# Properties

 Label 1134.2.h.s.541.1 Level $1134$ Weight $2$ Character 1134.541 Analytic conductor $9.055$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.h (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.05503558921$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{2}, \sqrt{-3})$$ Defining polynomial: $$x^{4} + 2 x^{2} + 4$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$3$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 541.1 Root $$0.707107 + 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 1134.541 Dual form 1134.2.h.s.109.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 2.44949i) q^{7} -1.00000 q^{8} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 2.44949i) q^{7} -1.00000 q^{8} -4.24264 q^{11} +(-3.12132 - 5.40629i) q^{13} +(2.62132 - 0.358719i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.12132 + 5.40629i) q^{19} +(-2.12132 - 3.67423i) q^{22} -7.24264 q^{23} -5.00000 q^{25} +(3.12132 - 5.40629i) q^{26} +(1.62132 + 2.09077i) q^{28} +(-2.12132 + 3.67423i) q^{29} +(-0.378680 + 0.655892i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{37} -6.24264 q^{38} +(-2.74264 - 4.75039i) q^{41} +(3.24264 - 5.61642i) q^{43} +(2.12132 - 3.67423i) q^{44} +(-3.62132 - 6.27231i) q^{46} +(6.62132 + 11.4685i) q^{47} +(-5.00000 - 4.89898i) q^{49} +(-2.50000 - 4.33013i) q^{50} +6.24264 q^{52} +(2.12132 + 3.67423i) q^{53} +(-1.00000 + 2.44949i) q^{56} -4.24264 q^{58} +(-3.12132 - 5.40629i) q^{61} -0.757359 q^{62} +1.00000 q^{64} +(4.12132 - 7.13834i) q^{67} +7.24264 q^{71} +(3.50000 + 6.06218i) q^{73} +4.00000 q^{74} +(-3.12132 - 5.40629i) q^{76} +(-4.24264 + 10.3923i) q^{77} +(-4.62132 - 8.00436i) q^{79} +(2.74264 - 4.75039i) q^{82} +(3.87868 - 6.71807i) q^{83} +6.48528 q^{86} +4.24264 q^{88} +(-2.74264 + 4.75039i) q^{89} +(-16.3640 + 2.23936i) q^{91} +(3.62132 - 6.27231i) q^{92} +(-6.62132 + 11.4685i) q^{94} +(6.24264 - 10.8126i) q^{97} +(1.74264 - 6.77962i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{2} - 2q^{4} + 4q^{7} - 4q^{8} + O(q^{10})$$ $$4q + 2q^{2} - 2q^{4} + 4q^{7} - 4q^{8} - 4q^{13} + 2q^{14} - 2q^{16} - 4q^{19} - 12q^{23} - 20q^{25} + 4q^{26} - 2q^{28} - 10q^{31} + 2q^{32} + 8q^{37} - 8q^{38} + 6q^{41} - 4q^{43} - 6q^{46} + 18q^{47} - 20q^{49} - 10q^{50} + 8q^{52} - 4q^{56} - 4q^{61} - 20q^{62} + 4q^{64} + 8q^{67} + 12q^{71} + 14q^{73} + 16q^{74} - 4q^{76} - 10q^{79} - 6q^{82} + 24q^{83} - 8q^{86} + 6q^{89} - 40q^{91} + 6q^{92} - 18q^{94} + 8q^{97} - 10q^{98} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$$.

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$

## 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$6$$ 0 0
$$7$$ 1.00000 2.44949i 0.377964 0.925820i
$$8$$ −1.00000 −0.353553
$$9$$ 0 0
$$10$$ 0 0
$$11$$ −4.24264 −1.27920 −0.639602 0.768706i $$-0.720901\pi$$
−0.639602 + 0.768706i $$0.720901\pi$$
$$12$$ 0 0
$$13$$ −3.12132 5.40629i −0.865699 1.49943i −0.866352 0.499434i $$-0.833541\pi$$
0.000653431 1.00000i $$-0.499792\pi$$
$$14$$ 2.62132 0.358719i 0.700577 0.0958718i
$$15$$ 0 0
$$16$$ −0.500000 0.866025i −0.125000 0.216506i
$$17$$ 0 0 0.866025 0.500000i $$-0.166667\pi$$
−0.866025 + 0.500000i $$0.833333\pi$$
$$18$$ 0 0
$$19$$ −3.12132 + 5.40629i −0.716080 + 1.24029i 0.246462 + 0.969153i $$0.420732\pi$$
−0.962542 + 0.271134i $$0.912601\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −2.12132 3.67423i −0.452267 0.783349i
$$23$$ −7.24264 −1.51019 −0.755097 0.655613i $$-0.772410\pi$$
−0.755097 + 0.655613i $$0.772410\pi$$
$$24$$ 0 0
$$25$$ −5.00000 −1.00000
$$26$$ 3.12132 5.40629i 0.612141 1.06026i
$$27$$ 0 0
$$28$$ 1.62132 + 2.09077i 0.306401 + 0.395118i
$$29$$ −2.12132 + 3.67423i −0.393919 + 0.682288i −0.992963 0.118428i $$-0.962214\pi$$
0.599043 + 0.800717i $$0.295548\pi$$
$$30$$ 0 0
$$31$$ −0.378680 + 0.655892i −0.0680129 + 0.117802i −0.898027 0.439941i $$-0.854999\pi$$
0.830014 + 0.557743i $$0.188333\pi$$
$$32$$ 0.500000 0.866025i 0.0883883 0.153093i
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i $$-0.726690\pi$$
0.982274 + 0.187453i $$0.0600231\pi$$
$$38$$ −6.24264 −1.01269
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −2.74264 4.75039i −0.428329 0.741887i 0.568396 0.822755i $$-0.307564\pi$$
−0.996725 + 0.0808682i $$0.974231\pi$$
$$42$$ 0 0
$$43$$ 3.24264 5.61642i 0.494498 0.856496i −0.505482 0.862837i $$-0.668685\pi$$
0.999980 + 0.00634147i $$0.00201857\pi$$
$$44$$ 2.12132 3.67423i 0.319801 0.553912i
$$45$$ 0 0
