# Properties

 Label 570.2.c.f.569.1 Level $570$ Weight $2$ Character 570.569 Analytic conductor $4.551$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.1499238400.2 Defining polynomial: $$x^{8} - 4 x^{7} + 16 x^{6} - 34 x^{5} + 59 x^{4} - 66 x^{3} + 54 x^{2} - 26 x + 5$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 569.1 Root $$0.500000 + 0.0845405i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.569 Dual form 570.2.c.f.569.7

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} +(0.500000 - 1.65831i) q^{3} -1.00000 q^{4} +(-0.584541 + 2.15831i) q^{5} +(-1.65831 - 0.500000i) q^{6} -4.86140i q^{7} +1.00000i q^{8} +(-2.50000 - 1.65831i) q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} +(0.500000 - 1.65831i) q^{3} -1.00000 q^{4} +(-0.584541 + 2.15831i) q^{5} +(-1.65831 - 0.500000i) q^{6} -4.86140i q^{7} +1.00000i q^{8} +(-2.50000 - 1.65831i) q^{9} +(2.15831 + 0.584541i) q^{10} -2.31662i q^{11} +(-0.500000 + 1.65831i) q^{12} +3.31662 q^{13} -4.86140 q^{14} +(3.28689 + 2.04851i) q^{15} +1.00000 q^{16} -4.86140 q^{17} +(-1.65831 + 2.50000i) q^{18} +(2.31662 + 3.69232i) q^{19} +(0.584541 - 2.15831i) q^{20} +(-8.06173 - 2.43070i) q^{21} -2.31662 q^{22} -6.03049 q^{23} +(1.65831 + 0.500000i) q^{24} +(-4.31662 - 2.52324i) q^{25} -3.31662i q^{26} +(-4.00000 + 3.31662i) q^{27} +4.86140i q^{28} -1.35416 q^{29} +(2.04851 - 3.28689i) q^{30} -8.55373i q^{31} -1.00000i q^{32} +(-3.84169 - 1.15831i) q^{33} +4.86140i q^{34} +(10.4924 + 2.84169i) q^{35} +(2.50000 + 1.65831i) q^{36} +2.00000 q^{37} +(3.69232 - 2.31662i) q^{38} +(1.65831 - 5.50000i) q^{39} +(-2.15831 - 0.584541i) q^{40} -3.50724 q^{41} +(-2.43070 + 8.06173i) q^{42} -1.16908i q^{43} +2.31662i q^{44} +(5.04051 - 4.42643i) q^{45} +6.03049i q^{46} +5.04648 q^{47} +(0.500000 - 1.65831i) q^{48} -16.6332 q^{49} +(-2.52324 + 4.31662i) q^{50} +(-2.43070 + 8.06173i) q^{51} -3.31662 q^{52} -1.00000i q^{53} +(3.31662 + 4.00000i) q^{54} +(5.00000 + 1.35416i) q^{55} +4.86140 q^{56} +(7.28134 - 1.99553i) q^{57} +1.35416i q^{58} +9.90789 q^{59} +(-3.28689 - 2.04851i) q^{60} +4.31662 q^{61} -8.55373 q^{62} +(-8.06173 + 12.1535i) q^{63} -1.00000 q^{64} +(-1.93870 + 7.15831i) q^{65} +(-1.15831 + 3.84169i) q^{66} +7.00000 q^{67} +4.86140 q^{68} +(-3.01524 + 10.0004i) q^{69} +(2.84169 - 10.4924i) q^{70} +10.8919 q^{71} +(1.65831 - 2.50000i) q^{72} -11.0770i q^{73} -2.00000i q^{74} +(-6.34264 + 5.89669i) q^{75} +(-2.31662 - 3.69232i) q^{76} -11.2620 q^{77} +(-5.50000 - 1.65831i) q^{78} +4.67632i q^{79} +(-0.584541 + 2.15831i) q^{80} +(3.50000 + 8.29156i) q^{81} +3.50724i q^{82} +9.72281 q^{83} +(8.06173 + 2.43070i) q^{84} +(2.84169 - 10.4924i) q^{85} -1.16908 q^{86} +(-0.677081 + 2.24562i) q^{87} +2.31662 q^{88} +8.55373 q^{89} +(-4.42643 - 5.04051i) q^{90} -16.1235i q^{91} +6.03049 q^{92} +(-14.1848 - 4.27686i) q^{93} -5.04648i q^{94} +(-9.32335 + 2.84169i) q^{95} +(-1.65831 - 0.500000i) q^{96} +16.6332 q^{97} +16.6332i q^{98} +(-3.84169 + 5.79156i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{3} - 8q^{4} - 20q^{9} + O(q^{10})$$ $$8q + 4q^{3} - 8q^{4} - 20q^{9} + 4q^{10} - 4q^{12} + 22q^{15} + 8q^{16} - 8q^{19} + 8q^{22} - 8q^{25} - 32q^{27} + 2q^{30} - 44q^{33} + 20q^{36} + 16q^{37} - 4q^{40} + 22q^{45} + 4q^{48} - 80q^{49} + 40q^{55} - 4q^{57} - 22q^{60} + 8q^{61} - 8q^{64} + 4q^{66} + 56q^{67} + 36q^{70} - 4q^{75} + 8q^{76} - 44q^{78} + 28q^{81} + 36q^{85} - 8q^{88} - 10q^{90} + 80q^{97} - 44q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0.500000 1.65831i 0.288675 0.957427i
$$4$$ −1.00000 −0.500000
$$5$$ −0.584541 + 2.15831i −0.261414 + 0.965227i
$$6$$ −1.65831 0.500000i −0.677003 0.204124i
$$7$$ 4.86140i 1.83744i −0.394912 0.918719i $$-0.629225\pi$$
0.394912 0.918719i $$-0.370775\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ −2.50000 1.65831i −0.833333 0.552771i
$$10$$ 2.15831 + 0.584541i 0.682518 + 0.184848i
$$11$$ 2.31662i 0.698489i −0.937032 0.349244i $$-0.886438\pi$$
0.937032 0.349244i $$-0.113562\pi$$
$$12$$ −0.500000 + 1.65831i −0.144338 + 0.478714i
$$13$$ 3.31662 0.919866 0.459933 0.887954i $$-0.347873\pi$$
0.459933 + 0.887954i $$0.347873\pi$$
$$14$$ −4.86140 −1.29926
$$15$$ 3.28689 + 2.04851i 0.848670 + 0.528922i
$$16$$ 1.00000 0.250000
$$17$$ −4.86140 −1.17906 −0.589532 0.807745i $$-0.700688\pi$$
−0.589532 + 0.807745i $$0.700688\pi$$
$$18$$ −1.65831 + 2.50000i −0.390868 + 0.589256i
$$19$$ 2.31662 + 3.69232i 0.531470 + 0.847077i
$$20$$ 0.584541 2.15831i 0.130707 0.482613i
$$21$$ −8.06173 2.43070i −1.75921 0.530423i
$$22$$ −2.31662 −0.493906
$$23$$ −6.03049 −1.25744 −0.628722 0.777631i $$-0.716421\pi$$
−0.628722 + 0.777631i $$0.716421\pi$$
$$24$$ 1.65831 + 0.500000i 0.338502 + 0.102062i
$$25$$ −4.31662 2.52324i −0.863325 0.504648i
$$26$$ 3.31662i 0.650444i
$$27$$ −4.00000 + 3.31662i −0.769800 + 0.638285i
$$28$$ 4.86140i 0.918719i
$$29$$ −1.35416 −0.251461 −0.125731 0.992064i $$-0.540128\pi$$
−0.125731 + 0.992064i $$0.540128\pi$$
$$30$$ 2.04851 3.28689i 0.374004 0.600101i
$$31$$ 8.55373i 1.53629i −0.640273 0.768147i $$-0.721179\pi$$
0.640273 0.768147i $$-0.278821\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ −3.84169 1.15831i −0.668752 0.201636i
$$34$$ 4.86140i 0.833724i
$$35$$ 10.4924 + 2.84169i 1.77354 + 0.480333i
