# Properties

 Label 75.3.f.c.43.1 Level $75$ Weight $3$ Character 75.43 Analytic conductor $2.044$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$75 = 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 75.f (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.04360198270$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(i)$$ Coefficient field: $$\Q(i, \sqrt{6})$$ Defining polynomial: $$x^{4} + 9$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 15) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 43.1 Root $$-1.22474 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 75.43 Dual form 75.3.f.c.7.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.224745 + 0.224745i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.89898i q^{4} -0.550510 q^{6} +(-3.44949 + 3.44949i) q^{7} +(-1.77526 - 1.77526i) q^{8} +3.00000i q^{9} +O(q^{10})$$ $$q+(-0.224745 + 0.224745i) q^{2} +(1.22474 + 1.22474i) q^{3} +3.89898i q^{4} -0.550510 q^{6} +(-3.44949 + 3.44949i) q^{7} +(-1.77526 - 1.77526i) q^{8} +3.00000i q^{9} +11.3485 q^{11} +(-4.77526 + 4.77526i) q^{12} +(5.55051 + 5.55051i) q^{13} -1.55051i q^{14} -14.7980 q^{16} +(17.3485 - 17.3485i) q^{17} +(-0.674235 - 0.674235i) q^{18} -8.69694i q^{19} -8.44949 q^{21} +(-2.55051 + 2.55051i) q^{22} +(-11.5505 - 11.5505i) q^{23} -4.34847i q^{24} -2.49490 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-13.4495 - 13.4495i) q^{28} -35.1464i q^{29} +10.6969 q^{31} +(10.4268 - 10.4268i) q^{32} +(13.8990 + 13.8990i) q^{33} +7.79796i q^{34} -11.6969 q^{36} +(6.04541 - 6.04541i) q^{37} +(1.95459 + 1.95459i) q^{38} +13.5959i q^{39} +0.696938 q^{41} +(1.89898 - 1.89898i) q^{42} +(26.4949 + 26.4949i) q^{43} +44.2474i q^{44} +5.19184 q^{46} +(-44.2474 + 44.2474i) q^{47} +(-18.1237 - 18.1237i) q^{48} +25.2020i q^{49} +42.4949 q^{51} +(-21.6413 + 21.6413i) q^{52} +(0.696938 + 0.696938i) q^{53} -1.65153i q^{54} +12.2474 q^{56} +(10.6515 - 10.6515i) q^{57} +(7.89898 + 7.89898i) q^{58} +39.9342i q^{59} +5.90918 q^{61} +(-2.40408 + 2.40408i) q^{62} +(-10.3485 - 10.3485i) q^{63} -54.5051i q^{64} -6.24745 q^{66} +(45.1010 - 45.1010i) q^{67} +(67.6413 + 67.6413i) q^{68} -28.2929i q^{69} -68.0000 q^{71} +(5.32577 - 5.32577i) q^{72} +(-77.7878 - 77.7878i) q^{73} +2.71735i q^{74} +33.9092 q^{76} +(-39.1464 + 39.1464i) q^{77} +(-3.05561 - 3.05561i) q^{78} +24.4949i q^{79} -9.00000 q^{81} +(-0.156633 + 0.156633i) q^{82} +(-13.1464 - 13.1464i) q^{83} -32.9444i q^{84} -11.9092 q^{86} +(43.0454 - 43.0454i) q^{87} +(-20.1464 - 20.1464i) q^{88} -82.1816i q^{89} -38.2929 q^{91} +(45.0352 - 45.0352i) q^{92} +(13.1010 + 13.1010i) q^{93} -19.8888i q^{94} +25.5403 q^{96} +(24.5959 - 24.5959i) q^{97} +(-5.66403 - 5.66403i) q^{98} +34.0454i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 4q^{2} - 12q^{6} - 4q^{7} - 12q^{8} + O(q^{10})$$ $$4q + 4q^{2} - 12q^{6} - 4q^{7} - 12q^{8} + 16q^{11} - 24q^{12} + 32q^{13} - 20q^{16} + 40q^{17} + 12q^{18} - 24q^{21} - 20q^{22} - 56q^{23} + 88q^{26} - 44q^{28} - 16q^{31} + 76q^{32} + 36q^{33} + 12q^{36} - 64q^{37} + 96q^{38} - 56q^{41} - 12q^{42} + 8q^{43} - 136q^{46} - 128q^{47} - 48q^{48} + 72q^{51} + 80q^{52} - 56q^{53} + 72q^{57} + 12q^{58} + 200q^{61} - 88q^{62} - 12q^{63} + 24q^{66} + 200q^{67} + 104q^{68} - 272q^{71} + 36q^{72} - 76q^{73} + 312q^{76} - 88q^{77} - 120q^{78} - 36q^{81} - 128q^{82} + 16q^{83} - 224q^{86} + 84q^{87} - 12q^{88} - 16q^{91} - 104q^{92} + 72q^{93} - 84q^{96} + 20q^{97} + 188q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$$.

 $$n$$ $$26$$ $$52$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{3}{4}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.224745 + 0.224745i −0.112372 + 0.112372i −0.761057 0.648685i $$-0.775319\pi$$
0.648685 + 0.761057i $$0.275319\pi$$
$$3$$ 1.22474 + 1.22474i 0.408248 + 0.408248i
$$4$$ 3.89898i 0.974745i
$$5$$ 0 0
$$6$$ −0.550510 −0.0917517
$$7$$ −3.44949 + 3.44949i −0.492784 + 0.492784i −0.909182 0.416398i $$-0.863292\pi$$
0.416398 + 0.909182i $$0.363292\pi$$
$$8$$ −1.77526 1.77526i −0.221907 0.221907i
$$9$$ 3.00000i 0.333333i
$$10$$ 0 0
$$11$$ 11.3485 1.03168 0.515840 0.856685i $$-0.327480\pi$$
0.515840 + 0.856685i $$0.327480\pi$$
$$12$$ −4.77526 + 4.77526i −0.397938 + 0.397938i
$$13$$ 5.55051 + 5.55051i 0.426962 + 0.426962i 0.887592 0.460630i $$-0.152376\pi$$
−0.460630 + 0.887592i $$0.652376\pi$$
$$14$$ 1.55051i 0.110751i
$$15$$ 0 0
$$16$$ −14.7980 −0.924872
$$17$$ 17.3485 17.3485i 1.02050 1.02050i 0.0207127 0.999785i $$-0.493406\pi$$
0.999785 0.0207127i $$-0.00659354\pi$$
$$18$$ −0.674235 0.674235i −0.0374575 0.0374575i
$$19$$ 8.69694i 0.457734i −0.973458 0.228867i $$-0.926498\pi$$
0.973458 0.228867i $$-0.0735020\pi$$
$$20$$ 0 0
$$21$$ −8.44949 −0.402357
$$22$$ −2.55051 + 2.55051i −0.115932 + 0.115932i
$$23$$ −11.5505 11.5505i −0.502196 0.502196i 0.409924 0.912120i $$-0.365555\pi$$
−0.912120 + 0.409924i $$0.865555\pi$$
