# Properties

 Label 45.4.b.b.19.3 Level $45$ Weight $4$ Character 45.19 Analytic conductor $2.655$ Analytic rank $0$ Dimension $4$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$45 = 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 45.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$2.65508595026$$ 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: $$\Z[a_1, \ldots, a_{5}]$$ 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 19.3 Root $$2.70156i$$ of defining polynomial Character $$\chi$$ $$=$$ 45.19 Dual form 45.4.b.b.19.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.70156i q^{2} +5.10469 q^{4} +(8.10469 - 7.70156i) q^{5} +22.2094i q^{7} +22.2984i q^{8} +O(q^{10})$$ $$q+1.70156i q^{2} +5.10469 q^{4} +(8.10469 - 7.70156i) q^{5} +22.2094i q^{7} +22.2984i q^{8} +(13.1047 + 13.7906i) q^{10} +1.79063 q^{11} -58.2094i q^{13} -37.7906 q^{14} +2.89531 q^{16} -18.9844i q^{17} -104.837 q^{19} +(41.3719 - 39.3141i) q^{20} +3.04686i q^{22} -49.6125i q^{23} +(6.37188 - 124.837i) q^{25} +99.0469 q^{26} +113.372i q^{28} -293.466 q^{29} +64.4187 q^{31} +183.314i q^{32} +32.3031 q^{34} +(171.047 + 180.000i) q^{35} -19.8844i q^{37} -178.388i q^{38} +(171.733 + 180.722i) q^{40} +165.581 q^{41} +247.350i q^{43} +9.14059 q^{44} +84.4187 q^{46} -384.544i q^{47} -150.256 q^{49} +(212.419 + 10.8422i) q^{50} -297.141i q^{52} +463.528i q^{53} +(14.5125 - 13.7906i) q^{55} -495.234 q^{56} -499.350i q^{58} -73.7906 q^{59} -137.350 q^{61} +109.612i q^{62} -288.758 q^{64} +(-448.303 - 471.769i) q^{65} +173.906i q^{67} -96.9093i q^{68} +(-306.281 + 291.047i) q^{70} +594.281 q^{71} -320.231i q^{73} +33.8345 q^{74} -535.163 q^{76} +39.7687i q^{77} +770.469 q^{79} +(23.4656 - 22.2984i) q^{80} +281.747i q^{82} +173.925i q^{83} +(-146.209 - 153.862i) q^{85} -420.881 q^{86} +39.9282i q^{88} +1019.02 q^{89} +1292.79 q^{91} -253.256i q^{92} +654.325 q^{94} +(-849.675 + 807.412i) q^{95} +384.375i q^{97} -255.670i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 18 q^{4} - 6 q^{5}+O(q^{10})$$ 4 * q - 18 * q^4 - 6 * q^5 $$4 q - 18 q^{4} - 6 q^{5} + 14 q^{10} + 84 q^{11} - 228 q^{14} + 50 q^{16} - 112 q^{19} + 396 q^{20} + 256 q^{25} + 12 q^{26} - 636 q^{29} + 104 q^{31} - 716 q^{34} + 300 q^{35} + 418 q^{40} + 816 q^{41} - 1116 q^{44} + 184 q^{46} - 140 q^{49} + 696 q^{50} - 864 q^{55} - 60 q^{56} - 372 q^{59} + 680 q^{61} + 958 q^{64} - 948 q^{65} + 1080 q^{70} + 72 q^{71} + 3132 q^{74} - 2448 q^{76} - 760 q^{79} - 444 q^{80} - 508 q^{85} - 4296 q^{86} + 2232 q^{89} + 1944 q^{91} + 3232 q^{94} - 2784 q^{95}+O(q^{100})$$ 4 * q - 18 * q^4 - 6 * q^5 + 14 * q^10 + 84 * q^11 - 228 * q^14 + 50 * q^16 - 112 * q^19 + 396 * q^20 + 256 * q^25 + 12 * q^26 - 636 * q^29 + 104 * q^31 - 716 * q^34 + 300 * q^35 + 418 * q^40 + 816 * q^41 - 1116 * q^44 + 184 * q^46 - 140 * q^49 + 696 * q^50 - 864 * q^55 - 60 * q^56 - 372 * q^59 + 680 * q^61 + 958 * q^64 - 948 * q^65 + 1080 * q^70 + 72 * q^71 + 3132 * q^74 - 2448 * q^76 - 760 * q^79 - 444 * q^80 - 508 * q^85 - 4296 * q^86 + 2232 * q^89 + 1944 * q^91 + 3232 * q^94 - 2784 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$$.

