Properties

 Label 150.11.b.a.149.4 Level $150$ Weight $11$ Character 150.149 Analytic conductor $95.304$ Analytic rank $0$ Dimension $8$ CM no Inner twists $4$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$150 = 2 \cdot 3 \cdot 5^{2}$$ Weight: $$k$$ $$=$$ $$11$$ Character orbit: $$[\chi]$$ $$=$$ 150.b (of order $$2$$, degree $$1$$, not minimal)

Newform invariants

 Self dual: no Analytic conductor: $$95.3035879011$$ Analytic rank: $$0$$ Dimension: $$8$$ Coefficient field: 8.0.3421020160000.10 Defining polynomial: $$x^{8} + 967 x^{4} + 194481$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$2^{26}\cdot 3^{8}$$ Twist minimal: no (minimal twist has level 6) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

 Embedding label 149.4 Root $$2.90605 + 2.90605i$$ of defining polynomial Character $$\chi$$ $$=$$ 150.149 Dual form 150.11.b.a.149.3

$q$-expansion

 $$f(q)$$ $$=$$ $$q-22.6274 q^{2} +(18.8335 + 242.269i) q^{3} +512.000 q^{4} +(-426.153 - 5481.92i) q^{6} -670.530i q^{7} -11585.2 q^{8} +(-58339.6 + 9125.53i) q^{9} +O(q^{10})$$ $$q-22.6274 q^{2} +(18.8335 + 242.269i) q^{3} +512.000 q^{4} +(-426.153 - 5481.92i) q^{6} -670.530i q^{7} -11585.2 q^{8} +(-58339.6 + 9125.53i) q^{9} +233268. i q^{11} +(9642.73 + 124042. i) q^{12} +307781. i q^{13} +15172.4i q^{14} +262144. q^{16} +672324. q^{17} +(1.32007e6 - 206487. i) q^{18} +1.55119e6 q^{19} +(162449. - 12628.4i) q^{21} -5.27826e6i q^{22} -5.57551e6 q^{23} +(-218190. - 2.80674e6i) q^{24} -6.96428e6i q^{26} +(-3.30957e6 - 1.39620e7i) q^{27} -343311. i q^{28} +2.97313e7i q^{29} +3.09368e7 q^{31} -5.93164e6 q^{32} +(-5.65137e7 + 4.39325e6i) q^{33} -1.52130e7 q^{34} +(-2.98699e7 + 4.67227e6i) q^{36} +8.56690e7i q^{37} -3.50994e7 q^{38} +(-7.45657e7 + 5.79657e6i) q^{39} +3.59054e7i q^{41} +(-3.67579e6 + 285748. i) q^{42} -3.66253e7i q^{43} +1.19433e8i q^{44} +1.26159e8 q^{46} +3.28877e7 q^{47} +(4.93708e6 + 6.35094e7i) q^{48} +2.82026e8 q^{49} +(1.26622e7 + 1.62883e8i) q^{51} +1.57584e8i q^{52} -4.59194e8 q^{53} +(7.48870e7 + 3.15924e8i) q^{54} +7.76824e6i q^{56} +(2.92143e7 + 3.75805e8i) q^{57} -6.72743e8i q^{58} +4.88657e8i q^{59} -6.12928e7 q^{61} -7.00020e8 q^{62} +(6.11894e6 + 3.91184e7i) q^{63} +1.34218e8 q^{64} +(1.27876e9 - 9.94079e7i) q^{66} +6.70776e8i q^{67} +3.44230e8 q^{68} +(-1.05006e8 - 1.35077e9i) q^{69} +1.23330e9i q^{71} +(6.75878e8 - 1.05721e8i) q^{72} +1.08126e9i q^{73} -1.93847e9i q^{74} +7.94209e8 q^{76} +1.56413e8 q^{77} +(1.68723e9 - 1.31161e8i) q^{78} +1.86628e9 q^{79} +(3.32023e9 - 1.06476e9i) q^{81} -8.12446e8i q^{82} +1.09562e9 q^{83} +(8.31737e7 - 6.46574e6i) q^{84} +8.28736e8i q^{86} +(-7.20298e9 + 5.59944e8i) q^{87} -2.70247e9i q^{88} -5.19876e9i q^{89} +2.06376e8 q^{91} -2.85466e9 q^{92} +(5.82647e8 + 7.49503e9i) q^{93} -7.44163e8 q^{94} +(-1.11713e8 - 1.43705e9i) q^{96} +1.07471e10i q^{97} -6.38151e9 q^{98} +(-2.12870e9 - 1.36088e10i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9} + O(q^{10})$$ $$8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9} + 2097152 q^{16} + 3137456 q^{19} + 19256016 q^{21} + 5505024 q^{24} - 43571696 q^{31} - 302174208 q^{34} - 162828288 q^{36} - 434574480 q^{39} + 377628672 q^{46} + 100116840 q^{49} - 1417153536 q^{51} - 963325440 q^{54} - 2368077488 q^{61} + 1073741824 q^{64} + 6246890496 q^{66} - 1192536576 q^{69} + 1606377472 q^{76} - 398565136 q^{79} + 2917929096 q^{81} + 9859080192 q^{84} + 16634464160 q^{91} - 17010954240 q^{94} + 2818572288 q^{96} + 5253825024 q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$$.

 $$n$$ $$101$$ $$127$$ $$\chi(n)$$ $$-1$$ $$-1$$

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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −22.6274 −0.707107
$$3$$ 18.8335 + 242.269i 0.0775039 + 0.996992i
$$4$$ 512.000 0.500000
$$5$$ 0 0
$$6$$ −426.153 5481.92i −0.0548036 0.704980i
$$7$$ 670.530i 0.0398959i −0.999801 0.0199479i $$-0.993650\pi$$
0.999801 0.0199479i $$-0.00635004\pi$$
$$8$$ −11585.2 −0.353553
$$9$$ −58339.6 + 9125.53i −0.987986 + 0.154542i
$$10$$ 0 0
$$11$$ 233268.i 1.44841i 0.689583 + 0.724206i $$0.257794\pi$$
−0.689583 + 0.724206i $$0.742206\pi$$
$$12$$ 9642.73 + 124042.i 0.0387520 + 0.498496i
$$13$$ 307781.i 0.828943i 0.910062 + 0.414471i $$0.136033\pi$$
−0.910062 + 0.414471i $$0.863967\pi$$
$$14$$ 15172.4i 0.0282106i
$$15$$ 0 0
$$16$$ 262144. 0.250000
$$17$$ 672324. 0.473515 0.236758 0.971569i $$-0.423915\pi$$
0.236758 + 0.971569i $$0.423915\pi$$
$$18$$ 1.32007e6 206487.i 0.698612 0.109277i
$$19$$ 1.55119e6 0.626465 0.313233 0.949676i $$-0.398588\pi$$
0.313233 + 0.949676i $$0.398588\pi$$
$$20$$ 0 0
$$21$$ 162449. 12628.4i 0.0397758 0.00309209i
$$22$$ 5.27826e6i 1.02418i
$$23$$ −5.57551e6 −0.866255 −0.433127 0.901333i $$-0.642590\pi$$
−0.433127 + 0.901333i $$0.642590\pi$$
$$24$$ −218190. 2.80674e6i −0.0274018 0.352490i
$$25$$ 0 0
$$26$$ 6.96428e6i 0.586151i
