# Properties

 Label 637.2.u.h.361.3 Level $637$ Weight $2$ Character 637.361 Analytic conductor $5.086$ Analytic rank $0$ Dimension $12$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$637 = 7^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 637.u (of order $$6$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$5.08647060876$$ Analytic rank: $$0$$ Dimension: $$12$$ Relative dimension: $$6$$ over $$\Q(\zeta_{6})$$ Coefficient field: 12.0.58891012706304.1 Defining polynomial: $$x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64$$ Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{4}$$ Twist minimal: no (minimal twist has level 91) Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

## Embedding invariants

 Embedding label 361.3 Root $$-1.08105 - 0.911778i$$ of defining polynomial Character $$\chi$$ $$=$$ 637.361 Dual form 637.2.u.h.30.3

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(-0.713220 - 0.411778i) q^{2} +2.66029 q^{3} +(-0.660878 - 1.14467i) q^{4} +(-2.73845 + 1.58105i) q^{5} +(-1.89737 - 1.09545i) q^{6} +2.73565i q^{8} +4.07715 q^{9} +O(q^{10})$$ $$q+(-0.713220 - 0.411778i) q^{2} +2.66029 q^{3} +(-0.660878 - 1.14467i) q^{4} +(-2.73845 + 1.58105i) q^{5} +(-1.89737 - 1.09545i) q^{6} +2.73565i q^{8} +4.07715 q^{9} +2.60416 q^{10} +5.94270i q^{11} +(-1.75813 - 3.04517i) q^{12} +(-0.0766193 + 3.60474i) q^{13} +(-7.28508 + 4.20604i) q^{15} +(-0.195274 + 0.338225i) q^{16} +(-1.34982 - 2.33796i) q^{17} +(-2.90791 - 1.67888i) q^{18} -1.95705i q^{19} +(3.61956 + 2.08976i) q^{20} +(2.44707 - 4.23845i) q^{22} +(-1.36471 + 2.36374i) q^{23} +7.27763i q^{24} +(2.49941 - 4.32911i) q^{25} +(1.53900 - 2.53942i) q^{26} +2.86554 q^{27} +(2.99923 + 5.19481i) q^{29} +6.92783 q^{30} +(0.997270 + 0.575774i) q^{31} +(5.01684 - 2.89647i) q^{32} +15.8093i q^{33} +2.22331i q^{34} +(-2.69450 - 4.66701i) q^{36} +(5.63310 + 3.25227i) q^{37} +(-0.805869 + 1.39581i) q^{38} +(-0.203830 + 9.58965i) q^{39} +(-4.32519 - 7.49145i) q^{40} +(-3.23351 + 1.86687i) q^{41} +(3.49562 - 6.05460i) q^{43} +(6.80245 - 3.92740i) q^{44} +(-11.1651 + 6.44617i) q^{45} +(1.94667 - 1.12391i) q^{46} +(0.394969 - 0.228035i) q^{47} +(-0.519487 + 0.899778i) q^{48} +(-3.56527 + 2.05841i) q^{50} +(-3.59092 - 6.21965i) q^{51} +(4.17688 - 2.29459i) q^{52} +(-0.199643 + 0.345792i) q^{53} +(-2.04376 - 1.17997i) q^{54} +(-9.39568 - 16.2738i) q^{55} -5.20632i q^{57} -4.94006i q^{58} +(-4.16200 + 2.40293i) q^{59} +(9.62910 + 5.55936i) q^{60} -1.15703 q^{61} +(-0.474182 - 0.821308i) q^{62} -3.98971 q^{64} +(-5.48944 - 9.99254i) q^{65} +(6.50993 - 11.2755i) q^{66} -6.27918i q^{67} +(-1.78413 + 3.09021i) q^{68} +(-3.63052 + 6.28825i) q^{69} +(3.90335 + 2.25360i) q^{71} +11.1537i q^{72} +(-7.19299 - 4.15288i) q^{73} +(-2.67843 - 4.63917i) q^{74} +(6.64917 - 11.5167i) q^{75} +(-2.24018 + 1.29337i) q^{76} +(4.09418 - 6.75560i) q^{78} +(3.95705 + 6.85381i) q^{79} -1.23495i q^{80} -4.60828 q^{81} +3.07494 q^{82} +6.19795i q^{83} +(7.39284 + 4.26826i) q^{85} +(-4.98630 + 2.87884i) q^{86} +(7.97882 + 13.8197i) q^{87} -16.2571 q^{88} +(-3.08423 - 1.78068i) q^{89} +10.6176 q^{90} +3.60762 q^{92} +(2.65303 + 1.53173i) q^{93} -0.375600 q^{94} +(3.09418 + 5.35928i) q^{95} +(13.3462 - 7.70546i) q^{96} +(-2.96831 - 1.71375i) q^{97} +24.2293i q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} + O(q^{10})$$ $$12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29} - 16 q^{30} + 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} - 2 q^{38} - 10 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} + 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} + 26 q^{52} + 22 q^{53} - 12 q^{54} - 6 q^{55} - 18 q^{59} + 66 q^{60} - 28 q^{61} - 4 q^{62} - 52 q^{64} - 42 q^{65} + 26 q^{66} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 30 q^{73} + 6 q^{74} + 46 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} - 28 q^{82} - 48 q^{85} - 60 q^{86} - 2 q^{87} + 28 q^{88} + 12 q^{89} + 24 q^{90} + 24 q^{92} + 18 q^{93} - 8 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{97} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$$.

 $$n$$ $$197$$ $$248$$ $$\chi(n)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −0.713220 0.411778i −0.504323 0.291171i 0.226174 0.974087i $$-0.427378\pi$$
−0.730497 + 0.682916i $$0.760712\pi$$
$$3$$ 2.66029 1.53592 0.767960 0.640498i $$-0.221272\pi$$
0.767960 + 0.640498i $$0.221272\pi$$
$$4$$ −0.660878 1.14467i −0.330439 0.572337i
$$5$$ −2.73845 + 1.58105i −1.22467 + 0.707065i −0.965911 0.258876i $$-0.916648\pi$$
−0.258762 + 0.965941i $$0.583315\pi$$
$$6$$ −1.89737 1.09545i −0.774600 0.447215i
$$7$$ 0 0
$$8$$ 2.73565i 0.967199i
$$9$$ 4.07715 1.35905
$$10$$ 2.60416 0.823508
$$11$$ 5.94270i 1.79179i 0.444265 + 0.895895i $$0.353465\pi$$
−0.444265 + 0.895895i $$0.646535\pi$$
$$12$$ −1.75813 3.04517i −0.507528 0.879064i
$$13$$ −0.0766193 + 3.60474i −0.0212504 + 0.999774i
$$14$$ 0 0
$$15$$ −7.28508 + 4.20604i −1.88100 + 1.08600i
$$16$$ −0.195274 + 0.338225i −0.0488186 + 0.0845563i
$$17$$ −1.34982 2.33796i −0.327380 0.567038i 0.654611 0.755966i $$-0.272832\pi$$
−0.981991 + 0.188927i $$0.939499\pi$$
$$18$$ −2.90791 1.67888i −0.685401 0.395716i
$$19$$ 1.95705i 0.448978i −0.974477 0.224489i $$-0.927929\pi$$
0.974477 0.224489i $$-0.0720712\pi$$
$$20$$ 3.61956 + 2.08976i 0.809359 + 0.467284i
$$21$$ 0 0
$$22$$ 2.44707 4.23845i 0.521717 0.903641i
