LMFDB - Embedded newform 40.12.k.a.27.16

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			27.16
Character	$\chi$	$=$	40.27
Dual form			40.12.k.a.3.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-33.9596 - 29.9123i) 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} +(51991.2 - 76725.8i) q^{8} -249879. i q^{9} +(-88945.8 - 303461. i) q^{10} -126280. q^{11} +(1.05821e6 + 819306. i) 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} +(-7.47443e6 + 8.48579e6i) q^{18} -8.18436e6i q^{19} +(-6.05664e6 + 1.29660e7i) q^{20} +3.02474e7i q^{21} +(4.28843e6 + 3.77732e6i) 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} +(-7.49560e7 - 5.80337e7i) q^{28} +5.76467e7 q^{29} +(-1.81321e8 - 9.91220e7i) q^{30} +1.06494e8i q^{31} +(1.69318e8 + 8.57917e7i) 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} +(-2.44813e8 + 2.77938e8i) q^{38} +8.12916e8 q^{39} +(5.93523e8 - 2.59153e8i) q^{40} +1.16134e9 q^{41} +(9.04767e8 - 1.02719e9i) 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} +(-1.39095e9 + 2.36169e9i) q^{48} -1.65175e8i q^{49} +(6.07359e8 - 2.12460e9i) q^{50} +2.52350e9 q^{51} +(-1.55969e9 + 2.01449e9i) 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} +(-1.95766e9 - 1.72434e9i) q^{58} +3.77611e9i q^{59} +(3.19264e9 + 8.78987e9i) q^{60} -7.58909e9i q^{61} +(3.18549e9 - 3.61651e9i) 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} +(-4.84168e9 + 6.25349e9i) q^{68} +2.71729e10 q^{69} +(1.28435e10 + 7.02108e9i) q^{70} +2.81818e10i q^{71} +(-1.91721e10 - 1.29915e10i) 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} +(-2.76063e10 - 2.43161e10i) q^{78} +9.46251e9 q^{79} +(-2.79077e10 - 8.95288e9i) q^{80} +1.32070e10 q^{81} +(-3.94386e10 - 3.47382e10i) 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} +(-6.56546e9 + 9.68894e9i) q^{88} -9.09638e10i q^{89} +(-7.58284e10 + 2.22257e10i) q^{90} -5.75810e10 q^{91} +(-5.21349e10 + 6.73372e10i) 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} +(-4.94076e9 + 5.60928e9i) 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 $

$2$	−33.9596	−	29.9123i	−0.750409	−	0.660974i
$2$	−33.9596	−	29.9123i	−0.750409	−	0.660974i
$3$	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	−0.971811	−	0.235762i	$-0.924241\pi$
$7$	−32730.0	+	32730.0i	−0.736048	+	0.736048i	0.235762	+	0.971811i	$0.424241\pi$
$8$	51991.2	−	76725.8i	0.560964	−	0.827840i
$9$		−	249879.i		−	1.41057i
$10$	−88945.8	−	303461.i	−0.281271	−	0.959628i
$11$	−126280.			−0.236415			−0.118207	−	0.992989i	$-0.537715\pi$
$11$	−126280.			−0.236415			−0.118207	+	0.992989i	$0.537715\pi$
$12$	1.05821e6	+	819306.i	1.22765	+	0.950494i
$13$	879637.	+	879637.i	0.657075	+	0.657075i	0.954687	−	0.297612i	$-0.0961901\pi$
$13$	879637.	+	879637.i	0.657075	+	0.657075i	−0.297612	+	0.954687i	$0.596190\pi$
$14$	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	$0.643012\pi$
