# Properties

 Label 370.2.c.a.369.5 Level $370$ Weight $2$ Character 370.369 Analytic conductor $2.954$ Analytic rank $0$ Dimension $10$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$370 = 2 \cdot 5 \cdot 37$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 370.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.95446487479$$ Analytic rank: $$0$$ Dimension: $$10$$ Coefficient field: $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ Defining polynomial: $$x^{10} + 19 x^{8} + 103 x^{6} + 210 x^{4} + 140 x^{2} + 16$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 369.5 Root $$-0.377861i$$ of defining polynomial Character $$\chi$$ $$=$$ 370.369 Dual form 370.2.c.a.369.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} -0.377861i q^{3} +1.00000 q^{4} +(1.04797 - 1.97529i) q^{5} +0.377861i q^{6} -0.631751i q^{7} -1.00000 q^{8} +2.85722 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} -0.377861i q^{3} +1.00000 q^{4} +(1.04797 - 1.97529i) q^{5} +0.377861i q^{6} -0.631751i q^{7} -1.00000 q^{8} +2.85722 q^{9} +(-1.04797 + 1.97529i) q^{10} +1.24789 q^{11} -0.377861i q^{12} -3.34999 q^{13} +0.631751i q^{14} +(-0.746385 - 0.395986i) q^{15} +1.00000 q^{16} -3.10511 q^{17} -2.85722 q^{18} -5.97327i q^{19} +(1.04797 - 1.97529i) q^{20} -0.238714 q^{21} -1.24789 q^{22} +7.60706 q^{23} +0.377861i q^{24} +(-2.80353 - 4.14008i) q^{25} +3.34999 q^{26} -2.21322i q^{27} -0.631751i q^{28} +9.57629i q^{29} +(0.746385 + 0.395986i) q^{30} -7.26707i q^{31} -1.00000 q^{32} -0.471529i q^{33} +3.10511 q^{34} +(-1.24789 - 0.662054i) q^{35} +2.85722 q^{36} +(4.10511 - 4.48866i) q^{37} +5.97327i q^{38} +1.26583i q^{39} +(-1.04797 + 1.97529i) q^{40} -8.45510 q^{41} +0.238714 q^{42} +4.86640 q^{43} +1.24789 q^{44} +(2.99427 - 5.64384i) q^{45} -7.60706 q^{46} -13.1187i q^{47} -0.377861i q^{48} +6.60089 q^{49} +(2.80353 + 4.14008i) q^{50} +1.17330i q^{51} -3.34999 q^{52} +7.17340i q^{53} +2.21322i q^{54} +(1.30775 - 2.46494i) q^{55} +0.631751i q^{56} -2.25707 q^{57} -9.57629i q^{58} +4.36469i q^{59} +(-0.746385 - 0.395986i) q^{60} +2.14666i q^{61} +7.26707i q^{62} -1.80505i q^{63} +1.00000 q^{64} +(-3.51068 + 6.61720i) q^{65} +0.471529i q^{66} +11.3451i q^{67} -3.10511 q^{68} -2.87441i q^{69} +(1.24789 + 0.662054i) q^{70} -12.7183 q^{71} -2.85722 q^{72} +4.45836i q^{73} +(-4.10511 + 4.48866i) q^{74} +(-1.56437 + 1.05934i) q^{75} -5.97327i q^{76} -0.788355i q^{77} -1.26583i q^{78} +8.78679i q^{79} +(1.04797 - 1.97529i) q^{80} +7.73537 q^{81} +8.45510 q^{82} +6.63185i q^{83} -0.238714 q^{84} +(-3.25406 + 6.13349i) q^{85} -4.86640 q^{86} +3.61851 q^{87} -1.24789 q^{88} +13.7784i q^{89} +(-2.99427 + 5.64384i) q^{90} +2.11636i q^{91} +7.60706 q^{92} -2.74594 q^{93} +13.1187i q^{94} +(-11.7989 - 6.25979i) q^{95} +0.377861i q^{96} -11.0583 q^{97} -6.60089 q^{98} +3.56550 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + O(q^{10})$$ $$10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + 3q^{10} - 2q^{13} - 10q^{15} + 10q^{16} + 18q^{17} + 8q^{18} - 3q^{20} - 12q^{21} + 10q^{23} + 5q^{25} + 2q^{26} + 10q^{30} - 10q^{32} - 18q^{34} - 8q^{36} - 8q^{37} + 3q^{40} - 4q^{41} + 12q^{42} - 10q^{43} + 20q^{45} - 10q^{46} - 8q^{49} - 5q^{50} - 2q^{52} + 5q^{55} + 12q^{57} - 10q^{60} + 10q^{64} + 2q^{65} + 18q^{68} - 20q^{71} + 8q^{72} + 8q^{74} + 25q^{75} - 3q^{80} + 58q^{81} + 4q^{82} - 12q^{84} - 28q^{85} + 10q^{86} - 10q^{87} - 20q^{90} + 10q^{92} - 32q^{93} + 2q^{95} + 2q^{97} + 8q^{98} - 82q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$$.

 $$n$$ $$261$$ $$297$$ $$\chi(n)$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −0.707107
$$3$$ 0.377861i 0.218158i −0.994033 0.109079i $$-0.965210\pi$$
0.994033 0.109079i $$-0.0347902\pi$$
$$4$$ 1.00000 0.500000
$$5$$ 1.04797 1.97529i 0.468665 0.883376i
$$6$$ 0.377861i 0.154261i
$$7$$ 0.631751i 0.238779i −0.992847 0.119390i $$-0.961906\pi$$
0.992847 0.119390i $$-0.0380938\pi$$
$$8$$ −1.00000 −0.353553
$$9$$ 2.85722 0.952407
$$10$$ −1.04797 + 1.97529i −0.331396 + 0.624641i
$$11$$ 1.24789 0.376253 0.188126 0.982145i $$-0.439759\pi$$
0.188126 + 0.982145i $$0.439759\pi$$
$$12$$ 0.377861i 0.109079i
$$13$$ −3.34999 −0.929120 −0.464560 0.885542i $$-0.653788\pi$$
−0.464560 + 0.885542i $$0.653788\pi$$
$$14$$ 0.631751i 0.168843i
$$15$$ −0.746385 0.395986i −0.192716 0.102243i
$$16$$ 1.00000 0.250000
$$17$$ −3.10511 −0.753100 −0.376550 0.926396i $$-0.622890\pi$$
−0.376550 + 0.926396i $$0.622890\pi$$
$$18$$ −2.85722 −0.673453
$$19$$ 5.97327i 1.37036i −0.728373 0.685181i $$-0.759723\pi$$
0.728373 0.685181i $$-0.240277\pi$$
$$20$$ 1.04797 1.97529i 0.234333 0.441688i
$$21$$ −0.238714 −0.0520917
$$22$$ −1.24789 −0.266051
$$23$$ 7.60706 1.58618 0.793090 0.609104i $$-0.208471\pi$$
0.793090 + 0.609104i $$0.208471\pi$$
$$24$$ 0.377861i 0.0771306i