$$36$$ 2.50000 + 1.65831i 0.416667 + 0.276385i
$$37$$ 2.00000 0.328798 0.164399 0.986394i $$-0.447432\pi$$
0.164399 + 0.986394i $$0.447432\pi$$
$$38$$ 3.69232 2.31662i 0.598974 0.375806i
$$39$$ 1.65831 5.50000i 0.265543 0.880705i
$$40$$ −2.15831 0.584541i −0.341259 0.0924240i
$$41$$ −3.50724 −0.547739 −0.273870 0.961767i $$-0.588304\pi$$
−0.273870 + 0.961767i $$0.588304\pi$$
$$42$$ −2.43070 + 8.06173i −0.375065 + 1.24395i
$$43$$ 1.16908i 0.178283i −0.996019 0.0891416i $$-0.971588\pi$$
0.996019 0.0891416i $$-0.0284124\pi$$
$$44$$ 2.31662i 0.349244i
$$45$$ 5.04051 4.42643i 0.751394 0.659853i
$$46$$ 6.03049i 0.889147i
$$47$$ 5.04648 0.736105 0.368053 0.929805i $$-0.380025\pi$$
0.368053 + 0.929805i $$0.380025\pi$$
$$48$$ 0.500000 1.65831i 0.0721688 0.239357i
$$49$$ −16.6332 −2.37618
$$50$$ −2.52324 + 4.31662i −0.356840 + 0.610463i
$$51$$ −2.43070 + 8.06173i −0.340366 + 1.12887i
$$52$$ −3.31662 −0.459933
$$53$$ 1.00000i 0.137361i −0.997639 0.0686803i $$-0.978121\pi$$
0.997639 0.0686803i $$-0.0218788\pi$$
$$54$$ 3.31662 + 4.00000i 0.451335 + 0.544331i
$$55$$ 5.00000 + 1.35416i 0.674200 + 0.182595i
$$56$$ 4.86140 0.649632
$$57$$ 7.28134 1.99553i 0.964437 0.264314i
$$58$$ 1.35416i 0.177810i
$$59$$ 9.90789 1.28990 0.644949 0.764226i $$-0.276879\pi$$
0.644949 + 0.764226i $$0.276879\pi$$
$$60$$ −3.28689 2.04851i −0.424335 0.264461i
$$61$$ 4.31662 0.552687 0.276344 0.961059i $$-0.410877\pi$$
0.276344 + 0.961059i $$0.410877\pi$$
$$62$$ −8.55373 −1.08632
$$63$$ −8.06173 + 12.1535i −1.01568 + 1.53120i
$$64$$ −1.00000 −0.125000
$$65$$ −1.93870 + 7.15831i −0.240466 + 0.887879i
$$66$$ −1.15831 + 3.84169i −0.142578 + 0.472879i
$$67$$ 7.00000 0.855186 0.427593 0.903971i $$-0.359362\pi$$
0.427593 + 0.903971i $$0.359362\pi$$
$$68$$ 4.86140 0.589532
$$69$$ −3.01524 + 10.0004i −0.362993 + 1.20391i
$$70$$ 2.84169 10.4924i 0.339647 1.25409i
$$71$$ 10.8919 1.29263 0.646315 0.763071i $$-0.276309\pi$$
0.646315 + 0.763071i $$0.276309\pi$$
$$72$$ 1.65831 2.50000i 0.195434 0.294628i
$$73$$ 11.0770i 1.29646i −0.761444 0.648231i $$-0.775509\pi$$
0.761444 0.648231i $$-0.224491\pi$$
$$74$$ 2.00000i 0.232495i
$$75$$ −6.34264 + 5.89669i −0.732385 + 0.680891i
$$76$$ −2.31662 3.69232i −0.265735 0.423539i
$$77$$ −11.2620 −1.28343
$$78$$ −5.50000 1.65831i −0.622752 0.187767i
$$79$$ 4.67632i 0.526128i 0.964778 + 0.263064i $$0.0847330\pi$$
−0.964778 + 0.263064i $$0.915267\pi$$
$$80$$ −0.584541 + 2.15831i −0.0653536 + 0.241307i
$$81$$ 3.50000 + 8.29156i 0.388889 + 0.921285i
$$82$$ 3.50724i 0.387310i
$$83$$ 9.72281 1.06722 0.533608 0.845732i $$-0.320836\pi$$
0.533608 + 0.845732i $$0.320836\pi$$
$$84$$ 8.06173 + 2.43070i 0.879606 + 0.265211i
$$85$$ 2.84169 10.4924i 0.308224 1.13806i
$$86$$ −1.16908 −0.126065
$$87$$ −0.677081 + 2.24562i −0.0725907 + 0.240756i
$$88$$ 2.31662 0.246953
$$89$$ 8.55373 0.906693 0.453347 0.891334i $$-0.350230\pi$$
0.453347 + 0.891334i $$0.350230\pi$$
$$90$$ −4.42643 5.04051i −0.466587 0.531316i
$$91$$ 16.1235i 1.69020i
$$92$$ 6.03049 0.628722
$$93$$ −14.1848 4.27686i −1.47089 0.443490i
$$94$$ 5.04648i 0.520505i
$$95$$ −9.32335 + 2.84169i −0.956555 + 0.291551i
$$96$$ −1.65831 0.500000i −0.169251 0.0510310i
$$97$$ 16.6332 1.68885 0.844425 0.535673i $$-0.179942\pi$$
0.844425 + 0.535673i $$0.179942\pi$$
$$98$$ 16.6332i 1.68021i
$$99$$ −3.84169 + 5.79156i −0.386104 + 0.582074i
$$100$$ 4.31662 + 2.52324i 0.431662 + 0.252324i
$$101$$ 7.68338i 0.764524i −0.924054 0.382262i $$-0.875145\pi$$
0.924054 0.382262i $$-0.124855\pi$$
$$102$$ 8.06173 + 2.43070i 0.798230 + 0.240675i
$$103$$ −15.5831 −1.53545 −0.767725 0.640779i $$-0.778612\pi$$
−0.767725 + 0.640779i $$0.778612\pi$$
$$104$$ 3.31662i 0.325222i
$$105$$ 9.95862 15.9789i 0.971862 1.55938i
$$106$$ −1.00000 −0.0971286
$$107$$ 19.9499i 1.92863i −0.264763 0.964314i $$-0.585294\pi$$
0.264763 0.964314i $$-0.414706\pi$$
$$108$$ 4.00000 3.31662i 0.384900 0.319142i
$$109$$ 17.2925i 1.65632i 0.560489 + 0.828162i $$0.310613\pi$$
−0.560489 + 0.828162i $$0.689387\pi$$
$$110$$ 1.35416 5.00000i 0.129114 0.476731i
$$111$$ 1.00000 3.31662i 0.0949158 0.314800i
$$112$$ 4.86140i 0.459360i
$$113$$ 8.31662i 0.782362i −0.920314 0.391181i $$-0.872067\pi$$
0.920314 0.391181i $$-0.127933\pi$$
$$114$$ −1.99553 7.28134i −0.186898 0.681960i
$$115$$ 3.52506 13.0157i 0.328714 1.21372i
$$116$$ 1.35416 0.125731
$$117$$ −8.29156 5.50000i −0.766555 0.508475i
$$118$$ 9.90789i 0.912095i
$$119$$ 23.6332i 2.16646i
$$120$$ −2.04851 + 3.28689i −0.187002 + 0.300050i
$$121$$ 5.63325 0.512114
$$122$$ 4.31662i 0.390809i
$$123$$ −1.75362 + 5.81610i −0.158119 + 0.524420i
$$124$$ 8.55373i 0.768147i
$$125$$ 7.96919 7.84169i 0.712786 0.701382i
$$126$$ 12.1535 + 8.06173i 1.08272 + 0.718196i
$$127$$ −3.36675 −0.298751 −0.149375 0.988781i $$-0.547726\pi$$
−0.149375 + 0.988781i $$0.547726\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ −1.93870 0.584541i −0.170693 0.0514659i
$$130$$ 7.15831 + 1.93870i 0.627826 + 0.170035i
$$131$$ 10.0000i 0.873704i −0.899533 0.436852i $$-0.856093\pi$$
0.899533 0.436852i $$-0.143907\pi$$
$$132$$ 3.84169 + 1.15831i 0.334376 + 0.100818i
$$133$$ 17.9499 11.2620i 1.55645 0.976544i
$$134$$ 7.00000i 0.604708i
$$135$$ −4.82015 10.5720i −0.414852 0.909889i
$$136$$ 4.86140i 0.416862i
$$137$$ −4.86140 −0.415338 −0.207669 0.978199i $$-0.566588\pi$$