$$23$$ −1.36471 + 2.36374i −0.284561 + 0.492874i −0.972503 0.232892i $$-0.925181\pi$$
0.687941 + 0.725766i $$0.258515\pi$$
$$24$$ 7.27763i 1.48554i
$$25$$ 2.49941 4.32911i 0.499883 0.865822i
$$26$$ 1.53900 2.53942i 0.301822 0.498022i
$$27$$ 2.86554 0.551474
$$28$$ 0 0
$$29$$ 2.99923 + 5.19481i 0.556942 + 0.964652i 0.997750 + 0.0670505i $$0.0213589\pi$$
−0.440807 + 0.897602i $$0.645308\pi$$
$$30$$ 6.92783 1.26484
$$31$$ 0.997270 + 0.575774i 0.179115 + 0.103412i 0.586877 0.809676i $$-0.300357\pi$$
−0.407762 + 0.913088i $$0.633691\pi$$
$$32$$ 5.01684 2.89647i 0.886860 0.512029i
$$33$$ 15.8093i 2.75205i
$$34$$ 2.22331i 0.381294i
$$35$$ 0 0
$$36$$ −2.69450 4.66701i −0.449083 0.777835i
$$37$$ 5.63310 + 3.25227i 0.926075 + 0.534670i 0.885568 0.464509i $$-0.153769\pi$$
0.0405072 + 0.999179i $$0.487103\pi$$
$$38$$ −0.805869 + 1.39581i −0.130729 + 0.226430i
$$39$$ −0.203830 + 9.58965i −0.0326389 + 1.53557i
$$40$$ −4.32519 7.49145i −0.683873 1.18450i
$$41$$ −3.23351 + 1.86687i −0.504990 + 0.291556i −0.730772 0.682622i $$-0.760840\pi$$
0.225782 + 0.974178i $$0.427506\pi$$
$$42$$ 0 0
$$43$$ 3.49562 6.05460i 0.533078 0.923318i −0.466176 0.884692i $$-0.654369\pi$$
0.999254 0.0386258i $$-0.0122980\pi$$
$$44$$ 6.80245 3.92740i 1.02551 0.592077i
$$45$$ −11.1651 + 6.44617i −1.66439 + 0.960938i
$$46$$ 1.94667 1.12391i 0.287021 0.165712i
$$47$$ 0.394969 0.228035i 0.0576121 0.0332624i −0.470917 0.882177i $$-0.656077\pi$$
0.528529 + 0.848915i $$0.322744\pi$$
$$48$$ −0.519487 + 0.899778i −0.0749815 + 0.129872i
$$49$$ 0 0
$$50$$ −3.56527 + 2.05841i −0.504205 + 0.291103i
$$51$$ −3.59092 6.21965i −0.502829 0.870926i
$$52$$ 4.17688 2.29459i 0.579230 0.318202i
$$53$$ −0.199643 + 0.345792i −0.0274231 + 0.0474982i −0.879411 0.476063i $$-0.842063\pi$$
0.851988 + 0.523561i $$0.175397\pi$$
$$54$$ −2.04376 1.17997i −0.278121 0.160573i
$$55$$ −9.39568 16.2738i −1.26691 2.19436i
$$56$$ 0 0
$$57$$ 5.20632i 0.689594i
$$58$$ 4.94006i 0.648662i
$$59$$ −4.16200 + 2.40293i −0.541846 + 0.312835i −0.745827 0.666140i $$-0.767945\pi$$
0.203981 + 0.978975i $$0.434612\pi$$
$$60$$ 9.62910 + 5.55936i 1.24311 + 0.717711i
$$61$$ −1.15703 −0.148142 −0.0740711 0.997253i $$-0.523599\pi$$
−0.0740711 + 0.997253i $$0.523599\pi$$
$$62$$ −0.474182 0.821308i −0.0602212 0.104306i
$$63$$ 0 0
$$64$$ −3.98971 −0.498714
$$65$$ −5.48944 9.99254i −0.680881 1.23942i
$$66$$ 6.50993 11.2755i 0.801316 1.38792i
$$67$$ 6.27918i 0.767124i −0.923515 0.383562i $$-0.874697\pi$$
0.923515 0.383562i $$-0.125303\pi$$
$$68$$ −1.78413 + 3.09021i −0.216358 + 0.374743i
$$69$$ −3.63052 + 6.28825i −0.437063 + 0.757016i
$$70$$ 0 0
$$71$$ 3.90335 + 2.25360i 0.463242 + 0.267453i 0.713406 0.700751i $$-0.247151\pi$$
−0.250165 + 0.968203i $$0.580485\pi$$
$$72$$ 11.1537i 1.31447i
$$73$$ −7.19299 4.15288i −0.841876 0.486057i 0.0160254 0.999872i $$-0.494899\pi$$
−0.857901 + 0.513814i $$0.828232\pi$$
$$74$$ −2.67843 4.63917i −0.311361 0.539293i
$$75$$ 6.64917 11.5167i 0.767780 1.32983i
$$76$$ −2.24018 + 1.29337i −0.256966 + 0.148360i
$$77$$ 0 0
$$78$$ 4.09418 6.75560i 0.463575 0.764921i
$$79$$ 3.95705 + 6.85381i 0.445203 + 0.771114i 0.998066 0.0621581i $$-0.0197983\pi$$
−0.552864 + 0.833272i $$0.686465\pi$$
$$80$$ 1.23495i 0.138072i
$$81$$ −4.60828 −0.512031
$$82$$ 3.07494 0.339571
$$83$$ 6.19795i 0.680313i 0.940369 + 0.340156i $$0.110480\pi$$
−0.940369 + 0.340156i $$0.889520\pi$$
$$84$$ 0 0
$$85$$ 7.39284 + 4.26826i 0.801866 + 0.462958i
$$86$$ −4.98630 + 2.87884i −0.537687 + 0.310434i
$$87$$ 7.97882 + 13.8197i 0.855419 + 1.48163i
$$88$$ −16.2571 −1.73302
$$89$$ −3.08423 1.78068i −0.326928 0.188752i 0.327549 0.944834i $$-0.393778\pi$$
−0.654476 + 0.756083i $$0.727111\pi$$
$$90$$ 10.6176 1.11919
$$91$$ 0 0
$$92$$ 3.60762 0.376120
$$93$$ 2.65303 + 1.53173i 0.275106 + 0.158833i
$$94$$ −0.375600 −0.0387402
$$95$$ 3.09418 + 5.35928i 0.317457 + 0.549851i
$$96$$ 13.3462 7.70546i 1.36215 0.786435i
$$97$$ −2.96831 1.71375i −0.301386 0.174005i 0.341679 0.939817i $$-0.389004\pi$$
−0.643065 + 0.765811i $$0.722338\pi$$
$$98$$ 0 0
$$99$$ 24.2293i 2.43513i
$$100$$ −6.60723 −0.660723
$$101$$ 13.3295 1.32633 0.663167 0.748472i $$-0.269212\pi$$
0.663167 + 0.748472i $$0.269212\pi$$
$$102$$ 5.91465i 0.585637i
$$103$$ 5.82248 + 10.0848i 0.573706 + 0.993688i 0.996181 + 0.0873131i $$0.0278281\pi$$
−0.422475 + 0.906375i $$0.638839\pi$$
$$104$$ −9.86130 0.209604i −0.966981 0.0205533i
$$105$$ 0 0
$$106$$ 0.284779 0.164417i 0.0276602 0.0159696i
$$107$$ −1.96483 + 3.40318i −0.189947 + 0.328998i −0.945232 0.326398i $$-0.894165\pi$$
0.755285 + 0.655396i $$0.227498\pi$$
$$108$$ −1.89377 3.28011i −0.182228 0.315629i
$$109$$ −9.74566 5.62666i −0.933465 0.538936i −0.0455595 0.998962i $$-0.514507\pi$$
−0.887906 + 0.460025i $$0.847840\pi$$
$$110$$ 15.4757i 1.47555i
$$111$$ 14.9857 + 8.65199i 1.42238 + 0.821210i
$$112$$ 0 0
$$113$$ 2.88709 5.00059i 0.271595 0.470416i −0.697676 0.716414i $$-0.745782\pi$$
0.969270 + 0.245998i $$0.0791157\pi$$
$$114$$ −2.14385 + 3.71325i −0.200790 + 0.347778i
$$115$$ 8.63066i 0.804813i
$$116$$ 3.96424 6.86627i 0.368071 0.637517i
$$117$$ −0.312389 + 14.6971i −0.0288803 + 1.35874i
$$118$$ 3.95790 0.364354
$$119$$ 0 0
$$120$$ −11.5063 19.9294i −1.05037 1.81930i
$$121$$ −24.3156 −2.21051
$$122$$ 0.825215 + 0.476438i 0.0747115 + 0.0431347i
$$123$$ −8.60209 + 4.96642i −0.775625 + 0.447807i
$$124$$ 1.52207i 0.136686i
$$125$$ 0.00370455i 0.000331345i
$$126$$ 0 0
