# Properties

 Label 1134.2.d.a.1133.11 Level $1134$ Weight $2$ Character 1134.1133 Analytic conductor $9.055$ Analytic rank $0$ Dimension $16$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.d (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$9.05503558921$$ Analytic rank: $$0$$ Dimension: $$16$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 6 x^{14} + 9 x^{12} + 54 x^{10} - 288 x^{8} + 486 x^{6} + 729 x^{4} - 4374 x^{2} + 6561$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{8}\cdot 3^{6}$$ Twist minimal: no (minimal twist has level 126) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 1133.11 Root $$1.69547 + 0.354107i$$ of defining polynomial Character $$\chi$$ $$=$$ 1134.1133 Dual form 1134.2.d.a.1133.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000i q^{2} -1.00000 q^{4} -1.79035 q^{5} +(2.28052 + 1.34136i) q^{7} -1.00000i q^{8} +O(q^{10})$$ $$q+1.00000i q^{2} -1.00000 q^{4} -1.79035 q^{5} +(2.28052 + 1.34136i) q^{7} -1.00000i q^{8} -1.79035i q^{10} -2.40150i q^{11} -4.89133i q^{13} +(-1.34136 + 2.28052i) q^{14} +1.00000 q^{16} -3.66466 q^{17} +3.01701i q^{19} +1.79035 q^{20} +2.40150 q^{22} -3.76638i q^{23} -1.79465 q^{25} +4.89133 q^{26} +(-2.28052 - 1.34136i) q^{28} -6.56103i q^{29} -4.64661i q^{31} +1.00000i q^{32} -3.66466i q^{34} +(-4.08292 - 2.40150i) q^{35} +9.36404 q^{37} -3.01701 q^{38} +1.79035i q^{40} -8.08188 q^{41} +6.96254 q^{43} +2.40150i q^{44} +3.76638 q^{46} +5.13604 q^{47} +(3.40150 + 6.11799i) q^{49} -1.79465i q^{50} +4.89133i q^{52} +4.29953i q^{55} +(1.34136 - 2.28052i) q^{56} +6.56103 q^{58} +14.5900 q^{59} -11.3283i q^{61} +4.64661 q^{62} -1.00000 q^{64} +8.75718i q^{65} +0.570231 q^{67} +3.66466 q^{68} +(2.40150 - 4.08292i) q^{70} -5.96254i q^{71} -12.3814i q^{73} +9.36404i q^{74} -3.01701i q^{76} +(3.22128 - 5.47667i) q^{77} +3.03663 q^{79} -1.79035 q^{80} -8.08188i q^{82} -14.0054 q^{83} +6.56103 q^{85} +6.96254i q^{86} -2.40150 q^{88} +3.74863 q^{89} +(6.56103 - 11.1547i) q^{91} +3.76638i q^{92} +5.13604i q^{94} -5.40150i q^{95} -5.51087i q^{97} +(-6.11799 + 3.40150i) q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16 q - 16 q^{4} - 4 q^{7} + O(q^{10})$$ $$16 q - 16 q^{4} - 4 q^{7} + 16 q^{16} + 16 q^{25} + 4 q^{28} - 8 q^{37} - 8 q^{43} + 24 q^{46} + 16 q^{49} + 24 q^{58} - 16 q^{64} + 56 q^{67} + 8 q^{79} + 24 q^{85} + 24 q^{91} + O(q^{100})$$

## Character values

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

 $$n$$ $$325$$ $$407$$ $$\chi(n)$$ $$-1$$ $$-1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000i 0.707107i
$$3$$ 0 0
$$4$$ −1.00000 −0.500000
$$5$$ −1.79035 −0.800669 −0.400334 0.916369i $$-0.631106\pi$$
−0.400334 + 0.916369i $$0.631106\pi$$
$$6$$ 0 0
$$7$$ 2.28052 + 1.34136i 0.861954 + 0.506987i
$$8$$ 1.00000i 0.353553i
$$9$$ 0 0
$$10$$ 1.79035i 0.566158i
$$11$$ 2.40150i 0.724081i −0.932162 0.362040i $$-0.882080\pi$$
0.932162 0.362040i $$-0.117920\pi$$
$$12$$ 0 0
$$13$$ 4.89133i 1.35661i −0.734781 0.678305i $$-0.762715\pi$$
0.734781 0.678305i $$-0.237285\pi$$
$$14$$ −1.34136 + 2.28052i −0.358494 + 0.609493i
$$15$$ 0 0
$$16$$ 1.00000 0.250000
$$17$$ −3.66466 −0.888812 −0.444406 0.895826i $$-0.646585\pi$$
−0.444406 + 0.895826i $$0.646585\pi$$
$$18$$ 0 0
$$19$$ 3.01701i 0.692150i 0.938207 + 0.346075i $$0.112486\pi$$
−0.938207 + 0.346075i $$0.887514\pi$$
$$20$$ 1.79035 0.400334
$$21$$ 0 0
$$22$$ 2.40150 0.512002
$$23$$ 3.76638i 0.785345i −0.919678 0.392673i $$-0.871551\pi$$
0.919678 0.392673i $$-0.128449\pi$$
$$24$$ 0 0
$$25$$ −1.79465 −0.358930
$$26$$ 4.89133 0.959268
$$27$$ 0 0
$$28$$ −2.28052 1.34136i −0.430977 0.253493i
$$29$$ 6.56103i 1.21835i −0.793035 0.609176i $$-0.791500\pi$$
0.793035 0.609176i $$-0.208500\pi$$
$$30$$ 0 0
$$31$$ 4.64661i 0.834556i −0.908779 0.417278i $$-0.862984\pi$$
0.908779 0.417278i $$-0.137016\pi$$
$$32$$ 1.00000i 0.176777i
$$33$$ 0 0
$$34$$ 3.66466i 0.628485i
$$35$$ −4.08292 2.40150i −0.690140 0.405928i
$$36$$ 0 0
