# Properties

 Label 1300.2.i.e.1101.1 Level $1300$ Weight $2$ Character 1300.1101 Analytic conductor $10.381$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1300 = 2^{2} \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1300.i (of order $$3$$, degree $$2$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.3805522628$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{6})$$ Defining polynomial: $$x^{2} - x + 1$$ x^2 - x + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 260) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 1101.1 Root $$0.500000 + 0.866025i$$ of defining polynomial Character $$\chi$$ $$=$$ 1300.1101 Dual form 1300.2.i.e.601.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-1.00000 + 3.46410i) q^{13} +(-1.50000 - 2.59808i) q^{17} +(3.50000 + 6.06218i) q^{19} -1.00000 q^{21} +(-1.50000 + 2.59808i) q^{23} +5.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} -4.00000 q^{31} +(1.50000 + 2.59808i) q^{33} +(-3.50000 + 6.06218i) q^{37} +(2.50000 + 2.59808i) q^{39} +(4.50000 - 7.79423i) q^{41} +(5.50000 + 9.52628i) q^{43} +(3.00000 - 5.19615i) q^{49} -3.00000 q^{51} +6.00000 q^{53} +7.00000 q^{57} +(1.50000 + 2.59808i) q^{59} +(-5.50000 - 9.52628i) q^{61} +(1.00000 - 1.73205i) q^{63} +(-3.50000 + 6.06218i) q^{67} +(1.50000 + 2.59808i) q^{69} +(1.50000 + 2.59808i) q^{71} -2.00000 q^{73} +3.00000 q^{77} +8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} +(1.50000 + 2.59808i) q^{87} +(-7.50000 + 12.9904i) q^{89} +(3.50000 - 0.866025i) q^{91} +(-2.00000 + 3.46410i) q^{93} +(-3.50000 - 6.06218i) q^{97} -6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q + q^{3} - q^{7} + 2 q^{9}+O(q^{10})$$ 2 * q + q^3 - q^7 + 2 * q^9 $$2 q + q^{3} - q^{7} + 2 q^{9} - 3 q^{11} - 2 q^{13} - 3 q^{17} + 7 q^{19} - 2 q^{21} - 3 q^{23} + 10 q^{27} - 3 q^{29} - 8 q^{31} + 3 q^{33} - 7 q^{37} + 5 q^{39} + 9 q^{41} + 11 q^{43} + 6 q^{49} - 6 q^{51} + 12 q^{53} + 14 q^{57} + 3 q^{59} - 11 q^{61} + 2 q^{63} - 7 q^{67} + 3 q^{69} + 3 q^{71} - 4 q^{73} + 6 q^{77} + 16 q^{79} - q^{81} + 24 q^{83} + 3 q^{87} - 15 q^{89} + 7 q^{91} - 4 q^{93} - 7 q^{97} - 12 q^{99}+O(q^{100})$$ 2 * q + q^3 - q^7 + 2 * q^9 - 3 * q^11 - 2 * q^13 - 3 * q^17 + 7 * q^19 - 2 * q^21 - 3 * q^23 + 10 * q^27 - 3 * q^29 - 8 * q^31 + 3 * q^33 - 7 * q^37 + 5 * q^39 + 9 * q^41 + 11 * q^43 + 6 * q^49 - 6 * q^51 + 12 * q^53 + 14 * q^57 + 3 * q^59 - 11 * q^61 + 2 * q^63 - 7 * q^67 + 3 * q^69 + 3 * q^71 - 4 * q^73 + 6 * q^77 + 16 * q^79 - q^81 + 24 * q^83 + 3 * q^87 - 15 * q^89 + 7 * q^91 - 4 * q^93 - 7 * q^97 - 12 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$$.

 $$n$$ $$301$$ $$651$$ $$677$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i $$-0.740119\pi$$
0.973494 + 0.228714i $$0.0734519\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −0.500000 0.866025i −0.188982 0.327327i 0.755929 0.654654i $$-0.227186\pi$$
−0.944911 + 0.327327i $$0.893852\pi$$
$$8$$ 0 0
$$9$$ 1.00000 + 1.73205i 0.333333 + 0.577350i
$$10$$ 0 0
$$11$$ −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i $$-0.982718\pi$$
0.546259 + 0.837616i $$0.316051\pi$$
$$12$$ 0 0
$$13$$ −1.00000 + 3.46410i −0.277350 + 0.960769i
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i $$-0.285189\pi$$
−0.988583 + 0.150675i $$0.951855\pi$$
$$18$$ 0 0
$$19$$ 3.50000 + 6.06218i 0.802955 + 1.39076i 0.917663 + 0.397360i $$0.130073\pi$$
−0.114708 + 0.993399i $$0.536593\pi$$
$$20$$ 0 0
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i $$-0.934591\pi$$
0.666190 + 0.745782i $$0.267924\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 5.00000 0.962250
$$28$$ 0 0
$$29$$ −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i $$-0.923185\pi$$
0.692480 + 0.721437i $$0.256518\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0 0
$$33$$ 1.50000 + 2.59808i 0.261116 + 0.452267i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −3.50000 + 6.06218i −0.575396 + 0.996616i 0.420602 + 0.907245i $$0.361819\pi$$
