# Properties

 Label 76.2.i.a.17.2 Level $76$ Weight $2$ Character 76.17 Analytic conductor $0.607$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Learn more

## Newspace parameters

 Level: $$N$$ $$=$$ $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 76.i (of order $$9$$, degree $$6$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$0.606863055362$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$2$$ over $$\Q(\zeta_{9})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ Defining polynomial: $$x^{12} - 6 x^{11} - 3 x^{10} + 70 x^{9} - 15 x^{8} - 426 x^{7} + 64 x^{6} + 1659 x^{5} + 267 x^{4} - 3969 x^{3} - 2088 x^{2} + 4446 x + 4161$$ Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

## Embedding invariants

 Embedding label 17.2 Root $$-1.26253 + 0.984808i$$ of defining polynomial Character $$\chi$$ $$=$$ 76.17 Dual form 76.2.i.a.9.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.86622 + 1.56594i) q^{3} +(-2.06765 + 0.752564i) q^{5} +(-1.48413 - 2.57059i) q^{7} +(0.509650 + 2.89037i) q^{9} +O(q^{10})$$ $$q+(1.86622 + 1.56594i) q^{3} +(-2.06765 + 0.752564i) q^{5} +(-1.48413 - 2.57059i) q^{7} +(0.509650 + 2.89037i) q^{9} +(1.34956 - 2.33751i) q^{11} +(3.64418 - 3.05783i) q^{13} +(-5.03717 - 1.83338i) q^{15} +(-1.19836 + 6.79626i) q^{17} +(-4.33264 - 0.477728i) q^{19} +(1.25569 - 7.12136i) q^{21} +(-4.86497 - 1.77070i) q^{23} +(-0.121388 + 0.101857i) q^{25} +(0.0792304 - 0.137231i) q^{27} +(1.17057 + 6.63861i) q^{29} +(2.14339 + 3.71247i) q^{31} +(6.17900 - 2.24897i) q^{33} +(5.00321 + 4.19819i) q^{35} -5.02546 q^{37} +11.5892 q^{39} +(1.42844 + 1.19860i) q^{41} +(8.50895 - 3.09700i) q^{43} +(-3.22896 - 5.59273i) q^{45} +(0.108919 + 0.617710i) q^{47} +(-0.905299 + 1.56802i) q^{49} +(-12.8790 + 10.8067i) q^{51} +(-6.42007 - 2.33671i) q^{53} +(-1.03130 + 5.84880i) q^{55} +(-7.33756 - 7.67622i) q^{57} +(0.623372 - 3.53532i) q^{59} +(9.43969 + 3.43576i) q^{61} +(6.67357 - 5.59979i) q^{63} +(-5.23369 + 9.06501i) q^{65} +(-1.58002 - 8.96073i) q^{67} +(-6.30628 - 10.9228i) q^{69} +(-0.533286 + 0.194100i) q^{71} +(-0.598968 - 0.502594i) q^{73} -0.386038 q^{75} -8.01173 q^{77} +(2.42448 + 2.03438i) q^{79} +(8.63662 - 3.14347i) q^{81} +(3.64810 + 6.31870i) q^{83} +(-2.63682 - 14.9542i) q^{85} +(-8.21115 + 14.2221i) q^{87} +(7.84414 - 6.58201i) q^{89} +(-13.2689 - 4.82948i) q^{91} +(-1.81347 + 10.2847i) q^{93} +(9.31792 - 2.27281i) q^{95} +(-1.47083 + 8.34147i) q^{97} +(7.44408 + 2.70942i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12q - 3q^{3} + 3q^{7} - 3q^{9} + O(q^{10})$$ $$12q - 3q^{3} + 3q^{7} - 3q^{9} + 3q^{11} - 9q^{13} - 15q^{15} - 3q^{17} - 12q^{19} - 15q^{21} - 12q^{23} - 18q^{25} - 9q^{27} + 27q^{29} + 6q^{31} + 48q^{33} + 33q^{35} - 12q^{37} + 60q^{39} + 3q^{41} + 27q^{43} + 24q^{45} - 15q^{47} + 9q^{49} - 33q^{51} - 21q^{53} - 27q^{55} - 42q^{57} - 48q^{59} - 6q^{61} - 9q^{63} - 33q^{65} + 24q^{67} - 33q^{69} + 30q^{73} + 42q^{75} + 24q^{77} + 3q^{79} + 3q^{81} + 3q^{83} - 42q^{85} - 18q^{87} - 18q^{89} - 24q^{91} - 78q^{93} + 9q^{95} + 12q^{97} - 6q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$$.

 $$n$$ $$21$$ $$39$$ $$\chi(n)$$ $$e\left(\frac{5}{9}\right)$$ $$1$$

## 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 0
$$3$$ 1.86622 + 1.56594i 1.07746 + 0.904098i 0.995708 0.0925543i $$-0.0295032\pi$$
0.0817546 + 0.996652i $$0.473948\pi$$
$$4$$ 0 0
$$5$$ −2.06765 + 0.752564i −0.924682 + 0.336557i −0.760100 0.649806i $$-0.774850\pi$$
−0.164583 + 0.986363i $$0.552628\pi$$
$$6$$ 0 0
$$7$$ −1.48413 2.57059i −0.560949 0.971593i −0.997414 0.0718714i $$-0.977103\pi$$
0.436465 0.899721i $$-0.356230\pi$$
$$8$$ 0 0
$$9$$ 0.509650 + 2.89037i 0.169883 + 0.963456i
$$10$$ 0 0
$$11$$ 1.34956 2.33751i 0.406909 0.704787i −0.587633 0.809128i $$-0.699940\pi$$
0.994542 + 0.104341i $$0.0332733\pi$$
$$12$$ 0 0
$$13$$ 3.64418 3.05783i 1.01071 0.848090i 0.0222816 0.999752i $$-0.492907\pi$$
0.988432 + 0.151662i $$0.0484625\pi$$
$$14$$ 0 0
$$15$$ −5.03717 1.83338i −1.30059 0.473376i
$$16$$ 0 0
$$17$$ −1.19836 + 6.79626i −0.290646 + 1.64834i 0.393744 + 0.919220i $$0.371180\pi$$
−0.684390 + 0.729116i $$0.739931\pi$$
$$18$$ 0 0
$$19$$ −4.33264 0.477728i −0.993976 0.109598i
$$20$$ 0 0
$$21$$ 1.25569 7.12136i 0.274014 1.55401i
$$22$$ 0 0
$$23$$ −4.86497 1.77070i −1.01442 0.369217i −0.219289 0.975660i $$-0.570374\pi$$
−0.795127 + 0.606442i $$0.792596\pi$$
$$24$$ 0 0
$$25$$ −0.121388 + 0.101857i −0.0242776 + 0.0203713i
$$26$$ 0 0
$$27$$ 0.0792304 0.137231i 0.0152479 0.0264101i
$$28$$ 0 0
