# Properties

 Label 3150.2.bp.g.1349.6 Level 3150 Weight 2 Character 3150.1349 Analytic conductor 25.153 Analytic rank 0 Dimension 24 CM no Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3150.bp (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$25.1528766367$$ Analytic rank: $$0$$ Dimension: $$24$$ Relative dimension: $$12$$ over $$\Q(\zeta_{6})$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 1349.6 Character $$\chi$$ $$=$$ 3150.1349 Dual form 3150.2.bp.g.899.6

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.04195 + 2.43194i) q^{7} +1.00000 q^{8} +O(q^{10})$$ $$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.04195 + 2.43194i) q^{7} +1.00000 q^{8} +(1.38605 - 0.800236i) q^{11} -0.770726 q^{13} +(-1.58515 - 2.11833i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.05027 + 1.76107i) q^{17} +(-3.06818 - 1.77141i) q^{19} +1.60047i q^{22} +(-1.61385 + 2.79527i) q^{23} +(0.385363 - 0.667468i) q^{26} +(2.62710 - 0.313613i) q^{28} -0.700774i q^{29} +(1.13725 - 0.656589i) q^{31} +(-0.500000 - 0.866025i) q^{32} -3.52215i q^{34} +(0.792101 + 0.457320i) q^{37} +(3.06818 - 1.77141i) q^{38} +4.88167 q^{41} -9.26963i q^{43} +(-1.38605 - 0.800236i) q^{44} +(-1.61385 - 2.79527i) q^{46} +(-2.31462 - 1.33635i) q^{47} +(-4.82867 - 5.06793i) q^{49} +(0.385363 + 0.667468i) q^{52} +(4.64520 + 8.04572i) q^{53} +(-1.04195 + 2.43194i) q^{56} +(0.606888 + 0.350387i) q^{58} +(-1.56198 - 2.70542i) q^{59} +(-9.43214 - 5.44565i) q^{61} +1.31318i q^{62} +1.00000 q^{64} +(-5.90314 + 3.40818i) q^{67} +(3.05027 + 1.76107i) q^{68} -6.47930i q^{71} +(-5.51852 - 9.55835i) q^{73} +(-0.792101 + 0.457320i) q^{74} +3.54282i q^{76} +(0.501930 + 4.20460i) q^{77} +(1.45086 - 2.51296i) q^{79} +(-2.44083 + 4.22765i) q^{82} +11.9777i q^{83} +(8.02773 + 4.63481i) q^{86} +(1.38605 - 0.800236i) q^{88} +(-4.40369 + 7.62742i) q^{89} +(0.803059 - 1.87436i) q^{91} +3.22770 q^{92} +(2.31462 - 1.33635i) q^{94} -5.31224 q^{97} +(6.80329 - 1.64779i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$24q - 12q^{2} - 12q^{4} + 24q^{8} + O(q^{10})$$ $$24q - 12q^{2} - 12q^{4} + 24q^{8} - 12q^{16} + 24q^{17} - 12q^{19} - 8q^{23} - 12q^{32} + 12q^{38} - 8q^{46} - 24q^{47} + 52q^{49} - 32q^{53} - 12q^{61} + 24q^{64} - 24q^{68} - 16q^{77} - 4q^{79} + 68q^{91} + 16q^{92} + 24q^{94} - 20q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times$$.

 $$n$$ $$127$$ $$451$$ $$2801$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.500000 + 0.866025i −0.353553 + 0.612372i
$$3$$ 0 0
$$4$$ −0.500000 0.866025i −0.250000 0.433013i
$$5$$ 0 0
$$6$$ 0 0
$$7$$ −1.04195 + 2.43194i −0.393821 + 0.919187i
$$8$$ 1.00000 0.353553
$$9$$ 0 0
$$10$$ 0 0
$$11$$ 1.38605 0.800236i 0.417910 0.241280i −0.276273 0.961079i $$-0.589099\pi$$
0.694183 + 0.719799i $$0.255766\pi$$
$$12$$ 0 0
$$13$$ −0.770726 −0.213761 −0.106880 0.994272i $$-0.534086\pi$$
−0.106880 + 0.994272i $$0.534086\pi$$
$$14$$ −1.58515 2.11833i −0.423648 0.566147i
$$15$$ 0 0
$$16$$ −0.500000 + 0.866025i −0.125000 + 0.216506i
$$17$$ −3.05027 + 1.76107i −0.739799 + 0.427123i −0.821996 0.569493i $$-0.807140\pi$$
0.0821974 + 0.996616i $$0.473806\pi$$
$$18$$ 0 0
$$19$$ −3.06818 1.77141i −0.703888 0.406390i 0.104906 0.994482i $$-0.466546\pi$$
−0.808794 + 0.588092i $$0.799879\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 1.60047i 0.341222i
$$23$$ −1.61385 + 2.79527i −0.336511 + 0.582854i −0.983774 0.179413i $$-0.942580\pi$$
0.647263 + 0.762267i $$0.275914\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0.385363 0.667468i 0.0755759 0.130901i
$$27$$ 0 0
$$28$$ 2.62710 0.313613i 0.496475 0.0592674i
$$29$$ 0.700774i 0.130131i −0.997881 0.0650653i $$-0.979274\pi$$
0.997881 0.0650653i $$-0.0207256\pi$$
$$30$$ 0 0
$$31$$ 1.13725 0.656589i 0.204255 0.117927i −0.394383 0.918946i $$-0.629042\pi$$
0.598639 + 0.801019i $$0.295708\pi$$
$$32$$ −0.500000 0.866025i −0.0883883 0.153093i
$$33$$ 0 0
$$34$$ 3.52215i 0.604043i
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0.792101 + 0.457320i 0.130221 + 0.0751829i 0.563695 0.825983i $$-0.309379\pi$$
−0.433475 + 0.901166i $$0.642713\pi$$
$$38$$ 3.06818 1.77141i 0.497724 0.287361i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 4.88167 0.762388 0.381194 0.924495i $$-0.375513\pi$$
0.381194 + 0.924495i $$0.375513\pi$$
$$42$$ 0 0
$$43$$ 9.26963i 1.41361i −0.707411 0.706803i $$-0.750137\pi$$
0.707411 0.706803i $$-0.249863\pi$$
$$44$$ −1.38605 0.800236i −0.208955 0.120640i
$$45$$ 0 0
$$46$$ −1.61385 2.79527i −0.237949 0.412140i
