# Properties

 Label 966.2.g.d.643.1 Level $966$ Weight $2$ Character 966.643 Analytic conductor $7.714$ Analytic rank $0$ Dimension $4$ Inner twists $4$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(643,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("966.643");

S:= CuspForms(chi, 2);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$966 = 2 \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 966.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: $$7.71354883526$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{7})$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - 3x^{2} + 4$$ x^4 - 3*x^2 + 4 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 643.1 Root $$-1.32288 - 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 966.643 Dual form 966.2.g.d.643.3

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -2.64575 q^{5} +1.00000i q^{6} -2.64575 q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -1.00000i q^{3} +1.00000 q^{4} -2.64575 q^{5} +1.00000i q^{6} -2.64575 q^{7} -1.00000 q^{8} -1.00000 q^{9} +2.64575 q^{10} -1.00000i q^{12} -5.00000i q^{13} +2.64575 q^{14} +2.64575i q^{15} +1.00000 q^{16} -5.29150 q^{17} +1.00000 q^{18} +5.29150 q^{19} -2.64575 q^{20} +2.64575i q^{21} +(4.00000 + 2.64575i) q^{23} +1.00000i q^{24} +2.00000 q^{25} +5.00000i q^{26} +1.00000i q^{27} -2.64575 q^{28} -1.00000 q^{29} -2.64575i q^{30} +4.00000i q^{31} -1.00000 q^{32} +5.29150 q^{34} +7.00000 q^{35} -1.00000 q^{36} +7.93725i q^{37} -5.29150 q^{38} -5.00000 q^{39} +2.64575 q^{40} +9.00000i q^{41} -2.64575i q^{42} -2.64575i q^{43} +2.64575 q^{45} +(-4.00000 - 2.64575i) q^{46} +13.0000i q^{47} -1.00000i q^{48} +7.00000 q^{49} -2.00000 q^{50} +5.29150i q^{51} -5.00000i q^{52} +5.29150i q^{53} -1.00000i q^{54} +2.64575 q^{56} -5.29150i q^{57} +1.00000 q^{58} -14.0000i q^{59} +2.64575i q^{60} +10.5830 q^{61} -4.00000i q^{62} +2.64575 q^{63} +1.00000 q^{64} +13.2288i q^{65} -5.29150i q^{67} -5.29150 q^{68} +(2.64575 - 4.00000i) q^{69} -7.00000 q^{70} +6.00000 q^{71} +1.00000 q^{72} -4.00000i q^{73} -7.93725i q^{74} -2.00000i q^{75} +5.29150 q^{76} +5.00000 q^{78} +5.29150i q^{79} -2.64575 q^{80} +1.00000 q^{81} -9.00000i q^{82} -15.8745 q^{83} +2.64575i q^{84} +14.0000 q^{85} +2.64575i q^{86} +1.00000i q^{87} -2.64575 q^{90} +13.2288i q^{91} +(4.00000 + 2.64575i) q^{92} +4.00000 q^{93} -13.0000i q^{94} -14.0000 q^{95} +1.00000i q^{96} +2.64575 q^{97} -7.00000 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{9}+O(q^{10})$$ 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 4 * q^9 $$4 q - 4 q^{2} + 4 q^{4} - 4 q^{8} - 4 q^{9} + 4 q^{16} + 4 q^{18} + 16 q^{23} + 8 q^{25} - 4 q^{29} - 4 q^{32} + 28 q^{35} - 4 q^{36} - 20 q^{39} - 16 q^{46} + 28 q^{49} - 8 q^{50} + 4 q^{58} + 4 q^{64} - 28 q^{70} + 24 q^{71} + 4 q^{72} + 20 q^{78} + 4 q^{81} + 56 q^{85} + 16 q^{92} + 16 q^{93} - 56 q^{95} - 28 q^{98}+O(q^{100})$$ 4 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 - 4 * q^9 + 4 * q^16 + 4 * q^18 + 16 * q^23 + 8 * q^25 - 4 * q^29 - 4 * q^32 + 28 * q^35 - 4 * q^36 - 20 * q^39 - 16 * q^46 + 28 * q^49 - 8 * q^50 + 4 * q^58 + 4 * q^64 - 28 * q^70 + 24 * q^71 + 4 * q^72 + 20 * q^78 + 4 * q^81 + 56 * q^85 + 16 * q^92 + 16 * q^93 - 56 * q^95 - 28 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$$.

 $$n$$ $$323$$ $$829$$ $$925$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 1.00000i 0.577350i
$$4$$ 1.00000 0.500000
$$5$$ −2.64575 −1.18322 −0.591608 0.806226i $$-0.701507\pi$$
−0.591608 + 0.806226i $$0.701507\pi$$
$$6$$ 1.00000i 0.408248i
$$7$$ −2.64575 −1.00000
$$8$$ −1.00000 −0.353553
$$9$$ −1.00000 −0.333333
$$10$$ 2.64575 0.836660
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ 5.00000i 1.38675i −0.720577 0.693375i $$-0.756123\pi$$
0.720577 0.693375i $$-0.243877\pi$$
$$14$$ 2.64575 0.707107
$$15$$ 2.64575i 0.683130i
$$16$$ 1.00000 0.250000
$$17$$ −5.29150 −1.28338 −0.641689 0.766965i $$-0.721766\pi$$
−0.641689 + 0.766965i $$0.721766\pi$$
$$18$$ 1.00000 0.235702
$$19$$ 5.29150 1.21395 0.606977 0.794719i $$-0.292382\pi$$
0.606977 + 0.794719i $$0.292382\pi$$
$$20$$ −2.64575 −0.591608
$$21$$ 2.64575i 0.577350i
$$22$$ 0 0