−0.995998 + 0.0893706i $$0.971514\pi$$
$$38$$ 0 0
$$39$$ 2.50000 + 2.59808i 0.400320 + 0.416025i
$$40$$ 0 0
$$41$$ 4.50000 7.79423i 0.702782 1.21725i −0.264704 0.964330i $$-0.585274\pi$$
0.967486 0.252924i $$-0.0813924\pi$$
$$42$$ 0 0
$$43$$ 5.50000 + 9.52628i 0.838742 + 1.45274i 0.890947 + 0.454108i $$0.150042\pi$$
−0.0522047 + 0.998636i $$0.516625\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ 3.00000 5.19615i 0.428571 0.742307i
$$50$$ 0 0
$$51$$ −3.00000 −0.420084
$$52$$ 0 0
$$53$$ 6.00000 0.824163 0.412082 0.911147i $$-0.364802\pi$$
0.412082 + 0.911147i $$0.364802\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 7.00000 0.927173
$$58$$ 0 0
$$59$$ 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i $$-0.104104\pi$$
−0.751710 + 0.659494i $$0.770771\pi$$
$$60$$ 0 0
$$61$$ −5.50000 9.52628i −0.704203 1.21972i −0.966978 0.254858i $$-0.917971\pi$$
0.262776 0.964857i $$-0.415362\pi$$
$$62$$ 0 0
$$63$$ 1.00000 1.73205i 0.125988 0.218218i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −3.50000 + 6.06218i −0.427593 + 0.740613i −0.996659 0.0816792i $$-0.973972\pi$$
0.569066 + 0.822292i $$0.307305\pi$$
$$68$$ 0 0
$$69$$ 1.50000 + 2.59808i 0.180579 + 0.312772i
$$70$$ 0 0
$$71$$ 1.50000 + 2.59808i 0.178017 + 0.308335i 0.941201 0.337846i $$-0.109698\pi$$
−0.763184 + 0.646181i $$0.776365\pi$$
$$72$$ 0 0
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 3.00000 0.341882
$$78$$ 0 0
$$79$$ 8.00000 0.900070 0.450035 0.893011i $$-0.351411\pi$$
0.450035 + 0.893011i $$0.351411\pi$$
$$80$$ 0 0
$$81$$ −0.500000 + 0.866025i −0.0555556 + 0.0962250i
$$82$$ 0 0
$$83$$ 12.0000 1.31717 0.658586 0.752506i $$-0.271155\pi$$
0.658586 + 0.752506i $$0.271155\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 1.50000 + 2.59808i 0.160817 + 0.278543i
$$88$$ 0 0
$$89$$ −7.50000 + 12.9904i −0.794998 + 1.37698i 0.127842 + 0.991795i $$0.459195\pi$$
−0.922840 + 0.385183i $$0.874138\pi$$
$$90$$ 0 0
$$91$$ 3.50000 0.866025i 0.366900 0.0907841i
$$92$$ 0 0
$$93$$ −2.00000 + 3.46410i −0.207390 + 0.359211i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −3.50000 6.06218i −0.355371 0.615521i 0.631810 0.775123i $$-0.282312\pi$$
−0.987181 + 0.159602i $$0.948979\pi$$
$$98$$ 0 0
$$99$$ −6.00000 −0.603023
$$100$$ 0 0
$$101$$ 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i $$-0.685553\pi$$
0.998240 + 0.0592978i $$0.0188862\pi$$
$$102$$ 0 0
$$103$$ −8.00000 −0.788263 −0.394132 0.919054i $$-0.628955\pi$$
−0.394132 + 0.919054i $$0.628955\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 4.50000 7.79423i 0.435031 0.753497i −0.562267 0.826956i $$-0.690071\pi$$
0.997298 + 0.0734594i $$0.0234039\pi$$
$$108$$ 0 0
$$109$$ 2.00000 0.191565 0.0957826 0.995402i $$-0.469465\pi$$
0.0957826 + 0.995402i $$0.469465\pi$$
$$110$$ 0 0
$$111$$ 3.50000 + 6.06218i 0.332205 + 0.575396i
$$112$$ 0 0
$$113$$ 4.50000 + 7.79423i 0.423324 + 0.733219i 0.996262 0.0863794i $$-0.0275297\pi$$
−0.572938 + 0.819599i $$0.694196\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −7.00000 + 1.73205i −0.647150 + 0.160128i
$$118$$ 0 0
$$119$$ −1.50000 + 2.59808i −0.137505 + 0.238165i
$$120$$ 0 0
$$121$$ 1.00000 + 1.73205i 0.0909091 + 0.157459i
$$122$$ 0 0
$$123$$ −4.50000 7.79423i −0.405751 0.702782i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −9.50000 + 16.4545i −0.842989 + 1.46010i 0.0443678 + 0.999015i $$0.485873\pi$$
−0.887357 + 0.461084i $$0.847461\pi$$
$$128$$ 0 0
$$129$$ 11.0000 0.968496
$$130$$ 0 0
$$131$$ −12.0000 −1.04844 −0.524222 0.851581i $$-0.675644\pi$$
−0.524222 + 0.851581i $$0.675644\pi$$
$$132$$ 0 0
$$133$$ 3.50000 6.06218i 0.303488 0.525657i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ −7.50000 12.9904i −0.640768 1.10984i −0.985262 0.171054i $$-0.945283\pi$$
0.344493 0.938789i $$-0.388051\pi$$
$$138$$ 0 0
$$139$$ −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i $$-0.234680\pi$$
