# Properties

 Label 2760.3.g.a.2161.12 Level $2760$ Weight $3$ Character 2760.2161 Analytic conductor $75.205$ Analytic rank $0$ Dimension $96$ CM no Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2760,3,Mod(2161,2760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2760, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("2760.2161");

S:= CuspForms(chi, 3);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 2760.g (of order $$2$$, degree $$1$$, 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: $$75.2045529634$$ Analytic rank: $$0$$ Dimension: $$96$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 2161.12 Character $$\chi$$ $$=$$ 2760.2161 Dual form 2760.3.g.a.2161.37

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.73205 q^{3} -2.23607i q^{5} +0.00406525i q^{7} +3.00000 q^{9} +O(q^{10})$$ $$q-1.73205 q^{3} -2.23607i q^{5} +0.00406525i q^{7} +3.00000 q^{9} -15.2374i q^{11} -17.0059 q^{13} +3.87298i q^{15} -29.9683i q^{17} +2.23468i q^{19} -0.00704122i q^{21} +(8.01839 - 21.5570i) q^{23} -5.00000 q^{25} -5.19615 q^{27} +3.32327 q^{29} +50.1303 q^{31} +26.3920i q^{33} +0.00909018 q^{35} +9.14013i q^{37} +29.4550 q^{39} -25.2881 q^{41} -41.4922i q^{43} -6.70820i q^{45} -71.5342 q^{47} +49.0000 q^{49} +51.9066i q^{51} -35.1120i q^{53} -34.0719 q^{55} -3.87057i q^{57} -113.791 q^{59} +51.7271i q^{61} +0.0121958i q^{63} +38.0262i q^{65} +78.1826i q^{67} +(-13.8883 + 37.3379i) q^{69} -6.44793 q^{71} +116.232 q^{73} +8.66025 q^{75} +0.0619440 q^{77} +153.554i q^{79} +9.00000 q^{81} -94.1572i q^{83} -67.0112 q^{85} -5.75608 q^{87} -151.007i q^{89} -0.0691331i q^{91} -86.8281 q^{93} +4.99689 q^{95} -80.0084i q^{97} -45.7123i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$96 q + 288 q^{9}+O(q^{10})$$ 96 * q + 288 * q^9 $$96 q + 288 q^{9} - 16 q^{23} - 480 q^{25} - 80 q^{31} + 80 q^{35} + 48 q^{39} + 112 q^{41} + 32 q^{47} - 688 q^{49} - 80 q^{55} - 496 q^{59} - 96 q^{69} - 416 q^{71} - 320 q^{73} + 864 q^{81} + 192 q^{93}+O(q^{100})$$ 96 * q + 288 * q^9 - 16 * q^23 - 480 * q^25 - 80 * q^31 + 80 * q^35 + 48 * q^39 + 112 * q^41 + 32 * q^47 - 688 * q^49 - 80 * q^55 - 496 * q^59 - 96 * q^69 - 416 * q^71 - 320 * q^73 + 864 * q^81 + 192 * q^93

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2760\mathbb{Z}\right)^\times$$.

 $$n$$ $$1201$$ $$1381$$ $$1657$$ $$1841$$ $$2071$$ $$\chi(n)$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −1.73205 −0.577350
$$4$$ 0 0
$$5$$ 2.23607i 0.447214i
$$6$$ 0 0
$$7$$ 0.00406525i 0.000580750i 1.00000 0.000290375i $$9.24293e-5\pi$$
−1.00000 0.000290375i $$0.999908\pi$$
$$8$$ 0 0
$$9$$ 3.00000 0.333333
$$10$$ 0 0
$$11$$ 15.2374i 1.38522i −0.721312 0.692610i $$-0.756461\pi$$
0.721312 0.692610i $$-0.243539\pi$$
$$12$$ 0 0
$$13$$ −17.0059 −1.30814 −0.654071 0.756433i $$-0.726940\pi$$
−0.654071 + 0.756433i $$0.726940\pi$$
$$14$$ 0 0
$$15$$ 3.87298i 0.258199i
$$16$$ 0 0
$$17$$ 29.9683i 1.76284i −0.472331 0.881421i $$-0.656587\pi$$
0.472331 0.881421i $$-0.343413\pi$$
$$18$$ 0 0
$$19$$ 2.23468i 0.117614i 0.998269 + 0.0588072i $$0.0187297\pi$$
−0.998269 + 0.0588072i $$0.981270\pi$$
$$20$$ 0 0
$$21$$ 0.00704122i 0.000335296i
$$22$$ 0 0
$$23$$ 8.01839 21.5570i 0.348626 0.937262i
$$24$$ 0 0
$$25$$ −5.00000 −0.200000
$$26$$ 0 0
$$27$$ −5.19615 −0.192450
$$28$$ 0 0
$$29$$ 3.32327 0.114596 0.0572978 0.998357i $$-0.481752\pi$$
0.0572978 + 0.998357i $$0.481752\pi$$
$$30$$ 0 0
$$31$$ 50.1303 1.61710 0.808552 0.588424i $$-0.200251\pi$$
0.808552 + 0.588424i $$0.200251\pi$$
$$32$$ 0 0
$$33$$ 26.3920i 0.799758i
$$34$$ 0 0
