# Properties

 Label 136.3.p.a.19.1 Level $136$ Weight $3$ Character 136.19 Analytic conductor $3.706$ Analytic rank $0$ Dimension $4$ CM discriminant -8 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$136 = 2^{3} \cdot 17$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 136.p (of order $$8$$, degree $$4$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$3.70573159530$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(\zeta_{8})$$ Defining polynomial: $$x^{4} + 1$$ x^4 + 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{8}]$

## Embedding invariants

 Embedding label 19.1 Root $$0.707107 - 0.707107i$$ of defining polynomial Character $$\chi$$ $$=$$ 136.19 Dual form 136.3.p.a.43.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.41421 + 1.41421i) q^{2} +(-5.53553 + 2.29289i) q^{3} +4.00000i q^{4} +(-11.0711 - 4.58579i) q^{6} +(-5.65685 + 5.65685i) q^{8} +(19.0208 - 19.0208i) q^{9} +O(q^{10})$$ $$q+(1.41421 + 1.41421i) q^{2} +(-5.53553 + 2.29289i) q^{3} +4.00000i q^{4} +(-11.0711 - 4.58579i) q^{6} +(-5.65685 + 5.65685i) q^{8} +(19.0208 - 19.0208i) q^{9} +(-17.9497 - 7.43503i) q^{11} +(-9.17157 - 22.1421i) q^{12} -16.0000 q^{16} +(-11.2929 + 12.7071i) q^{17} +53.7990 q^{18} +(12.0000 + 12.0000i) q^{19} +(-14.8701 - 35.8995i) q^{22} +(18.3431 - 44.2843i) q^{24} +(-17.6777 + 17.6777i) q^{25} +(-41.0416 + 99.0833i) q^{27} +(-22.6274 - 22.6274i) q^{32} +116.409 q^{33} +(-33.9411 + 2.00000i) q^{34} +(76.0833 + 76.0833i) q^{36} +33.9411i q^{38} +(-6.32233 + 15.2635i) q^{41} +(-35.4264 + 35.4264i) q^{43} +(29.7401 - 71.7990i) q^{44} +(88.5685 - 36.6863i) q^{48} +(-34.6482 - 34.6482i) q^{49} -50.0000 q^{50} +(33.3762 - 96.2340i) q^{51} +(-198.167 + 82.0833i) q^{54} +(-93.9411 - 38.9117i) q^{57} +(-1.42641 + 1.42641i) q^{59} -64.0000i q^{64} +(164.627 + 164.627i) q^{66} +127.841 q^{67} +(-50.8284 - 45.1716i) q^{68} +215.196i q^{72} +(45.2340 + 109.205i) q^{73} +(57.3223 - 138.388i) q^{75} +(-48.0000 + 48.0000i) q^{76} -400.487i q^{81} +(-30.5269 + 12.6447i) q^{82} +(53.5442 + 53.5442i) q^{83} -100.201 q^{86} +(143.598 - 59.4802i) q^{88} +31.2376i q^{89} +(177.137 + 73.3726i) q^{96} +(73.7660 + 178.087i) q^{97} -98.0000i q^{98} +(-482.839 + 199.999i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 8 q^{3} - 16 q^{6} + 28 q^{9}+O(q^{10})$$ 4 * q - 8 * q^3 - 16 * q^6 + 28 * q^9 $$4 q - 8 q^{3} - 16 q^{6} + 28 q^{9} - 52 q^{11} - 48 q^{12} - 64 q^{16} - 48 q^{17} + 136 q^{18} + 48 q^{19} + 48 q^{22} + 96 q^{24} - 68 q^{27} + 64 q^{33} + 112 q^{36} - 96 q^{41} + 28 q^{43} - 96 q^{44} + 128 q^{48} - 200 q^{50} - 56 q^{51} - 408 q^{54} - 240 q^{57} + 164 q^{59} + 568 q^{66} + 336 q^{67} - 192 q^{68} + 48 q^{73} + 300 q^{75} - 192 q^{76} + 8 q^{82} + 316 q^{83} - 480 q^{86} + 416 q^{88} + 256 q^{96} + 428 q^{97} - 1080 q^{99}+O(q^{100})$$ 4 * q - 8 * q^3 - 16 * q^6 + 28 * q^9 - 52 * q^11 - 48 * q^12 - 64 * q^16 - 48 * q^17 + 136 * q^18 + 48 * q^19 + 48 * q^22 + 96 * q^24 - 68 * q^27 + 64 * q^33 + 112 * q^36 - 96 * q^41 + 28 * q^43 - 96 * q^44 + 128 * q^48 - 200 * q^50 - 56 * q^51 - 408 * q^54 - 240 * q^57 + 164 * q^59 + 568 * q^66 + 336 * q^67 - 192 * q^68 + 48 * q^73 + 300 * q^75 - 192 * q^76 + 8 * q^82 + 316 * q^83 - 480 * q^86 + 416 * q^88 + 256 * q^96 + 428 * q^97 - 1080 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$$.

