# Properties

 Label 588.4.i.l.373.3 Level $588$ Weight $4$ Character 588.373 Analytic conductor $34.693$ Analytic rank $0$ Dimension $8$ CM no Inner twists $2$

# Learn more about

## Newspace parameters

 Level: $$N$$ $$=$$ $$588 = 2^{2} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 588.i (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$34.6931230834$$ Analytic rank: $$0$$ Dimension: $$8$$ Relative dimension: $$4$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ Defining polynomial: $$x^{8} - 2 x^{7} + 27 x^{6} + 10 x^{5} + 446 x^{4} + 62 x^{3} + 3061 x^{2} + 2142 x + 14161$$ Coefficient ring: $$\Z[a_1, \ldots, a_{11}]$$ Coefficient ring index: $$2^{8}\cdot 7^{2}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 373.3 Root $$-1.65506 - 2.86665i$$ of defining polynomial Character $$\chi$$ $$=$$ 588.373 Dual form 588.4.i.l.361.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.50000 + 2.59808i) q^{3} +(4.08470 - 7.07491i) q^{5} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$$ $$q+(1.50000 + 2.59808i) q^{3} +(4.08470 - 7.07491i) q^{5} +(-4.50000 + 7.79423i) q^{9} +(-18.9094 - 32.7521i) q^{11} -39.9319 q^{13} +24.5082 q^{15} +(4.96798 + 8.60480i) q^{17} +(-45.2229 + 78.3284i) q^{19} +(-59.2973 + 102.706i) q^{23} +(29.1304 + 50.4554i) q^{25} -27.0000 q^{27} -78.4061 q^{29} +(46.0055 + 79.6838i) q^{31} +(56.7283 - 98.2563i) q^{33} +(-166.218 + 287.897i) q^{37} +(-59.8979 - 103.746i) q^{39} -71.7451 q^{41} -115.947 q^{43} +(36.7623 + 63.6742i) q^{45} +(153.964 - 266.673i) q^{47} +(-14.9039 + 25.8144i) q^{51} +(201.575 + 349.138i) q^{53} -308.958 q^{55} -271.337 q^{57} +(296.855 + 514.168i) q^{59} +(166.585 - 288.534i) q^{61} +(-163.110 + 282.515i) q^{65} +(371.756 + 643.900i) q^{67} -355.784 q^{69} -728.272 q^{71} +(-400.874 - 694.335i) q^{73} +(-87.3912 + 151.366i) q^{75} +(-533.953 + 924.833i) q^{79} +(-40.5000 - 70.1481i) q^{81} -906.756 q^{83} +81.1709 q^{85} +(-117.609 - 203.705i) q^{87} +(556.634 - 964.119i) q^{89} +(-138.016 + 239.051i) q^{93} +(369.444 + 639.896i) q^{95} -1480.94 q^{97} +340.370 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8q + 12q^{3} - 36q^{9} + O(q^{10})$$ $$8q + 12q^{3} - 36q^{9} + 48q^{17} + 192q^{19} - 192q^{23} - 324q^{25} - 216q^{27} + 192q^{29} + 48q^{31} - 256q^{37} - 2016q^{41} - 224q^{43} + 864q^{47} - 144q^{51} + 648q^{53} - 4704q^{55} + 1152q^{57} + 336q^{59} + 960q^{61} + 360q^{65} - 720q^{67} - 1152q^{69} - 2688q^{71} + 672q^{73} + 972q^{75} + 1984q^{79} - 324q^{81} - 6240q^{83} + 1360q^{85} + 288q^{87} + 2160q^{89} - 144q^{93} + 3744q^{95} - 4032q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$295$$ $$493$$ $$\chi(n)$$ $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0 0
$$3$$ 1.50000 + 2.59808i 0.288675 + 0.500000i
$$4$$ 0 0
$$5$$ 4.08470 7.07491i 0.365347 0.632799i −0.623485 0.781835i $$-0.714284\pi$$
0.988832 + 0.149036i $$0.0476170\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ 0 0
$$9$$ −4.50000 + 7.79423i −0.166667 + 0.288675i
$$10$$ 0 0
$$11$$ −18.9094 32.7521i −0.518310 0.897739i −0.999774 0.0212729i $$-0.993228\pi$$
0.481464 0.876466i $$-0.340105\pi$$
$$12$$ 0 0
$$13$$ −39.9319 −0.851933 −0.425966 0.904739i $$-0.640066\pi$$
−0.425966 + 0.904739i $$0.640066\pi$$
$$14$$ 0 0
$$15$$ 24.5082 0.421866
$$16$$ 0 0
$$17$$ 4.96798 + 8.60480i 0.0708772 + 0.122763i 0.899286 0.437361i $$-0.144087\pi$$
−0.828409 + 0.560124i $$0.810753\pi$$
$$18$$ 0 0
$$19$$ −45.2229 + 78.3284i −0.546045 + 0.945777i 0.452496 + 0.891767i $$0.350534\pi$$
−0.998540 + 0.0540105i $$0.982800\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ −59.2973 + 102.706i −0.537580 + 0.931116i 0.461454 + 0.887164i $$0.347328\pi$$
−0.999034 + 0.0439513i $$0.986005\pi$$
$$24$$ 0 0
$$25$$ 29.1304 + 50.4554i 0.233043 + 0.403643i
$$26$$ 0 0
$$27$$ −27.0000 −0.192450
$$28$$ 0 0
$$29$$ −78.4061 −0.502057 −0.251028 0.967980i $$-0.580769\pi$$
−0.251028 + 0.967980i $$0.580769\pi$$
$$30$$ 0 0
$$31$$ 46.0055 + 79.6838i 0.266543 + 0.461666i 0.967967 0.251079i $$-0.0807853\pi$$
−0.701424 + 0.712744i $$0.747452\pi$$
$$32$$ 0 0