$$37$$ 9.36404 1.53944 0.769719 0.638382i $$-0.220396\pi$$
0.769719 + 0.638382i $$0.220396\pi$$
$$38$$ −3.01701 −0.489424
$$39$$ 0 0
$$40$$ 1.79035i 0.283079i
$$41$$ −8.08188 −1.26218 −0.631088 0.775711i $$-0.717392\pi$$
−0.631088 + 0.775711i $$0.717392\pi$$
$$42$$ 0 0
$$43$$ 6.96254 1.06178 0.530888 0.847442i $$-0.321858\pi$$
0.530888 + 0.847442i $$0.321858\pi$$
$$44$$ 2.40150i 0.362040i
$$45$$ 0 0
$$46$$ 3.76638 0.555323
$$47$$ 5.13604 0.749169 0.374584 0.927193i $$-0.377785\pi$$
0.374584 + 0.927193i $$0.377785\pi$$
$$48$$ 0 0
$$49$$ 3.40150 + 6.11799i 0.485929 + 0.873998i
$$50$$ 1.79465i 0.253802i
$$51$$ 0 0
$$52$$ 4.89133i 0.678305i
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 4.29953i 0.579749i
$$56$$ 1.34136 2.28052i 0.179247 0.304747i
$$57$$ 0 0
$$58$$ 6.56103 0.861506
$$59$$ 14.5900 1.89946 0.949729 0.313073i $$-0.101359\pi$$
0.949729 + 0.313073i $$0.101359\pi$$
$$60$$ 0 0
$$61$$ 11.3283i 1.45044i −0.688518 0.725219i $$-0.741738\pi$$
0.688518 0.725219i $$-0.258262\pi$$
$$62$$ 4.64661 0.590120
$$63$$ 0 0
$$64$$ −1.00000 −0.125000
$$65$$ 8.75718i 1.08619i
$$66$$ 0 0
$$67$$ 0.570231 0.0696648 0.0348324 0.999393i $$-0.488910\pi$$
0.0348324 + 0.999393i $$0.488910\pi$$
$$68$$ 3.66466 0.444406
$$69$$ 0 0
$$70$$ 2.40150 4.08292i 0.287035 0.488002i
$$71$$ 5.96254i 0.707623i −0.935317 0.353811i $$-0.884885\pi$$
0.935317 0.353811i $$-0.115115\pi$$
$$72$$ 0 0
$$73$$ 12.3814i 1.44913i −0.689204 0.724567i $$-0.742040\pi$$
0.689204 0.724567i $$-0.257960\pi$$
$$74$$ 9.36404i 1.08855i
$$75$$ 0 0
$$76$$ 3.01701i 0.346075i
$$77$$ 3.22128 5.47667i 0.367099 0.624124i
$$78$$ 0 0
$$79$$ 3.03663 0.341647 0.170824 0.985302i $$-0.445357\pi$$
0.170824 + 0.985302i $$0.445357\pi$$
$$80$$ −1.79035 −0.200167
$$81$$ 0 0
$$82$$ 8.08188i 0.892494i
$$83$$ −14.0054 −1.53729 −0.768646 0.639674i $$-0.779069\pi$$
−0.768646 + 0.639674i $$0.779069\pi$$
$$84$$ 0 0
$$85$$ 6.56103 0.711644
$$86$$ 6.96254i 0.750790i
$$87$$ 0 0
$$88$$ −2.40150 −0.256001
$$89$$ 3.74863 0.397354 0.198677 0.980065i $$-0.436336\pi$$
0.198677 + 0.980065i $$0.436336\pi$$
$$90$$ 0 0
$$91$$ 6.56103 11.1547i 0.687783 1.16934i
$$92$$ 3.76638i 0.392673i
$$93$$ 0 0
$$94$$ 5.13604i 0.529742i
$$95$$ 5.40150i 0.554183i
$$96$$ 0 0
$$97$$ 5.51087i 0.559545i −0.960066 0.279772i $$-0.909741\pi$$
0.960066 0.279772i $$-0.0902590\pi$$
$$98$$ −6.11799 + 3.40150i −0.618010 + 0.343604i
$$99$$ 0 0
$$100$$ 1.79465 0.179465
$$101$$ −0.250324 −0.0249082 −0.0124541 0.999922i $$-0.503964\pi$$
−0.0124541 + 0.999922i $$0.503964\pi$$
$$102$$ 0 0
$$103$$ 0.167931i 0.0165468i 0.999966 + 0.00827339i $$0.00263353\pi$$
−0.999966 + 0.00827339i $$0.997366\pi$$
$$104$$ −4.89133 −0.479634
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 7.99080i 0.772500i 0.922394 + 0.386250i $$0.126230\pi$$
−0.922394 + 0.386250i $$0.873770\pi$$
$$108$$ 0 0
$$109$$ −18.9533 −1.81540 −0.907700 0.419619i $$-0.862164\pi$$
−0.907700 + 0.419619i $$0.862164\pi$$
$$110$$ −4.29953 −0.409944
$$111$$ 0 0
$$112$$ 2.28052 + 1.34136i 0.215488 + 0.126747i
$$113$$ 1.15953i 0.109079i 0.998512 + 0.0545396i $$0.0173691\pi$$
−0.998512 + 0.0545396i $$0.982631\pi$$
$$114$$ 0 0
$$115$$ 6.74314i 0.628801i
$$116$$ 6.56103i 0.609176i
$$117$$ 0 0
$$118$$ 14.5900i 1.34312i
$$119$$ −8.35733 4.91564i −0.766115 0.450616i
$$120$$ 0 0
$$121$$ 5.23278 0.475707
$$122$$ 11.3283 1.02561
$$123$$ 0 0
$$124$$ 4.64661i 0.417278i
$$125$$ 12.1648 1.08805
$$126$$ 0 0
$$127$$ 1.40150 0.124363 0.0621817 0.998065i $$-0.480194\pi$$
0.0621817 + 0.998065i $$0.480194\pi$$
$$128$$ 1.00000i 0.0883883i
$$129$$ 0 0
$$130$$ −8.75718 −0.768056
$$131$$ −10.4918 −0.916671 −0.458335 0.888779i $$-0.651554\pi$$
−0.458335 + 0.888779i $$0.651554\pi$$
$$132$$ 0 0
$$133$$ −4.04690 + 6.88034i −0.350911 + 0.596601i
$$134$$ 0.570231i 0.0492604i
$$135$$ 0 0
$$136$$ 3.66466i 0.314242i
$$137$$ 4.72056i 0.403305i −0.979457 0.201652i $$-0.935369\pi$$
0.979457 0.201652i $$-0.0646311\pi$$
$$138$$ 0 0
$$139$$ 2.36375i 0.200491i −0.994963 0.100245i $$-0.968037\pi$$