−0.207669 + 0.978199i $$0.566588\pi$$
$$138$$ 10.0004 + 3.01524i 0.851293 + 0.256674i
$$139$$ −10.0000 −0.848189 −0.424094 0.905618i $$-0.639408\pi$$
−0.424094 + 0.905618i $$0.639408\pi$$
$$140$$ −10.4924 2.84169i −0.886772 0.240166i
$$141$$ 2.52324 8.36865i 0.212495 0.704767i
$$142$$ 10.8919i 0.914027i
$$143$$ 7.68338i 0.642516i
$$144$$ −2.50000 1.65831i −0.208333 0.138193i
$$145$$ 0.791562 2.92270i 0.0657356 0.242717i
$$146$$ −11.0770 −0.916736
$$147$$ −8.31662 + 27.5831i −0.685944 + 2.27502i
$$148$$ −2.00000 −0.164399
$$149$$ 4.00000i 0.327693i 0.986486 + 0.163846i $$0.0523901\pi$$
−0.986486 + 0.163846i $$0.947610\pi$$
$$150$$ 5.89669 + 6.34264i 0.481463 + 0.517874i
$$151$$ 2.70832i 0.220400i −0.993909 0.110200i $$-0.964851\pi$$
0.993909 0.110200i $$-0.0351492\pi$$
$$152$$ −3.69232 + 2.31662i −0.299487 + 0.187903i
$$153$$ 12.1535 + 8.06173i 0.982553 + 0.651752i
$$154$$ 11.2620i 0.907522i
$$155$$ 18.4616 + 5.00000i 1.48287 + 0.401610i
$$156$$ −1.65831 + 5.50000i −0.132771 + 0.440352i
$$157$$ 2.33816i 0.186606i 0.995638 + 0.0933028i $$0.0297425\pi$$
−0.995638 + 0.0933028i $$0.970258\pi$$
$$158$$ 4.67632 0.372028
$$159$$ −1.65831 0.500000i −0.131513 0.0396526i
$$160$$ 2.15831 + 0.584541i 0.170630 + 0.0462120i
$$161$$ 29.3166i 2.31047i
$$162$$ 8.29156 3.50000i 0.651447 0.274986i
$$163$$ 15.9384i 1.24839i 0.781269 + 0.624195i $$0.214573\pi$$
−0.781269 + 0.624195i $$0.785427\pi$$
$$164$$ 3.50724 0.273870
$$165$$ 4.74562 7.61448i 0.369446 0.592787i
$$166$$ 9.72281i 0.754636i
$$167$$ 5.05013i 0.390790i 0.980725 + 0.195395i $$0.0625990\pi$$
−0.980725 + 0.195395i $$0.937401\pi$$
$$168$$ 2.43070 8.06173i 0.187533 0.621976i
$$169$$ −2.00000 −0.153846
$$170$$ −10.4924 2.84169i −0.804733 0.217947i
$$171$$ 0.331463 13.0725i 0.0253476 0.999679i
$$172$$ 1.16908i 0.0891416i
$$173$$ 13.2665i 1.00863i 0.863519 + 0.504317i $$0.168256\pi$$
−0.863519 + 0.504317i $$0.831744\pi$$
$$174$$ 2.24562 + 0.677081i 0.170240 + 0.0513293i
$$175$$ −12.2665 + 20.9849i −0.927260 + 1.58631i
$$176$$ 2.31662i 0.174622i
$$177$$ 4.95394 16.4304i 0.372361 1.23498i
$$178$$ 8.55373i 0.641129i
$$179$$ 2.70832 0.202429 0.101215 0.994865i $$-0.467727\pi$$
0.101215 + 0.994865i $$0.467727\pi$$
$$180$$ −5.04051 + 4.42643i −0.375697 + 0.329927i
$$181$$ 2.70832i 0.201308i 0.994921 + 0.100654i $$0.0320935\pi$$
−0.994921 + 0.100654i $$0.967906\pi$$
$$182$$ −16.1235 −1.19515
$$183$$ 2.15831 7.15831i 0.159547 0.529158i
$$184$$ 6.03049i 0.444573i
$$185$$ −1.16908 + 4.31662i −0.0859525 + 0.317365i
$$186$$ −4.27686 + 14.1848i −0.313595 + 1.04008i
$$187$$ 11.2620i 0.823563i
$$188$$ −5.04648 −0.368053
$$189$$ 16.1235 + 19.4456i 1.17281 + 1.41446i
$$190$$ 2.84169 + 9.32335i 0.206158 + 0.676387i
$$191$$ 5.00000i 0.361787i −0.983503 0.180894i $$-0.942101\pi$$
0.983503 0.180894i $$-0.0578990\pi$$
$$192$$ −0.500000 + 1.65831i −0.0360844 + 0.119678i
$$193$$ 6.00000 0.431889 0.215945 0.976406i $$-0.430717\pi$$
0.215945 + 0.976406i $$0.430717\pi$$
$$194$$ 16.6332i 1.19420i
$$195$$ 10.9014 + 6.79413i 0.780663 + 0.486538i
$$196$$ 16.6332 1.18809
$$197$$ −6.21557 −0.442841 −0.221420 0.975178i $$-0.571069\pi$$
−0.221420 + 0.975178i $$0.571069\pi$$
$$198$$ 5.79156 + 3.84169i 0.411588 + 0.273017i
$$199$$ 21.2164 1.50399 0.751994 0.659169i $$-0.229092\pi$$
0.751994 + 0.659169i $$0.229092\pi$$
$$200$$ 2.52324 4.31662i 0.178420 0.305231i
$$201$$ 3.50000 11.6082i 0.246871 0.818778i
$$202$$ −7.68338 −0.540600
$$203$$ 6.58312i 0.462045i
$$204$$ 2.43070 8.06173i 0.170183 0.564434i
$$205$$ 2.05013 7.56973i 0.143187 0.528693i
$$206$$ 15.5831i 1.08573i
$$207$$ 15.0762 + 10.0004i 1.04787 + 0.695078i
$$208$$ 3.31662 0.229967
$$209$$ 8.55373 5.36675i 0.591674 0.371226i
$$210$$ −15.9789 9.95862i −1.10265 0.687210i
$$211$$ 18.4616i 1.27095i 0.772121 + 0.635475i $$0.219196\pi$$
−0.772121 + 0.635475i $$0.780804\pi$$
$$212$$ 1.00000i 0.0686803i
$$213$$ 5.44594 18.0622i 0.373150 1.23760i
$$214$$ −19.9499 −1.36375
$$215$$ 2.52324 + 0.683375i 0.172084 + 0.0466058i
$$216$$ −3.31662 4.00000i −0.225668 0.272166i
$$217$$ −41.5831 −2.82285
$$218$$ 17.2925 1.17120
$$219$$ −18.3691 5.53848i −1.24127 0.374256i
$$220$$ −5.00000 1.35416i −0.337100 0.0912975i
$$221$$ −16.1235 −1.08458
$$222$$ −3.31662 1.00000i −0.222597 0.0671156i
$$223$$ −23.2665 −1.55804 −0.779020 0.626999i $$-0.784283\pi$$
−0.779020 + 0.626999i $$0.784283\pi$$
$$224$$ −4.86140 −0.324816
$$225$$ 6.60724 + 13.4664i 0.440483 + 0.897761i
$$226$$ −8.31662 −0.553214
$$227$$ 0.0501256i 0.00332695i 0.999999 + 0.00166348i $$0.000529502\pi$$
−0.999999 + 0.00166348i $$0.999470\pi$$
$$228$$ −7.28134 + 1.99553i −0.482218 + 0.132157i
$$229$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$230$$ −13.0157 3.52506i −0.858228 0.232436i
$$231$$ −5.63102 + 18.6760i −0.370494 + 1.22879i
$$232$$ 1.35416i 0.0889050i
$$233$$ 15.1395 0.991818 0.495909 0.868374i $$-0.334835\pi$$
0.495909 + 0.868374i $$0.334835\pi$$
$$234$$ −5.50000 + 8.29156i −0.359546 + 0.542036i
$$235$$ −2.94987 + 10.8919i −0.192429 + 0.710509i
$$236$$ −9.90789 −0.644949
$$237$$ 7.75481 + 2.33816i 0.503729 + 0.151880i
$$238$$ 23.6332 1.53192
$$239$$ 6.36675i 0.411831i −0.978570 0.205915i $$-0.933983\pi$$
0.978570 0.205915i $$-0.0660172\pi$$
$$240$$ 3.28689 + 2.04851i 0.212168 + 0.132231i