$$33$$ 56.7283 98.2563i 0.299246 0.518310i
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 0 0
$$37$$ −166.218 + 287.897i −0.738541 + 1.27919i 0.214611 + 0.976700i $$0.431152\pi$$
−0.953152 + 0.302491i $$0.902182\pi$$
$$38$$ 0 0
$$39$$ −59.8979 103.746i −0.245932 0.425966i
$$40$$ 0 0
$$41$$ −71.7451 −0.273285 −0.136643 0.990620i $$-0.543631\pi$$
−0.136643 + 0.990620i $$0.543631\pi$$
$$42$$ 0 0
$$43$$ −115.947 −0.411202 −0.205601 0.978636i $$-0.565915\pi$$
−0.205601 + 0.978636i $$0.565915\pi$$
$$44$$ 0 0
$$45$$ 36.7623 + 63.6742i 0.121782 + 0.210933i
$$46$$ 0 0
$$47$$ 153.964 266.673i 0.477828 0.827623i −0.521849 0.853038i $$-0.674758\pi$$
0.999677 + 0.0254154i $$0.00809085\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 0 0
$$51$$ −14.9039 + 25.8144i −0.0409210 + 0.0708772i
$$52$$ 0 0
$$53$$ 201.575 + 349.138i 0.522424 + 0.904865i 0.999660 + 0.0260895i $$0.00830548\pi$$
−0.477236 + 0.878775i $$0.658361\pi$$
$$54$$ 0 0
$$55$$ −308.958 −0.757451
$$56$$ 0 0
$$57$$ −271.337 −0.630518
$$58$$ 0 0
$$59$$ 296.855 + 514.168i 0.655038 + 1.13456i 0.981884 + 0.189481i $$0.0606806\pi$$
−0.326847 + 0.945077i $$0.605986\pi$$
$$60$$ 0 0
$$61$$ 166.585 288.534i 0.349657 0.605623i −0.636532 0.771250i $$-0.719632\pi$$
0.986188 + 0.165628i $$0.0529649\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ 0 0
$$65$$ −163.110 + 282.515i −0.311251 + 0.539102i
$$66$$ 0 0
$$67$$ 371.756 + 643.900i 0.677869 + 1.17410i 0.975622 + 0.219460i $$0.0704295\pi$$
−0.297753 + 0.954643i $$0.596237\pi$$
$$68$$ 0 0
$$69$$ −355.784 −0.620744
$$70$$ 0 0
$$71$$ −728.272 −1.21732 −0.608662 0.793429i $$-0.708294\pi$$
−0.608662 + 0.793429i $$0.708294\pi$$
$$72$$ 0 0
$$73$$ −400.874 694.335i −0.642723 1.11323i −0.984822 0.173566i $$-0.944471\pi$$
0.342099 0.939664i $$-0.388862\pi$$
$$74$$ 0 0
$$75$$ −87.3912 + 151.366i −0.134548 + 0.233043i
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −533.953 + 924.833i −0.760435 + 1.31711i 0.182191 + 0.983263i $$0.441681\pi$$
−0.942626 + 0.333849i $$0.891652\pi$$
$$80$$ 0 0
$$81$$ −40.5000 70.1481i −0.0555556 0.0962250i
$$82$$ 0 0
$$83$$ −906.756 −1.19915 −0.599575 0.800319i $$-0.704664\pi$$
−0.599575 + 0.800319i $$0.704664\pi$$
$$84$$ 0 0
$$85$$ 81.1709 0.103579
$$86$$ 0 0
$$87$$ −117.609 203.705i −0.144931 0.251028i
$$88$$ 0 0
$$89$$ 556.634 964.119i 0.662957 1.14827i −0.316878 0.948466i $$-0.602635\pi$$
0.979835 0.199808i $$-0.0640320\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ −138.016 + 239.051i −0.153889 + 0.266543i
$$94$$ 0 0
$$95$$ 369.444 + 639.896i 0.398991 + 0.691073i
$$96$$ 0 0
$$97$$ −1480.94 −1.55017 −0.775084 0.631858i $$-0.782293\pi$$
−0.775084 + 0.631858i $$0.782293\pi$$
$$98$$ 0 0
$$99$$ 340.370 0.345540
$$100$$ 0 0
$$101$$ −278.158 481.784i −0.274037 0.474647i 0.695854 0.718183i $$-0.255026\pi$$
−0.969892 + 0.243536i $$0.921693\pi$$
$$102$$ 0 0
$$103$$ 276.217 478.423i 0.264238 0.457674i −0.703126 0.711066i $$-0.748213\pi$$
0.967364 + 0.253392i $$0.0815462\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −266.902 + 462.288i −0.241144 + 0.417674i −0.961040 0.276408i $$-0.910856\pi$$
0.719896 + 0.694082i $$0.244189\pi$$
$$108$$ 0 0
$$109$$ −547.314 947.976i −0.480947 0.833025i 0.518814 0.854887i $$-0.326374\pi$$
−0.999761 + 0.0218626i $$0.993040\pi$$
$$110$$ 0 0
$$111$$ −997.306 −0.852794
$$112$$ 0 0
$$113$$ −1425.18 −1.18646 −0.593228 0.805035i $$-0.702147\pi$$
−0.593228 + 0.805035i $$0.702147\pi$$
$$114$$ 0 0
$$115$$ 484.423 + 839.046i 0.392806 + 0.680360i
$$116$$ 0 0
$$117$$ 179.694 311.239i 0.141989 0.245932i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −49.6330 + 85.9668i −0.0372900 + 0.0645882i
$$122$$ 0 0
$$123$$ −107.618 186.399i −0.0788907 0.136643i
$$124$$ 0 0
$$125$$ 1497.13 1.07126
$$126$$ 0 0
$$127$$ −786.485 −0.549522 −0.274761 0.961513i $$-0.588599\pi$$
−0.274761 + 0.961513i $$0.588599\pi$$
$$128$$ 0 0
$$129$$ −173.920 301.238i −0.118704 0.205601i
$$130$$ 0 0
$$131$$ −13.8651 + 24.0151i −0.00924735 + 0.0160169i −0.870612 0.491970i $$-0.836277\pi$$
0.861365 + 0.507987i $$0.169610\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ −110.287 + 191.023i −0.0703110 + 0.121782i