 $$n$$ $$69$$ $$103$$ $$105$$ $$\chi(n)$$ $$-1$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.41421 + 1.41421i 0.707107 + 0.707107i
$$3$$ −5.53553 + 2.29289i −1.84518 + 0.764298i −0.902369 + 0.430964i $$0.858173\pi$$
−0.942809 + 0.333333i $$0.891827\pi$$
$$4$$ 4.00000i 1.00000i
$$5$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$6$$ −11.0711 4.58579i −1.84518 0.764298i
$$7$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$8$$ −5.65685 + 5.65685i −0.707107 + 0.707107i
$$9$$ 19.0208 19.0208i 2.11342 2.11342i
$$10$$ 0 0
$$11$$ −17.9497 7.43503i −1.63180 0.675912i −0.636364 0.771389i $$-0.719562\pi$$
−0.995432 + 0.0954775i $$0.969562\pi$$
$$12$$ −9.17157 22.1421i −0.764298 1.84518i
$$13$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −16.0000 −1.00000
$$17$$ −11.2929 + 12.7071i −0.664288 + 0.747477i
$$18$$ 53.7990 2.98883
$$19$$ 12.0000 + 12.0000i 0.631579 + 0.631579i 0.948464 0.316885i $$-0.102637\pi$$
−0.316885 + 0.948464i $$0.602637\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −14.8701 35.8995i −0.675912 1.63180i
$$23$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$24$$ 18.3431 44.2843i 0.764298 1.84518i
$$25$$ −17.6777 + 17.6777i −0.707107 + 0.707107i
$$26$$ 0 0
$$27$$ −41.0416 + 99.0833i −1.52006 + 3.66975i
$$28$$ 0 0
$$29$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$30$$ 0 0
$$31$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$32$$ −22.6274 22.6274i −0.707107 0.707107i
$$33$$ 116.409 3.52755
$$34$$ −33.9411 + 2.00000i −0.998268 + 0.0588235i
$$35$$ 0 0
$$36$$ 76.0833 + 76.0833i 2.11342 + 2.11342i
$$37$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$38$$ 33.9411i 0.893188i
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −6.32233 + 15.2635i −0.154203 + 0.372279i −0.982036 0.188696i $$-0.939574\pi$$
0.827832 + 0.560976i $$0.189574\pi$$
$$42$$ 0 0
$$43$$ −35.4264 + 35.4264i −0.823870 + 0.823870i −0.986661 0.162791i $$-0.947950\pi$$
0.162791 + 0.986661i $$0.447950\pi$$
$$44$$ 29.7401 71.7990i 0.675912 1.63180i
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 88.5685 36.6863i 1.84518 0.764298i
$$49$$ −34.6482 34.6482i −0.707107 0.707107i
$$50$$ −50.0000 −1.00000
$$51$$ 33.3762 96.2340i 0.654434 1.88694i
$$52$$ 0 0
$$53$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$54$$ −198.167 + 82.0833i −3.66975 + 1.52006i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −93.9411 38.9117i −1.64809 0.682661i
$$58$$ 0 0
$$59$$ −1.42641 + 1.42641i −0.0241764 + 0.0241764i −0.719092 0.694915i $$-0.755442\pi$$
0.694915 + 0.719092i $$0.255442\pi$$
$$60$$ 0 0
$$61$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 64.0000i 1.00000i
$$65$$ 0 0
$$66$$ 164.627 + 164.627i 2.49435 + 2.49435i
$$67$$ 127.841 1.90807 0.954034 0.299697i $$-0.0968855\pi$$
0.954034 + 0.299697i $$0.0968855\pi$$
$$68$$ −50.8284 45.1716i −0.747477 0.664288i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$72$$ 215.196i 2.98883i
$$73$$ 45.2340 + 109.205i 0.619644 + 1.49595i 0.852118 + 0.523350i $$0.175318\pi$$
−0.232473 + 0.972603i $$0.574682\pi$$
$$74$$ 0 0
$$75$$ 57.3223 138.388i 0.764298 1.84518i
$$76$$ −48.0000 + 48.0000i −0.631579 + 0.631579i
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$80$$ 0 0
$$81$$ 400.487i 4.94429i
$$82$$ −30.5269 + 12.6447i −0.372279 + 0.154203i
$$83$$ 53.5442 + 53.5442i 0.645110 + 0.645110i 0.951807 0.306697i $$-0.0992238\pi$$
−0.306697 + 0.951807i $$0.599224\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ −100.201 −1.16513
$$87$$ 0 0
$$88$$ 143.598 59.4802i 1.63180 0.675912i
$$89$$ 31.2376i 0.350984i 0.984481 + 0.175492i $$0.0561516\pi$$
−0.984481 + 0.175492i $$0.943848\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 177.137 + 73.3726i 1.84518 + 0.764298i