$$27$$ −3.30957e6 1.39620e7i −0.230650 0.973037i
$$28$$ 343311.i 0.0199479i
$$29$$ 2.97313e7i 1.44952i 0.689001 + 0.724760i $$0.258049\pi$$
−0.689001 + 0.724760i $$0.741951\pi$$
$$30$$ 0 0
$$31$$ 3.09368e7 1.08061 0.540303 0.841471i $$-0.318310\pi$$
0.540303 + 0.841471i $$0.318310\pi$$
$$32$$ −5.93164e6 −0.176777
$$33$$ −5.65137e7 + 4.39325e6i −1.44406 + 0.112258i
$$34$$ −1.52130e7 −0.334826
$$35$$ 0 0
$$36$$ −2.98699e7 + 4.67227e6i −0.493993 + 0.0772708i
$$37$$ 8.56690e7i 1.23542i 0.786406 + 0.617711i $$0.211940\pi$$
−0.786406 + 0.617711i $$0.788060\pi$$
$$38$$ −3.50994e7 −0.442978
$$39$$ −7.45657e7 + 5.79657e6i −0.826449 + 0.0642463i
$$40$$ 0 0
$$41$$ 3.59054e7i 0.309913i 0.987921 + 0.154957i $$0.0495238\pi$$
−0.987921 + 0.154957i $$0.950476\pi$$
$$42$$ −3.67579e6 + 285748.i −0.0281258 + 0.00218644i
$$43$$ 3.66253e7i 0.249137i −0.992211 0.124569i $$-0.960245\pi$$
0.992211 0.124569i $$-0.0397547\pi$$
$$44$$ 1.19433e8i 0.724206i
$$45$$ 0 0
$$46$$ 1.26159e8 0.612535
$$47$$ 3.28877e7 0.143398 0.0716992 0.997426i $$-0.477158\pi$$
0.0716992 + 0.997426i $$0.477158\pi$$
$$48$$ 4.93708e6 + 6.35094e7i 0.0193760 + 0.249248i
$$49$$ 2.82026e8 0.998408
$$50$$ 0 0
$$51$$ 1.26622e7 + 1.62883e8i 0.0366993 + 0.472091i
$$52$$ 1.57584e8i 0.414471i
$$53$$ −4.59194e8 −1.09804 −0.549019 0.835810i $$-0.684998\pi$$
−0.549019 + 0.835810i $$0.684998\pi$$
$$54$$ 7.48870e7 + 3.15924e8i 0.163094 + 0.688041i
$$55$$ 0 0
$$56$$ 7.76824e6i 0.0141053i
$$57$$ 2.92143e7 + 3.75805e8i 0.0485535 + 0.624581i
$$58$$ 6.72743e8i 1.02497i
$$59$$ 4.88657e8i 0.683508i 0.939789 + 0.341754i $$0.111021\pi$$
−0.939789 + 0.341754i $$0.888979\pi$$
$$60$$ 0 0
$$61$$ −6.12928e7 −0.0725705 −0.0362852 0.999341i $$-0.511552\pi$$
−0.0362852 + 0.999341i $$0.511552\pi$$
$$62$$ −7.00020e8 −0.764103
$$63$$ 6.11894e6 + 3.91184e7i 0.00616557 + 0.0394166i
$$64$$ 1.34218e8 0.125000
$$65$$ 0 0
$$66$$ 1.27876e9 9.94079e7i 1.02110 0.0793782i
$$67$$ 6.70776e8i 0.496825i 0.968654 + 0.248413i $$0.0799089\pi$$
−0.968654 + 0.248413i $$0.920091\pi$$
$$68$$ 3.44230e8 0.236758
$$69$$ −1.05006e8 1.35077e9i −0.0671382 0.863649i
$$70$$ 0 0
$$71$$ 1.23330e9i 0.683561i 0.939780 + 0.341781i $$0.111030\pi$$
−0.939780 + 0.341781i $$0.888970\pi$$
$$72$$ 6.75878e8 1.05721e8i 0.349306 0.0546387i
$$73$$ 1.08126e9i 0.521573i 0.965396 + 0.260787i $$0.0839819\pi$$
−0.965396 + 0.260787i $$0.916018\pi$$
$$74$$ 1.93847e9i 0.873575i
$$75$$ 0 0
$$76$$ 7.94209e8 0.313233
$$77$$ 1.56413e8 0.0577857
$$78$$ 1.68723e9 1.31161e8i 0.584388 0.0454290i
$$79$$ 1.86628e9 0.606515 0.303258 0.952909i $$-0.401926\pi$$
0.303258 + 0.952909i $$0.401926\pi$$
$$80$$ 0 0
$$81$$ 3.32023e9 1.06476e9i 0.952234 0.305370i
$$82$$ 8.12446e8i 0.219142i
$$83$$ 1.09562e9 0.278145 0.139072 0.990282i $$-0.455588\pi$$
0.139072 + 0.990282i $$0.455588\pi$$
$$84$$ 8.31737e7 6.46574e6i 0.0198879 0.00154604i
$$85$$ 0 0
$$86$$ 8.28736e8i 0.176167i
$$87$$ −7.20298e9 + 5.59944e8i −1.44516 + 0.112344i
$$88$$ 2.70247e9i 0.512091i
$$89$$ 5.19876e9i 0.931000i −0.885048 0.465500i $$-0.845874\pi$$
0.885048 0.465500i $$-0.154126\pi$$
$$90$$ 0 0
$$91$$ 2.06376e8 0.0330714
$$92$$ −2.85466e9 −0.433127
$$93$$ 5.82647e8 + 7.49503e9i 0.0837512 + 1.07735i
$$94$$ −7.44163e8 −0.101398
$$95$$ 0 0
$$96$$ −1.11713e8 1.43705e9i −0.0137009 0.176245i
$$97$$ 1.07471e10i 1.25150i 0.780024 + 0.625750i $$0.215207\pi$$
−0.780024 + 0.625750i $$0.784793\pi$$
$$98$$ −6.38151e9 −0.705981
$$99$$ −2.12870e9 1.36088e10i −0.223840 1.43101i
$$100$$ 0 0
$$101$$ 1.08154e10i 1.02905i −0.857475 0.514525i $$-0.827968\pi$$
0.857475 0.514525i $$-0.172032\pi$$
$$102$$ −2.86513e8 3.68563e9i −0.0259503 0.333819i
$$103$$ 2.83446e9i 0.244503i −0.992499 0.122251i $$-0.960989\pi$$
0.992499 0.122251i $$-0.0390114\pi$$
$$104$$ 3.56571e9i 0.293075i
$$105$$ 0 0
$$106$$ 1.03904e10 0.776430
$$107$$ −2.41202e10 −1.71974 −0.859869 0.510515i $$-0.829455\pi$$
−0.859869 + 0.510515i $$0.829455\pi$$
$$108$$ −1.69450e9 7.14855e9i −0.115325 0.486518i
$$109$$ 5.43424e9 0.353188 0.176594 0.984284i $$-0.443492\pi$$
0.176594 + 0.984284i $$0.443492\pi$$
$$110$$ 0 0
$$111$$ −2.07549e10 + 1.61344e9i −1.23170 + 0.0957500i
$$112$$ 1.75775e8i 0.00997396i
$$113$$ −1.39305e10 −0.756092 −0.378046 0.925787i $$-0.623404\pi$$
−0.378046 + 0.925787i $$0.623404\pi$$
$$114$$ −6.61043e8 8.50350e9i −0.0343325 0.441645i
$$115$$ 0 0
$$116$$ 1.52224e10i 0.724760i
$$117$$ −2.80866e9 1.79558e10i −0.128106 0.818984i
$$118$$ 1.10570e10i 0.483313i
$$119$$ 4.50813e8i 0.0188913i
$$120$$ 0 0
$$121$$ −2.84767e10 −1.09790
$$122$$ 1.38690e9 0.0513151
$$123$$ −8.69877e9 + 6.76223e8i −0.308981 + 0.0240195i
$$124$$ 1.58396e10 0.540303
$$125$$ 0 0
$$126$$ −1.38456e8 8.85149e8i −0.00435972 0.0278717i
$$127$$ 4.08412e10i 1.23617i −0.786110 0.618087i $$-0.787908\pi$$
0.786110 0.618087i $$-0.212092\pi$$
$$128$$ −3.03700e9 −0.0883883
$$129$$ 8.87317e9 6.89781e8i 0.248388 0.0193091i
