# Properties

 Label 75.9.c.c.26.1 Level $75$ Weight $9$ Character 75.26 Analytic conductor $30.553$ Analytic rank $0$ Dimension $2$ CM no Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$75 = 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$9$$ Character orbit: $$[\chi]$$ $$=$$ 75.c (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$30.5533957546$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-14})$$ Defining polynomial: $$x^{2} + 14$$ x^2 + 14 Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$2\cdot 3$$ Twist minimal: no (minimal twist has level 3) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 26.1 Root $$-3.74166i$$ of defining polynomial Character $$\chi$$ $$=$$ 75.26 Dual form 75.9.c.c.26.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-22.4499i q^{2} +(-45.0000 + 67.3498i) q^{3} -248.000 q^{4} +(1512.00 + 1010.25i) q^{6} +1750.00 q^{7} -179.600i q^{8} +(-2511.00 - 6061.48i) q^{9} +O(q^{10})$$ $$q-22.4499i q^{2} +(-45.0000 + 67.3498i) q^{3} -248.000 q^{4} +(1512.00 + 1010.25i) q^{6} +1750.00 q^{7} -179.600i q^{8} +(-2511.00 - 6061.48i) q^{9} +6959.48i q^{11} +(11160.0 - 16702.8i) q^{12} -25730.0 q^{13} -39287.4i q^{14} -67520.0 q^{16} -74893.0i q^{17} +(-136080. + 56371.8i) q^{18} +18938.0 q^{19} +(-78750.0 + 117862. i) q^{21} +156240. q^{22} +470461. i q^{23} +(12096.0 + 8081.98i) q^{24} +577637. i q^{26} +(521235. + 103651. i) q^{27} -434000. q^{28} +460897. i q^{29} -351478. q^{31} +1.46984e6i q^{32} +(-468720. - 313177. i) q^{33} -1.68134e6 q^{34} +(622728. + 1.50325e6i) q^{36} -1.33517e6 q^{37} -425157. i q^{38} +(1.15785e6 - 1.73291e6i) q^{39} +1.87547e6i q^{41} +(2.64600e6 + 1.76793e6i) q^{42} +3.52615e6 q^{43} -1.72595e6i q^{44} +1.05618e7 q^{46} +4.08104e6i q^{47} +(3.03840e6 - 4.54746e6i) q^{48} -2.70230e6 q^{49} +(5.04403e6 + 3.37019e6i) q^{51} +6.38104e6 q^{52} +6.60177e6i q^{53} +(2.32697e6 - 1.17017e7i) q^{54} -314299. i q^{56} +(-852210. + 1.27547e6i) q^{57} +1.03471e7 q^{58} +1.37149e7i q^{59} +753602. q^{61} +7.89066e6i q^{62} +(-4.39425e6 - 1.06076e7i) q^{63} +1.57128e7 q^{64} +(-7.03080e6 + 1.05227e7i) q^{66} -2.26889e6 q^{67} +1.85735e7i q^{68} +(-3.16855e7 - 2.11707e7i) q^{69} +1.70220e7i q^{71} +(-1.08864e6 + 450974. i) q^{72} -2.76728e7 q^{73} +2.99745e7i q^{74} -4.69662e6 q^{76} +1.21791e7i q^{77} +(-3.89038e7 - 2.59937e7i) q^{78} -2.29810e7 q^{79} +(-3.04365e7 + 3.04408e7i) q^{81} +4.21042e7 q^{82} +4.63952e7i q^{83} +(1.95300e7 - 2.92298e7i) q^{84} -7.91619e7i q^{86} +(-3.10414e7 - 2.07404e7i) q^{87} +1.24992e6 q^{88} +7.26152e7i q^{89} -4.50275e7 q^{91} -1.16674e8i q^{92} +(1.58165e7 - 2.36720e7i) q^{93} +9.16191e7 q^{94} +(-9.89937e7 - 6.61429e7i) q^{96} -1.47271e8 q^{97} +6.06665e7i q^{98} +(4.21848e7 - 1.74753e7i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 90 q^{3} - 496 q^{4} + 3024 q^{6} + 3500 q^{7} - 5022 q^{9}+O(q^{10})$$ 2 * q - 90 * q^3 - 496 * q^4 + 3024 * q^6 + 3500 * q^7 - 5022 * q^9 $$2 q - 90 q^{3} - 496 q^{4} + 3024 q^{6} + 3500 q^{7} - 5022 q^{9} + 22320 q^{12} - 51460 q^{13} - 135040 q^{16} - 272160 q^{18} + 37876 q^{19} - 157500 q^{21} + 312480 q^{22} + 24192 q^{24} + 1042470 q^{27} - 868000 q^{28} - 702956 q^{31} - 937440 q^{33} - 3362688 q^{34} + 1245456 q^{36} - 2670340 q^{37} + 2315700 q^{39} + 5292000 q^{42} + 7052300 q^{43} + 21123648 q^{46} + 6076800 q^{48} - 5404602 q^{49} + 10088064 q^{51} + 12762080 q^{52} + 4653936 q^{54} - 1704420 q^{57} + 20694240 q^{58} + 1507204 q^{61} - 8788500 q^{63} + 31425536 q^{64} - 14061600 q^{66} - 4537780 q^{67} - 63370944 q^{69} - 2177280 q^{72} - 55345540 q^{73} - 9393248 q^{76} - 77807520 q^{78} - 45961964 q^{79} - 60872958 q^{81} + 84208320 q^{82} + 39060000 q^{84} - 62082720 q^{87} + 2499840 q^{88} - 90055000 q^{91} + 31633020 q^{93} + 183238272 q^{94} - 197987328 q^{96} - 294542020 q^{97} + 84369600 q^{99}+O(q^{100})$$ 2 * q - 90 * q^3 - 496 * q^4 + 3024 * q^6 + 3500 * q^7 - 5022 * q^9 + 22320 * q^12 - 51460 * q^13 - 135040 * q^16 - 272160 * q^18 + 37876 * q^19 - 157500 * q^21 + 312480 * q^22 + 24192 * q^24 + 1042470 * q^27 - 868000 * q^28 - 702956 * q^31 - 937440 * q^33 - 3362688 * q^34 + 1245456 * q^36 - 2670340 * q^37 + 2315700 * q^39 + 5292000 * q^42 + 7052300 * q^43 + 21123648 * q^46 + 6076800 * q^48 - 5404602 * q^49 + 10088064 * q^51 + 12762080 * q^52 + 4653936 * q^54 - 1704420 * q^57 + 20694240 * q^58 + 1507204 * q^61 - 8788500 * q^63 + 31425536 * q^64 - 14061600 * q^66 - 4537780 * q^67 - 63370944 * q^69 - 2177280 * q^72 - 55345540 * q^73 - 9393248 * q^76 - 77807520 * q^78 - 45961964 * q^79 - 60872958 * q^81 + 84208320 * q^82 + 39060000 * q^84 - 62082720 * q^87 + 2499840 * q^88 - 90055000 * q^91 + 31633020 * q^93 + 183238272 * q^94 - 197987328 * q^96 - 294542020 * q^97 + 84369600 * q^99

## Character values

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

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

## Coefficient data

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