$$29$$ 1.17057 + 6.63861i 0.217369 + 1.23276i 0.876749 + 0.480949i $$0.159708\pi$$
−0.659380 + 0.751810i $$0.729181\pi$$
$$30$$ 0 0
$$31$$ 2.14339 + 3.71247i 0.384965 + 0.666779i 0.991764 0.128076i $$-0.0408802\pi$$
−0.606799 + 0.794855i $$0.707547\pi$$
$$32$$ 0 0
$$33$$ 6.17900 2.24897i 1.07563 0.391496i
$$34$$ 0 0
$$35$$ 5.00321 + 4.19819i 0.845696 + 0.709623i
$$36$$ 0 0
$$37$$ −5.02546 −0.826181 −0.413091 0.910690i $$-0.635551\pi$$
−0.413091 + 0.910690i $$0.635551\pi$$
$$38$$ 0 0
$$39$$ 11.5892 1.85576
$$40$$ 0 0
$$41$$ 1.42844 + 1.19860i 0.223085 + 0.187190i 0.747479 0.664285i $$-0.231264\pi$$
−0.524395 + 0.851475i $$0.675708\pi$$
$$42$$ 0 0
$$43$$ 8.50895 3.09700i 1.29760 0.472289i 0.401387 0.915908i $$-0.368528\pi$$
0.896215 + 0.443620i $$0.146306\pi$$
$$44$$ 0 0
$$45$$ −3.22896 5.59273i −0.481346 0.833715i
$$46$$ 0 0
$$47$$ 0.108919 + 0.617710i 0.0158875 + 0.0901022i 0.991720 0.128415i $$-0.0409890\pi$$
−0.975833 + 0.218518i $$0.929878\pi$$
$$48$$ 0 0
$$49$$ −0.905299 + 1.56802i −0.129328 + 0.224003i
$$50$$ 0 0
$$51$$ −12.8790 + 10.8067i −1.80342 + 1.51325i
$$52$$ 0 0
$$53$$ −6.42007 2.33671i −0.881864 0.320972i −0.138902 0.990306i $$-0.544357\pi$$
−0.742962 + 0.669334i $$0.766580\pi$$
$$54$$ 0 0
$$55$$ −1.03130 + 5.84880i −0.139061 + 0.788652i
$$56$$ 0 0
$$57$$ −7.33756 7.67622i −0.971884 1.01674i
$$58$$ 0 0
$$59$$ 0.623372 3.53532i 0.0811561 0.460259i −0.916964 0.398970i $$-0.869368\pi$$
0.998120 0.0612890i $$-0.0195211\pi$$
$$60$$ 0 0
$$61$$ 9.43969 + 3.43576i 1.20863 + 0.439905i 0.866228 0.499650i $$-0.166538\pi$$
0.342400 + 0.939554i $$0.388760\pi$$
$$62$$ 0 0
$$63$$ 6.67357 5.59979i 0.840791 0.705507i
$$64$$ 0 0
$$65$$ −5.23369 + 9.06501i −0.649159 + 1.12438i
$$66$$ 0 0
$$67$$ −1.58002 8.96073i −0.193030 1.09473i −0.915196 0.403008i $$-0.867965\pi$$
0.722167 0.691719i $$-0.243146\pi$$
$$68$$ 0 0
$$69$$ −6.30628 10.9228i −0.759187 1.31495i
$$70$$ 0 0
$$71$$ −0.533286 + 0.194100i −0.0632894 + 0.0230355i −0.373471 0.927642i $$-0.621832\pi$$
0.310181 + 0.950677i $$0.399610\pi$$
$$72$$ 0 0
$$73$$ −0.598968 0.502594i −0.0701039 0.0588242i 0.607062 0.794654i $$-0.292348\pi$$
−0.677166 + 0.735830i $$0.736792\pi$$
$$74$$ 0 0
$$75$$ −0.386038 −0.0445759
$$76$$ 0 0
$$77$$ −8.01173 −0.913021
$$78$$ 0 0
$$79$$ 2.42448 + 2.03438i 0.272775 + 0.228885i 0.768905 0.639363i $$-0.220802\pi$$
−0.496130 + 0.868248i $$0.665246\pi$$
$$80$$ 0 0
$$81$$ 8.63662 3.14347i 0.959625 0.349275i
$$82$$ 0 0
$$83$$ 3.64810 + 6.31870i 0.400431 + 0.693568i 0.993778 0.111380i $$-0.0355269\pi$$
−0.593346 + 0.804947i $$0.702194\pi$$
$$84$$ 0 0
$$85$$ −2.63682 14.9542i −0.286003 1.62201i
$$86$$ 0 0
$$87$$ −8.21115 + 14.2221i −0.880328 + 1.52477i
$$88$$ 0 0
$$89$$ 7.84414 6.58201i 0.831477 0.697692i −0.124152 0.992263i $$-0.539621\pi$$
0.955630 + 0.294571i $$0.0951768\pi$$
$$90$$ 0 0
$$91$$ −13.2689 4.82948i −1.39096 0.506267i
$$92$$ 0 0
$$93$$ −1.81347 + 10.2847i −0.188048 + 1.06647i
$$94$$ 0 0
$$95$$ 9.31792 2.27281i 0.955998 0.233186i
$$96$$ 0 0
$$97$$ −1.47083 + 8.34147i −0.149340 + 0.846948i 0.814440 + 0.580248i $$0.197044\pi$$
−0.963780 + 0.266700i $$0.914067\pi$$
$$98$$ 0 0
$$99$$ 7.44408 + 2.70942i 0.748158 + 0.272307i
$$100$$ 0 0
$$101$$ 7.17480 6.02037i 0.713920 0.599050i −0.211776 0.977318i $$-0.567925\pi$$
0.925696 + 0.378269i $$0.123480\pi$$
$$102$$ 0 0
$$103$$ −6.00311 + 10.3977i −0.591504 + 1.02452i 0.402526 + 0.915409i $$0.368132\pi$$
−0.994030 + 0.109107i $$0.965201\pi$$
$$104$$ 0 0
$$105$$ 2.76295 + 15.6695i 0.269637 + 1.52918i
$$106$$ 0 0
$$107$$ −7.15153 12.3868i −0.691364 1.19748i −0.971391 0.237486i $$-0.923677\pi$$
0.280027 0.959992i $$-0.409657\pi$$
$$108$$ 0 0
$$109$$ 2.08076 0.757335i 0.199301 0.0725396i −0.240441 0.970664i $$-0.577292\pi$$
0.439742 + 0.898124i $$0.355070\pi$$
$$110$$ 0 0
$$111$$ −9.37862 7.86960i −0.890179 0.746949i
$$112$$ 0 0
$$113$$ −7.64213 −0.718911 −0.359455 0.933162i $$-0.617038\pi$$
−0.359455 + 0.933162i $$0.617038\pi$$
$$114$$ 0 0
$$115$$ 11.3916 1.06228
$$116$$ 0 0
$$117$$ 10.6955 + 8.97460i 0.988800 + 0.829702i
$$118$$ 0 0
$$119$$ 19.2490 7.00605i 1.76455 0.642244i
$$120$$ 0 0
$$121$$ 1.85735 + 3.21703i 0.168850 + 0.292457i
$$122$$ 0 0
$$123$$ 0.788836 + 4.47371i 0.0711270 + 0.403381i
$$124$$ 0 0
$$125$$ 5.67521 9.82975i 0.507606 0.879200i
$$126$$ 0 0
$$127$$ −3.55943 + 2.98672i −0.315848 + 0.265028i −0.786904 0.617075i $$-0.788317\pi$$
0.471056 + 0.882103i $$0.343873\pi$$
$$128$$ 0 0
$$129$$ 20.7293 + 7.54485i 1.82511 + 0.664287i
$$130$$ 0 0
