# Properties

 Label 1176.2.q.n.961.1 Level $1176$ Weight $2$ Character 1176.961 Analytic conductor $9.390$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1176 = 2^{3} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1176.q (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.39040727770$$ 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: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 961.1 Root $$-0.707107 - 1.22474i$$ of defining polynomial Character $$\chi$$ $$=$$ 1176.961 Dual form 1176.2.q.n.361.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.500000 + 0.866025i) q^{3} +(-1.70711 + 2.95680i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$$ $$q+(0.500000 + 0.866025i) q^{3} +(-1.70711 + 2.95680i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(-0.414214 - 0.717439i) q^{11} -4.24264 q^{13} -3.41421 q^{15} +(-3.70711 - 6.42090i) q^{17} +(-3.41421 + 5.91359i) q^{19} +(2.41421 - 4.18154i) q^{23} +(-3.32843 - 5.76500i) q^{25} -1.00000 q^{27} +2.82843 q^{29} +(1.41421 + 2.44949i) q^{31} +(0.414214 - 0.717439i) q^{33} +(0.828427 - 1.43488i) q^{37} +(-2.12132 - 3.67423i) q^{39} +10.2426 q^{41} -11.3137 q^{43} +(-1.70711 - 2.95680i) q^{45} +(2.24264 - 3.88437i) q^{47} +(3.70711 - 6.42090i) q^{51} +(1.00000 + 1.73205i) q^{53} +2.82843 q^{55} -6.82843 q^{57} +(-4.24264 - 7.34847i) q^{59} +(-5.53553 + 9.58783i) q^{61} +(7.24264 - 12.5446i) q^{65} +(-5.65685 - 9.79796i) q^{67} +4.82843 q^{69} -10.4853 q^{71} +(-3.87868 - 6.71807i) q^{73} +(3.32843 - 5.76500i) q^{75} +(-6.82843 + 11.8272i) q^{79} +(-0.500000 - 0.866025i) q^{81} -4.00000 q^{83} +25.3137 q^{85} +(1.41421 + 2.44949i) q^{87} +(-2.87868 + 4.98602i) q^{89} +(-1.41421 + 2.44949i) q^{93} +(-11.6569 - 20.1903i) q^{95} -0.242641 q^{97} +0.828427 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 2q^{3} - 4q^{5} - 2q^{9} + O(q^{10})$$ $$4q + 2q^{3} - 4q^{5} - 2q^{9} + 4q^{11} - 8q^{15} - 12q^{17} - 8q^{19} + 4q^{23} - 2q^{25} - 4q^{27} - 4q^{33} - 8q^{37} + 24q^{41} - 4q^{45} - 8q^{47} + 12q^{51} + 4q^{53} - 16q^{57} - 8q^{61} + 12q^{65} + 8q^{69} - 8q^{71} - 24q^{73} + 2q^{75} - 16q^{79} - 2q^{81} - 16q^{83} + 56q^{85} - 20q^{89} - 24q^{95} + 16q^{97} - 8q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$$.

 $$n$$ $$295$$ $$589$$ $$785$$ $$1081$$ $$\chi(n)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## 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 0
$$3$$ 0.500000 + 0.866025i 0.288675 + 0.500000i
$$4$$ 0 0
$$5$$ −1.70711 + 2.95680i −0.763441 + 1.32232i 0.177625 + 0.984098i $$0.443158\pi$$
−0.941067 + 0.338221i $$0.890175\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ −0.500000 + 0.866025i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ −0.414214 0.717439i −0.124890 0.216316i 0.796800 0.604243i $$-0.206524\pi$$
−0.921690 + 0.387927i $$0.873191\pi$$
$$12$$ 0 0
$$13$$ −4.24264 −1.17670 −0.588348 0.808608i $$-0.700222\pi$$
−0.588348 + 0.808608i $$0.700222\pi$$
$$14$$ 0 0
$$15$$ −3.41421 −0.881546
$$16$$ 0 0
$$17$$ −3.70711 6.42090i −0.899105 1.55730i −0.828640 0.559782i $$-0.810885\pi$$
−0.0704656 0.997514i $$-0.522449\pi$$
$$18$$ 0 0
$$19$$ −3.41421 + 5.91359i −0.783274 + 1.35667i 0.146750 + 0.989174i $$0.453119\pi$$
−0.930025 + 0.367497i $$0.880215\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 2.41421 4.18154i 0.503398 0.871911i −0.496594 0.867983i $$-0.665416\pi$$
0.999992 0.00392850i $$-0.00125049\pi$$
$$24$$ 0 0
$$25$$ −3.32843 5.76500i −0.665685 1.15300i
$$26$$ 0 0
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ 2.82843 0.525226 0.262613 0.964901i $$-0.415416\pi$$
0.262613 + 0.964901i $$0.415416\pi$$
$$30$$ 0 0
$$31$$ 1.41421 + 2.44949i 0.254000 + 0.439941i 0.964623 0.263631i $$-0.0849203\pi$$
−0.710623 + 0.703573i $$0.751587\pi$$
$$32$$ 0 0
$$33$$ 0.414214 0.717439i 0.0721053 0.124890i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 0.828427 1.43488i 0.136193 0.235892i −0.789860 0.613287i $$-0.789847\pi$$
0.926052 + 0.377395i $$0.123180\pi$$
$$38$$ 0 0
$$39$$ −2.12132 3.67423i −0.339683 0.588348i