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 22.4499i 1.40312i −0.712610 0.701561i $$-0.752487\pi$$
0.712610 0.701561i $$-0.247513\pi$$
$$3$$ −45.0000 + 67.3498i −0.555556 + 0.831479i
$$4$$ −248.000 −0.968750
$$5$$ 0 0
$$6$$ 1512.00 + 1010.25i 1.16667 + 0.779512i
$$7$$ 1750.00 0.728863 0.364431 0.931230i $$-0.381263\pi$$
0.364431 + 0.931230i $$0.381263\pi$$
$$8$$ 179.600i 0.0438475i
$$9$$ −2511.00 6061.48i −0.382716 0.923866i
$$10$$ 0 0
$$11$$ 6959.48i 0.475342i 0.971346 + 0.237671i $$0.0763840\pi$$
−0.971346 + 0.237671i $$0.923616\pi$$
$$12$$ 11160.0 16702.8i 0.538194 0.805496i
$$13$$ −25730.0 −0.900879 −0.450439 0.892807i $$-0.648733\pi$$
−0.450439 + 0.892807i $$0.648733\pi$$
$$14$$ 39287.4i 1.02268i
$$15$$ 0 0
$$16$$ −67520.0 −1.03027
$$17$$ 74893.0i 0.896697i −0.893859 0.448348i $$-0.852012\pi$$
0.893859 0.448348i $$-0.147988\pi$$
$$18$$ −136080. + 56371.8i −1.29630 + 0.536997i
$$19$$ 18938.0 0.145318 0.0726590 0.997357i $$-0.476852\pi$$
0.0726590 + 0.997357i $$0.476852\pi$$
$$20$$ 0 0
$$21$$ −78750.0 + 117862.i −0.404924 + 0.606035i
$$22$$ 156240. 0.666963
$$23$$ 470461.i 1.68117i 0.541678 + 0.840586i $$0.317789\pi$$
−0.541678 + 0.840586i $$0.682211\pi$$
$$24$$ 12096.0 + 8081.98i 0.0364583 + 0.0243597i
$$25$$ 0 0
$$26$$ 577637.i 1.26404i
$$27$$ 521235. + 103651.i 0.980796 + 0.195038i
$$28$$ −434000. −0.706086
$$29$$ 460897.i 0.651647i 0.945431 + 0.325823i $$0.105641\pi$$
−0.945431 + 0.325823i $$0.894359\pi$$
$$30$$ 0 0
$$31$$ −351478. −0.380585 −0.190292 0.981727i $$-0.560944\pi$$
−0.190292 + 0.981727i $$0.560944\pi$$
$$32$$ 1.46984e6i 1.40175i
$$33$$ −468720. 313177.i −0.395237 0.264079i
$$34$$ −1.68134e6 −1.25817
$$35$$ 0 0
$$36$$ 622728. + 1.50325e6i 0.370756 + 0.894995i
$$37$$ −1.33517e6 −0.712409 −0.356205 0.934408i $$-0.615929\pi$$
−0.356205 + 0.934408i $$0.615929\pi$$
$$38$$ 425157.i 0.203899i
$$39$$ 1.15785e6 1.73291e6i 0.500488 0.749062i
$$40$$ 0 0
$$41$$ 1.87547e6i 0.663704i 0.943331 + 0.331852i $$0.107673\pi$$
−0.943331 + 0.331852i $$0.892327\pi$$
$$42$$ 2.64600e6 + 1.76793e6i 0.850340 + 0.568157i
$$43$$ 3.52615e6 1.03140 0.515700 0.856769i $$-0.327532\pi$$
0.515700 + 0.856769i $$0.327532\pi$$
$$44$$ 1.72595e6i 0.460488i
$$45$$ 0 0
$$46$$ 1.05618e7 2.35889
$$47$$ 4.08104e6i 0.836333i 0.908370 + 0.418167i $$0.137327\pi$$
−0.908370 + 0.418167i $$0.862673\pi$$
$$48$$ 3.03840e6 4.54746e6i 0.572374 0.856651i
$$49$$ −2.70230e6 −0.468759
$$50$$ 0 0
$$51$$ 5.04403e6 + 3.37019e6i 0.745585 + 0.498165i
$$52$$ 6.38104e6 0.872726
$$53$$ 6.60177e6i 0.836675i 0.908292 + 0.418337i $$0.137387\pi$$
−0.908292 + 0.418337i $$0.862613\pi$$
$$54$$ 2.32697e6 1.17017e7i 0.273663 1.37618i
$$55$$ 0 0
$$56$$ 314299.i 0.0319589i
$$57$$ −852210. + 1.27547e6i −0.0807323 + 0.120829i
$$58$$ 1.03471e7 0.914340
$$59$$ 1.37149e7i 1.13184i 0.824461 + 0.565919i $$0.191479\pi$$
−0.824461 + 0.565919i $$0.808521\pi$$
$$60$$ 0 0
$$61$$ 753602. 0.0544280 0.0272140 0.999630i $$-0.491336\pi$$
0.0272140 + 0.999630i $$0.491336\pi$$
$$62$$ 7.89066e6i 0.534007i
$$63$$ −4.39425e6 1.06076e7i −0.278948 0.673372i
$$64$$ 1.57128e7 0.936554
$$65$$ 0 0
$$66$$ −7.03080e6 + 1.05227e7i −0.370535 + 0.554566i
$$67$$ −2.26889e6 −0.112594 −0.0562969 0.998414i $$-0.517929\pi$$
−0.0562969 + 0.998414i $$0.517929\pi$$
$$68$$ 1.85735e7i 0.868675i
$$69$$ −3.16855e7 2.11707e7i −1.39786 0.933985i
$$70$$ 0 0
$$71$$ 1.70220e7i 0.669849i 0.942245 + 0.334925i $$0.108711\pi$$
−0.942245 + 0.334925i $$0.891289\pi$$
$$72$$ −1.08864e6 + 450974.i −0.0405093 + 0.0167812i
$$73$$ −2.76728e7 −0.974454 −0.487227 0.873275i $$-0.661992\pi$$
−0.487227 + 0.873275i $$0.661992\pi$$
$$74$$ 2.99745e7i 0.999597i
$$75$$ 0 0
$$76$$ −4.69662e6 −0.140777
$$77$$ 1.21791e7i 0.346459i
$$78$$ −3.89038e7 2.59937e7i −1.05103 0.702246i
$$79$$ −2.29810e7 −0.590011 −0.295006 0.955496i $$-0.595322\pi$$
−0.295006 + 0.955496i $$0.595322\pi$$
$$80$$ 0 0
$$81$$ −3.04365e7 + 3.04408e7i −0.707057 + 0.707157i
$$82$$ 4.21042e7 0.931257
$$83$$ 4.63952e7i 0.977599i 0.872396 + 0.488799i $$0.162565\pi$$
−0.872396 + 0.488799i $$0.837435\pi$$
$$84$$ 1.95300e7 2.92298e7i 0.392270 0.587096i
$$85$$ 0 0
$$86$$ 7.91619e7i 1.44718i
$$87$$ −3.10414e7 2.07404e7i −0.541831 0.362026i
$$88$$ 1.24992e6 0.0208426
$$89$$ 7.26152e7i 1.15736i 0.815555 + 0.578679i $$0.196432\pi$$
−0.815555 + 0.578679i $$0.803568\pi$$
$$90$$ 0 0
$$91$$ −4.50275e7 −0.656617
$$92$$ 1.16674e8i 1.62864i
$$93$$ 1.58165e7 2.36720e7i 0.211436 0.316448i
$$94$$ 9.16191e7 1.17348
$$95$$ 0 0
$$96$$ −9.89937e7 6.61429e7i −1.16553 0.778751i
$$97$$ −1.47271e8 −1.66353 −0.831764 0.555129i $$-0.812669\pi$$
−0.831764 + 0.555129i $$0.812669\pi$$
$$98$$ 6.06665e7i 0.657726i
$$99$$ 4.21848e7 1.74753e7i 0.439152 0.181921i
$$100$$ 0 0
$$101$$ 1.03545e8i 0.995045i −0.867451 0.497522i $$-0.834243\pi$$
0.867451 0.497522i $$-0.165757\pi$$
$$102$$ 7.56605e7 1.13238e8i 0.698986 1.04615i
$$103$$ 1.66064e8 1.47545 0.737726 0.675100i $$-0.235899\pi$$
