# Properties

 Label 105.3.k.d.62.12 Level 105 Weight 3 Character 105.62 Analytic conductor 2.861 Analytic rank 0 Dimension 32 CM no Inner twists 8

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$105 = 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 105.k (of order $$4$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.86104277578$$ Analytic rank: $$0$$ Dimension: $$32$$ Relative dimension: $$16$$ over $$\Q(i)$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

## Embedding invariants

 Embedding label 62.12 Character $$\chi$$ $$=$$ 105.62 Dual form 105.3.k.d.83.12

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.88692 - 1.88692i) q^{2} +(1.39918 + 2.65373i) q^{3} -3.12092i q^{4} +(4.96950 + 0.551428i) q^{5} +(7.64751 + 2.36725i) q^{6} +(-6.68054 + 2.09055i) q^{7} +(1.65875 + 1.65875i) q^{8} +(-5.08462 + 7.42608i) q^{9} +O(q^{10})$$ $$q+(1.88692 - 1.88692i) q^{2} +(1.39918 + 2.65373i) q^{3} -3.12092i q^{4} +(4.96950 + 0.551428i) q^{5} +(7.64751 + 2.36725i) q^{6} +(-6.68054 + 2.09055i) q^{7} +(1.65875 + 1.65875i) q^{8} +(-5.08462 + 7.42608i) q^{9} +(10.4175 - 8.33654i) q^{10} -17.9060i q^{11} +(8.28210 - 4.36672i) q^{12} +(-11.1383 - 11.1383i) q^{13} +(-8.66093 + 16.5503i) q^{14} +(5.48986 + 13.9593i) q^{15} +18.7435 q^{16} +(-0.666845 - 0.666845i) q^{17} +(4.41815 + 23.6067i) q^{18} -10.8119 q^{19} +(1.72096 - 15.5094i) q^{20} +(-14.8950 - 14.8033i) q^{21} +(-33.7872 - 33.7872i) q^{22} +(-2.20425 - 2.20425i) q^{23} +(-2.08100 + 6.72276i) q^{24} +(24.3919 + 5.48064i) q^{25} -42.0343 q^{26} +(-26.8211 - 3.10283i) q^{27} +(6.52445 + 20.8494i) q^{28} -22.9708 q^{29} +(36.6989 + 15.9811i) q^{30} +26.1094i q^{31} +(28.7325 - 28.7325i) q^{32} +(47.5179 - 25.0537i) q^{33} -2.51656 q^{34} +(-34.3517 + 6.70517i) q^{35} +(23.1762 + 15.8687i) q^{36} +(41.6663 + 41.6663i) q^{37} +(-20.4011 + 20.4011i) q^{38} +(13.9737 - 45.1427i) q^{39} +(7.32848 + 9.15784i) q^{40} +6.85976 q^{41} +(-56.0383 + 0.173022i) q^{42} +(-37.6932 + 37.6932i) q^{43} -55.8834 q^{44} +(-29.3629 + 34.1001i) q^{45} -8.31847 q^{46} +(5.55606 + 5.55606i) q^{47} +(26.2255 + 49.7404i) q^{48} +(40.2592 - 27.9320i) q^{49} +(56.3670 - 35.6839i) q^{50} +(0.836596 - 2.70266i) q^{51} +(-34.7619 + 34.7619i) q^{52} +(32.4556 + 32.4556i) q^{53} +(-56.4640 + 44.7545i) q^{54} +(9.87390 - 88.9841i) q^{55} +(-14.5490 - 7.61364i) q^{56} +(-15.1277 - 28.6918i) q^{57} +(-43.3441 + 43.3441i) q^{58} -99.8940i q^{59} +(43.5658 - 17.1334i) q^{60} -44.6768i q^{61} +(49.2664 + 49.2664i) q^{62} +(18.4433 - 60.2399i) q^{63} -33.4577i q^{64} +(-49.2100 - 61.4940i) q^{65} +(42.3881 - 136.937i) q^{66} +(-18.0239 - 18.0239i) q^{67} +(-2.08117 + 2.08117i) q^{68} +(2.76536 - 8.93362i) q^{69} +(-52.1668 + 77.4710i) q^{70} +6.35575i q^{71} +(-20.7521 + 3.88391i) q^{72} +(55.3597 + 55.3597i) q^{73} +157.242 q^{74} +(19.5843 + 72.3979i) q^{75} +33.7430i q^{76} +(37.4336 + 119.622i) q^{77} +(-58.8133 - 111.548i) q^{78} -59.7832i q^{79} +(93.1460 + 10.3357i) q^{80} +(-29.2934 - 75.5175i) q^{81} +(12.9438 - 12.9438i) q^{82} +(-42.2387 + 42.2387i) q^{83} +(-46.2000 + 46.4862i) q^{84} +(-2.94617 - 3.68160i) q^{85} +142.248i q^{86} +(-32.1402 - 60.9585i) q^{87} +(29.7017 - 29.7017i) q^{88} +58.4197i q^{89} +(8.93864 + 119.750i) q^{90} +(97.6954 + 51.1248i) q^{91} +(-6.87928 + 6.87928i) q^{92} +(-69.2875 + 36.5317i) q^{93} +20.9677 q^{94} +(-53.7296 - 5.96197i) q^{95} +(116.450 + 36.0466i) q^{96} +(11.1921 - 11.1921i) q^{97} +(23.2603 - 128.671i) q^{98} +(132.972 + 91.0454i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$32q + O(q^{10})$$ $$32q - 48q^{15} - 24q^{16} - 92q^{18} - 60q^{21} + 112q^{22} - 72q^{25} + 88q^{28} - 108q^{30} + 416q^{36} + 72q^{37} + 300q^{42} - 328q^{43} + 32q^{46} + 148q^{51} - 748q^{57} - 392q^{58} + 544q^{60} - 220q^{63} - 648q^{67} - 8q^{70} - 8q^{72} + 500q^{78} - 948q^{81} + 672q^{85} + 1288q^{88} + 808q^{91} + 292q^{93} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$$.

 $$n$$ $$22$$ $$31$$ $$71$$ $$\chi(n)$$ $$e\left(\frac{1}{4}\right)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.88692 1.88692i 0.943459 0.943459i −0.0550258 0.998485i $$-0.517524\pi$$
0.998485 + 0.0550258i $$0.0175241\pi$$
$$3$$ 1.39918 + 2.65373i 0.466392 + 0.884578i
$$4$$ 3.12092i 0.780230i
$$5$$ 4.96950 + 0.551428i 0.993900 + 0.110286i
$$6$$ 7.64751 + 2.36725i 1.27459 + 0.394542i
$$7$$ −6.68054 + 2.09055i −0.954363 + 0.298651i
$$8$$ 1.65875 + 1.65875i 0.207344 + 0.207344i
$$9$$ −5.08462 + 7.42608i −0.564957 + 0.825120i
$$10$$ 10.4175 8.33654i 1.04175 0.833654i
$$11$$ 17.9060i 1.62782i −0.580989 0.813911i $$-0.697334\pi$$
0.580989 0.813911i $$-0.302666\pi$$
$$12$$ 8.28210 4.36672i 0.690175 0.363893i
$$13$$ −11.1383 11.1383i −0.856796 0.856796i 0.134164 0.990959i $$-0.457165\pi$$
−0.990959 + 0.134164i $$0.957165\pi$$
$$14$$ −8.66093 + 16.5503i −0.618638 + 1.18217i
$$15$$ 5.48986 + 13.9593i 0.365991 + 0.930619i
$$16$$ 18.7435 1.17147
$$17$$ −0.666845 0.666845i −0.0392262 0.0392262i 0.687222 0.726448i $$-0.258830\pi$$
−0.726448 + 0.687222i $$0.758830\pi$$
$$18$$ 4.41815 + 23.6067i 0.245453 + 1.31148i
$$19$$ −10.8119 −0.569046 −0.284523 0.958669i $$-0.591835\pi$$
−0.284523 + 0.958669i $$0.591835\pi$$
$$20$$ 1.72096 15.5094i 0.0860482 0.775471i
$$21$$ −14.8950 14.8033i −0.709287 0.704920i
$$22$$ −33.7872 33.7872i −1.53578 1.53578i
$$23$$ −2.20425 2.20425i −0.0958368 0.0958368i 0.657563 0.753400i $$-0.271587\pi$$
−0.753400 + 0.657563i $$0.771587\pi$$
$$24$$ −2.08100 + 6.72276i −0.0867083 + 0.280115i
$$25$$ 24.3919 + 5.48064i 0.975674 + 0.219226i
$$26$$ −42.0343 −1.61670
$$27$$ −26.8211 3.10283i −0.993375 0.114920i
$$28$$ 6.52445 + 20.8494i 0.233016 + 0.744623i
$$29$$ −22.9708 −0.792098 −0.396049 0.918229i $$-0.629619\pi$$
−0.396049 + 0.918229i $$0.629619\pi$$
$$30$$ 36.6989 + 15.9811i 1.22330 + 0.532703i