−0.952355 + 0.304991i $$0.901346\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −7.50000 7.79423i −0.627182 0.651786i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −3.00000 5.19615i −0.247436 0.428571i
$$148$$ 0 0
$$149$$ 10.5000 + 18.1865i 0.860194 + 1.48990i 0.871742 + 0.489966i $$0.162991\pi$$
−0.0115483 + 0.999933i $$0.503676\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 0 0
$$153$$ 3.00000 5.19615i 0.242536 0.420084i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 10.0000 0.798087 0.399043 0.916932i $$-0.369342\pi$$
0.399043 + 0.916932i $$0.369342\pi$$
$$158$$ 0 0
$$159$$ 3.00000 5.19615i 0.237915 0.412082i
$$160$$ 0 0
$$161$$ 3.00000 0.236433
$$162$$ 0 0
$$163$$ −0.500000 0.866025i −0.0391630 0.0678323i 0.845780 0.533533i $$-0.179136\pi$$
−0.884943 + 0.465700i $$0.845802\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −1.50000 + 2.59808i −0.116073 + 0.201045i −0.918208 0.396098i $$-0.870364\pi$$
0.802135 + 0.597143i $$0.203697\pi$$
$$168$$ 0 0
$$169$$ −11.0000 6.92820i −0.846154 0.532939i
$$170$$ 0 0
$$171$$ −7.00000 + 12.1244i −0.535303 + 0.927173i
$$172$$ 0 0
$$173$$ −1.50000 2.59808i −0.114043 0.197528i 0.803354 0.595502i $$-0.203047\pi$$
−0.917397 + 0.397974i $$0.869713\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 3.00000 0.225494
$$178$$ 0 0
$$179$$ 10.5000 18.1865i 0.784807 1.35933i −0.144308 0.989533i $$-0.546095\pi$$
0.929114 0.369792i $$-0.120571\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ −11.0000 −0.813143
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 9.00000 0.658145
$$188$$ 0 0
$$189$$ −2.50000 4.33013i −0.181848 0.314970i
$$190$$ 0 0
$$191$$ 1.50000 + 2.59808i 0.108536 + 0.187990i 0.915177 0.403051i $$-0.132050\pi$$
−0.806641 + 0.591041i $$0.798717\pi$$
$$192$$ 0 0
$$193$$ 2.50000 4.33013i 0.179954 0.311689i −0.761911 0.647682i $$-0.775738\pi$$
0.941865 + 0.335993i $$0.109072\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 10.5000 18.1865i 0.748094 1.29574i −0.200641 0.979665i $$-0.564303\pi$$
0.948735 0.316072i $$-0.102364\pi$$
$$198$$ 0 0
$$199$$ −8.50000 14.7224i −0.602549 1.04365i −0.992434 0.122782i $$-0.960818\pi$$
0.389885 0.920864i $$-0.372515\pi$$
$$200$$ 0 0
$$201$$ 3.50000 + 6.06218i 0.246871 + 0.427593i
$$202$$ 0 0
$$203$$ 3.00000 0.210559
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ −6.00000 −0.417029
$$208$$ 0 0
$$209$$ −21.0000 −1.45260
$$210$$ 0 0
$$211$$ −5.50000 + 9.52628i −0.378636 + 0.655816i −0.990864 0.134865i $$-0.956940\pi$$
0.612228 + 0.790681i $$0.290273\pi$$
$$212$$ 0 0
$$213$$ 3.00000 0.205557
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 2.00000 + 3.46410i 0.135769 + 0.235159i
$$218$$ 0 0
$$219$$ −1.00000 + 1.73205i −0.0675737 + 0.117041i
$$220$$ 0 0
$$221$$ 10.5000 2.59808i 0.706306 0.174766i
$$222$$ 0 0
$$223$$ −9.50000 + 16.4545i −0.636167 + 1.10187i 0.350100 + 0.936713i $$0.386148\pi$$
−0.986267 + 0.165161i $$0.947186\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 13.5000 + 23.3827i 0.896026 + 1.55196i 0.832529 + 0.553981i $$0.186892\pi$$
0.0634974 + 0.997982i $$0.479775\pi$$
$$228$$ 0 0
$$229$$ −22.0000 −1.45380 −0.726900 0.686743i $$-0.759040\pi$$
−0.726900 + 0.686743i $$0.759040\pi$$
$$230$$ 0 0
$$231$$ 1.50000 2.59808i 0.0986928 0.170941i
$$232$$ 0 0
$$233$$ −18.0000 −1.17922 −0.589610 0.807688i $$-0.700718\pi$$
−0.589610 + 0.807688i $$0.700718\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 4.00000 6.92820i 0.259828 0.450035i
$$238$$ 0 0
$$239$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$240$$ 0 0
$$241$$ 0.500000 + 0.866025i 0.0322078 + 0.0557856i 0.881680 0.471848i $$-0.156413\pi$$
−0.849472 + 0.527633i $$0.823079\pi$$
$$242$$ 0 0
$$243$$ 8.00000 + 13.8564i 0.513200 + 0.888889i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −24.5000 + 6.06218i −1.55890 + 0.385727i
$$248$$ 0 0
$$249$$ 6.00000 10.3923i 0.380235 0.658586i