$$136$$ 0 0
$$137$$ 1181.49 + 2046.40i 0.736798 + 1.27617i 0.953930 + 0.300029i $$0.0969964\pi$$
−0.217132 + 0.976142i $$0.569670\pi$$
$$138$$ 0 0
$$139$$ −2513.28 −1.53362 −0.766811 0.641873i $$-0.778158\pi$$
−0.766811 + 0.641873i $$0.778158\pi$$
$$140$$ 0 0
$$141$$ 923.782 0.551748
$$142$$ 0 0
$$143$$ 755.090 + 1307.85i 0.441565 + 0.764813i
$$144$$ 0 0
$$145$$ −320.266 + 554.716i −0.183425 + 0.317701i
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −1132.92 + 1962.27i −0.622900 + 1.07889i 0.366043 + 0.930598i $$0.380712\pi$$
−0.988943 + 0.148296i $$0.952621\pi$$
$$150$$ 0 0
$$151$$ −141.573 245.212i −0.0762984 0.132153i 0.825352 0.564619i $$-0.190977\pi$$
−0.901650 + 0.432466i $$0.857644\pi$$
$$152$$ 0 0
$$153$$ −89.4237 −0.0472515
$$154$$ 0 0
$$155$$ 751.675 0.389522
$$156$$ 0 0
$$157$$ 96.2904 + 166.780i 0.0489478 + 0.0847801i 0.889461 0.457011i $$-0.151080\pi$$
−0.840513 + 0.541791i $$0.817747\pi$$
$$158$$ 0 0
$$159$$ −604.725 + 1047.41i −0.301622 + 0.522424i
$$160$$ 0 0
$$161$$ 0 0
$$162$$ 0 0
$$163$$ 421.417 729.915i 0.202502 0.350744i −0.746832 0.665013i $$-0.768426\pi$$
0.949334 + 0.314269i $$0.101759\pi$$
$$164$$ 0 0
$$165$$ −463.436 802.695i −0.218657 0.378726i
$$166$$ 0 0
$$167$$ 3859.21 1.78823 0.894116 0.447836i $$-0.147805\pi$$
0.894116 + 0.447836i $$0.147805\pi$$
$$168$$ 0 0
$$169$$ −602.441 −0.274211
$$170$$ 0 0
$$171$$ −407.006 704.955i −0.182015 0.315259i
$$172$$ 0 0
$$173$$ 755.329 1308.27i 0.331946 0.574947i −0.650948 0.759123i $$-0.725628\pi$$
0.982893 + 0.184176i $$0.0589616\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −890.565 + 1542.50i −0.378186 + 0.655038i
$$178$$ 0 0
$$179$$ 1232.31 + 2134.43i 0.514566 + 0.891255i 0.999857 + 0.0169022i $$0.00538039\pi$$
−0.485291 + 0.874353i $$0.661286\pi$$
$$180$$ 0 0
$$181$$ 3297.36 1.35409 0.677047 0.735940i $$-0.263259\pi$$
0.677047 + 0.735940i $$0.263259\pi$$
$$182$$ 0 0
$$183$$ 999.511 0.403749
$$184$$ 0 0
$$185$$ 1357.90 + 2351.95i 0.539647 + 0.934696i
$$186$$ 0 0
$$187$$ 187.883 325.424i 0.0734727 0.127258i
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 2364.85 4096.05i 0.895889 1.55173i 0.0631890 0.998002i $$-0.479873\pi$$
0.832700 0.553724i $$-0.186794\pi$$
$$192$$ 0 0
$$193$$ −2276.59 3943.17i −0.849080 1.47065i −0.882030 0.471193i $$-0.843823\pi$$
0.0329498 0.999457i $$-0.489510\pi$$
$$194$$ 0 0
$$195$$ −978.660 −0.359402
$$196$$ 0 0
$$197$$ −3109.06 −1.12442 −0.562212 0.826993i $$-0.690050\pi$$
−0.562212 + 0.826993i $$0.690050\pi$$
$$198$$ 0 0
$$199$$ −221.756 384.092i −0.0789943 0.136822i 0.823822 0.566849i $$-0.191838\pi$$
−0.902816 + 0.430027i $$0.858504\pi$$
$$200$$ 0 0
$$201$$ −1115.27 + 1931.70i −0.391368 + 0.677869i
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −293.057 + 507.590i −0.0998439 + 0.172935i
$$206$$ 0 0
$$207$$ −533.675 924.353i −0.179193 0.310372i
$$208$$ 0 0
$$209$$ 3420.56 1.13208
$$210$$ 0 0
$$211$$ 4653.28 1.51822 0.759112 0.650960i $$-0.225633\pi$$
0.759112 + 0.650960i $$0.225633\pi$$
$$212$$ 0 0
$$213$$ −1092.41 1892.11i −0.351411 0.608662i
$$214$$ 0 0
$$215$$ −473.607 + 820.311i −0.150231 + 0.260208i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 1202.62 2083.00i 0.371077 0.642723i
$$220$$ 0 0
$$221$$ −198.381 343.606i −0.0603826 0.104586i
$$222$$ 0 0
$$223$$ −2778.90 −0.834481 −0.417240 0.908796i $$-0.637003\pi$$
−0.417240 + 0.908796i $$0.637003\pi$$
$$224$$ 0 0
$$225$$ −524.347 −0.155362
$$226$$ 0 0
$$227$$ 1608.61 + 2786.20i 0.470340 + 0.814653i 0.999425 0.0339159i $$-0.0107978\pi$$
−0.529084 + 0.848569i $$0.677464\pi$$
$$228$$ 0 0
$$229$$ −1864.01 + 3228.56i −0.537891 + 0.931655i 0.461126 + 0.887335i $$0.347446\pi$$
−0.999017 + 0.0443203i $$0.985888\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 1801.76 3120.73i 0.506596 0.877451i −0.493374 0.869817i $$-0.664237\pi$$
0.999971 0.00763377i $$-0.00242993\pi$$
$$234$$ 0 0
$$235$$ −1257.79 2178.56i −0.349146 0.604739i
$$236$$ 0 0
$$237$$ −3203.72 −0.878075
$$238$$ 0 0
$$239$$ 2348.76 0.635684 0.317842 0.948144i $$-0.397042\pi$$
0.317842 + 0.948144i $$0.397042\pi$$