$$31$$ 26.1094i 0.842240i 0.907005 + 0.421120i $$0.138363\pi$$
−0.907005 + 0.421120i $$0.861637\pi$$
$$32$$ 28.7325 28.7325i 0.897891 0.897891i
$$33$$ 47.5179 25.0537i 1.43994 0.759203i
$$34$$ −2.51656 −0.0740166
$$35$$ −34.3517 + 6.70517i −0.981478 + 0.191576i
$$36$$ 23.1762 + 15.8687i 0.643784 + 0.440797i
$$37$$ 41.6663 + 41.6663i 1.12612 + 1.12612i 0.990803 + 0.135314i $$0.0432044\pi$$
0.135314 + 0.990803i $$0.456796\pi$$
$$38$$ −20.4011 + 20.4011i −0.536871 + 0.536871i
$$39$$ 13.9737 45.1427i 0.358300 1.15751i
$$40$$ 7.32848 + 9.15784i 0.183212 + 0.228946i
$$41$$ 6.85976 0.167311 0.0836556 0.996495i $$-0.473340\pi$$
0.0836556 + 0.996495i $$0.473340\pi$$
$$42$$ −56.0383 + 0.173022i −1.33425 + 0.00411958i
$$43$$ −37.6932 + 37.6932i −0.876587 + 0.876587i −0.993180 0.116593i $$-0.962803\pi$$
0.116593 + 0.993180i $$0.462803\pi$$
$$44$$ −55.8834 −1.27008
$$45$$ −29.3629 + 34.1001i −0.652510 + 0.757780i
$$46$$ −8.31847 −0.180836
$$47$$ 5.55606 + 5.55606i 0.118214 + 0.118214i 0.763739 0.645525i $$-0.223361\pi$$
−0.645525 + 0.763739i $$0.723361\pi$$
$$48$$ 26.2255 + 49.7404i 0.546364 + 1.03626i
$$49$$ 40.2592 27.9320i 0.821616 0.570042i
$$50$$ 56.3670 35.6839i 1.12734 0.713678i
$$51$$ 0.836596 2.70266i 0.0164038 0.0529934i
$$52$$ −34.7619 + 34.7619i −0.668498 + 0.668498i
$$53$$ 32.4556 + 32.4556i 0.612369 + 0.612369i 0.943563 0.331194i $$-0.107451\pi$$
−0.331194 + 0.943563i $$0.607451\pi$$
$$54$$ −56.4640 + 44.7545i −1.04563 + 0.828787i
$$55$$ 9.87390 88.9841i 0.179525 1.61789i
$$56$$ −14.5490 7.61364i −0.259804 0.135958i
$$57$$ −15.1277 28.6918i −0.265398 0.503365i
$$58$$ −43.3441 + 43.3441i −0.747312 + 0.747312i
$$59$$ 99.8940i 1.69312i −0.532294 0.846559i $$-0.678670\pi$$
0.532294 0.846559i $$-0.321330\pi$$
$$60$$ 43.5658 17.1334i 0.726097 0.285557i
$$61$$ 44.6768i 0.732406i −0.930535 0.366203i $$-0.880658\pi$$
0.930535 0.366203i $$-0.119342\pi$$
$$62$$ 49.2664 + 49.2664i 0.794619 + 0.794619i
$$63$$ 18.4433 60.2399i 0.292752 0.956189i
$$64$$ 33.4577i 0.522776i
$$65$$ −49.2100 61.4940i −0.757077 0.946061i
$$66$$ 42.3881 136.937i 0.642244 2.07480i
$$67$$ −18.0239 18.0239i −0.269013 0.269013i 0.559689 0.828702i $$-0.310920\pi$$
−0.828702 + 0.559689i $$0.810920\pi$$
$$68$$ −2.08117 + 2.08117i −0.0306054 + 0.0306054i
$$69$$ 2.76536 8.93362i 0.0400777 0.129473i
$$70$$ −52.1668 + 77.4710i −0.745240 + 1.10673i
$$71$$ 6.35575i 0.0895177i 0.998998 + 0.0447588i $$0.0142519\pi$$
−0.998998 + 0.0447588i $$0.985748\pi$$
$$72$$ −20.7521 + 3.88391i −0.288224 + 0.0539431i
$$73$$ 55.3597 + 55.3597i 0.758352 + 0.758352i 0.976022 0.217671i $$-0.0698458\pi$$
−0.217671 + 0.976022i $$0.569846\pi$$
$$74$$ 157.242 2.12489
$$75$$ 19.5843 + 72.3979i 0.261124 + 0.965305i
$$76$$ 33.7430i 0.443987i
$$77$$ 37.4336 + 119.622i 0.486150 + 1.55353i
$$78$$ −58.8133 111.548i −0.754017 1.43010i
$$79$$ 59.7832i 0.756749i −0.925653 0.378375i $$-0.876483\pi$$
0.925653 0.378375i $$-0.123517\pi$$
$$80$$ 93.1460 + 10.3357i 1.16432 + 0.129196i
$$81$$ −29.2934 75.5175i −0.361646 0.932315i
$$82$$ 12.9438 12.9438i 0.157851 0.157851i
$$83$$ −42.2387 + 42.2387i −0.508900 + 0.508900i −0.914189 0.405289i $$-0.867171\pi$$
0.405289 + 0.914189i $$0.367171\pi$$
$$84$$ −46.2000 + 46.4862i −0.550000 + 0.553407i
$$85$$ −2.94617 3.68160i −0.0346608 0.0433130i
$$86$$ 142.248i 1.65405i
$$87$$ −32.1402 60.9585i −0.369428 0.700673i
$$88$$ 29.7017 29.7017i 0.337519 0.337519i
$$89$$ 58.4197i 0.656401i 0.944608 + 0.328200i $$0.106442\pi$$
−0.944608 + 0.328200i $$0.893558\pi$$
$$90$$ 8.93864 + 119.750i 0.0993182 + 1.33055i
$$91$$ 97.6954 + 51.1248i 1.07358 + 0.561811i
$$92$$ −6.87928 + 6.87928i −0.0747748 + 0.0747748i
$$93$$ −69.2875 + 36.5317i −0.745027 + 0.392814i
$$94$$ 20.9677 0.223060
$$95$$ −53.7296 5.96197i −0.565574 0.0627576i
$$96$$ 116.450 + 36.0466i 1.21302 + 0.375486i
$$97$$ 11.1921 11.1921i 0.115383 0.115383i −0.647058 0.762441i $$-0.724001\pi$$
0.762441 + 0.647058i $$0.224001\pi$$
$$98$$ 23.2603 128.671i 0.237350 1.31297i
$$99$$ 132.972 + 91.0454i 1.34315 + 0.919650i
$$100$$ 17.1047 76.1251i 0.171047 0.761251i
$$101$$ 11.9219 0.118038 0.0590191 0.998257i $$-0.481203\pi$$
0.0590191 + 0.998257i $$0.481203\pi$$
$$102$$ −3.52111 6.67829i −0.0345207 0.0654734i
$$103$$ −24.4345 24.4345i −0.237229 0.237229i 0.578473 0.815702i $$-0.303649\pi$$
−0.815702 + 0.578473i $$0.803649\pi$$
$$104$$ 36.9514i 0.355302i
$$105$$ −65.8578 81.7786i −0.627217 0.778844i
$$106$$ 122.482 1.15549
$$107$$ −36.8755 + 36.8755i −0.344631 + 0.344631i −0.858105 0.513474i $$-0.828358\pi$$
0.513474 + 0.858105i $$0.328358\pi$$
$$108$$ −9.68369 + 83.7066i −0.0896638 + 0.775061i
$$109$$ 53.8082i 0.493653i −0.969060 0.246827i $$-0.920612\pi$$
0.969060 0.246827i $$-0.0793879\pi$$
$$110$$ −149.274 186.537i −1.35704 1.69579i
$$111$$ −52.2729 + 168.870i −0.470927 + 1.52135i
$$112$$ −125.217 + 39.1844i −1.11801 + 0.349860i
$$113$$ 83.5360 + 83.5360i 0.739257 + 0.739257i 0.972434 0.233177i $$-0.0749122\pi$$
−0.233177 + 0.972434i $$0.574912\pi$$
$$114$$ −82.6839 25.5944i −0.725297 0.224512i
$$115$$ −9.73852 12.1695i −0.0846828 0.105822i
$$116$$ 71.6902i 0.618019i
$$117$$ 139.348 26.0800i 1.19101 0.222906i
$$118$$ −188.492 188.492i −1.59739 1.59739i
$$119$$ 5.84896 + 3.06081i 0.0491509 + 0.0257211i
$$120$$ −14.0486 + 32.2613i −0.117072 + 0.268844i
$$121$$ −199.627 −1.64981
$$122$$ −84.3014 84.3014i −0.690995 0.690995i
$$123$$ 9.59801 + 18.2040i 0.0780326 + 0.148000i
$$124$$ 81.4855 0.657141
$$125$$ 118.193 + 40.6864i 0.945545 + 0.325491i
$$126$$ −78.8666 148.469i −0.625926 1.17832i
$$127$$ 147.690 + 147.690i 1.16291 + 1.16291i 0.983835 + 0.179080i $$0.0573121\pi$$
0.179080 + 0.983835i $$0.442688\pi$$
$$128$$ 51.7981 + 51.7981i 0.404673 + 0.404673i
$$129$$ −152.767 47.2884i −1.18424 0.366577i
$$130$$ −208.889 23.1789i −1.60684 0.178299i