$$127$$ 3.06558 + 5.30975i 0.272027 + 0.471164i 0.969381 0.245563i $$-0.0789728\pi$$
−0.697354 + 0.716727i $$0.745639\pi$$
$$128$$ −7.18812 4.15007i −0.635346 0.366817i
$$129$$ 9.29938 16.1070i 0.818765 1.41814i
$$130$$ −0.199529 + 9.38731i −0.0174998 + 0.823322i
$$131$$ −5.11084 8.85224i −0.446537 0.773424i 0.551621 0.834095i $$-0.314009\pi$$
−0.998158 + 0.0606707i $$0.980676\pi$$
$$132$$ 18.0965 10.4480i 1.57510 0.909383i
$$133$$ 0 0
$$134$$ −2.58563 + 4.47844i −0.223364 + 0.386878i
$$135$$ −7.84715 + 4.53056i −0.675375 + 0.389928i
$$136$$ 6.39584 3.69264i 0.548439 0.316641i
$$137$$ 17.2751 9.97376i 1.47591 0.852116i 0.476278 0.879295i $$-0.341986\pi$$
0.999631 + 0.0271788i $$0.00865233\pi$$
$$138$$ 5.17872 2.98994i 0.440842 0.254520i
$$139$$ 10.1637 17.6041i 0.862077 1.49316i −0.00784365 0.999969i $$-0.502497\pi$$
0.869921 0.493192i $$-0.164170\pi$$
$$140$$ 0 0
$$141$$ 1.05073 0.606641i 0.0884877 0.0510884i
$$142$$ −1.85596 3.21462i −0.155749 0.269765i
$$143$$ −21.4219 0.455325i −1.79139 0.0380762i
$$144$$ −0.796164 + 1.37900i −0.0663470 + 0.114916i
$$145$$ −16.4265 9.48383i −1.36414 0.787589i
$$146$$ 3.42013 + 5.92383i 0.283052 + 0.490260i
$$147$$ 0 0
$$148$$ 8.59741i 0.706703i
$$149$$ 10.7162i 0.877901i 0.898511 + 0.438951i $$0.144650\pi$$
−0.898511 + 0.438951i $$0.855350\pi$$
$$150$$ −9.48465 + 5.47597i −0.774418 + 0.447111i
$$151$$ 7.57267 + 4.37208i 0.616255 + 0.355795i 0.775409 0.631459i $$-0.217544\pi$$
−0.159155 + 0.987254i $$0.550877\pi$$
$$152$$ 5.35380 0.434251
$$153$$ −5.50343 9.53222i −0.444926 0.770634i
$$154$$ 0 0
$$155$$ −3.64130 −0.292476
$$156$$ 11.1117 6.10427i 0.889651 0.488733i
$$157$$ −3.25367 + 5.63552i −0.259671 + 0.449763i −0.966154 0.257967i $$-0.916947\pi$$
0.706483 + 0.707730i $$0.250281\pi$$
$$158$$ 6.51770i 0.518520i
$$159$$ −0.531109 + 0.919907i −0.0421197 + 0.0729534i
$$160$$ −9.15891 + 15.8637i −0.724075 + 1.25414i
$$161$$ 0 0
$$162$$ 3.28672 + 1.89759i 0.258229 + 0.149089i
$$163$$ 2.61267i 0.204640i −0.994752 0.102320i $$-0.967373\pi$$
0.994752 0.102320i $$-0.0326266\pi$$
$$164$$ 4.27392 + 2.46755i 0.333737 + 0.192683i
$$165$$ −24.9952 43.2930i −1.94588 3.37036i
$$166$$ 2.55218 4.42050i 0.198087 0.343097i
$$167$$ −3.36558 + 1.94312i −0.260436 + 0.150363i −0.624534 0.780998i $$-0.714711\pi$$
0.364097 + 0.931361i $$0.381378\pi$$
$$168$$ 0 0
$$169$$ −12.9883 0.552385i −0.999097 0.0424911i
$$170$$ −3.51515 6.08842i −0.269600 0.466961i
$$171$$ 7.97919i 0.610184i
$$172$$ −9.24072 −0.704599
$$173$$ −13.9768 −1.06263 −0.531317 0.847173i $$-0.678303\pi$$
−0.531317 + 0.847173i $$0.678303\pi$$
$$174$$ 13.1420i 0.996293i
$$175$$ 0 0
$$176$$ −2.00997 1.16046i −0.151507 0.0874727i
$$177$$ −11.0721 + 6.39250i −0.832232 + 0.480490i
$$178$$ 1.46649 + 2.54004i 0.109918 + 0.190384i
$$179$$ 25.2843 1.88984 0.944919 0.327305i $$-0.106140\pi$$
0.944919 + 0.327305i $$0.106140\pi$$
$$180$$ 14.7575 + 8.52026i 1.09996 + 0.635063i
$$181$$ −0.864474 −0.0642559 −0.0321279 0.999484i $$-0.510228\pi$$
−0.0321279 + 0.999484i $$0.510228\pi$$
$$182$$ 0 0
$$183$$ −3.07803 −0.227535
$$184$$ −6.46638 3.73336i −0.476708 0.275227i
$$185$$ −20.5680 −1.51219
$$186$$ −1.26146 2.18492i −0.0924950 0.160206i
$$187$$ 13.8938 8.02158i 1.01601 0.586596i
$$188$$ −0.522052 0.301407i −0.0380746 0.0219824i
$$189$$ 0 0
$$190$$ 5.09647i 0.369737i
$$191$$ 14.6676 1.06131 0.530657 0.847587i $$-0.321945\pi$$
0.530657 + 0.847587i $$0.321945\pi$$
$$192$$ −10.6138 −0.765985
$$193$$ 16.4959i 1.18740i 0.804686 + 0.593700i $$0.202333\pi$$
−0.804686 + 0.593700i $$0.797667\pi$$
$$194$$ 1.41137 + 2.44457i 0.101331 + 0.175510i
$$195$$ −14.6035 26.5831i −1.04578 1.90365i
$$196$$ 0 0
$$197$$ 9.53510 5.50509i 0.679348 0.392222i −0.120262 0.992742i $$-0.538373\pi$$
0.799609 + 0.600521i $$0.205040\pi$$
$$198$$ 9.97709 17.2808i 0.709041 1.22809i
$$199$$ −10.6059 18.3699i −0.751829 1.30221i −0.946935 0.321425i $$-0.895838\pi$$
0.195106 0.980782i $$-0.437495\pi$$
$$200$$ 11.8429 + 6.83753i 0.837423 + 0.483486i
$$201$$ 16.7045i 1.17824i
$$202$$ −9.50686 5.48879i −0.668901 0.386190i
$$203$$ 0 0
$$204$$ −4.74632 + 8.22086i −0.332309 + 0.575576i
$$205$$ 5.90322 10.2247i 0.412299 0.714122i
$$206$$ 9.59027i 0.668186i
$$207$$ −5.56412 + 9.63734i −0.386733 + 0.669842i
$$208$$ −1.20425 0.729828i −0.0834998 0.0506044i
$$209$$ 11.6301 0.804474
$$210$$ 0 0
$$211$$ 8.96788 + 15.5328i 0.617375 + 1.06932i 0.989963 + 0.141327i $$0.0451370\pi$$
−0.372588 + 0.927997i $$0.621530\pi$$
$$212$$ 0.527759 0.0362466
$$213$$ 10.3840 + 5.99523i 0.711503 + 0.410786i
$$214$$ 2.80271 1.61815i 0.191589 0.110614i
$$215$$ 22.1070i 1.50768i
$$216$$ 7.83913i 0.533385i
$$217$$ 0 0
$$218$$ 4.63387 + 8.02610i 0.313845 + 0.543596i
$$219$$ −19.1355 11.0479i −1.29305 0.746545i
$$220$$ −12.4188 + 21.5100i −0.837275 + 1.45020i
$$221$$ 8.53115 4.68662i 0.573867 0.315256i
$$222$$ −7.12540 12.3415i −0.478225 0.828311i
$$223$$ −13.8834 + 8.01558i −0.929700 + 0.536763i −0.886717 0.462313i $$-0.847020\pi$$
−0.0429835 + 0.999076i $$0.513686\pi$$
$$224$$ 0 0
$$225$$ 10.1905 17.6505i 0.679366 1.17670i
$$226$$ −4.11826 + 2.37768i −0.273943 + 0.158161i
$$227$$ 14.1812 8.18751i 0.941239 0.543424i 0.0508902 0.998704i $$-0.483794\pi$$
0.890348 + 0.455280i $$0.150461\pi$$
$$228$$ −5.95954 + 3.44074i −0.394680 + 0.227869i
$$229$$ 23.3917 13.5052i 1.54577 0.892449i 0.547310 0.836930i $$-0.315652\pi$$
0.998458 0.0555193i $$-0.0176814\pi$$