$$241$$ 17.1075i 1.10199i −0.834509 0.550994i $$-0.814249\pi$$
0.834509 0.550994i $$-0.185751\pi$$
$$242$$ 5.63325i 0.362119i
$$243$$ 15.5000 1.65831i 0.994325 0.106381i
$$244$$ −4.31662 −0.276344
$$245$$ 9.72281 35.8997i 0.621167 2.29355i
$$246$$ 5.81610 + 1.75362i 0.370821 + 0.111807i
$$247$$ 7.68338 + 12.2461i 0.488881 + 0.779198i
$$248$$ 8.55373 0.543162
$$249$$ 4.86140 16.1235i 0.308079 1.02178i
$$250$$ −7.84169 7.96919i −0.495952 0.504016i
$$251$$ 1.58312i 0.0999259i −0.998751 0.0499629i $$-0.984090\pi$$
0.998751 0.0499629i $$-0.0159103\pi$$
$$252$$ 8.06173 12.1535i 0.507841 0.765599i
$$253$$ 13.9704i 0.878310i
$$254$$ 3.36675i 0.211249i
$$255$$ −15.9789 9.95862i −1.00064 0.623633i
$$256$$ 1.00000 0.0625000
$$257$$ 14.9499i 0.932548i −0.884640 0.466274i $$-0.845596\pi$$
0.884640 0.466274i $$-0.154404\pi$$
$$258$$ −0.584541 + 1.93870i −0.0363919 + 0.120698i
$$259$$ 9.72281i 0.604146i
$$260$$ 1.93870 7.15831i 0.120233 0.443940i
$$261$$ 3.38540 + 2.24562i 0.209551 + 0.139001i
$$262$$ −10.0000 −0.617802
$$263$$ −21.7838 −1.34325 −0.671623 0.740893i $$-0.734402\pi$$
−0.671623 + 0.740893i $$0.734402\pi$$
$$264$$ 1.15831 3.84169i 0.0712892 0.236440i
$$265$$ 2.15831 + 0.584541i 0.132584 + 0.0359080i
$$266$$ −11.2620 17.9499i −0.690521 1.10058i
$$267$$ 4.27686 14.1848i 0.261740 0.868093i
$$268$$ −7.00000 −0.427593
$$269$$ −14.3991 −0.877931 −0.438965 0.898504i $$-0.644655\pi$$
−0.438965 + 0.898504i $$0.644655\pi$$
$$270$$ −10.5720 + 4.82015i −0.643388 + 0.293345i
$$271$$ 9.31662 0.565945 0.282972 0.959128i $$-0.408680\pi$$
0.282972 + 0.959128i $$0.408680\pi$$
$$272$$ −4.86140 −0.294766
$$273$$ −26.7377 8.06173i −1.61824 0.487918i
$$274$$ 4.86140i 0.293688i
$$275$$ −5.84541 + 10.0000i −0.352491 + 0.603023i
$$276$$ 3.01524 10.0004i 0.181496 0.601955i
$$277$$ 12.0610i 0.724673i −0.932047 0.362337i $$-0.881979\pi$$
0.932047 0.362337i $$-0.118021\pi$$
$$278$$ 10.0000i 0.599760i
$$279$$ −14.1848 + 21.3843i −0.849219 + 1.28025i
$$280$$ −2.84169 + 10.4924i −0.169823 + 0.627043i
$$281$$ 13.6002 0.811321 0.405660 0.914024i $$-0.367042\pi$$
0.405660 + 0.914024i $$0.367042\pi$$
$$282$$ −8.36865 2.52324i −0.498346 0.150257i
$$283$$ 15.1395i 0.899947i −0.893042 0.449974i $$-0.851433\pi$$
0.893042 0.449974i $$-0.148567\pi$$
$$284$$ −10.8919 −0.646315
$$285$$ 0.0507319 + 16.8819i 0.00300510 + 0.999995i
$$286$$ −7.68338 −0.454328
$$287$$ 17.0501i 1.00644i
$$288$$ −1.65831 + 2.50000i −0.0977170 + 0.147314i
$$289$$ 6.63325 0.390191
$$290$$ −2.92270 0.791562i −0.171627 0.0464821i
$$291$$ 8.31662 27.5831i 0.487529 1.61695i
$$292$$ 11.0770i 0.648231i
$$293$$ 8.26650i 0.482934i 0.970409 + 0.241467i $$0.0776286\pi$$
−0.970409 + 0.241467i $$0.922371\pi$$
$$294$$ 27.5831 + 8.31662i 1.60868 + 0.485035i
$$295$$ −5.79156 + 21.3843i −0.337198 + 1.24504i
$$296$$ 2.00000i 0.116248i
$$297$$ 7.68338 + 9.26650i 0.445835 + 0.537697i
$$298$$ 4.00000 0.231714
$$299$$ −20.0009 −1.15668
$$300$$ 6.34264 5.89669i 0.366192 0.340446i
$$301$$ −5.68338 −0.327584
$$302$$ −2.70832 −0.155846
$$303$$ −12.7414 3.84169i −0.731976 0.220699i
$$304$$ 2.31662 + 3.69232i 0.132868 + 0.211769i
$$305$$ −2.52324 + 9.31662i −0.144480 + 0.533468i
$$306$$ 8.06173 12.1535i 0.460858 0.694770i
$$307$$ 2.00000 0.114146 0.0570730 0.998370i $$-0.481823\pi$$
0.0570730 + 0.998370i $$0.481823\pi$$
$$308$$ 11.2620 0.641715
$$309$$ −7.79156 + 25.8417i −0.443246 + 1.47008i
$$310$$ 5.00000 18.4616i 0.283981 1.04855i
$$311$$ 18.8997i 1.07171i 0.844311 + 0.535853i $$0.180010\pi$$
−0.844311 + 0.535853i $$0.819990\pi$$
$$312$$ 5.50000 + 1.65831i 0.311376 + 0.0938835i
$$313$$ 28.5546i 1.61400i 0.590551 + 0.807000i $$0.298910\pi$$
−0.590551 + 0.807000i $$0.701090\pi$$
$$314$$ 2.33816 0.131950
$$315$$ −21.5187 24.5039i −1.21244 1.38064i
$$316$$ 4.67632i 0.263064i
$$317$$ 17.0000i 0.954815i 0.878682 + 0.477408i $$0.158423\pi$$
−0.878682 + 0.477408i $$0.841577\pi$$
$$318$$ −0.500000 + 1.65831i −0.0280386 + 0.0929935i
$$319$$ 3.13708i 0.175643i
$$320$$ 0.584541 2.15831i 0.0326768 0.120653i
$$321$$ −33.0831 9.97494i −1.84652 0.556747i
$$322$$ 29.3166 1.63375
$$323$$ −11.2620 17.9499i −0.626637 0.998758i
$$324$$ −3.50000 8.29156i −0.194444 0.460642i
$$325$$ −14.3166 8.36865i −0.794143 0.464209i
$$326$$ 15.9384 0.882745
$$327$$ 28.6764 + 8.64627i 1.58581 + 0.478140i
$$328$$ 3.50724i 0.193655i
$$329$$ 24.5330i 1.35255i
$$330$$ −7.61448 4.74562i −0.419163 0.261238i
$$331$$ 15.7533i 0.865879i 0.901423 + 0.432940i $$0.142524\pi$$
−0.901423 + 0.432940i $$0.857476\pi$$
$$332$$ −9.72281 −0.533608
$$333$$ −5.00000 3.31662i −0.273998 0.181750i
$$334$$ 5.05013 0.276331
$$335$$ −4.09178 + 15.1082i −0.223558 + 0.825448i
$$336$$ −8.06173 2.43070i −0.439803 0.132606i
$$337$$ 18.2164 0.992309 0.496155 0.868234i $$-0.334745\pi$$
0.496155 + 0.868234i $$0.334745\pi$$
$$338$$ 2.00000i 0.108786i
$$339$$ −13.7916 4.15831i −0.749055 0.225849i
$$340$$ −2.84169 + 10.4924i −0.154112 + 0.569032i
$$341$$ −19.8158 −1.07308
$$342$$ −13.0725 0.331463i −0.706880 0.0179235i
$$343$$ 46.8311i 2.52864i
$$344$$ 1.16908 0.0630326
$$345$$ −19.8215 12.3535i −1.06715 0.665090i
$$346$$ 13.2665 0.713211
$$347$$ 24.8623 1.33468 0.667338 0.744755i $$-0.267434\pi$$
0.667338 + 0.744755i $$0.267434\pi$$
$$348$$ 0.677081 2.24562i 0.0362953 0.120378i
