# Properties

 Label 570.2.q.a.349.1 Level $570$ Weight $2$ Character 570.349 Analytic conductor $4.551$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$570 = 2 \cdot 3 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 570.q (of order $$6$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$4.55147291521$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{24})$$ Defining polynomial: $$x^{8} - x^{4} + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$3^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 349.1 Root $$-0.258819 + 0.965926i$$ of defining polynomial Character $$\chi$$ $$=$$ 570.349 Dual form 570.2.q.a.49.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.03906 + 0.917738i) q^{5} +(0.500000 - 0.866025i) q^{6} -3.00000i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.03906 + 0.917738i) q^{5} +(0.500000 - 0.866025i) q^{6} -3.00000i q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.30701 - 1.81431i) q^{10} +2.00000 q^{11} +1.00000i q^{12} +(2.98735 + 1.72474i) q^{13} +(1.50000 + 2.59808i) q^{14} +(1.30701 - 1.81431i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-4.24264 + 2.44949i) q^{17} +1.00000i q^{18} +(1.00000 + 4.24264i) q^{19} +(-0.224745 + 2.22474i) q^{20} +(1.50000 + 2.59808i) q^{21} +(-1.73205 + 1.00000i) q^{22} +(2.12132 + 1.22474i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.31552 - 3.74264i) q^{25} -3.44949 q^{26} +1.00000i q^{27} +(-2.59808 - 1.50000i) q^{28} +(-4.67423 + 8.09601i) q^{29} +(-0.224745 + 2.22474i) q^{30} -7.89898 q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.73205 + 1.00000i) q^{33} +(2.44949 - 4.24264i) q^{34} +(2.75321 + 6.11717i) q^{35} +(-0.500000 - 0.866025i) q^{36} +4.55051i q^{37} +(-2.98735 - 3.17423i) q^{38} -3.44949 q^{39} +(-0.917738 - 2.03906i) q^{40} +(-1.22474 - 2.12132i) q^{41} +(-2.59808 - 1.50000i) q^{42} +(0.476756 - 0.275255i) q^{43} +(1.00000 - 1.73205i) q^{44} +(-0.224745 + 2.22474i) q^{45} -2.44949 q^{46} +(3.07483 + 1.77526i) q^{47} +(0.866025 + 0.500000i) q^{48} -2.00000 q^{49} +(-1.00000 + 4.89898i) q^{50} +(2.44949 - 4.24264i) q^{51} +(2.98735 - 1.72474i) q^{52} +(2.68556 + 1.55051i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-4.07812 + 1.83548i) q^{55} +3.00000 q^{56} +(-2.98735 - 3.17423i) q^{57} -9.34847i q^{58} +(5.89898 + 10.2173i) q^{59} +(-0.917738 - 2.03906i) q^{60} +(-2.17423 + 3.76588i) q^{61} +(6.84072 - 3.94949i) q^{62} +(-2.59808 - 1.50000i) q^{63} -1.00000 q^{64} +(-7.67423 - 0.775255i) q^{65} +(1.00000 - 1.73205i) q^{66} +(1.25529 + 0.724745i) q^{67} +4.89898i q^{68} -2.44949 q^{69} +(-5.44294 - 3.92102i) q^{70} +(1.77526 + 3.07483i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-10.3048 + 5.94949i) q^{73} +(-2.27526 - 3.94086i) q^{74} +(-1.00000 + 4.89898i) q^{75} +(4.17423 + 1.25529i) q^{76} -6.00000i q^{77} +(2.98735 - 1.72474i) q^{78} +(8.39898 + 14.5475i) q^{79} +(1.81431 + 1.30701i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.12132 + 1.22474i) q^{82} +1.34847i q^{83} +3.00000 q^{84} +(6.40300 - 8.88828i) q^{85} +(-0.275255 + 0.476756i) q^{86} -9.34847i q^{87} +2.00000i q^{88} +(-5.77526 + 10.0030i) q^{89} +(-0.917738 - 2.03906i) q^{90} +(5.17423 - 8.96204i) q^{91} +(2.12132 - 1.22474i) q^{92} +(6.84072 - 3.94949i) q^{93} -3.55051 q^{94} +(-5.93269 - 7.73325i) q^{95} -1.00000 q^{96} +(16.1920 - 9.34847i) q^{97} +(1.73205 - 1.00000i) q^{98} +(1.00000 - 1.73205i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 4q^{4} + 4q^{5} + 4q^{6} + 4q^{9} + O(q^{10})$$ $$8q + 4q^{4} + 4q^{5} + 4q^{6} + 4q^{9} + 4q^{10} + 16q^{11} + 12q^{14} + 4q^{15} - 4q^{16} + 8q^{19} + 8q^{20} + 12q^{21} - 4q^{24} - 8q^{26} - 8q^{29} + 8q^{30} - 24q^{31} + 12q^{35} - 4q^{36} - 8q^{39} - 4q^{40} + 8q^{44} + 8q^{45} - 16q^{49} - 8q^{50} - 4q^{54} + 8q^{55} + 24q^{56} + 8q^{59} - 4q^{60} + 12q^{61} - 8q^{64} - 32q^{65} + 8q^{66} - 12q^{70} + 24q^{71} - 28q^{74} - 8q^{75} + 4q^{76} + 28q^{79} + 4q^{80} - 4q^{81} + 24q^{84} + 24q^{85} - 12q^{86} - 56q^{89} - 4q^{90} + 12q^{91} - 48q^{94} + 40q^{95} - 8q^{96} + 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$$.

 $$n$$ $$191$$ $$211$$ $$457$$ $$\chi(n)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.866025 + 0.500000i −0.612372 + 0.353553i
$$3$$ −0.866025 + 0.500000i −0.500000 + 0.288675i
$$4$$ 0.500000 0.866025i 0.250000 0.433013i
$$5$$ −2.03906 + 0.917738i −0.911894 + 0.410425i
$$6$$ 0.500000 0.866025i 0.204124 0.353553i
$$7$$ 3.00000i 1.13389i −0.823754 0.566947i $$-0.808125\pi$$
0.823754 0.566947i $$-0.191875\pi$$
$$8$$ 1.00000i 0.353553i
$$9$$ 0.500000 0.866025i 0.166667 0.288675i
$$10$$ 1.30701 1.81431i 0.413312 0.573736i
$$11$$ 2.00000 0.603023 0.301511 0.953463i $$-0.402509\pi$$
0.301511 + 0.953463i $$0.402509\pi$$
$$12$$ 1.00000i 0.288675i
$$13$$ 2.98735 + 1.72474i 0.828541 + 0.478358i 0.853353 0.521334i $$-0.174565\pi$$
−0.0248121 + 0.999692i $$0.507899\pi$$
$$14$$ 1.50000 + 2.59808i 0.400892 + 0.694365i
$$15$$ 1.30701 1.81431i 0.337468 0.468454i
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ −4.24264 + 2.44949i −1.02899 + 0.594089i −0.916696 0.399586i $$-0.869154\pi$$
−0.112296 + 0.993675i $$0.535820\pi$$
$$18$$ 1.00000i 0.235702i
$$19$$ 1.00000 + 4.24264i 0.229416 + 0.973329i
$$20$$ −0.224745 + 2.22474i −0.0502545 + 0.497468i
$$21$$ 1.50000 + 2.59808i 0.327327 + 0.566947i
$$22$$ −1.73205 + 1.00000i −0.369274 + 0.213201i
$$23$$ 2.12132 + 1.22474i 0.442326 + 0.255377i 0.704584 0.709621i $$-0.251134\pi$$
−0.262258 + 0.964998i $$0.584467\pi$$
$$24$$ −0.500000 0.866025i −0.102062 0.176777i
$$25$$ 3.31552 3.74264i 0.663103 0.748528i
$$26$$ −3.44949 −0.676501
$$27$$ 1.00000i 0.192450i
$$28$$ −2.59808 1.50000i −0.490990 0.283473i
$$29$$ −4.67423 + 8.09601i −0.867984 + 1.50339i −0.00392972 + 0.999992i $$0.501251\pi$$
−0.864054 + 0.503399i $$0.832082\pi$$
$$30$$ −0.224745 + 2.22474i −0.0410326 + 0.406181i