$$23$$ 4.00000 + 2.64575i 0.834058 + 0.551677i
$$24$$ 1.00000i 0.204124i
$$25$$ 2.00000 0.400000
$$26$$ 5.00000i 0.980581i
$$27$$ 1.00000i 0.192450i
$$28$$ −2.64575 −0.500000
$$29$$ −1.00000 −0.185695 −0.0928477 0.995680i $$-0.529597\pi$$
−0.0928477 + 0.995680i $$0.529597\pi$$
$$30$$ 2.64575i 0.483046i
$$31$$ 4.00000i 0.718421i 0.933257 + 0.359211i $$0.116954\pi$$
−0.933257 + 0.359211i $$0.883046\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0 0
$$34$$ 5.29150 0.907485
$$35$$ 7.00000 1.18322
$$36$$ −1.00000 −0.166667
$$37$$ 7.93725i 1.30488i 0.757842 + 0.652438i $$0.226254\pi$$
−0.757842 + 0.652438i $$0.773746\pi$$
$$38$$ −5.29150 −0.858395
$$39$$ −5.00000 −0.800641
$$40$$ 2.64575 0.418330
$$41$$ 9.00000i 1.40556i 0.711405 + 0.702782i $$0.248059\pi$$
−0.711405 + 0.702782i $$0.751941\pi$$
$$42$$ 2.64575i 0.408248i
$$43$$ 2.64575i 0.403473i −0.979440 0.201737i $$-0.935341\pi$$
0.979440 0.201737i $$-0.0646585\pi$$
$$44$$ 0 0
$$45$$ 2.64575 0.394405
$$46$$ −4.00000 2.64575i −0.589768 0.390095i
$$47$$ 13.0000i 1.89624i 0.317905 + 0.948122i $$0.397021\pi$$
−0.317905 + 0.948122i $$0.602979\pi$$
$$48$$ 1.00000i 0.144338i
$$49$$ 7.00000 1.00000
$$50$$ −2.00000 −0.282843
$$51$$ 5.29150i 0.740959i
$$52$$ 5.00000i 0.693375i
$$53$$ 5.29150i 0.726844i 0.931625 + 0.363422i $$0.118392\pi$$
−0.931625 + 0.363422i $$0.881608\pi$$
$$54$$ 1.00000i 0.136083i
$$55$$ 0 0
$$56$$ 2.64575 0.353553
$$57$$ 5.29150i 0.700877i
$$58$$ 1.00000 0.131306
$$59$$ 14.0000i 1.82264i −0.411693 0.911322i $$-0.635063\pi$$
0.411693 0.911322i $$-0.364937\pi$$
$$60$$ 2.64575i 0.341565i
$$61$$ 10.5830 1.35501 0.677507 0.735516i $$-0.263060\pi$$
0.677507 + 0.735516i $$0.263060\pi$$
$$62$$ 4.00000i 0.508001i
$$63$$ 2.64575 0.333333
$$64$$ 1.00000 0.125000
$$65$$ 13.2288i 1.64083i
$$66$$ 0 0
$$67$$ 5.29150i 0.646460i −0.946320 0.323230i $$-0.895231\pi$$
0.946320 0.323230i $$-0.104769\pi$$
$$68$$ −5.29150 −0.641689
$$69$$ 2.64575 4.00000i 0.318511 0.481543i
$$70$$ −7.00000 −0.836660
$$71$$ 6.00000 0.712069 0.356034 0.934473i $$-0.384129\pi$$
0.356034 + 0.934473i $$0.384129\pi$$
$$72$$ 1.00000 0.117851
$$73$$ 4.00000i 0.468165i −0.972217 0.234082i $$-0.924791\pi$$
0.972217 0.234082i $$-0.0752085\pi$$
$$74$$ 7.93725i 0.922687i
$$75$$ 2.00000i 0.230940i
$$76$$ 5.29150 0.606977
$$77$$ 0 0
$$78$$ 5.00000 0.566139
$$79$$ 5.29150i 0.595341i 0.954669 + 0.297670i $$0.0962096\pi$$
−0.954669 + 0.297670i $$0.903790\pi$$
$$80$$ −2.64575 −0.295804
$$81$$ 1.00000 0.111111
$$82$$ 9.00000i 0.993884i
$$83$$ −15.8745 −1.74245 −0.871227 0.490881i $$-0.836675\pi$$
−0.871227 + 0.490881i $$0.836675\pi$$
$$84$$ 2.64575i 0.288675i
$$85$$ 14.0000 1.51851
$$86$$ 2.64575i 0.285299i
$$87$$ 1.00000i 0.107211i
$$88$$ 0 0
$$89$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$90$$ −2.64575 −0.278887
$$91$$ 13.2288i 1.38675i
$$92$$ 4.00000 + 2.64575i 0.417029 + 0.275839i
$$93$$ 4.00000 0.414781
$$94$$ 13.0000i 1.34085i
$$95$$ −14.0000 −1.43637
$$96$$ 1.00000i 0.102062i
$$97$$ 2.64575 0.268635 0.134318 0.990938i $$-0.457116\pi$$
0.134318 + 0.990938i $$0.457116\pi$$
$$98$$ −7.00000 −0.707107
$$99$$ 0 0
$$100$$ 2.00000 0.200000
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 5.29150i 0.523937i
$$103$$ 2.64575 0.260694 0.130347 0.991468i $$-0.458391\pi$$
0.130347 + 0.991468i $$0.458391\pi$$
$$104$$ 5.00000i 0.490290i
$$105$$ 7.00000i 0.683130i
$$106$$ 5.29150i 0.513956i
$$107$$ 5.29150i 0.511549i −0.966736 0.255774i $$-0.917670\pi$$
0.966736 0.255774i $$-0.0823304\pi$$
$$108$$ 1.00000i 0.0962250i
$$109$$ 18.5203i 1.77392i 0.461847 + 0.886960i $$0.347187\pi$$
−0.461847 + 0.886960i $$0.652813\pi$$
$$110$$ 0 0
$$111$$ 7.93725 0.753371
$$112$$ −2.64575 −0.250000
$$113$$ 2.64575i 0.248891i 0.992226 + 0.124446i $$0.0397153\pi$$
−0.992226 + 0.124446i $$0.960285\pi$$
$$114$$ 5.29150i 0.495595i
$$115$$ −10.5830 7.00000i −0.986870 0.652753i
$$116$$ −1.00000 −0.0928477
$$117$$ 5.00000i 0.462250i
$$118$$ 14.0000i 1.28880i
$$119$$ 14.0000 1.28338
$$120$$ 2.64575i 0.241523i
$$121$$ 11.0000 1.00000
$$122$$ −10.5830 −0.958140
$$123$$ 9.00000 0.811503
$$124$$ 4.00000i 0.359211i
$$125$$ 7.93725 0.709930
$$126$$ −2.64575 −0.235702
