# Properties

 Label 637.2.q.g.491.1 Level $637$ Weight $2$ Character 637.491 Analytic conductor $5.086$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.q (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.08647060876$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{6})$$ Coefficient field: 12.0.2346760387617129.1 Defining polynomial: $$x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 491.1 Root $$1.21245 + 0.727987i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.491 Dual form 637.2.q.g.589.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-1.99469 + 1.15163i) q^{2} +(0.736680 + 1.27597i) q^{3} +(1.65252 - 2.86225i) q^{4} -0.847292i q^{5} +(-2.93889 - 1.69677i) q^{6} +3.00585i q^{8} +(0.414604 - 0.718115i) q^{9} +O(q^{10})$$ $$q+(-1.99469 + 1.15163i) q^{2} +(0.736680 + 1.27597i) q^{3} +(1.65252 - 2.86225i) q^{4} -0.847292i q^{5} +(-2.93889 - 1.69677i) q^{6} +3.00585i q^{8} +(0.414604 - 0.718115i) q^{9} +(0.975769 + 1.69008i) q^{10} +(-1.30198 + 0.751701i) q^{11} +4.86951 q^{12} +(-2.92329 - 2.11054i) q^{13} +(1.08112 - 0.624183i) q^{15} +(-0.156597 - 0.271234i) q^{16} +(1.03570 - 1.79389i) q^{17} +1.90989i q^{18} +(-0.0410731 - 0.0237136i) q^{19} +(-2.42516 - 1.40016i) q^{20} +(1.73137 - 2.99882i) q^{22} +(-3.90935 - 6.77119i) q^{23} +(-3.83536 + 2.21435i) q^{24} +4.28210 q^{25} +(8.26161 + 0.843323i) q^{26} +5.64180 q^{27} +(-0.679854 - 1.17754i) q^{29} +(-1.43766 + 2.49010i) q^{30} -7.86105i q^{31} +(-4.58156 - 2.64516i) q^{32} +(-1.91829 - 1.10753i) q^{33} +4.77099i q^{34} +(-1.37028 - 2.37340i) q^{36} +(5.80427 - 3.35110i) q^{37} +0.109237 q^{38} +(0.539460 - 5.28482i) q^{39} +2.54683 q^{40} +(-8.67622 + 5.00922i) q^{41} +(4.63283 - 8.02430i) q^{43} +4.96880i q^{44} +(-0.608453 - 0.351290i) q^{45} +(15.5959 + 9.00428i) q^{46} +0.360014i q^{47} +(0.230724 - 0.399625i) q^{48} +(-8.54144 + 4.93141i) q^{50} +3.05192 q^{51} +(-10.8717 + 4.87945i) q^{52} +2.71181 q^{53} +(-11.2536 + 6.49729i) q^{54} +(0.636910 + 1.10316i) q^{55} -0.0698773i q^{57} +(2.71219 + 1.56588i) q^{58} +(-1.42132 - 0.820598i) q^{59} -4.12590i q^{60} +(-2.26097 + 3.91612i) q^{61} +(9.05305 + 15.6803i) q^{62} +12.8114 q^{64} +(-1.78825 + 2.47688i) q^{65} +5.10186 q^{66} +(1.76900 - 1.02133i) q^{67} +(-3.42303 - 5.92886i) q^{68} +(5.75988 - 9.97641i) q^{69} +(12.3096 + 7.10697i) q^{71} +(2.15854 + 1.24624i) q^{72} +6.76150i q^{73} +(-7.71847 + 13.3688i) q^{74} +(3.15454 + 5.46382i) q^{75} +(-0.135748 + 0.0783743i) q^{76} +(5.01012 + 11.1628i) q^{78} +11.6590 q^{79} +(-0.229814 + 0.132683i) q^{80} +(2.91240 + 5.04442i) q^{81} +(11.5376 - 19.9837i) q^{82} -11.5362i q^{83} +(-1.51994 - 0.877541i) q^{85} +21.3413i q^{86} +(1.00167 - 1.73494i) q^{87} +(-2.25950 - 3.91357i) q^{88} +(-15.1652 + 8.75561i) q^{89} +1.61823 q^{90} -25.8411 q^{92} +(10.0304 - 5.79108i) q^{93} +(-0.414604 - 0.718115i) q^{94} +(-0.0200923 + 0.0348009i) q^{95} -7.79456i q^{96} +(0.369125 + 0.213115i) q^{97} +1.24663i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q - 3q^{3} + 4q^{4} - 9q^{6} - q^{9} + O(q^{10})$$ $$12q - 3q^{3} + 4q^{4} - 9q^{6} - q^{9} + 12q^{10} - 12q^{11} + 2q^{12} - 2q^{13} - 12q^{15} - 8q^{16} + 17q^{17} - 9q^{19} - 3q^{20} - 15q^{22} + 3q^{23} - 15q^{24} + 10q^{25} + 15q^{26} + 12q^{27} - q^{29} + 11q^{30} - 18q^{32} + 6q^{33} - 13q^{36} - 15q^{37} - 38q^{38} + 5q^{39} + 2q^{40} - 6q^{41} + 11q^{43} + 9q^{45} + 30q^{46} + 19q^{48} + 18q^{50} - 8q^{51} - 40q^{52} + 16q^{53} - 6q^{54} - 15q^{55} + 24q^{58} - 27q^{59} + 5q^{61} + 41q^{62} + 2q^{64} - 18q^{65} + 68q^{66} - 15q^{67} - 11q^{68} + 7q^{69} + 30q^{71} - 57q^{72} - 33q^{74} + q^{75} - 45q^{76} + 44q^{78} + 70q^{79} + 63q^{80} + 14q^{81} + 5q^{82} - 21q^{85} + 10q^{87} - 14q^{88} - 48q^{89} - 66q^{92} + 81q^{93} + q^{94} + 2q^{95} - 3q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.99469 + 1.15163i −1.41046 + 0.814328i −0.995431 0.0954820i $$-0.969561\pi$$
−0.415026 + 0.909810i $$0.636227\pi$$
$$3$$ 0.736680 + 1.27597i 0.425323 + 0.736680i 0.996451 0.0841807i $$-0.0268273\pi$$
−0.571128 + 0.820861i $$0.693494\pi$$
$$4$$ 1.65252 2.86225i 0.826259 1.43112i
$$5$$ 0.847292i 0.378920i −0.981888 0.189460i $$-0.939326\pi$$
0.981888 0.189460i $$-0.0606738\pi$$
$$6$$ −2.93889 1.69677i −1.19980 0.692704i
$$7$$ 0 0
$$8$$ 3.00585i 1.06273i
$$9$$ 0.414604 0.718115i 0.138201 0.239372i
$$10$$ 0.975769 + 1.69008i 0.308565 + 0.534451i
$$11$$ −1.30198 + 0.751701i −0.392563 + 0.226646i −0.683270 0.730166i $$-0.739443\pi$$
0.290707 + 0.956812i $$0.406110\pi$$
$$12$$ 4.86951 1.40571
$$13$$ −2.92329 2.11054i −0.810774 0.585360i
$$14$$ 0 0
$$15$$ 1.08112 0.624183i 0.279143 0.161163i
$$16$$ −0.156597 0.271234i −0.0391492 0.0678085i
$$17$$ 1.03570 1.79389i 0.251194 0.435081i −0.712661 0.701509i $$-0.752510\pi$$
0.963855 + 0.266428i $$0.0858434\pi$$
$$18$$ 1.90989i 0.450164i
$$19$$ −0.0410731 0.0237136i −0.00942282 0.00544027i 0.495281 0.868733i $$-0.335065\pi$$
−0.504704 + 0.863292i $$0.668398\pi$$
$$20$$ −2.42516 1.40016i −0.542282 0.313086i
$$21$$ 0 0
$$22$$ 1.73137 2.99882i 0.369129 0.639350i
$$23$$ −3.90935 6.77119i −0.815156 1.41189i −0.909216 0.416325i $$-0.863318\pi$$
0.0940598 0.995567i $$-0.470016\pi$$
$$24$$ −3.83536 + 2.21435i −0.782891 + 0.452002i
$$25$$ 4.28210 0.856419
$$26$$ 8.26161 + 0.843323i 1.62024 + 0.165389i
$$27$$ 5.64180 1.08577
$$28$$ 0 0
