Properties

 Label 1680.2.cz.d.433.8 Level 1680 Weight 2 Character 1680.433 Analytic conductor 13.415 Analytic rank 0 Dimension 16 CM no Inner twists 4

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1680.cz (of order $$4$$, degree $$2$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$13.4148675396$$ Analytic rank: $$0$$ Dimension: $$16$$ Relative dimension: $$8$$ over $$\Q(i)$$ Coefficient field: $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ Defining polynomial: $$x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256$$ Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2^{8}$$ Twist minimal: no (minimal twist has level 105) Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

 Embedding label 433.8 Root $$-0.944649 - 1.05244i$$ of defining polynomial Character $$\chi$$ $$=$$ 1680.433 Dual form 1680.2.cz.d.97.8

$q$-expansion

 $$f(q)$$ $$=$$ $$q+(0.707107 - 0.707107i) q^{3} +(1.28999 - 1.82645i) q^{5} +(1.75993 - 1.97552i) q^{7} -1.00000i q^{9} +O(q^{10})$$ $$q+(0.707107 - 0.707107i) q^{3} +(1.28999 - 1.82645i) q^{5} +(1.75993 - 1.97552i) q^{7} -1.00000i q^{9} +2.67187 q^{11} +(-1.22714 + 1.22714i) q^{13} +(-0.379340 - 2.20366i) q^{15} +(4.74624 + 4.74624i) q^{17} +6.01729 q^{19} +(-0.152445 - 2.64136i) q^{21} +(0.175684 + 0.175684i) q^{23} +(-1.67187 - 4.71220i) q^{25} +(-0.707107 - 0.707107i) q^{27} +0.304889i q^{29} +7.25379i q^{31} +(1.88930 - 1.88930i) q^{33} +(-1.33791 - 5.76281i) q^{35} +(-0.735441 + 0.735441i) q^{37} +1.73544i q^{39} -7.05736i q^{41} +(-0.304889 - 0.304889i) q^{43} +(-1.82645 - 1.28999i) q^{45} +(0.556866 + 0.556866i) q^{47} +(-0.805321 - 6.95352i) q^{49} +6.71220 q^{51} +(-4.99031 - 4.99031i) q^{53} +(3.44668 - 4.88005i) q^{55} +(4.25487 - 4.25487i) q^{57} -7.98837 q^{59} +5.53409i q^{61} +(-1.97552 - 1.75993i) q^{63} +(0.658323 + 3.82432i) q^{65} +(3.43055 - 3.43055i) q^{67} +0.248455 q^{69} -15.3087 q^{71} +(-10.0208 + 10.0208i) q^{73} +(-4.51422 - 2.14984i) q^{75} +(4.70230 - 5.27832i) q^{77} -11.2973i q^{79} -1.00000 q^{81} +(-4.88941 + 4.88941i) q^{83} +(14.7914 - 2.54621i) q^{85} +(0.215589 + 0.215589i) q^{87} -6.91251 q^{89} +(0.264559 + 4.58392i) q^{91} +(5.12921 + 5.12921i) q^{93} +(7.76222 - 10.9903i) q^{95} +(8.84137 + 8.84137i) q^{97} -2.67187i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$16q + 8q^{7} + O(q^{10})$$ $$16q + 8q^{7} + 16q^{11} - 8q^{15} + 8q^{21} + 40q^{23} + 8q^{35} + 32q^{37} + 16q^{43} + 16q^{51} + 24q^{53} + 8q^{57} - 8q^{63} + 40q^{65} + 32q^{67} - 64q^{71} - 24q^{77} - 16q^{81} + 48q^{85} + 48q^{91} + 24q^{93} + 72q^{95} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$$.

 $$n$$ $$241$$ $$337$$ $$421$$ $$1121$$ $$1471$$ $$\chi(n)$$ $$-1$$ $$e\left(\frac{3}{4}\right)$$ $$1$$ $$1$$ $$1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 0.707107 0.707107i 0.408248 0.408248i
$$4$$ 0 0
$$5$$ 1.28999 1.82645i 0.576899 0.816815i
$$6$$ 0 0
$$7$$ 1.75993 1.97552i 0.665189 0.746675i
$$8$$ 0 0
$$9$$ 1.00000i 0.333333i
$$10$$ 0 0
$$11$$ 2.67187 0.805600 0.402800 0.915288i $$-0.368037\pi$$
0.402800 + 0.915288i $$0.368037\pi$$
$$12$$ 0 0
$$13$$ −1.22714 + 1.22714i −0.340348 + 0.340348i −0.856498 0.516150i $$-0.827365\pi$$
0.516150 + 0.856498i $$0.327365\pi$$
$$14$$ 0 0
$$15$$ −0.379340 2.20366i −0.0979452 0.568982i
$$16$$ 0 0
$$17$$ 4.74624 + 4.74624i 1.15113 + 1.15113i 0.986326 + 0.164807i $$0.0527002\pi$$
0.164807 + 0.986326i $$0.447300\pi$$
$$18$$ 0 0
$$19$$ 6.01729 1.38046 0.690231 0.723589i $$-0.257509\pi$$
0.690231 + 0.723589i $$0.257509\pi$$
$$20$$ 0 0
$$21$$ −0.152445 2.64136i −0.0332662 0.576391i
$$22$$ 0 0
$$23$$ 0.175684 + 0.175684i 0.0366327 + 0.0366327i 0.725186 0.688553i $$-0.241754\pi$$
−0.688553 + 0.725186i $$0.741754\pi$$
$$24$$ 0 0
$$25$$ −1.67187 4.71220i −0.334374 0.942440i
$$26$$ 0 0
$$27$$ −0.707107 0.707107i −0.136083 0.136083i
$$28$$ 0 0
$$29$$ 0.304889i 0.0566165i 0.999599 + 0.0283083i $$0.00901200\pi$$
−0.999599 + 0.0283083i $$0.990988\pi$$
$$30$$ 0 0
$$31$$ 7.25379i 1.30282i 0.758726 + 0.651410i $$0.225822\pi$$
−0.758726 + 0.651410i $$0.774178\pi$$
$$32$$ 0 0
$$33$$ 1.88930 1.88930i 0.328885 0.328885i
$$34$$ 0 0
$$35$$ −1.33791 5.76281i −0.226148 0.974093i
$$36$$ 0 0