$$131$$ 0.00139646 0.00791975i 0.000122010 0.000691951i −0.984747 0.173994i $$-0.944333\pi$$
0.984869 + 0.173302i $$0.0554437\pi$$
$$132$$ 0 0
$$133$$ 5.20217 + 11.8465i 0.451085 + 1.02722i
$$134$$ 0 0
$$135$$ −0.0605457 + 0.343372i −0.00521095 + 0.0295528i
$$136$$ 0 0
$$137$$ −14.6907 5.34697i −1.25511 0.456822i −0.372984 0.927838i $$-0.621665\pi$$
−0.882125 + 0.471015i $$0.843888\pi$$
$$138$$ 0 0
$$139$$ −5.96207 + 5.00277i −0.505697 + 0.424330i −0.859612 0.510948i $$-0.829295\pi$$
0.353915 + 0.935278i $$0.384850\pi$$
$$140$$ 0 0
$$141$$ −0.764032 + 1.32334i −0.0643431 + 0.111446i
$$142$$ 0 0
$$143$$ −2.22967 12.6451i −0.186454 1.05743i
$$144$$ 0 0
$$145$$ −7.41630 12.8454i −0.615890 1.06675i
$$146$$ 0 0
$$147$$ −4.14493 + 1.50863i −0.341868 + 0.124430i
$$148$$ 0 0
$$149$$ −0.400779 0.336294i −0.0328331 0.0275502i 0.626223 0.779644i $$-0.284600\pi$$
−0.659057 + 0.752093i $$0.729044\pi$$
$$150$$ 0 0
$$151$$ 0.0730868 0.00594772 0.00297386 0.999996i $$-0.499053\pi$$
0.00297386 + 0.999996i $$0.499053\pi$$
$$152$$ 0 0
$$153$$ −20.2544 −1.63747
$$154$$ 0 0
$$155$$ −7.22566 6.06305i −0.580379 0.486996i
$$156$$ 0 0
$$157$$ −13.4211 + 4.88487i −1.07112 + 0.389855i −0.816594 0.577212i $$-0.804141\pi$$
−0.254523 + 0.967067i $$0.581918\pi$$
$$158$$ 0 0
$$159$$ −8.32209 14.4143i −0.659985 1.14313i
$$160$$ 0 0
$$161$$ 2.66850 + 15.1338i 0.210307 + 1.19271i
$$162$$ 0 0
$$163$$ −0.158689 + 0.274858i −0.0124295 + 0.0215286i −0.872173 0.489197i $$-0.837290\pi$$
0.859744 + 0.510726i $$0.170623\pi$$
$$164$$ 0 0
$$165$$ −11.0835 + 9.30018i −0.862851 + 0.724018i
$$166$$ 0 0
$$167$$ −0.822400 0.299329i −0.0636392 0.0231628i 0.310004 0.950735i $$-0.399669\pi$$
−0.373644 + 0.927572i $$0.621892\pi$$
$$168$$ 0 0
$$169$$ 1.67230 9.48408i 0.128638 0.729545i
$$170$$ 0 0
$$171$$ −0.827319 12.7664i −0.0632667 0.976271i
$$172$$ 0 0
$$173$$ 3.78253 21.4518i 0.287581 1.63095i −0.408338 0.912831i $$-0.633891\pi$$
0.695919 0.718121i $$-0.254997\pi$$
$$174$$ 0 0
$$175$$ 0.441988 + 0.160870i 0.0334111 + 0.0121607i
$$176$$ 0 0
$$177$$ 6.69946 5.62151i 0.503562 0.422539i
$$178$$ 0 0
$$179$$ 2.96398 5.13376i 0.221538 0.383715i −0.733737 0.679433i $$-0.762226\pi$$
0.955275 + 0.295718i $$0.0955590\pi$$
$$180$$ 0 0
$$181$$ 2.09038 + 11.8552i 0.155377 + 0.881187i 0.958440 + 0.285293i $$0.0920910\pi$$
−0.803063 + 0.595894i $$0.796798\pi$$
$$182$$ 0 0
$$183$$ 12.2363 + 21.1939i 0.904534 + 1.56670i
$$184$$ 0 0
$$185$$ 10.3909 3.78198i 0.763955 0.278057i
$$186$$ 0 0
$$187$$ 14.2691 + 11.9732i 1.04346 + 0.875566i
$$188$$ 0 0
$$189$$ −0.470353 −0.0342132
$$190$$ 0 0
$$191$$ −8.38465 −0.606692 −0.303346 0.952880i $$-0.598104\pi$$
−0.303346 + 0.952880i $$0.598104\pi$$
$$192$$ 0 0
$$193$$ 0.715575 + 0.600439i 0.0515082 + 0.0432205i 0.668178 0.744001i $$-0.267074\pi$$
−0.616670 + 0.787222i $$0.711519\pi$$
$$194$$ 0 0
$$195$$ −23.9625 + 8.72164i −1.71599 + 0.624570i
$$196$$ 0 0
$$197$$ 11.1803 + 19.3648i 0.796562 + 1.37969i 0.921843 + 0.387565i $$0.126684\pi$$
−0.125280 + 0.992121i $$0.539983\pi$$
$$198$$ 0 0
$$199$$ −2.50746 14.2205i −0.177749 1.00806i −0.934923 0.354851i $$-0.884532\pi$$
0.757174 0.653213i $$-0.226580\pi$$
$$200$$ 0 0
$$201$$ 11.0833 19.1969i 0.781758 1.35405i
$$202$$ 0 0
$$203$$ 15.3279 12.8616i 1.07581 0.902709i
$$204$$ 0 0
$$205$$ −3.85554 1.40330i −0.269283 0.0980109i
$$206$$ 0 0
$$207$$ 2.63855 14.9640i 0.183392 1.04007i
$$208$$ 0 0
$$209$$ −6.96387 + 9.48288i −0.481701 + 0.655945i
$$210$$ 0 0
$$211$$ −3.15065 + 17.8682i −0.216900 + 1.23010i 0.660679 + 0.750668i $$0.270268\pi$$
−0.877579 + 0.479432i $$0.840843\pi$$
$$212$$ 0 0
$$213$$ −1.29918 0.472863i −0.0890183 0.0324000i
$$214$$ 0 0
$$215$$ −15.2629 + 12.8071i −1.04092 + 0.873434i
$$216$$ 0 0
$$217$$ 6.36216 11.0196i 0.431892 0.748058i
$$218$$ 0 0
$$219$$ −0.330772 1.87590i −0.0223515 0.126762i
$$220$$ 0 0
$$221$$ 16.4148 + 28.4312i 1.10418 + 1.91249i
$$222$$ 0 0
$$223$$ −3.08215 + 1.12181i −0.206396 + 0.0751219i −0.443149 0.896448i $$-0.646139\pi$$
0.236754 + 0.971570i $$0.423917\pi$$
$$224$$ 0 0
$$225$$ −0.356268 0.298945i −0.0237512 0.0199296i
$$226$$ 0 0
$$227$$ 11.5190 0.764543 0.382272 0.924050i $$-0.375142\pi$$
0.382272 + 0.924050i $$0.375142\pi$$
$$228$$ 0 0
$$229$$ 15.3682 1.01556 0.507780 0.861487i $$-0.330466\pi$$
0.507780 + 0.861487i $$0.330466\pi$$
$$230$$ 0 0
$$231$$ −14.9516 12.5459i −0.983746 0.825461i
$$232$$ 0 0
$$233$$ −12.8920 + 4.69229i −0.844581 + 0.307402i −0.727829 0.685759i $$-0.759471\pi$$
−0.116752 + 0.993161i $$0.537248\pi$$
$$234$$ 0 0
$$235$$ −0.690073 1.19524i −0.0450154 0.0779689i
$$236$$ 0 0
