# Properties

 Label 240.4.f.f.49.3 Level $240$ Weight $4$ Character 240.49 Analytic conductor $14.160$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$240 = 2^{4} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 240.f (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$14.1604584014$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{41})$$ Defining polynomial: $$x^{4} + 21x^{2} + 100$$ x^4 + 21*x^2 + 100 Coefficient ring: $$\Z[a_1, \ldots, a_{7}]$$ Coefficient ring index: $$2\cdot 3^{2}$$ Twist minimal: no (minimal twist has level 15) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 49.3 Root $$-3.70156i$$ of defining polynomial Character $$\chi$$ $$=$$ 240.49 Dual form 240.4.f.f.49.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+3.00000i q^{3} +(-8.10469 + 7.70156i) q^{5} -22.2094i q^{7} -9.00000 q^{9} +O(q^{10})$$ $$q+3.00000i q^{3} +(-8.10469 + 7.70156i) q^{5} -22.2094i q^{7} -9.00000 q^{9} +1.79063 q^{11} -58.2094i q^{13} +(-23.1047 - 24.3141i) q^{15} +18.9844i q^{17} +104.837 q^{19} +66.6281 q^{21} -49.6125i q^{23} +(6.37188 - 124.837i) q^{25} -27.0000i q^{27} +293.466 q^{29} -64.4187 q^{31} +5.37188i q^{33} +(171.047 + 180.000i) q^{35} -19.8844i q^{37} +174.628 q^{39} -165.581 q^{41} -247.350i q^{43} +(72.9422 - 69.3141i) q^{45} -384.544i q^{47} -150.256 q^{49} -56.9531 q^{51} -463.528i q^{53} +(-14.5125 + 13.7906i) q^{55} +314.512i q^{57} -73.7906 q^{59} -137.350 q^{61} +199.884i q^{63} +(448.303 + 471.769i) q^{65} -173.906i q^{67} +148.837 q^{69} +594.281 q^{71} -320.231i q^{73} +(374.512 + 19.1156i) q^{75} -39.7687i q^{77} -770.469 q^{79} +81.0000 q^{81} +173.925i q^{83} +(-146.209 - 153.862i) q^{85} +880.397i q^{87} -1019.02 q^{89} -1292.79 q^{91} -193.256i q^{93} +(-849.675 + 807.412i) q^{95} +384.375i q^{97} -16.1156 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 6 q^{5} - 36 q^{9}+O(q^{10})$$ 4 * q + 6 * q^5 - 36 * q^9 $$4 q + 6 q^{5} - 36 q^{9} + 84 q^{11} - 54 q^{15} + 112 q^{19} + 36 q^{21} + 256 q^{25} + 636 q^{29} - 104 q^{31} + 300 q^{35} + 468 q^{39} - 816 q^{41} - 54 q^{45} - 140 q^{49} - 612 q^{51} + 864 q^{55} - 372 q^{59} + 680 q^{61} + 948 q^{65} + 288 q^{69} + 72 q^{71} + 576 q^{75} + 760 q^{79} + 324 q^{81} - 508 q^{85} - 2232 q^{89} - 1944 q^{91} - 2784 q^{95} - 756 q^{99}+O(q^{100})$$ 4 * q + 6 * q^5 - 36 * q^9 + 84 * q^11 - 54 * q^15 + 112 * q^19 + 36 * q^21 + 256 * q^25 + 636 * q^29 - 104 * q^31 + 300 * q^35 + 468 * q^39 - 816 * q^41 - 54 * q^45 - 140 * q^49 - 612 * q^51 + 864 * q^55 - 372 * q^59 + 680 * q^61 + 948 * q^65 + 288 * q^69 + 72 * q^71 + 576 * q^75 + 760 * q^79 + 324 * q^81 - 508 * q^85 - 2232 * q^89 - 1944 * q^91 - 2784 * q^95 - 756 * q^99

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$$.

 $$n$$ $$31$$ $$97$$ $$161$$ $$181$$ $$\chi(n)$$ $$1$$ $$-1$$ $$1$$ $$1$$

## 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
$$3$$ 3.00000i 0.577350i
$$4$$ 0 0
$$5$$ −8.10469 + 7.70156i −0.724905 + 0.688849i
$$6$$ 0 0
$$7$$ 22.2094i 1.19919i −0.800302 0.599597i $$-0.795328\pi$$
0.800302 0.599597i $$-0.204672\pi$$
$$8$$ 0 0
$$9$$ −9.00000 −0.333333
$$10$$ 0 0
$$11$$ 1.79063 0.0490813 0.0245407 0.999699i $$-0.492188\pi$$
0.0245407 + 0.999699i $$0.492188\pi$$
$$12$$ 0 0
$$13$$ 58.2094i 1.24188i −0.783860 0.620938i $$-0.786752\pi$$
0.783860 0.620938i $$-0.213248\pi$$
$$14$$ 0 0
$$15$$ −23.1047 24.3141i −0.397707 0.418524i
$$16$$ 0 0
$$17$$ 18.9844i 0.270846i 0.990788 + 0.135423i $$0.0432394\pi$$
−0.990788 + 0.135423i $$0.956761\pi$$
$$18$$ 0 0
$$19$$ 104.837 1.26586 0.632931 0.774208i $$-0.281852\pi$$
0.632931 + 0.774208i $$0.281852\pi$$
$$20$$ 0 0
$$21$$ 66.6281 0.692355
$$22$$ 0 0
$$23$$ 49.6125i 0.449779i −0.974384 0.224890i $$-0.927798\pi$$
0.974384 0.224890i $$-0.0722021\pi$$
$$24$$ 0 0
