# Properties

 Label 1300.2.bb.a.549.1 Level $1300$ Weight $2$ Character 1300.549 Analytic conductor $10.381$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1300 = 2^{2} \cdot 5^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1300.bb (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$10.3805522628$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{6})$$ Coefficient field: $$\Q(\zeta_{12})$$ Defining polynomial: $$x^{4} - x^{2} + 1$$ x^4 - x^2 + 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: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 549.1 Root $$-0.866025 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 1300.549 Dual form 1300.2.bb.a.1049.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})$$ $$q+(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{7} +(-1.00000 + 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} +(3.46410 - 1.00000i) q^{13} +(2.59808 + 1.50000i) q^{17} +(-3.50000 + 6.06218i) q^{19} -1.00000 q^{21} +(2.59808 - 1.50000i) q^{23} -5.00000i q^{27} +(1.50000 + 2.59808i) q^{29} -4.00000 q^{31} +(2.59808 + 1.50000i) q^{33} +(-6.06218 + 3.50000i) q^{37} +(-2.50000 + 2.59808i) q^{39} +(4.50000 + 7.79423i) q^{41} +(9.52628 + 5.50000i) q^{43} +(-3.00000 - 5.19615i) q^{49} -3.00000 q^{51} +6.00000i q^{53} -7.00000i q^{57} +(-1.50000 + 2.59808i) q^{59} +(-5.50000 + 9.52628i) q^{61} +(-1.73205 + 1.00000i) q^{63} +(-6.06218 + 3.50000i) q^{67} +(-1.50000 + 2.59808i) q^{69} +(1.50000 - 2.59808i) q^{71} -2.00000i q^{73} -3.00000i q^{77} -8.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000i q^{83} +(-2.59808 - 1.50000i) q^{87} +(7.50000 + 12.9904i) q^{89} +(3.50000 + 0.866025i) q^{91} +(3.46410 - 2.00000i) q^{93} +(6.06218 + 3.50000i) q^{97} +6.00000 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{9}+O(q^{10})$$ 4 * q - 4 * q^9 $$4 q - 4 q^{9} - 6 q^{11} - 14 q^{19} - 4 q^{21} + 6 q^{29} - 16 q^{31} - 10 q^{39} + 18 q^{41} - 12 q^{49} - 12 q^{51} - 6 q^{59} - 22 q^{61} - 6 q^{69} + 6 q^{71} - 32 q^{79} - 2 q^{81} + 30 q^{89} + 14 q^{91} + 24 q^{99}+O(q^{100})$$ 4 * q - 4 * q^9 - 6 * q^11 - 14 * q^19 - 4 * q^21 + 6 * q^29 - 16 * q^31 - 10 * q^39 + 18 * q^41 - 12 * q^49 - 12 * q^51 - 6 * q^59 - 22 * q^61 - 6 * q^69 + 6 * q^71 - 32 * q^79 - 2 * q^81 + 30 * q^89 + 14 * q^91 + 24 * q^99

## Character values

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

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

## 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
$$3$$ −0.866025 + 0.500000i −0.500000 + 0.288675i −0.728714 0.684819i $$-0.759881\pi$$
0.228714 + 0.973494i $$0.426548\pi$$
$$4$$ 0 0
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0.866025 + 0.500000i 0.327327 + 0.188982i 0.654654 0.755929i $$-0.272814\pi$$
−0.327327 + 0.944911i $$0.606148\pi$$
$$8$$ 0 0
$$9$$ −1.00000 + 1.73205i −0.333333 + 0.577350i
$$10$$ 0 0
$$11$$ −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i $$-0.316051\pi$$
−0.998526 + 0.0542666i $$0.982718\pi$$
$$12$$ 0 0
$$13$$ 3.46410 1.00000i 0.960769 0.277350i
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ 2.59808 + 1.50000i 0.630126 + 0.363803i 0.780801 0.624780i $$-0.214811\pi$$
−0.150675 + 0.988583i $$0.548145\pi$$
$$18$$ 0 0
$$19$$ −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i $$0.463407\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ 0 0
$$21$$ −1.00000 −0.218218
$$22$$ 0 0
$$23$$ 2.59808 1.50000i 0.541736 0.312772i −0.204046 0.978961i $$-0.565409\pi$$
0.745782 + 0.666190i $$0.232076\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 5.00000i 0.962250i
$$28$$ 0 0
$$29$$ 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i $$-0.0768152\pi$$
−0.692480 + 0.721437i $$0.743482\pi$$
$$30$$ 0 0
$$31$$ −4.00000 −0.718421 −0.359211 0.933257i $$-0.616954\pi$$
