# Properties

 Label 325.2.e.b.126.1 Level $325$ Weight $2$ Character 325.126 Analytic conductor $2.595$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$325 = 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 325.e (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.59513806569$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{5})$$ Defining polynomial: $$x^{4} - x^{3} + 2x^{2} + x + 1$$ x^4 - x^3 + 2*x^2 + x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 65) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 126.1 Root $$-0.309017 + 0.535233i$$ of defining polynomial Character $$\chi$$ $$=$$ 325.126 Dual form 325.2.e.b.276.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.309017 + 0.535233i) q^{2} +(1.11803 - 1.93649i) q^{3} +(0.809017 + 1.40126i) q^{4} +(0.690983 + 1.19682i) q^{6} +(2.11803 + 3.66854i) q^{7} -2.23607 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.309017 + 0.535233i) q^{2} +(1.11803 - 1.93649i) q^{3} +(0.809017 + 1.40126i) q^{4} +(0.690983 + 1.19682i) q^{6} +(2.11803 + 3.66854i) q^{7} -2.23607 q^{8} +(-1.00000 - 1.73205i) q^{9} +(0.118034 - 0.204441i) q^{11} +3.61803 q^{12} +(1.00000 + 3.46410i) q^{13} -2.61803 q^{14} +(-0.927051 + 1.60570i) q^{16} +(-1.73607 - 3.00696i) q^{17} +1.23607 q^{18} +(-2.11803 - 3.66854i) q^{19} +9.47214 q^{21} +(0.0729490 + 0.126351i) q^{22} +(1.88197 - 3.25966i) q^{23} +(-2.50000 + 4.33013i) q^{24} +(-2.16312 - 0.535233i) q^{26} +2.23607 q^{27} +(-3.42705 + 5.93583i) q^{28} +(3.73607 - 6.47106i) q^{29} +(-2.80902 - 4.86536i) q^{32} +(-0.263932 - 0.457144i) q^{33} +2.14590 q^{34} +(1.61803 - 2.80252i) q^{36} +(1.50000 - 2.59808i) q^{37} +2.61803 q^{38} +(7.82624 + 1.93649i) q^{39} +(-5.97214 + 10.3440i) q^{41} +(-2.92705 + 5.06980i) q^{42} +(-3.11803 - 5.40059i) q^{43} +0.381966 q^{44} +(1.16312 + 2.01458i) q^{46} +4.94427 q^{47} +(2.07295 + 3.59045i) q^{48} +(-5.47214 + 9.47802i) q^{49} -7.76393 q^{51} +(-4.04508 + 4.20378i) q^{52} -6.00000 q^{53} +(-0.690983 + 1.19682i) q^{54} +(-4.73607 - 8.20311i) q^{56} -9.47214 q^{57} +(2.30902 + 3.99933i) q^{58} +(0.354102 + 0.613323i) q^{59} +(-7.20820 - 12.4850i) q^{61} +(4.23607 - 7.33708i) q^{63} -0.236068 q^{64} +0.326238 q^{66} +(-1.35410 + 2.34537i) q^{67} +(2.80902 - 4.86536i) q^{68} +(-4.20820 - 7.28882i) q^{69} +(3.11803 + 5.40059i) q^{71} +(2.23607 + 3.87298i) q^{72} +6.00000 q^{73} +(0.927051 + 1.60570i) q^{74} +(3.42705 - 5.93583i) q^{76} +1.00000 q^{77} +(-3.45492 + 3.59045i) q^{78} +(5.50000 - 9.52628i) q^{81} +(-3.69098 - 6.39297i) q^{82} -8.94427 q^{83} +(7.66312 + 13.2729i) q^{84} +3.85410 q^{86} +(-8.35410 - 14.4697i) q^{87} +(-0.263932 + 0.457144i) q^{88} +(4.50000 - 7.79423i) q^{89} +(-10.5902 + 11.0056i) q^{91} +6.09017 q^{92} +(-1.52786 + 2.64634i) q^{94} -12.5623 q^{96} +(-1.73607 - 3.00696i) q^{97} +(-3.38197 - 5.85774i) q^{98} -0.472136 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + q^{2} + q^{4} + 5 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10})$$ 4 * q + q^2 + q^4 + 5 * q^6 + 4 * q^7 - 4 * q^9 $$4 q + q^{2} + q^{4} + 5 q^{6} + 4 q^{7} - 4 q^{9} - 4 q^{11} + 10 q^{12} + 4 q^{13} - 6 q^{14} + 3 q^{16} + 2 q^{17} - 4 q^{18} - 4 q^{19} + 20 q^{21} + 7 q^{22} + 12 q^{23} - 10 q^{24} + 7 q^{26} - 7 q^{28} + 6 q^{29} - 9 q^{32} - 10 q^{33} + 22 q^{34} + 2 q^{36} + 6 q^{37} + 6 q^{38} - 6 q^{41} - 5 q^{42} - 8 q^{43} + 6 q^{44} - 11 q^{46} - 16 q^{47} + 15 q^{48} - 4 q^{49} - 40 q^{51} - 5 q^{52} - 24 q^{53} - 5 q^{54} - 10 q^{56} - 20 q^{57} + 7 q^{58} - 12 q^{59} - 2 q^{61} + 8 q^{63} + 8 q^{64} - 30 q^{66} + 8 q^{67} + 9 q^{68} + 10 q^{69} + 8 q^{71} + 24 q^{73} - 3 q^{74} + 7 q^{76} + 4 q^{77} - 25 q^{78} + 22 q^{81} - 17 q^{82} + 15 q^{84} + 2 q^{86} - 20 q^{87} - 10 q^{88} + 18 q^{89} - 20 q^{91} + 2 q^{92} - 24 q^{94} - 10 q^{96} + 2 q^{97} - 18 q^{98} + 16 q^{99}+O(q^{100})$$ 4 * q + q^2 + q^4 + 5 * q^6 + 4 * q^7 - 4 * q^9 - 4 * q^11 + 10 * q^12 + 4 * q^13 - 6 * q^14 + 3 * q^16 + 2 * q^17 - 4 * q^18 - 4 * q^19 + 20 * q^21 + 7 * q^22 + 12 * q^23 - 10 * q^24 + 7 * q^26 - 7 * q^28 + 6 * q^29 - 9 * q^32 - 10 * q^33 + 22 * q^34 + 2 * q^36 + 6 * q^37 + 6 * q^38 - 6 * q^41 - 5 * q^42 - 8 * q^43 + 6 * q^44 - 11 * q^46 - 16 * q^47 + 15 * q^48 - 4 * q^49 - 40 * q^51 - 5 * q^52 - 24 * q^53 - 5 * q^54 - 10 * q^56 - 20 * q^57 + 7 * q^58 - 12 * q^59 - 2 * q^61 + 8 * q^63 + 8 * q^64 - 30 * q^66 + 8 * q^67 + 9 * q^68 + 10 * q^69 + 8 * q^71 + 24 * q^73 - 3 * q^74 + 7 * q^76 + 4 * q^77 - 25 * q^78 + 22 * q^81 - 17 * q^82 + 15 * q^84 + 2 * q^86 - 20 * q^87 - 10 * q^88 + 18 * q^89 - 20 * q^91 + 2 * q^92 - 24 * q^94 - 10 * q^96 + 2 * q^97 - 18 * q^98 + 16 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$$.