$$25$$ 6.37188 124.837i 0.0509751 0.998700i
$$26$$ 0 0
$$27$$ 27.0000i 0.192450i
$$28$$ 0 0
$$29$$ 293.466 1.87914 0.939572 0.342350i $$-0.111223\pi$$
0.939572 + 0.342350i $$0.111223\pi$$
$$30$$ 0 0
$$31$$ −64.4187 −0.373224 −0.186612 0.982434i $$-0.559751\pi$$
−0.186612 + 0.982434i $$0.559751\pi$$
$$32$$ 0 0
$$33$$ 5.37188i 0.0283371i
$$34$$ 0 0
$$35$$ 171.047 + 180.000i 0.826063 + 0.869302i
$$36$$ 0 0
$$37$$ 19.8844i 0.0883505i −0.999024 0.0441752i $$-0.985934\pi$$
0.999024 0.0441752i $$-0.0140660\pi$$
$$38$$ 0 0
$$39$$ 174.628 0.716997
$$40$$ 0 0
$$41$$ −165.581 −0.630718 −0.315359 0.948972i $$-0.602125\pi$$
−0.315359 + 0.948972i $$0.602125\pi$$
$$42$$ 0 0
$$43$$ 247.350i 0.877221i −0.898677 0.438611i $$-0.855471\pi$$
0.898677 0.438611i $$-0.144529\pi$$
$$44$$ 0 0
$$45$$ 72.9422 69.3141i 0.241635 0.229616i
$$46$$ 0 0
$$47$$ 384.544i 1.19344i −0.802451 0.596718i $$-0.796471\pi$$
0.802451 0.596718i $$-0.203529\pi$$
$$48$$ 0 0
$$49$$ −150.256 −0.438065
$$50$$ 0 0
$$51$$ −56.9531 −0.156373
$$52$$ 0 0
$$53$$ 463.528i 1.20133i −0.799501 0.600665i $$-0.794903\pi$$
0.799501 0.600665i $$-0.205097\pi$$
$$54$$ 0 0
$$55$$ −14.5125 + 13.7906i −0.0355793 + 0.0338096i
$$56$$ 0 0
$$57$$ 314.512i 0.730846i
$$58$$ 0 0
$$59$$ −73.7906 −0.162826 −0.0814129 0.996680i $$-0.525943\pi$$
−0.0814129 + 0.996680i $$0.525943\pi$$
$$60$$ 0 0
$$61$$ −137.350 −0.288293 −0.144146 0.989556i $$-0.546044\pi$$
−0.144146 + 0.989556i $$0.546044\pi$$
$$62$$ 0 0
$$63$$ 199.884i 0.399731i
$$64$$ 0 0
$$65$$ 448.303 + 471.769i 0.855464 + 0.900242i
$$66$$ 0 0
$$67$$ 173.906i 0.317105i −0.987351 0.158552i $$-0.949317\pi$$
0.987351 0.158552i $$-0.0506827\pi$$
$$68$$ 0 0
$$69$$ 148.837 0.259680
$$70$$ 0 0
$$71$$ 594.281 0.993355 0.496677 0.867935i $$-0.334553\pi$$
0.496677 + 0.867935i $$0.334553\pi$$
$$72$$ 0 0
$$73$$ 320.231i 0.513428i −0.966487 0.256714i $$-0.917360\pi$$
0.966487 0.256714i $$-0.0826398\pi$$
$$74$$ 0 0
$$75$$ 374.512 + 19.1156i 0.576600 + 0.0294305i
$$76$$ 0 0
$$77$$ 39.7687i 0.0588580i
$$78$$ 0 0
$$79$$ −770.469 −1.09727 −0.548636 0.836061i $$-0.684853\pi$$
−0.548636 + 0.836061i $$0.684853\pi$$
$$80$$ 0 0
$$81$$ 81.0000 0.111111
$$82$$ 0 0
$$83$$ 173.925i 0.230009i 0.993365 + 0.115004i $$0.0366882\pi$$
−0.993365 + 0.115004i $$0.963312\pi$$
$$84$$ 0 0
$$85$$ −146.209 153.862i −0.186572 0.196338i
$$86$$ 0 0
$$87$$ 880.397i 1.08492i
$$88$$ 0 0
$$89$$ −1019.02 −1.21367 −0.606834 0.794829i $$-0.707561\pi$$
−0.606834 + 0.794829i $$0.707561\pi$$
$$90$$ 0 0
$$91$$ −1292.79 −1.48925
$$92$$ 0 0
$$93$$ 193.256i 0.215481i
$$94$$ 0 0
$$95$$ −849.675 + 807.412i −0.917630 + 0.871987i
$$96$$ 0 0
$$97$$ 384.375i 0.402344i 0.979556 + 0.201172i $$0.0644750\pi$$
−0.979556 + 0.201172i $$0.935525\pi$$
$$98$$ 0 0
$$99$$ −16.1156 −0.0163604
$$100$$ 0 0
$$101$$ 34.4906 0.0339796 0.0169898 0.999856i $$-0.494592\pi$$
0.0169898 + 0.999856i $$0.494592\pi$$
$$102$$ 0 0
$$103$$ 1756.30i 1.68013i −0.542484 0.840066i $$-0.682516\pi$$
0.542484 0.840066i $$-0.317484\pi$$
$$104$$ 0 0
$$105$$ −540.000 + 513.141i −0.501891 + 0.476928i
$$106$$ 0 0
$$107$$ 1361.74i 1.23032i 0.788403 + 0.615159i $$0.210908\pi$$
−0.788403 + 0.615159i $$0.789092\pi$$
$$108$$ 0 0
$$109$$ −321.119 −0.282180 −0.141090 0.989997i $$-0.545061\pi$$
−0.141090 + 0.989997i $$0.545061\pi$$
$$110$$ 0 0
$$111$$ 59.6531 0.0510092
$$112$$ 0 0
$$113$$ 1582.25i 1.31721i 0.752487 + 0.658607i $$0.228854\pi$$
−0.752487 + 0.658607i $$0.771146\pi$$
$$114$$ 0 0
$$115$$ 382.094 + 402.094i 0.309830 + 0.326047i
$$116$$ 0 0
$$117$$ 523.884i 0.413958i
$$118$$ 0 0
$$119$$ 421.631 0.324797
$$120$$ 0 0
$$121$$ −1327.79 −0.997591
$$122$$ 0 0
$$123$$ 496.744i 0.364145i
$$124$$ 0 0
$$125$$ 909.802 + 1060.84i 0.651001 + 0.759077i
$$126$$ 0 0
$$127$$ 1197.14i 0.836449i 0.908344 + 0.418225i $$0.137348\pi$$
