LMFDB - Embedded newform 40.12.k.a.27.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [40,12,Mod(3,40)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("40.3"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	40.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$30.7337272224$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.18
Character	$\chi$	$=$	40.27
Dual form			40.12.k.a.3.18

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-29.9123 - 33.9596i) q^{2} +(462.074 - 462.074i) q^{3} +(-258.514 + 2031.62i) q^{4} +(-5907.12 - 3732.84i) q^{5} +(-29513.6 - 1870.19i) q^{6} +(32730.0 - 32730.0i) q^{7} +(76725.8 - 51991.2i) q^{8} -249879. i q^{9} +(49929.2 + 312261. i) q^{10} -126280. q^{11} +(819306. + 1.05821e6i) q^{12} +(-879637. - 879637. i) q^{13} +(-2.09053e6 - 132471. i) q^{14} +(-4.45438e6 + 1.00468e6i) q^{15} +(-4.06064e6 - 1.05040e6i) q^{16} +(2.73063e6 + 2.73063e6i) q^{17} +(-8.48579e6 + 7.47443e6i) q^{18} -8.18436e6i q^{19} +(9.11078e6 - 1.10360e7i) q^{20} -3.02474e7i q^{21} +(3.77732e6 + 4.28843e6i) q^{22} +(-2.94032e7 - 2.94032e7i) q^{23} +(1.14292e7 - 5.94768e7i) q^{24} +(2.09599e7 + 4.41007e7i) q^{25} +(-3.56023e6 + 5.61841e7i) q^{26} +(-3.36074e7 - 3.36074e7i) q^{27} +(5.80337e7 + 7.49560e7i) q^{28} -5.76467e7 q^{29} +(1.67359e8 + 1.21217e8i) q^{30} -1.06494e8i q^{31} +(8.57917e7 + 1.69318e8i) q^{32} +(-5.83508e7 + 5.83508e7i) q^{33} +(1.10519e7 - 1.74410e8i) q^{34} +(-3.15516e8 + 7.11639e7i) q^{35} +(5.07658e8 + 6.45972e7i) q^{36} +(-5.93042e8 + 5.93042e8i) q^{37} +(-2.77938e8 + 2.44813e8i) q^{38} -8.12916e8 q^{39} +(-6.47303e8 + 2.07131e7i) q^{40} +1.16134e9 q^{41} +(-1.02719e9 + 9.04767e8i) q^{42} +(-2.38195e8 + 2.38195e8i) q^{43} +(3.26452e7 - 2.56553e8i) q^{44} +(-9.32757e8 + 1.47606e9i) q^{45} +(-1.19006e8 + 1.87804e9i) q^{46} +(2.31393e8 - 2.31393e8i) q^{47} +(-2.36169e9 + 1.39095e9i) q^{48} -1.65175e8i q^{49} +(8.70684e8 - 2.03094e9i) q^{50} +2.52350e9 q^{51} +(2.01449e9 - 1.55969e9i) q^{52} +(3.34230e9 + 3.34230e9i) q^{53} +(-1.36022e8 + 2.14657e9i) q^{54} +(7.45951e8 + 4.71383e8i) q^{55} +(8.09561e8 - 4.21290e9i) q^{56} +(-3.78178e9 - 3.78178e9i) q^{57} +(1.72434e9 + 1.95766e9i) q^{58} +3.77611e9i q^{59} +(-8.89600e8 - 9.30932e9i) q^{60} +7.58909e9i q^{61} +(-3.61651e9 + 3.18549e9i) q^{62} +(-8.17852e9 - 8.17852e9i) q^{63} +(3.18376e9 - 7.97814e9i) q^{64} +(1.91257e9 + 8.47967e9i) q^{65} +(3.72697e9 + 2.36168e8i) q^{66} +(-1.18937e10 - 1.18937e10i) q^{67} +(-6.25349e9 + 4.84168e9i) q^{68} -2.71729e10 q^{69} +(1.18545e10 + 8.58612e9i) q^{70} -2.81818e10i q^{71} +(-1.29915e10 - 1.91721e10i) q^{72} +(-1.16546e10 + 1.16546e10i) q^{73} +(3.78787e10 + 2.40027e9i) q^{74} +(3.00628e10 + 1.06927e10i) q^{75} +(1.66275e10 + 2.11577e9i) q^{76} +(-4.13314e9 + 4.13314e9i) q^{77} +(2.43161e10 + 2.76063e10i) q^{78} -9.46251e9 q^{79} +(2.00657e10 + 2.13626e10i) q^{80} +1.32070e10 q^{81} +(-3.47382e10 - 3.94386e10i) q^{82} +(-3.26629e9 + 3.26629e9i) q^{83} +(6.14511e10 + 7.81937e9i) q^{84} +(-5.93713e9 - 2.63231e10i) q^{85} +(1.52140e10 + 9.64068e8i) q^{86} +(-2.66371e10 + 2.66371e10i) q^{87} +(-9.68894e9 + 6.56546e9i) q^{88} -9.09638e10i q^{89} +(7.80274e10 - 1.24762e10i) q^{90} -5.75810e10 q^{91} +(6.73372e10 - 5.21349e10i) q^{92} +(-4.92083e10 - 4.92083e10i) q^{93} +(-1.47795e10 - 9.36539e8i) q^{94} +(-3.05509e10 + 4.83460e10i) q^{95} +(1.17880e11 + 3.85954e10i) q^{96} +(6.74508e10 + 6.74508e10i) q^{97} +(-5.60928e9 + 4.94076e9i) q^{98} +3.15547e10i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 2 q^{2} - 4 q^{3} + 22352 q^{6} + 74836 q^{8} - 141690 q^{10} - 8 q^{11} - 114212 q^{12} - 1529272 q^{16} - 5279472 q^{17} - 7492118 q^{18} - 19078400 q^{20} + 110378148 q^{22} - 34182200 q^{25}+ \cdots - 277418419174 q^{98}+O(q^{100}) $ 128 * q - 2 * q^2 - 4 * q^3 + 22352 * q^6 + 74836 * q^8 - 141690 * q^10 - 8 * q^11 - 114212 * q^12 - 1529272 * q^16 - 5279472 * q^17 - 7492118 * q^18 - 19078400 * q^20 + 110378148 * q^22 - 34182200 * q^25 + 255826660 * q^26 + 708584 * q^27 + 94521900 * q^28 - 293248580 * q^30 - 472895712 * q^32 - 708592 * q^33 + 1064775860 * q^35 + 86525660 * q^36 + 3129197436 * q^38 + 3364165660 * q^40 - 8 * q^41 + 1572869820 * q^42 + 4763690652 * q^43 - 385692400 * q^46 + 382518896 * q^48 - 2735634410 * q^50 + 224442568 * q^51 + 4940288660 * q^52 + 5445667880 * q^56 + 708584 * q^57 + 10041578500 * q^58 + 15019215220 * q^60 + 2940684960 * q^62 - 5068308440 * q^65 - 18585180232 * q^66 - 44333852092 * q^67 - 24658647124 * q^68 - 2573940380 * q^70 + 52114546396 * q^72 + 30695219256 * q^73 - 114387554460 * q^75 + 64146613592 * q^76 + 58383192800 * q^78 - 6693485600 * q^80 - 353771564728 * q^81 - 30935854652 * q^82 - 122796947724 * q^83 - 64352390624 * q^86 - 192245775664 * q^88 + 306882997670 * q^90 + 93235242840 * q^91 + 185062591860 * q^92 + 345055140192 * q^96 - 144367002024 * q^97 - 277418419174 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$

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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−29.9123	−	33.9596i	−0.660974	−	0.750409i
$2$	−29.9123	−	33.9596i	−0.660974	−	0.750409i
$3$	462.074	−	462.074i	1.09786	−	1.09786i	0.103194	−	0.994661i	$-0.467094\pi$
$3$	462.074	−	462.074i	1.09786	−	1.09786i	0.994661	−	0.103194i	$-0.0329062\pi$
$4$	−258.514	+	2031.62i	−0.126228	+	0.992001i
$5$	−5907.12	−	3732.84i	−0.845358	−	0.534201i
$5$	−5907.12	−	3732.84i	−0.845358	−	0.534201i
$6$	−29513.6	−	1870.19i	−1.54949	−	0.0981872i
$7$	32730.0	−	32730.0i	0.736048	−	0.736048i	−0.235762	−	0.971811i	$-0.575759\pi$
$7$	32730.0	−	32730.0i	0.736048	−	0.736048i	0.971811	+	0.235762i	$0.0757587\pi$
$8$	76725.8	−	51991.2i	0.827840	−	0.560964i
$9$		−	249879.i		−	1.41057i
$10$	49929.2	+	312261.i	0.157890	+	0.987457i
$11$	−126280.			−0.236415			−0.118207	−	0.992989i	$-0.537715\pi$
$11$	−126280.			−0.236415			−0.118207	+	0.992989i	$0.537715\pi$
$12$	819306.	+	1.05821e6i	0.950494	+	1.22765i
$13$	−879637.	−	879637.i	−0.657075	−	0.657075i	0.297612	−	0.954687i	$-0.403810\pi$
$13$	−879637.	−	879637.i	−0.657075	−	0.657075i	−0.954687	+	0.297612i	$0.903810\pi$
$14$	−2.09053e6	−	132471.i	−1.03885	−	0.0658288i
$15$	−4.45438e6	+	1.00468e6i	−1.51456	+	0.341605i
$16$	−4.06064e6	−	1.05040e6i	−0.968133	−	0.250436i
$17$	2.73063e6	+	2.73063e6i	0.466437	+	0.466437i	0.900758	−	0.434321i	$-0.143012\pi$
$17$	2.73063e6	+	2.73063e6i	0.466437	+	0.466437i	−0.434321	+	0.900758i	$0.643012\pi$
$18$	−8.48579e6	+	7.47443e6i	−1.05851	+	0.932351i
$19$		−	8.18436e6i		−	0.758298i	−0.925336	−	0.379149i	$-0.876217\pi$
$19$		−	8.18436e6i		−	0.758298i	0.925336	−	0.379149i	$-0.123783\pi$
$20$	9.11078e6	−	1.10360e7i	0.636635	−	0.771165i
$21$		−	3.02474e7i		−	1.61615i
$22$	3.77732e6	+	4.28843e6i	0.156264	+	0.177408i
$23$	−2.94032e7	−	2.94032e7i	−0.952558	−	0.952558i	0.0463664	−	0.998925i	$-0.485236\pi$
$23$	−2.94032e7	−	2.94032e7i	−0.952558	−	0.952558i	−0.998925	+	0.0463664i	$0.985236\pi$
$24$	1.14292e7	−	5.94768e7i	0.292991	−	1.52471i
$25$	2.09599e7	+	4.41007e7i	0.429259	+	0.903181i
$26$	−3.56023e6	+	5.61841e7i	−0.0587658	+	0.927385i
$27$	−3.36074e7	−	3.36074e7i	−0.450748	−	0.450748i
$28$	5.80337e7	+	7.49560e7i	0.637251	+	0.823071i
$29$	−5.76467e7			−0.521898			−0.260949	−	0.965353i	$-0.584035\pi$
$29$	−5.76467e7			−0.521898			−0.260949	+	0.965353i	$0.584035\pi$
$30$	1.67359e8	+	1.21217e8i	1.25742	+	0.910744i
$31$		−	1.06494e8i		−	0.668093i	−0.942557	−	0.334047i	$-0.891586\pi$
$31$		−	1.06494e8i		−	0.668093i	0.942557	−	0.334047i	$-0.108414\pi$
$32$	8.57917e7	+	1.69318e8i	0.451981	+	0.892028i
$33$	−5.83508e7	+	5.83508e7i	−0.259549	+	0.259549i
$34$	1.10519e7	−	1.74410e8i	0.0417160	−	0.658321i
$35$	−3.15516e8	+	7.11639e7i	−1.01542	+	0.229026i
$36$	5.07658e8	+	6.45972e7i	1.39929	+	0.178053i
$37$	−5.93042e8	+	5.93042e8i	−1.40597	+	1.40597i	−0.626742	+	0.779227i	$0.715612\pi$
$37$	−5.93042e8	+	5.93042e8i	−1.40597	+	1.40597i	−0.779227	+	0.626742i	$0.784388\pi$
$38$	−2.77938e8	+	2.44813e8i	−0.569034	+	0.501215i
$39$	−8.12916e8			−1.44275
$40$	−6.47303e8	+	2.07131e7i	−0.999488	+	0.0319827i
$41$	1.16134e9			1.56548			0.782739	−	0.622350i	$-0.213822\pi$
$41$	1.16134e9			1.56548			0.782739	+	0.622350i	$0.213822\pi$
$42$	−1.02719e9	+	9.04767e8i	−1.21277	+	1.06823i
$43$	−2.38195e8	+	2.38195e8i	−0.247091	+	0.247091i	−0.819776	−	0.572685i	$-0.805902\pi$
$43$	−2.38195e8	+	2.38195e8i	−0.247091	+	0.247091i	0.572685	+	0.819776i	$0.305902\pi$
$44$	3.26452e7	−	2.56553e8i	0.0298421	−	0.234524i
$45$	−9.32757e8	+	1.47606e9i	−0.753529	+	1.19244i
$46$	−1.19006e8	+	1.87804e9i	−0.0851925	+	1.34442i
$47$	2.31393e8	−	2.31393e8i	0.147168	−	0.147168i	−0.629684	−	0.776852i	$-0.716816\pi$
$47$	2.31393e8	−	2.31393e8i	0.147168	−	0.147168i	0.776852	+	0.629684i	$0.216816\pi$
$48$	−2.36169e9	+	1.39095e9i	−1.33781	+	0.787928i
$49$		−	1.65175e8i		−	0.0835345i
$50$	8.70684e8	−	2.03094e9i	0.394027	−	0.919099i
$51$	2.52350e9			1.02416
$52$	2.01449e9	−	1.55969e9i	0.734761	−	0.568879i
$53$	3.34230e9	+	3.34230e9i	1.09781	+	1.09781i	0.994666	+	0.103146i	$0.0328909\pi$
$53$	3.34230e9	+	3.34230e9i	1.09781	+	1.09781i	0.103146	+	0.994666i	$0.467109\pi$
$54$	−1.36022e8	+	2.14657e9i	−0.0403129	+	0.636178i
$55$	7.45951e8	+	4.71383e8i	0.199855	+	0.126293i
$56$	8.09561e8	−	4.21290e9i	0.196433	−	1.02223i
$57$	−3.78178e9	−	3.78178e9i	−0.832501	−	0.832501i
$58$	1.72434e9	+	1.95766e9i	0.344961	+	0.391637i
$59$			3.77611e9i			0.687635i	0.939036	+	0.343818i	$0.111720\pi$
$59$			3.77611e9i			0.687635i	−0.939036	+	0.343818i	$0.888280\pi$
$60$	−8.89600e8	−	9.30932e9i	−0.147694	−	1.54556i
$61$			7.58909e9i			1.15047i	0.817988	+	0.575235i	$0.195089\pi$
$61$			7.58909e9i			1.15047i	−0.817988	+	0.575235i	$0.804911\pi$
$62$	−3.61651e9	+	3.18549e9i	−0.501343	+	0.441592i
$63$	−8.17852e9	−	8.17852e9i	−1.03825	−	1.03825i