0.994963 0.100245i $$-0.0319628\pi$$
$$140$$ 4.08292 + 2.40150i 0.345070 + 0.202964i
$$141$$ 0 0
$$142$$ 5.96254 0.500365
$$143$$ −11.7465 −0.982295
$$144$$ 0 0
$$145$$ 11.7465i 0.975497i
$$146$$ 12.3814 1.02469
$$147$$ 0 0
$$148$$ −9.36404 −0.769719
$$149$$ 17.3640i 1.42252i 0.702930 + 0.711259i $$0.251875\pi$$
−0.702930 + 0.711259i $$0.748125\pi$$
$$150$$ 0 0
$$151$$ −11.2328 −0.914110 −0.457055 0.889438i $$-0.651096\pi$$
−0.457055 + 0.889438i $$0.651096\pi$$
$$152$$ 3.01701 0.244712
$$153$$ 0 0
$$154$$ 5.47667 + 3.22128i 0.441322 + 0.259578i
$$155$$ 8.31905i 0.668203i
$$156$$ 0 0
$$157$$ 13.8431i 1.10480i 0.833580 + 0.552399i $$0.186287\pi$$
−0.833580 + 0.552399i $$0.813713\pi$$
$$158$$ 3.03663i 0.241581i
$$159$$ 0 0
$$160$$ 1.79035i 0.141540i
$$161$$ 5.05208 8.58930i 0.398159 0.676931i
$$162$$ 0 0
$$163$$ −4.33577 −0.339604 −0.169802 0.985478i $$-0.554313\pi$$
−0.169802 + 0.985478i $$0.554313\pi$$
$$164$$ 8.08188 0.631088
$$165$$ 0 0
$$166$$ 14.0054i 1.08703i
$$167$$ −12.4151 −0.960711 −0.480355 0.877074i $$-0.659492\pi$$
−0.480355 + 0.877074i $$0.659492\pi$$
$$168$$ 0 0
$$169$$ −10.9251 −0.840390
$$170$$ 6.56103i 0.503208i
$$171$$ 0 0
$$172$$ −6.96254 −0.530888
$$173$$ 17.4182 1.32428 0.662139 0.749381i $$-0.269649\pi$$
0.662139 + 0.749381i $$0.269649\pi$$
$$174$$ 0 0
$$175$$ −4.09272 2.40727i −0.309381 0.181973i
$$176$$ 2.40150i 0.181020i
$$177$$ 0 0
$$178$$ 3.74863i 0.280972i
$$179$$ 13.1221i 0.980789i −0.871501 0.490395i $$-0.836853\pi$$
0.871501 0.490395i $$-0.163147\pi$$
$$180$$ 0 0
$$181$$ 13.3577i 0.992873i 0.868073 + 0.496437i $$0.165359\pi$$
−0.868073 + 0.496437i $$0.834641\pi$$
$$182$$ 11.1547 + 6.56103i 0.826845 + 0.486336i
$$183$$ 0 0
$$184$$ −3.76638 −0.277661
$$185$$ −16.7649 −1.23258
$$186$$ 0 0
$$187$$ 8.80071i 0.643572i
$$188$$ −5.13604 −0.374584
$$189$$ 0 0
$$190$$ 5.40150 0.391866
$$191$$ 9.25333i 0.669547i −0.942299 0.334774i $$-0.891340\pi$$
0.942299 0.334774i $$-0.108660\pi$$
$$192$$ 0 0
$$193$$ −24.5602 −1.76788 −0.883941 0.467599i $$-0.845119\pi$$
−0.883941 + 0.467599i $$0.845119\pi$$
$$194$$ 5.51087 0.395658
$$195$$ 0 0
$$196$$ −3.40150 6.11799i −0.242965 0.436999i
$$197$$ 12.4861i 0.889598i 0.895630 + 0.444799i $$0.146725\pi$$
−0.895630 + 0.444799i $$0.853275\pi$$
$$198$$ 0 0
$$199$$ 0.179145i 0.0126993i 0.999980 + 0.00634964i $$0.00202117\pi$$
−0.999980 + 0.00634964i $$0.997979\pi$$
$$200$$ 1.79465i 0.126901i
$$201$$ 0 0
$$202$$ 0.250324i 0.0176127i
$$203$$ 8.80071 14.9625i 0.617689 1.05016i
$$204$$ 0 0
$$205$$ 14.4694 1.01059
$$206$$ −0.167931 −0.0117003
$$207$$ 0 0
$$208$$ 4.89133i 0.339152i
$$209$$ 7.24536 0.501172
$$210$$ 0 0
$$211$$ −15.1221 −1.04105 −0.520523 0.853848i $$-0.674263\pi$$
−0.520523 + 0.853848i $$0.674263\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ −7.99080 −0.546240
$$215$$ −12.4654 −0.850131
$$216$$ 0 0
$$217$$ 6.23278 10.5967i 0.423109 0.719348i
$$218$$ 18.9533i 1.28368i
$$219$$ 0 0
$$220$$ 4.29953i 0.289874i
$$221$$ 17.9251i 1.20577i
$$222$$ 0 0
$$223$$ 8.39524i 0.562187i 0.959680 + 0.281093i $$0.0906971\pi$$
−0.959680 + 0.281093i $$0.909303\pi$$
$$224$$ −1.34136 + 2.28052i −0.0896234 + 0.152373i
$$225$$ 0 0
$$226$$ −1.15953 −0.0771306
$$227$$ 2.42522 0.160967 0.0804836 0.996756i $$-0.474354\pi$$
0.0804836 + 0.996756i $$0.474354\pi$$
$$228$$ 0 0
$$229$$ 2.01975i 0.133469i 0.997771 + 0.0667344i $$0.0212580\pi$$
−0.997771 + 0.0667344i $$0.978742\pi$$
$$230$$ −6.74314 −0.444630
$$231$$ 0 0
$$232$$ −6.56103 −0.430753
$$233$$ 12.7289i 0.833899i −0.908930 0.416950i $$-0.863099\pi$$
0.908930 0.416950i $$-0.136901\pi$$
$$234$$ 0 0
$$235$$ −9.19531 −0.599836
$$236$$ −14.5900 −0.949729
$$237$$ 0 0
$$238$$ 4.91564 8.35733i 0.318633 0.541725i
$$239$$ 17.4495i 1.12871i −0.825531 0.564356i $$-0.809124\pi$$
0.825531 0.564356i $$-0.190876\pi$$
$$240$$ 0 0
$$241$$ 11.4332i 0.736476i −0.929732 0.368238i $$-0.879961\pi$$
0.929732 0.368238i $$-0.120039\pi$$
$$242$$ 5.23278i 0.336376i