$$130$$ 0 0
$$131$$ 4.15498e10i 1.07699i 0.842628 + 0.538495i $$0.181007\pi$$
−0.842628 + 0.538495i $$0.818993\pi$$
$$132$$ −2.89350e10 + 2.24934e9i −0.722028 + 0.0561289i
$$133$$ 1.04012e9i 0.0249934i
$$134$$ 1.51779e10i 0.351308i
$$135$$ 0 0
$$136$$ −7.78903e9 −0.167413
$$137$$ −9.25532e10 −1.91773 −0.958867 0.283854i $$-0.908387\pi$$
−0.958867 + 0.283854i $$0.908387\pi$$
$$138$$ 2.37602e9 + 3.05645e10i 0.0474739 + 0.610692i
$$139$$ −7.95575e10 −1.53323 −0.766615 0.642107i $$-0.778061\pi$$
−0.766615 + 0.642107i $$0.778061\pi$$
$$140$$ 0 0
$$141$$ 6.19389e8 + 7.96767e9i 0.0111139 + 0.142967i
$$142$$ 2.79064e10i 0.483351i
$$143$$ −7.17955e10 −1.20065
$$144$$ −1.52934e10 + 2.39220e9i −0.246997 + 0.0386354i
$$145$$ 0 0
$$146$$ 2.44661e10i 0.368808i
$$147$$ 5.31152e9 + 6.83261e10i 0.0773806 + 0.995405i
$$148$$ 4.38625e10i 0.617711i
$$149$$ 8.07804e10i 1.09995i −0.835180 0.549977i $$-0.814636\pi$$
0.835180 0.549977i $$-0.185364\pi$$
$$150$$ 0 0
$$151$$ 3.08654e10 0.393176 0.196588 0.980486i $$-0.437014\pi$$
0.196588 + 0.980486i $$0.437014\pi$$
$$152$$ −1.79709e10 −0.221489
$$153$$ −3.92231e10 + 6.13531e9i −0.467827 + 0.0731778i
$$154$$ −3.53923e9 −0.0408606
$$155$$ 0 0
$$156$$ −3.81776e10 + 2.96785e9i −0.413225 + 0.0321232i
$$157$$ 9.71322e10i 1.01828i −0.860685 0.509138i $$-0.829964\pi$$
0.860685 0.509138i $$-0.170036\pi$$
$$158$$ −4.22291e10 −0.428871
$$159$$ −8.64822e9 1.11249e11i −0.0851023 1.09473i
$$160$$ 0 0
$$161$$ 3.73855e9i 0.0345600i
$$162$$ −7.51283e10 + 2.40928e10i −0.673331 + 0.215929i
$$163$$ 1.39440e11i 1.21185i −0.795520 0.605927i $$-0.792802\pi$$
0.795520 0.605927i $$-0.207198\pi$$
$$164$$ 1.83836e10i 0.154957i
$$165$$ 0 0
$$166$$ −2.47911e10 −0.196678
$$167$$ −1.25840e11 −0.968804 −0.484402 0.874845i $$-0.660963\pi$$
−0.484402 + 0.874845i $$0.660963\pi$$
$$168$$ −1.88201e9 + 1.46303e8i −0.0140629 + 0.00109322i
$$169$$ 4.31296e10 0.312854
$$170$$ 0 0
$$171$$ −9.04958e10 + 1.41554e10i −0.618939 + 0.0968149i
$$172$$ 1.87521e10i 0.124569i
$$173$$ 1.26257e11 0.814750 0.407375 0.913261i $$-0.366444\pi$$
0.407375 + 0.913261i $$0.366444\pi$$
$$174$$ 1.62985e11 1.26701e10i 1.02188 0.0794389i
$$175$$ 0 0
$$176$$ 6.11499e10i 0.362103i
$$177$$ −1.18386e11 + 9.20310e9i −0.681452 + 0.0529746i
$$178$$ 1.17635e11i 0.658317i
$$179$$ 2.96543e11i 1.61370i −0.590758 0.806848i $$-0.701171\pi$$
0.590758 0.806848i $$-0.298829\pi$$
$$180$$ 0 0
$$181$$ 2.48451e11 1.27893 0.639466 0.768819i $$-0.279155\pi$$
0.639466 + 0.768819i $$0.279155\pi$$
$$182$$ −4.66976e9 −0.0233850
$$183$$ −1.15435e9 1.48493e10i −0.00562450 0.0723522i
$$184$$ 6.45936e10 0.306267
$$185$$ 0 0
$$186$$ −1.31838e10 1.69593e11i −0.0592210 0.761805i
$$187$$ 1.56832e11i 0.685846i
$$188$$ 1.68385e10 0.0716992
$$189$$ −9.36194e9 + 2.21916e9i −0.0388201 + 0.00920196i
$$190$$ 0 0
$$191$$ 1.58050e11i 0.621769i −0.950448 0.310884i $$-0.899375\pi$$
0.950448 0.310884i $$-0.100625\pi$$
$$192$$ 2.52778e9 + 3.25168e10i 0.00968799 + 0.124624i
$$193$$ 3.78369e11i 1.41296i −0.707734 0.706479i $$-0.750283\pi$$
0.707734 0.706479i $$-0.249717\pi$$
$$194$$ 2.43178e11i 0.884944i
$$195$$ 0 0
$$196$$ 1.44397e11 0.499204
$$197$$ −1.89406e11 −0.638356 −0.319178 0.947695i $$-0.603407\pi$$
−0.319178 + 0.947695i $$0.603407\pi$$
$$198$$ 4.81669e10 + 3.07932e11i 0.158279 + 1.01188i
$$199$$ −5.02942e10 −0.161158 −0.0805791 0.996748i $$-0.525677\pi$$
−0.0805791 + 0.996748i $$0.525677\pi$$
$$200$$ 0 0
$$201$$ −1.62508e11 + 1.26330e10i −0.495331 + 0.0385059i
$$202$$ 2.44725e11i 0.727648i
$$203$$ 1.99357e10 0.0578298
$$204$$ 6.48304e9 + 8.33962e10i 0.0183496 + 0.236045i
$$205$$ 0 0
$$206$$ 6.41365e10i 0.172890i
$$207$$ 3.25273e11 5.08795e10i 0.855848 0.133872i
$$208$$ 8.06828e10i 0.207236i
$$209$$ 3.61843e11i 0.907380i
$$210$$ 0 0
$$211$$ 4.74970e11 1.13567 0.567837 0.823141i $$-0.307780\pi$$
0.567837 + 0.823141i $$0.307780\pi$$
$$212$$ −2.35108e11 −0.549019
$$213$$ −2.98791e11 + 2.32273e10i −0.681505 + 0.0529787i
$$214$$ 5.45778e11 1.21604
$$215$$ 0 0
$$216$$ 3.83422e10 + 1.61753e11i 0.0815470 + 0.344020i
$$217$$ 2.07440e10i 0.0431117i
$$218$$ −1.22963e11 −0.249742
$$219$$ −2.61955e11 + 2.03638e10i −0.520004 + 0.0404240i
$$220$$ 0 0
$$221$$ 2.06928e11i 0.392517i
$$222$$ 4.69631e11 3.65081e10i 0.870947 0.0677055i
$$223$$ 2.35580e11i 0.427183i −0.976923 0.213592i $$-0.931484\pi$$
0.976923 0.213592i $$-0.0685162\pi$$
$$224$$ 3.97734e9i 0.00705266i
$$225$$ 0 0
$$226$$ 3.15211e11 0.534638
$$227$$ 4.27026e11 0.708475 0.354238 0.935155i $$-0.384740\pi$$
0.354238 + 0.935155i $$0.384740\pi$$
$$228$$ 1.49577e10 + 1.92412e11i 0.0242768 + 0.312290i
$$229$$ −1.03671e12 −1.64619 −0.823096 0.567902i $$-0.807755\pi$$
−0.823096 + 0.567902i $$0.807755\pi$$
$$230$$ 0 0
$$231$$ 2.94580e9 + 3.78941e10i 0.00447862 + 0.0576119i
$$232$$ 3.44444e11i 0.512483i
$$233$$ 1.03766e12 1.51103 0.755516 0.655130i $$-0.227386\pi$$