$64$	3.18376e9	−	7.97814e9i	0.370638	−	0.928777i
$65$	1.91257e9	+	8.47967e9i	0.204453	+	0.906474i
$66$	3.72697e9	+	2.36168e8i	0.366324	+	0.0232129i
$67$	−1.18937e10	−	1.18937e10i	−1.07624	−	1.07624i	−0.996843	−	0.0793918i	$-0.974702\pi$
$67$	−1.18937e10	−	1.18937e10i	−1.07624	−	1.07624i	−0.0793918	−	0.996843i	$-0.525298\pi$
$68$	−6.25349e9	+	4.84168e9i	−0.521583	+	0.403829i
$69$	−2.71729e10			−2.09154
$70$	1.18545e10	+	8.58612e9i	0.843031	+	0.610601i
$71$		−	2.81818e10i		−	1.85374i	−0.375386	−	0.926868i	$-0.622490\pi$
$71$		−	2.81818e10i		−	1.85374i	0.375386	−	0.926868i	$-0.377510\pi$
$72$	−1.29915e10	−	1.91721e10i	−0.791280	−	1.16773i
$73$	−1.16546e10	+	1.16546e10i	−0.657994	+	0.657994i	−0.954905	−	0.296911i	$-0.904043\pi$
$73$	−1.16546e10	+	1.16546e10i	−0.657994	+	0.657994i	0.296911	+	0.954905i	$0.404043\pi$
$74$	3.78787e10	+	2.40027e9i	1.98436	+	0.125743i
$75$	3.00628e10	+	1.06927e10i	1.46283	+	0.520298i
$76$	1.66275e10	+	2.11577e9i	0.752232	+	0.0957182i
$77$	−4.13314e9	+	4.13314e9i	−0.174013	+	0.174013i
$78$	2.43161e10	+	2.76063e10i	0.953618	+	1.08265i
$79$	−9.46251e9			−0.345985			−0.172993	−	0.984923i	$-0.555344\pi$
$79$	−9.46251e9			−0.345985			−0.172993	+	0.984923i	$0.555344\pi$
$80$	2.00657e10	+	2.13626e10i	0.684636	+	0.728885i
$81$	1.32070e10			0.420859
$82$	−3.47382e10	−	3.94386e10i	−1.03474	−	1.17475i
$83$	−3.26629e9	+	3.26629e9i	−0.0910176	+	0.0910176i	−0.751150	−	0.660132i	$-0.770500\pi$
$83$	−3.26629e9	+	3.26629e9i	−0.0910176	+	0.0910176i	0.660132	+	0.751150i	$0.270500\pi$
$84$	6.14511e10	+	7.81937e9i	1.60322	+	0.204003i
$85$	−5.93713e9	−	2.63231e10i	−0.145135	−	0.643477i
$86$	1.52140e10	+	9.64068e8i	0.348740	+	0.0220987i
$87$	−2.66371e10	+	2.66371e10i	−0.572968	+	0.572968i
$88$	−9.68894e9	+	6.56546e9i	−0.195714	+	0.132620i
$89$		−	9.09638e10i		−	1.72673i	−0.504582	−	0.863364i	$-0.668353\pi$
$89$		−	9.09638e10i		−	1.72673i	0.504582	−	0.863364i	$-0.331647\pi$
$90$	7.80274e10	−	1.24762e10i	1.39288	−	0.222715i
$91$	−5.75810e10			−0.967279
$92$	6.73372e10	−	5.21349e10i	1.06518	−	0.824700i
$93$	−4.92083e10	−	4.92083e10i	−0.733470	−	0.733470i
$94$	−1.47795e10	−	9.36539e8i	−0.207710	−	0.0131620i
$95$	−3.05509e10	+	4.83460e10i	−0.405083	+	0.641033i
$96$	1.17880e11	+	3.85954e10i	1.47553	+	0.483107i
$97$	6.74508e10	+	6.74508e10i	0.797522	+	0.797522i	0.982704	−	0.185182i	$-0.0592876\pi$
$97$	6.74508e10	+	6.74508e10i	0.797522	+	0.797522i	−0.185182	+	0.982704i	$0.559288\pi$
$98$	−5.60928e9	+	4.94076e9i	−0.0626850	+	0.0552141i
$99$			3.15547e10i			0.333480i
$100$	−9.50142e10	+	3.11819e10i	−0.950142	+	0.311819i
$101$		−	1.67506e11i		−	1.58585i	−0.609318	−	0.792926i	$-0.708557\pi$
$101$		−	1.67506e11i		−	1.58585i	0.609318	−	0.792926i	$-0.291443\pi$
$102$	−7.54837e10	−	8.56973e10i	−0.676943	−	0.768539i
$103$	−2.10811e10	−	2.10811e10i	−0.179180	−	0.179180i	0.611818	−	0.790998i	$-0.290438\pi$
$103$	−2.10811e10	−	2.10811e10i	−0.179180	−	0.179180i	−0.790998	+	0.611818i	$0.790438\pi$
$104$	−1.13224e11	−	2.17574e10i	−0.912549	−	0.175357i
$105$	−1.12909e11	+	1.78675e11i	−0.863348	+	1.36622i
$106$	1.35276e10	−	2.13479e11i	0.0981833	−	1.54943i
$107$	−7.74162e10	−	7.74162e10i	−0.533606	−	0.533606i	0.388037	−	0.921644i	$-0.373153\pi$
$107$	−7.74162e10	−	7.74162e10i	−0.533606	−	0.533606i	−0.921644	+	0.388037i	$0.873153\pi$
$108$	7.69654e10	−	5.95894e10i	0.504040	−	0.390246i
$109$	−1.61613e11			−1.00607			−0.503037	−	0.864265i	$-0.667784\pi$
$109$	−1.61613e11			−1.00607			−0.503037	+	0.864265i	$0.667784\pi$
$110$	−6.30506e9	−	3.94324e10i	−0.0373276	−	0.233450i
$111$			5.48059e11i			3.08710i
$112$	−1.67284e11	+	9.85251e10i	−0.896926	+	0.528260i
$113$	1.77988e11	−	1.77988e11i	0.908779	−	0.908779i	−0.0873943	−	0.996174i	$-0.527854\pi$
$113$	1.77988e11	−	1.77988e11i	0.908779	−	0.908779i	0.996174	+	0.0873943i	$0.0278540\pi$
$114$	−1.53063e10	+	2.41550e11i	−0.0744551	+	1.17498i
$115$	6.39306e10	+	2.83446e11i	0.296395	+	1.31411i
$116$	1.49025e10	−	1.17116e11i	0.0658780	−	0.517723i
$117$	−2.19802e11	+	2.19802e11i	−0.926852	+	0.926852i
$118$	1.28235e11	−	1.12952e11i	0.516008	−	0.454509i
$119$	1.78747e11			0.686640
$120$	−2.89531e11	+	3.08673e11i	−1.06218	+	1.13241i
$121$	−2.69365e11			−0.944108
$122$	2.57723e11	−	2.27007e11i	0.863323	−	0.760430i
$123$	5.36624e11	−	5.36624e11i	1.71867	−	1.71867i
$124$	2.16356e11	+	2.75303e10i	0.662750	+	0.0843319i
$125$	4.08081e10	−	3.38748e11i	0.119603	−	0.992822i
$126$	−3.31016e10	+	5.22377e11i	−0.0928563	+	1.46537i
$127$	2.86770e9	−	2.86770e9i	0.00770218	−	0.00770218i	−0.703245	−	0.710947i	$-0.748266\pi$
$127$	2.86770e9	−	2.86770e9i	0.00770218	−	0.00770218i	0.710947	+	0.703245i	$0.248266\pi$
$128$	−3.66168e11	+	1.30525e11i	−0.941945	+	0.335767i
$129$			2.20128e11i			0.542540i
$130$	2.30757e11	−	3.18596e11i	0.545088	−	0.752579i
$131$	−2.73761e11			−0.619982			−0.309991	−	0.950739i	$-0.600326\pi$
$131$	−2.73761e11			−0.619982			−0.309991	+	0.950739i	$0.600326\pi$
$132$	−1.03462e11	−	1.33631e11i	−0.224711	−	0.290236i
$133$	−2.67874e11	−	2.67874e11i	−0.558144	−	0.558144i
$134$	−4.81386e10	+	7.59676e11i	−0.0962536	+	1.51898i
$135$	7.30717e10	+	3.23974e11i	0.140253	+	0.621834i
$136$	3.51478e11	+	6.75408e10i	0.647790	+	0.124481i
$137$	−2.28212e11	−	2.28212e11i	−0.403994	−	0.403994i	0.475644	−	0.879638i	$-0.342215\pi$
$137$	−2.28212e11	−	2.28212e11i	−0.403994	−	0.403994i	−0.879638	+	0.475644i	$0.842215\pi$
$138$	8.12804e11	+	9.22783e11i	1.38245	+	1.56951i
$139$			5.03921e11i			0.823723i	0.911246	+	0.411862i	$0.135121\pi$
$139$			5.03921e11i			0.823723i	−0.911246	+	0.411862i	$0.864879\pi$
$140$	−6.30127e10	−	6.59404e11i	−0.0990203	−	1.03621i
$141$		−	2.13842e11i		−	0.323138i
$142$	−9.57044e11	+	8.42982e11i	−1.39106	+	1.22527i
$143$	1.11081e11	+	1.11081e11i	0.155342	+	0.155342i
$144$	−2.62474e11	+	1.01467e12i	−0.353258	+	1.36562i
$145$	3.40526e11	+	2.15186e11i	0.441190	+	0.278798i
$146$	7.44402e11	+	4.71707e10i	0.928681	+	0.0588480i
$147$	−7.63231e10	−	7.63231e10i	−0.0917088	−	0.0917088i
$148$	−1.05152e12	−	1.35814e12i	−1.21725	−	1.57220i
$149$	−3.44610e11			−0.384418			−0.192209	−	0.981354i	$-0.561565\pi$
$149$	−3.44610e11			−0.384418			−0.192209	+	0.981354i	$0.561565\pi$
$150$	−5.36125e11	−	1.34077e12i	−0.576453	−	1.44162i
$151$		−	8.62493e11i		−	0.894092i	−0.894511	−	0.447046i	$-0.852476\pi$
$151$		−	8.62493e11i		−	0.894092i	0.894511	−	0.447046i	$-0.147524\pi$
$152$	−4.25515e11	−	6.27951e11i	−0.425378	−	0.627749i
$153$	6.82325e11	−	6.82325e11i	0.657943	−	0.657943i
$154$	2.63992e11	+	1.67284e10i	0.245599	+	0.0155629i
$155$	−3.97527e11	+	6.29074e11i	−0.356896	+	0.564778i
$156$	2.10150e11	−	1.65153e12i	0.182115	−	1.43121i
$157$	4.31447e11	−	4.31447e11i	0.360977	−	0.360977i	−0.503196	−	0.864172i	$-0.667843\pi$
$157$	4.31447e11	−	4.31447e11i	0.360977	−	0.360977i	0.864172	+	0.503196i	$0.167843\pi$
$158$	2.83045e11	+	3.21344e11i	0.228687	+	0.259630i
$159$	3.08878e12			2.41048
$160$	1.25256e11	−	1.32043e12i	0.0944362	−	0.995531i
$161$	−1.92473e12			−1.40226
$162$	−3.95051e11	−	4.48505e11i	−0.278177	−	0.315816i
$163$	6.93048e11	−	6.93048e11i	0.471772	−	0.471772i	−0.430716	−	0.902488i	$-0.641739\pi$
$163$	6.93048e11	−	6.93048e11i	0.471772	−	0.471772i	0.902488	+	0.430716i	$0.141739\pi$
$164$	−3.00222e11	+	2.35939e12i	−0.197607	+	1.55296i
$165$	5.62499e11	−	1.26871e11i	0.358064	−	0.0807606i
$166$	2.08624e11	+	1.32199e10i	0.128461	+	0.00814020i
$167$	2.16220e12	−	2.16220e12i	1.28812	−	1.28812i	0.352189	−	0.935929i	$-0.385438\pi$
$167$	2.16220e12	−	2.16220e12i	1.28812	−	1.28812i	0.935929	−	0.352189i	$-0.114562\pi$
$168$	−1.57260e12	−	2.32075e12i	−0.906602	−	1.33791i
$169$		−	2.44637e11i		−	0.136504i
$170$	−7.16330e11	+	9.89006e11i	−0.386941	+	0.534232i
$171$	−2.04510e12			−1.06963
$172$	−4.22345e11	−	5.45499e11i	−0.213925	−	0.276304i
$173$	9.35656e11	+	9.35656e11i	0.459053	+	0.459053i	0.898345	−	0.439292i	$-0.144771\pi$
$173$	9.35656e11	+	9.35656e11i	0.459053	+	0.459053i	−0.439292	+	0.898345i	$0.644771\pi$
$174$	1.70136e12	+	1.07811e11i	0.808678	+	0.0512437i
$175$	2.12943e12	+	7.57396e11i	0.980741	+	0.348830i
$176$	5.12778e11	+	1.32645e11i	0.228881	+	0.0592068i
$177$	1.74484e12	+	1.74484e12i	0.754924	+	0.754924i
$178$	−3.08910e12	+	2.72093e12i	−1.29575	+	1.14132i
$179$		−	3.89013e12i		−	1.58224i	−0.611662	−	0.791119i	$-0.709499\pi$
$179$		−	3.89013e12i		−	1.58224i	0.611662	−	0.791119i	$-0.290501\pi$
$180$	−2.75766e12	−	2.27659e12i	−1.08778	−	0.898020i
$181$		−	9.66903e11i		−	0.369957i	−0.982743	−	0.184978i	$-0.940778\pi$
$181$		−	9.66903e11i		−	0.369957i	0.982743	−	0.184978i	$-0.0592215\pi$
$182$	1.72238e12	+	1.95543e12i	0.639346	+	0.725855i
$183$	3.50672e12	+	3.50672e12i	1.26305	+	1.26305i
$184$	−3.78469e12	−	7.27275e11i	−1.32292	−	0.254215i
$185$	5.71690e12	−	1.28944e12i	1.93962	−	0.437477i
$186$	−1.99165e11	+	3.14303e12i	−0.0655982	+	1.03521i
$187$	−3.44823e11	−	3.44823e11i	−0.110273	−	0.110273i
$188$	4.10285e11	+	5.29922e11i	0.127414	+	0.164567i
$189$	−2.19994e12			−0.663545
$190$	2.55566e12	−	4.08638e11i	0.748786	−	0.119728i
$191$			5.99831e12i			1.70744i	0.520732	+	0.853720i	$0.325659\pi$
$191$			5.99831e12i			1.70744i	−0.520732	+	0.853720i	$0.674341\pi$
$192$	−2.21536e12	−	5.15763e12i	−0.612756	−	1.42657i
$193$	−1.60923e12	+	1.60923e12i	−0.432566	+	0.432566i	−0.889500	−	0.456935i	$-0.848947\pi$
$193$	−1.60923e12	+	1.60923e12i	−0.432566	+	0.432566i	0.456935	+	0.889500i	$0.348947\pi$
$194$	2.72999e11	−	4.30821e12i	0.0713267	−	1.12561i
$195$	4.80199e12	+	3.03449e12i	1.21964	+	0.770717i
$196$	3.35573e11	+	4.27001e10i	0.0828663	+	0.0105444i
$197$	1.45943e12	−	1.45943e12i	0.350444	−	0.350444i	−0.509830	−	0.860275i	$-0.670292\pi$
$197$	1.45943e12	−	1.45943e12i	0.350444	−	0.350444i	0.860275	+	0.509830i	$0.170292\pi$
$198$	1.07159e12	−	9.43872e11i	0.250247	−	0.220422i