 $$n$$ $$11$$ $$37$$ $$\chi(n)$$ $$1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.70156i 0.601593i 0.953688 + 0.300797i $$0.0972525\pi$$
−0.953688 + 0.300797i $$0.902747\pi$$
$$3$$ 0 0
$$4$$ 5.10469 0.638086
$$5$$ 8.10469 7.70156i 0.724905 0.688849i
$$6$$ 0 0
$$7$$ 22.2094i 1.19919i 0.800302 + 0.599597i $$0.204672\pi$$
−0.800302 + 0.599597i $$0.795328\pi$$
$$8$$ 22.2984i 0.985461i
$$9$$ 0 0
$$10$$ 13.1047 + 13.7906i 0.414407 + 0.436098i
$$11$$ 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 $$-0.213248\pi$$
$$14$$ −37.7906 −0.721426
$$15$$ 0 0
$$16$$ 2.89531 0.0452393
$$17$$ 18.9844i 0.270846i −0.990788 0.135423i $$-0.956761\pi$$
0.990788 0.135423i $$-0.0432394\pi$$
$$18$$ 0 0
$$19$$ −104.837 −1.26586 −0.632931 0.774208i $$-0.718148\pi$$
−0.632931 + 0.774208i $$0.718148\pi$$
$$20$$ 41.3719 39.3141i 0.462552 0.439545i
$$21$$ 0 0
$$22$$ 3.04686i 0.0295270i
$$23$$ 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
$$26$$ 99.0469 0.747103
$$27$$ 0 0
$$28$$ 113.372i 0.765188i
$$29$$ −293.466 −1.87914 −0.939572 0.342350i $$-0.888777\pi$$
−0.939572 + 0.342350i $$0.888777\pi$$
$$30$$ 0 0
$$31$$ 64.4187 0.373224 0.186612 0.982434i $$-0.440249\pi$$
0.186612 + 0.982434i $$0.440249\pi$$
$$32$$ 183.314i 1.01268i
$$33$$ 0 0
$$34$$ 32.3031 0.162939
$$35$$ 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 $$-0.0140660\pi$$
$$38$$ 178.388i 0.761534i
$$39$$ 0 0
$$40$$ 171.733 + 180.722i 0.678834 + 0.714366i
$$41$$ 165.581 0.630718 0.315359 0.948972i $$-0.397875\pi$$
0.315359 + 0.948972i $$0.397875\pi$$
$$42$$ 0 0
$$43$$ 247.350i 0.877221i 0.898677 + 0.438611i $$0.144529\pi$$
−0.898677 + 0.438611i $$0.855471\pi$$
$$44$$ 9.14059 0.0313181
$$45$$ 0 0
$$46$$ 84.4187 0.270584
$$47$$ 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
$$50$$ 212.419 + 10.8422i 0.600811 + 0.0306662i
$$51$$ 0 0
$$52$$ 297.141i 0.792423i
$$53$$ 463.528i 1.20133i 0.799501 + 0.600665i $$0.205097\pi$$
−0.799501 + 0.600665i $$0.794903\pi$$
$$54$$ 0 0
$$55$$ 14.5125 13.7906i 0.0355793 0.0338096i
$$56$$ −495.234 −1.18176
$$57$$ 0 0
$$58$$ 499.350i 1.13048i
$$59$$ −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 $$0.546044\pi$$
$$62$$ 109.612i 0.224529i
$$63$$ 0 0
$$64$$ −288.758 −0.563980
$$65$$ −448.303 471.769i −0.855464 0.900242i
$$66$$ 0 0
$$67$$ 173.906i 0.317105i 0.987351 + 0.158552i $$0.0506827\pi$$
−0.987351 + 0.158552i $$0.949317\pi$$
$$68$$ 96.9093i 0.172823i
$$69$$ 0 0
$$70$$ −306.281 + 291.047i −0.522966 + 0.496954i
$$71$$ 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 $$-0.0826398\pi$$
$$74$$ 33.8345 0.0531510
$$75$$ 0 0
$$76$$ −535.163 −0.807728
$$77$$ 39.7687i 0.0588580i
$$78$$ 0 0
$$79$$ 770.469 1.09727 0.548636 0.836061i $$-0.315147\pi$$
0.548636 + 0.836061i $$0.315147\pi$$
$$80$$ 23.4656 22.2984i 0.0327942 0.0311630i
$$81$$ 0 0
$$82$$ 281.747i 0.379436i
$$83$$ 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
$$86$$ −420.881 −0.527730
$$87$$ 0 0
$$88$$ 39.9282i 0.0483677i
$$89$$ 1019.02 1.21367 0.606834 0.794829i $$-0.292439\pi$$
0.606834 + 0.794829i $$0.292439\pi$$
$$90$$ 0 0
$$91$$ 1292.79 1.48925
$$92$$ 253.256i 0.286998i
$$93$$ 0 0
$$94$$ 654.325 0.717962
$$95$$ −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 $$0.935525\pi$$
$$98$$ 255.670i 0.263537i
$$99$$ 0 0
$$100$$ 32.5265 637.256i 0.0325265 0.637256i
$$101$$ −34.4906 −0.0339796 −0.0169898 0.999856i $$-0.505408\pi$$
−0.0169898 + 0.999856i $$0.505408\pi$$
$$102$$ 0 0
$$103$$ 1756.30i 1.68013i 0.542484 + 0.840066i $$0.317484\pi$$
−0.542484 + 0.840066i $$0.682516\pi$$
$$104$$ 1297.98 1.22382
$$105$$ 0 0
$$106$$ −788.722 −0.722712