−0.908344 + 0.418225i $$0.862652\pi$$
$$128$$ 0 0
$$129$$ 742.050 0.506464
$$130$$ 0 0
$$131$$ 321.647 0.214522 0.107261 0.994231i $$-0.465792\pi$$
0.107261 + 0.994231i $$0.465792\pi$$
$$132$$ 0 0
$$133$$ 2328.37i 1.51801i
$$134$$ 0 0
$$135$$ 207.942 + 218.827i 0.132569 + 0.139508i
$$136$$ 0 0
$$137$$ 354.291i 0.220942i 0.993879 + 0.110471i $$0.0352360\pi$$
−0.993879 + 0.110471i $$0.964764\pi$$
$$138$$ 0 0
$$139$$ 77.2562 0.0471424 0.0235712 0.999722i $$-0.492496\pi$$
0.0235712 + 0.999722i $$0.492496\pi$$
$$140$$ 0 0
$$141$$ 1153.63 0.689030
$$142$$ 0 0
$$143$$ 104.231i 0.0609529i
$$144$$ 0 0
$$145$$ −2378.45 + 2260.14i −1.36220 + 1.29445i
$$146$$ 0 0
$$147$$ 450.769i 0.252917i
$$148$$ 0 0
$$149$$ 1705.38 0.937651 0.468826 0.883291i $$-0.344677\pi$$
0.468826 + 0.883291i $$0.344677\pi$$
$$150$$ 0 0
$$151$$ −758.281 −0.408663 −0.204331 0.978902i $$-0.565502\pi$$
−0.204331 + 0.978902i $$0.565502\pi$$
$$152$$ 0 0
$$153$$ 170.859i 0.0902821i
$$154$$ 0 0
$$155$$ 522.094 496.125i 0.270552 0.257095i
$$156$$ 0 0
$$157$$ 1769.05i 0.899273i −0.893212 0.449636i $$-0.851554\pi$$
0.893212 0.449636i $$-0.148446\pi$$
$$158$$ 0 0
$$159$$ 1390.58 0.693588
$$160$$ 0 0
$$161$$ −1101.86 −0.539372
$$162$$ 0 0
$$163$$ 881.719i 0.423690i −0.977303 0.211845i $$-0.932053\pi$$
0.977303 0.211845i $$-0.0679473\pi$$
$$164$$ 0 0
$$165$$ −41.3719 43.5374i −0.0195200 0.0205417i
$$166$$ 0 0
$$167$$ 216.900i 0.100504i 0.998737 + 0.0502522i $$0.0160025\pi$$
−0.998737 + 0.0502522i $$0.983997\pi$$
$$168$$ 0 0
$$169$$ −1191.33 −0.542254
$$170$$ 0 0
$$171$$ −943.537 −0.421954
$$172$$ 0 0
$$173$$ 4125.91i 1.81322i −0.421970 0.906610i $$-0.638661\pi$$
0.421970 0.906610i $$-0.361339\pi$$
$$174$$ 0 0
$$175$$ −2772.56 141.515i −1.19763 0.0611289i
$$176$$ 0 0
$$177$$ 221.372i 0.0940075i
$$178$$ 0 0
$$179$$ −3213.14 −1.34168 −0.670842 0.741600i $$-0.734067\pi$$
−0.670842 + 0.741600i $$0.734067\pi$$
$$180$$ 0 0
$$181$$ 3394.42 1.39395 0.696976 0.717095i $$-0.254529\pi$$
0.696976 + 0.717095i $$0.254529\pi$$
$$182$$ 0 0
$$183$$ 412.050i 0.166446i
$$184$$ 0 0
$$185$$ 153.141 + 161.156i 0.0608601 + 0.0640457i
$$186$$ 0 0
$$187$$ 33.9939i 0.0132935i
$$188$$ 0 0
$$189$$ −599.653 −0.230785
$$190$$ 0 0
$$191$$ 3467.49 1.31361 0.656804 0.754062i $$-0.271908\pi$$
0.656804 + 0.754062i $$0.271908\pi$$
$$192$$ 0 0
$$193$$ 1792.14i 0.668401i −0.942502 0.334200i $$-0.891534\pi$$
0.942502 0.334200i $$-0.108466\pi$$
$$194$$ 0 0
$$195$$ −1415.31 + 1344.91i −0.519755 + 0.493902i
$$196$$ 0 0
$$197$$ 1678.19i 0.606935i 0.952842 + 0.303467i $$0.0981443\pi$$
−0.952842 + 0.303467i $$0.901856\pi$$
$$198$$ 0 0
$$199$$ 3108.23 1.10722 0.553610 0.832776i $$-0.313250\pi$$
0.553610 + 0.832776i $$0.313250\pi$$
$$200$$ 0 0
$$201$$ 521.719 0.183081
$$202$$ 0 0
$$203$$ 6517.69i 2.25346i
$$204$$ 0 0
$$205$$ 1341.98 1275.23i 0.457211 0.434469i
$$206$$ 0 0
$$207$$ 446.512i 0.149926i
$$208$$ 0 0
$$209$$ 187.725 0.0621301
$$210$$ 0 0
$$211$$ 4473.27 1.45949 0.729745 0.683719i $$-0.239639\pi$$
0.729745 + 0.683719i $$0.239639\pi$$
$$212$$ 0 0
$$213$$ 1782.84i 0.573514i
$$214$$ 0 0
$$215$$ 1904.98 + 2004.69i 0.604273 + 0.635902i
$$216$$ 0 0
$$217$$ 1430.70i 0.447568i
$$218$$ 0 0
$$219$$ 960.694 0.296428
$$220$$ 0 0
$$221$$ 1105.07 0.336357
$$222$$ 0 0
$$223$$ 1753.42i 0.526535i −0.964723 0.263268i $$-0.915200\pi$$
0.964723 0.263268i $$-0.0848003\pi$$
$$224$$ 0 0
$$225$$ −57.3469 + 1123.54i −0.0169917 + 0.332900i
$$226$$ 0 0
$$227$$ 936.900i 0.273939i 0.990575 + 0.136970i $$0.0437363\pi$$
−0.990575 + 0.136970i $$0.956264\pi$$
$$228$$ 0 0
$$229$$ 2582.06 0.745096 0.372548 0.928013i $$-0.378484\pi$$
0.372548 + 0.928013i $$0.378484\pi$$
$$230$$ 0 0
$$231$$ 119.306 0.0339817
$$232$$ 0 0
$$233$$ 2295.01i 0.645284i −0.946521 0.322642i $$-0.895429\pi$$