$$37$$ −0.735441 + 0.735441i −0.120906 + 0.120906i −0.764971 0.644065i $$-0.777247\pi$$
0.644065 + 0.764971i $$0.277247\pi$$
$$38$$ 0 0
$$39$$ 1.73544i 0.277893i
$$40$$ 0 0
$$41$$ 7.05736i 1.10217i −0.834447 0.551087i $$-0.814213\pi$$
0.834447 0.551087i $$-0.185787\pi$$
$$42$$ 0 0
$$43$$ −0.304889 0.304889i −0.0464952 0.0464952i 0.683477 0.729972i $$-0.260467\pi$$
−0.729972 + 0.683477i $$0.760467\pi$$
$$44$$ 0 0
$$45$$ −1.82645 1.28999i −0.272272 0.192300i
$$46$$ 0 0
$$47$$ 0.556866 + 0.556866i 0.0812273 + 0.0812273i 0.746553 0.665326i $$-0.231707\pi$$
−0.665326 + 0.746553i $$0.731707\pi$$
$$48$$ 0 0
$$49$$ −0.805321 6.95352i −0.115046 0.993360i
$$50$$ 0 0
$$51$$ 6.71220 0.939896
$$52$$ 0 0
$$53$$ −4.99031 4.99031i −0.685472 0.685472i 0.275756 0.961228i $$-0.411072\pi$$
−0.961228 + 0.275756i $$0.911072\pi$$
$$54$$ 0 0
$$55$$ 3.44668 4.88005i 0.464750 0.658026i
$$56$$ 0 0
$$57$$ 4.25487 4.25487i 0.563571 0.563571i
$$58$$ 0 0
$$59$$ −7.98837 −1.04000 −0.519999 0.854167i $$-0.674068\pi$$
−0.519999 + 0.854167i $$0.674068\pi$$
$$60$$ 0 0
$$61$$ 5.53409i 0.708567i 0.935138 + 0.354284i $$0.115275\pi$$
−0.935138 + 0.354284i $$0.884725\pi$$
$$62$$ 0 0
$$63$$ −1.97552 1.75993i −0.248892 0.221730i
$$64$$ 0 0
$$65$$ 0.658323 + 3.82432i 0.0816549 + 0.474348i
$$66$$ 0 0
$$67$$ 3.43055 3.43055i 0.419109 0.419109i −0.465788 0.884896i $$-0.654229\pi$$
0.884896 + 0.465788i $$0.154229\pi$$
$$68$$ 0 0
$$69$$ 0.248455 0.0299104
$$70$$ 0 0
$$71$$ −15.3087 −1.81681 −0.908407 0.418087i $$-0.862701\pi$$
−0.908407 + 0.418087i $$0.862701\pi$$
$$72$$ 0 0
$$73$$ −10.0208 + 10.0208i −1.17285 + 1.17285i −0.191323 + 0.981527i $$0.561278\pi$$
−0.981527 + 0.191323i $$0.938722\pi$$
$$74$$ 0 0
$$75$$ −4.51422 2.14984i −0.521257 0.248242i
$$76$$ 0 0
$$77$$ 4.70230 5.27832i 0.535876 0.601521i
$$78$$ 0 0
$$79$$ 11.2973i 1.27104i −0.772084 0.635521i $$-0.780785\pi$$
0.772084 0.635521i $$-0.219215\pi$$
$$80$$ 0 0
$$81$$ −1.00000 −0.111111
$$82$$ 0 0
$$83$$ −4.88941 + 4.88941i −0.536682 + 0.536682i −0.922553 0.385871i $$-0.873901\pi$$
0.385871 + 0.922553i $$0.373901\pi$$
$$84$$ 0 0
$$85$$ 14.7914 2.54621i 1.60435 0.276175i
$$86$$ 0 0
$$87$$ 0.215589 + 0.215589i 0.0231136 + 0.0231136i
$$88$$ 0 0
$$89$$ −6.91251 −0.732725 −0.366363 0.930472i $$-0.619397\pi$$
−0.366363 + 0.930472i $$0.619397\pi$$
$$90$$ 0 0
$$91$$ 0.264559 + 4.58392i 0.0277333 + 0.480525i
$$92$$ 0 0
$$93$$ 5.12921 + 5.12921i 0.531874 + 0.531874i
$$94$$ 0 0
$$95$$ 7.76222 10.9903i 0.796387 1.12758i
$$96$$ 0 0
$$97$$ 8.84137 + 8.84137i 0.897705 + 0.897705i 0.995233 0.0975276i $$-0.0310934\pi$$
−0.0975276 + 0.995233i $$0.531093\pi$$
$$98$$ 0 0
$$99$$ 2.67187i 0.268533i
$$100$$ 0 0
$$101$$ 7.22962i 0.719374i −0.933073 0.359687i $$-0.882883\pi$$
0.933073 0.359687i $$-0.117117\pi$$
$$102$$ 0 0
$$103$$ −6.94538 + 6.94538i −0.684349 + 0.684349i −0.960977 0.276628i $$-0.910783\pi$$
0.276628 + 0.960977i $$0.410783\pi$$
$$104$$ 0 0
$$105$$ −5.02097 3.12888i −0.489996 0.305347i
$$106$$ 0 0
$$107$$ 7.47295 7.47295i 0.722437 0.722437i −0.246664 0.969101i $$-0.579334\pi$$
0.969101 + 0.246664i $$0.0793344\pi$$
$$108$$ 0 0
$$109$$ 5.95352i 0.570244i 0.958491 + 0.285122i $$0.0920341\pi$$
−0.958491 + 0.285122i $$0.907966\pi$$
$$110$$ 0 0
$$111$$ 1.04007i 0.0987192i
$$112$$ 0 0
$$113$$ 6.99031 + 6.99031i 0.657593 + 0.657593i 0.954810 0.297217i $$-0.0960585\pi$$
−0.297217 + 0.954810i $$0.596058\pi$$
$$114$$ 0 0
$$115$$ 0.547509 0.0942489i 0.0510555 0.00878876i
$$116$$ 0 0
$$117$$ 1.22714 + 1.22714i 0.113449 + 0.113449i
$$118$$ 0 0
$$119$$ 17.7293 1.02324i 1.62524 0.0938002i
$$120$$ 0 0
$$121$$ −3.86110 −0.351009
$$122$$ 0 0
$$123$$ −4.99031 4.99031i −0.449961 0.449961i
$$124$$ 0 0
$$125$$ −10.7633 3.02508i −0.962700 0.270571i
$$126$$ 0 0
$$127$$ −2.86110 + 2.86110i −0.253882 + 0.253882i −0.822560 0.568678i $$-0.807455\pi$$
0.568678 + 0.822560i $$0.307455\pi$$
$$128$$ 0 0
$$129$$ −0.431179 −0.0379632
$$130$$ 0 0
$$131$$ 9.34764i 0.816707i −0.912824 0.408353i $$-0.866103\pi$$
0.912824 0.408353i $$-0.133897\pi$$
$$132$$ 0 0
$$133$$ 10.5900 11.8873i 0.918268 1.03076i
$$134$$ 0 0
$$135$$ −2.20366 + 0.379340i −0.189661 + 0.0326484i
$$136$$ 0 0
$$137$$ 7.51943 7.51943i 0.642428 0.642428i −0.308724 0.951152i $$-0.599902\pi$$