$$25$$ −2.80353 4.14008i −0.560706 0.828015i
$$26$$ 3.34999 0.656987
$$27$$ 2.21322i 0.425934i
$$28$$ 0.631751i 0.119390i
$$29$$ 9.57629i 1.77827i 0.457643 + 0.889136i $$0.348694\pi$$
−0.457643 + 0.889136i $$0.651306\pi$$
$$30$$ 0.746385 + 0.395986i 0.136271 + 0.0722969i
$$31$$ 7.26707i 1.30520i −0.757701 0.652602i $$-0.773677\pi$$
0.757701 0.652602i $$-0.226323\pi$$
$$32$$ −1.00000 −0.176777
$$33$$ 0.471529i 0.0820827i
$$34$$ 3.10511 0.532522
$$35$$ −1.24789 0.662054i −0.210932 0.111908i
$$36$$ 2.85722 0.476203
$$37$$ 4.10511 4.48866i 0.674876 0.737931i
$$38$$ 5.97327i 0.968992i
$$39$$ 1.26583i 0.202695i
$$40$$ −1.04797 + 1.97529i −0.165698 + 0.312321i
$$41$$ −8.45510 −1.32046 −0.660232 0.751061i $$-0.729542\pi$$
−0.660232 + 0.751061i $$0.729542\pi$$
$$42$$ 0.238714 0.0368344
$$43$$ 4.86640 0.742119 0.371059 0.928609i $$-0.378995\pi$$
0.371059 + 0.928609i $$0.378995\pi$$
$$44$$ 1.24789 0.188126
$$45$$ 2.99427 5.64384i 0.446360 0.841333i
$$46$$ −7.60706 −1.12160
$$47$$ 13.1187i 1.91356i −0.290815 0.956779i $$-0.593926\pi$$
0.290815 0.956779i $$-0.406074\pi$$
$$48$$ 0.377861i 0.0545396i
$$49$$ 6.60089 0.942984
$$50$$ 2.80353 + 4.14008i 0.396479 + 0.585495i
$$51$$ 1.17330i 0.164295i
$$52$$ −3.34999 −0.464560
$$53$$ 7.17340i 0.985343i 0.870215 + 0.492671i $$0.163980\pi$$
−0.870215 + 0.492671i $$0.836020\pi$$
$$54$$ 2.21322i 0.301181i
$$55$$ 1.30775 2.46494i 0.176337 0.332373i
$$56$$ 0.631751i 0.0844213i
$$57$$ −2.25707 −0.298956
$$58$$ 9.57629i 1.25743i
$$59$$ 4.36469i 0.568234i 0.958790 + 0.284117i $$0.0917004\pi$$
−0.958790 + 0.284117i $$0.908300\pi$$
$$60$$ −0.746385 0.395986i −0.0963579 0.0511216i
$$61$$ 2.14666i 0.274852i 0.990512 + 0.137426i $$0.0438829\pi$$
−0.990512 + 0.137426i $$0.956117\pi$$
$$62$$ 7.26707i 0.922919i
$$63$$ 1.80505i 0.227415i
$$64$$ 1.00000 0.125000
$$65$$ −3.51068 + 6.61720i −0.435446 + 0.820762i
$$66$$ 0.471529i 0.0580412i
$$67$$ 11.3451i 1.38602i 0.720926 + 0.693012i $$0.243717\pi$$
−0.720926 + 0.693012i $$0.756283\pi$$
$$68$$ −3.10511 −0.376550
$$69$$ 2.87441i 0.346038i
$$70$$ 1.24789 + 0.662054i 0.149151 + 0.0791306i
$$71$$ −12.7183 −1.50939 −0.754694 0.656077i $$-0.772215\pi$$
−0.754694 + 0.656077i $$0.772215\pi$$
$$72$$ −2.85722 −0.336727
$$73$$ 4.45836i 0.521811i 0.965364 + 0.260906i $$0.0840211\pi$$
−0.965364 + 0.260906i $$0.915979\pi$$
$$74$$ −4.10511 + 4.48866i −0.477209 + 0.521796i
$$75$$ −1.56437 + 1.05934i −0.180638 + 0.122323i
$$76$$ 5.97327i 0.685181i
$$77$$ 0.788355i 0.0898414i
$$78$$ 1.26583i 0.143327i
$$79$$ 8.78679i 0.988592i 0.869294 + 0.494296i $$0.164574\pi$$
−0.869294 + 0.494296i $$0.835426\pi$$
$$80$$ 1.04797 1.97529i 0.117166 0.220844i
$$81$$ 7.73537 0.859486
$$82$$ 8.45510 0.933710
$$83$$ 6.63185i 0.727941i 0.931411 + 0.363970i $$0.118579\pi$$
−0.931411 + 0.363970i $$0.881421\pi$$
$$84$$ −0.238714 −0.0260458
$$85$$ −3.25406 + 6.13349i −0.352952 + 0.665270i
$$86$$ −4.86640 −0.524757
$$87$$ 3.61851 0.387945
$$88$$ −1.24789 −0.133026
$$89$$ 13.7784i 1.46051i 0.683175 + 0.730255i $$0.260599\pi$$
−0.683175 + 0.730255i $$0.739401\pi$$
$$90$$ −2.99427 + 5.64384i −0.315624 + 0.594912i
$$91$$ 2.11636i 0.221855i
$$92$$ 7.60706 0.793090
$$93$$ −2.74594 −0.284741
$$94$$ 13.1187i 1.35309i
$$95$$ −11.7989 6.25979i −1.21054 0.642241i
$$96$$ 0.377861i 0.0385653i
$$97$$ −11.0583 −1.12280 −0.561398 0.827546i $$-0.689736\pi$$
−0.561398 + 0.827546i $$0.689736\pi$$
$$98$$ −6.60089 −0.666791
$$99$$ 3.56550 0.358346
$$100$$ −2.80353 4.14008i −0.280353 0.414008i
$$101$$ 8.65314 0.861019 0.430510 0.902586i $$-0.358334\pi$$
0.430510 + 0.902586i $$0.358334\pi$$
$$102$$ 1.17330i 0.116174i
$$103$$ 4.57336 0.450627 0.225313 0.974286i $$-0.427659\pi$$
0.225313 + 0.974286i $$0.427659\pi$$
$$104$$ 3.34999 0.328494
$$105$$ −0.250165 + 0.471529i −0.0244136 + 0.0460165i
$$106$$ 7.17340i 0.696743i
$$107$$ 11.4715i 1.10900i 0.832185 + 0.554498i $$0.187090\pi$$
−0.832185 + 0.554498i $$0.812910\pi$$
$$108$$ 2.21322i 0.212967i
$$109$$ 0.727748i 0.0697057i −0.999392 0.0348528i $$-0.988904\pi$$
0.999392 0.0348528i $$-0.0110962\pi$$
$$110$$ −1.30775 + 2.46494i −0.124689 + 0.235023i
$$111$$ −1.69609 1.55116i −0.160986 0.147230i
$$112$$ 0.631751i 0.0596948i
$$113$$ 17.9970 1.69301 0.846506 0.532379i $$-0.178702\pi$$
0.846506 + 0.532379i $$0.178702\pi$$
$$114$$ 2.25707 0.211394
$$115$$ 7.97195 15.0261i 0.743388 1.40119i
$$116$$ 9.57629i 0.889136i
$$117$$ −9.57166 −0.884901
$$118$$ 4.36469i 0.401802i
$$119$$ 1.96166i 0.179825i
$$120$$ 0.746385 + 0.395986i 0.0681353 + 0.0361484i
$$121$$ −9.44277 −0.858434
$$122$$ 2.14666i 0.194350i
$$123$$ 3.19485i 0.288070i
$$124$$ 7.26707i 0.652602i
$$125$$ −11.1159 + 1.19911i −0.994232 + 0.107252i
$$126$$ 1.80505i 0.160807i
$$127$$ 15.4830i 1.37389i −0.726707 0.686947i $$-0.758950\pi$$
0.726707 0.686947i $$-0.241050\pi$$
$$128$$ −1.00000 −0.0883883