$$349$$ −4.63325 −0.248012 −0.124006 0.992281i $$-0.539574\pi$$
−0.124006 + 0.992281i $$0.539574\pi$$
$$350$$ 20.9849 + 12.2665i 1.12169 + 0.655672i
$$351$$ −13.2665 + 11.0000i −0.708113 + 0.587137i
$$352$$ −2.31662 −0.123477
$$353$$ −20.0009 −1.06454 −0.532269 0.846575i $$-0.678661\pi$$
−0.532269 + 0.846575i $$0.678661\pi$$
$$354$$ −16.4304 4.95394i −0.873265 0.263299i
$$355$$ −6.36675 + 23.5081i −0.337912 + 1.24768i
$$356$$ −8.55373 −0.453347
$$357$$ 39.1913 + 11.8166i 2.07422 + 0.625402i
$$358$$ 2.70832i 0.143139i
$$359$$ 34.8997i 1.84194i −0.389636 0.920969i $$-0.627399\pi$$
0.389636 0.920969i $$-0.372601\pi$$
$$360$$ 4.42643 + 5.04051i 0.233293 + 0.265658i
$$361$$ −8.26650 + 17.1075i −0.435079 + 0.900392i
$$362$$ 2.70832 0.142346
$$363$$ 2.81662 9.34169i 0.147834 0.490311i
$$364$$ 16.1235i 0.845099i
$$365$$ 23.9076 + 6.47494i 1.25138 + 0.338914i
$$366$$ −7.15831 2.15831i −0.374171 0.112817i
$$367$$ 2.33816i 0.122051i 0.998136 + 0.0610255i $$0.0194371\pi$$
−0.998136 + 0.0610255i $$0.980563\pi$$
$$368$$ −6.03049 −0.314361
$$369$$ 8.76811 + 5.81610i 0.456449 + 0.302774i
$$370$$ 4.31662 + 1.16908i 0.224411 + 0.0607776i
$$371$$ −4.86140 −0.252392
$$372$$ 14.1848 + 4.27686i 0.735445 + 0.221745i
$$373$$ −16.6834 −0.863832 −0.431916 0.901914i $$-0.642162\pi$$
−0.431916 + 0.901914i $$0.642162\pi$$
$$374$$ 11.2620 0.582347
$$375$$ −9.01937 17.1362i −0.465758 0.884912i
$$376$$ 5.04648i 0.260253i
$$377$$ −4.49124 −0.231311
$$378$$ 19.4456 16.1235i 1.00017 0.829301i
$$379$$ 22.7678i 1.16950i −0.811213 0.584751i $$-0.801192\pi$$
0.811213 0.584751i $$-0.198808\pi$$
$$380$$ 9.32335 2.84169i 0.478278 0.145775i
$$381$$ −1.68338 + 5.58312i −0.0862419 + 0.286032i
$$382$$ −5.00000 −0.255822
$$383$$ 25.5831i 1.30724i 0.756824 + 0.653618i $$0.226750\pi$$
−0.756824 + 0.653618i $$0.773250\pi$$
$$384$$ 1.65831 + 0.500000i 0.0846254 + 0.0255155i
$$385$$ 6.58312 24.3070i 0.335507 1.23880i
$$386$$ 6.00000i 0.305392i
$$387$$ −1.93870 + 2.92270i −0.0985497 + 0.148569i
$$388$$ −16.6332 −0.844425
$$389$$ 30.2164i 1.53203i 0.642822 + 0.766015i $$0.277763\pi$$
−0.642822 + 0.766015i $$0.722237\pi$$
$$390$$ 6.79413 10.9014i 0.344034 0.552012i
$$391$$ 29.3166 1.48261
$$392$$ 16.6332i 0.840106i
$$393$$ −16.5831 5.00000i −0.836508 0.252217i
$$394$$ 6.21557i 0.313136i
$$395$$ −10.0930 2.73350i −0.507832 0.137537i
$$396$$ 3.84169 5.79156i 0.193052 0.291037i
$$397$$ 16.7373i 0.840021i 0.907519 + 0.420010i $$0.137974\pi$$
−0.907519 + 0.420010i $$0.862026\pi$$
$$398$$ 21.2164i 1.06348i
$$399$$ −9.70106 35.3975i −0.485660 1.77209i
$$400$$ −4.31662 2.52324i −0.215831 0.126162i
$$401$$ −8.92389 −0.445638 −0.222819 0.974860i $$-0.571526\pi$$
−0.222819 + 0.974860i $$0.571526\pi$$
$$402$$ −11.6082 3.50000i −0.578964 0.174564i
$$403$$ 28.3695i 1.41319i
$$404$$ 7.68338i 0.382262i
$$405$$ −19.9417 + 2.70734i −0.990910 + 0.134529i
$$406$$ 6.58312 0.326715
$$407$$ 4.63325i 0.229662i
$$408$$ −8.06173 2.43070i −0.399115 0.120338i
$$409$$ 1.16908i 0.0578073i −0.999582 0.0289037i $$-0.990798\pi$$
0.999582 0.0289037i $$-0.00920160\pi$$
$$410$$ −7.56973 2.05013i −0.373842 0.101248i
$$411$$ −2.43070 + 8.06173i −0.119898 + 0.397656i
$$412$$ 15.5831 0.767725
$$413$$ 48.1662i 2.37011i
$$414$$ 10.0004 15.0762i 0.491494 0.740955i
$$415$$ −5.68338 + 20.9849i −0.278986 + 1.03011i
$$416$$ 3.31662i 0.162611i
$$417$$ −5.00000 + 16.5831i −0.244851 + 0.812079i
$$418$$ −5.36675 8.55373i −0.262496 0.418376i
$$419$$ 22.9499i 1.12117i −0.828095 0.560587i $$-0.810575\pi$$
0.828095 0.560587i $$-0.189425\pi$$
$$420$$ −9.95862 + 15.9789i −0.485931 + 0.779690i
$$421$$ 24.3070i 1.18465i −0.805699 0.592326i $$-0.798210\pi$$
0.805699 0.592326i $$-0.201790\pi$$
$$422$$ 18.4616 0.898697
$$423$$ −12.6162 8.36865i −0.613421 0.406898i
$$424$$ 1.00000 0.0485643
$$425$$ 20.9849 + 12.2665i 1.01792 + 0.595013i
$$426$$ −18.0622 5.44594i −0.875114 0.263857i
$$427$$ 20.9849i 1.01553i
$$428$$ 19.9499i 0.964314i
$$429$$ −12.7414 3.84169i −0.615162 0.185478i
$$430$$ 0.683375 2.52324i 0.0329553 0.121682i
$$431$$ 33.4160 1.60959 0.804796 0.593552i $$-0.202275\pi$$
0.804796 + 0.593552i $$0.202275\pi$$
$$432$$ −4.00000 + 3.31662i −0.192450 + 0.159571i
$$433$$ 8.31662 0.399671 0.199836 0.979829i $$-0.435959\pi$$
0.199836 + 0.979829i $$0.435959\pi$$
$$434$$ 41.5831i 1.99605i
$$435$$ −4.45097 2.77401i −0.213408 0.133004i
$$436$$ 17.2925i 0.828162i
$$437$$ −13.9704 22.2665i −0.668293 1.06515i
$$438$$ −5.53848 + 18.3691i −0.264639 + 0.877708i
$$439$$ 1.16908i 0.0557972i −0.999611 0.0278986i $$-0.991118\pi$$
0.999611 0.0278986i $$-0.00888155\pi$$
$$440$$ −1.35416 + 5.00000i −0.0645571 + 0.238366i
$$441$$ 41.5831 + 27.5831i 1.98015 + 1.31348i
$$442$$ 16.1235i 0.766914i
$$443$$ 3.87740 0.184221 0.0921105 0.995749i $$-0.470639\pi$$
0.0921105 + 0.995749i $$0.470639\pi$$
$$444$$ −1.00000 + 3.31662i −0.0474579 + 0.157400i
$$445$$ −5.00000 + 18.4616i −0.237023 + 0.875164i
$$446$$ 23.2665i 1.10170i
$$447$$ 6.63325 + 2.00000i 0.313742 + 0.0945968i
$$448$$ 4.86140i 0.229680i
$$449$$ 31.5066 1.48689 0.743444 0.668798i $$-0.233191\pi$$
0.743444 + 0.668798i $$0.233191\pi$$
$$450$$ 13.4664 6.60724i 0.634813 0.311468i
$$451$$ 8.12497i 0.382590i
$$452$$ 8.31662i 0.391181i
$$453$$ −4.49124 1.35416i −0.211017 0.0636240i
$$454$$ 0.0501256 0.00235251