$$127$$ −13.0000 −1.15356 −0.576782 0.816898i $$-0.695692\pi$$
−0.576782 + 0.816898i $$0.695692\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ −2.64575 −0.232945
$$130$$ 13.2288i 1.16024i
$$131$$ 22.0000i 1.92215i 0.276289 + 0.961074i $$0.410895\pi$$
−0.276289 + 0.961074i $$0.589105\pi$$
$$132$$ 0 0
$$133$$ −14.0000 −1.21395
$$134$$ 5.29150i 0.457116i
$$135$$ 2.64575i 0.227710i
$$136$$ 5.29150 0.453743
$$137$$ 7.93725i 0.678125i 0.940764 + 0.339063i $$0.110110\pi$$
−0.940764 + 0.339063i $$0.889890\pi$$
$$138$$ −2.64575 + 4.00000i −0.225221 + 0.340503i
$$139$$ 5.00000i 0.424094i 0.977259 + 0.212047i $$0.0680131\pi$$
−0.977259 + 0.212047i $$0.931987\pi$$
$$140$$ 7.00000 0.591608
$$141$$ 13.0000 1.09480
$$142$$ −6.00000 −0.503509
$$143$$ 0 0
$$144$$ −1.00000 −0.0833333
$$145$$ 2.64575 0.219718
$$146$$ 4.00000i 0.331042i
$$147$$ 7.00000i 0.577350i
$$148$$ 7.93725i 0.652438i
$$149$$ 15.8745i 1.30049i −0.759724 0.650245i $$-0.774666\pi$$
0.759724 0.650245i $$-0.225334\pi$$
$$150$$ 2.00000i 0.163299i
$$151$$ −5.00000 −0.406894 −0.203447 0.979086i $$-0.565214\pi$$
−0.203447 + 0.979086i $$0.565214\pi$$
$$152$$ −5.29150 −0.429198
$$153$$ 5.29150 0.427793
$$154$$ 0 0
$$155$$ 10.5830i 0.850047i
$$156$$ −5.00000 −0.400320
$$157$$ 10.5830 0.844616 0.422308 0.906452i $$-0.361220\pi$$
0.422308 + 0.906452i $$0.361220\pi$$
$$158$$ 5.29150i 0.420969i
$$159$$ 5.29150 0.419643
$$160$$ 2.64575 0.209165
$$161$$ −10.5830 7.00000i −0.834058 0.551677i
$$162$$ −1.00000 −0.0785674
$$163$$ −18.0000 −1.40987 −0.704934 0.709273i $$-0.749024\pi$$
−0.704934 + 0.709273i $$0.749024\pi$$
$$164$$ 9.00000i 0.702782i
$$165$$ 0 0
$$166$$ 15.8745 1.23210
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 2.64575i 0.204124i
$$169$$ −12.0000 −0.923077
$$170$$ −14.0000 −1.07375
$$171$$ −5.29150 −0.404651
$$172$$ 2.64575i 0.201737i
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 1.00000i 0.0758098i
$$175$$ −5.29150 −0.400000
$$176$$ 0 0
$$177$$ −14.0000 −1.05230
$$178$$ 0 0
$$179$$ 9.00000 0.672692 0.336346 0.941739i $$-0.390809\pi$$
0.336346 + 0.941739i $$0.390809\pi$$
$$180$$ 2.64575 0.197203
$$181$$ −15.8745 −1.17994 −0.589971 0.807424i $$-0.700861\pi$$
−0.589971 + 0.807424i $$0.700861\pi$$
$$182$$ 13.2288i 0.980581i
$$183$$ 10.5830i 0.782318i
$$184$$ −4.00000 2.64575i −0.294884 0.195047i
$$185$$ 21.0000i 1.54395i
$$186$$ −4.00000 −0.293294
$$187$$ 0 0
$$188$$ 13.0000i 0.948122i
$$189$$ 2.64575i 0.192450i
$$190$$ 14.0000 1.01567
$$191$$ 15.8745i 1.14864i −0.818631 0.574320i $$-0.805267\pi$$
0.818631 0.574320i $$-0.194733\pi$$
$$192$$ 1.00000i 0.0721688i
$$193$$ 19.0000 1.36765 0.683825 0.729646i $$-0.260315\pi$$
0.683825 + 0.729646i $$0.260315\pi$$
$$194$$ −2.64575 −0.189954
$$195$$ 13.2288 0.947331
$$196$$ 7.00000 0.500000
$$197$$ −1.00000 −0.0712470 −0.0356235 0.999365i $$-0.511342\pi$$
−0.0356235 + 0.999365i $$0.511342\pi$$
$$198$$ 0 0
$$199$$ −13.2288 −0.937762 −0.468881 0.883261i $$-0.655343\pi$$
−0.468881 + 0.883261i $$0.655343\pi$$
$$200$$ −2.00000 −0.141421
$$201$$ −5.29150 −0.373234
$$202$$ 0 0
$$203$$ 2.64575 0.185695
$$204$$ 5.29150i 0.370479i
$$205$$ 23.8118i 1.66309i
$$206$$ −2.64575 −0.184338
$$207$$ −4.00000 2.64575i −0.278019 0.183892i
$$208$$ 5.00000i 0.346688i
$$209$$ 0 0
$$210$$ 7.00000i 0.483046i
$$211$$ −16.0000 −1.10149 −0.550743 0.834675i $$-0.685655\pi$$
−0.550743 + 0.834675i $$0.685655\pi$$
$$212$$ 5.29150i 0.363422i
$$213$$ 6.00000i 0.411113i
$$214$$ 5.29150i 0.361720i
$$215$$ 7.00000i 0.477396i
$$216$$ 1.00000i 0.0680414i
$$217$$ 10.5830i 0.718421i
$$218$$ 18.5203i 1.25435i
$$219$$ −4.00000 −0.270295
$$220$$ 0 0
$$221$$ 26.4575i 1.77972i
$$222$$ −7.93725 −0.532714
$$223$$ 28.0000i 1.87502i 0.347960 + 0.937509i $$0.386874\pi$$
−0.347960 + 0.937509i $$0.613126\pi$$
$$224$$ 2.64575 0.176777
$$225$$ −2.00000 −0.133333
$$226$$ 2.64575i 0.175993i
$$227$$ −7.93725 −0.526814 −0.263407 0.964685i $$-0.584846\pi$$
−0.263407 + 0.964685i $$0.584846\pi$$
$$228$$ 5.29150i 0.350438i
$$229$$ 10.5830 0.699345 0.349672 0.936872i $$-0.386293\pi$$
0.349672 + 0.936872i $$0.386293\pi$$
$$230$$ 10.5830 + 7.00000i 0.697823 + 0.461566i
$$231$$ 0 0
$$232$$ 1.00000 0.0656532