$18$	−7.47443e6	+	8.48579e6i	−0.932351	+	1.05851i
$19$		−	8.18436e6i		−	0.758298i	−0.925336	−	0.379149i	$-0.876217\pi$
$19$		−	8.18436e6i		−	0.758298i	0.925336	−	0.379149i	$-0.123783\pi$
$20$	−6.05664e6	+	1.29660e7i	−0.423220	+	0.906027i
$21$			3.02474e7i			1.61615i
$22$	4.28843e6	+	3.77732e6i	0.177408	+	0.156264i
$23$	2.94032e7	+	2.94032e7i	0.952558	+	0.952558i	0.998925	−	0.0463664i	$-0.0147642\pi$
$23$	2.94032e7	+	2.94032e7i	0.952558	+	0.952558i	−0.0463664	+	0.998925i	$0.514764\pi$
$24$	−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
$28$	−7.49560e7	−	5.80337e7i	−0.823071	−	0.637251i
$29$	5.76467e7			0.521898			0.260949	−	0.965353i	$-0.415965\pi$
$29$	5.76467e7			0.521898			0.260949	+	0.965353i	$0.415965\pi$
$30$	−1.81321e8	−	9.91220e7i	−1.36233	−	0.744738i
$31$			1.06494e8i			0.668093i	0.942557	+	0.334047i	$0.108414\pi$
$31$			1.06494e8i			0.668093i	−0.942557	+	0.334047i	$0.891586\pi$
$32$	1.69318e8	+	8.57917e7i	0.892028	+	0.451981i
$33$	−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	$-0.284388\pi$
$37$	5.93042e8	−	5.93042e8i	1.40597	−	1.40597i	0.779227	−	0.626742i	$-0.215612\pi$
$38$	−2.44813e8	+	2.77938e8i	−0.501215	+	0.569034i
$39$	8.12916e8			1.44275
$40$	5.93523e8	−	2.59153e8i	0.916448	−	0.400153i
$41$	1.16134e9			1.56548			0.782739	−	0.622350i	$-0.213822\pi$
$41$	1.16134e9			1.56548			0.782739	+	0.622350i	$0.213822\pi$
$42$	9.04767e8	−	1.02719e9i	1.06823	−	1.21277i
$43$	−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	−0.776852	−	0.629684i	$-0.783184\pi$
$47$	−2.31393e8	+	2.31393e8i	−0.147168	+	0.147168i	0.629684	+	0.776852i	$0.283184\pi$
$48$	−1.39095e9	+	2.36169e9i	−0.787928	+	1.33781i
$49$		−	1.65175e8i		−	0.0835345i
$50$	6.07359e8	−	2.12460e9i	0.274859	−	0.961484i
$51$	2.52350e9			1.02416
$52$	−1.55969e9	+	2.01449e9i	−0.568879	+	0.734761i
$53$	−3.34230e9	−	3.34230e9i	−1.09781	−	1.09781i	−0.994666	−	0.103146i	$-0.967109\pi$
$53$	−3.34230e9	−	3.34230e9i	−1.09781	−	1.09781i	−0.103146	−	0.994666i	$-0.532891\pi$
$54$	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
$58$	−1.95766e9	−	1.72434e9i	−0.391637	−	0.344961i
$59$			3.77611e9i			0.687635i	0.939036	+	0.343818i	$0.111720\pi$
$59$			3.77611e9i			0.687635i	−0.939036	+	0.343818i	$0.888280\pi$
$60$	3.19264e9	+	8.78987e9i	0.530051	+	1.45932i
$61$		−	7.58909e9i		−	1.15047i	−0.817988	−	0.575235i	$-0.804911\pi$
$61$		−	7.58909e9i		−	1.15047i	0.817988	−	0.575235i	$-0.195089\pi$
$62$	3.18549e9	−	3.61651e9i	0.441592	−	0.501343i
$63$	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	$-0.525298\pi$
$68$	−4.84168e9	+	6.25349e9i	−0.403829	+	0.521583i
$69$	2.71729e10			2.09154
$70$	1.28435e10	+	7.02108e9i	0.913362	+	0.499303i
$71$			2.81818e10i			1.85374i	0.375386	+	0.926868i	$0.377510\pi$
$71$			2.81818e10i			1.85374i	−0.375386	+	0.926868i	$0.622490\pi$
$72$	−1.91721e10	−	1.29915e10i	−1.16773	−	0.791280i
$73$	−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
