081 + 0.685492i $$0.240413\pi$$
$$228$$ 0 0
$$229$$ −5.34275 5.34275i −0.353059 0.353059i 0.508188 0.861246i $$-0.330316\pi$$
−0.861246 + 0.508188i $$0.830316\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 23.2271i 1.52166i −0.648954 0.760828i $$-0.724793\pi$$
0.648954 0.760828i $$-0.275207\pi$$
$$234$$ 0 0
$$235$$ 4.94725 + 4.94725i 0.322723 + 0.322723i
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 26.9213 1.74140 0.870698 0.491817i $$-0.163667\pi$$
0.870698 + 0.491817i $$0.163667\pi$$
$$240$$ 0 0
$$241$$ −10.3494 −0.666664 −0.333332 0.942809i $$-0.608173\pi$$
−0.333332 + 0.942809i $$0.608173\pi$$
$$242$$ 0 0
$$243$$ 0 0
$$244$$ 0 0
$$245$$ 0.801866 + 0.801866i 0.0512293 + 0.0512293i
$$246$$ 0 0
$$247$$ 26.3235i 1.67492i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 9.75696 + 9.75696i 0.615854 + 0.615854i 0.944465 0.328611i $$-0.106581\pi$$
−0.328611 + 0.944465i $$0.606581\pi$$
$$252$$ 0 0
$$253$$ −1.33962 + 1.33962i −0.0842209 + 0.0842209i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ −16.9965 −1.06021 −0.530105 0.847932i $$-0.677848\pi$$
−0.530105 + 0.847932i $$0.677848\pi$$
$$258$$ 0 0
$$259$$ −6.98038 + 6.98038i −0.433740 + 0.433740i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 0 0
$$263$$ 29.9929i 1.84944i −0.380643 0.924722i $$-0.624297\pi$$
0.380643 0.924722i $$-0.375703\pi$$
$$264$$ 0 0
$$265$$ 9.01686i 0.553901i
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 20.6003 20.6003i 1.25602 1.25602i 0.303046 0.952976i $$-0.401996\pi$$
0.952976 0.303046i $$-0.0980037\pi$$
$$270$$ 0 0
$$271$$ 26.6506 1.61891 0.809453 0.587184i $$-0.199764\pi$$
0.809453 + 0.587184i $$0.199764\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0.529904 0.529904i 0.0319544 0.0319544i
$$276$$ 0 0
$$277$$ −12.1220 12.1220i −0.728338 0.728338i 0.241951 0.970289i $$-0.422213\pi$$
−0.970289 + 0.241951i $$0.922213\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 2.76588i 0.164999i −0.996591 0.0824993i $$-0.973710\pi$$
0.996591 0.0824993i $$-0.0262902\pi$$
$$282$$ 0 0
$$283$$ 4.48528 + 4.48528i 0.266622 + 0.266622i 0.827738 0.561115i $$-0.189628\pi$$
−0.561115 + 0.827738i $$0.689628\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −2.01704 −0.119062
$$288$$ 0 0
$$289$$ 24.5443 1.44378
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ −8.20793 8.20793i −0.479512 0.479512i 0.425463 0.904976i $$-0.360111\pi$$
−0.904976 + 0.425463i $$0.860111\pi$$
$$294$$ 0 0
$$295$$ 13.9929i 0.814700i
$$296$$ 0 0
$$297$$ 0 0
$$298$$ 0 0
$$299$$ 8.16804 + 8.16804i 0.472370 + 0.472370i
$$300$$ 0 0
$$301$$ 0.996470 0.996470i 0.0574356 0.0574356i
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 15.3435 0.878567
$$306$$ 0 0
$$307$$ 10.4549 10.4549i 0.596693 0.596693i −0.342738 0.939431i $$-0.611354\pi$$
0.939431 + 0.342738i $$0.111354\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 15.0761i 0.854885i 0.904043 + 0.427442i $$0.140585\pi$$
−0.904043 + 0.427442i $$0.859415\pi$$
$$312$$ 0 0
$$313$$ 23.0027i 1.30019i 0.759852 + 0.650096i $$0.225271\pi$$
−0.759852 + 0.650096i $$0.774729\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −6.75892 + 6.75892i −0.379618 + 0.379618i −0.870964 0.491346i $$-0.836505\pi$$