$$237$$ 1.33888 + 7.59318i 0.0869698 + 0.493230i
$$238$$ 0 0
$$239$$ −8.39945 + 14.5483i −0.543315 + 0.941050i 0.455396 + 0.890289i $$0.349498\pi$$
−0.998711 + 0.0507604i $$0.983836\pi$$
$$240$$ 0 0
$$241$$ 17.2571 14.4804i 1.11163 0.932765i 0.113474 0.993541i $$-0.463802\pi$$
0.998151 + 0.0607762i $$0.0193576\pi$$
$$242$$ 0 0
$$243$$ 20.5936 + 7.49547i 1.32108 + 0.480834i
$$244$$ 0 0
$$245$$ 0.691806 3.92342i 0.0441978 0.250658i
$$246$$ 0 0
$$247$$ −17.2497 + 11.5076i −1.09757 + 0.732208i
$$248$$ 0 0
$$249$$ −3.08657 + 17.5048i −0.195603 + 1.10932i
$$250$$ 0 0
$$251$$ 14.5743 + 5.30463i 0.919924 + 0.334825i 0.758208 0.652012i $$-0.226075\pi$$
0.161716 + 0.986837i $$0.448297\pi$$
$$252$$ 0 0
$$253$$ −10.7046 + 8.98226i −0.672995 + 0.564710i
$$254$$ 0 0
$$255$$ 18.4965 32.0369i 1.15830 2.00623i
$$256$$ 0 0
$$257$$ −5.05935 28.6930i −0.315594 1.78982i −0.568870 0.822427i $$-0.692619\pi$$
0.253277 0.967394i $$-0.418492\pi$$
$$258$$ 0 0
$$259$$ 7.45846 + 12.9184i 0.463446 + 0.802712i
$$260$$ 0 0
$$261$$ −18.5914 + 6.76673i −1.15078 + 0.418850i
$$262$$ 0 0
$$263$$ 2.90918 + 2.44110i 0.179388 + 0.150524i 0.728060 0.685513i $$-0.240422\pi$$
−0.548672 + 0.836038i $$0.684867\pi$$
$$264$$ 0 0
$$265$$ 15.0330 0.923470
$$266$$ 0 0
$$267$$ 24.9459 1.52667
$$268$$ 0 0
$$269$$ −6.09243 5.11215i −0.371462 0.311693i 0.437878 0.899035i $$-0.355730\pi$$
−0.809340 + 0.587341i $$0.800175\pi$$
$$270$$ 0 0
$$271$$ 0.640257 0.233034i 0.0388928 0.0141558i −0.322500 0.946569i $$-0.604523\pi$$
0.361393 + 0.932413i $$0.382301\pi$$
$$272$$ 0 0
$$273$$ −17.2000 29.7912i −1.04099 1.80305i
$$274$$ 0 0
$$275$$ 0.0742704 + 0.421208i 0.00447867 + 0.0253998i
$$276$$ 0 0
$$277$$ 6.97191 12.0757i 0.418901 0.725558i −0.576928 0.816795i $$-0.695749\pi$$
0.995829 + 0.0912367i $$0.0290820\pi$$
$$278$$ 0 0
$$279$$ −9.63801 + 8.08725i −0.577013 + 0.484171i
$$280$$ 0 0
$$281$$ −25.1212 9.14338i −1.49861 0.545448i −0.542908 0.839792i $$-0.682677\pi$$
−0.955700 + 0.294344i $$0.904899\pi$$
$$282$$ 0 0
$$283$$ 0.879102 4.98563i 0.0522572 0.296365i −0.947467 0.319854i $$-0.896366\pi$$
0.999724 + 0.0234886i $$0.00747733\pi$$
$$284$$ 0 0
$$285$$ 20.9484 + 10.3498i 1.24087 + 0.613067i
$$286$$ 0 0
$$287$$ 0.961127 5.45082i 0.0567335 0.321752i
$$288$$ 0 0
$$289$$ −28.7784 10.4745i −1.69284 0.616145i
$$290$$ 0 0
$$291$$ −15.8072 + 13.2638i −0.926632 + 0.777536i
$$292$$ 0 0
$$293$$ −0.625879 + 1.08405i −0.0365642 + 0.0633311i −0.883728 0.468000i $$-0.844975\pi$$
0.847164 + 0.531331i $$0.178308\pi$$
$$294$$ 0 0
$$295$$ 1.37164 + 7.77893i 0.0798597 + 0.452907i
$$296$$ 0 0
$$297$$ −0.213853 0.370404i −0.0124090 0.0214930i
$$298$$ 0 0
$$299$$ −23.1434 + 8.42349i −1.33841 + 0.487143i
$$300$$ 0 0
$$301$$ −20.5895 17.2767i −1.18676 0.995811i
$$302$$ 0 0
$$303$$ 22.8173 1.31082
$$304$$ 0 0
$$305$$ −22.1036 −1.26565
$$306$$ 0 0
$$307$$ −18.5543 15.5689i −1.05895 0.888564i −0.0649432 0.997889i $$-0.520687\pi$$
−0.994006 + 0.109325i $$0.965131\pi$$
$$308$$ 0 0
$$309$$ −27.4853 + 10.0038i −1.56359 + 0.569099i
$$310$$ 0 0
$$311$$ 15.7119 + 27.2139i 0.890942 + 1.54316i 0.838747 + 0.544521i $$0.183288\pi$$
0.0521949 + 0.998637i $$0.483378\pi$$
$$312$$ 0 0
$$313$$ 3.65444 + 20.7254i 0.206561 + 1.17147i 0.894964 + 0.446139i $$0.147201\pi$$
−0.688402 + 0.725329i $$0.741688\pi$$
$$314$$ 0 0
$$315$$ −9.58442 + 16.6007i −0.540021 + 0.935344i
$$316$$ 0 0
$$317$$ 7.82632 6.56706i 0.439570 0.368843i −0.395978 0.918260i $$-0.629595\pi$$
0.835548 + 0.549417i $$0.185150\pi$$
$$318$$ 0 0
$$319$$ 17.0976 + 6.22301i 0.957281 + 0.348422i
$$320$$ 0 0
$$321$$ 6.05073 34.3154i 0.337719 1.91530i
$$322$$ 0 0
$$323$$ 8.43885 28.8733i 0.469550 1.60655i
$$324$$ 0 0
$$325$$ −0.130899 + 0.742368i −0.00726100 + 0.0411792i
$$326$$ 0 0
$$327$$ 5.06910 + 1.84500i 0.280322 + 0.102029i
$$328$$ 0 0
$$329$$ 1.42623 1.19675i 0.0786306 0.0659789i
$$330$$ 0 0
$$331$$ 13.6834 23.7003i 0.752105 1.30268i −0.194695 0.980864i $$-0.562372\pi$$
0.946801 0.321821i $$-0.104295\pi$$
$$332$$ 0 0
$$333$$ −2.56123 14.5254i −0.140354 0.795989i
$$334$$ 0 0
$$335$$ 10.0104 + 17.3386i 0.546929 + 0.947309i
$$336$$ 0 0
$$337$$ −1.26806 + 0.461535i −0.0690754 + 0.0251414i −0.376327 0.926487i $$-0.622813\pi$$
0.307251 + 0.951628i $$0.400591\pi$$
$$338$$ 0 0
$$339$$ −14.2619 11.9671i −0.774599 0.649966i
$$340$$ 0 0
$$341$$ 11.5706 0.626583
$$342$$ 0 0
$$343$$ −15.4035 −0.831712
$$344$$ 0 0
$$345$$ 21.2593 + 17.8387i 1.14456 + 0.960402i
$$346$$ 0 0
$$347$$ −9.33198 + 3.39656i −0.500967 + 0.182337i −0.580129 0.814525i $$-0.696998\pi$$