$78$	−2.76063e10	−	2.43161e10i	−1.08265	−	0.953618i
$79$	9.46251e9			0.345985			0.172993	−	0.984923i	$-0.444656\pi$
$79$	9.46251e9			0.345985			0.172993	+	0.984923i	$0.444656\pi$
$80$	−2.79077e10	−	8.95288e9i	−0.952202	−	0.305470i
$81$	1.32070e10			0.420859
$82$	−3.94386e10	−	3.47382e10i	−1.17475	−	1.03474i
$83$	−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
$88$	−6.56546e9	+	9.68894e9i	−0.132620	+	0.195714i
$89$		−	9.09638e10i		−	1.72673i	−0.504582	−	0.863364i	$-0.668353\pi$
$89$		−	9.09638e10i		−	1.72673i	0.504582	−	0.863364i	$-0.331647\pi$
$90$	−7.58284e10	+	2.22257e10i	−1.35362	+	0.396753i
$91$	−5.75810e10			−0.967279
$92$	−5.21349e10	+	6.73372e10i	−0.824700	+	1.06518i
$93$	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	$0.559288\pi$
$98$	−4.94076e9	+	5.60928e9i	−0.0552141	+	0.0626850i
$99$			3.15547e10i			0.333480i
$100$	−8.41773e10	+	5.39832e10i	−0.841773	+	0.539832i
$101$			1.67506e11i			1.58585i	0.609318	+	0.792926i	$0.291443\pi$
$101$			1.67506e11i			1.58585i	−0.609318	+	0.792926i	$0.708557\pi$
$102$	−8.56973e10	−	7.54837e10i	−0.768539	−	0.676943i
$103$	2.10811e10	+	2.10811e10i	0.179180	+	0.179180i	0.790998	−	0.611818i	$-0.209562\pi$
$103$	2.10811e10	+	2.10811e10i	0.179180	+	0.179180i	−0.611818	+	0.790998i	$0.709562\pi$
$104$	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	$0.873153\pi$
$108$	5.95894e10	−	7.69654e10i	0.390246	−	0.504040i
$109$	1.61613e11			1.00607			0.503037	−	0.864265i	$-0.332216\pi$
$109$	1.61613e11			1.00607			0.503037	+	0.864265i	$0.332216\pi$
$110$	1.12321e10	+	3.83211e10i	0.0664968	+	0.226870i
$111$		−	5.48059e11i		−	3.08710i
$112$	9.85251e10	−	1.67284e11i	0.528260	−	0.896926i
$113$	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
$118$	1.12952e11	−	1.28235e11i	0.454509	−	0.516008i
$119$	−1.78747e11			−0.686640
$120$	1.54504e11	−	3.94000e11i	0.566817	−	1.44544i
$121$	−2.69365e11			−0.944108
$122$	−2.27007e11	+	2.57723e11i	−0.760430	+	0.863323i
$123$	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	−0.710947	−	0.703245i	$-0.751734\pi$
$127$	−2.86770e9	+	2.86770e9i	−0.00770218	+	0.00770218i	0.703245	+	0.710947i	$0.251734\pi$
$128$	−1.30525e11	+	3.66168e11i	−0.335767	+	0.941945i
$129$			2.20128e11i			0.542540i
$130$	1.88696e11	−	3.45176e11i	0.445732	−	0.815365i
$131$	−2.73761e11			−0.619982			−0.309991	−	0.950739i	$-0.600326\pi$
$131$	−2.73761e11			−0.619982			−0.309991	+	0.950739i	$0.600326\pi$
$132$	−1.33631e11	−	1.03462e11i	−0.290236	−	0.224711i
$133$	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	$0.842215\pi$
$138$	−9.22783e11	−	8.12804e11i	−1.56951	−	1.38245i
$139$			5.03921e11i			0.823723i	0.911246	+	0.411862i	$0.135121\pi$
$139$			5.03921e11i			0.823723i	−0.911246	+	0.411862i	$0.864879\pi$
$140$	−2.26143e11	−	6.22610e11i	−0.355369	−	0.978390i
$141$			2.13842e11i			0.323138i
$142$	8.42982e11	−	9.57044e11i	1.22527	−	1.39106i