$$35$$ 0.00909018 0.000259719
$$36$$ 0 0
$$37$$ 9.14013i 0.247031i 0.992343 + 0.123515i $$0.0394168\pi$$
−0.992343 + 0.123515i $$0.960583\pi$$
$$38$$ 0 0
$$39$$ 29.4550 0.755256
$$40$$ 0 0
$$41$$ −25.2881 −0.616782 −0.308391 0.951260i $$-0.599790\pi$$
−0.308391 + 0.951260i $$0.599790\pi$$
$$42$$ 0 0
$$43$$ 41.4922i 0.964935i −0.875914 0.482467i $$-0.839741\pi$$
0.875914 0.482467i $$-0.160259\pi$$
$$44$$ 0 0
$$45$$ 6.70820i 0.149071i
$$46$$ 0 0
$$47$$ −71.5342 −1.52200 −0.761002 0.648750i $$-0.775292\pi$$
−0.761002 + 0.648750i $$0.775292\pi$$
$$48$$ 0 0
$$49$$ 49.0000 1.00000
$$50$$ 0 0
$$51$$ 51.9066i 1.01778i
$$52$$ 0 0
$$53$$ 35.1120i 0.662491i −0.943545 0.331245i $$-0.892531\pi$$
0.943545 0.331245i $$-0.107469\pi$$
$$54$$ 0 0
$$55$$ −34.0719 −0.619490
$$56$$ 0 0
$$57$$ 3.87057i 0.0679048i
$$58$$ 0 0
$$59$$ −113.791 −1.92867 −0.964334 0.264689i $$-0.914731\pi$$
−0.964334 + 0.264689i $$0.914731\pi$$
$$60$$ 0 0
$$61$$ 51.7271i 0.847985i 0.905666 + 0.423993i $$0.139372\pi$$
−0.905666 + 0.423993i $$0.860628\pi$$
$$62$$ 0 0
$$63$$ 0.0121958i 0.000193583i
$$64$$ 0 0
$$65$$ 38.0262i 0.585019i
$$66$$ 0 0
$$67$$ 78.1826i 1.16690i 0.812148 + 0.583452i $$0.198298\pi$$
−0.812148 + 0.583452i $$0.801702\pi$$
$$68$$ 0 0
$$69$$ −13.8883 + 37.3379i −0.201279 + 0.541129i
$$70$$ 0 0
$$71$$ −6.44793 −0.0908159 −0.0454080 0.998969i $$-0.514459\pi$$
−0.0454080 + 0.998969i $$0.514459\pi$$
$$72$$ 0 0
$$73$$ 116.232 1.59221 0.796107 0.605157i $$-0.206889\pi$$
0.796107 + 0.605157i $$0.206889\pi$$
$$74$$ 0 0
$$75$$ 8.66025 0.115470
$$76$$ 0 0
$$77$$ 0.0619440 0.000804467
$$78$$ 0 0
$$79$$ 153.554i 1.94373i 0.235546 + 0.971863i $$0.424312\pi$$
−0.235546 + 0.971863i $$0.575688\pi$$
$$80$$ 0 0
$$81$$ 9.00000 0.111111
$$82$$ 0 0
$$83$$ 94.1572i 1.13442i −0.823572 0.567212i $$-0.808022\pi$$
0.823572 0.567212i $$-0.191978\pi$$
$$84$$ 0 0
$$85$$ −67.0112 −0.788367
$$86$$ 0 0
$$87$$ −5.75608 −0.0661618
$$88$$ 0 0
$$89$$ 151.007i 1.69671i −0.529426 0.848356i $$-0.677593\pi$$
0.529426 0.848356i $$-0.322407\pi$$
$$90$$ 0 0
$$91$$ 0.0691331i 0.000759704i
$$92$$ 0 0
$$93$$ −86.8281 −0.933636
$$94$$ 0 0
$$95$$ 4.99689 0.0525988
$$96$$ 0 0
$$97$$ 80.0084i 0.824828i −0.910996 0.412414i $$-0.864686\pi$$
0.910996 0.412414i $$-0.135314\pi$$
$$98$$ 0 0
$$99$$ 45.7123i 0.461740i
$$100$$ 0 0
$$101$$ 172.731 1.71021 0.855106 0.518453i $$-0.173492\pi$$
0.855106 + 0.518453i $$0.173492\pi$$
$$102$$ 0 0
$$103$$ 160.984i 1.56295i −0.623935 0.781476i $$-0.714467\pi$$
0.623935 0.781476i $$-0.285533\pi$$
$$104$$ 0 0
$$105$$ −0.0157447 −0.000149949
$$106$$ 0 0
$$107$$ 147.142i 1.37516i 0.726108 + 0.687580i $$0.241327\pi$$
−0.726108 + 0.687580i $$0.758673\pi$$
$$108$$ 0 0
$$109$$ 15.9321i 0.146166i 0.997326 + 0.0730832i $$0.0232839\pi$$
−0.997326 + 0.0730832i $$0.976716\pi$$
$$110$$ 0 0
$$111$$ 15.8312i 0.142623i
$$112$$ 0 0
$$113$$ 26.5616i 0.235059i −0.993069 0.117529i $$-0.962503\pi$$
0.993069 0.117529i $$-0.0374974\pi$$
$$114$$ 0 0
$$115$$ −48.2030 17.9297i −0.419156 0.155910i
$$116$$ 0 0
$$117$$ −51.0176 −0.436048
$$118$$ 0 0
$$119$$ 0.121829 0.00102377
$$120$$ 0 0
$$121$$ −111.179 −0.918837
$$122$$ 0 0
$$123$$ 43.8002 0.356099
$$124$$ 0 0
$$125$$ 11.1803i 0.0894427i
$$126$$ 0 0
$$127$$ 27.5246 0.216729 0.108365 0.994111i $$-0.465439\pi$$
0.108365 + 0.994111i $$0.465439\pi$$
$$128$$ 0 0
$$129$$ 71.8666i 0.557105i
$$130$$ 0 0
$$131$$ 38.1375 0.291126 0.145563 0.989349i $$-0.453501\pi$$
0.145563 + 0.989349i $$0.453501\pi$$
$$132$$ 0 0
$$133$$ −0.00908452 −6.83047e−5
$$134$$ 0 0
$$135$$ 11.6190i 0.0860663i
$$136$$ 0 0