$$24$$ 4.34847i 0.181186i
$$25$$ 0 0
$$26$$ −2.49490 −0.0959576
$$27$$ −3.67423 + 3.67423i −0.136083 + 0.136083i
$$28$$ −13.4495 13.4495i −0.480339 0.480339i
$$29$$ 35.1464i 1.21195i −0.795485 0.605973i $$-0.792784\pi$$
0.795485 0.605973i $$-0.207216\pi$$
$$30$$ 0 0
$$31$$ 10.6969 0.345063 0.172531 0.985004i $$-0.444805\pi$$
0.172531 + 0.985004i $$0.444805\pi$$
$$32$$ 10.4268 10.4268i 0.325837 0.325837i
$$33$$ 13.8990 + 13.8990i 0.421181 + 0.421181i
$$34$$ 7.79796i 0.229352i
$$35$$ 0 0
$$36$$ −11.6969 −0.324915
$$37$$ 6.04541 6.04541i 0.163389 0.163389i −0.620677 0.784066i $$-0.713142\pi$$
0.784066 + 0.620677i $$0.213142\pi$$
$$38$$ 1.95459 + 1.95459i 0.0514366 + 0.0514366i
$$39$$ 13.5959i 0.348613i
$$40$$ 0 0
$$41$$ 0.696938 0.0169985 0.00849925 0.999964i $$-0.497295\pi$$
0.00849925 + 0.999964i $$0.497295\pi$$
$$42$$ 1.89898 1.89898i 0.0452138 0.0452138i
$$43$$ 26.4949 + 26.4949i 0.616160 + 0.616160i 0.944544 0.328384i $$-0.106504\pi$$
−0.328384 + 0.944544i $$0.606504\pi$$
$$44$$ 44.2474i 1.00562i
$$45$$ 0 0
$$46$$ 5.19184 0.112866
$$47$$ −44.2474 + 44.2474i −0.941435 + 0.941435i −0.998377 0.0569424i $$-0.981865\pi$$
0.0569424 + 0.998377i $$0.481865\pi$$
$$48$$ −18.1237 18.1237i −0.377578 0.377578i
$$49$$ 25.2020i 0.514327i
$$50$$ 0 0
$$51$$ 42.4949 0.833233
$$52$$ −21.6413 + 21.6413i −0.416179 + 0.416179i
$$53$$ 0.696938 + 0.696938i 0.0131498 + 0.0131498i 0.713651 0.700501i $$-0.247040\pi$$
−0.700501 + 0.713651i $$0.747040\pi$$
$$54$$ 1.65153i 0.0305839i
$$55$$ 0 0
$$56$$ 12.2474 0.218704
$$57$$ 10.6515 10.6515i 0.186869 0.186869i
$$58$$ 7.89898 + 7.89898i 0.136189 + 0.136189i
$$59$$ 39.9342i 0.676851i 0.940993 + 0.338425i $$0.109894\pi$$
−0.940993 + 0.338425i $$0.890106\pi$$
$$60$$ 0 0
$$61$$ 5.90918 0.0968719 0.0484359 0.998826i $$-0.484576\pi$$
0.0484359 + 0.998826i $$0.484576\pi$$
$$62$$ −2.40408 + 2.40408i −0.0387755 + 0.0387755i
$$63$$ −10.3485 10.3485i −0.164261 0.164261i
$$64$$ 54.5051i 0.851642i
$$65$$ 0 0
$$66$$ −6.24745 −0.0946583
$$67$$ 45.1010 45.1010i 0.673150 0.673150i −0.285291 0.958441i $$-0.592090\pi$$
0.958441 + 0.285291i $$0.0920903\pi$$
$$68$$ 67.6413 + 67.6413i 0.994725 + 0.994725i
$$69$$ 28.2929i 0.410041i
$$70$$ 0 0
$$71$$ −68.0000 −0.957746 −0.478873 0.877884i $$-0.658955\pi$$
−0.478873 + 0.877884i $$0.658955\pi$$
$$72$$ 5.32577 5.32577i 0.0739690 0.0739690i
$$73$$ −77.7878 77.7878i −1.06559 1.06559i −0.997693 0.0678931i $$-0.978372\pi$$
−0.0678931 0.997693i $$-0.521628\pi$$
$$74$$ 2.71735i 0.0367209i
$$75$$ 0 0
$$76$$ 33.9092 0.446173
$$77$$ −39.1464 + 39.1464i −0.508395 + 0.508395i
$$78$$ −3.05561 3.05561i −0.0391745 0.0391745i
$$79$$ 24.4949i 0.310062i 0.987910 + 0.155031i $$0.0495477\pi$$
−0.987910 + 0.155031i $$0.950452\pi$$
$$80$$ 0 0
$$81$$ −9.00000 −0.111111
$$82$$ −0.156633 + 0.156633i −0.00191016 + 0.00191016i
$$83$$ −13.1464 13.1464i −0.158391 0.158391i 0.623463 0.781853i $$-0.285725\pi$$
−0.781853 + 0.623463i $$0.785725\pi$$
$$84$$ 32.9444i 0.392195i
$$85$$ 0 0
$$86$$ −11.9092 −0.138479
$$87$$ 43.0454 43.0454i 0.494775 0.494775i
$$88$$ −20.1464 20.1464i −0.228937 0.228937i
$$89$$ 82.1816i 0.923389i −0.887039 0.461695i $$-0.847242\pi$$
0.887039 0.461695i $$-0.152758\pi$$
$$90$$ 0 0
$$91$$ −38.2929 −0.420801
$$92$$ 45.0352 45.0352i 0.489513 0.489513i
$$93$$ 13.1010 + 13.1010i 0.140871 + 0.140871i
$$94$$ 19.8888i 0.211583i
$$95$$ 0 0
$$96$$ 25.5403 0.266045
$$97$$ 24.5959 24.5959i 0.253566 0.253566i −0.568865 0.822431i $$-0.692617\pi$$
0.822431 + 0.568865i $$0.192617\pi$$
$$98$$ −5.66403 5.66403i −0.0577962 0.0577962i
$$99$$ 34.0454i 0.343893i
$$100$$ 0 0
$$101$$ −105.621 −1.04575 −0.522876 0.852409i $$-0.675141\pi$$
−0.522876 + 0.852409i $$0.675141\pi$$
$$102$$ −9.55051 + 9.55051i −0.0936325 + 0.0936325i
$$103$$ 89.2474 + 89.2474i 0.866480 + 0.866480i 0.992081 0.125601i $$-0.0400858\pi$$
−0.125601 + 0.992081i $$0.540086\pi$$
$$104$$ 19.7071i 0.189492i
$$105$$ 0 0
$$106$$ −0.313267 −0.00295535
$$107$$ −68.7423 + 68.7423i −0.642452 + 0.642452i −0.951158 0.308706i $$-0.900104\pi$$
0.308706 + 0.951158i $$0.400104\pi$$
$$108$$ −14.3258 14.3258i −0.132646 0.132646i
$$109$$ 68.6969i 0.630247i −0.949051 0.315124i $$-0.897954\pi$$
0.949051 0.315124i $$-0.102046\pi$$
$$110$$ 0 0
$$111$$ 14.8082 0.133407
$$112$$ 51.0454 51.0454i 0.455763 0.455763i
$$113$$ −97.6413 97.6413i −0.864083 0.864083i 0.127727 0.991809i $$-0.459232\pi$$
−0.991809 + 0.127727i $$0.959232\pi$$
$$114$$ 4.78775i 0.0419978i
$$115$$ 0 0
$$116$$ 137.035 1.18134
$$117$$ −16.6515 + 16.6515i −0.142321 + 0.142321i
$$118$$ −8.97500 8.97500i −0.0760593 0.0760593i
$$119$$ 119.687i 1.00577i
$$120$$ 0 0
$$121$$ 7.78775 0.0643616
$$122$$ −1.32806 + 1.32806i −0.0108857 + 0.0108857i
$$123$$ 0.853572 + 0.853572i 0.00693961 + 0.00693961i
$$124$$ 41.7071i 0.336348i
$$125$$ 0 0
$$126$$ 4.65153 0.0369169
$$127$$ −164.621 + 164.621i −1.29623 + 1.29623i −0.365362 + 0.930865i $$0.619055\pi$$