$143$	−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
$148$	1.35814e12	+	1.05152e12i	1.57220	+	1.21725i
$149$	3.44610e11			0.384418			0.192209	−	0.981354i	$-0.438435\pi$
$149$	3.44610e11			0.384418			0.192209	+	0.981354i	$0.438435\pi$
$150$	−7.01079e11	−	1.26237e12i	−0.753815	−	1.35733i
$151$			8.62493e11i			0.894092i	0.894511	+	0.447046i	$0.147524\pi$
$151$			8.62493e11i			0.894092i	−0.894511	+	0.447046i	$0.852476\pi$
$152$	−6.27951e11	−	4.25515e11i	−0.627749	−	0.425378i
$153$	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	−0.864172	−	0.503196i	$-0.832157\pi$
$157$	−4.31447e11	+	4.31447e11i	−0.360977	+	0.360977i	0.503196	+	0.864172i	$0.332157\pi$
$158$	−3.21344e11	−	2.83045e11i	−0.259630	−	0.228687i
$159$	−3.08878e12			−2.41048
$160$	6.79934e11	+	1.13882e12i	0.512634	+	0.858607i
$161$	−1.92473e12			−1.40226
$162$	−4.48505e11	−	3.95051e11i	−0.315816	−	0.278177i
$163$	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	$0.614562\pi$
$167$	−2.16220e12	+	2.16220e12i	−1.28812	+	1.28812i	−0.935929	+	0.352189i	$0.885438\pi$
$168$	2.32075e12	+	1.57260e12i	1.33791	+	0.906602i
$169$		−	2.44637e11i		−	0.136504i
$170$	5.85761e11	−	1.07152e12i	0.316411	−	0.578802i
$171$	−2.04510e12			−1.06963
$172$	−5.45499e11	−	4.22345e11i	−0.276304	−	0.213925i
$173$	−9.35656e11	−	9.35656e11i	−0.459053	−	0.459053i	0.439292	−	0.898345i	$-0.355229\pi$
$173$	−9.35656e11	−	9.35656e11i	−0.459053	−	0.459053i	−0.898345	+	0.439292i	$0.855229\pi$
$174$	−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
$178$	−2.72093e12	+	3.08910e12i	−1.14132	+	1.29575i
$179$		−	3.89013e12i		−	1.58224i	−0.611662	−	0.791119i	$-0.709499\pi$
$179$		−	3.89013e12i		−	1.58224i	0.611662	−	0.791119i	$-0.290501\pi$
$180$	3.23993e12	+	1.51342e12i	1.27802	+	0.596983i
$181$			9.66903e11i			0.369957i	0.982743	+	0.184978i	$0.0592215\pi$
$181$			9.66903e11i			0.369957i	−0.982743	+	0.184978i	$0.940778\pi$
$182$	1.95543e12	+	1.72238e12i	0.725855	+	0.639346i
$183$	−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
$188$	−5.29922e11	−	4.10285e11i	−0.164567	−	0.127414i
$189$	2.19994e12			0.663545
$190$	−2.48363e12	+	7.27965e11i	−0.727684	+	0.213288i
$191$		−	5.99831e12i		−	1.70744i	−0.520732	−	0.853720i	$-0.674341\pi$
$191$		−	5.99831e12i		−	1.70744i	0.520732	−	0.853720i	$-0.325659\pi$
$192$	−5.15763e12	−	2.21536e12i	−1.42657	−	0.612756i
$193$	−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	−0.860275	−	0.509830i	$-0.829708\pi$
$197$	−1.45943e12	+	1.45943e12i	−0.350444	+	0.350444i	0.509830	+	0.860275i	$0.329708\pi$
$198$	9.43872e11	−	1.07159e12i	0.220422	−	0.250247i
$199$	3.04353e12			0.691330			0.345665	−	0.938358i	$-0.387653\pi$
$199$	3.04353e12			0.691330			0.345665	+	0.938358i	$0.387653\pi$
$200$	4.47339e12	+	6.84682e11i	0.988489	+	0.151295i
$201$	−1.09916e13			−2.36310
$202$	5.01048e12	−	5.68844e12i	1.04821	−	1.19004i