$$131$$ −131.274 −1.00209 −0.501046 0.865421i $$-0.667051\pi$$
−0.501046 + 0.865421i $$0.667051\pi$$
$$132$$ −78.1906 148.300i −0.592353 1.12348i
$$133$$ 72.2291 22.6028i 0.543076 0.169946i
$$134$$ −68.0192 −0.507606
$$135$$ −131.577 30.2094i −0.974641 0.223774i
$$136$$ 2.21226i 0.0162666i
$$137$$ 68.1163 68.1163i 0.497199 0.497199i −0.413366 0.910565i $$-0.635647\pi$$
0.910565 + 0.413366i $$0.135647\pi$$
$$138$$ −11.6390 22.0750i −0.0843406 0.159964i
$$139$$ −30.1138 −0.216646 −0.108323 0.994116i $$-0.534548\pi$$
−0.108323 + 0.994116i $$0.534548\pi$$
$$140$$ 20.9263 + 107.209i 0.149474 + 0.765779i
$$141$$ −6.97041 + 22.5182i −0.0494355 + 0.159704i
$$142$$ 11.9928 + 11.9928i 0.0844563 + 0.0844563i
$$143$$ −199.444 + 199.444i −1.39471 + 1.39471i
$$144$$ −95.3037 + 139.191i −0.661831 + 0.966604i
$$145$$ −114.154 12.6668i −0.787266 0.0873570i
$$146$$ 208.918 1.43095
$$147$$ 130.454 + 67.7553i 0.887441 + 0.460921i
$$148$$ 130.037 130.037i 0.878631 0.878631i
$$149$$ 92.4633 0.620559 0.310280 0.950645i $$-0.399577\pi$$
0.310280 + 0.950645i $$0.399577\pi$$
$$150$$ 173.563 + 99.6549i 1.15709 + 0.664366i
$$151$$ −12.2683 −0.0812472 −0.0406236 0.999175i $$-0.512934\pi$$
−0.0406236 + 0.999175i $$0.512934\pi$$
$$152$$ −17.9342 17.9342i −0.117988 0.117988i
$$153$$ 8.34269 1.56139i 0.0545274 0.0102052i
$$154$$ 296.351 + 155.083i 1.92436 + 1.00703i
$$155$$ −14.3975 + 129.751i −0.0928870 + 0.837102i
$$156$$ −140.887 43.6108i −0.903121 0.279557i
$$157$$ −63.9309 + 63.9309i −0.407203 + 0.407203i −0.880762 0.473559i $$-0.842969\pi$$
0.473559 + 0.880762i $$0.342969\pi$$
$$158$$ −112.806 112.806i −0.713962 0.713962i
$$159$$ −40.7174 + 131.540i −0.256084 + 0.827292i
$$160$$ 158.630 126.942i 0.991439 0.793390i
$$161$$ 19.3337 + 10.1175i 0.120085 + 0.0628414i
$$162$$ −197.770 87.2212i −1.22080 0.538403i
$$163$$ −10.2931 + 10.2931i −0.0631481 + 0.0631481i −0.737976 0.674827i $$-0.764218\pi$$
0.674827 + 0.737976i $$0.264218\pi$$
$$164$$ 21.4088i 0.130541i
$$165$$ 249.955 98.3017i 1.51488 0.595768i
$$166$$ 159.402i 0.960253i
$$167$$ −57.7311 57.7311i −0.345695 0.345695i 0.512808 0.858503i $$-0.328605\pi$$
−0.858503 + 0.512808i $$0.828605\pi$$
$$168$$ −0.152100 49.2621i −0.000905359 0.293227i
$$169$$ 79.1253i 0.468197i
$$170$$ −12.5061 1.38770i −0.0735650 0.00816296i
$$171$$ 54.9742 80.2898i 0.321487 0.469531i
$$172$$ 117.638 + 117.638i 0.683940 + 0.683940i
$$173$$ 179.111 179.111i 1.03532 1.03532i 0.0359688 0.999353i $$-0.488548\pi$$
0.999353 0.0359688i $$-0.0114517\pi$$
$$174$$ −175.670 54.3777i −1.00960 0.312516i
$$175$$ −174.408 + 14.3788i −0.996619 + 0.0821647i
$$176$$ 335.623i 1.90695i
$$177$$ 265.092 139.769i 1.49770 0.789657i
$$178$$ 110.233 + 110.233i 0.619287 + 0.619287i
$$179$$ −307.914 −1.72019 −0.860095 0.510133i $$-0.829596\pi$$
−0.860095 + 0.510133i $$0.829596\pi$$
$$180$$ 106.424 + 91.6394i 0.591243 + 0.509108i
$$181$$ 124.967i 0.690428i 0.938524 + 0.345214i $$0.112194\pi$$
−0.938524 + 0.345214i $$0.887806\pi$$
$$182$$ 280.812 87.8749i 1.54292 0.482829i
$$183$$ 118.560 62.5106i 0.647870 0.341588i
$$184$$ 7.31259i 0.0397423i
$$185$$ 184.085 + 230.037i 0.995053 + 1.24344i
$$186$$ −61.8076 + 199.672i −0.332299 + 1.07351i
$$187$$ −11.9406 + 11.9406i −0.0638532 + 0.0638532i
$$188$$ 17.3400 17.3400i 0.0922342 0.0922342i
$$189$$ 185.666 35.3424i 0.982361 0.186997i
$$190$$ −112.633 + 90.1336i −0.592806 + 0.474387i
$$191$$ 120.234i 0.629496i −0.949175 0.314748i $$-0.898080\pi$$
0.949175 0.314748i $$-0.101920\pi$$
$$192$$ 88.7878 46.8132i 0.462437 0.243819i
$$193$$ −12.8649 + 12.8649i −0.0666576 + 0.0666576i −0.739650 0.672992i $$-0.765009\pi$$
0.672992 + 0.739650i $$0.265009\pi$$
$$194$$ 42.2372i 0.217718i
$$195$$ 94.3353 216.631i 0.483771 1.11093i
$$196$$ −87.1737 125.646i −0.444764 0.641050i
$$197$$ −7.82035 + 7.82035i −0.0396972 + 0.0396972i −0.726677 0.686980i $$-0.758936\pi$$
0.686980 + 0.726677i $$0.258936\pi$$
$$198$$ 422.702 79.1117i 2.13486 0.399554i
$$199$$ 301.160 1.51336 0.756682 0.653783i $$-0.226819\pi$$
0.756682 + 0.653783i $$0.226819\pi$$
$$200$$ 31.3690 + 49.5510i 0.156845 + 0.247755i
$$201$$ 22.6120 73.0491i 0.112498 0.363429i
$$202$$ 22.4956 22.4956i 0.111364 0.111364i
$$203$$ 153.458 48.0218i 0.755949 0.236560i
$$204$$ −8.43479 2.61095i −0.0413470 0.0127988i
$$205$$ 34.0896 + 3.78266i 0.166291 + 0.0184520i
$$206$$ −92.2120 −0.447631
$$207$$ 27.5767 5.16117i 0.133221 0.0249332i
$$208$$ −208.772 208.772i −1.00371 1.00371i
$$209$$ 193.598i 0.926305i
$$210$$ −278.578 30.0413i −1.32656 0.143054i
$$211$$ −363.605 −1.72325 −0.861623 0.507549i $$-0.830552\pi$$
−0.861623 + 0.507549i $$0.830552\pi$$
$$212$$ 101.291 101.291i 0.477789 0.477789i
$$213$$ −16.8665 + 8.89282i −0.0791854 + 0.0417503i
$$214$$ 139.162i 0.650291i
$$215$$ −208.102 + 166.531i −0.967915 + 0.774565i
$$216$$ −39.3427 49.6363i −0.182142 0.229798i
$$217$$ −54.5832 174.425i −0.251535 0.803802i
$$218$$ −101.532 101.532i −0.465742 0.465742i
$$219$$ −69.4520 + 224.368i −0.317132 + 1.02451i
$$220$$ −277.712 30.8157i −1.26233 0.140071i
$$221$$ 14.8551i 0.0672176i
$$222$$ 220.009 + 417.278i 0.991032 + 1.87963i
$$223$$ −21.1671 21.1671i −0.0949198 0.0949198i 0.658052 0.752972i $$-0.271381\pi$$
−0.752972 + 0.658052i $$0.771381\pi$$
$$224$$ −131.882 + 252.016i −0.588758 + 1.12507i
$$225$$ −164.723 + 153.269i −0.732102 + 0.681195i
$$226$$ 315.251 1.39492
$$227$$ −190.960 190.960i −0.841234 0.841234i 0.147785 0.989019i $$-0.452785\pi$$
−0.989019 + 0.147785i $$0.952785\pi$$
$$228$$ −89.5449 + 47.2124i −0.392741 + 0.207072i
$$229$$ 84.1627 0.367523 0.183761 0.982971i $$-0.441173\pi$$
0.183761 + 0.982971i $$0.441173\pi$$
$$230$$ −41.3386 4.58704i −0.179733 0.0199436i
$$231$$ −265.069 + 266.711i −1.14748 + 1.15459i
$$232$$ −38.1029 38.1029i −0.164237 0.164237i
$$233$$ −227.465 227.465i −0.976246 0.976246i 0.0234784 0.999724i $$-0.492526\pi$$