$$230$$ −3.55392 + 6.15556i −0.234338 + 0.405886i
$$231$$ 0 0
$$232$$ −14.2112 + 8.20484i −0.933011 + 0.538674i
$$233$$ 5.78406 + 10.0183i 0.378926 + 0.656320i 0.990906 0.134554i $$-0.0429601\pi$$
−0.611980 + 0.790873i $$0.709627\pi$$
$$234$$ 6.27473 10.3536i 0.410192 0.676837i
$$235$$ −0.721069 + 1.24893i −0.0470374 + 0.0814711i
$$236$$ 5.50114 + 3.17609i 0.358094 + 0.206746i
$$237$$ 10.5269 + 18.2331i 0.683796 + 1.18437i
$$238$$ 0 0
$$239$$ 14.6731i 0.949122i −0.880223 0.474561i $$-0.842607\pi$$
0.880223 0.474561i $$-0.157393\pi$$
$$240$$ 3.28533i 0.212067i
$$241$$ −12.4246 + 7.17334i −0.800338 + 0.462076i −0.843589 0.536989i $$-0.819562\pi$$
0.0432510 + 0.999064i $$0.486228\pi$$
$$242$$ 17.3424 + 10.0126i 1.11481 + 0.643637i
$$243$$ −20.8560 −1.33791
$$244$$ 0.764654 + 1.32442i 0.0489519 + 0.0847872i
$$245$$ 0 0
$$246$$ 8.18025 0.521554
$$247$$ 7.05464 + 0.149948i 0.448876 + 0.00954094i
$$248$$ −1.57512 + 2.72818i −0.100020 + 0.173240i
$$249$$ 16.4883i 1.04491i
$$250$$ −0.00152545 + 0.00264216i −9.64781e−5 + 0.000167105i
$$251$$ 4.30726 7.46040i 0.271872 0.470896i −0.697469 0.716615i $$-0.745691\pi$$
0.969341 + 0.245719i $$0.0790239\pi$$
$$252$$ 0 0
$$253$$ −14.0470 8.11004i −0.883128 0.509874i
$$254$$ 5.04936i 0.316825i
$$255$$ 19.6671 + 11.3548i 1.23160 + 0.711066i
$$256$$ 7.40753 + 12.8302i 0.462970 + 0.801888i
$$257$$ 5.18197 8.97544i 0.323243 0.559873i −0.657912 0.753094i $$-0.728560\pi$$
0.981155 + 0.193222i $$0.0618936\pi$$
$$258$$ −13.2650 + 7.65856i −0.825844 + 0.476801i
$$259$$ 0 0
$$260$$ −7.81035 + 12.8875i −0.484377 + 0.799247i
$$261$$ 12.2283 + 21.1800i 0.756913 + 1.31101i
$$262$$ 8.41813i 0.520074i
$$263$$ −22.0826 −1.36167 −0.680835 0.732436i $$-0.738383\pi$$
−0.680835 + 0.732436i $$0.738383\pi$$
$$264$$ −43.2488 −2.66178
$$265$$ 1.26258i 0.0775596i
$$266$$ 0 0
$$267$$ −8.20495 4.73713i −0.502135 0.289908i
$$268$$ −7.18761 + 4.14977i −0.439053 + 0.253488i
$$269$$ −6.46995 11.2063i −0.394480 0.683259i 0.598555 0.801082i $$-0.295742\pi$$
−0.993035 + 0.117823i $$0.962409\pi$$
$$270$$ 7.46233 0.454143
$$271$$ 15.3069 + 8.83745i 0.929829 + 0.536837i 0.886757 0.462235i $$-0.152952\pi$$
0.0430712 + 0.999072i $$0.486286\pi$$
$$272$$ 1.05434 0.0639289
$$273$$ 0 0
$$274$$ −16.4279 −0.992446
$$275$$ 25.7266 + 14.8533i 1.55137 + 0.895685i
$$276$$ 9.59732 0.577691
$$277$$ −9.00751 15.6015i −0.541209 0.937401i −0.998835 0.0482562i $$-0.984634\pi$$
0.457626 0.889145i $$-0.348700\pi$$
$$278$$ −14.4980 + 8.37041i −0.869530 + 0.502024i
$$279$$ 4.06602 + 2.34752i 0.243426 + 0.140542i
$$280$$ 0 0
$$281$$ 2.44178i 0.145665i 0.997344 + 0.0728323i $$0.0232038\pi$$
−0.997344 + 0.0728323i $$0.976796\pi$$
$$282$$ −0.999205 −0.0595018
$$283$$ 28.7240 1.70746 0.853732 0.520713i $$-0.174334\pi$$
0.853732 + 0.520713i $$0.174334\pi$$
$$284$$ 5.95741i 0.353507i
$$285$$ 8.23143 + 14.2573i 0.487588 + 0.844527i
$$286$$ 15.0910 + 9.14580i 0.892350 + 0.540802i
$$287$$ 0 0
$$288$$ 20.4544 11.8094i 1.20529 0.695873i
$$289$$ 4.85596 8.41078i 0.285645 0.494752i
$$290$$ 7.81046 + 13.5281i 0.458646 + 0.794399i
$$291$$ −7.89657 4.55909i −0.462905 0.267258i
$$292$$ 10.9782i 0.642449i
$$293$$ 25.4013 + 14.6654i 1.48396 + 0.856763i 0.999834 0.0182359i $$-0.00580499\pi$$
0.484124 + 0.874999i $$0.339138\pi$$
$$294$$ 0 0
$$295$$ 7.59829 13.1606i 0.442390 0.766241i
$$296$$ −8.89708 + 15.4102i −0.517132 + 0.895699i
$$297$$ 17.0291i 0.988126i
$$298$$ 4.41267 7.64298i 0.255619 0.442746i
$$299$$ −8.41611 5.10052i −0.486716 0.294971i
$$300$$ −17.5772 −1.01482
$$301$$ 0 0
$$302$$ −3.60065 6.23651i −0.207194 0.358871i
$$303$$ 35.4603 2.03714
$$304$$ 0.661923 + 0.382161i 0.0379639 + 0.0219185i
$$305$$ 3.16846 1.82931i 0.181426 0.104746i
$$306$$ 9.06476i 0.518198i
$$307$$ 7.06910i 0.403455i −0.979442 0.201728i $$-0.935344\pi$$
0.979442 0.201728i $$-0.0646555\pi$$
$$308$$ 0 0
$$309$$ 15.4895 + 26.8286i 0.881166 + 1.52623i
$$310$$ 2.59705 + 1.49941i 0.147503 + 0.0851607i
$$311$$ −11.1343 + 19.2852i −0.631368 + 1.09356i 0.355904 + 0.934522i $$0.384173\pi$$
−0.987272 + 0.159039i $$0.949160\pi$$
$$312$$ −26.2340 0.557607i −1.48520 0.0315683i
$$313$$ 14.0420 + 24.3214i 0.793700 + 1.37473i 0.923661 + 0.383210i $$0.125181\pi$$
−0.129961 + 0.991519i $$0.541485\pi$$
$$314$$ 4.64117 2.67958i 0.261916 0.151217i
$$315$$ 0 0
$$316$$ 5.23025 9.05906i 0.294225 0.509612i
$$317$$ −16.9009 + 9.75774i −0.949249 + 0.548049i −0.892848 0.450359i $$-0.851296\pi$$
−0.0564015 + 0.998408i $$0.517963\pi$$
$$318$$ 0.757595 0.437398i 0.0424838 0.0245281i
$$319$$ −30.8712 + 17.8235i −1.72845 + 0.997924i
$$320$$ 10.9256 6.30792i 0.610762 0.352624i
$$321$$ −5.22702 + 9.05346i −0.291744 + 0.505315i
$$322$$ 0 0
$$323$$ −4.57550 + 2.64167i −0.254588 + 0.146986i
$$324$$ 3.04551 + 5.27498i 0.169195 + 0.293054i
$$325$$ 15.4138 + 9.34142i 0.855004 + 0.518169i
$$326$$ −1.07584 + 1.86341i −0.0595853 + 0.103205i
$$327$$ −25.9263 14.9686i −1.43373 0.827764i
$$328$$ −5.10711 8.84577i −0.281993 0.488426i
$$329$$ 0 0
$$330$$ 41.1700i 2.26633i
$$331$$ 15.6308i 0.859145i −0.903032 0.429573i $$-0.858664\pi$$
0.903032 0.429573i $$-0.141336\pi$$
$$332$$ 7.09463 4.09609i 0.389368 0.224802i
$$333$$ 22.9670 + 13.2600i 1.25858 + 0.726644i
$$334$$ 3.20053 0.175125
$$335$$ 9.92767 + 17.1952i 0.542407 + 0.939476i
$$336$$ 0 0
$$337$$ 21.7501 1.18480 0.592401 0.805643i $$-0.298180\pi$$
0.592401 + 0.805643i $$0.298180\pi$$
$$338$$ 9.03603 + 5.74225i 0.491495 + 0.312337i
