# Properties

 Label 1520.2.q.o.961.1 Level $1520$ Weight $2$ Character 1520.961 Analytic conductor $12.137$ Analytic rank $0$ Dimension $8$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,2,Mod(881,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1520.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$1520 = 2^{4} \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1520.q (of order $$3$$, 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: $$12.1372611072$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: 8.0.4601315889.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9$$ x^8 - x^7 + 6*x^6 - 3*x^5 + 26*x^4 - 14*x^3 + 31*x^2 + 12*x + 9 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 95) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 961.1 Root $$1.07988 - 1.87040i$$ of defining polynomial Character $$\chi$$ $$=$$ 1520.961 Dual form 1520.2.q.o.881.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+(-0.579878 + 1.00438i) q^{3} +(-0.500000 + 0.866025i) q^{5} +2.43525 q^{7} +(0.827483 + 1.43324i) q^{9} +O(q^{10})$$ $$q+(-0.579878 + 1.00438i) q^{3} +(-0.500000 + 0.866025i) q^{5} +2.43525 q^{7} +(0.827483 + 1.43324i) q^{9} +5.75477 q^{11} +(0.797505 + 1.38132i) q^{13} +(-0.579878 - 1.00438i) q^{15} +(2.99203 - 5.18234i) q^{17} +(-0.149412 - 4.35634i) q^{19} +(-1.41215 + 2.44592i) q^{21} +(-0.470022 - 0.814102i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.39862 q^{27} +(-1.30917 - 2.26755i) q^{29} +5.26913 q^{31} +(-3.33706 + 5.77996i) q^{33} +(-1.21763 + 2.10899i) q^{35} -2.89384 q^{37} -1.84982 q^{39} +(3.15767 - 5.46925i) q^{41} +(2.26961 - 3.93108i) q^{43} -1.65497 q^{45} +(4.47718 + 7.75471i) q^{47} -1.06953 q^{49} +(3.47002 + 6.01025i) q^{51} +(1.09819 + 1.90213i) q^{53} +(-2.87738 + 4.98377i) q^{55} +(4.46205 + 2.37608i) q^{57} +(-5.39939 + 9.35202i) q^{59} +(5.26434 + 9.11811i) q^{61} +(2.01513 + 3.49031i) q^{63} -1.59501 q^{65} +(0.504789 + 0.874320i) q^{67} +1.09022 q^{69} +(4.41694 - 7.65036i) q^{71} +(5.12499 - 8.87674i) q^{73} +1.15976 q^{75} +14.0143 q^{77} +(3.80229 - 6.58577i) q^{79} +(0.648093 - 1.12253i) q^{81} -3.11355 q^{83} +(2.99203 + 5.18234i) q^{85} +3.03663 q^{87} +(5.55706 + 9.62511i) q^{89} +(1.94213 + 3.36387i) q^{91} +(-3.05545 + 5.29220i) q^{93} +(3.84741 + 2.04877i) q^{95} +(-2.02888 + 3.51412i) q^{97} +(4.76197 + 8.24798i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9}+O(q^{10})$$ 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9 $$8 q + 3 q^{3} - 4 q^{5} + 8 q^{7} - q^{9} + 4 q^{11} - 7 q^{13} + 3 q^{15} + q^{17} - 5 q^{19} + 4 q^{21} + 2 q^{23} - 4 q^{25} - 24 q^{27} + q^{29} - 19 q^{33} - 4 q^{35} - 4 q^{37} - 30 q^{39} + 8 q^{41} + q^{43} + 2 q^{45} - 12 q^{47} - 20 q^{49} + 22 q^{51} + 5 q^{53} - 2 q^{55} + 7 q^{57} - 5 q^{59} - 3 q^{63} + 14 q^{65} + 4 q^{67} - 18 q^{69} + 20 q^{71} + 20 q^{73} - 6 q^{75} + 28 q^{77} + 17 q^{79} - 12 q^{81} - 2 q^{83} + q^{85} + 32 q^{87} - 11 q^{89} + 6 q^{91} + 8 q^{93} + 4 q^{95} - q^{97} + 38 q^{99}+O(q^{100})$$ 8 * q + 3 * q^3 - 4 * q^5 + 8 * q^7 - q^9 + 4 * q^11 - 7 * q^13 + 3 * q^15 + q^17 - 5 * q^19 + 4 * q^21 + 2 * q^23 - 4 * q^25 - 24 * q^27 + q^29 - 19 * q^33 - 4 * q^35 - 4 * q^37 - 30 * q^39 + 8 * q^41 + q^43 + 2 * q^45 - 12 * q^47 - 20 * q^49 + 22 * q^51 + 5 * q^53 - 2 * q^55 + 7 * q^57 - 5 * q^59 - 3 * q^63 + 14 * q^65 + 4 * q^67 - 18 * q^69 + 20 * q^71 + 20 * q^73 - 6 * q^75 + 28 * q^77 + 17 * q^79 - 12 * q^81 - 2 * q^83 + q^85 + 32 * q^87 - 11 * q^89 + 6 * q^91 + 8 * q^93 + 4 * q^95 - q^97 + 38 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$401$$ $$1141$$ $$1217$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ −0.579878 + 1.00438i −0.334793 + 0.579878i −0.983445 0.181207i $$-0.942000\pi$$
0.648652 + 0.761085i $$0.275333\pi$$
$$4$$ 0 0
$$5$$ −0.500000 + 0.866025i −0.223607 + 0.387298i
$$6$$ 0 0
$$7$$ 2.43525 0.920440 0.460220 0.887805i $$-0.347771\pi$$
0.460220 + 0.887805i $$0.347771\pi$$
$$8$$ 0 0
$$9$$ 0.827483 + 1.43324i 0.275828 + 0.477748i
$$10$$ 0 0
$$11$$ 5.75477 1.73513 0.867564 0.497326i $$-0.165685\pi$$
0.867564 + 0.497326i $$0.165685\pi$$
$$12$$ 0 0
$$13$$ 0.797505 + 1.38132i 0.221188 + 0.383109i 0.955169 0.296061i $$-0.0956732\pi$$
−0.733981 + 0.679170i $$0.762340\pi$$
$$14$$ 0 0
$$15$$ −0.579878 1.00438i −0.149724 0.259329i
$$16$$ 0 0