−0.930865 + 0.365362i $$0.880945\pi$$
$$128$$ 53.9569 + 53.9569i 0.421538 + 0.421538i
$$129$$ 64.8990i 0.503093i
$$130$$ 0 0
$$131$$ 106.136 0.810200 0.405100 0.914272i $$-0.367237\pi$$
0.405100 + 0.914272i $$0.367237\pi$$
$$132$$ −54.1918 + 54.1918i −0.410544 + 0.410544i
$$133$$ 30.0000 + 30.0000i 0.225564 + 0.225564i
$$134$$ 20.2724i 0.151287i
$$135$$ 0 0
$$136$$ −61.5959 −0.452911
$$137$$ 166.631 166.631i 1.21629 1.21629i 0.247363 0.968923i $$-0.420436\pi$$
0.968923 0.247363i $$-0.0795639\pi$$
$$138$$ 6.35867 + 6.35867i 0.0460774 + 0.0460774i
$$139$$ 191.171i 1.37533i 0.726026 + 0.687667i $$0.241365\pi$$
−0.726026 + 0.687667i $$0.758635\pi$$
$$140$$ 0 0
$$141$$ −108.384 −0.768679
$$142$$ 15.2827 15.2827i 0.107624 0.107624i
$$143$$ 62.9898 + 62.9898i 0.440488 + 0.440488i
$$144$$ 44.3939i 0.308291i
$$145$$ 0 0
$$146$$ 34.9648 0.239485
$$147$$ −30.8661 + 30.8661i −0.209973 + 0.209973i
$$148$$ 23.5709 + 23.5709i 0.159263 + 0.159263i
$$149$$ 84.8536i 0.569487i −0.958604 0.284744i $$-0.908092\pi$$
0.958604 0.284744i $$-0.0919084\pi$$
$$150$$ 0 0
$$151$$ 148.969 0.986552 0.493276 0.869873i $$-0.335799\pi$$
0.493276 + 0.869873i $$0.335799\pi$$
$$152$$ −15.4393 + 15.4393i −0.101574 + 0.101574i
$$153$$ 52.0454 + 52.0454i 0.340166 + 0.340166i
$$154$$ 17.5959i 0.114259i
$$155$$ 0 0
$$156$$ −53.0102 −0.339809
$$157$$ −16.8536 + 16.8536i −0.107348 + 0.107348i −0.758741 0.651393i $$-0.774185\pi$$
0.651393 + 0.758741i $$0.274185\pi$$
$$158$$ −5.50510 5.50510i −0.0348424 0.0348424i
$$159$$ 1.70714i 0.0107368i
$$160$$ 0 0
$$161$$ 79.6867 0.494949
$$162$$ 2.02270 2.02270i 0.0124858 0.0124858i
$$163$$ −130.606 130.606i −0.801265 0.801265i 0.182029 0.983293i $$-0.441734\pi$$
−0.983293 + 0.182029i $$0.941734\pi$$
$$164$$ 2.71735i 0.0165692i
$$165$$ 0 0
$$166$$ 5.90918 0.0355975
$$167$$ 45.0352 45.0352i 0.269672 0.269672i −0.559296 0.828968i $$-0.688929\pi$$
0.828968 + 0.559296i $$0.188929\pi$$
$$168$$ 15.0000 + 15.0000i 0.0892857 + 0.0892857i
$$169$$ 107.384i 0.635406i
$$170$$ 0 0
$$171$$ 26.0908 0.152578
$$172$$ −103.303 + 103.303i −0.600599 + 0.600599i
$$173$$ −146.631 146.631i −0.847579 0.847579i 0.142252 0.989831i $$-0.454566\pi$$
−0.989831 + 0.142252i $$0.954566\pi$$
$$174$$ 19.3485i 0.111198i
$$175$$ 0 0
$$176$$ −167.934 −0.954171
$$177$$ −48.9092 + 48.9092i −0.276323 + 0.276323i
$$178$$ 18.4699 + 18.4699i 0.103763 + 0.103763i
$$179$$ 183.712i 1.02632i −0.858292 0.513161i $$-0.828474\pi$$
0.858292 0.513161i $$-0.171526\pi$$
$$180$$ 0 0
$$181$$ −286.272 −1.58162 −0.790808 0.612064i $$-0.790339\pi$$
−0.790808 + 0.612064i $$0.790339\pi$$
$$182$$ 8.60612 8.60612i 0.0472864 0.0472864i
$$183$$ 7.23724 + 7.23724i 0.0395478 + 0.0395478i
$$184$$ 41.0102i 0.222882i
$$185$$ 0 0
$$186$$ −5.88877 −0.0316601
$$187$$ 196.879 196.879i 1.05283 1.05283i
$$188$$ −172.520 172.520i −0.917659 0.917659i
$$189$$ 25.3485i 0.134119i
$$190$$ 0 0
$$191$$ 48.0908 0.251784 0.125892 0.992044i $$-0.459821\pi$$
0.125892 + 0.992044i $$0.459821\pi$$
$$192$$ 66.7548 66.7548i 0.347681 0.347681i
$$193$$ 255.565 + 255.565i 1.32417 + 1.32417i 0.910364 + 0.413809i $$0.135802\pi$$
0.413809 + 0.910364i $$0.364198\pi$$
$$194$$ 11.0556i 0.0569877i
$$195$$ 0 0
$$196$$ −98.2622 −0.501338
$$197$$ 96.6969 96.6969i 0.490847 0.490847i −0.417726 0.908573i $$-0.637173\pi$$
0.908573 + 0.417726i $$0.137173\pi$$
$$198$$ −7.65153 7.65153i −0.0386441 0.0386441i
$$199$$ 192.606i 0.967870i −0.875104 0.483935i $$-0.839207\pi$$
0.875104 0.483935i $$-0.160793\pi$$
$$200$$ 0 0
$$201$$ 110.474 0.549624
$$202$$ 23.7378 23.7378i 0.117514 0.117514i
$$203$$ 121.237 + 121.237i 0.597228 + 0.597228i
$$204$$ 165.687i 0.812190i
$$205$$ 0 0
$$206$$ −40.1158 −0.194737
$$207$$ 34.6515 34.6515i 0.167399 0.167399i
$$208$$ −82.1362 82.1362i −0.394886 0.394886i
$$209$$ 98.6969i 0.472234i
$$210$$ 0 0
$$211$$ 147.212 0.697688 0.348844 0.937181i $$-0.386574\pi$$
0.348844 + 0.937181i $$0.386574\pi$$
$$212$$ −2.71735 + 2.71735i −0.0128177 + 0.0128177i
$$213$$ −83.2827 83.2827i −0.390998 0.390998i
$$214$$ 30.8990i 0.144388i
$$215$$ 0 0
$$216$$ 13.0454 0.0603954
$$217$$ −36.8990 + 36.8990i −0.170041 + 0.170041i
$$218$$ 15.4393 + 15.4393i 0.0708224 + 0.0708224i
$$219$$ 190.540i 0.870047i
$$220$$ 0 0
$$221$$ 192.586 0.871429
$$222$$ −3.32806 + 3.32806i −0.0149913 + 0.0149913i
$$223$$ −167.429 167.429i −0.750803 0.750803i 0.223826 0.974629i $$-0.428145\pi$$
−0.974629 + 0.223826i $$0.928145\pi$$
$$224$$ 71.9342i 0.321135i
$$225$$ 0 0
$$226$$ 43.8888 0.194198
$$227$$ −253.171 + 253.171i −1.11529 + 1.11529i −0.122870 + 0.992423i $$0.539210\pi$$
−0.992423 + 0.122870i $$0.960790\pi$$
$$228$$ 41.5301 + 41.5301i 0.182150 + 0.182150i
$$229$$ 224.202i 0.979048i 0.871990 + 0.489524i $$0.162829\pi$$
−0.871990 + 0.489524i $$0.837171\pi$$
$$230$$ 0 0
$$231$$ −95.8888 −0.415103
$$232$$ −62.3939 + 62.3939i −0.268939 + 0.268939i