$$339$$ 7.68050 13.3030i 0.417148 0.722521i
$$340$$ 11.2832i 0.611917i
$$341$$ −3.42165 + 5.92647i −0.185293 + 0.320937i
$$342$$ −3.28565 + 5.69092i −0.177668 + 0.307730i
$$343$$ 0 0
$$344$$ 16.5633 + 9.56281i 0.893032 + 0.515592i
$$345$$ 22.9601i 1.23613i
$$346$$ 9.96851 + 5.75532i 0.535910 + 0.309408i
$$347$$ 7.97952 + 13.8209i 0.428363 + 0.741946i 0.996728 0.0808303i $$-0.0257572\pi$$
−0.568365 + 0.822777i $$0.692424\pi$$
$$348$$ 10.5460 18.2663i 0.565327 0.979176i
$$349$$ 5.90375 3.40853i 0.316021 0.182455i −0.333597 0.942716i $$-0.608262\pi$$
0.649617 + 0.760261i $$0.274929\pi$$
$$350$$ 0 0
$$351$$ −0.219556 + 10.3295i −0.0117190 + 0.551349i
$$352$$ 17.2128 + 29.8135i 0.917448 + 1.58907i
$$353$$ 14.0033i 0.745318i 0.927968 + 0.372659i $$0.121554\pi$$
−0.927968 + 0.372659i $$0.878446\pi$$
$$354$$ 10.5292 0.559619
$$355$$ −14.2522 −0.756427
$$356$$ 4.70725i 0.249484i
$$357$$ 0 0
$$358$$ −18.0333 10.4115i −0.953088 0.550266i
$$359$$ 4.68947 2.70747i 0.247501 0.142895i −0.371119 0.928586i $$-0.621026\pi$$
0.618619 + 0.785691i $$0.287692\pi$$
$$360$$ −17.6345 30.5438i −0.929418 1.60980i
$$361$$ 15.1700 0.798419
$$362$$ 0.616561 + 0.355972i 0.0324057 + 0.0187094i
$$363$$ −64.6867 −3.39517
$$364$$ 0 0
$$365$$ 26.2636 1.37470
$$366$$ 2.19531 + 1.26747i 0.114751 + 0.0662515i
$$367$$ 30.0317 1.56764 0.783822 0.620985i $$-0.213267\pi$$
0.783822 + 0.620985i $$0.213267\pi$$
$$368$$ −0.532985 0.923157i −0.0277838 0.0481229i
$$369$$ −13.1835 + 7.61152i −0.686307 + 0.396240i
$$370$$ 14.6695 + 8.46943i 0.762630 + 0.440305i
$$371$$ 0 0
$$372$$ 4.04914i 0.209938i
$$373$$ 21.4098 1.10856 0.554278 0.832332i $$-0.312995\pi$$
0.554278 + 0.832332i $$0.312995\pi$$
$$374$$ −13.2124 −0.683199
$$375$$ 0.00985519i 0.000508920i
$$376$$ 0.623826 + 1.08050i 0.0321713 + 0.0557224i
$$377$$ −18.9557 + 10.4134i −0.976270 + 0.536317i
$$378$$ 0 0
$$379$$ −8.20693 + 4.73827i −0.421562 + 0.243389i −0.695745 0.718289i $$-0.744926\pi$$
0.274184 + 0.961677i $$0.411592\pi$$
$$380$$ 4.08975 7.08366i 0.209800 0.363384i
$$381$$ 8.15535 + 14.1255i 0.417811 + 0.723670i
$$382$$ −10.4613 6.03982i −0.535245 0.309024i
$$383$$ 5.43061i 0.277491i 0.990328 + 0.138746i $$0.0443070\pi$$
−0.990328 + 0.138746i $$0.955693\pi$$
$$384$$ −19.1225 11.0404i −0.975842 0.563402i
$$385$$ 0 0
$$386$$ 6.79264 11.7652i 0.345736 0.598833i
$$387$$ 14.2522 24.6855i 0.724480 1.25484i
$$388$$ 4.53033i 0.229993i
$$389$$ −5.32109 + 9.21640i −0.269790 + 0.467290i −0.968807 0.247815i $$-0.920288\pi$$
0.699018 + 0.715105i $$0.253621\pi$$
$$390$$ −0.530805 + 24.9730i −0.0268784 + 1.26456i
$$391$$ 7.36845 0.372638
$$392$$ 0 0
$$393$$ −13.5963 23.5495i −0.685845 1.18792i
$$394$$ −9.06750 −0.456814
$$395$$ −21.6724 12.5126i −1.09046 0.629575i
$$396$$ 27.7346 16.0126i 1.39372 0.804663i
$$397$$ 37.1854i 1.86628i −0.359512 0.933140i $$-0.617057\pi$$
0.359512 0.933140i $$-0.382943\pi$$
$$398$$ 17.4690i 0.875644i
$$399$$ 0 0
$$400$$ 0.976143 + 1.69073i 0.0488072 + 0.0845365i
$$401$$ 0.776487 + 0.448305i 0.0387759 + 0.0223873i 0.519263 0.854615i $$-0.326207\pi$$
−0.480487 + 0.877002i $$0.659540\pi$$
$$402$$ −6.87853 + 11.9140i −0.343070 + 0.594214i
$$403$$ −2.15192 + 3.55078i −0.107195 + 0.176877i
$$404$$ −8.80916 15.2579i −0.438272 0.759110i
$$405$$ 12.6196 7.28590i 0.627071 0.362039i
$$406$$ 0 0
$$407$$ −19.3273 + 33.4758i −0.958016 + 1.65933i
$$408$$ 17.0148 9.82350i 0.842359 0.486336i
$$409$$ −21.2846 + 12.2886i −1.05245 + 0.607635i −0.923335 0.383995i $$-0.874548\pi$$
−0.129119 + 0.991629i $$0.541215\pi$$
$$410$$ −8.42059 + 4.86163i −0.415863 + 0.240099i
$$411$$ 45.9567 26.5331i 2.26688 1.30878i
$$412$$ 7.69589 13.3297i 0.379149 0.656706i
$$413$$ 0 0
$$414$$ 7.93689 4.58237i 0.390077 0.225211i
$$415$$ −9.79924 16.9728i −0.481026 0.833161i
$$416$$ 10.0566 + 18.3063i 0.493067 + 0.897540i
$$417$$ 27.0385 46.8321i 1.32408 2.29338i
$$418$$ −8.29486 4.78904i −0.405715 0.234239i
$$419$$ 3.82279 + 6.62126i 0.186755 + 0.323470i 0.944167 0.329468i $$-0.106869\pi$$
−0.757411 + 0.652938i $$0.773536\pi$$
$$420$$ 0 0
$$421$$ 25.0780i 1.22223i 0.791544 + 0.611113i $$0.209278\pi$$
−0.791544 + 0.611113i $$0.790722\pi$$
$$422$$ 14.7711i 0.719046i
$$423$$ 1.61035 0.929736i 0.0782979 0.0452053i
$$424$$ −0.945966 0.546154i −0.0459402 0.0265236i
$$425$$ −13.4951 −0.654606
$$426$$ −4.93741 8.55184i −0.239218 0.414338i
$$427$$ 0 0
$$428$$ 5.19405 0.251064
$$429$$ −56.9884 1.21130i −2.75143 0.0584820i
$$430$$ 9.10317 15.7671i 0.438994 0.760359i
$$431$$ 7.75404i 0.373499i 0.982408 + 0.186750i $$0.0597953\pi$$
−0.982408 + 0.186750i $$0.940205\pi$$
$$432$$ −0.559567 + 0.969199i −0.0269222 + 0.0466306i
$$433$$ 17.9880 31.1561i 0.864448 1.49727i −0.00314644 0.999995i $$-0.501002\pi$$
0.867594 0.497273i $$-0.165665\pi$$
$$434$$ 0 0
$$435$$ −43.6992 25.2298i −2.09522 1.20967i
$$436$$ 14.8741i 0.712342i
$$437$$ 4.62596 + 2.67080i 0.221290 + 0.127762i
$$438$$ 9.09853 + 15.7591i 0.434745 + 0.753000i
$$439$$ −14.1175 + 24.4523i −0.673792 + 1.16704i 0.303028 + 0.952982i $$0.402002\pi$$
−0.976820 + 0.214061i $$0.931331\pi$$
$$440$$ 44.5194 25.7033i 2.12238 1.22536i
$$441$$ 0 0
$$442$$ −8.01444 0.170348i −0.381208 0.00810264i
$$443$$ −14.3959 24.9344i −0.683970 1.18467i −0.973759 0.227580i $$-0.926919\pi$$
0.289790 0.957090i $$-0.406415\pi$$
$$444$$ 22.8716i 1.08544i
$$445$$ 11.2614 0.533840
$$446$$ 13.2026 0.625159
$$447$$ 28.5081i 1.34839i
$$448$$ 0 0