0.491346 + 0.870964i $$0.336505\pi$$
$$318$$ 0 0
$$319$$ 2.91688 0.163314
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −29.3763 + 29.3763i −1.63454 + 1.63454i
$$324$$ 0 0
$$325$$ −3.23099 3.23099i −0.179223 0.179223i
$$326$$ 0 0
$$327$$ 0 0
$$328$$ 0 0
$$329$$ 7.23412i 0.398830i
$$330$$ 0 0
$$331$$ −19.6631 19.6631i −1.08078 1.08078i −0.996436 0.0843464i $$-0.973120\pi$$
−0.0843464 0.996436i $$-0.526880\pi$$
$$332$$ 0 0
$$333$$ 0 0
$$334$$ 0 0
$$335$$ −7.41215 −0.404969
$$336$$ 0 0
$$337$$ 3.00980 0.163954 0.0819771 0.996634i $$-0.473877\pi$$
0.0819771 + 0.996634i $$0.473877\pi$$
$$338$$ 0 0
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 3.10587 + 3.10587i 0.168192 + 0.168192i
$$342$$ 0 0
$$343$$ 19.0761i 1.03001i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −6.27521 6.27521i −0.336871 0.336871i 0.518317 0.855188i $$-0.326559\pi$$
−0.855188 + 0.518317i $$0.826559\pi$$
$$348$$ 0 0
$$349$$ 4.74255 4.74255i 0.253863 0.253863i −0.568690 0.822552i $$-0.692549\pi$$
0.822552 + 0.568690i $$0.192549\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 8.75882 0.466185 0.233093 0.972455i $$-0.425116\pi$$
0.233093 + 0.972455i $$0.425116\pi$$
$$354$$ 0 0
$$355$$ −8.94725 + 8.94725i −0.474871 + 0.474871i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 32.7917i 1.73068i 0.501184 + 0.865341i $$0.332898\pi$$
−0.501184 + 0.865341i $$0.667102\pi$$
$$360$$ 0 0
$$361$$ 22.5443i 1.18654i
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ −25.8382 + 25.8382i −1.35243 + 1.35243i
$$366$$ 0 0
$$367$$ −20.6435 −1.07758 −0.538791 0.842439i $$-0.681119\pi$$
−0.538791 + 0.842439i $$0.681119\pi$$
$$368$$ 0 0
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 6.59245 6.59245i 0.342263 0.342263i
$$372$$ 0 0
$$373$$ 16.6167 + 16.6167i 0.860378 + 0.860378i 0.991382 0.131004i $$-0.0418200\pi$$
−0.131004 + 0.991382i $$0.541820\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 17.7851i 0.915979i
$$378$$ 0 0
$$379$$ 7.77844 + 7.77844i 0.399552 + 0.399552i 0.878075 0.478523i $$-0.158828\pi$$
−0.478523 + 0.878075i $$0.658828\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ −17.2037 −0.879070 −0.439535 0.898225i $$-0.644857\pi$$
−0.439535 + 0.898225i $$0.644857\pi$$
$$384$$ 0 0
$$385$$ 4.23765 0.215971
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ −23.8515 23.8515i −1.20932 1.20932i −0.971248 0.238069i $$-0.923486\pi$$
−0.238069 0.971248i $$-0.576514\pi$$
$$390$$ 0 0
$$391$$ 18.2306i 0.921961i
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 11.0544 + 11.0544i 0.556208 + 0.556208i
$$396$$ 0 0
$$397$$ 10.2673 10.2673i 0.515299 0.515299i −0.400847 0.916145i $$-0.631284\pi$$
0.916145 + 0.400847i $$0.131284\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −32.2274 −1.60936 −0.804681 0.593708i $$-0.797663\pi$$
−0.804681 + 0.593708i $$0.797663\pi$$
$$402$$ 0 0
$$403$$ 18.9374 18.9374i 0.943341 0.943341i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 2.58526i 0.128146i
$$408$$ 0 0
$$409$$ 11.5702i 0.572110i −0.958213 0.286055i $$-0.907656\pi$$
0.958213 0.286055i $$-0.0923440\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 10.2306 10.2306i 0.503414 0.503414i
$$414$$ 0 0
