# Properties

 Label 1050.2.b.d.251.12 Level $1050$ Weight $2$ Character 1050.251 Analytic conductor $8.384$ Analytic rank $0$ Dimension $12$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1050.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$8.38429221223$$ Analytic rank: $$0$$ Dimension: $$12$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ Defining polynomial: $$x^{12} + 4 x^{8} - 30 x^{6} + 36 x^{4} + 729$$ 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 251.12 Root $$1.68439 + 0.403509i$$ of defining polynomial Character $$\chi$$ $$=$$ 1050.251 Dual form 1050.2.b.d.251.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} +(1.68439 - 0.403509i) q^{3} -1.00000 q^{4} +(0.403509 + 1.68439i) q^{6} +(-2.31502 - 1.28088i) q^{7} -1.00000i q^{8} +(2.67436 - 1.35934i) q^{9} +O(q^{10})$$ $$q+1.00000i q^{2} +(1.68439 - 0.403509i) q^{3} -1.00000 q^{4} +(0.403509 + 1.68439i) q^{6} +(-2.31502 - 1.28088i) q^{7} -1.00000i q^{8} +(2.67436 - 1.35934i) q^{9} +5.34872i q^{11} +(-1.68439 + 0.403509i) q^{12} +3.95617i q^{13} +(1.28088 - 2.31502i) q^{14} +1.00000 q^{16} +7.32496 q^{17} +(1.35934 + 2.67436i) q^{18} -0.807019i q^{19} +(-4.41626 - 1.22338i) q^{21} -5.34872 q^{22} -0.281327i q^{23} +(-0.403509 - 1.68439i) q^{24} -3.95617 q^{26} +(3.95617 - 3.36879i) q^{27} +(2.31502 + 1.28088i) q^{28} -0.281327i q^{29} +9.07971i q^{31} +1.00000i q^{32} +(2.15826 + 9.00935i) q^{33} +7.32496i q^{34} +(-2.67436 + 1.35934i) q^{36} +6.06739 q^{37} +0.807019 q^{38} +(1.59635 + 6.66375i) q^{39} +6.15019 q^{41} +(1.22338 - 4.41626i) q^{42} +6.34872 q^{43} -5.34872i q^{44} +0.281327 q^{46} -5.78984 q^{47} +(1.68439 - 0.403509i) q^{48} +(3.71867 + 5.93055i) q^{49} +(12.3381 - 2.95569i) q^{51} -3.95617i q^{52} -10.9788i q^{53} +(3.36879 + 3.95617i) q^{54} +(-1.28088 + 2.31502i) q^{56} +(-0.325639 - 1.35934i) q^{57} +0.281327 q^{58} -4.90390 q^{59} +13.2555i q^{61} -9.07971 q^{62} +(-7.93236 - 0.278649i) q^{63} -1.00000 q^{64} +(-9.00935 + 2.15826i) q^{66} -6.71867 q^{67} -7.32496 q^{68} +(-0.113518 - 0.473865i) q^{69} -3.36995i q^{71} +(-1.35934 - 2.67436i) q^{72} -4.98282i q^{73} +6.06739i q^{74} +0.807019i q^{76} +(6.85109 - 12.3824i) q^{77} +(-6.66375 + 1.59635i) q^{78} -3.26010 q^{79} +(5.30441 - 7.27071i) q^{81} +6.15019i q^{82} -1.53511 q^{83} +(4.41626 + 1.22338i) q^{84} +6.34872i q^{86} +(-0.113518 - 0.473865i) q^{87} +5.34872 q^{88} -4.31652 q^{89} +(5.06739 - 9.15863i) q^{91} +0.281327i q^{92} +(3.66375 + 15.2938i) q^{93} -5.78984i q^{94} +(0.403509 + 1.68439i) q^{96} -15.0892i q^{97} +(-5.93055 + 3.71867i) q^{98} +(7.27071 + 14.3044i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q - 12q^{4} - 4q^{7} + O(q^{10})$$ $$12q - 12q^{4} - 4q^{7} + 12q^{16} + 8q^{18} + 14q^{21} + 4q^{28} - 8q^{37} + 12q^{39} + 14q^{42} + 12q^{43} + 20q^{46} + 28q^{49} + 28q^{51} - 36q^{57} + 20q^{58} - 22q^{63} - 12q^{64} - 64q^{67} - 8q^{72} + 8q^{78} + 56q^{79} - 16q^{81} - 14q^{84} - 20q^{91} - 44q^{93} + 48q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$701$$ $$\chi(n)$$ $$1$$ $$-1$$ $$-1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 1.68439 0.403509i 0.972485 0.232966i
$$4$$ −1.00000 −0.500000
$$5$$ 0 0
$$6$$ 0.403509 + 1.68439i 0.164732 + 0.687651i
$$7$$ −2.31502 1.28088i −0.874997 0.484129i
$$8$$ 1.00000i 0.353553i
$$9$$ 2.67436 1.35934i 0.891454 0.453112i
$$10$$ 0 0
$$11$$ 5.34872i 1.61270i 0.591439 + 0.806350i $$0.298560\pi$$
−0.591439 + 0.806350i $$0.701440\pi$$
$$12$$ −1.68439 + 0.403509i −0.486242 + 0.116483i
$$13$$ 3.95617i 1.09724i 0.836070 + 0.548622i $$0.184847\pi$$
−0.836070 + 0.548622i $$0.815153\pi$$
$$14$$ 1.28088 2.31502i 0.342331 0.618716i
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ 7.32496 1.77656 0.888281 0.459300i $$-0.151900\pi$$
0.888281 + 0.459300i $$0.151900\pi$$
$$18$$ 1.35934 + 2.67436i 0.320399 + 0.630353i
$$19$$ 0.807019i 0.185143i −0.995706 0.0925714i $$-0.970491\pi$$
0.995706 0.0925714i $$-0.0295086\pi$$
$$20$$ 0 0
$$21$$ −4.41626 1.22338i −0.963707 0.266963i
$$22$$ −5.34872 −1.14035
$$23$$ 0.281327i 0.0586607i −0.999570 0.0293304i $$-0.990663\pi$$
0.999570 0.0293304i $$-0.00933749\pi$$
$$24$$ −0.403509 1.68439i −0.0823660 0.343825i
$$25$$ 0 0
$$26$$ −3.95617 −0.775869
$$27$$ 3.95617 3.36879i 0.761365 0.648323i
$$28$$ 2.31502 + 1.28088i 0.437498 + 0.242064i
$$29$$ 0.281327i 0.0522411i −0.999659 0.0261206i $$-0.991685\pi$$
0.999659 0.0261206i $$-0.00831538\pi$$
$$30$$ 0 0
$$31$$ 9.07971i 1.63076i 0.578924 + 0.815382i $$0.303473\pi$$
−0.578924 + 0.815382i $$0.696527\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 2.15826 + 9.00935i 0.375705 + 1.56833i
$$34$$ 7.32496i 1.25622i
$$35$$ 0 0
$$36$$ −2.67436 + 1.35934i −0.445727 + 0.226556i