 $$n$$ $$27$$ $$301$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.309017 + 0.535233i −0.218508 + 0.378467i −0.954352 0.298684i $$-0.903452\pi$$
0.735844 + 0.677151i $$0.236786\pi$$
$$3$$ 1.11803 1.93649i 0.645497 1.11803i −0.338689 0.940898i $$-0.609984\pi$$
0.984186 0.177136i $$-0.0566831\pi$$
$$4$$ 0.809017 + 1.40126i 0.404508 + 0.700629i
$$5$$ 0 0
$$6$$ 0.690983 + 1.19682i 0.282093 + 0.488599i
$$7$$ 2.11803 + 3.66854i 0.800542 + 1.38658i 0.919260 + 0.393651i $$0.128788\pi$$
−0.118718 + 0.992928i $$0.537879\pi$$
$$8$$ −2.23607 −0.790569
$$9$$ −1.00000 1.73205i −0.333333 0.577350i
$$10$$ 0 0
$$11$$ 0.118034 0.204441i 0.0355886 0.0616412i −0.847683 0.530504i $$-0.822003\pi$$
0.883271 + 0.468863i $$0.155336\pi$$
$$12$$ 3.61803 1.04444
$$13$$ 1.00000 + 3.46410i 0.277350 + 0.960769i
$$14$$ −2.61803 −0.699699
$$15$$ 0 0
$$16$$ −0.927051 + 1.60570i −0.231763 + 0.401425i
$$17$$ −1.73607 3.00696i −0.421058 0.729294i 0.574985 0.818164i $$-0.305008\pi$$
−0.996043 + 0.0888696i $$0.971675\pi$$
$$18$$ 1.23607 0.291344
$$19$$ −2.11803 3.66854i −0.485910 0.841621i 0.513959 0.857815i $$-0.328179\pi$$
−0.999869 + 0.0161937i $$0.994845\pi$$
$$20$$ 0 0
$$21$$ 9.47214 2.06699
$$22$$ 0.0729490 + 0.126351i 0.0155528 + 0.0269382i
$$23$$ 1.88197 3.25966i 0.392417 0.679686i −0.600351 0.799737i $$-0.704972\pi$$
0.992768 + 0.120051i $$0.0383057\pi$$
$$24$$ −2.50000 + 4.33013i −0.510310 + 0.883883i
$$25$$ 0 0
$$26$$ −2.16312 0.535233i −0.424223 0.104968i
$$27$$ 2.23607 0.430331
$$28$$ −3.42705 + 5.93583i −0.647652 + 1.12177i
$$29$$ 3.73607 6.47106i 0.693770 1.20165i −0.276823 0.960921i $$-0.589282\pi$$
0.970593 0.240725i $$-0.0773851\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$32$$ −2.80902 4.86536i −0.496569 0.860082i
$$33$$ −0.263932 0.457144i −0.0459447 0.0795785i
$$34$$ 2.14590 0.368018
$$35$$ 0 0
$$36$$ 1.61803 2.80252i 0.269672 0.467086i
$$37$$ 1.50000 2.59808i 0.246598 0.427121i −0.715981 0.698119i $$-0.754020\pi$$
0.962580 + 0.270998i $$0.0873538\pi$$
$$38$$ 2.61803 0.424701
$$39$$ 7.82624 + 1.93649i 1.25320 + 0.310087i
$$40$$ 0 0
$$41$$ −5.97214 + 10.3440i −0.932691 + 1.61547i −0.153990 + 0.988072i $$0.549212\pi$$
−0.778701 + 0.627396i $$0.784121\pi$$
$$42$$ −2.92705 + 5.06980i −0.451654 + 0.782287i
$$43$$ −3.11803 5.40059i −0.475496 0.823583i 0.524110 0.851650i $$-0.324398\pi$$
−0.999606 + 0.0280676i $$0.991065\pi$$
$$44$$ 0.381966 0.0575835
$$45$$ 0 0
$$46$$ 1.16312 + 2.01458i 0.171493 + 0.297034i
$$47$$ 4.94427 0.721196 0.360598 0.932721i $$-0.382573\pi$$
0.360598 + 0.932721i $$0.382573\pi$$
$$48$$ 2.07295 + 3.59045i 0.299204 + 0.518237i
$$49$$ −5.47214 + 9.47802i −0.781734 + 1.35400i
$$50$$ 0 0
$$51$$ −7.76393 −1.08717
$$52$$ −4.04508 + 4.20378i −0.560952 + 0.582959i
$$53$$ −6.00000 −0.824163 −0.412082 0.911147i $$-0.635198\pi$$
−0.412082 + 0.911147i $$0.635198\pi$$
$$54$$ −0.690983 + 1.19682i −0.0940309 + 0.162866i
$$55$$ 0 0
$$56$$ −4.73607 8.20311i −0.632884 1.09619i
$$57$$ −9.47214 −1.25462
$$58$$ 2.30902 + 3.99933i 0.303189 + 0.525138i
$$59$$ 0.354102 + 0.613323i 0.0461001 + 0.0798478i 0.888155 0.459545i $$-0.151987\pi$$
−0.842055 + 0.539392i $$0.818654\pi$$
$$60$$ 0 0
$$61$$ −7.20820 12.4850i −0.922916 1.59854i −0.794879 0.606768i $$-0.792466\pi$$
−0.128037 0.991769i $$-0.540868\pi$$
$$62$$ 0 0
$$63$$ 4.23607 7.33708i 0.533694 0.924386i
$$64$$ −0.236068 −0.0295085
$$65$$ 0 0
$$66$$ 0.326238 0.0401571
$$67$$ −1.35410 + 2.34537i −0.165430 + 0.286533i −0.936808 0.349844i $$-0.886234\pi$$
0.771378 + 0.636377i $$0.219568\pi$$
$$68$$ 2.80902 4.86536i 0.340643 0.590012i
$$69$$ −4.20820 7.28882i −0.506608 0.877471i
$$70$$ 0 0
$$71$$ 3.11803 + 5.40059i 0.370043 + 0.640933i 0.989572 0.144041i $$-0.0460098\pi$$
−0.619529 + 0.784974i $$0.712676\pi$$
$$72$$ 2.23607 + 3.87298i 0.263523 + 0.456435i
$$73$$ 6.00000 0.702247 0.351123 0.936329i $$-0.385800\pi$$
0.351123 + 0.936329i $$0.385800\pi$$
$$74$$ 0.927051 + 1.60570i 0.107767 + 0.186659i
$$75$$ 0 0
$$76$$ 3.42705 5.93583i 0.393110 0.680886i
$$77$$ 1.00000 0.113961
$$78$$ −3.45492 + 3.59045i −0.391192 + 0.406539i
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ 0 0
$$81$$ 5.50000 9.52628i 0.611111 1.05848i
$$82$$ −3.69098 6.39297i −0.407601 0.705985i
$$83$$ −8.94427 −0.981761 −0.490881 0.871227i $$-0.663325\pi$$
−0.490881 + 0.871227i $$0.663325\pi$$
$$84$$ 7.66312 + 13.2729i 0.836115 + 1.44819i
$$85$$ 0 0
$$86$$ 3.85410 0.415599
$$87$$ −8.35410 14.4697i −0.895654 1.55132i
$$88$$ −0.263932 + 0.457144i −0.0281352 + 0.0487317i
$$89$$ 4.50000 7.79423i 0.476999 0.826187i −0.522654 0.852545i $$-0.675058\pi$$
0.999653 + 0.0263586i $$0.00839118\pi$$
$$90$$ 0 0
$$91$$ −10.5902 + 11.0056i −1.11015 + 1.15370i
$$92$$ 6.09017 0.634944
$$93$$ 0 0
$$94$$ −1.52786 + 2.64634i −0.157587 + 0.272949i
$$95$$ 0 0
$$96$$ −12.5623 −1.28213
$$97$$ −1.73607 3.00696i −0.176271 0.305310i 0.764329 0.644826i $$-0.223070\pi$$
−0.940600 + 0.339516i $$0.889737\pi$$
$$98$$ −3.38197 5.85774i −0.341630 0.591721i
$$99$$ −0.472136 −0.0474514
$$100$$ 0 0
$$101$$ −0.263932 + 0.457144i −0.0262622 + 0.0454875i −0.878858 0.477084i $$-0.841694\pi$$
0.852596 + 0.522571i $$0.175027\pi$$
$$102$$ 2.39919 4.15551i 0.237555 0.411457i
$$103$$ −12.9443 −1.27544 −0.637719 0.770270i $$-0.720122\pi$$
−0.637719 + 0.770270i $$0.720122\pi$$