$$97$$ 73.7660 + 178.087i 0.760474 + 1.83595i 0.484536 + 0.874771i $$0.338988\pi$$
0.275938 + 0.961175i $$0.411012\pi$$
$$98$$ 98.0000i 1.00000i
$$99$$ −482.839 + 199.999i −4.87716 + 2.02019i
$$100$$ −70.7107 70.7107i −0.707107 0.707107i
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 183.296 88.8944i 1.79702 0.871514i
$$103$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −68.0675 164.329i −0.636145 1.53579i −0.831776 0.555112i $$-0.812675\pi$$
0.195631 0.980678i $$-0.437325\pi$$
$$108$$ −396.333 164.167i −3.66975 1.52006i
$$109$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ −139.175 57.6482i −1.23164 0.510161i −0.330547 0.943790i $$-0.607233\pi$$
−0.901092 + 0.433628i $$0.857233\pi$$
$$114$$ −77.8234 187.882i −0.682661 1.64809i
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0 0
$$118$$ −4.03449 −0.0341906
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 181.354 + 181.354i 1.49879 + 1.49879i
$$122$$ 0 0
$$123$$ 98.9878i 0.804779i
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$128$$ 90.5097 90.5097i 0.707107 0.707107i
$$129$$ 114.875 277.333i 0.890505 2.14987i
$$130$$ 0 0
$$131$$ 15.3589 + 37.0797i 0.117244 + 0.283051i 0.971597 0.236641i $$-0.0760466\pi$$
−0.854354 + 0.519692i $$0.826047\pi$$
$$132$$ 465.637i 3.52755i
$$133$$ 0 0
$$134$$ 180.794 + 180.794i 1.34921 + 1.34921i
$$135$$ 0 0
$$136$$ −8.00000 135.765i −0.0588235 0.998268i
$$137$$ −135.765 −0.990982 −0.495491 0.868613i $$-0.665012\pi$$
−0.495491 + 0.868613i $$0.665012\pi$$
$$138$$ 0 0
$$139$$ 86.5061 35.8320i 0.622346 0.257784i −0.0491511 0.998791i $$-0.515652\pi$$
0.671497 + 0.741007i $$0.265652\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −304.333 + 304.333i −2.11342 + 2.11342i
$$145$$ 0 0
$$146$$ −90.4680 + 218.409i −0.619644 + 1.49595i
$$147$$ 271.241 + 112.352i 1.84518 + 0.764298i
$$148$$ 0 0
$$149$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$150$$ 276.777 114.645i 1.84518 0.764298i
$$151$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$152$$ −135.765 −0.893188
$$153$$ 26.8995 + 456.500i 0.175814 + 2.98366i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 566.375 566.375i 3.49614 3.49614i
$$163$$ 29.1558 70.3883i 0.178870 0.431830i −0.808860 0.588001i $$-0.799915\pi$$
0.987730 + 0.156171i $$0.0499150\pi$$
$$164$$ −61.0538 25.2893i −0.372279 0.154203i
$$165$$ 0 0
$$166$$ 151.446i 0.912324i
$$167$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$168$$ 0 0
$$169$$ −169.000 −1.00000
$$170$$ 0 0
$$171$$ 456.500 2.66959
$$172$$ −141.706 141.706i −0.823870 0.823870i
$$173$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 287.196 + 118.960i 1.63180 + 0.675912i
$$177$$ 4.62532 11.1665i 0.0261318 0.0630877i
$$178$$ −44.1766 + 44.1766i −0.248183 + 0.248183i
$$179$$ −252.000 + 252.000i −1.40782 + 1.40782i −0.636755 + 0.771066i $$0.719724\pi$$
−0.771066 + 0.636755i $$0.780276\pi$$
$$180$$ 0 0
$$181$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 297.182 144.126i 1.58921 0.770729i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$192$$ 146.745 + 354.274i 0.764298 + 1.84518i
$$193$$ 353.324 + 146.352i 1.83070 + 0.758299i 0.967234 + 0.253886i $$0.0817088\pi$$
0.863462 + 0.504413i $$0.168291\pi$$
$$194$$ −147.532 + 356.174i −0.760474 + 1.83595i
$$195$$ 0 0
$$196$$ 138.593 138.593i 0.707107 0.707107i
$$197$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$198$$ −965.678 399.997i −4.87716 2.02019i
$$199$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$200$$ 200.000i 1.00000i
$$201$$ −707.666 + 293.125i −3.52073 + 1.45833i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 384.936 + 133.505i 1.88694 + 0.654434i