−0.359211 + 0.933257i $$0.616954\pi$$
$$32$$ 0 0
$$33$$ 2.59808 + 1.50000i 0.452267 + 0.261116i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −6.06218 + 3.50000i −0.996616 + 0.575396i −0.907245 0.420602i $$-0.861819\pi$$
−0.0893706 + 0.995998i $$0.528486\pi$$
$$38$$ 0 0
$$39$$ −2.50000 + 2.59808i −0.400320 + 0.416025i
$$40$$ 0 0
$$41$$ 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i $$0.0813924\pi$$
−0.264704 + 0.964330i $$0.585274\pi$$
$$42$$ 0 0
$$43$$ 9.52628 + 5.50000i 1.45274 + 0.838742i 0.998636 0.0522047i $$-0.0166248\pi$$
0.454108 + 0.890947i $$0.349958\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$48$$ 0 0
$$49$$ −3.00000 5.19615i −0.428571 0.742307i
$$50$$ 0 0
$$51$$ −3.00000 −0.420084
$$52$$ 0 0
$$53$$ 6.00000i 0.824163i 0.911147 + 0.412082i $$0.135198\pi$$
−0.911147 + 0.412082i $$0.864802\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 7.00000i 0.927173i
$$58$$ 0 0
$$59$$ −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i $$-0.895896\pi$$
0.751710 + 0.659494i $$0.229229\pi$$
$$60$$ 0 0
$$61$$ −5.50000 + 9.52628i −0.704203 + 1.21972i 0.262776 + 0.964857i $$0.415362\pi$$
−0.966978 + 0.254858i $$0.917971\pi$$
$$62$$ 0 0
$$63$$ −1.73205 + 1.00000i −0.218218 + 0.125988i
$$64$$ 0 0
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −6.06218 + 3.50000i −0.740613 + 0.427593i −0.822292 0.569066i $$-0.807305\pi$$
0.0816792 + 0.996659i $$0.473972\pi$$
$$68$$ 0 0
$$69$$ −1.50000 + 2.59808i −0.180579 + 0.312772i
$$70$$ 0 0
$$71$$ 1.50000 2.59808i 0.178017 0.308335i −0.763184 0.646181i $$-0.776365\pi$$
0.941201 + 0.337846i $$0.109698\pi$$
$$72$$ 0 0
$$73$$ 2.00000i 0.234082i −0.993127 0.117041i $$-0.962659\pi$$
0.993127 0.117041i $$-0.0373409\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 3.00000i 0.341882i
$$78$$ 0 0
$$79$$ −8.00000 −0.900070 −0.450035 0.893011i $$-0.648589\pi$$
−0.450035 + 0.893011i $$0.648589\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ 12.0000i 1.31717i 0.752506 + 0.658586i $$0.228845\pi$$
−0.752506 + 0.658586i $$0.771155\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ −2.59808 1.50000i −0.278543 0.160817i
$$88$$ 0 0
$$89$$ 7.50000 + 12.9904i 0.794998 + 1.37698i 0.922840 + 0.385183i $$0.125862\pi$$
−0.127842 + 0.991795i $$0.540805\pi$$
$$90$$ 0 0
$$91$$ 3.50000 + 0.866025i 0.366900 + 0.0907841i
$$92$$ 0 0
$$93$$ 3.46410 2.00000i 0.359211 0.207390i
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 6.06218 + 3.50000i 0.615521 + 0.355371i 0.775123 0.631810i $$-0.217688\pi$$
−0.159602 + 0.987181i $$0.551021\pi$$
$$98$$ 0 0
$$99$$ 6.00000 0.603023
$$100$$ 0 0
$$101$$ 4.50000 + 7.79423i 0.447767 + 0.775555i 0.998240 0.0592978i $$-0.0188862\pi$$
−0.550474 + 0.834853i $$0.685553\pi$$
$$102$$ 0 0
$$103$$ 8.00000i 0.788263i −0.919054 0.394132i $$-0.871045\pi$$
0.919054 0.394132i $$-0.128955\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 7.79423 4.50000i 0.753497 0.435031i −0.0734594 0.997298i $$-0.523404\pi$$
0.826956 + 0.562267i $$0.190071\pi$$
$$108$$ 0 0
$$109$$ −2.00000 −0.191565 −0.0957826 0.995402i $$-0.530535\pi$$
−0.0957826 + 0.995402i $$0.530535\pi$$
$$110$$ 0 0
$$111$$ 3.50000 6.06218i 0.332205 0.575396i
$$112$$ 0 0
$$113$$ 7.79423 + 4.50000i 0.733219 + 0.423324i 0.819599 0.572938i $$-0.194196\pi$$
−0.0863794 + 0.996262i $$0.527530\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ −1.73205 + 7.00000i −0.160128 + 0.647150i
$$118$$ 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
$$123$$ −7.79423 4.50000i −0.702782 0.405751i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ −16.4545 + 9.50000i −1.46010 + 0.842989i −0.999015 0.0443678i $$-0.985873\pi$$
−0.461084 + 0.887357i $$0.652539\pi$$
$$128$$ 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