0.0791620 + 0.996862i $$0.474776\pi$$
$$348$$ 0 0
$$349$$ 3.32804 + 5.76434i 0.178146 + 0.308558i 0.941246 0.337723i $$-0.109657\pi$$
−0.763100 + 0.646281i $$0.776323\pi$$
$$350$$ 0 0
$$351$$ −0.130899 0.742368i −0.00698690 0.0396247i
$$352$$ 0 0
$$353$$ −10.8285 + 18.7556i −0.576345 + 0.998259i 0.419549 + 0.907733i $$0.362188\pi$$
−0.995894 + 0.0905262i $$0.971145\pi$$
$$354$$ 0 0
$$355$$ 0.956578 0.802664i 0.0507699 0.0426010i
$$356$$ 0 0
$$357$$ 46.8939 + 17.0680i 2.48189 + 0.903333i
$$358$$ 0 0
$$359$$ −1.67956 + 9.52525i −0.0886437 + 0.502724i 0.907867 + 0.419258i $$0.137710\pi$$
−0.996511 + 0.0834652i $$0.973401\pi$$
$$360$$ 0 0
$$361$$ 18.5436 + 4.13965i 0.975976 + 0.217876i
$$362$$ 0 0
$$363$$ −1.57146 + 8.91219i −0.0824802 + 0.467769i
$$364$$ 0 0
$$365$$ 1.61669 + 0.588428i 0.0846215 + 0.0307997i
$$366$$ 0 0
$$367$$ 19.8828 16.6837i 1.03788 0.870881i 0.0461083 0.998936i $$-0.485318\pi$$
0.991767 + 0.128056i $$0.0408736\pi$$
$$368$$ 0 0
$$369$$ −2.73640 + 4.73958i −0.142451 + 0.246733i
$$370$$ 0 0
$$371$$ 3.52149 + 19.9714i 0.182827 + 1.03686i
$$372$$ 0 0
$$373$$ −9.13616 15.8243i −0.473052 0.819351i 0.526472 0.850193i $$-0.323515\pi$$
−0.999524 + 0.0308418i $$0.990181\pi$$
$$374$$ 0 0
$$375$$ 25.9840 9.45741i 1.34181 0.488379i
$$376$$ 0 0
$$377$$ 24.5655 + 20.6129i 1.26519 + 1.06162i
$$378$$ 0 0
$$379$$ −31.1455 −1.59983 −0.799917 0.600110i $$-0.795123\pi$$
−0.799917 + 0.600110i $$0.795123\pi$$
$$380$$ 0 0
$$381$$ −11.3197 −0.579926
$$382$$ 0 0
$$383$$ −22.1294 18.5687i −1.13076 0.948819i −0.131661 0.991295i $$-0.542031\pi$$
−0.999097 + 0.0424761i $$0.986475\pi$$
$$384$$ 0 0
$$385$$ 16.5655 6.02934i 0.844255 0.307284i
$$386$$ 0 0
$$387$$ 13.2881 + 23.0156i 0.675470 + 1.16995i
$$388$$ 0 0
$$389$$ −1.07456 6.09416i −0.0544826 0.308986i 0.945373 0.325991i $$-0.105698\pi$$
−0.999855 + 0.0170051i $$0.994587\pi$$
$$390$$ 0 0
$$391$$ 17.8642 30.9417i 0.903431 1.56479i
$$392$$ 0 0
$$393$$ 0.0150080 0.0125932i 0.000757053 0.000635243i
$$394$$ 0 0
$$395$$ −6.54397 2.38181i −0.329263 0.119842i
$$396$$ 0 0
$$397$$ −1.25366 + 7.10986i −0.0629194 + 0.356834i 0.937051 + 0.349191i $$0.113544\pi$$
−0.999971 + 0.00764217i $$0.997567\pi$$
$$398$$ 0 0
$$399$$ −8.84252 + 30.2544i −0.442680 + 1.51462i
$$400$$ 0 0
$$401$$ −4.01252 + 22.7561i −0.200376 + 1.13639i 0.704177 + 0.710025i $$0.251316\pi$$
−0.904552 + 0.426362i $$0.859795\pi$$
$$402$$ 0 0
$$403$$ 19.1630 + 6.97477i 0.954578 + 0.347438i
$$404$$ 0 0
$$405$$ −15.4919 + 12.9992i −0.769797 + 0.645937i
$$406$$ 0 0
$$407$$ −6.78219 + 11.7471i −0.336181 + 0.582282i
$$408$$ 0 0
$$409$$ −1.47083 8.34147i −0.0727276 0.412459i −0.999336 0.0364315i $$-0.988401\pi$$
0.926609 0.376027i $$-0.122710\pi$$
$$410$$ 0 0
$$411$$ −19.0430 32.9834i −0.939321 1.62695i
$$412$$ 0 0
$$413$$ −10.0130 + 3.64444i −0.492709 + 0.179331i
$$414$$ 0 0
$$415$$ −12.2982 10.3194i −0.603697 0.506562i
$$416$$ 0 0
$$417$$ −18.9606 −0.928505
$$418$$ 0 0
$$419$$ −34.4402 −1.68251 −0.841257 0.540635i $$-0.818184\pi$$
−0.841257 + 0.540635i $$0.818184\pi$$
$$420$$ 0 0
$$421$$ 8.18476 + 6.86783i 0.398901 + 0.334718i 0.820069 0.572265i $$-0.193935\pi$$
−0.421168 + 0.906983i $$0.638380\pi$$
$$422$$ 0 0
$$423$$ −1.72990 + 0.629631i −0.0841105 + 0.0306137i
$$424$$ 0 0
$$425$$ −0.546777 0.947046i −0.0265226 0.0459385i
$$426$$ 0 0
$$427$$ −5.17779 29.3647i −0.250571 1.42106i
$$428$$ 0 0
$$429$$ 15.6404 27.0900i 0.755126 1.30792i
$$430$$ 0 0
$$431$$ −9.45533 + 7.93396i −0.455447 + 0.382166i −0.841453 0.540331i $$-0.818299\pi$$
0.386005 + 0.922497i $$0.373855\pi$$
$$432$$ 0 0
$$433$$ 33.6628 + 12.2522i 1.61773 + 0.588805i 0.982948 0.183886i $$-0.0588676\pi$$
0.634782 + 0.772691i $$0.281090\pi$$
$$434$$ 0 0
$$435$$ 6.27475 35.5859i 0.300851 1.70621i
$$436$$ 0 0
$$437$$ 20.2323 + 9.99596i 0.967840 + 0.478172i
$$438$$ 0 0
$$439$$ −3.66200 + 20.7682i −0.174778 + 0.991213i 0.763623 + 0.645663i $$0.223419\pi$$
−0.938400 + 0.345550i $$0.887692\pi$$
$$440$$ 0 0
$$441$$ −4.99355 1.81750i −0.237788 0.0865478i
$$442$$ 0 0
$$443$$ 7.17585 6.02125i 0.340935 0.286078i −0.456203 0.889876i $$-0.650791\pi$$
0.797138 + 0.603797i $$0.206346\pi$$
$$444$$ 0 0
$$445$$ −11.2656 + 19.5125i −0.534039 + 0.924983i
$$446$$ 0 0
$$447$$ −0.221325 1.25520i −0.0104683 0.0593687i
$$448$$ 0 0
$$449$$ −4.05742 7.02766i −0.191481 0.331656i 0.754260 0.656576i $$-0.227996\pi$$
−0.945741 + 0.324920i $$0.894663\pi$$
$$450$$ 0 0
$$451$$ 4.72952 1.72141i 0.222704 0.0810578i
$$452$$ 0 0
$$453$$ 0.136396 + 0.114450i 0.00640844 + 0.00537732i
$$454$$ 0 0