$$233$$ 205.712 + 205.712i 0.882883 + 0.882883i 0.993827 0.110944i $$-0.0353873\pi$$
−0.110944 + 0.993827i $$0.535387\pi$$
$$234$$ 7.48469i 0.0319859i
$$235$$ 0 0
$$236$$ −155.703 −0.659757
$$237$$ −30.0000 + 30.0000i −0.126582 + 0.126582i
$$238$$ −26.8990 26.8990i −0.113021 0.113021i
$$239$$ 345.798i 1.44685i 0.690401 + 0.723427i $$0.257434\pi$$
−0.690401 + 0.723427i $$0.742566\pi$$
$$240$$ 0 0
$$241$$ 101.576 0.421475 0.210738 0.977543i $$-0.432413\pi$$
0.210738 + 0.977543i $$0.432413\pi$$
$$242$$ −1.75026 + 1.75026i −0.00723247 + 0.00723247i
$$243$$ −11.0227 11.0227i −0.0453609 0.0453609i
$$244$$ 23.0398i 0.0944254i
$$245$$ 0 0
$$246$$ −0.383672 −0.00155964
$$247$$ 48.2724 48.2724i 0.195435 0.195435i
$$248$$ −18.9898 18.9898i −0.0765718 0.0765718i
$$249$$ 32.2020i 0.129325i
$$250$$ 0 0
$$251$$ −331.258 −1.31975 −0.659876 0.751375i $$-0.729391\pi$$
−0.659876 + 0.751375i $$0.729391\pi$$
$$252$$ 40.3485 40.3485i 0.160113 0.160113i
$$253$$ −131.081 131.081i −0.518105 0.518105i
$$254$$ 73.9954i 0.291321i
$$255$$ 0 0
$$256$$ 193.767 0.756904
$$257$$ −33.2372 + 33.2372i −0.129328 + 0.129328i −0.768808 0.639480i $$-0.779150\pi$$
0.639480 + 0.768808i $$0.279150\pi$$
$$258$$ −14.5857 14.5857i −0.0565338 0.0565338i
$$259$$ 41.7071i 0.161031i
$$260$$ 0 0
$$261$$ 105.439 0.403982
$$262$$ −23.8536 + 23.8536i −0.0910442 + 0.0910442i
$$263$$ 278.157 + 278.157i 1.05763 + 1.05763i 0.998235 + 0.0593952i $$0.0189172\pi$$
0.0593952 + 0.998235i $$0.481083\pi$$
$$264$$ 49.3485i 0.186926i
$$265$$ 0 0
$$266$$ −13.4847 −0.0506943
$$267$$ 100.652 100.652i 0.376972 0.376972i
$$268$$ 175.848 + 175.848i 0.656149 + 0.656149i
$$269$$ 488.499i 1.81598i 0.418988 + 0.907992i $$0.362385\pi$$
−0.418988 + 0.907992i $$0.637615\pi$$
$$270$$ 0 0
$$271$$ 131.576 0.485518 0.242759 0.970087i $$-0.421947\pi$$
0.242759 + 0.970087i $$0.421947\pi$$
$$272$$ −256.722 + 256.722i −0.943831 + 0.943831i
$$273$$ −46.8990 46.8990i −0.171791 0.171791i
$$274$$ 74.8990i 0.273354i
$$275$$ 0 0
$$276$$ 110.313 0.399686
$$277$$ −101.510 + 101.510i −0.366461 + 0.366461i −0.866185 0.499724i $$-0.833435\pi$$
0.499724 + 0.866185i $$0.333435\pi$$
$$278$$ −42.9648 42.9648i −0.154550 0.154550i
$$279$$ 32.0908i 0.115021i
$$280$$ 0 0
$$281$$ 343.303 1.22172 0.610860 0.791739i $$-0.290824\pi$$
0.610860 + 0.791739i $$0.290824\pi$$
$$282$$ 24.3587 24.3587i 0.0863783 0.0863783i
$$283$$ −1.19184 1.19184i −0.00421143 0.00421143i 0.704998 0.709209i $$-0.250948\pi$$
−0.709209 + 0.704998i $$0.750948\pi$$
$$284$$ 265.131i 0.933558i
$$285$$ 0 0
$$286$$ −28.3133 −0.0989974
$$287$$ −2.40408 + 2.40408i −0.00837659 + 0.00837659i
$$288$$ 31.2804 + 31.2804i 0.108612 + 0.108612i
$$289$$ 312.939i 1.08283i
$$290$$ 0 0
$$291$$ 60.2474 0.207036
$$292$$ 303.293 303.293i 1.03867 1.03867i
$$293$$ −96.5653 96.5653i −0.329574 0.329574i 0.522850 0.852425i $$-0.324869\pi$$
−0.852425 + 0.522850i $$0.824869\pi$$
$$294$$ 13.8740i 0.0471904i
$$295$$ 0 0
$$296$$ −21.4643 −0.0725145
$$297$$ −41.6969 + 41.6969i −0.140394 + 0.140394i
$$298$$ 19.0704 + 19.0704i 0.0639946 + 0.0639946i
$$299$$ 128.222i 0.428838i
$$300$$ 0 0
$$301$$ −182.788 −0.607268
$$302$$ −33.4801 + 33.4801i −0.110861 + 0.110861i
$$303$$ −129.359 129.359i −0.426926 0.426926i
$$304$$ 128.697i 0.423345i
$$305$$ 0 0
$$306$$ −23.3939 −0.0764506
$$307$$ 124.969 124.969i 0.407066 0.407066i −0.473648 0.880714i $$-0.657063\pi$$
0.880714 + 0.473648i $$0.157063\pi$$
$$308$$ −152.631 152.631i −0.495556 0.495556i
$$309$$ 218.611i 0.707478i
$$310$$ 0 0
$$311$$ −586.302 −1.88522 −0.942608 0.333902i $$-0.891635\pi$$
−0.942608 + 0.333902i $$0.891635\pi$$
$$312$$ 24.1362 24.1362i 0.0773597 0.0773597i
$$313$$ 102.373 + 102.373i 0.327072 + 0.327072i 0.851472 0.524400i $$-0.175710\pi$$
−0.524400 + 0.851472i $$0.675710\pi$$
$$314$$ 7.57551i 0.0241258i
$$315$$ 0 0
$$316$$ −95.5051 −0.302231
$$317$$ 108.783 108.783i 0.343165 0.343165i −0.514391 0.857556i $$-0.671982\pi$$
0.857556 + 0.514391i $$0.171982\pi$$
$$318$$ −0.383672 0.383672i −0.00120651 0.00120651i
$$319$$ 398.858i 1.25034i
$$320$$ 0 0
$$321$$ −168.384 −0.524560
$$322$$ −17.9092 + 17.9092i −0.0556186 + 0.0556186i
$$323$$ −150.879 150.879i −0.467116 0.467116i
$$324$$ 35.0908i 0.108305i
$$325$$ 0 0
$$326$$ 58.7061 0.180080
$$327$$ 84.1362 84.1362i 0.257297 0.257297i
$$328$$ −1.23724 1.23724i −0.00377208 0.00377208i
$$329$$ 305.262i 0.927849i
$$330$$ 0 0
$$331$$ −245.423 −0.741461 −0.370730 0.928741i $$-0.620893\pi$$
−0.370730 + 0.928741i $$0.620893\pi$$
$$332$$ 51.2577 51.2577i 0.154391 0.154391i
$$333$$ 18.1362 + 18.1362i 0.0544631 + 0.0544631i
$$334$$ 20.2429i 0.0606074i
$$335$$ 0 0
$$336$$ 125.035 0.372129
$$337$$ −213.808 + 213.808i −0.634446 + 0.634446i −0.949180 0.314734i $$-0.898085\pi$$
0.314734 + 0.949180i $$0.398085\pi$$
$$338$$ 24.1339 + 24.1339i 0.0714022 + 0.0714022i
$$339$$ 239.171i 0.705520i
$$340$$ 0 0
$$341$$ 121.394 0.355994
$$342$$ −5.86378 + 5.86378i −0.0171455 + 0.0171455i