$$133$$ −6.06218 + 3.50000i −0.525657 + 0.303488i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 12.9904 + 7.50000i 1.10984 + 0.640768i 0.938789 0.344493i $$-0.111949\pi$$
0.171054 + 0.985262i $$0.445283\pi$$
$$138$$ 0 0
$$139$$ 2.50000 4.33013i 0.212047 0.367277i −0.740308 0.672268i $$-0.765320\pi$$
0.952355 + 0.304991i $$0.0986536\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ −7.79423 7.50000i −0.651786 0.627182i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 5.19615 + 3.00000i 0.428571 + 0.247436i
$$148$$ 0 0
$$149$$ −10.5000 + 18.1865i −0.860194 + 1.48990i 0.0115483 + 0.999933i $$0.496324\pi$$
−0.871742 + 0.489966i $$0.837009\pi$$
$$150$$ 0 0
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ 0 0
$$153$$ −5.19615 + 3.00000i −0.420084 + 0.242536i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 10.0000i 0.798087i −0.916932 0.399043i $$-0.869342\pi$$
0.916932 0.399043i $$-0.130658\pi$$
$$158$$ 0 0
$$159$$ −3.00000 5.19615i −0.237915 0.412082i
$$160$$ 0 0
$$161$$ 3.00000 0.236433
$$162$$ 0 0
$$163$$ −0.866025 0.500000i −0.0678323 0.0391630i 0.465700 0.884943i $$-0.345802\pi$$
−0.533533 + 0.845780i $$0.679136\pi$$
$$164$$ 0 0
$$165$$ 0 0
$$166$$ 0 0
$$167$$ −2.59808 + 1.50000i −0.201045 + 0.116073i −0.597143 0.802135i $$-0.703697\pi$$
0.396098 + 0.918208i $$0.370364\pi$$
$$168$$ 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
$$173$$ −2.59808 1.50000i −0.197528 0.114043i 0.397974 0.917397i $$-0.369713\pi$$
−0.595502 + 0.803354i $$0.703047\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 3.00000i 0.225494i
$$178$$ 0 0
$$179$$ −10.5000 18.1865i −0.784807 1.35933i −0.929114 0.369792i $$-0.879429\pi$$
0.144308 0.989533i $$-0.453905\pi$$
$$180$$ 0 0
$$181$$ 2.00000 0.148659 0.0743294 0.997234i $$-0.476318\pi$$
0.0743294 + 0.997234i $$0.476318\pi$$
$$182$$ 0 0
$$183$$ 11.0000i 0.813143i
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 9.00000i 0.658145i
$$188$$ 0 0
$$189$$ 2.50000 4.33013i 0.181848 0.314970i
$$190$$ 0 0
$$191$$ 1.50000 2.59808i 0.108536 0.187990i −0.806641 0.591041i $$-0.798717\pi$$
0.915177 + 0.403051i $$0.132050\pi$$
$$192$$ 0 0
$$193$$ −4.33013 + 2.50000i −0.311689 + 0.179954i −0.647682 0.761911i $$-0.724262\pi$$
0.335993 + 0.941865i $$0.390928\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 18.1865 10.5000i 1.29574 0.748094i 0.316072 0.948735i $$-0.397636\pi$$
0.979665 + 0.200641i $$0.0643025\pi$$
$$198$$ 0 0
$$199$$ 8.50000 14.7224i 0.602549 1.04365i −0.389885 0.920864i $$-0.627485\pi$$
0.992434 0.122782i $$-0.0391815\pi$$
$$200$$ 0 0
$$201$$ 3.50000 6.06218i 0.246871 0.427593i
$$202$$ 0 0
$$203$$ 3.00000i 0.210559i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 6.00000i 0.417029i
$$208$$ 0 0
$$209$$ 21.0000 1.45260
$$210$$ 0 0
$$211$$ −5.50000 9.52628i −0.378636 0.655816i 0.612228 0.790681i $$-0.290273\pi$$
−0.990864 + 0.134865i $$0.956940\pi$$
$$212$$ 0 0
$$213$$ 3.00000i 0.205557i
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ −3.46410 2.00000i −0.235159 0.135769i
$$218$$ 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
$$223$$ 16.4545 9.50000i 1.10187 0.636167i 0.165161 0.986267i $$-0.447186\pi$$
0.936713 + 0.350100i $$0.113852\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −23.3827 13.5000i −1.55196 0.896026i −0.997982 0.0634974i $$-0.979775\pi$$
−0.553981 0.832529i $$-0.686892\pi$$
$$228$$ 0 0
$$229$$ 22.0000 1.45380 0.726900 0.686743i $$-0.240960\pi$$
0.726900 + 0.686743i $$0.240960\pi$$
$$230$$ 0 0
$$231$$ 1.50000 + 2.59808i 0.0986928 + 0.170941i
$$232$$ 0 0
$$233$$ 18.0000i 1.17922i −0.807688 0.589610i $$-0.799282\pi$$
0.807688 0.589610i $$-0.200718\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 6.92820 4.00000i 0.450035 0.259828i