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −126.177 304.617i −0.603716 1.45750i
$$210$$ 0 0
$$211$$ 132.094 318.903i 0.626038 1.51139i −0.218469 0.975844i $$-0.570106\pi$$
0.844507 0.535545i $$-0.179894\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 136.135 328.659i 0.636145 1.53579i
$$215$$ 0 0
$$216$$ −328.333 792.666i −1.52006 3.66975i
$$217$$ 0 0
$$218$$ 0 0
$$219$$ −500.789 500.789i −2.28671 2.28671i
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$224$$ 0 0
$$225$$ 672.487i 2.98883i
$$226$$ −115.296 278.350i −0.510161 1.23164i
$$227$$ −85.2584 35.3152i −0.375588 0.155574i 0.186900 0.982379i $$-0.440156\pi$$
−0.562488 + 0.826805i $$0.690156\pi$$
$$228$$ 155.647 375.765i 0.682661 1.64809i
$$229$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 123.558 + 298.295i 0.530291 + 1.28024i 0.931330 + 0.364175i $$0.118649\pi$$
−0.401039 + 0.916061i $$0.631351\pi$$
$$234$$ 0 0
$$235$$ 0 0
$$236$$ −5.70563 5.70563i −0.0241764 0.0241764i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ −321.589 + 133.207i −1.33440 + 0.552725i −0.931906 0.362700i $$-0.881855\pi$$
−0.402490 + 0.915425i $$0.631855\pi$$
$$242$$ 512.946i 2.11961i
$$243$$ 548.900 + 1325.16i 2.25885 + 5.45334i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 139.990 139.990i 0.569065 0.569065i
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −419.167 173.624i −1.68340 0.697287i
$$250$$ 0 0
$$251$$ 197.512i 0.786899i −0.919346 0.393450i $$-0.871282\pi$$
0.919346 0.393450i $$-0.128718\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 256.000 1.00000
$$257$$ −362.706 362.706i −1.41131 1.41131i −0.750973 0.660333i $$-0.770415\pi$$
−0.660333 0.750973i $$-0.729585\pi$$
$$258$$ 554.666 229.750i 2.14987 0.890505i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −30.7178 + 74.1594i −0.117244 + 0.283051i
$$263$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$264$$ −658.510 + 658.510i −2.49435 + 2.49435i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −71.6245 172.917i −0.268256 0.647628i
$$268$$ 511.362i 1.90807i
$$269$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 180.686 203.314i 0.664288 0.747477i
$$273$$ 0 0
$$274$$ −192.000 192.000i −0.700730 0.700730i
$$275$$ 448.744 185.876i 1.63180 0.675912i
$$276$$ 0 0
$$277$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$278$$ 173.012 + 71.6640i 0.622346 + 0.257784i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 360.000 360.000i 1.28114 1.28114i 0.341118 0.940020i $$-0.389194\pi$$
0.940020 0.341118i $$-0.110806\pi$$
$$282$$ 0 0
$$283$$ 128.009 + 53.0229i 0.452327 + 0.187360i 0.597204 0.802090i $$-0.296278\pi$$
−0.144876 + 0.989450i $$0.546278\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ −860.784 −2.98883
$$289$$ −33.9411 287.000i −0.117443 0.993080i
$$290$$ 0 0
$$291$$ −816.668 816.668i −2.80642 2.80642i
$$292$$ −436.818 + 180.936i −1.49595 + 0.619644i
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 224.704 + 542.482i 0.764298 + 1.84518i
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 1473.37 1473.37i 4.96085 4.96085i
$$298$$ 0 0
$$299$$ 0 0
$$300$$ 553.553 + 229.289i 1.84518 + 0.764298i
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ −192.000 192.000i −0.631579 0.631579i
$$305$$ 0 0
$$306$$ −607.546 + 683.630i −1.98545 + 2.23408i
$$307$$ −542.000 −1.76547 −0.882736 0.469869i $$-0.844301\pi$$
−0.882736 + 0.469869i $$0.844301\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$312$$ 0 0
$$313$$ −42.9691 + 103.737i −0.137281 + 0.331427i −0.977537 0.210764i $$-0.932405\pi$$
0.840256 + 0.542191i $$0.182405\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 753.580 + 753.580i 2.34760 + 2.34760i