$$31$$ −7.89898 −1.41870 −0.709349 0.704857i $$-0.751011\pi$$
−0.709349 + 0.704857i $$0.751011\pi$$
$$32$$ 0.866025 + 0.500000i 0.153093 + 0.0883883i
$$33$$ −1.73205 + 1.00000i −0.301511 + 0.174078i
$$34$$ 2.44949 4.24264i 0.420084 0.727607i
$$35$$ 2.75321 + 6.11717i 0.465378 + 1.03399i
$$36$$ −0.500000 0.866025i −0.0833333 0.144338i
$$37$$ 4.55051i 0.748099i 0.927409 + 0.374050i $$0.122031\pi$$
−0.927409 + 0.374050i $$0.877969\pi$$
$$38$$ −2.98735 3.17423i −0.484611 0.514929i
$$39$$ −3.44949 −0.552360
$$40$$ −0.917738 2.03906i −0.145107 0.322403i
$$41$$ −1.22474 2.12132i −0.191273 0.331295i 0.754399 0.656416i $$-0.227928\pi$$
−0.945672 + 0.325121i $$0.894595\pi$$
$$42$$ −2.59808 1.50000i −0.400892 0.231455i
$$43$$ 0.476756 0.275255i 0.0727046 0.0419760i −0.463207 0.886250i $$-0.653301\pi$$
0.535912 + 0.844274i $$0.319968\pi$$
$$44$$ 1.00000 1.73205i 0.150756 0.261116i
$$45$$ −0.224745 + 2.22474i −0.0335030 + 0.331645i
$$46$$ −2.44949 −0.361158
$$47$$ 3.07483 + 1.77526i 0.448510 + 0.258948i 0.707201 0.707013i $$-0.249958\pi$$
−0.258691 + 0.965960i $$0.583291\pi$$
$$48$$ 0.866025 + 0.500000i 0.125000 + 0.0721688i
$$49$$ −2.00000 −0.285714
$$50$$ −1.00000 + 4.89898i −0.141421 + 0.692820i
$$51$$ 2.44949 4.24264i 0.342997 0.594089i
$$52$$ 2.98735 1.72474i 0.414270 0.239179i
$$53$$ 2.68556 + 1.55051i 0.368890 + 0.212979i 0.672974 0.739667i $$-0.265017\pi$$
−0.304083 + 0.952645i $$0.598350\pi$$
$$54$$ −0.500000 0.866025i −0.0680414 0.117851i
$$55$$ −4.07812 + 1.83548i −0.549893 + 0.247495i
$$56$$ 3.00000 0.400892
$$57$$ −2.98735 3.17423i −0.395684 0.420438i
$$58$$ 9.34847i 1.22751i
$$59$$ 5.89898 + 10.2173i 0.767982 + 1.33018i 0.938656 + 0.344856i $$0.112072\pi$$
−0.170674 + 0.985328i $$0.554594\pi$$
$$60$$ −0.917738 2.03906i −0.118479 0.263241i
$$61$$ −2.17423 + 3.76588i −0.278382 + 0.482172i −0.970983 0.239149i $$-0.923132\pi$$
0.692601 + 0.721321i $$0.256465\pi$$
$$62$$ 6.84072 3.94949i 0.868772 0.501586i
$$63$$ −2.59808 1.50000i −0.327327 0.188982i
$$64$$ −1.00000 −0.125000
$$65$$ −7.67423 0.775255i −0.951872 0.0961586i
$$66$$ 1.00000 1.73205i 0.123091 0.213201i
$$67$$ 1.25529 + 0.724745i 0.153359 + 0.0885417i 0.574716 0.818353i $$-0.305113\pi$$
−0.421357 + 0.906895i $$0.638446\pi$$
$$68$$ 4.89898i 0.594089i
$$69$$ −2.44949 −0.294884
$$70$$ −5.44294 3.92102i −0.650556 0.468652i
$$71$$ 1.77526 + 3.07483i 0.210684 + 0.364915i 0.951929 0.306319i $$-0.0990976\pi$$
−0.741245 + 0.671235i $$0.765764\pi$$
$$72$$ 0.866025 + 0.500000i 0.102062 + 0.0589256i
$$73$$ −10.3048 + 5.94949i −1.20609 + 0.696335i −0.961902 0.273393i $$-0.911854\pi$$
−0.244185 + 0.969729i $$0.578521\pi$$
$$74$$ −2.27526 3.94086i −0.264493 0.458115i
$$75$$ −1.00000 + 4.89898i −0.115470 + 0.565685i
$$76$$ 4.17423 + 1.25529i 0.478818 + 0.143992i
$$77$$ 6.00000i 0.683763i
$$78$$ 2.98735 1.72474i 0.338250 0.195289i
$$79$$ 8.39898 + 14.5475i 0.944959 + 1.63672i 0.755833 + 0.654764i $$0.227232\pi$$
0.189126 + 0.981953i $$0.439435\pi$$
$$80$$ 1.81431 + 1.30701i 0.202846 + 0.146128i
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 2.12132 + 1.22474i 0.234261 + 0.135250i
$$83$$ 1.34847i 0.148014i 0.997258 + 0.0740069i $$0.0235787\pi$$
−0.997258 + 0.0740069i $$0.976421\pi$$
$$84$$ 3.00000 0.327327
$$85$$ 6.40300 8.88828i 0.694503 0.964070i
$$86$$ −0.275255 + 0.476756i −0.0296815 + 0.0514099i
$$87$$ 9.34847i 1.00226i
$$88$$ 2.00000i 0.213201i
$$89$$ −5.77526 + 10.0030i −0.612176 + 1.06032i 0.378697 + 0.925521i $$0.376372\pi$$
−0.990873 + 0.134799i $$0.956961\pi$$
$$90$$ −0.917738 2.03906i −0.0967380 0.214936i
$$91$$ 5.17423 8.96204i 0.542407 0.939477i
$$92$$ 2.12132 1.22474i 0.221163 0.127688i
$$93$$ 6.84072 3.94949i 0.709349 0.409543i
$$94$$ −3.55051 −0.366207
$$95$$ −5.93269 7.73325i −0.608681 0.793415i
$$96$$ −1.00000 −0.102062
$$97$$ 16.1920 9.34847i 1.64405 0.949193i 0.664679 0.747129i $$-0.268569\pi$$
0.979372 0.202064i $$-0.0647648\pi$$
$$98$$ 1.73205 1.00000i 0.174964 0.101015i
$$99$$ 1.00000 1.73205i 0.100504 0.174078i
$$100$$ −1.58346 4.74264i −0.158346 0.474264i
$$101$$ 1.89898 3.28913i 0.188956 0.327281i −0.755947 0.654633i $$-0.772823\pi$$
0.944902 + 0.327353i $$0.106156\pi$$
$$102$$ 4.89898i 0.485071i
$$103$$ 9.89898i 0.975375i 0.873018 + 0.487688i $$0.162160\pi$$
−0.873018 + 0.487688i $$0.837840\pi$$
$$104$$ −1.72474 + 2.98735i −0.169125 + 0.292933i
$$105$$ −5.44294 3.92102i −0.531176 0.382653i
$$106$$ −3.10102 −0.301198
$$107$$ 10.4495i 1.01019i −0.863064 0.505095i $$-0.831457\pi$$
0.863064 0.505095i $$-0.168543\pi$$
$$108$$ 0.866025 + 0.500000i 0.0833333 + 0.0481125i
$$109$$ −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i $$-0.932756\pi$$
0.307290 0.951616i $$-0.400578\pi$$
$$110$$ 2.61401 3.62863i 0.249236 0.345976i
$$111$$ −2.27526 3.94086i −0.215958 0.374050i
$$112$$ −2.59808 + 1.50000i −0.245495 + 0.141737i
$$113$$ 14.8990i 1.40158i −0.713369 0.700789i $$-0.752831\pi$$
0.713369 0.700789i $$-0.247169\pi$$
$$114$$ 4.17423 + 1.25529i 0.390953 + 0.117569i
$$115$$ −5.44949 0.550510i −0.508168 0.0513353i
$$116$$ 4.67423 + 8.09601i 0.433992 + 0.751696i
$$117$$ 2.98735 1.72474i 0.276180 0.159453i
$$118$$ −10.2173 5.89898i −0.940582 0.543045i
$$119$$ 7.34847 + 12.7279i 0.673633 + 1.16677i
$$120$$ 1.81431 + 1.30701i 0.165623 + 0.119313i
$$121$$ −7.00000 −0.636364
$$122$$ 4.34847i 0.393692i
$$123$$ 2.12132 + 1.22474i 0.191273 + 0.110432i
$$124$$ −3.94949 + 6.84072i −0.354675 + 0.614315i
$$125$$ −3.32577 + 10.6742i −0.297465 + 0.954733i
$$126$$ 3.00000 0.267261
$$127$$ 14.4600 + 8.34847i 1.28312 + 0.740807i 0.977417 0.211322i $$-0.0677767\pi$$
0.305699 + 0.952128i $$0.401110\pi$$
$$128$$ 0.866025 0.500000i 0.0765466 0.0441942i
$$129$$ −0.275255 + 0.476756i −0.0242349 + 0.0419760i
$$130$$ 7.03371 3.16573i 0.616897 0.277653i
$$131$$ −3.89898 6.75323i −0.340655 0.590032i 0.643899 0.765110i $$-0.277316\pi$$
−0.984555 + 0.175078i $$0.943982\pi$$