$$455$$ 34.7994 + 9.42481i 1.63142 + 0.441842i
$$456$$ 1.99553 + 7.28134i 0.0934491 + 0.340980i
$$457$$ 18.8318i 0.880913i −0.897774 0.440457i $$-0.854817\pi$$
0.897774 0.440457i $$-0.145183\pi$$
$$458$$ 0 0
$$459$$ 19.4456 16.1235i 0.907644 0.752578i
$$460$$ −3.52506 + 13.0157i −0.164357 + 0.606859i
$$461$$ 11.5831i 0.539480i −0.962933 0.269740i $$-0.913062\pi$$
0.962933 0.269740i $$-0.0869377\pi$$
$$462$$ 18.6760 + 5.63102i 0.868886 + 0.261979i
$$463$$ 4.67632i 0.217327i 0.994079 + 0.108664i $$0.0346571\pi$$
−0.994079 + 0.108664i $$0.965343\pi$$
$$464$$ −1.35416 −0.0628653
$$465$$ 17.5224 28.1151i 0.812580 1.30381i
$$466$$ 15.1395i 0.701322i
$$467$$ 8.18357 0.378690 0.189345 0.981911i $$-0.439363\pi$$
0.189345 + 0.981911i $$0.439363\pi$$
$$468$$ 8.29156 + 5.50000i 0.383278 + 0.254238i
$$469$$ 34.0298i 1.57135i
$$470$$ 10.8919 + 2.94987i 0.502405 + 0.136068i
$$471$$ 3.87740 + 1.16908i 0.178661 + 0.0538684i
$$472$$ 9.90789i 0.456048i
$$473$$ −2.70832 −0.124529
$$474$$ 2.33816 7.75481i 0.107395 0.356190i
$$475$$ −0.683375 21.7838i −0.0313554 0.999508i
$$476$$ 23.6332i 1.08323i
$$477$$ −1.65831 + 2.50000i −0.0759289 + 0.114467i
$$478$$ −6.36675 −0.291208
$$479$$ 14.0000i 0.639676i 0.947472 + 0.319838i $$0.103629\pi$$
−0.947472 + 0.319838i $$0.896371\pi$$
$$480$$ 2.04851 3.28689i 0.0935011 0.150025i
$$481$$ 6.63325 0.302450
$$482$$ −17.1075 −0.779223
$$483$$ 48.6161 + 14.6583i 2.21211 + 0.666976i
$$484$$ −5.63325 −0.256057
$$485$$ −9.72281 + 35.8997i −0.441490 + 1.63012i
$$486$$ −1.65831 15.5000i −0.0752226 0.703094i
$$487$$ −16.5330 −0.749182 −0.374591 0.927190i $$-0.622217\pi$$
−0.374591 + 0.927190i $$0.622217\pi$$
$$488$$ 4.31662i 0.195404i
$$489$$ 26.4308 + 7.96919i 1.19524 + 0.360379i
$$490$$ −35.8997 9.72281i −1.62179 0.439232i
$$491$$ 41.5831i 1.87662i 0.345795 + 0.938310i $$0.387609\pi$$
−0.345795 + 0.938310i $$0.612391\pi$$
$$492$$ 1.75362 5.81610i 0.0790594 0.262210i
$$493$$ 6.58312 0.296489
$$494$$ 12.2461 7.68338i 0.550976 0.345691i
$$495$$ −10.2544 11.6770i −0.460900 0.524841i
$$496$$ 8.55373i 0.384074i
$$497$$ 52.9499i 2.37513i
$$498$$ −16.1235 4.86140i −0.722509 0.217845i
$$499$$ 41.5831 1.86152 0.930758 0.365635i $$-0.119148\pi$$
0.930758 + 0.365635i $$0.119148\pi$$
$$500$$ −7.96919 + 7.84169i −0.356393 + 0.350691i
$$501$$ 8.37469 + 2.52506i 0.374153 + 0.112811i
$$502$$ −1.58312 −0.0706583
$$503$$ 13.7853 0.614656 0.307328 0.951604i $$-0.400565\pi$$
0.307328 + 0.951604i $$0.400565\pi$$
$$504$$ −12.1535 8.06173i −0.541360 0.359098i
$$505$$ 16.5831 + 4.49124i 0.737939 + 0.199858i
$$506$$ 13.9704 0.621059
$$507$$ −1.00000 + 3.31662i −0.0444116 + 0.147296i
$$508$$ 3.36675 0.149375
$$509$$ −17.1075 −0.758275 −0.379137 0.925340i $$-0.623779\pi$$
−0.379137 + 0.925340i $$0.623779\pi$$
$$510$$ −9.95862 + 15.9789i −0.440975 + 0.707557i
$$511$$ −53.8496 −2.38217
$$512$$ 1.00000i 0.0441942i
$$513$$ −21.5125 7.08592i −0.949802 0.312851i
$$514$$ −14.9499 −0.659411
$$515$$ 9.10897 33.6332i 0.401389 1.48206i
$$516$$ 1.93870 + 0.584541i 0.0853466 + 0.0257330i
$$517$$ 11.6908i 0.514161i
$$518$$ −9.72281 −0.427196
$$519$$ 22.0000 + 6.63325i 0.965693 + 0.291167i
$$520$$ −7.15831 1.93870i −0.313913 0.0850177i
$$521$$ 41.9697 1.83873 0.919363 0.393410i $$-0.128705\pi$$
0.919363 + 0.393410i $$0.128705\pi$$
$$522$$ 2.24562 3.38540i 0.0982882 0.148175i
$$523$$ −29.0000 −1.26808 −0.634041 0.773300i $$-0.718605\pi$$
−0.634041 + 0.773300i $$0.718605\pi$$
$$524$$ 10.0000i 0.436852i
$$525$$ 28.6662 + 30.8341i 1.25110 + 1.34571i
$$526$$ 21.7838i 0.949818i
$$527$$ 41.5831i 1.81139i
$$528$$ −3.84169 1.15831i −0.167188 0.0504091i
$$529$$ 13.3668 0.581163
$$530$$ 0.584541 2.15831i 0.0253908 0.0937511i
$$531$$ −24.7697 16.4304i −1.07491 0.713017i
$$532$$ −17.9499 + 11.2620i −0.778226 + 0.488272i
$$533$$ −11.6322 −0.503847
$$534$$ −14.1848 4.27686i −0.613834 0.185078i
$$535$$ 43.0581 + 11.6615i 1.86156 + 0.504171i
$$536$$ 7.00000i 0.302354i
$$537$$ 1.35416 4.49124i 0.0584364 0.193811i
$$538$$ 14.3991i 0.620791i
$$539$$ 38.5330i 1.65973i
$$540$$ 4.82015 + 10.5720i 0.207426 + 0.454944i
$$541$$ −28.8496 −1.24034 −0.620171 0.784467i $$-0.712937\pi$$
−0.620171 + 0.784467i $$0.712937\pi$$
$$542$$ 9.31662i 0.400183i
$$543$$ 4.49124 + 1.35416i 0.192738 + 0.0581126i
$$544$$ 4.86140i 0.208431i
$$545$$ −37.3227 10.1082i −1.59873 0.432987i
$$546$$ −8.06173 + 26.7377i −0.345010 + 1.14427i
$$547$$ 12.0000 0.513083 0.256541 0.966533i $$-0.417417\pi$$
0.256541 + 0.966533i $$0.417417\pi$$
$$548$$ 4.86140 0.207669
$$549$$ −10.7916 7.15831i −0.460573 0.305509i
$$550$$ 10.0000 + 5.84541i 0.426401 + 0.249249i
$$551$$ −3.13708 5.00000i −0.133644 0.213007i
$$552$$ −10.0004 3.01524i −0.425646 0.128337i
$$553$$ 22.7335 0.966727
$$554$$ −12.0610 −0.512422
$$555$$ 6.57377 + 4.09701i 0.279041 + 0.173909i
$$556$$ 10.0000 0.424094
$$557$$ −34.5851 −1.46542 −0.732708 0.680543i $$-0.761744\pi$$
−0.732708 + 0.680543i $$0.761744\pi$$
$$558$$ 21.3843 + 14.1848i 0.905270 + 0.600488i
$$559$$ 3.87740i 0.163997i
$$560$$ 10.4924 + 2.84169i 0.443386 + 0.120083i
$$561$$ 18.6760 + 5.63102i 0.788501 + 0.237742i
$$562$$ 13.6002i 0.573690i
$$563$$ 9.89975i 0.417225i −0.977998 0.208612i $$-0.933105\pi$$
0.977998 0.208612i $$-0.0668947\pi$$
$$564$$ −2.52324 + 8.36865i −0.106248 + 0.352384i