0.755516 + 0.655130i $$0.227386\pi$$
$$234$$ 6.35527e10 + 4.06293e11i 0.0905847 + 0.579109i
$$235$$ 0 0
$$236$$ 2.50192e11i 0.341754i
$$237$$ 3.51485e10 + 4.52142e11i 0.0470073 + 0.604691i
$$238$$ 1.02007e10i 0.0133582i
$$239$$ 1.23687e12i 1.58612i 0.609144 + 0.793060i $$0.291513\pi$$
−0.609144 + 0.793060i $$0.708487\pi$$
$$240$$ 0 0
$$241$$ −1.03912e12 −1.27814 −0.639072 0.769147i $$-0.720682\pi$$
−0.639072 + 0.769147i $$0.720682\pi$$
$$242$$ 6.44354e11 0.776333
$$243$$ 3.20490e11 + 7.84337e11i 0.378253 + 0.925702i
$$244$$ −3.13819e10 −0.0362852
$$245$$ 0 0
$$246$$ 1.96831e11 1.53012e10i 0.218483 0.0169844i
$$247$$ 4.77426e11i 0.519304i
$$248$$ −3.58410e11 −0.382052
$$249$$ 2.06344e10 + 2.65436e11i 0.0215573 + 0.277308i
$$250$$ 0 0
$$251$$ 5.66781e11i 0.568914i 0.958689 + 0.284457i $$0.0918133\pi$$
−0.958689 + 0.284457i $$0.908187\pi$$
$$252$$ 3.13290e9 + 2.00286e10i 0.00308279 + 0.0197083i
$$253$$ 1.30059e12i 1.25469i
$$254$$ 9.24130e11i 0.874107i
$$255$$ 0 0
$$256$$ 6.87195e10 0.0625000
$$257$$ 1.27943e12 1.14117 0.570584 0.821239i $$-0.306717\pi$$
0.570584 + 0.821239i $$0.306717\pi$$
$$258$$ −2.00777e11 + 1.56080e10i −0.175637 + 0.0136536i
$$259$$ 5.74436e10 0.0492882
$$260$$ 0 0
$$261$$ −2.71314e11 1.73451e12i −0.224011 1.43211i
$$262$$ 9.40164e11i 0.761548i
$$263$$ −1.68583e12 −1.33978 −0.669892 0.742459i $$-0.733660\pi$$
−0.669892 + 0.742459i $$0.733660\pi$$
$$264$$ 6.54725e11 5.08968e10i 0.510551 0.0396891i
$$265$$ 0 0
$$266$$ 2.35352e10i 0.0176730i
$$267$$ 1.25950e12 9.79107e10i 0.928200 0.0721562i
$$268$$ 3.43437e11i 0.248413i
$$269$$ 1.34023e12i 0.951523i 0.879574 + 0.475761i $$0.157827\pi$$
−0.879574 + 0.475761i $$0.842173\pi$$
$$270$$ 0 0
$$271$$ −1.75349e12 −1.19966 −0.599829 0.800129i $$-0.704765\pi$$
−0.599829 + 0.800129i $$0.704765\pi$$
$$272$$ 1.76246e11 0.118379
$$273$$ 3.88677e9 + 4.99985e10i 0.00256316 + 0.0329719i
$$274$$ 2.09424e12 1.35604
$$275$$ 0 0
$$276$$ −5.37632e10 6.91597e11i −0.0335691 0.431825i
$$277$$ 1.69580e12i 1.03986i −0.854209 0.519930i $$-0.825958\pi$$
0.854209 0.519930i $$-0.174042\pi$$
$$278$$ 1.80018e12 1.08416
$$279$$ −1.80484e12 + 2.82315e11i −1.06762 + 0.166999i
$$280$$ 0 0
$$281$$ 2.44175e11i 0.139370i 0.997569 + 0.0696851i $$0.0221995\pi$$
−0.997569 + 0.0696851i $$0.977801\pi$$
$$282$$ −1.40152e10 1.80288e11i −0.00785874 0.101093i
$$283$$ 9.96409e11i 0.548916i −0.961599 0.274458i $$-0.911502\pi$$
0.961599 0.274458i $$-0.0884984\pi$$
$$284$$ 6.31450e11i 0.341781i
$$285$$ 0 0
$$286$$ 1.62455e12 0.848989
$$287$$ 2.40756e10 0.0123643
$$288$$ 3.46050e11 5.41294e10i 0.174653 0.0273194i
$$289$$ −1.56397e12 −0.775783
$$290$$ 0 0
$$291$$ −2.60368e12 + 2.02404e11i −1.24774 + 0.0969962i
$$292$$ 5.53604e11i 0.260787i
$$293$$ 1.57571e12 0.729690 0.364845 0.931068i $$-0.381122\pi$$
0.364845 + 0.931068i $$0.381122\pi$$
$$294$$ −1.20186e11 1.54604e12i −0.0547163 0.703858i
$$295$$ 0 0
$$296$$ 9.92496e11i 0.436787i
$$297$$ 3.25690e12 7.72018e11i 1.40936 0.334076i
$$298$$ 1.82785e12i 0.777786i
$$299$$ 1.71603e12i 0.718076i
$$300$$ 0 0
$$301$$ −2.45583e10 −0.00993955
$$302$$ −6.98405e11 −0.278018
$$303$$ 2.62024e12 2.03692e11i 1.02595 0.0797554i
$$304$$ 4.06635e11 0.156616
$$305$$ 0 0
$$306$$ 8.87518e11 1.38826e11i 0.330803 0.0517445i
$$307$$ 3.29823e12i 1.20945i 0.796434 + 0.604726i $$0.206717\pi$$
−0.796434 + 0.604726i $$0.793283\pi$$
$$308$$ 8.00836e10 0.0288928
$$309$$ 6.86702e11 5.33827e10i 0.243768 0.0189499i
$$310$$ 0 0
$$311$$ 1.67301e12i 0.575038i 0.957775 + 0.287519i $$0.0928304\pi$$
−0.957775 + 0.287519i $$0.907170\pi$$
$$312$$ 8.63862e11 6.71547e10i 0.292194 0.0227145i
$$313$$ 1.73318e12i 0.576930i 0.957490 + 0.288465i $$0.0931449\pi$$
−0.957490 + 0.288465i $$0.906855\pi$$
$$314$$ 2.19785e12i 0.720029i
$$315$$ 0 0
$$316$$ 9.55536e11 0.303258
$$317$$ −1.33100e12 −0.415798 −0.207899 0.978150i $$-0.566663\pi$$
−0.207899 + 0.978150i $$0.566663\pi$$
$$318$$ 1.95687e11 + 2.51727e12i 0.0601764 + 0.774094i
$$319$$ −6.93538e12 −2.09950
$$320$$ 0 0
$$321$$ −4.54267e11 5.84358e12i −0.133286 1.71456i
$$322$$ 8.45937e10i 0.0244376i
$$323$$ 1.04290e12 0.296641
$$324$$ 1.69996e12 5.45157e11i 0.476117 0.152685i
$$325$$ 0 0
$$326$$ 3.15518e12i 0.856911i
$$327$$ 1.02345e11 + 1.31655e12i 0.0273735 + 0.352126i
$$328$$ 4.15973e11i 0.109571i
$$329$$ 2.20522e10i 0.00572100i
$$330$$ 0 0
$$331$$ 4.71961e12 1.18786 0.593931 0.804516i $$-0.297575\pi$$
0.593931 + 0.804516i $$0.297575\pi$$
$$332$$ 5.60959e11 0.139072
$$333$$ −7.81775e11 4.99789e12i −0.190924 1.22058i
$$334$$ 2.84743e12 0.685048
$$335$$ 0 0
$$336$$ 4.25849e10 3.31046e9i 0.00994396 0.000773022i
$$337$$ 4.15283e12i 0.955422i −0.878517 0.477711i $$-0.841467\pi$$
0.878517 0.477711i $$-0.158533\pi$$
$$338$$ −9.75911e11 −0.221221
$$339$$ −2.62360e11 3.37493e12i −0.0586001 0.753818i
$$340$$ 0 0
$$341$$ 7.21658e12i 1.56516i
$$342$$ 2.04769e12 3.20301e11i 0.437656 0.0684585i