$199$	−3.04353e12			−0.691330			−0.345665	−	0.938358i	$-0.612347\pi$
$199$	−3.04353e12			−0.691330			−0.345665	+	0.938358i	$0.612347\pi$
$200$	3.90101e12	+	2.29393e12i	0.862010	+	0.506891i
$201$	−1.09916e13			−2.36310
$202$	−5.68844e12	+	5.01048e12i	−1.19004	+	1.04821i
$203$	−1.88678e12	+	1.88678e12i	−0.384142	+	0.384142i
$204$	−6.52362e11	+	5.12680e12i	−0.129277	+	1.01597i
$205$	−6.86015e12	−	4.33508e12i	−1.32339	−	0.836279i
$206$	−8.53235e10	+	1.34649e12i	−0.0160250	+	0.252891i
$207$	−7.34723e12	+	7.34723e12i	−1.34365	+	1.34365i
$208$	2.64792e12	+	4.49587e12i	0.471581	+	0.800692i
$209$			1.03352e12i			0.179273i
$210$	9.44508e12	−	1.51023e12i	1.59588	−	0.255174i
$211$	6.06514e12			0.998360			0.499180	−	0.866498i	$-0.333635\pi$
$211$	6.06514e12			0.998360			0.499180	+	0.866498i	$0.333635\pi$
$212$	−7.65431e12	+	5.92625e12i	−1.22761	+	0.950457i
$213$	−1.30221e13	−	1.30221e13i	−2.03513	−	2.03513i
$214$	−3.13333e11	+	4.94472e12i	−0.0477233	+	0.753123i
$215$	2.29619e12	−	5.17902e11i	0.340876	−	0.0768840i
$216$	−4.32584e12	−	8.31263e11i	−0.626001	−	0.120294i
$217$	−3.48556e12	−	3.48556e12i	−0.491749	−	0.491749i
$218$	4.83420e12	+	5.48831e12i	0.664989	+	0.754968i
$219$			1.07706e13i			1.44476i
$220$	−1.15051e12	+	1.39363e12i	−0.150510	+	0.182315i
$221$		−	4.80392e12i		−	0.612969i
$222$	1.86119e13	−	1.63937e13i	2.31659	−	2.04049i
$223$	2.00321e12	+	2.00321e12i	0.243248	+	0.243248i	0.818192	−	0.574945i	$-0.194976\pi$
$223$	2.00321e12	+	2.00321e12i	0.243248	+	0.243248i	−0.574945	+	0.818192i	$0.694976\pi$
$224$	8.34973e12	+	2.73381e12i	0.989255	+	0.323895i
$225$	1.10198e13	−	5.23743e12i	1.27400	−	0.605501i
$226$	−1.13684e13	−	7.20385e11i	−1.28264	−	0.0812771i
$227$	−1.04876e13	−	1.04876e13i	−1.15487	−	1.15487i	−0.985563	−	0.169311i	$-0.945846\pi$
$227$	−1.04876e13	−	1.04876e13i	−1.15487	−	1.15487i	−0.169311	−	0.985563i	$-0.554154\pi$
$228$	8.66079e12	−	6.70550e12i	0.930927	−	0.720758i
$229$	−3.79569e12			−0.398287			−0.199143	−	0.979970i	$-0.563816\pi$
$229$	−3.79569e12			−0.398287			−0.199143	+	0.979970i	$0.563816\pi$
$230$	7.71340e12	−	1.06496e13i	0.790211	−	1.09101i
$231$			3.81964e12i			0.382082i
$232$	−4.42299e12	+	2.99712e12i	−0.432048	+	0.292766i
$233$	−7.03342e12	+	7.03342e12i	−0.670979	+	0.670979i	−0.957942	−	0.286962i	$-0.907355\pi$
$233$	−7.03342e12	+	7.03342e12i	−0.670979	+	0.670979i	0.286962	+	0.957942i	$0.407355\pi$
$234$	1.40392e13	+	8.89626e11i	1.30814	+	0.0828934i
$235$	−2.23062e12	+	5.03113e11i	−0.203027	+	0.0457923i
$236$	−7.67161e12	−	9.76177e11i	−0.682135	−	0.0867986i
$237$	−4.37239e12	+	4.37239e12i	−0.379842	+	0.379842i
$238$	−5.34671e12	−	6.07017e12i	−0.453851	−	0.515261i
$239$	6.28756e12			0.521547			0.260774	−	0.965400i	$-0.416022\pi$
$239$	6.28756e12			0.521547			0.260774	+	0.965400i	$0.416022\pi$
$240$	1.91430e13	+	5.99264e11i	1.55184	+	0.0485799i
$241$	8.07661e12			0.639934			0.319967	−	0.947429i	$-0.396328\pi$
$241$	8.07661e12			0.639934			0.319967	+	0.947429i	$0.396328\pi$
$242$	8.05731e12	+	9.14754e12i	0.624030	+	0.708467i
$243$	1.20561e13	−	1.20561e13i	0.912791	−	0.912791i
$244$	−1.54181e13	−	1.96189e12i	−1.14127	−	0.145221i
$245$	−6.16572e11	+	9.75708e11i	−0.0446242	+	0.0706165i
$246$	−3.42752e13	−	2.17192e12i	−2.42570	−	0.153710i
$247$	−7.19927e12	+	7.19927e12i	−0.498259	+	0.498259i
$248$	−5.53677e12	−	8.17086e12i	−0.374777	−	0.553074i
$249$			3.01854e12i			0.199848i
$250$	−1.27244e13	+	8.74688e12i	−0.824077	+	0.566478i
$251$	6.61521e12			0.419120			0.209560	−	0.977796i	$-0.432797\pi$
$251$	6.61521e12			0.419120			0.209560	+	0.977796i	$0.432797\pi$
$252$	1.87299e13	−	1.45014e13i	1.16100	−	0.898889i
$253$	3.71304e12	+	3.71304e12i	0.225199	+	0.225199i
$254$	−1.83166e11	−	1.16067e10i	−0.0108707	−	0.000688848i
$255$	−1.49066e13	−	9.41984e12i	−0.865782	−	0.547107i
$256$	1.53855e13	+	8.53064e12i	0.874564	+	0.484911i
$257$	1.81436e13	+	1.81436e13i	1.00947	+	1.00947i	0.999955	+	0.00951270i	$0.00302803\pi$
$257$	1.81436e13	+	1.81436e13i	1.00947	+	1.00947i	0.00951270	+	0.999955i	$0.496972\pi$
$258$	7.47546e12	−	6.58452e12i	0.407127	−	0.358604i
$259$			3.88205e13i			2.06972i
$260$	−1.77219e13	+	1.69350e12i	−0.925031	+	0.0883961i
$261$			1.44047e13i			0.736175i
$262$	8.18881e12	+	9.29682e12i	0.409792	+	0.465240i
$263$	6.53910e12	+	6.53910e12i	0.320451	+	0.320451i	0.848940	−	0.528489i	$-0.177241\pi$
$263$	6.53910e12	+	6.53910e12i	0.320451	+	0.320451i	−0.528489	+	0.848940i	$0.677241\pi$
$264$	−1.44328e12	+	7.51074e12i	−0.0692674	+	0.360463i
$265$	−7.26708e12	−	3.22196e13i	−0.341592	−	1.51450i
$266$	−1.08419e12	+	1.71096e13i	−0.0499179	+	0.787755i
$267$	−4.20321e13	−	4.20321e13i	−1.89570	−	1.89570i
$268$	2.72383e13	−	2.10889e13i	1.20348	−	0.931776i
$269$	2.41637e13			1.04599			0.522994	−	0.852336i	$-0.324815\pi$
$269$	2.41637e13			1.04599			0.522994	+	0.852336i	$0.324815\pi$
$270$	8.81630e12	−	1.21723e13i	0.373926	−	0.516263i
$271$		−	3.29811e13i		−	1.37068i	−0.728225	−	0.685338i	$-0.759655\pi$
$271$		−	3.29811e13i		−	1.37068i	0.728225	−	0.685338i	$-0.240345\pi$
$272$	−8.21984e12	−	1.39564e13i	−0.334761	−	0.568386i
$273$	−2.66067e13	+	2.66067e13i	−1.06193	+	1.06193i
$274$	−9.23661e11	+	1.45763e13i	−0.0361314	+	0.570190i
$275$	−2.64682e12	−	5.56903e12i	−0.101483	−	0.213526i
$276$	7.02459e12	−	5.52050e13i	0.264010	−	2.07481i
$277$	−1.13610e12	+	1.13610e12i	−0.0418580	+	0.0418580i	−0.727726	−	0.685868i	$-0.759423\pi$
$277$	−1.13610e12	+	1.13610e12i	−0.0418580	+	0.0418580i	0.685868	+	0.727726i	$0.259423\pi$
$278$	1.71130e13	−	1.50734e13i	0.618130	−	0.544460i
$279$	−2.66107e13			−0.942394
$280$	−2.05083e13	+	2.18642e13i	−0.712131	+	0.759213i
$281$	1.09119e13			0.371547			0.185774	−	0.982593i	$-0.440521\pi$
$281$	1.09119e13			0.371547			0.185774	+	0.982593i	$0.440521\pi$
$282$	−7.26200e12	+	6.39650e12i	−0.242486	+	0.213586i
$283$	−5.76184e12	+	5.76184e12i	−0.188684	+	0.188684i	−0.795127	−	0.606443i	$-0.792596\pi$
$283$	−5.76184e12	+	5.76184e12i	−0.188684	+	0.188684i	0.606443	+	0.795127i	$0.292596\pi$
$284$	5.72547e13	+	7.28540e12i	1.83891	+	0.233993i
$285$	8.22263e12	+	3.64562e13i	0.259038	+	1.14848i
$286$	4.49586e11	−	7.09493e12i	0.0138931	−	0.219248i
$287$	3.80105e13	−	3.80105e13i	1.15227	−	1.15227i
$288$	4.23089e13	−	2.14375e13i	1.25827	−	0.637552i
$289$		−	1.93593e13i		−	0.564873i
$290$	−2.87825e12	−	1.80008e13i	−0.0824025	−	0.515352i
$291$	6.23346e13			1.75113
$292$	−2.06648e13	−	2.66906e13i	−0.569674	−	0.735788i
$293$	2.34633e13	+	2.34633e13i	0.634772	+	0.634772i	0.949261	−	0.314489i	$-0.101833\pi$
$293$	2.34633e13	+	2.34633e13i	0.634772	+	0.634772i	−0.314489	+	0.949261i	$0.601833\pi$
$294$	−3.08909e11	+	4.87490e12i	−0.00820201	+	0.129436i
$295$	1.40956e13	−	2.23059e13i	0.367335	−	0.581298i
$296$	−1.46686e13	+	7.63346e13i	−0.375219	+	1.95262i
$297$	4.24394e12	+	4.24394e12i	0.106564	+	0.106564i
$298$	1.03081e13	+	1.17028e13i	0.254090	+	0.288471i
$299$			5.17283e13i			1.25180i
$300$	−2.94952e13	+	5.83120e13i	−0.700786	+	1.38545i
$301$			1.55922e13i			0.363741i
$302$	−2.92899e13	+	2.57991e13i	−0.670935	+	0.590971i
$303$	−7.74002e13	−	7.74002e13i	−1.74104	−	1.74104i
$304$	−8.59689e12	+	3.32338e13i	−0.189905	+	0.734133i
$305$	2.83289e13	−	4.48296e13i	0.614582	−	0.972559i
$306$	−4.35814e13	−	2.76163e12i	−0.928609	−	0.0588434i
$307$	−3.95702e13	−	3.95702e13i	−0.828147	−	0.828147i	0.159114	−	0.987260i	$-0.449136\pi$
$307$	−3.95702e13	−	3.95702e13i	−0.828147	−	0.828147i	−0.987260	+	0.159114i	$0.949136\pi$
$308$	−7.32849e12	−	9.46544e12i	−0.150656	−	0.194586i
$309$	−1.94821e13			−0.393427
$310$	3.32541e13	−	5.31718e12i	0.659713	−	0.105485i
$311$		−	3.00071e13i		−	0.584847i	−0.956289	−	0.292424i	$-0.905538\pi$
$311$		−	3.00071e13i		−	0.584847i	0.956289	−	0.292424i	$-0.0944617\pi$
$312$	−6.23716e13	+	4.22645e13i	−1.19436	+	0.809330i
$313$	−1.78435e13	+	1.78435e13i	−0.335726	+	0.335726i	−0.854756	−	0.519030i	$-0.826293\pi$
$313$	−1.78435e13	+	1.78435e13i	−0.335726	+	0.335726i	0.519030	+	0.854756i	$0.326293\pi$
$314$	−2.75573e13	−	1.74623e12i	−0.509476	−	0.0322841i
$315$	1.77823e13	+	7.88406e13i	0.323058	+	1.43233i
$316$	2.44619e12	−	1.92242e13i	0.0436729	−	0.343218i
$317$	−2.60242e12	+	2.60242e12i	−0.0456617	+	0.0456617i	−0.729569	−	0.683907i	$-0.760279\pi$
$317$	−2.60242e12	+	2.60242e12i	−0.0456617	+	0.0456617i	0.683907	+	0.729569i	$0.260279\pi$
$318$	−9.23924e13	−	1.04894e14i	−1.59326	−	1.80884i
$319$	7.27963e12			0.123384
$320$	−4.85879e13	+	3.52433e13i	−0.809475	+	0.587154i
$321$	−7.15441e13			−1.17164
$322$	5.75731e13	+	6.53632e13i	0.926855	+	1.05227i
$323$	2.23484e13	−	2.23484e13i	0.353698	−	0.353698i
$324$	−3.41420e12	+	2.68316e13i	−0.0531241	+	0.417493i
$325$	2.03555e13	−	5.72297e13i	0.311403	−	0.875514i
$326$	−4.42663e13	−	2.80503e12i	−0.665850	−	0.0421931i
$327$	−7.46772e13	+	7.46772e13i	−1.10452	+	1.10452i
$328$	8.91044e13	−	6.03793e13i	1.29596	−	0.878177i
$329$		−	1.51470e13i		−	0.216645i
$330$	−2.11341e13	−	1.53073e13i	−0.297274	−	0.215314i
$331$	5.59085e13			0.773435			0.386717	−	0.922198i	$-0.373609\pi$
$331$	5.59085e13			0.773435			0.386717	+	0.922198i	$0.373609\pi$
$332$	−5.79147e12	−	7.48024e12i	−0.0788006	−	0.101778i
$333$	1.48188e14	+	1.48188e14i	1.98322	+	1.98322i
$334$	−1.38104e14	−	8.75126e12i	−1.81803	−	0.115203i
$335$	2.58603e13	+	1.14655e14i	0.334878	+	1.48473i
$336$	−3.17720e13	+	1.22824e14i	−0.404742	+	1.56465i
$337$	−5.29356e12	−	5.29356e12i	−0.0663412	−	0.0663412i	0.673158	−	0.739499i	$-0.264938\pi$
$337$	−5.29356e12	−	5.29356e12i	−0.0663412	−	0.0663412i	−0.739499	+	0.673158i	$0.764938\pi$
$338$	−8.30778e12	+	7.31764e12i	−0.102434	+	0.0902255i
$339$		−	1.64487e14i		−	1.99542i
$340$	5.50134e13	−	5.25708e12i	0.656650	−	0.0627496i
$341$			1.34481e13i			0.157947i
$342$	6.11734e13	+	6.94507e13i	0.707000	+	0.802663i
$343$	5.93117e13	+	5.93117e13i	0.674563	+	0.674563i