$$129$$ 1.83882i 0.161899i
$$130$$ 3.51068 6.61720i 0.307907 0.580367i
$$131$$ 6.22121i 0.543550i 0.962361 + 0.271775i $$0.0876106\pi$$
−0.962361 + 0.271775i $$0.912389\pi$$
$$132$$ 0.471529i 0.0410413i
$$133$$ −3.77362 −0.327214
$$134$$ 11.3451i 0.980066i
$$135$$ −4.37174 2.31938i −0.376260 0.199620i
$$136$$ 3.10511 0.266261
$$137$$ 14.1258i 1.20685i 0.797419 + 0.603426i $$0.206198\pi$$
−0.797419 + 0.603426i $$0.793802\pi$$
$$138$$ 2.87441i 0.244686i
$$139$$ 8.43675 0.715596 0.357798 0.933799i $$-0.383528\pi$$
0.357798 + 0.933799i $$0.383528\pi$$
$$140$$ −1.24789 0.662054i −0.105466 0.0559538i
$$141$$ −4.95705 −0.417459
$$142$$ 12.7183 1.06730
$$143$$ −4.18042 −0.349584
$$144$$ 2.85722 0.238102
$$145$$ 18.9159 + 10.0356i 1.57088 + 0.833414i
$$146$$ 4.45836i 0.368976i
$$147$$ 2.49422i 0.205720i
$$148$$ 4.10511 4.48866i 0.337438 0.368966i
$$149$$ 13.6447 1.11782 0.558909 0.829229i $$-0.311220\pi$$
0.558909 + 0.829229i $$0.311220\pi$$
$$150$$ 1.56437 1.05934i 0.127731 0.0864951i
$$151$$ −3.17741 −0.258574 −0.129287 0.991607i $$-0.541269\pi$$
−0.129287 + 0.991607i $$0.541269\pi$$
$$152$$ 5.97327i 0.484496i
$$153$$ −8.87199 −0.717258
$$154$$ 0.788355i 0.0635275i
$$155$$ −14.3546 7.61566i −1.15299 0.611704i
$$156$$ 1.26583i 0.101348i
$$157$$ 0.215310i 0.0171836i −0.999963 0.00859180i $$-0.997265\pi$$
0.999963 0.00859180i $$-0.00273489\pi$$
$$158$$ 8.78679i 0.699040i
$$159$$ 2.71055 0.214961
$$160$$ −1.04797 + 1.97529i −0.0828491 + 0.156160i
$$161$$ 4.80576i 0.378747i
$$162$$ −7.73537 −0.607748
$$163$$ −1.66609 −0.130498 −0.0652490 0.997869i $$-0.520784\pi$$
−0.0652490 + 0.997869i $$0.520784\pi$$
$$164$$ −8.45510 −0.660232
$$165$$ −0.931406 0.494147i −0.0725099 0.0384693i
$$166$$ 6.63185i 0.514732i
$$167$$ 5.92242 0.458290 0.229145 0.973392i $$-0.426407\pi$$
0.229145 + 0.973392i $$0.426407\pi$$
$$168$$ 0.238714 0.0184172
$$169$$ −1.77756 −0.136736
$$170$$ 3.25406 6.13349i 0.249575 0.470417i
$$171$$ 17.0669i 1.30514i
$$172$$ 4.86640 0.371059
$$173$$ 2.88008i 0.218968i 0.993989 + 0.109484i $$0.0349199\pi$$
−0.993989 + 0.109484i $$0.965080\pi$$
$$174$$ −3.61851 −0.274318
$$175$$ −2.61550 + 1.77113i −0.197713 + 0.133885i
$$176$$ 1.24789 0.0940632
$$177$$ 1.64925 0.123965
$$178$$ 13.7784i 1.03274i
$$179$$ 4.46182i 0.333492i −0.986000 0.166746i $$-0.946674\pi$$
0.986000 0.166746i $$-0.0533260\pi$$
$$180$$ 2.99427 5.64384i 0.223180 0.420667i
$$181$$ 3.93480 0.292472 0.146236 0.989250i $$-0.453284\pi$$
0.146236 + 0.989250i $$0.453284\pi$$
$$182$$ 2.11636i 0.156875i
$$183$$ 0.811140 0.0599612
$$184$$ −7.60706 −0.560800
$$185$$ −4.56437 12.8127i −0.335579 0.942012i
$$186$$ 2.74594 0.201342
$$187$$ −3.87484 −0.283356
$$188$$ 13.1187i 0.956779i
$$189$$ −1.39820 −0.101704
$$190$$ 11.7989 + 6.25979i 0.855984 + 0.454133i
$$191$$ 7.76296i 0.561708i −0.959751 0.280854i $$-0.909382\pi$$
0.959751 0.280854i $$-0.0906177\pi$$
$$192$$ 0.377861i 0.0272698i
$$193$$ −3.49189 −0.251352 −0.125676 0.992071i $$-0.540110\pi$$
−0.125676 + 0.992071i $$0.540110\pi$$
$$194$$ 11.0583 0.793937
$$195$$ 2.50038 + 1.32655i 0.179056 + 0.0949962i
$$196$$ 6.60089 0.471492
$$197$$ 1.07617i 0.0766736i −0.999265 0.0383368i $$-0.987794\pi$$
0.999265 0.0383368i $$-0.0122060\pi$$
$$198$$ −3.56550 −0.253389
$$199$$ 5.71343i 0.405014i 0.979281 + 0.202507i $$0.0649090\pi$$
−0.979281 + 0.202507i $$0.935091\pi$$
$$200$$ 2.80353 + 4.14008i 0.198239 + 0.292748i
$$201$$ 4.28687 0.302372
$$202$$ −8.65314 −0.608833
$$203$$ 6.04983 0.424615
$$204$$ 1.17330i 0.0821475i
$$205$$ −8.86067 + 16.7013i −0.618856 + 1.16647i
$$206$$ −4.57336 −0.318641
$$207$$ 21.7350 1.51069
$$208$$ −3.34999 −0.232280
$$209$$ 7.45398i 0.515603i
$$210$$ 0.250165 0.471529i 0.0172630 0.0325386i
$$211$$ 22.8397 1.57235 0.786176 0.618003i $$-0.212058\pi$$
0.786176 + 0.618003i $$0.212058\pi$$
$$212$$ 7.17340i 0.492671i
$$213$$ 4.80576i 0.329286i
$$214$$ 11.4715i 0.784178i
$$215$$ 5.09983 9.61254i 0.347805 0.655570i
$$216$$ 2.21322i 0.150590i
$$217$$ −4.59098 −0.311656
$$218$$ 0.727748i 0.0492893i
$$219$$ 1.68464 0.113837
$$220$$ 1.30775 2.46494i 0.0881684 0.166186i
$$221$$ 10.4021 0.699720
$$222$$ 1.69609 + 1.55116i 0.113834 + 0.104107i
$$223$$ 3.32116i 0.222401i 0.993798 + 0.111201i $$0.0354696\pi$$
−0.993798 + 0.111201i $$0.964530\pi$$
$$224$$ 0.631751i 0.0422106i
$$225$$ −8.01030 11.8291i −0.534020 0.788607i
$$226$$ −17.9970 −1.19714
$$227$$ 5.62938 0.373635 0.186818 0.982395i $$-0.440183\pi$$
0.186818 + 0.982395i $$0.440183\pi$$
$$228$$ −2.25707 −0.149478
$$229$$ −0.973208 −0.0643114 −0.0321557 0.999483i $$-0.510237\pi$$
−0.0321557 + 0.999483i $$0.510237\pi$$
$$230$$ −7.97195 + 15.0261i −0.525655 + 0.990794i
$$231$$ −0.297889 −0.0195997
$$232$$ 9.57629i 0.628714i
$$233$$ 14.4150i 0.944357i 0.881503 + 0.472178i $$0.156532\pi$$
−0.881503 + 0.472178i $$0.843468\pi$$