$$240$$ 0 0
$$241$$ −2546.70 4411.01i −0.680693 1.17900i −0.974770 0.223213i $$-0.928345\pi$$
0.294076 0.955782i $$-0.404988\pi$$
$$242$$ 0 0
$$243$$ 121.500 210.444i 0.0320750 0.0555556i
$$244$$ 0 0
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 1805.84 3127.80i 0.465193 0.805738i
$$248$$ 0 0
$$249$$ −1360.13 2355.82i −0.346165 0.599575i
$$250$$ 0 0
$$251$$ 5939.02 1.49350 0.746749 0.665106i $$-0.231614\pi$$
0.746749 + 0.665106i $$0.231614\pi$$
$$252$$ 0 0
$$253$$ 4485.11 1.11453
$$254$$ 0 0
$$255$$ 121.756 + 210.888i 0.0299007 + 0.0517895i
$$256$$ 0 0
$$257$$ −757.944 + 1312.80i −0.183966 + 0.318638i −0.943228 0.332147i $$-0.892227\pi$$
0.759262 + 0.650785i $$0.225560\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 352.827 611.115i 0.0836761 0.144931i
$$262$$ 0 0
$$263$$ 3216.96 + 5571.94i 0.754244 + 1.30639i 0.945749 + 0.324898i $$0.105330\pi$$
−0.191505 + 0.981492i $$0.561337\pi$$
$$264$$ 0 0
$$265$$ 3293.50 0.763464
$$266$$ 0 0
$$267$$ 3339.81 0.765516
$$268$$ 0 0
$$269$$ −3474.90 6018.69i −0.787614 1.36419i −0.927425 0.374009i $$-0.877983\pi$$
0.139811 0.990178i $$-0.455350\pi$$
$$270$$ 0 0
$$271$$ −480.997 + 833.111i −0.107817 + 0.186745i −0.914886 0.403713i $$-0.867719\pi$$
0.807068 + 0.590458i $$0.201053\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 1101.68 1908.16i 0.241577 0.418424i
$$276$$ 0 0
$$277$$ −380.005 658.188i −0.0824271 0.142768i 0.821865 0.569682i $$-0.192934\pi$$
−0.904292 + 0.426915i $$0.859600\pi$$
$$278$$ 0 0
$$279$$ −828.099 −0.177695
$$280$$ 0 0
$$281$$ −4412.07 −0.936662 −0.468331 0.883553i $$-0.655145\pi$$
−0.468331 + 0.883553i $$0.655145\pi$$
$$282$$ 0 0
$$283$$ −1301.07 2253.53i −0.273289 0.473351i 0.696413 0.717641i $$-0.254778\pi$$
−0.969702 + 0.244291i $$0.921445\pi$$
$$284$$ 0 0
$$285$$ −1108.33 + 1919.69i −0.230358 + 0.398991i
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 2407.14 4169.29i 0.489953 0.848623i
$$290$$ 0 0
$$291$$ −2221.41 3847.59i −0.447495 0.775084i
$$292$$ 0 0
$$293$$ 9332.18 1.86072 0.930361 0.366644i $$-0.119493\pi$$
0.930361 + 0.366644i $$0.119493\pi$$
$$294$$ 0 0
$$295$$ 4850.26 0.957264
$$296$$ 0 0
$$297$$ 510.555 + 884.306i 0.0997488 + 0.172770i
$$298$$ 0 0
$$299$$ 2367.85 4101.24i 0.457982 0.793248i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 834.474 1445.35i 0.158216 0.274037i
$$304$$ 0 0
$$305$$ −1360.90 2357.15i −0.255492 0.442525i
$$306$$ 0 0
$$307$$ −4895.51 −0.910103 −0.455051 0.890465i $$-0.650379\pi$$
−0.455051 + 0.890465i $$0.650379\pi$$
$$308$$ 0 0
$$309$$ 1657.30 0.305116
$$310$$ 0 0
$$311$$ 3752.64 + 6499.77i 0.684221 + 1.18511i 0.973681 + 0.227916i $$0.0731910\pi$$
−0.289460 + 0.957190i $$0.593476\pi$$
$$312$$ 0 0
$$313$$ −3174.64 + 5498.63i −0.573294 + 0.992974i 0.422931 + 0.906162i $$0.361001\pi$$
−0.996225 + 0.0868124i $$0.972332\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 3999.80 6927.86i 0.708679 1.22747i −0.256669 0.966499i $$-0.582625\pi$$
0.965347 0.260968i $$-0.0840417\pi$$
$$318$$ 0 0
$$319$$ 1482.61 + 2567.96i 0.260221 + 0.450716i
$$320$$ 0 0
$$321$$ −1601.41 −0.278449
$$322$$ 0 0
$$323$$ −898.666 −0.154808
$$324$$ 0 0
$$325$$ −1163.23 2014.78i −0.198537 0.343876i
$$326$$ 0 0
$$327$$ 1641.94 2843.93i 0.277675 0.480947i
$$328$$ 0 0
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 1060.78 1837.32i 0.176150 0.305101i −0.764409 0.644732i $$-0.776969\pi$$
0.940559 + 0.339631i $$0.110302\pi$$
$$332$$ 0 0
$$333$$ −1495.96 2591.08i −0.246180 0.426397i
$$334$$ 0 0
$$335$$ 6074.05 0.990629
$$336$$ 0 0
$$337$$ −9114.19 −1.47324 −0.736620 0.676307i $$-0.763579\pi$$
−0.736620 + 0.676307i $$0.763579\pi$$
$$338$$ 0 0
$$339$$ −2137.77 3702.72i −0.342500 0.593228i
$$340$$ 0 0
$$341$$ 1739.87 3013.55i 0.276303 0.478572i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ −1453.27 + 2517.14i −0.226787 + 0.392806i
$$346$$ 0 0
$$347$$ 836.534 + 1448.92i 0.129416 + 0.224156i 0.923451 0.383717i $$-0.125356\pi$$
−0.794034 + 0.607873i $$0.792023\pi$$
$$348$$ 0 0
$$349$$ 3467.56 0.531845 0.265923 0.963994i $$-0.414323\pi$$
0.265923 + 0.963994i $$0.414323\pi$$
$$350$$ 0 0