$$132$$ 2.00000i 0.174078i
$$133$$ 12.7279 3.00000i 1.10365 0.260133i
$$134$$ −1.44949 −0.125217
$$135$$ −0.917738 2.03906i −0.0789863 0.175494i
$$136$$ −2.44949 4.24264i −0.210042 0.363803i
$$137$$ 0.953512 + 0.550510i 0.0814640 + 0.0470333i 0.540179 0.841550i $$-0.318357\pi$$
−0.458715 + 0.888584i $$0.651690\pi$$
$$138$$ 2.12132 1.22474i 0.180579 0.104257i
$$139$$ 3.27526 5.67291i 0.277804 0.481170i −0.693035 0.720904i $$-0.743727\pi$$
0.970839 + 0.239734i $$0.0770602\pi$$
$$140$$ 6.67423 + 0.674235i 0.564076 + 0.0569832i
$$141$$ −3.55051 −0.299007
$$142$$ −3.07483 1.77526i −0.258034 0.148976i
$$143$$ 5.97469 + 3.44949i 0.499629 + 0.288461i
$$144$$ −1.00000 −0.0833333
$$145$$ 2.10102 20.7980i 0.174480 1.72718i
$$146$$ 5.94949 10.3048i 0.492383 0.852833i
$$147$$ 1.73205 1.00000i 0.142857 0.0824786i
$$148$$ 3.94086 + 2.27526i 0.323936 + 0.187025i
$$149$$ 1.89898 + 3.28913i 0.155570 + 0.269456i 0.933267 0.359184i $$-0.116945\pi$$
−0.777696 + 0.628640i $$0.783612\pi$$
$$150$$ −1.58346 4.74264i −0.129289 0.387235i
$$151$$ 19.7980 1.61114 0.805568 0.592504i $$-0.201861\pi$$
0.805568 + 0.592504i $$0.201861\pi$$
$$152$$ −4.24264 + 1.00000i −0.344124 + 0.0811107i
$$153$$ 4.89898i 0.396059i
$$154$$ 3.00000 + 5.19615i 0.241747 + 0.418718i
$$155$$ 16.1065 7.24919i 1.29370 0.582269i
$$156$$ −1.72474 + 2.98735i −0.138090 + 0.239179i
$$157$$ −4.71940 + 2.72474i −0.376649 + 0.217458i −0.676359 0.736572i $$-0.736443\pi$$
0.299710 + 0.954030i $$0.403110\pi$$
$$158$$ −14.5475 8.39898i −1.15733 0.668187i
$$159$$ −3.10102 −0.245927
$$160$$ −2.22474 0.224745i −0.175882 0.0177676i
$$161$$ 3.67423 6.36396i 0.289570 0.501550i
$$162$$ 0.866025 + 0.500000i 0.0680414 + 0.0392837i
$$163$$ 6.34847i 0.497250i 0.968600 + 0.248625i $$0.0799788\pi$$
−0.968600 + 0.248625i $$0.920021\pi$$
$$164$$ −2.44949 −0.191273
$$165$$ 2.61401 3.62863i 0.203501 0.282488i
$$166$$ −0.674235 1.16781i −0.0523308 0.0906395i
$$167$$ −13.6814 7.89898i −1.05870 0.611241i −0.133628 0.991032i $$-0.542663\pi$$
−0.925073 + 0.379790i $$0.875996\pi$$
$$168$$ −2.59808 + 1.50000i −0.200446 + 0.115728i
$$169$$ −0.550510 0.953512i −0.0423469 0.0733471i
$$170$$ −1.10102 + 10.8990i −0.0844444 + 0.835914i
$$171$$ 4.17423 + 1.25529i 0.319212 + 0.0959948i
$$172$$ 0.550510i 0.0419760i
$$173$$ −3.85337 + 2.22474i −0.292966 + 0.169144i −0.639279 0.768975i $$-0.720767\pi$$
0.346312 + 0.938119i $$0.387434\pi$$
$$174$$ 4.67423 + 8.09601i 0.354353 + 0.613757i
$$175$$ −11.2279 9.94655i −0.848751 0.751888i
$$176$$ −1.00000 1.73205i −0.0753778 0.130558i
$$177$$ −10.2173 5.89898i −0.767982 0.443394i
$$178$$ 11.5505i 0.865747i
$$179$$ 18.2474 1.36388 0.681939 0.731409i $$-0.261137\pi$$
0.681939 + 0.731409i $$0.261137\pi$$
$$180$$ 1.81431 + 1.30701i 0.135231 + 0.0974186i
$$181$$ 5.55051 9.61377i 0.412566 0.714586i −0.582603 0.812757i $$-0.697966\pi$$
0.995170 + 0.0981710i $$0.0312992\pi$$
$$182$$ 10.3485i 0.767080i
$$183$$ 4.34847i 0.321448i
$$184$$ −1.22474 + 2.12132i −0.0902894 + 0.156386i
$$185$$ −4.17617 9.27875i −0.307038 0.682188i
$$186$$ −3.94949 + 6.84072i −0.289591 + 0.501586i
$$187$$ −8.48528 + 4.89898i −0.620505 + 0.358249i
$$188$$ 3.07483 1.77526i 0.224255 0.129474i
$$189$$ 3.00000 0.218218
$$190$$ 9.00449 + 3.73085i 0.653254 + 0.270664i
$$191$$ −14.6969 −1.06343 −0.531717 0.846922i $$-0.678453\pi$$
−0.531717 + 0.846922i $$0.678453\pi$$
$$192$$ 0.866025 0.500000i 0.0625000 0.0360844i
$$193$$ −1.81954 + 1.05051i −0.130973 + 0.0756174i −0.564055 0.825737i $$-0.690759\pi$$
0.433082 + 0.901355i $$0.357426\pi$$
$$194$$ −9.34847 + 16.1920i −0.671181 + 1.16252i
$$195$$ 7.03371 3.16573i 0.503694 0.226702i
$$196$$ −1.00000 + 1.73205i −0.0714286 + 0.123718i
$$197$$ 16.6969i 1.18961i −0.803871 0.594804i $$-0.797230\pi$$
0.803871 0.594804i $$-0.202770\pi$$
$$198$$ 2.00000i 0.142134i
$$199$$ −4.05051 + 7.01569i −0.287133 + 0.497329i −0.973124 0.230281i $$-0.926036\pi$$
0.685991 + 0.727610i $$0.259369\pi$$
$$200$$ 3.74264 + 3.31552i 0.264645 + 0.234442i
$$201$$ −1.44949 −0.102239
$$202$$ 3.79796i 0.267223i
$$203$$ 24.2880 + 14.0227i 1.70469 + 0.984201i
$$204$$ −2.44949 4.24264i −0.171499 0.297044i
$$205$$ 4.44414 + 3.20150i 0.310392 + 0.223603i
$$206$$ −4.94949 8.57277i −0.344847 0.597293i
$$207$$ 2.12132 1.22474i 0.147442 0.0851257i
$$208$$ 3.44949i 0.239179i
$$209$$ 2.00000 + 8.48528i 0.138343 + 0.586939i
$$210$$ 6.67423 + 0.674235i 0.460566 + 0.0465266i
$$211$$ −1.17423 2.03383i −0.0808376 0.140015i 0.822772 0.568371i $$-0.192426\pi$$
−0.903610 + 0.428356i $$0.859093\pi$$
$$212$$ 2.68556 1.55051i 0.184445 0.106489i
$$213$$ −3.07483 1.77526i −0.210684 0.121638i
$$214$$ 5.22474 + 9.04952i 0.357156 + 0.618613i
$$215$$ −0.719521 + 0.998798i −0.0490709 + 0.0681175i
$$216$$ −1.00000 −0.0680414
$$217$$ 23.6969i 1.60865i
$$218$$ 12.1244 + 7.00000i 0.821165 + 0.474100i
$$219$$ 5.94949 10.3048i 0.402029 0.696335i
$$220$$ −0.449490 + 4.44949i −0.0303046 + 0.299985i
$$221$$ −16.8990 −1.13675
$$222$$ 3.94086 + 2.27526i 0.264493 + 0.152705i
$$223$$ −11.8619 + 6.84847i −0.794331 + 0.458607i −0.841485 0.540280i $$-0.818318\pi$$
0.0471538 + 0.998888i $$0.484985\pi$$
$$224$$ 1.50000 2.59808i 0.100223 0.173591i
$$225$$ −1.58346 4.74264i −0.105564 0.316176i
$$226$$ 7.44949 + 12.9029i 0.495533 + 0.858288i
$$227$$ 13.3485i 0.885969i 0.896529 + 0.442985i $$0.146080\pi$$
−0.896529 + 0.442985i $$0.853920\pi$$
$$228$$ −4.24264 + 1.00000i −0.280976 + 0.0662266i
$$229$$ −27.0454 −1.78721 −0.893605 0.448853i $$-0.851833\pi$$
−0.893605 + 0.448853i $$0.851833\pi$$
$$230$$ 4.99465 2.24799i 0.329338 0.148228i
$$231$$ 3.00000 + 5.19615i 0.197386 + 0.341882i
$$232$$ −8.09601 4.67423i −0.531529 0.306879i
$$233$$ −12.6886 + 7.32577i −0.831258 + 0.479927i −0.854283 0.519808i $$-0.826003\pi$$
0.0230254 + 0.999735i $$0.492670\pi$$
$$234$$ −1.72474 + 2.98735i −0.112750 + 0.195289i
$$235$$ −7.89898 0.797959i −0.515273 0.0520531i
