# Properties

 Label 75.3.d.c.74.1 Level $75$ Weight $3$ Character 75.74 Analytic conductor $2.044$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$75 = 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 75.d (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.04360198270$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{11})$$ Defining polynomial: $$x^{4} - 5 x^{2} + 9$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$5^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 74.1 Root $$-1.65831 + 0.500000i$$ of defining polynomial Character $$\chi$$ $$=$$ 75.74 Dual form 75.3.d.c.74.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-3.31662 q^{2} +(1.65831 - 2.50000i) q^{3} +7.00000 q^{4} +(-5.50000 + 8.29156i) q^{6} -9.94987 q^{8} +(-3.50000 - 8.29156i) q^{9} +O(q^{10})$$ $$q-3.31662 q^{2} +(1.65831 - 2.50000i) q^{3} +7.00000 q^{4} +(-5.50000 + 8.29156i) q^{6} -9.94987 q^{8} +(-3.50000 - 8.29156i) q^{9} -16.5831i q^{11} +(11.6082 - 17.5000i) q^{12} -10.0000i q^{13} +5.00000 q^{16} -3.31662 q^{17} +(11.6082 + 27.5000i) q^{18} -7.00000 q^{19} +55.0000i q^{22} +19.8997 q^{23} +(-16.5000 + 24.8747i) q^{24} +33.1662i q^{26} +(-26.5330 - 5.00000i) q^{27} +33.1662i q^{29} +42.0000 q^{31} +23.2164 q^{32} +(-41.4578 - 27.5000i) q^{33} +11.0000 q^{34} +(-24.5000 - 58.0409i) q^{36} -40.0000i q^{37} +23.2164 q^{38} +(-25.0000 - 16.5831i) q^{39} +16.5831i q^{41} +50.0000i q^{43} -116.082i q^{44} -66.0000 q^{46} +46.4327 q^{47} +(8.29156 - 12.5000i) q^{48} +49.0000 q^{49} +(-5.50000 + 8.29156i) q^{51} -70.0000i q^{52} -46.4327 q^{53} +(88.0000 + 16.5831i) q^{54} +(-11.6082 + 17.5000i) q^{57} -110.000i q^{58} +66.3325i q^{59} -8.00000 q^{61} -139.298 q^{62} -97.0000 q^{64} +(137.500 + 91.2072i) q^{66} +45.0000i q^{67} -23.2164 q^{68} +(33.0000 - 49.7494i) q^{69} -33.1662i q^{71} +(34.8246 + 82.5000i) q^{72} +35.0000i q^{73} +132.665i q^{74} -49.0000 q^{76} +(82.9156 + 55.0000i) q^{78} -12.0000 q^{79} +(-56.5000 + 58.0409i) q^{81} -55.0000i q^{82} +69.6491 q^{83} -165.831i q^{86} +(82.9156 + 55.0000i) q^{87} +165.000i q^{88} -149.248i q^{89} +139.298 q^{92} +(69.6491 - 105.000i) q^{93} -154.000 q^{94} +(38.5000 - 58.0409i) q^{96} -70.0000i q^{97} -162.515 q^{98} +(-137.500 + 58.0409i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 28q^{4} - 22q^{6} - 14q^{9} + O(q^{10})$$ $$4q + 28q^{4} - 22q^{6} - 14q^{9} + 20q^{16} - 28q^{19} - 66q^{24} + 168q^{31} + 44q^{34} - 98q^{36} - 100q^{39} - 264q^{46} + 196q^{49} - 22q^{51} + 352q^{54} - 32q^{61} - 388q^{64} + 550q^{66} + 132q^{69} - 196q^{76} - 48q^{79} - 226q^{81} - 616q^{94} + 154q^{96} - 550q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$$.

 $$n$$ $$26$$ $$52$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −3.31662 −1.65831 −0.829156 0.559017i $$-0.811179\pi$$
−0.829156 + 0.559017i $$0.811179\pi$$
$$3$$ 1.65831 2.50000i 0.552771 0.833333i
$$4$$ 7.00000 1.75000
$$5$$ 0 0
$$6$$ −5.50000 + 8.29156i −0.916667 + 1.38193i
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ −9.94987 −1.24373
$$9$$ −3.50000 8.29156i −0.388889 0.921285i
$$10$$ 0 0
$$11$$ 16.5831i 1.50756i −0.657129 0.753778i $$-0.728229\pi$$
0.657129 0.753778i $$-0.271771\pi$$
$$12$$ 11.6082 17.5000i 0.967349 1.45833i
$$13$$ 10.0000i 0.769231i −0.923077 0.384615i $$-0.874334\pi$$
0.923077 0.384615i $$-0.125666\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 5.00000 0.312500
$$17$$ −3.31662 −0.195096 −0.0975478 0.995231i $$-0.531100\pi$$
−0.0975478 + 0.995231i $$0.531100\pi$$
$$18$$ 11.6082 + 27.5000i 0.644899 + 1.52778i
$$19$$ −7.00000 −0.368421 −0.184211 0.982887i $$-0.558973\pi$$
−0.184211 + 0.982887i $$0.558973\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 55.0000i 2.50000i
$$23$$ 19.8997 0.865206 0.432603 0.901584i $$-0.357595\pi$$
0.432603 + 0.901584i $$0.357595\pi$$
$$24$$ −16.5000 + 24.8747i −0.687500 + 1.03645i
$$25$$ 0 0
$$26$$ 33.1662i 1.27562i
$$27$$ −26.5330 5.00000i −0.982704 0.185185i
$$28$$ 0 0
$$29$$ 33.1662i 1.14366i 0.820371 + 0.571832i $$0.193767\pi$$
−0.820371 + 0.571832i $$0.806233\pi$$
$$30$$ 0 0
$$31$$ 42.0000 1.35484 0.677419 0.735597i $$-0.263098\pi$$
0.677419 + 0.735597i $$0.263098\pi$$
$$32$$ 23.2164 0.725512
$$33$$ −41.4578 27.5000i −1.25630 0.833333i
$$34$$ 11.0000 0.323529
$$35$$ 0 0
$$36$$ −24.5000 58.0409i −0.680556 1.61225i