0.946521 0.322642i $$-0.104571\pi$$
$$234$$ 0 0
$$235$$ 2961.59 + 3116.61i 0.822096 + 0.865128i
$$236$$ 0 0
$$237$$ 2311.41i 0.633510i
$$238$$ 0 0
$$239$$ −2294.01 −0.620866 −0.310433 0.950595i $$-0.600474\pi$$
−0.310433 + 0.950595i $$0.600474\pi$$
$$240$$ 0 0
$$241$$ 382.287 0.102180 0.0510898 0.998694i $$-0.483731\pi$$
0.0510898 + 0.998694i $$0.483731\pi$$
$$242$$ 0 0
$$243$$ 243.000i 0.0641500i
$$244$$ 0 0
$$245$$ 1217.78 1157.21i 0.317555 0.301760i
$$246$$ 0 0
$$247$$ 6102.52i 1.57204i
$$248$$ 0 0
$$249$$ −521.775 −0.132796
$$250$$ 0 0
$$251$$ 2259.98 0.568322 0.284161 0.958777i $$-0.408285\pi$$
0.284161 + 0.958777i $$0.408285\pi$$
$$252$$ 0 0
$$253$$ 88.8375i 0.0220758i
$$254$$ 0 0
$$255$$ 461.587 438.628i 0.113356 0.107717i
$$256$$ 0 0
$$257$$ 92.7843i 0.0225203i −0.999937 0.0112602i $$-0.996416\pi$$
0.999937 0.0112602i $$-0.00358430\pi$$
$$258$$ 0 0
$$259$$ −441.619 −0.105949
$$260$$ 0 0
$$261$$ −2641.19 −0.626382
$$262$$ 0 0
$$263$$ 568.312i 0.133246i −0.997778 0.0666229i $$-0.978778\pi$$
0.997778 0.0666229i $$-0.0212224\pi$$
$$264$$ 0 0
$$265$$ 3569.89 + 3756.75i 0.827534 + 0.870850i
$$266$$ 0 0
$$267$$ 3057.07i 0.700711i
$$268$$ 0 0
$$269$$ −7582.41 −1.71862 −0.859309 0.511458i $$-0.829106\pi$$
−0.859309 + 0.511458i $$0.829106\pi$$
$$270$$ 0 0
$$271$$ −7943.69 −1.78061 −0.890304 0.455366i $$-0.849508\pi$$
−0.890304 + 0.455366i $$0.849508\pi$$
$$272$$ 0 0
$$273$$ 3878.38i 0.859818i
$$274$$ 0 0
$$275$$ 11.4097 223.537i 0.00250192 0.0490175i
$$276$$ 0 0
$$277$$ 6823.00i 1.47998i 0.672618 + 0.739990i $$0.265170\pi$$
−0.672618 + 0.739990i $$0.734830\pi$$
$$278$$ 0 0
$$279$$ 579.769 0.124408
$$280$$ 0 0
$$281$$ 3315.86 0.703942 0.351971 0.936011i $$-0.385512\pi$$
0.351971 + 0.936011i $$0.385512\pi$$
$$282$$ 0 0
$$283$$ 6602.76i 1.38690i 0.720504 + 0.693451i $$0.243910\pi$$
−0.720504 + 0.693451i $$0.756090\pi$$
$$284$$ 0 0
$$285$$ −2422.24 2549.02i −0.503442 0.529794i
$$286$$ 0 0
$$287$$ 3677.46i 0.756353i
$$288$$ 0 0
$$289$$ 4552.59 0.926642
$$290$$ 0 0
$$291$$ −1153.12 −0.232293
$$292$$ 0 0
$$293$$ 5814.14i 1.15927i −0.814877 0.579634i $$-0.803195\pi$$
0.814877 0.579634i $$-0.196805\pi$$
$$294$$ 0 0
$$295$$ 598.050 568.303i 0.118033 0.112162i
$$296$$ 0 0
$$297$$ 48.3469i 0.00944570i
$$298$$ 0 0
$$299$$ −2887.91 −0.558570
$$300$$ 0 0
$$301$$ −5493.49 −1.05196
$$302$$ 0 0
$$303$$ 103.472i 0.0196181i
$$304$$ 0 0
$$305$$ 1113.18 1057.81i 0.208985 0.198590i
$$306$$ 0 0
$$307$$ 8124.86i 1.51046i 0.655462 + 0.755229i $$0.272474\pi$$
−0.655462 + 0.755229i $$0.727526\pi$$
$$308$$ 0 0
$$309$$ 5268.91 0.970025
$$310$$ 0 0
$$311$$ −7336.26 −1.33762 −0.668812 0.743432i $$-0.733197\pi$$
−0.668812 + 0.743432i $$0.733197\pi$$
$$312$$ 0 0
$$313$$ 2202.66i 0.397768i 0.980023 + 0.198884i $$0.0637318\pi$$
−0.980023 + 0.198884i $$0.936268\pi$$
$$314$$ 0 0
$$315$$ −1539.42 1620.00i −0.275354 0.289767i
$$316$$ 0 0
$$317$$ 10008.9i 1.77336i 0.462386 + 0.886679i $$0.346993\pi$$
−0.462386 + 0.886679i $$0.653007\pi$$
$$318$$ 0 0
$$319$$ 525.488 0.0922309
$$320$$ 0 0
$$321$$ −4085.21 −0.710325
$$322$$ 0 0
$$323$$ 1990.27i 0.342854i
$$324$$ 0 0
$$325$$ −7266.71 370.903i −1.24026 0.0633046i
$$326$$ 0 0
$$327$$ 963.356i 0.162917i
$$328$$ 0 0
$$329$$ −8540.47 −1.43116
$$330$$ 0 0
$$331$$ 8695.94 1.44402 0.722012 0.691881i $$-0.243218\pi$$
0.722012 + 0.691881i $$0.243218\pi$$
$$332$$ 0 0
$$333$$ 178.959i 0.0294502i
$$334$$ 0 0
$$335$$ 1339.35 + 1409.46i 0.218437 + 0.229871i
$$336$$ 0 0
$$337$$ 7400.61i 1.19625i −0.801402 0.598126i $$-0.795912\pi$$
0.801402 0.598126i $$-0.204088\pi$$
$$338$$ 0 0
$$339$$ −4746.74 −0.760494
$$340$$ 0 0
$$341$$ −115.350 −0.0183183
$$342$$ 0 0
$$343$$ 4280.72i 0.673869i
$$344$$ 0 0
$$345$$ −1206.28 + 1146.28i −0.188243 + 0.178880i