$344$	−5.89165e12	+	3.06598e13i	−0.0659425	+	0.343161i
$345$	1.60514e14	+	1.01432e14i	1.76810	+	1.11730i
$346$	3.78696e12	−	5.97621e13i	0.0410556	−	0.647899i
$347$	−8.67646e13	−	8.67646e13i	−0.925829	−	0.925829i	0.0716045	−	0.997433i	$-0.477188\pi$
$347$	−8.67646e13	−	8.67646e13i	−0.925829	−	0.925829i	−0.997433	+	0.0716045i	$0.977188\pi$
$348$	−4.72303e13	−	6.10024e13i	−0.496061	−	0.640710i
$349$	1.39724e14			1.44455			0.722273	−	0.691608i	$-0.243097\pi$
$349$	1.39724e14			1.44455			0.722273	+	0.691608i	$0.243097\pi$
$350$	−3.79752e13	−	9.49701e13i	−0.386479	−	0.966524i
$351$			5.91246e13i			0.592351i
$352$	−1.08338e13	−	2.13815e13i	−0.106855	−	0.210889i
$353$	−7.60363e13	+	7.60363e13i	−0.738346	+	0.738346i	−0.972258	−	0.233911i	$-0.924847\pi$
$353$	−7.60363e13	+	7.60363e13i	−0.738346	+	0.738346i	0.233911	+	0.972258i	$0.424847\pi$
$354$	7.06205e12	−	1.11446e14i	0.0675170	−	1.06549i
$355$	−1.05198e14	+	1.66473e14i	−0.990268	+	1.56707i
$356$	1.84804e14	+	2.35154e13i	1.71292	+	0.217961i
$357$	8.25942e13	−	8.25942e13i	0.753832	−	0.753832i
$358$	−1.32107e14	+	1.16362e14i	−1.18733	+	1.04582i
$359$	7.34475e13			0.650066			0.325033	−	0.945703i	$-0.394625\pi$
$359$	7.34475e13			0.650066			0.325033	+	0.945703i	$0.394625\pi$
$360$	5.17576e12	+	1.61747e14i	0.0451139	+	1.40985i
$361$	4.95065e13			0.424984
$362$	−3.28357e13	+	2.89223e13i	−0.277619	+	0.244532i
$363$	−1.24467e14	+	1.24467e14i	−1.03649	+	1.03649i
$364$	1.48855e13	−	1.16983e14i	0.122097	−	0.959542i
$365$	1.12350e14	−	2.53403e13i	0.907741	−	0.204739i
$366$	1.41931e13	−	2.23981e14i	0.112961	−	1.78265i
$367$	6.80496e13	−	6.80496e13i	0.533534	−	0.533534i	−0.388088	−	0.921622i	$-0.626864\pi$
$367$	6.80496e13	−	6.80496e13i	0.533534	−	0.533534i	0.921622	+	0.388088i	$0.126864\pi$
$368$	8.85107e13	+	1.50281e14i	0.683648	+	1.16076i
$369$		−	2.90193e14i		−	2.20822i
$370$	−2.14794e14	−	1.55574e14i	−1.61032	−	1.16634i
$371$	2.18787e14			1.61609
$372$	1.12694e14	−	8.72515e13i	0.820187	−	0.635019i
$373$	−1.51178e14	−	1.51178e14i	−1.08415	−	1.08415i	−0.996117	−	0.0880346i	$-0.971941\pi$
$373$	−1.51178e14	−	1.51178e14i	−1.08415	−	1.08415i	−0.0880346	−	0.996117i	$-0.528059\pi$
$374$	−1.39563e12	+	2.20245e13i	−0.00986229	+	0.155637i
$375$	−1.37670e14	−	1.75383e14i	−0.958668	−	1.22128i
$376$	5.72341e12	−	2.97843e13i	0.0392755	−	0.204387i
$377$	5.07082e13	+	5.07082e13i	0.342926	+	0.342926i
$378$	6.58051e13	+	7.47091e13i	0.438586	+	0.497930i
$379$		−	1.87498e14i		−	1.23163i	−0.787890	−	0.615817i	$-0.788826\pi$
$379$		−	1.87498e14i		−	1.23163i	0.787890	−	0.615817i	$-0.211174\pi$
$380$	−9.03227e13	−	7.45659e13i	−0.584773	−	0.482759i
$381$		−	2.65019e12i		−	0.0169118i
$382$	2.03700e14	−	1.79423e14i	1.28128	−	1.12857i
$383$	−8.37765e13	−	8.37765e13i	−0.519432	−	0.519432i	0.397967	−	0.917400i	$-0.369716\pi$
$383$	−8.37765e13	−	8.37765e13i	−0.519432	−	0.519432i	−0.917400	+	0.397967i	$0.869716\pi$
$384$	−1.08885e14	+	2.29509e14i	−0.665495	+	1.40274i
$385$	3.98433e13	−	8.98659e12i	0.240061	−	0.0541453i
$386$	1.02784e14	+	6.51316e12i	0.610516	+	0.0386867i
$387$	5.95199e13	+	5.95199e13i	0.348539	+	0.348539i
$388$	−1.54471e14	+	1.19597e14i	−0.891812	+	0.690473i
$389$	−2.66479e14			−1.51684			−0.758421	−	0.651765i	$-0.774029\pi$
$389$	−2.66479e14			−1.51684			−0.758421	+	0.651765i	$0.774029\pi$
$390$	−4.05882e13	−	2.53842e14i	−0.227795	−	1.42465i
$391$		−	1.60578e14i		−	0.888617i
$392$	−8.58765e12	−	1.26732e13i	−0.0468599	−	0.0691532i
$393$	−1.26498e14	+	1.26498e14i	−0.680651	+	0.680651i
$394$	−9.32166e13	−	5.90688e12i	−0.494611	−	0.0313422i
$395$	5.58962e13	+	3.53221e13i	0.292481	+	0.184826i
$396$	−6.41071e13	−	8.15733e12i	−0.330813	−	0.0420944i
$397$	−1.54200e14	+	1.54200e14i	−0.784760	+	0.784760i	−0.980630	−	0.195870i	$-0.937247\pi$
$397$	−1.54200e14	+	1.54200e14i	−0.784760	+	0.784760i	0.195870	+	0.980630i	$0.437247\pi$
$398$	9.10388e13	+	1.03357e14i	0.456951	+	0.518781i
$399$	−2.47555e14			−1.22552
$400$	−3.87872e13	−	2.01093e14i	−0.189391	−	0.981902i
$401$	−2.50513e14			−1.20653			−0.603263	−	0.797542i	$-0.706133\pi$
$401$	−2.50513e14			−1.20653			−0.603263	+	0.797542i	$0.706133\pi$
$402$	3.28783e14	+	3.73270e14i	1.56195	+	1.77329i
$403$	−9.36764e13	+	9.36764e13i	−0.438988	+	0.438988i
$404$	3.40308e14	+	4.33027e13i	1.57317	+	0.200178i
$405$	−7.80153e13	−	4.92997e13i	−0.355776	−	0.224823i
$406$	1.20512e14	+	7.63651e12i	0.542172	+	0.0343559i
$407$	7.48893e13	−	7.48893e13i	0.332392	−	0.332392i
$408$	1.93618e14	−	1.31200e14i	0.847841	−	0.574518i
$409$		−	2.82442e14i		−	1.22025i	−0.792304	−	0.610127i	$-0.791118\pi$
$409$		−	2.82442e14i		−	1.22025i	0.792304	−	0.610127i	$-0.208882\pi$
$410$	5.79846e13	+	3.62640e14i	0.247173	+	1.54584i
$411$	−2.10902e14			−0.887054
$412$	4.82786e13	−	3.73791e13i	0.200364	−	0.155129i
$413$	1.23592e14	+	1.23592e14i	0.506133	+	0.506133i
$414$	4.69281e14	+	2.97371e13i	1.89641	+	0.120170i
$415$	3.14869e13	−	7.10181e12i	0.125564	−	0.0283207i
$416$	7.34729e13	−	2.24404e14i	0.289144	−	0.883115i
$417$	2.32849e14	+	2.32849e14i	0.904329	+	0.904329i
$418$	3.50980e13	−	3.09149e13i	0.134528	−	0.118495i
$419$		−	1.35926e14i		−	0.514194i	−0.966386	−	0.257097i	$-0.917234\pi$
$419$		−	1.35926e14i		−	0.514194i	0.966386	−	0.257097i	$-0.0827659\pi$
$420$	−3.33810e14	−	2.75577e14i	−1.24632	−	1.02890i
$421$		−	1.21644e14i		−	0.448268i	−0.974558	−	0.224134i	$-0.928045\pi$
$421$		−	1.21644e14i		−	0.448268i	0.974558	−	0.224134i	$-0.0719553\pi$
$422$	−1.81422e14	−	2.05970e14i	−0.659890	−	0.749179i
$423$	−5.78203e13	−	5.78203e13i	−0.207591	−	0.207591i
$424$	4.30211e14	+	8.26702e13i	1.52465	+	0.292979i
$425$	−6.31887e13	+	1.77656e14i	−0.221055	+	0.621500i
$426$	−5.27055e13	+	8.31746e14i	−0.182013	+	2.87235i
$427$	2.48391e14	+	2.48391e14i	0.846802	+	0.846802i
$428$	1.77293e14	−	1.37267e14i	0.596694	−	0.461982i
$429$	1.02655e14			0.341087
$430$	−8.62720e13	−	6.24862e13i	−0.283005	−	0.204978i
$431$			3.16656e14i			1.02557i	0.858518	+	0.512783i	$0.171385\pi$
$431$			3.16656e14i			1.02557i	−0.858518	+	0.512783i	$0.828615\pi$
$432$	1.01166e14	+	1.71769e14i	0.323501	+	0.549268i
$433$	−3.39021e13	+	3.39021e13i	−0.107039	+	0.107039i	−0.758598	−	0.651559i	$-0.774115\pi$
$433$	−3.39021e13	+	3.39021e13i	−0.107039	+	0.107039i	0.651559	+	0.758598i	$0.274115\pi$
$434$	−1.41074e13	+	2.22629e14i	−0.0439798	+	0.694046i
$435$	2.56780e14	−	5.79163e13i	0.790443	−	0.178283i
$436$	4.17792e13	−	3.28336e14i	0.126994	−	0.998027i
$437$	−2.40646e14	+	2.40646e14i	−0.722323	+	0.722323i
$438$	3.65765e14	−	3.22173e14i	1.08416	−	0.954951i
$439$	−2.16011e14			−0.632297			−0.316148	−	0.948710i	$-0.602390\pi$
$439$	−2.16011e14			−0.632297			−0.316148	+	0.948710i	$0.602390\pi$
$440$	8.17415e13	−	2.61565e12i	0.236294	−	0.00756119i
$441$	−4.12737e13			−0.117831
$442$	−1.63139e14	+	1.43696e14i	−0.459977	+	0.405156i
$443$	5.57787e13	−	5.57787e13i	0.155327	−	0.155327i	−0.625165	−	0.780492i	$-0.714968\pi$
$443$	5.57787e13	−	5.57787e13i	0.155327	−	0.155327i	0.780492	+	0.625165i	$0.214968\pi$
$444$	−1.11345e15	−	1.41681e14i	−3.06241	−	0.389677i
$445$	−3.39554e14	+	5.37334e14i	−0.922419	+	1.45970i
$446$	8.10775e12	−	1.27949e14i	0.0217550	−	0.343316i
$447$	−1.59236e14	+	1.59236e14i	−0.422035	+	0.422035i
$448$	−1.56920e14	−	3.65328e14i	−0.410818	−	0.956433i
$449$		−	1.45737e14i		−	0.376891i	−0.982084	−	0.188445i	$-0.939655\pi$
$449$		−	1.45737e14i		−	0.376891i	0.982084	−	0.188445i	$-0.0603448\pi$
$450$	−5.07489e14	−	2.17565e14i	−1.29646	−	0.555803i
$451$	−1.46654e14			−0.370102
$452$	3.15591e14	+	4.07615e14i	0.786797	+	1.01622i
$453$	−3.98536e14	−	3.98536e14i	−0.981584	−	0.981584i
$454$	−4.24474e13	+	6.69864e14i	−0.103287	+	1.62997i
$455$	3.40138e14	+	2.14941e14i	0.817696	+	0.516721i
$456$	−4.86780e14	−	9.35407e13i	−1.15618	−	0.222174i
$457$	−3.45539e13	−	3.45539e13i	−0.0810883	−	0.0810883i	0.665399	−	0.746488i	$-0.268261\pi$
$457$	−3.45539e13	−	3.45539e13i	−0.0810883	−	0.0810883i	−0.746488	+	0.665399i	$0.768261\pi$
$458$	1.13538e14	+	1.28900e14i	0.263257	+	0.298878i
$459$		−	1.83538e14i		−	0.420491i
$460$	−5.92380e14	+	5.66079e13i	−1.34101	+	0.128147i
$461$			5.95337e14i			1.33170i	0.746084	+	0.665852i	$0.231932\pi$
$461$			5.95337e14i			1.33170i	−0.746084	+	0.665852i	$0.768068\pi$
$462$	1.29714e14	−	1.14254e14i	0.286718	−	0.252546i
$463$	5.26906e14	+	5.26906e14i	1.15090	+	1.15090i	0.986373	+	0.164527i	$0.0526097\pi$
$463$	5.26906e14	+	5.26906e14i	1.15090	+	1.15090i	0.164527	+	0.986373i	$0.447390\pi$
$464$	2.34083e14	+	6.05524e13i	0.505267	+	0.130702i
$465$	1.06992e14	+	4.74366e14i	0.228224	+	1.01186i
$466$	4.49238e14	+	2.84670e13i	0.947009	+	0.0600093i
$467$	−3.47468e14	−	3.47468e14i	−0.723889	−	0.723889i	0.245506	−	0.969395i	$-0.421046\pi$
$467$	−3.47468e14	−	3.47468e14i	−0.723889	−	0.723889i	−0.969395	+	0.245506i	$0.921046\pi$
$468$	−3.89733e14	−	5.03377e14i	−0.802444	−	1.03643i
$469$	−7.78564e14			−1.58432
$470$	8.38085e13	+	6.07019e13i	0.168558	+	0.122086i
$471$		−	3.98721e14i		−	0.792600i
$472$	1.96324e14	+	2.89725e14i	0.385739	+	0.569252i
$473$	3.00793e13	−	3.00793e13i	0.0584159	−	0.0584159i
$474$	2.79273e14	+	1.76967e13i	0.536102	+	0.0339713i
$475$	3.60936e14	−	1.71543e14i	0.684881	−	0.325506i
$476$	−4.62085e13	+	3.63145e14i	−0.0866730	+	0.681148i
$477$	8.35169e14	−	8.35169e14i	1.54854	−	1.54854i
$478$	−1.88075e14	−	2.13523e14i	−0.344729	−	0.391374i
$479$	4.52427e14			0.819791			0.409895	−	0.912133i	$-0.365565\pi$
$479$	4.52427e14			0.819791			0.409895	+	0.912133i	$0.365565\pi$
$480$	−5.52258e14	−	6.68013e14i	−0.989271	−	1.19663i
$481$	1.04332e15			1.84765
$482$	−2.41590e14	−	2.74279e14i	−0.422980	−	0.480212i
$483$	−8.89369e14	+	8.89369e14i	−1.53948	+	1.53948i
$484$	6.96347e13	−	5.47247e14i	0.119173	−	0.936556i
$485$	−1.46657e14	−	6.50223e14i	−0.248154	−	1.10023i
