# Properties

 Label 230.3.f.b.47.4 Level $230$ Weight $3$ Character 230.47 Analytic conductor $6.267$ Analytic rank $0$ Dimension $24$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$230 = 2 \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 230.f (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$6.26704608029$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 47.4 Character $$\chi$$ $$=$$ 230.47 Dual form 230.3.f.b.93.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 + 1.00000i) q^{2} +(-1.36040 + 1.36040i) q^{3} +2.00000i q^{4} +(-3.17264 - 3.86450i) q^{5} -2.72079 q^{6} +(7.21891 + 7.21891i) q^{7} +(-2.00000 + 2.00000i) q^{8} +5.29864i q^{9} +O(q^{10})$$ $$q+(1.00000 + 1.00000i) q^{2} +(-1.36040 + 1.36040i) q^{3} +2.00000i q^{4} +(-3.17264 - 3.86450i) q^{5} -2.72079 q^{6} +(7.21891 + 7.21891i) q^{7} +(-2.00000 + 2.00000i) q^{8} +5.29864i q^{9} +(0.691863 - 7.03714i) q^{10} -14.8137 q^{11} +(-2.72079 - 2.72079i) q^{12} +(-4.91350 + 4.91350i) q^{13} +14.4378i q^{14} +(9.57330 + 0.941208i) q^{15} -4.00000 q^{16} +(-17.8271 - 17.8271i) q^{17} +(-5.29864 + 5.29864i) q^{18} +29.6011i q^{19} +(7.72900 - 6.34528i) q^{20} -19.6412 q^{21} +(-14.8137 - 14.8137i) q^{22} +(-3.39116 + 3.39116i) q^{23} -5.44159i q^{24} +(-4.86874 + 24.5213i) q^{25} -9.82700 q^{26} +(-19.4518 - 19.4518i) q^{27} +(-14.4378 + 14.4378i) q^{28} -11.0158i q^{29} +(8.63209 + 10.5145i) q^{30} +42.3661 q^{31} +(-4.00000 - 4.00000i) q^{32} +(20.1526 - 20.1526i) q^{33} -35.6542i q^{34} +(4.99449 - 50.8005i) q^{35} -10.5973 q^{36} +(14.7295 + 14.7295i) q^{37} +(-29.6011 + 29.6011i) q^{38} -13.3686i q^{39} +(14.0743 + 1.38373i) q^{40} +23.9580 q^{41} +(-19.6412 - 19.6412i) q^{42} +(0.419945 - 0.419945i) q^{43} -29.6275i q^{44} +(20.4766 - 16.8107i) q^{45} -6.78233 q^{46} +(53.0162 + 53.0162i) q^{47} +(5.44159 - 5.44159i) q^{48} +55.2252i q^{49} +(-29.3901 + 19.6526i) q^{50} +48.5039 q^{51} +(-9.82700 - 9.82700i) q^{52} +(-58.3755 + 58.3755i) q^{53} -38.9036i q^{54} +(46.9987 + 57.2477i) q^{55} -28.8756 q^{56} +(-40.2692 - 40.2692i) q^{57} +(11.0158 - 11.0158i) q^{58} +13.7747i q^{59} +(-1.88242 + 19.1466i) q^{60} +39.0198 q^{61} +(42.3661 + 42.3661i) q^{62} +(-38.2504 + 38.2504i) q^{63} -8.00000i q^{64} +(34.5770 + 3.39947i) q^{65} +40.3051 q^{66} +(-16.9106 - 16.9106i) q^{67} +(35.6542 - 35.6542i) q^{68} -9.22666i q^{69} +(55.7949 - 45.8060i) q^{70} +103.112 q^{71} +(-10.5973 - 10.5973i) q^{72} +(41.5993 - 41.5993i) q^{73} +29.4590i q^{74} +(-26.7353 - 39.9821i) q^{75} -59.2022 q^{76} +(-106.939 - 106.939i) q^{77} +(13.3686 - 13.3686i) q^{78} -155.484i q^{79} +(12.6906 + 15.4580i) q^{80} +5.23660 q^{81} +(23.9580 + 23.9580i) q^{82} +(12.7160 - 12.7160i) q^{83} -39.2823i q^{84} +(-12.3339 + 125.452i) q^{85} +0.839889 q^{86} +(14.9859 + 14.9859i) q^{87} +(29.6275 - 29.6275i) q^{88} +141.715i q^{89} +(37.2873 + 3.66593i) q^{90} -70.9402 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-57.6347 + 57.6347i) q^{93} +106.032i q^{94} +(114.393 - 93.9135i) q^{95} +10.8832 q^{96} +(-29.4379 - 29.4379i) q^{97} +(-55.2252 + 55.2252i) q^{98} -78.4927i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10})$$ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 $$24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100})$$ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$$.

 $$n$$ $$47$$ $$51$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$1$$

## 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 + 1.00000i 0.500000 + 0.500000i
$$3$$ −1.36040 + 1.36040i −0.453466 + 0.453466i −0.896503 0.443038i $$-0.853901\pi$$
0.443038 + 0.896503i $$0.353901\pi$$
$$4$$ 2.00000i 0.500000i
$$5$$ −3.17264 3.86450i −0.634528 0.772900i
$$6$$ −2.72079 −0.453466
$$7$$ 7.21891 + 7.21891i 1.03127 + 1.03127i 0.999495 + 0.0317775i $$0.0101168\pi$$
0.0317775 + 0.999495i $$0.489883\pi$$
$$8$$ −2.00000 + 2.00000i −0.250000 + 0.250000i
$$9$$ 5.29864i 0.588738i
$$10$$ 0.691863 7.03714i 0.0691863 0.703714i
$$11$$ −14.8137 −1.34670 −0.673352 0.739322i $$-0.735146\pi$$
−0.673352 + 0.739322i $$0.735146\pi$$
$$12$$ −2.72079 2.72079i −0.226733 0.226733i
$$13$$ −4.91350 + 4.91350i −0.377962 + 0.377962i −0.870366 0.492405i $$-0.836118\pi$$
0.492405 + 0.870366i $$0.336118\pi$$
$$14$$ 14.4378i 1.03127i
$$15$$ 9.57330 + 0.941208i 0.638220 + 0.0627472i
$$16$$ −4.00000 −0.250000
$$17$$ −17.8271 17.8271i −1.04865 1.04865i −0.998754 0.0499002i $$-0.984110\pi$$
−0.0499002 0.998754i $$-0.515890\pi$$
$$18$$ −5.29864 + 5.29864i −0.294369 + 0.294369i
$$19$$ 29.6011i 1.55795i 0.627054 + 0.778976i $$0.284261\pi$$
−0.627054 + 0.778976i $$0.715739\pi$$
$$20$$ 7.72900 6.34528i 0.386450 0.317264i
$$21$$ −19.6412 −0.935293
$$22$$ −14.8137 14.8137i −0.673352 0.673352i
$$23$$ −3.39116 + 3.39116i −0.147442 + 0.147442i
$$24$$ 5.44159i 0.226733i
$$25$$ −4.86874 + 24.5213i −0.194749 + 0.980853i
$$26$$ −9.82700 −0.377962
$$27$$ −19.4518 19.4518i −0.720438 0.720438i
$$28$$ −14.4378 + 14.4378i −0.515636 + 0.515636i
$$29$$ 11.0158i 0.379856i −0.981798 0.189928i $$-0.939175\pi$$
0.981798 0.189928i $$-0.0608255\pi$$
$$30$$ 8.63209 + 10.5145i 0.287736 + 0.350484i
$$31$$ 42.3661 1.36665 0.683325 0.730115i $$-0.260533\pi$$
0.683325 + 0.730115i $$0.260533\pi$$
$$32$$ −4.00000 4.00000i −0.125000 0.125000i
$$33$$ 20.1526 20.1526i 0.610684 0.610684i
$$34$$ 35.6542i 1.04865i
$$35$$ 4.99449 50.8005i 0.142700 1.45144i
$$36$$ −10.5973 −0.294369
$$37$$ 14.7295 + 14.7295i 0.398095 + 0.398095i 0.877561 0.479466i $$-0.159169\pi$$