$$46$$ −3.62132 6.27231i −0.533935 0.924802i
$$47$$ 6.62132 + 11.4685i 0.965819 + 1.67285i 0.707399 + 0.706815i $$0.249869\pi$$
0.258420 + 0.966033i $$0.416798\pi$$
$$48$$ 0 0
$$49$$ −5.00000 4.89898i −0.714286 0.699854i
$$50$$ −2.50000 4.33013i −0.353553 0.612372i
$$51$$ 0 0
$$52$$ 6.24264 0.865699
$$53$$ 2.12132 + 3.67423i 0.291386 + 0.504695i 0.974138 0.225955i $$-0.0725503\pi$$
−0.682752 + 0.730650i $$0.739217\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ −1.00000 + 2.44949i −0.133631 + 0.327327i
$$57$$ 0 0
$$58$$ −4.24264 −0.557086
$$59$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$60$$ 0 0
$$61$$ −3.12132 5.40629i −0.399644 0.692204i 0.594038 0.804437i $$-0.297533\pi$$
−0.993682 + 0.112233i $$0.964200\pi$$
$$62$$ −0.757359 −0.0961847
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 4.12132 7.13834i 0.503499 0.872087i −0.496492 0.868041i $$-0.665379\pi$$
0.999992 0.00404550i $$-0.00128773\pi$$
$$68$$ 0 0
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 7.24264 0.859543 0.429772 0.902938i $$-0.358594\pi$$
0.429772 + 0.902938i $$0.358594\pi$$
$$72$$ 0 0
$$73$$ 3.50000 + 6.06218i 0.409644 + 0.709524i 0.994850 0.101361i $$-0.0323196\pi$$
−0.585206 + 0.810885i $$0.698986\pi$$
$$74$$ 4.00000 0.464991
$$75$$ 0 0
$$76$$ −3.12132 5.40629i −0.358040 0.620143i
$$77$$ −4.24264 + 10.3923i −0.483494 + 1.18431i
$$78$$ 0 0
$$79$$ −4.62132 8.00436i −0.519939 0.900561i −0.999731 0.0231789i $$-0.992621\pi$$
0.479792 0.877382i $$-0.340712\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 2.74264 4.75039i 0.302874 0.524593i
$$83$$ 3.87868 6.71807i 0.425740 0.737404i −0.570749 0.821125i $$-0.693347\pi$$
0.996489 + 0.0837207i $$0.0266803\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 6.48528 0.699326
$$87$$ 0 0
$$88$$ 4.24264 0.452267
$$89$$ −2.74264 + 4.75039i −0.290719 + 0.503541i −0.973980 0.226634i $$-0.927228\pi$$
0.683261 + 0.730175i $$0.260561\pi$$
$$90$$ 0 0
$$91$$ −16.3640 + 2.23936i −1.71541 + 0.234748i
$$92$$ 3.62132 6.27231i 0.377549 0.653934i
$$93$$ 0 0
$$94$$ −6.62132 + 11.4685i −0.682937 + 1.18288i
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 6.24264 10.8126i 0.633844 1.09785i −0.352915 0.935656i $$-0.614809\pi$$
0.986759 0.162195i $$-0.0518573\pi$$
$$98$$ 1.74264 6.77962i 0.176033 0.684845i
$$99$$ 0 0
$$100$$ 2.50000 4.33013i 0.250000 0.433013i
$$101$$ −7.75736 −0.771886 −0.385943 0.922523i $$-0.626124\pi$$
−0.385943 + 0.922523i $$0.626124\pi$$
$$102$$ 0 0
$$103$$ 0.757359 0.0746248 0.0373124 0.999304i $$-0.488120\pi$$
0.0373124 + 0.999304i $$0.488120\pi$$
$$104$$ 3.12132 + 5.40629i 0.306071 + 0.530130i
$$105$$ 0 0
$$106$$ −2.12132 + 3.67423i −0.206041 + 0.356873i
$$107$$ −1.24264 + 2.15232i −0.120131 + 0.208072i −0.919819 0.392343i $$-0.871665\pi$$
0.799688 + 0.600415i $$0.204998\pi$$
$$108$$ 0 0
$$109$$ 1.12132 + 1.94218i 0.107403 + 0.186027i 0.914717 0.404094i $$-0.132413\pi$$
−0.807314 + 0.590122i $$0.799080\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −2.62132 + 0.358719i −0.247691 + 0.0338958i
$$113$$ −10.2426 17.7408i −0.963547 1.66891i −0.713470 0.700686i $$-0.752878\pi$$
−0.250076 0.968226i $$-0.580456\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −2.12132 3.67423i −0.196960 0.341144i
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 7.00000 0.636364
$$122$$ 3.12132 5.40629i 0.282591 0.489462i
$$123$$ 0 0
$$124$$ −0.378680 0.655892i −0.0340064 0.0589009i
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 6.75736 0.599619 0.299809 0.953999i $$-0.403077\pi$$
0.299809 + 0.953999i $$0.403077\pi$$
$$128$$ 0.500000 + 0.866025i 0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 7.75736 0.677764 0.338882 0.940829i $$-0.389951\pi$$
0.338882 + 0.940829i $$0.389951\pi$$
$$132$$ 0 0
$$133$$ 10.1213 + 13.0519i 0.877630 + 1.13175i
$$134$$ 8.24264 0.712056
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 19.9706 1.70620 0.853100 0.521747i $$-0.174720\pi$$
0.853100 + 0.521747i $$0.174720\pi$$
$$138$$ 0 0
$$139$$ 2.36396 + 4.09450i 0.200509 + 0.347291i 0.948692 0.316200i $$-0.102407\pi$$
−0.748184 + 0.663491i $$0.769074\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 3.62132 + 6.27231i 0.303894 + 0.526361i
$$143$$ 13.2426 + 22.9369i 1.10741 + 1.91808i
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −3.50000 + 6.06218i −0.289662 + 0.501709i
$$147$$ 0 0
$$148$$ 2.00000 + 3.46410i 0.164399 + 0.284747i
$$149$$ −16.2426 −1.33065 −0.665324 0.746554i $$-0.731707\pi$$