$$107$$ 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 $$0.545061\pi$$
$$110$$ 23.4656 + 24.6939i 0.0203396 + 0.0214043i
$$111$$ 0 0
$$112$$ 64.3031i 0.0542506i
$$113$$ 1582.25i 1.31721i −0.752487 0.658607i $$-0.771146\pi$$
0.752487 0.658607i $$-0.228854\pi$$
$$114$$ 0 0
$$115$$ −382.094 402.094i −0.309830 0.326047i
$$116$$ −1498.05 −1.19906
$$117$$ 0 0
$$118$$ 125.559i 0.0979549i
$$119$$ 421.631 0.324797
$$120$$ 0 0
$$121$$ −1327.79 −0.997591
$$122$$ 233.709i 0.173435i
$$123$$ 0 0
$$124$$ 328.837 0.238149
$$125$$ −909.802 1060.84i −0.651001 0.759077i
$$126$$ 0 0
$$127$$ 1197.14i 0.836449i −0.908344 0.418225i $$-0.862652\pi$$
0.908344 0.418225i $$-0.137348\pi$$
$$128$$ 975.173i 0.673390i
$$129$$ 0 0
$$130$$ 802.744 762.816i 0.541579 0.514641i
$$131$$ 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
$$134$$ −295.912 −0.190768
$$135$$ 0 0
$$136$$ 423.322 0.266909
$$137$$ 354.291i 0.220942i −0.993879 0.110471i $$-0.964764\pi$$
0.993879 0.110471i $$-0.0352360\pi$$
$$138$$ 0 0
$$139$$ −77.2562 −0.0471424 −0.0235712 0.999722i $$-0.507504\pi$$
−0.0235712 + 0.999722i $$0.507504\pi$$
$$140$$ 873.141 + 918.844i 0.527099 + 0.554689i
$$141$$ 0 0
$$142$$ 1011.21i 0.597595i
$$143$$ 104.231i 0.0609529i
$$144$$ 0 0
$$145$$ −2378.45 + 2260.14i −1.36220 + 1.29445i
$$146$$ 544.893 0.308875
$$147$$ 0 0
$$148$$ 101.503i 0.0563752i
$$149$$ −1705.38 −0.937651 −0.468826 0.883291i $$-0.655323\pi$$
−0.468826 + 0.883291i $$0.655323\pi$$
$$150$$ 0 0
$$151$$ 758.281 0.408663 0.204331 0.978902i $$-0.434498\pi$$
0.204331 + 0.978902i $$0.434498\pi$$
$$152$$ 2337.71i 1.24746i
$$153$$ 0 0
$$154$$ −67.6689 −0.0354086
$$155$$ 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 $$-0.148446\pi$$
$$158$$ 1311.00i 0.660111i
$$159$$ 0 0
$$160$$ 1411.80 + 1485.70i 0.697581 + 0.734095i
$$161$$ 1101.86 0.539372
$$162$$ 0 0
$$163$$ 881.719i 0.423690i 0.977303 + 0.211845i $$0.0679473\pi$$
−0.977303 + 0.211845i $$0.932053\pi$$
$$164$$ 845.240 0.402452
$$165$$ 0 0
$$166$$ −295.944 −0.138372
$$167$$ 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
$$170$$ 261.806 248.784i 0.118116 0.112241i
$$171$$ 0 0
$$172$$ 1262.64i 0.559742i
$$173$$ 4125.91i 1.81322i 0.421970 + 0.906610i $$0.361339\pi$$
−0.421970 + 0.906610i $$0.638661\pi$$
$$174$$ 0 0
$$175$$ 2772.56 + 141.515i 1.19763 + 0.0611289i
$$176$$ 5.18443 0.00222040
$$177$$ 0 0
$$178$$ 1733.93i 0.730134i
$$179$$ −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 $$0.254529\pi$$
$$182$$ 2199.77i 0.895921i
$$183$$ 0 0
$$184$$ 1106.28 0.443240
$$185$$ −153.141 161.156i −0.0608601 0.0640457i
$$186$$ 0 0
$$187$$ 33.9939i 0.0132935i
$$188$$ 1962.98i 0.761514i
$$189$$ 0 0
$$190$$ −1373.86 1445.77i −0.524581 0.552040i
$$191$$ 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 $$-0.108466\pi$$
$$194$$ −654.038 −0.242047
$$195$$ 0 0
$$196$$ −767.011 −0.279523
$$197$$ 1678.19i 0.606935i −0.952842 0.303467i $$-0.901856\pi$$
0.952842 0.303467i $$-0.0981443\pi$$
$$198$$ 0 0
$$199$$ −3108.23 −1.10722 −0.553610 0.832776i $$-0.686750\pi$$
−0.553610 + 0.832776i $$0.686750\pi$$
$$200$$ 2783.68 + 142.083i 0.984180 + 0.0502339i
$$201$$ 0 0
$$202$$ 58.6878i 0.0204419i
$$203$$ 6517.69i 2.25346i
$$204$$ 0 0
$$205$$ 1341.98 1275.23i 0.457211 0.434469i
$$206$$ −2988.46 −1.01076
$$207$$ 0 0
$$208$$ 168.534i 0.0561815i
$$209$$ −187.725 −0.0621301
$$210$$ 0 0
$$211$$ −4473.27 −1.45949 −0.729745 0.683719i $$-0.760361\pi$$
−0.729745 + 0.683719i $$0.760361\pi$$
$$212$$ 2366.17i 0.766551i
$$213$$ 0 0
$$214$$ −2317.08 −0.740151
$$215$$ 1904.98 + 2004.69i 0.604273 + 0.635902i
$$216$$ 0 0
$$217$$ 1430.70i 0.447568i
$$218$$ 546.403i 0.169757i