$$415$$ −2.24471 −0.110188
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −6.74717 + 6.74717i −0.329621 + 0.329621i −0.852442 0.522822i $$-0.824879\pi$$
0.522822 + 0.852442i $$0.324879\pi$$
$$420$$ 0 0
$$421$$ 17.2239 + 17.2239i 0.839443 + 0.839443i 0.988785 0.149343i $$-0.0477158\pi$$
−0.149343 + 0.988785i $$0.547716\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 7.21137i 0.349803i
$$426$$ 0 0
$$427$$ 11.2180 + 11.2180i 0.542879 + 0.542879i
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 40.7088 1.96087 0.980437 0.196832i $$-0.0630654\pi$$
0.980437 + 0.196832i $$0.0630654\pi$$
$$432$$ 0 0
$$433$$ 7.31371 0.351474 0.175737 0.984437i $$-0.443769\pi$$
0.175737 + 0.984437i $$0.443769\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 12.8910 + 12.8910i 0.616659 + 0.616659i
$$438$$ 0 0
$$439$$ 17.7122i 0.845356i 0.906280 + 0.422678i $$0.138910\pi$$
−0.906280 + 0.422678i $$0.861090\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −15.6944 15.6944i −0.745664 0.745664i 0.227997 0.973662i $$-0.426782\pi$$
−0.973662 + 0.227997i $$0.926782\pi$$
$$444$$ 0 0
$$445$$ −11.0496 + 11.0496i −0.523801 + 0.523801i
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 28.3400 1.33745 0.668723 0.743511i $$-0.266841\pi$$
0.668723 + 0.743511i $$0.266841\pi$$
$$450$$ 0 0
$$451$$ 0.373517 0.373517i 0.0175882 0.0175882i
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 25.8382i 1.21131i
$$456$$ 0 0
$$457$$ 17.3396i 0.811113i 0.914070 + 0.405557i $$0.132922\pi$$
−0.914070 + 0.405557i $$0.867078\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ −1.69284 + 1.69284i −0.0788434 + 0.0788434i −0.745429 0.666585i $$-0.767755\pi$$
0.666585 + 0.745429i $$0.267755\pi$$
$$462$$ 0 0
$$463$$ −2.70238 −0.125590 −0.0627951 0.998026i $$-0.520001\pi$$
−0.0627951 + 0.998026i $$0.520001\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 17.1136 17.1136i 0.791924 0.791924i −0.189883 0.981807i $$-0.560811\pi$$
0.981807 + 0.189883i $$0.0608108\pi$$
$$468$$ 0 0
$$469$$ −5.41921 5.41921i −0.250236 0.250236i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0.369053i 0.0169691i
$$474$$ 0 0
$$475$$ −5.09921 5.09921i −0.233968 0.233968i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ −22.2251 −1.01549 −0.507745 0.861508i $$-0.669521\pi$$
−0.507745 + 0.861508i $$0.669521\pi$$
$$480$$ 0 0
$$481$$ −15.7631 −0.718735
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 22.1322 + 22.1322i 1.00497 + 1.00497i
$$486$$ 0 0
$$487$$ 13.9839i 0.633672i −0.948480 0.316836i $$-0.897380\pi$$
0.948480 0.316836i $$-0.102620\pi$$
$$488$$ 0 0
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −7.23412 7.23412i −0.326471 0.326471i 0.524772 0.851243i $$-0.324151\pi$$
−0.851243 + 0.524772i $$0.824151\pi$$
$$492$$ 0 0
$$493$$ −19.8476 + 19.8476i −0.893893 + 0.893893i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −13.0831 −0.586858
$$498$$ 0 0
$$499$$ 2.59078 2.59078i 0.115979 0.115979i −0.646735 0.762715i $$-0.723866\pi$$
0.762715 + 0.646735i $$0.223866\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 0 0
$$503$$ 39.6443i 1.76765i 0.467817 + 0.883825i $$0.345041\pi$$
−0.467817 + 0.883825i $$0.654959\pi$$
$$504$$ 0 0
$$505$$ 26.3235i 1.17138i