$$322$$ 0 0
$$323$$ −288.000 + 16.9706i −0.891641 + 0.0525404i
$$324$$ 1601.95 4.94429
$$325$$ 0 0
$$326$$ 140.777 58.3116i 0.431830 0.178870i
$$327$$ 0 0
$$328$$ −50.5786 122.108i −0.154203 0.372279i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −323.926 + 323.926i −0.978628 + 0.978628i −0.999776 0.0211480i $$-0.993268\pi$$
0.0211480 + 0.999776i $$0.493268\pi$$
$$332$$ −214.177 + 214.177i −0.645110 + 0.645110i
$$333$$ 0 0
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 236.589 97.9985i 0.702046 0.290797i −0.00296297 0.999996i $$-0.500943\pi$$
0.705009 + 0.709199i $$0.250943\pi$$
$$338$$ −239.002 239.002i −0.707107 0.707107i
$$339$$ 902.590 2.66251
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 645.588 + 645.588i 1.88768 + 1.88768i
$$343$$ 0 0
$$344$$ 400.804i 1.16513i
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −264.947 + 639.638i −0.763535 + 1.84334i −0.317892 + 0.948127i $$0.602975\pi$$
−0.445643 + 0.895211i $$0.647025\pi$$
$$348$$ 0 0
$$349$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 237.921 + 574.392i 0.675912 + 1.63180i
$$353$$ 617.179i 1.74838i −0.485583 0.874191i $$-0.661392\pi$$
0.485583 0.874191i $$-0.338608\pi$$
$$354$$ 22.3330 9.25065i 0.0630877 0.0261318i
$$355$$ 0 0
$$356$$ −124.950 −0.350984
$$357$$ 0 0
$$358$$ −712.764 −1.99096
$$359$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$360$$ 0 0
$$361$$ 73.0000i 0.202216i
$$362$$ 0 0
$$363$$ −1419.72 588.065i −3.91106 1.62001i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$368$$ 0 0
$$369$$ 170.067 + 410.579i 0.460888 + 1.11268i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 624.105 + 216.454i 1.66873 + 0.578753i
$$375$$ 0 0
$$376$$ 0 0
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 195.317 + 471.538i 0.515349 + 1.24416i 0.940733 + 0.339149i $$0.110139\pi$$
−0.425383 + 0.905013i $$0.639861\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$384$$ −293.490 + 708.548i −0.764298 + 1.84518i
$$385$$ 0 0
$$386$$ 292.704 + 706.649i 0.758299 + 1.83070i
$$387$$ 1347.68i 3.48237i
$$388$$ −712.347 + 295.064i −1.83595 + 0.760474i
$$389$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 392.000 1.00000
$$393$$ −170.040 170.040i −0.432671 0.432671i
$$394$$ 0 0
$$395$$ 0 0
$$396$$ −799.994 1931.36i −2.02019 4.87716i
$$397$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 282.843 282.843i 0.707107 0.707107i
$$401$$ −28.1781 + 68.0280i −0.0702696 + 0.169646i −0.955112 0.296244i $$-0.904266\pi$$
0.884843 + 0.465890i $$0.154266\pi$$
$$402$$ −1415.33 586.250i −3.52073 1.45833i
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 355.578 + 733.186i 0.871514 + 1.79702i
$$409$$ −291.826 −0.713512 −0.356756 0.934198i $$-0.616117\pi$$
−0.356756 + 0.934198i $$0.616117\pi$$
$$410$$ 0 0
$$411$$ 751.529 311.294i 1.82854 0.757405i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0 0
$$417$$ −396.698 + 396.698i −0.951315 + 0.951315i
$$418$$ 252.353 609.235i 0.603716 1.45750i
$$419$$ 383.200 + 158.726i 0.914557 + 0.378822i 0.789799 0.613365i $$-0.210185\pi$$
0.124758 + 0.992187i $$0.460185\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$422$$ 637.806 264.188i 1.51139 0.626038i
$$423$$ 0 0
$$424$$ 0 0
$$425$$ −25.0000 424.264i −0.0588235 0.998268i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 657.318 272.270i 1.53579 0.636145i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$432$$ 656.666 1585.33i 1.52006 3.66975i
$$433$$ −456.000 + 456.000i −1.05312 + 1.05312i −0.0546100 + 0.998508i $$0.517392\pi$$
−0.998508 + 0.0546100i $$0.982608\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 1416.44i 3.23389i