$$243$$ 0 0
$$244$$ 11.3283i 0.725219i
$$245$$ −6.08988 10.9533i −0.389068 0.699783i
$$246$$ 0 0
$$247$$ 14.7572 0.938977
$$248$$ −4.64661 −0.295060
$$249$$ 0 0
$$250$$ 12.1648i 0.769369i
$$251$$ 27.3560 1.72669 0.863347 0.504611i $$-0.168364\pi$$
0.863347 + 0.504611i $$0.168364\pi$$
$$252$$ 0 0
$$253$$ −9.04499 −0.568653
$$254$$ 1.40150i 0.0879382i
$$255$$ 0 0
$$256$$ 1.00000 0.0625000
$$257$$ 3.49673 0.218120 0.109060 0.994035i $$-0.465216\pi$$
0.109060 + 0.994035i $$0.465216\pi$$
$$258$$ 0 0
$$259$$ 21.3548 + 12.5606i 1.32693 + 0.780475i
$$260$$ 8.75718i 0.543097i
$$261$$ 0 0
$$262$$ 10.4918i 0.648184i
$$263$$ 9.64348i 0.594643i −0.954777 0.297321i $$-0.903907\pi$$
0.954777 0.297321i $$-0.0960932\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −6.88034 4.04690i −0.421861 0.248131i
$$267$$ 0 0
$$268$$ −0.570231 −0.0348324
$$269$$ 6.91107 0.421376 0.210688 0.977553i $$-0.432430\pi$$
0.210688 + 0.977553i $$0.432430\pi$$
$$270$$ 0 0
$$271$$ 20.6312i 1.25326i 0.779318 + 0.626629i $$0.215566\pi$$
−0.779318 + 0.626629i $$0.784434\pi$$
$$272$$ −3.66466 −0.222203
$$273$$ 0 0
$$274$$ 4.72056 0.285179
$$275$$ 4.30986i 0.259894i
$$276$$ 0 0
$$277$$ −15.5144 −0.932168 −0.466084 0.884740i $$-0.654336\pi$$
−0.466084 + 0.884740i $$0.654336\pi$$
$$278$$ 2.36375 0.141768
$$279$$ 0 0
$$280$$ −2.40150 + 4.08292i −0.143517 + 0.244001i
$$281$$ 13.5977i 0.811168i 0.914058 + 0.405584i $$0.132932\pi$$
−0.914058 + 0.405584i $$0.867068\pi$$
$$282$$ 0 0
$$283$$ 5.44783i 0.323840i −0.986804 0.161920i $$-0.948231\pi$$
0.986804 0.161920i $$-0.0517687\pi$$
$$284$$ 5.96254i 0.353811i
$$285$$ 0 0
$$286$$ 11.7465i 0.694587i
$$287$$ −18.4308 10.8407i −1.08794 0.639907i
$$288$$ 0 0
$$289$$ −3.57023 −0.210014
$$290$$ −11.7465 −0.689781
$$291$$ 0 0
$$292$$ 12.3814i 0.724567i
$$293$$ 24.4622 1.42910 0.714550 0.699585i $$-0.246632\pi$$
0.714550 + 0.699585i $$0.246632\pi$$
$$294$$ 0 0
$$295$$ −26.1212 −1.52084
$$296$$ 9.36404i 0.544274i
$$297$$ 0 0
$$298$$ −17.3640 −1.00587
$$299$$ −18.4226 −1.06541
$$300$$ 0 0
$$301$$ 15.8782 + 9.33927i 0.915203 + 0.538307i
$$302$$ 11.2328i 0.646374i
$$303$$ 0 0
$$304$$ 3.01701i 0.173037i
$$305$$ 20.2816i 1.16132i
$$306$$ 0 0
$$307$$ 31.2223i 1.78195i −0.454053 0.890975i $$-0.650022\pi$$
0.454053 0.890975i $$-0.349978\pi$$
$$308$$ −3.22128 + 5.47667i −0.183550 + 0.312062i
$$309$$ 0 0
$$310$$ −8.31905 −0.472491
$$311$$ −10.9100 −0.618651 −0.309325 0.950956i $$-0.600103\pi$$
−0.309325 + 0.950956i $$0.600103\pi$$
$$312$$ 0 0
$$313$$ 3.42405i 0.193539i −0.995307 0.0967694i $$-0.969149\pi$$
0.995307 0.0967694i $$-0.0308509\pi$$
$$314$$ −13.8431 −0.781210
$$315$$ 0 0
$$316$$ −3.03663 −0.170824
$$317$$ 19.0471i 1.06979i 0.844917 + 0.534897i $$0.179650\pi$$
−0.844917 + 0.534897i $$0.820350\pi$$
$$318$$ 0 0
$$319$$ −15.7563 −0.882186
$$320$$ 1.79035 0.100084
$$321$$ 0 0
$$322$$ 8.58930 + 5.05208i 0.478663 + 0.281541i
$$323$$ 11.0563i 0.615191i
$$324$$ 0 0
$$325$$ 8.77821i 0.486927i
$$326$$ 4.33577i 0.240136i
$$327$$ 0 0
$$328$$ 8.08188i 0.446247i
$$329$$ 11.7128 + 6.88929i 0.645749 + 0.379819i
$$330$$ 0 0
$$331$$ 0.0732502 0.00402620 0.00201310 0.999998i $$-0.499359\pi$$
0.00201310 + 0.999998i $$0.499359\pi$$
$$332$$ 14.0054 0.768646
$$333$$ 0 0
$$334$$ 12.4151i 0.679325i
$$335$$ −1.02091 −0.0557784
$$336$$ 0 0
$$337$$ −2.23278 −0.121627 −0.0608136 0.998149i $$-0.519370\pi$$
−0.0608136 + 0.998149i $$0.519370\pi$$
$$338$$ 10.9251i 0.594246i
$$339$$ 0 0
$$340$$ −6.56103 −0.355822
$$341$$ −11.1589 −0.604286
$$342$$ 0 0
$$343$$ −0.449242 + 18.5148i −0.0242568 + 0.999706i
$$344$$ 6.96254i 0.375395i
$$345$$ 0 0
$$346$$ 17.4182i 0.936406i
$$347$$ 31.8409i 1.70931i −0.519195 0.854656i $$-0.673768\pi$$
0.519195 0.854656i $$-0.326232\pi$$
$$348$$ 0 0
$$349$$ 14.7354i 0.788770i 0.918945 + 0.394385i $$0.129042\pi$$
−0.918945 + 0.394385i $$0.870958\pi$$
$$350$$ 2.40727 4.09272i 0.128674 0.218765i
$$351$$ 0 0
$$352$$ 2.40150 0.128001