$$104$$ −2.23607 7.74597i −0.219265 0.759555i
$$105$$ 0 0
$$106$$ 1.85410 3.21140i 0.180086 0.311919i
$$107$$ −2.88197 + 4.99171i −0.278610 + 0.482567i −0.971040 0.238919i $$-0.923207\pi$$
0.692429 + 0.721486i $$0.256540\pi$$
$$108$$ 1.80902 + 3.13331i 0.174073 + 0.301503i
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 0 0
$$111$$ −3.35410 5.80948i −0.318357 0.551411i
$$112$$ −7.85410 −0.742143
$$113$$ 0.736068 + 1.27491i 0.0692435 + 0.119933i 0.898568 0.438833i $$-0.144608\pi$$
−0.829325 + 0.558766i $$0.811275\pi$$
$$114$$ 2.92705 5.06980i 0.274143 0.474830i
$$115$$ 0 0
$$116$$ 12.0902 1.12254
$$117$$ 5.00000 5.19615i 0.462250 0.480384i
$$118$$ −0.437694 −0.0402930
$$119$$ 7.35410 12.7377i 0.674149 1.16766i
$$120$$ 0 0
$$121$$ 5.47214 + 9.47802i 0.497467 + 0.861638i
$$122$$ 8.90983 0.806658
$$123$$ 13.3541 + 23.1300i 1.20410 + 2.08556i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 2.61803 + 4.53457i 0.233233 + 0.403971i
$$127$$ −2.11803 + 3.66854i −0.187945 + 0.325531i −0.944565 0.328325i $$-0.893516\pi$$
0.756620 + 0.653855i $$0.226849\pi$$
$$128$$ 5.69098 9.85707i 0.503017 0.871250i
$$129$$ −13.9443 −1.22772
$$130$$ 0 0
$$131$$ −12.0000 −1.04844 −0.524222 0.851581i $$-0.675644\pi$$
−0.524222 + 0.851581i $$0.675644\pi$$
$$132$$ 0.427051 0.739674i 0.0371700 0.0643804i
$$133$$ 8.97214 15.5402i 0.777983 1.34751i
$$134$$ −0.836881 1.44952i −0.0722955 0.125219i
$$135$$ 0 0
$$136$$ 3.88197 + 6.72376i 0.332876 + 0.576558i
$$137$$ 0.736068 + 1.27491i 0.0628865 + 0.108923i 0.895755 0.444549i $$-0.146636\pi$$
−0.832868 + 0.553472i $$0.813303\pi$$
$$138$$ 5.20163 0.442792
$$139$$ 8.35410 + 14.4697i 0.708586 + 1.22731i 0.965382 + 0.260841i $$0.0839998\pi$$
−0.256796 + 0.966466i $$0.582667\pi$$
$$140$$ 0 0
$$141$$ 5.52786 9.57454i 0.465530 0.806322i
$$142$$ −3.85410 −0.323429
$$143$$ 0.826238 + 0.204441i 0.0690935 + 0.0170962i
$$144$$ 3.70820 0.309017
$$145$$ 0 0
$$146$$ −1.85410 + 3.21140i −0.153447 + 0.265777i
$$147$$ 12.2361 + 21.1935i 1.00921 + 1.74801i
$$148$$ 4.85410 0.399005
$$149$$ −2.26393 3.92125i −0.185469 0.321241i 0.758266 0.651946i $$-0.226047\pi$$
−0.943734 + 0.330705i $$0.892714\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 4.73607 + 8.20311i 0.384146 + 0.665360i
$$153$$ −3.47214 + 6.01392i −0.280706 + 0.486196i
$$154$$ −0.309017 + 0.535233i −0.0249013 + 0.0431303i
$$155$$ 0 0
$$156$$ 3.61803 + 12.5332i 0.289675 + 1.00346i
$$157$$ 18.0000 1.43656 0.718278 0.695756i $$-0.244931\pi$$
0.718278 + 0.695756i $$0.244931\pi$$
$$158$$ 0 0
$$159$$ −6.70820 + 11.6190i −0.531995 + 0.921443i
$$160$$ 0 0
$$161$$ 15.9443 1.25658
$$162$$ 3.39919 + 5.88756i 0.267065 + 0.462571i
$$163$$ 7.35410 + 12.7377i 0.576018 + 0.997692i 0.995930 + 0.0901274i $$0.0287274\pi$$
−0.419913 + 0.907565i $$0.637939\pi$$
$$164$$ −19.3262 −1.50913
$$165$$ 0 0
$$166$$ 2.76393 4.78727i 0.214523 0.371564i
$$167$$ −8.59017 + 14.8786i −0.664727 + 1.15134i 0.314632 + 0.949214i $$0.398119\pi$$
−0.979359 + 0.202128i $$0.935214\pi$$
$$168$$ −21.1803 −1.63410
$$169$$ −11.0000 + 6.92820i −0.846154 + 0.532939i
$$170$$ 0 0
$$171$$ −4.23607 + 7.33708i −0.323940 + 0.561081i
$$172$$ 5.04508 8.73834i 0.384684 0.666292i
$$173$$ −9.44427 16.3580i −0.718035 1.24367i −0.961777 0.273833i $$-0.911709\pi$$
0.243743 0.969840i $$-0.421625\pi$$
$$174$$ 10.3262 0.782830
$$175$$ 0 0
$$176$$ 0.218847 + 0.379054i 0.0164962 + 0.0285723i
$$177$$ 1.58359 0.119030
$$178$$ 2.78115 + 4.81710i 0.208456 + 0.361057i
$$179$$ 4.11803 7.13264i 0.307796 0.533119i −0.670084 0.742286i $$-0.733742\pi$$
0.977880 + 0.209167i $$0.0670751\pi$$
$$180$$ 0 0
$$181$$ 6.00000 0.445976 0.222988 0.974821i $$-0.428419\pi$$
0.222988 + 0.974821i $$0.428419\pi$$
$$182$$ −2.61803 9.06914i −0.194062 0.672249i
$$183$$ −32.2361 −2.38296
$$184$$ −4.20820 + 7.28882i −0.310233 + 0.537339i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −0.819660 −0.0599395
$$188$$ 4.00000 + 6.92820i 0.291730 + 0.505291i
$$189$$ 4.73607 + 8.20311i 0.344498 + 0.596688i
$$190$$ 0 0
$$191$$ 13.5902 + 23.5389i 0.983350 + 1.70321i 0.649050 + 0.760746i $$0.275167\pi$$
0.334300 + 0.942467i $$0.391500\pi$$
$$192$$ −0.263932 + 0.457144i −0.0190477 + 0.0329915i
$$193$$ −1.73607 + 3.00696i −0.124965 + 0.216446i −0.921719 0.387858i $$-0.873215\pi$$
0.796754 + 0.604303i $$0.206548\pi$$
$$194$$ 2.14590 0.154067
$$195$$ 0 0
$$196$$ −17.7082 −1.26487
$$197$$ 1.50000 2.59808i 0.106871 0.185105i −0.807630 0.589689i $$-0.799250\pi$$
0.914501 + 0.404584i $$0.132584\pi$$
$$198$$ 0.145898 0.252703i 0.0103685 0.0179588i
$$199$$ 0.645898 + 1.11873i 0.0457865 + 0.0793045i 0.888010 0.459823i $$-0.152087\pi$$
−0.842224 + 0.539128i $$0.818754\pi$$
$$200$$ 0 0
$$201$$ 3.02786 + 5.24441i 0.213569 + 0.369912i
$$202$$ −0.163119 0.282530i −0.0114770 0.0198788i
$$203$$ 31.6525 2.22157
$$204$$ −6.28115 10.8793i −0.439769 0.761702i
$$205$$ 0 0
$$206$$ 4.00000 6.92820i 0.278693 0.482711i
$$207$$ −7.52786 −0.523223
$$208$$ −6.48936 1.60570i −0.449956 0.111335i
$$209$$ −1.00000 −0.0691714
$$210$$ 0 0
$$211$$ 6.59017 11.4145i 0.453686 0.785807i −0.544926 0.838484i $$-0.683442\pi$$
0.998612 + 0.0526772i $$0.0167754\pi$$
$$212$$ −4.85410 8.40755i −0.333381 0.577433i
$$213$$ 13.9443 0.955446
$$214$$ −1.78115 3.08505i −0.121757 0.210889i
$$215$$ 0 0
$$216$$ −5.00000 −0.340207
$$217$$ 0 0