$$47$$ −2.31462 1.33635i −0.337623 0.194926i 0.321598 0.946876i $$-0.395780\pi$$
−0.659220 + 0.751950i $$0.729113\pi$$
$$48$$ 0 0
$$49$$ −4.82867 5.06793i −0.689810 0.723990i
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0.385363 + 0.667468i 0.0534402 + 0.0925612i
$$53$$ 4.64520 + 8.04572i 0.638067 + 1.10516i 0.985856 + 0.167592i $$0.0535991\pi$$
−0.347789 + 0.937573i $$0.613068\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −1.04195 + 2.43194i −0.139237 + 0.324982i
$$57$$ 0 0
$$58$$ 0.606888 + 0.350387i 0.0796883 + 0.0460081i
$$59$$ −1.56198 2.70542i −0.203352 0.352216i 0.746254 0.665661i $$-0.231850\pi$$
−0.949606 + 0.313445i $$0.898517\pi$$
$$60$$ 0 0
$$61$$ −9.43214 5.44565i −1.20766 0.697244i −0.245414 0.969418i $$-0.578924\pi$$
−0.962248 + 0.272175i $$0.912257\pi$$
$$62$$ 1.31318i 0.166774i
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −5.90314 + 3.40818i −0.721183 + 0.416375i −0.815188 0.579196i $$-0.803366\pi$$
0.0940048 + 0.995572i $$0.470033\pi$$
$$68$$ 3.05027 + 1.76107i 0.369899 + 0.213561i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 6.47930i 0.768951i −0.923135 0.384475i $$-0.874382\pi$$
0.923135 0.384475i $$-0.125618\pi$$
$$72$$ 0 0
$$73$$ −5.51852 9.55835i −0.645894 1.11872i −0.984094 0.177647i $$-0.943152\pi$$
0.338201 0.941074i $$-0.390182\pi$$
$$74$$ −0.792101 + 0.457320i −0.0920799 + 0.0531623i
$$75$$ 0 0
$$76$$ 3.54282i 0.406390i
$$77$$ 0.501930 + 4.20460i 0.0572002 + 0.479158i
$$78$$ 0 0
$$79$$ 1.45086 2.51296i 0.163234 0.282730i −0.772792 0.634659i $$-0.781141\pi$$
0.936027 + 0.351928i $$0.114474\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ −2.44083 + 4.22765i −0.269545 + 0.466865i
$$83$$ 11.9777i 1.31472i 0.753576 + 0.657361i $$0.228327\pi$$
−0.753576 + 0.657361i $$0.771673\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 8.02773 + 4.63481i 0.865653 + 0.499785i
$$87$$ 0 0
$$88$$ 1.38605 0.800236i 0.147753 0.0853055i
$$89$$ −4.40369 + 7.62742i −0.466791 + 0.808505i −0.999280 0.0379313i $$-0.987923\pi$$
0.532490 + 0.846437i $$0.321257\pi$$
$$90$$ 0 0
$$91$$ 0.803059 1.87436i 0.0841835 0.196486i
$$92$$ 3.22770 0.336511
$$93$$ 0 0
$$94$$ 2.31462 1.33635i 0.238735 0.137834i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ −5.31224 −0.539376 −0.269688 0.962948i $$-0.586921\pi$$
−0.269688 + 0.962948i $$0.586921\pi$$
$$98$$ 6.80329 1.64779i 0.687236 0.166452i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ −4.62663 8.01356i −0.460367 0.797379i 0.538612 0.842554i $$-0.318949\pi$$
−0.998979 + 0.0451749i $$0.985615\pi$$
$$102$$ 0 0
$$103$$ 7.91290 13.7055i 0.779681 1.35045i −0.152444 0.988312i $$-0.548714\pi$$
0.932125 0.362136i $$-0.117952\pi$$
$$104$$ −0.770726 −0.0755759
$$105$$ 0 0
$$106$$ −9.29040 −0.902363
$$107$$ −6.20735 + 10.7514i −0.600087 + 1.03938i 0.392720 + 0.919658i $$0.371534\pi$$
−0.992807 + 0.119724i $$0.961799\pi$$
$$108$$ 0 0
$$109$$ −5.51750 9.55659i −0.528480 0.915355i −0.999449 0.0332048i $$-0.989429\pi$$
0.470968 0.882150i $$-0.343905\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −1.58515 2.11833i −0.149782 0.200163i
$$113$$ 15.0301 1.41391 0.706957 0.707256i $$-0.250067\pi$$
0.706957 + 0.707256i $$0.250067\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −0.606888 + 0.350387i −0.0563482 + 0.0325326i
$$117$$ 0 0
$$118$$ 3.12395 0.287583
$$119$$ −1.10459 9.25303i −0.101258 0.848223i
$$120$$ 0 0
$$121$$ −4.21924 + 7.30795i −0.383568 + 0.664359i
$$122$$ 9.43214 5.44565i 0.853946 0.493026i
$$123$$ 0 0
$$124$$ −1.13725 0.656589i −0.102128 0.0589634i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 2.66506i 0.236486i −0.992985 0.118243i $$-0.962274\pi$$
0.992985 0.118243i $$-0.0377262\pi$$
$$128$$ −0.500000 + 0.866025i −0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 7.10987 12.3147i 0.621192 1.07594i −0.368071 0.929797i $$-0.619982\pi$$
0.989264 0.146139i $$-0.0466848\pi$$
$$132$$ 0 0
$$133$$ 7.50486 5.61590i 0.650754 0.486960i
$$134$$ 6.81636i 0.588844i
$$135$$ 0 0
$$136$$ −3.05027 + 1.76107i −0.261558 + 0.151011i
$$137$$ −0.0650662 0.112698i −0.00555898 0.00962843i 0.863233 0.504806i $$-0.168436\pi$$
−0.868792 + 0.495178i $$0.835103\pi$$
$$138$$ 0 0
$$139$$ 3.63572i 0.308378i 0.988041 + 0.154189i $$0.0492765\pi$$
−0.988041 + 0.154189i $$0.950724\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 5.61123 + 3.23965i 0.470884 + 0.271865i
$$143$$ −1.06826 + 0.616762i −0.0893327 + 0.0515763i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 11.0370 0.913432
$$147$$ 0 0
$$148$$ 0.914639i 0.0751829i