$$353$$ −2.15957 −0.114943 −0.0574713 0.998347i $$-0.518304\pi$$
−0.0574713 + 0.998347i $$0.518304\pi$$
$$354$$ 0 0
$$355$$ 10.6750i 0.566571i
$$356$$ −3.74863 −0.198677
$$357$$ 0 0
$$358$$ 13.1221 0.693523
$$359$$ 32.6448i 1.72293i 0.507820 + 0.861463i $$0.330451\pi$$
−0.507820 + 0.861463i $$0.669549\pi$$
$$360$$ 0 0
$$361$$ 9.89765 0.520929
$$362$$ −13.3577 −0.702067
$$363$$ 0 0
$$364$$ −6.56103 + 11.1547i −0.343891 + 0.584668i
$$365$$ 22.1670i 1.16028i
$$366$$ 0 0
$$367$$ 29.7003i 1.55034i −0.631751 0.775171i $$-0.717664\pi$$
0.631751 0.775171i $$-0.282336\pi$$
$$368$$ 3.76638i 0.196336i
$$369$$ 0 0
$$370$$ 16.7649i 0.871566i
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −2.01672 −0.104422 −0.0522109 0.998636i $$-0.516627\pi$$
−0.0522109 + 0.998636i $$0.516627\pi$$
$$374$$ −8.80071 −0.455074
$$375$$ 0 0
$$376$$ 5.13604i 0.264871i
$$377$$ −32.0921 −1.65283
$$378$$ 0 0
$$379$$ −18.8709 −0.969332 −0.484666 0.874699i $$-0.661059\pi$$
−0.484666 + 0.874699i $$0.661059\pi$$
$$380$$ 5.40150i 0.277091i
$$381$$ 0 0
$$382$$ 9.25333 0.473441
$$383$$ −0.836511 −0.0427437 −0.0213719 0.999772i $$-0.506803\pi$$
−0.0213719 + 0.999772i $$0.506803\pi$$
$$384$$ 0 0
$$385$$ −5.76722 + 9.80515i −0.293925 + 0.499717i
$$386$$ 24.5602i 1.25008i
$$387$$ 0 0
$$388$$ 5.51087i 0.279772i
$$389$$ 24.8219i 1.25852i 0.777195 + 0.629260i $$0.216642\pi$$
−0.777195 + 0.629260i $$0.783358\pi$$
$$390$$ 0 0
$$391$$ 13.8025i 0.698024i
$$392$$ 6.11799 3.40150i 0.309005 0.171802i
$$393$$ 0 0
$$394$$ −12.4861 −0.629041
$$395$$ −5.43662 −0.273546
$$396$$ 0 0
$$397$$ 3.03390i 0.152267i −0.997098 0.0761336i $$-0.975742\pi$$
0.997098 0.0761336i $$-0.0242575\pi$$
$$398$$ −0.179145 −0.00897975
$$399$$ 0 0
$$400$$ −1.79465 −0.0897324
$$401$$ 13.0771i 0.653038i −0.945191 0.326519i $$-0.894124\pi$$
0.945191 0.326519i $$-0.105876\pi$$
$$402$$ 0 0
$$403$$ −22.7281 −1.13217
$$404$$ 0.250324 0.0124541
$$405$$ 0 0
$$406$$ 14.9625 + 8.80071i 0.742578 + 0.436772i
$$407$$ 22.4878i 1.11468i
$$408$$ 0 0
$$409$$ 5.56709i 0.275275i 0.990483 + 0.137637i $$0.0439508\pi$$
−0.990483 + 0.137637i $$0.956049\pi$$
$$410$$ 14.4694i 0.714592i
$$411$$ 0 0
$$412$$ 0.167931i 0.00827339i
$$413$$ 33.2728 + 19.5705i 1.63725 + 0.963000i
$$414$$ 0 0
$$415$$ 25.0746 1.23086
$$416$$ 4.89133 0.239817
$$417$$ 0 0
$$418$$ 7.24536i 0.354382i
$$419$$ 16.3988 0.801132 0.400566 0.916268i $$-0.368814\pi$$
0.400566 + 0.916268i $$0.368814\pi$$
$$420$$ 0 0
$$421$$ 15.4578 0.753369 0.376684 0.926342i $$-0.377064\pi$$
0.376684 + 0.926342i $$0.377064\pi$$
$$422$$ 15.1221i 0.736131i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 6.57678 0.319021
$$426$$ 0 0
$$427$$ 15.1953 25.8343i 0.735353 1.25021i
$$428$$ 7.99080i 0.386250i
$$429$$ 0 0
$$430$$ 12.4654i 0.601134i
$$431$$ 25.0266i 1.20549i −0.797935 0.602744i $$-0.794074\pi$$
0.797935 0.602744i $$-0.205926\pi$$
$$432$$ 0 0
$$433$$ 2.25168i 0.108209i −0.998535 0.0541044i $$-0.982770\pi$$
0.998535 0.0541044i $$-0.0172304\pi$$
$$434$$ 10.5967 + 6.23278i 0.508656 + 0.299183i
$$435$$ 0 0
$$436$$ 18.9533 0.907700
$$437$$ 11.3632 0.543576
$$438$$ 0 0
$$439$$ 18.7400i 0.894412i −0.894431 0.447206i $$-0.852419\pi$$
0.894431 0.447206i $$-0.147581\pi$$
$$440$$ 4.29953 0.204972
$$441$$ 0 0
$$442$$ −17.9251 −0.852609
$$443$$ 1.20451i 0.0572281i −0.999591 0.0286141i $$-0.990891\pi$$
0.999591 0.0286141i $$-0.00910938\pi$$
$$444$$ 0 0
$$445$$ −6.71136 −0.318149
$$446$$ −8.39524 −0.397526
$$447$$ 0 0
$$448$$ −2.28052 1.34136i −0.107744 0.0633733i
$$449$$ 26.8022i 1.26487i 0.774612 + 0.632436i $$0.217945\pi$$
−0.774612 + 0.632436i $$0.782055\pi$$
$$450$$ 0 0
$$451$$ 19.4087i 0.913918i
$$452$$ 1.15953i 0.0545396i
$$453$$ 0 0
$$454$$ 2.42522i 0.113821i
$$455$$ −11.7465 + 19.9709i −0.550686 + 0.936250i
$$456$$ 0 0
$$457$$ 13.8488 0.647821 0.323911 0.946088i $$-0.395002\pi$$
0.323911 + 0.946088i $$0.395002\pi$$
$$458$$ −2.01975 −0.0943766
$$459$$ 0 0
$$460$$ 6.74314i 0.314401i
$$461$$ 4.80483 0.223783 0.111892 0.993720i $$-0.464309\pi$$