$$219$$ 0 0
$$220$$ 74.0816 70.3968i 0.0227026 0.0215734i
$$221$$ −1105.07 −0.336357
$$222$$ 0 0
$$223$$ 1753.42i 0.526535i 0.964723 + 0.263268i $$0.0848003\pi$$
−0.964723 + 0.263268i $$0.915200\pi$$
$$224$$ −4071.29 −1.21440
$$225$$ 0 0
$$226$$ 2692.29 0.792427
$$227$$ 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 $$0.378484\pi$$
$$230$$ 684.187 650.156i 0.196148 0.186391i
$$231$$ 0 0
$$232$$ 6543.82i 1.85182i
$$233$$ 2295.01i 0.645284i 0.946521 + 0.322642i $$0.104571\pi$$
−0.946521 + 0.322642i $$0.895429\pi$$
$$234$$ 0 0
$$235$$ −2961.59 3116.61i −0.822096 0.865128i
$$236$$ −376.678 −0.103897
$$237$$ 0 0
$$238$$ 717.432i 0.195396i
$$239$$ −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 $$0.483731\pi$$
$$242$$ 2259.32i 0.600144i
$$243$$ 0 0
$$244$$ −701.128 −0.183956
$$245$$ −1217.78 + 1157.21i −0.317555 + 0.301760i
$$246$$ 0 0
$$247$$ 6102.52i 1.57204i
$$248$$ 1436.44i 0.367798i
$$249$$ 0 0
$$250$$ 1805.09 1548.08i 0.456655 0.391638i
$$251$$ 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
$$254$$ 2037.01 0.503202
$$255$$ 0 0
$$256$$ −3969.38 −0.969087
$$257$$ 92.7843i 0.0225203i 0.999937 + 0.0112602i $$0.00358430\pi$$
−0.999937 + 0.0112602i $$0.996416\pi$$
$$258$$ 0 0
$$259$$ 441.619 0.105949
$$260$$ −2288.45 2408.23i −0.545859 0.574431i
$$261$$ 0 0
$$262$$ 547.302i 0.129055i
$$263$$ 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
$$266$$ 3961.87 0.913226
$$267$$ 0 0
$$268$$ 887.737i 0.202340i
$$269$$ 7582.41 1.71862 0.859309 0.511458i $$-0.170894\pi$$
0.859309 + 0.511458i $$0.170894\pi$$
$$270$$ 0 0
$$271$$ 7943.69 1.78061 0.890304 0.455366i $$-0.150492\pi$$
0.890304 + 0.455366i $$0.150492\pi$$
$$272$$ 54.9657i 0.0122529i
$$273$$ 0 0
$$274$$ 602.847 0.132917
$$275$$ 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 $$0.734830\pi$$
$$278$$ 131.456i 0.0283605i
$$279$$ 0 0
$$280$$ −4013.72 + 3814.08i −0.856663 + 0.814053i
$$281$$ −3315.86 −0.703942 −0.351971 0.936011i $$-0.614488\pi$$
−0.351971 + 0.936011i $$0.614488\pi$$
$$282$$ 0 0
$$283$$ 6602.76i 1.38690i −0.720504 0.693451i $$-0.756090\pi$$
0.720504 0.693451i $$-0.243910\pi$$
$$284$$ 3033.62 0.633846
$$285$$ 0 0
$$286$$ 177.356 0.0366688
$$287$$ 3677.46i 0.756353i
$$288$$ 0 0
$$289$$ 4552.59 0.926642
$$290$$ −3845.77 4047.07i −0.778730 0.819491i
$$291$$ 0 0
$$292$$ 1634.68i 0.327611i
$$293$$ 5814.14i 1.15927i 0.814877 + 0.579634i $$0.196805\pi$$
−0.814877 + 0.579634i $$0.803195\pi$$
$$294$$ 0 0
$$295$$ −598.050 + 568.303i −0.118033 + 0.112162i
$$296$$ 443.390 0.0870660
$$297$$ 0 0
$$298$$ 2901.81i 0.564084i
$$299$$ −2887.91 −0.558570
$$300$$ 0 0
$$301$$ −5493.49 −1.05196
$$302$$ 1290.26i 0.245849i
$$303$$ 0 0
$$304$$ −303.537 −0.0572667
$$305$$ −1113.18 + 1057.81i −0.208985 + 0.198590i
$$306$$ 0 0
$$307$$ 8124.86i 1.51046i −0.655462 0.755229i $$-0.727526\pi$$
0.655462 0.755229i $$-0.272474\pi$$
$$308$$ 203.007i 0.0375564i
$$309$$ 0 0
$$310$$ 844.187 + 888.375i 0.154667 + 0.162762i
$$311$$ −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 $$0.936268\pi$$
$$314$$ 3010.15 0.540996
$$315$$ 0 0
$$316$$ 3933.00 0.700154
$$317$$ 10008.9i 1.77336i −0.462386 0.886679i $$-0.653007\pi$$
0.462386 0.886679i $$-0.346993\pi$$
$$318$$ 0 0
$$319$$ −525.488 −0.0922309
$$320$$ −2340.29 + 2223.89i −0.408832 + 0.388497i
$$321$$ 0 0
$$322$$ 1874.89i 0.324483i
$$323$$ 1990.27i 0.342854i
$$324$$ 0 0
$$325$$ −7266.71 370.903i −1.24026 0.0633046i
$$326$$ −1500.30 −0.254889
$$327$$ 0 0
$$328$$ 3692.20i 0.621548i
$$329$$ 8540.47 1.43116
$$330$$ 0 0
$$331$$ −8695.94 −1.44402 −0.722012 0.691881i $$-0.756782\pi$$
−0.722012 + 0.691881i $$0.756782\pi$$