$$439$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$440$$ 0 0
$$441$$ −1318.08 −2.98883
$$442$$ 0 0
$$443$$ 704.840 1.59106 0.795530 0.605914i $$-0.207192\pi$$
0.795530 + 0.605914i $$0.207192\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 210.823 508.971i 0.469538 1.13357i −0.494827 0.868992i $$-0.664769\pi$$
0.964365 0.264574i $$-0.0852315\pi$$
$$450$$ −951.041 + 951.041i −2.11342 + 2.11342i
$$451$$ 226.968 226.968i 0.503256 0.503256i
$$452$$ 230.593 556.701i 0.510161 1.23164i
$$453$$ 0 0
$$454$$ −70.6304 170.517i −0.155574 0.375588i
$$455$$ 0 0
$$456$$ 751.529 311.294i 1.64809 0.682661i
$$457$$ 624.000 + 624.000i 1.36543 + 1.36543i 0.866840 + 0.498587i $$0.166148\pi$$
0.498587 + 0.866840i $$0.333852\pi$$
$$458$$ 0 0
$$459$$ −795.583 1640.46i −1.73330 3.57398i
$$460$$ 0 0
$$461$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ −247.116 + 596.590i −0.530291 + 1.28024i
$$467$$ −660.000 + 660.000i −1.41328 + 1.41328i −0.680898 + 0.732379i $$0.738410\pi$$
−0.732379 + 0.680898i $$0.761590\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 16.1380i 0.0341906i
$$473$$ 899.291 372.499i 1.90125 0.787524i
$$474$$ 0 0
$$475$$ −424.264 −0.893188
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −643.179 266.413i −1.33440 0.552725i
$$483$$ 0 0
$$484$$ −725.415 + 725.415i −1.49879 + 1.49879i
$$485$$ 0 0
$$486$$ −1097.80 + 2650.32i −2.25885 + 5.45334i
$$487$$ 0 0 −0.923880 0.382683i $$-0.875000\pi$$
0.923880 + 0.382683i $$0.125000\pi$$
$$488$$ 0 0
$$489$$ 456.488i 0.933514i
$$490$$ 0 0
$$491$$ 420.000 + 420.000i 0.855397 + 0.855397i 0.990792 0.135395i $$-0.0432302\pi$$
−0.135395 + 0.990792i $$0.543230\pi$$
$$492$$ 395.951 0.804779
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ −347.249 838.333i −0.697287 1.68340i
$$499$$ 474.550 + 196.565i 0.951002 + 0.393918i 0.803607 0.595160i $$-0.202911\pi$$
0.147394 + 0.989078i $$0.452911\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ 279.324 279.324i 0.556422 0.556422i
$$503$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 935.505 387.499i 1.84518 0.764298i
$$508$$ 0 0
$$509$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 362.039 + 362.039i 0.707107 + 0.707107i
$$513$$ −1681.50 + 696.500i −3.27778 + 1.35770i
$$514$$ 1025.89i 1.99589i
$$515$$ 0 0
$$516$$ 1109.33 + 459.500i 2.14987 + 0.890505i
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 954.675 + 395.439i 1.83239 + 0.759000i 0.965451 + 0.260584i $$0.0839152\pi$$
0.866938 + 0.498416i $$0.166085\pi$$
$$522$$ 0 0
$$523$$ 965.428i 1.84594i −0.384868 0.922972i $$-0.625753\pi$$
0.384868 0.922972i $$-0.374247\pi$$
$$524$$ −148.319 + 61.4356i −0.283051 + 0.117244i
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ −1862.55 −3.52755
$$529$$ 374.059 + 374.059i 0.707107 + 0.707107i
$$530$$ 0 0
$$531$$ 54.2628i 0.102190i
$$532$$ 0 0
$$533$$ 0 0
$$534$$ 143.249 345.833i 0.268256 0.647628i
$$535$$ 0 0
$$536$$ −723.176 + 723.176i −1.34921 + 1.34921i
$$537$$ 817.145 1972.76i 1.52169 3.67368i
$$538$$ 0 0
$$539$$ 364.316 + 879.538i 0.675912 + 1.63180i
$$540$$ 0 0
$$541$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 543.058 32.0000i 0.998268 0.0588235i
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −694.493 + 287.668i −1.26964 + 0.525902i −0.912855 0.408284i $$-0.866127\pi$$
−0.356785 + 0.934186i $$0.616127\pi$$
$$548$$ 543.058i 0.990982i
$$549$$ 0 0
$$550$$ 897.487 + 371.751i 1.63180 + 0.675912i
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 143.328 + 346.024i 0.257784 + 0.622346i
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ −1314.60 + 1479.22i −2.34331 + 2.63676i
$$562$$ 1018.23 1.81180
$$563$$ 664.543 + 664.543i 1.18036 + 1.18036i 0.979651 + 0.200710i $$0.0643251\pi$$