$$137$$ 146.494i 1.06930i 0.845075 + 0.534649i $$0.179556\pi$$
−0.845075 + 0.534649i $$0.820444\pi$$
$$138$$ 0 0
$$139$$ −154.014 −1.10801 −0.554005 0.832513i $$-0.686901\pi$$
−0.554005 + 0.832513i $$0.686901\pi$$
$$140$$ 0 0
$$141$$ 123.901 0.878729
$$142$$ 0 0
$$143$$ 259.125i 1.81207i
$$144$$ 0 0
$$145$$ 7.43106i 0.0512487i
$$146$$ 0 0
$$147$$ −84.8705 −0.577350
$$148$$ 0 0
$$149$$ 52.1230i 0.349819i −0.984585 0.174910i $$-0.944037\pi$$
0.984585 0.174910i $$-0.0559633\pi$$
$$150$$ 0 0
$$151$$ −183.173 −1.21307 −0.606534 0.795057i $$-0.707441\pi$$
−0.606534 + 0.795057i $$0.707441\pi$$
$$152$$ 0 0
$$153$$ 89.9050i 0.587614i
$$154$$ 0 0
$$155$$ 112.095i 0.723191i
$$156$$ 0 0
$$157$$ 38.4422i 0.244855i −0.992477 0.122427i $$-0.960932\pi$$
0.992477 0.122427i $$-0.0390678\pi$$
$$158$$ 0 0
$$159$$ 60.8158i 0.382489i
$$160$$ 0 0
$$161$$ 0.0876348 + 0.0325968i 0.000544315 + 0.000202464i
$$162$$ 0 0
$$163$$ 27.3583 0.167842 0.0839211 0.996472i $$-0.473256\pi$$
0.0839211 + 0.996472i $$0.473256\pi$$
$$164$$ 0 0
$$165$$ 59.0143 0.357662
$$166$$ 0 0
$$167$$ 103.548 0.620050 0.310025 0.950728i $$-0.399663\pi$$
0.310025 + 0.950728i $$0.399663\pi$$
$$168$$ 0 0
$$169$$ 120.199 0.711237
$$170$$ 0 0
$$171$$ 6.70403i 0.0392048i
$$172$$ 0 0
$$173$$ −37.0300 −0.214046 −0.107023 0.994257i $$-0.534132\pi$$
−0.107023 + 0.994257i $$0.534132\pi$$
$$174$$ 0 0
$$175$$ 0.0203263i 0.000116150i
$$176$$ 0 0
$$177$$ 197.092 1.11352
$$178$$ 0 0
$$179$$ −331.734 −1.85326 −0.926631 0.375973i $$-0.877309\pi$$
−0.926631 + 0.375973i $$0.877309\pi$$
$$180$$ 0 0
$$181$$ 286.944i 1.58533i 0.609659 + 0.792664i $$0.291306\pi$$
−0.609659 + 0.792664i $$0.708694\pi$$
$$182$$ 0 0
$$183$$ 89.5940i 0.489584i
$$184$$ 0 0
$$185$$ 20.4380 0.110475
$$186$$ 0 0
$$187$$ −456.640 −2.44193
$$188$$ 0 0
$$189$$ 0.0211237i 0.000111765i
$$190$$ 0 0
$$191$$ 10.2870i 0.0538584i −0.999637 0.0269292i $$-0.991427\pi$$
0.999637 0.0269292i $$-0.00857287\pi$$
$$192$$ 0 0
$$193$$ −212.862 −1.10291 −0.551455 0.834205i $$-0.685927\pi$$
−0.551455 + 0.834205i $$0.685927\pi$$
$$194$$ 0 0
$$195$$ 65.8634i 0.337761i
$$196$$ 0 0
$$197$$ 119.362 0.605901 0.302950 0.953006i $$-0.402028\pi$$
0.302950 + 0.953006i $$0.402028\pi$$
$$198$$ 0 0
$$199$$ 75.6515i 0.380158i 0.981769 + 0.190079i $$0.0608744\pi$$
−0.981769 + 0.190079i $$0.939126\pi$$
$$200$$ 0 0
$$201$$ 135.416i 0.673712i
$$202$$ 0 0
$$203$$ 0.0135099i 6.65514e-5i
$$204$$ 0 0
$$205$$ 56.5458i 0.275833i
$$206$$ 0 0
$$207$$ 24.0552 64.6711i 0.116209 0.312421i
$$208$$ 0 0
$$209$$ 34.0507 0.162922
$$210$$ 0 0
$$211$$ −302.528 −1.43378 −0.716890 0.697186i $$-0.754435\pi$$
−0.716890 + 0.697186i $$0.754435\pi$$
$$212$$ 0 0
$$213$$ 11.1681 0.0524326
$$214$$ 0 0
$$215$$ −92.7794 −0.431532
$$216$$ 0 0
$$217$$ 0.203792i 0.000939134i
$$218$$ 0 0
$$219$$ −201.319 −0.919265
$$220$$ 0 0
$$221$$ 509.637i 2.30605i
$$222$$ 0 0
$$223$$ 41.3082 0.185238 0.0926192 0.995702i $$-0.470476\pi$$
0.0926192 + 0.995702i $$0.470476\pi$$
$$224$$ 0 0
$$225$$ −15.0000 −0.0666667
$$226$$ 0 0
$$227$$ 124.502i 0.548466i −0.961663 0.274233i $$-0.911576\pi$$
0.961663 0.274233i $$-0.0884240\pi$$
$$228$$ 0 0
$$229$$ 253.060i 1.10506i 0.833492 + 0.552532i $$0.186338\pi$$
−0.833492 + 0.552532i $$0.813662\pi$$
$$230$$ 0 0
$$231$$ −0.107290 −0.000464459
$$232$$ 0 0
$$233$$ −332.346 −1.42638 −0.713188 0.700973i $$-0.752750\pi$$
−0.713188 + 0.700973i $$0.752750\pi$$
$$234$$ 0 0
$$235$$ 159.955i 0.680661i
$$236$$ 0 0
$$237$$ 265.964i 1.12221i
$$238$$ 0 0
$$239$$ −73.2581 −0.306519 −0.153260 0.988186i $$-0.548977\pi$$