−0.479466 + 0.877561i $$0.659169\pi$$
$$38$$ −29.6011 + 29.6011i −0.778976 + 0.778976i
$$39$$ 13.3686i 0.342785i
$$40$$ 14.0743 + 1.38373i 0.351857 + 0.0345931i
$$41$$ 23.9580 0.584341 0.292171 0.956366i $$-0.405622\pi$$
0.292171 + 0.956366i $$0.405622\pi$$
$$42$$ −19.6412 19.6412i −0.467646 0.467646i
$$43$$ 0.419945 0.419945i 0.00976615 0.00976615i −0.702207 0.711973i $$-0.747802\pi$$
0.711973 + 0.702207i $$0.247802\pi$$
$$44$$ 29.6275i 0.673352i
$$45$$ 20.4766 16.8107i 0.455036 0.373571i
$$46$$ −6.78233 −0.147442
$$47$$ 53.0162 + 53.0162i 1.12800 + 1.12800i 0.990502 + 0.137502i $$0.0439073\pi$$
0.137502 + 0.990502i $$0.456093\pi$$
$$48$$ 5.44159 5.44159i 0.113366 0.113366i
$$49$$ 55.2252i 1.12705i
$$50$$ −29.3901 + 19.6526i −0.587801 + 0.393052i
$$51$$ 48.5039 0.951057
$$52$$ −9.82700 9.82700i −0.188981 0.188981i
$$53$$ −58.3755 + 58.3755i −1.10142 + 1.10142i −0.107186 + 0.994239i $$0.534184\pi$$
−0.994239 + 0.107186i $$0.965816\pi$$
$$54$$ 38.9036i 0.720438i
$$55$$ 46.9987 + 57.2477i 0.854521 + 1.04087i
$$56$$ −28.8756 −0.515636
$$57$$ −40.2692 40.2692i −0.706477 0.706477i
$$58$$ 11.0158 11.0158i 0.189928 0.189928i
$$59$$ 13.7747i 0.233469i 0.993163 + 0.116735i $$0.0372427\pi$$
−0.993163 + 0.116735i $$0.962757\pi$$
$$60$$ −1.88242 + 19.1466i −0.0313736 + 0.319110i
$$61$$ 39.0198 0.639670 0.319835 0.947473i $$-0.396373\pi$$
0.319835 + 0.947473i $$0.396373\pi$$
$$62$$ 42.3661 + 42.3661i 0.683325 + 0.683325i
$$63$$ −38.2504 + 38.2504i −0.607149 + 0.607149i
$$64$$ 8.00000i 0.125000i
$$65$$ 34.5770 + 3.39947i 0.531954 + 0.0522995i
$$66$$ 40.3051 0.610684
$$67$$ −16.9106 16.9106i −0.252397 0.252397i 0.569556 0.821953i $$-0.307115\pi$$
−0.821953 + 0.569556i $$0.807115\pi$$
$$68$$ 35.6542 35.6542i 0.524327 0.524327i
$$69$$ 9.22666i 0.133720i
$$70$$ 55.7949 45.8060i 0.797071 0.654371i
$$71$$ 103.112 1.45229 0.726143 0.687544i $$-0.241311\pi$$
0.726143 + 0.687544i $$0.241311\pi$$
$$72$$ −10.5973 10.5973i −0.147185 0.147185i
$$73$$ 41.5993 41.5993i 0.569853 0.569853i −0.362234 0.932087i $$-0.617986\pi$$
0.932087 + 0.362234i $$0.117986\pi$$
$$74$$ 29.4590i 0.398095i
$$75$$ −26.7353 39.9821i −0.356471 0.533095i
$$76$$ −59.2022 −0.778976
$$77$$ −106.939 106.939i −1.38882 1.38882i
$$78$$ 13.3686 13.3686i 0.171393 0.171393i
$$79$$ 155.484i 1.96815i −0.177757 0.984074i $$-0.556884\pi$$
0.177757 0.984074i $$-0.443116\pi$$
$$80$$ 12.6906 + 15.4580i 0.158632 + 0.193225i
$$81$$ 5.23660 0.0646494
$$82$$ 23.9580 + 23.9580i 0.292171 + 0.292171i
$$83$$ 12.7160 12.7160i 0.153205 0.153205i −0.626343 0.779548i $$-0.715449\pi$$
0.779548 + 0.626343i $$0.215449\pi$$
$$84$$ 39.2823i 0.467646i
$$85$$ −12.3339 + 125.452i −0.145105 + 1.47591i
$$86$$ 0.839889 0.00976615
$$87$$ 14.9859 + 14.9859i 0.172252 + 0.172252i
$$88$$ 29.6275 29.6275i 0.336676 0.336676i
$$89$$ 141.715i 1.59230i 0.605101 + 0.796149i $$0.293133\pi$$
−0.605101 + 0.796149i $$0.706867\pi$$
$$90$$ 37.2873 + 3.66593i 0.414303 + 0.0407326i
$$91$$ −70.9402 −0.779563
$$92$$ −6.78233 6.78233i −0.0737210 0.0737210i
$$93$$ −57.6347 + 57.6347i −0.619728 + 0.619728i
$$94$$ 106.032i 1.12800i
$$95$$ 114.393 93.9135i 1.20414 0.988563i
$$96$$ 10.8832 0.113366
$$97$$ −29.4379 29.4379i −0.303483 0.303483i 0.538892 0.842375i $$-0.318843\pi$$
−0.842375 + 0.538892i $$0.818843\pi$$
$$98$$ −55.2252 + 55.2252i −0.563523 + 0.563523i
$$99$$ 78.4927i 0.792856i
$$100$$ −49.0427 9.73747i −0.490427 0.0973747i
$$101$$ 105.739 1.04692 0.523459 0.852051i $$-0.324641\pi$$
0.523459 + 0.852051i $$0.324641\pi$$
$$102$$ 48.5039 + 48.5039i 0.475529 + 0.475529i
$$103$$ −15.4223 + 15.4223i −0.149732 + 0.149732i −0.777998 0.628267i $$-0.783765\pi$$
0.628267 + 0.777998i $$0.283765\pi$$
$$104$$ 19.6540i 0.188981i
$$105$$ 62.3143 + 75.9033i 0.593469 + 0.722888i
$$106$$ −116.751 −1.10142
$$107$$ −38.0079 38.0079i −0.355214 0.355214i 0.506831 0.862045i $$-0.330817\pi$$
−0.862045 + 0.506831i $$0.830817\pi$$
$$108$$ 38.9036 38.9036i 0.360219 0.360219i
$$109$$ 146.178i 1.34108i 0.741873 + 0.670540i $$0.233938\pi$$
−0.741873 + 0.670540i $$0.766062\pi$$
$$110$$ −10.2491 + 104.246i −0.0931735 + 0.947694i
$$111$$ −40.0760 −0.361045
$$112$$ −28.8756 28.8756i −0.257818 0.257818i
$$113$$ 2.38693 2.38693i 0.0211232 0.0211232i −0.696466 0.717590i $$-0.745245\pi$$
0.717590 + 0.696466i $$0.245245\pi$$
$$114$$ 80.5384i 0.706477i
$$115$$ 23.8641 + 2.34622i 0.207514 + 0.0204019i
$$116$$ 22.0317 0.189928
$$117$$ −26.0349 26.0349i −0.222520 0.222520i
$$118$$ −13.7747 + 13.7747i −0.116735 + 0.116735i
$$119$$ 257.385i 2.16290i
$$120$$ −21.0290 + 17.2642i −0.175242 + 0.143868i
$$121$$ 98.4471 0.813612
$$122$$ 39.0198 + 39.0198i 0.319835 + 0.319835i
$$123$$ −32.5924 + 32.5924i −0.264979 + 0.264979i
$$124$$ 84.7322i 0.683325i
$$125$$ 110.209 58.9821i 0.881675 0.471856i
$$126$$ −76.5008 −0.607149
$$127$$ −134.874 134.874i −1.06200 1.06200i −0.997946 0.0640551i $$-0.979597\pi$$
−0.0640551 0.997946i $$-0.520403\pi$$
$$128$$ 8.00000 8.00000i 0.0625000 0.0625000i
$$129$$ 1.14258i 0.00885723i
$$130$$ 31.1775 + 37.9765i 0.239827 + 0.292127i
$$131$$ −48.2924 −0.368644 −0.184322 0.982866i $$-0.559009\pi$$
−0.184322 + 0.982866i $$0.559009\pi$$
$$132$$ 40.3051 + 40.3051i 0.305342 + 0.305342i
$$133$$ −213.687 + 213.687i −1.60667 + 1.60667i
$$134$$ 33.8212i 0.252397i
$$135$$ −13.4580 + 136.885i −0.0996889 + 1.01396i
$$136$$ 71.3085 0.524327
$$137$$ −3.29075 3.29075i −0.0240200 0.0240200i 0.694995 0.719015i $$-0.255407\pi$$
−0.719015 + 0.694995i $$0.755407\pi$$
$$138$$ 9.22666 9.22666i 0.0668598 0.0668598i