$$343$$ −255.959 255.959i −0.746237 0.746237i
$$344$$ 94.0704i 0.273460i
$$345$$ 0 0
$$346$$ 65.9092 0.190489
$$347$$ 160.050 160.050i 0.461239 0.461239i −0.437822 0.899062i $$-0.644250\pi$$
0.899062 + 0.437822i $$0.144250\pi$$
$$348$$ 167.833 + 167.833i 0.482279 + 0.482279i
$$349$$ 298.009i 0.853894i 0.904277 + 0.426947i $$0.140411\pi$$
−0.904277 + 0.426947i $$0.859589\pi$$
$$350$$ 0 0
$$351$$ −40.7878 −0.116204
$$352$$ 118.328 118.328i 0.336159 0.336159i
$$353$$ 22.5199 + 22.5199i 0.0637957 + 0.0637957i 0.738285 0.674489i $$-0.235636\pi$$
−0.674489 + 0.738285i $$0.735636\pi$$
$$354$$ 21.9842i 0.0621022i
$$355$$ 0 0
$$356$$ 320.424 0.900069
$$357$$ −146.586 + 146.586i −0.410604 + 0.410604i
$$358$$ 41.2883 + 41.2883i 0.115330 + 0.115330i
$$359$$ 48.2724i 0.134464i −0.997737 0.0672318i $$-0.978583\pi$$
0.997737 0.0672318i $$-0.0214167\pi$$
$$360$$ 0 0
$$361$$ 285.363 0.790480
$$362$$ 64.3383 64.3383i 0.177730 0.177730i
$$363$$ 9.53801 + 9.53801i 0.0262755 + 0.0262755i
$$364$$ 149.303i 0.410173i
$$365$$ 0 0
$$366$$ −3.25307 −0.00888816
$$367$$ −146.510 + 146.510i −0.399209 + 0.399209i −0.877954 0.478745i $$-0.841092\pi$$
0.478745 + 0.877954i $$0.341092\pi$$
$$368$$ 170.924 + 170.924i 0.464467 + 0.464467i
$$369$$ 2.09082i 0.00566617i
$$370$$ 0 0
$$371$$ −4.80816 −0.0129600
$$372$$ −51.0806 + 51.0806i −0.137313 + 0.137313i
$$373$$ −86.2066 86.2066i −0.231117 0.231117i 0.582042 0.813159i $$-0.302254\pi$$
−0.813159 + 0.582042i $$0.802254\pi$$
$$374$$ 88.4949i 0.236617i
$$375$$ 0 0
$$376$$ 157.101 0.417822
$$377$$ 195.081 195.081i 0.517455 0.517455i
$$378$$ 5.69694 + 5.69694i 0.0150713 + 0.0150713i
$$379$$ 210.000i 0.554090i 0.960857 + 0.277045i $$0.0893551\pi$$
−0.960857 + 0.277045i $$0.910645\pi$$
$$380$$ 0 0
$$381$$ −403.237 −1.05837
$$382$$ −10.8082 + 10.8082i −0.0282936 + 0.0282936i
$$383$$ 10.6311 + 10.6311i 0.0277575 + 0.0277575i 0.720849 0.693092i $$-0.243752\pi$$
−0.693092 + 0.720849i $$0.743752\pi$$
$$384$$ 132.167i 0.344184i
$$385$$ 0 0
$$386$$ −114.874 −0.297601
$$387$$ −79.4847 + 79.4847i −0.205387 + 0.205387i
$$388$$ 95.8990 + 95.8990i 0.247162 + 0.247162i
$$389$$ 535.337i 1.37619i 0.725621 + 0.688094i $$0.241552\pi$$
−0.725621 + 0.688094i $$0.758448\pi$$
$$390$$ 0 0
$$391$$ −400.767 −1.02498
$$392$$ 44.7401 44.7401i 0.114133 0.114133i
$$393$$ 129.990 + 129.990i 0.330763 + 0.330763i
$$394$$ 43.4643i 0.110315i
$$395$$ 0 0
$$396$$ −132.742 −0.335208
$$397$$ −118.742 + 118.742i −0.299099 + 0.299099i −0.840661 0.541562i $$-0.817833\pi$$
0.541562 + 0.840661i $$0.317833\pi$$
$$398$$ 43.2872 + 43.2872i 0.108762 + 0.108762i
$$399$$ 73.4847i 0.184172i
$$400$$ 0 0
$$401$$ 420.302 1.04813 0.524067 0.851677i $$-0.324414\pi$$
0.524067 + 0.851677i $$0.324414\pi$$
$$402$$ −24.8286 + 24.8286i −0.0617626 + 0.0617626i
$$403$$ 59.3735 + 59.3735i 0.147329 + 0.147329i
$$404$$ 411.814i 1.01934i
$$405$$ 0 0
$$406$$ −54.4949 −0.134224
$$407$$ 68.6061 68.6061i 0.168565 0.168565i
$$408$$ −75.4393 75.4393i −0.184900 0.184900i
$$409$$ 515.110i 1.25944i 0.776823 + 0.629719i $$0.216830\pi$$
−0.776823 + 0.629719i $$0.783170\pi$$
$$410$$ 0 0
$$411$$ 408.161 0.993093
$$412$$ −347.974 + 347.974i −0.844597 + 0.844597i
$$413$$ −137.753 137.753i −0.333541 0.333541i
$$414$$ 15.5755i 0.0376220i
$$415$$ 0 0
$$416$$ 115.748 0.278240
$$417$$ −234.136 + 234.136i −0.561478 + 0.561478i
$$418$$ 22.1816 + 22.1816i 0.0530661 + 0.0530661i
$$419$$ 88.6015i 0.211460i 0.994395 + 0.105730i $$0.0337178\pi$$
−0.994395 + 0.105730i $$0.966282\pi$$
$$420$$ 0 0
$$421$$ −257.151 −0.610810 −0.305405 0.952223i $$-0.598792\pi$$
−0.305405 + 0.952223i $$0.598792\pi$$
$$422$$ −33.0852 + 33.0852i −0.0784009 + 0.0784009i
$$423$$ −132.742 132.742i −0.313812 0.313812i
$$424$$ 2.47449i 0.00583605i
$$425$$ 0 0
$$426$$ 37.4347 0.0878749
$$427$$ −20.3837 + 20.3837i −0.0477369 + 0.0477369i
$$428$$ −268.025 268.025i −0.626227 0.626227i
$$429$$ 154.293i 0.359657i
$$430$$ 0 0
$$431$$ 804.636 1.86690 0.933452 0.358702i $$-0.116781\pi$$
0.933452 + 0.358702i $$0.116781\pi$$
$$432$$ 54.3712 54.3712i 0.125859 0.125859i
$$433$$ 344.848 + 344.848i 0.796416 + 0.796416i 0.982528 0.186113i $$-0.0595890\pi$$
−0.186113 + 0.982528i $$0.559589\pi$$
$$434$$ 16.5857i 0.0382159i
$$435$$ 0 0
$$436$$ 267.848 0.614330
$$437$$ −100.454 + 100.454i −0.229872 + 0.229872i
$$438$$ 42.8230 + 42.8230i 0.0977693 + 0.0977693i
$$439$$ 432.929i 0.986170i −0.869981 0.493085i $$-0.835869\pi$$
0.869981 0.493085i $$-0.164131\pi$$
$$440$$ 0 0
$$441$$ −75.6061 −0.171442
$$442$$ −43.2827 + 43.2827i −0.0979246 + 0.0979246i
$$443$$ −245.131 245.131i −0.553342 0.553342i 0.374062 0.927404i $$-0.377965\pi$$
−0.927404 + 0.374062i $$0.877965\pi$$
$$444$$ 57.7367i 0.130038i
$$445$$ 0 0
$$446$$ 75.2577 0.168739
$$447$$ 103.924 103.924i 0.232492 0.232492i
$$448$$ 188.015 + 188.015i 0.419676 + 0.419676i
$$449$$ 386.091i 0.859890i −0.902855 0.429945i $$-0.858533\pi$$