−0.153260 + 0.988186i $$0.548977\pi$$
$$240$$ 0 0
$$241$$ 132.842i 0.551212i −0.961271 0.275606i $$-0.911121\pi$$
0.961271 0.275606i $$-0.0888786\pi$$
$$242$$ 0 0
$$243$$ −15.5885 −0.0641500
$$244$$ 0 0
$$245$$ 109.567i 0.447213i
$$246$$ 0 0
$$247$$ 38.0026i 0.153857i
$$248$$ 0 0
$$249$$ 163.085i 0.654960i
$$250$$ 0 0
$$251$$ 148.237i 0.590587i 0.955407 + 0.295294i $$0.0954174\pi$$
−0.955407 + 0.295294i $$0.904583\pi$$
$$252$$ 0 0
$$253$$ −328.474 122.180i −1.29831 0.482923i
$$254$$ 0 0
$$255$$ 116.067 0.455164
$$256$$ 0 0
$$257$$ −51.5948 −0.200758 −0.100379 0.994949i $$-0.532006\pi$$
−0.100379 + 0.994949i $$0.532006\pi$$
$$258$$ 0 0
$$259$$ −0.0371569 −0.000143463
$$260$$ 0 0
$$261$$ 9.96982 0.0381985
$$262$$ 0 0
$$263$$ 344.329i 1.30924i −0.755959 0.654619i $$-0.772829\pi$$
0.755959 0.654619i $$-0.227171\pi$$
$$264$$ 0 0
$$265$$ −78.5128 −0.296275
$$266$$ 0 0
$$267$$ 261.553i 0.979598i
$$268$$ 0 0
$$269$$ 120.491 0.447924 0.223962 0.974598i $$-0.428101\pi$$
0.223962 + 0.974598i $$0.428101\pi$$
$$270$$ 0 0
$$271$$ −278.237 −1.02670 −0.513352 0.858178i $$-0.671596\pi$$
−0.513352 + 0.858178i $$0.671596\pi$$
$$272$$ 0 0
$$273$$ 0.119742i 0.000438615i
$$274$$ 0 0
$$275$$ 76.1871i 0.277044i
$$276$$ 0 0
$$277$$ 85.0056 0.306879 0.153440 0.988158i $$-0.450965\pi$$
0.153440 + 0.988158i $$0.450965\pi$$
$$278$$ 0 0
$$279$$ 150.391 0.539035
$$280$$ 0 0
$$281$$ 176.685i 0.628773i 0.949295 + 0.314387i $$0.101799\pi$$
−0.949295 + 0.314387i $$0.898201\pi$$
$$282$$ 0 0
$$283$$ 335.765i 1.18645i 0.805037 + 0.593224i $$0.202145\pi$$
−0.805037 + 0.593224i $$0.797855\pi$$
$$284$$ 0 0
$$285$$ −8.65486 −0.0303679
$$286$$ 0 0
$$287$$ 0.102802i 0.000358196i
$$288$$ 0 0
$$289$$ −609.100 −2.10761
$$290$$ 0 0
$$291$$ 138.579i 0.476215i
$$292$$ 0 0
$$293$$ 70.7243i 0.241380i 0.992690 + 0.120690i $$0.0385107\pi$$
−0.992690 + 0.120690i $$0.961489\pi$$
$$294$$ 0 0
$$295$$ 254.445i 0.862526i
$$296$$ 0 0
$$297$$ 79.1760i 0.266586i
$$298$$ 0 0
$$299$$ −136.360 + 366.596i −0.456052 + 1.22607i
$$300$$ 0 0
$$301$$ 0.168676 0.000560386
$$302$$ 0 0
$$303$$ −299.180 −0.987391
$$304$$ 0 0
$$305$$ 115.665 0.379230
$$306$$ 0 0
$$307$$ −100.740 −0.328145 −0.164072 0.986448i $$-0.552463\pi$$
−0.164072 + 0.986448i $$0.552463\pi$$
$$308$$ 0 0
$$309$$ 278.833i 0.902371i
$$310$$ 0 0
$$311$$ −564.238 −1.81427 −0.907136 0.420838i $$-0.861736\pi$$
−0.907136 + 0.420838i $$0.861736\pi$$
$$312$$ 0 0
$$313$$ 220.516i 0.704524i −0.935901 0.352262i $$-0.885413\pi$$
0.935901 0.352262i $$-0.114587\pi$$
$$314$$ 0 0
$$315$$ 0.0272705 8.65731e−5
$$316$$ 0 0
$$317$$ −467.676 −1.47532 −0.737659 0.675173i $$-0.764069\pi$$
−0.737659 + 0.675173i $$0.764069\pi$$
$$318$$ 0 0
$$319$$ 50.6381i 0.158740i
$$320$$ 0 0
$$321$$ 254.858i 0.793949i
$$322$$ 0 0
$$323$$ 66.9695 0.207336
$$324$$ 0 0
$$325$$ 85.0293 0.261629
$$326$$ 0 0
$$327$$ 27.5953i 0.0843892i
$$328$$ 0 0
$$329$$ 0.290804i 0.000883904i
$$330$$ 0 0
$$331$$ −35.3046 −0.106660 −0.0533302 0.998577i $$-0.516984\pi$$
−0.0533302 + 0.998577i $$0.516984\pi$$
$$332$$ 0 0
$$333$$ 27.4204i 0.0823435i
$$334$$ 0 0
$$335$$ 174.822 0.521855
$$336$$ 0 0
$$337$$ 55.7782i 0.165514i 0.996570 + 0.0827570i $$0.0263725\pi$$
−0.996570 + 0.0827570i $$0.973627\pi$$
$$338$$ 0 0
$$339$$ 46.0061i 0.135711i
$$340$$ 0 0
$$341$$ 763.856i 2.24005i
$$342$$ 0 0
$$343$$ 0.398395i 0.00116150i
$$344$$ 0 0
$$345$$ 83.4900 + 31.0551i 0.242000 + 0.0900147i
$$346$$ 0 0
$$347$$ 400.411 1.15392 0.576961 0.816772i $$-0.304238\pi$$
0.576961 + 0.816772i $$0.304238\pi$$
$$348$$ 0 0
$$349$$ 349.176 1.00051 0.500253 0.865880i $$-0.333240\pi$$