$$236$$ 11.7980 0.767982
$$237$$ −14.5475 8.39898i −0.944959 0.545572i
$$238$$ −12.7279 7.34847i −0.825029 0.476331i
$$239$$ −8.65153 −0.559621 −0.279811 0.960055i $$-0.590272\pi$$
−0.279811 + 0.960055i $$0.590272\pi$$
$$240$$ −2.22474 0.224745i −0.143607 0.0145072i
$$241$$ −5.50000 + 9.52628i −0.354286 + 0.613642i −0.986996 0.160748i $$-0.948609\pi$$
0.632709 + 0.774389i $$0.281943\pi$$
$$242$$ 6.06218 3.50000i 0.389692 0.224989i
$$243$$ 0.866025 + 0.500000i 0.0555556 + 0.0320750i
$$244$$ 2.17423 + 3.76588i 0.139191 + 0.241086i
$$245$$ 4.07812 1.83548i 0.260541 0.117264i
$$246$$ −2.44949 −0.156174
$$247$$ −4.33013 + 14.3990i −0.275519 + 0.916185i
$$248$$ 7.89898i 0.501586i
$$249$$ −0.674235 1.16781i −0.0427279 0.0740069i
$$250$$ −2.45692 10.9070i −0.155389 0.689822i
$$251$$ 10.3485 17.9241i 0.653190 1.13136i −0.329155 0.944276i $$-0.606764\pi$$
0.982344 0.187082i $$-0.0599029\pi$$
$$252$$ −2.59808 + 1.50000i −0.163663 + 0.0944911i
$$253$$ 4.24264 + 2.44949i 0.266733 + 0.153998i
$$254$$ −16.6969 −1.04766
$$255$$ −1.10102 + 10.8990i −0.0689486 + 0.682521i
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −21.7774 12.5732i −1.35844 0.784296i −0.369026 0.929419i $$-0.620309\pi$$
−0.989414 + 0.145123i $$0.953642\pi$$
$$258$$ 0.550510i 0.0342733i
$$259$$ 13.6515 0.848265
$$260$$ −4.50851 + 6.25845i −0.279606 + 0.388133i
$$261$$ 4.67423 + 8.09601i 0.289328 + 0.501131i
$$262$$ 6.75323 + 3.89898i 0.417216 + 0.240880i
$$263$$ −12.1244 + 7.00000i −0.747620 + 0.431638i −0.824833 0.565376i $$-0.808731\pi$$
0.0772134 + 0.997015i $$0.475398\pi$$
$$264$$ −1.00000 1.73205i −0.0615457 0.106600i
$$265$$ −6.89898 0.696938i −0.423801 0.0428126i
$$266$$ −9.52270 + 8.96204i −0.583874 + 0.549498i
$$267$$ 11.5505i 0.706880i
$$268$$ 1.25529 0.724745i 0.0766793 0.0442708i
$$269$$ −13.2474 22.9453i −0.807711 1.39900i −0.914445 0.404709i $$-0.867373\pi$$
0.106734 0.994288i $$-0.465961\pi$$
$$270$$ 1.81431 + 1.30701i 0.110416 + 0.0795419i
$$271$$ 2.55051 + 4.41761i 0.154932 + 0.268351i 0.933034 0.359787i $$-0.117151\pi$$
−0.778102 + 0.628138i $$0.783817\pi$$
$$272$$ 4.24264 + 2.44949i 0.257248 + 0.148522i
$$273$$ 10.3485i 0.626318i
$$274$$ −1.10102 −0.0665151
$$275$$ 6.63103 7.48528i 0.399866 0.451379i
$$276$$ −1.22474 + 2.12132i −0.0737210 + 0.127688i
$$277$$ 32.4949i 1.95243i 0.216807 + 0.976215i $$0.430436\pi$$
−0.216807 + 0.976215i $$0.569564\pi$$
$$278$$ 6.55051i 0.392873i
$$279$$ −3.94949 + 6.84072i −0.236450 + 0.409543i
$$280$$ −6.11717 + 2.75321i −0.365571 + 0.164536i
$$281$$ 13.2247 22.9059i 0.788922 1.36645i −0.137706 0.990473i $$-0.543973\pi$$
0.926628 0.375980i $$-0.122694\pi$$
$$282$$ 3.07483 1.77526i 0.183104 0.105715i
$$283$$ 7.70674 4.44949i 0.458118 0.264495i −0.253134 0.967431i $$-0.581461\pi$$
0.711253 + 0.702936i $$0.248128\pi$$
$$284$$ 3.55051 0.210684
$$285$$ 9.00449 + 3.73085i 0.533380 + 0.220996i
$$286$$ −6.89898 −0.407945
$$287$$ −6.36396 + 3.67423i −0.375653 + 0.216883i
$$288$$ 0.866025 0.500000i 0.0510310 0.0294628i
$$289$$ 3.50000 6.06218i 0.205882 0.356599i
$$290$$ 8.57944 + 19.0621i 0.503802 + 1.11936i
$$291$$ −9.34847 + 16.1920i −0.548017 + 0.949193i
$$292$$ 11.8990i 0.696335i
$$293$$ 18.8990i 1.10409i 0.833814 + 0.552045i $$0.186152\pi$$
−0.833814 + 0.552045i $$0.813848\pi$$
$$294$$ −1.00000 + 1.73205i −0.0583212 + 0.101015i
$$295$$ −21.4052 15.4200i −1.24626 0.897788i
$$296$$ −4.55051 −0.264493
$$297$$ 2.00000i 0.116052i
$$298$$ −3.28913 1.89898i −0.190534 0.110005i
$$299$$ 4.22474 + 7.31747i 0.244323 + 0.423180i
$$300$$ 3.74264 + 3.31552i 0.216081 + 0.191421i
$$301$$ −0.825765 1.43027i −0.0475963 0.0824393i
$$302$$ −17.1455 + 9.89898i −0.986615 + 0.569622i
$$303$$ 3.79796i 0.218187i
$$304$$ 3.17423 2.98735i 0.182055 0.171336i
$$305$$ 0.977296 9.67423i 0.0559598 0.553945i
$$306$$ −2.44949 4.24264i −0.140028 0.242536i
$$307$$ −1.90702 + 1.10102i −0.108840 + 0.0628386i −0.553432 0.832895i $$-0.686682\pi$$
0.444592 + 0.895733i $$0.353349\pi$$
$$308$$ −5.19615 3.00000i −0.296078 0.170941i
$$309$$ −4.94949 8.57277i −0.281567 0.487688i
$$310$$ −10.3240 + 14.3312i −0.586365 + 0.813959i
$$311$$ 10.8990 0.618024 0.309012 0.951058i $$-0.400002\pi$$
0.309012 + 0.951058i $$0.400002\pi$$
$$312$$ 3.44949i 0.195289i
$$313$$ 13.0779 + 7.55051i 0.739205 + 0.426780i 0.821780 0.569805i $$-0.192981\pi$$
−0.0825753 + 0.996585i $$0.526315\pi$$
$$314$$ 2.72474 4.71940i 0.153766 0.266331i
$$315$$ 6.67423 + 0.674235i 0.376051 + 0.0379888i
$$316$$ 16.7980 0.944959
$$317$$ 5.41045 + 3.12372i 0.303881 + 0.175446i 0.644185 0.764870i $$-0.277197\pi$$
−0.340304 + 0.940315i $$0.610530\pi$$
$$318$$ 2.68556 1.55051i 0.150599 0.0869483i
$$319$$ −9.34847 + 16.1920i −0.523414 + 0.906579i
$$320$$ 2.03906 0.917738i 0.113987 0.0513031i
$$321$$ 5.22474 + 9.04952i 0.291617 + 0.505095i
$$322$$ 7.34847i 0.409514i
$$323$$ −14.6349 15.5505i −0.814310 0.865254i
$$324$$ −1.00000 −0.0555556
$$325$$ 16.3597 5.46214i 0.907472 0.302985i
$$326$$ −3.17423 5.49794i −0.175805 0.304502i
$$327$$ 12.1244 + 7.00000i 0.670478 + 0.387101i
$$328$$ 2.12132 1.22474i 0.117130 0.0676252i
$$329$$ 5.32577 9.22450i 0.293619 0.508563i
$$330$$ −0.449490 + 4.44949i −0.0247436 + 0.244936i
$$331$$ 23.2474 1.27780 0.638898 0.769292i $$-0.279391\pi$$
0.638898 + 0.769292i $$0.279391\pi$$
$$332$$ 1.16781 + 0.674235i 0.0640918 + 0.0370034i
$$333$$ 3.94086 + 2.27526i 0.215958 + 0.124683i
$$334$$ 15.7980 0.864426
$$335$$ −3.22474 0.325765i −0.176187 0.0177985i
$$336$$ 1.50000 2.59808i 0.0818317 0.141737i
$$337$$ 3.55159 2.05051i 0.193467 0.111698i −0.400137 0.916455i $$-0.631038\pi$$
0.593605 + 0.804757i $$0.297704\pi$$
$$338$$ 0.953512 + 0.550510i 0.0518642 + 0.0299438i
$$339$$ 7.44949 + 12.9029i 0.404601 + 0.700789i
$$340$$ −4.49598 9.98930i −0.243829 0.541746i
$$341$$ −15.7980 −0.855507
$$342$$ −4.24264 + 1.00000i −0.229416 + 0.0540738i
$$343$$ 15.0000i 0.809924i