0.902855 0.429945i $$-0.141467\pi$$
$$450$$ 0 0
$$451$$ 7.90918 0.0175370
$$452$$ 380.702 380.702i 0.842260 0.842260i
$$453$$ 182.449 + 182.449i 0.402758 + 0.402758i
$$454$$ 113.798i 0.250656i
$$455$$ 0 0
$$456$$ −37.8184 −0.0829350
$$457$$ 223.747 223.747i 0.489599 0.489599i −0.418580 0.908180i $$-0.637472\pi$$
0.908180 + 0.418580i $$0.137472\pi$$
$$458$$ −50.3883 50.3883i −0.110018 0.110018i
$$459$$ 127.485i 0.277744i
$$460$$ 0 0
$$461$$ −722.620 −1.56751 −0.783753 0.621073i $$-0.786697\pi$$
−0.783753 + 0.621073i $$0.786697\pi$$
$$462$$ 21.5505 21.5505i 0.0466461 0.0466461i
$$463$$ 129.702 + 129.702i 0.280133 + 0.280133i 0.833162 0.553029i $$-0.186528\pi$$
−0.553029 + 0.833162i $$0.686528\pi$$
$$464$$ 520.095i 1.12090i
$$465$$ 0 0
$$466$$ −92.4653 −0.198423
$$467$$ −415.258 + 415.258i −0.889203 + 0.889203i −0.994446 0.105244i $$-0.966438\pi$$
0.105244 + 0.994446i $$0.466438\pi$$
$$468$$ −64.9240 64.9240i −0.138726 0.138726i
$$469$$ 311.151i 0.663435i
$$470$$ 0 0
$$471$$ −41.2827 −0.0876489
$$472$$ 70.8934 70.8934i 0.150198 0.150198i
$$473$$ 300.677 + 300.677i 0.635680 + 0.635680i
$$474$$ 13.4847i 0.0284487i
$$475$$ 0 0
$$476$$ −466.656 −0.980370
$$477$$ −2.09082 + 2.09082i −0.00438326 + 0.00438326i
$$478$$ −77.7163 77.7163i −0.162586 0.162586i
$$479$$ 304.949i 0.636637i −0.947984 0.318318i $$-0.896882\pi$$
0.947984 0.318318i $$-0.103118\pi$$
$$480$$ 0 0
$$481$$ 67.1102 0.139522
$$482$$ −22.8286 + 22.8286i −0.0473622 + 0.0473622i
$$483$$ 97.5959 + 97.5959i 0.202062 + 0.202062i
$$484$$ 30.3643i 0.0627361i
$$485$$ 0 0
$$486$$ 4.95459 0.0101946
$$487$$ 429.318 429.318i 0.881556 0.881556i −0.112137 0.993693i $$-0.535769\pi$$
0.993693 + 0.112137i $$0.0357694\pi$$
$$488$$ −10.4903 10.4903i −0.0214965 0.0214965i
$$489$$ 319.918i 0.654230i
$$490$$ 0 0
$$491$$ −414.318 −0.843825 −0.421912 0.906637i $$-0.638641\pi$$
−0.421912 + 0.906637i $$0.638641\pi$$
$$492$$ −3.32806 + 3.32806i −0.00676435 + 0.00676435i
$$493$$ −609.737 609.737i −1.23679 1.23679i
$$494$$ 21.6980i 0.0439230i
$$495$$ 0 0
$$496$$ −158.293 −0.319139
$$497$$ 234.565 234.565i 0.471962 0.471962i
$$498$$ 7.23724 + 7.23724i 0.0145326 + 0.0145326i
$$499$$ 367.585i 0.736643i −0.929699 0.368321i $$-0.879933\pi$$
0.929699 0.368321i $$-0.120067\pi$$
$$500$$ 0 0
$$501$$ 110.313 0.220186
$$502$$ 74.4485 74.4485i 0.148304 0.148304i
$$503$$ 9.59133 + 9.59133i 0.0190683 + 0.0190683i 0.716577 0.697508i $$-0.245708\pi$$
−0.697508 + 0.716577i $$0.745708\pi$$
$$504$$ 36.7423i 0.0729015i
$$505$$ 0 0
$$506$$ 58.9194 0.116441
$$507$$ 131.518 131.518i 0.259404 0.259404i
$$508$$ −641.854 641.854i −1.26349 1.26349i
$$509$$ 777.489i 1.52748i −0.645522 0.763742i $$-0.723360\pi$$
0.645522 0.763742i $$-0.276640\pi$$
$$510$$ 0 0
$$511$$ 536.656 1.05021
$$512$$ −259.376 + 259.376i −0.506593 + 0.506593i
$$513$$ 31.9546 + 31.9546i 0.0622897 + 0.0622897i
$$514$$ 14.9398i 0.0290658i
$$515$$ 0 0
$$516$$ −253.040 −0.490387
$$517$$ −502.141 + 502.141i −0.971259 + 0.971259i
$$518$$ −9.37347 9.37347i −0.0180955 0.0180955i
$$519$$ 359.171i 0.692045i
$$520$$ 0 0
$$521$$ 321.605 0.617284 0.308642 0.951178i $$-0.400125\pi$$
0.308642 + 0.951178i $$0.400125\pi$$
$$522$$ −23.6969 + 23.6969i −0.0453964 + 0.0453964i
$$523$$ 582.454 + 582.454i 1.11368 + 1.11368i 0.992649 + 0.121030i $$0.0386198\pi$$
0.121030 + 0.992649i $$0.461380\pi$$
$$524$$ 413.823i 0.789738i
$$525$$ 0 0
$$526$$ −125.029 −0.237697
$$527$$ 185.576 185.576i 0.352136 0.352136i
$$528$$ −205.677 205.677i −0.389539 0.389539i
$$529$$ 262.171i 0.495598i
$$530$$ 0 0
$$531$$ −119.803 −0.225617
$$532$$ −116.969 + 116.969i −0.219867 + 0.219867i
$$533$$ 3.86836 + 3.86836i 0.00725772 + 0.00725772i
$$534$$ 45.2418i 0.0847225i
$$535$$ 0 0
$$536$$ −160.132 −0.298753
$$537$$ 225.000 225.000i 0.418994 0.418994i
$$538$$ −109.788 109.788i −0.204066 0.204066i
$$539$$ 286.005i 0.530621i
$$540$$ 0 0
$$541$$ 460.697 0.851566 0.425783 0.904825i $$-0.359999\pi$$
0.425783 + 0.904825i $$0.359999\pi$$
$$542$$ −29.5709 + 29.5709i −0.0545589 + 0.0545589i
$$543$$ −350.611 350.611i −0.645692 0.645692i
$$544$$ 361.778i 0.665032i
$$545$$ 0 0
$$546$$ 21.0806 0.0386092
$$547$$ 661.778 661.778i 1.20983 1.20983i 0.238750 0.971081i $$-0.423262\pi$$
0.971081 0.238750i $$-0.0767376\pi$$
$$548$$ 649.691 + 649.691i 1.18557 + 1.18557i
$$549$$ 17.7276i 0.0322906i
$$550$$ 0 0
$$551$$ −305.666 −0.554748
$$552$$ −50.2270 + 50.2270i −0.0909910 + 0.0909910i
$$553$$ −84.4949 84.4949i −0.152794 0.152794i
$$554$$ 45.6276i 0.0823602i
$$555$$ 0 0
$$556$$ −745.373 −1.34060
$$557$$ −125.909 + 125.909i −0.226049 + 0.226049i −0.811040 0.584991i $$-0.801098\pi$$
0.584991 + 0.811040i $$0.301098\pi$$
$$558$$ −7.21225 7.21225i −0.0129252 0.0129252i
$$559$$ 294.120i 0.526155i
$$560$$ 0 0
$$561$$ 482.252 0.859629
$$562$$ −77.1556 + 77.1556i −0.137288 + 0.137288i
$$563$$ 200.009 + 200.009i 0.355256 + 0.355256i 0.862061 0.506805i $$-0.169174\pi$$