$$218$$ 0.618034 1.07047i 0.0418585 0.0725011i
$$219$$ 6.70820 11.6190i 0.453298 0.785136i
$$220$$ 0 0
$$221$$ 8.68034 9.02087i 0.583903 0.606810i
$$222$$ 4.14590 0.278254
$$223$$ 0.354102 0.613323i 0.0237124 0.0410711i −0.853926 0.520395i $$-0.825785\pi$$
0.877638 + 0.479324i $$0.159118\pi$$
$$224$$ 11.8992 20.6100i 0.795048 1.37706i
$$225$$ 0 0
$$226$$ −0.909830 −0.0605210
$$227$$ −3.11803 5.40059i −0.206951 0.358450i 0.743801 0.668401i $$-0.233021\pi$$
−0.950753 + 0.309951i $$0.899687\pi$$
$$228$$ −7.66312 13.2729i −0.507502 0.879020i
$$229$$ 15.8885 1.04994 0.524972 0.851119i $$-0.324076\pi$$
0.524972 + 0.851119i $$0.324076\pi$$
$$230$$ 0 0
$$231$$ 1.11803 1.93649i 0.0735612 0.127412i
$$232$$ −8.35410 + 14.4697i −0.548474 + 0.949984i
$$233$$ 15.8885 1.04089 0.520447 0.853894i $$-0.325765\pi$$
0.520447 + 0.853894i $$0.325765\pi$$
$$234$$ 1.23607 + 4.28187i 0.0808043 + 0.279914i
$$235$$ 0 0
$$236$$ −0.572949 + 0.992377i −0.0372958 + 0.0645982i
$$237$$ 0 0
$$238$$ 4.54508 + 7.87232i 0.294614 + 0.510287i
$$239$$ −25.8885 −1.67459 −0.837295 0.546751i $$-0.815864\pi$$
−0.837295 + 0.546751i $$0.815864\pi$$
$$240$$ 0 0
$$241$$ −7.50000 12.9904i −0.483117 0.836784i 0.516695 0.856170i $$-0.327162\pi$$
−0.999812 + 0.0193858i $$0.993829\pi$$
$$242$$ −6.76393 −0.434802
$$243$$ −8.94427 15.4919i −0.573775 0.993808i
$$244$$ 11.6631 20.2011i 0.746655 1.29324i
$$245$$ 0 0
$$246$$ −16.5066 −1.05242
$$247$$ 10.5902 11.0056i 0.673836 0.700271i
$$248$$ 0 0
$$249$$ −10.0000 + 17.3205i −0.633724 + 1.09764i
$$250$$ 0 0
$$251$$ −10.1180 17.5249i −0.638645 1.10616i −0.985730 0.168332i $$-0.946162\pi$$
0.347086 0.937833i $$-0.387171\pi$$
$$252$$ 13.7082 0.863536
$$253$$ −0.444272 0.769502i −0.0279311 0.0483781i
$$254$$ −1.30902 2.26728i −0.0821350 0.142262i
$$255$$ 0 0
$$256$$ 3.28115 + 5.68312i 0.205072 + 0.355195i
$$257$$ 8.73607 15.1313i 0.544941 0.943865i −0.453670 0.891170i $$-0.649885\pi$$
0.998611 0.0526955i $$-0.0167813\pi$$
$$258$$ 4.30902 7.46344i 0.268268 0.464653i
$$259$$ 12.7082 0.789649
$$260$$ 0 0
$$261$$ −14.9443 −0.925027
$$262$$ 3.70820 6.42280i 0.229094 0.396802i
$$263$$ 1.88197 3.25966i 0.116047 0.200999i −0.802151 0.597122i $$-0.796311\pi$$
0.918198 + 0.396122i $$0.129644\pi$$
$$264$$ 0.590170 + 1.02220i 0.0363224 + 0.0629123i
$$265$$ 0 0
$$266$$ 5.54508 + 9.60437i 0.339991 + 0.588882i
$$267$$ −10.0623 17.4284i −0.615803 1.06660i
$$268$$ −4.38197 −0.267671
$$269$$ 3.26393 + 5.65330i 0.199005 + 0.344688i 0.948206 0.317655i $$-0.102896\pi$$
−0.749201 + 0.662343i $$0.769562\pi$$
$$270$$ 0 0
$$271$$ −0.645898 + 1.11873i −0.0392355 + 0.0679579i −0.884976 0.465636i $$-0.845826\pi$$
0.845741 + 0.533594i $$0.179159\pi$$
$$272$$ 6.43769 0.390343
$$273$$ 9.47214 + 32.8124i 0.573280 + 1.98590i
$$274$$ −0.909830 −0.0549648
$$275$$ 0 0
$$276$$ 6.80902 11.7936i 0.409855 0.709889i
$$277$$ 8.44427 + 14.6259i 0.507367 + 0.878786i 0.999964 + 0.00852782i $$0.00271452\pi$$
−0.492597 + 0.870258i $$0.663952\pi$$
$$278$$ −10.3262 −0.619327
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −15.8885 −0.947831 −0.473916 0.880570i $$-0.657160\pi$$
−0.473916 + 0.880570i $$0.657160\pi$$
$$282$$ 3.41641 + 5.91739i 0.203444 + 0.352376i
$$283$$ −5.35410 + 9.27358i −0.318268 + 0.551257i −0.980127 0.198372i $$-0.936435\pi$$
0.661859 + 0.749629i $$0.269768\pi$$
$$284$$ −5.04508 + 8.73834i −0.299371 + 0.518525i
$$285$$ 0 0
$$286$$ −0.364745 + 0.379054i −0.0215678 + 0.0224139i
$$287$$ −50.5967 −2.98663
$$288$$ −5.61803 + 9.73072i −0.331046 + 0.573388i
$$289$$ 2.47214 4.28187i 0.145420 0.251874i
$$290$$ 0 0
$$291$$ −7.76393 −0.455130
$$292$$ 4.85410 + 8.40755i 0.284065 + 0.492015i
$$293$$ −14.9721 25.9325i −0.874682 1.51499i −0.857102 0.515147i $$-0.827737\pi$$
−0.0175799 0.999845i $$-0.505596\pi$$
$$294$$ −15.1246 −0.882085
$$295$$ 0 0
$$296$$ −3.35410 + 5.80948i −0.194953 + 0.337669i
$$297$$ 0.263932 0.457144i 0.0153149 0.0265262i
$$298$$ 2.79837 0.162105
$$299$$ 13.1738 + 3.25966i 0.761858 + 0.188511i
$$300$$ 0 0
$$301$$ 13.2082 22.8773i 0.761308 1.31862i
$$302$$ −2.47214 + 4.28187i −0.142255 + 0.246394i
$$303$$ 0.590170 + 1.02220i 0.0339044 + 0.0587241i
$$304$$ 7.85410 0.450464
$$305$$ 0 0
$$306$$ −2.14590 3.71680i −0.122673 0.212476i
$$307$$ −24.9443 −1.42364 −0.711822 0.702360i $$-0.752130\pi$$
−0.711822 + 0.702360i $$0.752130\pi$$
$$308$$ 0.809017 + 1.40126i 0.0460980 + 0.0798441i
$$309$$ −14.4721 + 25.0665i −0.823291 + 1.42598i
$$310$$ 0 0
$$311$$ −24.0000 −1.36092 −0.680458 0.732787i $$-0.738219\pi$$
−0.680458 + 0.732787i $$0.738219\pi$$
$$312$$ −17.5000 4.33013i −0.990742 0.245145i
$$313$$ −3.88854 −0.219793 −0.109897 0.993943i $$-0.535052\pi$$
−0.109897 + 0.993943i $$0.535052\pi$$
$$314$$ −5.56231 + 9.63420i −0.313899 + 0.543689i
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 11.8885 0.667727 0.333864 0.942621i $$-0.391648\pi$$
0.333864 + 0.942621i $$0.391648\pi$$
$$318$$ −4.14590 7.18091i −0.232490 0.402685i
$$319$$ −0.881966 1.52761i −0.0493806 0.0855297i
$$320$$ 0 0
$$321$$ 6.44427 + 11.1618i 0.359684 + 0.622991i
$$322$$ −4.92705 + 8.53390i −0.274574 + 0.475576i
$$323$$ −7.35410 + 12.7377i −0.409193 + 0.708743i
$$324$$ 17.7984 0.988799
$$325$$ 0 0
$$326$$ −9.09017 −0.503458
$$327$$ −2.23607 + 3.87298i −0.123655 + 0.214176i
$$328$$ 13.3541 23.1300i 0.737357 1.27714i