−0.665324 + 0.746554i $$0.731707\pi$$
$$150$$ 0 0
$$151$$ −2.75736 −0.224391 −0.112195 0.993686i $$-0.535788\pi$$
−0.112195 + 0.993686i $$0.535788\pi$$
$$152$$ 3.12132 5.40629i 0.253173 0.438508i
$$153$$ 0 0
$$154$$ −11.1213 + 1.52192i −0.896182 + 0.122640i
$$155$$ 0 0
$$156$$ 0 0
$$157$$ −7.00000 + 12.1244i −0.558661 + 0.967629i 0.438948 + 0.898513i $$0.355351\pi$$
−0.997609 + 0.0691164i $$0.977982\pi$$
$$158$$ 4.62132 8.00436i 0.367653 0.636793i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −7.24264 + 17.7408i −0.570800 + 1.39817i
$$162$$ 0 0
$$163$$ 5.87868 10.1822i 0.460454 0.797529i −0.538530 0.842606i $$-0.681020\pi$$
0.998984 + 0.0450772i $$0.0143534\pi$$
$$164$$ 5.48528 0.428329
$$165$$ 0 0
$$166$$ 7.75736 0.602088
$$167$$ 12.1066 + 20.9692i 0.936837 + 1.62265i 0.771325 + 0.636441i $$0.219594\pi$$
0.165512 + 0.986208i $$0.447072\pi$$
$$168$$ 0 0
$$169$$ −12.9853 + 22.4912i −0.998868 + 1.73009i
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 3.24264 + 5.61642i 0.247249 + 0.428248i
$$173$$ −5.48528 9.50079i −0.417038 0.722331i 0.578602 0.815610i $$-0.303599\pi$$
−0.995640 + 0.0932788i $$0.970265\pi$$
$$174$$ 0 0
$$175$$ −5.00000 + 12.2474i −0.377964 + 0.925820i
$$176$$ 2.12132 + 3.67423i 0.159901 + 0.276956i
$$177$$ 0 0
$$178$$ −5.48528 −0.411139
$$179$$ −8.12132 14.0665i −0.607016 1.05138i −0.991729 0.128346i $$-0.959033\pi$$
0.384713 0.923036i $$-0.374300\pi$$
$$180$$ 0 0
$$181$$ −20.2426 −1.50462 −0.752312 0.658807i $$-0.771061\pi$$
−0.752312 + 0.658807i $$0.771061\pi$$
$$182$$ −10.1213 13.0519i −0.750242 0.967473i
$$183$$ 0 0
$$184$$ 7.24264 0.533935
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ −13.2426 −0.965819
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 4.24264 + 7.34847i 0.306987 + 0.531717i 0.977702 0.209999i $$-0.0673460\pi$$
−0.670715 + 0.741715i $$0.734013\pi$$
$$192$$ 0 0
$$193$$ 2.25736 3.90986i 0.162488 0.281438i −0.773272 0.634074i $$-0.781381\pi$$
0.935760 + 0.352636i $$0.114715\pi$$
$$194$$ 12.4853 0.896391
$$195$$ 0 0
$$196$$ 6.74264 1.88064i 0.481617 0.134331i
$$197$$ −16.9706 −1.20910 −0.604551 0.796566i $$-0.706648\pi$$
−0.604551 + 0.796566i $$0.706648\pi$$
$$198$$ 0 0
$$199$$ 7.37868 + 12.7802i 0.523061 + 0.905968i 0.999640 + 0.0268362i $$0.00854325\pi$$
−0.476579 + 0.879132i $$0.658123\pi$$
$$200$$ 5.00000 0.353553
$$201$$ 0 0
$$202$$ −3.87868 6.71807i −0.272903 0.472682i
$$203$$ 6.87868 + 8.87039i 0.482789 + 0.622579i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0.378680 + 0.655892i 0.0263839 + 0.0456982i
$$207$$ 0 0
$$208$$ −3.12132 + 5.40629i −0.216425 + 0.374858i
$$209$$ 13.2426 22.9369i 0.916013 1.58658i
$$210$$ 0 0
$$211$$ 3.24264 + 5.61642i 0.223233 + 0.386650i 0.955788 0.294058i $$-0.0950057\pi$$
−0.732555 + 0.680708i $$0.761672\pi$$
$$212$$ −4.24264 −0.291386
$$213$$ 0 0
$$214$$ −2.48528 −0.169890
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 1.22792 + 1.58346i 0.0833568 + 0.107493i
$$218$$ −1.12132 + 1.94218i −0.0759454 + 0.131541i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ −5.86396 + 10.1567i −0.392680 + 0.680141i −0.992802 0.119767i $$-0.961785\pi$$
0.600122 + 0.799908i $$0.295119\pi$$
$$224$$ −1.62132 2.09077i −0.108329 0.139695i
$$225$$ 0 0
$$226$$ 10.2426 17.7408i 0.681330 1.18010i
$$227$$ −26.4853 −1.75789 −0.878945 0.476923i $$-0.841752\pi$$
−0.878945 + 0.476923i $$0.841752\pi$$
$$228$$ 0 0
$$229$$ 24.9706 1.65010 0.825051 0.565059i $$-0.191147\pi$$
0.825051 + 0.565059i $$0.191147\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 2.12132 3.67423i 0.139272 0.241225i
$$233$$ 10.2426 17.7408i 0.671018 1.16224i −0.306598 0.951839i $$-0.599191\pi$$
0.977616 0.210398i $$-0.0674759\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 1.86396 + 3.22848i 0.120570 + 0.208833i 0.919992 0.391936i $$-0.128195\pi$$
−0.799423 + 0.600769i $$0.794861\pi$$
$$240$$ 0 0
$$241$$ 8.51472 0.548481 0.274241 0.961661i $$-0.411574\pi$$
0.274241 + 0.961661i $$0.411574\pi$$
$$242$$ 3.50000 + 6.06218i 0.224989 + 0.389692i
$$243$$ 0 0
$$244$$ 6.24264 0.399644
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 38.9706 2.47964
$$248$$ 0.378680 0.655892i 0.0240462 0.0416492i
$$249$$ 0 0
$$250$$ 0 0
$$251$$ −18.7279 −1.18210 −0.591048 0.806636i $$-0.701286\pi$$
−0.591048 + 0.806636i $$0.701286\pi$$
$$252$$ 0 0
$$253$$ 30.7279 1.93185
$$254$$ 3.37868 + 5.85204i 0.211997 + 0.367190i
$$255$$ 0 0
$$256$$ −0.500000 + 0.866025i −0.0312500 + 0.0541266i