−0.506805 + 0.862061i $$0.669174\pi$$
$$564$$ 422.586i 0.749265i
$$565$$ 0 0
$$566$$ 0.535718 0.000946498
$$567$$ 31.0454 31.0454i 0.0547538 0.0547538i
$$568$$ 120.717 + 120.717i 0.212531 + 0.212531i
$$569$$ 599.839i 1.05420i 0.849804 + 0.527099i $$0.176720\pi$$
−0.849804 + 0.527099i $$0.823280\pi$$
$$570$$ 0 0
$$571$$ −247.970 −0.434274 −0.217137 0.976141i $$-0.569672\pi$$
−0.217137 + 0.976141i $$0.569672\pi$$
$$572$$ −245.596 + 245.596i −0.429363 + 0.429363i
$$573$$ 58.8990 + 58.8990i 0.102791 + 0.102791i
$$574$$ 1.08061i 0.00188260i
$$575$$ 0 0
$$576$$ 163.515 0.283881
$$577$$ 292.121 292.121i 0.506276 0.506276i −0.407105 0.913381i $$-0.633462\pi$$
0.913381 + 0.407105i $$0.133462\pi$$
$$578$$ 70.3314 + 70.3314i 0.121681 + 0.121681i
$$579$$ 626.005i 1.08118i
$$580$$ 0 0
$$581$$ 90.6969 0.156105
$$582$$ −13.5403 + 13.5403i −0.0232651 + 0.0232651i
$$583$$ 7.90918 + 7.90918i 0.0135664 + 0.0135664i
$$584$$ 276.186i 0.472922i
$$585$$ 0 0
$$586$$ 43.4051 0.0740702
$$587$$ −611.217 + 611.217i −1.04126 + 1.04126i −0.0421437 + 0.999112i $$0.513419\pi$$
−0.999112 + 0.0421437i $$0.986581\pi$$
$$588$$ −120.346 120.346i −0.204670 0.204670i
$$589$$ 93.0306i 0.157947i
$$590$$ 0 0
$$591$$ 236.858 0.400775
$$592$$ −89.4597 + 89.4597i −0.151114 + 0.151114i
$$593$$ −524.742 524.742i −0.884894 0.884894i 0.109133 0.994027i $$-0.465193\pi$$
−0.994027 + 0.109133i $$0.965193\pi$$
$$594$$ 18.7423i 0.0315528i
$$595$$ 0 0
$$596$$ 330.842 0.555105
$$597$$ 235.893 235.893i 0.395131 0.395131i
$$598$$ 28.8173 + 28.8173i 0.0481895 + 0.0481895i
$$599$$ 368.858i 0.615790i 0.951420 + 0.307895i $$0.0996245\pi$$
−0.951420 + 0.307895i $$0.900375\pi$$
$$600$$ 0 0
$$601$$ 932.484 1.55155 0.775777 0.631007i $$-0.217358\pi$$
0.775777 + 0.631007i $$0.217358\pi$$
$$602$$ 41.0806 41.0806i 0.0682402 0.0682402i
$$603$$ 135.303 + 135.303i 0.224383 + 0.224383i
$$604$$ 580.829i 0.961637i
$$605$$ 0 0
$$606$$ 58.1454 0.0959495
$$607$$ −513.611 + 513.611i −0.846146 + 0.846146i −0.989650 0.143504i $$-0.954163\pi$$
0.143504 + 0.989650i $$0.454163\pi$$
$$608$$ −90.6811 90.6811i −0.149147 0.149147i
$$609$$ 296.969i 0.487634i
$$610$$ 0 0
$$611$$ −491.192 −0.803915
$$612$$ −202.924 + 202.924i −0.331575 + 0.331575i
$$613$$ 615.287 + 615.287i 1.00373 + 1.00373i 0.999993 + 0.00373821i $$0.00118991\pi$$
0.00373821 + 0.999993i $$0.498810\pi$$
$$614$$ 56.1725i 0.0914861i
$$615$$ 0 0
$$616$$ 138.990 0.225633
$$617$$ −546.752 + 546.752i −0.886145 + 0.886145i −0.994150 0.108005i $$-0.965554\pi$$
0.108005 + 0.994150i $$0.465554\pi$$
$$618$$ −49.1316 49.1316i −0.0795010 0.0795010i
$$619$$ 152.869i 0.246962i −0.992347 0.123481i $$-0.960594\pi$$
0.992347 0.123481i $$-0.0394058\pi$$
$$620$$ 0 0
$$621$$ 84.8786 0.136680
$$622$$ 131.768 131.768i 0.211846 0.211846i
$$623$$ 283.485 + 283.485i 0.455032 + 0.455032i
$$624$$ 201.192i 0.322423i
$$625$$ 0 0
$$626$$ −46.0158 −0.0735077
$$627$$ 120.879 120.879i 0.192789 0.192789i
$$628$$ −65.7117 65.7117i −0.104637 0.104637i
$$629$$ 209.757i 0.333477i
$$630$$ 0 0
$$631$$ −41.4847 −0.0657444 −0.0328722 0.999460i $$-0.510465\pi$$
−0.0328722 + 0.999460i $$0.510465\pi$$
$$632$$ 43.4847 43.4847i 0.0688049 0.0688049i
$$633$$ 180.297 + 180.297i 0.284830 + 0.284830i
$$634$$ 48.8969i 0.0771245i
$$635$$ 0 0
$$636$$ −6.65612 −0.0104656
$$637$$ −139.884 + 139.884i −0.219598 + 0.219598i
$$638$$ 89.6413 + 89.6413i 0.140504 + 0.140504i
$$639$$ 204.000i 0.319249i
$$640$$ 0 0
$$641$$ 47.2122 0.0736541 0.0368270 0.999322i $$-0.488275\pi$$
0.0368270 + 0.999322i $$0.488275\pi$$
$$642$$ 37.8434 37.8434i 0.0589461 0.0589461i
$$643$$ −460.372 460.372i −0.715976 0.715976i 0.251803 0.967779i $$-0.418977\pi$$
−0.967779 + 0.251803i $$0.918977\pi$$
$$644$$ 310.697i 0.482449i
$$645$$ 0 0
$$646$$ 67.8184 0.104982
$$647$$ 281.287 281.287i 0.434756 0.434756i −0.455487 0.890243i $$-0.650535\pi$$
0.890243 + 0.455487i $$0.150535\pi$$
$$648$$ 15.9773 + 15.9773i 0.0246563 + 0.0246563i
$$649$$ 453.192i 0.698293i
$$650$$ 0 0
$$651$$ −90.3837 −0.138838
$$652$$ 509.231 509.231i 0.781029 0.781029i
$$653$$ −89.8230 89.8230i −0.137554 0.137554i 0.634977 0.772531i $$-0.281010\pi$$
−0.772531 + 0.634977i $$0.781010\pi$$
$$654$$ 37.8184i 0.0578263i
$$655$$ 0 0
$$656$$ −10.3133 −0.0157214
$$657$$ 233.363 233.363i 0.355195 0.355195i
$$658$$ 68.6061 + 68.6061i 0.104265 + 0.104265i
$$659$$ 1081.24i 1.64072i −0.571844 0.820362i $$-0.693772\pi$$
0.571844 0.820362i $$-0.306228\pi$$
$$660$$ 0 0
$$661$$ −632.393 −0.956721 −0.478361 0.878163i $$-0.658769\pi$$
−0.478361 + 0.878163i $$0.658769\pi$$
$$662$$ 55.1577 55.1577i 0.0833197 0.0833197i
$$663$$ 235.868 + 235.868i 0.355759 + 0.355759i
$$664$$ 46.6765i 0.0702960i
$$665$$ 0 0
$$666$$ −8.15205 −0.0122403
$$667$$ −405.959 + 405.959i −0.608634 + 0.608634i
$$668$$ 175.591 + 175.591i 0.262861 + 0.262861i
$$669$$ 410.116i 0.613028i
$$670$$ 0 0
$$671$$ 67.0602 0.0999407