$$449$$ −25.2795 14.5951i −1.19301 0.688785i −0.234023 0.972231i $$-0.575189\pi$$
−0.958988 + 0.283446i $$0.908522\pi$$
$$450$$ −14.5361 + 8.39244i −0.685240 + 0.395624i
$$451$$ −11.0942 19.2158i −0.522408 0.904836i
$$452$$ −7.63205 −0.358982
$$453$$ 20.1455 + 11.6310i 0.946518 + 0.546473i
$$454$$ −13.4858 −0.632918
$$455$$ 0 0
$$456$$ 14.2427 0.666974
$$457$$ 27.4399 + 15.8424i 1.28358 + 0.741077i 0.977501 0.210929i $$-0.0676489\pi$$
0.306081 + 0.952006i $$0.400982\pi$$
$$458$$ −22.2446 −1.03942
$$459$$ −3.86797 6.69952i −0.180541 0.312707i
$$460$$ −9.87929 + 5.70381i −0.460624 + 0.265942i
$$461$$ −19.1407 11.0509i −0.891471 0.514691i −0.0170480 0.999855i $$-0.505427\pi$$
−0.874424 + 0.485163i $$0.838760\pi$$
$$462$$ 0 0
$$463$$ 38.8811i 1.80696i −0.428632 0.903479i $$-0.641004\pi$$
0.428632 0.903479i $$-0.358996\pi$$
$$464$$ −2.34269 −0.108757
$$465$$ −9.68693 −0.449220
$$466$$ 9.52699i 0.441329i
$$467$$ 6.64116 + 11.5028i 0.307316 + 0.532287i 0.977774 0.209660i $$-0.0672358\pi$$
−0.670458 + 0.741947i $$0.733902\pi$$
$$468$$ 17.0298 9.35538i 0.787203 0.432453i
$$469$$ 0 0
$$470$$ 1.02856 0.593841i 0.0474440 0.0273918i
$$471$$ −8.65571 + 14.9921i −0.398834 + 0.690801i
$$472$$ −6.57358 11.3858i −0.302574 0.524073i
$$473$$ 35.9807 + 20.7734i 1.65439 + 0.955164i
$$474$$ 17.3390i 0.796406i
$$475$$ −8.47228 4.89147i −0.388735 0.224436i
$$476$$ 0 0
$$477$$ −0.813975 + 1.40985i −0.0372694 + 0.0645524i
$$478$$ −6.04205 + 10.4651i −0.276357 + 0.478664i
$$479$$ 6.63512i 0.303166i 0.988445 + 0.151583i $$0.0484371\pi$$
−0.988445 + 0.151583i $$0.951563\pi$$
$$480$$ −24.3654 + 42.2021i −1.11212 + 1.92625i
$$481$$ −12.1552 + 20.0566i −0.554229 + 0.914504i
$$482$$ 11.8153 0.538172
$$483$$ 0 0
$$484$$ 16.0697 + 27.8335i 0.730439 + 1.26516i
$$485$$ 10.8381 0.492133
$$486$$ 14.8749 + 8.58804i 0.674740 + 0.389561i
$$487$$ −28.9860 + 16.7351i −1.31348 + 0.758338i −0.982671 0.185359i $$-0.940655\pi$$
−0.330809 + 0.943698i $$0.607322\pi$$
$$488$$ 3.16522i 0.143283i
$$489$$ 6.95047i 0.314311i
$$490$$ 0 0
$$491$$ −18.6643 32.3276i −0.842310 1.45892i −0.887937 0.459966i $$-0.847862\pi$$
0.0456264 0.998959i $$-0.485472\pi$$
$$492$$ 11.3699 + 6.56439i 0.512593 + 0.295946i
$$493$$ 8.09684 14.0241i 0.364663 0.631615i
$$494$$ −4.96977 3.01189i −0.223601 0.135511i
$$495$$ −38.3076 66.3507i −1.72180 2.98224i
$$496$$ −0.389483 + 0.224868i −0.0174883 + 0.0100969i
$$497$$ 0 0
$$498$$ 6.78954 11.7598i 0.304246 0.526970i
$$499$$ −29.5598 + 17.0663i −1.32328 + 0.763994i −0.984250 0.176783i $$-0.943431\pi$$
−0.339027 + 0.940777i $$0.610098\pi$$
$$500$$ −0.00424050 + 0.00244826i −0.000189641 + 0.000109489i
$$501$$ −8.95342 + 5.16926i −0.400009 + 0.230946i
$$502$$ −6.14405 + 3.54727i −0.274223 + 0.158322i
$$503$$ −7.65447 + 13.2579i −0.341296 + 0.591142i −0.984674 0.174407i $$-0.944199\pi$$
0.643378 + 0.765549i $$0.277533\pi$$
$$504$$ 0 0
$$505$$ −36.5022 + 21.0745i −1.62433 + 0.937805i
$$506$$ 6.67907 + 11.5685i 0.296921 + 0.514282i
$$507$$ −34.5526 1.46950i −1.53453 0.0652630i
$$508$$ 4.05195 7.01819i 0.179776 0.311382i
$$509$$ 16.0189 + 9.24851i 0.710025 + 0.409933i 0.811070 0.584949i $$-0.198885\pi$$
−0.101046 + 0.994882i $$0.532219\pi$$
$$510$$ −9.35133 16.1970i −0.414084 0.717214i
$$511$$ 0 0
$$512$$ 4.39924i 0.194421i
$$513$$ 5.60801i 0.247599i
$$514$$ −7.39178 + 4.26765i −0.326037 + 0.188238i
$$515$$ −31.8892 18.4112i −1.40520 0.811295i
$$516$$ −24.5830 −1.08221
$$517$$ 1.35515 + 2.34718i 0.0595992 + 0.103229i
$$518$$ 0 0
$$519$$ −37.1823 −1.63212
$$520$$ 27.3361 15.0172i 1.19877 0.658547i
$$521$$ −11.7932 + 20.4265i −0.516671 + 0.894901i 0.483141 + 0.875542i $$0.339496\pi$$
−0.999813 + 0.0193585i $$0.993838\pi$$
$$522$$ 20.1414i 0.881564i
$$523$$ −6.15294 + 10.6572i −0.269049 + 0.466007i −0.968617 0.248560i $$-0.920043\pi$$
0.699567 + 0.714567i $$0.253376\pi$$
$$524$$ −6.75529 + 11.7005i −0.295106 + 0.511139i
$$525$$ 0 0
$$526$$ 15.7498 + 9.09312i 0.686722 + 0.396479i
$$527$$ 3.10877i 0.135420i
$$528$$ −5.34711 3.08715i −0.232703 0.134351i
$$529$$ 7.77515 + 13.4670i 0.338050 + 0.585520i
$$530$$ −0.519902 + 0.900497i −0.0225831 + 0.0391151i
$$531$$ −16.9691 + 9.79712i −0.736397 + 0.425159i
$$532$$ 0 0
$$533$$ −6.48183 11.7990i −0.280759 0.511072i
$$534$$ 3.90129 + 6.75724i 0.168825 + 0.292414i
$$535$$ 12.4259i 0.537220i
$$536$$ 17.1777 0.741962
$$537$$ 67.2636 2.90264
$$538$$ 10.6567i 0.459444i
$$539$$ 0 0
$$540$$ 10.3720 + 5.98829i 0.446341 + 0.257695i
$$541$$ 16.8365 9.72054i 0.723857 0.417919i −0.0923139 0.995730i $$-0.529426\pi$$
0.816170 + 0.577811i $$0.196093\pi$$
$$542$$ −7.27813 12.6061i −0.312623 0.541478i
$$543$$ −2.29975 −0.0986919
$$544$$ −13.5437 7.81944i −0.580680 0.335256i
$$545$$ 35.5841 1.52425
$$546$$ 0 0
$$547$$ 40.2163 1.71953 0.859763 0.510693i $$-0.170611\pi$$
0.859763 + 0.510693i $$0.170611\pi$$
$$548$$ −22.8334 13.1829i −0.975395 0.563145i
$$549$$ −4.71738 −0.201333
$$550$$ −12.2325 21.1873i −0.521595 0.903429i
$$551$$ 10.1665 5.86963i 0.433107 0.250055i
$$552$$ −17.2024 9.93184i −0.732185 0.422727i
$$553$$ 0 0
$$554$$ 14.8364i 0.630337i
$$555$$ −54.7168 −2.32260
$$556$$ −26.8680 −1.13945
$$557$$ 7.96399i 0.337445i 0.985664 + 0.168722i $$0.0539642\pi$$
−0.985664 + 0.168722i $$0.946036\pi$$
$$558$$ −1.93331 3.34860i −0.0818437 0.141757i
$$559$$ 21.5574 + 13.0647i 0.911781 + 0.552578i
$$560$$ 0 0
$$561$$ 36.9615 21.3397i 1.56052 0.900965i
$$562$$ 1.00547 1.74153i 0.0424133 0.0734620i