$$29$$ −0.679854 1.17754i −0.126246 0.218664i 0.795973 0.605331i $$-0.206959\pi$$
−0.922219 + 0.386668i $$0.873626\pi$$
$$30$$ −1.43766 + 2.49010i −0.262480 + 0.454628i
$$31$$ 7.86105i 1.41189i −0.708269 0.705943i $$-0.750523\pi$$
0.708269 0.705943i $$-0.249477\pi$$
$$32$$ −4.58156 2.64516i −0.809912 0.467603i
$$33$$ −1.91829 1.10753i −0.333932 0.192796i
$$34$$ 4.77099i 0.818218i
$$35$$ 0 0
$$36$$ −1.37028 2.37340i −0.228380 0.395566i
$$37$$ 5.80427 3.35110i 0.954216 0.550917i 0.0598278 0.998209i $$-0.480945\pi$$
0.894388 + 0.447292i $$0.147612\pi$$
$$38$$ 0.109237 0.0177206
$$39$$ 0.539460 5.28482i 0.0863827 0.846248i
$$40$$ 2.54683 0.402689
$$41$$ −8.67622 + 5.00922i −1.35500 + 0.782309i −0.988945 0.148285i $$-0.952625\pi$$
−0.366054 + 0.930594i $$0.619291\pi$$
$$42$$ 0 0
$$43$$ 4.63283 8.02430i 0.706500 1.22369i −0.259647 0.965704i $$-0.583606\pi$$
0.966147 0.257991i $$-0.0830604\pi$$
$$44$$ 4.96880i 0.749075i
$$45$$ −0.608453 0.351290i −0.0907028 0.0523673i
$$46$$ 15.5959 + 9.00428i 2.29948 + 1.32761i
$$47$$ 0.360014i 0.0525134i 0.999655 + 0.0262567i $$0.00835873\pi$$
−0.999655 + 0.0262567i $$0.991641\pi$$
$$48$$ 0.230724 0.399625i 0.0333021 0.0576810i
$$49$$ 0 0
$$50$$ −8.54144 + 4.93141i −1.20794 + 0.697406i
$$51$$ 3.05192 0.427355
$$52$$ −10.8717 + 4.87945i −1.50763 + 0.676658i
$$53$$ 2.71181 0.372496 0.186248 0.982503i $$-0.440367\pi$$
0.186248 + 0.982503i $$0.440367\pi$$
$$54$$ −11.2536 + 6.49729i −1.53143 + 0.884169i
$$55$$ 0.636910 + 1.10316i 0.0858809 + 0.148750i
$$56$$ 0 0
$$57$$ 0.0698773i 0.00925548i
$$58$$ 2.71219 + 1.56588i 0.356128 + 0.205611i
$$59$$ −1.42132 0.820598i −0.185040 0.106833i 0.404619 0.914486i $$-0.367404\pi$$
−0.589658 + 0.807653i $$0.700738\pi$$
$$60$$ 4.12590i 0.532651i
$$61$$ −2.26097 + 3.91612i −0.289488 + 0.501407i −0.973688 0.227887i $$-0.926818\pi$$
0.684200 + 0.729295i $$0.260152\pi$$
$$62$$ 9.05305 + 15.6803i 1.14974 + 1.99140i
$$63$$ 0 0
$$64$$ 12.8114 1.60143
$$65$$ −1.78825 + 2.47688i −0.221805 + 0.307219i
$$66$$ 5.10186 0.627995
$$67$$ 1.76900 1.02133i 0.216117 0.124775i −0.388034 0.921645i $$-0.626846\pi$$
0.604151 + 0.796870i $$0.293512\pi$$
$$68$$ −3.42303 5.92886i −0.415103 0.718980i
$$69$$ 5.75988 9.97641i 0.693409 1.20102i
$$70$$ 0 0
$$71$$ 12.3096 + 7.10697i 1.46088 + 0.843442i 0.999052 0.0435255i $$-0.0138590\pi$$
0.461832 + 0.886967i $$0.347192\pi$$
$$72$$ 2.15854 + 1.24624i 0.254387 + 0.146870i
$$73$$ 6.76150i 0.791373i 0.918386 + 0.395687i $$0.129493\pi$$
−0.918386 + 0.395687i $$0.870507\pi$$
$$74$$ −7.71847 + 13.3688i −0.897253 + 1.55409i
$$75$$ 3.15454 + 5.46382i 0.364255 + 0.630907i
$$76$$ −0.135748 + 0.0783743i −0.0155714 + 0.00899015i
$$77$$ 0 0
$$78$$ 5.01012 + 11.1628i 0.567284 + 1.26394i
$$79$$ 11.6590 1.31175 0.655873 0.754871i $$-0.272301\pi$$
0.655873 + 0.754871i $$0.272301\pi$$
$$80$$ −0.229814 + 0.132683i −0.0256940 + 0.0148344i
$$81$$ 2.91240 + 5.04442i 0.323600 + 0.560491i
$$82$$ 11.5376 19.9837i 1.27411 2.20683i
$$83$$ 11.5362i 1.26627i −0.774043 0.633133i $$-0.781768\pi$$
0.774043 0.633133i $$-0.218232\pi$$
$$84$$ 0 0
$$85$$ −1.51994 0.877541i −0.164861 0.0951826i
$$86$$ 21.3413i 2.30129i
$$87$$ 1.00167 1.73494i 0.107390 0.186006i
$$88$$ −2.25950 3.91357i −0.240863 0.417188i
$$89$$ −15.1652 + 8.75561i −1.60750 + 0.928093i −0.617577 + 0.786510i $$0.711886\pi$$
−0.989927 + 0.141582i $$0.954781\pi$$
$$90$$ 1.61823 0.170576
$$91$$ 0 0
$$92$$ −25.8411 −2.69412
$$93$$ 10.0304 5.79108i 1.04011 0.600507i
$$94$$ −0.414604 0.718115i −0.0427631 0.0740679i
$$95$$ −0.0200923 + 0.0348009i −0.00206143 + 0.00357050i
$$96$$ 7.79456i 0.795529i
$$97$$ 0.369125 + 0.213115i 0.0374790 + 0.0216385i 0.518622 0.855003i $$-0.326445\pi$$
−0.481143 + 0.876642i $$0.659778\pi$$
$$98$$ 0 0
$$99$$ 1.24663i 0.125291i
$$100$$ 7.07624 12.2564i 0.707624 1.22564i
$$101$$ 4.83499 + 8.37444i 0.481099 + 0.833288i 0.999765 0.0216891i $$-0.00690441\pi$$
−0.518666 + 0.854977i $$0.673571\pi$$
$$102$$ −6.08763 + 3.51469i −0.602765 + 0.348007i
$$103$$ 9.97823 0.983185 0.491592 0.870825i $$-0.336415\pi$$
0.491592 + 0.870825i $$0.336415\pi$$
$$104$$ 6.34397 8.78695i 0.622078 0.861631i
$$105$$ 0 0
$$106$$ −5.40922 + 3.12301i −0.525390 + 0.303334i
$$107$$ −4.93111 8.54094i −0.476709 0.825684i 0.522935 0.852373i $$-0.324837\pi$$
−0.999644 + 0.0266888i $$0.991504\pi$$
$$108$$ 9.32319 16.1482i 0.897124 1.55386i
$$109$$ 11.6055i 1.11161i −0.831314 0.555803i $$-0.812411\pi$$
0.831314 0.555803i $$-0.187589\pi$$
$$110$$ −2.54087 1.46697i −0.242263 0.139870i
$$111$$ 8.55178 + 4.93737i 0.811699 + 0.468635i
$$112$$ 0 0
$$113$$ 1.73879 3.01167i 0.163572 0.283314i −0.772576 0.634923i $$-0.781032\pi$$
0.936147 + 0.351609i $$0.114365\pi$$
$$114$$ 0.0804731 + 0.139383i 0.00753699 + 0.0130545i
$$115$$ −5.73718 + 3.31236i −0.534994 + 0.308879i
$$116$$ −4.49388 −0.417247
$$117$$ −2.72762 + 1.22422i −0.252168 + 0.113179i
$$118$$ 3.78011 0.347987
$$119$$ 0 0
$$120$$ 1.87620 + 3.24967i 0.171273 + 0.296653i
$$121$$ −4.36989 + 7.56887i −0.397263 + 0.688079i
$$122$$ 10.4152i 0.942951i
$$123$$ −12.7832 7.38039i −1.15262 0.665467i
$$124$$ −22.5003 12.9905i −2.02058 1.16658i
$$125$$ 7.86464i 0.703435i
$$126$$ 0 0
$$127$$ −7.84992 13.5965i −0.696567 1.20649i −0.969649 0.244499i $$-0.921376\pi$$
0.273082 0.961991i $$-0.411957\pi$$
$$128$$ −16.3917 + 9.46373i −1.44883 + 0.836483i
$$129$$ 13.6517 1.20196
$$130$$ 0.714541 7.00000i 0.0626694 0.613940i