$$40$$ 0 0
$$41$$ 10.2426 1.59963 0.799816 0.600245i $$-0.204930\pi$$
0.799816 + 0.600245i $$0.204930\pi$$
$$42$$ 0 0
$$43$$ −11.3137 −1.72532 −0.862662 0.505781i $$-0.831205\pi$$
−0.862662 + 0.505781i $$0.831205\pi$$
$$44$$ 0 0
$$45$$ −1.70711 2.95680i −0.254480 0.440773i
$$46$$ 0 0
$$47$$ 2.24264 3.88437i 0.327123 0.566593i −0.654817 0.755788i $$-0.727254\pi$$
0.981940 + 0.189194i $$0.0605876\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ 3.70711 6.42090i 0.519099 0.899105i
$$52$$ 0 0
$$53$$ 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i $$-0.122805\pi$$
−0.789136 + 0.614218i $$0.789471\pi$$
$$54$$ 0 0
$$55$$ 2.82843 0.381385
$$56$$ 0 0
$$57$$ −6.82843 −0.904447
$$58$$ 0 0
$$59$$ −4.24264 7.34847i −0.552345 0.956689i −0.998105 0.0615367i $$-0.980400\pi$$
0.445760 0.895152i $$-0.352933\pi$$
$$60$$ 0 0
$$61$$ −5.53553 + 9.58783i −0.708752 + 1.22760i 0.256568 + 0.966526i $$0.417408\pi$$
−0.965320 + 0.261069i $$0.915925\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ 7.24264 12.5446i 0.898339 1.55597i
$$66$$ 0 0
$$67$$ −5.65685 9.79796i −0.691095 1.19701i −0.971480 0.237124i $$-0.923795\pi$$
0.280385 0.959888i $$-0.409538\pi$$
$$68$$ 0 0
$$69$$ 4.82843 0.581274
$$70$$ 0 0
$$71$$ −10.4853 −1.24437 −0.622187 0.782869i $$-0.713756\pi$$
−0.622187 + 0.782869i $$0.713756\pi$$
$$72$$ 0 0
$$73$$ −3.87868 6.71807i −0.453965 0.786291i 0.544663 0.838655i $$-0.316658\pi$$
−0.998628 + 0.0523644i $$0.983324\pi$$
$$74$$ 0 0
$$75$$ 3.32843 5.76500i 0.384334 0.665685i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −6.82843 + 11.8272i −0.768258 + 1.33066i 0.170249 + 0.985401i $$0.445543\pi$$
−0.938507 + 0.345261i $$0.887790\pi$$
$$80$$ 0 0
$$81$$ −0.500000 0.866025i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ 0 0
$$85$$ 25.3137 2.74566
$$86$$ 0 0
$$87$$ 1.41421 + 2.44949i 0.151620 + 0.262613i
$$88$$ 0 0
$$89$$ −2.87868 + 4.98602i −0.305139 + 0.528517i −0.977292 0.211895i $$-0.932036\pi$$
0.672153 + 0.740412i $$0.265370\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −1.41421 + 2.44949i −0.146647 + 0.254000i
$$94$$ 0 0
$$95$$ −11.6569 20.1903i −1.19597 2.07148i
$$96$$ 0 0
$$97$$ −0.242641 −0.0246364 −0.0123182 0.999924i $$-0.503921\pi$$
−0.0123182 + 0.999924i $$0.503921\pi$$
$$98$$ 0 0
$$99$$ 0.828427 0.0832601
$$100$$ 0 0
$$101$$ 5.36396 + 9.29065i 0.533734 + 0.924455i 0.999223 + 0.0394011i $$0.0125450\pi$$
−0.465489 + 0.885053i $$0.654122\pi$$
$$102$$ 0 0
$$103$$ −7.07107 + 12.2474i −0.696733 + 1.20678i 0.272860 + 0.962054i $$0.412030\pi$$
−0.969593 + 0.244723i $$0.921303\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −6.41421 + 11.1097i −0.620085 + 1.07402i 0.369384 + 0.929277i $$0.379569\pi$$
−0.989469 + 0.144743i $$0.953765\pi$$
$$108$$ 0 0
$$109$$ 1.65685 + 2.86976i 0.158698 + 0.274873i 0.934399 0.356227i $$-0.115937\pi$$
−0.775702 + 0.631100i $$0.782604\pi$$
$$110$$ 0 0
$$111$$ 1.65685 0.157262
$$112$$ 0 0
$$113$$ −10.0000 −0.940721 −0.470360 0.882474i $$-0.655876\pi$$
−0.470360 + 0.882474i $$0.655876\pi$$
$$114$$ 0 0
$$115$$ 8.24264 + 14.2767i 0.768630 + 1.33131i
$$116$$ 0 0
$$117$$ 2.12132 3.67423i 0.196116 0.339683i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 5.15685 8.93193i 0.468805 0.811994i
$$122$$ 0 0
$$123$$ 5.12132 + 8.87039i 0.461774 + 0.799816i
$$124$$ 0 0
$$125$$ 5.65685 0.505964
$$126$$ 0 0
$$127$$ 20.0000 1.77471 0.887357 0.461084i $$-0.152539\pi$$
0.887357 + 0.461084i $$0.152539\pi$$
$$128$$ 0 0
$$129$$ −5.65685 9.79796i −0.498058 0.862662i
$$130$$ 0 0
$$131$$ 2.00000 3.46410i 0.174741 0.302660i −0.765331 0.643637i $$-0.777425\pi$$
0.940072 + 0.340977i $$0.110758\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 1.70711 2.95680i 0.146924 0.254480i
$$136$$ 0 0
$$137$$ 4.58579 + 7.94282i 0.391790 + 0.678600i 0.992686 0.120727i $$-0.0385226\pi$$
−0.600896 + 0.799328i $$0.705189\pi$$
$$138$$ 0 0
$$139$$ −20.9706 −1.77870 −0.889350 0.457227i $$-0.848843\pi$$
−0.889350 + 0.457227i $$0.848843\pi$$
$$140$$ 0 0
$$141$$ 4.48528 0.377729
$$142$$ 0 0