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ 20.2875 20.2875i 0.899229 0.899229i −0.0961393 0.995368i $$-0.530649\pi$$
0.995368 + 0.0961393i $$0.0306494\pi$$
$$510$$ 0 0
$$511$$ −37.7819 −1.67137
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 5.83655 5.83655i 0.257189 0.257189i
$$516$$ 0 0
$$517$$ −1.33962 1.33962i −0.0589162 0.0589162i
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 23.1784i 1.01546i 0.861515 + 0.507732i $$0.169516\pi$$
−0.861515 + 0.507732i $$0.830484\pi$$
$$522$$ 0 0
$$523$$ −5.78550 5.78550i −0.252982 0.252982i 0.569210 0.822192i $$-0.307249\pi$$
−0.822192 + 0.569210i $$0.807249\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −42.2672 −1.84119
$$528$$ 0 0
$$529$$ 15.0000 0.652174
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −2.27744 2.27744i −0.0986470 0.0986470i
$$534$$ 0 0
$$535$$ 49.1941i 2.12685i
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 0 0
$$539$$ −0.217129 0.217129i −0.00935241 0.00935241i
$$540$$ 0 0
$$541$$ −4.55175 + 4.55175i −0.195695 + 0.195695i −0.798152 0.602457i $$-0.794189\pi$$
0.602457 + 0.798152i $$0.294189\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 0 0
$$545$$ −9.68667 −0.414931
$$546$$ 0 0
$$547$$ −27.7355 + 27.7355i −1.18588 + 1.18588i −0.207689 + 0.978195i $$0.566594\pi$$
−0.978195 + 0.207689i $$0.933406\pi$$
$$548$$ 0 0
$$549$$ 0 0
$$550$$ 0 0
$$551$$ 28.0688i 1.19577i
$$552$$ 0 0
$$553$$ 16.1643i 0.687377i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −1.17538 + 1.17538i −0.0498026 + 0.0498026i −0.731569 0.681767i $$-0.761212\pi$$
0.681767 + 0.731569i $$0.261212\pi$$
$$558$$ 0 0
$$559$$ 2.25023 0.0951745
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 28.7346 28.7346i 1.21102 1.21102i 0.240326 0.970692i $$-0.422746\pi$$
0.970692 0.240326i $$-0.0772544\pi$$
$$564$$ 0 0
$$565$$ −3.91391 3.91391i −0.164659 0.164659i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 27.0004i 1.13191i 0.824435 + 0.565957i $$0.191493\pi$$
−0.824435 + 0.565957i $$0.808507\pi$$
$$570$$ 0 0
$$571$$ −14.8284 14.8284i −0.620550 0.620550i 0.325122 0.945672i $$-0.394595\pi$$
−0.945672 + 0.325122i $$0.894595\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 3.16451 0.131969
$$576$$ 0 0
$$577$$ −37.6372 −1.56686 −0.783429 0.621481i $$-0.786531\pi$$
−0.783429 + 0.621481i $$0.786531\pi$$
$$578$$ 0 0
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −1.64116 1.64116i −0.0680869 0.0680869i
$$582$$ 0 0
$$583$$ 2.44158i 0.101120i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 31.2574 + 31.2574i 1.29013 + 1.29013i 0.934703 + 0.355429i $$0.115665\pi$$
0.355429 + 0.934703i $$0.384335\pi$$
$$588$$ 0 0
$$589$$ 29.8874 29.8874i 1.23149 1.23149i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 3.59611 0.147675 0.0738373 0.997270i $$-0.476475\pi$$
0.0738373 + 0.997270i $$0.476475\pi$$
$$594$$ 0 0
$$595$$ −28.8347 + 28.8347i −1.18211 + 1.18211i
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 22.0296i 0.900104i −0.893002 0.450052i $$-0.851405\pi$$
0.893002 0.450052i $$-0.148595\pi$$
$$600$$ 0 0
$$601$$ 10.7721i 0.439405i 0.975567 + 0.219703i $$0.0705087\pi$$
−0.975567 + 0.219703i $$0.929491\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 18.4556 18.4556i 0.750325 0.750325i