$$565$$ 17.9499 + 4.86140i 0.755157 + 0.204521i
$$566$$ −15.1395 −0.636359
$$567$$ 40.3086 17.0149i 1.69280 0.714559i
$$568$$ 10.8919i 0.457014i
$$569$$ −17.1075 −0.717182 −0.358591 0.933495i $$-0.616743\pi$$
−0.358591 + 0.933495i $$0.616743\pi$$
$$570$$ 16.8819 0.0507319i 0.707104 0.00212493i
$$571$$ −25.6834 −1.07482 −0.537408 0.843322i $$-0.680596\pi$$
−0.537408 + 0.843322i $$0.680596\pi$$
$$572$$ 7.68338i 0.321258i
$$573$$ −8.29156 2.50000i −0.346385 0.104439i
$$574$$ 17.0501 0.711658
$$575$$ 26.0313 + 15.2164i 1.08558 + 0.634567i
$$576$$ 2.50000 + 1.65831i 0.104167 + 0.0690963i
$$577$$ 6.40065i 0.266462i 0.991085 + 0.133231i $$0.0425353\pi$$
−0.991085 + 0.133231i $$0.957465\pi$$
$$578$$ 6.63325i 0.275907i
$$579$$ 3.00000 9.94987i 0.124676 0.413503i
$$580$$ −0.791562 + 2.92270i −0.0328678 + 0.121359i
$$581$$ 47.2665i 1.96094i
$$582$$ −27.5831 8.31662i −1.14336 0.344735i
$$583$$ −2.31662 −0.0959448
$$584$$ 11.0770 0.458368
$$585$$ 16.7175 14.6808i 0.691182 0.606977i
$$586$$ 8.26650 0.341486
$$587$$ −26.0313 −1.07443 −0.537214 0.843446i $$-0.680523\pi$$
−0.537214 + 0.843446i $$0.680523\pi$$
$$588$$ 8.31662 27.5831i 0.342972 1.13751i
$$589$$ 31.5831 19.8158i 1.30136 0.816495i
$$590$$ 21.3843 + 5.79156i 0.880378 + 0.238435i
$$591$$ −3.10778 + 10.3073i −0.127837 + 0.423988i
$$592$$ 2.00000 0.0821995
$$593$$ −21.7838 −0.894553 −0.447276 0.894396i $$-0.647606\pi$$
−0.447276 + 0.894396i $$0.647606\pi$$
$$594$$ 9.26650 7.68338i 0.380209 0.315253i
$$595$$ −51.0079 13.8146i −2.09112 0.566343i
$$596$$ 4.00000i 0.163846i
$$597$$ 10.6082 35.1834i 0.434164 1.43996i
$$598$$ 20.0009i 0.817896i
$$599$$ 48.1853 1.96880 0.984399 0.175953i $$-0.0563007\pi$$
0.984399 + 0.175953i $$0.0563007\pi$$
$$600$$ −5.89669 6.34264i −0.240731 0.258937i
$$601$$ 22.9529i 0.936267i 0.883658 + 0.468133i $$0.155073\pi$$
−0.883658 + 0.468133i $$0.844927\pi$$
$$602$$ 5.68338i 0.231637i
$$603$$ −17.5000 11.6082i −0.712655 0.472722i
$$604$$ 2.70832i 0.110200i
$$605$$ −3.29286 + 12.1583i −0.133874 + 0.494306i
$$606$$ −3.84169 + 12.7414i −0.156058 + 0.517585i
$$607$$ −23.3668 −0.948427 −0.474214 0.880410i $$-0.657268\pi$$
−0.474214 + 0.880410i $$0.657268\pi$$
$$608$$ 3.69232 2.31662i 0.149743 0.0939515i
$$609$$ 10.9169 + 3.29156i 0.442374 + 0.133381i
$$610$$ 9.31662 + 2.52324i 0.377219 + 0.102163i
$$611$$ 16.7373 0.677118
$$612$$ −12.1535 8.06173i −0.491277 0.325876i
$$613$$ 13.2301i 0.534357i 0.963647 + 0.267178i $$0.0860913\pi$$
−0.963647 + 0.267178i $$0.913909\pi$$
$$614$$ 2.00000i 0.0807134i
$$615$$ −11.5279 7.18461i −0.464850 0.289712i
$$616$$ 11.2620i 0.453761i
$$617$$ −17.4776 −0.703622 −0.351811 0.936071i $$-0.614434\pi$$
−0.351811 + 0.936071i $$0.614434\pi$$
$$618$$ 25.8417 + 7.79156i 1.03951 + 0.313423i
$$619$$ −31.5831 −1.26943 −0.634716 0.772745i $$-0.718883\pi$$
−0.634716 + 0.772745i $$0.718883\pi$$
$$620$$ −18.4616 5.00000i −0.741436 0.200805i
$$621$$ 24.1219 20.0009i 0.967980 0.802607i
$$622$$ 18.8997 0.757811
$$623$$ 41.5831i 1.66599i
$$624$$ 1.65831 5.50000i 0.0663856 0.220176i
$$625$$ 12.2665 + 21.7838i 0.490660 + 0.871351i
$$626$$ 28.5546 1.14127
$$627$$ −4.62289 16.8681i −0.184620 0.673648i
$$628$$ 2.33816i 0.0933028i
$$629$$ −9.72281 −0.387674
$$630$$ −24.5039 + 21.5187i −0.976260 + 0.857324i
$$631$$ 15.8997 0.632959 0.316480 0.948599i $$-0.397499\pi$$
0.316480 + 0.948599i $$0.397499\pi$$
$$632$$ −4.67632 −0.186014
$$633$$ 30.6151 + 9.23081i 1.21684 + 0.366892i
$$634$$ 17.0000 0.675156
$$635$$ 1.96800 7.26650i 0.0780978 0.288362i
$$636$$ 1.65831 + 0.500000i 0.0657564 + 0.0198263i
$$637$$ −55.1662 −2.18577
$$638$$ 3.13708 0.124198
$$639$$ −27.2297 18.0622i −1.07719 0.714528i
$$640$$ −2.15831 0.584541i −0.0853148 0.0231060i
$$641$$ −23.3230 −0.921204 −0.460602 0.887607i $$-0.652366\pi$$
−0.460602 + 0.887607i $$0.652366\pi$$
$$642$$ −9.97494 + 33.0831i −0.393679 + 1.30569i
$$643$$ 46.6460i 1.83954i −0.392458 0.919770i $$-0.628375\pi$$
0.392458 0.919770i $$-0.371625\pi$$
$$644$$ 29.3166i 1.15524i
$$645$$ 2.39487 3.84264i 0.0942979 0.151304i
$$646$$ −17.9499 + 11.2620i −0.706228 + 0.443099i
$$647$$ 3.69232 0.145160 0.0725801 0.997363i $$-0.476877\pi$$
0.0725801 + 0.997363i $$0.476877\pi$$
$$648$$ −8.29156 + 3.50000i −0.325723 + 0.137493i
$$649$$ 22.9529i 0.900979i
$$650$$ −8.36865 + 14.3166i −0.328245 + 0.561544i
$$651$$ −20.7916 + 68.9578i −0.814886 + 2.70267i
$$652$$ 15.9384i 0.624195i
$$653$$ 26.8303 1.04995 0.524975 0.851118i $$-0.324075\pi$$
0.524975 + 0.851118i $$0.324075\pi$$
$$654$$ 8.64627 28.6764i 0.338096 1.12134i
$$655$$ 21.5831 + 5.84541i 0.843322 + 0.228399i
$$656$$ −3.50724 −0.136935
$$657$$ −18.3691 + 27.6924i −0.716646 + 1.08038i
$$658$$ −24.5330 −0.956396
$$659$$ −12.6162 −0.491458 −0.245729 0.969339i $$-0.579027\pi$$
−0.245729 + 0.969339i $$0.579027\pi$$
$$660$$ −4.74562 + 7.61448i −0.184723 + 0.296393i
$$661$$ 21.5987i 0.840092i 0.907503 + 0.420046i $$0.137986\pi$$
−0.907503 + 0.420046i $$0.862014\pi$$
$$662$$ 15.7533 0.612269
$$663$$ −8.06173 + 26.7377i −0.313092 + 1.03841i
$$664$$ 9.72281i 0.377318i
$$665$$ 13.8146 + 45.3246i 0.535707 + 1.75761i
$$666$$ −3.31662 + 5.00000i −0.128517 + 0.193746i
$$667$$ 8.16625 0.316198
$$668$$ 5.05013i 0.195395i
$$669$$ −11.6332 + 38.5831i −0.449767 + 1.49171i
$$670$$ 15.1082 + 4.09178i 0.583680 + 0.158079i