$$37$$ 40.0000i 1.08108i −0.841318 0.540541i $$-0.818220\pi$$
0.841318 0.540541i $$-0.181780\pi$$
$$38$$ 23.2164 0.610957
$$39$$ −25.0000 16.5831i −0.641026 0.425208i
$$40$$ 0 0
$$41$$ 16.5831i 0.404466i 0.979337 + 0.202233i $$0.0648199\pi$$
−0.979337 + 0.202233i $$0.935180\pi$$
$$42$$ 0 0
$$43$$ 50.0000i 1.16279i 0.813621 + 0.581395i $$0.197493\pi$$
−0.813621 + 0.581395i $$0.802507\pi$$
$$44$$ 116.082i 2.63822i
$$45$$ 0 0
$$46$$ −66.0000 −1.43478
$$47$$ 46.4327 0.987931 0.493965 0.869482i $$-0.335547\pi$$
0.493965 + 0.869482i $$0.335547\pi$$
$$48$$ 8.29156 12.5000i 0.172741 0.260417i
$$49$$ 49.0000 1.00000
$$50$$ 0 0
$$51$$ −5.50000 + 8.29156i −0.107843 + 0.162580i
$$52$$ 70.0000i 1.34615i
$$53$$ −46.4327 −0.876090 −0.438045 0.898953i $$-0.644329\pi$$
−0.438045 + 0.898953i $$0.644329\pi$$
$$54$$ 88.0000 + 16.5831i 1.62963 + 0.307095i
$$55$$ 0 0
$$56$$ 0 0
$$57$$ −11.6082 + 17.5000i −0.203652 + 0.307018i
$$58$$ 110.000i 1.89655i
$$59$$ 66.3325i 1.12428i 0.827042 + 0.562140i $$0.190022\pi$$
−0.827042 + 0.562140i $$0.809978\pi$$
$$60$$ 0 0
$$61$$ −8.00000 −0.131148 −0.0655738 0.997848i $$-0.520888\pi$$
−0.0655738 + 0.997848i $$0.520888\pi$$
$$62$$ −139.298 −2.24675
$$63$$ 0 0
$$64$$ −97.0000 −1.51562
$$65$$ 0 0
$$66$$ 137.500 + 91.2072i 2.08333 + 1.38193i
$$67$$ 45.0000i 0.671642i 0.941926 + 0.335821i $$0.109014\pi$$
−0.941926 + 0.335821i $$0.890986\pi$$
$$68$$ −23.2164 −0.341417
$$69$$ 33.0000 49.7494i 0.478261 0.721005i
$$70$$ 0 0
$$71$$ 33.1662i 0.467130i −0.972341 0.233565i $$-0.924961\pi$$
0.972341 0.233565i $$-0.0750392\pi$$
$$72$$ 34.8246 + 82.5000i 0.483674 + 1.14583i
$$73$$ 35.0000i 0.479452i 0.970841 + 0.239726i $$0.0770576\pi$$
−0.970841 + 0.239726i $$0.922942\pi$$
$$74$$ 132.665i 1.79277i
$$75$$ 0 0
$$76$$ −49.0000 −0.644737
$$77$$ 0 0
$$78$$ 82.9156 + 55.0000i 1.06302 + 0.705128i
$$79$$ −12.0000 −0.151899 −0.0759494 0.997112i $$-0.524199\pi$$
−0.0759494 + 0.997112i $$0.524199\pi$$
$$80$$ 0 0
$$81$$ −56.5000 + 58.0409i −0.697531 + 0.716555i
$$82$$ 55.0000i 0.670732i
$$83$$ 69.6491 0.839146 0.419573 0.907722i $$-0.362180\pi$$
0.419573 + 0.907722i $$0.362180\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 165.831i 1.92827i
$$87$$ 82.9156 + 55.0000i 0.953053 + 0.632184i
$$88$$ 165.000i 1.87500i
$$89$$ 149.248i 1.67695i −0.544944 0.838473i $$-0.683449\pi$$
0.544944 0.838473i $$-0.316551\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 139.298 1.51411
$$93$$ 69.6491 105.000i 0.748915 1.12903i
$$94$$ −154.000 −1.63830
$$95$$ 0 0
$$96$$ 38.5000 58.0409i 0.401042 0.604593i
$$97$$ 70.0000i 0.721649i −0.932634 0.360825i $$-0.882495\pi$$
0.932634 0.360825i $$-0.117505\pi$$
$$98$$ −162.515 −1.65831
$$99$$ −137.500 + 58.0409i −1.38889 + 0.586272i
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 18.2414 27.5000i 0.178838 0.269608i
$$103$$ 70.0000i 0.679612i 0.940496 + 0.339806i $$0.110361\pi$$
−0.940496 + 0.339806i $$0.889639\pi$$
$$104$$ 99.4987i 0.956719i
$$105$$ 0 0
$$106$$ 154.000 1.45283
$$107$$ −69.6491 −0.650926 −0.325463 0.945555i $$-0.605520\pi$$
−0.325463 + 0.945555i $$0.605520\pi$$
$$108$$ −185.731 35.0000i −1.71973 0.324074i
$$109$$ 88.0000 0.807339 0.403670 0.914905i $$-0.367734\pi$$
0.403670 + 0.914905i $$0.367734\pi$$
$$110$$ 0 0
$$111$$ −100.000 66.3325i −0.900901 0.597590i
$$112$$ 0 0
$$113$$ 102.815 0.909871 0.454935 0.890525i $$-0.349662\pi$$
0.454935 + 0.890525i $$0.349662\pi$$
$$114$$ 38.5000 58.0409i 0.337719 0.509131i
$$115$$ 0 0
$$116$$ 232.164i 2.00141i
$$117$$ −82.9156 + 35.0000i −0.708681 + 0.299145i
$$118$$ 220.000i 1.86441i
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −154.000 −1.27273
$$122$$ 26.5330 0.217484
$$123$$ 41.4578 + 27.5000i 0.337055 + 0.223577i
$$124$$ 294.000 2.37097
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 190.000i 1.49606i 0.663663 + 0.748031i $$0.269001\pi$$
−0.663663 + 0.748031i $$0.730999\pi$$
$$128$$ 228.847 1.78787
$$129$$ 125.000 + 82.9156i 0.968992 + 0.642757i
$$130$$ 0 0
$$131$$ 198.997i 1.51906i 0.650469 + 0.759532i $$0.274572\pi$$
−0.650469 + 0.759532i $$0.725428\pi$$
$$132$$ −290.205 192.500i −2.19852 1.45833i
$$133$$ 0 0
$$134$$ 149.248i 1.11379i
$$135$$ 0 0
$$136$$ 33.0000 0.242647
$$137$$ −69.6491 −0.508388 −0.254194 0.967153i $$-0.581810\pi$$
−0.254194 + 0.967153i $$0.581810\pi$$
$$138$$ −109.449 + 165.000i −0.793106 + 1.19565i