$$143$$ 1.75736 + 3.04384i 0.146958 + 0.254538i
$$144$$ 0 0
$$145$$ −4.82843 + 8.36308i −0.400979 + 0.694516i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −0.656854 + 1.13770i −0.0538116 + 0.0932044i −0.891676 0.452673i $$-0.850470\pi$$
0.837865 + 0.545878i $$0.183804\pi$$
$$150$$ 0 0
$$151$$ 4.82843 + 8.36308i 0.392932 + 0.680578i 0.992835 0.119495i $$-0.0381275\pi$$
−0.599903 + 0.800073i $$0.704794\pi$$
$$152$$ 0 0
$$153$$ 7.41421 0.599404
$$154$$ 0 0
$$155$$ −9.65685 −0.775657
$$156$$ 0 0
$$157$$ −0.121320 0.210133i −0.00968242 0.0167704i 0.861144 0.508362i $$-0.169749\pi$$
−0.870826 + 0.491591i $$0.836415\pi$$
$$158$$ 0 0
$$159$$ −1.00000 + 1.73205i −0.0793052 + 0.137361i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −2.82843 + 4.89898i −0.221540 + 0.383718i −0.955276 0.295717i $$-0.904442\pi$$
0.733736 + 0.679435i $$0.237775\pi$$
$$164$$ 0 0
$$165$$ 1.41421 + 2.44949i 0.110096 + 0.190693i
$$166$$ 0 0
$$167$$ −14.8284 −1.14746 −0.573729 0.819045i $$-0.694504\pi$$
−0.573729 + 0.819045i $$0.694504\pi$$
$$168$$ 0 0
$$169$$ 5.00000 0.384615
$$170$$ 0 0
$$171$$ −3.41421 5.91359i −0.261091 0.452224i
$$172$$ 0 0
$$173$$ 8.29289 14.3637i 0.630497 1.09205i −0.356953 0.934122i $$-0.616184\pi$$
0.987450 0.157931i $$-0.0504822\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 4.24264 7.34847i 0.318896 0.552345i
$$178$$ 0 0
$$179$$ 3.24264 + 5.61642i 0.242366 + 0.419791i 0.961388 0.275197i $$-0.0887431\pi$$
−0.719022 + 0.694988i $$0.755410\pi$$
$$180$$ 0 0
$$181$$ −7.07107 −0.525588 −0.262794 0.964852i $$-0.584644\pi$$
−0.262794 + 0.964852i $$0.584644\pi$$
$$182$$ 0 0
$$183$$ −11.0711 −0.818397
$$184$$ 0 0
$$185$$ 2.82843 + 4.89898i 0.207950 + 0.360180i
$$186$$ 0 0
$$187$$ −3.07107 + 5.31925i −0.224579 + 0.388982i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ −6.07107 + 10.5154i −0.439287 + 0.760867i −0.997635 0.0687396i $$-0.978102\pi$$
0.558348 + 0.829607i $$0.311436\pi$$
$$192$$ 0 0
$$193$$ −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i $$-0.189599\pi$$
−0.899770 + 0.436365i $$0.856266\pi$$
$$194$$ 0 0
$$195$$ 14.4853 1.03731
$$196$$ 0 0
$$197$$ −2.68629 −0.191390 −0.0956952 0.995411i $$-0.530507\pi$$
−0.0956952 + 0.995411i $$0.530507\pi$$
$$198$$ 0 0
$$199$$ 2.82843 + 4.89898i 0.200502 + 0.347279i 0.948690 0.316207i $$-0.102409\pi$$
−0.748188 + 0.663486i $$0.769076\pi$$
$$200$$ 0 0
$$201$$ 5.65685 9.79796i 0.399004 0.691095i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −17.4853 + 30.2854i −1.22123 + 2.11522i
$$206$$ 0 0
$$207$$ 2.41421 + 4.18154i 0.167799 + 0.290637i
$$208$$ 0 0
$$209$$ 5.65685 0.391293
$$210$$ 0 0
$$211$$ 1.65685 0.114063 0.0570313 0.998372i $$-0.481837\pi$$
0.0570313 + 0.998372i $$0.481837\pi$$
$$212$$ 0 0
$$213$$ −5.24264 9.08052i −0.359220 0.622187i
$$214$$ 0 0
$$215$$ 19.3137 33.4523i 1.31718 2.28143i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 3.87868 6.71807i 0.262097 0.453965i
$$220$$ 0 0
$$221$$ 15.7279 + 27.2416i 1.05797 + 1.83247i
$$222$$ 0 0
$$223$$ 13.6569 0.914531 0.457265 0.889330i $$-0.348829\pi$$
0.457265 + 0.889330i $$0.348829\pi$$
$$224$$ 0 0
$$225$$ 6.65685 0.443790
$$226$$ 0 0
$$227$$ 2.58579 + 4.47871i 0.171625 + 0.297263i 0.938988 0.343950i $$-0.111765\pi$$
−0.767363 + 0.641213i $$0.778432\pi$$
$$228$$ 0 0
$$229$$ 12.7071 22.0094i 0.839709 1.45442i −0.0504286 0.998728i $$-0.516059\pi$$
0.890138 0.455691i $$-0.150608\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 7.41421 12.8418i 0.485721 0.841294i −0.514144 0.857704i $$-0.671890\pi$$
0.999865 + 0.0164099i $$0.00522367\pi$$
$$234$$ 0 0
$$235$$ 7.65685 + 13.2621i 0.499478 + 0.865121i
$$236$$ 0 0
$$237$$ −13.6569 −0.887108
$$238$$ 0 0
$$239$$ −12.8284 −0.829802 −0.414901 0.909867i $$-0.636184\pi$$
−0.414901 + 0.909867i $$0.636184\pi$$
$$240$$ 0 0
$$241$$ −6.94975 12.0373i −0.447673 0.775392i 0.550561 0.834795i $$-0.314414\pi$$
−0.998234 + 0.0594029i $$0.981080\pi$$
$$242$$ 0 0
$$243$$ 0.500000 0.866025i 0.0320750 0.0555556i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 14.4853 25.0892i 0.921676 1.59639i