−0.999724 + 0.0234784i $$0.992526\pi$$
$$234$$ 213.728 312.150i 0.913368 1.33397i
$$235$$ 24.5471 + 30.6746i 0.104456 + 0.130530i
$$236$$ −311.761 −1.32102
$$237$$ 158.649 83.6472i 0.669404 0.352942i
$$238$$ 16.8120 5.26101i 0.0706386 0.0221051i
$$239$$ 19.0852 0.0798543 0.0399272 0.999203i $$-0.487287\pi$$
0.0399272 + 0.999203i $$0.487287\pi$$
$$240$$ 102.899 + 261.646i 0.428747 + 1.09019i
$$241$$ 345.423i 1.43329i −0.697438 0.716645i $$-0.745677\pi$$
0.697438 0.716645i $$-0.254323\pi$$
$$242$$ −376.679 + 376.679i −1.55652 + 1.55652i
$$243$$ 159.417 183.399i 0.656037 0.754729i
$$244$$ −139.433 −0.571445
$$245$$ 215.470 116.608i 0.879471 0.475952i
$$246$$ 52.4601 + 16.2388i 0.213252 + 0.0660112i
$$247$$ 120.426 + 120.426i 0.487556 + 0.487556i
$$248$$ −43.3090 + 43.3090i −0.174633 + 0.174633i
$$249$$ −171.190 52.9910i −0.687509 0.212815i
$$250$$ 299.793 146.249i 1.19917 0.584995i
$$251$$ 253.938 1.01170 0.505852 0.862620i $$-0.331178\pi$$
0.505852 + 0.862620i $$0.331178\pi$$
$$252$$ −188.004 57.5602i −0.746047 0.228414i
$$253$$ −39.4694 + 39.4694i −0.156005 + 0.156005i
$$254$$ 557.358 2.19432
$$255$$ 5.64779 12.9696i 0.0221482 0.0508610i
$$256$$ 329.309 1.28636
$$257$$ −295.955 295.955i −1.15158 1.15158i −0.986237 0.165340i $$-0.947128\pi$$
−0.165340 0.986237i $$-0.552872\pi$$
$$258$$ −377.489 + 199.030i −1.46313 + 0.771435i
$$259$$ −365.459 191.248i −1.41104 0.738408i
$$260$$ −191.918 + 153.581i −0.738146 + 0.590694i
$$261$$ 116.798 170.583i 0.447502 0.653576i
$$262$$ −247.703 + 247.703i −0.945433 + 0.945433i
$$263$$ −1.73180 1.73180i −0.00658477 0.00658477i 0.703807 0.710392i $$-0.251482\pi$$
−0.710392 + 0.703807i $$0.751482\pi$$
$$264$$ 120.378 + 37.2625i 0.455978 + 0.141146i
$$265$$ 143.391 + 179.185i 0.541098 + 0.676169i
$$266$$ 93.6408 178.940i 0.352033 0.672707i
$$267$$ −155.030 + 81.7394i −0.580638 + 0.306140i
$$268$$ −56.2511 + 56.2511i −0.209892 + 0.209892i
$$269$$ 400.956i 1.49054i −0.666761 0.745272i $$-0.732320\pi$$
0.666761 0.745272i $$-0.267680\pi$$
$$270$$ −305.277 + 191.271i −1.13066 + 0.708413i
$$271$$ 395.831i 1.46063i 0.683109 + 0.730316i $$0.260627\pi$$
−0.683109 + 0.730316i $$0.739373\pi$$
$$272$$ −12.4990 12.4990i −0.0459523 0.0459523i
$$273$$ 1.02134 + 330.790i 0.00374117 + 1.21169i
$$274$$ 257.060i 0.938174i
$$275$$ 98.1367 436.762i 0.356861 1.58822i
$$276$$ −27.8811 8.63047i −0.101019 0.0312698i
$$277$$ −40.6213 40.6213i −0.146647 0.146647i 0.629971 0.776618i $$-0.283067\pi$$
−0.776618 + 0.629971i $$0.783067\pi$$
$$278$$ −56.8222 + 56.8222i −0.204397 + 0.204397i
$$279$$ −193.891 132.756i −0.694949 0.475830i
$$280$$ −68.1031 45.8587i −0.243225 0.163781i
$$281$$ 284.890i 1.01384i 0.861992 + 0.506922i $$0.169217\pi$$
−0.861992 + 0.506922i $$0.830783\pi$$
$$282$$ 29.3374 + 55.6426i 0.104033 + 0.197314i
$$283$$ 102.657 + 102.657i 0.362744 + 0.362744i 0.864822 0.502078i $$-0.167431\pi$$
−0.502078 + 0.864822i $$0.667431\pi$$
$$284$$ 19.8358 0.0698444
$$285$$ −59.3556 150.926i −0.208265 0.529565i
$$286$$ 752.668i 2.63171i
$$287$$ −45.8269 + 14.3407i −0.159676 + 0.0499676i
$$288$$ 67.2762 + 359.464i 0.233598 + 1.24814i
$$289$$ 288.111i 0.996923i
$$290$$ −239.300 + 191.497i −0.825171 + 0.660336i
$$291$$ 45.3606 + 14.0412i 0.155879 + 0.0482515i
$$292$$ 172.773 172.773i 0.591689 0.591689i
$$293$$ −204.227 + 204.227i −0.697021 + 0.697021i −0.963767 0.266746i $$-0.914052\pi$$
0.266746 + 0.963767i $$0.414052\pi$$
$$294$$ 374.005 118.307i 1.27212 0.402405i
$$295$$ 55.0844 496.423i 0.186727 1.68279i
$$296$$ 138.228i 0.466987i
$$297$$ −55.5594 + 480.260i −0.187069 + 1.61704i
$$298$$ 174.471 174.471i 0.585472 0.585472i
$$299$$ 49.1033i 0.164225i
$$300$$ 225.948 61.1211i 0.753160 0.203737i
$$301$$ 173.011 330.611i 0.574789 1.09838i
$$302$$ −23.1493 + 23.1493i −0.0766534 + 0.0766534i
$$303$$ 16.6808 + 31.6374i 0.0550520 + 0.104414i
$$304$$ −202.653 −0.666621
$$305$$ 24.6360 222.021i 0.0807738 0.727938i
$$306$$ 12.7958 18.6882i 0.0418162 0.0610725i
$$307$$ 209.811 209.811i 0.683425 0.683425i −0.277345 0.960770i $$-0.589455\pi$$
0.960770 + 0.277345i $$0.0894547\pi$$
$$308$$ 373.331 116.827i 1.21211 0.379309i
$$309$$ 30.6546 99.0310i 0.0992058 0.320489i
$$310$$ 217.662 + 271.996i 0.702137 + 0.877407i
$$311$$ 414.961 1.33428 0.667141 0.744932i $$-0.267518\pi$$
0.667141 + 0.744932i $$0.267518\pi$$
$$312$$ 98.0593 51.7016i 0.314293 0.165710i
$$313$$ 6.05318 + 6.05318i 0.0193392 + 0.0193392i 0.716710 0.697371i $$-0.245647\pi$$
−0.697371 + 0.716710i $$0.745647\pi$$
$$314$$ 241.265i 0.768359i
$$315$$ 124.872 289.192i 0.396420 0.918069i
$$316$$ −186.579 −0.590439
$$317$$ −255.502 + 255.502i −0.805999 + 0.805999i −0.984026 0.178027i $$-0.943029\pi$$
0.178027 + 0.984026i $$0.443029\pi$$
$$318$$ 171.374 + 325.035i 0.538911 + 1.02212i
$$319$$ 411.317i 1.28939i
$$320$$ 18.4495 166.268i 0.0576547 0.519588i
$$321$$ −149.453 46.2625i −0.465586 0.144120i
$$322$$ 55.5719 17.3902i 0.172583 0.0540069i
$$323$$ 7.20984 + 7.20984i 0.0223215 + 0.0223215i
$$324$$ −235.684 + 91.4223i −0.727421 + 0.282168i
$$325$$ −210.640 332.730i −0.648122 1.02378i
$$326$$ 38.8446i 0.119155i
$$327$$ 142.793 75.2872i 0.436675 0.230236i
$$328$$ 11.3786 + 11.3786i 0.0346909 + 0.0346909i
$$329$$ −48.7327 25.5022i −0.148124 0.0775144i
$$330$$ 286.158 657.133i 0.867147 1.99131i
$$331$$ 148.520 0.448702 0.224351 0.974508i $$-0.427974\pi$$
0.224351 + 0.974508i $$0.427974\pi$$
$$332$$ 131.824 + 131.824i 0.397059 + 0.397059i
$$333$$ −521.275 + 97.5603i −1.56539 + 0.292974i
$$334$$ −217.868 −0.652299
$$335$$ −79.6308 99.5085i −0.237704 0.297040i
$$336$$ −279.185 277.467i −0.830909 0.825794i
$$337$$ 225.218 + 225.218i 0.668303 + 0.668303i 0.957323 0.289020i $$-0.0933294\pi$$
−0.289020 + 0.957323i $$0.593329\pi$$
$$338$$ 149.303 + 149.303i 0.441725 + 0.441725i
$$339$$ −104.801 + 338.564i −0.309147 + 0.998714i