$$329$$ 10.4721 + 18.1383i 0.577348 + 0.999995i
$$330$$ 0 0
$$331$$ 2.82624 + 4.89519i 0.155344 + 0.269064i 0.933184 0.359398i $$-0.117018\pi$$
−0.777840 + 0.628462i $$0.783685\pi$$
$$332$$ −7.23607 12.5332i −0.397131 0.687851i
$$333$$ −6.00000 −0.328798
$$334$$ −5.30902 9.19549i −0.290496 0.503155i
$$335$$ 0 0
$$336$$ −8.78115 + 15.2094i −0.479051 + 0.829741i
$$337$$ 7.88854 0.429716 0.214858 0.976645i $$-0.431071\pi$$
0.214858 + 0.976645i $$0.431071\pi$$
$$338$$ −0.309017 8.02850i −0.0168083 0.436693i
$$339$$ 3.29180 0.178786
$$340$$ 0 0
$$341$$ 0 0
$$342$$ −2.61803 4.53457i −0.141567 0.245201i
$$343$$ −16.7082 −0.902158
$$344$$ 6.97214 + 12.0761i 0.375912 + 0.651099i
$$345$$ 0 0
$$346$$ 11.6738 0.627585
$$347$$ 15.3541 + 26.5941i 0.824251 + 1.42765i 0.902490 + 0.430711i $$0.141737\pi$$
−0.0782387 + 0.996935i $$0.524930\pi$$
$$348$$ 13.5172 23.4125i 0.724599 1.25504i
$$349$$ −1.20820 + 2.09267i −0.0646737 + 0.112018i −0.896549 0.442944i $$-0.853934\pi$$
0.831876 + 0.554962i $$0.187267\pi$$
$$350$$ 0 0
$$351$$ 2.23607 + 7.74597i 0.119352 + 0.413449i
$$352$$ −1.32624 −0.0706887
$$353$$ −9.73607 + 16.8634i −0.518199 + 0.897546i 0.481578 + 0.876403i $$0.340064\pi$$
−0.999776 + 0.0211430i $$0.993269\pi$$
$$354$$ −0.489357 + 0.847591i −0.0260090 + 0.0450490i
$$355$$ 0 0
$$356$$ 14.5623 0.771801
$$357$$ −16.4443 28.4823i −0.870323 1.50744i
$$358$$ 2.54508 + 4.40822i 0.134512 + 0.232981i
$$359$$ 17.8885 0.944121 0.472061 0.881566i $$-0.343510\pi$$
0.472061 + 0.881566i $$0.343510\pi$$
$$360$$ 0 0
$$361$$ 0.527864 0.914287i 0.0277823 0.0481204i
$$362$$ −1.85410 + 3.21140i −0.0974494 + 0.168787i
$$363$$ 24.4721 1.28445
$$364$$ −23.9894 5.93583i −1.25738 0.311122i
$$365$$ 0 0
$$366$$ 9.96149 17.2538i 0.520696 0.901871i
$$367$$ 2.82624 4.89519i 0.147528 0.255527i −0.782785 0.622292i $$-0.786202\pi$$
0.930313 + 0.366766i $$0.119535\pi$$
$$368$$ 3.48936 + 6.04374i 0.181895 + 0.315052i
$$369$$ 23.8885 1.24359
$$370$$ 0 0
$$371$$ −12.7082 22.0113i −0.659777 1.14277i
$$372$$ 0 0
$$373$$ 13.9721 + 24.2004i 0.723450 + 1.25305i 0.959609 + 0.281337i $$0.0907780\pi$$
−0.236159 + 0.971714i $$0.575889\pi$$
$$374$$ 0.253289 0.438709i 0.0130973 0.0226851i
$$375$$ 0 0
$$376$$ −11.0557 −0.570156
$$377$$ 26.1525 + 6.47106i 1.34692 + 0.333277i
$$378$$ −5.85410 −0.301103
$$379$$ −5.40983 + 9.37010i −0.277884 + 0.481310i −0.970859 0.239652i $$-0.922967\pi$$
0.692974 + 0.720962i $$0.256300\pi$$
$$380$$ 0 0
$$381$$ 4.73607 + 8.20311i 0.242636 + 0.420258i
$$382$$ −16.7984 −0.859480
$$383$$ 2.11803 + 3.66854i 0.108226 + 0.187454i 0.915052 0.403336i $$-0.132149\pi$$
−0.806825 + 0.590790i $$0.798816\pi$$
$$384$$ −12.7254 22.0411i −0.649392 1.12478i
$$385$$ 0 0
$$386$$ −1.07295 1.85840i −0.0546117 0.0945902i
$$387$$ −6.23607 + 10.8012i −0.316997 + 0.549055i
$$388$$ 2.80902 4.86536i 0.142606 0.247001i
$$389$$ −0.111456 −0.00565105 −0.00282553 0.999996i $$-0.500899\pi$$
−0.00282553 + 0.999996i $$0.500899\pi$$
$$390$$ 0 0
$$391$$ −13.0689 −0.660922
$$392$$ 12.2361 21.1935i 0.618015 1.07043i
$$393$$ −13.4164 + 23.2379i −0.676768 + 1.17220i
$$394$$ 0.927051 + 1.60570i 0.0467042 + 0.0808940i
$$395$$ 0 0
$$396$$ −0.381966 0.661585i −0.0191945 0.0332459i
$$397$$ 13.9721 + 24.2004i 0.701241 + 1.21459i 0.968031 + 0.250831i $$0.0807038\pi$$
−0.266790 + 0.963755i $$0.585963\pi$$
$$398$$ −0.798374 −0.0400189
$$399$$ −20.0623 34.7489i −1.00437 1.73962i
$$400$$ 0 0
$$401$$ −4.44427 + 7.69770i −0.221936 + 0.384405i −0.955396 0.295328i $$-0.904571\pi$$
0.733460 + 0.679733i $$0.237904\pi$$
$$402$$ −3.74265 −0.186666
$$403$$ 0 0
$$404$$ −0.854102 −0.0424932
$$405$$ 0 0
$$406$$ −9.78115 + 16.9415i −0.485430 + 0.840790i
$$407$$ −0.354102 0.613323i −0.0175522 0.0304013i
$$408$$ 17.3607 0.859482
$$409$$ −12.4443 21.5541i −0.615330 1.06578i −0.990327 0.138756i $$-0.955690\pi$$
0.374997 0.927026i $$-0.377644\pi$$
$$410$$ 0 0
$$411$$ 3.29180 0.162372
$$412$$ −10.4721 18.1383i −0.515925 0.893609i
$$413$$ −1.50000 + 2.59808i −0.0738102 + 0.127843i
$$414$$ 2.32624 4.02916i 0.114328 0.198023i
$$415$$ 0 0
$$416$$ 14.0451 14.5961i 0.688617 0.715632i
$$417$$ 37.3607 1.82956
$$418$$ 0.309017 0.535233i 0.0151145 0.0261791i
$$419$$ −8.82624 + 15.2875i −0.431190 + 0.746843i −0.996976 0.0777091i $$-0.975239\pi$$
0.565786 + 0.824552i $$0.308573\pi$$
$$420$$ 0 0
$$421$$ 6.00000 0.292422 0.146211 0.989253i $$-0.453292\pi$$
0.146211 + 0.989253i $$0.453292\pi$$
$$422$$ 4.07295 + 7.05455i 0.198268 + 0.343410i
$$423$$ −4.94427 8.56373i −0.240399 0.416383i
$$424$$ 13.4164 0.651558
$$425$$ 0 0
$$426$$ −4.30902 + 7.46344i −0.208773 + 0.361605i
$$427$$ 30.5344 52.8872i 1.47767 2.55939i
$$428$$ −9.32624 −0.450801
$$429$$ 1.31966 1.37143i 0.0637138 0.0662133i
$$430$$ 0 0
$$431$$ −13.5902 + 23.5389i −0.654615 + 1.13383i 0.327375 + 0.944895i $$0.393836\pi$$
−0.981990 + 0.188933i $$0.939497\pi$$
$$432$$ −2.07295 + 3.59045i −0.0997348 + 0.172746i
$$433$$ −7.26393 12.5815i −0.349082 0.604628i 0.637004 0.770860i $$-0.280173\pi$$
−0.986087 + 0.166232i $$0.946840\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −1.61803 2.80252i −0.0774898 0.134216i
$$437$$ −15.9443 −0.762718
$$438$$ 4.14590 + 7.18091i 0.198099 + 0.343117i
$$439$$ 11.3541 19.6659i 0.541902 0.938601i −0.456893 0.889522i $$-0.651038\pi$$
0.998795 0.0490797i $$-0.0156288\pi$$