$$17$$ 2.99203 5.18234i 0.725673 1.25690i −0.233023 0.972471i $$-0.574862\pi$$
0.958696 0.284432i $$-0.0918050\pi$$
$$18$$ 0 0
$$19$$ −0.149412 4.35634i −0.0342775 0.999412i
$$20$$ 0 0
$$21$$ −1.41215 + 2.44592i −0.308156 + 0.533743i
$$22$$ 0 0
$$23$$ −0.470022 0.814102i −0.0980064 0.169752i 0.812853 0.582469i $$-0.197913\pi$$
−0.910859 + 0.412717i $$0.864580\pi$$
$$24$$ 0 0
$$25$$ −0.500000 0.866025i −0.100000 0.173205i
$$26$$ 0 0
$$27$$ −5.39862 −1.03897
$$28$$ 0 0
$$29$$ −1.30917 2.26755i −0.243106 0.421073i 0.718491 0.695536i $$-0.244833\pi$$
−0.961598 + 0.274463i $$0.911500\pi$$
$$30$$ 0 0
$$31$$ 5.26913 0.946364 0.473182 0.880965i $$-0.343105\pi$$
0.473182 + 0.880965i $$0.343105\pi$$
$$32$$ 0 0
$$33$$ −3.33706 + 5.77996i −0.580908 + 1.00616i
$$34$$ 0 0
$$35$$ −1.21763 + 2.10899i −0.205817 + 0.356485i
$$36$$ 0 0
$$37$$ −2.89384 −0.475744 −0.237872 0.971297i $$-0.576450\pi$$
−0.237872 + 0.971297i $$0.576450\pi$$
$$38$$ 0 0
$$39$$ −1.84982 −0.296209
$$40$$ 0 0
$$41$$ 3.15767 5.46925i 0.493145 0.854153i −0.506823 0.862050i $$-0.669180\pi$$
0.999969 + 0.00789701i $$0.00251372\pi$$
$$42$$ 0 0
$$43$$ 2.26961 3.93108i 0.346113 0.599485i −0.639443 0.768839i $$-0.720835\pi$$
0.985555 + 0.169354i $$0.0541682\pi$$
$$44$$ 0 0
$$45$$ −1.65497 −0.246708
$$46$$ 0 0
$$47$$ 4.47718 + 7.75471i 0.653064 + 1.13114i 0.982375 + 0.186919i $$0.0598502\pi$$
−0.329311 + 0.944221i $$0.606816\pi$$
$$48$$ 0 0
$$49$$ −1.06953 −0.152791
$$50$$ 0 0
$$51$$ 3.47002 + 6.01025i 0.485900 + 0.841604i
$$52$$ 0 0
$$53$$ 1.09819 + 1.90213i 0.150848 + 0.261277i 0.931540 0.363640i $$-0.118466\pi$$
−0.780691 + 0.624917i $$0.785133\pi$$
$$54$$ 0 0
$$55$$ −2.87738 + 4.98377i −0.387986 + 0.672012i
$$56$$ 0 0
$$57$$ 4.46205 + 2.37608i 0.591013 + 0.314719i
$$58$$ 0 0
$$59$$ −5.39939 + 9.35202i −0.702941 + 1.21753i 0.264489 + 0.964389i $$0.414797\pi$$
−0.967430 + 0.253140i $$0.918537\pi$$
$$60$$ 0 0
$$61$$ 5.26434 + 9.11811i 0.674030 + 1.16745i 0.976751 + 0.214375i $$0.0687716\pi$$
−0.302721 + 0.953079i $$0.597895\pi$$
$$62$$ 0 0
$$63$$ 2.01513 + 3.49031i 0.253883 + 0.439738i
$$64$$ 0 0
$$65$$ −1.59501 −0.197837
$$66$$ 0 0
$$67$$ 0.504789 + 0.874320i 0.0616698 + 0.106815i 0.895212 0.445641i $$-0.147024\pi$$
−0.833542 + 0.552456i $$0.813691\pi$$
$$68$$ 0 0
$$69$$ 1.09022 0.131247
$$70$$ 0 0
$$71$$ 4.41694 7.65036i 0.524194 0.907931i −0.475409 0.879765i $$-0.657700\pi$$
0.999603 0.0281662i $$-0.00896677\pi$$
$$72$$ 0 0
$$73$$ 5.12499 8.87674i 0.599835 1.03894i −0.393011 0.919534i $$-0.628566\pi$$
0.992845 0.119410i $$-0.0381003\pi$$
$$74$$ 0 0
$$75$$ 1.15976 0.133917
$$76$$ 0 0
$$77$$ 14.0143 1.59708
$$78$$ 0 0
$$79$$ 3.80229 6.58577i 0.427792 0.740957i −0.568885 0.822417i $$-0.692625\pi$$
0.996677 + 0.0814604i $$0.0259584\pi$$
$$80$$ 0 0
$$81$$ 0.648093 1.12253i 0.0720103 0.124726i
$$82$$ 0 0
$$83$$ −3.11355 −0.341756 −0.170878 0.985292i $$-0.554660\pi$$
−0.170878 + 0.985292i $$0.554660\pi$$
$$84$$ 0 0
$$85$$ 2.99203 + 5.18234i 0.324531 + 0.562104i
$$86$$ 0 0
$$87$$ 3.03663 0.325561
$$88$$ 0 0
$$89$$ 5.55706 + 9.62511i 0.589047 + 1.02026i 0.994358 + 0.106081i $$0.0338302\pi$$
−0.405310 + 0.914179i $$0.632837\pi$$
$$90$$ 0 0
$$91$$ 1.94213 + 3.36387i 0.203590 + 0.352629i
$$92$$ 0 0
$$93$$ −3.05545 + 5.29220i −0.316836 + 0.548776i
$$94$$ 0 0
$$95$$ 3.84741 + 2.04877i 0.394735 + 0.210200i
$$96$$ 0 0
$$97$$ −2.02888 + 3.51412i −0.206002 + 0.356805i −0.950451 0.310873i $$-0.899379\pi$$
0.744450 + 0.667678i $$0.232712\pi$$
$$98$$ 0 0
$$99$$ 4.76197 + 8.24798i 0.478596 + 0.828953i
$$100$$ 0 0
$$101$$ 5.56503 + 9.63892i 0.553741 + 0.959108i 0.998000 + 0.0632098i $$0.0201337\pi$$
−0.444259 + 0.895898i $$0.646533\pi$$
$$102$$ 0 0
$$103$$ −11.5791 −1.14092 −0.570460 0.821326i $$-0.693235\pi$$
−0.570460 + 0.821326i $$0.693235\pi$$
$$104$$ 0 0
$$105$$ −1.41215 2.44592i −0.137812 0.238697i
$$106$$ 0 0
$$107$$ −17.9177 −1.73217 −0.866086 0.499894i $$-0.833372\pi$$
−0.866086 + 0.499894i $$0.833372\pi$$
$$108$$ 0 0
$$109$$ −2.81235 + 4.87113i −0.269374 + 0.466570i −0.968700 0.248233i $$-0.920150\pi$$
0.699326 + 0.714803i $$0.253484\pi$$
$$110$$ 0 0
$$111$$ 1.67807 2.90650i 0.159275 0.275873i
$$112$$ 0 0
$$113$$ −15.6789 −1.47494 −0.737472 0.675378i $$-0.763981\pi$$
−0.737472 + 0.675378i $$0.763981\pi$$
$$114$$ 0 0
$$115$$ 0.940044 0.0876595
$$116$$ 0 0
$$117$$ −1.31984 + 2.28604i −0.122020 + 0.211344i