0.951152 + 0.308724i $$0.0999019\pi$$
$$138$$ 0 0
$$139$$ 7.78902 0.660656 0.330328 0.943866i $$-0.392841\pi$$
0.330328 + 0.943866i $$0.392841\pi$$
$$140$$ 0 0
$$141$$ 0.787528 0.0663218
$$142$$ 0 0
$$143$$ −3.27877 + 3.27877i −0.274184 + 0.274184i
$$144$$ 0 0
$$145$$ 0.556866 + 0.393303i 0.0462452 + 0.0326620i
$$146$$ 0 0
$$147$$ −5.48633 4.34743i −0.452505 0.358570i
$$148$$ 0 0
$$149$$ 14.2855i 1.17031i −0.810920 0.585157i $$-0.801033\pi$$
0.810920 0.585157i $$-0.198967\pi$$
$$150$$ 0 0
$$151$$ −9.77990 −0.795877 −0.397939 0.917412i $$-0.630274\pi$$
−0.397939 + 0.917412i $$0.630274\pi$$
$$152$$ 0 0
$$153$$ 4.74624 4.74624i 0.383711 0.383711i
$$154$$ 0 0
$$155$$ 13.2487 + 9.35729i 1.06416 + 0.751596i
$$156$$ 0 0
$$157$$ −2.17731 2.17731i −0.173768 0.173768i 0.614864 0.788633i $$-0.289211\pi$$
−0.788633 + 0.614864i $$0.789211\pi$$
$$158$$ 0 0
$$159$$ −7.05736 −0.559685
$$160$$ 0 0
$$161$$ 0.656257 0.0378756i 0.0517203 0.00298502i
$$162$$ 0 0
$$163$$ 13.6757 + 13.6757i 1.07117 + 1.07117i 0.997266 + 0.0739001i $$0.0235446\pi$$
0.0739001 + 0.997266i $$0.476455\pi$$
$$164$$ 0 0
$$165$$ −1.01355 5.88789i −0.0789046 0.458371i
$$166$$ 0 0
$$167$$ −6.23288 6.23288i −0.482315 0.482315i 0.423555 0.905870i $$-0.360782\pi$$
−0.905870 + 0.423555i $$0.860782\pi$$
$$168$$ 0 0
$$169$$ 9.98824i 0.768326i
$$170$$ 0 0
$$171$$ 6.01729i 0.460154i
$$172$$ 0 0
$$173$$ −6.76935 + 6.76935i −0.514664 + 0.514664i −0.915952 0.401288i $$-0.868563\pi$$
0.401288 + 0.915952i $$0.368563\pi$$
$$174$$ 0 0
$$175$$ −12.2514 4.99032i −0.926119 0.377233i
$$176$$ 0 0
$$177$$ −5.64863 + 5.64863i −0.424577 + 0.424577i
$$178$$ 0 0
$$179$$ 1.30103i 0.0972437i 0.998817 + 0.0486218i $$0.0154829\pi$$
−0.998817 + 0.0486218i $$0.984517\pi$$
$$180$$ 0 0
$$181$$ 8.48528i 0.630706i 0.948974 + 0.315353i $$0.102123\pi$$
−0.948974 + 0.315353i $$0.897877\pi$$
$$182$$ 0 0
$$183$$ 3.91319 + 3.91319i 0.289271 + 0.289271i
$$184$$ 0 0
$$185$$ 0.394541 + 2.29196i 0.0290072 + 0.168508i
$$186$$ 0 0
$$187$$ 12.6814 + 12.6814i 0.927352 + 0.927352i
$$188$$ 0 0
$$189$$ −2.64136 + 0.152445i −0.192130 + 0.0110887i
$$190$$ 0 0
$$191$$ −1.93791 −0.140222 −0.0701110 0.997539i $$-0.522335\pi$$
−0.0701110 + 0.997539i $$0.522335\pi$$
$$192$$ 0 0
$$193$$ −7.82786 7.82786i −0.563462 0.563462i 0.366827 0.930289i $$-0.380444\pi$$
−0.930289 + 0.366827i $$0.880444\pi$$
$$194$$ 0 0
$$195$$ 3.16970 + 2.23870i 0.226987 + 0.160316i
$$196$$ 0 0
$$197$$ −8.50767 + 8.50767i −0.606146 + 0.606146i −0.941937 0.335790i $$-0.890997\pi$$
0.335790 + 0.941937i $$0.390997\pi$$
$$198$$ 0 0
$$199$$ −3.25460 −0.230712 −0.115356 0.993324i $$-0.536801\pi$$
−0.115356 + 0.993324i $$0.536801\pi$$
$$200$$ 0 0
$$201$$ 4.85153i 0.342201i
$$202$$ 0 0
$$203$$ 0.602314 + 0.536583i 0.0422741 + 0.0376607i
$$204$$ 0 0
$$205$$ −12.8900 9.10390i −0.900273 0.635844i
$$206$$ 0 0
$$207$$ 0.175684 0.175684i 0.0122109 0.0122109i
$$208$$ 0 0
$$209$$ 16.0774 1.11210
$$210$$ 0 0
$$211$$ 17.2508 1.18759 0.593797 0.804615i $$-0.297628\pi$$
0.593797 + 0.804615i $$0.297628\pi$$
$$212$$ 0 0
$$213$$ −10.8249 + 10.8249i −0.741711 + 0.741711i
$$214$$ 0 0
$$215$$ −0.950169 + 0.163563i −0.0648010 + 0.0111549i
$$216$$ 0 0
$$217$$ 14.3300 + 12.7661i 0.972782 + 0.866622i
$$218$$ 0 0
$$219$$ 14.1716i 0.957628i
$$220$$ 0 0
$$221$$ −11.6486 −0.783572
$$222$$ 0 0
$$223$$ −4.58392 + 4.58392i −0.306962 + 0.306962i −0.843730 0.536768i $$-0.819645\pi$$
0.536768 + 0.843730i $$0.319645\pi$$
$$224$$ 0 0
$$225$$ −4.71220 + 1.67187i −0.314147 + 0.111458i
$$226$$ 0 0
$$227$$ 14.1613 + 14.1613i 0.939918 + 0.939918i 0.998295 0.0583764i $$-0.0185924\pi$$
−0.0583764 + 0.998295i $$0.518592\pi$$
$$228$$ 0 0
$$229$$ 28.9307 1.91180 0.955898 0.293699i $$-0.0948864\pi$$
0.955898 + 0.293699i $$0.0948864\pi$$
$$230$$ 0 0
$$231$$ −0.407313 7.05736i −0.0267992 0.464340i
$$232$$ 0 0
$$233$$ −4.78546 4.78546i −0.313506 0.313506i 0.532760 0.846266i $$-0.321155\pi$$
−0.846266 + 0.532760i $$0.821155\pi$$
$$234$$ 0 0
$$235$$ 1.73544 0.298741i 0.113208 0.0194877i
$$236$$ 0 0
$$237$$ −7.98837 7.98837i −0.518901 0.518901i
$$238$$ 0 0
$$239$$ 16.1769i 1.04640i 0.852210 + 0.523200i $$0.175262\pi$$
−0.852210 + 0.523200i $$0.824738\pi$$
$$240$$ 0 0