$$340$$ −11.4900 + 9.19476i −0.0337941 + 0.0270434i
$$341$$ 467.517 1.37102
$$342$$ −47.7685 255.232i −0.139674 0.746293i
$$343$$ −210.559 + 270.765i −0.613876 + 0.789402i
$$344$$ −125.047 −0.363510
$$345$$ 18.6687 42.8707i 0.0541122 0.124263i
$$346$$ 675.934i 1.95357i
$$347$$ −81.8789 + 81.8789i −0.235962 + 0.235962i −0.815176 0.579214i $$-0.803360\pi$$
0.579214 + 0.815176i $$0.303360\pi$$
$$348$$ −190.247 + 100.307i −0.546686 + 0.288239i
$$349$$ −356.670 −1.02198 −0.510989 0.859587i $$-0.670721\pi$$
−0.510989 + 0.859587i $$0.670721\pi$$
$$350$$ −301.963 + 356.226i −0.862750 + 1.01779i
$$351$$ 264.182 + 333.303i 0.752656 + 0.949582i
$$352$$ −514.486 514.486i −1.46161 1.46161i
$$353$$ 305.766 305.766i 0.866191 0.866191i −0.125857 0.992048i $$-0.540168\pi$$
0.992048 + 0.125857i $$0.0401681\pi$$
$$354$$ 236.474 763.940i 0.668006 2.15802i
$$355$$ −3.50474 + 31.5849i −0.00987251 + 0.0889716i
$$356$$ 182.323 0.512144
$$357$$ 0.0611469 + 19.8042i 0.000171280 + 0.0554739i
$$358$$ −581.009 + 581.009i −1.62293 + 1.62293i
$$359$$ 356.776 0.993806 0.496903 0.867806i $$-0.334470\pi$$
0.496903 + 0.867806i $$0.334470\pi$$
$$360$$ −105.269 + 7.85776i −0.292415 + 0.0218271i
$$361$$ −244.103 −0.676187
$$362$$ 235.803 + 235.803i 0.651390 + 0.651390i
$$363$$ −279.313 529.756i −0.769456 1.45938i
$$364$$ 159.557 304.900i 0.438342 0.837637i
$$365$$ 244.583 + 305.637i 0.670090 + 0.837361i
$$366$$ 105.761 341.666i 0.288965 0.933514i
$$367$$ 185.321 185.321i 0.504963 0.504963i −0.408013 0.912976i $$-0.633778\pi$$
0.912976 + 0.408013i $$0.133778\pi$$
$$368$$ −41.3154 41.3154i −0.112270 0.112270i
$$369$$ −34.8792 + 50.9411i −0.0945237 + 0.138052i
$$370$$ 781.414 + 86.7076i 2.11193 + 0.234345i
$$371$$ −284.671 148.971i −0.767307 0.401538i
$$372$$ 114.013 + 216.241i 0.306485 + 0.581293i
$$373$$ −231.949 + 231.949i −0.621848 + 0.621848i −0.946004 0.324155i $$-0.894920\pi$$
0.324155 + 0.946004i $$0.394920\pi$$
$$374$$ 45.0617i 0.120486i
$$375$$ 57.4020 + 370.581i 0.153072 + 0.988215i
$$376$$ 18.4322i 0.0490219i
$$377$$ 255.857 + 255.857i 0.678666 + 0.678666i
$$378$$ 283.649 417.025i 0.750393 1.10324i
$$379$$ 33.7232i 0.0889794i −0.999010 0.0444897i $$-0.985834\pi$$
0.999010 0.0444897i $$-0.0141662\pi$$
$$380$$ −18.6068 + 167.686i −0.0489654 + 0.441278i
$$381$$ −185.286 + 598.575i −0.486315 + 1.57106i
$$382$$ −226.871 226.871i −0.593904 0.593904i
$$383$$ −353.025 + 353.025i −0.921735 + 0.921735i −0.997152 0.0754169i $$-0.975971\pi$$
0.0754169 + 0.997152i $$0.475971\pi$$
$$384$$ −64.9838 + 209.933i −0.169229 + 0.546701i
$$385$$ 120.063 + 615.104i 0.311852 + 1.59767i
$$386$$ 48.5501i 0.125777i
$$387$$ −88.2574 471.569i −0.228055 1.21852i
$$388$$ −34.9297 34.9297i −0.0900250 0.0900250i
$$389$$ 222.963 0.573170 0.286585 0.958055i $$-0.407480\pi$$
0.286585 + 0.958055i $$0.407480\pi$$
$$390$$ −230.762 586.768i −0.591698 1.50453i
$$391$$ 2.93978i 0.00751862i
$$392$$ 113.112 + 20.4476i 0.288551 + 0.0521623i
$$393$$ −183.675 348.366i −0.467367 0.886429i
$$394$$ 29.5127i 0.0749054i
$$395$$ 32.9661 297.093i 0.0834586 0.752133i
$$396$$ 284.145 414.994i 0.717539 1.04797i
$$397$$ −518.609 + 518.609i −1.30632 + 1.30632i −0.382270 + 0.924051i $$0.624857\pi$$
−0.924051 + 0.382270i $$0.875143\pi$$
$$398$$ 568.264 568.264i 1.42780 1.42780i
$$399$$ 161.043 + 160.052i 0.403617 + 0.401132i
$$400$$ 457.190 + 102.727i 1.14297 + 0.256817i
$$401$$ 333.028i 0.830494i 0.909709 + 0.415247i $$0.136305\pi$$
−0.909709 + 0.415247i $$0.863695\pi$$
$$402$$ −95.1707 180.505i −0.236743 0.449017i
$$403$$ 290.816 290.816i 0.721628 0.721628i
$$404$$ 37.2072i 0.0920969i
$$405$$ −103.931 391.438i −0.256619 0.966513i
$$406$$ 198.949 380.175i 0.490022 0.936392i
$$407$$ 746.079 746.079i 1.83312 1.83312i
$$408$$ 5.87074 3.09534i 0.0143891 0.00758661i
$$409$$ 634.549 1.55146 0.775732 0.631062i $$-0.217381\pi$$
0.775732 + 0.631062i $$0.217381\pi$$
$$410$$ 71.4618 57.1866i 0.174297 0.139480i
$$411$$ 276.069 + 85.4559i 0.671701 + 0.207922i
$$412$$ −76.2583 + 76.2583i −0.185093 + 0.185093i
$$413$$ 208.834 + 667.346i 0.505651 + 1.61585i
$$414$$ 42.2962 61.7736i 0.102165 0.149212i
$$415$$ −233.197 + 186.614i −0.561920 + 0.449671i
$$416$$ −640.065 −1.53862
$$417$$ −42.1345 79.9140i −0.101042 0.191640i
$$418$$ 365.303 + 365.303i 0.873931 + 0.873931i
$$419$$ 415.098i 0.990687i −0.868697 0.495343i $$-0.835042\pi$$
0.868697 0.495343i $$-0.164958\pi$$
$$420$$ −255.225 + 205.537i −0.607678 + 0.489374i
$$421$$ 425.874 1.01158 0.505789 0.862657i $$-0.331201\pi$$
0.505789 + 0.862657i $$0.331201\pi$$
$$422$$ −686.093 + 686.093i −1.62581 + 1.62581i
$$423$$ −69.5102 + 13.0093i −0.164327 + 0.0307549i
$$424$$ 107.671i 0.253942i
$$425$$ −12.6108 19.9203i −0.0296726 0.0468713i
$$426$$ −15.0457 + 48.6057i −0.0353185 + 0.114098i
$$427$$ 93.3992 + 298.465i 0.218733 + 0.698981i
$$428$$ 115.086 + 115.086i 0.268892 + 0.268892i
$$429$$ −808.327 250.214i −1.88421 0.583249i
$$430$$ −78.4396 + 706.902i −0.182418 + 1.64396i
$$431$$ 217.914i 0.505600i −0.967519 0.252800i $$-0.918649\pi$$
0.967519 0.252800i $$-0.0813514\pi$$
$$432$$ −502.723 58.1580i −1.16371 0.134625i
$$433$$ 377.736 + 377.736i 0.872369 + 0.872369i 0.992730 0.120361i $$-0.0384052\pi$$
−0.120361 + 0.992730i $$0.538405\pi$$
$$434$$ −432.120 226.132i −0.995668 0.521041i
$$435$$ −126.107 320.656i −0.289900 0.737141i
$$436$$ −167.931 −0.385163
$$437$$ 23.8320 + 23.8320i 0.0545355 + 0.0545355i
$$438$$ 292.313 + 554.414i 0.667382 + 1.26579i
$$439$$ 18.8677 0.0429789 0.0214894 0.999769i $$-0.493159\pi$$
0.0214894 + 0.999769i $$0.493159\pi$$
$$440$$ 163.981 131.224i 0.372683 0.298236i
$$441$$ 2.72321 + 440.992i 0.00617509 + 0.999981i
$$442$$ 28.0303 + 28.0303i 0.0634171 + 0.0634171i
$$443$$ −484.487 484.487i −1.09365 1.09365i −0.995136 0.0985149i $$-0.968591\pi$$
−0.0985149 0.995136i $$-0.531409\pi$$