0.111892 + 0.993720i $$0.464309\pi$$
$$462$$ 0 0
$$463$$ −21.0388 −0.977755 −0.488877 0.872353i $$-0.662593\pi$$
−0.488877 + 0.872353i $$0.662593\pi$$
$$464$$ 6.56103i 0.304588i
$$465$$ 0 0
$$466$$ 12.7289 0.589656
$$467$$ −5.82302 −0.269457 −0.134729 0.990883i $$-0.543016\pi$$
−0.134729 + 0.990883i $$0.543016\pi$$
$$468$$ 0 0
$$469$$ 1.30042 + 0.764885i 0.0600478 + 0.0353191i
$$470$$ 9.19531i 0.424148i
$$471$$ 0 0
$$472$$ 14.5900i 0.671560i
$$473$$ 16.7206i 0.768812i
$$474$$ 0 0
$$475$$ 5.41447i 0.248433i
$$476$$ 8.35733 + 4.91564i 0.383057 + 0.225308i
$$477$$ 0 0
$$478$$ 17.4495 0.798121
$$479$$ 26.9561 1.23166 0.615828 0.787881i $$-0.288822\pi$$
0.615828 + 0.787881i $$0.288822\pi$$
$$480$$ 0 0
$$481$$ 45.8026i 2.08842i
$$482$$ 11.4332 0.520767
$$483$$ 0 0
$$484$$ −5.23278 −0.237854
$$485$$ 9.86639i 0.448010i
$$486$$ 0 0
$$487$$ −13.6268 −0.617487 −0.308744 0.951145i $$-0.599909\pi$$
−0.308744 + 0.951145i $$0.599909\pi$$
$$488$$ −11.3283 −0.512807
$$489$$ 0 0
$$490$$ 10.9533 6.08988i 0.494821 0.275113i
$$491$$ 38.9630i 1.75838i 0.476475 + 0.879188i $$0.341914\pi$$
−0.476475 + 0.879188i $$0.658086\pi$$
$$492$$ 0 0
$$493$$ 24.0440i 1.08289i
$$494$$ 14.7572i 0.663957i
$$495$$ 0 0
$$496$$ 4.64661i 0.208639i
$$497$$ 7.99791 13.5977i 0.358755 0.609938i
$$498$$ 0 0
$$499$$ 26.0097 1.16435 0.582176 0.813063i $$-0.302201\pi$$
0.582176 + 0.813063i $$0.302201\pi$$
$$500$$ −12.1648 −0.544026
$$501$$ 0 0
$$502$$ 27.3560i 1.22096i
$$503$$ −10.5271 −0.469378 −0.234689 0.972070i $$-0.575407\pi$$
−0.234689 + 0.972070i $$0.575407\pi$$
$$504$$ 0 0
$$505$$ 0.448168 0.0199432
$$506$$ 9.04499i 0.402099i
$$507$$ 0 0
$$508$$ −1.40150 −0.0621817
$$509$$ 0.938871 0.0416147 0.0208074 0.999784i $$-0.493376\pi$$
0.0208074 + 0.999784i $$0.493376\pi$$
$$510$$ 0 0
$$511$$ 16.6079 28.2360i 0.734692 1.24909i
$$512$$ 1.00000i 0.0441942i
$$513$$ 0 0
$$514$$ 3.49673i 0.154234i
$$515$$ 0.300656i 0.0132485i
$$516$$ 0 0
$$517$$ 12.3342i 0.542459i
$$518$$ −12.5606 + 21.3548i −0.551879 + 0.938278i
$$519$$ 0 0
$$520$$ 8.75718 0.384028
$$521$$ 39.5054 1.73076 0.865382 0.501112i $$-0.167076\pi$$
0.865382 + 0.501112i $$0.167076\pi$$
$$522$$ 0 0
$$523$$ 24.3292i 1.06384i −0.846794 0.531922i $$-0.821470\pi$$
0.846794 0.531922i $$-0.178530\pi$$
$$524$$ 10.4918 0.458335
$$525$$ 0 0
$$526$$ 9.64348 0.420476
$$527$$ 17.0283i 0.741763i
$$528$$ 0 0
$$529$$ 8.81436 0.383233
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 4.04690 6.88034i 0.175455 0.298301i
$$533$$ 39.5311i 1.71228i
$$534$$ 0 0
$$535$$ 14.3063i 0.618516i
$$536$$ 0.570231i 0.0246302i
$$537$$ 0 0
$$538$$ 6.91107i 0.297958i
$$539$$ 14.6924 8.16873i 0.632845 0.351852i
$$540$$ 0 0
$$541$$ 42.7281 1.83702 0.918512 0.395394i $$-0.129392\pi$$
0.918512 + 0.395394i $$0.129392\pi$$
$$542$$ −20.6312 −0.886187
$$543$$ 0 0
$$544$$ 3.66466i 0.157121i
$$545$$ 33.9331 1.45353
$$546$$ 0 0
$$547$$ 24.4953 1.04734 0.523672 0.851920i $$-0.324562\pi$$
0.523672 + 0.851920i $$0.324562\pi$$
$$548$$ 4.72056i 0.201652i
$$549$$ 0 0
$$550$$ −4.30986 −0.183773
$$551$$ 19.7947 0.843283
$$552$$ 0 0
$$553$$ 6.92507 + 4.07321i 0.294484 + 0.173210i
$$554$$ 15.5144i 0.659142i
$$555$$ 0 0
$$556$$ 2.36375i 0.100245i
$$557$$ 2.54431i 0.107806i −0.998546 0.0539030i $$-0.982834\pi$$
0.998546 0.0539030i $$-0.0171662\pi$$
$$558$$ 0 0
$$559$$ 34.0560i 1.44042i
$$560$$ −4.08292 2.40150i −0.172535 0.101482i
$$561$$ 0 0
$$562$$ −13.5977 −0.573583
$$563$$ −15.8141 −0.666487 −0.333243 0.942841i $$-0.608143\pi$$
−0.333243 + 0.942841i $$0.608143\pi$$
$$564$$ 0 0
$$565$$ 2.07596i 0.0873363i
$$566$$ 5.44783 0.228990
$$567$$ 0 0
$$568$$ −5.96254 −0.250182
$$569$$ 6.38311i 0.267594i −0.991009 0.133797i $$-0.957283\pi$$
0.991009 0.133797i $$-0.0427170\pi$$
$$570$$ 0 0
$$571$$ −7.82375 −0.327414 −0.163707 0.986509i $$-0.552345\pi$$
−0.163707 + 0.986509i $$0.552345\pi$$
$$572$$ 11.7465 0.491148
$$573$$ 0 0
$$574$$ 10.8407 18.4308i 0.452482 0.769289i
$$575$$ 6.75933i 0.281884i