$$37$$ 6.06739 0.997473 0.498737 0.866754i $$-0.333797\pi$$
0.498737 + 0.866754i $$0.333797\pi$$
$$38$$ 0.807019 0.130916
$$39$$ 1.59635 + 6.66375i 0.255621 + 1.06705i
$$40$$ 0 0
$$41$$ 6.15019 0.960498 0.480249 0.877132i $$-0.340546\pi$$
0.480249 + 0.877132i $$0.340546\pi$$
$$42$$ 1.22338 4.41626i 0.188771 0.681444i
$$43$$ 6.34872 0.968171 0.484085 0.875021i $$-0.339152\pi$$
0.484085 + 0.875021i $$0.339152\pi$$
$$44$$ 5.34872i 0.806350i
$$45$$ 0 0
$$46$$ 0.281327 0.0414794
$$47$$ −5.78984 −0.844535 −0.422268 0.906471i $$-0.638766\pi$$
−0.422268 + 0.906471i $$0.638766\pi$$
$$48$$ 1.68439 0.403509i 0.243121 0.0582415i
$$49$$ 3.71867 + 5.93055i 0.531239 + 0.847222i
$$50$$ 0 0
$$51$$ 12.3381 2.95569i 1.72768 0.413879i
$$52$$ 3.95617i 0.548622i
$$53$$ 10.9788i 1.50805i −0.656846 0.754025i $$-0.728110\pi$$
0.656846 0.754025i $$-0.271890\pi$$
$$54$$ 3.36879 + 3.95617i 0.458434 + 0.538367i
$$55$$ 0 0
$$56$$ −1.28088 + 2.31502i −0.171165 + 0.309358i
$$57$$ −0.325639 1.35934i −0.0431320 0.180049i
$$58$$ 0.281327 0.0369401
$$59$$ −4.90390 −0.638433 −0.319217 0.947682i $$-0.603420\pi$$
−0.319217 + 0.947682i $$0.603420\pi$$
$$60$$ 0 0
$$61$$ 13.2555i 1.69719i 0.529040 + 0.848597i $$0.322552\pi$$
−0.529040 + 0.848597i $$0.677448\pi$$
$$62$$ −9.07971 −1.15312
$$63$$ −7.93236 0.278649i −0.999384 0.0351064i
$$64$$ −1.00000 −0.125000
$$65$$ 0 0
$$66$$ −9.00935 + 2.15826i −1.10897 + 0.265663i
$$67$$ −6.71867 −0.820817 −0.410408 0.911902i $$-0.634614\pi$$
−0.410408 + 0.911902i $$0.634614\pi$$
$$68$$ −7.32496 −0.888281
$$69$$ −0.113518 0.473865i −0.0136660 0.0570467i
$$70$$ 0 0
$$71$$ 3.36995i 0.399940i −0.979802 0.199970i $$-0.935916\pi$$
0.979802 0.199970i $$-0.0640844\pi$$
$$72$$ −1.35934 2.67436i −0.160199 0.315176i
$$73$$ 4.98282i 0.583195i −0.956541 0.291598i $$-0.905813\pi$$
0.956541 0.291598i $$-0.0941868\pi$$
$$74$$ 6.06739i 0.705320i
$$75$$ 0 0
$$76$$ 0.807019i 0.0925714i
$$77$$ 6.85109 12.3824i 0.780754 1.41111i
$$78$$ −6.66375 + 1.59635i −0.754521 + 0.180751i
$$79$$ −3.26010 −0.366789 −0.183395 0.983039i $$-0.558709\pi$$
−0.183395 + 0.983039i $$0.558709\pi$$
$$80$$ 0 0
$$81$$ 5.30441 7.27071i 0.589379 0.807857i
$$82$$ 6.15019i 0.679175i
$$83$$ −1.53511 −0.168501 −0.0842503 0.996445i $$-0.526850\pi$$
−0.0842503 + 0.996445i $$0.526850\pi$$
$$84$$ 4.41626 + 1.22338i 0.481853 + 0.133482i
$$85$$ 0 0
$$86$$ 6.34872i 0.684600i
$$87$$ −0.113518 0.473865i −0.0121704 0.0508037i
$$88$$ 5.34872 0.570176
$$89$$ −4.31652 −0.457550 −0.228775 0.973479i $$-0.573472\pi$$
−0.228775 + 0.973479i $$0.573472\pi$$
$$90$$ 0 0
$$91$$ 5.06739 9.15863i 0.531207 0.960085i
$$92$$ 0.281327i 0.0293304i
$$93$$ 3.66375 + 15.2938i 0.379913 + 1.58589i
$$94$$ 5.78984i 0.597177i
$$95$$ 0 0
$$96$$ 0.403509 + 1.68439i 0.0411830 + 0.171913i
$$97$$ 15.0892i 1.53207i −0.642796 0.766037i $$-0.722226\pi$$
0.642796 0.766037i $$-0.277774\pi$$
$$98$$ −5.93055 + 3.71867i −0.599076 + 0.375643i
$$99$$ 7.27071 + 14.3044i 0.730734 + 1.43765i
$$100$$ 0 0
$$101$$ −5.78984 −0.576111 −0.288055 0.957614i $$-0.593009\pi$$
−0.288055 + 0.957614i $$0.593009\pi$$
$$102$$ 2.95569 + 12.3381i 0.292657 + 1.22165i
$$103$$ 6.95721i 0.685514i 0.939424 + 0.342757i $$0.111361\pi$$
−0.939424 + 0.342757i $$0.888639\pi$$
$$104$$ 3.95617 0.387934
$$105$$ 0 0
$$106$$ 10.9788 1.06635
$$107$$ 10.6088i 1.02559i −0.858510 0.512797i $$-0.828610\pi$$
0.858510 0.512797i $$-0.171390\pi$$
$$108$$ −3.95617 + 3.36879i −0.380683 + 0.324162i
$$109$$ −18.1348 −1.73700 −0.868499 0.495691i $$-0.834915\pi$$
−0.868499 + 0.495691i $$0.834915\pi$$
$$110$$ 0 0
$$111$$ 10.2199 2.44825i 0.970028 0.232378i
$$112$$ −2.31502 1.28088i −0.218749 0.121032i
$$113$$ 8.54142i 0.803510i −0.915747 0.401755i $$-0.868400\pi$$
0.915747 0.401755i $$-0.131600\pi$$
$$114$$ 1.35934 0.325639i 0.127314 0.0304989i
$$115$$ 0 0
$$116$$ 0.281327i 0.0261206i
$$117$$ 5.37777 + 10.5802i 0.497175 + 0.978142i
$$118$$ 4.90390i 0.451441i
$$119$$ −16.9574 9.38242i −1.55449 0.860085i
$$120$$ 0 0
$$121$$ −17.6088 −1.60080
$$122$$ −13.2555 −1.20010
$$123$$ 10.3593 2.48166i 0.934070 0.223764i
$$124$$ 9.07971i 0.815382i
$$125$$ 0 0
$$126$$ 0.278649 7.93236i 0.0248240 0.706671i
$$127$$ 2.00000 0.177471 0.0887357 0.996055i $$-0.471717\pi$$
0.0887357 + 0.996055i $$0.471717\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 10.6937 2.56177i 0.941532 0.225551i
$$130$$ 0 0
$$131$$ 16.5454 1.44558 0.722788 0.691070i $$-0.242860\pi$$
0.722788 + 0.691070i $$0.242860\pi$$
$$132$$ −2.15826 9.00935i −0.187852 0.784163i
$$133$$ −1.03370 + 1.86827i −0.0896329 + 0.161999i
$$134$$ 6.71867i 0.580405i
$$135$$ 0 0
$$136$$ 7.32496i 0.628110i
$$137$$ 7.41612i 0.633601i 0.948492 + 0.316801i $$0.102609\pi$$