$$241$$ 11.3707i 0.732454i −0.930526 0.366227i $$-0.880649\pi$$
0.930526 0.366227i $$-0.119351\pi$$
$$242$$ 0 0
$$243$$ −0.707107 + 0.707107i −0.0453609 + 0.0453609i
$$244$$ 0 0
$$245$$ −13.7391 7.49906i −0.877762 0.479098i
$$246$$ 0 0
$$247$$ −7.38407 + 7.38407i −0.469837 + 0.469837i
$$248$$ 0 0
$$249$$ 6.91467i 0.438199i
$$250$$ 0 0
$$251$$ 6.95039i 0.438705i −0.975646 0.219352i $$-0.929606\pi$$
0.975646 0.219352i $$-0.0703944\pi$$
$$252$$ 0 0
$$253$$ 0.469405 + 0.469405i 0.0295112 + 0.0295112i
$$254$$ 0 0
$$255$$ 8.65865 12.2595i 0.542226 0.767722i
$$256$$ 0 0
$$257$$ −10.0889 10.0889i −0.629329 0.629329i 0.318570 0.947899i $$-0.396797\pi$$
−0.947899 + 0.318570i $$0.896797\pi$$
$$258$$ 0 0
$$259$$ 0.158553 + 2.74720i 0.00985202 + 0.170703i
$$260$$ 0 0
$$261$$ 0.304889 0.0188722
$$262$$ 0 0
$$263$$ −18.1984 18.1984i −1.12216 1.12216i −0.991416 0.130744i $$-0.958263\pi$$
−0.130744 0.991416i $$-0.541737\pi$$
$$264$$ 0 0
$$265$$ −15.5520 + 2.67714i −0.955352 + 0.164456i
$$266$$ 0 0
$$267$$ −4.88789 + 4.88789i −0.299134 + 0.299134i
$$268$$ 0 0
$$269$$ 15.5119 0.945775 0.472888 0.881123i $$-0.343212\pi$$
0.472888 + 0.881123i $$0.343212\pi$$
$$270$$ 0 0
$$271$$ 13.3418i 0.810458i −0.914215 0.405229i $$-0.867192\pi$$
0.914215 0.405229i $$-0.132808\pi$$
$$272$$ 0 0
$$273$$ 3.42839 + 3.05425i 0.207496 + 0.184852i
$$274$$ 0 0
$$275$$ −4.46702 12.5904i −0.269372 0.759229i
$$276$$ 0 0
$$277$$ −2.00561 + 2.00561i −0.120505 + 0.120505i −0.764788 0.644282i $$-0.777156\pi$$
0.644282 + 0.764788i $$0.277156\pi$$
$$278$$ 0 0
$$279$$ 7.25379 0.434273
$$280$$ 0 0
$$281$$ 13.5557 0.808664 0.404332 0.914612i $$-0.367504\pi$$
0.404332 + 0.914612i $$0.367504\pi$$
$$282$$ 0 0
$$283$$ −16.2444 + 16.2444i −0.965627 + 0.965627i −0.999429 0.0338017i $$-0.989239\pi$$
0.0338017 + 0.999429i $$0.489239\pi$$
$$284$$ 0 0
$$285$$ −2.28260 13.2600i −0.135210 0.785457i
$$286$$ 0 0
$$287$$ −13.9419 12.4204i −0.822966 0.733155i
$$288$$ 0 0
$$289$$ 28.0537i 1.65021i
$$290$$ 0 0
$$291$$ 12.5036 0.732973
$$292$$ 0 0
$$293$$ 2.41765 2.41765i 0.141240 0.141240i −0.632951 0.774192i $$-0.718157\pi$$
0.774192 + 0.632951i $$0.218157\pi$$
$$294$$ 0 0
$$295$$ −10.3049 + 14.5904i −0.599974 + 0.849486i
$$296$$ 0 0
$$297$$ −1.88930 1.88930i −0.109628 0.109628i
$$298$$ 0 0
$$299$$ −0.431179 −0.0249357
$$300$$ 0 0
$$301$$ −1.13890 + 0.0657309i −0.0656449 + 0.00378867i
$$302$$ 0 0
$$303$$ −5.11211 5.11211i −0.293683 0.293683i
$$304$$ 0 0
$$305$$ 10.1078 + 7.13890i 0.578769 + 0.408772i
$$306$$ 0 0
$$307$$ 7.21300 + 7.21300i 0.411667 + 0.411667i 0.882319 0.470652i $$-0.155981\pi$$
−0.470652 + 0.882319i $$0.655981\pi$$
$$308$$ 0 0
$$309$$ 9.82225i 0.558768i
$$310$$ 0 0
$$311$$ 10.2542i 0.581460i −0.956805 0.290730i $$-0.906102\pi$$
0.956805 0.290730i $$-0.0938981\pi$$
$$312$$ 0 0
$$313$$ −22.0904 + 22.0904i −1.24862 + 1.24862i −0.292293 + 0.956329i $$0.594418\pi$$
−0.956329 + 0.292293i $$0.905582\pi$$
$$314$$ 0 0
$$315$$ −5.76281 + 1.33791i −0.324698 + 0.0753826i
$$316$$ 0 0
$$317$$ −12.2563 + 12.2563i −0.688385 + 0.688385i −0.961875 0.273490i $$-0.911822\pi$$
0.273490 + 0.961875i $$0.411822\pi$$
$$318$$ 0 0
$$319$$ 0.814625i 0.0456102i
$$320$$ 0 0
$$321$$ 10.5683i 0.589867i
$$322$$ 0 0
$$323$$ 28.5595 + 28.5595i 1.58909 + 1.58909i
$$324$$ 0 0
$$325$$ 7.83417 + 3.73092i 0.434561 + 0.206954i
$$326$$ 0 0
$$327$$ 4.20978 + 4.20978i 0.232801 + 0.232801i
$$328$$ 0 0
$$329$$ 2.08014 0.120054i 0.114682 0.00661882i
$$330$$ 0 0
$$331$$ −1.26308 −0.0694252 −0.0347126 0.999397i $$-0.511052\pi$$
−0.0347126 + 0.999397i $$0.511052\pi$$
$$332$$ 0 0
$$333$$ 0.735441 + 0.735441i 0.0403019 + 0.0403019i
$$334$$ 0 0
$$335$$ −1.84038 10.6911i −0.100551 0.584118i
$$336$$ 0 0
$$337$$ −9.55621 + 9.55621i −0.520560 + 0.520560i −0.917741 0.397180i $$-0.869989\pi$$
0.397180 + 0.917741i $$0.369989\pi$$
$$338$$ 0 0
$$339$$ 9.88579 0.536922
$$340$$ 0 0
$$341$$ 19.3812i 1.04955i
$$342$$ 0 0
$$343$$ −15.1541 10.6468i −0.818244 0.574871i
$$344$$ 0 0
$$345$$ 0.320503 0.453791i 0.0172553 0.0244313i
$$346$$ 0 0
$$347$$ −6.54975 + 6.54975i −0.351609 + 0.351609i −0.860708 0.509099i $$-0.829979\pi$$
0.509099 + 0.860708i $$0.329979\pi$$
$$348$$ 0 0
$$349$$ 2.77139 0.148349 0.0741746 0.997245i $$-0.476368\pi$$