$$257$$ −5.48528 −0.342162 −0.171081 0.985257i $$-0.554726\pi$$
−0.171081 + 0.985257i $$0.554726\pi$$
$$258$$ 0 0
$$259$$ −6.48528 8.36308i −0.402976 0.519657i
$$260$$ 0 0
$$261$$ 0 0
$$262$$ 3.87868 + 6.71807i 0.239626 + 0.415044i
$$263$$ −22.9706 −1.41643 −0.708213 0.705999i $$-0.750498\pi$$
−0.708213 + 0.705999i $$0.750498\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −6.24264 + 15.2913i −0.382761 + 0.937569i
$$267$$ 0 0
$$268$$ 4.12132 + 7.13834i 0.251750 + 0.436043i
$$269$$ −5.48528 9.50079i −0.334444 0.579273i 0.648934 0.760844i $$-0.275215\pi$$
−0.983378 + 0.181571i $$0.941882\pi$$
$$270$$ 0 0
$$271$$ 6.24264 10.8126i 0.379213 0.656817i −0.611735 0.791063i $$-0.709528\pi$$
0.990948 + 0.134246i $$0.0428613\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 9.98528 + 17.2950i 0.603233 + 1.04483i
$$275$$ 21.2132 1.27920
$$276$$ 0 0
$$277$$ −19.2132 −1.15441 −0.577205 0.816599i $$-0.695857\pi$$
−0.577205 + 0.816599i $$0.695857\pi$$
$$278$$ −2.36396 + 4.09450i −0.141781 + 0.245572i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 11.2279 19.4473i 0.669802 1.16013i −0.308158 0.951335i $$-0.599712\pi$$
0.977959 0.208795i $$-0.0669542\pi$$
$$282$$ 0 0
$$283$$ −12.4853 + 21.6251i −0.742173 + 1.28548i 0.209331 + 0.977845i $$0.432871\pi$$
−0.951504 + 0.307636i $$0.900462\pi$$
$$284$$ −3.62132 + 6.27231i −0.214886 + 0.372193i
$$285$$ 0 0
$$286$$ −13.2426 + 22.9369i −0.783054 + 1.35629i
$$287$$ −14.3787 + 1.96768i −0.848747 + 0.116148i
$$288$$ 0 0
$$289$$ 8.50000 14.7224i 0.500000 0.866025i
$$290$$ 0 0
$$291$$ 0 0
$$292$$ −7.00000 −0.409644
$$293$$ −5.48528 9.50079i −0.320454 0.555042i 0.660128 0.751153i $$-0.270502\pi$$
−0.980582 + 0.196111i $$0.937169\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ −2.00000 + 3.46410i −0.116248 + 0.201347i
$$297$$ 0 0
$$298$$ −8.12132 14.0665i −0.470455 0.814853i
$$299$$ 22.6066 + 39.1558i 1.30737 + 2.26444i
$$300$$ 0 0
$$301$$ −10.5147 13.5592i −0.606058 0.781541i
$$302$$ −1.37868 2.38794i −0.0793341 0.137411i
$$303$$ 0 0
$$304$$ 6.24264 0.358040
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −28.0000 −1.59804 −0.799022 0.601302i $$-0.794649\pi$$
−0.799022 + 0.601302i $$0.794649\pi$$
$$308$$ −6.87868 8.87039i −0.391949 0.505437i
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −5.48528 + 9.50079i −0.311042 + 0.538740i −0.978588 0.205828i $$-0.934011\pi$$
0.667546 + 0.744568i $$0.267345\pi$$
$$312$$ 0 0
$$313$$ 8.98528 + 15.5630i 0.507878 + 0.879671i 0.999958 + 0.00912090i $$0.00290331\pi$$
−0.492080 + 0.870550i $$0.663763\pi$$
$$314$$ −14.0000 −0.790066
$$315$$ 0 0
$$316$$ 9.24264 0.519939
$$317$$ −8.48528 14.6969i −0.476581 0.825462i 0.523059 0.852296i $$-0.324791\pi$$
−0.999640 + 0.0268342i $$0.991457\pi$$
$$318$$ 0 0
$$319$$ 9.00000 15.5885i 0.503903 0.872786i
$$320$$ 0 0
$$321$$ 0 0
$$322$$ −18.9853 + 2.59808i −1.05801 + 0.144785i
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 15.6066 + 27.0314i 0.865699 + 1.49943i
$$326$$ 11.7574 0.651180
$$327$$ 0 0
$$328$$ 2.74264 + 4.75039i 0.151437 + 0.262297i
$$329$$ 34.7132 4.75039i 1.91380 0.261898i
$$330$$ 0 0
$$331$$ 9.24264 + 16.0087i 0.508021 + 0.879919i 0.999957 + 0.00928730i $$0.00295628\pi$$
−0.491935 + 0.870632i $$0.663710\pi$$
$$332$$ 3.87868 + 6.71807i 0.212870 + 0.368702i
$$333$$ 0 0
$$334$$ −12.1066 + 20.9692i −0.662444 + 1.14739i
$$335$$ 0 0
$$336$$ 0 0
$$337$$ −2.24264 3.88437i −0.122164 0.211595i 0.798457 0.602052i $$-0.205650\pi$$
−0.920621 + 0.390457i $$0.872317\pi$$
$$338$$ −25.9706 −1.41261
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 1.60660 2.78272i 0.0870024 0.150693i
$$342$$ 0 0
$$343$$ −17.0000 + 7.34847i −0.917914 + 0.396780i
$$344$$ −3.24264 + 5.61642i −0.174831 + 0.302817i
$$345$$ 0 0
$$346$$ 5.48528 9.50079i 0.294891 0.510765i
$$347$$ −3.36396 + 5.82655i −0.180587 + 0.312786i −0.942081 0.335387i $$-0.891133\pi$$
0.761494 + 0.648172i $$0.224466\pi$$
$$348$$ 0 0
$$349$$ −12.4853 + 21.6251i −0.668322 + 1.15757i 0.310051 + 0.950720i $$0.399654\pi$$
−0.978373 + 0.206848i $$0.933680\pi$$
$$350$$ −13.1066 + 1.79360i −0.700577 + 0.0958718i
$$351$$ 0 0
$$352$$ −2.12132 + 3.67423i −0.113067 + 0.195837i
$$353$$ −21.0000 −1.11772 −0.558859 0.829263i $$-0.688761\pi$$
−0.558859 + 0.829263i $$0.688761\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ −2.74264 4.75039i −0.145360 0.251770i
$$357$$ 0 0
$$358$$ 8.12132 14.0665i 0.429225 0.743440i
$$359$$ 5.37868 9.31615i 0.283876 0.491687i −0.688460 0.725274i $$-0.741713\pi$$