$$233$$ −18.0000 −1.17922 −0.589610 0.807688i $$-0.700718\pi$$
−0.589610 + 0.807688i $$0.700718\pi$$
$$234$$ 5.00000i 0.326860i
$$235$$ 34.3948i 2.24367i
$$236$$ 14.0000i 0.911322i
$$237$$ 5.29150 0.343720
$$238$$ −14.0000 −0.907485
$$239$$ −20.0000 −1.29369 −0.646846 0.762620i $$-0.723912\pi$$
−0.646846 + 0.762620i $$0.723912\pi$$
$$240$$ 2.64575i 0.170783i
$$241$$ −23.8118 −1.53385 −0.766925 0.641736i $$-0.778214\pi$$
−0.766925 + 0.641736i $$0.778214\pi$$
$$242$$ −11.0000 −0.707107
$$243$$ 1.00000i 0.0641500i
$$244$$ 10.5830 0.677507
$$245$$ −18.5203 −1.18322
$$246$$ −9.00000 −0.573819
$$247$$ 26.4575i 1.68345i
$$248$$ 4.00000i 0.254000i
$$249$$ 15.8745i 1.00601i
$$250$$ −7.93725 −0.501996
$$251$$ 18.5203 1.16899 0.584494 0.811398i $$-0.301293\pi$$
0.584494 + 0.811398i $$0.301293\pi$$
$$252$$ 2.64575 0.166667
$$253$$ 0 0
$$254$$ 13.0000 0.815693
$$255$$ 14.0000i 0.876714i
$$256$$ 1.00000 0.0625000
$$257$$ 6.00000i 0.374270i 0.982334 + 0.187135i $$0.0599201\pi$$
−0.982334 + 0.187135i $$0.940080\pi$$
$$258$$ 2.64575 0.164717
$$259$$ 21.0000i 1.30488i
$$260$$ 13.2288i 0.820413i
$$261$$ 1.00000 0.0618984
$$262$$ 22.0000i 1.35916i
$$263$$ 23.8118i 1.46830i −0.678989 0.734148i $$-0.737582\pi$$
0.678989 0.734148i $$-0.262418\pi$$
$$264$$ 0 0
$$265$$ 14.0000i 0.860013i
$$266$$ 14.0000 0.858395
$$267$$ 0 0
$$268$$ 5.29150i 0.323230i
$$269$$ 10.0000i 0.609711i 0.952399 + 0.304855i $$0.0986081\pi$$
−0.952399 + 0.304855i $$0.901392\pi$$
$$270$$ 2.64575i 0.161015i
$$271$$ 14.0000i 0.850439i 0.905090 + 0.425220i $$0.139803\pi$$
−0.905090 + 0.425220i $$0.860197\pi$$
$$272$$ −5.29150 −0.320844
$$273$$ 13.2288 0.800641
$$274$$ 7.93725i 0.479507i
$$275$$ 0 0
$$276$$ 2.64575 4.00000i 0.159256 0.240772i
$$277$$ 2.00000 0.120168 0.0600842 0.998193i $$-0.480863\pi$$
0.0600842 + 0.998193i $$0.480863\pi$$
$$278$$ 5.00000i 0.299880i
$$279$$ 4.00000i 0.239474i
$$280$$ −7.00000 −0.418330
$$281$$ 7.93725i 0.473497i 0.971571 + 0.236748i $$0.0760817\pi$$
−0.971571 + 0.236748i $$0.923918\pi$$
$$282$$ −13.0000 −0.774139
$$283$$ 10.5830 0.629094 0.314547 0.949242i $$-0.398147\pi$$
0.314547 + 0.949242i $$0.398147\pi$$
$$284$$ 6.00000 0.356034
$$285$$ 14.0000i 0.829288i
$$286$$ 0 0
$$287$$ 23.8118i 1.40556i
$$288$$ 1.00000 0.0589256
$$289$$ 11.0000 0.647059
$$290$$ −2.64575 −0.155364
$$291$$ 2.64575i 0.155097i
$$292$$ 4.00000i 0.234082i
$$293$$ 21.1660 1.23653 0.618266 0.785969i $$-0.287836\pi$$
0.618266 + 0.785969i $$0.287836\pi$$
$$294$$ 7.00000i 0.408248i
$$295$$ 37.0405i 2.15658i
$$296$$ 7.93725i 0.461344i
$$297$$ 0 0
$$298$$ 15.8745i 0.919586i
$$299$$ 13.2288 20.0000i 0.765039 1.15663i
$$300$$ 2.00000i 0.115470i
$$301$$ 7.00000i 0.403473i
$$302$$ 5.00000 0.287718
$$303$$ 0 0
$$304$$ 5.29150 0.303488
$$305$$ −28.0000 −1.60328
$$306$$ −5.29150 −0.302495
$$307$$ 21.0000i 1.19853i 0.800549 + 0.599267i $$0.204541\pi$$
−0.800549 + 0.599267i $$0.795459\pi$$
$$308$$ 0 0
$$309$$ 2.64575i 0.150512i
$$310$$ 10.5830i 0.601074i
$$311$$ 24.0000i 1.36092i −0.732787 0.680458i $$-0.761781\pi$$
0.732787 0.680458i $$-0.238219\pi$$
$$312$$ 5.00000 0.283069
$$313$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$314$$ −10.5830 −0.597234
$$315$$ −7.00000 −0.394405
$$316$$ 5.29150i 0.297670i
$$317$$ 27.0000 1.51647 0.758236 0.651981i $$-0.226062\pi$$
0.758236 + 0.651981i $$0.226062\pi$$
$$318$$ −5.29150 −0.296733
$$319$$ 0 0
$$320$$ −2.64575 −0.147902
$$321$$ −5.29150 −0.295343
$$322$$ 10.5830 + 7.00000i 0.589768 + 0.390095i
$$323$$ −28.0000 −1.55796
$$324$$ 1.00000 0.0555556
$$325$$ 10.0000i 0.554700i
$$326$$ 18.0000 0.996928
$$327$$ 18.5203 1.02417
$$328$$ 9.00000i 0.496942i
$$329$$ 34.3948i 1.89624i
$$330$$ 0 0
$$331$$ 4.00000 0.219860 0.109930 0.993939i $$-0.464937\pi$$
0.109930 + 0.993939i $$0.464937\pi$$
$$332$$ −15.8745 −0.871227
$$333$$ 7.93725i 0.434959i
$$334$$ 0 0
$$335$$ 14.0000i 0.764902i
$$336$$ 2.64575i 0.144338i
$$337$$ 26.4575i 1.44123i −0.693334 0.720616i $$-0.743859\pi$$
0.693334 0.720616i $$-0.256141\pi$$
$$338$$ 12.0000 0.652714
$$339$$ 2.64575 0.143697
$$340$$ 14.0000 0.759257
$$341$$ 0 0
$$342$$ 5.29150 0.286132
$$343$$ −18.5203 −1.00000
$$344$$ 2.64575i 0.142649i
$$345$$ −7.00000 + 10.5830i −0.376867 + 0.569770i