$$118$$ 0 0
$$119$$ 7.28635 12.6203i 0.667939 1.15690i
$$120$$ 0 0
$$121$$ 22.1173 2.01067
$$122$$ 0 0
$$123$$ 3.66213 + 6.34299i 0.330203 + 0.571928i
$$124$$ 0 0
$$125$$ 1.00000 0.0894427
$$126$$ 0 0
$$127$$ 3.05996 + 5.30000i 0.271527 + 0.470299i 0.969253 0.246066i $$-0.0791380\pi$$
−0.697726 + 0.716365i $$0.745805\pi$$
$$128$$ 0 0
$$129$$ 2.63220 + 4.55910i 0.231752 + 0.401406i
$$130$$ 0 0
$$131$$ −7.44055 + 12.8874i −0.650084 + 1.12598i 0.333018 + 0.942920i $$0.391933\pi$$
−0.983102 + 0.183058i $$0.941400\pi$$
$$132$$ 0 0
$$133$$ −0.363857 10.6088i −0.0315504 0.919899i
$$134$$ 0 0
$$135$$ 2.69931 4.67535i 0.232320 0.402390i
$$136$$ 0 0
$$137$$ −8.67518 15.0258i −0.741170 1.28374i −0.951963 0.306214i $$-0.900938\pi$$
0.210793 0.977531i $$-0.432396\pi$$
$$138$$ 0 0
$$139$$ −3.35267 5.80700i −0.284370 0.492543i 0.688086 0.725629i $$-0.258451\pi$$
−0.972456 + 0.233086i $$0.925118\pi$$
$$140$$ 0 0
$$141$$ −10.3849 −0.874564
$$142$$ 0 0
$$143$$ 4.58946 + 7.94917i 0.383790 + 0.664743i
$$144$$ 0 0
$$145$$ 2.61834 0.217441
$$146$$ 0 0
$$147$$ 0.620199 1.07422i 0.0511532 0.0885999i
$$148$$ 0 0
$$149$$ −7.19642 + 12.4646i −0.589553 + 1.02114i 0.404737 + 0.914433i $$0.367363\pi$$
−0.994291 + 0.106704i $$0.965970\pi$$
$$150$$ 0 0
$$151$$ −12.7219 −1.03529 −0.517645 0.855595i $$-0.673191\pi$$
−0.517645 + 0.855595i $$0.673191\pi$$
$$152$$ 0 0
$$153$$ 9.90341 0.800644
$$154$$ 0 0
$$155$$ −2.63457 + 4.56320i −0.211614 + 0.366525i
$$156$$ 0 0
$$157$$ 1.68765 2.92309i 0.134689 0.233288i −0.790790 0.612088i $$-0.790330\pi$$
0.925479 + 0.378800i $$0.123663\pi$$
$$158$$ 0 0
$$159$$ −2.54727 −0.202012
$$160$$ 0 0
$$161$$ −1.14462 1.98255i −0.0902089 0.156246i
$$162$$ 0 0
$$163$$ −0.307960 −0.0241213 −0.0120607 0.999927i $$-0.503839\pi$$
−0.0120607 + 0.999927i $$0.503839\pi$$
$$164$$ 0 0
$$165$$ −3.33706 5.77996i −0.259790 0.449969i
$$166$$ 0 0
$$167$$ 7.13215 + 12.3532i 0.551902 + 0.955923i 0.998137 + 0.0610070i $$0.0194312\pi$$
−0.446235 + 0.894916i $$0.647235\pi$$
$$168$$ 0 0
$$169$$ 5.22797 9.05511i 0.402152 0.696547i
$$170$$ 0 0
$$171$$ 6.12005 3.81894i 0.468012 0.292042i
$$172$$ 0 0
$$173$$ −6.67357 + 11.5590i −0.507382 + 0.878811i 0.492581 + 0.870266i $$0.336053\pi$$
−0.999963 + 0.00854514i $$0.997280\pi$$
$$174$$ 0 0
$$175$$ −1.21763 2.10899i −0.0920440 0.159425i
$$176$$ 0 0
$$177$$ −6.26197 10.8461i −0.470679 0.815239i
$$178$$ 0 0
$$179$$ 14.2207 1.06291 0.531454 0.847087i $$-0.321646\pi$$
0.531454 + 0.847087i $$0.321646\pi$$
$$180$$ 0 0
$$181$$ −4.94132 8.55861i −0.367285 0.636157i 0.621855 0.783133i $$-0.286379\pi$$
−0.989140 + 0.146976i $$0.953046\pi$$
$$182$$ 0 0
$$183$$ −12.2107 −0.902641
$$184$$ 0 0
$$185$$ 1.44692 2.50613i 0.106379 0.184255i
$$186$$ 0 0
$$187$$ 17.2184 29.8232i 1.25914 2.18089i
$$188$$ 0 0
$$189$$ −13.1470 −0.956305
$$190$$ 0 0
$$191$$ 12.9942 0.940228 0.470114 0.882606i $$-0.344213\pi$$
0.470114 + 0.882606i $$0.344213\pi$$
$$192$$ 0 0
$$193$$ −7.25795 + 12.5711i −0.522439 + 0.904890i 0.477221 + 0.878784i $$0.341644\pi$$
−0.999659 + 0.0261066i $$0.991689\pi$$
$$194$$ 0 0
$$195$$ 0.924911 1.60199i 0.0662343 0.114721i
$$196$$ 0 0
$$197$$ −25.0010 −1.78125 −0.890624 0.454740i $$-0.849732\pi$$
−0.890624 + 0.454740i $$0.849732\pi$$
$$198$$ 0 0
$$199$$ −1.12769 1.95322i −0.0799401 0.138460i 0.823284 0.567630i $$-0.192140\pi$$
−0.903224 + 0.429170i $$0.858806\pi$$
$$200$$ 0 0
$$201$$ −1.17086 −0.0825864
$$202$$ 0 0
$$203$$ −3.18816 5.52205i −0.223765 0.387572i
$$204$$ 0 0
$$205$$ 3.15767 + 5.46925i 0.220541 + 0.381989i
$$206$$ 0 0
$$207$$ 0.777871 1.34731i 0.0540657 0.0936446i
$$208$$ 0 0
$$209$$ −0.859833 25.0697i −0.0594759 1.73411i
$$210$$ 0 0
$$211$$ 11.1081 19.2397i 0.764710 1.32452i −0.175689 0.984446i $$-0.556215\pi$$
0.940400 0.340071i $$-0.110451\pi$$
$$212$$ 0 0
$$213$$ 5.12257 + 8.87255i 0.350993 + 0.607937i
$$214$$ 0 0
$$215$$ 2.26961 + 3.93108i 0.154786 + 0.268098i
$$216$$ 0 0
$$217$$ 12.8317 0.871071
$$218$$ 0 0
$$219$$ 5.94373 + 10.2949i 0.401640 + 0.695662i
$$220$$ 0 0
$$221$$ 9.54463 0.642041
$$222$$ 0 0
$$223$$ 5.10799 8.84730i 0.342056 0.592459i −0.642758 0.766069i $$-0.722210\pi$$
0.984814 + 0.173610i $$0.0555432\pi$$
$$224$$ 0 0
$$225$$ 0.827483 1.43324i 0.0551656 0.0955495i
$$226$$ 0 0
$$227$$ −4.15180 −0.275565 −0.137782 0.990463i $$-0.543997\pi$$
−0.137782 + 0.990463i $$0.543997\pi$$