0.972336 + 0.233587i $$0.0750463\pi$$
$$360$$ 0 0
$$361$$ −9.98528 17.2950i −0.525541 0.910264i
$$362$$ −10.1213 17.5306i −0.531965 0.921390i
$$363$$ 0 0
$$364$$ 6.24264 15.2913i 0.327203 0.801481i
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 11.7279 0.612193 0.306096 0.952001i $$-0.400977\pi$$
0.306096 + 0.952001i $$0.400977\pi$$
$$368$$ 3.62132 + 6.27231i 0.188774 + 0.326967i
$$369$$ 0 0
$$370$$ 0 0
$$371$$ 11.1213 1.52192i 0.577390 0.0790140i
$$372$$ 0 0
$$373$$ −7.21320 −0.373486 −0.186743 0.982409i $$-0.559793\pi$$
−0.186743 + 0.982409i $$0.559793\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −6.62132 11.4685i −0.341469 0.591441i
$$377$$ 26.4853 1.36406
$$378$$ 0 0
$$379$$ 1.27208 0.0653423 0.0326711 0.999466i $$-0.489599\pi$$
0.0326711 + 0.999466i $$0.489599\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −4.24264 + 7.34847i −0.217072 + 0.375980i
$$383$$ 24.2132 1.23724 0.618618 0.785692i $$-0.287693\pi$$
0.618618 + 0.785692i $$0.287693\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 4.51472 0.229793
$$387$$ 0 0
$$388$$ 6.24264 + 10.8126i 0.316922 + 0.548925i
$$389$$ −10.2426 −0.519322 −0.259661 0.965700i $$-0.583611\pi$$
−0.259661 + 0.965700i $$0.583611\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 5.00000 + 4.89898i 0.252538 + 0.247436i
$$393$$ 0 0
$$394$$ −8.48528 14.6969i −0.427482 0.740421i
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 10.1213 17.5306i 0.507975 0.879838i −0.491983 0.870605i $$-0.663728\pi$$
0.999957 0.00923278i $$-0.00293893\pi$$
$$398$$ −7.37868 + 12.7802i −0.369860 + 0.640616i
$$399$$ 0 0
$$400$$ 2.50000 + 4.33013i 0.125000 + 0.216506i
$$401$$ −29.4853 −1.47242 −0.736212 0.676751i $$-0.763388\pi$$
−0.736212 + 0.676751i $$0.763388\pi$$
$$402$$ 0 0
$$403$$ 4.72792 0.235515
$$404$$ 3.87868 6.71807i 0.192972 0.334236i
$$405$$ 0 0
$$406$$ −4.24264 + 10.3923i −0.210559 + 0.515761i
$$407$$ −8.48528 + 14.6969i −0.420600 + 0.728500i
$$408$$ 0 0
$$409$$ −17.5000 + 30.3109i −0.865319 + 1.49878i 0.00141047 + 0.999999i $$0.499551\pi$$
−0.866730 + 0.498778i $$0.833782\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −0.378680 + 0.655892i −0.0186562 + 0.0323135i
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −6.24264 −0.306071
$$417$$ 0 0
$$418$$ 26.4853 1.29544
$$419$$ −3.87868 6.71807i −0.189486 0.328199i 0.755593 0.655041i $$-0.227349\pi$$
−0.945079 + 0.326842i $$0.894015\pi$$
$$420$$ 0 0
$$421$$ 7.12132 12.3345i 0.347072 0.601146i −0.638656 0.769492i $$-0.720509\pi$$
0.985728 + 0.168346i $$0.0538426\pi$$
$$422$$ −3.24264 + 5.61642i −0.157849 + 0.273403i
$$423$$ 0 0
$$424$$ −2.12132 3.67423i −0.103020 0.178437i
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −16.3640 + 2.23936i −0.791908 + 0.108370i
$$428$$ −1.24264 2.15232i −0.0600653 0.104036i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −18.6213 32.2531i −0.896957 1.55358i −0.831363 0.555729i $$-0.812439\pi$$
−0.0655943 0.997846i $$-0.520894\pi$$
$$432$$ 0 0
$$433$$ 3.97056 0.190813 0.0954065 0.995438i $$-0.469585\pi$$
0.0954065 + 0.995438i $$0.469585\pi$$
$$434$$ −0.757359 + 1.85514i −0.0363544 + 0.0890498i
$$435$$ 0 0
$$436$$ −2.24264 −0.107403
$$437$$ 22.6066 39.1558i 1.08142 1.87308i
$$438$$ 0 0
$$439$$ −5.86396 10.1567i −0.279872 0.484752i 0.691481 0.722395i $$-0.256959\pi$$
−0.971353 + 0.237643i $$0.923625\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 4.75736 + 8.23999i 0.226029 + 0.391494i 0.956628 0.291313i $$-0.0940923\pi$$
−0.730599 + 0.682807i $$0.760759\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −11.7279 −0.555333
$$447$$ 0 0
$$448$$ 1.00000 2.44949i 0.0472456 0.115728i
$$449$$ 4.97056 0.234575 0.117288 0.993098i $$-0.462580\pi$$
0.117288 + 0.993098i $$0.462580\pi$$
$$450$$ 0 0
$$451$$ 11.6360 + 20.1542i 0.547920 + 0.949025i
$$452$$ 20.4853 0.963547
$$453$$ 0 0
$$454$$ −13.2426 22.9369i −0.621508 1.07648i
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −5.75736 9.97204i −0.269318 0.466472i 0.699368 0.714762i $$-0.253465\pi$$
−0.968686 + 0.248290i $$0.920132\pi$$
$$458$$ 12.4853 + 21.6251i 0.583399 + 1.01048i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 17.1213 29.6550i 0.797419 1.38117i −0.123872 0.992298i $$-0.539531\pi$$
0.921291 0.388873i $$-0.127135\pi$$
$$462$$ 0 0
$$463$$ 4.37868 + 7.58410i 0.203495 + 0.352463i 0.949652 0.313307i $$-0.101437\pi$$
−0.746158 + 0.665769i $$0.768103\pi$$
$$464$$ 4.24264 0.196960
$$465$$ 0 0
$$466$$ 20.4853 0.948962