$203$	−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
$208$	−4.49587e12	−	2.64792e12i	−0.800692	−	0.471581i
$209$			1.03352e12i			0.179273i
$210$	9.17890e12	−	2.69038e12i	1.55090	−	0.454576i
$211$	6.06514e12			0.998360			0.499180	−	0.866498i	$-0.333635\pi$
$211$	6.06514e12			0.998360			0.499180	+	0.866498i	$0.333635\pi$
$212$	5.92625e12	−	7.65431e12i	0.950457	−	1.22761i
$213$	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
$218$	−5.48831e12	−	4.83420e12i	−0.754968	−	0.664989i
$219$			1.07706e13i			1.44476i
$220$	7.64832e11	−	1.63735e12i	0.100056	−	0.214198i
$221$			4.80392e12i			0.612969i
$222$	−1.63937e13	+	1.86119e13i	−2.04049	+	2.31659i
$223$	−2.00321e12	−	2.00321e12i	−0.243248	−	0.243248i	0.574945	−	0.818192i	$-0.305024\pi$
$223$	−2.00321e12	−	2.00321e12i	−0.243248	−	0.243248i	−0.818192	+	0.574945i	$0.805024\pi$
$224$	−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	$-0.554154\pi$
$228$	6.70550e12	−	8.66079e12i	0.720758	−	0.930927i
$229$	3.79569e12			0.398287			0.199143	−	0.979970i	$-0.436184\pi$
$229$	3.79569e12			0.398287			0.199143	+	0.979970i	$0.436184\pi$
$230$	6.30744e12	−	1.15380e13i	0.646174	−	1.18203i
$231$		−	3.81964e12i		−	0.382082i
$232$	2.99712e12	−	4.42299e12i	0.292766	−	0.432048i
$233$	−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
$238$	6.07017e12	+	5.34671e12i	0.515261	+	0.453851i
$239$	−6.28756e12			−0.521547			−0.260774	−	0.965400i	$-0.583978\pi$
$239$	−6.28756e12			−0.521547			−0.260774	+	0.965400i	$0.583978\pi$
$240$	−1.70323e13	+	8.75853e12i	−1.38074	+	0.710018i
$241$	8.07661e12			0.639934			0.319967	−	0.947429i	$-0.396328\pi$
$241$	8.07661e12			0.639934			0.319967	+	0.947429i	$0.396328\pi$
$242$	9.14754e12	+	8.05731e12i	0.708467	+	0.624030i
$243$	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
$248$	8.17086e12	+	5.53677e12i	0.553074	+	0.374777i
$249$			3.01854e12i			0.199848i
$250$	1.15185e13	−	1.02831e13i	0.745980	−	0.665968i
$251$	6.61521e12			0.419120			0.209560	−	0.977796i	$-0.432797\pi$
$251$	6.61521e12			0.419120			0.209560	+	0.977796i	$0.432797\pi$
$252$	−1.45014e13	+	1.87299e13i	−0.898889	+	1.16100i
$253$	−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	$0.496972\pi$
$258$	6.58452e12	−	7.47546e12i	0.358604	−	0.407127i
$259$			3.88205e13i			2.06972i
$260$	−1.67330e13	+	6.07773e12i	−0.873416	+	0.317240i
$261$		−	1.44047e13i		−	0.736175i
$262$	9.29682e12	+	8.18881e12i	0.465240	+	0.409792i
$263$	−6.53910e12	−	6.53910e12i	−0.320451	−	0.320451i	0.528489	−	0.848940i	$-0.322759\pi$
$263$	−6.53910e12	−	6.53910e12i	−0.320451	−	0.320451i	−0.848940	+	0.528489i	$0.822759\pi$
$264$	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
$268$	2.10889e13	−	2.72383e13i	0.931776	−	1.20348i
$269$	−2.41637e13			−1.04599			−0.522994	−	0.852336i	$-0.675185\pi$
$269$	−2.41637e13			−1.04599			−0.522994	+	0.852336i	$0.675185\pi$
$270$	−7.20930e12	+	1.31878e13i	−0.305768	+	0.559333i