0.737726 + 0.675100i $$0.235899\pi$$
$$104$$ 4.62110e6i 0.0395013i
$$105$$ 0 0
$$106$$ 1.48209e8 1.17396
$$107$$ 2.25540e7i 0.172063i 0.996292 + 0.0860316i $$0.0274186\pi$$
−0.996292 + 0.0860316i $$0.972581\pi$$
$$108$$ −1.29266e8 2.57055e7i −0.950146 0.188943i
$$109$$ −1.09975e8 −0.779091 −0.389546 0.921007i $$-0.627368\pi$$
−0.389546 + 0.921007i $$0.627368\pi$$
$$110$$ 0 0
$$111$$ 6.00826e7 8.99235e7i 0.395783 0.592354i
$$112$$ −1.18160e8 −0.750928
$$113$$ 2.87748e8i 1.76481i −0.470490 0.882405i $$-0.655923\pi$$
0.470490 0.882405i $$-0.344077\pi$$
$$114$$ 2.86343e7 + 1.91321e7i 0.169538 + 0.113277i
$$115$$ 0 0
$$116$$ 1.14303e8i 0.631283i
$$117$$ 6.46080e7 + 1.55962e8i 0.344781 + 0.832291i
$$118$$ 3.07899e8 1.58811
$$119$$ 1.31063e8i 0.653569i
$$120$$ 0 0
$$121$$ 1.65924e8 0.774050
$$122$$ 1.69183e7i 0.0763692i
$$123$$ −1.26312e8 8.43961e7i −0.551856 0.368724i
$$124$$ 8.71665e7 0.368691
$$125$$ 0 0
$$126$$ −2.38140e8 + 9.86507e7i −0.944822 + 0.391397i
$$127$$ −2.75994e8 −1.06092 −0.530462 0.847708i $$-0.677982\pi$$
−0.530462 + 0.847708i $$0.677982\pi$$
$$128$$ 2.35290e7i 0.0876523i
$$129$$ −1.58677e8 + 2.37486e8i −0.573000 + 0.857588i
$$130$$ 0 0
$$131$$ 2.89118e8i 0.981725i 0.871237 + 0.490862i $$0.163318\pi$$
−0.871237 + 0.490862i $$0.836682\pi$$
$$132$$ 1.16243e8 + 7.76678e7i 0.382886 + 0.255826i
$$133$$ 3.31415e7 0.105917
$$134$$ 5.09365e7i 0.157983i
$$135$$ 0 0
$$136$$ −1.34508e7 −0.0393180
$$137$$ 2.07562e8i 0.589205i 0.955620 + 0.294602i $$0.0951872\pi$$
−0.955620 + 0.294602i $$0.904813\pi$$
$$138$$ −4.75282e8 + 7.11337e8i −1.31049 + 1.96137i
$$139$$ −1.42668e8 −0.382180 −0.191090 0.981573i $$-0.561202\pi$$
−0.191090 + 0.981573i $$0.561202\pi$$
$$140$$ 0 0
$$141$$ −2.74857e8 1.83647e8i −0.695394 0.464630i
$$142$$ 3.82143e8 0.939880
$$143$$ 1.79067e8i 0.428226i
$$144$$ 1.69543e8 + 4.09271e8i 0.394302 + 0.951835i
$$145$$ 0 0
$$146$$ 6.21252e8i 1.36728i
$$147$$ 1.21604e8 1.82000e8i 0.260422 0.389763i
$$148$$ 3.31122e8 0.690147
$$149$$ 8.19236e8i 1.66213i −0.556179 0.831063i $$-0.687733\pi$$
0.556179 0.831063i $$-0.312267\pi$$
$$150$$ 0 0
$$151$$ 4.23861e8 0.815296 0.407648 0.913139i $$-0.366349\pi$$
0.407648 + 0.913139i $$0.366349\pi$$
$$152$$ 3.40126e6i 0.00637184i
$$153$$ −4.53963e8 + 1.88056e8i −0.828428 + 0.343180i
$$154$$ 2.73420e8 0.486124
$$155$$ 0 0
$$156$$ −2.87147e8 + 4.29762e8i −0.484848 + 0.725654i
$$157$$ 7.59851e8 1.25063 0.625316 0.780371i $$-0.284970\pi$$
0.625316 + 0.780371i $$0.284970\pi$$
$$158$$ 5.15922e8i 0.827857i
$$159$$ −4.44628e8 2.97079e8i −0.695678 0.464819i
$$160$$ 0 0
$$161$$ 8.23307e8i 1.22534i
$$162$$ 6.83394e8 + 6.83297e8i 0.992227 + 0.992087i
$$163$$ −6.68160e8 −0.946520 −0.473260 0.880923i $$-0.656923\pi$$
−0.473260 + 0.880923i $$0.656923\pi$$
$$164$$ 4.65116e8i 0.642963i
$$165$$ 0 0
$$166$$ 1.04157e9 1.37169
$$167$$ 1.96306e8i 0.252387i −0.992006 0.126194i $$-0.959724\pi$$
0.992006 0.126194i $$-0.0402761\pi$$
$$168$$ 2.11680e7 + 1.41435e7i 0.0265731 + 0.0177549i
$$169$$ −1.53698e8 −0.188417
$$170$$ 0 0
$$171$$ −4.75533e7 1.14792e8i −0.0556156 0.134254i
$$172$$ −8.74485e8 −0.999168
$$173$$ 1.02319e9i 1.14228i −0.820852 0.571141i $$-0.806501\pi$$
0.820852 0.571141i $$-0.193499\pi$$
$$174$$ −4.65620e8 + 6.96877e8i −0.507966 + 0.760255i
$$175$$ 0 0
$$176$$ 4.69904e8i 0.489732i
$$177$$ −9.23696e8 6.17170e8i −0.941100 0.628799i
$$178$$ 1.63021e9 1.62391
$$179$$ 1.28895e9i 1.25552i −0.778408 0.627759i $$-0.783972\pi$$
0.778408 0.627759i $$-0.216028\pi$$
$$180$$ 0 0
$$181$$ 4.71707e8 0.439499 0.219749 0.975556i $$-0.429476\pi$$
0.219749 + 0.975556i $$0.429476\pi$$
$$182$$ 1.01086e9i 0.921314i
$$183$$ −3.39121e7 + 5.07550e7i −0.0302378 + 0.0452558i
$$184$$ 8.44946e7 0.0737153
$$185$$ 0 0
$$186$$ −5.31435e8 3.55080e8i −0.444016 0.296670i
$$187$$ 5.21217e8 0.426238
$$188$$ 1.01210e9i 0.810198i
$$189$$ 9.12161e8 + 1.81390e8i 0.714866 + 0.142156i
$$190$$ 0 0
$$191$$ 1.61787e8i 0.121565i −0.998151 0.0607827i $$-0.980640\pi$$
0.998151 0.0607827i $$-0.0193597\pi$$
$$192$$ −7.07075e8 + 1.05825e9i −0.520308 + 0.778725i
$$193$$ 1.58840e9 1.14480 0.572401 0.819974i $$-0.306012\pi$$
0.572401 + 0.819974i $$0.306012\pi$$
$$194$$ 3.30623e9i 2.33413i
$$195$$ 0 0
$$196$$ 6.70171e8 0.454110
$$197$$ 5.37769e8i 0.357052i 0.983935 + 0.178526i $$0.0571328\pi$$
−0.983935 + 0.178526i $$0.942867\pi$$
$$198$$ −3.92319e8 9.47046e8i −0.255257 0.616184i
$$199$$ 6.47586e8 0.412938 0.206469 0.978453i $$-0.433803\pi$$
0.206469 + 0.978453i $$0.433803\pi$$
$$200$$ 0 0
$$201$$ 1.02100e8 1.52809e8i 0.0625521 0.0936194i
$$202$$ −2.32457e9 −1.39617
$$203$$ 8.06570e8i 0.474961i
$$204$$ −1.25092e9 8.35806e8i −0.722285 0.482597i
$$205$$ 0 0
$$206$$ 3.72812e9i 2.07024i
$$207$$ 2.85169e9 1.18133e9i 1.55318 0.643412i
$$208$$ 1.73729e9 0.928152
$$209$$ 1.31799e8i 0.0690758i
$$210$$ 0 0
$$211$$ 5.81104e7 0.0293173 0.0146586 0.999893i $$-0.495334\pi$$
0.0146586 + 0.999893i $$0.495334\pi$$
$$212$$ 1.63724e9i 0.810529i
$$213$$ −1.14643e9 7.65990e8i −0.556966 0.372139i