$$346$$ 0 0
$$347$$ −11.0000 −0.590511 −0.295255 0.955418i $$-0.595405\pi$$
−0.295255 + 0.955418i $$0.595405\pi$$
$$348$$ 1.00000i 0.0536056i
$$349$$ 30.0000i 1.60586i 0.596071 + 0.802932i $$0.296728\pi$$
−0.596071 + 0.802932i $$0.703272\pi$$
$$350$$ 5.29150 0.282843
$$351$$ 5.00000 0.266880
$$352$$ 0 0
$$353$$ 25.0000i 1.33062i 0.746569 + 0.665308i $$0.231700\pi$$
−0.746569 + 0.665308i $$0.768300\pi$$
$$354$$ 14.0000 0.744092
$$355$$ −15.8745 −0.842531
$$356$$ 0 0
$$357$$ 14.0000i 0.740959i
$$358$$ −9.00000 −0.475665
$$359$$ 23.8118i 1.25674i 0.777916 + 0.628368i $$0.216277\pi$$
−0.777916 + 0.628368i $$0.783723\pi$$
$$360$$ −2.64575 −0.139443
$$361$$ 9.00000 0.473684
$$362$$ 15.8745 0.834346
$$363$$ 11.0000i 0.577350i
$$364$$ 13.2288i 0.693375i
$$365$$ 10.5830i 0.553940i
$$366$$ 10.5830i 0.553183i
$$367$$ −18.5203 −0.966750 −0.483375 0.875413i $$-0.660589\pi$$
−0.483375 + 0.875413i $$0.660589\pi$$
$$368$$ 4.00000 + 2.64575i 0.208514 + 0.137919i
$$369$$ 9.00000i 0.468521i
$$370$$ 21.0000i 1.09174i
$$371$$ 14.0000i 0.726844i
$$372$$ 4.00000 0.207390
$$373$$ 21.1660i 1.09593i 0.836500 + 0.547967i $$0.184598\pi$$
−0.836500 + 0.547967i $$0.815402\pi$$
$$374$$ 0 0
$$375$$ 7.93725i 0.409878i
$$376$$ 13.0000i 0.670424i
$$377$$ 5.00000i 0.257513i
$$378$$ 2.64575i 0.136083i
$$379$$ 23.8118i 1.22313i −0.791195 0.611564i $$-0.790541\pi$$
0.791195 0.611564i $$-0.209459\pi$$
$$380$$ −14.0000 −0.718185
$$381$$ 13.0000i 0.666010i
$$382$$ 15.8745i 0.812210i
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 1.00000i 0.0510310i
$$385$$ 0 0
$$386$$ −19.0000 −0.967075
$$387$$ 2.64575i 0.134491i
$$388$$ 2.64575 0.134318
$$389$$ 21.1660i 1.07316i 0.843850 + 0.536580i $$0.180284\pi$$
−0.843850 + 0.536580i $$0.819716\pi$$
$$390$$ −13.2288 −0.669864
$$391$$ −21.1660 14.0000i −1.07041 0.708010i
$$392$$ −7.00000 −0.353553
$$393$$ 22.0000 1.10975
$$394$$ 1.00000 0.0503793
$$395$$ 14.0000i 0.704416i
$$396$$ 0 0
$$397$$ 34.0000i 1.70641i 0.521575 + 0.853206i $$0.325345\pi$$
−0.521575 + 0.853206i $$0.674655\pi$$
$$398$$ 13.2288 0.663098
$$399$$ 14.0000i 0.700877i
$$400$$ 2.00000 0.100000
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 5.29150 0.263916
$$403$$ 20.0000 0.996271
$$404$$ 0 0
$$405$$ −2.64575 −0.131468
$$406$$ −2.64575 −0.131306
$$407$$ 0 0
$$408$$ 5.29150i 0.261968i
$$409$$ 18.0000i 0.890043i −0.895520 0.445021i $$-0.853196\pi$$
0.895520 0.445021i $$-0.146804\pi$$
$$410$$ 23.8118i 1.17598i
$$411$$ 7.93725 0.391516
$$412$$ 2.64575 0.130347
$$413$$ 37.0405i 1.82264i
$$414$$ 4.00000 + 2.64575i 0.196589 + 0.130032i
$$415$$ 42.0000 2.06170
$$416$$ 5.00000i 0.245145i
$$417$$ 5.00000 0.244851
$$418$$ 0 0
$$419$$ 15.8745 0.775520 0.387760 0.921760i $$-0.373249\pi$$
0.387760 + 0.921760i $$0.373249\pi$$
$$420$$ 7.00000i 0.341565i
$$421$$ 29.1033i 1.41841i 0.705004 + 0.709203i $$0.250945\pi$$
−0.705004 + 0.709203i $$0.749055\pi$$
$$422$$ 16.0000 0.778868
$$423$$ 13.0000i 0.632082i
$$424$$ 5.29150i 0.256978i
$$425$$ −10.5830 −0.513351
$$426$$ 6.00000i 0.290701i
$$427$$ −28.0000 −1.35501
$$428$$ 5.29150i 0.255774i
$$429$$ 0 0
$$430$$ 7.00000i 0.337570i
$$431$$ 13.2288i 0.637207i 0.947888 + 0.318603i $$0.103214\pi$$
−0.947888 + 0.318603i $$0.896786\pi$$
$$432$$ 1.00000i 0.0481125i
$$433$$ −13.2288 −0.635733 −0.317867 0.948135i $$-0.602966\pi$$
−0.317867 + 0.948135i $$0.602966\pi$$
$$434$$ 10.5830i 0.508001i
$$435$$ 2.64575i 0.126854i
$$436$$ 18.5203i 0.886960i
$$437$$ 21.1660 + 14.0000i 1.01251 + 0.669711i
$$438$$ 4.00000 0.191127
$$439$$ 6.00000i 0.286364i 0.989696 + 0.143182i $$0.0457335\pi$$
−0.989696 + 0.143182i $$0.954267\pi$$
$$440$$ 0 0
$$441$$ −7.00000 −0.333333
$$442$$ 26.4575i 1.25846i
$$443$$ 3.00000 0.142534 0.0712672 0.997457i $$-0.477296\pi$$
0.0712672 + 0.997457i $$0.477296\pi$$
$$444$$ 7.93725 0.376685
$$445$$ 0 0
$$446$$ 28.0000i 1.32584i
$$447$$ −15.8745 −0.750838
$$448$$ −2.64575 −0.125000
$$449$$ 12.0000 0.566315 0.283158 0.959073i $$-0.408618\pi$$
0.283158 + 0.959073i $$0.408618\pi$$
$$450$$ 2.00000 0.0942809
$$451$$ 0 0
$$452$$ 2.64575i 0.124446i
$$453$$ 5.00000i 0.234920i
$$454$$ 7.93725 0.372514
$$455$$ 35.0000i 1.64083i