$$344$$ 0.275255 + 0.476756i 0.0148408 + 0.0257050i
$$345$$ 4.99465 2.24799i 0.268903 0.121028i
$$346$$ 2.22474 3.85337i 0.119603 0.207159i
$$347$$ 24.6773 14.2474i 1.32475 0.764843i 0.340265 0.940329i $$-0.389483\pi$$
0.984482 + 0.175486i $$0.0561498\pi$$
$$348$$ −8.09601 4.67423i −0.433992 0.250565i
$$349$$ 26.5505 1.42122 0.710608 0.703588i $$-0.248420\pi$$
0.710608 + 0.703588i $$0.248420\pi$$
$$350$$ 14.6969 + 3.00000i 0.785584 + 0.160357i
$$351$$ −1.72474 + 2.98735i −0.0920601 + 0.159453i
$$352$$ 1.73205 + 1.00000i 0.0923186 + 0.0533002i
$$353$$ 21.1464i 1.12551i 0.826623 + 0.562755i $$0.190259\pi$$
−0.826623 + 0.562755i $$0.809741\pi$$
$$354$$ 11.7980 0.627054
$$355$$ −6.44174 4.64054i −0.341892 0.246294i
$$356$$ 5.77526 + 10.0030i 0.306088 + 0.530160i
$$357$$ −12.7279 7.34847i −0.673633 0.388922i
$$358$$ −15.8028 + 9.12372i −0.835202 + 0.482204i
$$359$$ −10.1237 17.5348i −0.534310 0.925452i −0.999196 0.0400814i $$-0.987238\pi$$
0.464887 0.885370i $$-0.346095\pi$$
$$360$$ −2.22474 0.224745i −0.117254 0.0118451i
$$361$$ −17.0000 + 8.48528i −0.894737 + 0.446594i
$$362$$ 11.1010i 0.583457i
$$363$$ 6.06218 3.50000i 0.318182 0.183702i
$$364$$ −5.17423 8.96204i −0.271204 0.469738i
$$365$$ 15.5521 21.5885i 0.814032 1.12999i
$$366$$ 2.17423 + 3.76588i 0.113649 + 0.196846i
$$367$$ 14.3725 + 8.29796i 0.750238 + 0.433150i 0.825780 0.563993i $$-0.190735\pi$$
−0.0755421 + 0.997143i $$0.524069\pi$$
$$368$$ 2.44949i 0.127688i
$$369$$ −2.44949 −0.127515
$$370$$ 8.25605 + 5.94755i 0.429212 + 0.309198i
$$371$$ 4.65153 8.05669i 0.241495 0.418282i
$$372$$ 7.89898i 0.409543i
$$373$$ 25.1010i 1.29968i 0.760070 + 0.649841i $$0.225164\pi$$
−0.760070 + 0.649841i $$0.774836\pi$$
$$374$$ 4.89898 8.48528i 0.253320 0.438763i
$$375$$ −2.45692 10.9070i −0.126875 0.563237i
$$376$$ −1.77526 + 3.07483i −0.0915518 + 0.158572i
$$377$$ −27.9271 + 16.1237i −1.43832 + 0.830414i
$$378$$ −2.59808 + 1.50000i −0.133631 + 0.0771517i
$$379$$ −8.75255 −0.449588 −0.224794 0.974406i $$-0.572171\pi$$
−0.224794 + 0.974406i $$0.572171\pi$$
$$380$$ −9.66354 + 1.27123i −0.495729 + 0.0652129i
$$381$$ −16.6969 −0.855410
$$382$$ 12.7279 7.34847i 0.651217 0.375980i
$$383$$ 1.16781 0.674235i 0.0596722 0.0344518i −0.469867 0.882737i $$-0.655698\pi$$
0.529539 + 0.848285i $$0.322365\pi$$
$$384$$ −0.500000 + 0.866025i −0.0255155 + 0.0441942i
$$385$$ 5.50643 + 12.2343i 0.280633 + 0.623520i
$$386$$ 1.05051 1.81954i 0.0534696 0.0926120i
$$387$$ 0.550510i 0.0279840i
$$388$$ 18.6969i 0.949193i
$$389$$ 7.12372 12.3387i 0.361187 0.625595i −0.626969 0.779044i $$-0.715705\pi$$
0.988157 + 0.153449i $$0.0490382\pi$$
$$390$$ −4.50851 + 6.25845i −0.228297 + 0.316909i
$$391$$ −12.0000 −0.606866
$$392$$ 2.00000i 0.101015i
$$393$$ 6.75323 + 3.89898i 0.340655 + 0.196677i
$$394$$ 8.34847 + 14.4600i 0.420590 + 0.728483i
$$395$$ −30.4768 21.9551i −1.53345 1.10468i
$$396$$ −1.00000 1.73205i −0.0502519 0.0870388i
$$397$$ −8.00853 + 4.62372i −0.401936 + 0.232058i −0.687319 0.726356i $$-0.741213\pi$$
0.285383 + 0.958414i $$0.407879\pi$$
$$398$$ 8.10102i 0.406067i
$$399$$ −9.52270 + 8.96204i −0.476731 + 0.448663i
$$400$$ −4.89898 1.00000i −0.244949 0.0500000i
$$401$$ −16.1464 27.9664i −0.806314 1.39658i −0.915400 0.402545i $$-0.868126\pi$$
0.109086 0.994032i $$-0.465208\pi$$
$$402$$ 1.25529 0.724745i 0.0626084 0.0361470i
$$403$$ −23.5970 13.6237i −1.17545 0.678646i
$$404$$ −1.89898 3.28913i −0.0944778 0.163640i
$$405$$ 1.81431 + 1.30701i 0.0901539 + 0.0649457i
$$406$$ −28.0454 −1.39187
$$407$$ 9.10102i 0.451121i
$$408$$ 4.24264 + 2.44949i 0.210042 + 0.121268i
$$409$$ −5.55051 + 9.61377i −0.274455 + 0.475370i −0.969997 0.243115i $$-0.921831\pi$$
0.695542 + 0.718485i $$0.255164\pi$$
$$410$$ −5.44949 0.550510i −0.269131 0.0271878i
$$411$$ −1.10102 −0.0543093
$$412$$ 8.57277 + 4.94949i 0.422350 + 0.243844i
$$413$$ 30.6520 17.6969i 1.50829 0.870809i
$$414$$ −1.22474 + 2.12132i −0.0601929 + 0.104257i
$$415$$ −1.23754 2.74961i −0.0607485 0.134973i
$$416$$ 1.72474 + 2.98735i 0.0845626 + 0.146467i
$$417$$ 6.55051i 0.320780i
$$418$$ −5.97469 6.34847i −0.292232 0.310514i
$$419$$ 26.0454 1.27240 0.636201 0.771524i $$-0.280505\pi$$
0.636201 + 0.771524i $$0.280505\pi$$
$$420$$ −6.11717 + 2.75321i −0.298488 + 0.134343i
$$421$$ 10.7980 + 18.7026i 0.526260 + 0.911510i 0.999532 + 0.0305930i $$0.00973959\pi$$
−0.473272 + 0.880917i $$0.656927\pi$$
$$422$$ 2.03383 + 1.17423i 0.0990055 + 0.0571608i
$$423$$ 3.07483 1.77526i 0.149503 0.0863159i
$$424$$ −1.55051 + 2.68556i −0.0752994 + 0.130422i
$$425$$ −4.89898 + 24.0000i −0.237635 + 1.16417i
$$426$$ 3.55051 0.172023
$$427$$ 11.2977 + 6.52270i 0.546732 + 0.315656i
$$428$$ −9.04952 5.22474i −0.437425 0.252548i
$$429$$ −6.89898 −0.333086
$$430$$ 0.123724 1.22474i 0.00596652 0.0590624i
$$431$$ −15.1237 + 26.1951i −0.728484 + 1.26177i 0.229040 + 0.973417i $$0.426441\pi$$
−0.957524 + 0.288354i $$0.906892\pi$$
$$432$$ 0.866025 0.500000i 0.0416667 0.0240563i
$$433$$ 16.2795 + 9.39898i 0.782343 + 0.451686i 0.837260 0.546805i $$-0.184156\pi$$
−0.0549168 + 0.998491i $$0.517489\pi$$
$$434$$ −11.8485 20.5222i −0.568745 0.985095i
$$435$$ 8.57944 + 19.0621i 0.411353 + 0.913956i
$$436$$ −14.0000 −0.670478
$$437$$ −3.07483 + 10.2247i −0.147089 + 0.489116i
$$438$$ 11.8990i 0.568555i
$$439$$ −8.74745 15.1510i −0.417493 0.723119i 0.578194 0.815900i $$-0.303758\pi$$
−0.995687 + 0.0927806i $$0.970424\pi$$
$$440$$ −1.83548 4.07812i −0.0875029 0.194417i
$$441$$ −1.00000 + 1.73205i −0.0476190 + 0.0824786i
$$442$$ 14.6349 8.44949i 0.696113 0.401901i
$$443$$ −8.48528 4.89898i −0.403148 0.232758i 0.284693 0.958619i $$-0.408108\pi$$
−0.687841 + 0.725861i $$0.741442\pi$$
$$444$$ −4.55051 −0.215958
$$445$$ 2.59592 25.6969i 0.123058 1.21815i
$$446$$ 6.84847 11.8619i 0.324284 0.561677i
$$447$$ −3.28913 1.89898i −0.155570 0.0898186i
$$448$$ 3.00000i 0.141737i
$$449$$ 10.6969 0.504820 0.252410 0.967620i $$-0.418777\pi$$