$$467$$ 0 0 −0.866025 0.500000i $$-0.833333\pi$$
0.866025 + 0.500000i $$0.166667\pi$$
$$468$$ 0 0
$$469$$ −13.3640 17.2335i −0.617090 0.795768i
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ −13.7574 + 23.8284i −0.632564 + 1.09563i
$$474$$ 0 0
$$475$$ 15.6066 27.0314i 0.716080 1.24029i
$$476$$ 0 0
$$477$$ 0 0
$$478$$ −1.86396 + 3.22848i −0.0852556 + 0.147667i
$$479$$ 13.2426 0.605072 0.302536 0.953138i $$-0.402167\pi$$
0.302536 + 0.953138i $$0.402167\pi$$
$$480$$ 0 0
$$481$$ −24.9706 −1.13856
$$482$$ 4.25736 + 7.37396i 0.193917 + 0.335875i
$$483$$ 0 0
$$484$$ −3.50000 + 6.06218i −0.159091 + 0.275554i
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 1.37868 + 2.38794i 0.0624739 + 0.108208i 0.895571 0.444919i $$-0.146768\pi$$
−0.833097 + 0.553127i $$0.813434\pi$$
$$488$$ 3.12132 + 5.40629i 0.141296 + 0.244731i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 3.36396 + 5.82655i 0.151813 + 0.262949i 0.931894 0.362730i $$-0.118155\pi$$
−0.780081 + 0.625679i $$0.784822\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 19.4853 + 33.7495i 0.876684 + 1.51846i
$$495$$ 0 0
$$496$$ 0.757359 0.0340064
$$497$$ 7.24264 17.7408i 0.324877 0.795782i
$$498$$ 0 0
$$499$$ −10.7279 −0.480248 −0.240124 0.970742i $$-0.577188\pi$$
−0.240124 + 0.970742i $$0.577188\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −9.36396 16.2189i −0.417934 0.723883i
$$503$$ 24.2132 1.07961 0.539807 0.841789i $$-0.318497\pi$$
0.539807 + 0.841789i $$0.318497\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 15.3640 + 26.6112i 0.683011 + 1.18301i
$$507$$ 0 0
$$508$$ −3.37868 + 5.85204i −0.149905 + 0.259643i
$$509$$ −7.75736 −0.343839 −0.171919 0.985111i $$-0.554997\pi$$
−0.171919 + 0.985111i $$0.554997\pi$$
$$510$$ 0 0
$$511$$ 18.3492 2.51104i 0.811723 0.111082i
$$512$$ −1.00000 −0.0441942
$$513$$ 0 0
$$514$$ −2.74264 4.75039i −0.120973 0.209531i
$$515$$ 0 0
$$516$$ 0 0
$$517$$ −28.0919 48.6566i −1.23548 2.13991i
$$518$$ 4.00000 9.79796i 0.175750 0.430498i
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 8.22792 + 14.2512i 0.360472 + 0.624355i 0.988039 0.154207i $$-0.0492824\pi$$
−0.627567 + 0.778563i $$0.715949\pi$$
$$522$$ 0 0
$$523$$ 10.1213 17.5306i 0.442574 0.766561i −0.555305 0.831647i $$-0.687399\pi$$
0.997880 + 0.0650852i $$0.0207319\pi$$
$$524$$ −3.87868 + 6.71807i −0.169441 + 0.293480i
$$525$$ 0 0
$$526$$ −11.4853 19.8931i −0.500782 0.867380i
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 29.4558 1.28069
$$530$$ 0 0
$$531$$ 0 0
$$532$$ −16.3640 + 2.23936i −0.709468 + 0.0970884i
$$533$$ −17.1213 + 29.6550i −0.741607 + 1.28450i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ −4.12132 + 7.13834i −0.178014 + 0.308329i
$$537$$ 0 0
$$538$$ 5.48528 9.50079i 0.236487 0.409608i
$$539$$ 21.2132 + 20.7846i 0.913717 + 0.895257i
$$540$$ 0 0
$$541$$ 7.48528 12.9649i 0.321817 0.557404i −0.659046 0.752103i $$-0.729040\pi$$
0.980863 + 0.194699i $$0.0623730\pi$$
$$542$$ 12.4853 0.536289
$$543$$ 0 0
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 3.24264 5.61642i 0.138645 0.240141i −0.788339 0.615241i $$-0.789059\pi$$
0.926984 + 0.375101i $$0.122392\pi$$
$$548$$ −9.98528 + 17.2950i −0.426550 + 0.738806i
$$549$$ 0 0
$$550$$ 10.6066 + 18.3712i 0.452267 + 0.783349i
$$551$$ −13.2426 22.9369i −0.564155 0.977146i
$$552$$ 0 0
$$553$$ −24.2279 + 3.31552i −1.03028 + 0.140990i
$$554$$ −9.60660 16.6391i −0.408145 0.706929i
$$555$$ 0 0
$$556$$ −4.72792 −0.200509
$$557$$ −20.4853 35.4815i −0.867989 1.50340i −0.864048 0.503409i $$-0.832079\pi$$
−0.00394110 0.999992i $$-0.501254\pi$$
$$558$$ 0 0
$$559$$ −40.4853 −1.71234
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 22.4558 0.947243
$$563$$ 9.36396 16.2189i 0.394644 0.683543i −0.598412 0.801189i $$-0.704201\pi$$
0.993056 + 0.117645i $$0.0375346\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ −24.9706 −1.04959
$$567$$ 0 0
$$568$$ −7.24264 −0.303894
$$569$$ 12.4706 + 21.5996i 0.522793 + 0.905504i 0.999648 + 0.0265224i $$0.00844333\pi$$
−0.476855 + 0.878982i $$0.658223\pi$$
$$570$$ 0 0
$$571$$ 10.4853 18.1610i 0.438795 0.760016i −0.558801 0.829301i $$-0.688739\pi$$
0.997597 + 0.0692856i $$0.0220720\pi$$
$$572$$ −26.4853 −1.10741
$$573$$ 0 0
$$574$$ −8.89340 11.4685i −0.371203 0.478684i
$$575$$ 36.2132 1.51019
$$576$$ 0 0
$$577$$ −17.9706 31.1259i −0.748124 1.29579i −0.948721 0.316115i $$-0.897621\pi$$
0.200596 0.979674i $$-0.435712\pi$$
$$578$$ 17.0000 0.707107
$$579$$ 0 0
$$580$$ 0 0