$$139$$ −77.0000 −0.553957 −0.276978 0.960876i $$-0.589333\pi$$
−0.276978 + 0.960876i $$0.589333\pi$$
$$140$$ 0 0
$$141$$ 77.0000 116.082i 0.546099 0.823276i
$$142$$ 110.000i 0.774648i
$$143$$ −165.831 −1.15966
$$144$$ −17.5000 41.4578i −0.121528 0.287901i
$$145$$ 0 0
$$146$$ 116.082i 0.795081i
$$147$$ 81.2573 122.500i 0.552771 0.833333i
$$148$$ 280.000i 1.89189i
$$149$$ 165.831i 1.11296i −0.830861 0.556481i $$-0.812151\pi$$
0.830861 0.556481i $$-0.187849\pi$$
$$150$$ 0 0
$$151$$ 172.000 1.13907 0.569536 0.821966i $$-0.307123\pi$$
0.569536 + 0.821966i $$0.307123\pi$$
$$152$$ 69.6491 0.458218
$$153$$ 11.6082 + 27.5000i 0.0758705 + 0.179739i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ −175.000 116.082i −1.12179 0.744115i
$$157$$ 250.000i 1.59236i −0.605062 0.796178i $$-0.706852\pi$$
0.605062 0.796178i $$-0.293148\pi$$
$$158$$ 39.7995 0.251896
$$159$$ −77.0000 + 116.082i −0.484277 + 0.730075i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 187.389 192.500i 1.15672 1.18827i
$$163$$ 35.0000i 0.214724i −0.994220 0.107362i $$-0.965760\pi$$
0.994220 0.107362i $$-0.0342404\pi$$
$$164$$ 116.082i 0.707816i
$$165$$ 0 0
$$166$$ −231.000 −1.39157
$$167$$ 179.098 1.07244 0.536221 0.844078i $$-0.319851\pi$$
0.536221 + 0.844078i $$0.319851\pi$$
$$168$$ 0 0
$$169$$ 69.0000 0.408284
$$170$$ 0 0
$$171$$ 24.5000 + 58.0409i 0.143275 + 0.339421i
$$172$$ 350.000i 2.03488i
$$173$$ −278.596 −1.61038 −0.805192 0.593014i $$-0.797938\pi$$
−0.805192 + 0.593014i $$0.797938\pi$$
$$174$$ −275.000 182.414i −1.58046 1.04836i
$$175$$ 0 0
$$176$$ 82.9156i 0.471111i
$$177$$ 165.831 + 110.000i 0.936900 + 0.621469i
$$178$$ 495.000i 2.78090i
$$179$$ 116.082i 0.648502i 0.945971 + 0.324251i $$0.105112\pi$$
−0.945971 + 0.324251i $$0.894888\pi$$
$$180$$ 0 0
$$181$$ 182.000 1.00552 0.502762 0.864425i $$-0.332317\pi$$
0.502762 + 0.864425i $$0.332317\pi$$
$$182$$ 0 0
$$183$$ −13.2665 + 20.0000i −0.0724945 + 0.109290i
$$184$$ −198.000 −1.07609
$$185$$ 0 0
$$186$$ −231.000 + 348.246i −1.24194 + 1.87229i
$$187$$ 55.0000i 0.294118i
$$188$$ 325.029 1.72888
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 232.164i 1.21552i −0.794122 0.607758i $$-0.792069\pi$$
0.794122 0.607758i $$-0.207931\pi$$
$$192$$ −160.856 + 242.500i −0.837793 + 1.26302i
$$193$$ 25.0000i 0.129534i 0.997900 + 0.0647668i $$0.0206304\pi$$
−0.997900 + 0.0647668i $$0.979370\pi$$
$$194$$ 232.164i 1.19672i
$$195$$ 0 0
$$196$$ 343.000 1.75000
$$197$$ −218.897 −1.11115 −0.555577 0.831465i $$-0.687502\pi$$
−0.555577 + 0.831465i $$0.687502\pi$$
$$198$$ 456.036 192.500i 2.30321 0.972222i
$$199$$ 68.0000 0.341709 0.170854 0.985296i $$-0.445347\pi$$
0.170854 + 0.985296i $$0.445347\pi$$
$$200$$ 0 0
$$201$$ 112.500 + 74.6241i 0.559701 + 0.371264i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ −38.5000 + 58.0409i −0.188725 + 0.284514i
$$205$$ 0 0
$$206$$ 232.164i 1.12701i
$$207$$ −69.6491 165.000i −0.336469 0.797101i
$$208$$ 50.0000i 0.240385i
$$209$$ 116.082i 0.555416i
$$210$$ 0 0
$$211$$ 77.0000 0.364929 0.182464 0.983212i $$-0.441593\pi$$
0.182464 + 0.983212i $$0.441593\pi$$
$$212$$ −325.029 −1.53316
$$213$$ −82.9156 55.0000i −0.389275 0.258216i
$$214$$ 231.000 1.07944
$$215$$ 0 0
$$216$$ 264.000 + 49.7494i 1.22222 + 0.230321i
$$217$$ 0 0
$$218$$ −291.863 −1.33882
$$219$$ 87.5000 + 58.0409i 0.399543 + 0.265027i
$$220$$ 0 0
$$221$$ 33.1662i 0.150074i
$$222$$ 331.662 + 220.000i 1.49398 + 0.990991i
$$223$$ 140.000i 0.627803i −0.949456 0.313901i $$-0.898364\pi$$
0.949456 0.313901i $$-0.101636\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ −341.000 −1.50885
$$227$$ −185.731 −0.818198 −0.409099 0.912490i $$-0.634157\pi$$
−0.409099 + 0.912490i $$0.634157\pi$$
$$228$$ −81.2573 + 122.500i −0.356392 + 0.537281i
$$229$$ −372.000 −1.62445 −0.812227 0.583341i $$-0.801745\pi$$
−0.812227 + 0.583341i $$0.801745\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 330.000i 1.42241i
$$233$$ 119.398 0.512440 0.256220 0.966619i $$-0.417523\pi$$
0.256220 + 0.966619i $$0.417523\pi$$
$$234$$ 275.000 116.082i 1.17521 0.496076i
$$235$$ 0 0
$$236$$ 464.327i 1.96749i
$$237$$ −19.8997 + 30.0000i −0.0839652 + 0.126582i
$$238$$ 0 0
$$239$$ 232.164i 0.971396i −0.874127 0.485698i $$-0.838565\pi$$
0.874127 0.485698i $$-0.161435\pi$$
$$240$$ 0 0
$$241$$ −413.000 −1.71369 −0.856846 0.515572i $$-0.827580\pi$$