$$238$$ 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 −0.849472 0.527633i $$-0.823079\pi$$
0.881680 + 0.471848i $$0.156413\pi$$
$$242$$ 0 0
$$243$$ 13.8564 + 8.00000i 0.888889 + 0.513200i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −6.06218 + 24.5000i −0.385727 + 1.55890i
$$248$$ 0 0
$$249$$ −6.00000 10.3923i −0.380235 0.658586i
$$250$$ 0 0
$$251$$ −10.5000 + 18.1865i −0.662754 + 1.14792i 0.317135 + 0.948380i $$0.397279\pi$$
−0.979889 + 0.199543i $$0.936054\pi$$
$$252$$ 0 0
$$253$$ −7.79423 4.50000i −0.490019 0.282913i
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 0 0
$$257$$ 7.79423 4.50000i 0.486191 0.280702i −0.236802 0.971558i $$-0.576099\pi$$
0.722993 + 0.690856i $$0.242766\pi$$
$$258$$ 0 0
$$259$$ −7.00000 −0.434959
$$260$$ 0 0
$$261$$ −6.00000 −0.371391
$$262$$ 0 0
$$263$$ 2.59808 1.50000i 0.160204 0.0924940i −0.417755 0.908560i $$-0.637183\pi$$
0.577959 + 0.816066i $$0.303849\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −12.9904 7.50000i −0.794998 0.458993i
$$268$$ 0 0
$$269$$ 13.5000 23.3827i 0.823110 1.42567i −0.0802460 0.996775i $$-0.525571\pi$$
0.903356 0.428892i $$-0.141096\pi$$
$$270$$ 0 0
$$271$$ −11.5000 19.9186i −0.698575 1.20997i −0.968960 0.247216i $$-0.920484\pi$$
0.270385 0.962752i $$-0.412849\pi$$
$$272$$ 0 0
$$273$$ −3.46410 + 1.00000i −0.209657 + 0.0605228i
$$274$$ 0 0
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 16.4545 + 9.50000i 0.988654 + 0.570800i 0.904872 0.425684i $$-0.139967\pi$$
0.0837823 + 0.996484i $$0.473300\pi$$
$$278$$ 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
$$283$$ −4.33013 + 2.50000i −0.257399 + 0.148610i −0.623148 0.782104i $$-0.714146\pi$$
0.365748 + 0.930714i $$0.380813\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 9.00000i 0.531253i
$$288$$ 0 0
$$289$$ −4.00000 6.92820i −0.235294 0.407541i
$$290$$ 0 0
$$291$$ −7.00000 −0.410347
$$292$$ 0 0
$$293$$ −23.3827 13.5000i −1.36603 0.788678i −0.375613 0.926777i $$-0.622568\pi$$
−0.990419 + 0.138098i $$0.955901\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ −12.9904 + 7.50000i −0.753778 + 0.435194i
$$298$$ 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
$$303$$ −7.79423 4.50000i −0.447767 0.258518i
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 20.0000i 1.14146i 0.821138 + 0.570730i $$0.193340\pi$$
−0.821138 + 0.570730i $$0.806660\pi$$
$$308$$ 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
$$313$$ 22.0000i 1.24351i 0.783210 + 0.621757i $$0.213581\pi$$
−0.783210 + 0.621757i $$0.786419\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 18.0000i 1.01098i −0.862832 0.505490i $$-0.831312\pi$$
0.862832 0.505490i $$-0.168688\pi$$
$$318$$ 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
$$323$$ −18.1865 + 10.5000i −1.01193 + 0.584236i
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 1.73205 1.00000i 0.0957826 0.0553001i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 9.50000 16.4545i 0.522167 0.904420i −0.477500 0.878632i $$-0.658457\pi$$
0.999667 0.0257885i $$-0.00820965\pi$$
$$332$$ 0 0
$$333$$ 14.0000i 0.767195i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 34.0000i 1.85210i −0.377403 0.926049i $$-0.623183\pi$$
0.377403 0.926049i $$-0.376817\pi$$
$$338$$ 0 0
$$339$$ −9.00000 −0.488813
$$340$$ 0 0
$$341$$ 6.00000 + 10.3923i 0.324918 + 0.562775i
$$342$$ 0 0
$$343$$ 13.0000i 0.701934i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 28.5788 + 16.5000i 1.53419 + 0.885766i 0.999162 + 0.0409337i $$0.0130332\pi$$
0.535031 + 0.844833i $$0.320300\pi$$
$$348$$ 0 0
$$349$$ −0.500000 0.866025i −0.0267644 0.0463573i 0.852333 0.523000i $$-0.175187\pi$$
−0.879097 + 0.476642i $$0.841854\pi$$
$$350$$ 0 0
$$351$$ −5.00000 17.3205i −0.266880 0.924500i
$$352$$ 0 0