$$149$$ 2.53957 + 1.46622i 0.208049 + 0.120117i 0.600405 0.799696i $$-0.295006\pi$$
−0.392355 + 0.919814i $$0.628340\pi$$
$$150$$ 0 0
$$151$$ −3.56919 6.18201i −0.290456 0.503085i 0.683461 0.729987i $$-0.260474\pi$$
−0.973918 + 0.226902i $$0.927140\pi$$
$$152$$ −3.06818 1.77141i −0.248862 0.143681i
$$153$$ 0 0
$$154$$ −3.89225 1.66762i −0.313647 0.134380i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −7.15702 12.3963i −0.571192 0.989334i −0.996444 0.0842589i $$-0.973148\pi$$
0.425252 0.905075i $$-0.360186\pi$$
$$158$$ 1.45086 + 2.51296i 0.115424 + 0.199921i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −5.11638 6.83732i −0.403227 0.538857i
$$162$$ 0 0
$$163$$ 6.24313 + 3.60448i 0.489000 + 0.282324i 0.724160 0.689632i $$-0.242228\pi$$
−0.235159 + 0.971957i $$0.575561\pi$$
$$164$$ −2.44083 4.22765i −0.190597 0.330124i
$$165$$ 0 0
$$166$$ −10.3730 5.98884i −0.805099 0.464824i
$$167$$ 13.8952i 1.07524i −0.843187 0.537620i $$-0.819323\pi$$
0.843187 0.537620i $$-0.180677\pi$$
$$168$$ 0 0
$$169$$ −12.4060 −0.954306
$$170$$ 0 0
$$171$$ 0 0
$$172$$ −8.02773 + 4.63481i −0.612109 + 0.353401i
$$173$$ −2.05023 1.18370i −0.155876 0.0899951i 0.420033 0.907509i $$-0.362018\pi$$
−0.575909 + 0.817514i $$0.695352\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 1.60047i 0.120640i
$$177$$ 0 0
$$178$$ −4.40369 7.62742i −0.330071 0.571700i
$$179$$ 15.4837 8.93953i 1.15731 0.668172i 0.206650 0.978415i $$-0.433744\pi$$
0.950657 + 0.310243i $$0.100410\pi$$
$$180$$ 0 0
$$181$$ 16.6673i 1.23887i −0.785049 0.619434i $$-0.787362\pi$$
0.785049 0.619434i $$-0.212638\pi$$
$$182$$ 1.22171 + 1.63265i 0.0905594 + 0.121020i
$$183$$ 0 0
$$184$$ −1.61385 + 2.79527i −0.118975 + 0.206070i
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −2.81855 + 4.88187i −0.206113 + 0.356998i
$$188$$ 2.67270i 0.194926i
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −21.4359 12.3760i −1.55104 0.895496i −0.998057 0.0623063i $$-0.980154\pi$$
−0.552987 0.833190i $$-0.686512\pi$$
$$192$$ 0 0
$$193$$ 10.8917 6.28835i 0.784005 0.452645i −0.0538428 0.998549i $$-0.517147\pi$$
0.837848 + 0.545904i $$0.183814\pi$$
$$194$$ 2.65612 4.60054i 0.190698 0.330299i
$$195$$ 0 0
$$196$$ −1.97462 + 6.71572i −0.141044 + 0.479694i
$$197$$ −19.7360 −1.40613 −0.703066 0.711125i $$-0.748186\pi$$
−0.703066 + 0.711125i $$0.748186\pi$$
$$198$$ 0 0
$$199$$ −9.82275 + 5.67117i −0.696316 + 0.402018i −0.805974 0.591951i $$-0.798358\pi$$
0.109658 + 0.993969i $$0.465025\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 9.25326 0.651057
$$203$$ 1.70424 + 0.730173i 0.119614 + 0.0512481i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 7.91290 + 13.7055i 0.551318 + 0.954911i
$$207$$ 0 0
$$208$$ 0.385363 0.667468i 0.0267201 0.0462806i
$$209$$ −5.67019 −0.392215
$$210$$ 0 0
$$211$$ 16.0647 1.10594 0.552970 0.833201i $$-0.313494\pi$$
0.552970 + 0.833201i $$0.313494\pi$$
$$212$$ 4.64520 8.04572i 0.319034 0.552582i
$$213$$ 0 0
$$214$$ −6.20735 10.7514i −0.424326 0.734954i
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0.411830 + 3.44985i 0.0279569 + 0.234191i
$$218$$ 11.0350 0.747384
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 2.35092 1.35730i 0.158140 0.0913022i
$$222$$ 0 0
$$223$$ −2.00917 −0.134544 −0.0672720 0.997735i $$-0.521430\pi$$
−0.0672720 + 0.997735i $$0.521430\pi$$
$$224$$ 2.62710 0.313613i 0.175530 0.0209542i
$$225$$ 0 0
$$226$$ −7.51506 + 13.0165i −0.499894 + 0.865842i
$$227$$ 3.38249 1.95288i 0.224504 0.129617i −0.383530 0.923528i $$-0.625292\pi$$
0.608034 + 0.793911i $$0.291958\pi$$
$$228$$ 0 0
$$229$$ −11.5904 6.69174i −0.765918 0.442203i 0.0654987 0.997853i $$-0.479136\pi$$
−0.831416 + 0.555650i $$0.812470\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0.700774i 0.0460081i
$$233$$ −5.14808 + 8.91673i −0.337262 + 0.584154i −0.983917 0.178628i $$-0.942834\pi$$
0.646655 + 0.762783i $$0.276167\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −1.56198 + 2.70542i −0.101676 + 0.176108i
$$237$$ 0 0
$$238$$ 8.56565 + 3.66991i 0.555229 + 0.237885i
$$239$$ 17.5460i 1.13495i −0.823389 0.567477i $$-0.807920\pi$$
0.823389 0.567477i $$-0.192080\pi$$
$$240$$ 0 0
$$241$$ 8.66068 5.00024i 0.557883 0.322094i −0.194412 0.980920i $$-0.562280\pi$$
0.752295 + 0.658826i $$0.228947\pi$$
$$242$$ −4.21924 7.30795i −0.271223 0.469773i
$$243$$ 0 0
$$244$$ 10.8913i 0.697244i
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 2.36472 + 1.36527i 0.150464 + 0.0868702i
$$248$$ 1.13725 0.656589i 0.0722152 0.0416935i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 3.55412 0.224334 0.112167 0.993689i $$-0.464221\pi$$