0.252410 + 0.967620i $$0.418777\pi$$
$$450$$ 3.74264 + 3.31552i 0.176430 + 0.156295i
$$451$$ −2.44949 4.24264i −0.115342 0.199778i
$$452$$ −12.9029 7.44949i −0.606901 0.350395i
$$453$$ −17.1455 + 9.89898i −0.805568 + 0.465095i
$$454$$ −6.67423 11.5601i −0.313237 0.542543i
$$455$$ −2.32577 + 23.0227i −0.109034 + 1.07932i
$$456$$ 3.17423 2.98735i 0.148647 0.139895i
$$457$$ 14.1010i 0.659618i −0.944048 0.329809i $$-0.893016\pi$$
0.944048 0.329809i $$-0.106984\pi$$
$$458$$ 23.4220 13.5227i 1.09444 0.631874i
$$459$$ −2.44949 4.24264i −0.114332 0.198030i
$$460$$ −3.20150 + 4.44414i −0.149271 + 0.207209i
$$461$$ 12.1237 + 20.9989i 0.564658 + 0.978017i 0.997081 + 0.0763458i $$0.0243253\pi$$
−0.432423 + 0.901671i $$0.642341\pi$$
$$462$$ −5.19615 3.00000i −0.241747 0.139573i
$$463$$ 39.2929i 1.82609i −0.407854 0.913047i $$-0.633723\pi$$
0.407854 0.913047i $$-0.366277\pi$$
$$464$$ 9.34847 0.433992
$$465$$ −10.3240 + 14.3312i −0.478765 + 0.664595i
$$466$$ 7.32577 12.6886i 0.339360 0.587788i
$$467$$ 3.55051i 0.164298i −0.996620 0.0821490i $$-0.973822\pi$$
0.996620 0.0821490i $$-0.0261783\pi$$
$$468$$ 3.44949i 0.159453i
$$469$$ 2.17423 3.76588i 0.100397 0.173892i
$$470$$ 7.23970 3.25844i 0.333942 0.150300i
$$471$$ 2.72474 4.71940i 0.125550 0.217458i
$$472$$ −10.2173 + 5.89898i −0.470291 + 0.271523i
$$473$$ 0.953512 0.550510i 0.0438425 0.0253125i
$$474$$ 16.7980 0.771556
$$475$$ 19.1942 + 10.3239i 0.880690 + 0.473693i
$$476$$ 14.6969 0.673633
$$477$$ 2.68556 1.55051i 0.122963 0.0709930i
$$478$$ 7.49245 4.32577i 0.342696 0.197856i
$$479$$ 14.3485 24.8523i 0.655598 1.13553i −0.326145 0.945320i $$-0.605750\pi$$
0.981743 0.190210i $$-0.0609168\pi$$
$$480$$ 2.03906 0.917738i 0.0930698 0.0418888i
$$481$$ −7.84847 + 13.5939i −0.357859 + 0.619831i
$$482$$ 11.0000i 0.501036i
$$483$$ 7.34847i 0.334367i
$$484$$ −3.50000 + 6.06218i −0.159091 + 0.275554i
$$485$$ −24.4370 + 33.9221i −1.10963 + 1.54032i
$$486$$ −1.00000 −0.0453609
$$487$$ 34.8990i 1.58142i −0.612188 0.790712i $$-0.709711\pi$$
0.612188 0.790712i $$-0.290289\pi$$
$$488$$ −3.76588 2.17423i −0.170474 0.0984230i
$$489$$ −3.17423 5.49794i −0.143544 0.248625i
$$490$$ −2.61401 + 3.62863i −0.118089 + 0.163925i
$$491$$ 5.02270 + 8.69958i 0.226671 + 0.392606i 0.956820 0.290682i $$-0.0938823\pi$$
−0.730148 + 0.683289i $$0.760549\pi$$
$$492$$ 2.12132 1.22474i 0.0956365 0.0552158i
$$493$$ 45.7980i 2.06264i
$$494$$ −3.44949 14.6349i −0.155200 0.658457i
$$495$$ −0.449490 + 4.44949i −0.0202031 + 0.199990i
$$496$$ 3.94949 + 6.84072i 0.177337 + 0.307157i
$$497$$ 9.22450 5.32577i 0.413775 0.238893i
$$498$$ 1.16781 + 0.674235i 0.0523308 + 0.0302132i
$$499$$ −16.4217 28.4432i −0.735136 1.27329i −0.954664 0.297686i $$-0.903785\pi$$
0.219528 0.975606i $$-0.429548\pi$$
$$500$$ 7.58128 + 8.21731i 0.339045 + 0.367489i
$$501$$ 15.7980 0.705801
$$502$$ 20.6969i 0.923750i
$$503$$ 5.02118 + 2.89898i 0.223883 + 0.129259i 0.607747 0.794131i $$-0.292073\pi$$
−0.383864 + 0.923390i $$0.625407\pi$$
$$504$$ 1.50000 2.59808i 0.0668153 0.115728i
$$505$$ −0.853572 + 8.44949i −0.0379834 + 0.375997i
$$506$$ −4.89898 −0.217786
$$507$$ 0.953512 + 0.550510i 0.0423469 + 0.0244490i
$$508$$ 14.4600 8.34847i 0.641558 0.370403i
$$509$$ −7.22474 + 12.5136i −0.320231 + 0.554657i −0.980536 0.196341i $$-0.937094\pi$$
0.660304 + 0.750998i $$0.270427\pi$$
$$510$$ −4.49598 9.98930i −0.199085 0.442334i
$$511$$ 17.8485 + 30.9145i 0.789570 + 1.36757i
$$512$$ 1.00000i 0.0441942i
$$513$$ −4.24264 + 1.00000i −0.187317 + 0.0441511i
$$514$$ 25.1464 1.10916
$$515$$ −9.08467 20.1846i −0.400318 0.889439i
$$516$$ 0.275255 + 0.476756i 0.0121174 + 0.0209880i
$$517$$ 6.14966 + 3.55051i 0.270462 + 0.156151i
$$518$$ −11.8226 + 6.82577i −0.519454 + 0.299907i
$$519$$ 2.22474 3.85337i 0.0976555 0.169144i
$$520$$ 0.775255 7.67423i 0.0339972 0.336537i
$$521$$ 18.2474 0.799435 0.399718 0.916638i $$-0.369108\pi$$
0.399718 + 0.916638i $$0.369108\pi$$
$$522$$ −8.09601 4.67423i −0.354353 0.204586i
$$523$$ −14.1582 8.17423i −0.619094 0.357434i 0.157422 0.987531i $$-0.449682\pi$$
−0.776516 + 0.630097i $$0.783015\pi$$
$$524$$ −7.79796 −0.340655
$$525$$ 14.6969 + 3.00000i 0.641427 + 0.130931i
$$526$$ 7.00000 12.1244i 0.305215 0.528647i
$$527$$ 33.5125 19.3485i 1.45983 0.842833i
$$528$$ 1.73205 + 1.00000i 0.0753778 + 0.0435194i
$$529$$ −8.50000 14.7224i −0.369565 0.640106i
$$530$$ 6.32316 2.84592i 0.274661 0.123619i
$$531$$ 11.7980 0.511988
$$532$$ 3.76588 12.5227i 0.163272 0.542928i
$$533$$ 8.44949i 0.365988i
$$534$$ 5.77526 + 10.0030i 0.249920 + 0.432874i
$$535$$ 9.58989 + 21.3071i 0.414607 + 0.921187i
$$536$$ −0.724745 + 1.25529i −0.0313042 + 0.0542205i
$$537$$ −15.8028 + 9.12372i −0.681939 + 0.393718i
$$538$$ 22.9453 + 13.2474i 0.989240 + 0.571138i
$$539$$ −4.00000 −0.172292
$$540$$ −2.22474 0.224745i −0.0957378 0.00967148i
$$541$$ 7.17423 12.4261i 0.308444 0.534241i −0.669578 0.742742i $$-0.733525\pi$$
0.978022 + 0.208500i $$0.0668583\pi$$
$$542$$ −4.41761 2.55051i −0.189753 0.109554i
$$543$$ 11.1010i 0.476390i
$$544$$ −4.89898 −0.210042
$$545$$ 25.4004 + 18.2981i 1.08803 + 0.783805i
$$546$$ −5.17423 8.96204i −0.221437 0.383540i
$$547$$ 12.2512 + 7.07321i 0.523822 + 0.302429i 0.738497 0.674257i $$-0.235536\pi$$
−0.214675 + 0.976686i $$0.568869\pi$$
$$548$$ 0.953512 0.550510i 0.0407320 0.0235166i
$$549$$ 2.17423 + 3.76588i 0.0927941 + 0.160724i
$$550$$ −2.00000 + 9.79796i −0.0852803 + 0.417786i
$$551$$ −39.0227 11.7351i −1.66242 0.499931i
$$552$$ 2.44949i 0.104257i
$$553$$ 43.6424 25.1969i 1.85586 1.07148i
$$554$$ −16.2474 28.1414i −0.690288 1.19561i
$$555$$ 8.25605 + 5.94755i 0.350450 + 0.252459i
$$556$$ −3.27526 5.67291i −0.138902 0.240585i
$$557$$ −31.8198 18.3712i −1.34825 0.778412i −0.360247 0.932857i $$-0.617308\pi$$
−0.988001 + 0.154445i $$0.950641\pi$$
$$558$$ 7.89898i 0.334390i
$$559$$ 1.89898 0.0803183