$$353$$ −7.79423 + 4.50000i −0.414845 + 0.239511i −0.692869 0.721063i $$-0.743654\pi$$
0.278024 + 0.960574i $$0.410320\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ −2.59808 1.50000i −0.137505 0.0793884i
$$358$$ 0 0
$$359$$ 24.0000 1.26667 0.633336 0.773877i $$-0.281685\pi$$
0.633336 + 0.773877i $$0.281685\pi$$
$$360$$ 0 0
$$361$$ −15.0000 25.9808i −0.789474 1.36741i
$$362$$ 0 0
$$363$$ 2.00000i 0.104973i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 4.33013 2.50000i 0.226031 0.130499i −0.382709 0.923869i $$-0.625009\pi$$
0.608740 + 0.793370i $$0.291675\pi$$
$$368$$ 0 0
$$369$$ −18.0000 −0.937043
$$370$$ 0 0
$$371$$ −3.00000 + 5.19615i −0.155752 + 0.269771i
$$372$$ 0 0
$$373$$ −26.8468 15.5000i −1.39007 0.802560i −0.396751 0.917926i $$-0.629862\pi$$
−0.993323 + 0.115367i $$0.963196\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 7.79423 + 7.50000i 0.401423 + 0.386270i
$$378$$ 0 0
$$379$$ −0.500000 0.866025i −0.0256833 0.0444847i 0.852898 0.522077i $$-0.174843\pi$$
−0.878581 + 0.477593i $$0.841509\pi$$
$$380$$ 0 0
$$381$$ 9.50000 16.4545i 0.486700 0.842989i
$$382$$ 0 0
$$383$$ −7.79423 4.50000i −0.398266 0.229939i 0.287469 0.957790i $$-0.407186\pi$$
−0.685736 + 0.727851i $$0.740519\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ −19.0526 + 11.0000i −0.968496 + 0.559161i
$$388$$ 0 0
$$389$$ −18.0000 −0.912636 −0.456318 0.889817i $$-0.650832\pi$$
−0.456318 + 0.889817i $$0.650832\pi$$
$$390$$ 0 0
$$391$$ 9.00000 0.455150
$$392$$ 0 0
$$393$$ 10.3923 6.00000i 0.524222 0.302660i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −4.33013 2.50000i −0.217323 0.125471i 0.387387 0.921917i $$-0.373378\pi$$
−0.604710 + 0.796446i $$0.706711\pi$$
$$398$$ 0 0
$$399$$ 3.50000 6.06218i 0.175219 0.303488i
$$400$$ 0 0
$$401$$ 16.5000 + 28.5788i 0.823971 + 1.42716i 0.902703 + 0.430263i $$0.141579\pi$$
−0.0787327 + 0.996896i $$0.525087\pi$$
$$402$$ 0 0
$$403$$ −13.8564 + 4.00000i −0.690237 + 0.199254i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 18.1865 + 10.5000i 0.901473 + 0.520466i
$$408$$ 0 0
$$409$$ −12.5000 + 21.6506i −0.618085 + 1.07056i 0.371750 + 0.928333i $$0.378758\pi$$
−0.989835 + 0.142222i $$0.954575\pi$$
$$410$$ 0 0
$$411$$ −15.0000 −0.739895
$$412$$ 0 0
$$413$$ −2.59808 + 1.50000i −0.127843 + 0.0738102i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 5.00000i 0.244851i
$$418$$ 0 0
$$419$$ −4.50000 7.79423i −0.219839 0.380773i 0.734919 0.678155i $$-0.237220\pi$$
−0.954759 + 0.297382i $$0.903887\pi$$
$$420$$ 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
$$427$$ −9.52628 + 5.50000i −0.461009 + 0.266164i
$$428$$ 0 0
$$429$$ 10.5000 + 2.59808i 0.506945 + 0.125436i
$$430$$ 0 0
$$431$$ 4.50000 + 7.79423i 0.216757 + 0.375435i 0.953815 0.300395i $$-0.0971186\pi$$
−0.737057 + 0.675830i $$0.763785\pi$$
$$432$$ 0 0
$$433$$ 25.1147 + 14.5000i 1.20694 + 0.696826i 0.962089 0.272736i $$-0.0879285\pi$$
0.244848 + 0.969561i $$0.421262\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 21.0000i 1.00457i
$$438$$ 0 0
$$439$$ 5.50000 + 9.52628i 0.262501 + 0.454665i 0.966906 0.255134i $$-0.0821195\pi$$
−0.704405 + 0.709798i $$0.748786\pi$$
$$440$$ 0 0
$$441$$ 12.0000 0.571429
$$442$$ 0 0
$$443$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 21.0000i 0.993266i
$$448$$ 0 0
$$449$$ 1.50000 2.59808i 0.0707894 0.122611i −0.828458 0.560051i $$-0.810782\pi$$
0.899247 + 0.437440i $$0.144115\pi$$
$$450$$ 0 0
$$451$$ 13.5000 23.3827i 0.635690 1.10105i
$$452$$ 0 0
$$453$$ −6.92820 + 4.00000i −0.325515 + 0.187936i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 4.33013 2.50000i 0.202555 0.116945i −0.395292 0.918556i $$-0.629357\pi$$
0.597847 + 0.801611i $$0.296023\pi$$
$$458$$ 0 0
$$459$$ 7.50000 12.9904i 0.350070 0.606339i
$$460$$ 0 0