$$455$$ 31.0699 1.45658
$$456$$ 0 0
$$457$$ 4.33380 0.202727 0.101363 0.994849i $$-0.467680\pi$$
0.101363 + 0.994849i $$0.467680\pi$$
$$458$$ 0 0
$$459$$ 0.837711 + 0.702923i 0.0391010 + 0.0328097i
$$460$$ 0 0
$$461$$ 24.1245 8.78061i 1.12359 0.408954i 0.287629 0.957742i $$-0.407133\pi$$
0.835962 + 0.548788i $$0.184911\pi$$
$$462$$ 0 0
$$463$$ −0.875824 1.51697i −0.0407030 0.0704996i 0.844956 0.534835i $$-0.179626\pi$$
−0.885659 + 0.464336i $$0.846293\pi$$
$$464$$ 0 0
$$465$$ −3.99027 22.6300i −0.185044 1.04944i
$$466$$ 0 0
$$467$$ −8.64997 + 14.9822i −0.400273 + 0.693293i −0.993759 0.111551i $$-0.964418\pi$$
0.593486 + 0.804844i $$0.297751\pi$$
$$468$$ 0 0
$$469$$ −20.6894 + 17.3605i −0.955349 + 0.801633i
$$470$$ 0 0
$$471$$ −32.6961 11.9004i −1.50656 0.548341i
$$472$$ 0 0
$$473$$ 4.24408 24.0694i 0.195143 1.10671i
$$474$$ 0 0
$$475$$ 0.574590 0.383318i 0.0263640 0.0175878i
$$476$$ 0 0
$$477$$ 3.48197 19.7473i 0.159429 0.904165i
$$478$$ 0 0
$$479$$ −8.04717 2.92893i −0.367684 0.133826i 0.151569 0.988447i $$-0.451568\pi$$
−0.519253 + 0.854621i $$0.673790\pi$$
$$480$$ 0 0
$$481$$ −18.3137 + 15.3670i −0.835033 + 0.700676i
$$482$$ 0 0
$$483$$ −18.7187 + 32.4218i −0.851731 + 1.47524i
$$484$$ 0 0
$$485$$ −3.23633 18.3541i −0.146954 0.833419i
$$486$$ 0 0
$$487$$ −2.01043 3.48216i −0.0911011 0.157792i 0.816874 0.576817i $$-0.195705\pi$$
−0.907975 + 0.419025i $$0.862372\pi$$
$$488$$ 0 0
$$489$$ −0.726562 + 0.264447i −0.0328563 + 0.0119587i
$$490$$ 0 0
$$491$$ 6.40117 + 5.37122i 0.288881 + 0.242400i 0.775698 0.631104i $$-0.217398\pi$$
−0.486817 + 0.873504i $$0.661842\pi$$
$$492$$ 0 0
$$493$$ −46.5205 −2.09518
$$494$$ 0 0
$$495$$ −17.4308 −0.783455
$$496$$ 0 0
$$497$$ 1.29042 + 1.08279i 0.0578833 + 0.0485698i
$$498$$ 0 0
$$499$$ 7.57293 2.75632i 0.339011 0.123390i −0.166904 0.985973i $$-0.553377\pi$$
0.505915 + 0.862583i $$0.331155\pi$$
$$500$$ 0 0
$$501$$ −1.06605 1.84645i −0.0476274 0.0824931i
$$502$$ 0 0
$$503$$ −1.17379 6.65690i −0.0523367 0.296816i 0.947393 0.320073i $$-0.103708\pi$$
−0.999730 + 0.0232569i $$0.992596\pi$$
$$504$$ 0 0
$$505$$ −10.3043 + 17.8475i −0.458535 + 0.794205i
$$506$$ 0 0
$$507$$ 17.9724 15.0807i 0.798183 0.669755i
$$508$$ 0 0
$$509$$ −8.14794 2.96561i −0.361151 0.131448i 0.155070 0.987903i $$-0.450440\pi$$
−0.516221 + 0.856455i $$0.672662\pi$$
$$510$$ 0 0
$$511$$ −0.403016 + 2.28562i −0.0178284 + 0.101110i
$$512$$ 0 0
$$513$$ −0.408836 + 0.556722i −0.0180505 + 0.0245799i
$$514$$ 0 0
$$515$$ 4.58742 26.0165i 0.202146 1.14643i
$$516$$ 0 0
$$517$$ 1.59090 + 0.579040i 0.0699676 + 0.0254661i
$$518$$ 0 0
$$519$$ 40.6514 34.1106i 1.78440 1.49729i
$$520$$ 0 0
$$521$$ −18.9134 + 32.7589i −0.828610 + 1.43519i 0.0705193 + 0.997510i $$0.477534\pi$$
−0.899129 + 0.437684i $$0.855799\pi$$
$$522$$ 0 0
$$523$$ 1.16685 + 6.61751i 0.0510226 + 0.289363i 0.999633 0.0270822i $$-0.00862160\pi$$
−0.948611 + 0.316446i $$0.897510\pi$$
$$524$$ 0 0
$$525$$ 0.572932 + 0.992347i 0.0250048 + 0.0433096i
$$526$$ 0 0
$$527$$ −27.7995 + 10.1182i −1.21096 + 0.440755i
$$528$$ 0 0
$$529$$ 2.91353 + 2.44474i 0.126675 + 0.106293i
$$530$$ 0 0
$$531$$ 10.5361 0.457226
$$532$$ 0 0
$$533$$ 8.87062 0.384229
$$534$$ 0 0
$$535$$ 24.1087 + 20.2296i 1.04231 + 0.874603i
$$536$$ 0 0
$$537$$ 13.5706 4.93930i 0.585615 0.213146i
$$538$$ 0 0
$$539$$ 2.44352 + 4.23230i 0.105250 + 0.182298i
$$540$$ 0 0
$$541$$ 6.42812 + 36.4557i 0.276366 + 1.56735i 0.734588 + 0.678514i $$0.237376\pi$$
−0.458222 + 0.888838i $$0.651513\pi$$
$$542$$ 0 0
$$543$$ −14.6634 + 25.3977i −0.629267 + 1.08992i
$$544$$ 0 0
$$545$$ −3.73235 + 3.13181i −0.159876 + 0.134152i
$$546$$ 0 0
$$547$$ 32.4038 + 11.7940i 1.38549 + 0.504275i 0.923837 0.382787i $$-0.125036\pi$$
0.461649 + 0.887063i $$0.347258\pi$$
$$548$$ 0 0
$$549$$ −5.11969 + 29.0352i −0.218503 + 1.23919i
$$550$$ 0 0
$$551$$ −1.90019 29.3219i −0.0809508 1.24916i
$$552$$ 0 0
$$553$$ 1.63131 9.25162i 0.0693704 0.393419i
$$554$$ 0 0
$$555$$ 25.3141 + 9.21358i 1.07452 + 0.391095i
$$556$$ 0 0
$$557$$ 32.0493 26.8925i 1.35797 1.13947i 0.381369 0.924423i $$-0.375453\pi$$
0.976603 0.215051i $$-0.0689917\pi$$
$$558$$ 0 0
$$559$$ 21.5380 37.3050i 0.910962 1.57783i
$$560$$ 0 0
$$561$$ 7.87991 + 44.6892i 0.332690 + 1.88678i
$$562$$ 0 0
$$563$$ 7.86717 + 13.6263i 0.331562 + 0.574282i 0.982818 0.184576i $$-0.0590912\pi$$
−0.651257 + 0.758858i $$0.725758\pi$$
$$564$$ 0 0
$$565$$ 15.8013 5.75119i 0.664764 0.241954i
$$566$$ 0 0
$$567$$ −20.8985 17.5359i −0.877654 0.736439i
$$568$$ 0 0
$$569$$ 41.4620 1.73818 0.869089 0.494656i $$-0.164706\pi$$