−0.856846 + 0.515572i $$0.827580\pi$$
$$242$$ 510.760 2.11058
$$243$$ 51.4077 + 237.500i 0.211554 + 0.977366i
$$244$$ −56.0000 −0.229508
$$245$$ 0 0
$$246$$ −137.500 91.2072i −0.558943 0.370761i
$$247$$ 70.0000i 0.283401i
$$248$$ −417.895 −1.68506
$$249$$ 115.500 174.123i 0.463855 0.699288i
$$250$$ 0 0
$$251$$ 248.747i 0.991023i −0.868601 0.495512i $$-0.834981\pi$$
0.868601 0.495512i $$-0.165019\pi$$
$$252$$ 0 0
$$253$$ 330.000i 1.30435i
$$254$$ 630.159i 2.48094i
$$255$$ 0 0
$$256$$ −371.000 −1.44922
$$257$$ 278.596 1.08403 0.542017 0.840368i $$-0.317661\pi$$
0.542017 + 0.840368i $$0.317661\pi$$
$$258$$ −414.578 275.000i −1.60689 1.06589i
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 275.000 116.082i 1.05364 0.444758i
$$262$$ 660.000i 2.51908i
$$263$$ 285.230 1.08452 0.542262 0.840210i $$-0.317568\pi$$
0.542262 + 0.840210i $$0.317568\pi$$
$$264$$ 412.500 + 273.622i 1.56250 + 1.03645i
$$265$$ 0 0
$$266$$ 0 0
$$267$$ −373.120 247.500i −1.39745 0.926966i
$$268$$ 315.000i 1.17537i
$$269$$ 464.327i 1.72612i 0.505098 + 0.863062i $$0.331456\pi$$
−0.505098 + 0.863062i $$0.668544\pi$$
$$270$$ 0 0
$$271$$ 22.0000 0.0811808 0.0405904 0.999176i $$-0.487076\pi$$
0.0405904 + 0.999176i $$0.487076\pi$$
$$272$$ −16.5831 −0.0609674
$$273$$ 0 0
$$274$$ 231.000 0.843066
$$275$$ 0 0
$$276$$ 231.000 348.246i 0.836957 1.26176i
$$277$$ 210.000i 0.758123i −0.925372 0.379061i $$-0.876247\pi$$
0.925372 0.379061i $$-0.123753\pi$$
$$278$$ 255.380 0.918633
$$279$$ −147.000 348.246i −0.526882 1.24819i
$$280$$ 0 0
$$281$$ 198.997i 0.708176i 0.935212 + 0.354088i $$0.115209\pi$$
−0.935212 + 0.354088i $$0.884791\pi$$
$$282$$ −255.380 + 385.000i −0.905603 + 1.36525i
$$283$$ 345.000i 1.21908i −0.792755 0.609541i $$-0.791354\pi$$
0.792755 0.609541i $$-0.208646\pi$$
$$284$$ 232.164i 0.817478i
$$285$$ 0 0
$$286$$ 550.000 1.92308
$$287$$ 0 0
$$288$$ −81.2573 192.500i −0.282143 0.668403i
$$289$$ −278.000 −0.961938
$$290$$ 0 0
$$291$$ −175.000 116.082i −0.601375 0.398907i
$$292$$ 245.000i 0.839041i
$$293$$ 318.396 1.08668 0.543338 0.839514i $$-0.317160\pi$$
0.543338 + 0.839514i $$0.317160\pi$$
$$294$$ −269.500 + 406.287i −0.916667 + 1.38193i
$$295$$ 0 0
$$296$$ 397.995i 1.34458i
$$297$$ −82.9156 + 440.000i −0.279177 + 1.48148i
$$298$$ 550.000i 1.84564i
$$299$$ 198.997i 0.665543i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −570.459 −1.88894
$$303$$ 0 0
$$304$$ −35.0000 −0.115132
$$305$$ 0 0
$$306$$ −38.5000 91.2072i −0.125817 0.298063i
$$307$$ 325.000i 1.05863i 0.848425 + 0.529316i $$0.177551\pi$$
−0.848425 + 0.529316i $$0.822449\pi$$
$$308$$ 0 0
$$309$$ 175.000 + 116.082i 0.566343 + 0.375669i
$$310$$ 0 0
$$311$$ 397.995i 1.27973i 0.768489 + 0.639863i $$0.221009\pi$$
−0.768489 + 0.639863i $$0.778991\pi$$
$$312$$ 248.747 + 165.000i 0.797266 + 0.528846i
$$313$$ 490.000i 1.56550i 0.622339 + 0.782748i $$0.286182\pi$$
−0.622339 + 0.782748i $$0.713818\pi$$
$$314$$ 829.156i 2.64062i
$$315$$ 0 0
$$316$$ −84.0000 −0.265823
$$317$$ 212.264 0.669602 0.334801 0.942289i $$-0.391331\pi$$
0.334801 + 0.942289i $$0.391331\pi$$
$$318$$ 255.380 385.000i 0.803082 1.21069i
$$319$$ 550.000 1.72414
$$320$$ 0 0
$$321$$ −115.500 + 174.123i −0.359813 + 0.542439i
$$322$$ 0 0
$$323$$ 23.2164 0.0718773
$$324$$ −395.500 + 406.287i −1.22068 + 1.25397i
$$325$$ 0 0
$$326$$ 116.082i 0.356079i
$$327$$ 145.931 220.000i 0.446274 0.672783i
$$328$$ 165.000i 0.503049i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −243.000 −0.734139 −0.367069 0.930194i $$-0.619639\pi$$
−0.367069 + 0.930194i $$0.619639\pi$$
$$332$$ 487.544 1.46851
$$333$$ −331.662 + 140.000i −0.995983 + 0.420420i
$$334$$ −594.000 −1.77844
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 385.000i 1.14243i 0.820799 + 0.571217i $$0.193528\pi$$
−0.820799 + 0.571217i $$0.806472\pi$$
$$338$$ −228.847 −0.677062
$$339$$ 170.500 257.038i 0.502950 0.758225i
$$340$$ 0 0
$$341$$ 696.491i 2.04250i
$$342$$ −81.2573 192.500i −0.237594 0.562865i
$$343$$ 0 0
$$344$$ 497.494i 1.44620i
$$345$$ 0 0
$$346$$ 924.000 2.67052
$$347$$ 295.180 0.850662 0.425331 0.905038i $$-0.360158\pi$$
0.425331 + 0.905038i $$0.360158\pi$$
$$348$$ 580.409 + 385.000i 1.66784 + 1.10632i
$$349$$ −532.000 −1.52436 −0.762178 0.647368i $$-0.775870\pi$$
−0.762178 + 0.647368i $$0.775870\pi$$
$$350$$ 0 0
$$351$$ −50.0000 + 265.330i −0.142450 + 0.755926i
$$352$$ 385.000i 1.09375i