$$440$$ 0 0
$$441$$ 21.8885 1.04231
$$442$$ 2.14590 + 7.43361i 0.102070 + 0.353581i
$$443$$ −0.944272 −0.0448637 −0.0224319 0.999748i $$-0.507141\pi$$
−0.0224319 + 0.999748i $$0.507141\pi$$
$$444$$ 5.42705 9.39993i 0.257556 0.446101i
$$445$$ 0 0
$$446$$ 0.218847 + 0.379054i 0.0103627 + 0.0179487i
$$447$$ −10.1246 −0.478878
$$448$$ −0.500000 0.866025i −0.0236228 0.0409159i
$$449$$ −1.97214 3.41584i −0.0930709 0.161203i 0.815731 0.578431i $$-0.196335\pi$$
−0.908802 + 0.417228i $$0.863002\pi$$
$$450$$ 0 0
$$451$$ 1.40983 + 2.44190i 0.0663863 + 0.114984i
$$452$$ −1.19098 + 2.06284i −0.0560191 + 0.0970280i
$$453$$ 8.94427 15.4919i 0.420239 0.727875i
$$454$$ 3.85410 0.180882
$$455$$ 0 0
$$456$$ 21.1803 0.991860
$$457$$ −0.791796 + 1.37143i −0.0370387 + 0.0641528i −0.883950 0.467580i $$-0.845126\pi$$
0.846912 + 0.531733i $$0.178459\pi$$
$$458$$ −4.90983 + 8.50408i −0.229421 + 0.397369i
$$459$$ −3.88197 6.72376i −0.181195 0.313838i
$$460$$ 0 0
$$461$$ 0.791796 + 1.37143i 0.0368776 + 0.0638739i 0.883875 0.467723i $$-0.154925\pi$$
−0.846998 + 0.531597i $$0.821592\pi$$
$$462$$ 0.690983 + 1.19682i 0.0321474 + 0.0556810i
$$463$$ −11.0557 −0.513803 −0.256902 0.966438i $$-0.582702\pi$$
−0.256902 + 0.966438i $$0.582702\pi$$
$$464$$ 6.92705 + 11.9980i 0.321580 + 0.556993i
$$465$$ 0 0
$$466$$ −4.90983 + 8.50408i −0.227443 + 0.393944i
$$467$$ −8.94427 −0.413892 −0.206946 0.978352i $$-0.566352\pi$$
−0.206946 + 0.978352i $$0.566352\pi$$
$$468$$ 11.3262 + 2.80252i 0.523556 + 0.129546i
$$469$$ −11.4721 −0.529734
$$470$$ 0 0
$$471$$ 20.1246 34.8569i 0.927293 1.60612i
$$472$$ −0.791796 1.37143i −0.0364454 0.0631252i
$$473$$ −1.47214 −0.0676889
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 23.7984 1.09080
$$477$$ 6.00000 + 10.3923i 0.274721 + 0.475831i
$$478$$ 8.00000 13.8564i 0.365911 0.633777i
$$479$$ −16.0623 + 27.8207i −0.733905 + 1.27116i 0.221296 + 0.975207i $$0.428971\pi$$
−0.955202 + 0.295955i $$0.904362\pi$$
$$480$$ 0 0
$$481$$ 10.5000 + 2.59808i 0.478759 + 0.118462i
$$482$$ 9.27051 0.422260
$$483$$ 17.8262 30.8759i 0.811122 1.40490i
$$484$$ −8.85410 + 15.3358i −0.402459 + 0.697080i
$$485$$ 0 0
$$486$$ 11.0557 0.501498
$$487$$ 7.06231 + 12.2323i 0.320024 + 0.554297i 0.980493 0.196556i $$-0.0629758\pi$$
−0.660469 + 0.750853i $$0.729642\pi$$
$$488$$ 16.1180 + 27.9173i 0.729629 + 1.26375i
$$489$$ 32.8885 1.48727
$$490$$ 0 0
$$491$$ 0.118034 0.204441i 0.00532680 0.00922629i −0.863350 0.504606i $$-0.831638\pi$$
0.868677 + 0.495380i $$0.164971\pi$$
$$492$$ −21.6074 + 37.4251i −0.974136 + 1.68725i
$$493$$ −25.9443 −1.16847
$$494$$ 2.61803 + 9.06914i 0.117791 + 0.408040i
$$495$$ 0 0
$$496$$ 0 0
$$497$$ −13.2082 + 22.8773i −0.592469 + 1.02619i
$$498$$ −6.18034 10.7047i −0.276948 0.479687i
$$499$$ −21.8885 −0.979866 −0.489933 0.871760i $$-0.662979\pi$$
−0.489933 + 0.871760i $$0.662979\pi$$
$$500$$ 0 0
$$501$$ 19.2082 + 33.2696i 0.858159 + 1.48638i
$$502$$ 12.5066 0.558196
$$503$$ 4.59017 + 7.95041i 0.204666 + 0.354491i 0.950026 0.312170i $$-0.101056\pi$$
−0.745361 + 0.666662i $$0.767723\pi$$
$$504$$ −9.47214 + 16.4062i −0.421922 + 0.730791i
$$505$$ 0 0
$$506$$ 0.549150 0.0244127
$$507$$ 1.11803 + 29.0474i 0.0496536 + 1.29004i
$$508$$ −6.85410 −0.304102
$$509$$ 16.6803 28.8912i 0.739343 1.28058i −0.213448 0.976954i $$-0.568470\pi$$
0.952791 0.303625i $$-0.0981971\pi$$
$$510$$ 0 0
$$511$$ 12.7082 + 22.0113i 0.562178 + 0.973721i
$$512$$ 18.7082 0.826794
$$513$$ −4.73607 8.20311i −0.209103 0.362176i
$$514$$ 5.39919 + 9.35167i 0.238148 + 0.412484i
$$515$$ 0 0
$$516$$ −11.2812 19.5395i −0.496625 0.860180i
$$517$$ 0.583592 1.01081i 0.0256664 0.0444554i
$$518$$ −3.92705 + 6.80185i −0.172545 + 0.298856i
$$519$$ −42.2361 −1.85396
$$520$$ 0 0
$$521$$ 29.7771 1.30456 0.652279 0.757979i $$-0.273813\pi$$
0.652279 + 0.757979i $$0.273813\pi$$
$$522$$ 4.61803 7.99867i 0.202126 0.350092i
$$523$$ 2.64590 4.58283i 0.115697 0.200393i −0.802361 0.596839i $$-0.796423\pi$$
0.918058 + 0.396446i $$0.129756\pi$$
$$524$$ −9.70820 16.8151i −0.424105 0.734571i
$$525$$ 0 0
$$526$$ 1.16312 + 2.01458i 0.0507144 + 0.0878399i
$$527$$ 0 0
$$528$$ 0.978714 0.0425930
$$529$$ 4.41641 + 7.64944i 0.192018 + 0.332584i
$$530$$ 0 0
$$531$$ 0.708204 1.22665i 0.0307334 0.0532319i
$$532$$ 29.0344 1.25880
$$533$$ −41.8050 10.3440i −1.81077 0.448050i
$$534$$ 12.4377 0.538232
$$535$$ 0 0
$$536$$ 3.02786 5.24441i 0.130784 0.226524i
$$537$$ −9.20820 15.9491i −0.397363 0.688253i
$$538$$ −4.03444 −0.173937
$$539$$ 1.29180 + 2.23746i 0.0556416 + 0.0963741i
$$540$$ 0 0
$$541$$ −27.8885 −1.19902 −0.599511 0.800366i $$-0.704638\pi$$
−0.599511 + 0.800366i $$0.704638\pi$$
$$542$$ −0.399187 0.691412i −0.0171465 0.0296987i
$$543$$ 6.70820 11.6190i 0.287877 0.498617i
$$544$$ −9.75329 + 16.8932i −0.418169 + 0.724290i
$$545$$ 0 0
$$546$$ −20.4894 5.06980i −0.876864 0.216967i
$$547$$ −18.8328 −0.805233 −0.402617 0.915369i $$-0.631899\pi$$
−0.402617 + 0.915369i $$0.631899\pi$$
$$548$$ −1.19098 + 2.06284i −0.0508763 + 0.0881203i
$$549$$ −14.4164 + 24.9700i −0.615277 + 1.06569i
$$550$$ 0 0
$$551$$ −31.6525 −1.34844
$$552$$ 9.40983 + 16.2983i 0.400509 + 0.693702i
$$553$$ 0 0
$$554$$ −10.4377 −0.443455
$$555$$ 0 0
$$556$$ −13.5172 + 23.4125i −0.573258 + 0.992912i
$$557$$ −4.97214 + 8.61199i −0.210676 + 0.364902i −0.951926 0.306327i $$-0.900900\pi$$