0.500253 + 0.865880i $$0.333240\pi$$
$$350$$ 0 0
$$351$$ 88.3650 0.251752
$$352$$ 0 0
$$353$$ 170.286 0.482396 0.241198 0.970476i $$-0.422460\pi$$
0.241198 + 0.970476i $$0.422460\pi$$
$$354$$ 0 0
$$355$$ 14.4180i 0.0406141i
$$356$$ 0 0
$$357$$ −0.211014 −0.000591075
$$358$$ 0 0
$$359$$ 339.758i 0.946402i −0.880954 0.473201i $$-0.843098\pi$$
0.880954 0.473201i $$-0.156902\pi$$
$$360$$ 0 0
$$361$$ 356.006 0.986167
$$362$$ 0 0
$$363$$ 192.568 0.530491
$$364$$ 0 0
$$365$$ 259.902i 0.712059i
$$366$$ 0 0
$$367$$ 359.169i 0.978662i 0.872098 + 0.489331i $$0.162759\pi$$
−0.872098 + 0.489331i $$0.837241\pi$$
$$368$$ 0 0
$$369$$ −75.8642 −0.205594
$$370$$ 0 0
$$371$$ 0.142739 0.000384742
$$372$$ 0 0
$$373$$ 123.592i 0.331345i −0.986181 0.165672i $$-0.947021\pi$$
0.986181 0.165672i $$-0.0529794\pi$$
$$374$$ 0 0
$$375$$ 19.3649i 0.0516398i
$$376$$ 0 0
$$377$$ −56.5151 −0.149907
$$378$$ 0 0
$$379$$ 195.626i 0.516163i 0.966123 + 0.258082i $$0.0830903\pi$$
−0.966123 + 0.258082i $$0.916910\pi$$
$$380$$ 0 0
$$381$$ −47.6740 −0.125129
$$382$$ 0 0
$$383$$ 438.104i 1.14387i 0.820297 + 0.571937i $$0.193808\pi$$
−0.820297 + 0.571937i $$0.806192\pi$$
$$384$$ 0 0
$$385$$ 0.138511i 0.000359769i
$$386$$ 0 0
$$387$$ 124.477i 0.321645i
$$388$$ 0 0
$$389$$ 189.600i 0.487403i 0.969850 + 0.243701i $$0.0783617\pi$$
−0.969850 + 0.243701i $$0.921638\pi$$
$$390$$ 0 0
$$391$$ −646.028 240.298i −1.65225 0.614572i
$$392$$ 0 0
$$393$$ −66.0560 −0.168082
$$394$$ 0 0
$$395$$ 343.358 0.869261
$$396$$ 0 0
$$397$$ −202.827 −0.510899 −0.255450 0.966822i $$-0.582224\pi$$
−0.255450 + 0.966822i $$0.582224\pi$$
$$398$$ 0 0
$$399$$ 0.0157348 3.94357e−5
$$400$$ 0 0
$$401$$ 634.552i 1.58242i −0.611541 0.791212i $$-0.709450\pi$$
0.611541 0.791212i $$-0.290550\pi$$
$$402$$ 0 0
$$403$$ −852.508 −2.11540
$$404$$ 0 0
$$405$$ 20.1246i 0.0496904i
$$406$$ 0 0
$$407$$ 139.272 0.342192
$$408$$ 0 0
$$409$$ 409.129 1.00031 0.500157 0.865934i $$-0.333275\pi$$
0.500157 + 0.865934i $$0.333275\pi$$
$$410$$ 0 0
$$411$$ 253.735i 0.617359i
$$412$$ 0 0
$$413$$ 0.462591i 0.00112007i
$$414$$ 0 0
$$415$$ −210.542 −0.507330
$$416$$ 0 0
$$417$$ 266.759 0.639710
$$418$$ 0 0
$$419$$ 533.372i 1.27296i 0.771292 + 0.636482i $$0.219611\pi$$
−0.771292 + 0.636482i $$0.780389\pi$$
$$420$$ 0 0
$$421$$ 227.712i 0.540883i 0.962736 + 0.270442i $$0.0871697\pi$$
−0.962736 + 0.270442i $$0.912830\pi$$
$$422$$ 0 0
$$423$$ −214.603 −0.507335
$$424$$ 0 0
$$425$$ 149.842i 0.352568i
$$426$$ 0 0
$$427$$ −0.210284 −0.000492468
$$428$$ 0 0
$$429$$ 448.819i 1.04620i
$$430$$ 0 0
$$431$$ 131.051i 0.304062i 0.988376 + 0.152031i $$0.0485814\pi$$
−0.988376 + 0.152031i $$0.951419\pi$$
$$432$$ 0 0
$$433$$ 517.145i 1.19433i −0.802118 0.597166i $$-0.796294\pi$$
0.802118 0.597166i $$-0.203706\pi$$
$$434$$ 0 0
$$435$$ 12.8710i 0.0295885i
$$436$$ 0 0
$$437$$ 48.1730 + 17.9185i 0.110236 + 0.0410034i
$$438$$ 0 0
$$439$$ 527.882 1.20247 0.601233 0.799074i $$-0.294676\pi$$
0.601233 + 0.799074i $$0.294676\pi$$
$$440$$ 0 0
$$441$$ 147.000 0.333333
$$442$$ 0 0
$$443$$ −800.259 −1.80645 −0.903227 0.429164i $$-0.858808\pi$$
−0.903227 + 0.429164i $$0.858808\pi$$
$$444$$ 0 0
$$445$$ −337.663 −0.758793
$$446$$ 0 0
$$447$$ 90.2798i 0.201968i
$$448$$ 0 0
$$449$$ 476.816 1.06195 0.530975 0.847387i $$-0.321826\pi$$
0.530975 + 0.847387i $$0.321826\pi$$
$$450$$ 0 0
$$451$$ 385.325i 0.854379i
$$452$$ 0 0
$$453$$ 317.266 0.700365
$$454$$ 0 0
$$455$$ −0.154586 −0.000339750
$$456$$ 0 0
$$457$$ 334.499i 0.731946i −0.930625 0.365973i $$-0.880736\pi$$
0.930625 0.365973i $$-0.119264\pi$$