0.0741746 + 0.997245i $$0.476368\pi$$
$$350$$ 0 0
$$351$$ 1.73544 0.0926310
$$352$$ 0 0
$$353$$ 0.970568 0.970568i 0.0516581 0.0516581i −0.680806 0.732464i $$-0.738370\pi$$
0.732464 + 0.680806i $$0.238370\pi$$
$$354$$ 0 0
$$355$$ −19.7481 + 27.9607i −1.04812 + 1.48400i
$$356$$ 0 0
$$357$$ 11.8130 13.2601i 0.625209 0.701797i
$$358$$ 0 0
$$359$$ 9.32813i 0.492320i −0.969229 0.246160i $$-0.920831\pi$$
0.969229 0.246160i $$-0.0791688\pi$$
$$360$$ 0 0
$$361$$ 17.2078 0.905674
$$362$$ 0 0
$$363$$ −2.73021 + 2.73021i −0.143299 + 0.143299i
$$364$$ 0 0
$$365$$ 5.37586 + 31.2293i 0.281385 + 1.63462i
$$366$$ 0 0
$$367$$ 13.0035 + 13.0035i 0.678776 + 0.678776i 0.959723 0.280948i $$-0.0906487\pi$$
−0.280948 + 0.959723i $$0.590649\pi$$
$$368$$ 0 0
$$369$$ −7.05736 −0.367392
$$370$$ 0 0
$$371$$ −18.6410 + 1.07586i −0.967793 + 0.0558557i
$$372$$ 0 0
$$373$$ 20.6757 + 20.6757i 1.07055 + 1.07055i 0.997315 + 0.0732339i $$0.0233320\pi$$
0.0732339 + 0.997315i $$0.476668\pi$$
$$374$$ 0 0
$$375$$ −9.74986 + 5.47176i −0.503481 + 0.282560i
$$376$$ 0 0
$$377$$ −0.374143 0.374143i −0.0192693 0.0192693i
$$378$$ 0 0
$$379$$ 22.0077i 1.13046i 0.824933 + 0.565230i $$0.191213\pi$$
−0.824933 + 0.565230i $$0.808787\pi$$
$$380$$ 0 0
$$381$$ 4.04621i 0.207294i
$$382$$ 0 0
$$383$$ −0.390382 + 0.390382i −0.0199476 + 0.0199476i −0.717010 0.697063i $$-0.754490\pi$$
0.697063 + 0.717010i $$0.254490\pi$$
$$384$$ 0 0
$$385$$ −3.57472 15.3975i −0.182185 0.784729i
$$386$$ 0 0
$$387$$ −0.304889 + 0.304889i −0.0154984 + 0.0154984i
$$388$$ 0 0
$$389$$ 25.9300i 1.31470i −0.753584 0.657352i $$-0.771677\pi$$
0.753584 0.657352i $$-0.228323\pi$$
$$390$$ 0 0
$$391$$ 1.66768i 0.0843381i
$$392$$ 0 0
$$393$$ −6.60978 6.60978i −0.333419 0.333419i
$$394$$ 0 0
$$395$$ −20.6339 14.5733i −1.03821 0.733263i
$$396$$ 0 0
$$397$$ 17.1631 + 17.1631i 0.861391 + 0.861391i 0.991500 0.130109i $$-0.0415327\pi$$
−0.130109 + 0.991500i $$0.541533\pi$$
$$398$$ 0 0
$$399$$ −0.917304 15.8938i −0.0459226 0.795686i
$$400$$ 0 0
$$401$$ −12.9418 −0.646281 −0.323140 0.946351i $$-0.604739\pi$$
−0.323140 + 0.946351i $$0.604739\pi$$
$$402$$ 0 0
$$403$$ −8.90143 8.90143i −0.443412 0.443412i
$$404$$ 0 0
$$405$$ −1.28999 + 1.82645i −0.0640999 + 0.0907572i
$$406$$ 0 0
$$407$$ −1.96500 + 1.96500i −0.0974016 + 0.0974016i
$$408$$ 0 0
$$409$$ 2.64278 0.130677 0.0653386 0.997863i $$-0.479187\pi$$
0.0653386 + 0.997863i $$0.479187\pi$$
$$410$$ 0 0
$$411$$ 10.6341i 0.524540i
$$412$$ 0 0
$$413$$ −14.0589 + 15.7812i −0.691795 + 0.776540i
$$414$$ 0 0
$$415$$ 2.62301 + 15.2376i 0.128759 + 0.747982i
$$416$$ 0 0
$$417$$ 5.50767 5.50767i 0.269712 0.269712i
$$418$$ 0 0
$$419$$ 10.0302 0.490007 0.245003 0.969522i $$-0.421211\pi$$
0.245003 + 0.969522i $$0.421211\pi$$
$$420$$ 0 0
$$421$$ −26.6440 −1.29855 −0.649274 0.760555i $$-0.724927\pi$$
−0.649274 + 0.760555i $$0.724927\pi$$
$$422$$ 0 0
$$423$$ 0.556866 0.556866i 0.0270758 0.0270758i
$$424$$ 0 0
$$425$$ 14.4301 30.3004i 0.699965 1.46978i
$$426$$ 0 0
$$427$$ 10.9327 + 9.73958i 0.529069 + 0.471332i
$$428$$ 0 0
$$429$$ 4.63688i 0.223870i
$$430$$ 0 0
$$431$$ −22.3747 −1.07775 −0.538876 0.842385i $$-0.681151\pi$$
−0.538876 + 0.842385i $$0.681151\pi$$
$$432$$ 0 0
$$433$$ −13.4723 + 13.4723i −0.647438 + 0.647438i −0.952373 0.304935i $$-0.901365\pi$$
0.304935 + 0.952373i $$0.401365\pi$$
$$434$$ 0 0
$$435$$ 0.671871 0.115657i 0.0322138 0.00554532i
$$436$$ 0 0
$$437$$ 1.05714 + 1.05714i 0.0505700 + 0.0505700i
$$438$$ 0 0
$$439$$ 25.6790 1.22559 0.612795 0.790242i $$-0.290045\pi$$
0.612795 + 0.790242i $$0.290045\pi$$
$$440$$ 0 0
$$441$$ −6.95352 + 0.805321i −0.331120 + 0.0383486i
$$442$$ 0 0
$$443$$ 15.6351 + 15.6351i 0.742845 + 0.742845i 0.973125 0.230279i $$-0.0739640\pi$$
−0.230279 + 0.973125i $$0.573964\pi$$
$$444$$ 0 0
$$445$$ −8.91705 + 12.6254i −0.422709 + 0.598501i
$$446$$ 0 0
$$447$$ −10.1014 10.1014i −0.477779 0.477779i
$$448$$ 0 0
$$449$$ 7.01947i 0.331269i 0.986187 + 0.165635i $$0.0529673\pi$$
−0.986187 + 0.165635i $$0.947033\pi$$
$$450$$ 0 0
$$451$$ 18.8564i 0.887912i
$$452$$ 0 0
$$453$$ −6.91544 + 6.91544i −0.324916 + 0.324916i
$$454$$ 0 0
$$455$$ 8.71359 + 5.42999i 0.408500 + 0.254562i
$$456$$ 0 0
$$457$$ 11.2119 11.2119i 0.524472 0.524472i −0.394447 0.918919i $$-0.629064\pi$$