$$456$$ 5.29150i 0.247797i
$$457$$ 5.29150i 0.247526i 0.992312 + 0.123763i $$0.0394963\pi$$
−0.992312 + 0.123763i $$0.960504\pi$$
$$458$$ −10.5830 −0.494511
$$459$$ 5.29150i 0.246986i
$$460$$ −10.5830 7.00000i −0.493435 0.326377i
$$461$$ 12.0000i 0.558896i 0.960161 + 0.279448i $$0.0901514\pi$$
−0.960161 + 0.279448i $$0.909849\pi$$
$$462$$ 0 0
$$463$$ 19.0000 0.883005 0.441502 0.897260i $$-0.354446\pi$$
0.441502 + 0.897260i $$0.354446\pi$$
$$464$$ −1.00000 −0.0464238
$$465$$ −10.5830 −0.490775
$$466$$ 18.0000 0.833834
$$467$$ −13.2288 −0.612154 −0.306077 0.952007i $$-0.599016\pi$$
−0.306077 + 0.952007i $$0.599016\pi$$
$$468$$ 5.00000i 0.231125i
$$469$$ 14.0000i 0.646460i
$$470$$ 34.3948i 1.58651i
$$471$$ 10.5830i 0.487639i
$$472$$ 14.0000i 0.644402i
$$473$$ 0 0
$$474$$ −5.29150 −0.243047
$$475$$ 10.5830 0.485582
$$476$$ 14.0000 0.641689
$$477$$ 5.29150i 0.242281i
$$478$$ 20.0000 0.914779
$$479$$ 5.29150 0.241775 0.120887 0.992666i $$-0.461426\pi$$
0.120887 + 0.992666i $$0.461426\pi$$
$$480$$ 2.64575i 0.120761i
$$481$$ 39.6863 1.80954
$$482$$ 23.8118 1.08460
$$483$$ −7.00000 + 10.5830i −0.318511 + 0.481543i
$$484$$ 11.0000 0.500000
$$485$$ −7.00000 −0.317854
$$486$$ 1.00000i 0.0453609i
$$487$$ −23.0000 −1.04223 −0.521115 0.853487i $$-0.674484\pi$$
−0.521115 + 0.853487i $$0.674484\pi$$
$$488$$ −10.5830 −0.479070
$$489$$ 18.0000i 0.813988i
$$490$$ 18.5203 0.836660
$$491$$ 20.0000 0.902587 0.451294 0.892375i $$-0.350963\pi$$
0.451294 + 0.892375i $$0.350963\pi$$
$$492$$ 9.00000 0.405751
$$493$$ 5.29150 0.238317
$$494$$ 26.4575i 1.19038i
$$495$$ 0 0
$$496$$ 4.00000i 0.179605i
$$497$$ −15.8745 −0.712069
$$498$$ 15.8745i 0.711354i
$$499$$ 4.00000 0.179065 0.0895323 0.995984i $$-0.471463\pi$$
0.0895323 + 0.995984i $$0.471463\pi$$
$$500$$ 7.93725 0.354965
$$501$$ 0 0
$$502$$ −18.5203 −0.826600
$$503$$ 26.4575 1.17968 0.589841 0.807519i $$-0.299190\pi$$
0.589841 + 0.807519i $$0.299190\pi$$
$$504$$ −2.64575 −0.117851
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 12.0000i 0.532939i
$$508$$ −13.0000 −0.576782
$$509$$ 20.0000i 0.886484i 0.896402 + 0.443242i $$0.146172\pi$$
−0.896402 + 0.443242i $$0.853828\pi$$
$$510$$ 14.0000i 0.619930i
$$511$$ 10.5830i 0.468165i
$$512$$ −1.00000 −0.0441942
$$513$$ 5.29150i 0.233626i
$$514$$ 6.00000i 0.264649i
$$515$$ −7.00000 −0.308457
$$516$$ −2.64575 −0.116473
$$517$$ 0 0
$$518$$ 21.0000i 0.922687i
$$519$$ 0 0
$$520$$ 13.2288i 0.580119i
$$521$$ 15.8745 0.695475 0.347737 0.937592i $$-0.386950\pi$$
0.347737 + 0.937592i $$0.386950\pi$$
$$522$$ −1.00000 −0.0437688
$$523$$ −21.1660 −0.925525 −0.462763 0.886482i $$-0.653142\pi$$
−0.462763 + 0.886482i $$0.653142\pi$$
$$524$$ 22.0000i 0.961074i
$$525$$ 5.29150i 0.230940i
$$526$$ 23.8118i 1.03824i
$$527$$ 21.1660i 0.922006i
$$528$$ 0 0
$$529$$ 9.00000 + 21.1660i 0.391304 + 0.920261i
$$530$$ 14.0000i 0.608121i
$$531$$ 14.0000i 0.607548i
$$532$$ −14.0000 −0.606977
$$533$$ 45.0000 1.94917
$$534$$ 0 0
$$535$$ 14.0000i 0.605273i
$$536$$ 5.29150i 0.228558i
$$537$$ 9.00000i 0.388379i
$$538$$ 10.0000i 0.431131i
$$539$$ 0 0
$$540$$ 2.64575i 0.113855i
$$541$$ −24.0000 −1.03184 −0.515920 0.856637i $$-0.672550\pi$$
−0.515920 + 0.856637i $$0.672550\pi$$
$$542$$ 14.0000i 0.601351i
$$543$$ 15.8745i 0.681240i
$$544$$ 5.29150 0.226871
$$545$$ 49.0000i 2.09893i
$$546$$ −13.2288 −0.566139
$$547$$ −34.0000 −1.45374 −0.726868 0.686778i $$-0.759025\pi$$
−0.726868 + 0.686778i $$0.759025\pi$$
$$548$$ 7.93725i 0.339063i
$$549$$ −10.5830 −0.451672
$$550$$ 0 0
$$551$$ −5.29150 −0.225426
$$552$$ −2.64575 + 4.00000i −0.112611 + 0.170251i
$$553$$ 14.0000i 0.595341i
$$554$$ −2.00000 −0.0849719
$$555$$ −21.0000 −0.891400
$$556$$ 5.00000i 0.212047i
$$557$$ 31.7490i 1.34525i −0.739984 0.672624i $$-0.765167\pi$$
0.739984 0.672624i $$-0.234833\pi$$
$$558$$ 4.00000i 0.169334i
$$559$$ −13.2288 −0.559517
$$560$$ 7.00000 0.295804
$$561$$ 0 0
$$562$$ 7.93725i 0.334813i
$$563$$ 23.8118 1.00355 0.501773 0.864999i $$-0.332681\pi$$
0.501773 + 0.864999i $$0.332681\pi$$
$$564$$ 13.0000 0.547399
$$565$$ 7.00000i 0.294492i
$$566$$ −10.5830 −0.444837
$$567$$ −2.64575 −0.111111
$$568$$ −6.00000 −0.251754
$$569$$ 23.8118i 0.998241i −0.866533 0.499120i $$-0.833657\pi$$