$$351$$ 1078.16 0.163955
$$352$$ 0 0
$$353$$ 1992.12 + 3450.45i 0.300368 + 0.520252i 0.976219 0.216785i $$-0.0695572\pi$$
−0.675851 + 0.737038i $$0.736224\pi$$
$$354$$ 0 0
$$355$$ −2974.78 + 5152.46i −0.444746 + 0.770322i
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 0 0
$$359$$ −1085.47 + 1880.08i −0.159579 + 0.276398i −0.934717 0.355394i $$-0.884347\pi$$
0.775138 + 0.631792i $$0.217680\pi$$
$$360$$ 0 0
$$361$$ −660.724 1144.41i −0.0963295 0.166848i
$$362$$ 0 0
$$363$$ −297.798 −0.0430588
$$364$$ 0 0
$$365$$ −6549.81 −0.939268
$$366$$ 0 0
$$367$$ 1796.06 + 3110.86i 0.255459 + 0.442468i 0.965020 0.262176i $$-0.0844400\pi$$
−0.709561 + 0.704644i $$0.751107\pi$$
$$368$$ 0 0
$$369$$ 322.853 559.197i 0.0455475 0.0788907i
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −3719.90 + 6443.05i −0.516378 + 0.894393i 0.483441 + 0.875377i $$0.339387\pi$$
−0.999819 + 0.0190163i $$0.993947\pi$$
$$374$$ 0 0
$$375$$ 2245.70 + 3889.66i 0.309246 + 0.535630i
$$376$$ 0 0
$$377$$ 3130.91 0.427719
$$378$$ 0 0
$$379$$ 11243.9 1.52390 0.761951 0.647635i $$-0.224242\pi$$
0.761951 + 0.647635i $$0.224242\pi$$
$$380$$ 0 0
$$381$$ −1179.73 2043.35i −0.158633 0.274761i
$$382$$ 0 0
$$383$$ 1770.62 3066.81i 0.236226 0.409156i −0.723402 0.690427i $$-0.757423\pi$$
0.959628 + 0.281271i $$0.0907561\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 521.759 903.714i 0.0685336 0.118704i
$$388$$ 0 0
$$389$$ 5279.10 + 9143.66i 0.688074 + 1.19178i 0.972460 + 0.233070i $$0.0748770\pi$$
−0.284386 + 0.958710i $$0.591790\pi$$
$$390$$ 0 0
$$391$$ −1178.35 −0.152409
$$392$$ 0 0
$$393$$ −83.1908 −0.0106779
$$394$$ 0 0
$$395$$ 4362.08 + 7555.34i 0.555645 + 0.962406i
$$396$$ 0 0
$$397$$ −270.287 + 468.151i −0.0341696 + 0.0591834i −0.882604 0.470116i $$-0.844212\pi$$
0.848435 + 0.529300i $$0.177545\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −1083.52 + 1876.70i −0.134933 + 0.233711i −0.925572 0.378572i $$-0.876415\pi$$
0.790639 + 0.612283i $$0.209749\pi$$
$$402$$ 0 0
$$403$$ −1837.09 3181.93i −0.227077 0.393308i
$$404$$ 0 0
$$405$$ −661.722 −0.0811882
$$406$$ 0 0
$$407$$ 12572.3 1.53117
$$408$$ 0 0
$$409$$ −478.845 829.384i −0.0578908 0.100270i 0.835628 0.549296i $$-0.185104\pi$$
−0.893518 + 0.449027i $$0.851771\pi$$
$$410$$ 0 0
$$411$$ −3544.46 + 6139.19i −0.425390 + 0.736798i
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −3703.83 + 6415.22i −0.438105 + 0.758821i
$$416$$ 0 0
$$417$$ −3769.92 6529.69i −0.442719 0.766811i
$$418$$ 0 0
$$419$$ −6464.42 −0.753718 −0.376859 0.926271i $$-0.622996\pi$$
−0.376859 + 0.926271i $$0.622996\pi$$
$$420$$ 0 0
$$421$$ −6201.23 −0.717885 −0.358943 0.933360i $$-0.616863\pi$$
−0.358943 + 0.933360i $$0.616863\pi$$
$$422$$ 0 0
$$423$$ 1385.67 + 2400.06i 0.159276 + 0.275874i
$$424$$ 0 0
$$425$$ −289.439 + 501.322i −0.0330349 + 0.0572181i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ −2265.27 + 3923.56i −0.254938 + 0.441565i
$$430$$ 0 0
$$431$$ −707.796 1225.94i −0.0791029 0.137010i 0.823760 0.566938i $$-0.191872\pi$$
−0.902863 + 0.429928i $$0.858539\pi$$
$$432$$ 0 0
$$433$$ −8905.73 −0.988411 −0.494206 0.869345i $$-0.664541\pi$$
−0.494206 + 0.869345i $$0.664541\pi$$
$$434$$ 0 0
$$435$$ −1921.59 −0.211801
$$436$$ 0 0
$$437$$ −5363.19 9289.32i −0.587085 1.01686i
$$438$$ 0 0
$$439$$ 5438.25 9419.33i 0.591238 1.02405i −0.402828 0.915276i $$-0.631973\pi$$
0.994066 0.108779i $$-0.0346940\pi$$
$$440$$ 0 0
$$441$$ 0 0
$$442$$ 0 0
$$443$$ −5701.48 + 9875.25i −0.611479 + 1.05911i 0.379512 + 0.925187i $$0.376092\pi$$
−0.990991 + 0.133927i $$0.957241\pi$$
$$444$$ 0 0
$$445$$ −4547.37 7876.28i −0.484418 0.839037i
$$446$$ 0 0
$$447$$ −6797.49 −0.719262
$$448$$ 0 0
$$449$$ −12689.0 −1.33370 −0.666852 0.745190i $$-0.732359\pi$$
−0.666852 + 0.745190i $$0.732359\pi$$
$$450$$ 0 0
$$451$$ 1356.66 + 2349.80i 0.141646 + 0.245339i
$$452$$ 0 0
$$453$$ 424.720 735.636i 0.0440509 0.0762984i
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −1135.02 + 1965.92i −0.116180 + 0.201229i −0.918251 0.395999i $$-0.870398\pi$$
0.802071 + 0.597229i $$0.203732\pi$$
$$458$$ 0 0
$$459$$ −134.135 232.329i −0.0136403 0.0236257i