$$576$$ 0 0
$$577$$ 14.3197i 0.596138i 0.954544 + 0.298069i $$0.0963425\pi$$
−0.954544 + 0.298069i $$0.903657\pi$$
$$578$$ 3.57023i 0.148502i
$$579$$ 0 0
$$580$$ 11.7465i 0.487749i
$$581$$ −31.9395 18.7863i −1.32508 0.779387i
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −12.3814 −0.512346
$$585$$ 0 0
$$586$$ 24.4622i 1.01053i
$$587$$ −4.75150 −0.196115 −0.0980577 0.995181i $$-0.531263\pi$$
−0.0980577 + 0.995181i $$0.531263\pi$$
$$588$$ 0 0
$$589$$ 14.0189 0.577637
$$590$$ 26.1212i 1.07539i
$$591$$ 0 0
$$592$$ 9.36404 0.384860
$$593$$ −3.58070 −0.147042 −0.0735208 0.997294i $$-0.523424\pi$$
−0.0735208 + 0.997294i $$0.523424\pi$$
$$594$$ 0 0
$$595$$ 14.9625 + 8.80071i 0.613404 + 0.360794i
$$596$$ 17.3640i 0.711259i
$$597$$ 0 0
$$598$$ 18.4226i 0.753357i
$$599$$ 15.0655i 0.615561i 0.951457 + 0.307780i $$0.0995862\pi$$
−0.951457 + 0.307780i $$0.900414\pi$$
$$600$$ 0 0
$$601$$ 22.9444i 0.935920i 0.883750 + 0.467960i $$0.155011\pi$$
−0.883750 + 0.467960i $$0.844989\pi$$
$$602$$ −9.33927 + 15.8782i −0.380640 + 0.647146i
$$603$$ 0 0
$$604$$ 11.2328 0.457055
$$605$$ −9.36850 −0.380884
$$606$$ 0 0
$$607$$ 24.4832i 0.993741i 0.867825 + 0.496870i $$0.165518\pi$$
−0.867825 + 0.496870i $$0.834482\pi$$
$$608$$ −3.01701 −0.122356
$$609$$ 0 0
$$610$$ −20.2816 −0.821178
$$611$$ 25.1221i 1.01633i
$$612$$ 0 0
$$613$$ −0.880086 −0.0355463 −0.0177732 0.999842i $$-0.505658\pi$$
−0.0177732 + 0.999842i $$0.505658\pi$$
$$614$$ 31.2223 1.26003
$$615$$ 0 0
$$616$$ −5.47667 3.22128i −0.220661 0.129789i
$$617$$ 13.5801i 0.546714i 0.961913 + 0.273357i $$0.0881341\pi$$
−0.961913 + 0.273357i $$0.911866\pi$$
$$618$$ 0 0
$$619$$ 35.4869i 1.42634i 0.700992 + 0.713169i $$0.252741\pi$$
−0.700992 + 0.713169i $$0.747259\pi$$
$$620$$ 8.31905i 0.334101i
$$621$$ 0 0
$$622$$ 10.9100i 0.437452i
$$623$$ 8.54881 + 5.02826i 0.342501 + 0.201453i
$$624$$ 0 0
$$625$$ −12.8060 −0.512240
$$626$$ 3.42405 0.136853
$$627$$ 0 0
$$628$$ 13.8431i 0.552399i
$$629$$ −34.3161 −1.36827
$$630$$ 0 0
$$631$$ 26.9822 1.07415 0.537073 0.843536i $$-0.319530\pi$$
0.537073 + 0.843536i $$0.319530\pi$$
$$632$$ 3.03663i 0.120790i
$$633$$ 0 0
$$634$$ −19.0471 −0.756458
$$635$$ −2.50918 −0.0995739
$$636$$ 0 0
$$637$$ 29.9251 16.6379i 1.18567 0.659216i
$$638$$ 15.7563i 0.623800i
$$639$$ 0 0
$$640$$ 1.79035i 0.0707698i
$$641$$ 1.07708i 0.0425420i 0.999774 + 0.0212710i $$0.00677128\pi$$
−0.999774 + 0.0212710i $$0.993229\pi$$
$$642$$ 0 0
$$643$$ 38.4661i 1.51695i 0.651700 + 0.758477i $$0.274056\pi$$
−0.651700 + 0.758477i $$0.725944\pi$$
$$644$$ −5.05208 + 8.58930i −0.199080 + 0.338466i
$$645$$ 0 0
$$646$$ 11.0563 0.435006
$$647$$ 8.95210 0.351943 0.175972 0.984395i $$-0.443693\pi$$
0.175972 + 0.984395i $$0.443693\pi$$
$$648$$ 0 0
$$649$$ 35.0380i 1.37536i
$$650$$ −8.77821 −0.344310
$$651$$ 0 0
$$652$$ 4.33577 0.169802
$$653$$ 11.3846i 0.445513i 0.974874 + 0.222757i $$0.0715055\pi$$
−0.974874 + 0.222757i $$0.928494\pi$$
$$654$$ 0 0
$$655$$ 18.7839 0.733949
$$656$$ −8.08188 −0.315544
$$657$$ 0 0
$$658$$ −6.88929 + 11.7128i −0.268572 + 0.456614i
$$659$$ 36.3007i 1.41407i 0.707177 + 0.707036i $$0.249968\pi$$
−0.707177 + 0.707036i $$0.750032\pi$$
$$660$$ 0 0
$$661$$ 36.0758i 1.40319i −0.712578 0.701593i $$-0.752473\pi$$
0.712578 0.701593i $$-0.247527\pi$$
$$662$$ 0.0732502i 0.00284695i
$$663$$ 0 0
$$664$$ 14.0054i 0.543515i
$$665$$ 7.24536 12.3182i 0.280963 0.477680i
$$666$$ 0 0
$$667$$ −24.7114 −0.956828
$$668$$ 12.4151 0.480355
$$669$$ 0 0
$$670$$ 1.02091i 0.0394413i
$$671$$ −27.2049 −1.05023
$$672$$ 0 0
$$673$$ −9.57023 −0.368905 −0.184453 0.982841i $$-0.559051\pi$$
−0.184453 + 0.982841i $$0.559051\pi$$
$$674$$ 2.23278i 0.0860034i
$$675$$ 0 0
$$676$$ 10.9251 0.420195
$$677$$ 15.6282 0.600639 0.300320 0.953839i $$-0.402907\pi$$
0.300320 + 0.953839i $$0.402907\pi$$
$$678$$ 0 0
$$679$$ 7.39207 12.5676i 0.283682 0.482302i
$$680$$ 6.56103i 0.251604i
$$681$$ 0 0
$$682$$ 11.1589i 0.427294i
$$683$$ 11.1313i 0.425926i 0.977060 + 0.212963i $$0.0683114\pi$$