$$332$$ 887.832i 0.146765i
$$333$$ 0 0
$$334$$ −369.069 −0.0604627
$$335$$ 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 $$-0.204088\pi$$
$$338$$ 2027.12i 0.326216i
$$339$$ 0 0
$$340$$ −746.353 785.419i −0.119049 0.125280i
$$341$$ 115.350 0.0183183
$$342$$ 0 0
$$343$$ 4280.72i 0.673869i
$$344$$ −5515.52 −0.864467
$$345$$ 0 0
$$346$$ −7020.49 −1.09082
$$347$$ 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 $$0.375761\pi$$
$$350$$ −240.797 + 4717.69i −0.0367748 + 0.720489i
$$351$$ 0 0
$$352$$ 328.247i 0.0497035i
$$353$$ 12163.0i 1.83392i −0.398981 0.916959i $$-0.630636\pi$$
0.398981 0.916959i $$-0.369364\pi$$
$$354$$ 0 0
$$355$$ 4816.46 4576.89i 0.720088 0.684271i
$$356$$ 5201.80 0.774424
$$357$$ 0 0
$$358$$ 5467.36i 0.807148i
$$359$$ 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
$$362$$ 5775.81i 0.838591i
$$363$$ 0 0
$$364$$ 6599.31 0.950268
$$365$$ −2466.28 2595.37i −0.353674 0.372187i
$$366$$ 0 0
$$367$$ 6086.09i 0.865644i −0.901479 0.432822i $$-0.857518\pi$$
0.901479 0.432822i $$-0.142482\pi$$
$$368$$ 143.644i 0.0203477i
$$369$$ 0 0
$$370$$ 274.218 260.578i 0.0385295 0.0366130i
$$371$$ −10294.7 −1.44063
$$372$$ 0 0
$$373$$ 10581.9i 1.46893i 0.678646 + 0.734466i $$0.262567\pi$$
−0.678646 + 0.734466i $$0.737433\pi$$
$$374$$ 57.8428 0.00799727
$$375$$ 0 0
$$376$$ 8574.72 1.17608
$$377$$ 17082.4i 2.33366i
$$378$$ 0 0
$$379$$ −11655.2 −1.57964 −0.789822 0.613336i $$-0.789827\pi$$
−0.789822 + 0.613336i $$0.789827\pi$$
$$380$$ −4337.32 + 4121.59i −0.585526 + 0.556403i
$$381$$ 0 0
$$382$$ 5900.16i 0.790257i
$$383$$ 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
$$386$$ 3049.44 0.402105
$$387$$ 0 0
$$388$$ 1962.11i 0.256730i
$$389$$ 6134.33 0.799545 0.399773 0.916614i $$-0.369089\pi$$
0.399773 + 0.916614i $$0.369089\pi$$
$$390$$ 0 0
$$391$$ −941.862 −0.121821
$$392$$ 3350.48i 0.431696i
$$393$$ 0 0
$$394$$ 2855.55 0.365128
$$395$$ 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 $$0.788723\pi$$
$$398$$ 5288.85i 0.666096i
$$399$$ 0 0
$$400$$ 18.4486 361.444i 0.00230607 0.0451805i
$$401$$ 1306.44 0.162695 0.0813474 0.996686i $$-0.474078\pi$$
0.0813474 + 0.996686i $$0.474078\pi$$
$$402$$ 0 0
$$403$$ 3749.77i 0.463498i
$$404$$ −176.063 −0.0216819
$$405$$ 0 0
$$406$$ 11090.2 1.35566
$$407$$ 35.6055i 0.00433636i
$$408$$ 0 0
$$409$$ 3876.93 0.468709 0.234354 0.972151i $$-0.424702\pi$$
0.234354 + 0.972151i $$0.424702\pi$$
$$410$$ 2169.89 + 2283.47i 0.261374 + 0.275055i
$$411$$ 0 0
$$412$$ 8965.38i 1.07207i
$$413$$ 1638.84i 0.195260i
$$414$$ 0 0
$$415$$ 1339.49 + 1409.61i 0.158441 + 0.166735i
$$416$$ 10670.6 1.25762
$$417$$ 0 0
$$418$$ 319.426i 0.0373771i
$$419$$ −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 $$0.655742\pi$$
$$422$$ 7611.54i 0.878019i
$$423$$ 0 0
$$424$$ −10336.0 −1.18386
$$425$$ −2369.96 120.966i −0.270494 0.0138064i
$$426$$ 0 0
$$427$$ 3050.46i 0.345719i
$$428$$ 6951.24i 0.785049i
$$429$$ 0 0
$$430$$ −3411.11 + 3241.44i −0.382554 + 0.363526i
$$431$$ 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 $$-0.112768\pi$$
$$434$$ −2434.42 −0.269254
$$435$$ 0 0
$$436$$ −1639.21 −0.180055
$$437$$ 5201.25i 0.569358i
$$438$$ 0 0
$$439$$ 4230.97 0.459984 0.229992 0.973192i $$-0.426130\pi$$
0.229992 + 0.973192i $$0.426130\pi$$
$$440$$ 307.509 + 323.605i 0.0333180 + 0.0350620i
$$441$$ 0 0
$$442$$ 1880.34i 0.202350i
$$443$$ 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
$$446$$ −2983.55 −0.316760
$$447$$ 0 0
$$448$$ 6413.13i 0.676321i
$$449$$ −9349.71 −0.982717 −0.491358 0.870957i $$-0.663499\pi$$
−0.491358 + 0.870957i $$0.663499\pi$$
$$450$$ 0 0
$$451$$ 296.494 0.0309565