$$353$$ −278.596 −0.789225 −0.394613 0.918848i $$-0.629121\pi$$
−0.394613 + 0.918848i $$0.629121\pi$$
$$354$$ −550.000 364.829i −1.55367 1.03059i
$$355$$ 0 0
$$356$$ 1044.74i 2.93465i
$$357$$ 0 0
$$358$$ 385.000i 1.07542i
$$359$$ 397.995i 1.10862i 0.832310 + 0.554311i $$0.187018\pi$$
−0.832310 + 0.554311i $$0.812982\pi$$
$$360$$ 0 0
$$361$$ −312.000 −0.864266
$$362$$ −603.626 −1.66747
$$363$$ −255.380 + 385.000i −0.703526 + 1.06061i
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 44.0000 66.3325i 0.120219 0.181236i
$$367$$ 180.000i 0.490463i −0.969465 0.245232i $$-0.921136\pi$$
0.969465 0.245232i $$-0.0788640\pi$$
$$368$$ 99.4987 0.270377
$$369$$ 137.500 58.0409i 0.372629 0.157293i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 487.544 735.000i 1.31060 1.97581i
$$373$$ 110.000i 0.294906i 0.989069 + 0.147453i $$0.0471075\pi$$
−0.989069 + 0.147453i $$0.952892\pi$$
$$374$$ 182.414i 0.487739i
$$375$$ 0 0
$$376$$ −462.000 −1.22872
$$377$$ 331.662 0.879741
$$378$$ 0 0
$$379$$ 533.000 1.40633 0.703166 0.711025i $$-0.251769\pi$$
0.703166 + 0.711025i $$0.251769\pi$$
$$380$$ 0 0
$$381$$ 475.000 + 315.079i 1.24672 + 0.826980i
$$382$$ 770.000i 2.01571i
$$383$$ −79.5990 −0.207830 −0.103915 0.994586i $$-0.533137\pi$$
−0.103915 + 0.994586i $$0.533137\pi$$
$$384$$ 379.500 572.118i 0.988281 1.48989i
$$385$$ 0 0
$$386$$ 82.9156i 0.214807i
$$387$$ 414.578 175.000i 1.07126 0.452196i
$$388$$ 490.000i 1.26289i
$$389$$ 99.4987i 0.255781i 0.991788 + 0.127890i $$0.0408206\pi$$
−0.991788 + 0.127890i $$0.959179\pi$$
$$390$$ 0 0
$$391$$ −66.0000 −0.168798
$$392$$ −487.544 −1.24373
$$393$$ 497.494 + 330.000i 1.26589 + 0.839695i
$$394$$ 726.000 1.84264
$$395$$ 0 0
$$396$$ −962.500 + 406.287i −2.43056 + 1.02598i
$$397$$ 20.0000i 0.0503778i −0.999683 0.0251889i $$-0.991981\pi$$
0.999683 0.0251889i $$-0.00801873\pi$$
$$398$$ −225.530 −0.566660
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 746.241i 1.86095i 0.366357 + 0.930475i $$0.380605\pi$$
−0.366357 + 0.930475i $$0.619395\pi$$
$$402$$ −373.120 247.500i −0.928160 0.615672i
$$403$$ 420.000i 1.04218i
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −663.325 −1.62979
$$408$$ 54.7243 82.5000i 0.134128 0.202206i
$$409$$ −77.0000 −0.188264 −0.0941320 0.995560i $$-0.530008\pi$$
−0.0941320 + 0.995560i $$0.530008\pi$$
$$410$$ 0 0
$$411$$ −115.500 + 174.123i −0.281022 + 0.423656i
$$412$$ 490.000i 1.18932i
$$413$$ 0 0
$$414$$ 231.000 + 547.243i 0.557971 + 1.32184i
$$415$$ 0 0
$$416$$ 232.164i 0.558086i
$$417$$ −127.690 + 192.500i −0.306211 + 0.461631i
$$418$$ 385.000i 0.921053i
$$419$$ 116.082i 0.277045i −0.990359 0.138523i $$-0.955765\pi$$
0.990359 0.138523i $$-0.0442353\pi$$
$$420$$ 0 0
$$421$$ 412.000 0.978622 0.489311 0.872109i $$-0.337248\pi$$
0.489311 + 0.872109i $$0.337248\pi$$
$$422$$ −255.380 −0.605166
$$423$$ −162.515 385.000i −0.384195 0.910165i
$$424$$ 462.000 1.08962
$$425$$ 0 0
$$426$$ 275.000 + 182.414i 0.645540 + 0.428203i
$$427$$ 0 0
$$428$$ −487.544 −1.13912
$$429$$ −275.000 + 414.578i −0.641026 + 0.966383i
$$430$$ 0 0
$$431$$ 198.997i 0.461711i 0.972988 + 0.230856i $$0.0741525\pi$$
−0.972988 + 0.230856i $$0.925848\pi$$
$$432$$ −132.665 25.0000i −0.307095 0.0578704i
$$433$$ 455.000i 1.05081i 0.850853 + 0.525404i $$0.176086\pi$$
−0.850853 + 0.525404i $$0.823914\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 616.000 1.41284
$$437$$ −139.298 −0.318760
$$438$$ −290.205 192.500i −0.662568 0.439498i
$$439$$ −22.0000 −0.0501139 −0.0250569 0.999686i $$-0.507977\pi$$
−0.0250569 + 0.999686i $$0.507977\pi$$
$$440$$ 0 0
$$441$$ −171.500 406.287i −0.388889 0.921285i
$$442$$ 110.000i 0.248869i
$$443$$ −527.343 −1.19039 −0.595196 0.803581i $$-0.702925\pi$$
−0.595196 + 0.803581i $$0.702925\pi$$
$$444$$ −700.000 464.327i −1.57658 1.04578i
$$445$$ 0 0
$$446$$ 464.327i 1.04109i
$$447$$ −414.578 275.000i −0.927468 0.615213i
$$448$$ 0 0
$$449$$ 82.9156i 0.184667i −0.995728 0.0923337i $$-0.970567\pi$$
0.995728 0.0923337i $$-0.0294326\pi$$
$$450$$ 0 0
$$451$$ 275.000 0.609756
$$452$$ 719.708 1.59227
$$453$$ 285.230 430.000i 0.629646 0.949227i
$$454$$ 616.000 1.35683
$$455$$ 0 0
$$456$$ 115.500 174.123i 0.253289 0.381848i
$$457$$ 275.000i 0.601751i −0.953663 0.300875i $$-0.902721\pi$$
0.953663 0.300875i $$-0.0972788\pi$$
$$458$$ 1233.78 2.69385
$$459$$ 88.0000 + 16.5831i 0.191721 + 0.0361288i