−0.948492 + 0.316801i $$0.897391\pi$$
$$138$$ 0.473865 0.113518i 0.0403381 0.00966330i
$$139$$ 6.36982i 0.540281i 0.962821 + 0.270141i $$0.0870702\pi$$
−0.962821 + 0.270141i $$0.912930\pi$$
$$140$$ 0 0
$$141$$ −9.75237 + 2.33625i −0.821298 + 0.196748i
$$142$$ 3.36995 0.282800
$$143$$ −21.1604 −1.76953
$$144$$ 2.67436 1.35934i 0.222863 0.113278i
$$145$$ 0 0
$$146$$ 4.98282 0.412381
$$147$$ 8.65674 + 8.48887i 0.713996 + 0.700150i
$$148$$ −6.06739 −0.498737
$$149$$ 7.60882i 0.623339i −0.950191 0.311669i $$-0.899112\pi$$
0.950191 0.311669i $$-0.100888\pi$$
$$150$$ 0 0
$$151$$ −4.63005 −0.376788 −0.188394 0.982094i $$-0.560328\pi$$
−0.188394 + 0.982094i $$0.560328\pi$$
$$152$$ −0.807019 −0.0654578
$$153$$ 19.5896 9.95708i 1.58372 0.804982i
$$154$$ 12.3824 + 6.85109i 0.997804 + 0.552077i
$$155$$ 0 0
$$156$$ −1.59635 6.66375i −0.127810 0.533527i
$$157$$ 15.3162i 1.22237i 0.791489 + 0.611184i $$0.209306\pi$$
−0.791489 + 0.611184i $$0.790694\pi$$
$$158$$ 3.26010i 0.259359i
$$159$$ −4.43004 18.4926i −0.351325 1.46656i
$$160$$ 0 0
$$161$$ −0.360347 + 0.651279i −0.0283993 + 0.0513280i
$$162$$ 7.27071 + 5.30441i 0.571241 + 0.416754i
$$163$$ −3.06739 −0.240257 −0.120128 0.992758i $$-0.538331\pi$$
−0.120128 + 0.992758i $$0.538331\pi$$
$$164$$ −6.15019 −0.480249
$$165$$ 0 0
$$166$$ 1.53511i 0.119148i
$$167$$ −1.89546 −0.146675 −0.0733376 0.997307i $$-0.523365\pi$$
−0.0733376 + 0.997307i $$0.523365\pi$$
$$168$$ −1.22338 + 4.41626i −0.0943857 + 0.340722i
$$169$$ −2.65128 −0.203945
$$170$$ 0 0
$$171$$ −1.09701 2.15826i −0.0838904 0.165046i
$$172$$ −6.34872 −0.484085
$$173$$ 8.86007 0.673619 0.336809 0.941573i $$-0.390652\pi$$
0.336809 + 0.941573i $$0.390652\pi$$
$$174$$ 0.473865 0.113518i 0.0359236 0.00860578i
$$175$$ 0 0
$$176$$ 5.34872i 0.403175i
$$177$$ −8.26010 + 1.97877i −0.620867 + 0.148733i
$$178$$ 4.31652i 0.323537i
$$179$$ 11.3487i 0.848243i 0.905605 + 0.424122i $$0.139417\pi$$
−0.905605 + 0.424122i $$0.860583\pi$$
$$180$$ 0 0
$$181$$ 8.63303i 0.641688i −0.947132 0.320844i $$-0.896033\pi$$
0.947132 0.320844i $$-0.103967\pi$$
$$182$$ 9.15863 + 5.06739i 0.678883 + 0.375620i
$$183$$ 5.34872 + 22.3275i 0.395389 + 1.65050i
$$184$$ −0.281327 −0.0207397
$$185$$ 0 0
$$186$$ −15.2938 + 3.66375i −1.12140 + 0.268639i
$$187$$ 39.1791i 2.86506i
$$188$$ 5.78984 0.422268
$$189$$ −13.4737 + 2.73143i −0.980064 + 0.198682i
$$190$$ 0 0
$$191$$ 7.78607i 0.563380i −0.959505 0.281690i $$-0.909105\pi$$
0.959505 0.281690i $$-0.0908950\pi$$
$$192$$ −1.68439 + 0.403509i −0.121561 + 0.0291208i
$$193$$ −25.1715 −1.81188 −0.905941 0.423404i $$-0.860835\pi$$
−0.905941 + 0.423404i $$0.860835\pi$$
$$194$$ 15.0892 1.08334
$$195$$ 0 0
$$196$$ −3.71867 5.93055i −0.265619 0.423611i
$$197$$ 2.52597i 0.179968i 0.995943 + 0.0899840i $$0.0286816\pi$$
−0.995943 + 0.0899840i $$0.971318\pi$$
$$198$$ −14.3044 + 7.27071i −1.01657 + 0.516707i
$$199$$ 0.947731i 0.0671828i −0.999436 0.0335914i $$-0.989306\pi$$
0.999436 0.0335914i $$-0.0106945\pi$$
$$200$$ 0 0
$$201$$ −11.3169 + 2.71105i −0.798232 + 0.191222i
$$202$$ 5.78984i 0.407372i
$$203$$ −0.360347 + 0.651279i −0.0252914 + 0.0457108i
$$204$$ −12.3381 + 2.95569i −0.863840 + 0.206940i
$$205$$ 0 0
$$206$$ −6.95721 −0.484732
$$207$$ −0.382418 0.752370i −0.0265799 0.0522933i
$$208$$ 3.95617i 0.274311i
$$209$$ 4.31652 0.298580
$$210$$ 0 0
$$211$$ −12.8901 −0.887394 −0.443697 0.896177i $$-0.646333\pi$$
−0.443697 + 0.896177i $$0.646333\pi$$
$$212$$ 10.9788i 0.754025i
$$213$$ −1.35981 5.67632i −0.0931724 0.388935i
$$214$$ 10.6088 0.725204
$$215$$ 0 0
$$216$$ −3.36879 3.95617i −0.229217 0.269183i
$$217$$ 11.6300 21.0197i 0.789499 1.42691i
$$218$$ 18.1348i 1.22824i
$$219$$ −2.01062 8.39303i −0.135865 0.567149i
$$220$$ 0 0
$$221$$ 28.9788i 1.94932i
$$222$$ 2.44825 + 10.2199i 0.164316 + 0.685913i
$$223$$ 23.7296i 1.58905i −0.607230 0.794526i $$-0.707719\pi$$
0.607230 0.794526i $$-0.292281\pi$$
$$224$$ 1.28088 2.31502i 0.0855827 0.154679i
$$225$$ 0 0
$$226$$ 8.54142 0.568167
$$227$$ 10.4667 0.694700 0.347350 0.937736i $$-0.387082\pi$$
0.347350 + 0.937736i $$0.387082\pi$$
$$228$$ 0.325639 + 1.35934i 0.0215660 + 0.0900243i
$$229$$ 16.4762i 1.08878i −0.838833 0.544388i $$-0.816762\pi$$
0.838833 0.544388i $$-0.183238\pi$$
$$230$$ 0 0
$$231$$ 6.54351 23.6213i 0.430531 1.55417i
$$232$$ −0.281327 −0.0184700
$$233$$ 27.9575i 1.83156i −0.401681 0.915780i $$-0.631574\pi$$
0.401681 0.915780i $$-0.368426\pi$$
$$234$$ −10.5802 + 5.37777i −0.691651 + 0.351556i
$$235$$ 0 0
$$236$$ 4.90390 0.319217
$$237$$ −5.49128 + 1.31548i −0.356697 + 0.0854495i
$$238$$ 9.38242 16.9574i 0.608172 1.09919i
$$239$$ 17.2601i 1.11646i −0.829685 0.558231i $$-0.811480\pi$$
0.829685 0.558231i $$-0.188520\pi$$