$$452$$ 8076.87i 0.840496i
$$453$$ 0 0
$$454$$ −1594.19 −0.164800
$$455$$ 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 $$-0.162505\pi$$
$$458$$ 4393.53i 0.448245i
$$459$$ 0 0
$$460$$ −1950.47 2052.56i −0.197698 0.208046i
$$461$$ −6237.23 −0.630145 −0.315073 0.949068i $$-0.602029\pi$$
−0.315073 + 0.949068i $$0.602029\pi$$
$$462$$ 0 0
$$463$$ 6469.98i 0.649428i −0.945812 0.324714i $$-0.894732\pi$$
0.945812 0.324714i $$-0.105268\pi$$
$$464$$ −849.675 −0.0850111
$$465$$ 0 0
$$466$$ −3905.10 −0.388198
$$467$$ 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
$$470$$ 5303.10 5039.32i 0.520455 0.494567i
$$471$$ 0 0
$$472$$ 1645.42i 0.160458i
$$473$$ 442.912i 0.0430552i
$$474$$ 0 0
$$475$$ −668.012 + 13087.6i −0.0645274 + 1.26422i
$$476$$ 2152.29 0.207248
$$477$$ 0 0
$$478$$ 3903.39i 0.373509i
$$479$$ −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
$$482$$ 650.485i 0.0614705i
$$483$$ 0 0
$$484$$ −6777.97 −0.636549
$$485$$ 2960.29 + 3115.24i 0.277154 + 0.291661i
$$486$$ 0 0
$$487$$ 12757.1i 1.18702i 0.804827 + 0.593510i $$0.202258\pi$$
−0.804827 + 0.593510i $$0.797742\pi$$
$$488$$ 3062.69i 0.284101i
$$489$$ 0 0
$$490$$ −1969.06 2072.13i −0.181537 0.191039i
$$491$$ 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
$$494$$ −10383.8 −0.945729
$$495$$ 0 0
$$496$$ 186.512 0.0168844
$$497$$ 13198.6i 1.19122i
$$498$$ 0 0
$$499$$ −11372.3 −1.02023 −0.510113 0.860107i $$-0.670396\pi$$
−0.510113 + 0.860107i $$0.670396\pi$$
$$500$$ −4644.25 5415.27i −0.415395 0.484356i
$$501$$ 0 0
$$502$$ 3845.50i 0.341899i
$$503$$ 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
$$506$$ 151.163 0.0132806
$$507$$ 0 0
$$508$$ 6111.03i 0.533726i
$$509$$ 16256.7 1.41565 0.707825 0.706388i $$-0.249676\pi$$
0.707825 + 0.706388i $$0.249676\pi$$
$$510$$ 0 0
$$511$$ 7112.14 0.615699
$$512$$ 1047.24i 0.0903943i
$$513$$ 0 0
$$514$$ −157.878 −0.0135481
$$515$$ 13526.3 + 14234.3i 1.15736 + 1.21794i
$$516$$ 0 0
$$517$$ 688.574i 0.0585754i
$$518$$ 751.442i 0.0637384i
$$519$$ 0 0
$$520$$ 10519.7 9996.46i 0.887153 0.843026i
$$521$$ −19748.4 −1.66064 −0.830320 0.557286i $$-0.811843\pi$$
−0.830320 + 0.557286i $$0.811843\pi$$
$$522$$ 0 0
$$523$$ 7843.44i 0.655774i 0.944717 + 0.327887i $$0.106337\pi$$
−0.944717 + 0.327887i $$0.893663\pi$$
$$524$$ 1641.91 0.136884
$$525$$ 0 0
$$526$$ 967.019 0.0801597
$$527$$ 1222.95i 0.101086i
$$528$$ 0 0
$$529$$ 9705.60 0.797699
$$530$$ −6392.34 + 6074.39i −0.523897 + 0.497839i
$$531$$ 0 0
$$532$$ 11885.6i 0.968622i
$$533$$ 9638.38i 0.783273i
$$534$$ 0 0
$$535$$ 10487.5 + 11036.5i 0.847504 + 0.891865i
$$536$$ −3877.84 −0.312495
$$537$$ 0 0
$$538$$ 12902.0i 1.03391i
$$539$$ −269.053 −0.0215008
$$540$$ 0 0
$$541$$ 7383.29 0.586751 0.293376 0.955997i $$-0.405221\pi$$
0.293376 + 0.955997i $$0.405221\pi$$
$$542$$ 13516.7i 1.07120i
$$543$$ 0 0
$$544$$ 3480.10 0.274280
$$545$$ −2602.57 + 2473.12i −0.204554 + 0.194379i
$$546$$ 0 0
$$547$$ 3354.90i 0.262240i −0.991367 0.131120i $$-0.958143\pi$$
0.991367 0.131120i $$-0.0418573\pi$$
$$548$$ 1808.54i 0.140980i
$$549$$ 0 0
$$550$$ 380.363 + 19.4143i 0.0294886 + 0.00150514i
$$551$$ 30766.2 2.37874
$$552$$ 0 0
$$553$$ 17111.6i 1.31584i
$$554$$ −11609.8 −0.890346
$$555$$ 0 0
$$556$$ −394.369 −0.0300809
$$557$$ 20771.8i 1.58012i −0.613028 0.790061i $$-0.710049\pi$$
0.613028 0.790061i $$-0.289951\pi$$
$$558$$ 0 0
$$559$$ 14398.1 1.08940
$$560$$ 495.234 + 521.156i 0.0373705 + 0.0393266i
$$561$$ 0 0
$$562$$ 5642.15i 0.423487i
$$563$$ 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
$$566$$ 11235.0 0.834350
$$567$$ 0 0
$$568$$ 13251.5i 0.978913i
$$569$$ 11549.5 0.850931 0.425466 0.904975i $$-0.360110\pi$$