0.112167 + 0.993689i $$0.464221\pi$$
$$252$$ 0 0
$$253$$ 5.16584i 0.324774i
$$254$$ 2.30801 + 1.33253i 0.144818 + 0.0836105i
$$255$$ 0 0
$$256$$ −0.500000 0.866025i −0.0312500 0.0541266i
$$257$$ −6.15756 3.55507i −0.384098 0.221759i 0.295502 0.955342i $$-0.404513\pi$$
−0.679600 + 0.733583i $$0.737847\pi$$
$$258$$ 0 0
$$259$$ −1.93751 + 1.44984i −0.120391 + 0.0900885i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 7.10987 + 12.3147i 0.439249 + 0.760802i
$$263$$ −14.2752 24.7253i −0.880245 1.52463i −0.851069 0.525054i $$-0.824045\pi$$
−0.0291760 0.999574i $$-0.509288\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 1.11108 + 9.30735i 0.0681245 + 0.570670i
$$267$$ 0 0
$$268$$ 5.90314 + 3.40818i 0.360592 + 0.208188i
$$269$$ 12.9628 + 22.4523i 0.790359 + 1.36894i 0.925745 + 0.378149i $$0.123439\pi$$
−0.135386 + 0.990793i $$0.543228\pi$$
$$270$$ 0 0
$$271$$ −24.1643 13.9513i −1.46788 0.847479i −0.468523 0.883451i $$-0.655214\pi$$
−0.999353 + 0.0359726i $$0.988547\pi$$
$$272$$ 3.52215i 0.213561i
$$273$$ 0 0
$$274$$ 0.130132 0.00786158
$$275$$ 0 0
$$276$$ 0 0
$$277$$ −8.98042 + 5.18485i −0.539581 + 0.311527i −0.744909 0.667166i $$-0.767507\pi$$
0.205328 + 0.978693i $$0.434174\pi$$
$$278$$ −3.14863 1.81786i −0.188842 0.109028i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 21.0412i 1.25521i −0.778530 0.627607i $$-0.784035\pi$$
0.778530 0.627607i $$-0.215965\pi$$
$$282$$ 0 0
$$283$$ −13.6859 23.7046i −0.813541 1.40909i −0.910371 0.413794i $$-0.864203\pi$$
0.0968293 0.995301i $$-0.469130\pi$$
$$284$$ −5.61123 + 3.23965i −0.332965 + 0.192238i
$$285$$ 0 0
$$286$$ 1.23352i 0.0729399i
$$287$$ −5.08646 + 11.8719i −0.300244 + 0.700777i
$$288$$ 0 0
$$289$$ −2.29724 + 3.97894i −0.135132 + 0.234055i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −5.51852 + 9.55835i −0.322947 + 0.559360i
$$293$$ 16.9059i 0.987654i 0.869560 + 0.493827i $$0.164402\pi$$
−0.869560 + 0.493827i $$0.835598\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0.792101 + 0.457320i 0.0460399 + 0.0265812i
$$297$$ 0 0
$$298$$ −2.53957 + 1.46622i −0.147113 + 0.0849358i
$$299$$ 1.24384 2.15439i 0.0719328 0.124591i
$$300$$ 0 0
$$301$$ 22.5432 + 9.65851i 1.29937 + 0.556707i
$$302$$ 7.13837 0.410767
$$303$$ 0 0
$$304$$ 3.06818 1.77141i 0.175972 0.101597i
$$305$$ 0 0
$$306$$ 0 0
$$307$$ 14.0139 0.799813 0.399906 0.916556i $$-0.369043\pi$$
0.399906 + 0.916556i $$0.369043\pi$$
$$308$$ 3.39032 2.53698i 0.193182 0.144558i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 6.72211 + 11.6430i 0.381176 + 0.660216i 0.991231 0.132143i $$-0.0421859\pi$$
−0.610055 + 0.792359i $$0.708853\pi$$
$$312$$ 0 0
$$313$$ −2.12904 + 3.68760i −0.120340 + 0.208436i −0.919902 0.392149i $$-0.871732\pi$$
0.799562 + 0.600584i $$0.205065\pi$$
$$314$$ 14.3140 0.807788
$$315$$ 0 0
$$316$$ −2.90172 −0.163234
$$317$$ −0.0987910 + 0.171111i −0.00554866 + 0.00961055i −0.868786 0.495187i $$-0.835100\pi$$
0.863238 + 0.504798i $$0.168433\pi$$
$$318$$ 0 0
$$319$$ −0.560785 0.971308i −0.0313979 0.0543828i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 8.47948 1.01225i 0.472543 0.0564105i
$$323$$ 12.4783 0.694314
$$324$$ 0 0
$$325$$ 0 0
$$326$$ −6.24313 + 3.60448i −0.345775 + 0.199633i
$$327$$ 0 0
$$328$$ 4.88167 0.269545
$$329$$ 5.66165 4.23662i 0.312137 0.233572i
$$330$$ 0 0
$$331$$ −2.29740 + 3.97922i −0.126277 + 0.218718i −0.922231 0.386639i $$-0.873636\pi$$
0.795955 + 0.605356i $$0.206969\pi$$
$$332$$ 10.3730 5.98884i 0.569291 0.328680i
$$333$$ 0 0
$$334$$ 12.0336 + 6.94758i 0.658447 + 0.380155i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 6.05076i 0.329606i −0.986327 0.164803i $$-0.947301\pi$$
0.986327 0.164803i $$-0.0526988\pi$$
$$338$$ 6.20299 10.7439i 0.337398 0.584391i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.05085 1.82013i 0.0569069 0.0985656i
$$342$$ 0 0
$$343$$ 17.3562 6.46250i 0.937144 0.348942i
$$344$$ 9.26963i 0.499785i
$$345$$ 0 0
$$346$$ 2.05023 1.18370i 0.110221 0.0636362i
$$347$$ −1.59102 2.75573i −0.0854104 0.147935i 0.820156 0.572140i $$-0.193887\pi$$
−0.905566 + 0.424205i $$0.860553\pi$$
$$348$$ 0 0
$$349$$ 29.0573i 1.55540i 0.628636 + 0.777700i $$0.283614\pi$$
−0.628636 + 0.777700i $$0.716386\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −1.38605 0.800236i −0.0738767 0.0426527i
$$353$$ 6.63942 3.83327i 0.353381 0.204025i −0.312792 0.949822i $$-0.601264\pi$$
0.666173 + 0.745797i $$0.267931\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 8.80739 0.466791
$$357$$ 0 0
$$358$$ 17.8791i 0.944938i