$$228$$ 0 0
$$229$$ 6.53286 0.431703 0.215852 0.976426i $$-0.430747\pi$$
0.215852 + 0.976426i $$0.430747\pi$$
$$230$$ 0 0
$$231$$ −8.12660 + 14.0757i −0.534691 + 0.926111i
$$232$$ 0 0
$$233$$ −2.57410 + 4.45848i −0.168635 + 0.292084i −0.937940 0.346797i $$-0.887269\pi$$
0.769305 + 0.638882i $$0.220603\pi$$
$$234$$ 0 0
$$235$$ −8.95437 −0.584118
$$236$$ 0 0
$$237$$ 4.40973 + 7.63788i 0.286443 + 0.496134i
$$238$$ 0 0
$$239$$ −13.9962 −0.905338 −0.452669 0.891679i $$-0.649528\pi$$
−0.452669 + 0.891679i $$0.649528\pi$$
$$240$$ 0 0
$$241$$ −7.61285 13.1858i −0.490387 0.849375i 0.509552 0.860440i $$-0.329811\pi$$
−0.999939 + 0.0110652i $$0.996478\pi$$
$$242$$ 0 0
$$243$$ −7.34631 12.7242i −0.471266 0.816256i
$$244$$ 0 0
$$245$$ 0.534767 0.926244i 0.0341650 0.0591756i
$$246$$ 0 0
$$247$$ 5.89834 3.68059i 0.375302 0.234190i
$$248$$ 0 0
$$249$$ 1.80548 3.12718i 0.114417 0.198177i
$$250$$ 0 0
$$251$$ −3.05630 5.29366i −0.192912 0.334133i 0.753302 0.657674i $$-0.228460\pi$$
−0.946214 + 0.323542i $$0.895126\pi$$
$$252$$ 0 0
$$253$$ −2.70487 4.68497i −0.170053 0.294541i
$$254$$ 0 0
$$255$$ −6.94004 −0.434602
$$256$$ 0 0
$$257$$ −0.0613414 0.106246i −0.00382637 0.00662747i 0.864106 0.503310i $$-0.167885\pi$$
−0.867932 + 0.496683i $$0.834551\pi$$
$$258$$ 0 0
$$259$$ −7.04723 −0.437893
$$260$$ 0 0
$$261$$ 2.16663 3.75271i 0.134111 0.232287i
$$262$$ 0 0
$$263$$ −5.03027 + 8.71267i −0.310179 + 0.537247i −0.978401 0.206716i $$-0.933722\pi$$
0.668222 + 0.743962i $$0.267056\pi$$
$$264$$ 0 0
$$265$$ −2.19639 −0.134923
$$266$$ 0 0
$$267$$ −12.8897 −0.788835
$$268$$ 0 0
$$269$$ −2.85614 + 4.94698i −0.174142 + 0.301623i −0.939864 0.341549i $$-0.889049\pi$$
0.765722 + 0.643172i $$0.222382\pi$$
$$270$$ 0 0
$$271$$ −6.35560 + 11.0082i −0.386075 + 0.668702i −0.991918 0.126883i $$-0.959503\pi$$
0.605843 + 0.795585i $$0.292836\pi$$
$$272$$ 0 0
$$273$$ −4.50479 −0.272642
$$274$$ 0 0
$$275$$ −2.87738 4.98377i −0.173513 0.300533i
$$276$$ 0 0
$$277$$ 17.6019 1.05760 0.528799 0.848747i $$-0.322642\pi$$
0.528799 + 0.848747i $$0.322642\pi$$
$$278$$ 0 0
$$279$$ 4.36012 + 7.55195i 0.261034 + 0.452123i
$$280$$ 0 0
$$281$$ 10.2502 + 17.7539i 0.611476 + 1.05911i 0.990992 + 0.133922i $$0.0427571\pi$$
−0.379516 + 0.925185i $$0.623910\pi$$
$$282$$ 0 0
$$283$$ −5.92805 + 10.2677i −0.352386 + 0.610350i −0.986667 0.162752i $$-0.947963\pi$$
0.634281 + 0.773103i $$0.281296\pi$$
$$284$$ 0 0
$$285$$ −4.28877 + 2.67621i −0.254045 + 0.158525i
$$286$$ 0 0
$$287$$ 7.68973 13.3190i 0.453911 0.786196i
$$288$$ 0 0
$$289$$ −9.40447 16.2890i −0.553204 0.958177i
$$290$$ 0 0
$$291$$ −2.35301 4.07552i −0.137936 0.238911i
$$292$$ 0 0
$$293$$ −24.9814 −1.45943 −0.729715 0.683751i $$-0.760347\pi$$
−0.729715 + 0.683751i $$0.760347\pi$$
$$294$$ 0 0
$$295$$ −5.39939 9.35202i −0.314365 0.544495i
$$296$$ 0 0
$$297$$ −31.0678 −1.80274
$$298$$ 0 0
$$299$$ 0.749690 1.29850i 0.0433557 0.0750943i
$$300$$ 0 0
$$301$$ 5.52708 9.57319i 0.318576 0.551789i
$$302$$ 0 0
$$303$$ −12.9082 −0.741554
$$304$$ 0 0
$$305$$ −10.5287 −0.602871
$$306$$ 0 0
$$307$$ 8.45997 14.6531i 0.482836 0.836296i −0.516970 0.856003i $$-0.672940\pi$$
0.999806 + 0.0197074i $$0.00627348\pi$$
$$308$$ 0 0
$$309$$ 6.71444 11.6298i 0.381971 0.661594i
$$310$$ 0 0
$$311$$ 15.2133 0.862670 0.431335 0.902192i $$-0.358043\pi$$
0.431335 + 0.902192i $$0.358043\pi$$
$$312$$ 0 0
$$313$$ −12.4637 21.5877i −0.704488 1.22021i −0.966876 0.255246i $$-0.917844\pi$$
0.262389 0.964962i $$-0.415490\pi$$
$$314$$ 0 0
$$315$$ −4.03027 −0.227080
$$316$$ 0 0
$$317$$ 12.6152 + 21.8502i 0.708541 + 1.22723i 0.965398 + 0.260780i $$0.0839798\pi$$
−0.256857 + 0.966449i $$0.582687\pi$$
$$318$$ 0 0
$$319$$ −7.53396 13.0492i −0.421821 0.730615i
$$320$$ 0 0
$$321$$ 10.3901 17.9962i 0.579919 1.00445i
$$322$$ 0 0
$$323$$ −23.0231 12.2600i −1.28104 0.682163i
$$324$$ 0 0
$$325$$ 0.797505 1.38132i 0.0442376 0.0766218i
$$326$$ 0 0
$$327$$ −3.26164 5.64933i −0.180369 0.312408i
$$328$$ 0 0
$$329$$ 10.9031 + 18.8847i 0.601106 + 1.04115i
$$330$$ 0 0
$$331$$ 20.2063 1.11064 0.555320 0.831637i $$-0.312596\pi$$
0.555320 + 0.831637i $$0.312596\pi$$
$$332$$ 0 0
$$333$$ −2.39460 4.14757i −0.131223 0.227285i
$$334$$ 0 0
$$335$$ −1.00958 −0.0551592
$$336$$ 0 0
$$337$$ 15.9123 27.5610i 0.866800 1.50134i 0.00155051 0.999999i $$-0.499506\pi$$
0.865249 0.501342i $$-0.167160\pi$$