$$563$$ −0.711981 1.23319i −0.0300064 0.0519726i 0.850632 0.525761i $$-0.176219\pi$$
−0.880639 + 0.473789i $$0.842886\pi$$
$$564$$ −1.38881 0.801831i −0.0584795 0.0337632i
$$565$$ 18.2585i 0.768140i
$$566$$ −20.4865 11.8279i −0.861113 0.497164i
$$567$$ 0 0
$$568$$ −6.16506 + 10.6782i −0.258680 + 0.448047i
$$569$$ −9.25946 + 16.0379i −0.388177 + 0.672342i −0.992204 0.124622i $$-0.960228\pi$$
0.604028 + 0.796963i $$0.293562\pi$$
$$570$$ 13.5581i 0.567886i
$$571$$ 2.17883 3.77384i 0.0911812 0.157930i −0.816827 0.576882i $$-0.804269\pi$$
0.908008 + 0.418952i $$0.137602\pi$$
$$572$$ 13.6360 + 24.8220i 0.570151 + 1.03786i
$$573$$ 39.0202 1.63009
$$574$$ 0 0
$$575$$ 6.82194 + 11.8159i 0.284494 + 0.492759i
$$576$$ −16.2667 −0.677778
$$577$$ −8.28280 4.78208i −0.344818 0.199081i 0.317583 0.948231i $$-0.397129\pi$$
−0.662400 + 0.749150i $$0.730462\pi$$
$$578$$ −6.92674 + 3.99916i −0.288115 + 0.166343i
$$579$$ 43.8839i 1.82375i
$$580$$ 25.0706i 1.04100i
$$581$$ 0 0
$$582$$ 3.75466 + 6.50327i 0.155636 + 0.269569i
$$583$$ −2.05494 1.18642i −0.0851068 0.0491364i
$$584$$ 11.3608 19.6775i 0.470114 0.814262i
$$585$$ −22.3813 40.7411i −0.925352 1.68444i
$$586$$ −12.0778 20.9194i −0.498929 0.864171i
$$587$$ −2.04428 + 1.18027i −0.0843765 + 0.0487148i −0.541595 0.840640i $$-0.682179\pi$$
0.457218 + 0.889355i $$0.348846\pi$$
$$588$$ 0 0
$$589$$ 1.12682 1.95171i 0.0464297 0.0804186i
$$590$$ −10.8385 + 6.25762i −0.446214 + 0.257622i
$$591$$ 25.3661 14.6452i 1.04342 0.602421i
$$592$$ −2.20000 + 1.27017i −0.0904194 + 0.0522037i
$$593$$ 35.0127 20.2146i 1.43780 0.830114i 0.440103 0.897947i $$-0.354942\pi$$
0.997697 + 0.0678337i $$0.0216087\pi$$
$$594$$ 7.01219 12.1455i 0.287714 0.498335i
$$595$$ 0 0
$$596$$ 12.2665 7.08207i 0.502455 0.290093i
$$597$$ −28.2147 48.8693i −1.15475 2.00009i
$$598$$ 3.90226 + 7.10336i 0.159575 + 0.290478i
$$599$$ 19.2936 33.4176i 0.788316 1.36540i −0.138681 0.990337i $$-0.544286\pi$$
0.926998 0.375067i $$-0.122380\pi$$
$$600$$ 31.5057 + 18.1898i 1.28621 + 0.742596i
$$601$$ −4.08115 7.06877i −0.166474 0.288341i 0.770704 0.637193i $$-0.219905\pi$$
−0.937178 + 0.348852i $$0.886571\pi$$
$$602$$ 0 0
$$603$$ 25.6012i 1.04256i
$$604$$ 11.5576i 0.470274i
$$605$$ 66.5872 38.4442i 2.70716 1.56298i
$$606$$ −25.2910 14.6018i −1.02738 0.593157i
$$607$$ 7.58525 0.307876 0.153938 0.988081i $$-0.450804\pi$$
0.153938 + 0.988081i $$0.450804\pi$$
$$608$$ −5.66853 9.81819i −0.229889 0.398180i
$$609$$ 0 0
$$610$$ −3.01308 −0.121996
$$611$$ 0.791746 + 1.44123i 0.0320306 + 0.0583060i
$$612$$ −7.27419 + 12.5993i −0.294042 + 0.509295i
$$613$$ 15.5778i 0.629183i −0.949227 0.314592i $$-0.898132\pi$$
0.949227 0.314592i $$-0.101868\pi$$
$$614$$ −2.91090 + 5.04183i −0.117474 + 0.203472i
$$615$$ 15.7043 27.2006i 0.633258 1.09683i
$$616$$ 0 0
$$617$$ 20.6709 + 11.9343i 0.832177 + 0.480458i 0.854598 0.519291i $$-0.173804\pi$$
−0.0224202 + 0.999749i $$0.507137\pi$$
$$618$$ 25.5129i 1.02628i
$$619$$ 16.8843 + 9.74814i 0.678636 + 0.391811i 0.799341 0.600878i $$-0.205182\pi$$
−0.120705 + 0.992688i $$0.538515\pi$$
$$620$$ 2.40646 + 4.16810i 0.0966456 + 0.167395i
$$621$$ −3.91063 + 6.77341i −0.156928 + 0.271807i
$$622$$ 15.8824 9.16972i 0.636827 0.367672i
$$623$$ 0 0
$$624$$ −3.20366 1.94155i −0.128249 0.0777244i
$$625$$ 12.5029 + 21.6557i 0.500117 + 0.866228i
$$626$$ 23.1287i 0.924410i
$$627$$ 30.9396 1.23561
$$628$$ 8.60111 0.343222
$$629$$ 17.5599i 0.700161i
$$630$$ 0 0
$$631$$ −22.2239 12.8309i −0.884718 0.510792i −0.0125066 0.999922i $$-0.503981\pi$$
−0.872211 + 0.489130i $$0.837314\pi$$
$$632$$ −18.7496 + 10.8251i −0.745820 + 0.430600i
$$633$$ 23.8572 + 41.3219i 0.948238 + 1.64240i
$$634$$ 16.0721 0.638304
$$635$$ −16.7899 9.69366i −0.666287 0.384681i
$$636$$ 1.40399 0.0556719
$$637$$ 0 0
$$638$$ 29.3573 1.16227
$$639$$ 15.9145 + 9.18826i 0.629569 + 0.363482i
$$640$$ 26.2458 1.03746
$$641$$ −0.553020 0.957859i −0.0218430 0.0378332i 0.854897 0.518797i $$-0.173620\pi$$
−0.876740 + 0.480964i $$0.840287\pi$$
$$642$$ 7.45603 4.30474i 0.294266 0.169895i
$$643$$ 10.9437 + 6.31833i 0.431576 + 0.249171i 0.700018 0.714125i $$-0.253175\pi$$
−0.268442 + 0.963296i $$0.586509\pi$$
$$644$$ 0 0
$$645$$ 58.8110i 2.31568i
$$646$$ 4.35112 0.171192
$$647$$ −25.7148 −1.01095 −0.505477 0.862840i $$-0.668683\pi$$
−0.505477 + 0.862840i $$0.668683\pi$$
$$648$$ 12.6066i 0.495236i
$$649$$ −14.2799 24.7335i −0.560535 0.970875i
$$650$$ −7.14685 13.0096i −0.280323 0.510277i
$$651$$ 0 0
$$652$$ −2.99066 + 1.72666i −0.117123 + 0.0676211i
$$653$$ −12.6303 + 21.8764i −0.494263 + 0.856089i −0.999978 0.00661158i $$-0.997895\pi$$
0.505715 + 0.862701i $$0.331229\pi$$
$$654$$ 12.3275 + 21.3518i 0.482041 + 0.834920i
$$655$$ 27.9916 + 16.1610i 1.09372 + 0.631461i
$$656$$ 1.45821i 0.0569335i
$$657$$ −29.3269 16.9319i −1.14415 0.660577i
$$658$$ 0 0
$$659$$ −11.4882 + 19.8982i −0.447517 + 0.775123i −0.998224 0.0595764i $$-0.981025\pi$$
0.550707 + 0.834699i $$0.314358\pi$$
$$660$$ −33.0376 + 57.2228i −1.28599 + 2.22739i
$$661$$ 30.4326i 1.18369i 0.806051 + 0.591845i $$0.201600\pi$$
−0.806051 + 0.591845i $$0.798400\pi$$
$$662$$ −6.43641 + 11.1482i −0.250158 + 0.433287i
$$663$$ 22.6954 12.4678i 0.881415 0.484208i
$$664$$ −16.9554 −0.657998
$$665$$ 0 0
$$666$$ −10.9204 18.9146i −0.423155 0.732926i
$$667$$ −16.3723 −0.633937
$$668$$ 4.44847 + 2.56833i 0.172117 + 0.0993715i
$$669$$ −36.9339 + 21.3238i −1.42795 + 0.824425i