$$343$$ 3.78515e11i 0.0797282i
$$344$$ 4.24313e11i 0.0880833i
$$345$$ 0 0
$$346$$ −2.85687e12 −0.576115
$$347$$ −4.39939e12 −0.874470 −0.437235 0.899347i $$-0.644042\pi$$
−0.437235 + 0.899347i $$0.644042\pi$$
$$348$$ −3.68793e12 + 2.86691e11i −0.722580 + 0.0561718i
$$349$$ 9.24002e12 1.78462 0.892310 0.451423i $$-0.149083\pi$$
0.892310 + 0.451423i $$0.149083\pi$$
$$350$$ 0 0
$$351$$ 4.29724e12 1.01862e12i 0.806592 0.191195i
$$352$$ 1.38366e12i 0.256046i
$$353$$ −9.20733e11 −0.167981 −0.0839905 0.996467i $$-0.526767\pi$$
−0.0839905 + 0.996467i $$0.526767\pi$$
$$354$$ 2.67878e12 2.08242e11i 0.481860 0.0374587i
$$355$$ 0 0
$$356$$ 2.66177e12i 0.465500i
$$357$$ 1.09218e11 8.49037e9i 0.0188345 0.00146415i
$$358$$ 6.70999e12i 1.14106i
$$359$$ 6.17595e12i 1.03569i 0.855473 + 0.517847i $$0.173267\pi$$
−0.855473 + 0.517847i $$0.826733\pi$$
$$360$$ 0 0
$$361$$ −3.72488e12 −0.607542
$$362$$ −5.62180e12 −0.904342
$$363$$ −5.36315e11 6.89902e12i −0.0850916 1.09460i
$$364$$ 1.05665e11 0.0165357
$$365$$ 0 0
$$366$$ 2.61201e10 + 3.36002e11i 0.00397712 + 0.0511607i
$$367$$ 8.19379e12i 1.23071i 0.788252 + 0.615353i $$0.210987\pi$$
−0.788252 + 0.615353i $$0.789013\pi$$
$$368$$ −1.46159e12 −0.216564
$$369$$ −3.27656e11 2.09471e12i −0.0478945 0.306190i
$$370$$ 0 0
$$371$$ 3.07903e11i 0.0438072i
$$372$$ 2.98315e11 + 3.83746e12i 0.0418756 + 0.538677i
$$373$$ 9.07322e12i 1.25666i −0.777947 0.628329i $$-0.783739\pi$$
0.777947 0.628329i $$-0.216261\pi$$
$$374$$ 3.54870e12i 0.484966i
$$375$$ 0 0
$$376$$ −3.81012e11 −0.0506990
$$377$$ −9.15072e12 −1.20157
$$378$$ 2.11837e11 5.02140e10i 0.0274500 0.00650677i
$$379$$ −1.17817e13 −1.50665 −0.753324 0.657650i $$-0.771551\pi$$
−0.753324 + 0.657650i $$0.771551\pi$$
$$380$$ 0 0
$$381$$ 9.89455e12 7.69180e11i 1.23246 0.0958083i
$$382$$ 3.57627e12i 0.439657i
$$383$$ −6.82336e12 −0.827950 −0.413975 0.910288i $$-0.635860\pi$$
−0.413975 + 0.910288i $$0.635860\pi$$
$$384$$ −5.71972e10 7.35771e11i −0.00685045 0.0881225i
$$385$$ 0 0
$$386$$ 8.56152e12i 0.999112i
$$387$$ 3.34225e11 + 2.13670e12i 0.0385021 + 0.246144i
$$388$$ 5.50249e12i 0.625750i
$$389$$ 7.07814e11i 0.0794642i −0.999210 0.0397321i $$-0.987350\pi$$
0.999210 0.0397321i $$-0.0126504\pi$$
$$390$$ 0 0
$$391$$ −3.74855e12 −0.410185
$$392$$ −3.26733e12 −0.352991
$$393$$ −1.00662e13 + 7.82526e11i −1.07375 + 0.0834710i
$$394$$ 4.28577e12 0.451386
$$395$$ 0 0
$$396$$ −1.08989e12 6.96770e12i −0.111920 0.715506i
$$397$$ 1.26553e12i 0.128328i −0.997939 0.0641639i $$-0.979562\pi$$
0.997939 0.0641639i $$-0.0204380\pi$$
$$398$$ 1.13803e12 0.113956
$$399$$ 2.51989e11 1.95890e10i 0.0249182 0.00193708i
$$400$$ 0 0
$$401$$ 1.50259e13i 1.44917i 0.689187 + 0.724583i $$0.257968\pi$$
−0.689187 + 0.724583i $$0.742032\pi$$
$$402$$ 3.67714e12 2.85853e11i 0.350252 0.0272278i
$$403$$ 9.52175e12i 0.895760i
$$404$$ 5.53749e12i 0.514525i
$$405$$ 0 0
$$406$$ −4.51094e11 −0.0408919
$$407$$ −1.99839e13 −1.78940
$$408$$ −1.46694e11 1.88704e12i −0.0129752 0.166909i
$$409$$ 1.70362e12 0.148852 0.0744261 0.997227i $$-0.476288\pi$$
0.0744261 + 0.997227i $$0.476288\pi$$
$$410$$ 0 0
$$411$$ −1.74310e12 2.24228e13i −0.148632 1.91197i
$$412$$ 1.45124e12i 0.122251i
$$413$$ 3.27659e11 0.0272692
$$414$$ −7.36009e12 + 1.15127e12i −0.605176 + 0.0946621i
$$415$$ 0 0
$$416$$ 1.82564e12i 0.146538i
$$417$$ −1.49834e12 1.92743e13i −0.118831 1.52862i
$$418$$ 8.18758e12i 0.641615i
$$419$$ 2.22448e13i 1.72250i −0.508185 0.861248i $$-0.669683\pi$$
0.508185 0.861248i $$-0.330317\pi$$
$$420$$ 0 0
$$421$$ 1.82948e11 0.0138330 0.00691650 0.999976i $$-0.497798\pi$$
0.00691650 + 0.999976i $$0.497798\pi$$
$$422$$ −1.07473e13 −0.803043
$$423$$ −1.91865e12 + 3.00118e11i −0.141676 + 0.0221610i
$$424$$ 5.31988e12 0.388215
$$425$$ 0 0
$$426$$ 6.76086e12 5.25574e11i 0.481897 0.0374616i
$$427$$ 4.10986e10i 0.00289526i
$$428$$ −1.23495e13 −0.859869
$$429$$ −1.35216e12 1.73938e13i −0.0930552 1.19704i
$$430$$ 0 0
$$431$$ 6.64491e12i 0.446789i 0.974728 + 0.223395i $$0.0717139\pi$$
−0.974728 + 0.223395i $$0.928286\pi$$
$$432$$ −8.67584e11 3.66006e12i −0.0576624 0.243259i
$$433$$ 7.28337e12i 0.478512i 0.970956 + 0.239256i $$0.0769036\pi$$
−0.970956 + 0.239256i $$0.923096\pi$$
$$434$$ 4.69384e11i 0.0304846i
$$435$$ 0 0
$$436$$ 2.78233e12 0.176594
$$437$$ −8.64868e12 −0.542678
$$438$$ 5.92738e12 4.60781e11i 0.367699 0.0285841i
$$439$$ 1.52600e13 0.935907 0.467954 0.883753i $$-0.344991\pi$$
0.467954 + 0.883753i $$0.344991\pi$$
$$440$$ 0 0
$$441$$ −1.64533e13 + 2.57363e12i −0.986414 + 0.154296i
$$442$$ 4.68225e12i 0.277551i
$$443$$ 1.83304e13 1.07437 0.537184 0.843465i $$-0.319488\pi$$
0.537184 + 0.843465i $$0.319488\pi$$
$$444$$ −1.06265e13 + 8.26083e11i −0.615852 + 0.0478750i
$$445$$ 0 0
$$446$$ 5.33057e12i 0.302064i
$$447$$ 1.95706e13 1.52138e12i 1.09665 0.0852508i
$$448$$ 8.99970e10i 0.00498698i