0.918919 + 0.394447i $$0.129064\pi$$
$$458$$ 0 0
$$459$$ 6.71220i 0.313299i
$$460$$ 0 0
$$461$$ 29.9845i 1.39652i −0.715846 0.698259i $$-0.753959\pi$$
0.715846 0.698259i $$-0.246041\pi$$
$$462$$ 0 0
$$463$$ −7.70220 7.70220i −0.357951 0.357951i 0.505106 0.863057i $$-0.331453\pi$$
−0.863057 + 0.505106i $$0.831453\pi$$
$$464$$ 0 0
$$465$$ 15.9849 2.75166i 0.741280 0.127605i
$$466$$ 0 0
$$467$$ 1.80961 + 1.80961i 0.0837386 + 0.0837386i 0.747735 0.663997i $$-0.231141\pi$$
−0.663997 + 0.747735i $$0.731141\pi$$
$$468$$ 0 0
$$469$$ −0.739590 12.8146i −0.0341511 0.591724i
$$470$$ 0 0
$$471$$ −3.07918 −0.141881
$$472$$ 0 0
$$473$$ −0.814625 0.814625i −0.0374565 0.0374565i
$$474$$ 0 0
$$475$$ −10.0601 28.3547i −0.461591 1.30100i
$$476$$ 0 0
$$477$$ −4.99031 + 4.99031i −0.228491 + 0.228491i
$$478$$ 0 0
$$479$$ 4.09455 0.187085 0.0935425 0.995615i $$-0.470181\pi$$
0.0935425 + 0.995615i $$0.470181\pi$$
$$480$$ 0 0
$$481$$ 1.80498i 0.0823001i
$$482$$ 0 0
$$483$$ 0.437262 0.490826i 0.0198961 0.0223334i
$$484$$ 0 0
$$485$$ 27.5536 4.74311i 1.25114 0.215374i
$$486$$ 0 0
$$487$$ 10.3049 10.3049i 0.466959 0.466959i −0.433969 0.900928i $$-0.642887\pi$$
0.900928 + 0.433969i $$0.142887\pi$$
$$488$$ 0 0
$$489$$ 19.3404 0.874603
$$490$$ 0 0
$$491$$ 8.55953 0.386286 0.193143 0.981171i $$-0.438132\pi$$
0.193143 + 0.981171i $$0.438132\pi$$
$$492$$ 0 0
$$493$$ −1.44708 + 1.44708i −0.0651732 + 0.0651732i
$$494$$ 0 0
$$495$$ −4.88005 3.44668i −0.219342 0.154917i
$$496$$ 0 0
$$497$$ −26.9423 + 30.2427i −1.20853 + 1.35657i
$$498$$ 0 0
$$499$$ 23.7564i 1.06348i 0.846907 + 0.531741i $$0.178462\pi$$
−0.846907 + 0.531741i $$0.821538\pi$$
$$500$$ 0 0
$$501$$ −8.81463 −0.393808
$$502$$ 0 0
$$503$$ −17.9504 + 17.9504i −0.800367 + 0.800367i −0.983153 0.182786i $$-0.941489\pi$$
0.182786 + 0.983153i $$0.441489\pi$$
$$504$$ 0 0
$$505$$ −13.2046 9.32611i −0.587596 0.415007i
$$506$$ 0 0
$$507$$ 7.06275 + 7.06275i 0.313668 + 0.313668i
$$508$$ 0 0
$$509$$ −16.8977 −0.748979 −0.374489 0.927231i $$-0.622182\pi$$
−0.374489 + 0.927231i $$0.622182\pi$$
$$510$$ 0 0
$$511$$ 2.16039 + 37.4322i 0.0955698 + 1.65590i
$$512$$ 0 0
$$513$$ −4.25487 4.25487i −0.187857 0.187857i
$$514$$ 0 0
$$515$$ 3.72598 + 21.6449i 0.164186 + 0.953787i
$$516$$ 0 0
$$517$$ 1.48788 + 1.48788i 0.0654367 + 0.0654367i
$$518$$ 0 0
$$519$$ 9.57331i 0.420221i
$$520$$ 0 0
$$521$$ 7.88477i 0.345438i −0.984971 0.172719i $$-0.944745\pi$$
0.984971 0.172719i $$-0.0552552\pi$$
$$522$$ 0 0
$$523$$ −1.23149 + 1.23149i −0.0538493 + 0.0538493i −0.733519 0.679669i $$-0.762123\pi$$
0.679669 + 0.733519i $$0.262123\pi$$
$$524$$ 0 0
$$525$$ −12.1917 + 5.13436i −0.532091 + 0.224082i
$$526$$ 0 0
$$527$$ −34.4283 + 34.4283i −1.49972 + 1.49972i
$$528$$ 0 0
$$529$$ 22.9383i 0.997316i
$$530$$ 0 0
$$531$$ 7.98837i 0.346666i
$$532$$ 0 0
$$533$$ 8.66039 + 8.66039i 0.375123 + 0.375123i
$$534$$ 0 0
$$535$$ −4.00900 23.2890i −0.173324 1.00687i
$$536$$ 0 0
$$537$$ 0.919968 + 0.919968i 0.0396996 + 0.0396996i
$$538$$ 0 0
$$539$$ −2.15171 18.5789i −0.0926809 0.800250i
$$540$$ 0 0
$$541$$ 34.9495 1.50260 0.751298 0.659963i $$-0.229428\pi$$
0.751298 + 0.659963i $$0.229428\pi$$
$$542$$ 0 0
$$543$$ 6.00000 + 6.00000i 0.257485 + 0.257485i
$$544$$ 0 0
$$545$$ 10.8738 + 7.67996i 0.465784 + 0.328973i
$$546$$ 0 0
$$547$$ −3.83548 + 3.83548i −0.163993 + 0.163993i −0.784333 0.620340i $$-0.786995\pi$$
0.620340 + 0.784333i $$0.286995\pi$$
$$548$$ 0 0
$$549$$ 5.53409 0.236189
$$550$$ 0 0
$$551$$ 1.83461i 0.0781569i
$$552$$ 0 0
$$553$$ −22.3179 19.8823i −0.949054 0.845483i
$$554$$ 0 0
$$555$$ 1.89964 + 1.34168i 0.0806353 + 0.0569510i
$$556$$ 0 0
$$557$$ −16.3147 + 16.3147i −0.691275 + 0.691275i −0.962512 0.271238i $$-0.912567\pi$$
0.271238 + 0.962512i $$0.412567\pi$$
$$558$$ 0 0
$$559$$ 0.748285 0.0316491
$$560$$ 0 0
$$561$$ 17.9341 0.757180
$$562$$ 0 0
$$563$$ 23.7521 23.7521i 1.00103 1.00103i 0.00103054 0.999999i $$-0.499672\pi$$
0.999999 0.00103054i $$-0.000328032\pi$$
$$564$$ 0 0
$$565$$ 21.7849 3.75008i 0.916497 0.157767i
$$566$$ 0 0
$$567$$ −1.75993 + 1.97552i −0.0739099 + 0.0829638i
$$568$$ 0 0
$$569$$ 0.277792i 0.0116457i 0.999983 + 0.00582283i $$0.00185348\pi$$
−0.999983 + 0.00582283i $$0.998147\pi$$