$486$	−7.70044e14	−	4.87956e13i	−1.28830	−	0.0816358i
$487$	−3.05458e14	+	3.05458e14i	−0.505292	+	0.505292i	−0.913078	−	0.407786i	$-0.866301\pi$
$487$	−3.05458e14	+	3.05458e14i	−0.505292	+	0.505292i	0.407786	+	0.913078i	$0.366301\pi$
$488$	3.94566e14	+	5.82278e14i	0.645373	+	0.952405i
$489$		−	6.40480e14i		−	1.03587i
$490$	5.15777e13	−	8.24705e12i	0.0824867	−	0.0131893i
$491$	5.09391e14			0.805570			0.402785	−	0.915295i	$-0.368042\pi$
$491$	5.09391e14			0.805570			0.402785	+	0.915295i	$0.368042\pi$
$492$	9.51490e14	+	1.22894e15i	1.48798	+	1.92186i
$493$	−1.57412e14	−	1.57412e14i	−0.243433	−	0.243433i
$494$	4.59831e14	+	2.91382e13i	0.703234	+	0.0445620i
$495$	1.17789e14	−	1.86397e14i	0.178145	−	0.281910i
$496$	−1.11862e14	+	4.32436e14i	−0.167315	+	0.646803i
$497$	−9.22390e14	−	9.22390e14i	−1.36444	−	1.36444i
$498$	1.02508e14	−	9.02913e13i	0.149968	−	0.132094i
$499$		−	2.62021e14i		−	0.379126i	−0.981869	−	0.189563i	$-0.939293\pi$
$499$		−	2.62021e14i		−	0.379126i	0.981869	−	0.189563i	$-0.0607071\pi$
$500$	6.77657e14	+	1.70478e14i	0.969783	+	0.243968i
$501$		−	1.99820e15i		−	2.82833i
$502$	−1.97876e14	−	2.24650e14i	−0.277027	−	0.314511i
$503$	9.59059e14	+	9.59059e14i	1.32807	+	1.32807i	0.907052	+	0.421020i	$0.138328\pi$
$503$	9.59059e14	+	9.59059e14i	1.32807	+	1.32807i	0.421020	+	0.907052i	$0.361672\pi$
$504$	−1.05271e15	−	2.02292e14i	−1.44192	−	0.277083i
$505$	−6.25273e14	+	9.89477e14i	−0.847163	+	1.34061i
$506$	1.50281e13	−	2.37159e14i	0.0201408	−	0.317842i
$507$	−1.13040e14	−	1.13040e14i	−0.149862	−	0.149862i
$508$	5.08474e12	+	6.56742e12i	0.00666835	+	0.00861280i
$509$	2.42915e14			0.315142			0.157571	−	0.987508i	$-0.449634\pi$
$509$	2.42915e14			0.315142			0.157571	+	0.987508i	$0.449634\pi$
$510$	1.25997e14	+	7.87992e14i	0.161705	+	1.01131i
$511$			7.62910e14i			0.968631i
$512$	−1.70517e14	−	7.77656e14i	−0.214182	−	0.976794i
$513$	−2.75055e14	+	2.75055e14i	−0.341801	+	0.341801i
$514$	7.34343e13	−	1.15887e15i	0.0902822	−	1.42474i
$515$	4.58362e13	+	2.03221e14i	0.0557530	+	0.247189i
$516$	−4.47216e14	−	5.69062e13i	−0.538200	−	0.0684835i
$517$	−2.92204e13	+	2.92204e13i	−0.0347927	+	0.0347927i
$518$	1.31833e15	−	1.16121e15i	1.55314	−	1.36803i
$519$	8.64686e14			1.00795
$520$	5.87612e14	+	5.51172e14i	0.677754	+	0.635724i
$521$	1.22559e15			1.39874			0.699371	−	0.714758i	$-0.253463\pi$
$521$	1.22559e15			1.39874			0.699371	+	0.714758i	$0.253463\pi$
$522$	4.89178e14	−	4.30876e14i	0.552432	−	0.486592i
$523$	−3.98497e14	+	3.98497e14i	−0.445313	+	0.445313i	−0.893793	−	0.448480i	$-0.851966\pi$
$523$	−3.98497e14	+	3.98497e14i	−0.445313	+	0.445313i	0.448480	+	0.893793i	$0.351966\pi$
$524$	7.07711e13	−	5.56178e14i	0.0782589	−	0.615023i
$525$	1.33393e15	−	6.33982e14i	1.45968	−	0.693747i
$526$	2.64663e13	−	4.17665e14i	0.0286597	−	0.452279i
$527$	2.90796e14	−	2.90796e14i	0.311624	−	0.311624i
$528$	2.98234e14	−	1.75650e14i	0.316279	−	0.186278i
$529$			7.76286e14i			0.814734i
$530$	−8.76792e14	+	1.21055e15i	−0.910708	+	1.25738i
$531$	9.43568e14			0.969959
$532$	6.13467e14	−	4.74968e14i	0.624133	−	0.483226i
$533$	−1.02155e15	−	1.02155e15i	−1.02864	−	1.02864i
$534$	−1.70120e14	+	2.68467e15i	−0.169542	+	2.67555i
$535$	1.68324e14	+	7.46289e14i	0.166035	+	0.736141i
$536$	−1.53093e15	−	2.94186e14i	−1.49468	−	0.287221i
$537$	−1.79753e15	−	1.79753e15i	−1.73707	−	1.73707i
$538$	−7.22792e14	−	8.20592e14i	−0.691370	−	0.784919i
$539$			2.08583e13i			0.0197488i
$540$	−6.77081e14	+	6.47020e13i	−0.634564	+	0.0606390i
$541$			7.62437e14i			0.707325i	0.935373	+	0.353663i	$0.115064\pi$
$541$			7.62437e14i			0.707325i	−0.935373	+	0.353663i	$0.884936\pi$
$542$	−1.12003e15	+	9.86540e14i	−1.02857	+	0.905980i
$543$	−4.46781e14	−	4.46781e14i	−0.406159	−	0.406159i
$544$	−2.28079e14	+	6.96609e14i	−0.205254	+	0.626895i
$545$	9.54666e14	+	6.03275e14i	0.850493	+	0.537446i
$546$	1.69942e15	+	1.07688e14i	1.49879	+	0.0949743i
$547$	−4.72318e14	−	4.72318e14i	−0.412386	−	0.412386i	0.470183	−	0.882569i	$-0.344188\pi$
$547$	−4.72318e14	−	4.72318e14i	−0.412386	−	0.412386i	−0.882569	+	0.470183i	$0.844188\pi$
$548$	5.22635e14	−	4.04643e14i	0.451758	−	0.349767i
$549$	1.89635e15			1.62282
$550$	−1.09950e14	+	2.56467e14i	−0.0931538	+	0.217289i
$551$			4.71801e14i			0.395754i
$552$	−2.08486e15	+	1.41275e15i	−1.73146	+	1.17328i
$553$	−3.09708e14	+	3.09708e14i	−0.254662	+	0.254662i
$554$	7.25649e13	+	4.59824e12i	0.0590776	+	0.00374359i
$555$	2.04582e15	−	3.23745e15i	1.64913	−	2.60970i
$556$	−1.02378e15	−	1.30271e14i	−0.817135	−	0.103977i
$557$	−8.64876e14	+	8.64876e14i	−0.683519	+	0.683519i	−0.960791	−	0.277273i	$-0.910569\pi$
$557$	−8.64876e14	+	8.64876e14i	−0.683519	+	0.683519i	0.277273	+	0.960791i	$0.410569\pi$
$558$	7.95985e14	+	9.03688e14i	0.622897	+	0.707181i
$559$	4.19051e14			0.324714
$560$	1.35595e15	+	4.24475e13i	1.04042	+	0.0325700i
$561$	−3.18668e14			−0.242127
$562$	−3.26398e14	−	3.70563e14i	−0.245583	−	0.278812i
$563$	−1.38765e15	+	1.38765e15i	−1.03391	+	1.03391i	−0.0345095	+	0.999404i	$0.510987\pi$
$563$	−1.38765e15	+	1.38765e15i	−1.03391	+	1.03391i	−0.999404	+	0.0345095i	$0.989013\pi$
$564$	4.34445e14	+	5.52812e13i	0.320553	+	0.0407889i
$565$	−1.71579e15	+	3.86994e14i	−1.25371	+	0.282773i
$566$	3.68020e14	+	2.33204e13i	0.266306	+	0.0168751i
$567$	4.32265e14	−	4.32265e14i	0.309773	−	0.309773i
$568$	−1.46521e15	−	2.16227e15i	−1.03988	−	1.53460i
$569$			1.13013e15i			0.794350i	0.917743	+	0.397175i	$0.130009\pi$
$569$			1.13013e15i			0.794350i	−0.917743	+	0.397175i	$0.869991\pi$
$570$	9.92083e14	−	1.36973e15i	0.690615	−	0.953502i
$571$	7.85962e14			0.541880			0.270940	−	0.962596i	$-0.412666\pi$
$571$	7.85962e14			0.541880			0.270940	+	0.962596i	$0.412666\pi$
$572$	−2.54389e14	+	1.96958e14i	−0.173708	+	0.134491i
$573$	2.77167e15	+	2.77167e15i	1.87452	+	1.87452i
$574$	−2.42780e15	−	1.53843e14i	−1.62629	−	0.103054i
$575$	6.80412e14	−	1.91299e15i	0.451439	−	1.26923i
$576$	−1.99357e15	−	7.95552e14i	−1.31011	−	0.522811i
$577$	−7.62365e14	−	7.62365e14i	−0.496245	−	0.496245i	0.414022	−	0.910267i	$-0.364124\pi$
$577$	−7.62365e14	−	7.62365e14i	−0.496245	−	0.496245i	−0.910267	+	0.414022i	$0.864124\pi$
$578$	−6.57434e14	+	5.79079e14i	−0.423886	+	0.373366i
$579$			1.48716e15i			0.949789i
$580$	−5.25207e14	+	6.36190e14i	−0.332259	+	0.402469i
$581$			2.13811e14i			0.133987i
$582$	−1.86457e15	−	2.11686e15i	−1.15745	−	1.31406i
$583$	−4.22066e14	−	4.22066e14i	−0.259539	−	0.259539i
$584$	−2.88271e14	+	1.50015e15i	−0.175603	+	0.913825i
$585$	2.11889e15	−	4.77911e14i	1.27865	−	0.288396i
$586$	9.49652e13	−	1.49865e15i	0.0567712	−	0.895907i
$587$	6.26772e14	+	6.26772e14i	0.371193	+	0.371193i	0.867912	−	0.496718i	$-0.165462\pi$
$587$	6.26772e14	+	6.26772e14i	0.371193	+	0.371193i	−0.496718	+	0.867912i	$0.665462\pi$
$588$	1.74790e14	−	1.35329e14i	0.102551	−	0.0793990i
$589$	−8.71588e14			−0.506614
$590$	−1.17913e15	+	1.88538e14i	−0.679010	+	0.108571i
$591$		−	1.34873e15i		−	0.769475i
$592$	3.03107e15	−	1.78520e15i	1.71327	−	1.00906i
$593$	1.63801e15	−	1.63801e15i	0.917308	−	0.917308i	−0.0795248	−	0.996833i	$-0.525340\pi$
$593$	1.63801e15	−	1.63801e15i	0.917308	−	0.917308i	0.996833	+	0.0795248i	$0.0253403\pi$
$594$	1.71769e13	−	2.71069e14i	0.00953057	−	0.150402i
$595$	−1.05588e15	−	6.67233e14i	−0.580457	−	0.366804i
$596$	8.90866e13	−	7.00117e14i	0.0485242	−	0.381343i
$597$	−1.40634e15	+	1.40634e15i	−0.758980	+	0.758980i
$598$	1.75667e15	−	1.54731e15i	0.939366	−	0.827410i
$599$	8.14020e13			0.0431308			0.0215654	−	0.999767i	$-0.493135\pi$
$599$	8.14020e13			0.0431308			0.0215654	+	0.999767i	$0.493135\pi$
$600$	2.86252e15	−	7.42594e14i	1.50286	−	0.389870i
$601$	−1.05056e15			−0.546527			−0.273264	−	0.961939i	$-0.588103\pi$
$601$	−1.05056e15			−0.546527			−0.273264	+	0.961939i	$0.588103\pi$
$602$	5.29507e14	−	4.66399e14i	0.272955	−	0.240424i
$603$	−2.97199e15	+	2.97199e15i	−1.51811	+	1.51811i
$604$	1.75226e15	+	2.22967e14i	0.886941	+	0.112859i
$605$	1.59117e15	+	1.00550e15i	0.798109	+	0.504343i
$606$	−3.13269e14	+	4.94370e15i	−0.155710	+	2.45727i
$607$	−5.37289e14	+	5.37289e14i	−0.264649	+	0.264649i	−0.826940	−	0.562291i	$-0.809920\pi$
$607$	−5.37289e14	+	5.37289e14i	−0.264649	+	0.264649i	0.562291	+	0.826940i	$0.309920\pi$
$608$	1.38576e15	−	7.02150e14i	0.676423	−	0.342736i
$609$			1.74366e15i			0.843465i
$610$	−2.36978e15	+	3.78917e14i	−1.13604	+	0.181648i
$611$	−4.07085e14			−0.193401
$612$	1.20983e15	+	1.56261e15i	0.569630	+	0.735731i
$613$	7.77970e14	+	7.77970e14i	0.363020	+	0.363020i	0.864923	−	0.501904i	$-0.167367\pi$
$613$	7.77970e14	+	7.77970e14i	0.363020	+	0.363020i	−0.501904	+	0.864923i	$0.667367\pi$
$614$	−1.60156e14	+	2.52742e15i	−0.0740657	+	1.16883i
$615$	−5.17303e15	+	1.16677e15i	−2.37100	+	0.534775i
$616$	−1.02231e14	+	5.32006e14i	−0.0464398	+	0.241670i
$617$	1.80526e14	+	1.80526e14i	0.0812777	+	0.0812777i	0.746577	−	0.665299i	$-0.231696\pi$
$617$	1.80526e14	+	1.80526e14i	0.0812777	+	0.0812777i	−0.665299	+	0.746577i	$0.731696\pi$
$618$	5.82754e14	+	6.61605e14i	0.260045	+	0.295231i
$619$		−	1.67025e15i		−	0.738724i	−0.929286	−	0.369362i	$-0.879576\pi$
$619$		−	1.67025e15i		−	0.738724i	0.929286	−	0.369362i	$-0.120424\pi$
$620$	−1.17527e15	−	9.70247e14i	−0.515210	−	0.425332i
$621$			1.97633e15i			0.858728i
$622$	−1.01903e15	+	8.97581e14i	−0.438875	+	0.386569i
$623$	−2.97724e15	−	2.97724e15i	−1.27095	−	1.27095i
$624$	3.30096e15	+	8.53890e14i	1.39677	+	0.361316i
$625$	−1.50555e15	+	1.84869e15i	−0.631473	+	0.775398i
$626$	1.13970e15	+	7.22194e13i	0.473838	+	0.0300258i
$627$	4.77564e14	+	4.77564e14i	0.196816	+	0.196816i
$628$	7.65000e14	+	9.88071e14i	0.312524	+	0.403655i
$629$	−3.23875e15			−1.31159
$630$	2.14549e15	−	2.96218e15i	0.861297	−	1.18916i
$631$		−	1.35945e15i		−	0.541004i	−0.962719	−	0.270502i	$-0.912810\pi$