$$606$$ 0 0
$$607$$ −5.47453 −0.222204 −0.111102 0.993809i $$-0.535438\pi$$
−0.111102 + 0.993809i $$0.535438\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −8.16804 + 8.16804i −0.330444 + 0.330444i
$$612$$ 0 0
$$613$$ 10.5049 + 10.5049i 0.424289 + 0.424289i 0.886677 0.462389i $$-0.153007\pi$$
−0.462389 + 0.886677i $$0.653007\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 22.2235i 0.894686i 0.894363 + 0.447343i $$0.147630\pi$$
−0.894363 + 0.447343i $$0.852370\pi$$
$$618$$ 0 0
$$619$$ 11.6398 + 11.6398i 0.467843 + 0.467843i 0.901215 0.433372i $$-0.142676\pi$$
−0.433372 + 0.901215i $$0.642676\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ −16.1573 −0.647327
$$624$$ 0 0
$$625$$ 29.3424 1.17369
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 17.5912 + 17.5912i 0.701405 + 0.701405i
$$630$$ 0 0
$$631$$ 4.06977i 0.162015i −0.996713 0.0810075i $$-0.974186\pi$$
0.996713 0.0810075i $$-0.0258138\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ −21.3646 21.3646i −0.847828 0.847828i
$$636$$ 0 0
$$637$$ −1.32390 + 1.32390i −0.0524549 + 0.0524549i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 8.41958 0.332553 0.166277 0.986079i $$-0.446826\pi$$
0.166277 + 0.986079i $$0.446826\pi$$
$$642$$ 0 0
$$643$$ −7.37275 + 7.37275i −0.290753 + 0.290753i −0.837378 0.546625i $$-0.815912\pi$$
0.546625 + 0.837378i $$0.315912\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 11.6132i 0.456560i 0.973595 + 0.228280i $$0.0733102\pi$$
−0.973595 + 0.228280i $$0.926690\pi$$
$$648$$ 0 0
$$649$$ 3.78901i 0.148731i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −1.93049 + 1.93049i −0.0755458 + 0.0755458i −0.743870 0.668324i $$-0.767012\pi$$
0.668324 + 0.743870i $$0.267012\pi$$
$$654$$ 0 0
$$655$$ 13.2082 0.516088
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −22.3102 + 22.3102i −0.869081 + 0.869081i −0.992371 0.123290i $$-0.960656\pi$$
0.123290 + 0.992371i $$0.460656\pi$$
$$660$$ 0 0
$$661$$ −10.7033 10.7033i −0.416311 0.416311i 0.467619 0.883930i $$-0.345112\pi$$
−0.883930 + 0.467619i $$0.845112\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 40.7784i 1.58132i
$$666$$ 0 0
$$667$$ 8.70960 + 8.70960i 0.337237 + 0.337237i
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −4.15472 −0.160391
$$672$$ 0 0
$$673$$ −20.6345 −0.795401 −0.397700 0.917515i $$-0.630192\pi$$
−0.397700 + 0.917515i $$0.630192\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 26.8246 + 26.8246i 1.03095 + 1.03095i 0.999505 + 0.0314484i $$0.0100120\pi$$
0.0314484 + 0.999505i $$0.489988\pi$$
$$678$$ 0 0
$$679$$ 32.3627i 1.24197i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ −12.9026 12.9026i −0.493705 0.493705i 0.415766 0.909472i $$-0.363513\pi$$
−0.909472 + 0.415766i $$0.863513\pi$$
$$684$$ 0 0
$$685$$ 8.93077 8.93077i 0.341227 0.341227i
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 14.8871 0.567152
$$690$$ 0 0
$$691$$ −21.3923 + 21.3923i −0.813803 + 0.813803i −0.985202 0.171399i $$-0.945171\pi$$
0.171399 + 0.985202i $$0.445171\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 41.1941i 1.56258i
$$696$$ 0 0