$$560$$ 3.92102 5.44294i 0.165693 0.230006i
$$561$$ 4.89898 8.48528i 0.206835 0.358249i
$$562$$ 26.4495i 1.11570i
$$563$$ 25.5959i 1.07874i 0.842069 + 0.539370i $$0.181337\pi$$
−0.842069 + 0.539370i $$0.818663\pi$$
$$564$$ −1.77526 + 3.07483i −0.0747517 + 0.129474i
$$565$$ 13.6734 + 30.3799i 0.575242 + 1.27809i
$$566$$ −4.44949 + 7.70674i −0.187026 + 0.323939i
$$567$$ −2.59808 + 1.50000i −0.109109 + 0.0629941i
$$568$$ −3.07483 + 1.77526i −0.129017 + 0.0744881i
$$569$$ 32.8990 1.37920 0.689598 0.724192i $$-0.257787\pi$$
0.689598 + 0.724192i $$0.257787\pi$$
$$570$$ −9.66354 + 1.27123i −0.404761 + 0.0532461i
$$571$$ −20.5505 −0.860012 −0.430006 0.902826i $$-0.641489\pi$$
−0.430006 + 0.902826i $$0.641489\pi$$
$$572$$ 5.97469 3.44949i 0.249814 0.144230i
$$573$$ 12.7279 7.34847i 0.531717 0.306987i
$$574$$ 3.67423 6.36396i 0.153360 0.265627i
$$575$$ 11.6170 3.87868i 0.484464 0.161752i
$$576$$ −0.500000 + 0.866025i −0.0208333 + 0.0360844i
$$577$$ 22.0000i 0.915872i −0.888985 0.457936i $$-0.848589\pi$$
0.888985 0.457936i $$-0.151411\pi$$
$$578$$ 7.00000i 0.291162i
$$579$$ 1.05051 1.81954i 0.0436577 0.0756174i
$$580$$ −16.9611 12.2185i −0.704269 0.507346i
$$581$$ 4.04541 0.167832
$$582$$ 18.6969i 0.775013i
$$583$$ 5.37113 + 3.10102i 0.222449 + 0.128431i
$$584$$ −5.94949 10.3048i −0.246192 0.426416i
$$585$$ −4.50851 + 6.25845i −0.186404 + 0.258755i
$$586$$ −9.44949 16.3670i −0.390355 0.676114i
$$587$$ 27.9664 16.1464i 1.15430 0.666434i 0.204367 0.978894i $$-0.434486\pi$$
0.949931 + 0.312460i $$0.101153\pi$$
$$588$$ 2.00000i 0.0824786i
$$589$$ −7.89898 33.5125i −0.325472 1.38086i
$$590$$ 26.2474 + 2.65153i 1.08059 + 0.109162i
$$591$$ 8.34847 + 14.4600i 0.343410 + 0.594804i
$$592$$ 3.94086 2.27526i 0.161968 0.0935124i
$$593$$ −16.5813 9.57321i −0.680912 0.393125i 0.119287 0.992860i $$-0.461939\pi$$
−0.800199 + 0.599735i $$0.795273\pi$$
$$594$$ −1.00000 1.73205i −0.0410305 0.0710669i
$$595$$ −26.6648 19.2090i −1.09315 0.787492i
$$596$$ 3.79796 0.155570
$$597$$ 8.10102i 0.331553i
$$598$$ −7.31747 4.22474i −0.299234 0.172763i
$$599$$ −15.1237 + 26.1951i −0.617939 + 1.07030i 0.371923 + 0.928264i $$0.378699\pi$$
−0.989861 + 0.142037i $$0.954635\pi$$
$$600$$ −4.89898 1.00000i −0.200000 0.0408248i
$$601$$ −15.0000 −0.611863 −0.305931 0.952054i $$-0.598968\pi$$
−0.305931 + 0.952054i $$0.598968\pi$$
$$602$$ 1.43027 + 0.825765i 0.0582934 + 0.0336557i
$$603$$ 1.25529 0.724745i 0.0511196 0.0295139i
$$604$$ 9.89898 17.1455i 0.402784 0.697642i
$$605$$ 14.2734 6.42416i 0.580296 0.261179i
$$606$$ −1.89898 3.28913i −0.0771408 0.133612i
$$607$$ 27.0000i 1.09590i 0.836512 + 0.547948i $$0.184591\pi$$
−0.836512 + 0.547948i $$0.815409\pi$$
$$608$$ −1.25529 + 4.17423i −0.0509089 + 0.169288i
$$609$$ −28.0454 −1.13646
$$610$$ 3.99075 + 8.86678i 0.161581 + 0.359005i
$$611$$ 6.12372 + 10.6066i 0.247739 + 0.429097i
$$612$$ 4.24264 + 2.44949i 0.171499 + 0.0990148i
$$613$$ 26.7593 15.4495i 1.08080 0.623999i 0.149686 0.988734i $$-0.452174\pi$$
0.931112 + 0.364735i $$0.118840\pi$$
$$614$$ 1.10102 1.90702i 0.0444336 0.0769612i
$$615$$ −5.44949 0.550510i −0.219745 0.0221987i
$$616$$ 6.00000 0.241747
$$617$$ −7.74607 4.47219i −0.311845 0.180044i 0.335907 0.941895i $$-0.390957\pi$$
−0.647752 + 0.761851i $$0.724291\pi$$
$$618$$ 8.57277 + 4.94949i 0.344847 + 0.199098i
$$619$$ 11.0454 0.443952 0.221976 0.975052i $$-0.428749\pi$$
0.221976 + 0.975052i $$0.428749\pi$$
$$620$$ 1.77526 17.5732i 0.0712960 0.705757i
$$621$$ −1.22474 + 2.12132i −0.0491473 + 0.0851257i
$$622$$ −9.43879 + 5.44949i −0.378461 + 0.218505i
$$623$$ 30.0091 + 17.3258i 1.20229 + 0.694142i
$$624$$ 1.72474 + 2.98735i 0.0690451 + 0.119590i
$$625$$ −3.01472 24.8176i −0.120589 0.992703i
$$626$$ −15.1010 −0.603558
$$627$$ −5.97469 6.34847i −0.238606 0.253533i
$$628$$ 5.44949i 0.217458i
$$629$$ −11.1464 19.3062i −0.444437 0.769788i
$$630$$ −6.11717 + 2.75321i −0.243714 + 0.109691i
$$631$$ −20.9495 + 36.2856i −0.833986 + 1.44451i 0.0608673 + 0.998146i $$0.480613\pi$$
−0.894853 + 0.446360i $$0.852720\pi$$
$$632$$ −14.5475 + 8.39898i −0.578667 + 0.334093i
$$633$$ 2.03383 + 1.17423i 0.0808376 + 0.0466716i
$$634$$ −6.24745 −0.248118
$$635$$ −37.1464 3.75255i −1.47411 0.148915i
$$636$$ −1.55051 + 2.68556i −0.0614817 + 0.106489i
$$637$$ −5.97469 3.44949i −0.236726 0.136674i
$$638$$ 18.6969i 0.740219i
$$639$$ 3.55051 0.140456
$$640$$ −1.30701 + 1.81431i −0.0516640 + 0.0717170i
$$641$$ 21.1237 + 36.5874i 0.834337 + 1.44511i 0.894569 + 0.446930i $$0.147483\pi$$
−0.0602322 + 0.998184i $$0.519184\pi$$
$$642$$ −9.04952 5.22474i −0.357156 0.206204i
$$643$$ −31.4787 + 18.1742i −1.24140 + 0.716722i −0.969379 0.245570i $$-0.921025\pi$$
−0.272020 + 0.962292i $$0.587692\pi$$
$$644$$ −3.67423 6.36396i −0.144785 0.250775i
$$645$$ 0.123724 1.22474i 0.00487164 0.0482243i
$$646$$ 20.4495 + 6.14966i 0.804574 + 0.241955i
$$647$$ 31.8434i 1.25189i −0.779866 0.625946i $$-0.784713\pi$$
0.779866 0.625946i $$-0.215287\pi$$
$$648$$ 0.866025 0.500000i 0.0340207 0.0196419i
$$649$$ 11.7980 + 20.4347i 0.463110 + 0.802131i
$$650$$ −11.4368 + 12.9102i −0.448590 + 0.506380i
$$651$$ −11.8485 20.5222i −0.464378 0.804327i
$$652$$ 5.49794 + 3.17423i 0.215316 + 0.124313i
$$653$$ 2.44949i 0.0958559i 0.998851 + 0.0479280i $$0.0152618\pi$$
−0.998851 + 0.0479280i $$0.984738\pi$$
$$654$$ −14.0000 −0.547443
$$655$$ 14.1479 + 10.1920i 0.552806 + 0.398234i
$$656$$ −1.22474 + 2.12132i −0.0478183 + 0.0828236i
$$657$$ 11.8990i 0.464223i
$$658$$ 10.6515i 0.415240i
$$659$$ 0.348469 0.603566i 0.0135744 0.0235116i −0.859158 0.511710i $$-0.829012\pi$$
0.872733 + 0.488198i $$0.162346\pi$$
$$660$$ −1.83548 4.07812i −0.0714458 0.158740i
$$661$$ 3.44949 5.97469i 0.134170 0.232389i −0.791110 0.611673i $$-0.790497\pi$$
0.925280 + 0.379285i $$0.123830\pi$$
$$662$$ −20.1329 + 11.6237i −0.782487 + 0.451769i
$$663$$ 14.6349 8.44949i 0.568374 0.328151i
$$664$$ −1.34847 −0.0523308