$$131$$ −2.54517 −0.222373 −0.111186 0.993800i $$-0.535465\pi$$
−0.111186 + 0.993800i $$0.535465\pi$$
$$132$$ −6.34003 + 3.66042i −0.551829 + 0.318598i
$$133$$ 0 0
$$134$$ −2.35240 + 4.07447i −0.203216 + 0.351981i
$$135$$ 4.78025i 0.411419i
$$136$$ 5.39215 + 3.11316i 0.462373 + 0.266951i
$$137$$ 1.61490 + 0.932362i 0.137970 + 0.0796571i 0.567396 0.823445i $$-0.307951\pi$$
−0.429426 + 0.903102i $$0.641284\pi$$
$$138$$ 26.5331i 2.25865i
$$139$$ −7.80462 + 13.5180i −0.661979 + 1.14658i 0.318116 + 0.948052i $$0.396950\pi$$
−0.980095 + 0.198530i $$0.936383\pi$$
$$140$$ 0 0
$$141$$ −0.459366 + 0.265215i −0.0386856 + 0.0223351i
$$142$$ −32.7385 −2.74735
$$143$$ 5.39257 + 0.550459i 0.450949 + 0.0460317i
$$144$$ −0.259703 −0.0216419
$$145$$ −0.997721 + 0.576035i −0.0828562 + 0.0478371i
$$146$$ −7.78676 13.4871i −0.644437 1.11620i
$$147$$ 0 0
$$148$$ 22.1510i 1.82080i
$$149$$ −5.51106 3.18181i −0.451484 0.260664i 0.256973 0.966419i $$-0.417275\pi$$
−0.708457 + 0.705754i $$0.750608\pi$$
$$150$$ −12.5846 7.26574i −1.02753 0.593245i
$$151$$ 0.664094i 0.0540432i 0.999635 + 0.0270216i $$0.00860228\pi$$
−0.999635 + 0.0270216i $$0.991398\pi$$
$$152$$ 0.0712794 0.123460i 0.00578152 0.0100139i
$$153$$ −0.858811 1.48750i −0.0694307 0.120258i
$$154$$ 0 0
$$155$$ −6.66060 −0.534992
$$156$$ −14.2350 10.2773i −1.13971 0.822844i
$$157$$ −16.5760 −1.32291 −0.661453 0.749986i $$-0.730060\pi$$
−0.661453 + 0.749986i $$0.730060\pi$$
$$158$$ −23.2562 + 13.4269i −1.85016 + 1.06819i
$$159$$ 1.99774 + 3.46019i 0.158431 + 0.274411i
$$160$$ −2.24122 + 3.88191i −0.177184 + 0.306892i
$$161$$ 0 0
$$162$$ −11.6186 6.70802i −0.912846 0.527032i
$$163$$ −7.83863 4.52563i −0.613969 0.354475i 0.160548 0.987028i $$-0.448674\pi$$
−0.774517 + 0.632553i $$0.782007\pi$$
$$164$$ 33.1113i 2.58556i
$$165$$ −0.938398 + 1.62535i −0.0730542 + 0.126534i
$$166$$ 13.2855 + 23.0112i 1.03116 + 1.78601i
$$167$$ −2.30156 + 1.32880i −0.178100 + 0.102826i −0.586400 0.810022i $$-0.699455\pi$$
0.408300 + 0.912848i $$0.366122\pi$$
$$168$$ 0 0
$$169$$ 4.09120 + 12.3395i 0.314708 + 0.949189i
$$170$$ 4.04242 0.310039
$$171$$ −0.0340582 + 0.0196635i −0.00260449 + 0.00150370i
$$172$$ −15.3117 26.5206i −1.16750 2.02218i
$$173$$ 9.79352 16.9629i 0.744588 1.28966i −0.205799 0.978594i $$-0.565979\pi$$
0.950387 0.311070i $$-0.100687\pi$$
$$174$$ 4.61423i 0.349804i
$$175$$ 0 0
$$176$$ 0.407774 + 0.235428i 0.0307371 + 0.0177461i
$$177$$ 2.41807i 0.181754i
$$178$$ 20.1665 34.9294i 1.51154 2.61807i
$$179$$ −1.44666 2.50569i −0.108129 0.187284i 0.806884 0.590711i $$-0.201152\pi$$
−0.915012 + 0.403426i $$0.867819\pi$$
$$180$$ −2.01096 + 1.16103i −0.149888 + 0.0865379i
$$181$$ −1.36804 −0.101686 −0.0508429 0.998707i $$-0.516191\pi$$
−0.0508429 + 0.998707i $$0.516191\pi$$
$$182$$ 0 0
$$183$$ −6.66245 −0.492503
$$184$$ 20.3532 11.7509i 1.50046 0.866289i
$$185$$ −2.83936 4.91791i −0.208754 0.361572i
$$186$$ −13.3384 + 23.1028i −0.978019 + 1.69398i
$$187$$ 3.11415i 0.227729i
$$188$$ 1.03045 + 0.594929i 0.0751531 + 0.0433897i
$$189$$ 0 0
$$190$$ 0.0925559i 0.00671471i
$$191$$ 0.756625 1.31051i 0.0547475 0.0948254i −0.837353 0.546663i $$-0.815898\pi$$
0.892100 + 0.451837i $$0.149231\pi$$
$$192$$ 9.43792 + 16.3470i 0.681123 + 1.17974i
$$193$$ 6.02229 3.47697i 0.433494 0.250278i −0.267340 0.963602i $$-0.586145\pi$$
0.700834 + 0.713324i $$0.252811\pi$$
$$194$$ −0.981719 −0.0704834
$$195$$ −4.47778 0.457080i −0.320661 0.0327322i
$$196$$ 0 0
$$197$$ −13.4037 + 7.73860i −0.954971 + 0.551353i −0.894622 0.446825i $$-0.852555\pi$$
−0.0603494 + 0.998177i $$0.519221\pi$$
$$198$$ −1.43566 2.48664i −0.102028 0.176718i
$$199$$ 3.30764 5.72901i 0.234473 0.406118i −0.724647 0.689121i $$-0.757997\pi$$
0.959119 + 0.283002i $$0.0913304\pi$$
$$200$$ 12.8713i 0.910140i
$$201$$ 2.60637 + 1.50479i 0.183839 + 0.106140i
$$202$$ −19.2886 11.1363i −1.35714 0.783545i
$$203$$ 0 0
$$204$$ 5.04336 8.73535i 0.353106 0.611597i
$$205$$ 4.24427 + 7.35129i 0.296433 + 0.513436i
$$206$$ −19.9035 + 11.4913i −1.38674 + 0.800634i
$$207$$ −6.48333 −0.450622
$$208$$ −0.114674 + 1.12340i −0.00795118 + 0.0778937i
$$209$$ 0.0713021 0.00493207
$$210$$ 0 0
$$211$$ 4.04714 + 7.00986i 0.278617 + 0.482578i 0.971041 0.238912i $$-0.0767907\pi$$
−0.692424 + 0.721490i $$0.743457\pi$$
$$212$$ 4.48132 7.76187i 0.307778 0.533088i
$$213$$ 20.9423i 1.43494i
$$214$$ 19.6721 + 11.3577i 1.34475 + 0.776394i
$$215$$ −6.79892 3.92536i −0.463683 0.267707i
$$216$$ 16.9584i 1.15387i
$$217$$ 0 0
$$218$$ 13.3653 + 23.1493i 0.905211 + 1.56787i
$$219$$ −8.62745 + 4.98106i −0.582989 + 0.336589i
$$220$$ 4.21002 0.283840
$$221$$ −6.81373 + 3.05815i −0.458341 + 0.205713i
$$222$$ −22.7442 −1.52649
$$223$$ 13.9067 8.02903i 0.931261 0.537664i 0.0440506 0.999029i $$-0.485974\pi$$
0.887210 + 0.461366i $$0.152640\pi$$
$$224$$ 0 0
$$225$$ 1.77537 3.07504i 0.118358 0.205002i
$$226$$ 8.00979i 0.532804i
$$227$$ 1.12220 + 0.647903i 0.0744831 + 0.0430029i 0.536779 0.843723i $$-0.319641\pi$$
−0.462296 + 0.886726i $$0.652974\pi$$
$$228$$ −0.200006 0.115474i −0.0132457 0.00764742i
$$229$$ 20.8175i 1.37566i −0.725871 0.687831i $$-0.758563\pi$$
0.725871 0.687831i $$-0.241437\pi$$
$$230$$ 7.62925 13.2142i 0.503058 0.871322i
$$231$$ 0 0
$$232$$ 3.53951 2.04354i 0.232380 0.134165i
$$233$$ 13.3043 0.871591 0.435796 0.900046i $$-0.356467\pi$$
0.435796 + 0.900046i $$0.356467\pi$$
$$234$$ 4.03090 5.58314i 0.263508 0.364981i