$$139$$ 108.941i 0.783751i −0.920018 0.391876i $$-0.871826\pi$$
0.920018 0.391876i $$-0.128174\pi$$
$$140$$ 101.601 + 9.98899i 0.725721 + 0.0713499i
$$141$$ −144.246 −1.02302
$$142$$ 103.112 + 103.112i 0.726143 + 0.726143i
$$143$$ 72.7874 72.7874i 0.509002 0.509002i
$$144$$ 21.1946i 0.147185i
$$145$$ −42.5707 + 34.9492i −0.293591 + 0.241029i
$$146$$ 83.1985 0.569853
$$147$$ −75.1282 75.1282i −0.511076 0.511076i
$$148$$ −29.4590 + 29.4590i −0.199048 + 0.199048i
$$149$$ 68.8768i 0.462260i 0.972923 + 0.231130i $$0.0742423\pi$$
−0.972923 + 0.231130i $$0.925758\pi$$
$$150$$ 13.2468 66.7175i 0.0883121 0.444783i
$$151$$ 138.399 0.916549 0.458275 0.888811i $$-0.348468\pi$$
0.458275 + 0.888811i $$0.348468\pi$$
$$152$$ −59.2022 59.2022i −0.389488 0.389488i
$$153$$ 94.4596 94.4596i 0.617383 0.617383i
$$154$$ 213.878i 1.38882i
$$155$$ −134.412 163.724i −0.867177 1.05628i
$$156$$ 26.7372 0.171393
$$157$$ −135.287 135.287i −0.861699 0.861699i 0.129836 0.991535i $$-0.458555\pi$$
−0.991535 + 0.129836i $$0.958555\pi$$
$$158$$ 155.484 155.484i 0.984074 0.984074i
$$159$$ 158.828i 0.998916i
$$160$$ −2.76745 + 28.1486i −0.0172966 + 0.175928i
$$161$$ −48.9610 −0.304106
$$162$$ 5.23660 + 5.23660i 0.0323247 + 0.0323247i
$$163$$ −84.3740 + 84.3740i −0.517632 + 0.517632i −0.916854 0.399222i $$-0.869280\pi$$
0.399222 + 0.916854i $$0.369280\pi$$
$$164$$ 47.9160i 0.292171i
$$165$$ −141.816 13.9428i −0.859494 0.0845019i
$$166$$ 25.4320 0.153205
$$167$$ 217.730 + 217.730i 1.30378 + 1.30378i 0.925826 + 0.377949i $$0.123371\pi$$
0.377949 + 0.925826i $$0.376629\pi$$
$$168$$ 39.2823 39.2823i 0.233823 0.233823i
$$169$$ 120.715i 0.714290i
$$170$$ −137.786 + 113.118i −0.810505 + 0.665400i
$$171$$ −156.846 −0.917225
$$172$$ 0.839889 + 0.839889i 0.00488308 + 0.00488308i
$$173$$ −222.534 + 222.534i −1.28632 + 1.28632i −0.349321 + 0.937003i $$0.613588\pi$$
−0.937003 + 0.349321i $$0.886412\pi$$
$$174$$ 29.9718i 0.172252i
$$175$$ −212.164 + 141.870i −1.21237 + 0.810687i
$$176$$ 59.2550 0.336676
$$177$$ −18.7390 18.7390i −0.105870 0.105870i
$$178$$ −141.715 + 141.715i −0.796149 + 0.796149i
$$179$$ 194.058i 1.08412i 0.840339 + 0.542061i $$0.182356\pi$$
−0.840339 + 0.542061i $$0.817644\pi$$
$$180$$ 33.6214 + 40.9532i 0.186785 + 0.227518i
$$181$$ −0.412795 −0.00228064 −0.00114032 0.999999i $$-0.500363\pi$$
−0.00114032 + 0.999999i $$0.500363\pi$$
$$182$$ −70.9402 70.9402i −0.389781 0.389781i
$$183$$ −53.0825 + 53.0825i −0.290068 + 0.290068i
$$184$$ 13.5647i 0.0737210i
$$185$$ 10.1908 103.654i 0.0550855 0.560290i
$$186$$ −115.269 −0.619728
$$187$$ 264.086 + 264.086i 1.41223 + 1.41223i
$$188$$ −106.032 + 106.032i −0.564002 + 0.564002i
$$189$$ 280.842i 1.48594i
$$190$$ 208.307 + 20.4799i 1.09635 + 0.107789i
$$191$$ −313.636 −1.64207 −0.821036 0.570877i $$-0.806603\pi$$
−0.821036 + 0.570877i $$0.806603\pi$$
$$192$$ 10.8832 + 10.8832i 0.0566832 + 0.0566832i
$$193$$ −11.9642 + 11.9642i −0.0619909 + 0.0619909i −0.737423 0.675432i $$-0.763957\pi$$
0.675432 + 0.737423i $$0.263957\pi$$
$$194$$ 58.8757i 0.303483i
$$195$$ −51.6630 + 42.4138i −0.264939 + 0.217507i
$$196$$ −110.450 −0.563523
$$197$$ −57.7317 57.7317i −0.293054 0.293054i 0.545231 0.838286i $$-0.316442\pi$$
−0.838286 + 0.545231i $$0.816442\pi$$
$$198$$ 78.4927 78.4927i 0.396428 0.396428i
$$199$$ 263.722i 1.32524i 0.748957 + 0.662619i $$0.230555\pi$$
−0.748957 + 0.662619i $$0.769445\pi$$
$$200$$ −39.3052 58.7801i −0.196526 0.293901i
$$201$$ 46.0102 0.228907
$$202$$ 105.739 + 105.739i 0.523459 + 0.523459i
$$203$$ 79.5222 79.5222i 0.391735 0.391735i
$$204$$ 97.0078i 0.475529i
$$205$$ −76.0101 92.5857i −0.370781 0.451638i
$$206$$ −30.8447 −0.149732
$$207$$ −17.9686 17.9686i −0.0868047 0.0868047i
$$208$$ 19.6540 19.6540i 0.0944904 0.0944904i
$$209$$ 438.503i 2.09810i
$$210$$ −13.5890 + 138.218i −0.0647095 + 0.658179i
$$211$$ 321.514 1.52376 0.761881 0.647717i $$-0.224276\pi$$
0.761881 + 0.647717i $$0.224276\pi$$
$$212$$ −116.751 116.751i −0.550712 0.550712i
$$213$$ −140.274 + 140.274i −0.658561 + 0.658561i
$$214$$ 76.0158i 0.355214i
$$215$$ −2.95521 0.290544i −0.0137452 0.00135137i
$$216$$ 77.8073 0.360219
$$217$$ 305.837 + 305.837i 1.40939 + 1.40939i
$$218$$ −146.178 + 146.178i −0.670540 + 0.670540i
$$219$$ 113.183i 0.516817i
$$220$$ −114.495 + 93.9973i −0.520434 + 0.427261i
$$221$$ 175.187 0.792702
$$222$$ −40.0760 40.0760i −0.180522 0.180522i
$$223$$ −75.9702 + 75.9702i −0.340674 + 0.340674i −0.856621 0.515947i $$-0.827440\pi$$
0.515947 + 0.856621i $$0.327440\pi$$
$$224$$ 57.7513i 0.257818i
$$225$$ −129.930 25.7977i −0.577466 0.114656i
$$226$$ 4.77385 0.0211232
$$227$$ −63.6613 63.6613i −0.280446 0.280446i 0.552841 0.833287i $$-0.313544\pi$$
−0.833287 + 0.552841i $$0.813544\pi$$
$$228$$ 80.5384 80.5384i 0.353239 0.353239i
$$229$$ 103.156i 0.450462i −0.974305 0.225231i $$-0.927686\pi$$
0.974305 0.225231i $$-0.0723137\pi$$
$$230$$ 21.5179 + 26.2103i 0.0935560 + 0.113958i
$$231$$ 290.959 1.25956
$$232$$ 22.0317 + 22.0317i 0.0949640 + 0.0949640i
$$233$$ −211.803 + 211.803i −0.909026 + 0.909026i −0.996194 0.0871679i $$-0.972218\pi$$
0.0871679 + 0.996194i $$0.472218\pi$$
$$234$$ 52.0698i 0.222520i
$$235$$ 36.6799 373.082i 0.156085 1.58758i
$$236$$ −27.5494 −0.116735
$$237$$ 211.520 + 211.520i 0.892488 + 0.892488i
$$238$$ 257.385 257.385i 1.08145 1.08145i
$$239$$ 89.5138i 0.374535i −0.982309 0.187267i $$-0.940037\pi$$
0.982309 0.187267i $$-0.0599631\pi$$
$$240$$ −38.2932 3.76483i −0.159555 0.0156868i
$$241$$ 175.324 0.727487 0.363744 0.931499i $$-0.381498\pi$$