$$449$$ 8.33876e12i 0.456951i −0.973550 0.228475i $$-0.926626\pi$$
0.973550 0.228475i $$-0.0733741\pi$$
$$450$$ 0 0
$$451$$ −8.37559e12 −0.448883
$$452$$ −7.13242e12 −0.378046
$$453$$ 5.81303e11 + 7.47774e12i 0.0304727 + 0.391994i
$$454$$ −9.66249e12 −0.500968
$$455$$ 0 0
$$456$$ −3.38454e11 4.35379e12i −0.0171663 0.220823i
$$457$$ 4.12288e11i 0.0206833i −0.999947 0.0103416i $$-0.996708\pi$$
0.999947 0.0103416i $$-0.00329191\pi$$
$$458$$ 2.34581e13 1.16403
$$459$$ −2.22510e12 9.38700e12i −0.109216 0.460748i
$$460$$ 0 0
$$461$$ 1.66247e11i 0.00798453i 0.999992 + 0.00399226i $$0.00127078\pi$$
−0.999992 + 0.00399226i $$0.998729\pi$$
$$462$$ −6.66559e10 8.57446e11i −0.00316686 0.0407377i
$$463$$ 1.27323e13i 0.598416i 0.954188 + 0.299208i $$0.0967224\pi$$
−0.954188 + 0.299208i $$0.903278\pi$$
$$464$$ 7.79389e12i 0.362380i
$$465$$ 0 0
$$466$$ −2.34795e13 −1.06846
$$467$$ −2.26689e13 −1.02058 −0.510288 0.860004i $$-0.670461\pi$$
−0.510288 + 0.860004i $$0.670461\pi$$
$$468$$ −1.43803e12 9.19337e12i −0.0640531 0.409492i
$$469$$ 4.49775e11 0.0198213
$$470$$ 0 0
$$471$$ 2.35321e13 1.82934e12i 1.01521 0.0789203i
$$472$$ 5.66120e12i 0.241657i
$$473$$ 8.54352e12 0.360854
$$474$$ −7.95321e11 1.02308e13i −0.0332392 0.427581i
$$475$$ 0 0
$$476$$ 2.30816e11i 0.00944565i
$$477$$ 2.67892e13 4.19039e12i 1.08485 0.169693i
$$478$$ 2.79873e13i 1.12156i
$$479$$ 2.39654e13i 0.950402i 0.879877 + 0.475201i $$0.157625\pi$$
−0.879877 + 0.475201i $$0.842375\pi$$
$$480$$ 0 0
$$481$$ −2.63673e13 −1.02409
$$482$$ 2.35126e13 0.903785
$$483$$ −9.05734e11 + 7.04098e10i −0.0344560 + 0.00267853i
$$484$$ −1.45801e13 −0.548950
$$485$$ 0 0
$$486$$ −7.25186e12 1.77475e13i −0.267466 0.654570i
$$487$$ 1.13824e13i 0.415516i 0.978180 + 0.207758i $$0.0666167\pi$$
−0.978180 + 0.207758i $$0.933383\pi$$
$$488$$ 7.10091e11 0.0256575
$$489$$ 3.37821e13 2.62615e12i 1.20821 0.0939235i
$$490$$ 0 0
$$491$$ 3.59512e13i 1.25981i 0.776672 + 0.629906i $$0.216906\pi$$
−0.776672 + 0.629906i $$0.783094\pi$$
$$492$$ −4.45377e12 + 3.46226e11i −0.154491 + 0.0120098i
$$493$$ 1.99891e13i 0.686370i
$$494$$ 1.08029e13i 0.367203i
$$495$$ 0 0
$$496$$ 8.10990e12 0.270151
$$497$$ 8.26965e11 0.0272713
$$498$$ −4.66903e11 6.00612e12i −0.0152433 0.196086i
$$499$$ 1.33630e13 0.431917 0.215958 0.976403i $$-0.430712\pi$$
0.215958 + 0.976403i $$0.430712\pi$$
$$500$$ 0 0
$$501$$ −2.37000e12 3.04871e13i −0.0750862 0.965890i
$$502$$ 1.28248e13i 0.402283i
$$503$$ −3.54934e13 −1.10232 −0.551160 0.834399i $$-0.685815\pi$$
−0.551160 + 0.834399i $$0.685815\pi$$
$$504$$ −7.08893e10 4.53196e11i −0.00217986 0.0139359i
$$505$$ 0 0
$$506$$ 2.94290e13i 0.887203i
$$507$$ 8.12280e11 + 1.04490e13i 0.0242474 + 0.311913i
$$508$$ 2.09107e13i 0.618087i
$$509$$ 6.07337e13i 1.77763i 0.458269 + 0.888813i $$0.348470\pi$$
−0.458269 + 0.888813i $$0.651530\pi$$
$$510$$ 0 0
$$511$$ 7.25016e11 0.0208086
$$512$$ −1.55494e12 −0.0441942
$$513$$ −5.13377e12 2.16577e13i −0.144494 0.609574i
$$514$$ −2.89501e13 −0.806928
$$515$$ 0 0
$$516$$ 4.54307e12 3.53168e11i 0.124194 0.00965456i
$$517$$ 7.67166e12i 0.207700i
$$518$$ −1.29980e12 −0.0348520
$$519$$ 2.37785e12 + 3.05881e13i 0.0631464 + 0.812299i
$$520$$ 0 0
$$521$$ 2.06244e13i 0.537270i −0.963242 0.268635i $$-0.913427\pi$$
0.963242 0.268635i $$-0.0865726\pi$$
$$522$$ 6.13914e12 + 3.92476e13i 0.158400 + 1.01265i
$$523$$ 5.24376e13i 1.34009i 0.742320 + 0.670045i $$0.233725\pi$$
−0.742320 + 0.670045i $$0.766275\pi$$
$$524$$ 2.12735e13i 0.538495i
$$525$$ 0 0
$$526$$ 3.81460e13 0.947370
$$527$$ 2.07996e13 0.511683
$$528$$ −1.48147e13 + 1.15166e12i −0.361014 + 0.0280644i
$$529$$ −1.03402e13 −0.249603
$$530$$ 0 0
$$531$$ −4.45925e12 2.85080e13i −0.105631 0.675297i
$$532$$ 5.32541e11i 0.0124967i
$$533$$ −1.10510e13 −0.256900
$$534$$ −2.84992e13 + 2.21547e12i −0.656337 + 0.0510221i
$$535$$ 0 0
$$536$$ 7.77110e12i 0.175654i
$$537$$ 7.18431e13 5.58492e12i 1.60884 0.125068i
$$538$$ 3.03260e13i 0.672828i
$$539$$ 6.57877e13i 1.44611i
$$540$$ 0 0
$$541$$ 8.20249e13 1.76994 0.884972 0.465645i $$-0.154178\pi$$
0.884972 + 0.465645i $$0.154178\pi$$
$$542$$ 3.96770e13 0.848286
$$543$$ 4.67919e12 + 6.01919e13i 0.0991223 + 1.27509i
$$544$$ −3.98798e12 −0.0837064
$$545$$ 0 0
$$546$$ −8.79477e10 1.13134e12i −0.00181243 0.0233147i
$$547$$ 1.62332e13i 0.331488i 0.986169 + 0.165744i $$0.0530025\pi$$
−0.986169 + 0.165744i $$0.946997\pi$$
$$548$$ −4.73872e13 −0.958867
$$549$$ 3.57580e12 5.59329e11i 0.0716987 0.0112152i
$$550$$ 0 0
$$551$$ 4.61189e13i 0.908074i
$$552$$ 1.21652e12 + 1.56490e13i 0.0237369 + 0.305346i
$$553$$ 1.25140e12i 0.0241974i
$$554$$ 3.83715e13i 0.735292i
$$555$$ 0 0
$$556$$ −4.07335e13 −0.766615
$$557$$ −1.12168e13 −0.209215 −0.104608 0.994514i $$-0.533359\pi$$
−0.104608 + 0.994514i $$0.533359\pi$$
$$558$$ 4.08389e13 6.38805e12i 0.754924 0.118086i
$$559$$ 1.12726e13 0.206521
$$560$$ 0 0
$$561$$ −3.79955e13 + 2.95369e12i −0.683783 + 0.0531557i