$$338$$ 0 0
$$339$$ 9.09183 15.7475i 0.493800 0.855287i
$$340$$ 0 0
$$341$$ 30.3226 1.64206
$$342$$ 0 0
$$343$$ −19.6514 −1.06107
$$344$$ 0 0
$$345$$ −0.545111 + 0.944159i −0.0293478 + 0.0508318i
$$346$$ 0 0
$$347$$ −1.65128 + 2.86009i −0.0886451 + 0.153538i −0.906939 0.421263i $$-0.861587\pi$$
0.818294 + 0.574801i $$0.194920\pi$$
$$348$$ 0 0
$$349$$ 17.8486 0.955416 0.477708 0.878519i $$-0.341468\pi$$
0.477708 + 0.878519i $$0.341468\pi$$
$$350$$ 0 0
$$351$$ −4.30543 7.45723i −0.229807 0.398037i
$$352$$ 0 0
$$353$$ −8.29523 −0.441511 −0.220755 0.975329i $$-0.570852\pi$$
−0.220755 + 0.975329i $$0.570852\pi$$
$$354$$ 0 0
$$355$$ 4.41694 + 7.65036i 0.234427 + 0.406039i
$$356$$ 0 0
$$357$$ 8.45039 + 14.6365i 0.447242 + 0.774646i
$$358$$ 0 0
$$359$$ 4.17511 7.23150i 0.220354 0.381664i −0.734562 0.678542i $$-0.762612\pi$$
0.954915 + 0.296878i $$0.0959455\pi$$
$$360$$ 0 0
$$361$$ −18.9554 + 1.30178i −0.997650 + 0.0685148i
$$362$$ 0 0
$$363$$ −12.8254 + 22.2142i −0.673156 + 1.16594i
$$364$$ 0 0
$$365$$ 5.12499 + 8.87674i 0.268254 + 0.464630i
$$366$$ 0 0
$$367$$ 7.20988 + 12.4879i 0.376353 + 0.651862i 0.990528 0.137307i $$-0.0438448\pi$$
−0.614176 + 0.789169i $$0.710511\pi$$
$$368$$ 0 0
$$369$$ 10.4517 0.544093
$$370$$ 0 0
$$371$$ 2.67438 + 4.63216i 0.138847 + 0.240490i
$$372$$ 0 0
$$373$$ −24.1157 −1.24866 −0.624332 0.781159i $$-0.714629\pi$$
−0.624332 + 0.781159i $$0.714629\pi$$
$$374$$ 0 0
$$375$$ −0.579878 + 1.00438i −0.0299448 + 0.0518659i
$$376$$ 0 0
$$377$$ 2.08814 3.61676i 0.107545 0.186273i
$$378$$ 0 0
$$379$$ −16.6757 −0.856571 −0.428285 0.903644i $$-0.640882\pi$$
−0.428285 + 0.903644i $$0.640882\pi$$
$$380$$ 0 0
$$381$$ −7.09760 −0.363621
$$382$$ 0 0
$$383$$ −5.43895 + 9.42053i −0.277917 + 0.481367i −0.970867 0.239619i $$-0.922977\pi$$
0.692950 + 0.720986i $$0.256311\pi$$
$$384$$ 0 0
$$385$$ −7.00716 + 12.1368i −0.357118 + 0.618546i
$$386$$ 0 0
$$387$$ 7.51226 0.381870
$$388$$ 0 0
$$389$$ −18.2272 31.5704i −0.924154 1.60068i −0.792917 0.609330i $$-0.791438\pi$$
−0.131237 0.991351i $$-0.541895\pi$$
$$390$$ 0 0
$$391$$ −5.62528 −0.284482
$$392$$ 0 0
$$393$$ −8.62922 14.9463i −0.435287 0.753939i
$$394$$ 0 0
$$395$$ 3.80229 + 6.58577i 0.191314 + 0.331366i
$$396$$ 0 0
$$397$$ −4.29191 + 7.43380i −0.215405 + 0.373092i −0.953398 0.301717i $$-0.902440\pi$$
0.737993 + 0.674808i $$0.235774\pi$$
$$398$$ 0 0
$$399$$ 10.8662 + 5.78635i 0.543992 + 0.289680i
$$400$$ 0 0
$$401$$ 8.52785 14.7707i 0.425860 0.737612i −0.570640 0.821200i $$-0.693305\pi$$
0.996500 + 0.0835885i $$0.0266381\pi$$
$$402$$ 0 0
$$403$$ 4.20216 + 7.27836i 0.209325 + 0.362561i
$$404$$ 0 0
$$405$$ 0.648093 + 1.12253i 0.0322040 + 0.0557790i
$$406$$ 0 0
$$407$$ −16.6533 −0.825476
$$408$$ 0 0
$$409$$ 5.89702 + 10.2139i 0.291589 + 0.505047i 0.974186 0.225749i $$-0.0724828\pi$$
−0.682597 + 0.730795i $$0.739149\pi$$
$$410$$ 0 0
$$411$$ 20.1222 0.992553
$$412$$ 0 0
$$413$$ −13.1489 + 22.7745i −0.647015 + 1.12066i
$$414$$ 0 0
$$415$$ 1.55677 2.69641i 0.0764190 0.132362i
$$416$$ 0 0
$$417$$ 7.77656 0.380820
$$418$$ 0 0
$$419$$ −1.14280 −0.0558292 −0.0279146 0.999610i $$-0.508887\pi$$
−0.0279146 + 0.999610i $$0.508887\pi$$
$$420$$ 0 0
$$421$$ −9.75944 + 16.9039i −0.475646 + 0.823843i −0.999611 0.0278967i $$-0.991119\pi$$
0.523965 + 0.851740i $$0.324452\pi$$
$$422$$ 0 0
$$423$$ −7.40959 + 12.8338i −0.360266 + 0.624000i
$$424$$ 0 0
$$425$$ −5.98406 −0.290269
$$426$$ 0 0
$$427$$ 12.8200 + 22.2049i 0.620404 + 1.07457i
$$428$$ 0 0
$$429$$ −10.6453 −0.513960
$$430$$ 0 0
$$431$$ −18.4392 31.9377i −0.888187 1.53838i −0.842017 0.539451i $$-0.818632\pi$$
−0.0461694 0.998934i $$-0.514701\pi$$
$$432$$ 0 0
$$433$$ −0.184467 0.319506i −0.00886490 0.0153545i 0.861559 0.507658i $$-0.169488\pi$$
−0.870424 + 0.492303i $$0.836155\pi$$
$$434$$ 0 0
$$435$$ −1.51832 + 2.62980i −0.0727976 + 0.126089i
$$436$$ 0 0
$$437$$ −3.47628 + 2.16921i −0.166293 + 0.103767i
$$438$$ 0 0
$$439$$ −1.13220 + 1.96102i −0.0540367 + 0.0935944i −0.891778 0.452472i $$-0.850542\pi$$
0.837742 + 0.546067i $$0.183875\pi$$
$$440$$ 0 0
$$441$$ −0.885022 1.53290i −0.0421439 0.0729954i
$$442$$ 0 0
$$443$$ −8.23137 14.2572i −0.391084 0.677378i 0.601508 0.798866i $$-0.294567\pi$$
−0.992593 + 0.121488i $$0.961233\pi$$
$$444$$ 0 0
$$445$$ −11.1141 −0.526860
$$446$$ 0 0
$$447$$ −8.34609 14.4558i −0.394756 0.683738i
$$448$$ 0 0