$$240$$ 0 0
$$241$$ 19.1935i 1.23636i −0.786037 0.618180i $$-0.787870\pi$$
0.786037 0.618180i $$-0.212130\pi$$
$$242$$ 17.6088i 1.13194i
$$243$$ 6.00091 14.3871i 0.384959 0.922934i
$$244$$ 13.2555i 0.848597i
$$245$$ 0 0
$$246$$ 2.48166 + 10.3593i 0.158225 + 0.660487i
$$247$$ 3.19270 0.203147
$$248$$ 9.07971 0.576562
$$249$$ −2.58574 + 0.619433i −0.163864 + 0.0392550i
$$250$$ 0 0
$$251$$ 21.0271 1.32722 0.663611 0.748078i $$-0.269023\pi$$
0.663611 + 0.748078i $$0.269023\pi$$
$$252$$ 7.93236 + 0.278649i 0.499692 + 0.0175532i
$$253$$ 1.50474 0.0946022
$$254$$ 2.00000i 0.125491i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ −14.5881 −0.909982 −0.454991 0.890496i $$-0.650358\pi$$
−0.454991 + 0.890496i $$0.650358\pi$$
$$258$$ 2.56177 + 10.6937i 0.159489 + 0.665763i
$$259$$ −14.0462 7.77163i −0.872786 0.482905i
$$260$$ 0 0
$$261$$ −0.382418 0.752370i −0.0236711 0.0465705i
$$262$$ 16.5454i 1.02218i
$$263$$ 8.91138i 0.549499i 0.961516 + 0.274749i $$0.0885949\pi$$
−0.961516 + 0.274749i $$0.911405\pi$$
$$264$$ 9.00935 2.15826i 0.554487 0.132832i
$$265$$ 0 0
$$266$$ −1.86827 1.03370i −0.114551 0.0633800i
$$267$$ −7.27071 + 1.74175i −0.444960 + 0.106594i
$$268$$ 6.71867 0.410408
$$269$$ 22.3352 1.36180 0.680901 0.732375i $$-0.261588\pi$$
0.680901 + 0.732375i $$0.261588\pi$$
$$270$$ 0 0
$$271$$ 7.17684i 0.435962i 0.975953 + 0.217981i $$0.0699471\pi$$
−0.975953 + 0.217981i $$0.930053\pi$$
$$272$$ 7.32496 0.444141
$$273$$ 4.83989 17.4715i 0.292924 1.05742i
$$274$$ −7.41612 −0.448024
$$275$$ 0 0
$$276$$ 0.113518 + 0.473865i 0.00683298 + 0.0285233i
$$277$$ 9.32749 0.560435 0.280217 0.959937i $$-0.409593\pi$$
0.280217 + 0.959937i $$0.409593\pi$$
$$278$$ −6.36982 −0.382037
$$279$$ 12.3424 + 24.2824i 0.738919 + 1.45375i
$$280$$ 0 0
$$281$$ 17.4373i 1.04022i −0.854098 0.520112i $$-0.825890\pi$$
0.854098 0.520112i $$-0.174110\pi$$
$$282$$ −2.33625 9.75237i −0.139122 0.580745i
$$283$$ 16.1776i 0.961660i 0.876814 + 0.480830i $$0.159665\pi$$
−0.876814 + 0.480830i $$0.840335\pi$$
$$284$$ 3.36995i 0.199970i
$$285$$ 0 0
$$286$$ 21.1604i 1.25124i
$$287$$ −14.2378 7.87768i −0.840433 0.465005i
$$288$$ 1.35934 + 2.67436i 0.0800997 + 0.157588i
$$289$$ 36.6550 2.15618
$$290$$ 0 0
$$291$$ −6.08862 25.4161i −0.356922 1.48992i
$$292$$ 4.98282i 0.291598i
$$293$$ 22.5623 1.31810 0.659050 0.752099i $$-0.270958\pi$$
0.659050 + 0.752099i $$0.270958\pi$$
$$294$$ −8.48887 + 8.65674i −0.495081 + 0.504871i
$$295$$ 0 0
$$296$$ 6.06739i 0.352660i
$$297$$ 18.0187 + 21.1604i 1.04555 + 1.22785i
$$298$$ 7.60882 0.440767
$$299$$ 1.11298 0.0643652
$$300$$ 0 0
$$301$$ −14.6974 8.13197i −0.847146 0.468719i
$$302$$ 4.63005i 0.266429i
$$303$$ −9.75237 + 2.33625i −0.560259 + 0.134214i
$$304$$ 0.807019i 0.0462857i
$$305$$ 0 0
$$306$$ 9.95708 + 19.5896i 0.569208 + 1.11986i
$$307$$ 19.4057i 1.10754i −0.832669 0.553771i $$-0.813188\pi$$
0.832669 0.553771i $$-0.186812\pi$$
$$308$$ −6.85109 + 12.3824i −0.390377 + 0.705554i
$$309$$ 2.80730 + 11.7187i 0.159702 + 0.666652i
$$310$$ 0 0
$$311$$ 6.73757 0.382053 0.191026 0.981585i $$-0.438818\pi$$
0.191026 + 0.981585i $$0.438818\pi$$
$$312$$ 6.66375 1.59635i 0.377260 0.0903756i
$$313$$ 21.3875i 1.20889i 0.796646 + 0.604446i $$0.206606\pi$$
−0.796646 + 0.604446i $$0.793394\pi$$
$$314$$ −15.3162 −0.864344
$$315$$ 0 0
$$316$$ 3.26010 0.183395
$$317$$ 3.47403i 0.195121i 0.995230 + 0.0975605i $$0.0311039\pi$$
−0.995230 + 0.0975605i $$0.968896\pi$$
$$318$$ 18.4926 4.43004i 1.03701 0.248424i
$$319$$ 1.50474 0.0842493
$$320$$ 0 0
$$321$$ −4.28076 17.8694i −0.238929 0.997374i
$$322$$ −0.651279 0.360347i −0.0362944 0.0200814i
$$323$$ 5.91138i 0.328918i
$$324$$ −5.30441 + 7.27071i −0.294689 + 0.403928i
$$325$$ 0 0
$$326$$ 3.06739i 0.169887i
$$327$$ −30.5461 + 7.31755i −1.68920 + 0.404662i
$$328$$ 6.15019i 0.339587i
$$329$$ 13.4036 + 7.41612i 0.738966 + 0.408864i
$$330$$ 0 0
$$331$$ −8.93261 −0.490980 −0.245490 0.969399i $$-0.578949\pi$$
−0.245490 + 0.969399i $$0.578949\pi$$
$$332$$ 1.53511 0.0842503
$$333$$ 16.2264 8.24763i 0.889201 0.451967i
$$334$$ 1.89546i 0.103715i
$$335$$ 0 0
$$336$$ −4.41626 1.22338i −0.240927 0.0667408i
$$337$$ 34.2176 1.86395 0.931977 0.362518i $$-0.118083\pi$$
0.931977 + 0.362518i $$0.118083\pi$$
$$338$$ 2.65128i 0.144211i
$$339$$ −3.44654 14.3871i −0.187191 0.781401i
$$340$$ 0 0
$$341$$ −48.5648 −2.62993
$$342$$ 2.15826 1.09701i 0.116705 0.0593195i
$$343$$ −1.01247 18.4926i −0.0546680 0.998505i
$$344$$ 6.34872i 0.342300i
$$345$$ 0 0
$$346$$ 8.86007i 0.476320i
$$347$$ 11.5260i 0.618747i −0.950941 0.309373i $$-0.899881\pi$$
0.950941 0.309373i $$-0.100119\pi$$
$$348$$ 0.113518 + 0.473865i 0.00608521 + 0.0254018i
$$349$$ 21.8342i 1.16876i 0.811482 + 0.584378i $$0.198661\pi$$