$$461$$ −13.5000 + 23.3827i −0.628758 + 1.08904i 0.359044 + 0.933321i $$0.383103\pi$$
−0.987801 + 0.155719i $$0.950230\pi$$
$$462$$ 0 0
$$463$$ 4.00000i 0.185896i 0.995671 + 0.0929479i $$0.0296290\pi$$
−0.995671 + 0.0929479i $$0.970371\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 36.0000i 1.66588i −0.553362 0.832941i $$-0.686655\pi$$
0.553362 0.832941i $$-0.313345\pi$$
$$468$$ 0 0
$$469$$ −7.00000 −0.323230
$$470$$ 0 0
$$471$$ 5.00000 + 8.66025i 0.230388 + 0.399043i
$$472$$ 0 0
$$473$$ 33.0000i 1.51734i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ −10.3923 6.00000i −0.475831 0.274721i
$$478$$ 0 0
$$479$$ 19.5000 + 33.7750i 0.890978 + 1.54322i 0.838705 + 0.544586i $$0.183313\pi$$
0.0522726 + 0.998633i $$0.483354\pi$$
$$480$$ 0 0
$$481$$ −17.5000 + 18.1865i −0.797931 + 0.829235i
$$482$$ 0 0
$$483$$ −2.59808 + 1.50000i −0.118217 + 0.0682524i
$$484$$ 0 0
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −9.52628 5.50000i −0.431677 0.249229i 0.268384 0.963312i $$-0.413510\pi$$
−0.700061 + 0.714083i $$0.746844\pi$$
$$488$$ 0 0
$$489$$ 1.00000 0.0452216
$$490$$ 0 0
$$491$$ 4.50000 + 7.79423i 0.203082 + 0.351749i 0.949520 0.313707i $$-0.101571\pi$$
−0.746438 + 0.665455i $$0.768237\pi$$
$$492$$ 0 0
$$493$$ 9.00000i 0.405340i
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 2.59808 1.50000i 0.116540 0.0672842i
$$498$$ 0 0
$$499$$ −32.0000 −1.43252 −0.716258 0.697835i $$-0.754147\pi$$
−0.716258 + 0.697835i $$0.754147\pi$$
$$500$$ 0 0
$$501$$ 1.50000 2.59808i 0.0670151 0.116073i
$$502$$ 0 0
$$503$$ 12.9904 + 7.50000i 0.579212 + 0.334408i 0.760820 0.648963i $$-0.224797\pi$$
−0.181608 + 0.983371i $$0.558130\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ −6.06218 + 11.5000i −0.269231 + 0.510733i
$$508$$ 0 0
$$509$$ −4.50000 7.79423i −0.199459 0.345473i 0.748894 0.662690i $$-0.230585\pi$$
−0.948353 + 0.317217i $$0.897252\pi$$
$$510$$ 0 0
$$511$$ 1.00000 1.73205i 0.0442374 0.0766214i
$$512$$ 0 0
$$513$$ 30.3109 + 17.5000i 1.33826 + 0.772644i
$$514$$ 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
$$523$$ −25.1147 + 14.5000i −1.09819 + 0.634041i −0.935745 0.352677i $$-0.885272\pi$$
−0.162446 + 0.986718i $$0.551938\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −10.3923 6.00000i −0.452696 0.261364i
$$528$$ 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
$$533$$ 23.3827 + 22.5000i 1.01282 + 0.974583i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 18.1865 + 10.5000i 0.784807 + 0.453108i
$$538$$ 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
$$543$$ −1.73205 + 1.00000i −0.0743294 + 0.0429141i
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 8.00000i 0.342055i 0.985266 + 0.171028i $$0.0547087\pi$$
−0.985266 + 0.171028i $$0.945291\pi$$
$$548$$ 0 0
$$549$$ −11.0000 19.0526i −0.469469 0.813143i
$$550$$ 0 0
$$551$$ −21.0000 −0.894630
$$552$$ 0 0
$$553$$ −6.92820 4.00000i −0.294617 0.170097i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ −33.7750 + 19.5000i −1.43109 + 0.826242i −0.997204 0.0747252i $$-0.976192\pi$$
−0.433888 + 0.900967i $$0.642859\pi$$
$$558$$ 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
$$563$$ 33.7750 + 19.5000i 1.42345 + 0.821827i 0.996592 0.0824933i $$-0.0262883\pi$$
0.426855 + 0.904320i $$0.359622\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 1.00000i 0.0419961i
$$568$$ 0 0
$$569$$ 13.5000 + 23.3827i 0.565949 + 0.980253i 0.996961 + 0.0779066i $$0.0248236\pi$$
−0.431011 + 0.902347i $$0.641843\pi$$
$$570$$ 0 0
$$571$$ −40.0000 −1.67395 −0.836974 0.547243i $$-0.815677\pi$$
−0.836974 + 0.547243i $$0.815677\pi$$
$$572$$ 0 0
$$573$$ 3.00000i 0.125327i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 0 0
$$577$$ 2.00000i 0.0832611i 0.999133 + 0.0416305i $$0.0132552\pi$$