$$460$$ 0 0
$$461$$ 596.992i 1.29499i −0.762068 0.647497i $$-0.775816\pi$$
0.762068 0.647497i $$-0.224184\pi$$
$$462$$ 0 0
$$463$$ 240.000i 0.518359i 0.965829 + 0.259179i $$0.0834520\pi$$
−0.965829 + 0.259179i $$0.916548\pi$$
$$464$$ 165.831i 0.357395i
$$465$$ 0 0
$$466$$ −396.000 −0.849785
$$467$$ 13.2665 0.0284079 0.0142040 0.999899i $$-0.495479\pi$$
0.0142040 + 0.999899i $$0.495479\pi$$
$$468$$ −580.409 + 245.000i −1.24019 + 0.523504i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −625.000 414.578i −1.32696 0.880208i
$$472$$ 660.000i 1.39831i
$$473$$ 829.156 1.75297
$$474$$ 66.0000 99.4987i 0.139241 0.209913i
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 162.515 + 385.000i 0.340701 + 0.807128i
$$478$$ 770.000i 1.61088i
$$479$$ 298.496i 0.623165i −0.950219 0.311583i $$-0.899141\pi$$
0.950219 0.311583i $$-0.100859\pi$$
$$480$$ 0 0
$$481$$ −400.000 −0.831601
$$482$$ 1369.77 2.84184
$$483$$ 0 0
$$484$$ −1078.00 −2.22727
$$485$$ 0 0
$$486$$ −170.500 787.698i −0.350823 1.62078i
$$487$$ 410.000i 0.841889i 0.907086 + 0.420945i $$0.138301\pi$$
−0.907086 + 0.420945i $$0.861699\pi$$
$$488$$ 79.5990 0.163113
$$489$$ −87.5000 58.0409i −0.178937 0.118693i
$$490$$ 0 0
$$491$$ 265.330i 0.540387i 0.962806 + 0.270193i $$0.0870877\pi$$
−0.962806 + 0.270193i $$0.912912\pi$$
$$492$$ 290.205 + 192.500i 0.589847 + 0.391260i
$$493$$ 110.000i 0.223124i
$$494$$ 232.164i 0.469967i
$$495$$ 0 0
$$496$$ 210.000 0.423387
$$497$$ 0 0
$$498$$ −383.070 + 577.500i −0.769217 + 1.15964i
$$499$$ −322.000 −0.645291 −0.322645 0.946520i $$-0.604572\pi$$
−0.322645 + 0.946520i $$0.604572\pi$$
$$500$$ 0 0
$$501$$ 297.000 447.744i 0.592814 0.893701i
$$502$$ 825.000i 1.64343i
$$503$$ −411.261 −0.817617 −0.408809 0.912620i $$-0.634056\pi$$
−0.408809 + 0.912620i $$0.634056\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 1094.49i 2.16302i
$$507$$ 114.424 172.500i 0.225687 0.340237i
$$508$$ 1330.00i 2.61811i
$$509$$ 431.161i 0.847075i −0.905879 0.423538i $$-0.860788\pi$$
0.905879 0.423538i $$-0.139212\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 315.079 0.615389
$$513$$ 185.731 + 35.0000i 0.362049 + 0.0682261i
$$514$$ −924.000 −1.79767
$$515$$ 0 0
$$516$$ 875.000 + 580.409i 1.69574 + 1.12482i
$$517$$ 770.000i 1.48936i
$$518$$ 0 0
$$519$$ −462.000 + 696.491i −0.890173 + 1.34199i
$$520$$ 0 0
$$521$$ 281.913i 0.541100i −0.962706 0.270550i $$-0.912794\pi$$
0.962706 0.270550i $$-0.0872055\pi$$
$$522$$ −912.072 + 385.000i −1.74726 + 0.737548i
$$523$$ 1015.00i 1.94073i −0.241651 0.970363i $$-0.577689\pi$$
0.241651 0.970363i $$-0.422311\pi$$
$$524$$ 1392.98i 2.65836i
$$525$$ 0 0
$$526$$ −946.000 −1.79848
$$527$$ −139.298 −0.264323
$$528$$ −207.289 137.500i −0.392593 0.260417i
$$529$$ −133.000 −0.251418
$$530$$ 0 0
$$531$$ 550.000 232.164i 1.03578 0.437220i
$$532$$ 0 0
$$533$$ 165.831 0.311128
$$534$$ 1237.50 + 820.865i 2.31742 + 1.53720i
$$535$$ 0 0
$$536$$ 447.744i 0.835344i
$$537$$ 290.205 + 192.500i 0.540418 + 0.358473i
$$538$$ 1540.00i 2.86245i
$$539$$ 812.573i 1.50756i
$$540$$ 0 0
$$541$$ 912.000 1.68577 0.842884 0.538096i $$-0.180856\pi$$
0.842884 + 0.538096i $$0.180856\pi$$
$$542$$ −72.9657 −0.134623
$$543$$ 301.813 455.000i 0.555825 0.837937i
$$544$$ −77.0000 −0.141544
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 55.0000i 0.100548i 0.998735 + 0.0502742i $$0.0160095\pi$$
−0.998735 + 0.0502742i $$0.983990\pi$$
$$548$$ −487.544 −0.889679
$$549$$ 28.0000 + 66.3325i 0.0510018 + 0.120824i
$$550$$ 0 0
$$551$$ 232.164i 0.421350i
$$552$$ −328.346 + 495.000i −0.594829 + 0.896739i
$$553$$ 0 0
$$554$$ 696.491i 1.25720i
$$555$$ 0 0
$$556$$ −539.000 −0.969424
$$557$$ −1014.89 −1.82206 −0.911030 0.412341i $$-0.864711\pi$$
−0.911030 + 0.412341i $$0.864711\pi$$
$$558$$ 487.544 + 1155.00i 0.873734 + 2.06989i
$$559$$ 500.000 0.894454
$$560$$ 0 0
$$561$$ 137.500 + 91.2072i 0.245098 + 0.162580i
$$562$$ 660.000i 1.17438i
$$563$$ 119.398 0.212075 0.106038 0.994362i $$-0.466184\pi$$
0.106038 + 0.994362i $$0.466184\pi$$
$$564$$ 539.000 812.573i 0.955674 1.44073i
$$565$$ 0 0
$$566$$ 1144.24i 2.02162i
$$567$$ 0 0
$$568$$ 330.000i 0.580986i
$$569$$ 49.7494i 0.0874330i 0.999044 + 0.0437165i $$0.0139198\pi$$
−0.999044 + 0.0437165i $$0.986080\pi$$
$$570$$ 0 0
$$571$$ 242.000 0.423818 0.211909 0.977289i $$-0.432032\pi$$
0.211909 + 0.977289i $$0.432032\pi$$