−0.811482 + 0.584378i $$0.801339\pi$$
$$350$$ 0 0
$$351$$ 13.3275 + 15.6513i 0.711369 + 0.835403i
$$352$$ −5.34872 −0.285088
$$353$$ −4.84211 −0.257720 −0.128860 0.991663i $$-0.541132\pi$$
−0.128860 + 0.991663i $$0.541132\pi$$
$$354$$ −1.97877 8.26010i −0.105170 0.439019i
$$355$$ 0 0
$$356$$ 4.31652 0.228775
$$357$$ −32.3489 8.96119i −1.71209 0.474277i
$$358$$ −11.3487 −0.599799
$$359$$ 30.3063i 1.59950i 0.600331 + 0.799752i $$0.295035\pi$$
−0.600331 + 0.799752i $$0.704965\pi$$
$$360$$ 0 0
$$361$$ 18.3487 0.965722
$$362$$ 8.63303 0.453742
$$363$$ −29.6602 + 7.10532i −1.55676 + 0.372933i
$$364$$ −5.06739 + 9.15863i −0.265604 + 0.480043i
$$365$$ 0 0
$$366$$ −22.3275 + 5.34872i −1.16708 + 0.279582i
$$367$$ 13.9910i 0.730325i −0.930944 0.365162i $$-0.881013\pi$$
0.930944 0.365162i $$-0.118987\pi$$
$$368$$ 0.281327i 0.0146652i
$$369$$ 16.4478 8.36018i 0.856239 0.435213i
$$370$$ 0 0
$$371$$ −14.0625 + 25.4161i −0.730090 + 1.31954i
$$372$$ −3.66375 15.2938i −0.189956 0.792946i
$$373$$ 4.24464 0.219779 0.109890 0.993944i $$-0.464950\pi$$
0.109890 + 0.993944i $$0.464950\pi$$
$$374$$ −39.1791 −2.02591
$$375$$ 0 0
$$376$$ 5.78984i 0.298588i
$$377$$ 1.11298 0.0573213
$$378$$ −2.73143 13.4737i −0.140489 0.693010i
$$379$$ −1.63005 −0.0837299 −0.0418650 0.999123i $$-0.513330\pi$$
−0.0418650 + 0.999123i $$0.513330\pi$$
$$380$$ 0 0
$$381$$ 3.36879 0.807019i 0.172588 0.0413448i
$$382$$ 7.78607 0.398370
$$383$$ −16.9994 −0.868631 −0.434316 0.900761i $$-0.643010\pi$$
−0.434316 + 0.900761i $$0.643010\pi$$
$$384$$ −0.403509 1.68439i −0.0205915 0.0859563i
$$385$$ 0 0
$$386$$ 25.1715i 1.28119i
$$387$$ 16.9788 8.63005i 0.863079 0.438690i
$$388$$ 15.0892i 0.766037i
$$389$$ 29.4623i 1.49380i −0.664938 0.746898i $$-0.731542\pi$$
0.664938 0.746898i $$-0.268458\pi$$
$$390$$ 0 0
$$391$$ 2.06071i 0.104214i
$$392$$ 5.93055 3.71867i 0.299538 0.187821i
$$393$$ 27.8689 6.67621i 1.40580 0.336770i
$$394$$ −2.52597 −0.127257
$$395$$ 0 0
$$396$$ −7.27071 14.3044i −0.365367 0.718824i
$$397$$ 17.8706i 0.896899i 0.893808 + 0.448449i $$0.148024\pi$$
−0.893808 + 0.448449i $$0.851976\pi$$
$$398$$ 0.947731 0.0475054
$$399$$ −0.987289 + 3.56400i −0.0494263 + 0.178423i
$$400$$ 0 0
$$401$$ 12.6762i 0.633020i 0.948589 + 0.316510i $$0.102511\pi$$
−0.948589 + 0.316510i $$0.897489\pi$$
$$402$$ −2.71105 11.3169i −0.135215 0.564435i
$$403$$ −35.9209 −1.78935
$$404$$ 5.78984 0.288055
$$405$$ 0 0
$$406$$ −0.651279 0.360347i −0.0323224 0.0178837i
$$407$$ 32.4528i 1.60863i
$$408$$ −2.95569 12.3381i −0.146328 0.610827i
$$409$$ 5.26425i 0.260300i −0.991494 0.130150i $$-0.958454\pi$$
0.991494 0.130150i $$-0.0415459\pi$$
$$410$$ 0 0
$$411$$ 2.99247 + 12.4917i 0.147608 + 0.616168i
$$412$$ 6.95721i 0.342757i
$$413$$ 11.3526 + 6.28133i 0.558627 + 0.309084i
$$414$$ 0.752370 0.382418i 0.0369770 0.0187948i
$$415$$ 0 0
$$416$$ −3.95617 −0.193967
$$417$$ 2.57028 + 10.7293i 0.125867 + 0.525416i
$$418$$ 4.31652i 0.211128i
$$419$$ −13.1148 −0.640700 −0.320350 0.947299i $$-0.603800\pi$$
−0.320350 + 0.947299i $$0.603800\pi$$
$$420$$ 0 0
$$421$$ 3.86521 0.188379 0.0941895 0.995554i $$-0.469974\pi$$
0.0941895 + 0.995554i $$0.469974\pi$$
$$422$$ 12.8901i 0.627482i
$$423$$ −15.4841 + 7.87034i −0.752864 + 0.382669i
$$424$$ −10.9788 −0.533176
$$425$$ 0 0
$$426$$ 5.67632 1.35981i 0.275019 0.0658829i
$$427$$ 16.9788 30.6868i 0.821660 1.48504i
$$428$$ 10.6088i 0.512797i
$$429$$ −35.6425 + 8.53844i −1.72084 + 0.412240i
$$430$$ 0 0
$$431$$ 10.2389i 0.493189i −0.969119 0.246594i $$-0.920688\pi$$
0.969119 0.246594i $$-0.0793115\pi$$
$$432$$ 3.95617 3.36879i 0.190341 0.162081i
$$433$$ 22.7030i 1.09103i 0.838099 + 0.545517i $$0.183667\pi$$
−0.838099 + 0.545517i $$0.816333\pi$$
$$434$$ 21.0197 + 11.6300i 1.00898 + 0.558260i
$$435$$ 0 0
$$436$$ 18.1348 0.868499
$$437$$ −0.227036 −0.0108606
$$438$$ 8.39303 2.01062i 0.401035 0.0960709i
$$439$$ 26.4492i 1.26235i −0.775639 0.631176i $$-0.782572\pi$$
0.775639 0.631176i $$-0.217428\pi$$
$$440$$ 0 0
$$441$$ 18.0067 + 10.8055i 0.857461 + 0.514548i
$$442$$ −28.9788 −1.37838
$$443$$ 27.8689i 1.32409i 0.749463 + 0.662046i $$0.230312\pi$$
−0.749463 + 0.662046i $$0.769688\pi$$
$$444$$ −10.2199 + 2.44825i −0.485014 + 0.116189i
$$445$$ 0 0
$$446$$ 23.7296 1.12363
$$447$$ −3.07023 12.8162i −0.145217 0.606187i
$$448$$ 2.31502 + 1.28088i 0.109375 + 0.0605161i
$$449$$ 9.45858i 0.446378i −0.974775 0.223189i $$-0.928353\pi$$
0.974775 0.223189i $$-0.0716467\pi$$
$$450$$ 0 0
$$451$$ 32.8956i 1.54900i
$$452$$ 8.54142i 0.401755i
$$453$$ −7.79882 + 1.86827i −0.366421 + 0.0877789i
$$454$$ 10.4667i 0.491227i
$$455$$ 0 0
$$456$$ −1.35934 + 0.325639i −0.0636568 + 0.0152495i
$$457$$ −31.8322 −1.48905 −0.744524 0.667595i $$-0.767324\pi$$