$$214$$ 5.06336e8 0.241426
$$215$$ 0 0
$$216$$ 1.86157e7 9.36136e7i 0.00855195 0.0430055i
$$217$$ −6.15086e8 −0.277394
$$218$$ 2.46893e9i 1.09316i
$$219$$ 1.24527e9 1.86376e9i 0.541363 0.810238i
$$220$$ 0 0
$$221$$ 1.92700e9i 0.807815i
$$222$$ −2.01878e9 1.34885e9i −0.831144 0.555332i
$$223$$ −4.40200e9 −1.78004 −0.890021 0.455920i $$-0.849310\pi$$
−0.890021 + 0.455920i $$0.849310\pi$$
$$224$$ 2.57222e9i 1.02168i
$$225$$ 0 0
$$226$$ −6.45992e9 −2.47624
$$227$$ 3.53592e9i 1.33168i −0.746095 0.665839i $$-0.768074\pi$$
0.746095 0.665839i $$-0.231926\pi$$
$$228$$ 2.11348e8 3.16317e8i 0.0782094 0.117053i
$$229$$ −1.86569e9 −0.678420 −0.339210 0.940711i $$-0.610160\pi$$
−0.339210 + 0.940711i $$0.610160\pi$$
$$230$$ 0 0
$$231$$ −8.20260e8 5.48059e8i −0.288074 0.192477i
$$232$$ 8.27770e7 0.0285731
$$233$$ 2.72132e9i 0.923328i 0.887055 + 0.461664i $$0.152747\pi$$
−0.887055 + 0.461664i $$0.847253\pi$$
$$234$$ 3.50134e9 1.45045e9i 1.16781 0.483769i
$$235$$ 0 0
$$236$$ 3.40129e9i 1.09647i
$$237$$ 1.03414e9 1.54777e9i 0.327784 0.490582i
$$238$$ −2.94235e9 −0.917037
$$239$$ 2.27461e9i 0.697132i −0.937284 0.348566i $$-0.886669\pi$$
0.937284 0.348566i $$-0.113331\pi$$
$$240$$ 0 0
$$241$$ −1.74667e9 −0.517778 −0.258889 0.965907i $$-0.583356\pi$$
−0.258889 + 0.965907i $$0.583356\pi$$
$$242$$ 3.72500e9i 1.08609i
$$243$$ −6.80540e8 3.41973e9i −0.195177 0.980768i
$$244$$ −1.86893e8 −0.0527272
$$245$$ 0 0
$$246$$ −1.89469e9 + 2.83571e9i −0.517365 + 0.774321i
$$247$$ −4.87275e8 −0.130914
$$248$$ 6.31253e7i 0.0166877i
$$249$$ −3.12471e9 2.08778e9i −0.812853 0.543110i
$$250$$ 0 0
$$251$$ 1.37549e9i 0.346547i 0.984874 + 0.173274i $$0.0554345\pi$$
−0.984874 + 0.173274i $$0.944566\pi$$
$$252$$ 1.08977e9 + 2.63068e9i 0.270230 + 0.652329i
$$253$$ −3.27417e9 −0.799132
$$254$$ 6.19605e9i 1.48861i
$$255$$ 0 0
$$256$$ 4.55069e9 1.05954
$$257$$ 7.93672e9i 1.81932i 0.415356 + 0.909659i $$0.363657\pi$$
−0.415356 + 0.909659i $$0.636343\pi$$
$$258$$ 5.33154e9 + 3.56228e9i 1.20330 + 0.803988i
$$259$$ −2.33655e9 −0.519249
$$260$$ 0 0
$$261$$ 2.79372e9 1.15731e9i 0.602034 0.249396i
$$262$$ 6.49068e9 1.37748
$$263$$ 3.22555e8i 0.0674187i −0.999432 0.0337093i $$-0.989268\pi$$
0.999432 0.0337093i $$-0.0107320\pi$$
$$264$$ −5.62464e7 + 8.41819e7i −0.0115792 + 0.0173302i
$$265$$ 0 0
$$266$$ 7.44025e8i 0.148614i
$$267$$ −4.89062e9 3.26769e9i −0.962319 0.642977i
$$268$$ 5.62685e8 0.109075
$$269$$ 3.47314e9i 0.663304i 0.943402 + 0.331652i $$0.107606\pi$$
−0.943402 + 0.331652i $$0.892394\pi$$
$$270$$ 0 0
$$271$$ −1.44216e9 −0.267385 −0.133693 0.991023i $$-0.542683\pi$$
−0.133693 + 0.991023i $$0.542683\pi$$
$$272$$ 5.05678e9i 0.923843i
$$273$$ 2.02624e9 3.03259e9i 0.364787 0.545964i
$$274$$ 4.65976e9 0.826726
$$275$$ 0 0
$$276$$ 7.85800e9 + 5.25035e9i 1.35418 + 0.904798i
$$277$$ −3.38046e9 −0.574192 −0.287096 0.957902i $$-0.592690\pi$$
−0.287096 + 0.957902i $$0.592690\pi$$
$$278$$ 3.20289e9i 0.536245i
$$279$$ 8.82561e8 + 2.13048e9i 0.145656 + 0.351609i
$$280$$ 0 0
$$281$$ 4.02262e9i 0.645184i 0.946538 + 0.322592i $$0.104554\pi$$
−0.946538 + 0.322592i $$0.895446\pi$$
$$282$$ −4.12286e9 + 6.17053e9i −0.651932 + 0.975722i
$$283$$ 1.04253e10 1.62533 0.812666 0.582730i $$-0.198016\pi$$
0.812666 + 0.582730i $$0.198016\pi$$
$$284$$ 4.22146e9i 0.648917i
$$285$$ 0 0
$$286$$ −4.02006e9 −0.600853
$$287$$ 3.28207e9i 0.483749i
$$288$$ 8.90943e9 3.69078e9i 1.29503 0.536473i
$$289$$ 1.36679e9 0.195935
$$290$$ 0 0
$$291$$ 6.62720e9 9.91868e9i 0.924183 1.38319i
$$292$$ 6.86285e9 0.944002
$$293$$ 1.03927e10i 1.41012i −0.709146 0.705061i $$-0.750919\pi$$
0.709146 0.705061i $$-0.249081\pi$$
$$294$$ −4.08588e9 2.72999e9i −0.546885 0.365403i
$$295$$ 0 0
$$296$$ 2.39796e8i 0.0312374i
$$297$$ −7.21360e8 + 3.62753e9i −0.0927099 + 0.466213i
$$298$$ −1.83918e10 −2.33216
$$299$$ 1.21050e10i 1.51453i
$$300$$ 0 0
$$301$$ 6.17076e9 0.751749
$$302$$ 9.51565e9i 1.14396i
$$303$$ 6.97372e9 + 4.65951e9i 0.827359 + 0.552803i
$$304$$ −1.27869e9 −0.149717
$$305$$ 0 0
$$306$$ 4.22185e9 + 1.01914e10i 0.481524 + 1.16238i
$$307$$ 2.99309e9 0.336951 0.168476 0.985706i $$-0.446116\pi$$
0.168476 + 0.985706i $$0.446116\pi$$
$$308$$ 3.02042e9i 0.335632i
$$309$$ −7.47286e9 + 1.11843e10i −0.819696 + 1.22681i
$$310$$ 0 0
$$311$$ 6.44832e9i 0.689295i 0.938732 + 0.344647i $$0.112002\pi$$
−0.938732 + 0.344647i $$0.887998\pi$$
$$312$$ −3.11230e8 2.07949e8i −0.0328445 0.0219452i
$$313$$ −3.27737e7 −0.00341467 −0.00170733 0.999999i $$-0.500543\pi$$
−0.00170733 + 0.999999i $$0.500543\pi$$
$$314$$ 1.70586e10i 1.75479i
$$315$$ 0 0
$$316$$ 5.69928e9 0.571573
$$317$$ 1.17797e10i 1.16653i 0.812282 + 0.583264i $$0.198225\pi$$
−0.812282 + 0.583264i $$0.801775\pi$$
$$318$$ −6.66942e9 + 9.98187e9i −0.652198 + 0.976120i
$$319$$ −3.20761e9 −0.309755
$$320$$ 0 0
$$321$$ −1.51901e9 1.01493e9i −0.143067 0.0955907i
$$322$$ 1.84832e10 1.71931
$$323$$ 1.41832e9i 0.130306i
$$324$$ 7.54825e9 7.54931e9i 0.684961 0.685058i
$$325$$ 0 0