$$460$$ 0 0
$$461$$ −10731.2 −1.08417 −0.542085 0.840324i $$-0.682365\pi$$
−0.542085 + 0.840324i $$0.682365\pi$$
$$462$$ 0 0
$$463$$ −3307.74 −0.332017 −0.166008 0.986124i $$-0.553088\pi$$
−0.166008 + 0.986124i $$0.553088\pi$$
$$464$$ 0 0
$$465$$ 1127.51 + 1952.91i 0.112445 + 0.194761i
$$466$$ 0 0
$$467$$ −4623.35 + 8007.87i −0.458122 + 0.793490i −0.998862 0.0476996i $$-0.984811\pi$$
0.540740 + 0.841190i $$0.318144\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ 0 0
$$471$$ −288.871 + 500.339i −0.0282600 + 0.0489478i
$$472$$ 0 0
$$473$$ 2192.48 + 3797.49i 0.213130 + 0.369152i
$$474$$ 0 0
$$475$$ −5269.45 −0.509008
$$476$$ 0 0
$$477$$ −3628.35 −0.348283
$$478$$ 0 0
$$479$$ 7611.66 + 13183.8i 0.726066 + 1.25758i 0.958534 + 0.284978i $$0.0919865\pi$$
−0.232468 + 0.972604i $$0.574680\pi$$
$$480$$ 0 0
$$481$$ 6637.39 11496.3i 0.629187 1.08978i
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0 0
$$485$$ −6049.19 + 10477.5i −0.566349 + 0.980946i
$$486$$ 0 0
$$487$$ 3879.36 + 6719.25i 0.360966 + 0.625212i 0.988120 0.153683i $$-0.0491136\pi$$
−0.627154 + 0.778895i $$0.715780\pi$$
$$488$$ 0 0
$$489$$ 2528.50 0.233830
$$490$$ 0 0
$$491$$ −8342.30 −0.766767 −0.383384 0.923589i $$-0.625241\pi$$
−0.383384 + 0.923589i $$0.625241\pi$$
$$492$$ 0 0
$$493$$ −389.520 674.668i −0.0355844 0.0616340i
$$494$$ 0 0
$$495$$ 1390.31 2408.09i 0.126242 0.218657i
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 1293.47 2240.36i 0.116040 0.200987i −0.802155 0.597116i $$-0.796313\pi$$
0.918195 + 0.396129i $$0.129647\pi$$
$$500$$ 0 0
$$501$$ 5788.82 + 10026.5i 0.516218 + 0.894116i
$$502$$ 0 0
$$503$$ −409.682 −0.0363157 −0.0181578 0.999835i $$-0.505780\pi$$
−0.0181578 + 0.999835i $$0.505780\pi$$
$$504$$ 0 0
$$505$$ −4544.77 −0.400475
$$506$$ 0 0
$$507$$ −903.662 1565.19i −0.0791578 0.137105i
$$508$$ 0 0
$$509$$ 2195.25 3802.29i 0.191165 0.331107i −0.754472 0.656333i $$-0.772107\pi$$
0.945637 + 0.325225i $$0.105440\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 1221.02 2114.87i 0.105086 0.182015i
$$514$$ 0 0
$$515$$ −2256.53 3908.43i −0.193077 0.334419i
$$516$$ 0 0
$$517$$ −11645.5 −0.990652
$$518$$ 0 0
$$519$$ 4531.98 0.383298
$$520$$ 0 0
$$521$$ −9714.76 16826.5i −0.816912 1.41493i −0.907947 0.419086i $$-0.862351\pi$$
0.0910341 0.995848i $$-0.470983\pi$$
$$522$$ 0 0
$$523$$ 8974.35 15544.0i 0.750326 1.29960i −0.197338 0.980336i $$-0.563230\pi$$
0.947664 0.319268i $$-0.103437\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ −457.109 + 791.735i −0.0377836 + 0.0654431i
$$528$$ 0 0
$$529$$ −948.833 1643.43i −0.0779841 0.135072i
$$530$$ 0 0
$$531$$ −5343.39 −0.436692
$$532$$ 0 0
$$533$$ 2864.92 0.232821
$$534$$ 0 0
$$535$$ 2180.43 + 3776.62i 0.176202 + 0.305192i
$$536$$ 0 0
$$537$$ −3696.94 + 6403.28i −0.297085 + 0.514566i
$$538$$ 0 0
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −11547.0 + 20000.0i −0.917641 + 1.58940i −0.114652 + 0.993406i $$0.536575\pi$$
−0.802989 + 0.595994i $$0.796758\pi$$
$$542$$ 0 0
$$543$$ 4946.04 + 8566.80i 0.390893 + 0.677047i
$$544$$ 0 0
$$545$$ −8942.47 −0.702850
$$546$$ 0 0
$$547$$ −2266.68 −0.177178 −0.0885889 0.996068i $$-0.528236\pi$$
−0.0885889 + 0.996068i $$0.528236\pi$$
$$548$$ 0 0
$$549$$ 1499.27 + 2596.81i 0.116552 + 0.201874i
$$550$$ 0 0
$$551$$ 3545.75 6141.42i 0.274145 0.474834i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ −4073.70 + 7055.85i −0.311565 + 0.539647i
$$556$$ 0 0
$$557$$ 5519.27 + 9559.65i 0.419854 + 0.727209i 0.995924 0.0901913i $$-0.0287478\pi$$
−0.576070 + 0.817400i $$0.695415\pi$$
$$558$$ 0 0
$$559$$ 4629.97 0.350316
$$560$$ 0 0
$$561$$ 1127.30 0.0848390
$$562$$ 0 0
$$563$$ −3529.68 6113.58i −0.264224 0.457650i 0.703136 0.711055i $$-0.251783\pi$$
−0.967360 + 0.253406i $$0.918449\pi$$
$$564$$ 0 0
$$565$$ −5821.43 + 10083.0i −0.433468 + 0.750788i
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ 676.403 1171.56i 0.0498353 0.0863172i −0.840032 0.542537i $$-0.817464\pi$$
0.889867 + 0.456220i $$0.150797\pi$$
$$570$$ 0 0
$$571$$ 10419.6 + 18047.3i 0.763655 + 1.32269i 0.940955 + 0.338532i $$0.109930\pi$$