$631$		−	1.35945e15i		−	0.541004i	0.962719	−	0.270502i	$-0.0871897\pi$
$632$	−7.26019e14	+	4.91968e14i	−0.286420	+	0.194085i
$633$	2.80255e15	−	2.80255e15i	1.09605	−	1.09605i
$634$	1.66222e14	+	1.05330e13i	0.0644461	+	0.00408377i
$635$	−2.76445e13	+	6.23518e12i	−0.0106256	+	0.00239659i
$636$	−7.98494e14	+	6.27523e15i	−0.304269	+	2.39120i
$637$	−1.45294e14	+	1.45294e14i	−0.0548885	+	0.0548885i
$638$	−2.17750e14	−	2.47214e14i	−0.0815539	−	0.0925888i
$639$	−7.04203e15			−2.61483
$640$	2.65023e15	+	5.95822e14i	0.975648	+	0.219344i
$641$	−2.53848e15			−0.926520			−0.463260	−	0.886223i	$-0.653320\pi$
$641$	−2.53848e15			−0.926520			−0.463260	+	0.886223i	$0.653320\pi$
$642$	2.14004e15	+	2.42961e15i	0.774426	+	0.879213i
$643$	3.55281e15	−	3.55281e15i	1.27471	−	1.27471i	0.331122	−	0.943588i	$-0.392573\pi$
$643$	3.55281e15	−	3.55281e15i	1.27471	−	1.27471i	0.943588	−	0.331122i	$-0.107427\pi$
$644$	4.97570e14	−	3.91032e15i	0.177004	−	1.39104i
$645$	8.21702e14	−	1.30032e15i	0.289825	−	0.458640i
$646$	−1.42744e15	−	9.04527e13i	−0.499204	−	0.0316332i
$647$	1.69427e15	−	1.69427e15i	0.587503	−	0.587503i	−0.349451	−	0.936954i	$-0.613632\pi$
$647$	1.69427e15	−	1.69427e15i	0.587503	−	0.587503i	0.936954	+	0.349451i	$0.113632\pi$
$648$	1.01332e15	−	6.86649e14i	0.348404	−	0.236087i
$649$		−	4.76847e14i		−	0.162567i
$650$	−2.55238e15	+	1.02061e15i	−0.862823	+	0.345012i
$651$	−3.22117e15			−1.07974
$652$	1.22885e15	+	1.58717e15i	0.408447	+	0.527549i
$653$	−2.27945e15	−	2.27945e15i	−0.751291	−	0.751291i	0.223429	−	0.974720i	$-0.428275\pi$
$653$	−2.27945e15	−	2.27945e15i	−0.751291	−	0.751291i	−0.974720	+	0.223429i	$0.928275\pi$
$654$	4.76977e15	+	3.02247e14i	1.55891	+	0.0987836i
$655$	1.61714e15	+	1.02191e15i	0.524107	+	0.331195i
$656$	−4.71577e15	−	1.21987e15i	−1.51559	−	0.392052i
$657$	2.91224e15	+	2.91224e15i	0.928148	+	0.928148i
$658$	−5.14387e14	+	4.53081e14i	−0.162573	+	0.143197i
$659$			2.48138e15i			0.777721i	0.921297	+	0.388860i	$0.127131\pi$
$659$			2.48138e15i			0.777721i	−0.921297	+	0.388860i	$0.872869\pi$
$660$	1.12339e14	+	1.17558e15i	0.0349171	+	0.365394i
$661$			3.17662e15i			0.979169i	0.871956	+	0.489585i	$0.162852\pi$
$661$			3.17662e15i			0.979169i	−0.871956	+	0.489585i	$0.837148\pi$
$662$	−1.67235e15	−	1.89863e15i	−0.511220	−	0.580393i
$663$	−2.21977e15	−	2.21977e15i	−0.672951	−	0.672951i
$664$	−8.07902e13	+	4.20427e14i	−0.0242904	+	0.126406i
$665$	5.82431e14	+	2.58229e15i	0.173670	+	0.769992i
$666$	5.99776e14	−	9.46507e15i	0.177370	−	2.79908i
$667$	1.69500e15	+	1.69500e15i	0.497138	+	0.497138i
$668$	3.83381e15	+	4.95173e15i	1.11522	+	1.44041i
$669$	1.85126e15			0.534101
$670$	3.12011e15	−	4.30780e15i	0.892809	−	1.23266i
$671$		−	9.58350e14i		−	0.271988i
$672$	5.12142e15	−	2.59497e15i	1.44165	−	0.730469i
$673$	2.62930e15	−	2.62930e15i	0.734104	−	0.734104i	−0.237326	−	0.971430i	$-0.576271\pi$
$673$	2.62930e15	−	2.62930e15i	0.734104	−	0.734104i	0.971430	+	0.237326i	$0.0762710\pi$
$674$	−2.14251e13	+	3.38110e14i	−0.00593326	+	0.0936329i
$675$	7.77700e14	−	2.18652e15i	0.213620	−	0.600595i
$676$	4.97009e14	+	6.32421e13i	0.135412	+	0.0172306i
$677$	2.93460e15	−	2.93460e15i	0.793069	−	0.793069i	−0.188923	−	0.981992i	$-0.560500\pi$
$677$	2.93460e15	−	2.93460e15i	0.793069	−	0.793069i	0.981992	+	0.188923i	$0.0604996\pi$
$678$	−5.58592e15	+	4.92018e15i	−1.49738	+	1.31892i
$679$	4.41533e15			1.17403
$680$	−1.82410e15	−	1.71098e15i	−0.481116	−	0.451280i
$681$	−9.69212e15			−2.53577
$682$	4.56693e14	−	4.02263e14i	0.118525	−	0.104399i
$683$	6.81191e14	−	6.81191e14i	0.175370	−	0.175370i	−0.613964	−	0.789334i	$-0.710426\pi$
$683$	6.81191e14	−	6.81191e14i	0.175370	−	0.175370i	0.789334	+	0.613964i	$0.210426\pi$
$684$	5.28686e14	−	4.15485e15i	0.135017	−	1.06108i
$685$	4.96195e14	+	2.19995e15i	0.125705	+	0.557333i
$686$	2.40057e14	−	3.78835e15i	0.0603298	−	0.952067i
$687$	−1.75389e15	+	1.75389e15i	−0.437261	+	0.437261i
$688$	1.21743e15	−	7.17025e14i	0.301097	−	0.177336i
$689$		−	5.88002e15i		−	1.44269i
$690$	−1.35672e15	−	8.48505e15i	−0.330233	−	2.06531i
$691$	2.33044e15			0.562742			0.281371	−	0.959599i	$-0.409211\pi$
$691$	2.33044e15			0.562742			0.281371	+	0.959599i	$0.409211\pi$
$692$	−2.14278e15	+	1.65902e15i	−0.513326	+	0.397436i
$693$	1.03278e15	+	1.03278e15i	0.245458	+	0.245458i
$694$	−3.51170e14	+	5.54182e15i	−0.0828019	+	1.30670i
$695$	1.88106e15	−	2.97672e15i	0.440034	−	0.696341i
$696$	−6.58856e14	+	3.42864e15i	−0.152911	+	0.795741i
$697$	3.17117e15	+	3.17117e15i	0.730197	+	0.730197i
$698$	−4.17946e15	−	4.74498e15i	−0.954807	−	1.08400i
$699$			6.49993e15i			1.47328i
$700$	−2.08923e15	+	4.13039e15i	−0.469836	+	0.928864i
$701$		−	6.75327e15i		−	1.50683i	−0.657544	−	0.753416i	$-0.728405\pi$
$701$		−	6.75327e15i		−	1.50683i	0.657544	−	0.753416i	$-0.271595\pi$
$702$	2.00785e15	−	1.76855e15i	0.444506	−	0.391529i
$703$	4.85367e15	+	4.85367e15i	1.06614	+	1.06614i
$704$	−4.02045e14	+	1.00748e15i	−0.0876244	+	0.219577i
$705$	−7.98238e14	+	1.26319e15i	−0.172621	+	0.273167i
$706$	4.85658e15	+	3.07748e14i	1.04209	+	0.0660343i
$707$	−5.48246e15	−	5.48246e15i	−1.16726	−	1.16726i
$708$	−3.99592e15	+	3.09379e15i	−0.844178	+	0.653593i
$709$	7.86850e15			1.64945			0.824723	−	0.565538i	$-0.191331\pi$
$709$	7.86850e15			1.64945			0.824723	+	0.565538i	$0.191331\pi$
$710$	8.80009e15	−	1.40710e15i	1.83048	−	0.292686i
$711$			2.36448e15i			0.488037i
$712$	−4.72932e15	−	6.97927e15i	−0.968632	−	1.42945i
$713$	−3.13127e15	+	3.13127e15i	−0.636398	+	0.636398i
$714$	−5.27545e15	−	3.34291e14i	−1.06395	−	0.0674193i
$715$	−2.41520e14	−	1.07081e15i	−0.0483359	−	0.214304i
$716$	7.90325e15	+	1.00565e15i	1.56958	+	0.199722i
$717$	2.90532e15	−	2.90532e15i	0.572584	−	0.572584i
$718$	−2.19698e15	−	2.49425e15i	−0.429677	−	0.487816i
$719$	−8.23402e14			−0.159810			−0.0799048	−	0.996802i	$-0.525462\pi$
$719$	−8.23402e14			−0.159810			−0.0799048	+	0.996802i	$0.525462\pi$
$720$	5.33806e15	−	5.01399e15i	1.02815	−	0.965728i
$721$	−1.37997e15			−0.263770
$722$	−1.48085e15	−	1.68122e15i	−0.280903	−	0.318912i
$723$	3.73199e15	−	3.73199e15i	0.702555	−	0.702555i
$724$	1.96438e15	+	2.49958e14i	0.366998	+	0.0466988i
$725$	−1.20827e15	−	2.54226e15i	−0.224029	−	0.471369i
$726$	7.94992e15	+	5.03765e14i	1.46289	+	0.0926993i
$727$	−5.05866e15	+	5.05866e15i	−0.923840	+	0.923840i	−0.997298	−	0.0734587i	$-0.976596\pi$
$727$	−5.05866e15	+	5.05866e15i	−0.923840	+	0.923840i	0.0734587	+	0.997298i	$0.476596\pi$
$728$	−4.41795e15	+	2.99371e15i	−0.800752	+	0.542609i
$729$		−	8.80202e15i		−	1.58336i
$730$	−4.22119e15	−	3.05738e15i	−0.753631	−	0.545850i
$731$	−1.30084e15			−0.230505
$732$	−8.03086e15	+	6.21778e15i	−1.41238	+	1.09351i
$733$	2.69997e15	+	2.69997e15i	0.471288	+	0.471288i	0.902331	−	0.431043i	$-0.141854\pi$
$733$	2.69997e15	+	2.69997e15i	0.471288	+	0.471288i	−0.431043	+	0.902331i	$0.641854\pi$
$734$	−4.34645e15	−	2.75423e14i	−0.753020	−	0.0477168i
$735$	1.65947e14	+	7.35752e14i	0.0285358	+	0.126518i
$736$	2.45594e15	−	7.50104e15i	0.419170	−	1.28025i
$737$	1.50194e15	+	1.50194e15i	0.254438	+	0.254438i
$738$	−9.85485e15	+	8.68033e15i	−1.65707	+	1.45957i
$739$			6.30115e15i			1.05166i	0.850589	+	0.525830i	$0.176245\pi$
$739$			6.30115e15i			1.05166i	−0.850589	+	0.525830i	$0.823755\pi$
$740$	1.14174e15	+	1.19479e16i	0.189144	+	1.97932i
$741$			6.65319e15i			1.09403i
$742$	−6.54440e15	−	7.42992e15i	−1.06819	−	1.21273i
$743$	−1.39645e15	−	1.39645e15i	−0.226248	−	0.226248i	0.584875	−	0.811123i	$-0.301144\pi$
$743$	−1.39645e15	−	1.39645e15i	−0.226248	−	0.226248i	−0.811123	+	0.584875i	$0.801144\pi$
$744$	−6.33395e15	−	1.21714e15i	−1.01865	−	0.195745i
$745$	2.03565e15	+	1.28638e15i	0.324971	+	0.205356i
$746$	−6.11876e14	+	9.65603e15i	−0.0969616	+	1.53015i
$747$	8.16176e14	+	8.16176e14i	0.128387	+	0.128387i
$748$	7.89692e14	−	6.11408e14i	0.123310	−	0.0954712i
$749$	−5.06766e15			−0.785520
$750$	−1.83792e15	+	9.92133e15i	−0.282806	+	1.52663i
$751$			2.91690e15i			0.445556i	0.974869	+	0.222778i	$0.0715125\pi$
$751$			2.91690e15i			0.445556i	−0.974869	+	0.222778i	$0.928488\pi$
$752$	−1.18266e15	+	6.96550e14i	−0.179334	+	0.105622i
$753$	3.05672e15	−	3.05672e15i	0.460133	−	0.460133i
$754$	2.05236e14	−	3.23883e15i	0.0306698	−	0.484000i
$755$	−3.21955e15	+	5.09485e15i	−0.477625	+	0.755828i
$756$	5.68715e14	−	4.46943e15i	0.0837577	−	0.658238i
$757$	−2.18243e15	+	2.18243e15i	−0.319090	+	0.319090i	−0.848418	−	0.529328i	$-0.822444\pi$
$757$	−2.18243e15	+	2.18243e15i	−0.319090	+	0.319090i	0.529328	+	0.848418i	$0.322444\pi$
$758$	−6.36737e15	+	5.60849e15i	−0.924229	+	0.814077i
$759$	3.43140e15			0.494472
$760$	1.69524e14	+	5.29776e15i	0.0242524	+	0.757910i
$761$	3.33090e14			0.0473093			0.0236546	−	0.999720i	$-0.492470\pi$
$761$	3.33090e14			0.0473093			0.0236546	+	0.999720i	$0.492470\pi$
$762$	−8.99993e13	+	7.92730e13i	−0.0126907	+	0.0111782i
$763$	−5.28958e15	+	5.28958e15i	−0.740520	+	0.740520i
$764$	−1.21863e16	−	1.55065e15i	−1.69378	−	0.215526i
$765$	−6.57758e15	+	1.48356e15i	−0.907671	+	0.204723i
$766$	−3.39076e14	+	5.35096e15i	−0.0464556	+	0.733117i
$767$	3.32160e15	−	3.32160e15i	0.451828	−	0.451828i
$768$	1.10510e16	−	3.16745e15i	1.49251	−	0.427782i
$769$		−	5.52657e15i		−	0.741073i	−0.928818	−	0.370536i	$-0.879174\pi$
$769$		−	5.52657e15i		−	0.741073i	0.928818	−	0.370536i	$-0.120826\pi$
$770$	−1.49698e15	−	1.08426e15i	−0.199305	−	0.144355i
$771$	1.67674e16			2.21650
$772$	−2.85333e15	−	3.68534e15i	−0.374504	−	0.483707i
$773$	−1.66942e15	−	1.66942e15i	−0.217560	−	0.217560i	0.589910	−	0.807469i	$-0.299163\pi$
$773$	−1.66942e15	−	1.66942e15i	−0.217560	−	0.217560i	−0.807469	+	0.589910i	$0.799163\pi$
$774$	2.40900e14	−	3.80165e15i	0.0311718	−	0.491922i
$775$	4.69647e15	−	2.23211e15i	0.603410	−	0.286785i
$776$	8.68207e15	+	1.66836e15i	1.10760	+	0.212839i
$777$	1.79379e16	+	1.79379e16i	2.27226	+	2.27226i