$$346$$ 0 0
$$347$$ 7841.44i 1.21311i −0.795040 0.606557i $$-0.792550\pi$$
0.795040 0.606557i $$-0.207450\pi$$
$$348$$ 0 0
$$349$$ 4961.26 0.760946 0.380473 0.924792i $$-0.375761\pi$$
0.380473 + 0.924792i $$0.375761\pi$$
$$350$$ 0 0
$$351$$ −1571.65 −0.238999
$$352$$ 0 0
$$353$$ 12163.0i 1.83392i 0.398981 + 0.916959i $$0.369364\pi$$
−0.398981 + 0.916959i $$0.630636\pi$$
$$354$$ 0 0
$$355$$ −4816.46 + 4576.89i −0.720088 + 0.684271i
$$356$$ 0 0
$$357$$ 1264.89i 0.187522i
$$358$$ 0 0
$$359$$ 5193.79 0.763559 0.381779 0.924253i $$-0.375311\pi$$
0.381779 + 0.924253i $$0.375311\pi$$
$$360$$ 0 0
$$361$$ 4131.90 0.602406
$$362$$ 0 0
$$363$$ 3983.38i 0.575959i
$$364$$ 0 0
$$365$$ 2466.28 + 2595.37i 0.353674 + 0.372187i
$$366$$ 0 0
$$367$$ 6086.09i 0.865644i 0.901479 + 0.432822i $$0.142482\pi$$
−0.901479 + 0.432822i $$0.857518\pi$$
$$368$$ 0 0
$$369$$ 1490.23 0.210239
$$370$$ 0 0
$$371$$ −10294.7 −1.44063
$$372$$ 0 0
$$373$$ 10581.9i 1.46893i 0.678646 + 0.734466i $$0.262567\pi$$
−0.678646 + 0.734466i $$0.737433\pi$$
$$374$$ 0 0
$$375$$ −3182.53 + 2729.40i −0.438253 + 0.375856i
$$376$$ 0 0
$$377$$ 17082.4i 2.33366i
$$378$$ 0 0
$$379$$ 11655.2 1.57964 0.789822 0.613336i $$-0.210173\pi$$
0.789822 + 0.613336i $$0.210173\pi$$
$$380$$ 0 0
$$381$$ −3591.42 −0.482924
$$382$$ 0 0
$$383$$ 6364.97i 0.849177i 0.905387 + 0.424588i $$0.139581\pi$$
−0.905387 + 0.424588i $$0.860419\pi$$
$$384$$ 0 0
$$385$$ 306.281 + 322.313i 0.0405442 + 0.0426665i
$$386$$ 0 0
$$387$$ 2226.15i 0.292407i
$$388$$ 0 0
$$389$$ −6134.33 −0.799545 −0.399773 0.916614i $$-0.630911\pi$$
−0.399773 + 0.916614i $$0.630911\pi$$
$$390$$ 0 0
$$391$$ 941.862 0.121821
$$392$$ 0 0
$$393$$ 964.941i 0.123855i
$$394$$ 0 0
$$395$$ 6244.41 5933.81i 0.795418 0.755854i
$$396$$ 0 0
$$397$$ 9746.46i 1.23214i 0.787690 + 0.616072i $$0.211277\pi$$
−0.787690 + 0.616072i $$0.788723\pi$$
$$398$$ 0 0
$$399$$ 6985.12 0.876425
$$400$$ 0 0
$$401$$ −1306.44 −0.162695 −0.0813474 0.996686i $$-0.525922\pi$$
−0.0813474 + 0.996686i $$0.525922\pi$$
$$402$$ 0 0
$$403$$ 3749.77i 0.463498i
$$404$$ 0 0
$$405$$ −656.480 + 623.827i −0.0805450 + 0.0765387i
$$406$$ 0 0
$$407$$ 35.6055i 0.00433636i
$$408$$ 0 0
$$409$$ 3876.93 0.468709 0.234354 0.972151i $$-0.424702\pi$$
0.234354 + 0.972151i $$0.424702\pi$$
$$410$$ 0 0
$$411$$ −1062.87 −0.127561
$$412$$ 0 0
$$413$$ 1638.84i 0.195260i
$$414$$ 0 0
$$415$$ −1339.49 1409.61i −0.158441 0.166735i
$$416$$ 0 0
$$417$$ 231.769i 0.0272177i
$$418$$ 0 0
$$419$$ −16022.5 −1.86814 −0.934071 0.357088i $$-0.883770\pi$$
−0.934071 + 0.357088i $$0.883770\pi$$
$$420$$ 0 0
$$421$$ −8119.73 −0.939980 −0.469990 0.882672i $$-0.655742\pi$$
−0.469990 + 0.882672i $$0.655742\pi$$
$$422$$ 0 0
$$423$$ 3460.89i 0.397812i
$$424$$ 0 0
$$425$$ 2369.96 + 120.966i 0.270494 + 0.0138064i
$$426$$ 0 0
$$427$$ 3050.46i 0.345719i
$$428$$ 0 0
$$429$$ 312.694 0.0351911
$$430$$ 0 0
$$431$$ 5713.99 0.638592 0.319296 0.947655i $$-0.396554\pi$$
0.319296 + 0.947655i $$0.396554\pi$$
$$432$$ 0 0
$$433$$ 6251.34i 0.693811i −0.937900 0.346906i $$-0.887232\pi$$
0.937900 0.346906i $$-0.112768\pi$$
$$434$$ 0 0
$$435$$ −6780.43 7135.34i −0.747349 0.786468i
$$436$$ 0 0
$$437$$ 5201.25i 0.569358i
$$438$$ 0 0
$$439$$ −4230.97 −0.459984 −0.229992 0.973192i $$-0.573870\pi$$
−0.229992 + 0.973192i $$0.573870\pi$$
$$440$$ 0 0
$$441$$ 1352.31 0.146022
$$442$$ 0 0
$$443$$ 6314.29i 0.677203i 0.940930 + 0.338601i $$0.109954\pi$$
−0.940930 + 0.338601i $$0.890046\pi$$
$$444$$ 0 0
$$445$$ 8258.88 7848.08i 0.879794 0.836033i
$$446$$ 0 0
$$447$$ 5116.13i 0.541353i
$$448$$ 0 0
$$449$$ 9349.71 0.982717 0.491358 0.870957i $$-0.336501\pi$$
0.491358 + 0.870957i $$0.336501\pi$$
$$450$$ 0 0
$$451$$ −296.494 −0.0309565
$$452$$ 0 0
$$453$$ 2274.84i 0.235941i
$$454$$ 0 0
$$455$$ 10477.7 9956.53i 1.07956 1.02587i