$271$			3.29811e13i			1.37068i	0.728225	+	0.685338i	$0.240345\pi$
$271$			3.29811e13i			1.37068i	−0.728225	+	0.685338i	$0.759655\pi$
$272$	−1.39564e13	−	8.21984e12i	−0.568386	−	0.334761i
$273$	−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	−0.685868	−	0.727726i	$-0.740577\pi$
$277$	1.13610e12	−	1.13610e12i	0.0418580	−	0.0418580i	0.727726	+	0.685868i	$0.240577\pi$
$278$	1.50734e13	−	1.71130e13i	0.544460	−	0.618130i
$279$	2.66107e13			0.942394
$280$	−1.09439e13	+	2.79081e13i	−0.380018	+	0.969082i
$281$	1.09119e13			0.371547			0.185774	−	0.982593i	$-0.440521\pi$
$281$	1.09119e13			0.371547			0.185774	+	0.982593i	$0.440521\pi$
$282$	6.39650e12	−	7.26200e12i	0.213586	−	0.242486i
$283$	−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
$288$	2.14375e13	−	4.23089e13i	0.637552	−	1.25827i
$289$		−	1.93593e13i		−	0.564873i
$290$	−5.12743e12	−	1.74935e13i	−0.146795	−	0.500828i
$291$	6.23346e13			1.75113
$292$	−2.66906e13	−	2.06648e13i	−0.735788	−	0.569674i
$293$	−2.34633e13	−	2.34633e13i	−0.634772	−	0.634772i	0.314489	−	0.949261i	$-0.398167\pi$
$293$	−2.34633e13	−	2.34633e13i	−0.634772	−	0.634772i	−0.949261	+	0.314489i	$0.898167\pi$
$294$	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
$298$	−1.17028e13	−	1.03081e13i	−0.288471	−	0.254090i
$299$			5.17283e13i			1.25180i
$300$	−1.39519e13	+	6.38404e13i	−0.331487	+	1.51680i
$301$		−	1.55922e13i		−	0.363741i
$302$	2.57991e13	−	2.92899e13i	0.590971	−	0.670935i
$303$	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	$0.949136\pi$
$308$	9.46544e12	+	7.32849e12i	0.194586	+	0.150656i
$309$	1.94821e13			0.393427
$310$	3.23169e13	−	9.47223e12i	0.641121	−	0.187916i
$311$			3.00071e13i			0.584847i	0.956289	+	0.292424i	$0.0944617\pi$
$311$			3.00071e13i			0.584847i	−0.956289	+	0.292424i	$0.905538\pi$
$312$	4.22645e13	−	6.23716e13i	0.809330	−	1.19436i
$313$	−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	−0.683907	−	0.729569i	$-0.739721\pi$
$317$	2.60242e12	−	2.60242e12i	0.0456617	−	0.0456617i	0.729569	+	0.683907i	$0.239721\pi$
$318$	1.04894e14	+	9.23924e13i	1.80884	+	1.59326i
$319$	−7.27963e12			−0.123384
$320$	1.09743e13	−	5.90122e13i	0.182832	−	0.983144i
$321$	−7.15441e13			−1.17164
$322$	6.53632e13	+	5.75731e13i	1.05227	+	0.926855i
$323$	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
$328$	6.03793e13	−	8.91044e13i	0.878177	−	1.29596i
$329$		−	1.51470e13i		−	0.216645i
$330$	2.28973e13	+	1.25171e13i	0.322075	+	0.176067i
$331$	5.59085e13			0.773435			0.386717	−	0.922198i	$-0.373609\pi$
$331$	5.59085e13			0.773435			0.386717	+	0.922198i	$0.373609\pi$
$332$	−7.48024e12	−	5.79147e12i	−0.101778	−	0.0788006i
$333$	−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	$0.764938\pi$
$338$	−7.31764e12	+	8.30778e12i	−0.0902255	+	0.102434i
$339$		−	1.64487e14i		−	1.99542i
$340$	−5.19437e13	+	1.88669e13i	−0.620010	+	0.225199i