0.363744 + 0.931499i $$0.381498\pi$$
$$242$$ 98.4471 + 98.4471i 0.406806 + 0.406806i
$$243$$ 167.943 167.943i 0.691122 0.691122i
$$244$$ 78.0397i 0.319835i
$$245$$ 213.418 175.210i 0.871094 0.715142i
$$246$$ −65.1848 −0.264979
$$247$$ −145.445 145.445i −0.588846 0.588846i
$$248$$ −84.7322 + 84.7322i −0.341662 + 0.341662i
$$249$$ 34.5976i 0.138946i
$$250$$ 169.191 + 51.2274i 0.676766 + 0.204909i
$$251$$ 326.776 1.30190 0.650948 0.759122i $$-0.274371\pi$$
0.650948 + 0.759122i $$0.274371\pi$$
$$252$$ −76.5008 76.5008i −0.303575 0.303575i
$$253$$ 50.2359 50.2359i 0.198561 0.198561i
$$254$$ 269.748i 1.06200i
$$255$$ −153.885 187.443i −0.603472 0.735072i
$$256$$ 16.0000 0.0625000
$$257$$ −44.9594 44.9594i −0.174939 0.174939i 0.614206 0.789146i $$-0.289476\pi$$
−0.789146 + 0.614206i $$0.789476\pi$$
$$258$$ −1.14258 + 1.14258i −0.00442861 + 0.00442861i
$$259$$ 212.662i 0.821089i
$$260$$ −6.79894 + 69.1540i −0.0261498 + 0.265977i
$$261$$ 58.3689 0.223636
$$262$$ −48.2924 48.2924i −0.184322 0.184322i
$$263$$ 123.550 123.550i 0.469771 0.469771i −0.432070 0.901840i $$-0.642217\pi$$
0.901840 + 0.432070i $$0.142217\pi$$
$$264$$ 80.6103i 0.305342i
$$265$$ 410.797 + 40.3879i 1.55018 + 0.152407i
$$266$$ −427.375 −1.60667
$$267$$ −192.788 192.788i −0.722052 0.722052i
$$268$$ 33.8212 33.8212i 0.126198 0.126198i
$$269$$ 237.309i 0.882189i 0.897461 + 0.441094i $$0.145410\pi$$
−0.897461 + 0.441094i $$0.854590\pi$$
$$270$$ −150.343 + 123.427i −0.556827 + 0.457138i
$$271$$ 26.2193 0.0967502 0.0483751 0.998829i $$-0.484596\pi$$
0.0483751 + 0.998829i $$0.484596\pi$$
$$272$$ 71.3085 + 71.3085i 0.262164 + 0.262164i
$$273$$ 96.5068 96.5068i 0.353505 0.353505i
$$274$$ 6.58149i 0.0240200i
$$275$$ 72.1242 363.253i 0.262270 1.32092i
$$276$$ 18.4533 0.0668598
$$277$$ −225.480 225.480i −0.814007 0.814007i 0.171225 0.985232i $$-0.445228\pi$$
−0.985232 + 0.171225i $$0.945228\pi$$
$$278$$ 108.941 108.941i 0.391876 0.391876i
$$279$$ 224.483i 0.804598i
$$280$$ 91.6119 + 111.590i 0.327185 + 0.398535i
$$281$$ −70.2491 −0.249997 −0.124998 0.992157i $$-0.539893\pi$$
−0.124998 + 0.992157i $$0.539893\pi$$
$$282$$ −144.246 144.246i −0.511511 0.511511i
$$283$$ 49.1215 49.1215i 0.173574 0.173574i −0.614974 0.788548i $$-0.710833\pi$$
0.788548 + 0.614974i $$0.210833\pi$$
$$284$$ 206.225i 0.726143i
$$285$$ −27.8608 + 283.380i −0.0977571 + 0.994316i
$$286$$ 145.575 0.509002
$$287$$ 172.951 + 172.951i 0.602615 + 0.602615i
$$288$$ 21.1946 21.1946i 0.0735923 0.0735923i
$$289$$ 346.613i 1.19935i
$$290$$ −77.5199 7.62144i −0.267310 0.0262808i
$$291$$ 80.0943 0.275238
$$292$$ 83.1985 + 83.1985i 0.284926 + 0.284926i
$$293$$ 369.904 369.904i 1.26247 1.26247i 0.312580 0.949891i $$-0.398807\pi$$
0.949891 0.312580i $$-0.101193\pi$$
$$294$$ 150.256i 0.511076i
$$295$$ 53.2323 43.7021i 0.180448 0.148143i
$$296$$ −58.9181 −0.199048
$$297$$ 288.154 + 288.154i 0.970217 + 0.970217i
$$298$$ −68.8768 + 68.8768i −0.231130 + 0.231130i
$$299$$ 33.3250i 0.111455i
$$300$$ 79.9643 53.4706i 0.266548 0.178235i
$$301$$ 6.06308 0.0201431
$$302$$ 138.399 + 138.399i 0.458275 + 0.458275i
$$303$$ −143.847 + 143.847i −0.474741 + 0.474741i
$$304$$ 118.404i 0.389488i
$$305$$ −123.796 150.792i −0.405888 0.494401i
$$306$$ 188.919 0.617383
$$307$$ 4.17039 + 4.17039i 0.0135843 + 0.0135843i 0.713866 0.700282i $$-0.246942\pi$$
−0.700282 + 0.713866i $$0.746942\pi$$
$$308$$ 213.878 213.878i 0.694409 0.694409i
$$309$$ 41.9610i 0.135796i
$$310$$ 29.3115 298.136i 0.0945534 0.961730i
$$311$$ −385.664 −1.24008 −0.620039 0.784571i $$-0.712883\pi$$
−0.620039 + 0.784571i $$0.712883\pi$$
$$312$$ 26.7372 + 26.7372i 0.0856963 + 0.0856963i
$$313$$ −156.465 + 156.465i −0.499888 + 0.499888i −0.911403 0.411515i $$-0.865000\pi$$
0.411515 + 0.911403i $$0.365000\pi$$
$$314$$ 270.574i 0.861699i
$$315$$ 269.173 + 26.4640i 0.854519 + 0.0840128i
$$316$$ 310.967 0.984074
$$317$$ −172.672 172.672i −0.544708 0.544708i 0.380198 0.924905i $$-0.375856\pi$$
−0.924905 + 0.380198i $$0.875856\pi$$
$$318$$ 158.828 158.828i 0.499458 0.499458i
$$319$$ 163.186i 0.511554i
$$320$$ −30.9160 + 25.3811i −0.0966125 + 0.0793160i
$$321$$ 103.412 0.322155
$$322$$ −48.9610 48.9610i −0.152053 0.152053i
$$323$$ 527.702 527.702i 1.63375 1.63375i
$$324$$ 10.4732i 0.0323247i
$$325$$ −96.5630 144.408i −0.297117 0.444333i
$$326$$ −168.748 −0.517632
$$327$$ −198.860 198.860i −0.608134 0.608134i
$$328$$ −47.9160 + 47.9160i −0.146085 + 0.146085i
$$329$$ 765.437i 2.32656i
$$330$$ −127.874 155.759i −0.387496 0.471998i
$$331$$ 594.585 1.79633 0.898165 0.439659i $$-0.144901\pi$$
0.898165 + 0.439659i $$0.144901\pi$$
$$332$$ 25.4320 + 25.4320i 0.0766024 + 0.0766024i
$$333$$ −78.0465 + 78.0465i −0.234374 + 0.234374i
$$334$$ 435.461i 1.30378i
$$335$$ −11.6998 + 119.002i −0.0349248 + 0.355231i
$$336$$ 78.5646 0.233823
$$337$$ −318.172 318.172i −0.944130 0.944130i 0.0543895 0.998520i $$-0.482679\pi$$
−0.998520 + 0.0543895i $$0.982679\pi$$
$$338$$ −120.715 + 120.715i −0.357145 + 0.357145i
$$339$$ 6.49433i 0.0191573i
$$340$$ −250.904 24.6679i −0.737953 0.0725525i
$$341$$ −627.601 −1.84047
$$342$$ −156.846 156.846i −0.458613 0.458613i
$$343$$ −44.9394 + 44.9394i −0.131019 + 0.131019i
$$344$$ 1.67978i 0.00488308i
$$345$$ −35.6564 + 29.2728i −0.103352 + 0.0848488i
$$346$$ −445.068 −1.28632
$$347$$ 161.848 + 161.848i 0.466422 + 0.466422i 0.900753 0.434331i $$-0.143015\pi$$
−0.434331 + 0.900753i $$0.643015\pi$$
$$348$$ −29.9718 + 29.9718i −0.0861258 + 0.0861258i