$$359$$ 19.6694 + 11.3561i 1.03811 + 0.599353i 0.919297 0.393564i $$-0.128758\pi$$
0.118812 + 0.992917i $$0.462091\pi$$
$$360$$ 0 0
$$361$$ −3.22420 5.58447i −0.169695 0.293920i
$$362$$ 14.4343 + 8.33363i 0.758649 + 0.438006i
$$363$$ 0 0
$$364$$ −2.02477 + 0.241710i −0.106127 + 0.0126690i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −9.37433 16.2368i −0.489336 0.847555i 0.510589 0.859825i $$-0.329427\pi$$
−0.999925 + 0.0122703i $$0.996094\pi$$
$$368$$ −1.61385 2.79527i −0.0841277 0.145713i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ −24.4068 + 2.91359i −1.26714 + 0.151266i
$$372$$ 0 0
$$373$$ 2.46050 + 1.42057i 0.127400 + 0.0735545i 0.562346 0.826902i $$-0.309899\pi$$
−0.434946 + 0.900457i $$0.643232\pi$$
$$374$$ −2.81855 4.88187i −0.145744 0.252435i
$$375$$ 0 0
$$376$$ −2.31462 1.33635i −0.119368 0.0689169i
$$377$$ 0.540105i 0.0278168i
$$378$$ 0 0
$$379$$ 27.2750 1.40102 0.700510 0.713642i $$-0.252956\pi$$
0.700510 + 0.713642i $$0.252956\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 21.4359 12.3760i 1.09675 0.633211i
$$383$$ −26.1843 15.1175i −1.33796 0.772469i −0.351451 0.936206i $$-0.614312\pi$$
−0.986504 + 0.163737i $$0.947645\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 12.5767i 0.640137i
$$387$$ 0 0
$$388$$ 2.65612 + 4.60054i 0.134844 + 0.233557i
$$389$$ −4.29588 + 2.48023i −0.217810 + 0.125752i −0.604936 0.796274i $$-0.706801\pi$$
0.387126 + 0.922027i $$0.373468\pi$$
$$390$$ 0 0
$$391$$ 11.3684i 0.574926i
$$392$$ −4.82867 5.06793i −0.243885 0.255969i
$$393$$ 0 0
$$394$$ 9.86800 17.0919i 0.497143 0.861077i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −7.30213 + 12.6477i −0.366483 + 0.634768i −0.989013 0.147828i $$-0.952772\pi$$
0.622530 + 0.782596i $$0.286105\pi$$
$$398$$ 11.3423i 0.568540i
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −17.5622 10.1395i −0.877014 0.506345i −0.00734158 0.999973i $$-0.502337\pi$$
−0.869673 + 0.493629i $$0.835670\pi$$
$$402$$ 0 0
$$403$$ −0.876505 + 0.506050i −0.0436618 + 0.0252082i
$$404$$ −4.62663 + 8.01356i −0.230183 + 0.398689i
$$405$$ 0 0
$$406$$ −1.48447 + 1.11083i −0.0736730 + 0.0551296i
$$407$$ 1.46385 0.0725606
$$408$$ 0 0
$$409$$ −4.26877 + 2.46458i −0.211077 + 0.121865i −0.601812 0.798638i $$-0.705554\pi$$
0.390735 + 0.920503i $$0.372221\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −15.8258 −0.779681
$$413$$ 8.20693 0.979714i 0.403837 0.0482086i
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0.385363 + 0.667468i 0.0188940 + 0.0327253i
$$417$$ 0 0
$$418$$ 2.83510 4.91053i 0.138669 0.240182i
$$419$$ 24.0686 1.17583 0.587913 0.808924i $$-0.299950\pi$$
0.587913 + 0.808924i $$0.299950\pi$$
$$420$$ 0 0
$$421$$ 16.0657 0.782995 0.391498 0.920179i $$-0.371957\pi$$
0.391498 + 0.920179i $$0.371957\pi$$
$$422$$ −8.03236 + 13.9125i −0.391009 + 0.677248i
$$423$$ 0 0
$$424$$ 4.64520 + 8.04572i 0.225591 + 0.390735i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 23.0713 17.2643i 1.11650 0.835478i
$$428$$ 12.4147 0.600087
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −0.373691 + 0.215751i −0.0180001 + 0.0103923i −0.508973 0.860782i $$-0.669975\pi$$
0.490973 + 0.871175i $$0.336641\pi$$
$$432$$ 0 0
$$433$$ −30.5287 −1.46711 −0.733557 0.679628i $$-0.762141\pi$$
−0.733557 + 0.679628i $$0.762141\pi$$
$$434$$ −3.19357 1.36827i −0.153296 0.0656790i
$$435$$ 0 0
$$436$$ −5.51750 + 9.55659i −0.264240 + 0.457677i
$$437$$ 9.90315 5.71759i 0.473732 0.273509i
$$438$$ 0 0
$$439$$ 32.9059 + 18.9982i 1.57051 + 0.906735i 0.996106 + 0.0881648i $$0.0281002\pi$$
0.574406 + 0.818571i $$0.305233\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 2.71461i 0.129121i
$$443$$ −11.6503 + 20.1789i −0.553522 + 0.958728i 0.444495 + 0.895781i $$0.353383\pi$$
−0.998017 + 0.0629464i $$0.979950\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 1.00459 1.73999i 0.0475685 0.0823911i
$$447$$ 0 0
$$448$$ −1.04195 + 2.43194i −0.0492276 + 0.114898i
$$449$$ 21.9119i 1.03409i 0.855960 + 0.517043i $$0.172967\pi$$
−0.855960 + 0.517043i $$0.827033\pi$$
$$450$$ 0 0
$$451$$ 6.76623 3.90648i 0.318609 0.183949i
$$452$$ −7.51506 13.0165i −0.353479 0.612243i
$$453$$ 0 0
$$454$$ 3.90576i 0.183306i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 34.0904 + 19.6821i 1.59468 + 0.920691i 0.992488 + 0.122341i $$0.0390403\pi$$
0.602195 + 0.798349i $$0.294293\pi$$
$$458$$ 11.5904 6.69174i 0.541586 0.312685i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 2.35282 0.109582 0.0547909 0.998498i $$-0.482551\pi$$
0.0547909 + 0.998498i $$0.482551\pi$$