$$581$$ −12.5772 16.2189i −0.521789 0.672872i
$$582$$ 0 0
$$583$$ −9.00000 15.5885i −0.372742 0.645608i
$$584$$ −3.50000 6.06218i −0.144831 0.250855i
$$585$$ 0 0
$$586$$ 5.48528 9.50079i 0.226595 0.392474i
$$587$$ −1.60660 + 2.78272i −0.0663115 + 0.114855i −0.897275 0.441472i $$-0.854456\pi$$
0.830963 + 0.556327i $$0.187790\pi$$
$$588$$ 0 0
$$589$$ −2.36396 4.09450i −0.0974053 0.168711i
$$590$$ 0 0
$$591$$ 0 0
$$592$$ −4.00000 −0.164399
$$593$$ −2.74264 + 4.75039i −0.112627 + 0.195075i −0.916829 0.399281i $$-0.869260\pi$$
0.804202 + 0.594356i $$0.202593\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 8.12132 14.0665i 0.332662 0.576188i
$$597$$ 0 0
$$598$$ −22.6066 + 39.1558i −0.924453 + 1.60120i
$$599$$ 11.4853 19.8931i 0.469276 0.812810i −0.530107 0.847931i $$-0.677848\pi$$
0.999383 + 0.0351210i $$0.0111817\pi$$
$$600$$ 0 0
$$601$$ 8.98528 15.5630i 0.366517 0.634827i −0.622501 0.782619i $$-0.713883\pi$$
0.989018 + 0.147792i $$0.0472167\pi$$
$$602$$ 6.48528 15.8856i 0.264320 0.647450i
$$603$$ 0 0
$$604$$ 1.37868 2.38794i 0.0560977 0.0971640i
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −38.9706 −1.58177 −0.790883 0.611967i $$-0.790378\pi$$
−0.790883 + 0.611967i $$0.790378\pi$$
$$608$$ 3.12132 + 5.40629i 0.126586 + 0.219254i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 41.3345 71.5935i 1.67222 2.89636i
$$612$$ 0 0
$$613$$ 18.9706 + 32.8580i 0.766214 + 1.32712i 0.939602 + 0.342268i $$0.111195\pi$$
−0.173389 + 0.984853i $$0.555472\pi$$
$$614$$ −14.0000 24.2487i −0.564994 0.978598i
$$615$$ 0 0
$$616$$ 4.24264 10.3923i 0.170941 0.418718i
$$617$$ −14.2279 24.6435i −0.572795 0.992109i −0.996277 0.0862052i $$-0.972526\pi$$
0.423483 0.905904i $$-0.360807\pi$$
$$618$$ 0 0
$$619$$ −1.51472 −0.0608817 −0.0304408 0.999537i $$-0.509691\pi$$
−0.0304408 + 0.999537i $$0.509691\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ −10.9706 −0.439879
$$623$$ 8.89340 + 11.4685i 0.356306 + 0.459474i
$$624$$ 0 0
$$625$$ 25.0000 1.00000
$$626$$ −8.98528 + 15.5630i −0.359124 + 0.622021i
$$627$$ 0 0
$$628$$ −7.00000 12.1244i −0.279330 0.483814i
$$629$$ 0 0
$$630$$ 0 0
$$631$$ −24.4853 −0.974744 −0.487372 0.873195i $$-0.662044\pi$$
−0.487372 + 0.873195i $$0.662044\pi$$
$$632$$ 4.62132 + 8.00436i 0.183826 + 0.318396i
$$633$$ 0 0
$$634$$ 8.48528 14.6969i 0.336994 0.583690i
$$635$$ 0 0
$$636$$ 0 0
$$637$$ −10.8787 + 42.3227i −0.431029 + 1.67689i
$$638$$ 18.0000 0.712627
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 4.45584 0.175995 0.0879976 0.996121i $$-0.471953\pi$$
0.0879976 + 0.996121i $$0.471953\pi$$
$$642$$ 0 0
$$643$$ 23.3640 + 40.4676i 0.921385 + 1.59589i 0.797275 + 0.603617i $$0.206274\pi$$
0.124110 + 0.992268i $$0.460392\pi$$
$$644$$ −11.7426 15.1427i −0.462725 0.596706i
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 1.13604 + 1.96768i 0.0446623 + 0.0773574i 0.887492 0.460822i $$-0.152445\pi$$
−0.842830 + 0.538180i $$0.819112\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ −15.6066 + 27.0314i −0.612141 + 1.06026i
$$651$$ 0 0
$$652$$ 5.87868 + 10.1822i 0.230227 + 0.398765i
$$653$$ −24.0000 −0.939193 −0.469596 0.882881i $$-0.655601\pi$$
−0.469596 + 0.882881i $$0.655601\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −2.74264 + 4.75039i −0.107082 + 0.185472i
$$657$$ 0 0
$$658$$ 21.4706 + 27.6873i 0.837010 + 1.07936i
$$659$$ −19.6066 + 33.9596i −0.763765 + 1.32288i 0.177132 + 0.984187i $$0.443318\pi$$
−0.940897 + 0.338692i $$0.890015\pi$$
$$660$$ 0 0
$$661$$ 21.0919 36.5322i 0.820379 1.42094i −0.0850210 0.996379i $$-0.527096\pi$$
0.905400 0.424559i $$-0.139571\pi$$
$$662$$ −9.24264 + 16.0087i −0.359225 + 0.622197i
$$663$$ 0 0
$$664$$ −3.87868 + 6.71807i −0.150522 + 0.260712i
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 15.3640 26.6112i 0.594895 1.03039i
$$668$$ −24.2132 −0.936837
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 13.2426 + 22.9369i 0.511226 + 0.885470i
$$672$$ 0 0
$$673$$ 13.7426 23.8030i 0.529740 0.917536i −0.469658 0.882848i $$-0.655623\pi$$
0.999398 0.0346881i $$-0.0110438\pi$$
$$674$$ 2.24264 3.88437i 0.0863833 0.149620i
$$675$$ 0 0
$$676$$ −12.9853 22.4912i −0.499434 0.865045i
$$677$$ 17.1213 + 29.6550i 0.658026 + 1.13973i 0.981126 + 0.193369i $$0.0619416\pi$$
−0.323100 + 0.946365i $$0.604725\pi$$
$$678$$ 0 0
$$679$$ −20.2426 26.1039i −0.776841 1.00177i
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 3.21320 0.123040
$$683$$ 20.8492 + 36.1119i 0.797774 + 1.38179i 0.921063 + 0.389414i $$0.127323\pi$$