0.866533 0.499120i $$-0.166343\pi$$
$$570$$ 14.0000i 0.586395i
$$571$$ 26.4575i 1.10721i 0.832779 + 0.553606i $$0.186749\pi$$
−0.832779 + 0.553606i $$0.813251\pi$$
$$572$$ 0 0
$$573$$ −15.8745 −0.663167
$$574$$ 23.8118i 0.993884i
$$575$$ 8.00000 + 5.29150i 0.333623 + 0.220671i
$$576$$ −1.00000 −0.0416667
$$577$$ 10.0000i 0.416305i −0.978096 0.208153i $$-0.933255\pi$$
0.978096 0.208153i $$-0.0667451\pi$$
$$578$$ −11.0000 −0.457540
$$579$$ 19.0000i 0.789613i
$$580$$ 2.64575 0.109859
$$581$$ 42.0000 1.74245
$$582$$ 2.64575i 0.109670i
$$583$$ 0 0
$$584$$ 4.00000i 0.165521i
$$585$$ 13.2288i 0.546942i
$$586$$ −21.1660 −0.874360
$$587$$ 2.00000i 0.0825488i 0.999148 + 0.0412744i $$0.0131418\pi$$
−0.999148 + 0.0412744i $$0.986858\pi$$
$$588$$ 7.00000i 0.288675i
$$589$$ 21.1660i 0.872130i
$$590$$ 37.0405i 1.52493i
$$591$$ 1.00000i 0.0411345i
$$592$$ 7.93725i 0.326219i
$$593$$ 21.0000i 0.862367i −0.902264 0.431183i $$-0.858096\pi$$
0.902264 0.431183i $$-0.141904\pi$$
$$594$$ 0 0
$$595$$ −37.0405 −1.51851
$$596$$ 15.8745i 0.650245i
$$597$$ 13.2288i 0.541417i
$$598$$ −13.2288 + 20.0000i −0.540964 + 0.817861i
$$599$$ −46.0000 −1.87951 −0.939755 0.341850i $$-0.888947\pi$$
−0.939755 + 0.341850i $$0.888947\pi$$
$$600$$ 2.00000i 0.0816497i
$$601$$ 2.00000i 0.0815817i −0.999168 0.0407909i $$-0.987012\pi$$
0.999168 0.0407909i $$-0.0129877\pi$$
$$602$$ 7.00000i 0.285299i
$$603$$ 5.29150i 0.215487i
$$604$$ −5.00000 −0.203447
$$605$$ −29.1033 −1.18322
$$606$$ 0 0
$$607$$ 14.0000i 0.568242i −0.958788 0.284121i $$-0.908298\pi$$
0.958788 0.284121i $$-0.0917018\pi$$
$$608$$ −5.29150 −0.214599
$$609$$ 2.64575i 0.107211i
$$610$$ 28.0000 1.13369
$$611$$ 65.0000 2.62962
$$612$$ 5.29150 0.213896
$$613$$ 13.2288i 0.534304i −0.963654 0.267152i $$-0.913917\pi$$
0.963654 0.267152i $$-0.0860827\pi$$
$$614$$ 21.0000i 0.847491i
$$615$$ −23.8118 −0.960183
$$616$$ 0 0
$$617$$ 21.1660i 0.852111i 0.904697 + 0.426056i $$0.140097\pi$$
−0.904697 + 0.426056i $$0.859903\pi$$
$$618$$ 2.64575i 0.106428i
$$619$$ −21.1660 −0.850734 −0.425367 0.905021i $$-0.639855\pi$$
−0.425367 + 0.905021i $$0.639855\pi$$
$$620$$ 10.5830i 0.425024i
$$621$$ −2.64575 + 4.00000i −0.106170 + 0.160514i
$$622$$ 24.0000i 0.962312i
$$623$$ 0 0
$$624$$ −5.00000 −0.200160
$$625$$ −31.0000 −1.24000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 10.5830 0.422308
$$629$$ 42.0000i 1.67465i
$$630$$ 7.00000 0.278887
$$631$$ 31.7490i 1.26391i 0.775006 + 0.631954i $$0.217747\pi$$
−0.775006 + 0.631954i $$0.782253\pi$$
$$632$$ 5.29150i 0.210485i
$$633$$ 16.0000i 0.635943i
$$634$$ −27.0000 −1.07231
$$635$$ 34.3948 1.36491
$$636$$ 5.29150 0.209822
$$637$$ 35.0000i 1.38675i
$$638$$ 0 0
$$639$$ −6.00000 −0.237356
$$640$$ 2.64575 0.104583
$$641$$ 2.64575i 0.104501i 0.998634 + 0.0522504i $$0.0166394\pi$$
−0.998634 + 0.0522504i $$0.983361\pi$$
$$642$$ 5.29150 0.208839
$$643$$ 31.7490 1.25206 0.626029 0.779799i $$-0.284679\pi$$
0.626029 + 0.779799i $$0.284679\pi$$
$$644$$ −10.5830 7.00000i −0.417029 0.275839i
$$645$$ 7.00000 0.275625
$$646$$ 28.0000 1.10165
$$647$$ 24.0000i 0.943537i −0.881722 0.471769i $$-0.843616\pi$$
0.881722 0.471769i $$-0.156384\pi$$
$$648$$ −1.00000 −0.0392837
$$649$$ 0 0
$$650$$ 10.0000i 0.392232i
$$651$$ −10.5830 −0.414781
$$652$$ −18.0000 −0.704934
$$653$$ −3.00000 −0.117399 −0.0586995 0.998276i $$-0.518695\pi$$
−0.0586995 + 0.998276i $$0.518695\pi$$
$$654$$ −18.5203 −0.724199
$$655$$ 58.2065i 2.27432i
$$656$$ 9.00000i 0.351391i
$$657$$ 4.00000i 0.156055i
$$658$$ 34.3948i 1.34085i
$$659$$ 42.3320i 1.64902i −0.565846 0.824511i $$-0.691450\pi$$
0.565846 0.824511i $$-0.308550\pi$$
$$660$$ 0 0
$$661$$ 26.4575 1.02908 0.514539 0.857467i $$-0.327963\pi$$
0.514539 + 0.857467i $$0.327963\pi$$
$$662$$ −4.00000 −0.155464
$$663$$ 26.4575 1.02752
$$664$$ 15.8745 0.616050
$$665$$ 37.0405 1.43637
$$666$$ 7.93725i 0.307562i
$$667$$ −4.00000 2.64575i −0.154881 0.102444i
$$668$$ 0 0
$$669$$ 28.0000 1.08254
$$670$$ 14.0000i 0.540867i
$$671$$ 0 0
$$672$$ 2.64575i 0.102062i
$$673$$ −29.0000 −1.11787 −0.558934 0.829212i $$-0.688789\pi$$
−0.558934 + 0.829212i $$0.688789\pi$$
$$674$$ 26.4575i 1.01911i