$$671$$ 10.0000i 0.386046i
$$672$$ −2.43070 + 8.06173i −0.0937664 + 0.310988i
$$673$$ −13.2665 −0.511386 −0.255693 0.966758i $$-0.582304\pi$$
−0.255693 + 0.966758i $$0.582304\pi$$
$$674$$ 18.2164i 0.701668i
$$675$$ 25.6351 4.22366i 0.986697 0.162569i
$$676$$ 2.00000 0.0769231
$$677$$ 20.1662i 0.775052i 0.921859 + 0.387526i $$0.126670\pi$$
−0.921859 + 0.387526i $$0.873330\pi$$
$$678$$ −4.15831 + 13.7916i −0.159699 + 0.529662i
$$679$$ 80.8609i 3.10316i
$$680$$ 10.4924 + 2.84169i 0.402366 + 0.108974i
$$681$$ 0.0831240 + 0.0250628i 0.00318532 + 0.000960409i
$$682$$ 19.8158i 0.758785i
$$683$$ 24.0000i 0.918334i 0.888350 + 0.459167i $$0.151852\pi$$
−0.888350 + 0.459167i $$0.848148\pi$$
$$684$$ −0.331463 + 13.0725i −0.0126738 + 0.499839i
$$685$$ 2.84169 10.4924i 0.108575 0.400895i
$$686$$ 46.8311 1.78802
$$687$$ 0 0
$$688$$ 1.16908i 0.0445708i
$$689$$ 3.31662i 0.126353i
$$690$$ −12.3535 + 19.8215i −0.470289 + 0.754592i
$$691$$ 25.8997 0.985273 0.492636 0.870235i $$-0.336033\pi$$
0.492636 + 0.870235i $$0.336033\pi$$
$$692$$ 13.2665i 0.504317i
$$693$$ 28.1551 + 18.6760i 1.06952 + 0.709442i
$$694$$ 24.8623i 0.943758i
$$695$$ 5.84541 21.5831i 0.221729 0.818695i
$$696$$ −2.24562 0.677081i −0.0851201 0.0256647i
$$697$$ 17.0501 0.645820
$$698$$ 4.63325i 0.175371i
$$699$$ 7.56973 25.1059i 0.286313 0.949594i
$$700$$ 12.2665 20.9849i 0.463630 0.793153i
$$701$$ 10.7335i 0.405399i −0.979241 0.202699i $$-0.935029\pi$$
0.979241 0.202699i $$-0.0649714\pi$$
$$702$$ 11.0000 + 13.2665i 0.415168 + 0.500712i
$$703$$ 4.63325 + 7.38465i 0.174746 + 0.278517i
$$704$$ 2.31662i 0.0873111i
$$705$$ 16.5872 + 10.3378i 0.624711 + 0.389342i
$$706$$ 20.0009i 0.752742i
$$707$$ −37.3520 −1.40477
$$708$$ −4.95394 + 16.4304i −0.186181 + 0.617491i
$$709$$ 15.3668 0.577110 0.288555 0.957463i $$-0.406825\pi$$
0.288555 + 0.957463i $$0.406825\pi$$
$$710$$ 23.5081 + 6.36675i 0.882243 + 0.238940i
$$711$$ 7.75481 11.6908i 0.290828 0.438440i
$$712$$ 8.55373i 0.320564i
$$713$$ 51.5831i 1.93180i
$$714$$ 11.8166 39.1913i 0.442226 1.46670i
$$715$$ 16.5831 + 4.49124i 0.620174 + 0.167963i
$$716$$ −2.70832 −0.101215
$$717$$ −10.5581 3.18338i −0.394298 0.118885i
$$718$$ −34.8997 −1.30245
$$719$$ 4.89975i 0.182730i −0.995817 0.0913649i $$-0.970877\pi$$
0.995817 0.0913649i $$-0.0291230\pi$$
$$720$$ 5.04051 4.42643i 0.187849 0.164963i
$$721$$ 75.7559i 2.82130i
$$722$$ 17.1075 + 8.26650i 0.636674 + 0.307647i
$$723$$ −28.3695 8.55373i −1.05507 0.318117i
$$724$$ 2.70832i 0.100654i
$$725$$ 5.84541 + 3.41688i 0.217093 + 0.126900i
$$726$$ −9.34169 2.81662i −0.346703 0.104535i
$$727$$ 7.56973i 0.280746i −0.990099 0.140373i $$-0.955170\pi$$
0.990099 0.140373i $$-0.0448301\pi$$
$$728$$ 16.1235 0.597575
$$729$$ 5.00000 26.5330i 0.185185 0.982704i
$$730$$ 6.47494 23.9076i 0.239648 0.884858i
$$731$$ 5.68338i 0.210207i
$$732$$ −2.15831 + 7.15831i −0.0797735 + 0.264579i
$$733$$ 9.72281i 0.359120i −0.983747 0.179560i $$-0.942533\pi$$
0.983747 0.179560i $$-0.0574674\pi$$
$$734$$ 2.33816 0.0863031
$$735$$ −54.6716 34.0733i −2.01659 1.25681i
$$736$$ 6.03049i 0.222287i
$$737$$ 16.2164i 0.597338i
$$738$$ 5.81610 8.76811i 0.214094 0.322759i
$$739$$ 36.2164 1.33224 0.666120 0.745844i $$-0.267954\pi$$
0.666120 + 0.745844i $$0.267954\pi$$
$$740$$ 1.16908 4.31662i 0.0429763 0.158682i
$$741$$ 24.1495 6.61841i 0.887153 0.243133i
$$742$$ 4.86140i 0.178468i
$$743$$ 14.8496i 0.544780i 0.962187 + 0.272390i $$0.0878141\pi$$
−0.962187 + 0.272390i $$0.912186\pi$$
$$744$$ 4.27686 14.1848i 0.156797 0.520038i
$$745$$ −8.63325 2.33816i −0.316298 0.0856636i
$$746$$ 16.6834i 0.610822i
$$747$$ −24.3070 16.1235i −0.889347 0.589926i
$$748$$ 11.2620i 0.411781i
$$749$$ −96.9844 −3.54373
$$750$$ −17.1362 + 9.01937i −0.625727 + 0.329341i
$$751$$ 22.9529i 0.837562i 0.908087 + 0.418781i $$0.137542\pi$$
−0.908087 + 0.418781i $$0.862458\pi$$
$$752$$ 5.04648 0.184026
$$753$$ −2.62531 0.791562i −0.0956718 0.0288461i
$$754$$ 4.49124i 0.163561i
$$755$$ 5.84541 + 1.58312i 0.212736 + 0.0576158i
$$756$$ −16.1235 19.4456i −0.586404 0.707230i
$$757$$ 19.4456i 0.706763i 0.935479 + 0.353381i $$0.114968\pi$$
−0.935479 + 0.353381i $$0.885032\pi$$
$$758$$ −22.7678 −0.826963
$$759$$ 23.1672 + 6.98519i 0.840918 + 0.253546i
$$760$$ −2.84169 9.32335i −0.103079 0.338193i
$$761$$ 17.3166i 0.627727i −0.949468 0.313864i $$-0.898377\pi$$
0.949468 0.313864i $$-0.101623\pi$$
$$762$$ 5.58312 + 1.68338i 0.202255 + 0.0609822i
$$763$$ 84.0660 3.04339
$$764$$ 5.00000i 0.180894i
$$765$$ −24.5039 + 21.5187i −0.885942 + 0.778009i
$$766$$ 25.5831 0.924356
$$767$$ 32.8607 1.18653
$$768$$ 0.500000 1.65831i 0.0180422 0.0598392i
$$769$$ 18.1662 0.655092 0.327546 0.944835i $$-0.393778\pi$$
0.327546 + 0.944835i $$0.393778\pi$$
$$770$$ −24.3070 6.58312i −0.875964 0.237239i
$$771$$ −24.7916 7.47494i −0.892846 0.269203i
$$772$$ −6.00000 −0.215945
$$773$$ 42.1662i 1.51661i 0.651897 + 0.758307i $$0.273973\pi$$
−0.651897 + 0.758307i $$0.726027\pi$$
$$774$$ 2.92270 + 1.93870i 0.105054 + 0.0696852i
$$775$$ −21.5831 + 36.9232i −0.775289 + 1.32632i
$$776$$ 16.6332i 0.597099i
$$777$$ −16.1235 4.86140i −0.578426 0.174402i
$$778$$ 30.2164 1.08331
$$779$$ −8.12497 12.9499i −0.291107 0.463977i
$$780$$ −10.9014 6.79413i −0.390332 0.243269i
$$781$$ 25.2324i 0.902887i