$$349$$ 66.1242i 0.189468i 0.995503 + 0.0947339i $$0.0302000\pi$$
−0.995503 + 0.0947339i $$0.969800\pi$$
$$350$$ −354.034 70.2939i −1.01153 0.200840i
$$351$$ 191.153 0.544596
$$352$$ 59.2550 + 59.2550i 0.168338 + 0.168338i
$$353$$ 331.118 331.118i 0.938012 0.938012i −0.0601762 0.998188i $$-0.519166\pi$$
0.998188 + 0.0601762i $$0.0191662\pi$$
$$354$$ 37.4780i 0.105870i
$$355$$ −327.138 398.478i −0.921515 1.12247i
$$356$$ −283.429 −0.796149
$$357$$ 350.145 + 350.145i 0.980799 + 0.980799i
$$358$$ −194.058 + 194.058i −0.542061 + 0.542061i
$$359$$ 134.587i 0.374893i 0.982275 + 0.187447i $$0.0600211\pi$$
−0.982275 + 0.187447i $$0.939979\pi$$
$$360$$ −7.33187 + 74.5746i −0.0203663 + 0.207152i
$$361$$ −515.224 −1.42721
$$362$$ −0.412795 0.412795i −0.00114032 0.00114032i
$$363$$ −133.927 + 133.927i −0.368945 + 0.368945i
$$364$$ 141.880i 0.389781i
$$365$$ −292.740 28.7810i −0.802027 0.0788520i
$$366$$ −106.165 −0.290068
$$367$$ 451.660 + 451.660i 1.23068 + 1.23068i 0.963702 + 0.266979i $$0.0860254\pi$$
0.266979 + 0.963702i $$0.413975\pi$$
$$368$$ 13.5647 13.5647i 0.0368605 0.0368605i
$$369$$ 126.945i 0.344024i
$$370$$ 113.845 93.4629i 0.307688 0.252602i
$$371$$ −842.815 −2.27174
$$372$$ −115.269 115.269i −0.309864 0.309864i
$$373$$ 451.866 451.866i 1.21144 1.21144i 0.240883 0.970554i $$-0.422563\pi$$
0.970554 0.240883i $$-0.0774369\pi$$
$$374$$ 528.173i 1.41223i
$$375$$ −69.6895 + 230.168i −0.185839 + 0.613780i
$$376$$ −212.065 −0.564002
$$377$$ 54.1263 + 54.1263i 0.143571 + 0.143571i
$$378$$ 280.842 280.842i 0.742968 0.742968i
$$379$$ 230.954i 0.609377i 0.952452 + 0.304688i $$0.0985524\pi$$
−0.952452 + 0.304688i $$0.901448\pi$$
$$380$$ 187.827 + 228.787i 0.494282 + 0.602071i
$$381$$ 366.965 0.963162
$$382$$ −313.636 313.636i −0.821036 0.821036i
$$383$$ 183.834 183.834i 0.479985 0.479985i −0.425142 0.905127i $$-0.639776\pi$$
0.905127 + 0.425142i $$0.139776\pi$$
$$384$$ 21.7663i 0.0566832i
$$385$$ −73.9872 + 752.545i −0.192174 + 1.95466i
$$386$$ −23.9285 −0.0619909
$$387$$ 2.22514 + 2.22514i 0.00574971 + 0.00574971i
$$388$$ 58.8757 58.8757i 0.151742 0.151742i
$$389$$ 468.206i 1.20362i −0.798641 0.601808i $$-0.794447\pi$$
0.798641 0.601808i $$-0.205553\pi$$
$$390$$ −94.0768 9.24925i −0.241223 0.0237160i
$$391$$ 120.909 0.309231
$$392$$ −110.450 110.450i −0.281761 0.281761i
$$393$$ 65.6968 65.6968i 0.167168 0.167168i
$$394$$ 115.463i 0.293054i
$$395$$ −600.867 + 493.294i −1.52118 + 1.24884i
$$396$$ 156.985 0.396428
$$397$$ 53.6961 + 53.6961i 0.135255 + 0.135255i 0.771493 0.636238i $$-0.219510\pi$$
−0.636238 + 0.771493i $$0.719510\pi$$
$$398$$ −263.722 + 263.722i −0.662619 + 0.662619i
$$399$$ 581.399i 1.45714i
$$400$$ 19.4749 98.0853i 0.0486874 0.245213i
$$401$$ 248.645 0.620062 0.310031 0.950727i $$-0.399661\pi$$
0.310031 + 0.950727i $$0.399661\pi$$
$$402$$ 46.0102 + 46.0102i 0.114453 + 0.114453i
$$403$$ −208.166 + 208.166i −0.516541 + 0.516541i
$$404$$ 211.477i 0.523459i
$$405$$ −16.6138 20.2369i −0.0410218 0.0499675i
$$406$$ 159.044 0.391735
$$407$$ −218.199 218.199i −0.536117 0.536117i
$$408$$ −97.0078 + 97.0078i −0.237764 + 0.237764i
$$409$$ 561.926i 1.37390i 0.726703 + 0.686952i $$0.241052\pi$$
−0.726703 + 0.686952i $$0.758948\pi$$
$$410$$ 16.5756 168.596i 0.0404284 0.411209i
$$411$$ 8.95344 0.0217845
$$412$$ −30.8447 30.8447i −0.0748658 0.0748658i
$$413$$ −99.4381 + 99.4381i −0.240770 + 0.240770i
$$414$$ 35.9371i 0.0868047i
$$415$$ −89.4842 8.79772i −0.215625 0.0211993i
$$416$$ 39.3080 0.0944904
$$417$$ 148.204 + 148.204i 0.355404 + 0.355404i
$$418$$ 438.503 438.503i 1.04905 1.04905i
$$419$$ 453.494i 1.08233i −0.840918 0.541163i $$-0.817984\pi$$
0.840918 0.541163i $$-0.182016\pi$$
$$420$$ −151.807 + 124.629i −0.361444 + 0.296735i
$$421$$ −62.8563 −0.149302 −0.0746512 0.997210i $$-0.523784\pi$$
−0.0746512 + 0.997210i $$0.523784\pi$$
$$422$$ 321.514 + 321.514i 0.761881 + 0.761881i
$$423$$ −280.914 + 280.914i −0.664099 + 0.664099i
$$424$$ 233.502i 0.550712i
$$425$$ 523.940 350.349i 1.23280 0.824351i
$$426$$ −280.547 −0.658561
$$427$$ 281.681 + 281.681i 0.659674 + 0.659674i
$$428$$ 76.0158 76.0158i 0.177607 0.177607i
$$429$$ 198.039i 0.461630i
$$430$$ −2.66466 3.24575i −0.00619689 0.00754826i
$$431$$ −175.877 −0.408068 −0.204034 0.978964i $$-0.565405\pi$$
−0.204034 + 0.978964i $$0.565405\pi$$
$$432$$ 77.8073 + 77.8073i 0.180109 + 0.180109i
$$433$$ −342.932 + 342.932i −0.791991 + 0.791991i −0.981818 0.189827i $$-0.939207\pi$$
0.189827 + 0.981818i $$0.439207\pi$$
$$434$$ 611.674i 1.40939i
$$435$$ 10.3682 105.458i 0.0238349 0.242432i
$$436$$ −292.356 −0.670540
$$437$$ −100.382 100.382i −0.229707 0.229707i
$$438$$ −113.183 + 113.183i −0.258409 + 0.258409i
$$439$$ 55.4496i 0.126309i 0.998004 + 0.0631544i $$0.0201161\pi$$
−0.998004 + 0.0631544i $$0.979884\pi$$
$$440$$ −208.493 20.4982i −0.473847 0.0465867i
$$441$$ −292.619 −0.663535
$$442$$ 175.187 + 175.187i 0.396351 + 0.396351i
$$443$$ −154.793 + 154.793i −0.349420 + 0.349420i −0.859894 0.510473i $$-0.829470\pi$$
0.510473 + 0.859894i $$0.329470\pi$$
$$444$$ 80.1520i 0.180522i
$$445$$ 547.656 449.609i 1.23069 1.01036i
$$446$$ −151.940 −0.340674
$$447$$ −93.6997 93.6997i −0.209619 0.209619i
$$448$$ 57.7513 57.7513i 0.128909 0.128909i
$$449$$ 658.321i 1.46619i −0.680124 0.733097i $$-0.738074\pi$$
0.680124 0.733097i $$-0.261926\pi$$
$$450$$ −104.132 155.727i −0.231405 0.346061i
$$451$$ −354.908 −0.786935
$$452$$ 4.77385 + 4.77385i 0.0105616 + 0.0105616i
$$453$$ −188.277 + 188.277i −0.415623 + 0.415623i
$$454$$ 127.323i 0.280446i