−0.977060 + 0.212963i $$0.931689\pi$$
$$684$$ 0 0
$$685$$ 8.45145i 0.322913i
$$686$$ −18.5148 0.449242i −0.706899 0.0171522i
$$687$$ 0 0
$$688$$ 6.96254 0.265444
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 3.02419i 0.115046i −0.998344 0.0575228i $$-0.981680\pi$$
0.998344 0.0575228i $$-0.0183202\pi$$
$$692$$ −17.4182 −0.662139
$$693$$ 0 0
$$694$$ 31.8409 1.20867
$$695$$ 4.23194i 0.160527i
$$696$$ 0 0
$$697$$ 29.6174 1.12184
$$698$$ −14.7354 −0.557745
$$699$$ 0 0
$$700$$ 4.09272 + 2.40727i 0.154690 + 0.0909863i
$$701$$ 50.1486i 1.89409i 0.321103 + 0.947044i $$0.395946\pi$$
−0.321103 + 0.947044i $$0.604054\pi$$
$$702$$ 0 0
$$703$$ 28.2514i 1.06552i
$$704$$ 2.40150i 0.0905101i
$$705$$ 0 0
$$706$$ 2.15957i 0.0812766i
$$707$$ −0.570868 0.335775i −0.0214697 0.0126281i
$$708$$ 0 0
$$709$$ −3.60770 −0.135490 −0.0677449 0.997703i $$-0.521580\pi$$
−0.0677449 + 0.997703i $$0.521580\pi$$
$$710$$ −10.6750 −0.400626
$$711$$ 0 0
$$712$$ 3.74863i 0.140486i
$$713$$ −17.5009 −0.655414
$$714$$ 0 0
$$715$$ 21.0304 0.786493
$$716$$ 13.1221i 0.490395i
$$717$$ 0 0
$$718$$ −32.6448 −1.21829
$$719$$ 34.3161 1.27977 0.639887 0.768469i $$-0.278981\pi$$
0.639887 + 0.768469i $$0.278981\pi$$
$$720$$ 0 0
$$721$$ −0.225257 + 0.382970i −0.00838899 + 0.0142626i
$$722$$ 9.89765i 0.368352i
$$723$$ 0 0
$$724$$ 13.3577i 0.496437i
$$725$$ 11.7747i 0.437303i
$$726$$ 0 0
$$727$$ 22.4886i 0.834057i −0.908893 0.417029i $$-0.863071\pi$$
0.908893 0.417029i $$-0.136929\pi$$
$$728$$ −11.1547 6.56103i −0.413422 0.243168i
$$729$$ 0 0
$$730$$ −22.1670 −0.820439
$$731$$ −25.5154 −0.943720
$$732$$ 0 0
$$733$$ 31.1845i 1.15182i 0.817512 + 0.575912i $$0.195353\pi$$
−0.817512 + 0.575912i $$0.804647\pi$$
$$734$$ 29.7003 1.09626
$$735$$ 0 0
$$736$$ 3.76638 0.138831
$$737$$ 1.36941i 0.0504429i
$$738$$ 0 0
$$739$$ 4.08628 0.150316 0.0751581 0.997172i $$-0.476054\pi$$
0.0751581 + 0.997172i $$0.476054\pi$$
$$740$$ 16.7649 0.616290
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 2.05821i 0.0755083i 0.999287 + 0.0377542i $$0.0120204\pi$$
−0.999287 + 0.0377542i $$0.987980\pi$$
$$744$$ 0 0
$$745$$ 31.0877i 1.13897i
$$746$$ 2.01672i 0.0738374i
$$747$$ 0 0
$$748$$ 8.80071i 0.321786i
$$749$$ −10.7185 + 18.2231i −0.391647 + 0.665859i
$$750$$ 0 0
$$751$$ 23.8105 0.868859 0.434429 0.900706i $$-0.356950\pi$$
0.434429 + 0.900706i $$0.356950\pi$$
$$752$$ 5.13604 0.187292
$$753$$ 0 0
$$754$$ 32.0921i 1.16873i
$$755$$ 20.1106 0.731900
$$756$$ 0 0
$$757$$ 10.0754 0.366197 0.183098 0.983095i $$-0.441387\pi$$
0.183098 + 0.983095i $$0.441387\pi$$
$$758$$ 18.8709i 0.685421i
$$759$$ 0 0
$$760$$ −5.40150 −0.195933
$$761$$ 27.8735 1.01041 0.505207 0.862998i $$-0.331416\pi$$
0.505207 + 0.862998i $$0.331416\pi$$
$$762$$ 0 0
$$763$$ −43.2234 25.4233i −1.56479 0.920384i
$$764$$ 9.25333i 0.334774i
$$765$$ 0 0
$$766$$ 0.836511i 0.0302244i
$$767$$ 71.3645i 2.57682i
$$768$$ 0 0
$$769$$ 7.17261i 0.258651i −0.991602 0.129326i $$-0.958719\pi$$
0.991602 0.129326i $$-0.0412812\pi$$
$$770$$ −9.80515 5.76722i −0.353353 0.207836i
$$771$$ 0 0
$$772$$ 24.5602 0.883941
$$773$$ 2.14153 0.0770255 0.0385128 0.999258i $$-0.487738\pi$$
0.0385128 + 0.999258i $$0.487738\pi$$
$$774$$ 0 0
$$775$$ 8.33903i 0.299547i
$$776$$ −5.51087 −0.197829
$$777$$ 0 0
$$778$$ −24.8219 −0.889907
$$779$$ 24.3831i 0.873615i
$$780$$ 0 0
$$781$$ −14.3191 −0.512376
$$782$$ −13.8025 −0.493578
$$783$$ 0 0
$$784$$ 3.40150 + 6.11799i 0.121482 + 0.218500i
$$785$$ 24.7839i 0.884577i
$$786$$ 0 0
$$787$$ 18.3552i 0.654292i 0.944974 + 0.327146i $$0.106087\pi$$
−0.944974 + 0.327146i $$0.893913\pi$$
$$788$$ 12.4861i 0.444799i
$$789$$ 0 0
$$790$$ 5.43662i 0.193426i
$$791$$ −1.55534 + 2.64432i −0.0553017 + 0.0940212i
$$792$$ 0 0
$$793$$ −55.4103 −1.96768
$$794$$ 3.03390 0.107669
$$795$$ 0 0
$$796$$ 0.179145i 0.00634964i
$$797$$ 24.8452 0.880062 0.440031 0.897982i $$-0.354967\pi$$
0.440031 + 0.897982i $$0.354967\pi$$
$$798$$ 0 0
$$799$$ −18.8219 −0.665870