$$248$$ 0 0
$$249$$ −2.00000 3.46410i −0.126745 0.219529i
$$250$$ 0 0
$$251$$ −6.14214 −0.387688 −0.193844 0.981032i $$-0.562096\pi$$
−0.193844 + 0.981032i $$0.562096\pi$$
$$252$$ 0 0
$$253$$ −4.00000 −0.251478
$$254$$ 0 0
$$255$$ 12.6569 + 21.9223i 0.792603 + 1.37283i
$$256$$ 0 0
$$257$$ 1.70711 2.95680i 0.106486 0.184440i −0.807858 0.589377i $$-0.799373\pi$$
0.914345 + 0.404937i $$0.132707\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −1.41421 + 2.44949i −0.0875376 + 0.151620i
$$262$$ 0 0
$$263$$ 10.0711 + 17.4436i 0.621009 + 1.07562i 0.989298 + 0.145907i $$0.0466102\pi$$
−0.368290 + 0.929711i $$0.620057\pi$$
$$264$$ 0 0
$$265$$ −6.82843 −0.419467
$$266$$ 0 0
$$267$$ −5.75736 −0.352345
$$268$$ 0 0
$$269$$ 0.0502525 + 0.0870399i 0.00306395 + 0.00530692i 0.867553 0.497344i $$-0.165691\pi$$
−0.864489 + 0.502651i $$0.832358\pi$$
$$270$$ 0 0
$$271$$ −3.07107 + 5.31925i −0.186554 + 0.323121i −0.944099 0.329662i $$-0.893065\pi$$
0.757545 + 0.652783i $$0.226399\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ −2.75736 + 4.77589i −0.166275 + 0.287997i
$$276$$ 0 0
$$277$$ 14.3137 + 24.7921i 0.860027 + 1.48961i 0.871901 + 0.489682i $$0.162887\pi$$
−0.0118739 + 0.999930i $$0.503780\pi$$
$$278$$ 0 0
$$279$$ −2.82843 −0.169334
$$280$$ 0 0
$$281$$ 1.17157 0.0698902 0.0349451 0.999389i $$-0.488874\pi$$
0.0349451 + 0.999389i $$0.488874\pi$$
$$282$$ 0 0
$$283$$ 13.0711 + 22.6398i 0.776994 + 1.34579i 0.933667 + 0.358143i $$0.116590\pi$$
−0.156672 + 0.987651i $$0.550077\pi$$
$$284$$ 0 0
$$285$$ 11.6569 20.1903i 0.690492 1.19597i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ −18.9853 + 32.8835i −1.11678 + 1.93432i
$$290$$ 0 0
$$291$$ −0.121320 0.210133i −0.00711192 0.0123182i
$$292$$ 0 0
$$293$$ −1.75736 −0.102666 −0.0513330 0.998682i $$-0.516347\pi$$
−0.0513330 + 0.998682i $$0.516347\pi$$
$$294$$ 0 0
$$295$$ 28.9706 1.68673
$$296$$ 0 0
$$297$$ 0.414214 + 0.717439i 0.0240351 + 0.0416300i
$$298$$ 0 0
$$299$$ −10.2426 + 17.7408i −0.592347 + 1.02598i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ −5.36396 + 9.29065i −0.308152 + 0.533734i
$$304$$ 0 0
$$305$$ −18.8995 32.7349i −1.08218 1.87439i
$$306$$ 0 0
$$307$$ −11.5147 −0.657180 −0.328590 0.944473i $$-0.606573\pi$$
−0.328590 + 0.944473i $$0.606573\pi$$
$$308$$ 0 0
$$309$$ −14.1421 −0.804518
$$310$$ 0 0
$$311$$ −11.8995 20.6105i −0.674758 1.16872i −0.976539 0.215339i $$-0.930914\pi$$
0.301781 0.953377i $$-0.402419\pi$$
$$312$$ 0 0
$$313$$ −14.3640 + 24.8791i −0.811899 + 1.40625i 0.0996342 + 0.995024i $$0.468233\pi$$
−0.911533 + 0.411226i $$0.865101\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 11.0000 19.0526i 0.617822 1.07010i −0.372061 0.928208i $$-0.621349\pi$$
0.989882 0.141890i $$-0.0453179\pi$$
$$318$$ 0 0
$$319$$ −1.17157 2.02922i −0.0655955 0.113615i
$$320$$ 0 0
$$321$$ −12.8284 −0.716013
$$322$$ 0 0
$$323$$ 50.6274 2.81698
$$324$$ 0 0
$$325$$ 14.1213 + 24.4588i 0.783310 + 1.35673i
$$326$$ 0 0
$$327$$ −1.65685 + 2.86976i −0.0916242 + 0.158698i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −3.65685 + 6.33386i −0.200999 + 0.348140i −0.948851 0.315726i $$-0.897752\pi$$
0.747852 + 0.663866i $$0.231085\pi$$
$$332$$ 0 0
$$333$$ 0.828427 + 1.43488i 0.0453975 + 0.0786308i
$$334$$ 0 0
$$335$$ 38.6274 2.11044
$$336$$ 0 0
$$337$$ 10.3431 0.563427 0.281714 0.959499i $$-0.409097\pi$$
0.281714 + 0.959499i $$0.409097\pi$$
$$338$$ 0 0
$$339$$ −5.00000 8.66025i −0.271563 0.470360i
$$340$$ 0 0
$$341$$ 1.17157 2.02922i 0.0634442 0.109889i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −8.24264 + 14.2767i −0.443769 + 0.768630i
$$346$$ 0 0
$$347$$ 1.24264 + 2.15232i 0.0667084 + 0.115542i 0.897451 0.441115i $$-0.145417\pi$$
−0.830742 + 0.556657i $$0.812084\pi$$
$$348$$ 0 0
$$349$$ 10.5858 0.566644 0.283322 0.959025i $$-0.408563\pi$$
0.283322 + 0.959025i $$0.408563\pi$$
$$350$$ 0 0
$$351$$ 4.24264 0.226455
$$352$$ 0 0
$$353$$ 13.8492 + 23.9876i 0.737121 + 1.27673i 0.953787 + 0.300485i $$0.0971485\pi$$
−0.216666 + 0.976246i $$0.569518\pi$$
$$354$$ 0 0