$$250$$ 0 0
$$251$$ −10.5000 18.1865i −0.662754 1.14792i −0.979889 0.199543i $$-0.936054\pi$$
0.317135 0.948380i $$-0.397279\pi$$
$$252$$ 0 0
$$253$$ −4.50000 7.79423i −0.282913 0.490019i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 4.50000 7.79423i 0.280702 0.486191i −0.690856 0.722993i $$-0.742766\pi$$
0.971558 + 0.236802i $$0.0760993\pi$$
$$258$$ 0 0
$$259$$ 7.00000 0.434959
$$260$$ 0 0
$$261$$ −6.00000 −0.371391
$$262$$ 0 0
$$263$$ −1.50000 + 2.59808i −0.0924940 + 0.160204i −0.908560 0.417755i $$-0.862817\pi$$
0.816066 + 0.577959i $$0.196151\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 7.50000 + 12.9904i 0.458993 + 0.794998i
$$268$$ 0 0
$$269$$ −13.5000 23.3827i −0.823110 1.42567i −0.903356 0.428892i $$-0.858904\pi$$
0.0802460 0.996775i $$-0.474429\pi$$
$$270$$ 0 0
$$271$$ −11.5000 + 19.9186i −0.698575 + 1.20997i 0.270385 + 0.962752i $$0.412849\pi$$
−0.968960 + 0.247216i $$0.920484\pi$$
$$272$$ 0 0
$$273$$ 1.00000 3.46410i 0.0605228 0.209657i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −9.50000 16.4545i −0.570800 0.988654i −0.996484 0.0837823i $$-0.973300\pi$$
0.425684 0.904872i $$-0.360033\pi$$
$$278$$ 0 0
$$279$$ −4.00000 6.92820i −0.239474 0.414781i
$$280$$ 0 0
$$281$$ 6.00000 0.357930 0.178965 0.983855i $$-0.442725\pi$$
0.178965 + 0.983855i $$0.442725\pi$$
$$282$$ 0 0
$$283$$ 2.50000 4.33013i 0.148610 0.257399i −0.782104 0.623148i $$-0.785854\pi$$
0.930714 + 0.365748i $$0.119187\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ −9.00000 −0.531253
$$288$$ 0 0
$$289$$ 4.00000 6.92820i 0.235294 0.407541i
$$290$$ 0 0
$$291$$ −7.00000 −0.410347
$$292$$ 0 0
$$293$$ −13.5000 23.3827i −0.788678 1.36603i −0.926777 0.375613i $$-0.877432\pi$$
0.138098 0.990419i $$-0.455901\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −7.50000 + 12.9904i −0.435194 + 0.753778i
$$298$$ 0 0
$$299$$ −7.50000 7.79423i −0.433736 0.450752i
$$300$$ 0 0
$$301$$ 5.50000 9.52628i 0.317015 0.549086i
$$302$$ 0 0
$$303$$ −4.50000 7.79423i −0.258518 0.447767i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −20.0000 −1.14146 −0.570730 0.821138i $$-0.693340\pi$$
−0.570730 + 0.821138i $$0.693340\pi$$
$$308$$ 0 0
$$309$$ −4.00000 + 6.92820i −0.227552 + 0.394132i
$$310$$ 0 0
$$311$$ 24.0000 1.36092 0.680458 0.732787i $$-0.261781\pi$$
0.680458 + 0.732787i $$0.261781\pi$$
$$312$$ 0 0
$$313$$ 22.0000 1.24351 0.621757 0.783210i $$-0.286419\pi$$
0.621757 + 0.783210i $$0.286419\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 18.0000 1.01098 0.505490 0.862832i $$-0.331312\pi$$
0.505490 + 0.862832i $$0.331312\pi$$
$$318$$ 0 0
$$319$$ −4.50000 7.79423i −0.251952 0.436393i
$$320$$ 0 0
$$321$$ −4.50000 7.79423i −0.251166 0.435031i
$$322$$ 0 0
$$323$$ 10.5000 18.1865i 0.584236 1.01193i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 1.00000 1.73205i 0.0553001 0.0957826i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 9.50000 + 16.4545i 0.522167 + 0.904420i 0.999667 + 0.0257885i $$0.00820965\pi$$
−0.477500 + 0.878632i $$0.658457\pi$$
$$332$$ 0 0
$$333$$ −14.0000 −0.767195
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 34.0000 1.85210 0.926049 0.377403i $$-0.123183\pi$$
0.926049 + 0.377403i $$0.123183\pi$$
$$338$$ 0 0
$$339$$ 9.00000 0.488813
$$340$$ 0 0
$$341$$ 6.00000 10.3923i 0.324918 0.562775i
$$342$$ 0 0
$$343$$ −13.0000 −0.701934
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −16.5000 28.5788i −0.885766 1.53419i −0.844833 0.535031i $$-0.820300\pi$$
−0.0409337 0.999162i $$-0.513033\pi$$
$$348$$ 0 0
$$349$$ 0.500000 0.866025i 0.0267644 0.0463573i −0.852333 0.523000i $$-0.824813\pi$$
0.879097 + 0.476642i $$0.158146\pi$$
$$350$$ 0 0
$$351$$ −5.00000 + 17.3205i −0.266880 + 0.924500i
$$352$$ 0 0
$$353$$ 4.50000 7.79423i 0.239511 0.414845i −0.721063 0.692869i $$-0.756346\pi$$
0.960574 + 0.278024i $$0.0896796\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 1.50000 + 2.59808i 0.0793884 + 0.137505i