$$570$$ 0 0
$$571$$ 3.11538 0.130375 0.0651874 0.997873i $$-0.479235\pi$$
0.0651874 + 0.997873i $$0.479235\pi$$
$$572$$ 0 0
$$573$$ −1.37031 + 1.37031i −0.0572454 + 0.0572454i
$$574$$ 0 0
$$575$$ 0.534138 1.12158i 0.0222751 0.0467731i
$$576$$ 0 0
$$577$$ −29.5905 29.5905i −1.23187 1.23187i −0.963245 0.268625i $$-0.913431\pi$$
−0.268625 0.963245i $$-0.586569\pi$$
$$578$$ 0 0
$$579$$ −11.0703 −0.460064
$$580$$ 0 0
$$581$$ 1.05410 + 18.2641i 0.0437316 + 0.757722i
$$582$$ 0 0
$$583$$ −13.3335 13.3335i −0.552216 0.552216i
$$584$$ 0 0
$$585$$ 3.82432 0.658323i 0.158116 0.0272183i
$$586$$ 0 0
$$587$$ 26.6462 + 26.6462i 1.09981 + 1.09981i 0.994433 + 0.105375i $$0.0336041\pi$$
0.105375 + 0.994433i $$0.466396\pi$$
$$588$$ 0 0
$$589$$ 43.6482i 1.79849i
$$590$$ 0 0
$$591$$ 12.0317i 0.494916i
$$592$$ 0 0
$$593$$ −15.1889 + 15.1889i −0.623733 + 0.623733i −0.946484 0.322751i $$-0.895392\pi$$
0.322751 + 0.946484i $$0.395392\pi$$
$$594$$ 0 0
$$595$$ 21.0017 33.7017i 0.860985 1.38164i
$$596$$ 0 0
$$597$$ −2.30135 + 2.30135i −0.0941878 + 0.0941878i
$$598$$ 0 0
$$599$$ 22.2776i 0.910238i −0.890431 0.455119i $$-0.849597\pi$$
0.890431 0.455119i $$-0.150403\pi$$
$$600$$ 0 0
$$601$$ 22.3458i 0.911503i 0.890107 + 0.455752i $$0.150629\pi$$
−0.890107 + 0.455752i $$0.849371\pi$$
$$602$$ 0 0
$$603$$ −3.43055 3.43055i −0.139703 0.139703i
$$604$$ 0 0
$$605$$ −4.98077 + 7.05213i −0.202497 + 0.286710i
$$606$$ 0 0
$$607$$ −0.576027 0.576027i −0.0233802 0.0233802i 0.695320 0.718700i $$-0.255263\pi$$
−0.718700 + 0.695320i $$0.755263\pi$$
$$608$$ 0 0
$$609$$ 0.805321 0.0464788i 0.0326333 0.00188341i
$$610$$ 0 0
$$611$$ −1.36671 −0.0552911
$$612$$ 0 0
$$613$$ −16.4709 16.4709i −0.665253 0.665253i 0.291361 0.956613i $$-0.405892\pi$$
−0.956613 + 0.291361i $$0.905892\pi$$
$$614$$ 0 0
$$615$$ −15.5520 + 2.67714i −0.627117 + 0.107953i
$$616$$ 0 0
$$617$$ −3.70013 + 3.70013i −0.148962 + 0.148962i −0.777654 0.628692i $$-0.783590\pi$$
0.628692 + 0.777654i $$0.283590\pi$$
$$618$$ 0 0
$$619$$ −39.8840 −1.60307 −0.801536 0.597946i $$-0.795984\pi$$
−0.801536 + 0.597946i $$0.795984\pi$$
$$620$$ 0 0
$$621$$ 0.248455i 0.00997015i
$$622$$ 0 0
$$623$$ −12.1655 + 13.6558i −0.487401 + 0.547107i
$$624$$ 0 0
$$625$$ −19.4097 + 15.7564i −0.776388 + 0.630256i
$$626$$ 0 0
$$627$$ 11.3685 11.3685i 0.454013 0.454013i
$$628$$ 0 0
$$629$$ −6.98117 −0.278357
$$630$$ 0 0
$$631$$ 33.9725 1.35242 0.676211 0.736708i $$-0.263621\pi$$
0.676211 + 0.736708i $$0.263621\pi$$
$$632$$ 0 0
$$633$$ 12.1981 12.1981i 0.484833 0.484833i
$$634$$ 0 0
$$635$$ 1.53489 + 8.91646i 0.0609103 + 0.353839i
$$636$$ 0 0
$$637$$ 9.52120 + 7.54472i 0.377244 + 0.298933i
$$638$$ 0 0
$$639$$ 15.3087i 0.605605i
$$640$$ 0 0
$$641$$ −18.1113 −0.715352 −0.357676 0.933846i $$-0.616431\pi$$
−0.357676 + 0.933846i $$0.616431\pi$$
$$642$$ 0 0
$$643$$ 32.1062 32.1062i 1.26614 1.26614i 0.318082 0.948063i $$-0.396961\pi$$
0.948063 0.318082i $$-0.103039\pi$$
$$644$$ 0 0
$$645$$ −0.556214 + 0.787528i −0.0219009 + 0.0310089i
$$646$$ 0 0
$$647$$ 12.9277 + 12.9277i 0.508241 + 0.508241i 0.913986 0.405745i $$-0.132988\pi$$
−0.405745 + 0.913986i $$0.632988\pi$$
$$648$$ 0 0
$$649$$ −21.3439 −0.837821
$$650$$ 0 0
$$651$$ 19.1598 1.10580i 0.750934 0.0433398i
$$652$$ 0 0
$$653$$ −9.39937 9.39937i −0.367826 0.367826i 0.498858 0.866684i $$-0.333753\pi$$
−0.866684 + 0.498858i $$0.833753\pi$$
$$654$$ 0 0
$$655$$ −17.0730 12.0583i −0.667099 0.471158i
$$656$$ 0 0
$$657$$ 10.0208 + 10.0208i 0.390950 + 0.390950i
$$658$$ 0 0
$$659$$ 9.13808i 0.355969i −0.984033 0.177985i $$-0.943042\pi$$
0.984033 0.177985i $$-0.0569577\pi$$
$$660$$ 0 0
$$661$$ 28.4837i 1.10789i −0.832554 0.553943i $$-0.813122\pi$$
0.832554 0.553943i $$-0.186878\pi$$
$$662$$ 0 0
$$663$$ −8.23683 + 8.23683i −0.319892 + 0.319892i
$$664$$ 0 0
$$665$$ −8.05059 34.6765i −0.312188 1.34470i
$$666$$ 0 0
$$667$$ −0.0535642 + 0.0535642i −0.00207401 + 0.00207401i
$$668$$ 0 0
$$669$$ 6.48264i 0.250633i
$$670$$ 0 0
$$671$$ 14.7864i 0.570821i
$$672$$ 0 0
$$673$$ 26.8815 + 26.8815i 1.03621 + 1.03621i 0.999319 + 0.0368867i $$0.0117441\pi$$
0.0368867 + 0.999319i $$0.488256\pi$$
$$674$$ 0 0
$$675$$ −2.14984 + 4.51422i −0.0827473 + 0.173752i
$$676$$ 0 0