$$665$$ −23.1998 + 17.7981i −0.899648 + 0.690179i
$$666$$ −4.55051 −0.176329
$$667$$ −19.8311 + 11.4495i −0.767863 + 0.443326i
$$668$$ −13.6814 + 7.89898i −0.529351 + 0.305621i
$$669$$ 6.84847 11.8619i 0.264777 0.458607i
$$670$$ 2.95559 1.33025i 0.114185 0.0513921i
$$671$$ −4.34847 + 7.53177i −0.167871 + 0.290761i
$$672$$ 3.00000i 0.115728i
$$673$$ 10.3031i 0.397154i −0.980085 0.198577i $$-0.936368\pi$$
0.980085 0.198577i $$-0.0636320\pi$$
$$674$$ −2.05051 + 3.55159i −0.0789827 + 0.136802i
$$675$$ 3.74264 + 3.31552i 0.144054 + 0.127614i
$$676$$ −1.10102 −0.0423469
$$677$$ 6.85357i 0.263404i −0.991289 0.131702i $$-0.957956\pi$$
0.991289 0.131702i $$-0.0420442\pi$$
$$678$$ −12.9029 7.44949i −0.495533 0.286096i
$$679$$ −28.0454 48.5761i −1.07628 1.86418i
$$680$$ 8.88828 + 6.40300i 0.340850 + 0.245544i
$$681$$ −6.67423 11.5601i −0.255757 0.442985i
$$682$$ 13.6814 7.89898i 0.523889 0.302468i
$$683$$ 39.1918i 1.49963i 0.661645 + 0.749817i $$0.269858\pi$$
−0.661645 + 0.749817i $$0.730142\pi$$
$$684$$ 3.17423 2.98735i 0.121370 0.114224i
$$685$$ −2.44949 0.247449i −0.0935902 0.00945453i
$$686$$ 7.50000 + 12.9904i 0.286351 + 0.495975i
$$687$$ 23.4220 13.5227i 0.893605 0.515923i
$$688$$ −0.476756 0.275255i −0.0181761 0.0104940i
$$689$$ 5.34847 + 9.26382i 0.203760 + 0.352923i
$$690$$ −3.20150 + 4.44414i −0.121879 + 0.169186i
$$691$$ 0.404082 0.0153720 0.00768600 0.999970i $$-0.497553\pi$$
0.00768600 + 0.999970i $$0.497553\pi$$
$$692$$ 4.44949i 0.169144i
$$693$$ −5.19615 3.00000i −0.197386 0.113961i
$$694$$ −14.2474 + 24.6773i −0.540826 + 0.936738i
$$695$$ −1.47219 + 14.5732i −0.0558435 + 0.552794i
$$696$$ 9.34847 0.354353
$$697$$ 10.3923 + 6.00000i 0.393637 + 0.227266i
$$698$$ −22.9934 + 13.2753i −0.870314 + 0.502476i
$$699$$ 7.32577 12.6886i 0.277086 0.479927i
$$700$$ −14.2279 + 4.75039i −0.537765 + 0.179548i
$$701$$ 9.10102 + 15.7634i 0.343741 + 0.595377i 0.985124 0.171844i $$-0.0549725\pi$$
−0.641383 + 0.767221i $$0.721639\pi$$
$$702$$ 3.44949i 0.130193i
$$703$$ −19.3062 + 4.55051i −0.728146 + 0.171626i
$$704$$ −2.00000 −0.0753778
$$705$$ 7.23970 3.25844i 0.272663 0.122720i
$$706$$ −10.5732 18.3133i −0.397928 0.689232i
$$707$$ −9.86739 5.69694i −0.371101 0.214255i
$$708$$ −10.2173 + 5.89898i −0.383991 + 0.221697i
$$709$$ −20.6237 + 35.7213i −0.774540 + 1.34154i 0.160512 + 0.987034i $$0.448685\pi$$
−0.935053 + 0.354509i $$0.884648\pi$$
$$710$$ 7.89898 + 0.797959i 0.296443 + 0.0299469i
$$711$$ 16.7980 0.629973
$$712$$ −10.0030 5.77526i −0.374880 0.216437i
$$713$$ −16.7563 9.67423i −0.627527 0.362303i
$$714$$ 14.6969 0.550019
$$715$$ −15.3485 1.55051i −0.574000 0.0579858i
$$716$$ 9.12372 15.8028i 0.340970 0.590577i
$$717$$ 7.49245 4.32577i 0.279811 0.161549i
$$718$$ 17.5348 + 10.1237i 0.654393 + 0.377814i
$$719$$ 16.7753 + 29.0556i 0.625611 + 1.08359i 0.988422 + 0.151728i $$0.0484838\pi$$
−0.362811 + 0.931863i $$0.618183\pi$$
$$720$$ 2.03906 0.917738i 0.0759912 0.0342021i
$$721$$ 29.6969 1.10597
$$722$$ 10.4798 15.8485i 0.390017 0.589819i
$$723$$ 11.0000i 0.409094i
$$724$$ −5.55051 9.61377i −0.206283 0.357293i
$$725$$ 14.8030 + 44.3364i 0.549768 + 1.64661i
$$726$$ −3.50000 + 6.06218i −0.129897 + 0.224989i
$$727$$ −23.2077 + 13.3990i −0.860726 + 0.496941i −0.864255 0.503053i $$-0.832210\pi$$
0.00352905 + 0.999994i $$0.498877\pi$$
$$728$$ 8.96204 + 5.17423i 0.332155 + 0.191770i
$$729$$ −1.00000 −0.0370370
$$730$$ −2.67423 + 26.4722i −0.0989779 + 0.979780i
$$731$$ −1.34847 + 2.33562i −0.0498749 + 0.0863859i
$$732$$ −3.76588 2.17423i −0.139191 0.0803620i
$$733$$ 30.6969i 1.13382i 0.823781 + 0.566909i $$0.191861\pi$$
−0.823781 + 0.566909i $$0.808139\pi$$
$$734$$ −16.5959 −0.612567
$$735$$ −2.61401 + 3.62863i −0.0964194 + 0.133844i
$$736$$ 1.22474 + 2.12132i 0.0451447 + 0.0781929i
$$737$$ 2.51059 + 1.44949i 0.0924788 + 0.0533926i
$$738$$ 2.12132 1.22474i 0.0780869 0.0450835i
$$739$$ 10.8258 + 18.7508i 0.398232 + 0.689758i 0.993508 0.113763i $$-0.0362905\pi$$
−0.595276 + 0.803522i $$0.702957\pi$$
$$740$$ −10.1237 1.02270i −0.372156 0.0375953i
$$741$$ −3.44949 14.6349i −0.126720 0.537628i
$$742$$ 9.30306i 0.341526i
$$743$$ 39.8372 23.0000i 1.46148 0.843788i 0.462404 0.886669i $$-0.346987\pi$$
0.999080 + 0.0428813i $$0.0136537\pi$$
$$744$$ 3.94949 + 6.84072i 0.144795 + 0.250793i
$$745$$ −6.89069 4.96396i −0.252455 0.181865i
$$746$$ −12.5505 21.7381i −0.459507 0.795889i
$$747$$ 1.16781 + 0.674235i 0.0427279 + 0.0246690i
$$748$$ 9.79796i 0.358249i
$$749$$ −31.3485 −1.14545
$$750$$ 7.58128 + 8.21731i 0.276829 + 0.300054i
$$751$$ 10.1515 17.5830i 0.370435 0.641612i −0.619198 0.785235i $$-0.712542\pi$$
0.989632 + 0.143623i $$0.0458754\pi$$
$$752$$ 3.55051i 0.129474i
$$753$$ 20.6969i 0.754238i
$$754$$ 16.1237 27.9271i 0.587191 1.01705i
$$755$$ −40.3692 + 18.1693i −1.46919 + 0.661250i
$$756$$ 1.50000 2.59808i 0.0545545 0.0944911i
$$757$$ 10.6941 6.17423i 0.388683 0.224406i −0.292906 0.956141i $$-0.594622\pi$$
0.681589 + 0.731735i $$0.261289\pi$$
$$758$$ 7.57993 4.37628i 0.275316 0.158953i
$$759$$ −4.89898 −0.177822
$$760$$ 7.73325 5.93269i 0.280515 0.215201i
$$761$$ 34.8990 1.26509 0.632544 0.774525i $$-0.282011\pi$$
0.632544 + 0.774525i $$0.282011\pi$$
$$762$$ 14.4600 8.34847i 0.523830 0.302433i
$$763$$ −36.3731 + 21.0000i −1.31679 + 0.760251i
$$764$$ −7.34847 + 12.7279i −0.265858 + 0.460480i
$$765$$ −4.49598 9.98930i −0.162552 0.361164i
$$766$$ −0.674235 + 1.16781i −0.0243611 + 0.0421946i
$$767$$ 40.6969i 1.46948i
$$768$$ 1.00000i 0.0360844i
$$769$$ 0.297959 0.516080i 0.0107447 0.0186103i −0.860603 0.509276i $$-0.829913\pi$$
0.871348 + 0.490666i $$0.163246\pi$$
$$770$$ −10.8859 7.84204i −0.392300 0.282608i
$$771$$ 25.1464 0.905626
$$772$$ 2.10102i 0.0756174i
$$773$$ −33.6875 19.4495i −1.21166 0.699550i −0.248536 0.968623i $$-0.579949\pi$$
−0.963120 + 0.269073i $$0.913283\pi$$
$$774$$ 0.275255 + 0.476756i 0.00989384 + 0.0171366i
$$775$$ <