$$358$$ 0 0
$$359$$ −24.0000 −1.26667 −0.633336 0.773877i $$-0.718315\pi$$
−0.633336 + 0.773877i $$0.718315\pi$$
$$360$$ 0 0
$$361$$ −15.0000 + 25.9808i −0.789474 + 1.36741i
$$362$$ 0 0
$$363$$ 2.00000 0.104973
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 2.50000 4.33013i 0.130499 0.226031i −0.793370 0.608740i $$-0.791675\pi$$
0.923869 + 0.382709i $$0.125009\pi$$
$$368$$ 0 0
$$369$$ 18.0000 0.937043
$$370$$ 0 0
$$371$$ −3.00000 5.19615i −0.155752 0.269771i
$$372$$ 0 0
$$373$$ −15.5000 26.8468i −0.802560 1.39007i −0.917926 0.396751i $$-0.870138\pi$$
0.115367 0.993323i $$-0.463196\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ −7.50000 7.79423i −0.386270 0.401423i
$$378$$ 0 0
$$379$$ 0.500000 0.866025i 0.0256833 0.0444847i −0.852898 0.522077i $$-0.825157\pi$$
0.878581 + 0.477593i $$0.158491\pi$$
$$380$$ 0 0
$$381$$ 9.50000 + 16.4545i 0.486700 + 0.842989i
$$382$$ 0 0
$$383$$ −4.50000 7.79423i −0.229939 0.398266i 0.727851 0.685736i $$-0.240519\pi$$
−0.957790 + 0.287469i $$0.907186\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −11.0000 + 19.0526i −0.559161 + 0.968496i
$$388$$ 0 0
$$389$$ 18.0000 0.912636 0.456318 0.889817i $$-0.349168\pi$$
0.456318 + 0.889817i $$0.349168\pi$$
$$390$$ 0 0
$$391$$ 9.00000 0.455150
$$392$$ 0 0
$$393$$ −6.00000 + 10.3923i −0.302660 + 0.524222i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 2.50000 + 4.33013i 0.125471 + 0.217323i 0.921917 0.387387i $$-0.126622\pi$$
−0.796446 + 0.604710i $$0.793289\pi$$
$$398$$ 0 0
$$399$$ −3.50000 6.06218i −0.175219 0.303488i
$$400$$ 0 0
$$401$$ 16.5000 28.5788i 0.823971 1.42716i −0.0787327 0.996896i $$-0.525087\pi$$
0.902703 0.430263i $$-0.141579\pi$$
$$402$$ 0 0
$$403$$ 4.00000 13.8564i 0.199254 0.690237i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −10.5000 18.1865i −0.520466 0.901473i
$$408$$ 0 0
$$409$$ 12.5000 + 21.6506i 0.618085 + 1.07056i 0.989835 + 0.142222i $$0.0454247\pi$$
−0.371750 + 0.928333i $$0.621242\pi$$
$$410$$ 0 0
$$411$$ −15.0000 −0.739895
$$412$$ 0 0
$$413$$ 1.50000 2.59808i 0.0738102 0.127843i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −5.00000 −0.244851
$$418$$ 0 0
$$419$$ 4.50000 7.79423i 0.219839 0.380773i −0.734919 0.678155i $$-0.762780\pi$$
0.954759 + 0.297382i $$0.0961133\pi$$
$$420$$ 0 0
$$421$$ 2.00000 0.0974740 0.0487370 0.998812i $$-0.484480\pi$$
0.0487370 + 0.998812i $$0.484480\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −5.50000 + 9.52628i −0.266164 + 0.461009i
$$428$$ 0 0
$$429$$ −10.5000 + 2.59808i −0.506945 + 0.125436i
$$430$$ 0 0
$$431$$ 4.50000 7.79423i 0.216757 0.375435i −0.737057 0.675830i $$-0.763785\pi$$
0.953815 + 0.300395i $$0.0971186\pi$$
$$432$$ 0 0
$$433$$ 14.5000 + 25.1147i 0.696826 + 1.20694i 0.969561 + 0.244848i $$0.0787382\pi$$
−0.272736 + 0.962089i $$0.587929\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ −21.0000 −1.00457
$$438$$ 0 0
$$439$$ −5.50000 + 9.52628i −0.262501 + 0.454665i −0.966906 0.255134i $$-0.917881\pi$$
0.704405 + 0.709798i $$0.251214\pi$$
$$440$$ 0 0
$$441$$ 12.0000 0.571429
$$442$$ 0 0
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 21.0000 0.993266
$$448$$ 0 0
$$449$$ −1.50000 2.59808i −0.0707894 0.122611i 0.828458 0.560051i $$-0.189218\pi$$
−0.899247 + 0.437440i $$0.855885\pi$$
$$450$$ 0 0
$$451$$ 13.5000 + 23.3827i 0.635690 + 1.10105i
$$452$$ 0 0
$$453$$ 4.00000 6.92820i 0.187936 0.325515i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 2.50000 4.33013i 0.116945 0.202555i −0.801611 0.597847i $$-0.796023\pi$$
0.918556 + 0.395292i $$0.129357\pi$$
$$458$$ 0 0
$$459$$ −7.50000 12.9904i −0.350070 0.606339i
$$460$$ 0 0
$$461$$ −13.5000 23.3827i −0.628758 1.08904i −0.987801 0.155719i $$-0.950230\pi$$
0.359044 0.933321i $$-0.383103\pi$$
$$462$$ 0 0
$$463$$ 4.00000 0.185896 0.0929479 0.995671i $$-0.470371\pi$$