$$234$$ 9.57166 0.625719
$$235$$ −25.9132 13.7480i −1.69039 0.896819i
$$236$$ 4.36469i 0.284117i
$$237$$ 3.32019 0.215669
$$238$$ 1.96166i 0.127155i
$$239$$ 8.43344i 0.545514i −0.962083 0.272757i $$-0.912065\pi$$
0.962083 0.272757i $$-0.0879355\pi$$
$$240$$ −0.746385 0.395986i −0.0481789 0.0255608i
$$241$$ 18.6567i 1.20178i −0.799331 0.600891i $$-0.794812\pi$$
0.799331 0.600891i $$-0.205188\pi$$
$$242$$ 9.44277 0.607004
$$243$$ 9.56255i 0.613438i
$$244$$ 2.14666i 0.137426i
$$245$$ 6.91752 13.0387i 0.441944 0.833010i
$$246$$ 3.19485i 0.203696i
$$247$$ 20.0104i 1.27323i
$$248$$ 7.26707i 0.461460i
$$249$$ 2.50592 0.158806
$$250$$ 11.1159 1.19911i 0.703028 0.0758385i
$$251$$ 25.1189i 1.58549i 0.609553 + 0.792746i $$0.291349\pi$$
−0.609553 + 0.792746i $$0.708651\pi$$
$$252$$ 1.80505i 0.113708i
$$253$$ 9.49277 0.596805
$$254$$ 15.4830i 0.971490i
$$255$$ 2.31761 + 1.22958i 0.145134 + 0.0769994i
$$256$$ 1.00000 0.0625000
$$257$$ −20.3552 −1.26973 −0.634863 0.772625i $$-0.718943\pi$$
−0.634863 + 0.772625i $$0.718943\pi$$
$$258$$ 1.83882i 0.114480i
$$259$$ −2.83571 2.59341i −0.176203 0.161146i
$$260$$ −3.51068 + 6.61720i −0.217723 + 0.410381i
$$261$$ 27.3616i 1.69364i
$$262$$ 6.22121i 0.384348i
$$263$$ 22.2211i 1.37021i −0.728443 0.685107i $$-0.759756\pi$$
0.728443 0.685107i $$-0.240244\pi$$
$$264$$ 0.471529i 0.0290206i
$$265$$ 14.1695 + 7.51750i 0.870428 + 0.461796i
$$266$$ 3.77362 0.231375
$$267$$ 5.20633 0.318622
$$268$$ 11.3451i 0.693012i
$$269$$ −15.8411 −0.965850 −0.482925 0.875662i $$-0.660426\pi$$
−0.482925 + 0.875662i $$0.660426\pi$$
$$270$$ 4.37174 + 2.31938i 0.266056 + 0.141153i
$$271$$ −2.00602 −0.121857 −0.0609285 0.998142i $$-0.519406\pi$$
−0.0609285 + 0.998142i $$0.519406\pi$$
$$272$$ −3.10511 −0.188275
$$273$$ 0.799690 0.0483994
$$274$$ 14.1258i 0.853373i
$$275$$ −3.49849 5.16636i −0.210967 0.311543i
$$276$$ 2.87441i 0.173019i
$$277$$ −11.5671 −0.695000 −0.347500 0.937680i $$-0.612969\pi$$
−0.347500 + 0.937680i $$0.612969\pi$$
$$278$$ −8.43675 −0.506003
$$279$$ 20.7636i 1.24309i
$$280$$ 1.24789 + 0.662054i 0.0745757 + 0.0395653i
$$281$$ 14.2909i 0.852521i 0.904600 + 0.426261i $$0.140169\pi$$
−0.904600 + 0.426261i $$0.859831\pi$$
$$282$$ 4.95705 0.295188
$$283$$ −12.3837 −0.736137 −0.368068 0.929799i $$-0.619981\pi$$
−0.368068 + 0.929799i $$0.619981\pi$$
$$284$$ −12.7183 −0.754694
$$285$$ −2.36533 + 4.45836i −0.140110 + 0.264090i
$$286$$ 4.18042 0.247193
$$287$$ 5.34152i 0.315300i
$$288$$ −2.85722 −0.168363
$$289$$ −7.35829 −0.432840
$$290$$ −18.9159 10.0356i −1.11078 0.589313i
$$291$$ 4.17849i 0.244947i
$$292$$ 4.45836i 0.260906i
$$293$$ 27.8374i 1.62628i 0.582068 + 0.813140i $$0.302244\pi$$
−0.582068 + 0.813140i $$0.697756\pi$$
$$294$$ 2.49422i 0.145466i
$$295$$ 8.62152 + 4.57405i 0.501964 + 0.266312i
$$296$$ −4.10511 + 4.48866i −0.238605 + 0.260898i
$$297$$ 2.76185i 0.160259i
$$298$$ −13.6447 −0.790416
$$299$$ −25.4836 −1.47375
$$300$$ −1.56437 + 1.05934i −0.0903192 + 0.0611613i
$$301$$ 3.07435i 0.177203i
$$302$$ 3.17741 0.182839
$$303$$ 3.26968i 0.187838i
$$304$$ 5.97327i 0.342590i
$$305$$ 4.24028 + 2.24963i 0.242798 + 0.128814i
$$306$$ 8.87199 0.507178
$$307$$ 19.9411i 1.13810i 0.822304 + 0.569049i $$0.192688\pi$$
−0.822304 + 0.569049i $$0.807312\pi$$
$$308$$ 0.788355i 0.0449207i
$$309$$ 1.72810i 0.0983080i
$$310$$ 14.3546 + 7.61566i 0.815284 + 0.432540i
$$311$$ 4.96832i 0.281727i 0.990029 + 0.140864i $$0.0449879\pi$$
−0.990029 + 0.140864i $$0.955012\pi$$
$$312$$ 1.26583i 0.0716636i
$$313$$ −10.0000 −0.565233 −0.282617 0.959233i $$-0.591202\pi$$
−0.282617 + 0.959233i $$0.591202\pi$$
$$314$$ 0.215310i 0.0121506i
$$315$$ −3.56550 1.89164i −0.200893 0.106582i
$$316$$ 8.78679i 0.494296i
$$317$$ 22.9198i 1.28730i −0.765319 0.643651i $$-0.777419\pi$$
0.765319 0.643651i $$-0.222581\pi$$
$$318$$ −2.71055 −0.152000
$$319$$ 11.9502i 0.669080i
$$320$$ 1.04797 1.97529i 0.0585832 0.110422i
$$321$$ 4.33465 0.241937
$$322$$ 4.80576i 0.267815i
$$323$$ 18.5477i 1.03202i
$$324$$ 7.73537 0.429743
$$325$$ 9.39179 + 13.8692i 0.520963 + 0.769326i
$$326$$ 1.66609 0.0922760
$$327$$ −0.274988 −0.0152069
$$328$$ 8.45510 0.466855
$$329$$ −8.28775 −0.456918
$$330$$ 0.931406 + 0.494147i 0.0512722 + 0.0272019i
$$331$$ 5.54265i 0.304651i −0.988330 0.152326i $$-0.951324\pi$$
0.988330 0.152326i $$-0.0486763\pi$$
$$332$$ 6.63185i 0.363970i
$$333$$ 11.7292 12.8251i 0.642757 0.702811i
$$334$$ −5.92242 −0.324060
$$335$$ 22.4098 + 11.8893i 1.22438 + 0.649581i
$$336$$ −0.238714 −0.0130229
$$337$$ 25.6348i 1.39642i −0.715894 0.698209i $$-0.753981\pi$$
0.715894 0.698209i $$-0.246019\pi$$
$$338$$ 1.77756 0.0966867
$$339$$ 6.80035i 0.369344i
$$340$$ −3.25406 + 6.13349i −0.176476 + 0.332635i
$$341$$ 9.06851i 0.491087i
$$342$$ 17.0669i 0.922875i
$$343$$ 8.59237i 0.463945i
$$344$$ −4.86640 −0.262379