$$456$$ 0 0
$$457$$ 9547.46i 0.977268i −0.872489 0.488634i $$-0.837495\pi$$
0.872489 0.488634i $$-0.162505\pi$$
$$458$$ 0 0
$$459$$ 512.578 0.0521244
$$460$$ 0 0
$$461$$ 6237.23 0.630145 0.315073 0.949068i $$-0.397971\pi$$
0.315073 + 0.949068i $$0.397971\pi$$
$$462$$ 0 0
$$463$$ 6469.98i 0.649428i 0.945812 + 0.324714i $$0.105268\pi$$
−0.945812 + 0.324714i $$0.894732\pi$$
$$464$$ 0 0
$$465$$ 1488.37 + 1566.28i 0.148434 + 0.156203i
$$466$$ 0 0
$$467$$ 7206.64i 0.714097i −0.934086 0.357049i $$-0.883783\pi$$
0.934086 0.357049i $$-0.116217\pi$$
$$468$$ 0 0
$$469$$ −3862.35 −0.380270
$$470$$ 0 0
$$471$$ 5307.16 0.519195
$$472$$ 0 0
$$473$$ 442.912i 0.0430552i
$$474$$ 0 0
$$475$$ 668.012 13087.6i 0.0645274 1.26422i
$$476$$ 0 0
$$477$$ 4171.75i 0.400443i
$$478$$ 0 0
$$479$$ −10851.8 −1.03514 −0.517571 0.855640i $$-0.673164\pi$$
−0.517571 + 0.855640i $$0.673164\pi$$
$$480$$ 0 0
$$481$$ −1157.46 −0.109720
$$482$$ 0 0
$$483$$ 3305.59i 0.311407i
$$484$$ 0 0
$$485$$ −2960.29 3115.24i −0.277154 0.291661i
$$486$$ 0 0
$$487$$ 12757.1i 1.18702i −0.804827 0.593510i $$-0.797742\pi$$
0.804827 0.593510i $$-0.202258\pi$$
$$488$$ 0 0
$$489$$ 2645.16 0.244618
$$490$$ 0 0
$$491$$ 7016.52 0.644911 0.322455 0.946585i $$-0.395492\pi$$
0.322455 + 0.946585i $$0.395492\pi$$
$$492$$ 0 0
$$493$$ 5571.26i 0.508960i
$$494$$ 0 0
$$495$$ 130.612 124.116i 0.0118598 0.0112699i
$$496$$ 0 0
$$497$$ 13198.6i 1.19122i
$$498$$ 0 0
$$499$$ 11372.3 1.02023 0.510113 0.860107i $$-0.329604\pi$$
0.510113 + 0.860107i $$0.329604\pi$$
$$500$$ 0 0
$$501$$ −650.700 −0.0580262
$$502$$ 0 0
$$503$$ 5587.37i 0.495285i −0.968851 0.247643i $$-0.920344\pi$$
0.968851 0.247643i $$-0.0796559\pi$$
$$504$$ 0 0
$$505$$ −279.535 + 265.631i −0.0246320 + 0.0234068i
$$506$$ 0 0
$$507$$ 3573.99i 0.313070i
$$508$$ 0 0
$$509$$ −16256.7 −1.41565 −0.707825 0.706388i $$-0.750324\pi$$
−0.707825 + 0.706388i $$0.750324\pi$$
$$510$$ 0 0
$$511$$ −7112.14 −0.615699
$$512$$ 0 0
$$513$$ 2830.61i 0.243615i
$$514$$ 0 0
$$515$$ 13526.3 + 14234.3i 1.15736 + 1.21794i
$$516$$ 0 0
$$517$$ 688.574i 0.0585754i
$$518$$ 0 0
$$519$$ 12377.7 1.04686
$$520$$ 0 0
$$521$$ 19748.4 1.66064 0.830320 0.557286i $$-0.188157\pi$$
0.830320 + 0.557286i $$0.188157\pi$$
$$522$$ 0 0
$$523$$ 7843.44i 0.655774i −0.944717 0.327887i $$-0.893663\pi$$
0.944717 0.327887i $$-0.106337\pi$$
$$524$$ 0 0
$$525$$ 424.546 8317.69i 0.0352928 0.691455i
$$526$$ 0 0
$$527$$ 1222.95i 0.101086i
$$528$$ 0 0
$$529$$ 9705.60 0.797699
$$530$$ 0 0
$$531$$ 664.116 0.0542753
$$532$$ 0 0
$$533$$ 9638.38i 0.783273i
$$534$$ 0 0
$$535$$ −10487.5 11036.5i −0.847504 0.891865i
$$536$$ 0 0
$$537$$ 9639.42i 0.774622i
$$538$$ 0 0
$$539$$ −269.053 −0.0215008
$$540$$ 0 0
$$541$$ 7383.29 0.586751 0.293376 0.955997i $$-0.405221\pi$$
0.293376 + 0.955997i $$0.405221\pi$$
$$542$$ 0 0
$$543$$ 10183.3i 0.804798i
$$544$$ 0 0
$$545$$ 2602.57 2473.12i 0.204554 0.194379i
$$546$$ 0 0
$$547$$ 3354.90i 0.262240i 0.991367 + 0.131120i $$0.0418573\pi$$
−0.991367 + 0.131120i $$0.958143\pi$$
$$548$$ 0 0
$$549$$ 1236.15 0.0960976
$$550$$ 0 0
$$551$$ 30766.2 2.37874
$$552$$ 0 0
$$553$$ 17111.6i 1.31584i
$$554$$ 0 0
$$555$$ −483.469 + 459.422i −0.0369768 + 0.0351376i
$$556$$ 0 0
$$557$$ 20771.8i 1.58012i 0.613028 + 0.790061i $$0.289951\pi$$
−0.613028 + 0.790061i $$0.710049\pi$$
$$558$$ 0 0
$$559$$ −14398.1 −1.08940
$$560$$ 0 0
$$561$$ −101.982 −0.00767500
$$562$$ 0 0
$$563$$ 7194.86i 0.538592i 0.963057 + 0.269296i $$0.0867910\pi$$
−0.963057 + 0.269296i $$0.913209\pi$$
$$564$$ 0 0
$$565$$ −12185.8 12823.6i −0.907361 0.954856i
$$566$$ 0 0
$$567$$ 1798.96i 0.133244i
$$568$$ 0 0
$$569$$ −11549.5 −0.850931 −0.425466 0.904975i $$-0.639890\pi$$
−0.425466 + 0.904975i $$0.639890\pi$$
$$570$$ 0 0