$$455$$ 225.068 + 274.149i 0.494654 + 0.602524i
$$456$$ 161.077 0.353239
$$457$$ −630.005 630.005i −1.37857 1.37857i −0.847045 0.531522i $$-0.821620\pi$$
−0.531522 0.847045i $$-0.678380\pi$$
$$458$$ 103.156 103.156i 0.225231 0.225231i
$$459$$ 693.540i 1.51098i
$$460$$ −4.69244 + 47.7282i −0.0102010 + 0.103757i
$$461$$ −635.738 −1.37904 −0.689520 0.724266i $$-0.742179\pi$$
−0.689520 + 0.724266i $$0.742179\pi$$
$$462$$ 290.959 + 290.959i 0.629781 + 0.629781i
$$463$$ −30.8108 + 30.8108i −0.0665460 + 0.0665460i −0.739597 0.673051i $$-0.764984\pi$$
0.673051 + 0.739597i $$0.264984\pi$$
$$464$$ 44.0633i 0.0949640i
$$465$$ 405.584 + 39.8753i 0.872223 + 0.0857534i
$$466$$ −423.606 −0.909026
$$467$$ 273.937 + 273.937i 0.586588 + 0.586588i 0.936706 0.350118i $$-0.113858\pi$$
−0.350118 + 0.936706i $$0.613858\pi$$
$$468$$ 52.0698 52.0698i 0.111260 0.111260i
$$469$$ 244.152i 0.520580i
$$470$$ 409.762 336.402i 0.871834 0.715749i
$$471$$ 368.087 0.781502
$$472$$ −27.5494 27.5494i −0.0583673 0.0583673i
$$473$$ −6.22095 + 6.22095i −0.0131521 + 0.0131521i
$$474$$ 423.039i 0.892488i
$$475$$ −725.858 144.120i −1.52812 0.303410i
$$476$$ 514.769 1.08145
$$477$$ −309.311 309.311i −0.648451 0.648451i
$$478$$ 89.5138 89.5138i 0.187267 0.187267i
$$479$$ 617.839i 1.28985i 0.764245 + 0.644926i $$0.223112\pi$$
−0.764245 + 0.644926i $$0.776888\pi$$
$$480$$ −34.5284 42.0580i −0.0719341 0.0876209i
$$481$$ −144.747 −0.300929
$$482$$ 175.324 + 175.324i 0.363744 + 0.363744i
$$483$$ 66.6064 66.6064i 0.137901 0.137901i
$$484$$ 196.894i 0.406806i
$$485$$ −20.3670 + 207.158i −0.0419937 + 0.427130i
$$486$$ 335.885 0.691122
$$487$$ 182.634 + 182.634i 0.375019 + 0.375019i 0.869301 0.494283i $$-0.164569\pi$$
−0.494283 + 0.869301i $$0.664569\pi$$
$$488$$ −78.0397 + 78.0397i −0.159917 + 0.159917i
$$489$$ 229.564i 0.469456i
$$490$$ 388.628 + 38.2083i 0.793118 + 0.0779761i
$$491$$ −31.9547 −0.0650808 −0.0325404 0.999470i $$-0.510360\pi$$
−0.0325404 + 0.999470i $$0.510360\pi$$
$$492$$ −65.1848 65.1848i −0.132489 0.132489i
$$493$$ −196.381 + 196.381i −0.398338 + 0.398338i
$$494$$ 290.890i 0.588846i
$$495$$ −303.335 + 249.029i −0.612799 + 0.503089i
$$496$$ −169.464 −0.341662
$$497$$ 744.358 + 744.358i 1.49770 + 1.49770i
$$498$$ −34.5976 + 34.5976i −0.0694731 + 0.0694731i
$$499$$ 138.737i 0.278030i −0.990290 0.139015i $$-0.955606\pi$$
0.990290 0.139015i $$-0.0443936\pi$$
$$500$$ 117.964 + 220.419i 0.235928 + 0.440838i
$$501$$ −592.400 −1.18243
$$502$$ 326.776 + 326.776i 0.650948 + 0.650948i
$$503$$ 159.071 159.071i 0.316245 0.316245i −0.531078 0.847323i $$-0.678213\pi$$
0.847323 + 0.531078i $$0.178213\pi$$
$$504$$ 153.002i 0.303575i
$$505$$ −335.471 408.627i −0.664298 0.809163i
$$506$$ 100.472 0.198561
$$507$$ −164.220 164.220i −0.323906 0.323906i
$$508$$ 269.748 269.748i 0.531001 0.531001i
$$509$$ 128.670i 0.252790i −0.991980 0.126395i $$-0.959659\pi$$
0.991980 0.126395i $$-0.0403406\pi$$
$$510$$ 33.5581 341.329i 0.0658001 0.669272i
$$511$$ 600.602 1.17535
$$512$$ 16.0000 + 16.0000i 0.0312500 + 0.0312500i
$$513$$ 575.795 575.795i 1.12241 1.12241i
$$514$$ 89.9188i 0.174939i
$$515$$ 108.529 + 10.6701i 0.210736 + 0.0207187i
$$516$$ −2.28516 −0.00442861
$$517$$ −785.368 785.368i −1.51909 1.51909i
$$518$$ −212.662 + 212.662i −0.410545 + 0.410545i
$$519$$ 605.469i 1.16661i
$$520$$ −75.9529 + 62.3550i −0.146063 + 0.119914i
$$521$$ 452.310 0.868157 0.434078 0.900875i $$-0.357074\pi$$
0.434078 + 0.900875i $$0.357074\pi$$
$$522$$ 58.3689 + 58.3689i 0.111818 + 0.111818i
$$523$$ 66.3514 66.3514i 0.126867 0.126867i −0.640822 0.767689i $$-0.721406\pi$$
0.767689 + 0.640822i $$0.221406\pi$$
$$524$$ 96.5848i 0.184322i
$$525$$ 95.6276 481.627i 0.182148 0.917385i
$$526$$ 247.099 0.469771
$$527$$ −755.266 755.266i −1.43314 1.43314i
$$528$$ −80.6103 + 80.6103i −0.152671 + 0.152671i
$$529$$ 23.0000i 0.0434783i
$$530$$ 370.409 + 451.184i 0.698884 + 0.851291i
$$531$$ −72.9871 −0.137452
$$532$$ −427.375 427.375i −0.803336 0.803336i
$$533$$ −117.718 + 117.718i −0.220859 + 0.220859i
$$534$$ 385.576i 0.722052i
$$535$$ −26.2962 + 267.467i −0.0491519 + 0.499938i
$$536$$ 67.6424 0.126198
$$537$$ −263.996 263.996i −0.491612 0.491612i
$$538$$ −237.309 + 237.309i −0.441094 + 0.441094i
$$539$$ 818.093i 1.51780i
$$540$$ −273.770 26.9160i −0.506982 0.0498444i
$$541$$ −598.507 −1.10630 −0.553148 0.833083i $$-0.686574\pi$$
−0.553148 + 0.833083i $$0.686574\pi$$
$$542$$ 26.2193 + 26.2193i 0.0483751 + 0.0483751i
$$543$$ 0.561565 0.561565i 0.00103419 0.00103419i
$$544$$ 142.617i 0.262164i
$$545$$ 564.904 463.769i 1.03652 0.850953i
$$546$$ 193.014 0.353505
$$547$$ 87.9130 + 87.9130i 0.160718 + 0.160718i 0.782885 0.622166i $$-0.213747\pi$$
−0.622166 + 0.782885i $$0.713747\pi$$
$$548$$ 6.58149 6.58149i 0.0120100 0.0120100i
$$549$$ 206.752i 0.376598i
$$550$$ 435.377 291.128i 0.791594 0.529325i
$$551$$ 326.080 0.591797
$$552$$ 18.4533 + 18.4533i 0.0334299 + 0.0334299i
$$553$$ 1122.42 1122.42i 2.02970 2.02970i
$$554$$ 450.960i 0.814007i
$$555$$ 127.147 + 154.874i 0.229093 + 0.279052i
$$556$$ 217.883 0.391876
$$557$$ 688.697 + 688.697i 1.23644 + 1.23644i 0.961446 + 0.274995i $$0.0886762\pi$$
0.274995 + 0.961446i $$0.411324\pi$$
$$558$$ −224.483 + 224.483i −0.402299 + 0.402299i
$$559$$ 4.12680i 0.00738246i
$$560$$ −19.9780 + 203.202i −0.0356750 + 0.362860i
$$561$$ −718.525 −1.28079
$$562$$ −70.2491 70.2491i −0.124998 0.124998i
$$563$$ 51.4275 51.4275i 0.0913454 0.0913454i −0.659958 0.751303i $$-0.729426\pi$$
0.751303 + 0.659958i $$0.229426\pi$$