−0.999133 + 0.0416305i $$0.986745\pi$$
$$578$$ 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
$$583$$ 15.5885 9.00000i 0.645608 0.372742i
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 28.5788 16.5000i 1.17957 0.681028i 0.223659 0.974668i $$-0.428200\pi$$
0.955916 + 0.293640i $$0.0948666\pi$$
$$588$$ 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
$$593$$ 6.00000i 0.246390i 0.992382 + 0.123195i $$0.0393141\pi$$
−0.992382 + 0.123195i $$0.960686\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 17.0000i 0.695764i
$$598$$ 0 0
$$599$$ −24.0000 −0.980613 −0.490307 0.871550i $$-0.663115\pi$$
−0.490307 + 0.871550i $$0.663115\pi$$
$$600$$ 0 0
$$601$$ −17.5000 30.3109i −0.713840 1.23641i −0.963405 0.268049i $$-0.913621\pi$$
0.249565 0.968358i $$-0.419712\pi$$
$$602$$ 0 0
$$603$$ 14.0000i 0.570124i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 11.2583 + 6.50000i 0.456962 + 0.263827i 0.710766 0.703429i $$-0.248349\pi$$
−0.253804 + 0.967256i $$0.581682\pi$$
$$608$$ 0 0
$$609$$ −1.50000 2.59808i −0.0607831 0.105279i
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 37.2391 21.5000i 1.50407 0.868377i 0.504084 0.863655i $$-0.331830\pi$$
0.999989 0.00472215i $$-0.00150311\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −28.5788 16.5000i −1.15054 0.664265i −0.201522 0.979484i $$-0.564589\pi$$
−0.949019 + 0.315219i $$0.897922\pi$$
$$618$$ 0 0
$$619$$ −44.0000 −1.76851 −0.884255 0.467005i $$-0.845333\pi$$
−0.884255 + 0.467005i $$0.845333\pi$$
$$620$$ 0 0
$$621$$ −7.50000 12.9904i −0.300965 0.521286i
$$622$$ 0 0
$$623$$ 15.0000i 0.600962i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ −18.1865 + 10.5000i −0.726300 + 0.419330i
$$628$$ 0 0
$$629$$ −21.0000 −0.837325
$$630$$ 0 0
$$631$$ −8.50000 + 14.7224i −0.338380 + 0.586091i −0.984128 0.177459i $$-0.943212\pi$$
0.645748 + 0.763550i $$0.276545\pi$$
$$632$$ 0 0
$$633$$ 9.52628 + 5.50000i 0.378636 + 0.218605i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −15.5885 15.0000i −0.617637 0.594322i
$$638$$ 0 0
$$639$$ 3.00000 + 5.19615i 0.118678 + 0.205557i
$$640$$ 0 0
$$641$$ −13.5000 + 23.3827i −0.533218 + 0.923561i 0.466029 + 0.884769i $$0.345684\pi$$
−0.999247 + 0.0387913i $$0.987649\pi$$
$$642$$ 0 0
$$643$$ 9.52628 + 5.50000i 0.375680 + 0.216899i 0.675937 0.736959i $$-0.263739\pi$$
−0.300257 + 0.953858i $$0.597072\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 38.9711 22.5000i 1.53211 0.884566i 0.532850 0.846210i $$-0.321121\pi$$
0.999264 0.0383563i $$-0.0122122\pi$$
$$648$$ 0 0
$$649$$ 9.00000 0.353281
$$650$$ 0 0
$$651$$ 4.00000 0.156772
$$652$$ 0 0
$$653$$ 33.7750 19.5000i 1.32172 0.763094i 0.337715 0.941248i $$-0.390346\pi$$
0.984003 + 0.178154i $$0.0570127\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 3.46410 + 2.00000i 0.135147 + 0.0780274i
$$658$$ 0 0
$$659$$ −19.5000 + 33.7750i −0.759612 + 1.31569i 0.183436 + 0.983032i $$0.441278\pi$$
−0.943049 + 0.332655i $$0.892055\pi$$
$$660$$ 0 0
$$661$$ 0.500000 + 0.866025i 0.0194477 + 0.0336845i 0.875585 0.483063i $$-0.160476\pi$$
−0.856138 + 0.516748i $$0.827143\pi$$
$$662$$ 0 0
$$663$$ −10.3923 + 3.00000i −0.403604 + 0.116510i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 7.79423 + 4.50000i 0.301794 + 0.174241i
$$668$$ 0 0
$$669$$ −9.50000 + 16.4545i −0.367291 + 0.636167i
$$670$$ 0 0
$$671$$ 33.0000 1.27395
$$672$$ 0 0
$$673$$ −14.7224 + 8.50000i −0.567508 + 0.327651i −0.756153 0.654394i $$-0.772924\pi$$
0.188645 + 0.982045i $$0.439590\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 0 0
$$677$$ 42.0000i 1.61419i −0.590421 0.807096i $$-0.701038\pi$$
0.590421 0.807096i $$-0.298962\pi$$
$$678$$ 0 0
$$679$$ 3.50000 + 6.06218i 0.134318 + 0.232645i
$$680$$ 0 0
$$681$$ 27.0000 1.03464
$$682$$ 0 0