$$235$$ 0.305037 0.0198984
$$236$$ −4.69751 + 2.71211i −0.305782 + 0.176543i
$$237$$ 8.58899 + 14.8766i 0.557915 + 0.966337i
$$238$$ 0 0
$$239$$ 13.3652i 0.864525i −0.901748 0.432263i $$-0.857715\pi$$
0.901748 0.432263i $$-0.142285\pi$$
$$240$$ −0.338599 0.195490i −0.0218565 0.0126188i
$$241$$ 0.722398 + 0.417076i 0.0465337 + 0.0268663i 0.523086 0.852280i $$-0.324781\pi$$
−0.476553 + 0.879146i $$0.658114\pi$$
$$242$$ 20.1300i 1.29401i
$$243$$ 4.17170 7.22559i 0.267614 0.463522i
$$244$$ 7.47259 + 12.9429i 0.478384 + 0.828585i
$$245$$ 0 0
$$246$$ 33.9980 2.16763
$$247$$ 0.0700199 + 0.156008i 0.00445526 + 0.00992657i
$$248$$ 23.6291 1.50045
$$249$$ 14.7199 8.49852i 0.932834 0.538572i
$$250$$ 9.05718 + 15.6875i 0.572827 + 0.992165i
$$251$$ 13.6360 23.6183i 0.860699 1.49078i −0.0105555 0.999944i $$-0.503360\pi$$
0.871255 0.490831i $$-0.163307\pi$$
$$252$$ 0 0
$$253$$ 10.1798 + 5.87733i 0.640000 + 0.369504i
$$254$$ 31.3163 + 18.0804i 1.96496 + 1.13447i
$$255$$ 2.58587i 0.161933i
$$256$$ 8.98607 15.5643i 0.561630 0.972771i
$$257$$ 3.27594 + 5.67409i 0.204348 + 0.353940i 0.949925 0.312479i $$-0.101159\pi$$
−0.745577 + 0.666419i $$0.767826\pi$$
$$258$$ −27.2308 + 15.7217i −1.69532 + 0.978791i
$$259$$ 0 0
$$260$$ 4.13432 + 9.21148i 0.256399 + 0.571272i
$$261$$ −1.12748 −0.0697893
$$262$$ 5.07682 2.93110i 0.313647 0.181084i
$$263$$ 11.2945 + 19.5627i 0.696450 + 1.20629i 0.969689 + 0.244341i $$0.0785717\pi$$
−0.273239 + 0.961946i $$0.588095\pi$$
$$264$$ 3.32906 5.76610i 0.204889 0.354879i
$$265$$ 2.29770i 0.141146i
$$266$$ 0 0
$$267$$ −22.3437 12.9002i −1.36742 0.789478i
$$268$$ 6.75107i 0.412387i
$$269$$ −8.00065 + 13.8575i −0.487808 + 0.844909i −0.999902 0.0140210i $$-0.995537\pi$$
0.512093 + 0.858930i $$0.328870\pi$$
$$270$$ 5.50510 + 9.53511i 0.335030 + 0.580288i
$$271$$ 7.58582 4.37967i 0.460806 0.266046i −0.251577 0.967837i $$-0.580949\pi$$
0.712383 + 0.701791i $$0.247616\pi$$
$$272$$ −0.648750 −0.0393363
$$273$$ 0 0
$$274$$ −4.29496 −0.259468
$$275$$ −5.57522 + 3.21886i −0.336199 + 0.194104i
$$276$$ −19.0366 32.9724i −1.14587 1.98471i
$$277$$ −9.95914 + 17.2497i −0.598387 + 1.03644i 0.394673 + 0.918822i $$0.370858\pi$$
−0.993059 + 0.117614i $$0.962475\pi$$
$$278$$ 35.9522i 2.15627i
$$279$$ −5.64514 3.25922i −0.337965 0.195124i
$$280$$ 0 0
$$281$$ 14.0234i 0.836566i 0.908317 + 0.418283i $$0.137368\pi$$
−0.908317 + 0.418283i $$0.862632\pi$$
$$282$$ 0.610861 1.05804i 0.0363762 0.0630055i
$$283$$ 0.506295 + 0.876929i 0.0300961 + 0.0521280i 0.880681 0.473710i $$-0.157085\pi$$
−0.850585 + 0.525838i $$0.823752\pi$$
$$284$$ 40.6838 23.4888i 2.41414 1.39380i
$$285$$ −0.0592065 −0.00350709
$$286$$ −11.3904 + 5.11227i −0.673530 + 0.302295i
$$287$$ 0 0
$$288$$ −3.79906 + 2.19339i −0.223862 + 0.129247i
$$289$$ 6.35465 + 11.0066i 0.373803 + 0.647446i
$$290$$ 1.32676 2.29802i 0.0779101 0.134944i
$$291$$ 0.627989i 0.0368134i
$$292$$ 19.3531 + 11.1735i 1.13255 + 0.653879i
$$293$$ −0.172543 0.0996176i −0.0100801 0.00581972i 0.494952 0.868921i $$-0.335186\pi$$
−0.505032 + 0.863101i $$0.668519\pi$$
$$294$$ 0 0
$$295$$ −0.695286 + 1.20427i −0.0404811 + 0.0701153i
$$296$$ 10.0729 + 17.4467i 0.585474 + 1.01407i
$$297$$ −7.34554 + 4.24095i −0.426232 + 0.246085i
$$298$$ 14.6571 0.849065
$$299$$ −2.86276 + 28.0450i −0.165558 + 1.62188i
$$300$$ 20.8517 1.20387
$$301$$ 0 0
$$302$$ −0.764792 1.32466i −0.0440088 0.0762256i
$$303$$ −7.12368 + 12.3386i −0.409245 + 0.708833i
$$304$$ 0.0148539i 0.000851930i
$$305$$ 3.31809 + 1.91570i 0.189993 + 0.109693i
$$306$$ 3.42612 + 1.97807i 0.195858 + 0.113079i
$$307$$ 27.2004i 1.55241i 0.630482 + 0.776204i $$0.282857\pi$$
−0.630482 + 0.776204i $$0.717143\pi$$
$$308$$ 0 0
$$309$$ 7.35077 + 12.7319i 0.418171 + 0.724293i
$$310$$ 13.2858 7.67057i 0.754584 0.435659i
$$311$$ −27.1009 −1.53675 −0.768376 0.639999i $$-0.778935\pi$$
−0.768376 + 0.639999i $$0.778935\pi$$
$$312$$ 15.8854 + 1.62153i 0.899331 + 0.0918013i
$$313$$ −22.0785 −1.24795 −0.623975 0.781445i $$-0.714483\pi$$
−0.623975 + 0.781445i $$0.714483\pi$$
$$314$$ 33.0639 19.0894i 1.86590 1.07728i
$$315$$ 0 0
$$316$$ 19.2668 33.3711i 1.08384 1.87727i
$$317$$ 7.06823i 0.396991i 0.980102 + 0.198496i $$0.0636056\pi$$
−0.980102 + 0.198496i $$0.936394\pi$$
$$318$$ −7.96973 4.60133i −0.446920 0.258030i
$$319$$ 1.77032 + 1.02209i 0.0991188 + 0.0572263i
$$320$$ 10.8550i 0.606813i
$$321$$ 7.26531 12.5839i 0.405510 0.702364i
$$322$$ 0 0
$$323$$ −0.0850789 + 0.0491204i −0.00473392 + 0.00273313i
$$324$$ 19.2512 1.06951
$$325$$ −12.5178 9.03756i −0.694362 0.501313i
$$326$$ 20.8475 1.15464
$$327$$ 14.8082 8.54955i 0.818898 0.472791i
$$328$$ −15.0569 26.0794i −0.831381 1.43999i
$$329$$ 0 0
$$330$$ 4.32276i 0.237960i
$$331$$ −5.70588 3.29429i −0.313623 0.181071i 0.334923 0.942245i $$-0.391290\pi$$
−0.648547 + 0.761175i $$0.724623\pi$$
$$332$$ −33.0195 19.0638i −1.81218 1.04626i
$$333$$ 5.55751i 0.304550i
$$334$$ 3.06059 5.30110i 0.167468 0.290063i
$$335$$ −0.865365 1.49886i −0.0472799 0.0818912i
$$336$$ 0 0
$$337$$ −4.22290 −0.230036 −0.115018 0.993363i $$-0.536693\pi$$
−0.115018 + 0.993363i $$0.536693\pi$$
$$338$$ −22.3712 19.9018i −1.21683 1.08251i
$$339$$ 5.12373 0.278283
$$340$$ −5.02347 + 2.90030i −0.272436 + 0.157291i
$$341$$ 5.90916 + 10.2350i 0.319999 + 0.554254i
$$342$$ 0.0452902 0.0784450i 0.00244902 0.00424182i
$$343$$ 0 0
$$344$$ 24.1198 + 13.9256i 1.30045 + 0.750817i