$$677$$ 1.19694 + 1.19694i 0.0460022 + 0.0460022i 0.729734 0.683731i $$-0.239644\pi$$
−0.683731 + 0.729734i $$0.739644\pi$$
$$678$$ 0 0
$$679$$ 33.0264 1.90611i 1.26744 0.0731496i
$$680$$ 0 0
$$681$$ 20.0271 0.767440
$$682$$ 0 0
$$683$$ −2.41553 2.41553i −0.0924275 0.0924275i 0.659381 0.751809i $$-0.270818\pi$$
−0.751809 + 0.659381i $$0.770818\pi$$
$$684$$ 0 0
$$685$$ −4.03393 23.4338i −0.154129 0.895361i
$$686$$ 0 0
$$687$$ 20.4571 20.4571i 0.780487 0.780487i
$$688$$ 0 0
$$689$$ 12.2476 0.466598
$$690$$ 0 0
$$691$$ 41.6703i 1.58521i −0.609735 0.792606i $$-0.708724\pi$$
0.609735 0.792606i $$-0.291276\pi$$
$$692$$ 0 0
$$693$$ −5.27832 4.70230i −0.200507 0.178625i
$$694$$ 0 0
$$695$$ 10.0477 14.2263i 0.381132 0.539634i
$$696$$ 0 0
$$697$$ 33.4960 33.4960i 1.26875 1.26875i
$$698$$ 0 0
$$699$$ −6.76767 −0.255977
$$700$$ 0 0
$$701$$ 13.7870 0.520727 0.260364 0.965511i $$-0.416158\pi$$
0.260364 + 0.965511i $$0.416158\pi$$
$$702$$ 0 0
$$703$$ −4.42536 + 4.42536i −0.166906 + 0.166906i
$$704$$ 0 0
$$705$$ 1.01590 1.43838i 0.0382610 0.0541727i
$$706$$ 0 0
$$707$$ −14.2822 12.7236i −0.537138 0.478520i
$$708$$ 0 0
$$709$$ 24.6722i 0.926585i −0.886205 0.463293i $$-0.846668\pi$$
0.886205 0.463293i $$-0.153332\pi$$
$$710$$ 0 0
$$711$$ −11.2973 −0.423680
$$712$$ 0 0
$$713$$ −1.27438 + 1.27438i −0.0477257 + 0.0477257i
$$714$$ 0 0
$$715$$ 1.75895 + 10.2181i 0.0657811 + 0.382135i
$$716$$ 0 0
$$717$$ 11.4388 + 11.4388i 0.427191 + 0.427191i
$$718$$ 0 0
$$719$$ −29.9117 −1.11552 −0.557758 0.830003i $$-0.688338\pi$$
−0.557758 + 0.830003i $$0.688338\pi$$
$$720$$ 0 0
$$721$$ 1.49735 + 25.9441i 0.0557642 + 0.966207i
$$722$$ 0 0
$$723$$ −8.04033 8.04033i −0.299023 0.299023i
$$724$$ 0 0
$$725$$ 1.43670 0.509736i 0.0533577 0.0189311i
$$726$$ 0 0
$$727$$ −29.8488 29.8488i −1.10703 1.10703i −0.993539 0.113491i $$-0.963797\pi$$
−0.113491 0.993539i $$-0.536203\pi$$
$$728$$ 0 0
$$729$$ 1.00000i 0.0370370i
$$730$$ 0 0
$$731$$ 2.89416i 0.107044i
$$732$$ 0 0
$$733$$ 3.86707 3.86707i 0.142834 0.142834i −0.632074 0.774908i $$-0.717796\pi$$
0.774908 + 0.632074i $$0.217796\pi$$
$$734$$ 0 0
$$735$$ −15.0177 + 4.41240i −0.553935 + 0.162754i
$$736$$ 0 0
$$737$$ 9.16599 9.16599i 0.337634 0.337634i
$$738$$ 0 0
$$739$$ 11.9735i 0.440454i −0.975449 0.220227i $$-0.929320\pi$$
0.975449 0.220227i $$-0.0706797\pi$$
$$740$$ 0 0
$$741$$ 10.4427i 0.383621i
$$742$$ 0 0
$$743$$ 12.0406 + 12.0406i 0.441728 + 0.441728i 0.892593 0.450864i $$-0.148884\pi$$
−0.450864 + 0.892593i $$0.648884\pi$$
$$744$$ 0 0
$$745$$ −26.0918 18.4281i −0.955931 0.675154i
$$746$$ 0 0
$$747$$ 4.88941 + 4.88941i 0.178894 + 0.178894i
$$748$$ 0 0
$$749$$ −1.61109 27.9148i −0.0588679 1.01998i
$$750$$ 0 0
$$751$$ 24.1119 0.879855 0.439928 0.898033i $$-0.355004\pi$$
0.439928 + 0.898033i $$0.355004\pi$$
$$752$$ 0 0
$$753$$ −4.91467 4.91467i −0.179100 0.179100i
$$754$$ 0 0
$$755$$ −12.6159 + 17.8625i −0.459141 + 0.650085i
$$756$$ 0 0
$$757$$ 29.2896 29.2896i 1.06455 1.06455i 0.0667825 0.997768i $$-0.478727\pi$$
0.997768 0.0667825i $$-0.0212733\pi$$
$$758$$ 0 0
$$759$$ 0.663839 0.0240958
$$760$$ 0 0
$$761$$ 32.3002i 1.17088i −0.810716 0.585440i $$-0.800922\pi$$
0.810716 0.585440i $$-0.199078\pi$$
$$762$$ 0 0
$$763$$ 11.7613 + 10.4778i 0.425787 + 0.379320i
$$764$$ 0 0
$$765$$ −2.54621 14.7914i −0.0920584 0.534784i
$$766$$ 0 0
$$767$$ 9.80287 9.80287i 0.353961 0.353961i
$$768$$ 0 0
$$769$$ −18.4310 −0.664640 −0.332320 0.943167i $$-0.607831\pi$$
−0.332320 + 0.943167i $$0.607831\pi$$
$$770$$ 0 0
$$771$$ −14.2679 −0.513845
$$772$$ 0 0
$$773$$ −17.7963 + 17.7963i −0.640088 + 0.640088i −0.950577 0.310489i $$-0.899507\pi$$
0.310489 + 0.950577i $$0.399507\pi$$
$$774$$ 0 0
$$775$$ 34.1813 12.1274i 1.22783 0.435629i
$$776$$ 0 0
$$777$$ 2.05468 + 1.83045i 0.0737111 + 0.0656670i
$$778$$ 0 0
$$779$$ 42.4662i 1.52151i
$$780$$ 0 0
$$781$$ −40.9030 −1.46362
$$782$$ 0 0
$$783$$ 0.215589 0.215589i 0.00770453 0.00770453i
$$784$$ 0 0
$$785$$ −6.78546 + 1.16806i −0.242184 + 0.0416898i
$$786$$ 0 0
$$787$$ −16.0671 16.0671i −0.572730 0.572730i 0.360160 0.932890i $$-0.382722\pi$$
−0.932890 + 0.360160i $$0.882722\pi$$
$$788$$ 0 0
$$789$$ −25.7364 −0.916240
$$790$$ 0 0
$$791$$ 26.1119 1.50704i 0.928432 0.0535840i
$$792$$ 0 0