$$449$$ 14.1613 0.668315 0.334158 0.942517i $$-0.391548\pi$$
0.334158 + 0.942517i $$0.391548\pi$$
$$450$$ 0 0
$$451$$ 18.1717 31.4742i 0.855670 1.48206i
$$452$$ 0 0
$$453$$ 7.37713 12.7776i 0.346608 0.600342i
$$454$$ 0 0
$$455$$ −3.88426 −0.182097
$$456$$ 0 0
$$457$$ 1.22073 0.0571033 0.0285516 0.999592i $$-0.490910\pi$$
0.0285516 + 0.999592i $$0.490910\pi$$
$$458$$ 0 0
$$459$$ −16.1528 + 27.9775i −0.753950 + 1.30588i
$$460$$ 0 0
$$461$$ 4.34580 7.52714i 0.202404 0.350574i −0.746898 0.664938i $$-0.768458\pi$$
0.949303 + 0.314364i $$0.101791\pi$$
$$462$$ 0 0
$$463$$ 19.7149 0.916229 0.458114 0.888893i $$-0.348525\pi$$
0.458114 + 0.888893i $$0.348525\pi$$
$$464$$ 0 0
$$465$$ −3.05545 5.29220i −0.141693 0.245420i
$$466$$ 0 0
$$467$$ 11.4795 0.531207 0.265604 0.964082i $$-0.414429\pi$$
0.265604 + 0.964082i $$0.414429\pi$$
$$468$$ 0 0
$$469$$ 1.22929 + 2.12919i 0.0567633 + 0.0983170i
$$470$$ 0 0
$$471$$ 1.95726 + 3.39008i 0.0901858 + 0.156206i
$$472$$ 0 0
$$473$$ 13.0611 22.6225i 0.600549 1.04018i
$$474$$ 0 0
$$475$$ −3.69799 + 2.30756i −0.169676 + 0.105878i
$$476$$ 0 0
$$477$$ −1.81747 + 3.14796i −0.0832164 + 0.144135i
$$478$$ 0 0
$$479$$ 19.6316 + 34.0029i 0.896989 + 1.55363i 0.831324 + 0.555789i $$0.187584\pi$$
0.0656652 + 0.997842i $$0.479083\pi$$
$$480$$ 0 0
$$481$$ −2.30785 3.99731i −0.105229 0.182262i
$$482$$ 0 0
$$483$$ 2.65497 0.120805
$$484$$ 0 0
$$485$$ −2.02888 3.51412i −0.0921267 0.159568i
$$486$$ 0 0
$$487$$ −31.5943 −1.43168 −0.715838 0.698266i $$-0.753955\pi$$
−0.715838 + 0.698266i $$0.753955\pi$$
$$488$$ 0 0
$$489$$ 0.178579 0.309309i 0.00807564 0.0139874i
$$490$$ 0 0
$$491$$ −5.53187 + 9.58148i −0.249650 + 0.432406i −0.963429 0.267965i $$-0.913649\pi$$
0.713779 + 0.700371i $$0.246982\pi$$
$$492$$ 0 0
$$493$$ −15.6683 −0.705663
$$494$$ 0 0
$$495$$ −9.52395 −0.428070
$$496$$ 0 0
$$497$$ 10.7564 18.6306i 0.482489 0.835696i
$$498$$ 0 0
$$499$$ −10.1868 + 17.6440i −0.456023 + 0.789854i −0.998746 0.0500570i $$-0.984060\pi$$
0.542724 + 0.839911i $$0.317393\pi$$
$$500$$ 0 0
$$501$$ −16.5431 −0.739091
$$502$$ 0 0
$$503$$ −6.83622 11.8407i −0.304812 0.527950i 0.672407 0.740181i $$-0.265260\pi$$
−0.977219 + 0.212231i $$0.931927\pi$$
$$504$$ 0 0
$$505$$ −11.1301 −0.495281
$$506$$ 0 0
$$507$$ 6.06317 + 10.5017i 0.269275 + 0.466398i
$$508$$ 0 0
$$509$$ 3.86196 + 6.68912i 0.171179 + 0.296490i 0.938832 0.344375i $$-0.111909\pi$$
−0.767654 + 0.640865i $$0.778576\pi$$
$$510$$ 0 0
$$511$$ 12.4807 21.6171i 0.552112 0.956285i
$$512$$ 0 0
$$513$$ 0.806621 + 23.5182i 0.0356132 + 1.03836i
$$514$$ 0 0
$$515$$ 5.78953 10.0278i 0.255117 0.441876i
$$516$$ 0 0
$$517$$ 25.7651 + 44.6265i 1.13315 + 1.96267i
$$518$$ 0 0
$$519$$ −7.73971 13.4056i −0.339736 0.588439i
$$520$$ 0 0
$$521$$ −2.16876 −0.0950151 −0.0475075 0.998871i $$-0.515128\pi$$
−0.0475075 + 0.998871i $$0.515128\pi$$
$$522$$ 0 0
$$523$$ −11.9466 20.6921i −0.522389 0.904804i −0.999661 0.0260485i $$-0.991708\pi$$
0.477272 0.878756i $$-0.341626\pi$$
$$524$$ 0 0
$$525$$ 2.82430 0.123263
$$526$$ 0 0
$$527$$ 15.7654 27.3065i 0.686751 1.18949i
$$528$$ 0 0
$$529$$ 11.0582 19.1533i 0.480790 0.832752i
$$530$$ 0 0
$$531$$ −17.8716 −0.775562
$$532$$ 0 0
$$533$$ 10.0730 0.436312
$$534$$ 0 0
$$535$$ 8.95887 15.5172i 0.387326 0.670868i
$$536$$ 0 0
$$537$$ −8.24629 + 14.2830i −0.355854 + 0.616356i
$$538$$ 0 0
$$539$$ −6.15492 −0.265111
$$540$$ 0 0
$$541$$ −21.2275 36.7671i −0.912641 1.58074i −0.810319 0.585990i $$-0.800706\pi$$
−0.102323 0.994751i $$-0.532627\pi$$
$$542$$ 0 0
$$543$$ 11.4614 0.491858
$$544$$ 0 0
$$545$$ −2.81235 4.87113i −0.120468 0.208656i
$$546$$ 0 0
$$547$$ 6.01535 + 10.4189i 0.257198 + 0.445480i 0.965490 0.260439i $$-0.0838674\pi$$
−0.708292 + 0.705919i $$0.750534\pi$$
$$548$$ 0 0
$$549$$ −8.71231 + 15.0902i −0.371833 + 0.644033i
$$550$$ 0 0
$$551$$ −9.68259 + 6.04198i −0.412492 + 0.257397i
$$552$$ 0 0
$$553$$ 9.25956 16.0380i 0.393756 0.682006i
$$554$$ 0 0
$$555$$ 1.67807 + 2.90650i 0.0712301 + 0.123374i
$$556$$ 0 0
$$557$$ 4.37635 + 7.58006i 0.185432 + 0.321178i 0.943722 0.330740i $$-0.107298\pi$$
−0.758290 + 0.651917i $$0.773965\pi$$
$$558$$ 0 0
$$559$$ 7.24011 0.306224
$$560$$ 0 0
$$561$$ 19.9692 + 34.5876i 0.843099 + 1.46029i
$$562$$ 0 0
$$563$$ 35.9707 1.51598 0.757991 0.652265i $$-0.226181\pi$$
0.757991 + 0.652265i $$0.226181\pi$$
$$564$$ 0 0