$$683$$ 44.1673 + 25.5000i 1.69001 + 0.975730i 0.954495 + 0.298227i $$0.0963952\pi$$
0.735520 + 0.677503i $$0.236938\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −19.0526 + 11.0000i −0.726900 + 0.419676i
$$688$$ 0 0
$$689$$ 6.00000 + 20.7846i 0.228582 + 0.791831i
$$690$$ 0 0
$$691$$ −11.5000 19.9186i −0.437481 0.757739i 0.560014 0.828483i $$-0.310796\pi$$
−0.997494 + 0.0707446i $$0.977462\pi$$
$$692$$ 0 0
$$693$$ 5.19615 + 3.00000i 0.197386 + 0.113961i
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 27.0000i 1.02270i
$$698$$ 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
$$703$$ 49.0000i 1.84807i
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 9.00000i 0.338480i
$$708$$ 0 0
$$709$$ −18.5000 + 32.0429i −0.694782 + 1.20340i 0.275472 + 0.961309i $$0.411166\pi$$
−0.970254 + 0.242089i $$0.922167\pi$$
$$710$$ 0 0
$$711$$ 8.00000 13.8564i 0.300023 0.519656i
$$712$$ 0 0
$$713$$ −10.3923 + 6.00000i −0.389195 + 0.224702i
$$714$$ 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 $$-0.779660\pi$$
0.937654 + 0.347571i $$0.112993\pi$$
$$720$$ 0 0
$$721$$ 4.00000 6.92820i 0.148968 0.258020i
$$722$$ 0 0
$$723$$ 1.00000i 0.0371904i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 52.0000i 1.92857i −0.264861 0.964287i $$-0.585326\pi$$
0.264861 0.964287i $$-0.414674\pi$$
$$728$$ 0 0
$$729$$ −13.0000 −0.481481
$$730$$ 0 0
$$731$$ 16.5000 + 28.5788i 0.610275 + 1.05703i
$$732$$ 0 0
$$733$$ 34.0000i 1.25582i 0.778287 + 0.627909i $$0.216089\pi$$
−0.778287 + 0.627909i $$0.783911\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 18.1865 + 10.5000i 0.669910 + 0.386772i
$$738$$ 0 0
$$739$$ 23.5000 + 40.7032i 0.864461 + 1.49729i 0.867581 + 0.497296i $$0.165674\pi$$
−0.00311943 + 0.999995i $$0.500993\pi$$
$$740$$ 0 0
$$741$$ −7.00000 24.2487i −0.257151 0.890799i
$$742$$ 0 0
$$743$$ −18.1865 + 10.5000i −0.667199 + 0.385208i −0.795015 0.606590i $$-0.792537\pi$$
0.127815 + 0.991798i $$0.459204\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −20.7846 12.0000i −0.760469 0.439057i
$$748$$ 0 0
$$749$$ 9.00000 0.328853
$$750$$ 0 0
$$751$$ 6.50000 + 11.2583i 0.237188 + 0.410822i 0.959906 0.280321i $$-0.0904408\pi$$
−0.722718 + 0.691143i $$0.757107\pi$$
$$752$$ 0 0
$$753$$ 21.0000i 0.765283i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 25.1147 14.5000i 0.912811 0.527011i 0.0314762 0.999505i $$-0.489979\pi$$
0.881334 + 0.472493i $$0.156646\pi$$
$$758$$ 0 0
$$759$$ 9.00000 0.326679
$$760$$ 0 0
$$761$$ −1.50000 + 2.59808i −0.0543750 + 0.0941802i −0.891932 0.452170i $$-0.850650\pi$$
0.837557 + 0.546350i $$0.183983\pi$$
$$762$$ 0 0
$$763$$ −1.73205 1.00000i −0.0627044 0.0362024i
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ −2.59808 + 10.5000i −0.0938111 + 0.379133i
$$768$$ 0 0
$$769$$ −6.50000 11.2583i −0.234396 0.405986i 0.724701 0.689063i $$-0.241978\pi$$
−0.959097 + 0.283078i $$0.908645\pi$$
$$770$$ 0 0
$$771$$ −4.50000 + 7.79423i −0.162064 + 0.280702i
$$772$$ 0 0
$$773$$ −23.3827 13.5000i −0.841017 0.485561i 0.0165929 0.999862i $$-0.494718\pi$$
−0.857610 + 0.514301i $$0.828051\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 6.06218 3.50000i 0.217479 0.125562i
$$778$$ 0 0
$$779$$ −63.0000 −2.25721
$$780$$ 0 0
$$781$$ −9.00000 −0.322045
$$782$$ 0 0
$$783$$ 12.9904 7.50000i 0.464238 0.268028i
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 32.0429 + 18.5000i 1.14221 + 0.659454i 0.946976 0.321303i $$-0.104121\pi$$
0.195231 + 0.980757i $$0.437454\pi$$
$$788$$ 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
$$793$$ −9.52628 + 38.5000i −0.338288 + 1.36718i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 44.1673 + 25.5000i 1.56449 + 0.903256i 0.996794 + 0.0800155i $$0.0254970\pi$$
0.567692 + 0.823241i $$0.307836\pi$$
$$798$$ 0 0
$$799$$ 0