$$675$$ 2.00000i 0.0769800i
$$676$$ −12.0000 −0.461538
$$677$$ 31.7490 1.22021 0.610107 0.792319i $$-0.291126\pi$$
0.610107 + 0.792319i $$0.291126\pi$$
$$678$$ −2.64575 −0.101609
$$679$$ −7.00000 −0.268635
$$680$$ −14.0000 −0.536875
$$681$$ 7.93725i 0.304156i
$$682$$ 0 0
$$683$$ 12.0000 0.459167 0.229584 0.973289i $$-0.426264\pi$$
0.229584 + 0.973289i $$0.426264\pi$$
$$684$$ −5.29150 −0.202326
$$685$$ 21.0000i 0.802369i
$$686$$ 18.5203 0.707107
$$687$$ 10.5830i 0.403767i
$$688$$ 2.64575i 0.100868i
$$689$$ 26.4575 1.00795
$$690$$ 7.00000 10.5830i 0.266485 0.402888i
$$691$$ 35.0000i 1.33146i 0.746191 + 0.665731i $$0.231880\pi$$
−0.746191 + 0.665731i $$0.768120\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 11.0000 0.417554
$$695$$ 13.2288i 0.501795i
$$696$$ 1.00000i 0.0379049i
$$697$$ 47.6235i 1.80387i
$$698$$ 30.0000i 1.13552i
$$699$$ 18.0000i 0.680823i
$$700$$ −5.29150 −0.200000
$$701$$ 10.5830i 0.399715i −0.979825 0.199857i $$-0.935952\pi$$
0.979825 0.199857i $$-0.0640479\pi$$
$$702$$ −5.00000 −0.188713
$$703$$ 42.0000i 1.58406i
$$704$$ 0 0
$$705$$ −34.3948 −1.29538
$$706$$ 25.0000i 0.940887i
$$707$$ 0 0
$$708$$ −14.0000 −0.526152
$$709$$ 42.3320i 1.58981i 0.606732 + 0.794906i $$0.292480\pi$$
−0.606732 + 0.794906i $$0.707520\pi$$
$$710$$ 15.8745 0.595760
$$711$$ 5.29150i 0.198447i
$$712$$ 0 0
$$713$$ −10.5830 + 16.0000i −0.396337 + 0.599205i
$$714$$ 14.0000i 0.523937i
$$715$$ 0 0
$$716$$ 9.00000 0.336346
$$717$$ 20.0000i 0.746914i
$$718$$ 23.8118i 0.888647i
$$719$$ 21.0000i 0.783168i 0.920142 + 0.391584i $$0.128073\pi$$
−0.920142 + 0.391584i $$0.871927\pi$$
$$720$$ 2.64575 0.0986013
$$721$$ −7.00000 −0.260694
$$722$$ −9.00000 −0.334945
$$723$$ 23.8118i 0.885569i
$$724$$ −15.8745 −0.589971
$$725$$ −2.00000 −0.0742781
$$726$$ 11.0000i 0.408248i
$$727$$ 47.6235 1.76626 0.883129 0.469130i $$-0.155432\pi$$
0.883129 + 0.469130i $$0.155432\pi$$
$$728$$ 13.2288i 0.490290i
$$729$$ −1.00000 −0.0370370
$$730$$ 10.5830i 0.391695i
$$731$$ 14.0000i 0.517809i
$$732$$ 10.5830i 0.391159i
$$733$$ −37.0405 −1.36812 −0.684061 0.729424i $$-0.739788\pi$$
−0.684061 + 0.729424i $$0.739788\pi$$
$$734$$ 18.5203 0.683595
$$735$$ 18.5203i 0.683130i
$$736$$ −4.00000 2.64575i −0.147442 0.0975237i
$$737$$ 0 0
$$738$$ 9.00000i 0.331295i
$$739$$ 40.0000 1.47142 0.735712 0.677295i $$-0.236848\pi$$
0.735712 + 0.677295i $$0.236848\pi$$
$$740$$ 21.0000i 0.771975i
$$741$$ −26.4575 −0.971941
$$742$$ 14.0000i 0.513956i
$$743$$ 15.8745i 0.582379i 0.956665 + 0.291190i $$0.0940511\pi$$
−0.956665 + 0.291190i $$0.905949\pi$$
$$744$$ −4.00000 −0.146647
$$745$$ 42.0000i 1.53876i
$$746$$ 21.1660i 0.774943i
$$747$$ 15.8745 0.580818
$$748$$ 0 0
$$749$$ 14.0000i 0.511549i
$$750$$ 7.93725i 0.289828i
$$751$$ 15.8745i 0.579269i −0.957137 0.289635i $$-0.906466\pi$$
0.957137 0.289635i $$-0.0935338\pi$$
$$752$$ 13.0000i 0.474061i
$$753$$ 18.5203i 0.674916i
$$754$$ 5.00000i 0.182089i
$$755$$ 13.2288 0.481444
$$756$$ 2.64575i 0.0962250i
$$757$$ 52.9150i 1.92323i 0.274403 + 0.961615i $$0.411520\pi$$
−0.274403 + 0.961615i $$0.588480\pi$$
$$758$$ 23.8118i 0.864882i
$$759$$ 0 0
$$760$$ 14.0000 0.507833
$$761$$ 6.00000i 0.217500i 0.994069 + 0.108750i $$0.0346848\pi$$
−0.994069 + 0.108750i $$0.965315\pi$$
$$762$$ 13.0000i 0.470940i
$$763$$ 49.0000i 1.77392i
$$764$$ 15.8745i 0.574320i
$$765$$ −14.0000 −0.506171
$$766$$ 0 0
$$767$$ −70.0000 −2.52755
$$768$$ 1.00000i 0.0360844i
$$769$$ 29.1033 1.04949 0.524745 0.851259i $$-0.324161\pi$$
0.524745 + 0.851259i $$0.324161\pi$$
$$770$$ 0 0
$$771$$ 6.00000 0.216085
$$772$$ 19.0000 0.683825
$$773$$ −34.3948 −1.23709 −0.618547 0.785748i $$-0.712278\pi$$
−0.618547 + 0.785748i $$0.712278\pi$$
$$774$$ 2.64575i 0.0950996i
$$775$$ 8.00000i 0.287368i
$$776$$ −2.64575 −0.0949769
$$777$$ −21.0000 −0.753371
$$778$$ 21.1660i 0.758838i
$$779$$ 47.6235i 1.70629i
$$780$$ 13.2288 0.473665
$$781$$ 0 0
$$782$$ 21.1660 + 14.0000i 0.756895 + 0.500639i
$$783$$ 1.00000i 0.0357371i
$$784$$ 7.00000 0.250000
$$785$$ −28.0000 −0.999363
$$786$$ −22.0000 −0.784714
$$787$$ 42.3320 1.50897 0.754487 0.656315i $$-0.227886\pi$$
0.754487 + 0.656315i $$0.227886\pi$$
$$788$$ −1.00000 −0.0356235
$$789$$ −23.8118