$$565$$ 7.83943 13.5783i 0.329807 0.571243i
$$566$$ 0 0
$$567$$ 1.57827 2.73365i 0.0662812 0.114802i
$$568$$ 0 0
$$569$$ −20.3125 −0.851543 −0.425772 0.904831i $$-0.639997\pi$$
−0.425772 + 0.904831i $$0.639997\pi$$
$$570$$ 0 0
$$571$$ −10.1773 −0.425906 −0.212953 0.977062i $$-0.568308\pi$$
−0.212953 + 0.977062i $$0.568308\pi$$
$$572$$ 0 0
$$573$$ −7.53505 + 13.0511i −0.314781 + 0.545217i
$$574$$ 0 0
$$575$$ −0.470022 + 0.814102i −0.0196013 + 0.0339504i
$$576$$ 0 0
$$577$$ −32.7441 −1.36316 −0.681578 0.731745i $$-0.738706\pi$$
−0.681578 + 0.731745i $$0.738706\pi$$
$$578$$ 0 0
$$579$$ −8.41745 14.5794i −0.349817 0.605901i
$$580$$ 0 0
$$581$$ −7.58228 −0.314566
$$582$$ 0 0
$$583$$ 6.31984 + 10.9463i 0.261741 + 0.453349i
$$584$$ 0 0
$$585$$ −1.31984 2.28604i −0.0545689 0.0945160i
$$586$$ 0 0
$$587$$ 4.38663 7.59786i 0.181056 0.313597i −0.761185 0.648535i $$-0.775382\pi$$
0.942240 + 0.334938i $$0.108715\pi$$
$$588$$ 0 0
$$589$$ −0.787274 22.9541i −0.0324390 0.945808i
$$590$$ 0 0
$$591$$ 14.4975 25.1105i 0.596349 1.03291i
$$592$$ 0 0
$$593$$ 16.1603 + 27.9905i 0.663625 + 1.14943i 0.979656 + 0.200684i $$0.0643163\pi$$
−0.316031 + 0.948749i $$0.602350\pi$$
$$594$$ 0 0
$$595$$ 7.28635 + 12.6203i 0.298711 + 0.517383i
$$596$$ 0 0
$$597$$ 2.61570 0.107053
$$598$$ 0 0
$$599$$ −9.77520 16.9311i −0.399404 0.691787i 0.594249 0.804281i $$-0.297449\pi$$
−0.993652 + 0.112494i $$0.964116\pi$$
$$600$$ 0 0
$$601$$ −0.401837 −0.0163913 −0.00819564 0.999966i $$-0.502609\pi$$
−0.00819564 + 0.999966i $$0.502609\pi$$
$$602$$ 0 0
$$603$$ −0.835409 + 1.44697i −0.0340205 + 0.0589252i
$$604$$ 0 0
$$605$$ −11.0587 + 19.1542i −0.449599 + 0.778728i
$$606$$ 0 0
$$607$$ −13.4453 −0.545727 −0.272863 0.962053i $$-0.587971\pi$$
−0.272863 + 0.962053i $$0.587971\pi$$
$$608$$ 0 0
$$609$$ 7.39497 0.299659
$$610$$ 0 0
$$611$$ −7.14115 + 12.3688i −0.288900 + 0.500390i
$$612$$ 0 0
$$613$$ 10.3527 17.9313i 0.418140 0.724239i −0.577613 0.816311i $$-0.696016\pi$$
0.995752 + 0.0920716i $$0.0293489\pi$$
$$614$$ 0 0
$$615$$ −7.32425 −0.295342
$$616$$ 0 0
$$617$$ 4.63936 + 8.03560i 0.186773 + 0.323501i 0.944173 0.329451i $$-0.106864\pi$$
−0.757399 + 0.652952i $$0.773530\pi$$
$$618$$ 0 0
$$619$$ 2.89129 0.116211 0.0581053 0.998310i $$-0.481494\pi$$
0.0581053 + 0.998310i $$0.481494\pi$$
$$620$$ 0 0
$$621$$ 2.53747 + 4.39503i 0.101825 + 0.176366i
$$622$$ 0 0
$$623$$ 13.5329 + 23.4396i 0.542183 + 0.939088i
$$624$$ 0 0
$$625$$ −0.500000 + 0.866025i −0.0200000 + 0.0346410i
$$626$$ 0 0
$$627$$ 25.6781 + 13.6738i 1.02548 + 0.546078i
$$628$$ 0 0
$$629$$ −8.65844 + 14.9969i −0.345234 + 0.597964i
$$630$$ 0 0
$$631$$ 15.2270 + 26.3740i 0.606178 + 1.04993i 0.991864 + 0.127301i $$0.0406314\pi$$
−0.385686 + 0.922630i $$0.626035\pi$$
$$632$$ 0 0
$$633$$ 12.8826 + 22.3134i 0.512039 + 0.886877i
$$634$$ 0 0
$$635$$ −6.11991 −0.242861
$$636$$ 0 0
$$637$$ −0.852959 1.47737i −0.0337955 0.0585355i
$$638$$ 0 0
$$639$$ 14.6198 0.578349
$$640$$ 0 0
$$641$$ 10.0369 17.3845i 0.396434 0.686645i −0.596849 0.802354i $$-0.703581\pi$$
0.993283 + 0.115709i $$0.0369141\pi$$
$$642$$ 0 0
$$643$$ −1.04457 + 1.80924i −0.0411937 + 0.0713496i −0.885887 0.463901i $$-0.846449\pi$$
0.844693 + 0.535250i $$0.179783\pi$$
$$644$$ 0 0
$$645$$ −5.26439 −0.207285
$$646$$ 0 0
$$647$$ 2.10623 0.0828043 0.0414021 0.999143i $$-0.486818\pi$$
0.0414021 + 0.999143i $$0.486818\pi$$
$$648$$ 0 0
$$649$$ −31.0722 + 53.8187i −1.21969 + 2.11257i
$$650$$ 0 0
$$651$$ −7.44081 + 12.8879i −0.291628 + 0.505115i
$$652$$ 0 0
$$653$$ 1.83067 0.0716395 0.0358197 0.999358i $$-0.488596\pi$$
0.0358197 + 0.999358i $$0.488596\pi$$
$$654$$ 0 0
$$655$$ −7.44055 12.8874i −0.290726 0.503553i
$$656$$ 0 0
$$657$$ 16.9634 0.661804
$$658$$ 0 0
$$659$$ 12.0268 + 20.8310i 0.468497 + 0.811460i 0.999352 0.0360024i $$-0.0114624\pi$$
−0.530855 + 0.847463i $$0.678129\pi$$
$$660$$ 0 0
$$661$$ 8.72110 + 15.1054i 0.339211 + 0.587531i 0.984285 0.176589i $$-0.0565065\pi$$
−0.645073 + 0.764121i $$0.723173\pi$$
$$662$$ 0 0
$$663$$ −5.53472 + 9.58642i −0.214951 + 0.372306i
$$664$$ 0 0
$$665$$ 9.36941 + 4.98929i 0.363330 + 0.193476i
$$666$$ 0 0
$$667$$ −1.23068 + 2.13159i −0.0476519 + 0.0825356i
$$668$$ 0 0
$$669$$ 5.92402 + 10.2607i 0.229036 + 0.396702i
$$670$$ 0 0
$$671$$ 30.2951 + 52.4726i 1.16953 + 2.02568i
$$672$$ 0 0
$$673$$ 47.5187 1.83171 0.915856 0.401506i $$-0.131513\pi$$