$$697$$ 5.08312i 0.192537i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 14.2040 14.2040i 0.536479 0.536479i −0.386014 0.922493i $$-0.626148\pi$$
0.922493 + 0.386014i $$0.126148\pi$$
$$702$$ 0 0
$$703$$ −24.8776 −0.938278
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −19.2458 + 19.2458i −0.723812 + 0.723812i
$$708$$ 0 0
$$709$$ 29.5474 + 29.5474i 1.10968 + 1.10968i 0.993192 + 0.116485i $$0.0371626\pi$$
0.116485 + 0.993192i $$0.462837\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 0 0
$$713$$ 18.5478i 0.694622i
$$714$$ 0 0
$$715$$ 4.78473 + 4.78473i 0.178939 + 0.178939i
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 28.3683 1.05796 0.528979 0.848635i $$-0.322575\pi$$
0.528979 + 0.848635i $$0.322575\pi$$
$$720$$ 0 0
$$721$$ 8.53450 0.317841
$$722$$ 0 0
$$723$$ 0 0
$$724$$ 0 0
$$725$$ −3.44521 3.44521i −0.127952 0.127952i
$$726$$ 0 0
$$727$$ 20.4843i 0.759722i −0.925044 0.379861i $$-0.875972\pi$$
0.925044 0.379861i $$-0.124028\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 0 0
$$731$$ −2.51119 2.51119i −0.0928797 0.0928797i
$$732$$ 0 0
$$733$$ −33.9961 + 33.9961i −1.25567 + 1.25567i −0.302536 + 0.953138i $$0.597833\pi$$
−0.953138 + 0.302536i $$0.902167\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 2.00706 0.0739310
$$738$$ 0 0
$$739$$ 15.1645 15.1645i 0.557836 0.557836i −0.370855 0.928691i $$-0.620935\pi$$
0.928691 + 0.370855i $$0.120935\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 2.17431i 0.0797677i 0.999204 + 0.0398839i $$0.0126988\pi$$
−0.999204 + 0.0398839i $$0.987301\pi$$
$$744$$ 0 0
$$745$$ 27.6631i 1.01350i
$$746$$ 0 0
$$747$$ 0 0
$$748$$ 0 0
$$749$$ −35.9670 + 35.9670i −1.31421 + 1.31421i
$$750$$ 0 0
$$751$$ −29.8980 −1.09099 −0.545497 0.838113i $$-0.683659\pi$$
−0.545497 + 0.838113i $$0.683659\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ −25.6256 + 25.6256i −0.932610 + 0.932610i
$$756$$ 0 0
$$757$$ 15.3294 + 15.3294i 0.557157 + 0.557157i 0.928497 0.371340i $$-0.121101\pi$$
−0.371340 + 0.928497i $$0.621101\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 4.29449i 0.155675i −0.996966 0.0778375i $$-0.975198\pi$$
0.996966 0.0778375i $$-0.0248015\pi$$
$$762$$ 0 0
$$763$$ −7.08216 7.08216i −0.256392 0.256392i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 23.1027 0.834191
$$768$$ 0 0
$$769$$ 33.8819 1.22181 0.610907 0.791703i $$-0.290805\pi$$
0.610907 + 0.791703i $$0.290805\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −35.0230 35.0230i −1.25969 1.25969i −0.951240 0.308450i $$-0.900190\pi$$
−0.308450 0.951240i $$-0.599810\pi$$
$$774$$ 0 0
$$775$$ 7.33686i 0.263548i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −3.59431 3.59431i −0.128779 0.128779i
$$780$$ 0 0
$$781$$ 2.42274 2.42274i 0.0866923 0.0866923i
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 11.0263 0.393545
$$786$$ 0 0
$$787$$ 24.1090 24.1090i 0.859393 0.859393i −0.131873 0.991267i $$-0.542099\pi$$
0.991267 + 0.131873i $$0.0420992\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 5.72312i 0.203491i
$$792$$ 0 0
$$793$$ 25.3326i 0.899585i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −28.7722 + 28.7722i −1.01917 + 1.01917i −0.0193524 + 0.999813i $$0.506160\pi$$
−0.999813 + 0.0193524i $$0.993840\pi$$
$$798$$ 0 0