$$326$$ 1.50002e10i 1.32808i
$$327$$ 4.94888e9 7.40680e9i 0.432829 0.647798i
$$328$$ 3.36833e8 0.0291018
$$329$$ 7.14182e9i 0.609573i
$$330$$ 0 0
$$331$$ −1.20100e10 −1.00053 −0.500265 0.865872i $$-0.666764\pi$$
−0.500265 + 0.865872i $$0.666764\pi$$
$$332$$ 1.15060e10i 0.947049i
$$333$$ 3.35261e9 + 8.09311e9i 0.272651 + 0.658171i
$$334$$ −4.40705e9 −0.354130
$$335$$ 0 0
$$336$$ 5.31720e9 7.95806e9i 0.417182 0.624381i
$$337$$ −1.59214e10 −1.23441 −0.617207 0.786801i $$-0.711736\pi$$
−0.617207 + 0.786801i $$0.711736\pi$$
$$338$$ 3.45051e9i 0.264372i
$$339$$ 1.93798e10 + 1.29486e10i 1.46740 + 0.980451i
$$340$$ 0 0
$$341$$ 2.44611e9i 0.180908i
$$342$$ −2.57708e9 + 1.06757e9i −0.188375 + 0.0780354i
$$343$$ −1.48174e10 −1.07052
$$344$$ 6.33295e8i 0.0452243i
$$345$$ 0 0
$$346$$ −2.29706e10 −1.60276
$$347$$ 4.94792e9i 0.341275i 0.985334 + 0.170638i $$0.0545828\pi$$
−0.985334 + 0.170638i $$0.945417\pi$$
$$348$$ 7.69826e9 + 5.14361e9i 0.524899 + 0.350713i
$$349$$ −7.29567e9 −0.491772 −0.245886 0.969299i $$-0.579079\pi$$
−0.245886 + 0.969299i $$0.579079\pi$$
$$350$$ 0 0
$$351$$ −1.34114e10 2.66695e9i −0.883578 0.175706i
$$352$$ −1.02293e10 −0.666311
$$353$$ 6.93875e9i 0.446871i 0.974719 + 0.223436i $$0.0717272\pi$$
−0.974719 + 0.223436i $$0.928273\pi$$
$$354$$ −1.38554e10 + 2.07369e10i −0.882282 + 1.32048i
$$355$$ 0 0
$$356$$ 1.80086e10i 1.12119i
$$357$$ 8.82706e9 + 5.89782e9i 0.543429 + 0.363094i
$$358$$ −2.89368e10 −1.76164
$$359$$ 1.60096e10i 0.963838i 0.876216 + 0.481919i $$0.160060\pi$$
−0.876216 + 0.481919i $$0.839940\pi$$
$$360$$ 0 0
$$361$$ −1.66249e10 −0.978883
$$362$$ 1.05898e10i 0.616670i
$$363$$ −7.46660e9 + 1.11750e10i −0.430028 + 0.643607i
$$364$$ 1.11668e10 0.636098
$$365$$ 0 0
$$366$$ 1.13945e9 + 7.61325e8i 0.0634994 + 0.0424273i
$$367$$ −1.36364e10 −0.751686 −0.375843 0.926683i $$-0.622647\pi$$
−0.375843 + 0.926683i $$0.622647\pi$$
$$368$$ 3.17655e10i 1.73207i
$$369$$ 1.13681e10 4.70930e9i 0.613173 0.254010i
$$370$$ 0 0
$$371$$ 1.15531e10i 0.609821i
$$372$$ −3.92249e9 + 5.87065e9i −0.204829 + 0.306559i
$$373$$ 2.44062e10 1.26085 0.630427 0.776248i $$-0.282880\pi$$
0.630427 + 0.776248i $$0.282880\pi$$
$$374$$ 1.17013e10i 0.598063i
$$375$$ 0 0
$$376$$ 7.32953e8 0.0366712
$$377$$ 1.18589e10i 0.587055i
$$378$$ 4.07219e9 2.04780e10i 0.199463 1.00304i
$$379$$ −1.98392e10 −0.961542 −0.480771 0.876846i $$-0.659643\pi$$
−0.480771 + 0.876846i $$0.659643\pi$$
$$380$$ 0 0
$$381$$ 1.24197e10 1.85881e10i 0.589403 0.882137i
$$382$$ −3.63211e9 −0.170571
$$383$$ 1.51133e10i 0.702366i 0.936307 + 0.351183i $$0.114220\pi$$
−0.936307 + 0.351183i $$0.885780\pi$$
$$384$$ −1.58467e9 1.05880e9i −0.0728811 0.0486957i
$$385$$ 0 0
$$386$$ 3.56594e10i 1.60630i
$$387$$ −8.85416e9 2.13737e10i −0.394733 0.952875i
$$388$$ 3.65232e10 1.61154
$$389$$ 1.79991e10i 0.786056i −0.919527 0.393028i $$-0.871428\pi$$
0.919527 0.393028i $$-0.128572\pi$$
$$390$$ 0 0
$$391$$ 3.52342e10 1.50750
$$392$$ 4.85332e8i 0.0205539i
$$393$$ −1.94720e10 1.30103e10i −0.816284 0.545403i
$$394$$ 1.20729e10 0.500987
$$395$$ 0 0
$$396$$ −1.04618e10 + 4.33386e9i −0.425429 + 0.176236i
$$397$$ 2.35673e10 0.948739 0.474370 0.880326i $$-0.342676\pi$$
0.474370 + 0.880326i $$0.342676\pi$$
$$398$$ 1.45383e10i 0.579403i
$$399$$ −1.49137e9 + 2.23207e9i −0.0588428 + 0.0880678i
$$400$$ 0 0
$$401$$ 1.37692e10i 0.532515i 0.963902 + 0.266257i $$0.0857871\pi$$
−0.963902 + 0.266257i $$0.914213\pi$$
$$402$$ −3.43056e9 2.29214e9i −0.131359 0.0877682i
$$403$$ 9.04353e9 0.342861
$$404$$ 2.56791e10i 0.963950i
$$405$$ 0 0
$$406$$ 1.81075e10 0.666428
$$407$$ 9.29209e9i 0.338638i
$$408$$ 6.05284e8 9.05906e8i 0.0218433 0.0326921i
$$409$$ 3.58480e10 1.28107 0.640533 0.767931i $$-0.278714\pi$$
0.640533 + 0.767931i $$0.278714\pi$$
$$410$$ 0 0
$$411$$ −1.39793e10 9.34031e9i −0.489912 0.327336i
$$412$$ −4.11838e10 −1.42934
$$413$$ 2.40011e10i 0.824955i
$$414$$ −2.65207e10 6.40203e10i −0.902785 2.17930i
$$415$$ 0 0
$$416$$ 3.78191e10i 1.26281i
$$417$$ 6.42007e9 9.60868e9i 0.212322 0.317775i
$$418$$ 2.95887e9 0.0969217
$$419$$ 2.23996e10i 0.726750i 0.931643 + 0.363375i $$0.118376\pi$$
−0.931643 + 0.363375i $$0.881624\pi$$
$$420$$ 0 0
$$421$$ −1.49535e10 −0.476008 −0.238004 0.971264i $$-0.576493\pi$$
−0.238004 + 0.971264i $$0.576493\pi$$
$$422$$ 1.30457e9i 0.0411357i
$$423$$ 2.47372e10 1.02475e10i 0.772660 0.320078i
$$424$$ 1.18567e9 0.0366861
$$425$$ 0 0
$$426$$ −1.71964e10 + 2.57373e10i −0.522156 + 0.781491i
$$427$$ 1.31880e9 0.0396706
$$428$$ 5.59339e9i 0.166686i
$$429$$ 1.20602e10 + 8.05804e9i 0.356061 + 0.237903i
$$430$$ 0 0
$$431$$ 6.40436e10i 1.85595i −0.372640 0.927976i $$-0.621547\pi$$
0.372640 0.927976i $$-0.378453\pi$$
$$432$$ −3.51938e10 6.99854e9i −1.01049 0.200943i
$$433$$ 5.22954e9 0.148769 0.0743843 0.997230i $$-0.476301\pi$$
0.0743843 + 0.997230i $$0.476301\pi$$
$$434$$ 1.38087e10i 0.389218i
$$435$$ 0 0
$$436$$ 2.72738e10 0.754745
$$437$$ 8.90959e9i 0.244305i
$$438$$ −4.18412e10 2.79563e10i −1.13686 0.759598i