−0.744524 + 0.667595i $$0.767324\pi$$
$$458$$ 16.4762 0.769881
$$459$$ 28.9788 24.6762i 1.35261 1.15179i
$$460$$ 0 0
$$461$$ 10.6320 0.495179 0.247590 0.968865i $$-0.420362\pi$$
0.247590 + 0.968865i $$0.420362\pi$$
$$462$$ 23.6213 + 6.54351i 1.09896 + 0.304432i
$$463$$ −12.8322 −0.596364 −0.298182 0.954509i $$-0.596380\pi$$
−0.298182 + 0.954509i $$0.596380\pi$$
$$464$$ 0.281327i 0.0130603i
$$465$$ 0 0
$$466$$ 27.9575 1.29511
$$467$$ −20.8716 −0.965824 −0.482912 0.875669i $$-0.660421\pi$$
−0.482912 + 0.875669i $$0.660421\pi$$
$$468$$ −5.37777 10.5802i −0.248587 0.489071i
$$469$$ 15.5539 + 8.60584i 0.718212 + 0.397381i
$$470$$ 0 0
$$471$$ 6.18024 + 25.7985i 0.284770 + 1.18873i
$$472$$ 4.90390i 0.225720i
$$473$$ 33.9575i 1.56137i
$$474$$ −1.31548 5.49128i −0.0604220 0.252223i
$$475$$ 0 0
$$476$$ 16.9574 + 9.38242i 0.777243 + 0.430042i
$$477$$ −14.9238 29.3612i −0.683316 1.34436i
$$478$$ 17.2601 0.789458
$$479$$ 33.6879 1.53924 0.769619 0.638504i $$-0.220446\pi$$
0.769619 + 0.638504i $$0.220446\pi$$
$$480$$ 0 0
$$481$$ 24.0036i 1.09447i
$$482$$ 19.1935 0.874238
$$483$$ −0.344169 + 1.24241i −0.0156603 + 0.0565318i
$$484$$ 17.6088 0.800401
$$485$$ 0 0
$$486$$ 14.3871 + 6.00091i 0.652613 + 0.272207i
$$487$$ −33.3524 −1.51134 −0.755671 0.654951i $$-0.772689\pi$$
−0.755671 + 0.654951i $$0.772689\pi$$
$$488$$ 13.2555 0.600049
$$489$$ −5.16670 + 1.23772i −0.233646 + 0.0559717i
$$490$$ 0 0
$$491$$ 30.0000i 1.35388i −0.736038 0.676941i $$-0.763305\pi$$
0.736038 0.676941i $$-0.236695\pi$$
$$492$$ −10.3593 + 2.48166i −0.467035 + 0.111882i
$$493$$ 2.06071i 0.0928096i
$$494$$ 3.19270i 0.143646i
$$495$$ 0 0
$$496$$ 9.07971i 0.407691i
$$497$$ −4.31652 + 7.80152i −0.193622 + 0.349946i
$$498$$ −0.619433 2.58574i −0.0277574 0.115870i
$$499$$ −19.1810 −0.858657 −0.429329 0.903148i $$-0.641250\pi$$
−0.429329 + 0.903148i $$0.641250\pi$$
$$500$$ 0 0
$$501$$ −3.19270 + 0.764836i −0.142639 + 0.0341704i
$$502$$ 21.0271i 0.938487i
$$503$$ −36.9851 −1.64909 −0.824543 0.565800i $$-0.808568\pi$$
−0.824543 + 0.565800i $$0.808568\pi$$
$$504$$ −0.278649 + 7.93236i −0.0124120 + 0.353335i
$$505$$ 0 0
$$506$$ 1.50474i 0.0668938i
$$507$$ −4.46580 + 1.06982i −0.198333 + 0.0475122i
$$508$$ −2.00000 −0.0887357
$$509$$ −36.0374 −1.59733 −0.798665 0.601776i $$-0.794460\pi$$
−0.798665 + 0.601776i $$0.794460\pi$$
$$510$$ 0 0
$$511$$ −6.38242 + 11.5354i −0.282342 + 0.510294i
$$512$$ 1.00000i 0.0441942i
$$513$$ −2.71867 3.19270i −0.120032 0.140961i
$$514$$ 14.5881i 0.643455i
$$515$$ 0 0
$$516$$ −10.6937 + 2.56177i −0.470766 + 0.112776i
$$517$$ 30.9682i 1.36198i
$$518$$ 7.77163 14.0462i 0.341466 0.617153i
$$519$$ 14.9238 3.57512i 0.655084 0.156930i
$$520$$ 0 0
$$521$$ −3.65761 −0.160243 −0.0801214 0.996785i $$-0.525531\pi$$
−0.0801214 + 0.996785i $$0.525531\pi$$
$$522$$ 0.752370 0.382418i 0.0329303 0.0167380i
$$523$$ 2.26321i 0.0989633i −0.998775 0.0494816i $$-0.984243\pi$$
0.998775 0.0494816i $$-0.0157569\pi$$
$$524$$ −16.5454 −0.722788
$$525$$ 0 0
$$526$$ −8.91138 −0.388554
$$527$$ 66.5084i 2.89715i
$$528$$ 2.15826 + 9.00935i 0.0939261 + 0.392082i
$$529$$ 22.9209 0.996559
$$530$$ 0 0
$$531$$ −13.1148 + 6.66605i −0.569134 + 0.289282i
$$532$$ 1.03370 1.86827i 0.0448164 0.0809997i
$$533$$ 24.3312i 1.05390i
$$534$$ −1.74175 7.27071i −0.0753731 0.314634i
$$535$$ 0 0
$$536$$ 6.71867i 0.290202i
$$537$$ 4.57931 + 19.1157i 0.197612 + 0.824904i
$$538$$ 22.3352i 0.962940i
$$539$$ −31.7209 + 19.8901i −1.36632 + 0.856729i
$$540$$ 0 0
$$541$$ 15.1502 0.651360 0.325680 0.945480i $$-0.394407\pi$$
0.325680 + 0.945480i $$0.394407\pi$$
$$542$$ −7.17684 −0.308272
$$543$$ −3.48351 14.5414i −0.149492 0.624032i
$$544$$ 7.32496i 0.314055i
$$545$$ 0 0
$$546$$ 17.4715 + 4.83989i 0.747710 + 0.207128i
$$547$$ −2.89014 −0.123574 −0.0617868 0.998089i $$-0.519680\pi$$
−0.0617868 + 0.998089i $$0.519680\pi$$
$$548$$ 7.41612i 0.316801i
$$549$$ 18.0187 + 35.4500i 0.769019 + 1.51297i
$$550$$ 0 0
$$551$$ −0.227036 −0.00967206
$$552$$ −0.473865 + 0.113518i −0.0201690 + 0.00483165i
$$553$$ 7.54720 + 4.17580i 0.320940 + 0.177573i
$$554$$ 9.32749i 0.396287i
$$555$$ 0 0
$$556$$ 6.36982i 0.270141i
$$557$$ 32.4777i 1.37613i −0.725651 0.688063i $$-0.758461\pi$$
0.725651 0.688063i $$-0.241539\pi$$
$$558$$ −24.2824 + 12.3424i −1.02796 + 0.522494i
$$559$$ 25.1166i 1.06232i
$$560$$ 0 0
$$561$$ 15.8091 + 65.9931i 0.667463 + 2.78623i
$$562$$ 17.4373 0.735550
$$563$$ −10.9208 −0.460256 −0.230128 0.973160i $$-0.573914\pi$$
−0.230128 + 0.973160i $$0.573914\pi$$
$$564$$ 9.75237 2.33625i 0.410649 0.0983741i
$$565$$ 0 0
$$566$$ −16.1776 −0.679996
$$567$$ −21.5928 + 10.0375i −0.906811 + 0.421537i
$$568$$ −3.36995 −0.141400