0.0929479 + 0.995671i $$0.470371\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 36.0000 1.66588 0.832941 0.553362i $$-0.186655\pi$$
0.832941 + 0.553362i $$0.186655\pi$$
$$468$$ 0 0
$$469$$ 7.00000 0.323230
$$470$$ 0 0
$$471$$ 5.00000 8.66025i 0.230388 0.399043i
$$472$$ 0 0
$$473$$ −33.0000 −1.51734
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 6.00000 + 10.3923i 0.274721 + 0.475831i
$$478$$ 0 0
$$479$$ −19.5000 + 33.7750i −0.890978 + 1.54322i −0.0522726 + 0.998633i $$0.516646\pi$$
−0.838705 + 0.544586i $$0.816687\pi$$
$$480$$ 0 0
$$481$$ −17.5000 18.1865i −0.797931 0.829235i
$$482$$ 0 0
$$483$$ 1.50000 2.59808i 0.0682524 0.118217i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 5.50000 + 9.52628i 0.249229 + 0.431677i 0.963312 0.268384i $$-0.0864896\pi$$
−0.714083 + 0.700061i $$0.753156\pi$$
$$488$$ 0 0
$$489$$ −1.00000 −0.0452216
$$490$$ 0 0
$$491$$ 4.50000 7.79423i 0.203082 0.351749i −0.746438 0.665455i $$-0.768237\pi$$
0.949520 + 0.313707i $$0.101571\pi$$
$$492$$ 0 0
$$493$$ 9.00000 0.405340
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 1.50000 2.59808i 0.0672842 0.116540i
$$498$$ 0 0
$$499$$ 32.0000 1.43252 0.716258 0.697835i $$-0.245853\pi$$
0.716258 + 0.697835i $$0.245853\pi$$
$$500$$ 0 0
$$501$$ 1.50000 + 2.59808i 0.0670151 + 0.116073i
$$502$$ 0 0
$$503$$ 7.50000 + 12.9904i 0.334408 + 0.579212i 0.983371 0.181608i $$-0.0581302\pi$$
−0.648963 + 0.760820i $$0.724797\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −11.5000 + 6.06218i −0.510733 + 0.269231i
$$508$$ 0 0
$$509$$ 4.50000 7.79423i 0.199459 0.345473i −0.748894 0.662690i $$-0.769415\pi$$
0.948353 + 0.317217i $$0.102748\pi$$
$$510$$ 0 0
$$511$$ 1.00000 + 1.73205i 0.0442374 + 0.0766214i
$$512$$ 0 0
$$513$$ 17.5000 + 30.3109i 0.772644 + 1.33826i
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ −3.00000 −0.131685
$$520$$ 0 0
$$521$$ 30.0000 1.31432 0.657162 0.753749i $$-0.271757\pi$$
0.657162 + 0.753749i $$0.271757\pi$$
$$522$$ 0 0
$$523$$ 14.5000 25.1147i 0.634041 1.09819i −0.352677 0.935745i $$-0.614728\pi$$
0.986718 0.162446i $$-0.0519382\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 6.00000 + 10.3923i 0.261364 + 0.452696i
$$528$$ 0 0
$$529$$ 7.00000 + 12.1244i 0.304348 + 0.527146i
$$530$$ 0 0
$$531$$ −3.00000 + 5.19615i −0.130189 + 0.225494i
$$532$$ 0 0
$$533$$ 22.5000 + 23.3827i 0.974583 + 1.01282i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ −10.5000 18.1865i −0.453108 0.784807i
$$538$$ 0 0
$$539$$ 9.00000 + 15.5885i 0.387657 + 0.671442i
$$540$$ 0 0
$$541$$ −22.0000 −0.945854 −0.472927 0.881102i $$-0.656803\pi$$
−0.472927 + 0.881102i $$0.656803\pi$$
$$542$$ 0 0
$$543$$ 1.00000 1.73205i 0.0429141 0.0743294i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −8.00000 −0.342055 −0.171028 0.985266i $$-0.554709\pi$$
−0.171028 + 0.985266i $$0.554709\pi$$
$$548$$ 0 0
$$549$$ 11.0000 19.0526i 0.469469 0.813143i
$$550$$ 0 0
$$551$$ −21.0000 −0.894630
$$552$$ 0 0
$$553$$ −4.00000 6.92820i −0.170097 0.294617i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −19.5000 + 33.7750i −0.826242 + 1.43109i 0.0747252 + 0.997204i $$0.476192\pi$$
−0.900967 + 0.433888i $$0.857141\pi$$
$$558$$ 0 0
$$559$$ −38.5000 + 9.52628i −1.62838 + 0.402919i
$$560$$ 0 0
$$561$$ 4.50000 7.79423i 0.189990 0.329073i
$$562$$ 0 0
$$563$$ 19.5000 + 33.7750i 0.821827 + 1.42345i 0.904320 + 0.426855i $$0.140378\pi$$
−0.0824933 + 0.996592i $$0.526288\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 1.00000 0.0419961
$$568$$ 0 0
$$569$$ −13.5000 + 23.3827i −0.565949 + 0.980253i 0.431011 + 0.902347i $$0.358157\pi$$
−0.996961 + 0.0779066i $$0.975176\pi$$
$$570$$ 0 0
$$571$$ −40.0000 −1.67395 −0.836974 0.547243i $$-0.815677\pi$$
−0.836974 + 0.547243i $$0.815677\pi$$
$$572$$ 0 0
$$573$$ 3.00000 0.125327
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −2.00000 −0.0832611 −0.0416305 0.999133i $$-0.513255\pi$$
−0.0416305 + 0.999133i $$0.513255\pi$$
$$578$$ 0 0