$$355$$ 17.8995 31.0028i 0.950007 1.64546i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −14.4142 + 24.9662i −0.760753 + 1.31766i 0.181710 + 0.983352i $$0.441837\pi$$
−0.942463 + 0.334311i $$0.891496\pi$$
$$360$$ 0 0
$$361$$ −13.8137 23.9260i −0.727037 1.25927i
$$362$$ 0 0
$$363$$ 10.3137 0.541329
$$364$$ 0 0
$$365$$ 26.4853 1.38630
$$366$$ 0 0
$$367$$ −2.34315 4.05845i −0.122311 0.211849i 0.798368 0.602171i $$-0.205697\pi$$
−0.920679 + 0.390321i $$0.872364\pi$$
$$368$$ 0 0
$$369$$ −5.12132 + 8.87039i −0.266605 + 0.461774i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −2.65685 + 4.60181i −0.137567 + 0.238273i −0.926575 0.376110i $$-0.877261\pi$$
0.789008 + 0.614383i $$0.210595\pi$$
$$374$$ 0 0
$$375$$ 2.82843 + 4.89898i 0.146059 + 0.252982i
$$376$$ 0 0
$$377$$ −12.0000 −0.618031
$$378$$ 0 0
$$379$$ −23.3137 −1.19754 −0.598772 0.800919i $$-0.704345\pi$$
−0.598772 + 0.800919i $$0.704345\pi$$
$$380$$ 0 0
$$381$$ 10.0000 + 17.3205i 0.512316 + 0.887357i
$$382$$ 0 0
$$383$$ 4.48528 7.76874i 0.229187 0.396964i −0.728380 0.685173i $$-0.759727\pi$$
0.957567 + 0.288209i $$0.0930599\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 5.65685 9.79796i 0.287554 0.498058i
$$388$$ 0 0
$$389$$ 17.8995 + 31.0028i 0.907540 + 1.57191i 0.817470 + 0.575971i $$0.195376\pi$$
0.0900701 + 0.995935i $$0.471291\pi$$
$$390$$ 0 0
$$391$$ −35.7990 −1.81043
$$392$$ 0 0
$$393$$ 4.00000 0.201773
$$394$$ 0 0
$$395$$ −23.3137 40.3805i −1.17304 2.03176i
$$396$$ 0 0
$$397$$ 8.12132 14.0665i 0.407597 0.705979i −0.587023 0.809571i $$-0.699700\pi$$
0.994620 + 0.103591i $$0.0330334\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −0.585786 + 1.01461i −0.0292528 + 0.0506673i −0.880281 0.474452i $$-0.842646\pi$$
0.851028 + 0.525120i $$0.175979\pi$$
$$402$$ 0 0
$$403$$ −6.00000 10.3923i −0.298881 0.517678i
$$404$$ 0 0
$$405$$ 3.41421 0.169654
$$406$$ 0 0
$$407$$ −1.37258 −0.0680364
$$408$$ 0 0
$$409$$ 4.12132 + 7.13834i 0.203786 + 0.352968i 0.949745 0.313024i $$-0.101342\pi$$
−0.745959 + 0.665992i $$0.768009\pi$$
$$410$$ 0 0
$$411$$ −4.58579 + 7.94282i −0.226200 + 0.391790i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 6.82843 11.8272i 0.335194 0.580574i
$$416$$ 0 0
$$417$$ −10.4853 18.1610i −0.513466 0.889350i
$$418$$ 0 0
$$419$$ 7.51472 0.367118 0.183559 0.983009i $$-0.441238\pi$$
0.183559 + 0.983009i $$0.441238\pi$$
$$420$$ 0 0
$$421$$ −25.3137 −1.23371 −0.616857 0.787075i $$-0.711594\pi$$
−0.616857 + 0.787075i $$0.711594\pi$$
$$422$$ 0 0
$$423$$ 2.24264 + 3.88437i 0.109041 + 0.188864i
$$424$$ 0 0
$$425$$ −24.6777 + 42.7430i −1.19704 + 2.07334i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −1.75736 + 3.04384i −0.0848461 + 0.146958i
$$430$$ 0 0
$$431$$ 4.07107 + 7.05130i 0.196096 + 0.339649i 0.947259 0.320468i $$-0.103840\pi$$
−0.751163 + 0.660117i $$0.770507\pi$$
$$432$$ 0 0
$$433$$ 0.928932 0.0446416 0.0223208 0.999751i $$-0.492894\pi$$
0.0223208 + 0.999751i $$0.492894\pi$$
$$434$$ 0 0
$$435$$ −9.65685 −0.463011
$$436$$ 0 0
$$437$$ 16.4853 + 28.5533i 0.788598 + 1.36589i
$$438$$ 0 0
$$439$$ −6.34315 + 10.9867i −0.302742 + 0.524364i −0.976756 0.214354i $$-0.931235\pi$$
0.674014 + 0.738718i $$0.264569\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ 5.58579 9.67487i 0.265389 0.459667i −0.702277 0.711904i $$-0.747833\pi$$
0.967665 + 0.252237i $$0.0811664\pi$$
$$444$$ 0 0
$$445$$ −9.82843 17.0233i −0.465912 0.806983i
$$446$$ 0 0
$$447$$ −1.31371 −0.0621363
$$448$$ 0 0
$$449$$ −16.6274 −0.784696 −0.392348 0.919817i $$-0.628337\pi$$
−0.392348 + 0.919817i $$0.628337\pi$$
$$450$$ 0 0
$$451$$ −4.24264 7.34847i −0.199778 0.346026i
$$452$$ 0 0
$$453$$ −4.82843 + 8.36308i −0.226859 + 0.392932i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 12.3137 21.3280i 0.576011 0.997680i −0.419920 0.907561i $$-0.637942\pi$$
0.995931 0.0901192i $$-0.0287248\pi$$
$$458$$ 0 0
$$459$$ 3.70711 + 6.42090i 0.173033 + 0.299702i
$$460$$ 0 0
$$461$$ 16.3848 0.763115 0.381558 0.924345i $$-0.375388\pi$$
0.381558 + 0.924345i $$0.375388\pi$$
$$462$$ 0 0