$$462$$ 0 0
$$463$$ 2.24550i 0.104357i −0.998638 0.0521787i $$-0.983383\pi$$
0.998638 0.0521787i $$-0.0166165\pi$$
$$464$$ 0.606888 + 0.350387i 0.0281741 + 0.0162663i
$$465$$ 0 0
$$466$$ −5.14808 8.91673i −0.238480 0.413059i
$$467$$ −27.8740 16.0931i −1.28986 0.744699i −0.311228 0.950335i $$-0.600740\pi$$
−0.978628 + 0.205636i $$0.934074\pi$$
$$468$$ 0 0
$$469$$ −2.13770 17.9072i −0.0987099 0.826880i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ −1.56198 2.70542i −0.0718958 0.124527i
$$473$$ −7.41789 12.8482i −0.341075 0.590759i
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −7.46106 + 5.58312i −0.341977 + 0.255902i
$$477$$ 0 0
$$478$$ 15.1952 + 8.77298i 0.695014 + 0.401267i
$$479$$ 3.30556 + 5.72539i 0.151035 + 0.261600i 0.931608 0.363464i $$-0.118406\pi$$
−0.780573 + 0.625064i $$0.785073\pi$$
$$480$$ 0 0
$$481$$ −0.610493 0.352468i −0.0278361 0.0160712i
$$482$$ 10.0005i 0.455510i
$$483$$ 0 0
$$484$$ 8.43849 0.383568
$$485$$ 0 0
$$486$$ 0 0
$$487$$ −4.99120 + 2.88167i −0.226173 + 0.130581i −0.608805 0.793320i $$-0.708351\pi$$
0.382632 + 0.923901i $$0.375018\pi$$
$$488$$ −9.43214 5.44565i −0.426973 0.246513i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 2.90529i 0.131114i 0.997849 + 0.0655570i $$0.0208824\pi$$
−0.997849 + 0.0655570i $$0.979118\pi$$
$$492$$ 0 0
$$493$$ 1.23411 + 2.13755i 0.0555817 + 0.0962704i
$$494$$ −2.36472 + 1.36527i −0.106394 + 0.0614265i
$$495$$ 0 0
$$496$$ 1.31318i 0.0589634i
$$497$$ 15.7573 + 6.75111i 0.706810 + 0.302829i
$$498$$ 0 0
$$499$$ 1.14104 1.97634i 0.0510800 0.0884732i −0.839355 0.543584i $$-0.817067\pi$$
0.890435 + 0.455111i $$0.150400\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −1.77706 + 3.07796i −0.0793141 + 0.137376i
$$503$$ 1.32664i 0.0591520i 0.999563 + 0.0295760i $$0.00941571\pi$$
−0.999563 + 0.0295760i $$0.990584\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ −4.47375 2.58292i −0.198882 0.114825i
$$507$$ 0 0
$$508$$ −2.30801 + 1.33253i −0.102402 + 0.0591215i
$$509$$ −21.5053 + 37.2483i −0.953207 + 1.65100i −0.214788 + 0.976661i $$0.568906\pi$$
−0.738419 + 0.674342i $$0.764427\pi$$
$$510$$ 0 0
$$511$$ 28.9954 3.46136i 1.28268 0.153122i
$$512$$ 1.00000 0.0441942
$$513$$ 0 0
$$514$$ 6.15756 3.55507i 0.271598 0.156807i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −4.27758 −0.188128
$$518$$ −0.286843 2.40285i −0.0126032 0.105575i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 19.8838 + 34.4397i 0.871124 + 1.50883i 0.860835 + 0.508884i $$0.169942\pi$$
0.0102890 + 0.999947i $$0.496725\pi$$
$$522$$ 0 0
$$523$$ −19.8804 + 34.4338i −0.869307 + 1.50568i −0.00660128 + 0.999978i $$0.502101\pi$$
−0.862706 + 0.505706i $$0.831232\pi$$
$$524$$ −14.2197 −0.621192
$$525$$ 0 0
$$526$$ 28.5503 1.24485
$$527$$ −2.31260 + 4.00555i −0.100739 + 0.174484i
$$528$$ 0 0
$$529$$ 6.29098 + 10.8963i 0.273521 + 0.473752i
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −8.61594 3.69145i −0.373548 0.160045i
$$533$$ −3.76242 −0.162969
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −5.90314 + 3.40818i −0.254977 + 0.147211i
$$537$$ 0 0
$$538$$ −25.9257 −1.11774
$$539$$ −10.7483 3.16033i −0.462963 0.136125i
$$540$$ 0 0
$$541$$ −10.1006 + 17.4947i −0.434258 + 0.752157i −0.997235 0.0743161i $$-0.976323\pi$$
0.562977 + 0.826473i $$0.309656\pi$$
$$542$$ 24.1643 13.9513i 1.03795 0.599258i
$$543$$ 0 0
$$544$$ 3.05027 + 1.76107i 0.130779 + 0.0755054i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 34.5631i 1.47781i −0.673810 0.738905i $$-0.735343\pi$$
0.673810 0.738905i $$-0.264657\pi$$
$$548$$ −0.0650662 + 0.112698i −0.00277949 + 0.00481422i
$$549$$ 0 0
$$550$$ 0 0
$$551$$ −1.24136 + 2.15010i −0.0528837 + 0.0915973i
$$552$$ 0 0
$$553$$ 4.59965 + 6.14679i 0.195597 + 0.261388i
$$554$$ 10.3697i 0.440566i
$$555$$ 0 0
$$556$$ 3.14863 1.81786i 0.133532 0.0770945i
$$557$$ 16.2396 + 28.1278i 0.688094 + 1.19181i 0.972454 + 0.233096i $$0.0748856\pi$$
−0.284360 + 0.958718i $$0.591781\pi$$
$$558$$ 0 0
$$559$$ 7.14434i 0.302173i
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 18.2222 + 10.5206i 0.768658 + 0.443785i
$$563$$ −12.4603 + 7.19395i −0.525139 + 0.303189i −0.739035 0.673668i $$-0.764718\pi$$
0.213896 + 0.976856i $$0.431385\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 27.3718 1.15052
$$567$$ 0 0
$$568$$ 6.47930i 0.271865i
$$569$$ −6.84504 3.95199i −0.286959 0.165676i 0.349611 0.936895i $$-0.386314\pi$$
−0.636570 + 0.771219i $$0.719647\pi$$
$$570$$ 0 0
$$571$$ 18.3198 + 31.7309i 0.766661 + 1.32789i 0.939364 + 0.342921i $$0.111416\pi$$