$$572$$ −1160.82 −2.02940
$$573$$ −580.409 385.000i −1.01293 0.671902i
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 339.500 + 804.282i 0.589410 + 1.39632i
$$577$$ 665.000i 1.15251i 0.817269 + 0.576256i $$0.195487\pi$$
−0.817269 + 0.576256i $$0.804513\pi$$
$$578$$ 922.022 1.59519
$$579$$ 62.5000 + 41.4578i 0.107945 + 0.0716024i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 580.409 + 385.000i 0.997267 + 0.661512i
$$583$$ 770.000i 1.32075i
$$584$$ 348.246i 0.596311i
$$585$$ 0 0
$$586$$ −1056.00 −1.80205
$$587$$ 626.842 1.06787 0.533937 0.845524i $$-0.320712\pi$$
0.533937 + 0.845524i $$0.320712\pi$$
$$588$$ 568.801 857.500i 0.967349 1.45833i
$$589$$ −294.000 −0.499151
$$590$$ 0 0
$$591$$ −363.000 + 547.243i −0.614213 + 0.925961i
$$592$$ 200.000i 0.337838i
$$593$$ −859.006 −1.44858 −0.724288 0.689497i $$-0.757831\pi$$
−0.724288 + 0.689497i $$0.757831\pi$$
$$594$$ 275.000 1459.31i 0.462963 2.45676i
$$595$$ 0 0
$$596$$ 1160.82i 1.94768i
$$597$$ 112.765 170.000i 0.188887 0.284757i
$$598$$ 660.000i 1.10368i
$$599$$ 331.662i 0.553694i 0.960914 + 0.276847i $$0.0892895\pi$$
−0.960914 + 0.276847i $$0.910711\pi$$
$$600$$ 0 0
$$601$$ −343.000 −0.570715 −0.285358 0.958421i $$-0.592112\pi$$
−0.285358 + 0.958421i $$0.592112\pi$$
$$602$$ 0 0
$$603$$ 373.120 157.500i 0.618773 0.261194i
$$604$$ 1204.00 1.99338
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 1100.00i 1.81219i −0.423073 0.906096i $$-0.639049\pi$$
0.423073 0.906096i $$-0.360951\pi$$
$$608$$ −162.515 −0.267294
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 464.327i 0.759947i
$$612$$ 81.2573 + 192.500i 0.132773 + 0.314542i
$$613$$ 290.000i 0.473083i 0.971621 + 0.236542i $$0.0760140\pi$$
−0.971621 + 0.236542i $$0.923986\pi$$
$$614$$ 1077.90i 1.75554i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 79.5990 0.129010 0.0645049 0.997917i $$-0.479453\pi$$
0.0645049 + 0.997917i $$0.479453\pi$$
$$618$$ −580.409 385.000i −0.939174 0.622977i
$$619$$ 58.0000 0.0936995 0.0468498 0.998902i $$-0.485082\pi$$
0.0468498 + 0.998902i $$0.485082\pi$$
$$620$$ 0 0
$$621$$ −528.000 99.4987i −0.850242 0.160223i
$$622$$ 1320.00i 2.12219i
$$623$$ 0 0
$$624$$ −125.000 82.9156i −0.200321 0.132878i
$$625$$ 0 0
$$626$$ 1625.15i 2.59608i
$$627$$ 290.205 + 192.500i 0.462846 + 0.307018i
$$628$$ 1750.00i 2.78662i
$$629$$ 132.665i 0.210914i
$$630$$ 0 0
$$631$$ 862.000 1.36609 0.683043 0.730378i $$-0.260656\pi$$
0.683043 + 0.730378i $$0.260656\pi$$
$$632$$ 119.398 0.188922
$$633$$ 127.690 192.500i 0.201722 0.304107i
$$634$$ −704.000 −1.11041
$$635$$ 0 0
$$636$$ −539.000 + 812.573i −0.847484 + 1.27763i
$$637$$ 490.000i 0.769231i
$$638$$ −1824.14 −2.85916
$$639$$ −275.000 + 116.082i −0.430360 + 0.181662i
$$640$$ 0 0
$$641$$ 596.992i 0.931345i 0.884957 + 0.465673i $$0.154188\pi$$
−0.884957 + 0.465673i $$0.845812\pi$$
$$642$$ 383.070 577.500i 0.596682 0.899533i
$$643$$ 1050.00i 1.63297i 0.577366 + 0.816485i $$0.304080\pi$$
−0.577366 + 0.816485i $$0.695920\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −77.0000 −0.119195
$$647$$ −252.063 −0.389588 −0.194794 0.980844i $$-0.562404\pi$$
−0.194794 + 0.980844i $$0.562404\pi$$
$$648$$ 562.168 577.500i 0.867543 0.891204i
$$649$$ 1100.00 1.69492
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 245.000i 0.375767i
$$653$$ −1207.25 −1.84878 −0.924389 0.381452i $$-0.875424\pi$$
−0.924389 + 0.381452i $$0.875424\pi$$
$$654$$ −484.000 + 729.657i −0.740061 + 1.11568i
$$655$$ 0 0
$$656$$ 82.9156i 0.126396i
$$657$$ 290.205 122.500i 0.441712 0.186454i
$$658$$ 0 0
$$659$$ 812.573i 1.23304i 0.787339 + 0.616520i $$0.211458\pi$$
−0.787339 + 0.616520i $$0.788542\pi$$
$$660$$ 0 0
$$661$$ −98.0000 −0.148260 −0.0741301 0.997249i $$-0.523618\pi$$
−0.0741301 + 0.997249i $$0.523618\pi$$
$$662$$ 805.940 1.21743
$$663$$ 82.9156 + 55.0000i 0.125061 + 0.0829563i
$$664$$ −693.000 −1.04367
$$665$$ 0 0
$$666$$ 1100.00 464.327i 1.65165 0.697188i
$$667$$ 660.000i 0.989505i
$$668$$ 1253.68 1.87677
$$669$$ −350.000 232.164i −0.523169 0.347031i
$$670$$ 0 0
$$671$$ 132.665i 0.197712i
$$672$$ 0 0
$$673$$ 210.000i 0.312036i 0.987754 + 0.156018i $$0.0498657\pi$$
−0.987754 + 0.156018i $$0.950134\pi$$
$$674$$ 1276.90i 1.89451i
$$675$$ 0 0
$$676$$ 483.000 0.714497
$$677$$ 79.5990 0.117576 0.0587880 0.998270i $$-0.481276\pi$$
0.0587880 + 0.998270i $$0.481276\pi$$