$$458$$ 0 0
$$459$$ 155.720i 0.339259i
$$460$$ 0 0
$$461$$ −352.571 −0.764796 −0.382398 0.923998i $$-0.624902\pi$$
−0.382398 + 0.923998i $$0.624902\pi$$
$$462$$ 0 0
$$463$$ −47.7318 −0.103092 −0.0515462 0.998671i $$-0.516415\pi$$
−0.0515462 + 0.998671i $$0.516415\pi$$
$$464$$ 0 0
$$465$$ 194.154i 0.417535i
$$466$$ 0 0
$$467$$ 447.079i 0.957343i 0.877994 + 0.478672i $$0.158882\pi$$
−0.877994 + 0.478672i $$0.841118\pi$$
$$468$$ 0 0
$$469$$ −0.317832 −0.000677680
$$470$$ 0 0
$$471$$ 66.5838i 0.141367i
$$472$$ 0 0
$$473$$ −632.234 −1.33665
$$474$$ 0 0
$$475$$ 11.1734i 0.0235229i
$$476$$ 0 0
$$477$$ 105.336i 0.220830i
$$478$$ 0 0
$$479$$ 131.715i 0.274979i −0.990503 0.137490i $$-0.956097\pi$$
0.990503 0.137490i $$-0.0439034\pi$$
$$480$$ 0 0
$$481$$ 155.436i 0.323151i
$$482$$ 0 0
$$483$$ −0.151788 0.0564592i −0.000314261 0.000116893i
$$484$$ 0 0
$$485$$ −178.904 −0.368874
$$486$$ 0 0
$$487$$ −910.350 −1.86930 −0.934651 0.355566i $$-0.884288\pi$$
−0.934651 + 0.355566i $$0.884288\pi$$
$$488$$ 0 0
$$489$$ −47.3859 −0.0969037
$$490$$ 0 0
$$491$$ 851.950 1.73513 0.867567 0.497321i $$-0.165683\pi$$
0.867567 + 0.497321i $$0.165683\pi$$
$$492$$ 0 0
$$493$$ 99.5929i 0.202014i
$$494$$ 0 0
$$495$$ −102.216 −0.206497
$$496$$ 0 0
$$497$$ 0.0262125i 5.27414e-5i
$$498$$ 0 0
$$499$$ 816.691 1.63665 0.818327 0.574752i $$-0.194902\pi$$
0.818327 + 0.574752i $$0.194902\pi$$
$$500$$ 0 0
$$501$$ −179.351 −0.357986
$$502$$ 0 0
$$503$$ 395.328i 0.785940i −0.919551 0.392970i $$-0.871448\pi$$
0.919551 0.392970i $$-0.128552\pi$$
$$504$$ 0 0
$$505$$ 386.239i 0.764830i
$$506$$ 0 0
$$507$$ −208.191 −0.410633
$$508$$ 0 0
$$509$$ 543.733 1.06824 0.534119 0.845409i $$-0.320643\pi$$
0.534119 + 0.845409i $$0.320643\pi$$
$$510$$ 0 0
$$511$$ 0.472511i 0.000924678i
$$512$$ 0 0
$$513$$ 11.6117i 0.0226349i
$$514$$ 0 0
$$515$$ −359.971 −0.698973
$$516$$ 0 0
$$517$$ 1090.00i 2.10831i
$$518$$ 0 0
$$519$$ 64.1379 0.123580
$$520$$ 0 0
$$521$$ 532.334i 1.02175i 0.859654 + 0.510877i $$0.170679\pi$$
−0.859654 + 0.510877i $$0.829321\pi$$
$$522$$ 0 0
$$523$$ 76.9293i 0.147092i 0.997292 + 0.0735462i $$0.0234316\pi$$
−0.997292 + 0.0735462i $$0.976568\pi$$
$$524$$ 0 0
$$525$$ 0.0352061i 6.70593e-5i
$$526$$ 0 0
$$527$$ 1502.32i 2.85070i
$$528$$ 0 0
$$529$$ −400.411 345.705i −0.756921 0.653507i
$$530$$ 0 0
$$531$$ −341.374 −0.642889
$$532$$ 0 0
$$533$$ 430.045 0.806839
$$534$$ 0 0
$$535$$ 329.020 0.614990
$$536$$ 0 0
$$537$$ 574.580 1.06998
$$538$$ 0 0
$$539$$ 746.634i 1.38522i
$$540$$ 0 0
$$541$$ −571.727 −1.05680 −0.528398 0.848997i $$-0.677207\pi$$
−0.528398 + 0.848997i $$0.677207\pi$$
$$542$$ 0 0
$$543$$ 497.002i 0.915290i
$$544$$ 0 0
$$545$$ 35.6254 0.0653676
$$546$$ 0 0
$$547$$ −1044.99 −1.91039 −0.955197 0.295971i $$-0.904357\pi$$
−0.955197 + 0.295971i $$0.904357\pi$$
$$548$$ 0 0
$$549$$ 155.181i 0.282662i
$$550$$ 0 0
$$551$$ 7.42644i 0.0134781i
$$552$$ 0 0
$$553$$ −0.624237 −0.00112882
$$554$$ 0 0
$$555$$ −35.3996 −0.0637830
$$556$$ 0 0
$$557$$ 108.890i 0.195494i −0.995211 0.0977468i $$-0.968836\pi$$
0.995211 0.0977468i $$-0.0311635\pi$$
$$558$$ 0 0
$$559$$ 705.610i 1.26227i
$$560$$ 0 0
$$561$$ 790.924 1.40985
$$562$$ 0 0
$$563$$ 81.5720i 0.144888i −0.997372 0.0724441i $$-0.976920\pi$$
0.997372 0.0724441i $$-0.0230799\pi$$
$$564$$ 0 0
$$565$$ −59.3936 −0.105121
$$566$$ 0 0
$$567$$ 0.0365873i 6.45278e-5i
$$568$$ 0 0
$$569$$ 450.698i 0.792089i 0.918231 + 0.396044i $$0.129617\pi$$
−0.918231 + 0.396044i $$0.870383\pi$$
$$570$$ 0 0
$$571$$ 24.2937i 0.0425459i 0.999774 + 0.0212730i $$0.00677191\pi$$