$778$	7.97099e15	+	9.04953e15i	1.00259	+	1.13825i
$779$		−	9.50479e15i		−	1.18710i
$780$	−7.40630e15	+	8.97135e15i	−0.918504	+	1.11260i
$781$			3.55880e15i			0.438251i
$782$	−5.45318e15	+	4.80326e15i	−0.666826	+	0.587352i
$783$	1.93736e15	+	1.93736e15i	0.235245	+	0.235245i
$784$	−1.73501e14	+	6.70717e14i	−0.0209200	+	0.0808725i
$785$	−4.15913e15	+	9.38084e14i	−0.497989	+	0.112320i
$786$	8.07966e15	+	5.11986e14i	0.960659	+	0.0608743i
$787$	−9.66512e15	−	9.66512e15i	−1.14116	−	1.14116i	−0.988239	−	0.152920i	$-0.951132\pi$
$787$	−9.66512e15	−	9.66512e15i	−1.14116	−	1.14116i	−0.152920	−	0.988239i	$-0.548868\pi$
$788$	2.58772e15	+	3.34229e15i	0.303406	+	0.391877i
$789$	6.04310e15			0.703617
$790$	−4.72456e14	−	2.95478e15i	−0.0546276	−	0.341645i
$791$		−	1.16511e16i		−	1.33781i
$792$	1.64057e15	+	2.42106e15i	0.187071	+	0.276068i
$793$	6.67564e15	−	6.67564e15i	0.755946	−	0.755946i
$794$	9.84906e15	+	6.24108e14i	1.10760	+	0.0701854i
$795$	−1.82458e16	−	1.15299e16i	−2.03772	−	1.28768i
$796$	7.86796e14	−	6.18329e15i	0.0872650	−	0.685800i
$797$	−4.67660e14	+	4.67660e14i	−0.0515121	+	0.0515121i	−0.732394	−	0.680882i	$-0.761597\pi$
$797$	−4.67660e14	+	4.67660e14i	−0.0515121	+	0.0515121i	0.680882	+	0.732394i	$0.261597\pi$
$798$	7.40494e15	+	8.40689e15i	0.810038	+	0.919643i
$799$	1.26370e15			0.137289
$800$	−5.66885e15	+	7.33236e15i	−0.611646	+	0.791132i
$801$	−2.27299e16			−2.43567
$802$	7.49342e15	+	8.50734e15i	0.797482	+	0.905388i
$803$	1.47174e15	−	1.47174e15i	0.155560	−	0.155560i
$804$	2.84148e15	−	2.23307e16i	0.298289	−	2.34420i
$805$	1.13696e16	+	7.18472e15i	1.18541	+	0.749087i
$806$	5.98329e15	+	3.79145e14i	0.619580	+	0.0392611i
$807$	1.11654e16	−	1.11654e16i	1.14834	−	1.14834i
$808$	−8.70884e15	−	1.28520e16i	−0.889606	−	1.31283i
$809$			3.69378e15i			0.374761i	0.982287	+	0.187381i	$0.0599997\pi$
$809$			3.69378e15i			0.374761i	−0.982287	+	0.187381i	$0.940000\pi$
$810$	6.59415e14	+	4.12404e15i	0.0664494	+	0.415580i
$811$	1.58975e16			1.59116			0.795578	−	0.605851i	$-0.207167\pi$
$811$	1.58975e16			1.59116			0.795578	+	0.605851i	$0.207167\pi$
$812$	−3.34545e15	−	4.32097e15i	−0.332580	−	0.429559i
$813$	−1.52397e16	−	1.52397e16i	−1.50480	−	1.50480i
$814$	−4.78332e15	−	3.03106e14i	−0.469132	−	0.0297276i
$815$	−6.68096e15	+	1.50688e15i	−0.650836	+	0.146795i
$816$	−1.02471e16	−	2.65070e15i	−0.991524	−	0.256487i
$817$	1.94947e15	+	1.94947e15i	0.187368	+	0.187368i
$818$	−9.59161e15	+	8.44846e15i	−0.915690	+	0.806556i
$819$			1.43883e16i			1.36442i
$820$	1.05807e16	−	1.28165e16i	0.996638	−	1.20724i
$821$			1.46304e15i			0.136889i	0.997655	+	0.0684446i	$0.0218036\pi$
$821$			1.46304e15i			0.136889i	−0.997655	+	0.0684446i	$0.978196\pi$
$822$	6.30854e15	+	7.16214e15i	0.586319	+	0.665653i
$823$	1.27813e16	+	1.27813e16i	1.17998	+	1.17998i	0.979749	+	0.200232i	$0.0641695\pi$
$823$	1.27813e16	+	1.27813e16i	1.17998	+	1.17998i	0.200232	+	0.979749i	$0.435831\pi$
$824$	−2.71350e15	−	5.21432e14i	−0.248846	−	0.0478187i
$825$	−3.79634e15	−	1.35028e15i	−0.345834	−	0.123006i
$826$	5.00224e14	−	7.89404e15i	0.0452662	−	0.714347i
$827$	4.50116e15	+	4.50116e15i	0.404617	+	0.404617i	0.879856	−	0.475240i	$-0.157639\pi$
$827$	4.50116e15	+	4.50116e15i	0.404617	+	0.404617i	−0.475240	+	0.879856i	$0.657639\pi$
$828$	−1.30274e16	−	1.68261e16i	−1.16330	−	1.50251i
$829$	−1.32392e16			−1.17439			−0.587193	−	0.809447i	$-0.699767\pi$
$829$	−1.32392e16			−1.17439			−0.587193	+	0.809447i	$0.699767\pi$
$830$	−1.18302e15	−	8.56852e14i	−0.104247	−	0.0755051i
$831$			1.04993e15i			0.0919080i
$832$	−9.81842e15	+	4.21732e15i	−0.853814	+	0.366740i
$833$	4.51031e14	−	4.51031e14i	0.0389636	−	0.0389636i
$834$	9.42431e14	−	1.48725e16i	0.0808791	−	1.27635i
$835$	−2.08435e16	+	4.70122e15i	−1.77703	+	0.400807i
$836$	−2.09972e15	−	2.67180e14i	−0.177839	−	0.0226292i
$837$	−3.57900e15	+	3.57900e15i	−0.301142	+	0.301142i
$838$	−4.61601e15	+	4.06586e15i	−0.385855	+	0.339868i
$839$	4.47473e14			0.0371600			0.0185800	−	0.999827i	$-0.494085\pi$
$839$	4.47473e14			0.0371600			0.0185800	+	0.999827i	$0.494085\pi$
$840$	6.26517e14	+	1.95792e16i	0.0516888	+	1.61532i
$841$	−8.87737e15			−0.727623
$842$	−4.13097e15	+	3.63863e15i	−0.336384	+	0.296293i
$843$	5.04209e15	−	5.04209e15i	0.407905	−	0.407905i
$844$	−1.56792e15	+	1.23220e16i	−0.126021	+	0.990375i
$845$	−9.13191e14	+	1.44510e15i	−0.0729205	+	0.115395i
$846$	−2.34021e14	+	3.69309e15i	−0.0185660	+	0.292990i
$847$	−8.81631e15	+	8.81631e15i	−0.694909	+	0.694909i
$848$	−1.00611e16	−	1.70827e16i	−0.787897	−	1.33776i
$849$			5.32480e15i			0.414296i
$850$	7.92325e15	−	3.16823e15i	0.612490	−	0.244913i
$851$	3.48746e16			2.67853
$852$	2.98223e16	−	2.30895e16i	2.27575	−	1.76197i
$853$	6.25567e15	+	6.25567e15i	0.474301	+	0.474301i	0.903303	−	0.429003i	$-0.141135\pi$
$853$	6.25567e15	+	6.25567e15i	0.474301	+	0.474301i	−0.429003	+	0.903303i	$0.641135\pi$
$854$	1.00533e15	−	1.58652e16i	0.0757341	−	1.19516i
$855$	1.20806e16	+	7.63402e15i	0.904223	+	0.571399i
$856$	−9.96478e15	−	1.91485e15i	−0.741075	−	0.142407i
$857$	−7.99523e15	−	7.99523e15i	−0.590795	−	0.590795i	0.347051	−	0.937846i	$-0.387183\pi$
$857$	−7.99523e15	−	7.99523e15i	−0.590795	−	0.590795i	−0.937846	+	0.347051i	$0.887183\pi$
$858$	−3.07064e15	−	3.48613e15i	−0.225450	−	0.255955i
$859$			2.41892e16i			1.76466i	0.470636	+	0.882328i	$0.344025\pi$
$859$			2.41892e16i			1.76466i	−0.470636	+	0.882328i	$0.655975\pi$
$860$	4.58581e14	+	4.79887e15i	0.0332410	+	0.347854i
$861$		−	3.51274e16i		−	2.53004i
$862$	1.07535e16	−	9.47191e15i	0.769594	−	0.677872i
$863$	−7.54062e15	−	7.54062e15i	−0.536226	−	0.536226i	0.386193	−	0.922418i	$-0.373790\pi$
$863$	−7.54062e15	−	7.54062e15i	−0.536226	−	0.536226i	−0.922418	+	0.386193i	$0.873790\pi$
$864$	2.80710e15	−	8.57357e15i	0.198350	−	0.605810i
$865$	−2.03437e15	−	9.01969e15i	−0.142837	−	0.633290i
$866$	2.16539e15	+	1.37215e14i	0.151073	+	0.00957310i
$867$	−8.94542e15	−	8.94542e15i	−0.620149	−	0.620149i
$868$	7.98239e15	−	6.18026e15i	0.549888	−	0.425743i
$869$	1.19493e15			0.0817961
$870$	−9.64769e15	−	6.98776e15i	−0.656247	−	0.475315i
$871$			2.09244e16i			1.41434i
$872$	−1.23999e16	+	8.40245e15i	−0.832869	+	0.564372i
$873$	1.68545e16	−	1.68545e16i	1.12496	−	1.12496i
$874$	1.53705e16	+	9.73989e14i	1.01947	+	0.0646013i
$875$	−9.75155e15	−	1.24229e16i	−0.642731	−	0.818798i
$876$	−2.18817e16	−	2.78435e15i	−1.43321	−	0.182369i
$877$	1.17806e16	−	1.17806e16i	0.766780	−	0.766780i	−0.210758	−	0.977538i	$-0.567593\pi$
$877$	1.17806e16	−	1.17806e16i	0.766780	−	0.766780i	0.977538	+	0.210758i	$0.0675933\pi$
$878$	6.46137e15	+	7.33565e15i	0.417931	+	0.474481i
$879$	2.16836e16			1.39378
$880$	−2.53390e15	−	2.69767e15i	−0.161858	−	0.172319i
$881$	4.60229e14			0.0292150			0.0146075	−	0.999893i	$-0.495350\pi$
$881$	4.60229e14			0.0292150			0.0146075	+	0.999893i	$0.495350\pi$
$882$	1.23459e15	+	1.40164e15i	0.0778834	+	0.0884218i
$883$	7.96470e15	−	7.96470e15i	0.499327	−	0.499327i	−0.411901	−	0.911229i	$-0.635135\pi$
$883$	7.96470e15	−	7.96470e15i	0.499327	−	0.499327i	0.911229	+	0.411901i	$0.135135\pi$
$884$	9.75973e15	+	1.24188e15i	0.608066	+	0.0773736i
$885$	−3.79377e15	−	1.68202e16i	−0.234900	−	1.04146i
$886$	−3.56269e15	−	2.25758e14i	−0.219226	−	0.0138918i
$887$	1.46450e15	−	1.46450e15i	0.0895593	−	0.0895593i	−0.660908	−	0.750467i	$-0.729829\pi$
$887$	1.46450e15	−	1.46450e15i	0.0895593	−	0.0895593i	0.750467	+	0.660908i	$0.229829\pi$
$888$	2.84943e16	+	4.20502e16i	1.73175	+	2.55562i
$889$		−	1.87720e14i		−	0.0113384i
$890$	2.84045e16	−	4.54175e15i	1.70507	−	0.272633i
$891$	−1.66778e15			−0.0994974
$892$	−4.58761e15	+	3.55189e15i	−0.272007	+	0.210597i
$893$	−1.89381e15	−	1.89381e15i	−0.111597	−	0.111597i
$894$	1.01707e16	+	6.44488e14i	0.595653	+	0.0377449i
$895$	−1.45212e16	+	2.29794e16i	−0.845233	+	1.33756i
$896$	−7.71259e15	+	1.62567e16i	−0.446176	+	0.940458i
$897$	2.39023e16	+	2.39023e16i	1.37430	+	1.37430i
$898$	−4.94918e15	+	4.35933e15i	−0.282822	+	0.249115i
$899$			6.13905e15i			0.348677i
$900$	7.79169e15	+	2.37420e16i	0.439843	+	1.34024i
$901$			1.82531e16i			1.02412i
$902$	4.38674e15	+	4.98030e15i	0.244628	+	0.277728i
$903$	7.20478e15	+	7.20478e15i	0.399335	+	0.399335i
$904$	4.40244e15	−	2.29100e16i	0.242531	−	1.26212i
$905$	−3.60930e15	+	5.71161e15i	−0.197631	+	0.312746i
$906$	−1.61303e15	+	2.54552e16i	−0.0877884	+	1.38539i
$907$	7.27189e15	+	7.27189e15i	0.393376	+	0.393376i	0.875889	−	0.482513i	$-0.160276\pi$
$907$	7.27189e15	+	7.27189e15i	0.393376	+	0.393376i	−0.482513	+	0.875889i	$0.660276\pi$
$908$	2.40180e16	−	1.85956e16i	1.29141	−	0.999859i
$909$	−4.18561e16			−2.23696
$910$	−2.87497e15	−	1.79803e16i	−0.152724	−	0.955146i
$911$			1.22841e15i			0.0648621i	0.999474	+	0.0324311i	$0.0103249\pi$
$911$			1.22841e15i			0.0648621i	−0.999474	+	0.0324311i	$0.989675\pi$
$912$	1.13841e16	+	1.93289e16i	0.597484	+	1.01446i
$913$	4.12467e14	−	4.12467e14i	0.0215179	−	0.0215179i
$914$	−1.39853e14	+	2.20702e15i	−0.00725217	+	0.114447i
$915$	−7.62458e15	−	3.38047e16i	−0.393006	−	1.74245i
$916$	9.81240e14	−	7.71140e15i	0.0502748	−	0.395101i
$917$	−8.96019e15	+	8.96019e15i	−0.456337	+	0.456337i
$918$	−6.23290e15	+	5.49005e15i	−0.315541	+	0.277934i
$919$	−1.82570e16			−0.918742			−0.459371	−	0.888245i	$-0.651925\pi$
$919$	−1.82570e16			−0.918742			−0.459371	+	0.888245i	$0.651925\pi$
$920$	1.96418e16	+	1.84238e16i	0.982536	+	0.921605i
$921$	−3.65688e16			−1.81837
$922$	2.02174e16	−	1.78079e16i	0.999322	−	0.880221i
$923$	−2.47898e16	+	2.47898e16i	−1.21804	+	1.21804i
$924$	−7.76005e15	−	9.87431e14i	−0.379026	−	0.0482293i
$925$	−3.85836e16	−	1.37234e16i	−1.87337	−	0.666320i
$926$	2.13259e15	−	3.36545e16i	0.102931	−	1.62436i
$927$	−5.26772e15	+	5.26772e15i	−0.252746	+	0.252746i
$928$	−4.94561e15	−	9.76063e15i	−0.235888	−	0.465547i