0.741250 + 0.671229i $$0.234233\pi$$
$$558$$ 0 0
$$559$$ 15.5902 16.2018i 0.659394 0.685262i
$$560$$ 0 0
$$561$$ −0.916408 + 1.58726i −0.0386908 + 0.0670144i
$$562$$ 4.90983 8.50408i 0.207109 0.358723i
$$563$$ 15.3541 + 26.5941i 0.647098 + 1.12081i 0.983813 + 0.179200i $$0.0573510\pi$$
−0.336714 + 0.941607i $$0.609316\pi$$
$$564$$ 17.8885 0.753244
$$565$$ 0 0
$$566$$ −3.30902 5.73139i −0.139088 0.240908i
$$567$$ 46.5967 1.95688
$$568$$ −6.97214 12.0761i −0.292544 0.506702i
$$569$$ −8.44427 + 14.6259i −0.354002 + 0.613150i −0.986947 0.161047i $$-0.948513\pi$$
0.632944 + 0.774197i $$0.281846\pi$$
$$570$$ 0 0
$$571$$ 28.0000 1.17176 0.585882 0.810397i $$-0.300748\pi$$
0.585882 + 0.810397i $$0.300748\pi$$
$$572$$ 0.381966 + 1.32317i 0.0159708 + 0.0553245i
$$573$$ 60.7771 2.53900
$$574$$ 15.6353 27.0811i 0.652603 1.13034i
$$575$$ 0 0
$$576$$ 0.236068 + 0.408882i 0.00983617 + 0.0170367i
$$577$$ −27.8885 −1.16102 −0.580508 0.814255i $$-0.697146\pi$$
−0.580508 + 0.814255i $$0.697146\pi$$
$$578$$ 1.52786 + 2.64634i 0.0635508 + 0.110073i
$$579$$ 3.88197 + 6.72376i 0.161329 + 0.279430i
$$580$$ 0 0
$$581$$ −18.9443 32.8124i −0.785941 1.36129i
$$582$$ 2.39919 4.15551i 0.0994495 0.172252i
$$583$$ −0.708204 + 1.22665i −0.0293308 + 0.0508025i
$$584$$ −13.4164 −0.555175
$$585$$ 0 0
$$586$$ 18.5066 0.764500
$$587$$ 5.11803 8.86469i 0.211244 0.365885i −0.740860 0.671659i $$-0.765582\pi$$
0.952104 + 0.305774i $$0.0989152\pi$$
$$588$$ −19.7984 + 34.2918i −0.816471 + 1.41417i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ −3.35410 5.80948i −0.137969 0.238970i
$$592$$ 2.78115 + 4.81710i 0.114305 + 0.197982i
$$593$$ 7.88854 0.323944 0.161972 0.986795i $$-0.448215\pi$$
0.161972 + 0.986795i $$0.448215\pi$$
$$594$$ 0.163119 + 0.282530i 0.00669285 + 0.0115924i
$$595$$ 0 0
$$596$$ 3.66312 6.34471i 0.150047 0.259889i
$$597$$ 2.88854 0.118220
$$598$$ −5.81559 + 6.04374i −0.237817 + 0.247147i
$$599$$ −24.0000 −0.980613 −0.490307 0.871550i $$-0.663115\pi$$
−0.490307 + 0.871550i $$0.663115\pi$$
$$600$$ 0 0
$$601$$ −21.9721 + 38.0569i −0.896262 + 1.55237i −0.0640274 + 0.997948i $$0.520394\pi$$
−0.832235 + 0.554423i $$0.812939\pi$$
$$602$$ 8.16312 + 14.1389i 0.332704 + 0.576260i
$$603$$ 5.41641 0.220573
$$604$$ 6.47214 + 11.2101i 0.263347 + 0.456131i
$$605$$ 0 0
$$606$$ −0.729490 −0.0296335
$$607$$ −0.354102 0.613323i −0.0143726 0.0248940i 0.858750 0.512395i $$-0.171242\pi$$
−0.873122 + 0.487501i $$0.837908\pi$$
$$608$$ −11.8992 + 20.6100i −0.482576 + 0.835846i
$$609$$ 35.3885 61.2948i 1.43402 2.48379i
$$610$$ 0 0
$$611$$ 4.94427 + 17.1275i 0.200024 + 0.692903i
$$612$$ −11.2361 −0.454191
$$613$$ 19.9721 34.5928i 0.806667 1.39719i −0.108493 0.994097i $$-0.534602\pi$$
0.915160 0.403091i $$-0.132064\pi$$
$$614$$ 7.70820 13.3510i 0.311078 0.538803i
$$615$$ 0 0
$$616$$ −2.23607 −0.0900937
$$617$$ −20.2082 35.0016i −0.813552 1.40911i −0.910363 0.413810i $$-0.864198\pi$$
0.0968116 0.995303i $$-0.469136\pi$$
$$618$$ −8.94427 15.4919i −0.359791 0.623177i
$$619$$ 12.0000 0.482321 0.241160 0.970485i $$-0.422472\pi$$
0.241160 + 0.970485i $$0.422472\pi$$
$$620$$ 0 0
$$621$$ 4.20820 7.28882i 0.168869 0.292490i
$$622$$ 7.41641 12.8456i 0.297371 0.515061i
$$623$$ 38.1246 1.52743
$$624$$ −10.3647 + 10.7714i −0.414922 + 0.431199i
$$625$$ 0 0
$$626$$ 1.20163 2.08128i 0.0480266 0.0831846i
$$627$$ −1.11803 + 1.93649i −0.0446500 + 0.0773360i
$$628$$ 14.5623 + 25.2227i 0.581099 + 1.00649i
$$629$$ −10.4164 −0.415329
$$630$$ 0 0
$$631$$ 8.06231 + 13.9643i 0.320955 + 0.555911i 0.980685 0.195592i $$-0.0626627\pi$$
−0.659730 + 0.751503i $$0.729329\pi$$
$$632$$ 0 0
$$633$$ −14.7361 25.5236i −0.585706 1.01447i
$$634$$ −3.67376 + 6.36314i −0.145904 + 0.252713i
$$635$$ 0 0
$$636$$ −21.7082 −0.860786
$$637$$ −38.3050 9.47802i −1.51770 0.375533i
$$638$$ 1.09017 0.0431602
$$639$$ 6.23607 10.8012i 0.246695 0.427288i
$$640$$ 0 0
$$641$$ −4.44427 7.69770i −0.175538 0.304041i 0.764809 0.644257i $$-0.222833\pi$$
−0.940347 + 0.340216i $$0.889500\pi$$
$$642$$ −7.96556 −0.314376
$$643$$ −8.64590 14.9751i −0.340961 0.590562i 0.643650 0.765320i $$-0.277419\pi$$
−0.984611 + 0.174758i $$0.944086\pi$$
$$644$$ 12.8992 + 22.3420i 0.508299 + 0.880400i
$$645$$ 0 0
$$646$$ −4.54508 7.87232i −0.178824 0.309732i
$$647$$ 1.29837 2.24885i 0.0510443 0.0884114i −0.839374 0.543554i $$-0.817078\pi$$
0.890419 + 0.455142i $$0.150412\pi$$
$$648$$ −12.2984 + 21.3014i −0.483126 + 0.836798i
$$649$$ 0.167184 0.00656256
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −11.8992 + 20.6100i −0.466008 + 0.807150i
$$653$$ −10.5000 + 18.1865i −0.410897 + 0.711694i −0.994988 0.0999939i $$-0.968118\pi$$
0.584091 + 0.811688i $$0.301451\pi$$
$$654$$ −1.38197 2.39364i −0.0540391 0.0935985i
$$655$$ 0 0
$$656$$ −11.0729 19.1789i −0.432326 0.748811i
$$657$$ −6.00000 10.3923i −0.234082 0.405442i
$$658$$ −12.9443 −0.504620
$$659$$ 21.8820 + 37.9007i 0.852400 + 1.47640i 0.879036 + 0.476756i $$0.158187\pi$$
−0.0266355 + 0.999645i $$0.508479\pi$$
$$660$$ 0 0
$$661$$ 20.6803 35.8194i 0.804372 1.39321i −0.112342 0.993670i $$-0.535835\pi$$
0.916714 0.399544i $$-0.130831\pi$$
$$662$$ −3.49342 −0.135776
$$663$$ −7.76393 26.8950i −0.301526 1.04452i
$$664$$ 20.0000 0.776151
$$665$$ 0 0
$$666$$ 1.85410 3.21140i 0.0718450 0.124439i
$$667$$ −14.0623 24.3566i −0.544495 0.943092i