$$562$$ 5.52506e12i 0.0985497i
$$563$$ 7.98522e13 1.41171 0.705854 0.708357i $$-0.250563\pi$$
0.705854 + 0.708357i $$0.250563\pi$$
$$564$$ 3.17127e11 + 4.07945e12i 0.00555697 + 0.0714835i
$$565$$ 0 0
$$566$$ 2.25462e13i 0.388142i
$$567$$ −7.13953e11 2.22632e12i −0.0121830 0.0379902i
$$568$$ 1.42881e13i 0.241675i
$$569$$ 9.95594e11i 0.0166925i 0.999965 + 0.00834624i $$0.00265672\pi$$
−0.999965 + 0.00834624i $$0.997343\pi$$
$$570$$ 0 0
$$571$$ 1.07836e14 1.77657 0.888283 0.459297i $$-0.151899\pi$$
0.888283 + 0.459297i $$0.151899\pi$$
$$572$$ −3.67593e13 −0.600326
$$573$$ 3.82907e13 2.97664e12i 0.619899 0.0481895i
$$574$$ −5.44769e11 −0.00874285
$$575$$ 0 0
$$576$$ −7.83021e12 + 1.22481e12i −0.123498 + 0.0193177i
$$577$$ 3.31000e13i 0.517546i −0.965938 0.258773i $$-0.916682\pi$$
0.965938 0.258773i $$-0.0833182\pi$$
$$578$$ 3.53887e13 0.548562
$$579$$ 9.16671e13 7.12600e12i 1.40871 0.109510i
$$580$$ 0 0
$$581$$ 7.34648e11i 0.0110968i
$$582$$ 5.89145e13 4.57989e12i 0.882282 0.0685867i
$$583$$ 1.07116e14i 1.59041i
$$584$$ 1.25266e13i 0.184404i
$$585$$ 0 0
$$586$$ −3.56543e13 −0.515969
$$587$$ 1.21022e14 1.73650 0.868248 0.496131i $$-0.165246\pi$$
0.868248 + 0.496131i $$0.165246\pi$$
$$588$$ 2.71950e12 + 3.49830e13i 0.0386903 + 0.497703i
$$589$$ 4.79889e13 0.676961
$$590$$ 0 0
$$591$$ −3.56717e12 4.58873e13i −0.0494751 0.636436i
$$592$$ 2.24576e13i 0.308855i
$$593$$ 8.43944e12 0.115091 0.0575453 0.998343i $$-0.481673\pi$$
0.0575453 + 0.998343i $$0.481673\pi$$
$$594$$ −7.36952e13 + 1.74688e13i −0.996567 + 0.236227i
$$595$$ 0 0
$$596$$ 4.13596e13i 0.549977i
$$597$$ −9.47213e11 1.21847e13i −0.0124904 0.160673i
$$598$$ 3.88294e13i 0.507756i
$$599$$ 3.11882e13i 0.404443i −0.979340 0.202221i $$-0.935184\pi$$
0.979340 0.202221i $$-0.0648160\pi$$
$$600$$ 0 0
$$601$$ 2.87401e13 0.366535 0.183267 0.983063i $$-0.441333\pi$$
0.183267 + 0.983063i $$0.441333\pi$$
$$602$$ 5.55692e11 0.00702832
$$603$$ −6.12119e12 3.91328e13i −0.0767802 0.490857i
$$604$$ 1.58031e13 0.196588
$$605$$ 0 0
$$606$$ −5.92893e13 + 4.60902e12i −0.725459 + 0.0563956i
$$607$$ 4.47536e13i 0.543106i 0.962423 + 0.271553i $$0.0875372\pi$$
−0.962423 + 0.271553i $$0.912463\pi$$
$$608$$ −9.20110e12 −0.110744
$$609$$ 3.75459e11 + 4.82981e12i 0.00448204 + 0.0576559i
$$610$$ 0 0
$$611$$ 1.01222e13i 0.118869i
$$612$$ −2.00822e13 + 3.14128e12i −0.233913 + 0.0365889i
$$613$$ 6.78051e13i 0.783358i 0.920102 + 0.391679i $$0.128106\pi$$
−0.920102 + 0.391679i $$0.871894\pi$$
$$614$$ 7.46303e13i 0.855211i
$$615$$ 0 0
$$616$$ −1.81209e12 −0.0204303
$$617$$ −2.48261e12 −0.0277641 −0.0138820 0.999904i $$-0.504419\pi$$
−0.0138820 + 0.999904i $$0.504419\pi$$
$$618$$ −1.55383e13 + 1.20791e12i −0.172370 + 0.0133996i
$$619$$ −1.64000e13 −0.180464 −0.0902320 0.995921i $$-0.528761\pi$$
−0.0902320 + 0.995921i $$0.528761\pi$$
$$620$$ 0 0
$$621$$ 1.84526e13 + 7.78454e13i 0.199801 + 0.842898i
$$622$$ 3.78559e13i 0.406613i
$$623$$ −3.48592e12 −0.0371431
$$624$$ −1.95470e13 + 1.51954e12i −0.206612 + 0.0160616i
$$625$$ 0 0
$$626$$ 3.92175e13i 0.407951i
$$627$$ −8.76635e13 + 6.81476e12i −0.904651 + 0.0703255i
$$628$$ 4.97317e13i 0.509138i
$$629$$ 5.75973e13i 0.584991i
$$630$$ 0 0
$$631$$ −1.37258e13 −0.137211 −0.0686056 0.997644i $$-0.521855\pi$$
−0.0686056 + 0.997644i $$0.521855\pi$$
$$632$$ −2.16213e13 −0.214435
$$633$$ 8.94532e12 + 1.15070e14i 0.0880192 + 1.13226i
$$634$$ 3.01171e13 0.294014
$$635$$ 0 0
$$636$$ −4.42789e12 5.69593e13i −0.0425511 0.547367i
$$637$$ 8.68020e13i 0.827623i
$$638$$ 1.56930e14 1.48457
$$639$$ −1.12545e13 7.19503e13i −0.105639 0.675349i
$$640$$ 0 0
$$641$$ 5.42348e13i 0.501173i −0.968094 0.250587i $$-0.919377\pi$$
0.968094 0.250587i $$-0.0806235\pi$$
$$642$$ 1.02789e13 + 1.32225e14i 0.0942477 + 1.21238i
$$643$$ 5.54693e13i 0.504659i −0.967641 0.252329i $$-0.918803\pi$$
0.967641 0.252329i $$-0.0811966\pi$$
$$644$$ 1.91414e12i 0.0172800i
$$645$$ 0 0
$$646$$ −2.35982e13 −0.209757
$$647$$ 5.56652e13 0.490979 0.245489 0.969399i $$-0.421051\pi$$
0.245489 + 0.969399i $$0.421051\pi$$
$$648$$ −3.84657e13 + 1.23355e13i −0.336665 + 0.107965i
$$649$$ −1.13988e14 −0.990002
$$650$$ 0 0
$$651$$ 5.02564e12 3.90682e11i 0.0429820 0.00334132i
$$652$$ 7.13935e13i 0.605927i
$$653$$ 5.56792e13 0.468951 0.234475 0.972122i $$-0.424663\pi$$
0.234475 + 0.972122i $$0.424663\pi$$
$$654$$ −2.31581e12 2.97901e13i −0.0193560 0.248991i
$$655$$ 0 0
$$656$$ 9.41238e12i 0.0774784i
$$657$$ −9.86706e12 6.30802e13i −0.0806048 0.515307i
$$658$$ 4.98984e11i 0.00404536i
$$659$$ 1.52699e14i 1.22860i −0.789074 0.614298i $$-0.789439\pi$$
0.789074 0.614298i $$-0.210561\pi$$
$$660$$ 0 0
$$661$$ −2.08036e14 −1.64866 −0.824329 0.566111i $$-0.808447\pi$$
−0.824329 + 0.566111i $$0.808447\pi$$
$$662$$ −1.06793e14 −0.839945
$$663$$ −5.01323e13 + 3.89717e12i −0.391336 + 0.0304216i
$$664$$ −1.26931e13 −0.0983390
$$665$$ 0 0