0.425466 + 0.904975i $$0.360110\pi$$
$$570$$ 0 0
$$571$$ 1482.54 0.108655 0.0543277 0.998523i $$-0.482698\pi$$
0.0543277 + 0.998523i $$0.482698\pi$$
$$572$$ 532.068i 0.0388932i
$$573$$ 0 0
$$574$$ −6257.42 −0.455017
$$575$$ −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 $$-0.185620\pi$$
$$578$$ 7746.52i 0.557462i
$$579$$ 0 0
$$580$$ −12141.2 + 11537.3i −0.869202 + 0.825968i
$$581$$ −3862.76 −0.275825
$$582$$ 0 0
$$583$$ 830.006i 0.0589628i
$$584$$ 7140.66 0.505963
$$585$$ 0 0
$$586$$ −9893.12 −0.697408
$$587$$ 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
$$590$$ −967.003 1017.62i −0.0674761 0.0710080i
$$591$$ 0 0
$$592$$ 57.5714i 0.00399691i
$$593$$ 11764.8i 0.814707i −0.913271 0.407353i $$-0.866452\pi$$
0.913271 0.407353i $$-0.133548\pi$$
$$594$$ 0 0
$$595$$ 3417.19 3247.22i 0.235447 0.223736i
$$596$$ −8705.42 −0.598302
$$597$$ 0 0
$$598$$ 4913.96i 0.336032i
$$599$$ −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 $$0.533895\pi$$
$$602$$ 9347.51i 0.632851i
$$603$$ 0 0
$$604$$ 3870.79 0.260762
$$605$$ −10761.4 + 10226.1i −0.723159 + 0.687189i
$$606$$ 0 0
$$607$$ 22700.8i 1.51795i 0.651120 + 0.758975i $$0.274300\pi$$
−0.651120 + 0.758975i $$0.725700\pi$$
$$608$$ 19218.2i 1.28191i
$$609$$ 0 0
$$610$$ −1799.93 1894.14i −0.119470 0.125724i
$$611$$ −22384.0 −1.48210
$$612$$ 0 0
$$613$$ 28911.6i 1.90494i −0.304629 0.952471i $$-0.598532\pi$$
0.304629 0.952471i $$-0.401468\pi$$
$$614$$ 13825.0 0.908681
$$615$$ 0 0
$$616$$ −886.780 −0.0580023
$$617$$ 5566.87i 0.363231i 0.983370 + 0.181616i $$0.0581326\pi$$
−0.983370 + 0.181616i $$0.941867\pi$$
$$618$$ 0 0
$$619$$ −4150.32 −0.269492 −0.134746 0.990880i $$-0.543022\pi$$
−0.134746 + 0.990880i $$0.543022\pi$$
$$620$$ 2665.12 2532.56i 0.172635 0.164049i
$$621$$ 0 0
$$622$$ 12483.1i 0.804705i
$$623$$ 22631.9i 1.45542i
$$624$$ 0 0
$$625$$ −15543.8 1590.90i −0.994803 0.101818i
$$626$$ −3747.96 −0.239295
$$627$$ 0 0
$$628$$ 9030.46i 0.573813i
$$629$$ −377.492 −0.0239294
$$630$$ 0 0
$$631$$ −4090.09 −0.258041 −0.129021 0.991642i $$-0.541183\pi$$
−0.129021 + 0.991642i $$0.541183\pi$$
$$632$$ 17180.2i 1.08132i
$$633$$ 0 0
$$634$$ 17030.7 1.06684
$$635$$ −9219.85 9702.45i −0.576187 0.606346i
$$636$$ 0 0
$$637$$ 8746.32i 0.544022i
$$638$$ 894.150i 0.0554855i
$$639$$ 0 0
$$640$$ 7510.36 + 7903.47i 0.463864 + 0.488144i
$$641$$ −3909.35 −0.240890 −0.120445 0.992720i $$-0.538432\pi$$
−0.120445 + 0.992720i $$0.538432\pi$$
$$642$$ 0 0
$$643$$ 30539.5i 1.87303i −0.350624 0.936516i $$-0.614031\pi$$
0.350624 0.936516i $$-0.385969\pi$$
$$644$$ 5624.66 0.344166
$$645$$ 0 0
$$646$$ −3386.58 −0.206259
$$647$$ 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
$$650$$ 631.115 12364.8i 0.0380836 0.746132i
$$651$$ 0 0
$$652$$ 4500.90i 0.270351i
$$653$$ 12777.6i 0.765737i 0.923803 + 0.382869i $$0.125064\pi$$
−0.923803 + 0.382869i $$0.874936\pi$$
$$654$$ 0 0
$$655$$ 2606.85 2477.18i 0.155508 0.147773i
$$656$$ 479.410 0.0285332
$$657$$ 0 0
$$658$$ 14532.1i 0.860976i
$$659$$ 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 $$0.540958\pi$$
$$662$$ 14796.7i 0.868715i
$$663$$ 0 0
$$664$$ −3878.25 −0.226665
$$665$$ −17932.1 18870.7i −1.04568 1.10042i
$$666$$ 0 0
$$667$$ 14559.6i 0.845200i
$$668$$ 1107.21i 0.0641304i
$$669$$ 0 0
$$670$$ −2398.28 + 2278.99i −0.138289 + 0.131410i
$$671$$ −245.943 −0.0141498
$$672$$ 0 0
$$673$$ 8203.52i 0.469870i 0.972011 + 0.234935i $$0.0754877\pi$$
−0.972011 + 0.234935i $$0.924512\pi$$
$$674$$ 12592.6 0.719657
$$675$$ 0 0
$$676$$ −6081.37 −0.346004
$$677$$ 28057.1i 1.59279i −0.604774 0.796397i $$-0.706737\pi$$