0.200710 + 0.979651i $$0.435675\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 106.046 + 256.017i 0.187360 + 0.452327i
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −162.176 + 162.176i −0.285019 + 0.285019i −0.835107 0.550088i $$-0.814594\pi$$
0.550088 + 0.835107i $$0.314594\pi$$
$$570$$ 0 0
$$571$$ −95.9477 + 231.638i −0.168034 + 0.405671i −0.985356 0.170511i $$-0.945458\pi$$
0.817321 + 0.576182i $$0.195458\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −1217.33 1217.33i −2.11342 2.11342i
$$577$$ 2.00000 0.00346620 0.00173310 0.999998i $$-0.499448\pi$$
0.00173310 + 0.999998i $$0.499448\pi$$
$$578$$ 357.879 453.879i 0.619168 0.785258i
$$579$$ −2291.41 −3.95753
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 2309.89i 3.96888i
$$583$$ 0 0
$$584$$ −873.637 361.872i −1.49595 0.619644i
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −804.688 + 804.688i −1.37085 + 1.37085i −0.511659 + 0.859189i $$0.670969\pi$$
−0.859189 + 0.511659i $$0.829031\pi$$
$$588$$ −449.407 + 1084.96i −0.764298 + 1.84518i
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ −23.7065 23.7065i −0.0399772 0.0399772i 0.686836 0.726813i $$-0.258999\pi$$
−0.726813 + 0.686836i $$0.758999\pi$$
$$594$$ 4167.33 7.01571
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$600$$ 458.579 + 1107.11i 0.764298 + 1.84518i
$$601$$ −343.175 142.148i −0.571007 0.236519i 0.0784489 0.996918i $$-0.475003\pi$$
−0.649456 + 0.760399i $$0.725003\pi$$
$$602$$ 0 0
$$603$$ 2431.63 2431.63i 4.03256 4.03256i
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$608$$ 543.058i 0.893188i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ −1826.00 + 107.598i −2.98366 + 0.175814i
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ −766.504 766.504i −1.24838 1.24838i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ −292.057 705.087i −0.473349 1.14277i −0.962674 0.270665i $$-0.912757\pi$$
0.489324 0.872102i $$-0.337243\pi$$
$$618$$ 0 0
$$619$$ 307.697 742.846i 0.497087 1.20007i −0.453958 0.891023i $$-0.649988\pi$$
0.951045 0.309052i $$-0.100012\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 625.000i 1.00000i
$$626$$ −207.473 + 85.9382i −0.331427 + 0.137281i
$$627$$ 1396.91 + 1396.91i 2.22793 + 2.22793i
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$632$$ 0 0
$$633$$ 2068.18i 3.26726i
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −3.55696 8.58727i −0.00554908 0.0133967i 0.921081 0.389372i $$-0.127308\pi$$
−0.926630 + 0.375975i $$0.877308\pi$$
$$642$$ 2131.45i 3.32001i
$$643$$ −886.214 + 367.082i −1.37825 + 0.570889i −0.944012 0.329910i $$-0.892982\pi$$
−0.434236 + 0.900799i $$0.642982\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −431.294 383.294i −0.667637 0.593334i
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ 2265.50 + 2265.50i 3.49614 + 3.49614i
$$649$$ 36.2090 14.9983i 0.0557920 0.0231098i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 281.553 + 116.623i 0.431830 + 0.178870i
$$653$$ 0 0 0.382683 0.923880i $$-0.375000\pi$$
−0.382683 + 0.923880i $$0.625000\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 101.157 244.215i 0.154203 0.372279i
$$657$$ 2937.55 + 1216.77i 4.47115 + 1.85201i
$$658$$ 0 0
$$659$$ 994.000i 1.50835i 0.656676 + 0.754173i $$0.271962\pi$$
−0.656676 + 0.754173i $$0.728038\pi$$
$$660$$ 0 0
$$661$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$662$$ −916.201 −1.38399
$$663$$ 0 0
$$664$$ −605.783 −0.912324
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 365.969 883.528i 0.543788 1.31282i −0.378244 0.925706i $$-0.623472\pi$$
0.922032 0.387114i $$-0.126528\pi$$
$$674$$ 473.179 + 195.997i 0.702046 + 0.290797i