$$444$$ 527.030 + 163.140i 1.18700 + 0.367431i
$$445$$ −32.2143 + 290.317i −0.0723916 + 0.652397i
$$446$$ −79.8812 −0.179106
$$447$$ 129.372 + 245.373i 0.289424 + 0.548933i
$$448$$ 69.9451 + 223.515i 0.156127 + 0.498918i
$$449$$ −801.204 −1.78442 −0.892209 0.451623i $$-0.850845\pi$$
−0.892209 + 0.451623i $$0.850845\pi$$
$$450$$ −21.6128 + 600.025i −0.0480283 + 1.33339i
$$451$$ 122.831i 0.272353i
$$452$$ 260.709 260.709i 0.576791 0.576791i
$$453$$ −17.1655 32.5569i −0.0378930 0.0718695i
$$454$$ −720.652 −1.58734
$$455$$ 457.306 + 307.937i 1.00507 + 0.676784i
$$456$$ 22.4995 72.6856i 0.0493410 0.159398i
$$457$$ −407.879 407.879i −0.892515 0.892515i 0.102244 0.994759i $$-0.467398\pi$$
−0.994759 + 0.102244i $$0.967398\pi$$
$$458$$ 158.808 158.808i 0.346743 0.346743i
$$459$$ 15.8164 + 19.9546i 0.0344584 + 0.0434741i
$$460$$ −37.9800 + 30.3932i −0.0825653 + 0.0660721i
$$461$$ −627.296 −1.36073 −0.680365 0.732874i $$-0.738179\pi$$
−0.680365 + 0.732874i $$0.738179\pi$$
$$462$$ 3.09815 + 1003.43i 0.00670595 + 2.17192i
$$463$$ 576.012 576.012i 1.24409 1.24409i 0.285797 0.958290i $$-0.407742\pi$$
0.958290 0.285797i $$-0.0922584\pi$$
$$464$$ −430.555 −0.927920
$$465$$ −364.469 + 143.337i −0.783804 + 0.308252i
$$466$$ −858.417 −1.84210
$$467$$ −239.537 239.537i −0.512928 0.512928i 0.402495 0.915422i $$-0.368143\pi$$
−0.915422 + 0.402495i $$0.868143\pi$$
$$468$$ −81.3938 434.895i −0.173918 0.929264i
$$469$$ 158.089 + 82.7293i 0.337077 + 0.176395i
$$470$$ 104.199 + 11.5622i 0.221700 + 0.0246003i
$$471$$ −259.106 80.2051i −0.550119 0.170287i
$$472$$ 165.699 165.699i 0.351058 0.351058i
$$473$$ 674.937 + 674.937i 1.42693 + 1.42693i
$$474$$ 141.522 457.193i 0.298569 0.964542i
$$475$$ −263.722 59.2560i −0.555203 0.124749i
$$476$$ 9.55254 18.2541i 0.0200684 0.0383490i
$$477$$ −406.042 + 75.9936i −0.851241 + 0.159316i
$$478$$ 36.0122 36.0122i 0.0753393 0.0753393i
$$479$$ 868.698i 1.81357i 0.421598 + 0.906783i $$0.361469\pi$$
−0.421598 + 0.906783i $$0.638531\pi$$
$$480$$ 558.823 + 243.348i 1.16421 + 0.506975i
$$481$$ 928.188i 1.92970i
$$482$$ −651.785 651.785i −1.35225 1.35225i
$$483$$ 0.202120 + 65.4625i 0.000418468 + 0.135533i
$$484$$ 623.019i 1.28723i
$$485$$ 61.7909 49.4476i 0.127404 0.101954i
$$486$$ −45.2524 646.866i −0.0931119 1.33100i
$$487$$ 1.87718 + 1.87718i 0.00385458 + 0.00385458i 0.709031 0.705177i $$-0.249132\pi$$
−0.705177 + 0.709031i $$0.749132\pi$$
$$488$$ 74.1076 74.1076i 0.151860 0.151860i
$$489$$ −41.7171 12.9133i −0.0853111 0.0264077i
$$490$$ 186.545 626.605i 0.380704 1.27879i
$$491$$ 125.302i 0.255198i −0.991826 0.127599i $$-0.959273\pi$$
0.991826 0.127599i $$-0.0407270\pi$$
$$492$$ 56.8132 29.9546i 0.115474 0.0608834i
$$493$$ 15.3180 + 15.3180i 0.0310710 + 0.0310710i
$$494$$ 454.469 0.919978
$$495$$ 610.598 + 525.774i 1.23353 + 1.06217i
$$496$$ 489.383i 0.986660i
$$497$$ −13.2870 42.4599i −0.0267345 0.0854323i
$$498$$ −423.011 + 223.031i −0.849419 + 0.447854i
$$499$$ 426.549i 0.854807i 0.904061 + 0.427403i $$0.140572\pi$$
−0.904061 + 0.427403i $$0.859428\pi$$
$$500$$ 126.979 368.871i 0.253958 0.737743i
$$501$$ 72.4271 233.979i 0.144565 0.467024i
$$502$$ 479.160 479.160i 0.954502 0.954502i
$$503$$ −606.100 + 606.100i −1.20497 + 1.20497i −0.232335 + 0.972636i $$0.574636\pi$$
−0.972636 + 0.232335i $$0.925364\pi$$
$$504$$ 130.516 69.3300i 0.258960 0.137559i
$$505$$ 59.2456 + 6.57404i 0.117318 + 0.0130179i
$$506$$ 148.951i 0.294369i
$$507$$ −209.978 + 110.710i −0.414157 + 0.218363i
$$508$$ 460.929 460.929i 0.907341 0.907341i
$$509$$ 3.90604i 0.00767394i −0.999993 0.00383697i $$-0.998779\pi$$
0.999993 0.00383697i $$-0.00122135\pi$$
$$510$$ −13.8156 35.1294i −0.0270894 0.0688812i
$$511$$ −485.565 254.100i −0.950225 0.497260i
$$512$$ 414.186 414.186i 0.808956 0.808956i
$$513$$ 289.986 + 33.5474i 0.565276 + 0.0653945i
$$514$$ −1116.89 −2.17293
$$515$$ −107.954 134.901i −0.209619 0.261944i
$$516$$ −147.583 + 476.775i −0.286014 + 0.923982i
$$517$$ 99.4871 99.4871i 0.192431 0.192431i
$$518$$ −1050.46 + 328.723i −2.02792 + 0.634600i
$$519$$ 725.919 + 224.705i 1.39869 + 0.432957i
$$520$$ 20.3761 183.630i 0.0391847 0.353135i
$$521$$ −556.444 −1.06803 −0.534015 0.845475i $$-0.679317\pi$$
−0.534015 + 0.845475i $$0.679317\pi$$
$$522$$ −101.489 542.265i −0.194423 1.03882i
$$523$$ −241.019 241.019i −0.460839 0.460839i 0.438092 0.898930i $$-0.355655\pi$$
−0.898930 + 0.438092i $$0.855655\pi$$
$$524$$ 409.696i 0.781862i
$$525$$ −282.185 442.715i −0.537496 0.843266i
$$526$$ −6.53551 −0.0124249
$$527$$ 17.4109 17.4109i 0.0330378 0.0330378i
$$528$$ 890.653 469.595i 1.68684 0.889384i
$$529$$ 519.283i 0.981631i
$$530$$ 608.674 + 67.5400i 1.14844 + 0.127434i
$$531$$ 741.821 + 507.923i 1.39703 + 0.956540i
$$532$$ −70.5415 225.421i −0.132597 0.423724i
$$533$$ −76.4063 76.4063i −0.143351 0.143351i
$$534$$ −138.294 + 446.765i −0.258978 + 0.836639i
$$535$$ −203.587 + 162.919i −0.380537 + 0.304521i
$$536$$ 59.7942i 0.111556i
$$537$$ −430.826 817.122i −0.802283 1.52164i
$$538$$ −756.572 756.572i −1.40627 1.40627i
$$539$$ −500.153 720.883i −0.927927 1.33744i
$$540$$ −94.2813 + 410.640i −0.174595 + 0.760445i
$$541$$ 255.515 0.472302 0.236151 0.971716i $$-0.424114\pi$$
0.236151 + 0.971716i $$0.424114\pi$$
$$542$$ 746.901 + 746.901i 1.37805 + 1.37805i
$$543$$ −331.630 + 174.851i −0.610737 + 0.322010i
$$544$$ −38.3203 −0.0704416
$$545$$ 29.6714 267.400i 0.0544429 0.490642i
$$546$$ 626.101 + 622.247i 1.14671 + 1.13965i
$$547$$ −80.6313 80.6313i −0.147406 0.147406i 0.629552 0.776958i $$-0.283238\pi$$
−0.776958 + 0.629552i $$0.783238\pi$$
$$548$$ −212.586 212.586i −0.387930 0.387930i
$$549$$ 331.773 + 227.164i 0.604323 + 0.413778i
$$550$$ −638.958 1009.31i −1.16174 1.83511i
$$551$$ 248.358 0.450740
$$552$$ 19.4057 10.2316i 0.0351552 0.0185355i
$$553$$ 124.980 + 399.384i 0.226004 + 0.722213i
$$554$$ −153.298 −0.276711