$$670$$ 16.3520i 0.631733i
$$671$$ 6.87586i 0.265440i
$$672$$ 0 0
$$673$$ 5.41933 + 9.38656i 0.208900 + 0.361825i 0.951368 0.308056i $$-0.0996784\pi$$
−0.742468 + 0.669881i $$0.766345\pi$$
$$674$$ −15.5126 8.95620i −0.597523 0.344980i
$$675$$ 7.16218 12.4053i 0.275672 0.477479i
$$676$$ 7.95135 + 15.2324i 0.305821 + 0.585861i
$$677$$ 9.06044 + 15.6931i 0.348221 + 0.603137i 0.985934 0.167138i $$-0.0534525\pi$$
−0.637712 + 0.770275i $$0.720119\pi$$
$$678$$ −10.9558 + 6.32532i −0.420754 + 0.242923i
$$679$$ 0 0
$$680$$ −11.6765 + 20.2242i −0.447772 + 0.775564i
$$681$$ 37.7261 21.7812i 1.44567 0.834656i
$$682$$ 4.88078 2.81792i 0.186895 0.107904i
$$683$$ −32.7662 + 18.9176i −1.25376 + 0.723861i −0.971855 0.235580i $$-0.924301\pi$$
−0.281909 + 0.959441i $$0.590968\pi$$
$$684$$ −9.13357 + 5.27327i −0.349231 + 0.201628i
$$685$$ −31.5380 + 54.6254i −1.20500 + 2.08713i
$$686$$ 0 0
$$687$$ 62.2288 35.9278i 2.37418 1.37073i
$$688$$ 1.36521 + 2.36462i 0.0520482 + 0.0901502i
$$689$$ −1.23119 0.746155i −0.0469047 0.0284262i
$$690$$ −9.45446 + 16.3756i −0.359925 + 0.623408i
$$691$$ −26.0034 15.0131i −0.989216 0.571124i −0.0841761 0.996451i $$-0.526826\pi$$
−0.905040 + 0.425327i $$0.860159\pi$$
$$692$$ 9.23693 + 15.9988i 0.351135 + 0.608184i
$$693$$ 0 0
$$694$$ 13.1432i 0.498907i
$$695$$ 64.2774i 2.43818i
$$696$$ −37.8059 + 21.8273i −1.43303 + 0.827360i
$$697$$ 8.72934 + 5.03988i 0.330647 + 0.190899i
$$698$$ −5.61423 −0.212502
$$699$$ 15.3873 + 26.6516i 0.582001 + 1.00805i
$$700$$ 0 0
$$701$$ 0.116177 0.00438796 0.00219398 0.999998i $$-0.499302\pi$$
0.00219398 + 0.999998i $$0.499302\pi$$
$$702$$ 4.41006 7.27682i 0.166447 0.274646i
$$703$$ 6.36485 11.0242i 0.240055 0.415787i
$$704$$ 23.7097i 0.893591i
$$705$$ −1.91825 + 3.32251i −0.0722456 + 0.125133i
$$706$$ 5.76624 9.98741i 0.217015 0.375881i
$$707$$ 0 0
$$708$$ 14.6347 + 8.44932i 0.550004 + 0.317545i
$$709$$ 6.72993i 0.252748i −0.991983 0.126374i $$-0.959666\pi$$
0.991983 0.126374i $$-0.0403339\pi$$
$$710$$ 10.1649 + 5.86873i 0.381483 + 0.220249i
$$711$$ 16.1335 + 27.9440i 0.605053 + 1.04798i
$$712$$ 4.87132 8.43738i 0.182561 0.316204i
$$713$$ −2.72196 + 1.57153i −0.101938 + 0.0588541i
$$714$$ 0 0
$$715$$ 59.3826 32.6221i 2.22078 1.22000i
$$716$$ −16.7098 28.9423i −0.624476 1.08162i
$$717$$ 39.0347i 1.45778i
$$718$$ −4.45950 −0.166427
$$719$$ −46.8078 −1.74564 −0.872818 0.488046i $$-0.837710\pi$$
−0.872818 + 0.488046i $$0.837710\pi$$
$$720$$ 5.03509i 0.187647i
$$721$$ 0 0
$$722$$ −10.8195 6.24666i −0.402661 0.232476i
$$723$$ −33.0530 + 19.0832i −1.22926 + 0.709711i
$$724$$ 0.571312 + 0.989541i 0.0212326 + 0.0367760i
$$725$$ 29.9852 1.11362
$$726$$ 46.1359 + 26.6366i 1.71226 + 0.988576i
$$727$$ 13.3362 0.494611 0.247305 0.968938i $$-0.420455\pi$$
0.247305 + 0.968938i $$0.420455\pi$$
$$728$$ 0 0
$$729$$ −41.6582 −1.54290
$$730$$ −18.7317 10.8148i −0.693291 0.400272i
$$731$$ −18.8739 −0.698076
$$732$$ 2.03420 + 3.52334i 0.0751863 + 0.130226i
$$733$$ 25.5142 14.7306i 0.942387 0.544087i 0.0516792 0.998664i $$-0.483543\pi$$
0.890708 + 0.454576i $$0.150209\pi$$
$$734$$ −21.4193 12.3664i −0.790599 0.456453i
$$735$$ 0 0
$$736$$ 15.8113i 0.582814i
$$737$$ 37.3153 1.37453
$$738$$ 12.5370 0.461494
$$739$$ 12.0302i 0.442537i −0.975213 0.221269i $$-0.928980\pi$$
0.975213 0.221269i $$-0.0710198\pi$$
$$740$$ 13.5929 + 23.5436i 0.499685 + 0.865480i
$$741$$ 18.7674 + 0.398904i 0.689438 + 0.0146541i
$$742$$ 0 0
$$743$$ −18.9509 + 10.9413i −0.695242 + 0.401398i −0.805573 0.592497i $$-0.798142\pi$$
0.110331 + 0.993895i $$0.464809\pi$$
$$744$$ −4.19027 + 7.25777i −0.153623 + 0.266083i
$$745$$ −16.9427 29.3457i −0.620734 1.07514i
$$746$$ −15.2699 8.81607i −0.559070 0.322779i
$$747$$ 25.2700i 0.924580i
$$748$$ −18.3642 10.6026i −0.671461 0.387668i
$$749$$ 0 0
$$750$$ −0.00405815 + 0.00702892i −0.000148183 + 0.000256660i
$$751$$ 17.3746 30.0937i 0.634008 1.09813i −0.352717 0.935730i $$-0.614742\pi$$
0.986724 0.162403i $$-0.0519245\pi$$
$$752$$ 0.178118i 0.00649529i
$$753$$ 11.4586 19.8468i 0.417574 0.723259i
$$754$$ 17.8076 + 0.378504i 0.648515 + 0.0137843i
$$755$$ −27.6498 −1.00628
$$756$$ 0 0
$$757$$ −21.9632 38.0413i −0.798265 1.38264i −0.920745 0.390164i $$-0.872418\pi$$
0.122481 0.992471i $$-0.460915\pi$$
$$758$$ 7.80447 0.283471
$$759$$ −37.3691 21.5751i −1.35641 0.783126i
$$760$$ −14.6611 + 8.46461i −0.531815 + 0.307044i
$$761$$ 0.141391i 0.00512543i −0.999997 0.00256272i $$-0.999184\pi$$
0.999997 0.00256272i $$-0.000815739\pi$$
$$762$$ 13.4328i 0.486618i
$$763$$ 0 0
$$764$$ −9.69352 16.7897i −0.350699 0.607429i
$$765$$ 30.1418 + 17.4024i 1.08978 + 0.629183i
$$766$$ 2.23620 3.87322i 0.0807973 0.139945i
$$767$$ −8.34305 15.1870i −0.301250 0.548372i
$$768$$ 19.7062 + 34.1321i 0.711086 + 1.23164i
$$769$$ 11.8200 6.82429i 0.426241 0.246090i −0.271503 0.962438i $$-0.587521\pi$$
0.697744 + 0.716347i $$0.254187\pi$$
$$770$$ 0 0
$$771$$ 13.7856 23.8773i 0.496475 0.859920i
$$772$$ 18.8824 10.9018i 0.679593 0.392363i
$$773$$ −15.2328 + 8.79469i −0.547887 + 0.316323i −0.748269 0.663395i $$-0.769115\pi$$
0.200382 + 0.979718i $$0.435782\pi$$
$$774$$ −20.3299 + 11.7375i −0.730744 + 0.421895i
$$775$$ 4.98518 2.87820i 0.179073 0.103388i
$$776$$ 4.68824 8.12026i 0.168298 0.291500i
$$777$$ 0 0
$$778$$ 7.59022 4.38221i 0.272123 0.157110i
$$779$$ 3.65356 + 6.32814i 0.130902 + 0.226729i
$$780$$ −20.7778 + 34.2844i −0.743965 + 1.22758i
$$781$$