$$579$$ −2.50000 4.33013i −0.103896 0.179954i
$$580$$ 0 0
$$581$$ −6.00000 10.3923i −0.248922 0.431145i
$$582$$ 0 0
$$583$$ −9.00000 + 15.5885i −0.372742 + 0.645608i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 16.5000 28.5788i 0.681028 1.17957i −0.293640 0.955916i $$-0.594867\pi$$
0.974668 0.223659i $$-0.0718001\pi$$
$$588$$ 0 0
$$589$$ −14.0000 24.2487i −0.576860 0.999151i
$$590$$ 0 0
$$591$$ −10.5000 18.1865i −0.431912 0.748094i
$$592$$ 0 0
$$593$$ 6.00000 0.246390 0.123195 0.992382i $$-0.460686\pi$$
0.123195 + 0.992382i $$0.460686\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −17.0000 −0.695764
$$598$$ 0 0
$$599$$ 24.0000 0.980613 0.490307 0.871550i $$-0.336885\pi$$
0.490307 + 0.871550i $$0.336885\pi$$
$$600$$ 0 0
$$601$$ −17.5000 + 30.3109i −0.713840 + 1.23641i 0.249565 + 0.968358i $$0.419712\pi$$
−0.963405 + 0.268049i $$0.913621\pi$$
$$602$$ 0 0
$$603$$ −14.0000 −0.570124
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −6.50000 11.2583i −0.263827 0.456962i 0.703429 0.710766i $$-0.251651\pi$$
−0.967256 + 0.253804i $$0.918318\pi$$
$$608$$ 0 0
$$609$$ 1.50000 2.59808i 0.0607831 0.105279i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ −21.5000 + 37.2391i −0.868377 + 1.50407i −0.00472215 + 0.999989i $$0.501503\pi$$
−0.863655 + 0.504084i $$0.831830\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 16.5000 + 28.5788i 0.664265 + 1.15054i 0.979484 + 0.201522i $$0.0645887\pi$$
−0.315219 + 0.949019i $$0.602078\pi$$
$$618$$ 0 0
$$619$$ 44.0000 1.76851 0.884255 0.467005i $$-0.154667\pi$$
0.884255 + 0.467005i $$0.154667\pi$$
$$620$$ 0 0
$$621$$ −7.50000 + 12.9904i −0.300965 + 0.521286i
$$622$$ 0 0
$$623$$ 15.0000 0.600962
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −10.5000 + 18.1865i −0.419330 + 0.726300i
$$628$$ 0 0
$$629$$ 21.0000 0.837325
$$630$$ 0 0
$$631$$ −8.50000 14.7224i −0.338380 0.586091i 0.645748 0.763550i $$-0.276545\pi$$
−0.984128 + 0.177459i $$0.943212\pi$$
$$632$$ 0 0
$$633$$ 5.50000 + 9.52628i 0.218605 + 0.378636i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 15.0000 + 15.5885i 0.594322 + 0.617637i
$$638$$ 0 0
$$639$$ −3.00000 + 5.19615i −0.118678 + 0.205557i
$$640$$ 0 0
$$641$$ −13.5000 23.3827i −0.533218 0.923561i −0.999247 0.0387913i $$-0.987649\pi$$
0.466029 0.884769i $$-0.345684\pi$$
$$642$$ 0 0
$$643$$ 5.50000 + 9.52628i 0.216899 + 0.375680i 0.953858 0.300257i $$-0.0970725\pi$$
−0.736959 + 0.675937i $$0.763739\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 22.5000 38.9711i 0.884566 1.53211i 0.0383563 0.999264i $$-0.487788\pi$$
0.846210 0.532850i $$-0.178879\pi$$
$$648$$ 0 0
$$649$$ −9.00000 −0.353281
$$650$$ 0 0
$$651$$ 4.00000 0.156772
$$652$$ 0 0
$$653$$ −19.5000 + 33.7750i −0.763094 + 1.32172i 0.178154 + 0.984003i $$0.442987\pi$$
−0.941248 + 0.337715i $$0.890346\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ −2.00000 3.46410i −0.0780274 0.135147i
$$658$$ 0 0
$$659$$ 19.5000 + 33.7750i 0.759612 + 1.31569i 0.943049 + 0.332655i $$0.107945\pi$$
−0.183436 + 0.983032i $$0.558722\pi$$
$$660$$ 0 0
$$661$$ 0.500000 0.866025i 0.0194477 0.0336845i −0.856138 0.516748i $$-0.827143\pi$$
0.875585 + 0.483063i $$0.160476\pi$$
$$662$$ 0 0
$$663$$ 3.00000 10.3923i 0.116510 0.403604i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ −4.50000 7.79423i −0.174241 0.301794i
$$668$$ 0 0
$$669$$ 9.50000 + 16.4545i 0.367291 + 0.636167i
$$670$$ 0 0
$$671$$ 33.0000 1.27395
$$672$$ 0 0
$$673$$ 8.50000 14.7224i 0.327651 0.567508i −0.654394 0.756153i $$-0.727076\pi$$
0.982045 + 0.188645i $$0.0604097\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 42.0000 1.61419 0.807096 0.590421i $$-0.201038\pi$$
0.807096 + 0.590421i $$0.201038\pi$$
$$678$$ 0 0
$$679$$ −3.50000 + 6.06218i −0.134318 + 0.232645i
$$680$$ 0 0
$$681$$ 27.0000 1.03464
$$682$$ 0 0
$$683$$ 25.5000 + 44.1673i 0.975730 + 1.69001i 0.677503 + 0.735520i $$0.263062\pi$$