0.915856 + 0.401506i $$0.131513\pi$$
$$674$$ 0 0
$$675$$ 2.69931 + 4.67535i 0.103897 + 0.179954i
$$676$$ 0 0
$$677$$ 14.5531 0.559321 0.279661 0.960099i $$-0.409778\pi$$
0.279661 + 0.960099i $$0.409778\pi$$
$$678$$ 0 0
$$679$$ −4.94084 + 8.55778i −0.189612 + 0.328418i
$$680$$ 0 0
$$681$$ 2.40754 4.16998i 0.0922570 0.159794i
$$682$$ 0 0
$$683$$ −3.33714 −0.127692 −0.0638460 0.997960i $$-0.520337\pi$$
−0.0638460 + 0.997960i $$0.520337\pi$$
$$684$$ 0 0
$$685$$ 17.3504 0.662923
$$686$$ 0 0
$$687$$ −3.78826 + 6.56146i −0.144531 + 0.250335i
$$688$$ 0 0
$$689$$ −1.75163 + 3.03391i −0.0667318 + 0.115583i
$$690$$ 0 0
$$691$$ 19.3318 0.735415 0.367708 0.929941i $$-0.380143\pi$$
0.367708 + 0.929941i $$0.380143\pi$$
$$692$$ 0 0
$$693$$ 11.5966 + 20.0859i 0.440519 + 0.763001i
$$694$$ 0 0
$$695$$ 6.70534 0.254348
$$696$$ 0 0
$$697$$ −18.8957 32.7283i −0.715725 1.23967i
$$698$$ 0 0
$$699$$ −2.98533 5.17074i −0.112916 0.195575i
$$700$$ 0 0
$$701$$ −4.96892 + 8.60643i −0.187674 + 0.325060i −0.944474 0.328586i $$-0.893428\pi$$
0.756801 + 0.653646i $$0.226761\pi$$
$$702$$ 0 0
$$703$$ 0.432375 + 12.6065i 0.0163073 + 0.475464i
$$704$$ 0 0
$$705$$ 5.19244 8.99357i 0.195559 0.338717i
$$706$$ 0 0
$$707$$ 13.5523 + 23.4732i 0.509686 + 0.882801i
$$708$$ 0 0
$$709$$ −18.6059 32.2264i −0.698760 1.21029i −0.968897 0.247466i $$-0.920402\pi$$
0.270136 0.962822i $$-0.412931\pi$$
$$710$$ 0 0
$$711$$ 12.5853 0.471987
$$712$$ 0 0
$$713$$ −2.47661 4.28961i −0.0927497 0.160647i
$$714$$ 0 0
$$715$$ −9.17891 −0.343272
$$716$$ 0 0
$$717$$ 8.11608 14.0575i 0.303100 0.524985i
$$718$$ 0 0
$$719$$ −1.32109 + 2.28819i −0.0492683 + 0.0853351i −0.889608 0.456725i $$-0.849022\pi$$
0.840340 + 0.542060i $$0.182356\pi$$
$$720$$ 0 0
$$721$$ −28.1980 −1.05015
$$722$$ 0 0
$$723$$ 17.6581 0.656711
$$724$$ 0 0
$$725$$ −1.30917 + 2.26755i −0.0486213 + 0.0842145i
$$726$$ 0 0
$$727$$ −5.08653 + 8.81013i −0.188649 + 0.326750i −0.944800 0.327647i $$-0.893744\pi$$
0.756151 + 0.654397i $$0.227077\pi$$
$$728$$ 0 0
$$729$$ 20.9284 0.775126
$$730$$ 0 0
$$731$$ −13.5815 23.5238i −0.502329 0.870060i
$$732$$ 0 0
$$733$$ 14.8222 0.547472 0.273736 0.961805i $$-0.411741\pi$$
0.273736 + 0.961805i $$0.411741\pi$$
$$734$$ 0 0
$$735$$ 0.620199 + 1.07422i 0.0228764 + 0.0396231i
$$736$$ 0 0
$$737$$ 2.90494 + 5.03151i 0.107005 + 0.185338i
$$738$$ 0 0
$$739$$ 17.7433 30.7323i 0.652697 1.13050i −0.329769 0.944062i $$-0.606971\pi$$
0.982466 0.186443i $$-0.0596959\pi$$
$$740$$ 0 0
$$741$$ 0.276386 + 8.05845i 0.0101533 + 0.296035i
$$742$$ 0 0
$$743$$ −4.36941 + 7.56804i −0.160298 + 0.277645i −0.934976 0.354712i $$-0.884579\pi$$
0.774677 + 0.632357i $$0.217912\pi$$
$$744$$ 0 0
$$745$$ −7.19642 12.4646i −0.263656 0.456666i
$$746$$ 0 0
$$747$$ −2.57641 4.46247i −0.0942658 0.163273i
$$748$$ 0 0
$$749$$ −43.6342 −1.59436
$$750$$ 0 0
$$751$$ 6.54957 + 11.3442i 0.238997 + 0.413955i 0.960427 0.278533i $$-0.0898480\pi$$
−0.721430 + 0.692488i $$0.756515\pi$$
$$752$$ 0 0
$$753$$ 7.08911 0.258342
$$754$$ 0 0
$$755$$ 6.36093 11.0175i 0.231498 0.400966i
$$756$$ 0 0
$$757$$ 8.21901 14.2357i 0.298725 0.517407i −0.677119 0.735873i $$-0.736772\pi$$
0.975845 + 0.218466i $$0.0701053\pi$$
$$758$$ 0 0
$$759$$ 6.27397 0.227731
$$760$$ 0 0
$$761$$ 16.3918 0.594203 0.297101 0.954846i $$-0.403980\pi$$
0.297101 + 0.954846i $$0.403980\pi$$
$$762$$ 0 0
$$763$$ −6.84879 + 11.8625i −0.247943 + 0.429450i
$$764$$ 0 0
$$765$$ −4.95171 + 8.57661i −0.179029 + 0.310088i
$$766$$ 0 0
$$767$$ −17.2242 −0.621929
$$768$$ 0 0
$$769$$ 25.0210 + 43.3377i 0.902282 + 1.56280i 0.824525 + 0.565825i $$0.191442\pi$$
0.0777564 + 0.996972i $$0.475224\pi$$
$$770$$ 0 0
$$771$$ 0.142282 0.00512416
$$772$$ 0 0
$$773$$ −24.3436 42.1644i −0.875580 1.51655i −0.856144 0.516737i $$-0.827146\pi$$
−0.0194356 0.999811i $$-0.506187\pi$$
$$774$$ 0 0
$$775$$ −2.63457 4.56320i −0.0946364 0.163915i
$$776$$ 0 0
$$777$$ 4.08653 7.07808i 0.146603 0.253925i
$$778$$ 0 0
$$779$$ −24.2977 12.9387i −0.870555 0.463577i
$$780$$ 0 0
$$781$$ 25.4185 44.0261i 0.909544 1.57538i
$$782$$ 0 0
$$783$$ 7.06771 + 12.2416i 0.252579 + 0.437480i
$$784$$ 0 0
$$785$$ 1.68765 + 2.92309i 0.0602348 + 0.104330i
$$786$$ 0 0
$$787$$ −6.51678 −0.232298 −0.116149 0.993232i $$-0.537055\pi$$
−0.116149 + 0.993232i $$0.537055\pi$$
$$788$$ 0 0
$$789$$ −5.83388 10.1046i −0.207692 0.359732i
$$790$$ 0 0
$$791$$