$$463$$ 1.65685 0.0770005 0.0385003 0.999259i $$-0.487742\pi$$
0.0385003 + 0.999259i $$0.487742\pi$$
$$464$$ 0 0
$$465$$ −4.82843 8.36308i −0.223913 0.387829i
$$466$$ 0 0
$$467$$ 9.41421 16.3059i 0.435638 0.754547i −0.561710 0.827334i $$-0.689856\pi$$
0.997347 + 0.0727876i $$0.0231895\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0.121320 0.210133i 0.00559015 0.00968242i
$$472$$ 0 0
$$473$$ 4.68629 + 8.11689i 0.215476 + 0.373215i
$$474$$ 0 0
$$475$$ 45.4558 2.08566
$$476$$ 0 0
$$477$$ −2.00000 −0.0915737
$$478$$ 0 0
$$479$$ −11.4142 19.7700i −0.521529 0.903314i −0.999686 0.0250403i $$-0.992029\pi$$
0.478158 0.878274i $$-0.341305\pi$$
$$480$$ 0 0
$$481$$ −3.51472 + 6.08767i −0.160257 + 0.277574i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 0.414214 0.717439i 0.0188085 0.0325772i
$$486$$ 0 0
$$487$$ −2.48528 4.30463i −0.112619 0.195062i 0.804207 0.594350i $$-0.202591\pi$$
−0.916825 + 0.399288i $$0.869257\pi$$
$$488$$ 0 0
$$489$$ −5.65685 −0.255812
$$490$$ 0 0
$$491$$ 19.1716 0.865201 0.432600 0.901586i $$-0.357596\pi$$
0.432600 + 0.901586i $$0.357596\pi$$
$$492$$ 0 0
$$493$$ −10.4853 18.1610i −0.472233 0.817932i
$$494$$ 0 0
$$495$$ −1.41421 + 2.44949i −0.0635642 + 0.110096i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 12.4853 21.6251i 0.558918 0.968074i −0.438669 0.898649i $$-0.644550\pi$$
0.997587 0.0694257i $$-0.0221167\pi$$
$$500$$ 0 0
$$501$$ −7.41421 12.8418i −0.331243 0.573729i
$$502$$ 0 0
$$503$$ −19.3137 −0.861156 −0.430578 0.902553i $$-0.641690\pi$$
−0.430578 + 0.902553i $$0.641690\pi$$
$$504$$ 0 0
$$505$$ −36.6274 −1.62990
$$506$$ 0 0
$$507$$ 2.50000 + 4.33013i 0.111029 + 0.192308i
$$508$$ 0 0
$$509$$ 18.1924 31.5101i 0.806363 1.39666i −0.109003 0.994041i $$-0.534766\pi$$
0.915367 0.402621i $$-0.131901\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 3.41421 5.91359i 0.150741 0.261091i
$$514$$ 0 0
$$515$$ −24.1421 41.8154i −1.06383 1.84261i
$$516$$ 0 0
$$517$$ −3.71573 −0.163418
$$518$$ 0 0
$$519$$ 16.5858 0.728035
$$520$$ 0 0
$$521$$ −7.12132 12.3345i −0.311991 0.540384i 0.666803 0.745234i $$-0.267662\pi$$
−0.978793 + 0.204851i $$0.934329\pi$$
$$522$$ 0 0
$$523$$ 2.48528 4.30463i 0.108674 0.188228i −0.806559 0.591153i $$-0.798673\pi$$
0.915233 + 0.402924i $$0.132006\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 10.4853 18.1610i 0.456746 0.791107i
$$528$$ 0 0
$$529$$ −0.156854 0.271680i −0.00681975 0.0118122i
$$530$$ 0 0
$$531$$ 8.48528 0.368230
$$532$$ 0 0
$$533$$ −43.4558 −1.88228
$$534$$ 0 0
$$535$$ −21.8995 37.9310i −0.946798 1.63990i
$$536$$ 0 0
$$537$$ −3.24264 + 5.61642i −0.139930 + 0.242366i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 9.00000 15.5885i 0.386940 0.670200i −0.605096 0.796152i $$-0.706865\pi$$
0.992036 + 0.125952i $$0.0401986\pi$$
$$542$$ 0 0
$$543$$ −3.53553 6.12372i −0.151724 0.262794i
$$544$$ 0 0
$$545$$ −11.3137 −0.484626
$$546$$ 0 0
$$547$$ −3.02944 −0.129529 −0.0647647 0.997901i $$-0.520630\pi$$
−0.0647647 + 0.997901i $$0.520630\pi$$
$$548$$ 0 0
$$549$$ −5.53553 9.58783i −0.236251 0.409198i
$$550$$ 0 0
$$551$$ −9.65685 + 16.7262i −0.411396 + 0.712558i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −2.82843 + 4.89898i −0.120060 + 0.207950i
$$556$$ 0 0
$$557$$ −16.3137 28.2562i −0.691234 1.19725i −0.971434 0.237311i $$-0.923734\pi$$
0.280200 0.959942i $$-0.409599\pi$$
$$558$$ 0 0
$$559$$ 48.0000 2.03018
$$560$$ 0 0
$$561$$ −6.14214 −0.259321
$$562$$ 0 0
$$563$$ −0.928932 1.60896i −0.0391498 0.0678095i 0.845787 0.533521i $$-0.179132\pi$$
−0.884936 + 0.465712i $$0.845798\pi$$
$$564$$ 0 0
$$565$$ 17.0711 29.5680i 0.718185 1.24393i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 2.92893 5.07306i 0.122787 0.212674i −0.798079 0.602553i $$-0.794150\pi$$
0.920866 + 0.389880i $$0.127483\pi$$
$$570$$ 0 0
$$571$$ 20.8284 + 36.0759i 0.871643 + 1.50973i 0.860297 + 0.509794i $$0.170278\pi$$
0.0113458 + 0.999936i $$0.496388\pi$$
$$572$$ 0 0
$$573$$ −12.1421 −0.507245
$$574$$ 0 0
$$575$$ −32.1421 −1.34042
$$576$$ 0 0