$$439$$ 4.34801e10 1.17066 0.585332 0.810793i $$-0.300964\pi$$
0.585332 + 0.810793i $$0.300964\pi$$
$$440$$ 0 0
$$441$$ 6.78548e9 + 1.63800e10i 0.179402 + 0.433070i
$$442$$ 4.32610e10 1.13346
$$443$$ 3.78737e10i 0.983383i 0.870770 + 0.491691i $$0.163621\pi$$
−0.870770 + 0.491691i $$0.836379\pi$$
$$444$$ −1.49005e10 + 2.23010e10i −0.383415 + 0.573843i
$$445$$ 0 0
$$446$$ 9.88246e10i 2.49761i
$$447$$ 5.51754e10 + 3.68656e10i 1.38202 + 0.923403i
$$448$$ 2.74973e10 0.682620
$$449$$ 2.95505e10i 0.727076i 0.931579 + 0.363538i $$0.118431\pi$$
−0.931579 + 0.363538i $$0.881569\pi$$
$$450$$ 0 0
$$451$$ −1.30523e10 −0.315486
$$452$$ 7.13614e10i 1.70966i
$$453$$ −1.90737e10 + 2.85469e10i −0.452942 + 0.677902i
$$454$$ −7.93813e10 −1.86851
$$455$$ 0 0
$$456$$ 2.29074e8 + 1.53057e8i 0.00529806 + 0.00353991i
$$457$$ 2.02181e10 0.463529 0.231764 0.972772i $$-0.425550\pi$$
0.231764 + 0.972772i $$0.425550\pi$$
$$458$$ 4.18847e10i 0.951905i
$$459$$ 7.76277e9 3.90369e10i 0.174890 0.879476i
$$460$$ 0 0
$$461$$ 7.01826e10i 1.55391i 0.629556 + 0.776955i $$0.283237\pi$$
−0.629556 + 0.776955i $$0.716763\pi$$
$$462$$ −1.23039e10 + 1.84148e10i −0.270069 + 0.404202i
$$463$$ −4.16009e9 −0.0905271 −0.0452635 0.998975i $$-0.514413\pi$$
−0.0452635 + 0.998975i $$0.514413\pi$$
$$464$$ 3.11198e10i 0.671374i
$$465$$ 0 0
$$466$$ 6.10935e10 1.29554
$$467$$ 2.88138e10i 0.605806i −0.953021 0.302903i $$-0.902044\pi$$
0.953021 0.302903i $$-0.0979558\pi$$
$$468$$ −1.60228e10 3.86786e10i −0.334006 0.806282i
$$469$$ −3.97056e9 −0.0820654
$$470$$ 0 0
$$471$$ −3.41933e10 + 5.11758e10i −0.694796 + 1.03988i
$$472$$ 2.46319e9 0.0496283
$$473$$ 2.45402e10i 0.490268i
$$474$$ −3.47472e10 2.32165e10i −0.688346 0.459921i
$$475$$ 0 0
$$476$$ 3.25036e10i 0.633145i
$$477$$ 4.00165e10 1.65770e10i 0.772975 0.320209i
$$478$$ −5.10649e10 −0.978161
$$479$$ 4.47149e10i 0.849395i 0.905335 + 0.424698i $$0.139620\pi$$
−0.905335 + 0.424698i $$0.860380\pi$$
$$480$$ 0 0
$$481$$ 3.43539e10 0.641795
$$482$$ 3.92127e10i 0.726505i
$$483$$ −5.54496e10 3.70488e10i −1.01885 0.680747i
$$484$$ −4.11493e10 −0.749861
$$485$$ 0 0
$$486$$ −7.67727e10 + 1.52781e10i −1.37614 + 0.273857i
$$487$$ −5.72836e10 −1.01839 −0.509195 0.860651i $$-0.670057\pi$$
−0.509195 + 0.860651i $$0.670057\pi$$
$$488$$ 1.35347e8i 0.00238654i
$$489$$ 3.00672e10 4.50005e10i 0.525845 0.787012i
$$490$$ 0 0
$$491$$ 7.25262e10i 1.24787i −0.781477 0.623934i $$-0.785533\pi$$
0.781477 0.623934i $$-0.214467\pi$$
$$492$$ 3.13255e10 + 2.09302e10i 0.534611 + 0.357202i
$$493$$ 3.45180e10 0.584330
$$494$$ 1.09393e10i 0.183688i
$$495$$ 0 0
$$496$$ 2.37318e10 0.392106
$$497$$ 2.97885e10i 0.488228i
$$498$$ −4.68706e10 + 7.01495e10i −0.762050 + 1.14053i
$$499$$ −2.64368e10 −0.426389 −0.213195 0.977010i $$-0.568387\pi$$
−0.213195 + 0.977010i $$0.568387\pi$$
$$500$$ 0 0
$$501$$ 1.32212e10 + 8.83376e9i 0.209855 + 0.140215i
$$502$$ 3.08797e10 0.486248
$$503$$ 7.52828e10i 1.17604i −0.808845 0.588022i $$-0.799907\pi$$
0.808845 0.588022i $$-0.200093\pi$$
$$504$$ −1.90512e9 + 7.89205e8i −0.0295257 + 0.0122312i
$$505$$ 0 0
$$506$$ 7.35048e10i 1.12128i
$$507$$ 6.91640e9 1.03515e10i 0.104676 0.156665i
$$508$$ 6.84465e10 1.02777
$$509$$ 6.45184e10i 0.961197i −0.876941 0.480599i $$-0.840419\pi$$
0.876941 0.480599i $$-0.159581\pi$$
$$510$$ 0 0
$$511$$ −4.84273e10 −0.710243
$$512$$ 9.61394e10i 1.39901i
$$513$$ 9.87115e9 + 1.96295e9i 0.142527 + 0.0283426i
$$514$$ 1.78179e11 2.55272
$$515$$ 0 0
$$516$$ 3.93518e10 5.88964e10i 0.555094 0.830788i
$$517$$ −2.84019e10 −0.397544
$$518$$ 5.24554e10i 0.728569i
$$519$$ 6.89119e10 + 4.60437e10i 0.949783 + 0.634601i
$$520$$ 0 0
$$521$$ 7.65146e10i 1.03847i −0.854632 0.519235i $$-0.826217\pi$$
0.854632 0.519235i $$-0.173783\pi$$
$$522$$ −2.59816e10 6.27189e10i −0.349932 0.844727i
$$523$$ 8.46771e10 1.13177 0.565886 0.824483i $$-0.308534\pi$$
0.565886 + 0.824483i $$0.308534\pi$$
$$524$$ 7.17012e10i 0.951046i
$$525$$ 0 0
$$526$$ −7.24133e9 −0.0945966
$$527$$ 2.63232e10i 0.341269i
$$528$$ 3.16480e10 + 2.11457e10i 0.407202 + 0.272073i
$$529$$ −1.43023e11 −1.82634
$$530$$ 0 0
$$531$$ 8.31326e10 3.44381e10i 1.04567 0.433173i
$$532$$ −8.21909e9 −0.102607
$$533$$ 4.82558e10i 0.597917i
$$534$$ −7.33594e10 + 1.09794e11i −0.902175 + 1.35025i
$$535$$ 0 0
$$536$$ 4.07492e8i 0.00493696i
$$537$$ 8.68104e10 + 5.80026e10i 1.04394 + 0.697510i
$$538$$ 7.79717e10 0.930696
$$539$$ 1.88066e10i 0.222821i
$$540$$ 0 0
$$541$$ 1.43470e11 1.67483 0.837415 0.546568i $$-0.184066\pi$$
0.837415 + 0.546568i $$0.184066\pi$$
$$542$$ 3.23765e10i 0.375174i
$$543$$ −2.12268e10 + 3.17694e10i −0.244166 + 0.365434i
$$544$$ 1.10081e11 1.25695
$$545$$ 0 0
$$546$$ −6.80816e10 4.54889e10i −0.766053 0.511841i
$$547$$ −1.64171e11 −1.83378 −0.916892 0.399134i $$-0.869311\pi$$
−0.916892 + 0.399134i $$0.869311\pi$$
$$548$$ 5.14755e10i 0.570792i
$$549$$ −1.89229e9 4.56795e9i −0.0208305 0.0502842i
$$550$$ 0 0
$$551$$ 8.72847e9i 0.0946961i
$$552$$ −3.80226e9 + 5.69070e9i −0.0409529 + 0.0612928i