−0.177300 + 0.984157i $$0.556736\pi$$
$$572$$ 0 0
$$573$$ 14189.1 1.03448
$$574$$ 0 0
$$575$$ −6909.42 −0.501117
$$576$$ 0 0
$$577$$ 5007.32 + 8672.92i 0.361278 + 0.625751i 0.988171 0.153353i $$-0.0490073\pi$$
−0.626894 + 0.779105i $$0.715674\pi$$
$$578$$ 0 0
$$579$$ 6829.77 11829.5i 0.490217 0.849080i
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 7623.34 13204.0i 0.541555 0.938001i
$$584$$ 0 0
$$585$$ −1467.99 2542.63i −0.103750 0.179701i
$$586$$ 0 0
$$587$$ −20864.8 −1.46709 −0.733546 0.679640i $$-0.762136\pi$$
−0.733546 + 0.679640i $$0.762136\pi$$
$$588$$ 0 0
$$589$$ −8322.01 −0.582177
$$590$$ 0 0
$$591$$ −4663.60 8077.59i −0.324593 0.562212i
$$592$$ 0 0
$$593$$ 8773.84 15196.7i 0.607586 1.05237i −0.384051 0.923312i $$-0.625471\pi$$
0.991637 0.129058i $$-0.0411952\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0 0
$$597$$ 665.268 1152.28i 0.0456074 0.0789943i
$$598$$ 0 0
$$599$$ 65.3409 + 113.174i 0.00445703 + 0.00771980i 0.868245 0.496135i $$-0.165248\pi$$
−0.863788 + 0.503855i $$0.831915\pi$$
$$600$$ 0 0
$$601$$ 5964.47 0.404818 0.202409 0.979301i $$-0.435123\pi$$
0.202409 + 0.979301i $$0.435123\pi$$
$$602$$ 0 0
$$603$$ −6691.60 −0.451912
$$604$$ 0 0
$$605$$ 405.472 + 702.298i 0.0272476 + 0.0471942i
$$606$$ 0 0
$$607$$ −4955.82 + 8583.73i −0.331384 + 0.573975i −0.982784 0.184761i $$-0.940849\pi$$
0.651399 + 0.758735i $$0.274182\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ −6148.07 + 10648.8i −0.407077 + 0.705079i
$$612$$ 0 0
$$613$$ 3241.26 + 5614.03i 0.213562 + 0.369900i 0.952827 0.303515i $$-0.0981602\pi$$
−0.739265 + 0.673415i $$0.764827\pi$$
$$614$$ 0 0
$$615$$ −1758.34 −0.115290
$$616$$ 0 0
$$617$$ 7189.36 0.469097 0.234548 0.972104i $$-0.424639\pi$$
0.234548 + 0.972104i $$0.424639\pi$$
$$618$$ 0 0
$$619$$ 930.696 + 1612.01i 0.0604327 + 0.104672i 0.894659 0.446750i $$-0.147419\pi$$
−0.834226 + 0.551422i $$0.814085\pi$$
$$620$$ 0 0
$$621$$ 1601.03 2773.06i 0.103457 0.179193i
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 2474.04 4285.16i 0.158338 0.274250i
$$626$$ 0 0
$$627$$ 5130.84 + 8886.87i 0.326804 + 0.566041i
$$628$$ 0 0
$$629$$ −3303.06 −0.209383
$$630$$ 0 0
$$631$$ −29032.0 −1.83161 −0.915803 0.401627i $$-0.868445\pi$$
−0.915803 + 0.401627i $$0.868445\pi$$
$$632$$ 0 0
$$633$$ 6979.93 + 12089.6i 0.438274 + 0.759112i
$$634$$ 0 0
$$635$$ −3212.56 + 5564.32i −0.200766 + 0.347737i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 3277.23 5676.32i 0.202887 0.351411i
$$640$$ 0 0
$$641$$ −12228.9 21181.0i −0.753527 1.30515i −0.946103 0.323866i $$-0.895017\pi$$
0.192576 0.981282i $$-0.438316\pi$$
$$642$$ 0 0
$$643$$ −10968.2 −0.672695 −0.336348 0.941738i $$-0.609192\pi$$
−0.336348 + 0.941738i $$0.609192\pi$$
$$644$$ 0 0
$$645$$ −2841.64 −0.173472
$$646$$ 0 0
$$647$$ 2742.37 + 4749.92i 0.166636 + 0.288622i 0.937235 0.348698i $$-0.113376\pi$$
−0.770599 + 0.637320i $$0.780043\pi$$
$$648$$ 0 0
$$649$$ 11226.7 19445.2i 0.679025 1.17611i
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 5164.98 8946.01i 0.309527 0.536117i −0.668732 0.743504i $$-0.733163\pi$$
0.978259 + 0.207387i $$0.0664959\pi$$
$$654$$ 0 0
$$655$$ 113.270 + 196.189i 0.00675698 + 0.0117034i
$$656$$ 0 0
$$657$$ 7215.74 0.428482
$$658$$ 0 0
$$659$$ 26822.2 1.58550 0.792751 0.609546i $$-0.208648\pi$$
0.792751 + 0.609546i $$0.208648\pi$$
$$660$$ 0 0
$$661$$ 1249.38 + 2163.99i 0.0735177 + 0.127336i 0.900441 0.434979i $$-0.143244\pi$$
−0.826923 + 0.562315i $$0.809911\pi$$
$$662$$ 0 0
$$663$$ 595.143 1030.82i 0.0348619 0.0603826i
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 4649.27 8052.77i 0.269896 0.467473i
$$668$$ 0 0
$$669$$ −4168.36 7219.81i −0.240894 0.417240i
$$670$$ 0 0
$$671$$ −12600.1 −0.724922
$$672$$ 0 0
$$673$$ 10092.1 0.578044 0.289022 0.957322i $$-0.406670\pi$$
0.289022 + 0.957322i $$0.406670\pi$$
$$674$$ 0 0
$$675$$ −786.521 1362.29i −0.0448492 0.0776811i
$$676$$ 0 0
$$677$$ −13183.2 + 22833.9i −0.748406 + 1.29628i 0.200181 + 0.979759i $$0.435847\pi$$
−0.948586 + 0.316518i $$0.897486\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −4825.83 + 8358.59i −0.271551 + 0.470340i