$$672$$ −88.1010 + 88.1010i −0.131103 + 0.131103i
$$673$$ −233.293 233.293i −0.346646 0.346646i 0.512213 0.858859i $$-0.328826\pi$$
−0.858859 + 0.512213i $$0.828826\pi$$
$$674$$ 96.1046i 0.142588i
$$675$$ 0 0
$$676$$ 418.687 0.619359
$$677$$ 48.3883 48.3883i 0.0714745 0.0714745i −0.670466 0.741940i $$-0.733906\pi$$
0.741940 + 0.670466i $$0.233906\pi$$
$$678$$ 53.7526 + 53.7526i 0.0792810 + 0.0792810i
$$679$$ 169.687i 0.249907i
$$680$$ 0 0
$$681$$ −620.141 −0.910633
$$682$$ −27.2827 + 27.2827i −0.0400039 + 0.0400039i
$$683$$ −213.410 213.410i −0.312459 0.312459i 0.533402 0.845862i $$-0.320913\pi$$
−0.845862 + 0.533402i $$0.820913\pi$$
$$684$$ 101.728i 0.148724i
$$685$$ 0 0
$$686$$ 115.051 0.167713
$$687$$ −274.590 + 274.590i −0.399695 + 0.399695i
$$688$$ −392.070 392.070i −0.569870 0.569870i
$$689$$ 7.73673i 0.0112289i
$$690$$ 0 0
$$691$$ 151.121 0.218700 0.109350 0.994003i $$-0.465123\pi$$
0.109350 + 0.994003i $$0.465123\pi$$
$$692$$ 571.712 571.712i 0.826173 0.826173i
$$693$$ −117.439 117.439i −0.169465 0.169465i
$$694$$ 71.9408i 0.103661i
$$695$$ 0 0
$$696$$ −152.833 −0.219588
$$697$$ 12.0908 12.0908i 0.0173469 0.0173469i
$$698$$ −66.9760 66.9760i −0.0959542 0.0959542i
$$699$$ 503.889i 0.720871i
$$700$$ 0 0
$$701$$ −745.680 −1.06374 −0.531869 0.846827i $$-0.678510\pi$$
−0.531869 + 0.846827i $$0.678510\pi$$
$$702$$ 9.16684 9.16684i 0.0130582 0.0130582i
$$703$$ −52.5765 52.5765i −0.0747888 0.0747888i
$$704$$ 618.549i 0.878621i
$$705$$ 0 0
$$706$$ −10.1225 −0.0143378
$$707$$ 364.338 364.338i 0.515330 0.515330i
$$708$$ −190.696 190.696i −0.269345 0.269345i
$$709$$ 719.049i 1.01417i −0.861895 0.507087i $$-0.830722\pi$$
0.861895 0.507087i $$-0.169278\pi$$
$$710$$ 0 0
$$711$$ −73.4847 −0.103354
$$712$$ −145.893 + 145.893i −0.204906 + 0.204906i
$$713$$ −123.555 123.555i −0.173289 0.173289i
$$714$$ 65.8888i 0.0922812i
$$715$$ 0 0
$$716$$ 716.288 1.00040
$$717$$ −423.514 + 423.514i −0.590675 + 0.590675i
$$718$$ 10.8490 + 10.8490i 0.0151100 + 0.0151100i
$$719$$ 605.271i 0.841824i 0.907101 + 0.420912i $$0.138290\pi$$
−0.907101 + 0.420912i $$0.861710\pi$$
$$720$$ 0 0
$$721$$ −615.716 −0.853975
$$722$$ −64.1339 + 64.1339i −0.0888282 + 0.0888282i
$$723$$ 124.404 + 124.404i 0.172067 + 0.172067i
$$724$$ 1116.17i 1.54167i
$$725$$ 0 0
$$726$$ −4.28724 −0.00590529
$$727$$ 246.126 246.126i 0.338550 0.338550i −0.517271 0.855821i $$-0.673052\pi$$
0.855821 + 0.517271i $$0.173052\pi$$
$$728$$ 67.9796 + 67.9796i 0.0933786 + 0.0933786i
$$729$$ 27.0000i 0.0370370i
$$730$$ 0 0
$$731$$ 919.292 1.25758
$$732$$ −28.2179 + 28.2179i −0.0385490 + 0.0385490i
$$733$$ 270.763 + 270.763i 0.369390 + 0.369390i 0.867255 0.497865i $$-0.165882\pi$$
−0.497865 + 0.867255i $$0.665882\pi$$
$$734$$ 65.8546i 0.0897202i
$$735$$ 0 0
$$736$$ −240.869 −0.327268
$$737$$ 511.828 511.828i 0.694474 0.694474i
$$738$$ −0.469900 0.469900i −0.000636721 0.000636721i
$$739$$ 515.666i 0.697789i 0.937162 + 0.348895i $$0.113443\pi$$
−0.937162 + 0.348895i $$0.886557\pi$$
$$740$$ 0 0
$$741$$ 118.243 0.159572
$$742$$ 1.08061 1.08061i 0.00145635 0.00145635i
$$743$$ −420.702 420.702i −0.566220 0.566220i 0.364847 0.931067i $$-0.381121\pi$$
−0.931067 + 0.364847i $$0.881121\pi$$
$$744$$ 46.5153i 0.0625206i
$$745$$ 0 0
$$746$$ 38.7490 0.0519424
$$747$$ 39.4393 39.4393i 0.0527969 0.0527969i
$$748$$ 767.626 + 767.626i 1.02624 + 1.02624i
$$749$$ 474.252i 0.633180i
$$750$$ 0 0
$$751$$ −859.787 −1.14486 −0.572428 0.819955i $$-0.693998\pi$$
−0.572428 + 0.819955i $$0.693998\pi$$
$$752$$ 654.772 654.772i 0.870707 0.870707i
$$753$$ −405.706 405.706i −0.538786 0.538786i
$$754$$ 87.6867i 0.116295i
$$755$$ 0 0
$$756$$ 98.8332 0.130732
$$757$$ 956.075 956.075i 1.26298 1.26298i 0.313337 0.949642i $$-0.398553\pi$$
0.949642 0.313337i $$-0.101447\pi$$
$$758$$ −47.1964 47.1964i −0.0622644 0.0622644i
$$759$$ 321.081i 0.423031i
$$760$$ 0 0
$$761$$ −322.758 −0.424124 −0.212062 0.977256i $$-0.568018\pi$$
−0.212062 + 0.977256i $$0.568018\pi$$
$$762$$ 90.6255 90.6255i 0.118931 0.118931i
$$763$$ 236.969 + 236.969i 0.310576 + 0.310576i
$$764$$ 187.505i 0.245426i
$$765$$ 0 0
$$766$$ −4.77858 −0.00623835
$$767$$ −221.655 + 221.655i −0.288990 + 0.288990i
$$768$$ 237.316 + 237.316i 0.309005 + 0.309005i
$$769$$ 692.402i 0.900393i −0.892930 0.450196i $$-0.851354\pi$$
0.892930 0.450196i $$-0.148646\pi$$
$$770$$ 0 0
$$771$$ −81.4143 −0.105596
$$772$$ −996.444 + 996.444i −1.29073 + 1.29073i
$$773$$ −375.226 375.226i −0.485415 0.485415i 0.421441 0.906856i $$-0.361525\pi$$
−0.906856 + 0.421441i $$0.861525\pi$$
$$774$$ 35.7276i 0.0461596i
$$775$$ 0 0
$$776$$ −87.3281 −0.112536
$$777$$ −51.0806 + 51.0806i −0.0657408 + 0.0657408i
$$778$$ −120.314 120.314i −0.154646 0.154646i
$$779$$ 6.06123i 0.00778078i
$$780$$ 0 0
$$781$$ −771.696 −0.988087
$$782$$ 90.0704 90.0704i 0.115180 0.115180i
$$783$$ 129.136 + 129.136i 0.164925 + 0.164925i
$$784$$ 372.939i 0.475687i
$$785$$ 0 0
$$786$$ −58.4291