$$555$$ −352.890 + 810.374i −0.635837 + 1.46013i
$$556$$ 93.9827i 0.169034i
$$557$$ 452.948 452.948i 0.813192 0.813192i −0.171919 0.985111i $$-0.554997\pi$$
0.985111 + 0.171919i $$0.0549967\pi$$
$$558$$ −616.357 + 115.356i −1.10458 + 0.206730i
$$559$$ 839.680 1.50211
$$560$$ −643.873 + 125.679i −1.14977 + 0.224426i
$$561$$ −48.3940 14.9801i −0.0862638 0.0267025i
$$562$$ 537.564 + 537.564i 0.956520 + 0.956520i
$$563$$ 534.797 534.797i 0.949906 0.949906i −0.0488978 0.998804i $$-0.515571\pi$$
0.998804 + 0.0488978i $$0.0155709\pi$$
$$564$$ 70.2776 + 21.7541i 0.124606 + 0.0385711i
$$565$$ 369.068 + 461.196i 0.653218 + 0.816277i
$$566$$ 387.409 0.684468
$$567$$ 353.569 + 443.258i 0.623578 + 0.781761i
$$568$$ −10.5426 + 10.5426i −0.0185609 + 0.0185609i
$$569$$ 527.903 0.927773 0.463886 0.885895i $$-0.346455\pi$$
0.463886 + 0.885895i $$0.346455\pi$$
$$570$$ −396.784 172.786i −0.696112 0.303133i
$$571$$ 249.965 0.437767 0.218884 0.975751i $$-0.429759\pi$$
0.218884 + 0.975751i $$0.429759\pi$$
$$572$$ 622.448 + 622.448i 1.08820 + 1.08820i
$$573$$ 319.069 168.228i 0.556839 0.293592i
$$574$$ −59.4118 + 113.531i −0.103505 + 0.197790i
$$575$$ −41.6850 65.8464i −0.0724956 0.114515i
$$576$$ 248.460 + 170.120i 0.431353 + 0.295346i
$$577$$ −63.8107 + 63.8107i −0.110590 + 0.110590i −0.760237 0.649646i $$-0.774917\pi$$
0.649646 + 0.760237i $$0.274917\pi$$
$$578$$ −543.641 543.641i −0.940556 0.940556i
$$579$$ −52.1404 16.1398i −0.0900524 0.0278753i
$$580$$ −39.5320 + 356.264i −0.0681586 + 0.614249i
$$581$$ 193.875 370.480i 0.333692 0.637658i
$$582$$ 112.086 59.0973i 0.192588 0.101542i
$$583$$ 581.151 581.151i 0.996828 0.996828i
$$584$$ 183.656i 0.314479i
$$585$$ 706.873 52.7641i 1.20833 0.0901951i
$$586$$ 770.720i 1.31522i
$$587$$ 748.348 + 748.348i 1.27487 + 1.27487i 0.943502 + 0.331366i $$0.107509\pi$$
0.331366 + 0.943502i $$0.392491\pi$$
$$588$$ 211.459 407.136i 0.359624 0.692409i
$$589$$ 282.292i 0.479273i
$$590$$ −832.770 1040.65i −1.41148 1.76381i
$$591$$ −31.6952 9.81110i −0.0536298 0.0166008i
$$592$$ 780.974 + 780.974i 1.31921 + 1.31921i
$$593$$ −88.6544 + 88.6544i −0.149502 + 0.149502i −0.777895 0.628394i $$-0.783713\pi$$
0.628394 + 0.777895i $$0.283713\pi$$
$$594$$ 801.376 + 1011.05i 1.34912 + 1.70210i
$$595$$ 27.3786 + 18.4360i 0.0460144 + 0.0309848i
$$596$$ 288.571i 0.484179i
$$597$$ 421.375 + 799.198i 0.705821 + 1.33869i
$$598$$ 92.6540 + 92.6540i 0.154940 + 0.154940i
$$599$$ 512.160 0.855025 0.427512 0.904009i $$-0.359390\pi$$
0.427512 + 0.904009i $$0.359390\pi$$
$$600$$ −87.6045 + 152.575i −0.146008 + 0.254292i
$$601$$ 148.766i 0.247530i 0.992312 + 0.123765i $$0.0394969\pi$$
−0.992312 + 0.123765i $$0.960503\pi$$
$$602$$ −297.377 950.294i −0.493982 1.57856i
$$603$$ 225.491 42.2023i 0.373949 0.0699872i
$$604$$ 38.2885i 0.0633915i
$$605$$ −992.044 110.080i −1.63974 0.181950i
$$606$$ 91.1725 + 28.2220i 0.150450 + 0.0465710i
$$607$$ 336.268 336.268i 0.553984 0.553984i −0.373604 0.927588i $$-0.621878\pi$$
0.927588 + 0.373604i $$0.121878\pi$$
$$608$$ −310.652 + 310.652i −0.510941 + 0.510941i
$$609$$ 342.151 + 340.045i 0.561825 + 0.558366i
$$610$$ −372.450 465.422i −0.610573 0.762987i
$$611$$ 123.771i 0.202571i
$$612$$ −4.87299 26.0369i −0.00796240 0.0425439i
$$613$$ −289.428 + 289.428i −0.472151 + 0.472151i −0.902610 0.430459i $$-0.858352\pi$$
0.430459 + 0.902610i $$0.358352\pi$$
$$614$$ 791.794i 1.28957i
$$615$$ 37.6591 + 95.7573i 0.0612343 + 0.155703i
$$616$$ −136.330 + 260.516i −0.221315 + 0.422915i
$$617$$ −759.979 + 759.979i −1.23173 + 1.23173i −0.268434 + 0.963298i $$0.586506\pi$$
−0.963298 + 0.268434i $$0.913494\pi$$
$$618$$ −129.021 244.706i −0.208771 0.395965i
$$619$$ 509.592 0.823251 0.411626 0.911353i $$-0.364961\pi$$
0.411626 + 0.911353i $$0.364961\pi$$
$$620$$ 404.942 + 44.9334i 0.653133 + 0.0724732i
$$621$$ 52.2810 + 65.9598i 0.0841884 + 0.106215i
$$622$$ 782.998 782.998i 1.25884 1.25884i
$$623$$ −122.129 390.275i −0.196034 0.626444i
$$624$$ 261.917 846.134i 0.419738 1.35598i
$$625$$ 564.925 + 267.366i 0.903880 + 0.427786i
$$626$$ 22.8437 0.0364915
$$627$$ −513.757 + 270.877i −0.819390 + 0.432021i
$$628$$ 199.523 + 199.523i 0.317712 + 0.317712i
$$629$$ 55.5699i 0.0883465i
$$630$$ −310.058 781.305i −0.492155 1.24017i
$$631$$ −647.514 −1.02617 −0.513086 0.858337i $$-0.671498\pi$$
−0.513086 + 0.858337i $$0.671498\pi$$
$$632$$ 99.1654 99.1654i 0.156907 0.156907i
$$633$$ −508.747 964.911i −0.803708 1.52435i
$$634$$ 964.221i 1.52085i
$$635$$ 652.506 + 815.387i 1.02757 + 1.28407i
$$636$$ 410.524 + 127.076i 0.645479 + 0.199805i
$$637$$ −759.537 137.304i −1.19237 0.215547i
$$638$$ 776.122 + 776.122i 1.21649 + 1.21649i
$$639$$ −47.1983 32.3166i −0.0738628 0.0505737i
$$640$$ 228.848 + 285.974i 0.357575 + 0.446834i
$$641$$ 428.281i 0.668145i 0.942547 + 0.334072i $$0.108423\pi$$
−0.942547 + 0.334072i $$0.891577\pi$$
$$642$$ −369.300 + 194.712i −0.575233 + 0.303290i
$$643$$ −251.455 251.455i −0.391065 0.391065i 0.484002 0.875067i $$-0.339183\pi$$
−0.875067 + 0.484002i $$0.839183\pi$$
$$644$$ 31.5758 60.3388i 0.0490307 0.0936938i
$$645$$ −733.101 319.240i −1.13659 0.494946i
$$646$$ 27.2087 0.0421188
$$647$$ 245.105 + 245.105i 0.378832 + 0.378832i 0.870681 0.491848i $$-0.163679\pi$$
−0.491848 + 0.870681i $$0.663679\pi$$
$$648$$ 76.6743 173.855i 0.118325 0.268295i
$$649$$ −1788.71 −2.75610
$$650$$ −1025.29 230.375i −1.57738 0.354423i
$$651$$ 386.507 388.901i 0.593712 0.597390i
$$652$$ 32.1241 + 32.1241i 0.0492700 + 0.0492700i
$$653$$ 253.883 + 253.883i 0.388794 + 0.388794i 0.874257 0.485463i $$-0.161349\pi$$
−0.485463 + 0.874257i $$0.661349\pi$$
$$654$$ 127.378 411.499i 0.194767 0.629203i
$$655$$ −652.366 72.3882i −0.995979 0.110516i
$$656$$ 128.576 0.196000
$$657$$ −692.588 + 129.623i −1.05417 + 0.197295i
$$658$$ −140.075 + 43.8340i −0.212880 + 0.0666170i