$$682$$ 0 0
$$683$$ −11285.4 19546.9i −0.632245 1.09508i −0.987092 0.160155i $$-0.948800\pi$$
0.354847 0.934924i $$-0.384533\pi$$
$$684$$ 0 0
$$685$$ 19304.1 1.07675
$$686$$ 0 0
$$687$$ −11184.0 −0.621103
$$688$$ 0 0
$$689$$ −8049.28 13941.8i −0.445070 0.770884i
$$690$$ 0 0
$$691$$ −5965.75 + 10333.0i −0.328434 + 0.568864i −0.982201 0.187832i $$-0.939854\pi$$
0.653768 + 0.756695i $$0.273187\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ −10266.0 + 17781.2i −0.560304 + 0.970475i
$$696$$ 0 0
$$697$$ −356.428 617.352i −0.0193697 0.0335493i
$$698$$ 0 0
$$699$$ 10810.5 0.584967
$$700$$ 0 0
$$701$$ 16592.6 0.893997 0.446999 0.894535i $$-0.352493\pi$$
0.446999 + 0.894535i $$0.352493\pi$$
$$702$$ 0 0
$$703$$ −15033.7 26039.1i −0.806553 1.39699i
$$704$$ 0 0
$$705$$ 3773.38 6535.68i 0.201580 0.349146i
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −9357.00 + 16206.8i −0.495641 + 0.858476i −0.999987 0.00502575i $$-0.998400\pi$$
0.504346 + 0.863502i $$0.331734\pi$$
$$710$$ 0 0
$$711$$ −4805.57 8323.50i −0.253478 0.439037i
$$712$$ 0 0
$$713$$ −10912.0 −0.573152
$$714$$ 0 0
$$715$$ 12337.3 0.645298
$$716$$ 0 0
$$717$$ 3523.14 + 6102.25i 0.183506 + 0.317842i
$$718$$ 0 0
$$719$$ −12427.4 + 21524.9i −0.644594 + 1.11647i 0.339801 + 0.940497i $$0.389640\pi$$
−0.984395 + 0.175972i $$0.943693\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 0 0
$$723$$ 7640.09 13233.0i 0.392998 0.680693i
$$724$$ 0 0
$$725$$ −2284.00 3956.01i −0.117001 0.202652i
$$726$$ 0 0
$$727$$ 22506.0 1.14814 0.574071 0.818805i $$-0.305363\pi$$
0.574071 + 0.818805i $$0.305363\pi$$
$$728$$ 0 0
$$729$$ 729.000 0.0370370
$$730$$ 0 0
$$731$$ −576.020 997.696i −0.0291448 0.0504803i
$$732$$ 0 0
$$733$$ −11896.0 + 20604.5i −0.599440 + 1.03826i 0.393464 + 0.919340i $$0.371277\pi$$
−0.992904 + 0.118920i $$0.962057\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 14059.4 24351.6i 0.702692 1.21710i
$$738$$ 0 0
$$739$$ −2401.62 4159.72i −0.119547 0.207061i 0.800041 0.599945i $$-0.204811\pi$$
−0.919588 + 0.392884i $$0.871477\pi$$
$$740$$ 0 0
$$741$$ 10835.0 0.537159
$$742$$ 0 0
$$743$$ 5076.10 0.250638 0.125319 0.992116i $$-0.460005\pi$$
0.125319 + 0.992116i $$0.460005\pi$$
$$744$$ 0 0
$$745$$ 9255.24 + 16030.6i 0.455149 + 0.788341i
$$746$$ 0 0
$$747$$ 4080.40 7067.46i 0.199858 0.346165i
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 4579.36 7931.68i 0.222508 0.385394i −0.733061 0.680163i $$-0.761909\pi$$
0.955569 + 0.294768i $$0.0952425\pi$$
$$752$$ 0 0
$$753$$ 8908.54 + 15430.0i 0.431136 + 0.746749i
$$754$$ 0 0
$$755$$ −2313.14 −0.111502
$$756$$ 0 0
$$757$$ 33682.2 1.61717 0.808587 0.588377i $$-0.200233\pi$$
0.808587 + 0.588377i $$0.200233\pi$$
$$758$$ 0 0
$$759$$ 6727.67 + 11652.7i 0.321738 + 0.557266i
$$760$$ 0 0
$$761$$ 6673.14 11558.2i 0.317873 0.550571i −0.662171 0.749352i $$-0.730365\pi$$
0.980044 + 0.198781i $$0.0636983\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ −365.269 + 632.665i −0.0172632 + 0.0299007i
$$766$$ 0 0
$$767$$ −11854.0 20531.7i −0.558048 0.966568i
$$768$$ 0 0
$$769$$ 15530.6 0.728281 0.364140 0.931344i $$-0.381363\pi$$
0.364140 + 0.931344i $$0.381363\pi$$
$$770$$ 0 0
$$771$$ −4547.66 −0.212425
$$772$$ 0 0
$$773$$ −5507.62 9539.47i −0.256268 0.443869i 0.708971 0.705238i $$-0.249160\pi$$
−0.965239 + 0.261368i $$0.915826\pi$$
$$774$$ 0 0
$$775$$ −2680.32 + 4642.45i −0.124232 + 0.215176i
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 0 0
$$779$$ 3244.52 5619.67i 0.149226 0.258467i
$$780$$ 0 0
$$781$$ 13771.2 + 23852.4i 0.630951 + 1.09284i
$$782$$ 0 0
$$783$$ 2116.96 0.0966209
$$784$$ 0 0
$$785$$ 1573.27 0.0715317
$$786$$ 0 0
$$787$$ 10596.3 + 18353.3i 0.479946 + 0.831291i 0.999735 0.0230036i $$-0.00732292\pi$$
−0.519789 + 0.854294i $$0.673990\pi$$
$$788$$ 0 0
$$789$$ −9650.88 + 16715.8i −0.435463 + 0.754244i
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −6652.07 + 11521.7i −0.297884 + 0.515950i
$$794$$ 0 0
$$795$$ 4940.25 + 8556.76i 0.220393 + 0.381732i
$$796$$ 0 0
$$797$$ −18189.9 −0.808432 −0.404216 0.914663i $$-0.632456\pi$$
−0.404216 + 0.914663i $$0.632456\pi$$