$$553$$ −4.02167e10 −0.430037
$$554$$ 7.58912e10i 0.805661i
$$555$$ 0 0
$$556$$ 3.53817e10 0.370237
$$557$$ 1.54420e11i 1.60429i −0.597130 0.802145i $$-0.703692\pi$$
0.597130 0.802145i $$-0.296308\pi$$
$$558$$ 4.78291e10 1.98135e10i 0.493351 0.204373i
$$559$$ −9.07278e10 −0.929166
$$560$$ 0 0
$$561$$ −2.34547e10 + 3.51039e10i −0.236799 + 0.354408i
$$562$$ 9.03075e10 0.905271
$$563$$ 1.54622e11i 1.53900i −0.638646 0.769500i $$-0.720505\pi$$
0.638646 0.769500i $$-0.279495\pi$$
$$564$$ 6.81646e10 + 4.55444e10i 0.673663 + 0.450110i
$$565$$ 0 0
$$566$$ 2.34047e11i 2.28054i
$$567$$ −5.32638e10 + 5.32714e10i −0.515348 + 0.515420i
$$568$$ 3.05714e9 0.0293712
$$569$$ 1.15380e11i 1.10073i −0.834925 0.550364i $$-0.814489\pi$$
0.834925 0.550364i $$-0.185511\pi$$
$$570$$ 0 0
$$571$$ −1.63410e11 −1.53722 −0.768608 0.639720i $$-0.779050\pi$$
−0.768608 + 0.639720i $$0.779050\pi$$
$$572$$ 4.44087e10i 0.414844i
$$573$$ 1.08963e10 + 7.28041e9i 0.101079 + 0.0675363i
$$574$$ 7.36823e10 0.678759
$$575$$ 0 0
$$576$$ −3.94548e10 9.52427e10i −0.358434 0.865250i
$$577$$ −7.42282e10 −0.669678 −0.334839 0.942275i $$-0.608682\pi$$
−0.334839 + 0.942275i $$0.608682\pi$$
$$578$$ 3.06844e10i 0.274920i
$$579$$ −7.14779e10 + 1.06978e11i −0.636001 + 0.951879i
$$580$$ 0 0
$$581$$ 8.11916e10i 0.712535i
$$582$$ −2.22674e11 1.48780e11i −1.94078 1.29674i
$$583$$ −4.59449e10 −0.397707
$$584$$ 4.97002e9i 0.0427274i
$$585$$ 0 0
$$586$$ −2.33315e11 −1.97857
$$587$$ 6.72877e10i 0.566739i 0.959011 + 0.283369i $$0.0914523\pi$$
−0.959011 + 0.283369i $$0.908548\pi$$
$$588$$ −3.01577e10 + 4.51359e10i −0.252283 + 0.377583i
$$589$$ −6.65629e9 −0.0553059
$$590$$ 0 0
$$591$$ −3.62187e10 2.41996e10i −0.296881 0.198362i
$$592$$ 9.01507e10 0.733977
$$593$$ 2.36444e10i 0.191210i 0.995419 + 0.0956048i $$0.0304785\pi$$
−0.995419 + 0.0956048i $$0.969521\pi$$
$$594$$ 8.14378e10 + 1.61945e10i 0.654154 + 0.130083i
$$595$$ 0 0
$$596$$ 2.03170e11i 1.61018i
$$597$$ −2.91414e10 + 4.36148e10i −0.229410 + 0.343350i
$$598$$ −2.71756e11 −2.12507
$$599$$ 3.03370e10i 0.235649i 0.993034 + 0.117825i $$0.0375921\pi$$
−0.993034 + 0.117825i $$0.962408\pi$$
$$600$$ 0 0
$$601$$ 3.37911e10 0.259003 0.129501 0.991579i $$-0.458662\pi$$
0.129501 + 0.991579i $$0.458662\pi$$
$$602$$ 1.38533e11i 1.05480i
$$603$$ 5.69718e9 + 1.37528e10i 0.0430914 + 0.104022i
$$604$$ −1.05117e11 −0.789818
$$605$$ 0 0
$$606$$ 1.04606e11 1.56560e11i 0.775649 1.16089i
$$607$$ 3.82366e10 0.281660 0.140830 0.990034i $$-0.455023\pi$$
0.140830 + 0.990034i $$0.455023\pi$$
$$608$$ 2.78359e10i 0.203700i
$$609$$ −5.43224e10 3.62957e10i −0.394920 0.263867i
$$610$$ 0 0
$$611$$ 1.05005e11i 0.753435i
$$612$$ 1.12583e11 4.66380e10i 0.802539 0.332456i
$$613$$ −1.08066e11 −0.765330 −0.382665 0.923887i $$-0.624994\pi$$
−0.382665 + 0.923887i $$0.624994\pi$$
$$614$$ 6.71948e10i 0.472783i
$$615$$ 0 0
$$616$$ 2.18736e9 0.0151914
$$617$$ 4.72538e9i 0.0326059i 0.999867 + 0.0163029i $$0.00518962\pi$$
−0.999867 + 0.0163029i $$0.994810\pi$$
$$618$$ 2.51088e11 + 1.67765e11i 1.72136 + 1.15013i
$$619$$ 2.29845e10 0.156557 0.0782786 0.996932i $$-0.475058\pi$$
0.0782786 + 0.996932i $$0.475058\pi$$
$$620$$ 0 0
$$621$$ −4.87639e10 + 2.45221e11i −0.327893 + 1.64889i
$$622$$ 1.44764e11 0.967165
$$623$$ 1.27077e11i 0.843555i
$$624$$ −7.81780e10 + 1.17006e11i −0.515640 + 0.771739i
$$625$$ 0 0
$$626$$ 7.35768e8i 0.00479119i
$$627$$ −8.87662e9 5.93094e9i −0.0574351 0.0383754i
$$628$$ −1.88443e11 −1.21155
$$629$$ 9.99949e10i 0.638815i
$$630$$ 0 0
$$631$$ −1.01892e11 −0.642722 −0.321361 0.946957i $$-0.604140\pi$$
−0.321361 + 0.946957i $$0.604140\pi$$
$$632$$ 4.12737e9i 0.0258705i
$$633$$ −2.61497e9 + 3.91372e9i −0.0162874 + 0.0243767i
$$634$$ 2.64453e11 1.63678
$$635$$ 0 0
$$636$$ 1.10268e11 + 7.36757e10i 0.673938 + 0.450294i
$$637$$ 6.95302e10 0.422295
$$638$$ 7.20106e10i 0.434624i
$$639$$ 1.03179e11 4.27422e10i 0.618851 0.256362i
$$640$$ 0 0
$$641$$ 1.17803e11i 0.697791i 0.937162 + 0.348896i $$0.113443\pi$$
−0.937162 + 0.348896i $$0.886557\pi$$
$$642$$ −2.27851e10 + 3.41016e10i −0.134125 + 0.200740i
$$643$$ 2.62680e10 0.153668 0.0768339 0.997044i $$-0.475519\pi$$
0.0768339 + 0.997044i $$0.475519\pi$$
$$644$$ 2.04180e11i 1.18705i
$$645$$ 0 0
$$646$$ −3.18413e10 −0.182836
$$647$$ 3.10527e11i 1.77208i −0.463612 0.886038i $$-0.653447\pi$$
0.463612 0.886038i $$-0.346553\pi$$
$$648$$ 5.46715e9 + 5.46638e9i 0.0310071 + 0.0310027i
$$649$$ −9.54486e10 −0.538010
$$650$$ 0 0
$$651$$ 2.76789e10 4.14260e10i 0.154108 0.230648i
$$652$$ 1.65704e11 0.916942
$$653$$ 3.48345e10i 0.191583i −0.995401 0.0957914i $$-0.969462\pi$$
0.995401 0.0957914i $$-0.0305382\pi$$
$$654$$ −1.66282e11 1.11102e11i −0.908940 0.607311i
$$655$$ 0 0
$$656$$ 1.26632e11i 0.683796i
$$657$$ 6.94863e10 + 1.67738e11i 0.372939 + 0.900265i
$$658$$ 1.60333e11 0.855304
$$659$$ 3.77120e10i 0.199957i 0.994990 + 0.0999787i $$0.0318775\pi$$
−0.994990 + 0.0999787i $$0.968123\pi$$
$$660$$ 0 0