−0.172704 + 0.984974i $$0.555250\pi$$
$$572$$ 1.06826 + 0.616762i 0.0446664 + 0.0257881i
$$573$$ 0 0
$$574$$ −7.73815 10.3410i −0.322984 0.431624i
$$575$$ 0 0
$$576$$ 0 0
$$577$$ −11.6961 20.2583i −0.486916 0.843363i 0.512971 0.858406i $$-0.328545\pi$$
−0.999887 + 0.0150431i $$0.995211\pi$$
$$578$$ −2.29724 3.97894i −0.0955527 0.165502i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −29.1290 12.4802i −1.20848 0.517765i
$$582$$ 0 0
$$583$$ 12.8770 + 7.43451i 0.533309 + 0.307906i
$$584$$ −5.51852 9.55835i −0.228358 0.395527i
$$585$$ 0 0
$$586$$ −14.6409 8.45295i −0.604812 0.349188i
$$587$$ 23.7776i 0.981407i −0.871327 0.490704i $$-0.836740\pi$$
0.871327 0.490704i $$-0.163260\pi$$
$$588$$ 0 0
$$589$$ −4.65236 −0.191697
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −0.792101 + 0.457320i −0.0325551 + 0.0187957i
$$593$$ −33.6979 19.4555i −1.38381 0.798942i −0.391200 0.920306i $$-0.627940\pi$$
−0.992608 + 0.121364i $$0.961273\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 2.93244i 0.120117i
$$597$$ 0 0
$$598$$ 1.24384 + 2.15439i 0.0508642 + 0.0880994i
$$599$$ −3.09380 + 1.78621i −0.126409 + 0.0729824i −0.561871 0.827225i $$-0.689918\pi$$
0.435462 + 0.900207i $$0.356585\pi$$
$$600$$ 0 0
$$601$$ 21.3183i 0.869591i 0.900529 + 0.434795i $$0.143179\pi$$
−0.900529 + 0.434795i $$0.856821\pi$$
$$602$$ −19.6361 + 14.6937i −0.800308 + 0.598871i
$$603$$ 0 0
$$604$$ −3.56919 + 6.18201i −0.145228 + 0.251543i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −0.285402 + 0.494331i −0.0115841 + 0.0200643i −0.871759 0.489934i $$-0.837021\pi$$
0.860175 + 0.509999i $$0.170354\pi$$
$$608$$ 3.54282i 0.143681i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 1.78394 + 1.02996i 0.0721705 + 0.0416676i
$$612$$ 0 0
$$613$$ −29.5954 + 17.0869i −1.19535 + 0.690134i −0.959514 0.281659i $$-0.909115\pi$$
−0.235833 + 0.971794i $$0.575782\pi$$
$$614$$ −7.00693 + 12.1364i −0.282777 + 0.489783i
$$615$$ 0 0
$$616$$ 0.501930 + 4.20460i 0.0202233 + 0.169408i
$$617$$ 20.1713 0.812066 0.406033 0.913858i $$-0.366912\pi$$
0.406033 + 0.913858i $$0.366912\pi$$
$$618$$ 0 0
$$619$$ −13.9621 + 8.06104i −0.561186 + 0.324001i −0.753621 0.657309i $$-0.771695\pi$$
0.192436 + 0.981310i $$0.438361\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −13.4442 −0.539064
$$623$$ −13.9610 18.6569i −0.559336 0.747474i
$$624$$ 0 0
$$625$$ 0 0
$$626$$ −2.12904 3.68760i −0.0850935 0.147386i
$$627$$ 0 0
$$628$$ −7.15702 + 12.3963i −0.285596 + 0.494667i
$$629$$ −3.22149 −0.128449
$$630$$ 0 0
$$631$$ 3.10655 0.123670 0.0618350 0.998086i $$-0.480305\pi$$
0.0618350 + 0.998086i $$0.480305\pi$$
$$632$$ 1.45086 2.51296i 0.0577121 0.0999603i
$$633$$ 0 0
$$634$$ −0.0987910 0.171111i −0.00392349 0.00679569i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 3.72158 + 3.90598i 0.147454 + 0.154761i
$$638$$ 1.12157 0.0444034
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 18.9248 10.9262i 0.747483 0.431559i −0.0773008 0.997008i $$-0.524630\pi$$
0.824784 + 0.565448i $$0.191297\pi$$
$$642$$ 0 0
$$643$$ −25.4873 −1.00512 −0.502560 0.864542i $$-0.667609\pi$$
−0.502560 + 0.864542i $$0.667609\pi$$
$$644$$ −3.36311 + 7.84957i −0.132525 + 0.309317i
$$645$$ 0 0
$$646$$ −6.23917 + 10.8066i −0.245477 + 0.425179i
$$647$$ −41.5745 + 24.0030i −1.63446 + 0.943657i −0.651768 + 0.758418i $$0.725973\pi$$
−0.982694 + 0.185239i $$0.940694\pi$$
$$648$$ 0 0
$$649$$ −4.32995 2.49990i −0.169966 0.0981296i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 7.20895i 0.282324i
$$653$$ −23.0213 + 39.8741i −0.900894 + 1.56039i −0.0745575 + 0.997217i $$0.523754\pi$$
−0.826336 + 0.563177i $$0.809579\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −2.44083 + 4.22765i −0.0952985 + 0.165062i
$$657$$ 0 0
$$658$$ 0.838194 + 7.02144i 0.0326762 + 0.273724i
$$659$$ 14.8751i 0.579453i −0.957109 0.289727i $$-0.906436\pi$$
0.957109 0.289727i $$-0.0935644\pi$$
$$660$$ 0 0
$$661$$ 36.7957 21.2440i 1.43119 0.826296i 0.433974 0.900925i $$-0.357111\pi$$
0.997211 + 0.0746297i $$0.0237775\pi$$
$$662$$ −2.29740 3.97922i −0.0892911 0.154657i
$$663$$ 0 0
$$664$$ 11.9777i 0.464824i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 1.95885 + 1.13094i 0.0758471 + 0.0437903i
$$668$$ −12.0336 + 6.94758i −0.465593 + 0.268810i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −17.4312 −0.672925
$$672$$ 0 0
$$673$$ 50.6101i 1.95088i 0.220270 + 0.975439i $$0.429306\pi$$
−0.220270 + 0.975439i $$0.570694\pi$$
$$674$$ 5.24011 + 3.02538i 0.201841 + 0.116533i
$$675$$ 0 0
$$676$$ 6.20299 + 10.7439i 0.238577 + 0.413227i