$$666$$ 1.76895e13 + 1.13089e14i 0.135004 + 0.863080i
$$667$$ 1.65767e14i 1.25565i
$$668$$ −6.44300e13 −0.484402
$$669$$ 5.70737e13 4.43679e12i 0.425898 0.0331084i
$$670$$ 0 0
$$671$$ 1.42977e13i 0.105112i
$$672$$ −9.63587e11 + 7.49071e10i −0.00703144 + 0.000546609i
$$673$$ 9.45260e13i 0.684662i −0.939579 0.342331i $$-0.888784\pi$$
0.939579 0.342331i $$-0.111216\pi$$
$$674$$ 9.39679e13i 0.675585i
$$675$$ 0 0
$$676$$ 2.20824e13 0.156427
$$677$$ −1.70106e14 −1.19612 −0.598060 0.801451i $$-0.704062\pi$$
−0.598060 + 0.801451i $$0.704062\pi$$
$$678$$ 5.93652e12 + 7.63660e13i 0.0414366 + 0.533030i
$$679$$ 7.20622e12 0.0499297
$$680$$ 0 0
$$681$$ 8.04237e12 + 1.03455e14i 0.0549096 + 0.706344i
$$682$$ 1.63293e14i 1.10674i
$$683$$ −2.23578e14 −1.50427 −0.752135 0.659009i $$-0.770976\pi$$
−0.752135 + 0.659009i $$0.770976\pi$$
$$684$$ −4.63338e13 + 7.24758e12i −0.309469 + 0.0484075i
$$685$$ 0 0
$$686$$ 8.56481e12i 0.0563764i
$$687$$ −1.95249e13 2.51163e14i −0.127586 1.64124i
$$688$$ 9.60110e12i 0.0622843i
$$689$$ 1.41331e14i 0.910210i
$$690$$ 0 0
$$691$$ −1.10134e13 −0.0699090 −0.0349545 0.999389i $$-0.511129\pi$$
−0.0349545 + 0.999389i $$0.511129\pi$$
$$692$$ 6.46435e13 0.407375
$$693$$ −9.12509e12 + 1.42735e12i −0.0570915 + 0.00893029i
$$694$$ 9.95468e13 0.618344
$$695$$ 0 0
$$696$$ 8.34482e13 6.48708e12i 0.510941 0.0397194i
$$697$$ 2.41401e13i 0.146749i
$$698$$ −2.09078e14 −1.26192
$$699$$ 1.95426e13 + 2.51392e14i 0.117111 + 1.50649i
$$700$$ 0 0
$$701$$ 1.10962e14i 0.655516i −0.944762 0.327758i $$-0.893707\pi$$
0.944762 0.327758i $$-0.106293\pi$$
$$702$$ −9.72354e13 + 2.30488e13i −0.570346 + 0.135195i
$$703$$ 1.32889e14i 0.773948i
$$704$$ 3.13087e13i 0.181052i
$$705$$ 0 0
$$706$$ 2.08338e13 0.118781
$$707$$ −7.25206e12 −0.0410548
$$708$$ −6.06138e13 + 4.71199e12i −0.340726 + 0.0264873i
$$709$$ −2.08219e14 −1.16222 −0.581112 0.813824i $$-0.697382\pi$$
−0.581112 + 0.813824i $$0.697382\pi$$
$$710$$ 0 0
$$711$$ −1.08878e14 + 1.70308e13i −0.599229 + 0.0937318i
$$712$$ 6.02289e13i 0.329158i
$$713$$ −1.72489e14 −0.936080
$$714$$ −2.47132e12 + 1.92115e11i −0.0133180 + 0.00103531i
$$715$$ 0 0
$$716$$ 1.51830e14i 0.806848i
$$717$$ −2.99656e14 + 2.32946e13i −1.58135 + 0.122931i
$$718$$ 1.39746e14i 0.732347i
$$719$$ 2.74910e14i 1.43069i −0.698771 0.715346i $$-0.746269\pi$$
0.698771 0.715346i $$-0.253731\pi$$
$$720$$ 0 0
$$721$$ −1.90059e12 −0.00975465
$$722$$ 8.42844e13 0.429597
$$723$$ −1.95702e13 2.51746e14i −0.0990613 1.27430i
$$724$$ 1.27207e14 0.639466
$$725$$ 0 0
$$726$$ 1.21354e13 + 1.56107e14i 0.0601688 + 0.773997i
$$727$$ 2.99071e14i 1.47266i 0.676622 + 0.736330i $$0.263443\pi$$
−0.676622 + 0.736330i $$0.736557\pi$$
$$728$$ −2.39092e12 −0.0116925
$$729$$ −1.83985e14 + 9.24165e13i −0.893602 + 0.448861i
$$730$$ 0 0
$$731$$ 2.46241e13i 0.117970i
$$732$$ −5.91030e11 7.60286e12i −0.00281225 0.0361761i
$$733$$ 1.19922e14i 0.566734i 0.959012 + 0.283367i $$0.0914514\pi$$
−0.959012 + 0.283367i $$0.908549\pi$$
$$734$$ 1.85404e14i 0.870241i
$$735$$ 0 0
$$736$$ 3.30719e13 0.153134
$$737$$ −1.56471e14 −0.719608
$$738$$ 7.41400e12 + 4.73978e13i 0.0338666 + 0.216509i
$$739$$ 7.29345e13 0.330911 0.165455 0.986217i $$-0.447091\pi$$
0.165455 + 0.986217i $$0.447091\pi$$
$$740$$ 0 0
$$741$$ −1.15666e14 + 8.99158e12i −0.517742 + 0.0402481i
$$742$$ 6.96706e12i 0.0309763i
$$743$$ 1.07061e14 0.472809 0.236405 0.971655i $$-0.424031\pi$$
0.236405 + 0.971655i $$0.424031\pi$$
$$744$$ −6.75011e12 8.68317e13i −0.0296105 0.380902i
$$745$$ 0 0
$$746$$ 2.05304e14i 0.888592i
$$747$$ −6.39183e13 + 9.99815e12i −0.274803 + 0.0429850i
$$748$$ 8.02979e13i 0.342923i
$$749$$ 1.61733e13i 0.0686104i
$$750$$ 0 0
$$751$$ 1.83777e14 0.769292 0.384646 0.923064i $$-0.374323\pi$$
0.384646 + 0.923064i $$0.374323\pi$$
$$752$$ 8.62131e12 0.0358496
$$753$$ −1.37313e14 + 1.06744e13i −0.567203 + 0.0440931i
$$754$$ 2.07057e14 0.849638
$$755$$ 0 0
$$756$$ −4.79332e12 + 1.13621e12i −0.0194101 + 0.00460098i
$$757$$ 1.73049e14i 0.696130i 0.937470 + 0.348065i $$0.113161\pi$$
−0.937470 + 0.348065i $$0.886839\pi$$
$$758$$ 2.66589e14 1.06536
$$759$$ 3.15093e14 2.44946e13i 1.25092 0.0972438i
$$760$$ 0 0
$$761$$ 1.10156e14i 0.431604i −0.976437 0.215802i $$-0.930764\pi$$
0.976437 0.215802i $$-0.0692365\pi$$
$$762$$ −2.23888e14 + 1.74046e13i −0.871477 + 0.0677467i
$$763$$ 3.64382e12i 0.0140907i
$$764$$ 8.09218e13i 0.310884i
$$765$$ 0 0
$$766$$ 1.54395e14 0.585449
$$767$$ −1.50399e14 −0.566589
$$768$$ 1.29423e12 + 1.66486e13i 0.00484400 + 0.0623120i
$$769$$ −2.30458e14 −0.856959 −0.428480 0.903551i $$-0.640951\pi$$
−0.428480 + 0.903551i $$0.640951\pi$$
$$770$$ 0 0
$$771$$ 2.40960e13 + 3.09965e14i 0.0884451 + 1.13774i
$$772$$ 1.93725e14i 0.706479i
$$773$$ 1.50965e14 0.546991 0.273495 0.961873i $$-0.411820\pi$$
0.273495 + 0.961873i $$0.411820\pi$$
$$774$$ −7.56265e12 4.83481e13i −0.0272251 0.174050i
$$775$$ 0