$$345$$ −8.45293 4.88030i −0.455091 0.262747i
$$346$$ 45.1142i 2.42535i
$$347$$ 4.54739 7.87631i 0.244117 0.422822i −0.717766 0.696284i $$-0.754835\pi$$
0.961883 + 0.273462i $$0.0881687\pi$$
$$348$$ −3.31056 5.73405i −0.177464 0.307378i
$$349$$ 7.98521 4.61026i 0.427439 0.246782i −0.270816 0.962631i $$-0.587294\pi$$
0.698255 + 0.715849i $$0.253960\pi$$
$$350$$ 0 0
$$351$$ −16.4926 11.9073i −0.880310 0.635564i
$$352$$ 7.95349 0.423922
$$353$$ −1.86584 + 1.07724i −0.0993087 + 0.0573359i −0.548832 0.835933i $$-0.684927\pi$$
0.449523 + 0.893269i $$0.351594\pi$$
$$354$$ 2.78473 + 4.82330i 0.148007 + 0.256356i
$$355$$ 6.02167 10.4298i 0.319597 0.553559i
$$356$$ 57.8752i 3.06738i
$$357$$ 0 0
$$358$$ 5.77128 + 3.33205i 0.305021 + 0.176104i
$$359$$ 8.55756i 0.451651i 0.974168 + 0.225825i $$0.0725079\pi$$
−0.974168 + 0.225825i $$0.927492\pi$$
$$360$$ 1.05593 1.82892i 0.0556521 0.0963923i
$$361$$ −9.49888 16.4525i −0.499941 0.865923i
$$362$$ 2.72881 1.57548i 0.143423 0.0828055i
$$363$$ −12.8769 −0.675860
$$364$$ 0 0
$$365$$ 5.72896 0.299867
$$366$$ 13.2895 7.67270i 0.694654 0.401059i
$$367$$ −1.14912 1.99033i −0.0599833 0.103894i 0.834474 0.551047i $$-0.185771\pi$$
−0.894458 + 0.447153i $$0.852438\pi$$
$$368$$ −1.22438 + 2.12070i −0.0638255 + 0.110549i
$$369$$ 8.30736i 0.432464i
$$370$$ 11.3273 + 6.53979i 0.588876 + 0.339988i
$$371$$ 0 0
$$372$$ 38.2795i 1.98470i
$$373$$ −5.88418 + 10.1917i −0.304672 + 0.527707i −0.977188 0.212375i $$-0.931880\pi$$
0.672517 + 0.740082i $$0.265213\pi$$
$$374$$ −3.58636 6.21175i −0.185446 0.321202i
$$375$$ 10.0350 5.79373i 0.518207 0.299187i
$$376$$ −1.08215 −0.0558074
$$377$$ −0.497847 + 4.87715i −0.0256404 + 0.251186i
$$378$$ 0 0
$$379$$ −6.92034 + 3.99546i −0.355474 + 0.205233i −0.667094 0.744974i $$-0.732462\pi$$
0.311619 + 0.950207i $$0.399129\pi$$
$$380$$ 0.0664059 + 0.115018i 0.00340655 + 0.00590032i
$$381$$ 11.5658 20.0325i 0.592532 1.02630i
$$382$$ 3.48542i 0.178329i
$$383$$ 24.4605 + 14.1223i 1.24988 + 0.721616i 0.971084 0.238736i $$-0.0767331\pi$$
0.278791 + 0.960352i $$0.410066\pi$$
$$384$$ −24.1508 13.9435i −1.23244 0.711551i
$$385$$ 0 0
$$386$$ −8.00839 + 13.8709i −0.407616 + 0.706012i
$$387$$ −3.84158 6.65381i −0.195278 0.338232i
$$388$$ 1.21997 0.704352i 0.0619347 0.0357580i
$$389$$ −7.68086 −0.389435 −0.194717 0.980859i $$-0.562379\pi$$
−0.194717 + 0.980859i $$0.562379\pi$$
$$390$$ 9.45816 4.24503i 0.478933 0.214955i
$$391$$ −16.1957 −0.819050
$$392$$ 0 0
$$393$$ −1.87498 3.24756i −0.0945801 0.163818i
$$394$$ 17.8241 30.8722i 0.897964 1.55532i
$$395$$ 9.87862i 0.497047i
$$396$$ 3.56817 + 2.06008i 0.179307 + 0.103523i
$$397$$ −6.45433 3.72641i −0.323933 0.187023i 0.329211 0.944256i $$-0.393217\pi$$
−0.653144 + 0.757233i $$0.726551\pi$$
$$398$$ 15.2368i 0.763750i
$$399$$ 0 0
$$400$$ −0.670563 1.16145i −0.0335282 0.0580725i
$$401$$ 15.7601 9.09912i 0.787024 0.454389i −0.0518898 0.998653i $$-0.516524\pi$$
0.838914 + 0.544264i $$0.183191\pi$$
$$402$$ −6.93186 −0.345730
$$403$$ −16.5911 + 22.9801i −0.826461 + 1.14472i
$$404$$ 31.9596 1.59005
$$405$$ 4.27409 2.46765i 0.212381 0.122618i
$$406$$ 0 0
$$407$$ −5.03804 + 8.72615i −0.249727 + 0.432539i
$$408$$ 9.17361i 0.454161i
$$409$$ 25.3594 + 14.6413i 1.25394 + 0.723964i 0.971890 0.235435i $$-0.0756514\pi$$
0.282053 + 0.959399i $$0.408985\pi$$
$$410$$ −16.9320 9.77568i −0.836211 0.482787i
$$411$$ 2.74741i 0.135520i
$$412$$ 16.4892 28.5602i 0.812365 1.40706i
$$413$$ 0 0
$$414$$ 12.9322 7.46641i 0.635583 0.366954i
$$415$$ −9.77456 −0.479814
$$416$$ 7.81047 + 17.4021i 0.382940 + 0.853210i
$$417$$ −22.9980 −1.12622
$$418$$ −0.142225 + 0.0821139i −0.00695647 + 0.00401632i
$$419$$ 10.3697 + 17.9608i 0.506591 + 0.877441i 0.999971 + 0.00762733i $$0.00242788\pi$$
−0.493380 + 0.869814i $$0.664239\pi$$
$$420$$ 0 0
$$421$$ 24.8696i 1.21207i 0.795437 + 0.606036i $$0.207241\pi$$
−0.795437 + 0.606036i $$0.792759\pi$$
$$422$$ −16.1456 9.32165i −0.785954 0.453771i
$$423$$ 0.258531 + 0.149263i 0.0125702 + 0.00725742i
$$424$$ 8.15130i 0.395862i
$$425$$ 4.43497 7.68159i 0.215128 0.372612i
$$426$$ −24.1178 41.7733i −1.16851 2.02392i
$$427$$ 0 0
$$428$$ −32.5950 −1.57554
$$429$$ 3.27023 + 7.28626i 0.157888 + 0.351784i
$$430$$ 18.0823 0.872006
$$431$$ 18.3327 10.5844i 0.883055 0.509832i 0.0113906 0.999935i $$-0.496374\pi$$
0.871665 + 0.490103i $$0.163041\pi$$
$$432$$ −0.883489 1.53025i −0.0425069 0.0736241i
$$433$$ −11.7148 + 20.2906i −0.562977 + 0.975105i 0.434258 + 0.900789i $$0.357011\pi$$
−0.997235 + 0.0743163i $$0.976323\pi$$
$$434$$ 0 0
$$435$$ −1.47000 0.848707i −0.0704813 0.0406924i
$$436$$ −33.2178 19.1783i −1.59084 0.918474i
$$437$$ 0.370819i 0.0177387i
$$438$$ 11.4727 19.8713i 0.548187 0.949488i
$$439$$ −6.01919 10.4256i −0.287280 0.497584i 0.685879 0.727715i $$-0.259418\pi$$
−0.973160 + 0.230131i $$0.926085\pi$$
$$440$$ −3.31593 + 1.91445i −0.158081 + 0.0912680i
$$441$$ 0 0
$$442$$ 10.0694 13.9470i 0.478952 0.663390i
$$443$$ 15.7331 0.747503 0.373752 0.927529i $$-0.378071\pi$$
0.373752 + 0.927529i $$0.378071\pi$$
$$444$$ 28.2640 16.3182i 1.34135 0.774427i
$$445$$ 7.41855 + 12.8493i 0.351673 + 0.609116i
$$446$$ −18.4930 + 32.0308i −0.875669 + 1.51670i
$$447$$ 9.37592i 0.443466i
$$448$$ 0 0
$$449$$ 22.5177 + 13.0006i 1.06268 + 0.613536i 0.926171 0.377104i $$-0.123080\pi$$
0.136504 + 0.990640i $$0.456413\pi$$
$$450$$ 8.17832i 0.385530i