$$571$$ −1482.54 −0.108655 −0.0543277 0.998523i $$-0.517302\pi$$
−0.0543277 + 0.998523i $$0.517302\pi$$
$$572$$ 0 0
$$573$$ 10402.5i 0.758412i
$$574$$ 0 0
$$575$$ −6193.50 316.125i −0.449194 0.0229275i
$$576$$ 0 0
$$577$$ 15264.0i 1.10130i −0.834737 0.550649i $$-0.814380\pi$$
0.834737 0.550649i $$-0.185620\pi$$
$$578$$ 0 0
$$579$$ 5376.43 0.385901
$$580$$ 0 0
$$581$$ 3862.76 0.275825
$$582$$ 0 0
$$583$$ 830.006i 0.0589628i
$$584$$ 0 0
$$585$$ −4034.73 4245.92i −0.285155 0.300081i
$$586$$ 0 0
$$587$$ 1736.89i 0.122128i −0.998134 0.0610639i $$-0.980551\pi$$
0.998134 0.0610639i $$-0.0194493\pi$$
$$588$$ 0 0
$$589$$ −6753.50 −0.472450
$$590$$ 0 0
$$591$$ −5034.57 −0.350414
$$592$$ 0 0
$$593$$ 11764.8i 0.814707i 0.913271 + 0.407353i $$0.133548\pi$$
−0.913271 + 0.407353i $$0.866452\pi$$
$$594$$ 0 0
$$595$$ −3417.19 + 3247.22i −0.235447 + 0.223736i
$$596$$ 0 0
$$597$$ 9324.69i 0.639253i
$$598$$ 0 0
$$599$$ −9451.99 −0.644737 −0.322369 0.946614i $$-0.604479\pi$$
−0.322369 + 0.946614i $$0.604479\pi$$
$$600$$ 0 0
$$601$$ −3131.93 −0.212569 −0.106285 0.994336i $$-0.533895\pi$$
−0.106285 + 0.994336i $$0.533895\pi$$
$$602$$ 0 0
$$603$$ 1565.16i 0.105702i
$$604$$ 0 0
$$605$$ 10761.4 10226.1i 0.723159 0.687189i
$$606$$ 0 0
$$607$$ 22700.8i 1.51795i −0.651120 0.758975i $$-0.725700\pi$$
0.651120 0.758975i $$-0.274300\pi$$
$$608$$ 0 0
$$609$$ 19553.1 1.30103
$$610$$ 0 0
$$611$$ −22384.0 −1.48210
$$612$$ 0 0
$$613$$ 28911.6i 1.90494i −0.304629 0.952471i $$-0.598532\pi$$
0.304629 0.952471i $$-0.401468\pi$$
$$614$$ 0 0
$$615$$ 3825.70 + 4025.95i 0.250841 + 0.263971i
$$616$$ 0 0
$$617$$ 5566.87i 0.363231i −0.983370 0.181616i $$-0.941867\pi$$
0.983370 0.181616i $$-0.0581326\pi$$
$$618$$ 0 0
$$619$$ 4150.32 0.269492 0.134746 0.990880i $$-0.456978\pi$$
0.134746 + 0.990880i $$0.456978\pi$$
$$620$$ 0 0
$$621$$ −1339.54 −0.0865600
$$622$$ 0 0
$$623$$ 22631.9i 1.45542i
$$624$$ 0 0
$$625$$ −15543.8 1590.90i −0.994803 0.101818i
$$626$$ 0 0
$$627$$ 563.175i 0.0358709i
$$628$$ 0 0
$$629$$ 377.492 0.0239294
$$630$$ 0 0
$$631$$ 4090.09 0.258041 0.129021 0.991642i $$-0.458817\pi$$
0.129021 + 0.991642i $$0.458817\pi$$
$$632$$ 0 0
$$633$$ 13419.8i 0.842637i
$$634$$ 0 0
$$635$$ −9219.85 9702.45i −0.576187 0.606346i
$$636$$ 0 0
$$637$$ 8746.32i 0.544022i
$$638$$ 0 0
$$639$$ −5348.53 −0.331118
$$640$$ 0 0
$$641$$ 3909.35 0.240890 0.120445 0.992720i $$-0.461568\pi$$
0.120445 + 0.992720i $$0.461568\pi$$
$$642$$ 0 0
$$643$$ 30539.5i 1.87303i 0.350624 + 0.936516i $$0.385969\pi$$
−0.350624 + 0.936516i $$0.614031\pi$$
$$644$$ 0 0
$$645$$ −6014.08 + 5714.94i −0.367138 + 0.348877i
$$646$$ 0 0
$$647$$ 12707.7i 0.772167i 0.922464 + 0.386083i $$0.126172\pi$$
−0.922464 + 0.386083i $$0.873828\pi$$
$$648$$ 0 0
$$649$$ −132.132 −0.00799170
$$650$$ 0 0
$$651$$ −4292.10 −0.258403
$$652$$ 0 0
$$653$$ 12777.6i 0.765737i −0.923803 0.382869i $$-0.874936\pi$$
0.923803 0.382869i $$-0.125064\pi$$
$$654$$ 0 0
$$655$$ −2606.85 + 2477.18i −0.155508 + 0.147773i
$$656$$ 0 0
$$657$$ 2882.08i 0.171143i
$$658$$ 0 0
$$659$$ 23563.5 1.39287 0.696435 0.717620i $$-0.254768\pi$$
0.696435 + 0.717620i $$0.254768\pi$$
$$660$$ 0 0
$$661$$ −4361.31 −0.256634 −0.128317 0.991733i $$-0.540958\pi$$
−0.128317 + 0.991733i $$0.540958\pi$$
$$662$$ 0 0
$$663$$ 3315.21i 0.194196i
$$664$$ 0 0
$$665$$ 17932.1 + 18870.7i 1.04568 + 1.10042i
$$666$$ 0 0
$$667$$ 14559.6i 0.845200i
$$668$$ 0 0
$$669$$ 5260.25 0.303995
$$670$$ 0 0
$$671$$ −245.943 −0.0141498
$$672$$ 0 0
$$673$$ 8203.52i 0.469870i 0.972011 + 0.234935i $$0.0754877\pi$$
−0.972011 + 0.234935i $$0.924512\pi$$
$$674$$ 0 0
$$675$$ −3370.61 172.041i −0.192200 0.00981015i
$$676$$ 0 0
$$677$$ 28057.1i 1.59279i 0.604774 + 0.796397i $$0.293263\pi$$
−0.604774 + 0.796397i $$0.706737\pi$$
$$678$$ 0 0
$$679$$ 8536.73 0.482488
$$680$$ 0 0