$341$		−	1.34481e13i		−	0.157947i
$342$	6.94507e13	+	6.11734e13i	0.802663	+	0.707000i
$343$	−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	$0.977188\pi$
$348$	6.10024e13	+	4.72303e13i	0.640710	+	0.496061i
$349$	−1.39724e14			−1.44455			−0.722273	−	0.691608i	$-0.756903\pi$
$349$	−1.39724e14			−1.44455			−0.722273	+	0.691608i	$0.756903\pi$
$350$	4.96593e13	+	8.94169e13i	0.505389	+	0.910009i
$351$		−	5.91246e13i		−	0.592351i
$352$	−2.13815e13	−	1.08338e13i	−0.210889	−	0.106855i
$353$	−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
$358$	−1.16362e14	+	1.32107e14i	−1.04582	+	1.18733i
$359$	−7.34475e13			−0.650066			−0.325033	−	0.945703i	$-0.605375\pi$
$359$	−7.34475e13			−0.650066			−0.325033	+	0.945703i	$0.605375\pi$
$360$	−6.47568e13	−	1.48309e14i	−0.564445	−	1.29272i
$361$	4.95065e13			0.424984
$362$	2.89223e13	−	3.28357e13i	0.244532	−	0.277619i
$363$	−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	−0.921622	−	0.388088i	$-0.873136\pi$
$367$	−6.80496e13	+	6.80496e13i	−0.533534	+	0.533534i	0.388088	+	0.921622i	$0.373136\pi$
$368$	−1.50281e14	−	8.85107e13i	−1.16076	−	0.683648i
$369$		−	2.90193e14i		−	2.20822i
$370$	−2.32714e14	−	1.27216e14i	−1.74467	−	0.953749i
$371$	2.18787e14			1.61609
$372$	−8.72515e13	+	1.12694e14i	−0.635019	+	0.820187i
$373$	1.51178e14	+	1.51178e14i	1.08415	+	1.08415i	0.996117	+	0.0880346i	$0.0280586\pi$
$373$	1.51178e14	+	1.51178e14i	1.08415	+	1.08415i	0.0880346	+	0.996117i	$0.471941\pi$
$374$	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
$378$	−7.47091e13	−	6.58051e13i	−0.497930	−	0.438586i
$379$		−	1.87498e14i		−	1.23163i	−0.787890	−	0.615817i	$-0.788826\pi$
$379$		−	1.87498e14i		−	1.23163i	0.787890	−	0.615817i	$-0.211174\pi$
$380$	1.06118e14	+	4.95697e13i	0.687038	+	0.320927i
$381$			2.65019e12i			0.0169118i
$382$	−1.79423e14	+	2.03700e14i	−1.12857	+	1.28128i
$383$	8.37765e13	+	8.37765e13i	0.519432	+	0.519432i	0.917400	−	0.397967i	$-0.130284\pi$
$383$	8.37765e13	+	8.37765e13i	0.519432	+	0.519432i	−0.397967	+	0.917400i	$0.630284\pi$
$384$	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
$388$	−1.19597e14	+	1.54471e14i	−0.690473	+	0.891812i
$389$	2.66479e14			1.51684			0.758421	−	0.651765i	$-0.225971\pi$
$389$	2.66479e14			1.51684			0.758421	+	0.651765i	$0.225971\pi$
$390$	−7.23055e13	−	2.46688e14i	−0.405803	−	1.38450i
$391$			1.60578e14i			0.888617i
$392$	−1.26732e13	−	8.58765e12i	−0.0691532	−	0.0468599i
$393$	−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	−0.195870	−	0.980630i	$-0.562753\pi$
$397$	1.54200e14	−	1.54200e14i	0.784760	−	0.784760i	0.980630	+	0.195870i	$0.0627529\pi$
$398$	−1.03357e14	−	9.10388e13i	−0.518781	−	0.456951i
$399$	2.47555e14			1.22552
$400$	−1.31434e14	−	1.57061e14i	−0.641769	−	0.766898i
$401$	−2.50513e14			−1.20653			−0.603263	−	0.797542i	$-0.706133\pi$
$401$	−2.50513e14			−1.20653			−0.603263	+	0.797542i	$0.706133\pi$