$$564$$ 288.492i 0.511511i
$$565$$ −16.7971 1.65143i −0.0297294 0.00292288i
$$566$$ 98.2430 0.173574
$$567$$ 37.8025 + 37.8025i 0.0666712 + 0.0666712i
$$568$$ −206.225 + 206.225i −0.363071 + 0.363071i
$$569$$ 632.828i 1.11218i 0.831124 + 0.556088i $$0.187698\pi$$
−0.831124 + 0.556088i $$0.812302\pi$$
$$570$$ −311.241 + 255.519i −0.546036 + 0.448279i
$$571$$ 696.211 1.21928 0.609642 0.792677i $$-0.291313\pi$$
0.609642 + 0.792677i $$0.291313\pi$$
$$572$$ 145.575 + 145.575i 0.254501 + 0.254501i
$$573$$ 426.669 426.669i 0.744623 0.744623i
$$574$$ 345.901i 0.602615i
$$575$$ −66.6452 99.6665i −0.115905 0.173333i
$$576$$ 42.3891 0.0735923
$$577$$ −75.3419 75.3419i −0.130575 0.130575i 0.638799 0.769374i $$-0.279432\pi$$
−0.769374 + 0.638799i $$0.779432\pi$$
$$578$$ −346.613 + 346.613i −0.599676 + 0.599676i
$$579$$ 32.5522i 0.0562215i
$$580$$ −69.8985 85.1413i −0.120515 0.146795i
$$581$$ 183.591 0.315992
$$582$$ 80.0943 + 80.0943i 0.137619 + 0.137619i
$$583$$ 864.760 864.760i 1.48329 1.48329i
$$584$$ 166.397i 0.284926i
$$585$$ −18.0126 + 183.211i −0.0307907 + 0.313181i
$$586$$ 739.808 1.26247
$$587$$ 537.340 + 537.340i 0.915401 + 0.915401i 0.996691 0.0812898i $$-0.0259039\pi$$
−0.0812898 + 0.996691i $$0.525904\pi$$
$$588$$ 150.256 150.256i 0.255538 0.255538i
$$589$$ 1254.08i 2.12917i
$$590$$ 96.9343 + 9.53019i 0.164295 + 0.0161529i
$$591$$ 157.076 0.265780
$$592$$ −58.9181 58.9181i −0.0995238 0.0995238i
$$593$$ −100.376 + 100.376i −0.169268 + 0.169268i −0.786657 0.617390i $$-0.788190\pi$$
0.617390 + 0.786657i $$0.288190\pi$$
$$594$$ 576.309i 0.970217i
$$595$$ −994.663 + 816.589i −1.67170 + 1.37242i
$$596$$ −137.754 −0.231130
$$597$$ −358.767 358.767i −0.600949 0.600949i
$$598$$ 33.3250 33.3250i 0.0557274 0.0557274i
$$599$$ 57.7918i 0.0964805i −0.998836 0.0482403i $$-0.984639\pi$$
0.998836 0.0482403i $$-0.0153613\pi$$
$$600$$ 133.435 + 26.4936i 0.222392 + 0.0441561i
$$601$$ 855.388 1.42327 0.711637 0.702547i $$-0.247954\pi$$
0.711637 + 0.702547i $$0.247954\pi$$
$$602$$ 6.06308 + 6.06308i 0.0100716 + 0.0100716i
$$603$$ 89.6032 89.6032i 0.148596 0.148596i
$$604$$ 276.798i 0.458275i
$$605$$ −312.337 380.449i −0.516259 0.628841i
$$606$$ −287.693 −0.474741
$$607$$ 171.294 + 171.294i 0.282198 + 0.282198i 0.833985 0.551787i $$-0.186054\pi$$
−0.551787 + 0.833985i $$0.686054\pi$$
$$608$$ 118.404 118.404i 0.194744 0.194744i
$$609$$ 216.364i 0.355277i
$$610$$ 26.9964 274.588i 0.0442564 0.450144i
$$611$$ −520.990 −0.852684
$$612$$ 188.919 + 188.919i 0.308691 + 0.308691i
$$613$$ −107.859 + 107.859i −0.175952 + 0.175952i −0.789589 0.613636i $$-0.789706\pi$$
0.613636 + 0.789589i $$0.289706\pi$$
$$614$$ 8.34078i 0.0135843i
$$615$$ 229.357 + 22.5495i 0.372938 + 0.0366658i
$$616$$ 427.756 0.694409
$$617$$ 234.765 + 234.765i 0.380495 + 0.380495i 0.871280 0.490786i $$-0.163290\pi$$
−0.490786 + 0.871280i $$0.663290\pi$$
$$618$$ 41.9610 41.9610i 0.0678981 0.0678981i
$$619$$ 35.0950i 0.0566964i 0.999598 + 0.0283482i $$0.00902472\pi$$
−0.999598 + 0.0283482i $$0.990975\pi$$
$$620$$ 327.448 268.825i 0.528142 0.433588i
$$621$$ 131.929 0.212446
$$622$$ −385.664 385.664i −0.620039 0.620039i
$$623$$ −1023.02 + 1023.02i −1.64209 + 1.64209i
$$624$$ 53.4745i 0.0856963i
$$625$$ −577.591 238.776i −0.924145 0.382041i
$$626$$ −312.930 −0.499888
$$627$$ 596.538 + 596.538i 0.951416 + 0.951416i
$$628$$ 270.574 270.574i 0.430850 0.430850i
$$629$$ 525.170i 0.834929i
$$630$$ 242.709 + 295.637i 0.385253 + 0.469266i
$$631$$ −826.767 −1.31025 −0.655124 0.755521i $$-0.727384\pi$$
−0.655124 + 0.755521i $$0.727384\pi$$
$$632$$ 310.967 + 310.967i 0.492037 + 0.492037i
$$633$$ −437.386 + 437.386i −0.690974 + 0.690974i
$$634$$ 345.345i 0.544708i
$$635$$ −93.3144 + 949.128i −0.146952 + 1.49469i
$$636$$ 317.655 0.499458
$$637$$ −271.349 271.349i −0.425980 0.425980i
$$638$$ −163.186 + 163.186i −0.255777 + 0.255777i
$$639$$ 546.355i 0.855016i
$$640$$ −56.2971 5.53490i −0.0879642 0.00864829i
$$641$$ 52.1713 0.0813904 0.0406952 0.999172i $$-0.487043\pi$$
0.0406952 + 0.999172i $$0.487043\pi$$
$$642$$ 103.412 + 103.412i 0.161077 + 0.161077i
$$643$$ 241.431 241.431i 0.375476 0.375476i −0.493991 0.869467i $$-0.664463\pi$$
0.869467 + 0.493991i $$0.164463\pi$$
$$644$$ 97.9220i 0.152053i
$$645$$ 4.41551 3.62500i 0.00684575 0.00562016i
$$646$$ 1055.40 1.63375
$$647$$ −320.910 320.910i −0.495998 0.495998i 0.414192 0.910190i $$-0.364064\pi$$
−0.910190 + 0.414192i $$0.864064\pi$$
$$648$$ −10.4732 + 10.4732i −0.0161624 + 0.0161624i
$$649$$ 204.055i 0.314414i
$$650$$ 47.8451 240.971i 0.0736078 0.370725i
$$651$$ −832.119 −1.27822
$$652$$ −168.748 168.748i −0.258816 0.258816i
$$653$$ 358.411 358.411i 0.548869 0.548869i −0.377245 0.926114i $$-0.623128\pi$$
0.926114 + 0.377245i $$0.123128\pi$$
$$654$$ 397.720i 0.608134i
$$655$$ 153.214 + 186.626i 0.233915 + 0.284925i
$$656$$ −95.8320 −0.146085
$$657$$ 220.420 + 220.420i 0.335494 + 0.335494i
$$658$$ −765.437 + 765.437i −1.16328 + 1.16328i
$$659$$ 654.343i 0.992934i −0.868056 0.496467i $$-0.834630\pi$$
0.868056 0.496467i $$-0.165370\pi$$
$$660$$ 27.8856 283.633i 0.0422510 0.429747i
$$661$$ 205.380 0.310711 0.155355 0.987859i $$-0.450348\pi$$
0.155355 + 0.987859i $$0.450348\pi$$
$$662$$ 594.585 + 594.585i 0.898165 + 0.898165i
$$663$$ −238.324 + 238.324i −0.359463 + 0.359463i
$$664$$ 50.8640i 0.0766024i
$$665$$ 1503.75 + 147.842i 2.26128 + 0.222319i
$$666$$ −156.093 −0.234374
$$667$$ 37.3565 + 37.3565i 0.0560067 + 0.0560067i
$$668$$ −435.461 + 435.461i −0.651888 + 0.651888i