$$345$$ −5.67779 3.01229i −0.305682 0.162176i
$$346$$ 2.88008i 0.154834i
$$347$$ 19.6225 1.05339 0.526696 0.850054i $$-0.323431\pi$$
0.526696 + 0.850054i $$0.323431\pi$$
$$348$$ 3.61851 0.193972
$$349$$ −15.6263 −0.836459 −0.418230 0.908341i $$-0.637349\pi$$
−0.418230 + 0.908341i $$0.637349\pi$$
$$350$$ 2.61550 1.77113i 0.139804 0.0946709i
$$351$$ 7.41425i 0.395744i
$$352$$ −1.24789 −0.0665128
$$353$$ 23.5724 1.25463 0.627316 0.778765i $$-0.284153\pi$$
0.627316 + 0.778765i $$0.284153\pi$$
$$354$$ −1.64925 −0.0876564
$$355$$ −13.3284 + 25.1224i −0.707398 + 1.33336i
$$356$$ 13.7784i 0.730255i
$$357$$ 0.741234 0.0392302
$$358$$ 4.46182i 0.235815i
$$359$$ −9.34905 −0.493424 −0.246712 0.969089i $$-0.579350\pi$$
−0.246712 + 0.969089i $$0.579350\pi$$
$$360$$ −2.99427 + 5.64384i −0.157812 + 0.297456i
$$361$$ −16.6799 −0.877891
$$362$$ −3.93480 −0.206809
$$363$$ 3.56806i 0.187274i
$$364$$ 2.11636i 0.110927i
$$365$$ 8.80654 + 4.67221i 0.460955 + 0.244555i
$$366$$ −0.811140 −0.0423990
$$367$$ 12.2379i 0.638811i 0.947618 + 0.319406i $$0.103483\pi$$
−0.947618 + 0.319406i $$0.896517\pi$$
$$368$$ 7.60706 0.396545
$$369$$ −24.1581 −1.25762
$$370$$ 4.56437 + 12.8127i 0.237291 + 0.666103i
$$371$$ 4.53180 0.235280
$$372$$ −2.74594 −0.142371
$$373$$ 10.1918i 0.527712i −0.964562 0.263856i $$-0.915006\pi$$
0.964562 0.263856i $$-0.0849943\pi$$
$$374$$ 3.87484 0.200363
$$375$$ 0.453098 + 4.20025i 0.0233979 + 0.216900i
$$376$$ 13.1187i 0.676545i
$$377$$ 32.0805i 1.65223i
$$378$$ 1.39820 0.0719157
$$379$$ 20.7538 1.06605 0.533025 0.846099i $$-0.321055\pi$$
0.533025 + 0.846099i $$0.321055\pi$$
$$380$$ −11.7989 6.25979i −0.605272 0.321120i
$$381$$ −5.85042 −0.299726
$$382$$ 7.76296i 0.397188i
$$383$$ 17.7328 0.906103 0.453052 0.891484i $$-0.350335\pi$$
0.453052 + 0.891484i $$0.350335\pi$$
$$384$$ 0.377861i 0.0192826i
$$385$$ −1.55723 0.826171i −0.0793638 0.0421056i
$$386$$ 3.49189 0.177732
$$387$$ 13.9044 0.706799
$$388$$ −11.0583 −0.561398
$$389$$ 10.9054i 0.552923i −0.961025 0.276462i $$-0.910838\pi$$
0.961025 0.276462i $$-0.0891619\pi$$
$$390$$ −2.50038 1.32655i −0.126612 0.0671725i
$$391$$ −23.6208 −1.19455
$$392$$ −6.60089 −0.333395
$$393$$ 2.35075 0.118580
$$394$$ 1.07617i 0.0542164i
$$395$$ 17.3565 + 9.20827i 0.873298 + 0.463319i
$$396$$ 3.56550 0.179173
$$397$$ 23.0106i 1.15487i 0.816437 + 0.577435i $$0.195946\pi$$
−0.816437 + 0.577435i $$0.804054\pi$$
$$398$$ 5.71343i 0.286388i
$$399$$ 1.42590i 0.0713844i
$$400$$ −2.80353 4.14008i −0.140176 0.207004i
$$401$$ 16.5769i 0.827809i 0.910320 + 0.413904i $$0.135835\pi$$
−0.910320 + 0.413904i $$0.864165\pi$$
$$402$$ −4.28687 −0.213810
$$403$$ 24.3446i 1.21269i
$$404$$ 8.65314 0.430510
$$405$$ 8.10642 15.2796i 0.402811 0.759249i
$$406$$ −6.04983 −0.300248
$$407$$ 5.12273 5.60135i 0.253924 0.277649i
$$408$$ 1.17330i 0.0580870i
$$409$$ 5.05401i 0.249905i −0.992163 0.124952i $$-0.960122\pi$$
0.992163 0.124952i $$-0.0398778\pi$$
$$410$$ 8.86067 16.7013i 0.437597 0.824817i
$$411$$ 5.33760 0.263285
$$412$$ 4.57336 0.225313
$$413$$ 2.75740 0.135683
$$414$$ −21.7350 −1.06822
$$415$$ 13.0998 + 6.94997i 0.643045 + 0.341161i
$$416$$ 3.34999 0.164247
$$417$$ 3.18792i 0.156113i
$$418$$ 7.45398i 0.364586i
$$419$$ −24.2194 −1.18319 −0.591597 0.806234i $$-0.701502\pi$$
−0.591597 + 0.806234i $$0.701502\pi$$
$$420$$ −0.250165 + 0.471529i −0.0122068 + 0.0230083i
$$421$$ 20.8487i 1.01611i −0.861326 0.508053i $$-0.830365\pi$$
0.861326 0.508053i $$-0.169635\pi$$
$$422$$ −22.8397 −1.11182
$$423$$ 37.4830i 1.82249i
$$424$$ 7.17340i 0.348371i
$$425$$ 8.70527 + 12.8554i 0.422267 + 0.623578i
$$426$$ 4.80576i 0.232840i
$$427$$ 1.35616 0.0656290
$$428$$ 11.4715i 0.554498i
$$429$$ 1.57962i 0.0762647i
$$430$$ −5.09983 + 9.61254i −0.245935 + 0.463558i
$$431$$ 28.2298i 1.35978i −0.733314 0.679890i $$-0.762027\pi$$
0.733314 0.679890i $$-0.237973\pi$$
$$432$$ 2.21322i 0.106483i
$$433$$ 30.3997i 1.46091i 0.682958 + 0.730457i $$0.260693\pi$$
−0.682958 + 0.730457i $$0.739307\pi$$
$$434$$ 4.59098 0.220374
$$435$$ 3.79208 7.14759i 0.181816 0.342701i
$$436$$ 0.727748i 0.0348528i
$$437$$ 45.4390i 2.17364i
$$438$$ −1.68464 −0.0804952
$$439$$ 33.7591i 1.61123i −0.592438 0.805616i $$-0.701834\pi$$
0.592438 0.805616i $$-0.298166\pi$$
$$440$$ −1.30775 + 2.46494i −0.0623444 + 0.117512i
$$441$$ 18.8602 0.898105
$$442$$ −10.4021 −0.494777
$$443$$ 15.5413i 0.738388i −0.929352 0.369194i $$-0.879634\pi$$
0.929352 0.369194i $$-0.120366\pi$$
$$444$$ −1.69609 1.55116i −0.0804929 0.0736149i
$$445$$ 27.2164 + 14.4393i 1.29018 + 0.684490i
$$446$$ 3.32116i 0.157261i
$$447$$ 5.15580i 0.243861i
$$448$$ 0.631751i 0.0298474i
$$449$$ 14.2184i 0.671006i −0.942039 0.335503i $$-0.891094\pi$$
0.942039 0.335503i $$-0.108906\pi$$
$$450$$ 8.01030 + 11.8291i 0.377609 + 0.557630i
$$451$$ −10.5510 −0.496829
$$452$$ 17.9970 0.846506