−0.999774 + 0.0212730i $$0.993228\pi$$
$$572$$ 0 0
$$573$$ 17.8175i 0.0310952i
$$574$$ 0 0
$$575$$ −40.0919 + 107.785i −0.0697251 + 0.187452i
$$576$$ 0 0
$$577$$ 928.710 1.60955 0.804775 0.593581i $$-0.202286\pi$$
0.804775 + 0.593581i $$0.202286\pi$$
$$578$$ 0 0
$$579$$ 368.687 0.636765
$$580$$ 0 0
$$581$$ 0.382773 0.000658817
$$582$$ 0 0
$$583$$ −535.017 −0.917696
$$584$$ 0 0
$$585$$ 114.079i 0.195006i
$$586$$ 0 0
$$587$$ −573.154 −0.976413 −0.488207 0.872728i $$-0.662349\pi$$
−0.488207 + 0.872728i $$0.662349\pi$$
$$588$$ 0 0
$$589$$ 112.025i 0.190195i
$$590$$ 0 0
$$591$$ −206.742 −0.349817
$$592$$ 0 0
$$593$$ 853.534 1.43935 0.719674 0.694312i $$-0.244291\pi$$
0.719674 + 0.694312i $$0.244291\pi$$
$$594$$ 0 0
$$595$$ 0.272417i 0.000457844i
$$596$$ 0 0
$$597$$ 131.032i 0.219484i
$$598$$ 0 0
$$599$$ −354.069 −0.591100 −0.295550 0.955327i $$-0.595503\pi$$
−0.295550 + 0.955327i $$0.595503\pi$$
$$600$$ 0 0
$$601$$ 801.780 1.33408 0.667038 0.745024i $$-0.267562\pi$$
0.667038 + 0.745024i $$0.267562\pi$$
$$602$$ 0 0
$$603$$ 234.548i 0.388968i
$$604$$ 0 0
$$605$$ 248.604i 0.410916i
$$606$$ 0 0
$$607$$ −249.091 −0.410365 −0.205182 0.978724i $$-0.565779\pi$$
−0.205182 + 0.978724i $$0.565779\pi$$
$$608$$ 0 0
$$609$$ 0.0233999i 3.84235e-5i
$$610$$ 0 0
$$611$$ 1216.50 1.99100
$$612$$ 0 0
$$613$$ 588.293i 0.959694i −0.877352 0.479847i $$-0.840692\pi$$
0.877352 0.479847i $$-0.159308\pi$$
$$614$$ 0 0
$$615$$ 97.9402i 0.159252i
$$616$$ 0 0
$$617$$ 797.182i 1.29203i 0.763325 + 0.646014i $$0.223565\pi$$
−0.763325 + 0.646014i $$0.776435\pi$$
$$618$$ 0 0
$$619$$ 1018.87i 1.64599i −0.568047 0.822996i $$-0.692301\pi$$
0.568047 0.822996i $$-0.307699\pi$$
$$620$$ 0 0
$$621$$ −41.6648 + 112.014i −0.0670930 + 0.180376i
$$622$$ 0 0
$$623$$ 0.613883 0.000985366
$$624$$ 0 0
$$625$$ 25.0000 0.0400000
$$626$$ 0 0
$$627$$ −58.9776 −0.0940631
$$628$$ 0 0
$$629$$ 273.914 0.435476
$$630$$ 0 0
$$631$$ 627.621i 0.994645i 0.867566 + 0.497322i $$0.165683\pi$$
−0.867566 + 0.497322i $$0.834317\pi$$
$$632$$ 0 0
$$633$$ 523.993 0.827793
$$634$$ 0 0
$$635$$ 61.5468i 0.0969242i
$$636$$ 0 0
$$637$$ −833.287 −1.30814
$$638$$ 0 0
$$639$$ −19.3438 −0.0302720
$$640$$ 0 0
$$641$$ 892.382i 1.39217i 0.717958 + 0.696086i $$0.245077\pi$$
−0.717958 + 0.696086i $$0.754923\pi$$
$$642$$ 0 0
$$643$$ 233.345i 0.362900i 0.983400 + 0.181450i $$0.0580791\pi$$
−0.983400 + 0.181450i $$0.941921\pi$$
$$644$$ 0 0
$$645$$ 160.699 0.249145
$$646$$ 0 0
$$647$$ 1070.00 1.65379 0.826894 0.562358i $$-0.190106\pi$$
0.826894 + 0.562358i $$0.190106\pi$$
$$648$$ 0 0
$$649$$ 1733.89i 2.67163i
$$650$$ 0 0
$$651$$ 0.352978i 0.000542209i
$$652$$ 0 0
$$653$$ −99.1847 −0.151891 −0.0759454 0.997112i $$-0.524197\pi$$
−0.0759454 + 0.997112i $$0.524197\pi$$
$$654$$ 0 0
$$655$$ 85.2780i 0.130195i
$$656$$ 0 0
$$657$$ 348.695 0.530738
$$658$$ 0 0
$$659$$ 338.990i 0.514400i 0.966358 + 0.257200i $$0.0828000\pi$$
−0.966358 + 0.257200i $$0.917200\pi$$
$$660$$ 0 0
$$661$$ 1195.78i 1.80905i −0.426421 0.904525i $$-0.640226\pi$$
0.426421 0.904525i $$-0.359774\pi$$
$$662$$ 0 0
$$663$$ 882.717i 1.33140i
$$664$$ 0 0
$$665$$ 0.0203136i 3.05468e-5i
$$666$$ 0 0
$$667$$ 26.6473 71.6399i 0.0399510 0.107406i
$$668$$ 0 0
$$669$$ −71.5478 −0.106947
$$670$$ 0 0
$$671$$ 788.188 1.17465
$$672$$ 0 0
$$673$$ 381.479 0.566834 0.283417 0.958997i $$-0.408532\pi$$
0.283417 + 0.958997i $$0.408532\pi$$
$$674$$ 0 0
$$675$$ 25.9808 0.0384900
$$676$$ 0 0
$$677$$ 844.496i 1.24741i 0.781660 + 0.623704i $$0.214373\pi$$
−0.781660 + 0.623704i $$0.785627\pi$$
$$678$$ 0 0
$$679$$ 0.325254 0.000479019