$$661$$ −1.39619e11 −0.731372 −0.365686 0.930738i $$-0.619166\pi$$
−0.365686 + 0.930738i $$0.619166\pi$$
$$662$$ 2.69623e11i 1.40386i
$$663$$ −1.29783e11 8.67149e10i −0.671682 0.448786i
$$664$$ 8.33256e9 0.0428653
$$665$$ 0 0
$$666$$ 1.81690e11 7.52659e10i 0.923494 0.382562i
$$667$$ −2.16834e11 −1.09553
$$668$$ 4.86838e10i 0.244500i
$$669$$ 1.98090e11 2.96474e11i 0.988912 1.48007i
$$670$$ 0 0
$$671$$ 5.24468e9i 0.0258719i
$$672$$ −1.73239e11 1.15750e11i −0.849510 0.567603i
$$673$$ 1.29783e11 0.632642 0.316321 0.948652i $$-0.397552\pi$$
0.316321 + 0.948652i $$0.397552\pi$$
$$674$$ 3.57434e11i 1.73203i
$$675$$ 0 0
$$676$$ 3.81171e10 0.182529
$$677$$ 3.40648e11i 1.62163i 0.585306 + 0.810813i $$0.300975\pi$$
−0.585306 + 0.810813i $$0.699025\pi$$
$$678$$ 2.90696e11 4.35075e11i 1.37569 2.05895i
$$679$$ −2.57724e11 −1.21248
$$680$$ 0 0
$$681$$ 2.38144e11 + 1.59117e11i 1.10726 + 0.739821i
$$682$$ −5.49149e10 −0.253836
$$683$$ 1.02876e11i 0.472750i −0.971662 0.236375i $$-0.924041\pi$$
0.971662 0.236375i $$-0.0759593\pi$$
$$684$$ 1.17932e10 + 2.84685e10i 0.0538776 + 0.130059i
$$685$$ 0 0
$$686$$ 3.32650e11i 1.50208i
$$687$$ 8.39562e10 1.25654e11i 0.376900 0.564092i
$$688$$ −2.38086e11 −1.06262
$$689$$ 1.69863e11i 0.753742i
$$690$$ 0 0
$$691$$ 3.58259e11 1.57140 0.785698 0.618611i $$-0.212304\pi$$
0.785698 + 0.618611i $$0.212304\pi$$
$$692$$ 2.53752e11i 1.10659i
$$693$$ 7.38234e10 3.05817e10i 0.320082 0.132595i
$$694$$ 1.11081e11 0.478851
$$695$$ 0 0
$$696$$ −3.72496e9 + 5.57501e9i −0.0158740 + 0.0237580i
$$697$$ 1.40459e11 0.595141
$$698$$ 1.63787e11i 0.690016i
$$699$$ −1.83280e11 1.22459e11i −0.767728 0.512960i
$$700$$ 0 0
$$701$$ 2.49323e11i 1.03250i −0.856438 0.516250i $$-0.827327\pi$$
0.856438 0.516250i $$-0.172673\pi$$
$$702$$ −5.98729e10 + 3.01085e11i −0.246537 + 1.23977i
$$703$$ −2.52854e10 −0.103526
$$704$$ 1.09353e11i 0.445183i
$$705$$ 0 0
$$706$$ 1.55775e11 0.627015
$$707$$ 1.81203e11i 0.725251i
$$708$$ 2.29077e11 + 1.53058e11i 0.911691 + 0.609149i
$$709$$ −3.88874e11 −1.53895 −0.769474 0.638678i $$-0.779482\pi$$
−0.769474 + 0.638678i $$0.779482\pi$$
$$710$$ 0 0
$$711$$ 5.77052e10 + 1.39299e11i 0.225807 + 0.545091i
$$712$$ 1.30417e10 0.0507473
$$713$$ 1.65357e11i 0.639829i
$$714$$ 1.32406e11 1.98167e11i 0.509465 0.762497i
$$715$$ 0 0
$$716$$ 3.19659e11i 1.21628i
$$717$$ 1.53195e11 + 1.02357e11i 0.579651 + 0.387296i
$$718$$ 3.59416e11 1.35238
$$719$$ 3.35735e10i 0.125626i 0.998025 + 0.0628132i $$0.0200072\pi$$
−0.998025 + 0.0628132i $$0.979993\pi$$
$$720$$ 0 0
$$721$$ 2.90611e11 1.07540
$$722$$ 3.73228e11i 1.37349i
$$723$$ 7.86002e10 1.17638e11i 0.287654 0.430521i
$$724$$ −1.16983e11 −0.425764
$$725$$ 0 0
$$726$$ 2.50878e11 + 1.67625e11i 0.903058 + 0.603381i
$$727$$ −2.53113e11 −0.906102 −0.453051 0.891485i $$-0.649664\pi$$
−0.453051 + 0.891485i $$0.649664\pi$$
$$728$$ 8.08692e9i 0.0287911i
$$729$$ 2.60942e11 + 1.08053e11i 0.923920 + 0.382586i
$$730$$ 0 0
$$731$$ 2.64084e11i 0.924853i
$$732$$ 8.41020e9 1.25872e10i 0.0292929 0.0438416i
$$733$$ −2.07602e11 −0.719144 −0.359572 0.933117i $$-0.617077\pi$$
−0.359572 + 0.933117i $$0.617077\pi$$
$$734$$ 3.06137e11i 1.05471i
$$735$$ 0 0
$$736$$ −6.91504e11 −2.35659
$$737$$ 1.57903e10i 0.0535205i
$$738$$ −1.05724e11 2.55214e11i −0.356407 0.860357i
$$739$$ 4.15014e11 1.39151 0.695753 0.718281i $$-0.255071\pi$$
0.695753 + 0.718281i $$0.255071\pi$$
$$740$$ 0 0
$$741$$ 2.19274e10 3.28179e10i 0.0727300 0.108852i
$$742$$ 2.59366e11 0.855653
$$743$$ 3.30690e11i 1.08509i 0.840027 + 0.542545i $$0.182539\pi$$
−0.840027 + 0.542545i $$0.817461\pi$$
$$744$$ −4.25148e9 2.84064e9i −0.0138755 0.00927095i
$$745$$ 0 0
$$746$$ 5.47918e11i 1.76913i
$$747$$ 2.81224e11 1.16498e11i 0.903170 0.374143i
$$748$$ −1.29262e11 −0.412918
$$749$$ 3.94695e10i 0.125411i
$$750$$ 0 0
$$751$$ −4.77978e11 −1.50262 −0.751308 0.659952i $$-0.770577\pi$$
−0.751308 + 0.659952i $$0.770577\pi$$
$$752$$ 2.75552e11i 0.861652i
$$753$$ −9.26390e10 6.18970e10i −0.288147 0.192526i
$$754$$ −2.66231e11 −0.823709
$$755$$ 0 0
$$756$$ −2.26216e11 4.49847e10i −0.692526 0.137714i
$$757$$ 8.95066e10 0.272566 0.136283 0.990670i $$-0.456484\pi$$
0.136283 + 0.990670i $$0.456484\pi$$
$$758$$ 4.45390e11i 1.34916i
$$759$$ 1.47337e11 2.20514e11i 0.443962 0.664462i
$$760$$ 0 0
$$761$$ 5.71473e11i 1.70395i 0.523581 + 0.851976i $$0.324596\pi$$
−0.523581 + 0.851976i $$0.675404\pi$$
$$762$$ −4.17303e11 2.78822e11i −1.23775 0.827004i
$$763$$ −1.92456e11 −0.567851
$$764$$ 4.01231e10i 0.117766i
$$765$$ 0 0
$$766$$ 3.39292e11 0.985504
$$767$$ 3.52884e11i 1.01965i
$$768$$ −2.04781e11 + 3.06488e11i −0.588634 + 0.880986i
$$769$$ 2.56194e11 0.732596 0.366298 0.930498i $$-0.380625\pi$$
0.366298 + 0.930498i $$0.380625\pi$$
$$770$$ 0 0
$$771$$ −5.34537e11 3.57152e11i −1.51273 1.01073i
$$772$$ −3.93923e11 −1.10903
$$773$$ 1.00523e11i 0.281543i 0.990042 + 0.140772i $$0.0449584\pi$$
−0.990042 + 0.140772i $$0.955042\pi$$
$$774$$ −4.79838e11 + 1.98775e11i −1.33700 + 0.553859i