$$659$$ 508.205 0.771176 0.385588 0.922671i $$-0.373999\pi$$
0.385588 + 0.922671i $$0.373999\pi$$
$$660$$ −306.792 780.091i −0.464836 1.18196i
$$661$$ 392.220i 0.593373i 0.954975 + 0.296687i $$0.0958817\pi$$
−0.954975 + 0.296687i $$0.904118\pi$$
$$662$$ 280.246 280.246i 0.423332 0.423332i
$$663$$ −39.4215 + 20.7849i −0.0594592 + 0.0313497i
$$664$$ −140.127 −0.211034
$$665$$ 371.406 72.4954i 0.558506 0.109016i
$$666$$ −799.515 + 1167.69i −1.20047 + 1.75329i
$$667$$ 50.6334 + 50.6334i 0.0759122 + 0.0759122i
$$668$$ −180.174 + 180.174i −0.269722 + 0.269722i
$$669$$ 26.5554 85.7884i 0.0396942 0.128234i
$$670$$ −338.021 37.5077i −0.504509 0.0559816i
$$671$$ −799.984 −1.19223
$$672$$ −853.308 + 2.63465i −1.26980 + 0.00392061i
$$673$$ 335.327 335.327i 0.498257 0.498257i −0.412638 0.910895i $$-0.635393\pi$$
0.910895 + 0.412638i $$0.135393\pi$$
$$674$$ 849.936 1.26103
$$675$$ −637.211 222.681i −0.944017 0.329897i
$$676$$ 246.944 0.365302
$$677$$ −164.817 164.817i −0.243452 0.243452i 0.574825 0.818277i $$-0.305070\pi$$
−0.818277 + 0.574825i $$0.805070\pi$$
$$678$$ 441.092 + 836.593i 0.650578 + 1.23391i
$$679$$ −51.3716 + 98.1671i −0.0756578 + 0.144576i
$$680$$ 1.21990 10.9938i 0.00179397 0.0161674i
$$681$$ 239.571 773.944i 0.351793 1.13648i
$$682$$ 882.166 882.166i 1.29350 1.29350i
$$683$$ −707.818 707.818i −1.03634 1.03634i −0.999314 0.0370224i $$-0.988213\pi$$
−0.0370224 0.999314i $$-0.511787\pi$$
$$684$$ −250.578 171.570i −0.366342 0.250834i
$$685$$ 376.065 300.943i 0.549000 0.439332i
$$686$$ 113.603 + 908.220i 0.165602 + 1.32394i
$$687$$ 117.758 + 223.346i 0.171410 + 0.325103i
$$688$$ −706.505 + 706.505i −1.02690 + 1.02690i
$$689$$ 723.002i 1.04935i
$$690$$ −45.6672 116.120i −0.0661844 0.168290i
$$691$$ 603.312i 0.873101i −0.899680 0.436550i $$-0.856200\pi$$
0.899680 0.436550i $$-0.143800\pi$$
$$692$$ −558.990 558.990i −0.807789 0.807789i
$$693$$ −1078.66 330.247i −1.55651 0.476548i
$$694$$ 308.998i 0.445242i
$$695$$ −149.650 16.6056i −0.215324 0.0238929i
$$696$$ 47.8023 154.428i 0.0686815 0.221879i
$$697$$ −4.57439 4.57439i −0.00656297 0.00656297i
$$698$$ −673.008 + 673.008i −0.964195 + 0.964195i
$$699$$ 285.369 921.896i 0.408253 1.31888i
$$700$$ 44.8752 + 544.315i 0.0641074 + 0.777592i
$$701$$ 354.991i 0.506406i −0.967413 0.253203i $$-0.918516\pi$$
0.967413 0.253203i $$-0.0814841\pi$$
$$702$$ 1127.41 + 130.425i 1.60599 + 0.185791i
$$703$$ −450.491 450.491i −0.640812 0.640812i
$$704$$ −599.095 −0.850987
$$705$$ −47.0566 + 108.061i −0.0667470 + 0.153277i
$$706$$ 1153.91i 1.63443i
$$707$$ −79.6444 + 24.9233i −0.112651 + 0.0352521i
$$708$$ −436.209 827.332i −0.616114 1.16855i
$$709$$ 637.022i 0.898479i 0.893411 + 0.449240i $$0.148305\pi$$
−0.893411 + 0.449240i $$0.851695\pi$$
$$710$$ 52.9850 + 66.2113i 0.0746268 + 0.0932554i
$$711$$ 443.955 + 303.975i 0.624409 + 0.427531i
$$712$$ −96.9036 + 96.9036i −0.136101 + 0.136101i
$$713$$ 57.5517 57.5517i 0.0807176 0.0807176i
$$714$$ 37.4843 + 37.2535i 0.0524990 + 0.0521758i
$$715$$ −1101.11 + 881.156i −1.54002 + 1.23239i
$$716$$ 960.976i 1.34215i
$$717$$ 26.7035 + 50.6470i 0.0372434 + 0.0706374i
$$718$$ 673.208 673.208i 0.937616 0.937616i
$$719$$ 435.697i 0.605976i 0.952994 + 0.302988i $$0.0979843\pi$$
−0.952994 + 0.302988i $$0.902016\pi$$
$$720$$ −550.365 + 639.157i −0.764396 + 0.887717i
$$721$$ 214.318 + 112.154i 0.297251 + 0.155554i
$$722$$ −460.603 + 460.603i −0.637955 + 0.637955i
$$723$$ 916.661 483.307i 1.26786 0.668475i
$$724$$ 390.014 0.538693
$$725$$ −560.301 125.895i −0.772830 0.173648i
$$726$$ −1526.65 472.566i −2.10282 0.650917i
$$727$$ −757.367 + 757.367i −1.04177 + 1.04177i −0.0426819 + 0.999089i $$0.513590\pi$$
−0.999089 + 0.0426819i $$0.986410\pi$$
$$728$$ 77.2490 + 246.856i 0.106111 + 0.339087i
$$729$$ 709.745 + 166.443i 0.973587 + 0.228317i
$$730$$ 1038.22 + 115.203i 1.42222 + 0.157813i
$$731$$ 50.2711 0.0687703
$$732$$ −195.091 370.017i −0.266517 0.505488i
$$733$$ 672.443 + 672.443i 0.917385 + 0.917385i 0.996839 0.0794540i $$-0.0253177\pi$$
−0.0794540 + 0.996839i $$0.525318\pi$$
$$734$$ 699.372i 0.952823i
$$735$$ 610.928 + 408.646i 0.831195 + 0.555981i
$$736$$ −126.667 −0.172102
$$737$$ −322.736 + 322.736i −0.437906 + 0.437906i
$$738$$ 30.3075 + 161.936i 0.0410670 + 0.219425i
$$739$$ 540.207i 0.730997i 0.930812 + 0.365498i $$0.119101\pi$$
−0.930812 + 0.365498i $$0.880899\pi$$
$$740$$ 717.927 574.514i 0.970171 0.776371i
$$741$$ −151.082 + 488.077i −0.203889 + 0.658673i
$$742$$ −818.246 + 256.055i −1.10276 + 0.345088i
$$743$$ −164.151 164.151i −0.220931 0.220931i 0.587960 0.808890i $$-0.299931\pi$$
−0.808890 + 0.587960i $$0.799931\pi$$
$$744$$ −175.528 54.3337i −0.235924 0.0730292i
$$745$$ 459.497 + 50.9869i 0.616774 + 0.0684388i
$$746$$ 875.339i 1.17338i
$$747$$ −98.9005 528.436i −0.132397 0.707411i
$$748$$ 37.2655 + 37.2655i 0.0498202 + 0.0498202i
$$749$$ 169.258 323.439i 0.225979 0.431827i
$$750$$ 807.568 + 590.943i 1.07676 + 0.787923i
$$751$$ −12.8996 −0.0171766 −0.00858830 0.999963i $$-0.502734\pi$$
−0.00858830 + 0.999963i $$0.502734\pi$$
$$752$$ 104.140 + 104.140i 0.138484 + 0.138484i
$$753$$ 355.304 + 673.883i 0.471851 + 0.894932i
$$754$$ 965.563 1.28059
$$755$$ −60.9674 6.76510i −0.0807515 0.00896039i
$$756$$ −110.301 579.449i −0.145901 0.766467i
$$757$$ −328.630 328.630i −0.434121 0.434121i 0.455906 0.890028i $$-0.349315\pi$$
−0.890028 + 0.455906i $$0.849315\pi$$
$$758$$ −63.6329 63.6329i −0.0839484 0.0839484i
$$759$$ −159.966 49.5166i −0.210759 0.0652393i
$$760$$ −79.2345 99.0133i −0.104256 0.130281i
$$761$$ 984.602 1.29383 0.646913 0.762564i $$-0.276060\pi$$
0.646913 + 0.762564i $$0.276060\pi$$
$$762$$ 779.842 + 1479.08i 1.02342 + 1.94105i
$$763$$ 112.489 + 359.468i 0.147430 + 0.471124i
$$764$$ −375.240 −0.491152
$$765$$ 42.3200 3.15895i 0.0553203 0.00412935i
$$766$$ 1332.26i 1.73924i
$$767$$ −1112.65 + 1112.65i −1.45066 +