$$577$$ −6.60660 11.4430i −0.275036 0.476377i 0.695108 0.718905i $$-0.255357\pi$$
−0.970144 + 0.242528i $$0.922023\pi$$
$$578$$ 0 0
$$579$$ 1.00000 1.73205i 0.0415586 0.0719816i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0.828427 1.43488i 0.0343099 0.0594266i
$$584$$ 0 0
$$585$$ 7.24264 + 12.5446i 0.299446 + 0.518656i
$$586$$ 0 0
$$587$$ −35.7990 −1.47758 −0.738791 0.673934i $$-0.764603\pi$$
−0.738791 + 0.673934i $$0.764603\pi$$
$$588$$ 0 0
$$589$$ −19.3137 −0.795807
$$590$$ 0 0
$$591$$ −1.34315 2.32640i −0.0552496 0.0956952i
$$592$$ 0 0
$$593$$ −23.7071 + 41.0619i −0.973534 + 1.68621i −0.288844 + 0.957376i $$0.593271\pi$$
−0.684690 + 0.728835i $$0.740062\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ −2.82843 + 4.89898i −0.115760 + 0.200502i
$$598$$ 0 0
$$599$$ −11.7279 20.3134i −0.479190 0.829981i 0.520525 0.853846i $$-0.325736\pi$$
−0.999715 + 0.0238650i $$0.992403\pi$$
$$600$$ 0 0
$$601$$ −12.2426 −0.499388 −0.249694 0.968325i $$-0.580330\pi$$
−0.249694 + 0.968325i $$0.580330\pi$$
$$602$$ 0 0
$$603$$ 11.3137 0.460730
$$604$$ 0 0
$$605$$ 17.6066 + 30.4955i 0.715810 + 1.23982i
$$606$$ 0 0
$$607$$ −12.4853 + 21.6251i −0.506762 + 0.877737i 0.493207 + 0.869912i $$0.335824\pi$$
−0.999969 + 0.00782569i $$0.997509\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −9.51472 + 16.4800i −0.384924 + 0.666708i
$$612$$ 0 0
$$613$$ 5.17157 + 8.95743i 0.208878 + 0.361787i 0.951361 0.308077i $$-0.0996856\pi$$
−0.742483 + 0.669864i $$0.766352\pi$$
$$614$$ 0 0
$$615$$ −34.9706 −1.41015
$$616$$ 0 0
$$617$$ −4.48528 −0.180571 −0.0902853 0.995916i $$-0.528778\pi$$
−0.0902853 + 0.995916i $$0.528778\pi$$
$$618$$ 0 0
$$619$$ −16.8284 29.1477i −0.676392 1.17154i −0.976060 0.217501i $$-0.930209\pi$$
0.299668 0.954043i $$-0.403124\pi$$
$$620$$ 0 0
$$621$$ −2.41421 + 4.18154i −0.0968791 + 0.167799i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 6.98528 12.0989i 0.279411 0.483954i
$$626$$ 0 0
$$627$$ 2.82843 + 4.89898i 0.112956 + 0.195646i
$$628$$ 0 0
$$629$$ −12.2843 −0.489806
$$630$$ 0 0
$$631$$ −3.02944 −0.120600 −0.0603000 0.998180i $$-0.519206\pi$$
−0.0603000 + 0.998180i $$0.519206\pi$$
$$632$$ 0 0
$$633$$ 0.828427 + 1.43488i 0.0329270 + 0.0570313i
$$634$$ 0 0
$$635$$ −34.1421 + 59.1359i −1.35489 + 2.34674i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 5.24264 9.08052i 0.207396 0.359220i
$$640$$ 0 0
$$641$$ −17.5563 30.4085i −0.693434 1.20106i −0.970706 0.240272i $$-0.922764\pi$$
0.277272 0.960792i $$-0.410570\pi$$
$$642$$ 0 0
$$643$$ 31.7990 1.25403 0.627015 0.779007i $$-0.284277\pi$$
0.627015 + 0.779007i $$0.284277\pi$$
$$644$$ 0 0
$$645$$ 38.6274 1.52095
$$646$$ 0 0
$$647$$ 0.100505 + 0.174080i 0.00395126 + 0.00684379i 0.867994 0.496574i $$-0.165409\pi$$
−0.864043 + 0.503418i $$0.832076\pi$$
$$648$$ 0 0
$$649$$ −3.51472 + 6.08767i −0.137965 + 0.238962i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ −23.0711 + 39.9603i −0.902841 + 1.56377i −0.0790508 + 0.996871i $$0.525189\pi$$
−0.823790 + 0.566895i $$0.808144\pi$$
$$654$$ 0 0
$$655$$ 6.82843 + 11.8272i 0.266809 + 0.462126i
$$656$$ 0 0
$$657$$ 7.75736 0.302643
$$658$$ 0 0
$$659$$ 21.5147 0.838094 0.419047 0.907964i $$-0.362364\pi$$
0.419047 + 0.907964i $$0.362364\pi$$
$$660$$ 0 0
$$661$$ −2.46447 4.26858i −0.0958566 0.166029i 0.814109 0.580712i $$-0.197226\pi$$
−0.909966 + 0.414683i $$0.863892\pi$$
$$662$$ 0 0
$$663$$ −15.7279 + 27.2416i −0.610822 + 1.05797i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 6.82843 11.8272i 0.264398 0.457950i
$$668$$ 0 0
$$669$$ 6.82843 + 11.8272i 0.264002 + 0.457265i
$$670$$ 0 0
$$671$$ 9.17157 0.354065
$$672$$ 0 0
$$673$$ −23.3137 −0.898677 −0.449339 0.893361i $$-0.648340\pi$$
−0.449339 + 0.893361i $$0.648340\pi$$
$$674$$ 0 0
$$675$$ 3.32843 + 5.76500i 0.128111 + 0.221895i
$$676$$ 0 0
$$677$$ −13.8492 + 23.9876i −0.532270 + 0.921918i 0.467021 + 0.884246i $$0.345327\pi$$
−0.999290 + 0.0376716i $$0.988006\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −2.58579 + 4.47871i −0.0990876 + 0.171625i
$$682$$ 0 0