$$678$$ −565.485 + 852.500i −0.834048 + 1.25737i
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −308.000 + 464.327i −0.452276 + 0.681832i
$$682$$ 2310.00i 3.38710i
$$683$$ 169.148 0.247654 0.123827 0.992304i $$-0.460483\pi$$
0.123827 + 0.992304i $$0.460483\pi$$
$$684$$ 171.500 + 406.287i 0.250731 + 0.593986i
$$685$$ 0 0
$$686$$ 0 0
$$687$$ −616.892 + 930.000i −0.897951 + 1.35371i
$$688$$ 250.000i 0.363372i
$$689$$ 464.327i 0.673915i
$$690$$ 0 0
$$691$$ −713.000 −1.03184 −0.515919 0.856637i $$-0.672549\pi$$
−0.515919 + 0.856637i $$0.672549\pi$$
$$692$$ −1950.18 −2.81817
$$693$$ 0 0
$$694$$ −979.000 −1.41066
$$695$$ 0 0
$$696$$ −825.000 547.243i −1.18534 0.786269i
$$697$$ 55.0000i 0.0789096i
$$698$$ 1764.44 2.52786
$$699$$ 198.000 298.496i 0.283262 0.427033i
$$700$$ 0 0
$$701$$ 1160.82i 1.65595i 0.560767 + 0.827973i $$0.310506\pi$$
−0.560767 + 0.827973i $$0.689494\pi$$
$$702$$ 165.831 880.000i 0.236227 1.25356i
$$703$$ 280.000i 0.398293i
$$704$$ 1608.56i 2.28489i
$$705$$ 0 0
$$706$$ 924.000 1.30878
$$707$$ 0 0
$$708$$ 1160.82 + 770.000i 1.63957 + 1.08757i
$$709$$ 248.000 0.349788 0.174894 0.984587i $$-0.444042\pi$$
0.174894 + 0.984587i $$0.444042\pi$$
$$710$$ 0 0
$$711$$ 42.0000 + 99.4987i 0.0590717 + 0.139942i
$$712$$ 1485.00i 2.08567i
$$713$$ 835.789 1.17222
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 812.573i 1.13488i
$$717$$ −580.409 385.000i −0.809497 0.536960i
$$718$$ 1320.00i 1.83844i
$$719$$ 198.997i 0.276770i −0.990379 0.138385i $$-0.955809\pi$$
0.990379 0.138385i $$-0.0441911\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 1034.79 1.43322
$$723$$ −684.883 + 1032.50i −0.947279 + 1.42808i
$$724$$ 1274.00 1.75967
$$725$$ 0 0
$$726$$ 847.000 1276.90i 1.16667 1.75882i
$$727$$ 10.0000i 0.0137552i −0.999976 0.00687758i $$-0.997811\pi$$
0.999976 0.00687758i $$-0.00218922\pi$$
$$728$$ 0 0
$$729$$ 679.000 + 265.330i 0.931413 + 0.363964i
$$730$$ 0 0
$$731$$ 165.831i 0.226855i
$$732$$ −92.8655 + 140.000i −0.126865 + 0.191257i
$$733$$ 770.000i 1.05048i −0.850955 0.525239i $$-0.823976\pi$$
0.850955 0.525239i $$-0.176024\pi$$
$$734$$ 596.992i 0.813341i
$$735$$ 0 0
$$736$$ 462.000 0.627717
$$737$$ 746.241 1.01254
$$738$$ −456.036 + 192.500i −0.617935 + 0.260840i
$$739$$ −802.000 −1.08525 −0.542625 0.839975i $$-0.682570\pi$$
−0.542625 + 0.839975i $$0.682570\pi$$
$$740$$ 0 0
$$741$$ 175.000 + 116.082i 0.236167 + 0.156656i
$$742$$ 0 0
$$743$$ 1346.55 1.81231 0.906157 0.422941i $$-0.139002\pi$$
0.906157 + 0.422941i $$0.139002\pi$$
$$744$$ −693.000 + 1044.74i −0.931452 + 1.40422i
$$745$$ 0 0
$$746$$ 364.829i 0.489047i
$$747$$ −243.772 577.500i −0.326335 0.773092i
$$748$$ 385.000i 0.514706i
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 322.000 0.428762 0.214381 0.976750i $$-0.431227\pi$$
0.214381 + 0.976750i $$0.431227\pi$$
$$752$$ 232.164 0.308728
$$753$$ −621.867 412.500i −0.825853 0.547809i
$$754$$ −1100.00 −1.45889
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 400.000i 0.528402i 0.964468 + 0.264201i $$0.0851082\pi$$
−0.964468 + 0.264201i $$0.914892\pi$$
$$758$$ −1767.76 −2.33214
$$759$$ −825.000 547.243i −1.08696 0.721005i
$$760$$ 0 0
$$761$$ 348.246i 0.457616i −0.973472 0.228808i $$-0.926517\pi$$
0.973472 0.228808i $$-0.0734828\pi$$
$$762$$ −1575.40 1045.00i −2.06745 1.37139i
$$763$$ 0 0
$$764$$ 1625.15i 2.12715i
$$765$$ 0 0
$$766$$ 264.000 0.344648
$$767$$ 663.325 0.864830
$$768$$ −615.234 + 927.500i −0.801086 + 1.20768i
$$769$$ 193.000 0.250975 0.125488 0.992095i $$-0.459950\pi$$
0.125488 + 0.992095i $$0.459950\pi$$
$$770$$ 0 0
$$771$$ 462.000 696.491i 0.599222 0.903361i
$$772$$ 175.000i 0.226684i
$$773$$ 417.895 0.540614 0.270307 0.962774i $$-0.412875\pi$$
0.270307 + 0.962774i $$0.412875\pi$$
$$774$$ −1375.00 + 580.409i −1.77649 + 0.749883i
$$775$$ 0 0
$$776$$ 696.491i 0.897540i
$$777$$ 0 0
$$778$$ 330.000i 0.424165i
$$779$$ 116.082i 0.149014i
$$780$$ 0 0
$$781$$ −550.000 −0.704225
$$782$$ 218.897 0.279920
$$783$$ 165.831 880.000i 0.211790 1.12388i
$$784$$ 245.000 0.312500
$$785$$ 0 0
$$786$$ −1650.00 1094.49i −2.09924 1.39248i
$$787$$ 910.000i 1.15629i 0.815934 + 0.578145i $$0.196223\pi$$
−0.815934 + 0.578145i $$0.803777\pi$$
$$788$$ −1532.28 −1.94452
$$789$$ 473.000 713.074i 0.599493 0.903770i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 1368.11 577.500i 1.72741 0.729167