0.298227 + 0.954495i $$0.403605\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −11.0000 + 19.0526i −0.419676 + 0.726900i
$$688$$ 0 0
$$689$$ −6.00000 + 20.7846i −0.228582 + 0.791831i
$$690$$ 0 0
$$691$$ −11.5000 + 19.9186i −0.437481 + 0.757739i −0.997494 0.0707446i $$-0.977462\pi$$
0.560014 + 0.828483i $$0.310796\pi$$
$$692$$ 0 0
$$693$$ 3.00000 + 5.19615i 0.113961 + 0.197386i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −27.0000 −1.02270
$$698$$ 0 0
$$699$$ −9.00000 + 15.5885i −0.340411 + 0.589610i
$$700$$ 0 0
$$701$$ 18.0000 0.679851 0.339925 0.940452i $$-0.389598\pi$$
0.339925 + 0.940452i $$0.389598\pi$$
$$702$$ 0 0
$$703$$ −49.0000 −1.84807
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ −9.00000 −0.338480
$$708$$ 0 0
$$709$$ 18.5000 + 32.0429i 0.694782 + 1.20340i 0.970254 + 0.242089i $$0.0778325\pi$$
−0.275472 + 0.961309i $$0.588834\pi$$
$$710$$ 0 0
$$711$$ 8.00000 + 13.8564i 0.300023 + 0.519656i
$$712$$ 0 0
$$713$$ 6.00000 10.3923i 0.224702 0.389195i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −4.50000 7.79423i −0.167822 0.290676i 0.769832 0.638247i $$-0.220340\pi$$
−0.937654 + 0.347571i $$0.887007\pi$$
$$720$$ 0 0
$$721$$ 4.00000 + 6.92820i 0.148968 + 0.258020i
$$722$$ 0 0
$$723$$ 1.00000 0.0371904
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 52.0000 1.92857 0.964287 0.264861i $$-0.0853260\pi$$
0.964287 + 0.264861i $$0.0853260\pi$$
$$728$$ 0 0
$$729$$ 13.0000 0.481481
$$730$$ 0 0
$$731$$ 16.5000 28.5788i 0.610275 1.05703i
$$732$$ 0 0
$$733$$ 34.0000 1.25582 0.627909 0.778287i $$-0.283911\pi$$
0.627909 + 0.778287i $$0.283911\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −10.5000 18.1865i −0.386772 0.669910i
$$738$$ 0 0
$$739$$ −23.5000 + 40.7032i −0.864461 + 1.49729i 0.00311943 + 0.999995i $$0.499007\pi$$
−0.867581 + 0.497296i $$0.834326\pi$$
$$740$$ 0 0
$$741$$ −7.00000 + 24.2487i −0.257151 + 0.890799i
$$742$$ 0 0
$$743$$ 10.5000 18.1865i 0.385208 0.667199i −0.606590 0.795015i $$-0.707463\pi$$
0.991798 + 0.127815i $$0.0407965\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 12.0000 + 20.7846i 0.439057 + 0.760469i
$$748$$ 0 0
$$749$$ −9.00000 −0.328853
$$750$$ 0 0
$$751$$ 6.50000 11.2583i 0.237188 0.410822i −0.722718 0.691143i $$-0.757107\pi$$
0.959906 + 0.280321i $$0.0904408\pi$$
$$752$$ 0 0
$$753$$ −21.0000 −0.765283
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 14.5000 25.1147i 0.527011 0.912811i −0.472493 0.881334i $$-0.656646\pi$$
0.999505 0.0314762i $$-0.0100208\pi$$
$$758$$ 0 0
$$759$$ −9.00000 −0.326679
$$760$$ 0 0
$$761$$ −1.50000 2.59808i −0.0543750 0.0941802i 0.837557 0.546350i $$-0.183983\pi$$
−0.891932 + 0.452170i $$0.850650\pi$$
$$762$$ 0 0
$$763$$ −1.00000 1.73205i −0.0362024 0.0627044i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −10.5000 + 2.59808i −0.379133 + 0.0938111i
$$768$$ 0 0
$$769$$ 6.50000 11.2583i 0.234396 0.405986i −0.724701 0.689063i $$-0.758022\pi$$
0.959097 + 0.283078i $$0.0913554\pi$$
$$770$$ 0 0
$$771$$ −4.50000 7.79423i −0.162064 0.280702i
$$772$$ 0 0
$$773$$ −13.5000 23.3827i −0.485561 0.841017i 0.514301 0.857610i $$-0.328051\pi$$
−0.999862 + 0.0165929i $$0.994718\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 3.50000 6.06218i 0.125562 0.217479i
$$778$$ 0 0
$$779$$ 63.0000 2.25721
$$780$$ 0 0
$$781$$ −9.00000 −0.322045
$$782$$ 0 0
$$783$$ −7.50000 + 12.9904i −0.268028 + 0.464238i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −18.5000 32.0429i −0.659454 1.14221i −0.980757 0.195231i $$-0.937454\pi$$
0.321303 0.946976i $$-0.395879\pi$$
$$788$$ 0 0
$$789$$ 1.50000 + 2.59808i 0.0534014 + 0.0924940i
$$790$$ 0 0
$$791$$ 4.50000 7.79423i 0.160002 0.277131i
$$792$$ 0 0
$$793$$ 38.5000 9.52628i 1.36718 0.338288i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ −25.5000 44.1673i −0.903256 1.56449i −0.823241 0.567692i $$-0.807836\pi$$
−0.0800155 0.996794i $$-0.525497\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0