0.869089 + 0.494656i $$0.164706\pi$$
$$570$$ 0 0
$$571$$ 12.3160 0.515408 0.257704 0.966224i $$-0.417034\pi$$
0.257704 + 0.966224i $$0.417034\pi$$
$$572$$ 0 0
$$573$$ −15.6476 13.1299i −0.653688 0.548509i
$$574$$ 0 0
$$575$$ 0.770907 0.280587i 0.0321490 0.0117013i
$$576$$ 0 0
$$577$$ −5.49834 9.52341i −0.228899 0.396465i 0.728583 0.684957i $$-0.240179\pi$$
−0.957482 + 0.288493i $$0.906846\pi$$
$$578$$ 0 0
$$579$$ 0.395167 + 2.24110i 0.0164226 + 0.0931370i
$$580$$ 0 0
$$581$$ 10.8285 18.7556i 0.449244 0.778113i
$$582$$ 0 0
$$583$$ −14.1264 + 11.8535i −0.585055 + 0.490920i
$$584$$ 0 0
$$585$$ −28.8686 10.5073i −1.19357 0.434423i
$$586$$ 0 0
$$587$$ −7.13565 + 40.4683i −0.294520 + 1.67030i 0.374628 + 0.927175i $$0.377770\pi$$
−0.669148 + 0.743129i $$0.733341\pi$$
$$588$$ 0 0
$$589$$ −7.51300 17.1087i −0.309568 0.704954i
$$590$$ 0 0
$$591$$ −9.45936 + 53.6467i −0.389106 + 2.20673i
$$592$$ 0 0
$$593$$ 24.1916 + 8.80504i 0.993432 + 0.361580i 0.787048 0.616892i $$-0.211608\pi$$
0.206384 + 0.978471i $$0.433831\pi$$
$$594$$ 0 0
$$595$$ −34.5277 + 28.9722i −1.41550 + 1.18774i
$$596$$ 0 0
$$597$$ 17.5890 30.4651i 0.719871 1.24685i
$$598$$ 0 0
$$599$$ −4.76463 27.0215i −0.194677 1.10407i −0.912877 0.408234i $$-0.866145\pi$$
0.718200 0.695837i $$-0.244966\pi$$
$$600$$ 0 0
$$601$$ −12.5425 21.7242i −0.511618 0.886148i −0.999909 0.0134673i $$-0.995713\pi$$
0.488292 0.872681i $$-0.337620\pi$$
$$602$$ 0 0
$$603$$ 25.0945 9.13366i 1.02193 0.371951i
$$604$$ 0 0
$$605$$ −6.26138 5.25392i −0.254561 0.213602i
$$606$$ 0 0
$$607$$ 7.83141 0.317867 0.158934 0.987289i $$-0.449194\pi$$
0.158934 + 0.987289i $$0.449194\pi$$
$$608$$ 0 0
$$609$$ 48.7458 1.97528
$$610$$ 0 0
$$611$$ 2.28577 + 1.91799i 0.0924725 + 0.0775936i
$$612$$ 0 0
$$613$$ −8.42277 + 3.06564i −0.340193 + 0.123820i −0.506466 0.862260i $$-0.669049\pi$$
0.166274 + 0.986080i $$0.446826\pi$$
$$614$$ 0 0
$$615$$ −4.99779 8.65643i −0.201530 0.349061i
$$616$$ 0 0
$$617$$ 0.703095 + 3.98745i 0.0283055 + 0.160529i 0.995684 0.0928062i $$-0.0295837\pi$$
−0.967379 + 0.253335i $$0.918473\pi$$
$$618$$ 0 0
$$619$$ −13.0871 + 22.6676i −0.526016 + 0.911087i 0.473525 + 0.880781i $$0.342982\pi$$
−0.999541 + 0.0303060i $$0.990352\pi$$
$$620$$ 0 0
$$621$$ −0.628449 + 0.527331i −0.0252188 + 0.0211611i
$$622$$ 0 0
$$623$$ −28.5614 10.3955i −1.14429 0.416487i
$$624$$ 0 0
$$625$$ −4.19926 + 23.8152i −0.167970 + 0.952608i
$$626$$ 0 0
$$627$$ −27.8458 + 6.79210i −1.11205 + 0.271251i
$$628$$ 0 0
$$629$$ 6.02234 34.1544i 0.240126 1.36182i
$$630$$ 0 0
$$631$$ −41.3624 15.0547i −1.64661 0.599317i −0.658435 0.752638i $$-0.728781\pi$$
−0.988177 + 0.153321i $$0.951003\pi$$
$$632$$ 0 0
$$633$$ −33.8605 + 28.4123i −1.34583 + 1.12929i
$$634$$ 0 0
$$635$$ 5.11197 8.85419i 0.202862 0.351368i
$$636$$ 0 0
$$637$$ 1.49568 + 8.48242i 0.0592610 + 0.336086i
$$638$$ 0 0
$$639$$ −0.832810 1.44247i −0.0329455 0.0570632i
$$640$$ 0 0
$$641$$ 4.91616 1.78934i 0.194177 0.0706745i −0.243101 0.970001i $$-0.578165\pi$$
0.437278 + 0.899326i $$0.355943\pi$$
$$642$$ 0 0
$$643$$ 10.2920 + 8.63602i 0.405877 + 0.340571i 0.822760 0.568389i $$-0.192433\pi$$
−0.416883 + 0.908960i $$0.636878\pi$$
$$644$$ 0 0
$$645$$ −48.5390 −1.91122
$$646$$ 0 0
$$647$$ 15.4880 0.608895 0.304448 0.952529i $$-0.401528\pi$$
0.304448 + 0.952529i $$0.401528\pi$$
$$648$$ 0 0
$$649$$ −7.42257 6.22828i −0.291361 0.244481i
$$650$$ 0 0
$$651$$ 29.1292 10.6022i 1.14167 0.415532i
$$652$$ 0 0
$$653$$ −5.03649 8.72346i −0.197093 0.341375i 0.750492 0.660880i $$-0.229817\pi$$
−0.947585 + 0.319505i $$0.896483\pi$$
$$654$$ 0 0
$$655$$ 0.00307271 + 0.0174262i 0.000120061 + 0.000680898i
$$656$$ 0 0
$$657$$ 1.14742 1.98738i 0.0447650 0.0775352i
$$658$$ 0 0
$$659$$ 18.8606 15.8259i 0.734704 0.616490i −0.196706 0.980463i $$-0.563024\pi$$
0.931410 + 0.363973i $$0.118580\pi$$
$$660$$ 0 0
$$661$$ −44.4545 16.1801i −1.72908 0.629333i −0.730515 0.682897i $$-0.760720\pi$$
−0.998564 + 0.0535638i $$0.982942\pi$$
$$662$$ 0 0
$$663$$ −13.8881 + 78.7635i −0.539370 + 3.05892i
$$664$$ 0 0
$$665$$ −19.6715 20.5794i −0.762828 0.798035i
$$666$$ 0 0
$$667$$ 6.06024 34.3694i 0.234654 1.33079i
$$668$$ 0 0
$$669$$ −7.50865 2.73293i −0.290301 0.105661i
$$670$$ 0 0
$$671$$ 20.7706 17.4286i 0.801841 0.672824i
$$672$$ 0 0
$$673$$ 7.44102 12.8882i 0.286830 0.496805i −0.686221 0.727393i $$-0.740732\pi$$
0.973051 + 0.230588i $$0.0740651\pi$$
$$674$$ 0 0
$$675$$ 0.00436027 + 0.0247283i 0.000167827 + 0.000951794i
$$676$$ 0 0
$$677$$ 1.25311 + 2.17046i 0.0481611 + 0.0834175i 0.889101 0.457711i $$-0.151331\pi$$