$$681$$ −2810.70 −0.158159
$$682$$ 0 0
$$683$$ 3344.62i 0.187377i −0.995602 0.0936885i $$-0.970134\pi$$
0.995602 0.0936885i $$-0.0298658\pi$$
$$684$$ 0 0
$$685$$ −2728.59 2871.41i −0.152196 0.160162i
$$686$$ 0 0
$$687$$ 7746.17i 0.430182i
$$688$$ 0 0
$$689$$ −26981.7 −1.49190
$$690$$ 0 0
$$691$$ −12964.8 −0.713757 −0.356879 0.934151i $$-0.616159\pi$$
−0.356879 + 0.934151i $$0.616159\pi$$
$$692$$ 0 0
$$693$$ 357.918i 0.0196193i
$$694$$ 0 0
$$695$$ −626.138 + 594.994i −0.0341737 + 0.0324740i
$$696$$ 0 0
$$697$$ 3143.46i 0.170828i
$$698$$ 0 0
$$699$$ 6885.03 0.372555
$$700$$ 0 0
$$701$$ −16162.1 −0.870806 −0.435403 0.900236i $$-0.643394\pi$$
−0.435403 + 0.900236i $$0.643394\pi$$
$$702$$ 0 0
$$703$$ 2084.63i 0.111839i
$$704$$ 0 0
$$705$$ −9349.82 + 8884.76i −0.499482 + 0.474638i
$$706$$ 0 0
$$707$$ 766.014i 0.0407481i
$$708$$ 0 0
$$709$$ 14244.4 0.754529 0.377265 0.926105i $$-0.376865\pi$$
0.377265 + 0.926105i $$0.376865\pi$$
$$710$$ 0 0
$$711$$ 6934.22 0.365757
$$712$$ 0 0
$$713$$ 3195.97i 0.167868i
$$714$$ 0 0
$$715$$ 802.744 + 844.762i 0.0419873 + 0.0441850i
$$716$$ 0 0
$$717$$ 6882.02i 0.358457i
$$718$$ 0 0
$$719$$ −27638.5 −1.43358 −0.716790 0.697289i $$-0.754389\pi$$
−0.716790 + 0.697289i $$0.754389\pi$$
$$720$$ 0 0
$$721$$ −39006.4 −2.01480
$$722$$ 0 0
$$723$$ 1146.86i 0.0589934i
$$724$$ 0 0
$$725$$ 1869.93 36635.5i 0.0957895 1.87670i
$$726$$ 0 0
$$727$$ 2525.52i 0.128840i 0.997923 + 0.0644199i $$0.0205197\pi$$
−0.997923 + 0.0644199i $$0.979480\pi$$
$$728$$ 0 0
$$729$$ −729.000 −0.0370370
$$730$$ 0 0
$$731$$ 4695.79 0.237592
$$732$$ 0 0
$$733$$ 8400.27i 0.423289i 0.977347 + 0.211645i $$0.0678820\pi$$
−0.977347 + 0.211645i $$0.932118\pi$$
$$734$$ 0 0
$$735$$ 3471.62 + 3653.34i 0.174221 + 0.183341i
$$736$$ 0 0
$$737$$ 311.401i 0.0155639i
$$738$$ 0 0
$$739$$ −19689.1 −0.980074 −0.490037 0.871702i $$-0.663017\pi$$
−0.490037 + 0.871702i $$0.663017\pi$$
$$740$$ 0 0
$$741$$ 18307.6 0.907619
$$742$$ 0 0
$$743$$ 22526.6i 1.11227i −0.831091 0.556137i $$-0.812283\pi$$
0.831091 0.556137i $$-0.187717\pi$$
$$744$$ 0 0
$$745$$ −13821.6 + 13134.1i −0.679708 + 0.645900i
$$746$$ 0 0
$$747$$ 1565.32i 0.0766696i
$$748$$ 0 0
$$749$$ 30243.3 1.47539
$$750$$ 0 0
$$751$$ −34691.1 −1.68562 −0.842808 0.538215i $$-0.819099\pi$$
−0.842808 + 0.538215i $$0.819099\pi$$
$$752$$ 0 0
$$753$$ 6779.95i 0.328121i
$$754$$ 0 0
$$755$$ 6145.63 5839.95i 0.296242 0.281507i
$$756$$ 0 0
$$757$$ 6619.98i 0.317843i 0.987291 + 0.158922i $$0.0508017\pi$$
−0.987291 + 0.158922i $$0.949198\pi$$
$$758$$ 0 0
$$759$$ 266.512 0.0127454
$$760$$ 0 0
$$761$$ −29368.7 −1.39897 −0.699483 0.714649i $$-0.746586\pi$$
−0.699483 + 0.714649i $$0.746586\pi$$
$$762$$ 0 0
$$763$$ 7131.84i 0.338388i
$$764$$ 0 0
$$765$$ 1315.88 + 1384.76i 0.0621907 + 0.0654460i
$$766$$ 0 0
$$767$$ 4295.31i 0.202209i
$$768$$ 0 0
$$769$$ −32677.4 −1.53235 −0.766174 0.642633i $$-0.777842\pi$$
−0.766174 + 0.642633i $$0.777842\pi$$
$$770$$ 0 0
$$771$$ 278.353 0.0130021
$$772$$ 0 0
$$773$$ 28047.5i 1.30504i 0.757770 + 0.652522i $$0.226289\pi$$
−0.757770 + 0.652522i $$0.773711\pi$$
$$774$$ 0 0
$$775$$ −410.469 + 8041.87i −0.0190251 + 0.372739i
$$776$$ 0 0
$$777$$ 1324.86i 0.0611699i
$$778$$ 0 0
$$779$$ −17359.1 −0.798402
$$780$$ 0 0
$$781$$ 1064.14 0.0487552
$$782$$ 0 0
$$783$$ 7923.57i 0.361642i
$$784$$ 0 0
$$785$$ 13624.5 + 14337.6i 0.619463 + 0.651887i
$$786$$ 0 0
$$787$$ 22172.1i 1.00426i 0.864793 + 0.502128i $$0.167449\pi$$
−0.864793 + 0.502128i $$0.832551\pi$$
$$788$$ 0 0
$$789$$ 1704.94 0.0769295
$$790$$ 0 0
$$791$$ 35140.7 1.57960
$$792$$ 0 0
$$793$$ 7995.06i 0.358024i
$$794$$ 0 0
$$795$$ −11270.2 + 10709.7i −0.502786 + 0.477777i
$$796$$ 0 0
$$797$$ 24170.3i 1.07422i −0.843511 0.537112i $$-0.819515\pi$$
0.843511 0.537112i $$-0.180485\pi$$