$$669$$ 206.699i 0.308967i
$$670$$ −130.702 + 107.302i −0.195078 + 0.160153i
$$671$$ −578.030 −0.861446
$$672$$ 78.5646 + 78.5646i 0.116912 + 0.116912i
$$673$$ −181.364 + 181.364i −0.269486 + 0.269486i −0.828893 0.559407i $$-0.811029\pi$$
0.559407 + 0.828893i $$0.311029\pi$$
$$674$$ 636.344i 0.944130i
$$675$$ 571.690 382.279i 0.846949 0.566339i
$$676$$ −241.430 −0.357145
$$677$$ 49.6207 + 49.6207i 0.0732950 + 0.0732950i 0.742804 0.669509i $$-0.233495\pi$$
−0.669509 + 0.742804i $$0.733495\pi$$
$$678$$ −6.49433 + 6.49433i −0.00957866 + 0.00957866i
$$679$$ 425.018i 0.625947i
$$680$$ −226.236 275.572i −0.332700 0.405253i
$$681$$ 173.209 0.254345
$$682$$ −627.601 627.601i −0.920236 0.920236i
$$683$$ −665.906 + 665.906i −0.974972 + 0.974972i −0.999694 0.0247224i $$-0.992130\pi$$
0.0247224 + 0.999694i $$0.492130\pi$$
$$684$$ 313.691i 0.458613i
$$685$$ −2.27675 + 23.1574i −0.00332372 + 0.0338065i
$$686$$ −89.8789 −0.131019
$$687$$ 140.333 + 140.333i 0.204269 + 0.204269i
$$688$$ −1.67978 + 1.67978i −0.00244154 + 0.00244154i
$$689$$ 573.656i 0.832593i
$$690$$ −64.9293 6.38358i −0.0941004 0.00925157i
$$691$$ 868.900 1.25745 0.628727 0.777626i $$-0.283576\pi$$
0.628727 + 0.777626i $$0.283576\pi$$
$$692$$ −445.068 445.068i −0.643162 0.643162i
$$693$$ 566.632 566.632i 0.817651 0.817651i
$$694$$ 323.697i 0.466422i
$$695$$ −421.004 + 345.632i −0.605761 + 0.497312i
$$696$$ −59.9436 −0.0861258
$$697$$ −427.102 427.102i −0.612772 0.612772i
$$698$$ −66.1242 + 66.1242i −0.0947339 + 0.0947339i
$$699$$ 576.272i 0.824424i
$$700$$ −283.740 424.328i −0.405344 0.606183i
$$701$$ 769.630 1.09790 0.548952 0.835854i $$-0.315027\pi$$
0.548952 + 0.835854i $$0.315027\pi$$
$$702$$ 191.153 + 191.153i 0.272298 + 0.272298i
$$703$$ −436.010 + 436.010i −0.620213 + 0.620213i
$$704$$ 118.510i 0.168338i
$$705$$ 457.640 + 557.439i 0.649135 + 0.790693i
$$706$$ 662.236 0.938012
$$707$$ 763.318 + 763.318i 1.07966 + 1.07966i
$$708$$ 37.4780 37.4780i 0.0529351 0.0529351i
$$709$$ 1193.36i 1.68316i −0.540133 0.841580i $$-0.681626\pi$$
0.540133 0.841580i $$-0.318374\pi$$
$$710$$ 71.3396 725.615i 0.100478 1.02199i
$$711$$ 823.853 1.15872
$$712$$ −283.429 283.429i −0.398075 0.398075i
$$713$$ −143.671 + 143.671i −0.201501 + 0.201501i
$$714$$ 700.291i 0.980799i
$$715$$ −512.215 50.3589i −0.716384 0.0704320i
$$716$$ −388.116 −0.542061
$$717$$ 121.774 + 121.774i 0.169839 + 0.169839i
$$718$$ −134.587 + 134.587i −0.187447 + 0.187447i
$$719$$ 1266.00i 1.76078i −0.474252 0.880389i $$-0.657281\pi$$
0.474252 0.880389i $$-0.342719\pi$$
$$720$$ −81.9064 + 67.2427i −0.113759 + 0.0933926i
$$721$$ −222.665 −0.308828
$$722$$ −515.224 515.224i −0.713607 0.713607i
$$723$$ −238.511 + 238.511i −0.329890 + 0.329890i
$$724$$ 0.825590i 0.00114032i
$$725$$ 270.123 + 53.6331i 0.372583 + 0.0739768i
$$726$$ −267.854 −0.368945
$$727$$ −712.318 712.318i −0.979805 0.979805i 0.0199952 0.999800i $$-0.493635\pi$$
−0.999800 + 0.0199952i $$0.993635\pi$$
$$728$$ 141.880 141.880i 0.194891 0.194891i
$$729$$ 504.066i 0.691449i
$$730$$ −263.959 321.521i −0.361587 0.440439i
$$731$$ −14.9728 −0.0204826
$$732$$ −106.165 106.165i −0.145034 0.145034i
$$733$$ −785.498 + 785.498i −1.07162 + 1.07162i −0.0743915 + 0.997229i $$0.523701\pi$$
−0.997229 + 0.0743915i $$0.976299\pi$$
$$734$$ 903.320i 1.23068i
$$735$$ −51.9784 + 528.688i −0.0707190 + 0.719303i
$$736$$ 27.1293 0.0368605
$$737$$ 250.509 + 250.509i 0.339904 + 0.339904i
$$738$$ −126.945 + 126.945i −0.172012 + 0.172012i
$$739$$ 176.725i 0.239141i 0.992826 + 0.119570i $$0.0381517\pi$$
−0.992826 + 0.119570i $$0.961848\pi$$
$$740$$ 207.307 + 20.3816i 0.280145 + 0.0275427i
$$741$$ 395.726 0.534043
$$742$$ −842.815 842.815i −1.13587 1.13587i
$$743$$ −433.606 + 433.606i −0.583588 + 0.583588i −0.935887 0.352300i $$-0.885400\pi$$
0.352300 + 0.935887i $$0.385400\pi$$
$$744$$ 230.539i 0.309864i
$$745$$ 266.174 218.521i 0.357281 0.293317i
$$746$$ 903.732 1.21144
$$747$$ 67.3775 + 67.3775i 0.0901975 + 0.0901975i
$$748$$ −528.173 + 528.173i −0.706114 + 0.706114i
$$749$$ 548.751i 0.732645i
$$750$$ −299.857 + 160.478i −0.399809 + 0.213971i
$$751$$ 197.940 0.263569 0.131785 0.991278i $$-0.457929\pi$$
0.131785 + 0.991278i $$0.457929\pi$$
$$752$$ −212.065 212.065i −0.282001 0.282001i
$$753$$ −444.545 + 444.545i −0.590365 + 0.590365i
$$754$$ 108.253i 0.143571i
$$755$$ −439.090 534.843i −0.581576 0.708401i
$$756$$ 561.684 0.742968
$$757$$ −660.110 660.110i −0.872008 0.872008i 0.120683 0.992691i $$-0.461491\pi$$
−0.992691 + 0.120683i $$0.961491\pi$$
$$758$$ −230.954 + 230.954i −0.304688 + 0.304688i
$$759$$ 136.681i 0.180081i
$$760$$ −40.9598 + 416.614i −0.0538944 + 0.548176i
$$761$$ 886.095 1.16438 0.582191 0.813052i $$-0.302196\pi$$
0.582191 + 0.813052i $$0.302196\pi$$
$$762$$ 366.965 + 366.965i 0.481581 + 0.481581i
$$763$$ −1055.24 + 1055.24i −1.38302 + 1.38302i
$$764$$ 627.271i 0.821036i
$$765$$ −664.725 65.3531i −0.868922 0.0854288i
$$766$$ 367.668 0.479985
$$767$$ −67.6819 67.6819i −0.0882424 0.0882424i
$$768$$ −21.7663 + 21.7663i −0.0283416 + 0.0283416i
$$769$$ 666.097i 0.866185i −0.901349 0.433093i $$-0.857422\pi$$
0.901349 0.433093i $$-0.142578\pi$$
$$770$$ −826.532 + 678.558i −1.07342 + 0.881244i
$$771$$ 122.325 0.158658
$$772$$ −23.9285 23.9285i −0.0309955 0.0309955i
$$773$$ 686.942 686.942i 0.888670 0.888670i −0.105725 0.994395i $$-0.533716\pi$$
0.994395 + 0.105725i $$0.0337165\pi$$
$$774$$ 4.45027i 0.00574971i
$$775$$ −206.269 + 1038.87i −0.266154 + 1.34048i
$$776$$ 117.751 0.151742
$$777$$ −289.305