$$453$$ 1.20062i 0.0564100i
$$454$$ −5.62938 −0.264200
$$455$$ 4.18042 + 2.21788i 0.195981 + 0.103976i
$$456$$ 2.25707 0.105697
$$457$$ 9.17031 0.428969 0.214484 0.976727i $$-0.431193\pi$$
0.214484 + 0.976727i $$0.431193\pi$$
$$458$$ 0.973208 0.0454750
$$459$$ 6.87228i 0.320771i
$$460$$ 7.97195 15.0261i 0.371694 0.700597i
$$461$$ 10.3300i 0.481114i −0.970635 0.240557i $$-0.922670\pi$$
0.970635 0.240557i $$-0.0773301\pi$$
$$462$$ 0.297889 0.0138590
$$463$$ −25.8049 −1.19926 −0.599629 0.800278i $$-0.704685\pi$$
−0.599629 + 0.800278i $$0.704685\pi$$
$$464$$ 9.57629i 0.444568i
$$465$$ −2.87766 + 5.42403i −0.133448 + 0.251533i
$$466$$ 14.4150i 0.667761i
$$467$$ −34.4582 −1.59454 −0.797268 0.603625i $$-0.793722\pi$$
−0.797268 + 0.603625i $$0.793722\pi$$
$$468$$ −9.57166 −0.442450
$$469$$ 7.16727 0.330954
$$470$$ 25.9132 + 13.7480i 1.19529 + 0.634147i
$$471$$ −0.0813572 −0.00374874
$$472$$ 4.36469i 0.200901i
$$473$$ 6.07273 0.279224
$$474$$ −3.32019 −0.152501
$$475$$ −24.7298 + 16.7462i −1.13468 + 0.768369i
$$476$$ 1.96166i 0.0899124i
$$477$$ 20.4960i 0.938448i
$$478$$ 8.43344i 0.385737i
$$479$$ 29.6039i 1.35264i −0.736610 0.676318i $$-0.763574\pi$$
0.736610 0.676318i $$-0.236426\pi$$
$$480$$ 0.746385 + 0.395986i 0.0340676 + 0.0180742i
$$481$$ −13.7521 + 15.0370i −0.627041 + 0.685627i
$$482$$ 18.6567i 0.849789i
$$483$$ −1.81591 −0.0826268
$$484$$ −9.44277 −0.429217
$$485$$ −11.5887 + 21.8433i −0.526216 + 0.991852i
$$486$$ 9.56255i 0.433766i
$$487$$ −27.0961 −1.22784 −0.613920 0.789369i $$-0.710408\pi$$
−0.613920 + 0.789369i $$0.710408\pi$$
$$488$$ 2.14666i 0.0971749i
$$489$$ 0.629549i 0.0284692i
$$490$$ −6.91752 + 13.0387i −0.312502 + 0.589027i
$$491$$ 2.46033 0.111033 0.0555166 0.998458i $$-0.482319\pi$$
0.0555166 + 0.998458i $$0.482319\pi$$
$$492$$ 3.19485i 0.144035i
$$493$$ 29.7354i 1.33922i
$$494$$ 20.0104i 0.900310i
$$495$$ 3.73653 7.04289i 0.167944 0.316554i
$$496$$ 7.26707i 0.326301i
$$497$$ 8.03482i 0.360411i
$$498$$ −2.50592 −0.112293
$$499$$ 31.4091i 1.40606i 0.711158 + 0.703032i $$0.248171\pi$$
−0.711158 + 0.703032i $$0.751829\pi$$
$$500$$ −11.1159 + 1.19911i −0.497116 + 0.0536259i
$$501$$ 2.23785i 0.0999798i
$$502$$ 25.1189i 1.12111i
$$503$$ 1.78145 0.0794311 0.0397156 0.999211i $$-0.487355\pi$$
0.0397156 + 0.999211i $$0.487355\pi$$
$$504$$ 1.80505i 0.0804034i
$$505$$ 9.06821 17.0924i 0.403530 0.760604i
$$506$$ −9.49277 −0.422005
$$507$$ 0.671672i 0.0298300i
$$508$$ 15.4830i 0.686947i
$$509$$ 21.2370 0.941314 0.470657 0.882316i $$-0.344017\pi$$
0.470657 + 0.882316i $$0.344017\pi$$
$$510$$ −2.31761 1.22958i −0.102625 0.0544468i
$$511$$ 2.81657 0.124598
$$512$$ −1.00000 −0.0441942
$$513$$ −13.2201 −0.583683
$$514$$ 20.3552 0.897831
$$515$$ 4.79274 9.03371i 0.211193 0.398073i
$$516$$ 1.83882i 0.0809496i
$$517$$ 16.3707i 0.719982i
$$518$$ 2.83571 + 2.59341i 0.124594 + 0.113948i
$$519$$ 1.08827 0.0477698
$$520$$ 3.51068 6.61720i 0.153954 0.290183i
$$521$$ 2.52950 0.110819 0.0554097 0.998464i $$-0.482354\pi$$
0.0554097 + 0.998464i $$0.482354\pi$$
$$522$$ 27.3616i 1.19758i
$$523$$ −1.60848 −0.0703338 −0.0351669 0.999381i $$-0.511196\pi$$
−0.0351669 + 0.999381i $$0.511196\pi$$
$$524$$ 6.22121i 0.271775i
$$525$$ 0.669242 + 0.988294i 0.0292081 + 0.0431327i
$$526$$ 22.2211i 0.968887i
$$527$$ 22.5651i 0.982950i
$$528$$ 0.471529i 0.0205207i
$$529$$ 34.8673 1.51597
$$530$$ −14.1695 7.51750i −0.615486 0.326539i
$$531$$ 12.4709i 0.541190i
$$532$$ −3.77362 −0.163607
$$533$$ 28.3245 1.22687
$$534$$ −5.20633 −0.225300
$$535$$ 22.6596 + 12.0218i 0.979660 + 0.519748i
$$536$$ 11.3451i 0.490033i
$$537$$ −1.68595 −0.0727541
$$538$$ 15.8411 0.682959
$$539$$ 8.23719 0.354801
$$540$$ −4.37174 2.31938i −0.188130 0.0998102i
$$541$$ 3.12463i 0.134338i 0.997742 + 0.0671692i $$0.0213967\pi$$
−0.997742 + 0.0671692i $$0.978603\pi$$
$$542$$ 2.00602 0.0861660
$$543$$ 1.48681i 0.0638051i
$$544$$ 3.10511 0.133131
$$545$$ −1.43751 0.762657i −0.0615763 0.0326686i
$$546$$ −0.799690 −0.0342236
$$547$$ 5.44201 0.232683 0.116342 0.993209i $$-0.462883\pi$$
0.116342 + 0.993209i $$0.462883\pi$$
$$548$$ 14.1258i 0.603426i
$$549$$ 6.13349i 0.261771i
$$550$$ 3.49849 + 5.16636i 0.149176 + 0.220294i
$$551$$ 57.2017 2.43688
$$552$$ 2.87441i 0.122343i
$$553$$ 5.55106 0.236055
$$554$$ 11.5671 0.491440
$$555$$ −4.84144 + 1.72470i −0.205508 + 0.0732094i
$$556$$ 8.43675 0.357798
$$557$$ −36.3451 −1.53999 −0.769995 0.638050i $$-0.779741\pi$$
−0.769995 + 0.638050i $$0.779741\pi$$
$$558$$ 20.7636i 0.878995i
$$559$$ −16.3024 −0.689517
$$560$$ −1.24789 0.662054i −0.0527330 0.0279769i
$$561$$ 1.46415i 0.0618165i
$$562$$ 14.2909i 0.602824i
$$563$$ −38.4949 −1.62237 −0.811184 0.584791i $$-0.801177\pi$$
−0.811184 + 0.584791i $$0.801177\pi$$
$$564$$ −4.95705 −0.208729
$$565$$ 18.8602 35.5492i 0.793456 1.49557i
$$566$$ 12.3837 0.520527