$$451$$ 7.53087 13.0438i 0.354615 0.614211i
$$452$$ −5.74676 9.95369i −0.270305 0.468182i
$$453$$ −0.847362 + 0.489225i −0.0398125 + 0.0229858i
$$454$$ −2.98459 −0.140074
$$455$$ 0 0
$$456$$ 0.210041 0.00983605
$$457$$ −26.6700 + 15.3979i −1.24757 + 0.720284i −0.970624 0.240602i $$-0.922655\pi$$
−0.276945 + 0.960886i $$0.589322\pi$$
$$458$$ 23.9742 + 41.5245i 1.12024 + 1.94031i
$$459$$ 5.84322 10.1208i 0.272738 0.472396i
$$460$$ 21.8949i 1.02086i
$$461$$ −29.5278 17.0479i −1.37525 0.794000i −0.383665 0.923472i $$-0.625338\pi$$
−0.991583 + 0.129472i $$0.958672\pi$$
$$462$$ 0 0
$$463$$ 1.69184i 0.0786263i −0.999227 0.0393131i $$-0.987483\pi$$
0.999227 0.0393131i $$-0.0125170\pi$$
$$464$$ −0.212926 + 0.368799i −0.00988485 + 0.0171211i
$$465$$ −4.90674 8.49871i −0.227544 0.394118i
$$466$$ −26.5378 + 15.3216i −1.22934 + 0.709761i
$$467$$ −28.3524 −1.31199 −0.655996 0.754764i $$-0.727751\pi$$
−0.655996 + 0.754764i $$0.727751\pi$$
$$468$$ −1.00344 + 9.83015i −0.0463838 + 0.454399i
$$469$$ 0 0
$$470$$ −0.608453 + 0.351290i −0.0280658 + 0.0162038i
$$471$$ −12.2112 21.1504i −0.562662 0.974559i
$$472$$ 2.46659 4.27226i 0.113534 0.196647i
$$473$$ 13.9300i 0.640503i
$$474$$ −34.2647 19.7827i −1.57383 0.908651i
$$475$$ −0.175879 0.101544i −0.00806989 0.00465915i
$$476$$ 0 0
$$477$$ 1.12433 1.94739i 0.0514794 0.0891650i
$$478$$ 15.3918 + 26.6595i 0.704007 + 1.21938i
$$479$$ −5.44077 + 3.14123i −0.248595 + 0.143526i −0.619121 0.785296i $$-0.712511\pi$$
0.370526 + 0.928822i $$0.379178\pi$$
$$480$$ −6.60426 −0.301442
$$481$$ −24.0402 2.45396i −1.09614 0.111891i
$$482$$ −1.92128 −0.0875117
$$483$$ 0 0
$$484$$ 14.4427 + 25.0154i 0.656484 + 1.13706i
$$485$$ 0.180570 0.312757i 0.00819927 0.0142016i
$$486$$ 19.2171i 0.871703i
$$487$$ 11.2736 + 6.50879i 0.510854 + 0.294942i 0.733185 0.680030i $$-0.238033\pi$$
−0.222331 + 0.974971i $$0.571366\pi$$
$$488$$ −11.7712 6.79613i −0.532859 0.307647i
$$489$$ 13.3358i 0.603065i
$$490$$ 0 0
$$491$$ −6.17616 10.6974i −0.278726 0.482768i 0.692342 0.721569i $$-0.256579\pi$$
−0.971068 + 0.238801i $$0.923246\pi$$
$$492$$ −42.2490 + 24.3925i −1.90473 + 1.09970i
$$493$$ −2.81650 −0.126849
$$494$$ −0.319332 0.230550i −0.0143674 0.0103730i
$$495$$ 1.05626 0.0474754
$$496$$ −2.13218 + 1.23102i −0.0957378 + 0.0552743i
$$497$$ 0 0
$$498$$ −19.5744 + 33.9038i −0.877148 + 1.51926i
$$499$$ 9.15340i 0.409763i −0.978787 0.204881i $$-0.934319\pi$$
0.978787 0.204881i $$-0.0656808\pi$$
$$500$$ −22.5105 12.9965i −1.00670 0.581220i
$$501$$ −3.39102 1.95781i −0.151500 0.0874684i
$$502$$ 62.8149i 2.80357i
$$503$$ −11.2519 + 19.4888i −0.501696 + 0.868963i 0.498302 + 0.867003i $$0.333957\pi$$
−0.999998 + 0.00195935i $$0.999376\pi$$
$$504$$ 0 0
$$505$$ 7.09559 4.09664i 0.315750 0.182298i
$$506$$ −27.0741 −1.20359
$$507$$ −12.7308 + 14.3105i −0.565396 + 0.635551i
$$508$$ −51.8885 −2.30218
$$509$$ 33.4811 19.3303i 1.48402 0.856800i 0.484187 0.874965i $$-0.339116\pi$$
0.999835 + 0.0181646i $$0.00578229\pi$$
$$510$$ 2.97797 + 5.15800i 0.131867 + 0.228400i
$$511$$ 0 0
$$512$$ 3.53972i 0.156435i
$$513$$ −0.231727 0.133787i −0.0102310 0.00590686i
$$514$$ −13.0690 7.54536i −0.576447 0.332812i
$$515$$ 8.45447i 0.372549i
$$516$$ 22.5596 39.0744i 0.993132 1.72016i
$$517$$ −0.270623 0.468732i −0.0119020 0.0206148i
$$518$$ 0 0
$$519$$ 28.8588 1.26676
$$520$$ −7.44511 5.37520i −0.326490 0.235718i
$$521$$ 40.2351 1.76273 0.881366 0.472434i $$-0.156625\pi$$
0.881366 + 0.472434i $$0.156625\pi$$
$$522$$ 2.24897 1.29844i 0.0984348 0.0568313i
$$523$$ 0.366073 + 0.634057i 0.0160073 + 0.0277254i 0.873918 0.486073i $$-0.161571\pi$$
−0.857911 + 0.513799i $$0.828238\pi$$
$$524$$ −4.20594 + 7.28491i −0.183737 + 0.318243i
$$525$$ 0 0
$$526$$ −45.0581 26.0143i −1.96463 1.13428i
$$527$$ −14.1018 8.14169i −0.614285 0.354658i
$$528$$ 0.693741i 0.0301912i
$$529$$ −19.0660 + 33.0234i −0.828959 + 1.43580i
$$530$$ 2.64610 + 4.58319i 0.114939 + 0.199081i
$$531$$ −1.17857 + 0.680446i −0.0511455 + 0.0295288i
$$532$$ 0 0
$$533$$ 35.9353 + 3.66817i 1.55653 + 0.158886i
$$534$$ 59.4251 2.57157
$$535$$ −7.23667 + 4.17809i −0.312868 + 0.180635i
$$536$$ 3.06996 + 5.31733i 0.132602 + 0.229674i
$$537$$ 2.13146 3.69179i 0.0919791 0.159312i
$$538$$ 36.8553i 1.58894i
$$539$$ 0 0
$$540$$ −13.6823 7.89946i −0.588791 0.339939i
$$541$$ 23.6537i 1.01695i 0.861076 + 0.508476i $$0.169791\pi$$
−0.861076 + 0.508476i $$0.830209\pi$$
$$542$$ −10.0876 + 17.4722i −0.433298 + 0.750494i
$$543$$ −1.00781 1.74558i −0.0432492 0.0749099i
$$544$$ −9.49024 + 5.47919i −0.406891 + 0.234918i
$$545$$ −9.83325 −0.421210
$$546$$ 0 0
$$547$$ −12.9472 −0.553582 −0.276791 0.960930i $$-0.589271\pi$$
−0.276791 + 0.960930i $$0.589271\pi$$
$$548$$ 5.33730 3.08149i 0.227998 0.131635i
$$549$$ 1.87481 + 3.24727i 0.0800151 + 0.138590i
$$550$$ 7.41388 12.8412i 0.316129 0.547552i
$$551$$ 0.0644871i 0.00274724i
$$552$$ 29.9876 + 17.3133i 1.27636 + 0.736904i
$$553$$ 0 0
$$554$$ 45.8771i 1.94913i
$$555$$ 4.18340 7.24585i 0.177575 0.307569i
$$556$$ 25.7946 + 44.6775i 1.09393 + 1.89475i
$$557$$ −5.54845 + 3.20340i −0.235096 + 0.135732i −0.612921 0.790145i $$-0.710005\pi$$
0.377825 + 0.925877i $$0.376672\pi$$
$$558$$ 15.0137 0.635581
$$559$$ −30.4787 + 13.6795i −1.28911 + 0.578582i
$$560$$ 0 0
$$561$$ −3.97355 + 2.29413i −0.167764 + 0.0968584i
$$562$$ −16.1498 27.9723i −0.681239 1.17994i
$$563$$ 3.66042 6.34004i 0.154268 0.267201i −0.778524 0.627615i $$-0.784031\pi$$