−0.840940 + 0.541129i $$0.817997\pi$$
$$678$$ 0 0
$$679$$ 23.6254 8.59895i 0.906660 0.329997i
$$680$$ 0 0
$$681$$ 21.4970 + 18.0381i 0.823766 + 0.691222i
$$682$$ 0 0
$$683$$ −29.5227 −1.12965 −0.564827 0.825209i $$-0.691057\pi$$
−0.564827 + 0.825209i $$0.691057\pi$$
$$684$$ 0 0
$$685$$ 34.3992 1.31432
$$686$$ 0 0
$$687$$ 28.6805 + 24.0658i 1.09423 + 0.918166i
$$688$$ 0 0
$$689$$ −30.5412 + 11.1161i −1.16353 + 0.423489i
$$690$$ 0 0
$$691$$ −20.8238 36.0678i −0.792173 1.37208i −0.924619 0.380894i $$-0.875616\pi$$
0.132445 0.991190i $$-0.457717\pi$$
$$692$$ 0 0
$$693$$ −4.08317 23.1568i −0.155107 0.879655i
$$694$$ 0 0
$$695$$ 8.56259 14.8308i 0.324798 0.562566i
$$696$$ 0 0
$$697$$ −9.85781 + 8.27169i −0.373391 + 0.313313i
$$698$$ 0 0
$$699$$ −31.4071 11.4313i −1.18793 0.432370i
$$700$$ 0 0
$$701$$ 7.62364 43.2358i 0.287941 1.63299i −0.406647 0.913585i $$-0.633302\pi$$
0.694588 0.719408i $$-0.255587\pi$$
$$702$$ 0 0
$$703$$ 21.7735 + 2.40081i 0.821204 + 0.0905481i
$$704$$ 0 0
$$705$$ 0.583853 3.31120i 0.0219892 0.124707i
$$706$$ 0 0
$$707$$ −26.1243 9.50846i −0.982505 0.357603i
$$708$$ 0 0
$$709$$ 15.4412 12.9567i 0.579907 0.486599i −0.305010 0.952349i $$-0.598660\pi$$
0.884916 + 0.465750i $$0.154215\pi$$
$$710$$ 0 0
$$711$$ −4.64446 + 8.04444i −0.174181 + 0.301690i
$$712$$ 0 0
$$713$$ −3.85387 21.8564i −0.144328 0.818527i
$$714$$ 0 0
$$715$$ 14.1264 + 24.4676i 0.528297 + 0.915038i
$$716$$ 0 0
$$717$$ −38.4570 + 13.9972i −1.43620 + 0.522735i
$$718$$ 0 0
$$719$$ 17.5142 + 14.6962i 0.653170 + 0.548074i 0.908031 0.418903i $$-0.137585\pi$$
−0.254861 + 0.966978i $$0.582030\pi$$
$$720$$ 0 0
$$721$$ 35.6377 1.32722
$$722$$ 0 0
$$723$$ 54.8810 2.04105
$$724$$ 0 0
$$725$$ −0.818278 0.686617i −0.0303901 0.0255003i
$$726$$ 0 0
$$727$$ −10.1790 + 3.70485i −0.377518 + 0.137405i −0.523808 0.851836i $$-0.675489\pi$$
0.146290 + 0.989242i $$0.453267\pi$$
$$728$$ 0 0
$$729$$ 12.9084 + 22.3580i 0.478088 + 0.828073i
$$730$$ 0 0
$$731$$ 10.8512 + 61.5404i 0.401347 + 2.27615i
$$732$$ 0 0
$$733$$ −11.9702 + 20.7331i −0.442131 + 0.765794i −0.997847 0.0655783i $$-0.979111\pi$$
0.555716 + 0.831372i $$0.312444\pi$$
$$734$$ 0 0
$$735$$ 7.43492 6.23864i 0.274241 0.230116i
$$736$$ 0 0
$$737$$ −23.0782 8.39976i −0.850095 0.309409i
$$738$$ 0 0
$$739$$ 0.980265 5.55936i 0.0360596 0.204504i −0.961455 0.274962i $$-0.911335\pi$$
0.997515 + 0.0704574i $$0.0224459\pi$$
$$740$$ 0 0
$$741$$ −50.2120 5.53650i −1.84458 0.203389i
$$742$$ 0 0
$$743$$ 7.01282 39.7717i 0.257275 1.45908i −0.532889 0.846185i $$-0.678894\pi$$
0.790164 0.612895i $$-0.209995\pi$$
$$744$$ 0 0
$$745$$ 1.08175 + 0.393726i 0.0396324 + 0.0144250i
$$746$$ 0 0
$$747$$ −16.4041 + 13.7647i −0.600195 + 0.503623i
$$748$$ 0 0
$$749$$ −21.2276 + 36.7673i −0.775641 + 1.34345i
$$750$$ 0 0
$$751$$ 4.21819 + 23.9225i 0.153924 + 0.872946i 0.959763 + 0.280811i $$0.0906036\pi$$
−0.805839 + 0.592135i $$0.798285\pi$$
$$752$$ 0 0
$$753$$ 18.8922 + 32.7222i 0.688469 + 1.19246i
$$754$$ 0 0
$$755$$ −0.151118 + 0.0550025i −0.00549975 + 0.00200174i
$$756$$ 0 0
$$757$$ 6.92712 + 5.81254i 0.251770 + 0.211260i 0.759934 0.650000i $$-0.225231\pi$$
−0.508164 + 0.861260i $$0.669676\pi$$
$$758$$ 0 0
$$759$$ −34.0429 −1.23568
$$760$$ 0 0
$$761$$ −42.8970 −1.55502 −0.777508 0.628874i $$-0.783516\pi$$
−0.777508 + 0.628874i $$0.783516\pi$$
$$762$$ 0 0
$$763$$ −5.03493 4.22481i −0.182277 0.152948i
$$764$$ 0 0
$$765$$ 41.8791 15.2428i 1.51414 0.551103i
$$766$$ 0 0
$$767$$ −8.53872 14.7895i −0.308315 0.534018i
$$768$$ 0 0
$$769$$ 0.909951 + 5.16059i 0.0328137 + 0.186095i 0.996809 0.0798236i $$-0.0254357\pi$$
−0.963995 + 0.265919i $$0.914325\pi$$
$$770$$ 0 0
$$771$$ 35.4898 61.4701i 1.27813 2.21379i
$$772$$ 0 0
$$773$$ 27.4974 23.0731i 0.989014 0.829881i 0.00358889 0.999994i $$-0.498858\pi$$
0.985425 + 0.170113i $$0.0544132\pi$$
$$774$$ 0 0
$$775$$ −0.638321 0.232330i −0.0229292 0.00834554i
$$776$$ 0 0
$$777$$ −6.31041 + 35.7881i −0.226385 + 1.28389i
$$778$$ 0 0
$$779$$ −5.61631 5.87552i −0.201225 0.210512i
$$780$$ 0 0
$$781$$ −0.265992 + 1.50851i −0.00951794 + 0.0539789i
$$782$$ 0 0
$$783$$ 1.00377 + 0.365341i 0.0358717 + 0.0130562i
$$784$$ 0 0
$$785$$ 24.0739 20.2004i 0.859235 0.720984i
$$786$$ 0 0
$$787$$ −22.6443 + 39.2211i −0.807182 + 1.39808i 0.107625 + 0.994192i $$0.465675\pi$$
−0.914808 + 0.403890i $$0.867658\pi$$
$$788$$ 0 0
$$789$$ 1.60656 + 9.11124i 0.0571949 + 0.324369i
$$790$$ 0 0
$$791$$ 11.3419 + 19.6448i 0.403273 + 0.698489i
$$792$$ 0 0
$$793$$ 44.9059 16.3444i 1.59466 0.580407i
$$794$$ 0 0