0.604774 0.796397i $$-0.293263\pi$$
$$678$$ 0 0
$$679$$ −8536.73 −0.482488
$$680$$ 3430.89 3260.24i 0.193483 0.183860i
$$681$$ 0 0
$$682$$ 196.275i 0.0110202i
$$683$$ 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
$$686$$ −7283.91 −0.405395
$$687$$ 0 0
$$688$$ 716.156i 0.0396849i
$$689$$ 26981.7 1.49190
$$690$$ 0 0
$$691$$ 12964.8 0.713757 0.356879 0.934151i $$-0.383841\pi$$
0.356879 + 0.934151i $$0.383841\pi$$
$$692$$ 21061.5i 1.15699i
$$693$$ 0 0
$$694$$ 13342.7 0.729801
$$695$$ −626.138 + 594.994i −0.0341737 + 0.0324740i
$$696$$ 0 0
$$697$$ 3143.46i 0.170828i
$$698$$ 8441.90i 0.457780i
$$699$$ 0 0
$$700$$ 14153.1 + 722.392i 0.764193 + 0.0390055i
$$701$$ 16162.1 0.870806 0.435403 0.900236i $$-0.356606\pi$$
0.435403 + 0.900236i $$0.356606\pi$$
$$702$$ 0 0
$$703$$ 2084.63i 0.111839i
$$704$$ −517.058 −0.0276809
$$705$$ 0 0
$$706$$ 20696.2 1.10327
$$707$$ 766.014i 0.0407481i
$$708$$ 0 0
$$709$$ 14244.4 0.754529 0.377265 0.926105i $$-0.376865\pi$$
0.377265 + 0.926105i $$0.376865\pi$$
$$710$$ 7787.87 + 8195.51i 0.411653 + 0.433200i
$$711$$ 0 0
$$712$$ 22722.7i 1.19602i
$$713$$ 3195.97i 0.167868i
$$714$$ 0 0
$$715$$ −802.744 844.762i −0.0419873 0.0441850i
$$716$$ −16402.1 −0.856109
$$717$$ 0 0
$$718$$ 8837.55i 0.459352i
$$719$$ −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
$$722$$ 7030.68i 0.362403i
$$723$$ 0 0
$$724$$ 17327.4 0.889460
$$725$$ −1869.93 + 36635.5i −0.0957895 + 1.87670i
$$726$$ 0 0
$$727$$ 2525.52i 0.128840i −0.997923 0.0644199i $$-0.979480\pi$$
0.997923 0.0644199i $$-0.0205197\pi$$
$$728$$ 28827.3i 1.46760i
$$729$$ 0 0
$$730$$ 4416.19 4196.53i 0.223905 0.212768i
$$731$$ 4695.79 0.237592
$$732$$ 0 0
$$733$$ 8400.27i 0.423289i 0.977347 + 0.211645i $$0.0678820\pi$$
−0.977347 + 0.211645i $$0.932118\pi$$
$$734$$ 10355.9 0.520765
$$735$$ 0 0
$$736$$ 9094.67 0.455481
$$737$$ 311.401i 0.0155639i
$$738$$ 0 0
$$739$$ 19689.1 0.980074 0.490037 0.871702i $$-0.336983\pi$$
0.490037 + 0.871702i $$0.336983\pi$$
$$740$$ −781.735 822.653i −0.0388340 0.0408667i
$$741$$ 0 0
$$742$$ 17517.0i 0.866671i
$$743$$ 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
$$746$$ −18005.8 −0.883699
$$747$$ 0 0
$$748$$ 173.528i 0.00848239i
$$749$$ −30243.3 −1.47539
$$750$$ 0 0
$$751$$ 34691.1 1.68562 0.842808 0.538215i $$-0.180901\pi$$
0.842808 + 0.538215i $$0.180901\pi$$
$$752$$ 1113.37i 0.0539902i
$$753$$ 0 0
$$754$$ −29066.8 −1.40392
$$755$$ 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 $$0.949198\pi$$
$$758$$ 19832.0i 0.950303i
$$759$$ 0 0
$$760$$ −18004.0 18946.4i −0.859309 0.904288i
$$761$$ 29368.7 1.39897 0.699483 0.714649i $$-0.253414\pi$$
0.699483 + 0.714649i $$0.253414\pi$$
$$762$$ 0 0
$$763$$ 7131.84i 0.338388i
$$764$$ 17700.5 0.838194
$$765$$ 0 0
$$766$$ −10830.4 −0.510859
$$767$$ 4295.31i 0.202209i
$$768$$ 0 0
$$769$$ −32677.4 −1.53235 −0.766174 0.642633i $$-0.777842\pi$$
−0.766174 + 0.642633i $$0.777842\pi$$
$$770$$ −548.435 + 521.156i −0.0256678 + 0.0243911i
$$771$$ 0 0
$$772$$ 9148.33i 0.426497i
$$773$$ 28047.5i 1.30504i −0.757770 0.652522i $$-0.773711\pi$$
0.757770 0.652522i $$-0.226289\pi$$
$$774$$ 0 0
$$775$$ 410.469 8041.87i 0.0190251 0.372739i
$$776$$ −8570.96 −0.396494
$$777$$ 0 0
$$778$$ 10438.0i 0.481001i
$$779$$ −17359.1 −0.798402
$$780$$ 0 0
$$781$$ 1064.14 0.0487552
$$782$$ 1602.64i 0.0732867i
$$783$$ 0 0
$$784$$ −435.039 −0.0198177
$$785$$ −13624.5 14337.6i −0.619463 0.651887i
$$786$$ 0 0
$$787$$ 22172.1i 1.00426i −0.864793 0.502128i $$-0.832551\pi$$
0.864793 0.502128i $$-0.167449\pi$$
$$788$$ 8566.64i 0.387276i
$$789$$ 0 0
$$790$$ 10096.7 + 10625.2i 0.454717 + 0.478518i
$$791$$ 35140.7 1.57960