−0.123289 + 0.992371i $$0.539344\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −14.8640 11.0482i −0.567509 0.421822i
$$687$$ 0 0
$$688$$ −6.48528 −0.247249
$$689$$ 13.2426 22.9369i 0.504504 0.873827i
$$690$$ 0 0
$$691$$ −3.12132 5.40629i −0.118741 0.205665i 0.800528 0.599295i $$-0.204552\pi$$
−0.919269 + 0.393630i $$0.871219\pi$$
$$692$$ 10.9706 0.417038
$$693$$ 0 0
$$694$$ −6.72792 −0.255388
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 0 0
$$698$$ −24.9706 −0.945150
$$699$$ 0 0
$$700$$ −8.10660 10.4539i −0.306401 0.395118i
$$701$$ −13.7574 −0.519608 −0.259804 0.965661i $$-0.583658\pi$$
−0.259804 + 0.965661i $$0.583658\pi$$
$$702$$ 0 0
$$703$$ 12.4853 + 21.6251i 0.470891 + 0.815608i
$$704$$ −4.24264 −0.159901
$$705$$ 0 0
$$706$$ −10.5000 18.1865i −0.395173 0.684459i
$$707$$ −7.75736 + 19.0016i −0.291746 + 0.714628i
$$708$$ 0 0
$$709$$ −12.8492 22.2555i −0.482563 0.835824i 0.517236 0.855843i $$-0.326961\pi$$
−0.999800 + 0.0200183i $$0.993628\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ 2.74264 4.75039i 0.102785 0.178029i
$$713$$ 2.74264 4.75039i 0.102713 0.177904i
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 16.2426 0.607016
$$717$$ 0 0
$$718$$ 10.7574 0.401461
$$719$$ −1.13604 + 1.96768i −0.0423671 + 0.0733820i −0.886431 0.462860i $$-0.846823\pi$$
0.844064 + 0.536242i $$0.180157\pi$$
$$720$$ 0 0
$$721$$ 0.757359 1.85514i 0.0282055 0.0690892i
$$722$$ 9.98528 17.2950i 0.371614 0.643654i
$$723$$ 0 0
$$724$$ 10.1213 17.5306i 0.376156 0.651521i
$$725$$ 10.6066 18.3712i 0.393919 0.682288i
$$726$$ 0 0
$$727$$ 12.8640 22.2810i 0.477098 0.826358i −0.522558 0.852604i $$-0.675022\pi$$
0.999656 + 0.0262462i $$0.00835537\pi$$
$$728$$ 16.3640 2.23936i 0.606489 0.0829961i
$$729$$ 0 0
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ −38.9706 −1.43941 −0.719705 0.694280i $$-0.755723\pi$$
−0.719705 + 0.694280i $$0.755723\pi$$
$$734$$ 5.86396 + 10.1567i 0.216443 + 0.374890i
$$735$$ 0 0
$$736$$ −3.62132 + 6.27231i −0.133484 + 0.231200i
$$737$$ −17.4853 + 30.2854i −0.644079 + 1.11558i
$$738$$ 0 0
$$739$$ −5.24264 9.08052i −0.192854 0.334032i 0.753341 0.657630i $$-0.228441\pi$$
−0.946195 + 0.323598i $$0.895108\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 6.87868 + 8.87039i 0.252524 + 0.325642i
$$743$$ 17.3787 + 30.1008i 0.637562 + 1.10429i 0.985966 + 0.166945i $$0.0533903\pi$$
−0.348404 + 0.937344i $$0.613276\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −3.60660 6.24682i −0.132047 0.228712i
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 4.02944 + 5.19615i 0.147232 + 0.189863i
$$750$$ 0 0
$$751$$ −17.2426 −0.629193 −0.314596 0.949226i $$-0.601869\pi$$
−0.314596 + 0.949226i $$0.601869\pi$$
$$752$$ 6.62132 11.4685i 0.241455 0.418212i
$$753$$ 0 0
$$754$$ 13.2426 + 22.9369i 0.482269 + 0.835314i
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 12.9706 0.471423 0.235712 0.971823i $$-0.424258\pi$$
0.235712 + 0.971823i $$0.424258\pi$$
$$758$$ 0.636039 + 1.10165i 0.0231020 + 0.0400138i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −21.0000 −0.761249 −0.380625 0.924730i $$-0.624291\pi$$
−0.380625 + 0.924730i $$0.624291\pi$$
$$762$$ 0 0
$$763$$ 5.87868 0.804479i 0.212822 0.0291241i
$$764$$ −8.48528 −0.306987
$$765$$ 0 0
$$766$$ 12.1066 + 20.9692i 0.437429 + 0.757650i
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 6.24264 + 10.8126i 0.225115 + 0.389911i 0.956354 0.292210i $$-0.0943908\pi$$
−0.731239 + 0.682122i $$0.761057\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 2.25736 + 3.90986i 0.0812441 + 0.140719i
$$773$$ −22.6066 39.1558i −0.813103 1.40834i −0.910682 0.413108i $$-0.864443\pi$$
0.0975792 0.995228i $$-0.468890\pi$$
$$774$$ 0 0
$$775$$ 1.89340 3.27946i 0.0680129 0.117802i
$$776$$ −6.24264 + 10.8126i −0.224098 + 0.388149i
$$777$$ 0 0
$$778$$ −5.12132 8.87039i −0.183608 0.318019i
$$779$$ 34.2426 1.22687
$$780$$ 0 0
$$781$$ −30.7279 −1.09953
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −1.74264 + 6.77962i −0.0622372 + 0.242129i
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 15.6066 27.0314i 0.556315 0.963566i −0.441485 0.897269i $$-0.645548\pi$$
0.997800 0.0662975i $$-0.0211186\pi$$
$$788$$ 8.48528 14.6969i 0.302276 0.523557i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ −53.6985 + 7.34847i −1.90930 + 0.261281i
$$792$$ 0 0
$$793$$ −19.4853 + 33.7495i −0.691943 + 1.19848i
$$794$$ 20.2426 0.718384
$$795$$ 0 0
$$796$$ −14.7574 −0.523061