$$567$$ 4.88683i 0.205228i
$$568$$ 12.7183 0.533649
$$569$$ 41.2793i 1.73052i −0.501324 0.865260i $$-0.667154\pi$$
0.501324 0.865260i $$-0.332846\pi$$
$$570$$ 2.36533 4.45836i 0.0990728 0.186740i
$$571$$ −26.0635 −1.09072 −0.545362 0.838200i $$-0.683608\pi$$
−0.545362 + 0.838200i $$0.683608\pi$$
$$572$$ −4.18042 −0.174792
$$573$$ −2.93332 −0.122541
$$574$$ 5.34152i 0.222951i
$$575$$ −21.3266 31.4938i −0.889381 1.31338i
$$576$$ 2.85722 0.119051
$$577$$ 11.8411 0.492952 0.246476 0.969149i $$-0.420727\pi$$
0.246476 + 0.969149i $$0.420727\pi$$
$$578$$ 7.35829 0.306064
$$579$$ 1.31945i 0.0548344i
$$580$$ 18.9159 + 10.0356i 0.785441 + 0.416707i
$$581$$ 4.18968 0.173817
$$582$$ 4.17849i 0.173204i
$$583$$ 8.95162i 0.370738i
$$584$$ 4.45836i 0.184488i
$$585$$ −10.0308 + 18.9068i −0.414722 + 0.781700i
$$586$$ 27.8374i 1.14995i
$$587$$ −26.7315 −1.10333 −0.551663 0.834067i $$-0.686006\pi$$
−0.551663 + 0.834067i $$0.686006\pi$$
$$588$$ 2.49422i 0.102860i
$$589$$ −43.4082 −1.78860
$$590$$ −8.62152 4.57405i −0.354942 0.188311i
$$591$$ −0.406641 −0.0167270
$$592$$ 4.10511 4.48866i 0.168719 0.184483i
$$593$$ 22.6119i 0.928560i 0.885688 + 0.464280i $$0.153687\pi$$
−0.885688 + 0.464280i $$0.846313\pi$$
$$594$$ 2.76185i 0.113320i
$$595$$ 3.87484 + 2.05575i 0.158853 + 0.0842776i
$$596$$ 13.6447 0.558909
$$597$$ 2.15888 0.0883572
$$598$$ 25.4836 1.04210
$$599$$ 14.3406 0.585942 0.292971 0.956121i $$-0.405356\pi$$
0.292971 + 0.956121i $$0.405356\pi$$
$$600$$ 1.56437 1.05934i 0.0638653 0.0432476i
$$601$$ 15.0845 0.615308 0.307654 0.951498i $$-0.400456\pi$$
0.307654 + 0.951498i $$0.400456\pi$$
$$602$$ 3.07435i 0.125301i
$$603$$ 32.4154i 1.32006i
$$604$$ −3.17741 −0.129287
$$605$$ −9.89572 + 18.6522i −0.402318 + 0.758320i
$$606$$ 3.26968i 0.132822i
$$607$$ 41.5964 1.68835 0.844174 0.536070i $$-0.180092\pi$$
0.844174 + 0.536070i $$0.180092\pi$$
$$608$$ 5.97327i 0.242248i
$$609$$ 2.28599i 0.0926332i
$$610$$ −4.24028 2.24963i −0.171684 0.0910850i
$$611$$ 43.9475i 1.77793i
$$612$$ −8.87199 −0.358629
$$613$$ 30.4369i 1.22934i −0.788786 0.614668i $$-0.789290\pi$$
0.788786 0.614668i $$-0.210710\pi$$
$$614$$ 19.9411i 0.804756i
$$615$$ 6.31076 + 3.34810i 0.254474 + 0.135009i
$$616$$ 0.788355i 0.0317637i
$$617$$ 39.8195i 1.60307i −0.597946 0.801536i $$-0.704016\pi$$
0.597946 0.801536i $$-0.295984\pi$$
$$618$$ 1.72810i 0.0695142i
$$619$$ 39.4011 1.58367 0.791833 0.610738i $$-0.209127\pi$$
0.791833 + 0.610738i $$0.209127\pi$$
$$620$$ −14.3546 7.61566i −0.576493 0.305852i
$$621$$ 16.8361i 0.675608i
$$622$$ 4.96832i 0.199211i
$$623$$ 8.70453 0.348740
$$624$$ 1.26583i 0.0506738i
$$625$$ −9.28046 + 23.2136i −0.371218 + 0.928546i
$$626$$ 10.0000 0.399680
$$627$$ −2.81657 −0.112483
$$628$$ 0.215310i 0.00859180i
$$629$$ −12.7468 + 13.9378i −0.508249 + 0.555736i
$$630$$ 3.56550 + 1.89164i 0.142053 + 0.0753646i
$$631$$ 0.114985i 0.00457750i 0.999997 + 0.00228875i $$0.000728532\pi$$
−0.999997 + 0.00228875i $$0.999271\pi$$
$$632$$ 8.78679i 0.349520i
$$633$$ 8.63024i 0.343021i
$$634$$ 22.9198i 0.910260i
$$635$$ −30.5834 16.2257i −1.21366 0.643897i
$$636$$ 2.71055 0.107480
$$637$$ −22.1129 −0.876146
$$638$$ 11.9502i 0.473111i
$$639$$ −36.3391 −1.43755
$$640$$ −1.04797 + 1.97529i −0.0414246 + 0.0780801i
$$641$$ 34.9774 1.38153 0.690763 0.723081i $$-0.257275\pi$$
0.690763 + 0.723081i $$0.257275\pi$$
$$642$$ −4.33465 −0.171075
$$643$$ −25.2868 −0.997216 −0.498608 0.866828i $$-0.666155\pi$$
−0.498608 + 0.866828i $$0.666155\pi$$
$$644$$ 4.80576i 0.189374i
$$645$$ −3.63220 1.92703i −0.143018 0.0758766i
$$646$$ 18.5477i 0.729748i
$$647$$ 23.5824 0.927120 0.463560 0.886066i $$-0.346572\pi$$
0.463560 + 0.886066i $$0.346572\pi$$
$$648$$ −7.73537 −0.303874
$$649$$ 5.44665i 0.213800i
$$650$$ −9.39179 13.8692i −0.368376 0.543995i
$$651$$ 1.73475i 0.0679903i
$$652$$ −1.66609 −0.0652490
$$653$$ −9.89261 −0.387128 −0.193564 0.981088i $$-0.562005\pi$$
−0.193564 + 0.981088i $$0.562005\pi$$
$$654$$ 0.274988 0.0107529
$$655$$ 12.2887 + 6.51963i 0.480159 + 0.254743i
$$656$$ −8.45510 −0.330116
$$657$$ 12.7385i 0.496977i
$$658$$ 8.28775 0.323090
$$659$$ −25.4137 −0.989976 −0.494988 0.868900i $$-0.664827\pi$$
−0.494988 + 0.868900i $$0.664827\pi$$
$$660$$ −0.931406 0.494147i −0.0362549 0.0192347i
$$661$$ 28.4574i 1.10687i −0.832894 0.553433i $$-0.813318\pi$$
0.832894 0.553433i $$-0.186682\pi$$
$$662$$ 5.54265i 0.215421i
$$663$$ 3.93055i 0.152650i
$$664$$ 6.63185i 0.257366i
$$665$$ −3.95463 + 7.45398i −0.153354 + 0.289053i
$$666$$ −11.7292 + 12.8251i −0.454498 + 0.496962i
$$667$$ 72.8474i 2.82066i
$$668$$ 5.92242 0.229145
$$669$$ 1.25494 0.0485186
$$670$$ −22.4098 11.8893i −0.865767 0.459323i
$$671$$ 2.67880i 0.103414i
$$672$$ 0.238714 0.00920860
$$673$$ 20.4187i 0.787082i −0.919307 0.393541i $$-0.871250\pi$$
0.919307 0.393541i $$-0.128750\pi$$