0.932792 + 0.360414i $$0.117365\pi$$
$$564$$ 1.75309i 0.0738185i
$$565$$ −2.55176 1.47326i −0.107354 0.0619806i
$$566$$ −2.01980 1.16613i −0.0848986 0.0490162i
$$567$$ 0 0
$$568$$ −21.3625 + 37.0009i −0.896349 + 1.55252i
$$569$$ −2.15872 3.73901i −0.0904981 0.156747i 0.817223 0.576322i $$-0.195513\pi$$
−0.907721 + 0.419575i $$0.862179\pi$$
$$570$$ 0.118098 0.0681842i 0.00494660 0.00285592i
$$571$$ −34.1695 −1.42995 −0.714974 0.699152i $$-0.753561\pi$$
−0.714974 + 0.699152i $$0.753561\pi$$
$$572$$ 10.4869 14.5252i 0.438478 0.607330i
$$573$$ 2.22956 0.0931413
$$574$$ 0 0
$$575$$ −16.7402 28.9949i −0.698115 1.20917i
$$576$$ 5.31166 9.20007i 0.221319 0.383336i
$$577$$ 6.35656i 0.264627i −0.991208 0.132314i $$-0.957759\pi$$
0.991208 0.132314i $$-0.0422406\pi$$
$$578$$ −25.3511 14.6364i −1.05447 0.608796i
$$579$$ 8.87301 + 5.12283i 0.368750 + 0.212898i
$$580$$ 3.80763i 0.158103i
$$581$$ 0 0
$$582$$ −0.723214 1.25264i −0.0299782 0.0519237i
$$583$$ −3.53074 + 2.03847i −0.146228 + 0.0844249i
$$584$$ −20.3240 −0.841014
$$585$$ 1.03727 + 2.31109i 0.0428857 + 0.0955518i
$$586$$ 0.458892 0.0189566
$$587$$ 27.2036 15.7060i 1.12281 0.648256i 0.180695 0.983539i $$-0.442165\pi$$
0.942118 + 0.335283i $$0.108832\pi$$
$$588$$ 0 0
$$589$$ −0.186414 + 0.322878i −0.00768104 + 0.0133040i
$$590$$ 3.20286i 0.131860i
$$591$$ −19.7484 11.4018i −0.812342 0.469006i
$$592$$ −1.81786 1.04954i −0.0747136 0.0431359i
$$593$$ 0.473013i 0.0194243i −0.999953 0.00971215i $$-0.996908\pi$$
0.999953 0.00971215i $$-0.00309152\pi$$
$$594$$ 9.76804 16.9187i 0.400787 0.694184i
$$595$$ 0 0
$$596$$ −18.2143 + 10.5160i −0.746086 + 0.430753i
$$597$$ 9.74670 0.398906
$$598$$ −26.5872 59.2378i −1.08723 2.42242i
$$599$$ −9.62695 −0.393347 −0.196673 0.980469i $$-0.563014\pi$$
−0.196673 + 0.980469i $$0.563014\pi$$
$$600$$ −16.4234 + 9.48206i −0.670483 + 0.387103i
$$601$$ 20.5399 + 35.5762i 0.837842 + 1.45118i 0.891696 + 0.452635i $$0.149516\pi$$
−0.0538542 + 0.998549i $$0.517151\pi$$
$$602$$ 0 0
$$603$$ 1.69379i 0.0689765i
$$604$$ 1.90080 + 1.09743i 0.0773424 + 0.0446537i
$$605$$ 6.41304 + 3.70257i 0.260727 + 0.150531i
$$606$$ 32.8155i 1.33304i
$$607$$ −9.54289 + 16.5288i −0.387334 + 0.670882i −0.992090 0.125529i $$-0.959937\pi$$
0.604756 + 0.796411i $$0.293271\pi$$
$$608$$ 0.125453 + 0.217290i 0.00508777 + 0.00881228i
$$609$$ 0 0
$$610$$ −8.82474 −0.357303
$$611$$ 0.759825 1.05242i 0.0307392 0.0425765i
$$612$$ −5.67680 −0.229471
$$613$$ 32.9131 19.0024i 1.32935 0.767500i 0.344149 0.938915i $$-0.388167\pi$$
0.985199 + 0.171415i $$0.0548340\pi$$
$$614$$ −31.3249 54.2563i −1.26417 2.18961i
$$615$$ −6.25334 + 10.8311i −0.252159 + 0.436752i
$$616$$ 0 0
$$617$$ 7.20117 + 4.15759i 0.289908 + 0.167378i 0.637900 0.770119i $$-0.279803\pi$$
−0.347992 + 0.937497i $$0.613136\pi$$
$$618$$ −29.3250 16.9308i −1.17962 0.681056i
$$619$$ 44.4728i 1.78751i −0.448553 0.893756i $$-0.648060\pi$$
0.448553 0.893756i $$-0.351940\pi$$
$$620$$ −11.0068 + 19.0643i −0.442042 + 0.765640i
$$621$$ −22.0558 38.2018i −0.885069 1.53298i
$$622$$ 54.0579 31.2103i 2.16752 1.25142i
$$623$$ 0 0
$$624$$ −1.51790 + 0.681266i −0.0607646 + 0.0272725i
$$625$$ 14.7468 0.589874
$$626$$ 44.0397 25.4263i 1.76018 1.01624i
$$627$$ 0.0525269 + 0.0909792i 0.00209772 + 0.00363336i
$$628$$ −27.3921 + 47.4445i −1.09306 + 1.89324i
$$629$$ 13.8829i 0.553549i
$$630$$ 0 0
$$631$$ −10.1779 5.87622i −0.405177 0.233929i 0.283539 0.958961i $$-0.408492\pi$$
−0.688715 + 0.725032i $$0.741825\pi$$
$$632$$ 35.0453i 1.39403i
$$633$$ −5.96290 + 10.3280i −0.237004 + 0.410503i
$$634$$ −8.14001 14.0989i −0.323281 0.559939i
$$635$$ −11.5202 + 6.65117i −0.457164 + 0.263944i
$$636$$ 13.2052 0.523620
$$637$$ 0 0
$$638$$ −4.70831 −0.186404
$$639$$ 10.2072 5.89315i 0.403792 0.233129i
$$640$$ 8.01854 + 13.8885i 0.316961 + 0.548992i
$$641$$ 5.24342 9.08186i 0.207102 0.358712i −0.743698 0.668516i $$-0.766930\pi$$
0.950801 + 0.309804i $$0.100263\pi$$
$$642$$ 33.4679i 1.32087i
$$643$$ 27.0912 + 15.6411i 1.06837 + 0.616825i 0.927736 0.373237i $$-0.121752\pi$$
0.140635 + 0.990061i $$0.455085\pi$$
$$644$$ 0 0
$$645$$ 11.5669i 0.455448i
$$646$$ 0.113137 0.195959i 0.00445133 0.00770992i
$$647$$ −13.4337 23.2679i −0.528135 0.914757i −0.999462 0.0327983i $$-0.989558\pi$$
0.471327 0.881959i $$-0.343775\pi$$
$$648$$ −15.1627 + 8.75422i −0.595649 + 0.343898i
$$649$$ 2.46738 0.0968530
$$650$$ 35.3770 + 3.61119i 1.38760 + 0.141643i
$$651$$ 0 0
$$652$$ −25.9070 + 14.9574i −1.01459 + 0.585776i
$$653$$ 2.07081 + 3.58674i 0.0810369 + 0.140360i 0.903696 0.428176i $$-0.140844\pi$$
−0.822659 + 0.568536i $$0.807510\pi$$
$$654$$ −19.6919 + 34.1073i −0.770014 + 1.33370i
$$655$$ 2.15650i 0.0842615i
$$656$$ 2.71734 + 1.56886i 0.106094 + 0.0612536i
$$657$$ 4.85553 + 2.80334i 0.189432 + 0.109369i
$$658$$ 0 0
$$659$$ −10.7276 + 18.5807i −0.417887 + 0.723801i −0.995727 0.0923492i $$-0.970562\pi$$
0.577840 + 0.816150i $$0.303896\pi$$
$$660$$ 3.10144 + 5.37185i 0.120723 + 0.209099i
$$661$$ 36.7084 21.1936i 1.42779 0.824335i 0.430844 0.902426i $$-0.358216\pi$$
0.996946 + 0.0780909i $$0.0248824\pi$$
$$662$$ 15.1753 0.589803
$$663$$ −8.92164 6.44122i −0.346488 0.250156i
$$664$$ 34.6762 1.34570
$$665$$ 0 0
$$666$$ 6.40021 + 11.0855i 0.248003 + 0.429554i
$$667$$ −5.31558 + 9.20685i −0.205820 + 0.356491i
$$668$$ 8.78349i 0.339844i
$$669$$ 20.4896 + 11.8297i 0.792173 + 0.457361i