$$569$$ 4.58388i 0.192166i −0.995373 0.0960832i $$-0.969369\pi$$
0.995373 0.0960832i $$-0.0306315\pi$$
$$570$$ 0 0
$$571$$ 5.82853 0.243916 0.121958 0.992535i $$-0.461083\pi$$
0.121958 + 0.992535i $$0.461083\pi$$
$$572$$ 21.1604 0.884763
$$573$$ −3.14175 13.1148i −0.131248 0.547879i
$$574$$ 7.87768 14.2378i 0.328808 0.594276i
$$575$$ 0 0
$$576$$ −2.67436 + 1.35934i −0.111432 + 0.0566390i
$$577$$ 9.82493i 0.409017i 0.978865 + 0.204509i $$0.0655597\pi$$
−0.978865 + 0.204509i $$0.934440\pi$$
$$578$$ 36.6550i 1.52465i
$$579$$ −42.3987 + 10.1569i −1.76203 + 0.422107i
$$580$$ 0 0
$$581$$ 3.55383 + 1.96630i 0.147438 + 0.0815760i
$$582$$ 25.4161 6.08862i 1.05353 0.252382i
$$583$$ 58.7224 2.43203
$$584$$ −4.98282 −0.206191
$$585$$ 0 0
$$586$$ 22.5623i 0.932038i
$$587$$ 27.3106 1.12723 0.563615 0.826037i $$-0.309410\pi$$
0.563615 + 0.826037i $$0.309410\pi$$
$$588$$ −8.65674 8.48887i −0.356998 0.350075i
$$589$$ 7.32749 0.301924
$$590$$ 0 0
$$591$$ 1.01925 + 4.25473i 0.0419264 + 0.175016i
$$592$$ 6.06739 0.249368
$$593$$ 26.8788 1.10378 0.551889 0.833917i $$-0.313907\pi$$
0.551889 + 0.833917i $$0.313907\pi$$
$$594$$ −21.1604 + 18.0187i −0.868224 + 0.739316i
$$595$$ 0 0
$$596$$ 7.60882i 0.311669i
$$597$$ −0.382418 1.59635i −0.0156513 0.0653343i
$$598$$ 1.11298i 0.0455130i
$$599$$ 6.45858i 0.263890i 0.991257 + 0.131945i $$0.0421223\pi$$
−0.991257 + 0.131945i $$0.957878\pi$$
$$600$$ 0 0
$$601$$ 1.31548i 0.0536595i 0.999640 + 0.0268298i $$0.00854120\pi$$
−0.999640 + 0.0268298i $$0.991459\pi$$
$$602$$ 8.13197 14.6974i 0.331435 0.599023i
$$603$$ −17.9682 + 9.13294i −0.731720 + 0.371922i
$$604$$ 4.63005 0.188394
$$605$$ 0 0
$$606$$ −2.33625 9.75237i −0.0949039 0.396163i
$$607$$ 26.9651i 1.09448i −0.836976 0.547240i $$-0.815679\pi$$
0.836976 0.547240i $$-0.184321\pi$$
$$608$$ 0.807019 0.0327289
$$609$$ −0.344169 + 1.24241i −0.0139464 + 0.0503451i
$$610$$ 0 0
$$611$$ 22.9056i 0.926661i
$$612$$ −19.5896 + 9.95708i −0.791862 + 0.402491i
$$613$$ 33.9151 1.36982 0.684909 0.728629i $$-0.259842\pi$$
0.684909 + 0.728629i $$0.259842\pi$$
$$614$$ 19.4057 0.783150
$$615$$ 0 0
$$616$$ −12.3824 6.85109i −0.498902 0.276038i
$$617$$ 13.1253i 0.528405i 0.964467 + 0.264203i $$0.0851087\pi$$
−0.964467 + 0.264203i $$0.914891\pi$$
$$618$$ −11.7187 + 2.80730i −0.471394 + 0.112926i
$$619$$ 38.0907i 1.53099i 0.643439 + 0.765497i $$0.277507\pi$$
−0.643439 + 0.765497i $$0.722493\pi$$
$$620$$ 0 0
$$621$$ −0.947731 1.11298i −0.0380311 0.0446623i
$$622$$ 6.73757i 0.270152i
$$623$$ 9.99284 + 5.52896i 0.400355 + 0.221513i
$$624$$ 1.59635 + 6.66375i 0.0639052 + 0.266763i
$$625$$ 0 0
$$626$$ −21.3875 −0.854816
$$627$$ 7.27071 1.74175i 0.290364 0.0695590i
$$628$$ 15.3162i 0.611184i
$$629$$ 44.4434 1.77207
$$630$$ 0 0
$$631$$ −12.0674 −0.480395 −0.240198 0.970724i $$-0.577212\pi$$
−0.240198 + 0.970724i $$0.577212\pi$$
$$632$$ 3.26010i 0.129680i
$$633$$ −21.7121 + 5.20129i −0.862977 + 0.206733i
$$634$$ −3.47403 −0.137971
$$635$$ 0 0
$$636$$ 4.43004 + 18.4926i 0.175662 + 0.733278i
$$637$$ −23.4623 + 14.7117i −0.929609 + 0.582899i
$$638$$ 1.50474i 0.0595732i
$$639$$ −4.58090 9.01247i −0.181218 0.356528i
$$640$$ 0 0
$$641$$ 17.4373i 0.688734i 0.938835 + 0.344367i $$0.111906\pi$$
−0.938835 + 0.344367i $$0.888094\pi$$
$$642$$ 17.8694 4.28076i 0.705250 0.168948i
$$643$$ 6.01688i 0.237283i −0.992937 0.118641i $$-0.962146\pi$$
0.992937 0.118641i $$-0.0378538\pi$$
$$644$$ 0.360347 0.651279i 0.0141997 0.0256640i
$$645$$ 0 0
$$646$$ 5.91138 0.232580
$$647$$ −36.7581 −1.44511 −0.722555 0.691314i $$-0.757032\pi$$
−0.722555 + 0.691314i $$0.757032\pi$$
$$648$$ −7.27071 5.30441i −0.285621 0.208377i
$$649$$ 26.2296i 1.02960i
$$650$$ 0 0
$$651$$ 11.1079 40.0983i 0.435354 1.57158i
$$652$$ 3.06739 0.120128
$$653$$ 14.8073i 0.579454i −0.957109 0.289727i $$-0.906435\pi$$
0.957109 0.289727i $$-0.0935646\pi$$
$$654$$ −7.31755 30.5461i −0.286139 1.19445i
$$655$$ 0 0
$$656$$ 6.15019 0.240125
$$657$$ −6.77333 13.3259i −0.264253 0.519892i
$$658$$ −7.41612 + 13.4036i −0.289110 + 0.522528i
$$659$$ 11.3487i 0.442083i 0.975264 + 0.221042i $$0.0709457\pi$$
−0.975264 + 0.221042i $$0.929054\pi$$
$$660$$ 0 0
$$661$$ 19.7043i 0.766407i 0.923664 + 0.383203i $$0.125179\pi$$
−0.923664 + 0.383203i $$0.874821\pi$$
$$662$$ 8.93261i 0.347176i
$$663$$ 11.6932 + 48.8116i 0.454126 + 1.89569i
$$664$$ 1.53511i 0.0595740i
$$665$$ 0 0
$$666$$ 8.24763 + 16.2264i 0.319589 + 0.628760i
$$667$$ −0.0791449 −0.00306450
$$668$$ 1.89546 0.0733376
$$669$$ −9.57512 39.9700i −0.370196 1.54533i
$$670$$ 0 0
$$671$$ −70.9000 −2.73707
$$672$$ 1.22338 4.41626i 0.0471928 0.170361i
$$673$$ −21.7861 −0.839791 −0.419896 0.907572i $$-0.637933\pi$$
−0.419896 + 0.907572i $$0.637933\pi$$
$$674$$ 34.2176i 1.31801i