$$668$$ −27.7984 −1.07555
$$669$$ −0.791796 1.37143i −0.0306126 0.0530226i
$$670$$ 0 0
$$671$$ −3.40325 −0.131381
$$672$$ −26.6074 46.0854i −1.02640 1.77778i
$$673$$ −4.79180 + 8.29963i −0.184710 + 0.319927i −0.943479 0.331433i $$-0.892468\pi$$
0.758769 + 0.651360i $$0.225801\pi$$
$$674$$ −2.43769 + 4.22221i −0.0938965 + 0.162633i
$$675$$ 0 0
$$676$$ −18.6074 9.80881i −0.715669 0.377262i
$$677$$ −12.1115 −0.465481 −0.232741 0.972539i $$-0.574769\pi$$
−0.232741 + 0.972539i $$0.574769\pi$$
$$678$$ −1.01722 + 1.76188i −0.0390661 + 0.0676645i
$$679$$ 7.35410 12.7377i 0.282225 0.488827i
$$680$$ 0 0
$$681$$ −13.9443 −0.534346
$$682$$ 0 0
$$683$$ 12.8820 + 22.3122i 0.492915 + 0.853753i 0.999967 0.00816213i $$-0.00259812\pi$$
−0.507052 + 0.861915i $$0.669265\pi$$
$$684$$ −13.7082 −0.524146
$$685$$ 0 0
$$686$$ 5.16312 8.94278i 0.197129 0.341437i
$$687$$ 17.7639 30.7680i 0.677736 1.17387i
$$688$$ 11.5623 0.440809
$$689$$ −6.00000 20.7846i −0.228582 0.791831i
$$690$$ 0 0
$$691$$ −19.2984 + 33.4258i −0.734145 + 1.27158i 0.220953 + 0.975284i $$0.429083\pi$$
−0.955098 + 0.296291i $$0.904250\pi$$
$$692$$ 15.2812 26.4677i 0.580902 1.00615i
$$693$$ −1.00000 1.73205i −0.0379869 0.0657952i
$$694$$ −18.9787 −0.720422
$$695$$ 0 0
$$696$$ 18.6803 + 32.3553i 0.708076 + 1.22642i
$$697$$ 41.4721 1.57087
$$698$$ −0.746711 1.29334i −0.0282634 0.0489537i
$$699$$ 17.7639 30.7680i 0.671894 1.16375i
$$700$$ 0 0
$$701$$ 7.88854 0.297946 0.148973 0.988841i $$-0.452403\pi$$
0.148973 + 0.988841i $$0.452403\pi$$
$$702$$ −4.83688 1.19682i −0.182556 0.0451710i
$$703$$ −12.7082 −0.479299
$$704$$ −0.0278640 + 0.0482619i −0.00105017 + 0.00181894i
$$705$$ 0 0
$$706$$ −6.01722 10.4221i −0.226461 0.392242i
$$707$$ −2.23607 −0.0840960
$$708$$ 1.28115 + 2.21902i 0.0481487 + 0.0833960i
$$709$$ −12.1525 21.0487i −0.456396 0.790501i 0.542371 0.840139i $$-0.317527\pi$$
−0.998767 + 0.0496381i $$0.984193\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −10.0623 + 17.4284i −0.377101 + 0.653158i
$$713$$ 0 0
$$714$$ 20.3262 0.760690
$$715$$ 0 0
$$716$$ 13.3262 0.498025
$$717$$ −28.9443 + 50.1329i −1.08094 + 1.87225i
$$718$$ −5.52786 + 9.57454i −0.206298 + 0.357319i
$$719$$ 16.0623 + 27.8207i 0.599023 + 1.03754i 0.992966 + 0.118403i $$0.0377775\pi$$
−0.393943 + 0.919135i $$0.628889\pi$$
$$720$$ 0 0
$$721$$ −27.4164 47.4866i −1.02104 1.76849i
$$722$$ 0.326238 + 0.565061i 0.0121413 + 0.0210294i
$$723$$ −33.5410 −1.24740
$$724$$ 4.85410 + 8.40755i 0.180401 + 0.312464i
$$725$$ 0 0
$$726$$ −7.56231 + 13.0983i −0.280663 + 0.486123i
$$727$$ −28.9443 −1.07348 −0.536742 0.843747i $$-0.680345\pi$$
−0.536742 + 0.843747i $$0.680345\pi$$
$$728$$ 23.6803 24.6093i 0.877652 0.912082i
$$729$$ −7.00000 −0.259259
$$730$$ 0 0
$$731$$ −10.8262 + 18.7516i −0.400423 + 0.693553i
$$732$$ −26.0795 45.1711i −0.963927 1.66957i
$$733$$ 43.8885 1.62106 0.810530 0.585697i $$-0.199179\pi$$
0.810530 + 0.585697i $$0.199179\pi$$
$$734$$ 1.74671 + 3.02539i 0.0644723 + 0.111669i
$$735$$ 0 0
$$736$$ −21.1459 −0.779448
$$737$$ 0.319660 + 0.553668i 0.0117748 + 0.0203946i
$$738$$ −7.38197 + 12.7859i −0.271734 + 0.470657i
$$739$$ −13.7705 + 23.8512i −0.506556 + 0.877381i 0.493415 + 0.869794i $$0.335748\pi$$
−0.999971 + 0.00758729i $$0.997585\pi$$
$$740$$ 0 0
$$741$$ −9.47214 32.8124i −0.347968 1.20540i
$$742$$ 15.7082 0.576666
$$743$$ −19.0623 + 33.0169i −0.699328 + 1.21127i 0.269372 + 0.963036i $$0.413184\pi$$
−0.968700 + 0.248236i $$0.920149\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −17.2705 −0.632318
$$747$$ 8.94427 + 15.4919i 0.327254 + 0.566820i
$$748$$ −0.663119 1.14856i −0.0242460 0.0419954i
$$749$$ −24.4164 −0.892156
$$750$$ 0 0
$$751$$ 15.3541 26.5941i 0.560279 0.970432i −0.437193 0.899368i $$-0.644027\pi$$
0.997472 0.0710640i $$-0.0226395\pi$$
$$752$$ −4.58359 + 7.93901i −0.167146 + 0.289506i
$$753$$ −45.2492 −1.64897
$$754$$ −11.5451 + 11.9980i −0.420447 + 0.436942i
$$755$$ 0 0
$$756$$ −7.66312 + 13.2729i −0.278705 + 0.482731i
$$757$$ −3.44427 + 5.96565i −0.125184 + 0.216825i −0.921805 0.387654i $$-0.873286\pi$$
0.796621 + 0.604479i $$0.206619\pi$$
$$758$$ −3.34346 5.79104i −0.121440 0.210340i
$$759$$ −1.98684 −0.0721179
$$760$$ 0 0
$$761$$ 18.9721 + 32.8607i 0.687739 + 1.19120i 0.972567 + 0.232621i $$0.0747302\pi$$
−0.284828 + 0.958579i $$0.591937\pi$$
$$762$$ −5.85410 −0.212072
$$763$$ −4.23607 7.33708i −0.153356 0.265620i
$$764$$ −21.9894 + 38.0867i −0.795547 + 1.37793i
$$765$$ 0 0
$$766$$ −2.61803 −0.0945934
$$767$$ −1.77051 + 1.83997i −0.0639294 + 0.0664374i
$$768$$ 14.6738 0.529494
$$769$$ −14.9164 + 25.8360i −0.537899 + 0.931669i 0.461118 + 0.887339i $$0.347449\pi$$
−0.999017 + 0.0443301i $$0.985885\pi$$
$$770$$ 0 0
$$771$$ −19.5344 33.8346i −0.703516 1.21853i
$$772$$ −5.61803 −0.202197
$$773$$ −10.0279 17.3688i −0.360677 0.624711i 0.627395 0.778701i $$-0.284121\pi$$
−0.988072 + 0.153990i $$0.950788\pi$$
$$774$$ −3.85410 6.67550i −0.138533 0.239946i
$$775$$ 0 0
$$776$$ 3.88197 + 6.72376i 0.139354 + 0.241369i
$$777$$ 14.2082 24.6093i 0.509716 0.882855i
$$778$$ 0.0344419 0.0596550i 0.00123480 0.00213874i
$$779$$ 50.5967 1.81282
$$780$$ 0 0
$$781$$ 1.47214 0.0526772
$$782$$ 4.03851 6.99490i 0.144417 0.250137i
$$783$$ 8.35410 14.4697i 0.298551 0.517106i
$$784$$ −10.1459 17.5732i −0.362354 0.627615i