$$677$$ 29.9259 + 17.2777i 1.15015 + 0.664037i 0.948923 0.315508i $$-0.102175\pi$$
0.201223 + 0.979545i $$0.435508\pi$$
$$678$$ 0 0
$$679$$ 5.53510 12.9191i 0.212418 0.495788i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 1.05085 + 1.82013i 0.0402392 + 0.0696964i
$$683$$ −8.57731 14.8563i −0.328202 0.568462i 0.653953 0.756535i $$-0.273109\pi$$
−0.982155 + 0.188073i $$0.939776\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −3.08138 + 18.2621i −0.117648 + 0.697251i
$$687$$ 0 0
$$688$$ 8.02773 + 4.63481i 0.306055 + 0.176701i
$$689$$ −3.58017 6.20104i −0.136394 0.236241i
$$690$$ 0 0
$$691$$ −30.8635 17.8190i −1.17410 0.677869i −0.219460 0.975622i $$-0.570429\pi$$
−0.954643 + 0.297753i $$0.903763\pi$$
$$692$$ 2.36740i 0.0899951i
$$693$$ 0 0
$$694$$ 3.18204 0.120788
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −14.8904 + 8.59697i −0.564014 + 0.325633i
$$698$$ −25.1643 14.5286i −0.952484 0.549917i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 23.0808i 0.871751i 0.900007 + 0.435876i $$0.143561\pi$$
−0.900007 + 0.435876i $$0.856439\pi$$
$$702$$ 0 0
$$703$$ −1.62020 2.80627i −0.0611071 0.105841i
$$704$$ 1.38605 0.800236i 0.0522387 0.0301600i
$$705$$ 0 0
$$706$$ 7.66655i 0.288534i
$$707$$ 24.3092 2.90195i 0.914243 0.109139i
$$708$$ 0 0
$$709$$ 4.08362 7.07303i 0.153363 0.265633i −0.779098 0.626902i $$-0.784323\pi$$
0.932462 + 0.361268i $$0.117656\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −4.40369 + 7.62742i −0.165035 + 0.285850i
$$713$$ 4.23854i 0.158735i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −15.4837 8.93953i −0.578654 0.334086i
$$717$$ 0 0
$$718$$ −19.6694 + 11.3561i −0.734054 + 0.423806i
$$719$$ −0.377499 + 0.653847i −0.0140783 + 0.0243844i −0.872979 0.487758i $$-0.837815\pi$$
0.858900 + 0.512143i $$0.171148\pi$$
$$720$$ 0 0
$$721$$ 25.0862 + 33.5242i 0.934260 + 1.24851i
$$722$$ 6.44839 0.239984
$$723$$ 0 0
$$724$$ −14.4343 + 8.33363i −0.536446 + 0.309717i
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 4.27807 0.158665 0.0793325 0.996848i $$-0.474721\pi$$
0.0793325 + 0.996848i $$0.474721\pi$$
$$728$$ 0.803059 1.87436i 0.0297634 0.0694684i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 16.3245 + 28.2749i 0.603783 + 1.04578i
$$732$$ 0 0
$$733$$ −16.7810 + 29.0656i −0.619822 + 1.07356i 0.369696 + 0.929153i $$0.379462\pi$$
−0.989518 + 0.144410i $$0.953871\pi$$
$$734$$ 18.7487 0.692026
$$735$$ 0 0
$$736$$ 3.22770 0.118975
$$737$$ −5.45470 + 9.44781i −0.200926 + 0.348015i
$$738$$ 0 0
$$739$$ 17.3726 + 30.0902i 0.639060 + 1.10688i 0.985639 + 0.168864i $$0.0540099\pi$$
−0.346579 + 0.938021i $$0.612657\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 9.68015 22.5937i 0.355369 0.829441i
$$743$$ −14.3040 −0.524762 −0.262381 0.964964i $$-0.584508\pi$$
−0.262381 + 0.964964i $$0.584508\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −2.46050 + 1.42057i −0.0900854 + 0.0520109i
$$747$$ 0 0
$$748$$ 5.63710 0.206113
$$749$$ −19.6791 26.2984i −0.719060 0.960923i
$$750$$ 0 0
$$751$$ −21.3172 + 36.9224i −0.777874 + 1.34732i 0.155290 + 0.987869i $$0.450369\pi$$
−0.933165 + 0.359449i $$0.882965\pi$$
$$752$$ 2.31462 1.33635i 0.0844056 0.0487316i
$$753$$ 0 0
$$754$$ −0.467744 0.270052i −0.0170342 0.00983473i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 2.92253i 0.106221i −0.998589 0.0531107i $$-0.983086\pi$$
0.998589 0.0531107i $$-0.0169136\pi$$
$$758$$ −13.6375 + 23.6208i −0.495336 + 0.857946i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 15.2447 26.4046i 0.552621 0.957167i −0.445464 0.895300i $$-0.646961\pi$$
0.998084 0.0618669i $$-0.0197054\pi$$
$$762$$ 0 0
$$763$$ 28.9900 3.46072i 1.04951 0.125287i
$$764$$ 24.7520i 0.895496i
$$765$$ 0 0
$$766$$ 26.1843 15.1175i 0.946077 0.546218i
$$767$$ 1.20386 + 2.08514i 0.0434687 + 0.0752900i
$$768$$ 0 0
$$769$$ 42.7989i 1.54337i −0.636005 0.771685i $$-0.719414\pi$$
0.636005 0.771685i $$-0.280586\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −10.8917 6.28835i −0.392002 0.226323i
$$773$$ 34.9867 20.1996i 1.25838 0.726529i 0.285624 0.958342i $$-0.407799\pi$$
0.972760 + 0.231813i $$0.0744657\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ −5.31224 −0.190698
$$777$$ 0 0
$$778$$ 4.96045i 0.177841i
$$779$$ −14.9778 8.64744i −0.536636 0.309827i
$$780$$ 0 0
$$781$$ −5.18497 8.98062i −0.185533 0.321352i
$$782$$ 9.84535 + 5.68421i 0.352069 + 0.203267i
$$783$$ 0 0
$$784$$ 6.80329 1.64779i 0.242975 0.0588495i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ −15.8780 27.5015i −0.565990 0.