$$674$$ 25.6348i 0.987416i
$$675$$ −9.16288 + 6.20481i −0.352680 + 0.238823i
$$676$$ −1.77756 −0.0683678
$$677$$ 18.5163i 0.711641i 0.934554 + 0.355821i $$0.115799\pi$$
−0.934554 + 0.355821i $$0.884201\pi$$
$$678$$ 6.80035i 0.261166i
$$679$$ 6.98607i 0.268101i
$$680$$ 3.25406 6.13349i 0.124787 0.235209i
$$681$$ 2.12713i 0.0815116i
$$682$$ 9.06851i 0.347251i
$$683$$ −32.0667 −1.22700 −0.613499 0.789695i $$-0.710239\pi$$
−0.613499 + 0.789695i $$0.710239\pi$$
$$684$$ 17.0669i 0.652571i
$$685$$ 27.9026 + 14.8034i 1.06610 + 0.565609i
$$686$$ 8.59237i 0.328058i
$$687$$ 0.367738i 0.0140301i
$$688$$ 4.86640 0.185530
$$689$$ 24.0308i 0.915502i
$$690$$ 5.67779 + 3.01229i 0.216150 + 0.114676i
$$691$$ −6.57629 −0.250174 −0.125087 0.992146i $$-0.539921\pi$$
−0.125087 + 0.992146i $$0.539921\pi$$
$$692$$ 2.88008i 0.109484i
$$693$$ 2.25251i 0.0855656i
$$694$$ −19.6225 −0.744860
$$695$$ 8.84144 16.6650i 0.335375 0.632140i
$$696$$ −3.61851 −0.137159
$$697$$ 26.2540 0.994442
$$698$$ 15.6263 0.591466
$$699$$ 5.44686 0.206019
$$700$$ −2.61550 + 1.77113i −0.0988565 + 0.0669425i
$$701$$ 9.62168i 0.363406i 0.983353 + 0.181703i $$0.0581609\pi$$
−0.983353 + 0.181703i $$0.941839\pi$$
$$702$$ 7.41425i 0.279833i
$$703$$ −26.8120 24.5209i −1.01123 0.924824i
$$704$$ 1.24789 0.0470316
$$705$$ −5.19482 + 9.79160i −0.195648 + 0.368773i
$$706$$ −23.5724 −0.887159
$$707$$ 5.46663i 0.205594i
$$708$$ 1.64925 0.0619825
$$709$$ 8.65759i 0.325142i 0.986697 + 0.162571i $$0.0519787\pi$$
−0.986697 + 0.162571i $$0.948021\pi$$
$$710$$ 13.3284 25.1224i 0.500206 0.942826i
$$711$$ 25.1058i 0.941541i
$$712$$ 13.7784i 0.516368i
$$713$$ 55.2810i 2.07029i
$$714$$ −0.741234 −0.0277400
$$715$$ −4.38094 + 8.25753i −0.163838 + 0.308814i
$$716$$ 4.46182i 0.166746i
$$717$$ −3.18667 −0.119008
$$718$$ 9.34905 0.348904
$$719$$ 51.5303 1.92176 0.960878 0.276972i $$-0.0893310\pi$$
0.960878 + 0.276972i $$0.0893310\pi$$
$$720$$ 2.99427 5.64384i 0.111590 0.210333i
$$721$$ 2.88923i 0.107600i
$$722$$ 16.6799 0.620763
$$723$$ −7.04964 −0.262179
$$724$$ 3.93480 0.146236
$$725$$ 39.6466 26.8474i 1.47244 0.997087i
$$726$$ 3.56806i 0.132423i
$$727$$ 11.3224 0.419924 0.209962 0.977710i $$-0.432666\pi$$
0.209962 + 0.977710i $$0.432666\pi$$
$$728$$ 2.11636i 0.0784375i
$$729$$ 19.5928 0.725660
$$730$$ −8.80654 4.67221i −0.325945 0.172926i
$$731$$ −15.1107 −0.558890
$$732$$ 0.811140 0.0299806
$$733$$ 2.74231i 0.101290i 0.998717 + 0.0506448i $$0.0161276\pi$$
−0.998717 + 0.0506448i $$0.983872\pi$$
$$734$$ 12.2379i 0.451708i
$$735$$ −4.92680 2.61386i −0.181728 0.0964137i
$$736$$ −7.60706 −0.280400
$$737$$ 14.1574i 0.521495i
$$738$$ 24.1581 0.889272
$$739$$ 8.18878 0.301229 0.150614 0.988593i $$-0.451875\pi$$
0.150614 + 0.988593i $$0.451875\pi$$
$$740$$ −4.56437 12.8127i −0.167790 0.471006i
$$741$$ 7.56115 0.277766
$$742$$ −4.53180 −0.166368
$$743$$ 22.1217i 0.811567i −0.913969 0.405784i $$-0.866999\pi$$
0.913969 0.405784i $$-0.133001\pi$$
$$744$$ 2.74594 0.100671
$$745$$ 14.2992 26.9522i 0.523882 0.987453i
$$746$$ 10.1918i 0.373149i
$$747$$ 18.9487i 0.693296i
$$748$$ −3.87484 −0.141678
$$749$$ 7.24715 0.264805
$$750$$ −0.453098 4.20025i −0.0165448 0.153371i
$$751$$ −19.0818 −0.696306 −0.348153 0.937438i $$-0.613191\pi$$
−0.348153 + 0.937438i $$0.613191\pi$$
$$752$$ 13.1187i 0.478390i
$$753$$ 9.49146 0.345888
$$754$$ 32.0805i 1.16830i
$$755$$ −3.32982 + 6.27630i −0.121185 + 0.228418i
$$756$$ −1.39820 −0.0508521
$$757$$ 31.2209 1.13474 0.567372 0.823462i $$-0.307960\pi$$
0.567372 + 0.823462i $$0.307960\pi$$
$$758$$ −20.7538 −0.753811
$$759$$ 3.58695i 0.130198i
$$760$$ 11.7989 + 6.25979i 0.427992 + 0.227066i
$$761$$ −29.3163 −1.06271 −0.531357 0.847148i $$-0.678318\pi$$
−0.531357 + 0.847148i $$0.678318\pi$$
$$762$$ 5.85042 0.211939
$$763$$ −0.459756 −0.0166443
$$764$$ 7.76296i 0.280854i
$$765$$ −9.29756 + 17.5247i −0.336154 + 0.633608i
$$766$$ −17.7328 −0.640712
$$767$$ 14.6217i 0.527958i
$$768$$ 0.377861i 0.0136349i
$$769$$ 29.0289i 1.04681i 0.852084 + 0.523404i $$0.175338\pi$$
−0.852084 + 0.523404i $$0.824662\pi$$
$$770$$ 1.55723 + 0.826171i 0.0561187 + 0.0297731i
$$771$$ 7.69146i 0.277001i
$$772$$ −3.49189 −0.125676
$$773$$ 43.4153i 1.56154i 0.624819 + 0.780769i $$0.285173\pi$$
−0.624819 + 0.780769i $$0.714827\pi$$
$$774$$ −13.9044 −0.499782
$$775$$ −30.0862 + 20.3734i −1.08073 + 0.731836i
$$776$$ 11.0583 0.396969
$$777$$ −0.979948 + 1.07151i −0.0351554 + 0.0384401i
$$778$$ 10.9054i 0.390976i
$$779$$ 50.5046i 1.80951i
$$780$$ 2.50038 + 1.32655i 0.0895280 + 0.0474981i
$$781$$ −15.8711 −0.567912
$$782$$ 23.6208 0.844676
$$783$$ 21.1944 0.757426
$$784$$ 6.60089 0.235746
$$785$$ −0.425299 0.225638i −0.0151796 0.00805336i
$$786$$ −2.35075 −0.0838486
$$787$$ 18.9119i 0.674136i 0.941480 + 0.337068i $$0.109435\pi$$
−0.941480 + 0.337068i $$0.890565\pi$$