$$670$$ 3.45226 + 1.99317i 0.133373 + 0.0770027i
$$671$$ 6.79830i 0.262445i
$$672$$ 0 0
$$673$$ −14.7928 25.6219i −0.570220 0.987650i −0.996543 0.0830790i $$-0.973525\pi$$
0.426323 0.904571i $$-0.359809\pi$$
$$674$$ 8.42336 4.86323i 0.324456 0.187324i
$$675$$ 24.1588 0.929871
$$676$$ 42.0793 + 8.68114i 1.61844 + 0.333890i
$$677$$ 32.1659 1.23624 0.618118 0.786085i $$-0.287895\pi$$
0.618118 + 0.786085i $$0.287895\pi$$
$$678$$ −10.2202 + 5.90066i −0.392506 + 0.226613i
$$679$$ 0 0
$$680$$ 2.63775 4.56872i 0.101153 0.175202i
$$681$$ 1.90919i 0.0731604i
$$682$$ −23.5738 13.6104i −0.902689 0.521168i
$$683$$ 7.44986 + 4.30118i 0.285061 + 0.164580i 0.635712 0.771926i $$-0.280706\pi$$
−0.350651 + 0.936506i $$0.614040\pi$$
$$684$$ 0.129977i 0.00496980i
$$685$$ 0.789983 1.36829i 0.0301837 0.0522797i
$$686$$ 0 0
$$687$$ 26.5625 15.3359i 1.01342 0.585100i
$$688$$ −2.90195 −0.110636
$$689$$ −7.92740 5.72340i −0.302010 0.218044i
$$690$$ 22.4813 0.855847
$$691$$ −17.7033 + 10.2210i −0.673466 + 0.388826i −0.797388 0.603466i $$-0.793786\pi$$
0.123923 + 0.992292i $$0.460452\pi$$
$$692$$ −32.3680 56.0629i −1.23044 2.13119i
$$693$$ 0 0
$$694$$ 20.9477i 0.795164i
$$695$$ 11.4537 + 6.61279i 0.434463 + 0.250837i
$$696$$ 5.21498 + 3.01087i 0.197673 + 0.114127i
$$697$$ 20.7522i 0.786046i
$$698$$ −10.6187 + 18.3921i −0.401922 + 0.696150i
$$699$$ 9.80099 + 16.9758i 0.370708 + 0.642084i
$$700$$ 0 0
$$701$$ −25.1373 −0.949422 −0.474711 0.880142i $$-0.657447\pi$$
−0.474711 + 0.880142i $$0.657447\pi$$
$$702$$ 46.6104 + 4.75787i 1.75920 + 0.179574i
$$703$$ −0.317866 −0.0119885
$$704$$ −16.6803 + 9.63036i −0.628661 + 0.362958i
$$705$$ 0.224715 + 0.389217i 0.00846324 + 0.0146588i
$$706$$ 2.48118 4.29753i 0.0933804 0.161740i
$$707$$ 0 0
$$708$$ −6.92112 3.99591i −0.260112 0.150176i
$$709$$ 25.5416 + 14.7464i 0.959234 + 0.553814i 0.895937 0.444181i $$-0.146505\pi$$
0.0632970 + 0.997995i $$0.479838\pi$$
$$710$$ 27.7390i 1.04103i
$$711$$ 4.83389 8.37254i 0.181285 0.313995i
$$712$$ −26.3180 45.5841i −0.986309 1.70834i
$$713$$ −53.2287 + 30.7316i −1.99343 + 1.15091i
$$714$$ 0 0
$$715$$ 0.466399 4.56908i 0.0174423 0.170874i
$$716$$ −9.56254 −0.357369
$$717$$ 17.0536 9.84591i 0.636879 0.367702i
$$718$$ −9.85518 17.0697i −0.367792 0.637034i
$$719$$ −4.16576 + 7.21531i −0.155357 + 0.269086i −0.933189 0.359386i $$-0.882986\pi$$
0.777832 + 0.628472i $$0.216319\pi$$
$$720$$ 0.220044i 0.00820055i
$$721$$ 0 0
$$722$$ 37.8946 + 21.8784i 1.41029 + 0.814231i
$$723$$ 1.22901i 0.0457073i
$$724$$ −2.26071 + 3.91567i −0.0840188 + 0.145525i
$$725$$ −2.91120 5.04235i −0.108119 0.187268i
$$726$$ 25.6853 14.8294i 0.953271 0.550371i
$$727$$ 9.66141 0.358322 0.179161 0.983820i $$-0.442662\pi$$
0.179161 + 0.983820i $$0.442662\pi$$
$$728$$ 0 0
$$729$$ 29.7672 1.10249
$$730$$ −11.4275 + 6.59766i −0.422950 + 0.244190i
$$731$$ −9.59645 16.6215i −0.354938 0.614770i
$$732$$ −11.0098 + 19.0696i −0.406935 + 0.704832i
$$733$$ 14.0179i 0.517762i 0.965909 + 0.258881i $$0.0833538\pi$$
−0.965909 + 0.258881i $$0.916646\pi$$
$$734$$ 4.58425 + 2.64672i 0.169208 + 0.0976921i
$$735$$ 0 0
$$736$$ 41.3635i 1.52468i
$$737$$ −1.53547 + 2.65951i −0.0565598 + 0.0979644i
$$738$$ −9.56704 16.5706i −0.352168 0.609972i
$$739$$ −33.6145 + 19.4073i −1.23653 + 0.713910i −0.968383 0.249468i $$-0.919744\pi$$
−0.268146 + 0.963378i $$0.586411\pi$$
$$740$$ −18.7683 −0.689938
$$741$$ −0.147479 + 0.204271i −0.00541779 + 0.00750410i
$$742$$ 0 0
$$743$$ 29.7863 17.1971i 1.09275 0.630901i 0.158445 0.987368i $$-0.449352\pi$$
0.934308 + 0.356467i $$0.116019\pi$$
$$744$$ 17.4071 + 30.1500i 0.638175 + 1.10535i
$$745$$ −2.69592 + 4.66948i −0.0987710 + 0.171076i
$$746$$ 27.1057i 0.992410i
$$747$$ −8.28434 4.78297i −0.303108 0.175000i
$$748$$ 8.91346 + 5.14619i 0.325908 + 0.188163i
$$749$$ 0 0
$$750$$ −13.3445 + 23.1134i −0.487272 + 0.843980i
$$751$$ 24.0735 + 41.6965i 0.878454 + 1.52153i 0.853037 + 0.521850i $$0.174758\pi$$
0.0254165 + 0.999677i $$0.491909\pi$$
$$752$$ 0.0976479 0.0563770i 0.00356085 0.00205586i
$$753$$ 40.1816 1.46430
$$754$$ −4.62364 10.3017i −0.168383 0.375167i
$$755$$ 0.562681 0.0204781
$$756$$ 0 0
$$757$$ 3.45319 + 5.98110i 0.125508 + 0.217387i 0.921931 0.387353i $$-0.126611\pi$$
−0.796423 + 0.604740i $$0.793277\pi$$
$$758$$ 9.20262 15.9394i 0.334254 0.578945i
$$759$$ 17.3188i 0.628634i
$$760$$ −0.104606 0.0603945i −0.00379447 0.00219074i
$$761$$ 27.6895 + 15.9865i 1.00374 + 0.579511i 0.909353 0.416025i $$-0.136577\pi$$
0.0943888 + 0.995535i $$0.469910\pi$$
$$762$$ 53.2781i 1.93006i
$$763$$ 0 0
$$764$$ −2.50067 4.33129i −0.0904712 0.156701i
$$765$$ −1.26035 + 0.727663i −0.0455680 + 0.0263087i
$$766$$ −65.0548 −2.35053
$$767$$ 2.42301 + 5.39860i 0.0874898 + 0.194932i
$$768$$ 26.4795 0.955495
$$769$$ 12.4665 7.19752i 0.449553 0.259549i −0.258089 0.966121i $$-0.583093\pi$$
0.707641 + 0.706572i $$0.249759\pi$$
$$770$$ 0 0
$$771$$ −4.82664 + 8.35999i −0.173827 + 0.301078i
$$772$$ 22.9830i 0.827177i
$$773$$ 32.2829 + 18.6385i 1.16114 + 0.670382i 0.951576 0.307414i $$-0.0994636\pi$$
0.209560 + 0.977796i $$0.432797\pi$$
$$774$$ 15.3255 + 8.84818i 0.550864 + 0.318041i
$$775$$ 33.6618i 1.20917i
$$776$$ −0.640590 + 1.10953i −0.0229958 + 0.0398300i
$$777$$ 0 0
$$778$$ 15.3209 8.84553i 0.549281 0.317128i
$$779$$ 0.475146 0.0170239
$$780$$ −8.70789 + 12.0612i −0.311792 + 0.431859i
$$781$$ −21.3693 −0.764652