$$675$$ −1026.04 2477.08i −1.52006 3.66975i
$$676$$ 676.000i 1.00000i
$$677$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$678$$ 1276.45 + 1276.45i 1.88268 + 1.88268i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 552.925 0.811931
$$682$$ 0 0
$$683$$ −801.714 + 332.081i −1.17381 + 0.486209i −0.882451 0.470404i $$-0.844108\pi$$
−0.291362 + 0.956613i $$0.594108\pi$$
$$684$$ 1826.00i 2.66959i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 566.823 566.823i 0.823870 0.823870i
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 212.508 + 88.0238i 0.307537 + 0.127386i 0.531114 0.847300i $$-0.321773\pi$$
−0.223577 + 0.974686i $$0.571773\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ −1279.28 + 529.894i −1.84334 + 0.763535i
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −122.557 252.707i −0.175835 0.362564i
$$698$$ 0 0
$$699$$ −1367.92 1367.92i −1.95696 1.95696i
$$700$$ 0 0
$$701$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ −475.842 + 1148.78i −0.675912 + 1.63180i
$$705$$ 0 0
$$706$$ 872.823 872.823i 1.23629 1.23629i
$$707$$ 0 0
$$708$$ 44.6661 + 18.5013i 0.0630877 + 0.0261318i
$$709$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ −176.706 176.706i −0.248183 0.248183i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −1008.00 1008.00i −1.40782 1.40782i
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 103.238 103.238i 0.142988 0.142988i
$$723$$ 1474.74 1474.74i 2.03975 2.03975i
$$724$$ 0 0
$$725$$ 0 0
$$726$$ −1176.13 2839.43i −1.62001 3.91106i
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ −3528.22 3528.22i −4.83981 4.83981i
$$730$$ 0 0
$$731$$ −50.1005 850.234i −0.0685369 1.16311i
$$732$$ 0 0
$$733$$ 0 0 −0.707107 0.707107i $$-0.750000\pi$$
0.707107 + 0.707107i $$0.250000\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ −2294.71 950.499i −3.11358 1.28969i
$$738$$ −340.135 + 821.159i −0.460888 + 1.11268i
$$739$$ −227.688 + 227.688i −0.308103 + 0.308103i −0.844173 0.536070i $$-0.819908\pi$$
0.536070 + 0.844173i $$0.319908\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 −0.382683 0.923880i $$-0.625000\pi$$
0.382683 + 0.923880i $$0.375000\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 2036.91 2.72678
$$748$$ 576.505 + 1188.73i 0.770729 + 1.58921i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 0.923880 0.382683i $$-0.125000\pi$$
−0.923880 + 0.382683i $$0.875000\pi$$
$$752$$ 0 0
$$753$$ 452.873 + 1093.33i 0.601425 + 1.45197i
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$758$$ −390.635 + 943.075i −0.515349 + 1.24416i
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 610.940i 0.802812i 0.915900 + 0.401406i $$0.131478\pi$$
−0.915900 + 0.401406i $$0.868522\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ −1417.10 + 586.981i −1.84518 + 0.764298i
$$769$$ 1120.06i 1.45651i −0.685306 0.728256i $$-0.740331\pi$$
0.685306 0.728256i $$-0.259669\pi$$
$$770$$ 0 0
$$771$$ 2839.41 + 1176.12i 3.68277 + 1.52545i
$$772$$ −585.407 + 1413.30i −0.758299 + 1.83070i
$$773$$ 0 0 0.707107 0.707107i $$-0.250000\pi$$
−0.707107 + 0.707107i $$0.750000\pi$$
$$774$$ −1905.90 + 1905.90i −2.46241 + 2.46241i
$$775$$ 0 0
$$776$$ −1424.69 590.128i −1.83595 0.760474i
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −259.029 + 107.294i −0.332515 + 0.137732i
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 554.372 + 554.372i 0.707107 + 0.707107i
$$785$$ 0 0
$$786$$ 480.944i 0.611889i
$$787$$ −585.610 1413.79i −0.744104 1.79643i −0.588310 0.808635i $$-0.700207\pi$$
−0.155794 0.987790i $$-0.549793\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 1599.99 3862.71i 2.02019 4.87716i
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0