$$683$$ 0.899495 + 1.55797i 0.0344182 + 0.0596141i 0.882721 0.469897i $$-0.155709\pi$$
−0.848303 + 0.529511i $$0.822376\pi$$
$$684$$ 0 0
$$685$$ −31.3137 −1.19644
$$686$$ 0 0
$$687$$ 25.4142 0.969613
$$688$$ 0 0
$$689$$ −4.24264 7.34847i −0.161632 0.279954i
$$690$$ 0 0
$$691$$ −4.34315 + 7.52255i −0.165221 + 0.286171i −0.936734 0.350043i $$-0.886167\pi$$
0.771513 + 0.636214i $$0.219500\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 35.7990 62.0057i 1.35793 2.35201i
$$696$$ 0 0
$$697$$ −37.9706 65.7669i −1.43824 2.49110i
$$698$$ 0 0
$$699$$ 14.8284 0.560863
$$700$$ 0 0
$$701$$ −6.14214 −0.231985 −0.115993 0.993250i $$-0.537005\pi$$
−0.115993 + 0.993250i $$0.537005\pi$$
$$702$$ 0 0
$$703$$ 5.65685 + 9.79796i 0.213352 + 0.369537i
$$704$$ 0 0
$$705$$ −7.65685 + 13.2621i −0.288374 + 0.499478i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −3.31371 + 5.73951i −0.124449 + 0.215552i −0.921517 0.388337i $$-0.873050\pi$$
0.797068 + 0.603889i $$0.206383\pi$$
$$710$$ 0 0
$$711$$ −6.82843 11.8272i −0.256086 0.443554i
$$712$$ 0 0
$$713$$ 13.6569 0.511453
$$714$$ 0 0
$$715$$ −12.0000 −0.448775
$$716$$ 0 0
$$717$$ −6.41421 11.1097i −0.239543 0.414901i
$$718$$ 0 0
$$719$$ 3.31371 5.73951i 0.123580 0.214048i −0.797597 0.603191i $$-0.793896\pi$$
0.921177 + 0.389143i $$0.127229\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 6.94975 12.0373i 0.258464 0.447673i
$$724$$ 0 0
$$725$$ −9.41421 16.3059i −0.349635 0.605586i
$$726$$ 0 0
$$727$$ −9.85786 −0.365608 −0.182804 0.983149i $$-0.558517\pi$$
−0.182804 + 0.983149i $$0.558517\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 0 0
$$731$$ 41.9411 + 72.6442i 1.55125 + 2.68684i
$$732$$ 0 0
$$733$$ 4.02082 6.96426i 0.148512 0.257231i −0.782166 0.623071i $$-0.785885\pi$$
0.930678 + 0.365840i $$0.119218\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −4.68629 + 8.11689i −0.172622 + 0.298990i
$$738$$ 0 0
$$739$$ −16.4853 28.5533i −0.606421 1.05035i −0.991825 0.127604i $$-0.959271\pi$$
0.385404 0.922748i $$-0.374062\pi$$
$$740$$ 0 0
$$741$$ 28.9706 1.06426
$$742$$ 0 0
$$743$$ −4.82843 −0.177138 −0.0885689 0.996070i $$-0.528229\pi$$
−0.0885689 + 0.996070i $$0.528229\pi$$
$$744$$ 0 0
$$745$$ −2.24264 3.88437i −0.0821640 0.142312i
$$746$$ 0 0
$$747$$ 2.00000 3.46410i 0.0731762 0.126745i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ −10.1421 + 17.5667i −0.370092 + 0.641018i −0.989579 0.143989i $$-0.954007\pi$$
0.619488 + 0.785006i $$0.287340\pi$$
$$752$$ 0 0
$$753$$ −3.07107 5.31925i −0.111916 0.193844i
$$754$$ 0 0
$$755$$ −32.9706 −1.19992
$$756$$ 0 0
$$757$$ 41.9411 1.52438 0.762188 0.647356i $$-0.224125\pi$$
0.762188 + 0.647356i $$0.224125\pi$$
$$758$$ 0 0
$$759$$ −2.00000 3.46410i −0.0725954 0.125739i
$$760$$ 0 0
$$761$$ 15.9497 27.6258i 0.578178 1.00143i −0.417510 0.908672i $$-0.637097\pi$$
0.995688 0.0927614i $$-0.0295694\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −12.6569 + 21.9223i −0.457610 + 0.792603i
$$766$$ 0 0
$$767$$ 18.0000 + 31.1769i 0.649942 + 1.12573i
$$768$$ 0 0
$$769$$ 34.8701 1.25745 0.628723 0.777629i $$-0.283578\pi$$
0.628723 + 0.777629i $$0.283578\pi$$
$$770$$ 0 0
$$771$$ 3.41421 0.122960
$$772$$ 0 0
$$773$$ −16.6777 28.8866i −0.599854 1.03898i −0.992842 0.119434i $$-0.961892\pi$$
0.392988 0.919544i $$-0.371441\pi$$
$$774$$ 0 0
$$775$$ 9.41421 16.3059i 0.338169 0.585725i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −34.9706 + 60.5708i −1.25295 + 2.17017i
$$780$$ 0 0
$$781$$ 4.34315 + 7.52255i 0.155410 + 0.269178i
$$782$$ 0 0
$$783$$ −2.82843 −0.101080
$$784$$ 0 0
$$785$$ 0.828427 0.0295678
$$786$$ 0 0
$$787$$ −7.65685 13.2621i −0.272937 0.472741i 0.696675 0.717387i $$-0.254662\pi$$
−0.969613 + 0.244645i $$0.921329\pi$$
$$788$$ 0 0
$$789$$ −10.0711 + 17.4436i −0.358540 + 0.621009i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 23.4853 40.6777i 0.833987 1.44451i
$$794$$ 0 0
$$795$$ −3.41421 5.91359i −0.121090 0.209733i
$$796$$ 0 0
$$797$$ −39.4142 −1.39612 −0.698062 0.716038i $$-0.745954\pi$$
−0.698062 + 0.716038i $$0.745954\pi$$
$$798$$ 0 0
$$799$$ −33.2548 −1.17647