$929$		−	5.24697e15i		−	0.248784i	−0.992233	−	0.124392i	$-0.960302\pi$
$929$		−	5.24697e15i		−	0.248784i	0.992233	−	0.124392i	$-0.0396980\pi$
$930$	1.29089e16	−	1.78228e16i	0.608462	−	0.840077i
$931$	−1.35185e15			−0.0633440
$932$	−1.24710e16	−	1.61075e16i	−0.580916	−	0.750309i
$933$	−1.38655e16	−	1.38655e16i	−0.642078	−	0.642078i
$934$	−1.40634e15	+	2.21934e16i	−0.0647413	+	1.02168i
$935$	7.49741e14	+	3.32408e15i	0.0343121	+	0.152128i
$936$	−5.43671e15	+	2.82923e16i	−0.247354	+	1.28722i
$937$	1.31896e16	+	1.31896e16i	0.596575	+	0.596575i	0.939400	−	0.342824i	$-0.111384\pi$
$937$	1.31896e16	+	1.31896e16i	0.596575	+	0.596575i	−0.342824	+	0.939400i	$0.611384\pi$
$938$	2.32886e16	+	2.64397e16i	1.04720	+	1.18889i
$939$			1.64900e16i			0.737158i
$940$	−4.45486e14	−	4.66184e15i	−0.0197984	−	0.207183i
$941$		−	2.52020e16i		−	1.11350i	−0.830678	−	0.556752i	$-0.812047\pi$
$941$		−	2.52020e16i		−	1.11350i	0.830678	−	0.556752i	$-0.187953\pi$
$942$	−1.35404e16	+	1.19266e16i	−0.594775	+	0.523888i
$943$	−3.41470e16	−	3.41470e16i	−1.49121	−	1.49121i
$944$	3.96644e15	−	1.53334e16i	0.172209	−	0.665722i
$945$	1.29953e16	+	8.21202e15i	0.560933	+	0.354466i
$946$	−1.92122e15	−	1.21743e14i	−0.0824473	−	0.00522446i
$947$	−4.01804e15	−	4.01804e15i	−0.171431	−	0.171431i	0.616177	−	0.787608i	$-0.288681\pi$
$947$	−4.01804e15	−	4.01804e15i	−0.171431	−	0.171431i	−0.787608	+	0.616177i	$0.788681\pi$
$948$	−7.75270e15	−	1.00133e16i	−0.328857	−	0.424750i
$949$	2.05037e16			0.864703
$950$	−1.66219e16	−	7.12599e15i	−0.696951	−	0.298790i
$951$			2.40503e15i			0.100260i
$952$	1.37145e16	−	9.29326e15i	0.568428	−	0.385181i
$953$	−1.63918e16	+	1.63918e16i	−0.675487	+	0.675487i	−0.958976	−	0.283489i	$-0.908508\pi$
$953$	−1.63918e16	+	1.63918e16i	−0.675487	+	0.675487i	0.283489	+	0.958976i	$0.408508\pi$
$954$	−5.33438e16	−	3.38025e15i	−2.18559	−	0.138495i
$955$	2.23907e16	−	3.54327e16i	0.912116	−	1.44340i
$956$	−1.62542e15	+	1.27739e16i	−0.0658337	+	0.517376i
$957$	3.36373e15	−	3.36373e15i	0.135458	−	0.135458i
$958$	−1.35331e16	−	1.53643e16i	−0.541860	−	0.615178i
$959$	−1.49387e16			−0.594718
$960$	−6.16621e15	+	3.87363e16i	−0.244077	+	1.53330i
$961$	1.40674e16			0.553651
$962$	−3.12081e16	−	3.54309e16i	−1.22125	−	1.38650i
$963$	−1.93446e16	+	1.93446e16i	−0.752690	+	0.752690i
$964$	−2.08792e15	+	1.64086e16i	−0.0807774	+	0.634815i
$965$	1.55129e16	−	3.49890e15i	0.596749	−	0.134596i
$966$	5.68057e16	+	3.59962e15i	2.17279	+	0.137684i
$967$	−2.45132e16	+	2.45132e16i	−0.932299	+	0.932299i	−0.997849	−	0.0655502i	$-0.979120\pi$
$967$	−2.45132e16	+	2.45132e16i	−0.932299	+	0.932299i	0.0655502	+	0.997849i	$0.479120\pi$
$968$	−2.06672e16	+	1.40046e16i	−0.781570	+	0.529611i
$969$		−	2.06533e16i		−	0.776619i
$970$	−1.76945e16	+	2.44300e16i	−0.661598	+	0.913439i
$971$	1.14412e16			0.425370			0.212685	−	0.977121i	$-0.431779\pi$
$971$	1.14412e16			0.425370			0.212685	+	0.977121i	$0.431779\pi$
$972$	2.13767e16	+	2.76100e16i	0.790270	+	1.02071i
$973$	1.64933e16	+	1.64933e16i	0.606300	+	0.606300i
$974$	1.95102e16	+	1.23631e15i	0.713160	+	0.0451910i
$975$	−1.70386e16	−	3.58501e16i	−0.619312	−	1.30306i
$976$	7.97161e15	−	3.08166e16i	0.288119	−	1.11381i
$977$	9.14404e15	+	9.14404e15i	0.328638	+	0.328638i	0.852069	−	0.523430i	$-0.175348\pi$
$977$	9.14404e15	+	9.14404e15i	0.328638	+	0.328638i	−0.523430	+	0.852069i	$0.675348\pi$
$978$	−2.17505e16	+	1.91582e16i	−0.777329	+	0.684685i
$979$			1.14869e16i			0.408224i
$980$	−1.82287e15	−	1.50487e15i	−0.0644189	−	0.0531810i
$981$			4.03836e16i			1.41914i
$982$	−1.52370e16	−	1.72987e16i	−0.532460	−	0.604507i
$983$	2.02024e16	+	2.02024e16i	0.702034	+	0.702034i	0.964847	−	0.262813i	$-0.0846503\pi$
$983$	2.02024e16	+	2.02024e16i	0.702034	+	0.702034i	−0.262813	+	0.964847i	$0.584650\pi$
$984$	1.32731e16	−	6.90726e16i	0.458670	−	2.38689i
$985$	−1.40688e16	+	3.17320e15i	−0.483459	+	0.109043i
$986$	−6.37105e14	+	1.00542e16i	−0.0217715	+	0.343576i
$987$	−6.99904e15	−	6.99904e15i	−0.237845	−	0.237845i
$988$	−1.27651e16	−	1.64873e16i	−0.431379	−	0.557167i
$989$	1.40074e16			0.470737
$990$	−9.85330e15	+	1.57550e15i	−0.329297	+	0.0526532i
$991$		−	7.59051e15i		−	0.252270i	−0.992013	−	0.126135i	$-0.959743\pi$
$991$		−	7.59051e15i		−	0.252270i	0.992013	−	0.126135i	$-0.0402573\pi$
$992$	1.80314e16	−	9.13633e15i	0.595958	−	0.301966i
$993$	2.58339e16	−	2.58339e16i	0.849119	−	0.849119i
$994$	−3.73327e15	+	5.89148e16i	−0.122029	+	1.92575i
$995$	1.79785e16	+	1.13610e16i	0.584421	+	0.369309i
$996$	−6.13252e15	−	7.80335e14i	−0.198250	−	0.0252264i
$997$	−1.04726e16	+	1.04726e16i	−0.336691	+	0.336691i	−0.855120	−	0.518430i	$-0.826517\pi$
$997$	−1.04726e16	+	1.04726e16i	−0.336691	+	0.336691i	0.518430	+	0.855120i	$0.326517\pi$
$998$	−8.89815e15	+	7.83765e15i	−0.284500	+	0.250592i
$999$	3.98612e16			1.26748

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.12.k.a.27.18	yes	128
5.3	odd	4	inner	40.12.k.a.3.16	✓	128
8.3	odd	2	inner	40.12.k.a.27.16	yes	128
40.3	even	4	inner	40.12.k.a.3.18	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.12.k.a.3.16	✓	128	5.3	odd	4	inner
40.12.k.a.3.18	yes	128	40.3	even	4	inner
40.12.k.a.27.16	yes	128	8.3	odd	2	inner
40.12.k.a.27.18	yes	128	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-29.9123 - 33.9596i) q^{2} +(462.074 - 462.074i) q^{3} +(-258.514 + 2031.62i) q^{4} +(-5907.12 - 3732.84i) q^{5} +(-29513.6 - 1870.19i) q^{6} +(32730.0 - 32730.0i) q^{7} +(76725.8 - 51991.2i) q^{8} -249879. i q^{9} +(49929.2 + 312261. i) q^{10} -126280. q^{11} +(819306. + 1.05821e6i) q^{12} +(-879637. - 879637. i) q^{13} +(-2.09053e6 - 132471. i) q^{14} +(-4.45438e6 + 1.00468e6i) q^{15} +(-4.06064e6 - 1.05040e6i) q^{16} +(2.73063e6 + 2.73063e6i) q^{17} +(-8.48579e6 + 7.47443e6i) q^{18} -8.18436e6i q^{19} +(9.11078e6 - 1.10360e7i) q^{20} -3.02474e7i q^{21} +(3.77732e6 + 4.28843e6i) q^{22} +(-2.94032e7 - 2.94032e7i) q^{23} +(1.14292e7 - 5.94768e7i) q^{24} +(2.09599e7 + 4.41007e7i) q^{25} +(-3.56023e6 + 5.61841e7i) q^{26} +(-3.36074e7 - 3.36074e7i) q^{27} +(5.80337e7 + 7.49560e7i) q^{28} -5.76467e7 q^{29} +(1.67359e8 + 1.21217e8i) q^{30} -1.06494e8i q^{31} +(8.57917e7 + 1.69318e8i) q^{32} +(-5.83508e7 + 5.83508e7i) q^{33} +(1.10519e7 - 1.74410e8i) q^{34} +(-3.15516e8 + 7.11639e7i) q^{35} +(5.07658e8 + 6.45972e7i) q^{36} +(-5.93042e8 + 5.93042e8i) q^{37} +(-2.77938e8 + 2.44813e8i) q^{38} -8.12916e8 q^{39} +(-6.47303e8 + 2.07131e7i) q^{40} +1.16134e9 q^{41} +(-1.02719e9 + 9.04767e8i) q^{42} +(-2.38195e8 + 2.38195e8i) q^{43} +(3.26452e7 - 2.56553e8i) q^{44} +(-9.32757e8 + 1.47606e9i) q^{45} +(-1.19006e8 + 1.87804e9i) q^{46} +(2.31393e8 - 2.31393e8i) q^{47} +(-2.36169e9 + 1.39095e9i) q^{48} -1.65175e8i q^{49} +(8.70684e8 - 2.03094e9i) q^{50} +2.52350e9 q^{51} +(2.01449e9 - 1.55969e9i) q^{52} +(3.34230e9 + 3.34230e9i) q^{53} +(-1.36022e8 + 2.14657e9i) q^{54} +(7.45951e8 + 4.71383e8i) q^{55} +(8.09561e8 - 4.21290e9i) q^{56} +(-3.78178e9 - 3.78178e9i) q^{57} +(1.72434e9 + 1.95766e9i) q^{58} +3.77611e9i q^{59} +(-8.89600e8 - 9.30932e9i) q^{60} +7.58909e9i q^{61} +(-3.61651e9 + 3.18549e9i) q^{62} +(-8.17852e9 - 8.17852e9i) q^{63} +(3.18376e9 - 7.97814e9i) q^{64} +(1.91257e9 + 8.47967e9i) q^{65} +(3.72697e9 + 2.36168e8i) q^{66} +(-1.18937e10 - 1.18937e10i) q^{67} +(-6.25349e9 + 4.84168e9i) q^{68} -2.71729e10 q^{69} +(1.18545e10 + 8.58612e9i) q^{70} -2.81818e10i q^{71} +(-1.29915e10 - 1.91721e10i) q^{72} +(-1.16546e10 + 1.16546e10i) q^{73} +(3.78787e10 + 2.40027e9i) q^{74} +(3.00628e10 + 1.06927e10i) q^{75} +(1.66275e10 + 2.11577e9i) q^{76} +(-4.13314e9 + 4.13314e9i) q^{77} +(2.43161e10 + 2.76063e10i) q^{78} -9.46251e9 q^{79} +(2.00657e10 + 2.13626e10i) q^{80} +1.32070e10 q^{81} +(-3.47382e10 - 3.94386e10i) q^{82} +(-3.26629e9 + 3.26629e9i) q^{83} +(6.14511e10 + 7.81937e9i) q^{84} +(-5.93713e9 - 2.63231e10i) q^{85} +(1.52140e10 + 9.64068e8i) q^{86} +(-2.66371e10 + 2.66371e10i) q^{87} +(-9.68894e9 + 6.56546e9i) q^{88} -9.09638e10i q^{89} +(7.80274e10 - 1.24762e10i) q^{90} -5.75810e10 q^{91} +(6.73372e10 - 5.21349e10i) q^{92} +(-4.92083e10 - 4.92083e10i) q^{93} +(-1.47795e10 - 9.36539e8i) q^{94} +(-3.05509e10 + 4.83460e10i) q^{95} +(1.17880e11 + 3.85954e10i) q^{96} +(6.74508e10 + 6.74508e10i) q^{97} +(-5.60928e9 + 4.94076e9i) q^{98} +3.15547e10i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 2 q^{2} - 4 q^{3} + 22352 q^{6} + 74836 q^{8} - 141690 q^{10} - 8 q^{11} - 114212 q^{12} - 1529272 q^{16} - 5279472 q^{17} - 7492118 q^{18} - 19078400 q^{20} + 110378148 q^{22} - 34182200 q^{25}+ \cdots - 277418419174 q^{98}+O(q^{100}) \) 128 * q - 2 * q^2 - 4 * q^3 + 22352 * q^6 + 74836 * q^8 - 141690 * q^10 - 8 * q^11 - 114212 * q^12 - 1529272 * q^16 - 5279472 * q^17 - 7492118 * q^18 - 19078400 * q^20 + 110378148 * q^22 - 34182200 * q^25 + 255826660 * q^26 + 708584 * q^27 + 94521900 * q^28 - 293248580 * q^30 - 472895712 * q^32 - 708592 * q^33 + 1064775860 * q^35 + 86525660 * q^36 + 3129197436 * q^38 + 3364165660 * q^40 - 8 * q^41 + 1572869820 * q^42 + 4763690652 * q^43 - 385692400 * q^46 + 382518896 * q^48 - 2735634410 * q^50 + 224442568 * q^51 + 4940288660 * q^52 + 5445667880 * q^56 + 708584 * q^57 + 10041578500 * q^58 + 15019215220 * q^60 + 2940684960 * q^62 - 5068308440 * q^65 - 18585180232 * q^66 - 44333852092 * q^67 - 24658647124 * q^68 - 2573940380 * q^70 + 52114546396 * q^72 + 30695219256 * q^73 - 114387554460 * q^75 + 64146613592 * q^76 + 58383192800 * q^78 - 6693485600 * q^80 - 353771564728 * q^81 - 30935854652 * q^82 - 122796947724 * q^83 - 64352390624 * q^86 - 192245775664 * q^88 + 306882997670 * q^90 + 93235242840 * q^91 + 185062591860 * q^92 + 345055140192 * q^96 - 144367002024 * q^97 - 277418419174 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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