$$680$$ 0 0
$$681$$ 215.643i 0.316657i
$$682$$ 0 0
$$683$$ 1080.14 1.58147 0.790733 0.612162i $$-0.209700\pi$$
0.790733 + 0.612162i $$0.209700\pi$$
$$684$$ 0 0
$$685$$ 327.570 0.478204
$$686$$ 0 0
$$687$$ 438.312i 0.638009i
$$688$$ 0 0
$$689$$ 597.110i 0.866632i
$$690$$ 0 0
$$691$$ 241.213 0.349078 0.174539 0.984650i $$-0.444156\pi$$
0.174539 + 0.984650i $$0.444156\pi$$
$$692$$ 0 0
$$693$$ 0.185832 0.000268156
$$694$$ 0 0
$$695$$ 344.385i 0.495518i
$$696$$ 0 0
$$697$$ 757.840i 1.08729i
$$698$$ 0 0
$$699$$ 575.640 0.823519
$$700$$ 0 0
$$701$$ 1286.89i 1.83580i −0.396814 0.917899i $$-0.629884\pi$$
0.396814 0.917899i $$-0.370116\pi$$
$$702$$ 0 0
$$703$$ −20.4252 −0.0290544
$$704$$ 0 0
$$705$$ 277.051i 0.392980i
$$706$$ 0 0
$$707$$ 0.702197i 0.000993206i
$$708$$ 0 0
$$709$$ 661.784i 0.933404i −0.884415 0.466702i $$-0.845442\pi$$
0.884415 0.466702i $$-0.154558\pi$$
$$710$$ 0 0
$$711$$ 460.663i 0.647909i
$$712$$ 0 0
$$713$$ 401.964 1080.66i 0.563764 1.51565i
$$714$$ 0 0
$$715$$ 579.422 0.810381
$$716$$ 0 0
$$717$$ 126.887 0.176969
$$718$$ 0 0
$$719$$ 512.499 0.712794 0.356397 0.934335i $$-0.384005\pi$$
0.356397 + 0.934335i $$0.384005\pi$$
$$720$$ 0 0
$$721$$ 0.654441 0.000907685
$$722$$ 0 0
$$723$$ 230.089i 0.318243i
$$724$$ 0 0
$$725$$ −16.6164 −0.0229191
$$726$$ 0 0
$$727$$ 401.070i 0.551678i 0.961204 + 0.275839i $$0.0889556\pi$$
−0.961204 + 0.275839i $$0.911044\pi$$
$$728$$ 0 0
$$729$$ 27.0000 0.0370370
$$730$$ 0 0
$$731$$ −1243.45 −1.70103
$$732$$ 0 0
$$733$$ 990.923i 1.35187i −0.736960 0.675936i $$-0.763739\pi$$
0.736960 0.675936i $$-0.236261\pi$$
$$734$$ 0 0
$$735$$ 189.776i 0.258199i
$$736$$ 0 0
$$737$$ 1191.30 1.61642
$$738$$ 0 0
$$739$$ −798.831 −1.08096 −0.540481 0.841356i $$-0.681758\pi$$
−0.540481 + 0.841356i $$0.681758\pi$$
$$740$$ 0 0
$$741$$ 65.8224i 0.0888291i
$$742$$ 0 0
$$743$$ 1118.17i 1.50494i −0.658624 0.752472i $$-0.728861\pi$$
0.658624 0.752472i $$-0.271139\pi$$
$$744$$ 0 0
$$745$$ −116.551 −0.156444
$$746$$ 0 0
$$747$$ 282.472i 0.378141i
$$748$$ 0 0
$$749$$ −0.598170 −0.000798625
$$750$$ 0 0
$$751$$ 356.585i 0.474813i 0.971410 + 0.237407i $$0.0762973\pi$$
−0.971410 + 0.237407i $$0.923703\pi$$
$$752$$ 0 0
$$753$$ 256.755i 0.340976i
$$754$$ 0 0
$$755$$ 409.588i 0.542501i
$$756$$ 0 0
$$757$$ 1.81410i 0.00239643i −0.999999 0.00119822i $$-0.999619\pi$$
0.999999 0.00119822i $$-0.000381404\pi$$
$$758$$ 0 0
$$759$$ 568.933 + 211.621i 0.749583 + 0.278816i
$$760$$ 0 0
$$761$$ −1278.07 −1.67946 −0.839731 0.543003i $$-0.817287\pi$$
−0.839731 + 0.543003i $$0.817287\pi$$
$$762$$ 0 0
$$763$$ −0.0647682 −8.48862e−5
$$764$$ 0 0
$$765$$ −201.034 −0.262789
$$766$$ 0 0
$$767$$ 1935.12 2.52297
$$768$$ 0 0
$$769$$ 1344.09i 1.74784i 0.486067 + 0.873921i $$0.338431\pi$$
−0.486067 + 0.873921i $$0.661569\pi$$
$$770$$ 0 0
$$771$$ 89.3647 0.115908
$$772$$ 0 0
$$773$$ 169.656i 0.219477i −0.993960 0.109739i $$-0.964999\pi$$
0.993960 0.109739i $$-0.0350014\pi$$
$$774$$ 0 0
$$775$$ −250.651 −0.323421
$$776$$ 0 0
$$777$$ 0.0643577 8.28285e−5
$$778$$ 0 0
$$779$$ 56.5106i 0.0725425i
$$780$$ 0 0
$$781$$ 98.2499i 0.125800i
$$782$$ 0 0
$$783$$ −17.2682 −0.0220539
$$784$$ 0 0
$$785$$ −85.9593 −0.109502
$$786$$ 0 0
$$787$$ 772.353i 0.981389i −0.871332 0.490694i $$-0.836743\pi$$
0.871332 0.490694i $$-0.163257\pi$$
$$788$$ 0 0
$$789$$ 596.396i 0.755888i
$$790$$ 0 0
$$791$$ 0.107980 0.000136510
$$792$$ 0 0
$$793$$ 879.663i 1.10929i
$$794$$ 0 0
$$795$$ 135.988 0.171054
$$796$$ 0 0
$$797$$ 446.742i 0.560530i −0.959923 0.280265i $$-0.909578\pi$$
0.959923 0.280265i $$-0.0904223\pi$$
$$798$$ 0 0