$$675$$ 0 0
$$676$$ 2.65128 0.101972
$$677$$ 15.3706 0.590740 0.295370 0.955383i $$-0.404557\pi$$
0.295370 + 0.955383i $$0.404557\pi$$
$$678$$ 14.3871 3.44654i 0.552534 0.132364i
$$679$$ −19.3275 + 34.9318i −0.741721 + 1.34056i
$$680$$ 0 0
$$681$$ 17.6300 4.22341i 0.675585 0.161842i
$$682$$ 48.5648i 1.85964i
$$683$$ 22.0462i 0.843573i 0.906695 + 0.421786i $$0.138597\pi$$
−0.906695 + 0.421786i $$0.861403\pi$$
$$684$$ 1.09701 + 2.15826i 0.0419452 + 0.0825231i
$$685$$ 0 0
$$686$$ 18.4926 1.01247i 0.706049 0.0386561i
$$687$$ −6.64829 27.7524i −0.253648 1.05882i
$$688$$ 6.34872 0.242043
$$689$$ 43.4339 1.65470
$$690$$ 0 0
$$691$$ 31.7209i 1.20672i 0.797469 + 0.603360i $$0.206172\pi$$
−0.797469 + 0.603360i $$0.793828\pi$$
$$692$$ −8.86007 −0.336809
$$693$$ 1.49041 42.4280i 0.0566161 1.61171i
$$694$$ 11.5260 0.437520
$$695$$ 0 0
$$696$$ −0.473865 + 0.113518i −0.0179618 + 0.00430289i
$$697$$ 45.0499 1.70639
$$698$$ −21.8342 −0.826435
$$699$$ −11.2811 47.0915i −0.426691 1.78116i
$$700$$ 0 0
$$701$$ 49.4316i 1.86700i −0.358571 0.933502i $$-0.616736\pi$$
0.358571 0.933502i $$-0.383264\pi$$
$$702$$ −15.6513 + 13.3275i −0.590719 + 0.503014i
$$703$$ 4.89650i 0.184675i
$$704$$ 5.34872i 0.201588i
$$705$$ 0 0
$$706$$ 4.84211i 0.182235i
$$707$$ 13.4036 + 7.41612i 0.504095 + 0.278912i
$$708$$ 8.26010 1.97877i 0.310433 0.0743667i
$$709$$ −0.697442 −0.0261930 −0.0130965 0.999914i $$-0.504169\pi$$
−0.0130965 + 0.999914i $$0.504169\pi$$
$$710$$ 0 0
$$711$$ −8.71867 + 4.43157i −0.326976 + 0.166197i
$$712$$ 4.31652i 0.161768i
$$713$$ 2.55437 0.0956618
$$714$$ 8.96119 32.3489i 0.335364 1.21063i
$$715$$ 0 0
$$716$$ 11.3487i 0.424122i
$$717$$ −6.96461 29.0728i −0.260098 1.08574i
$$718$$ −30.3063 −1.13102
$$719$$ 32.1430 1.19873 0.599366 0.800475i $$-0.295419\pi$$
0.599366 + 0.800475i $$0.295419\pi$$
$$720$$ 0 0
$$721$$ 8.91138 16.1061i 0.331877 0.599823i
$$722$$ 18.3487i 0.682869i
$$723$$ −7.74474 32.3293i −0.288030 1.20234i
$$724$$ 8.63303i 0.320844i
$$725$$ 0 0
$$726$$ −7.10532 29.6602i −0.263703 1.10079i
$$727$$ 27.3970i 1.01610i 0.861328 + 0.508049i $$0.169633\pi$$
−0.861328 + 0.508049i $$0.830367\pi$$
$$728$$ −9.15863 5.06739i −0.339441 0.187810i
$$729$$ 4.30256 26.6550i 0.159354 0.987222i
$$730$$ 0 0
$$731$$ 46.5041 1.72002
$$732$$ −5.34872 22.3275i −0.197694 0.825248i
$$733$$ 0.0617893i 0.00228224i 0.999999 + 0.00114112i $$0.000363230\pi$$
−0.999999 + 0.00114112i $$0.999637\pi$$
$$734$$ 13.9910 0.516417
$$735$$ 0 0
$$736$$ 0.281327 0.0103699
$$737$$ 35.9363i 1.32373i
$$738$$ 8.36018 + 16.4478i 0.307742 + 0.605453i
$$739$$ −45.0037 −1.65549 −0.827744 0.561106i $$-0.810376\pi$$
−0.827744 + 0.561106i $$0.810376\pi$$
$$740$$ 0 0
$$741$$ 5.37777 1.28828i 0.197557 0.0473263i
$$742$$ −25.4161 14.0625i −0.933055 0.516252i
$$743$$ 38.1655i 1.40016i −0.714066 0.700078i $$-0.753148\pi$$
0.714066 0.700078i $$-0.246852\pi$$
$$744$$ 15.2938 3.66375i 0.560698 0.134319i
$$745$$ 0 0
$$746$$ 4.24464i 0.155407i
$$747$$ −4.10545 + 2.08674i −0.150211 + 0.0763497i
$$748$$ 39.1791i 1.43253i
$$749$$ −13.5887 + 24.5597i −0.496519 + 0.897391i
$$750$$ 0 0
$$751$$ −27.8901 −1.01773 −0.508863 0.860848i $$-0.669934\pi$$
−0.508863 + 0.860848i $$0.669934\pi$$
$$752$$ −5.78984 −0.211134
$$753$$ 35.4180 8.48464i 1.29070 0.309198i
$$754$$ 1.11298i 0.0405323i
$$755$$ 0 0
$$756$$ 13.4737 2.73143i 0.490032 0.0993411i
$$757$$ −38.5876 −1.40249 −0.701245 0.712921i $$-0.747372\pi$$
−0.701245 + 0.712921i $$0.747372\pi$$
$$758$$ 1.63005i 0.0592060i
$$759$$ 2.53457 0.607177i 0.0919992 0.0220391i
$$760$$ 0 0
$$761$$ −28.9173 −1.04825 −0.524125 0.851641i $$-0.675608\pi$$
−0.524125 + 0.851641i $$0.675608\pi$$
$$762$$ 0.807019 + 3.36879i 0.0292352 + 0.122038i
$$763$$ 41.9825 + 23.2286i 1.51987 + 0.840930i
$$764$$ 7.78607i 0.281690i
$$765$$ 0 0
$$766$$ 16.9994i 0.614215i
$$767$$ 19.4007i 0.700517i
$$768$$ 1.68439 0.403509i 0.0607803 0.0145604i
$$769$$ 30.3191i 1.09333i −0.837350 0.546667i $$-0.815896\pi$$
0.837350 0.546667i $$-0.184104\pi$$
$$770$$ 0 0
$$771$$ −24.5721 + 5.88644i −0.884944 + 0.211995i
$$772$$ 25.1715 0.905941
$$773$$ 23.7370 0.853761 0.426881 0.904308i $$-0.359612\pi$$
0.426881 + 0.904308i $$0.359612\pi$$
$$774$$ 8.63005 + 16.9788i 0.310201 + 0.610289i
$$775$$ 0 0
$$776$$ −15.0892 −0.541670
$$777$$ −26.7952 7.42272i −0.961272 0.266289i
$$778$$ 29.4623 1.05627
$$779$$ 4.96332i 0.177829i
$$780$$ 0 0
$$781$$ 18.0249 0.644983
$$782$$ 2.06071 0.0736908
$$783$$ −0.947731 1.11298i −0.0338691 0.0397746i
$$784$$ 3.71867 + 5.93055i 0.132810 + 0.211806i
$$785$$ 0 0
$$786$$ 6.67621 + 27.8689i 0.238133 + 0.994051i
$$787$$ 30.7560i 1.09633i 0.836369 + 0.548167i $$0.184674\pi$$
−0.836369 + 0.548167i $$0.815326\pi$$
$$788$$