$402$	3.73270e14	+	3.28783e14i	1.77329	+	1.56195i
$403$	−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
$408$	1.31200e14	−	1.93618e14i	0.574518	−	0.847841i
$409$		−	2.82442e14i		−	1.22025i	−0.792304	−	0.610127i	$-0.791118\pi$
$409$		−	2.82442e14i		−	1.22025i	0.792304	−	0.610127i	$-0.208882\pi$
$410$	−1.03296e14	−	3.52420e14i	−0.440324	−	1.50228i
$411$	−2.10902e14			−0.887054
$412$	−3.73791e13	+	4.82786e13i	−0.155129	+	0.200364i
$413$	−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
$418$	3.09149e13	−	3.50980e13i	0.118495	−	0.134528i
$419$		−	1.35926e14i		−	0.514194i	−0.966386	−	0.257097i	$-0.917234\pi$
$419$		−	1.35926e14i		−	0.514194i	0.966386	−	0.257097i	$-0.0827659\pi$
$420$	−3.92187e14	−	1.83197e14i	−1.46427	−	0.683987i
$421$			1.21644e14i			0.448268i	0.974558	+	0.224134i	$0.0719553\pi$
$421$			1.21644e14i			0.448268i	−0.974558	+	0.224134i	$0.928045\pi$
$422$	−2.05970e14	−	1.81422e14i	−0.749179	−	0.659890i
$423$	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
$428$	1.37267e14	−	1.77293e14i	0.461982	−	0.596694i
$429$	−1.02655e14			−0.341087
$430$	9.34694e13	+	5.10965e13i	0.306615	+	0.167616i
$431$		−	3.16656e14i		−	1.02557i	−0.858518	−	0.512783i	$-0.828615\pi$
$431$		−	3.16656e14i		−	1.02557i	0.858518	−	0.512783i	$-0.171385\pi$
$432$	1.71769e14	+	1.01166e14i	0.549268	+	0.323501i
$433$	−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
$438$	3.22173e14	−	3.65765e14i	0.954951	−	1.08416i
$439$	2.16011e14			0.632297			0.316148	−	0.948710i	$-0.397610\pi$
$439$	2.16011e14			0.632297			0.316148	+	0.948710i	$0.397610\pi$
$440$	−7.49502e13	+	3.27259e13i	−0.216662	+	0.0946022i
$441$	−4.12737e13			−0.117831
$442$	1.43696e14	−	1.63139e14i	0.405156	−	0.459977i
$443$	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
$448$	3.65328e14	+	1.56920e14i	0.956433	+	0.410818i
$449$		−	1.45737e14i		−	0.376891i	−0.982084	−	0.188445i	$-0.939655\pi$
$449$		−	1.45737e14i		−	0.376891i	0.982084	−	0.188445i	$-0.0603448\pi$
$450$	−5.30892e14	−	1.51766e14i	−1.35624	−	0.387709i
$451$	−1.46654e14			−0.370102
$452$	4.07615e14	+	3.15591e14i	1.01622	+	0.786797i
$453$	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	$0.768261\pi$
$458$	−1.28900e14	−	1.13538e14i	−0.298878	−	0.263257i
$459$		−	1.83538e14i		−	0.420491i
$460$	−5.59326e14	+	2.03157e14i	−1.26619	+	0.459901i
$461$		−	5.95337e14i		−	1.33170i	−0.746084	−	0.665852i	$-0.768068\pi$
$461$		−	5.95337e14i		−	1.33170i	0.746084	−	0.665852i	$-0.231932\pi$
$462$	−1.14254e14	+	1.29714e14i	−0.252546	+	0.286718i
$463$	−5.26906e14	−	5.26906e14i	−1.15090	−	1.15090i	−0.986373	−	0.164527i	$-0.947390\pi$
$463$	−5.26906e14	−	5.26906e14i	−1.15090	−	1.15090i	−0.164527	−	0.986373i	$-0.552610\pi$
$464$	−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	$0.921046\pi$
$468$	5.03377e14	+	3.89733e14i	1.03643	+	0.802444i
$469$	7.78564e14			1.58432
$470$	9.08004e13	+	4.96374e13i	0.182620	+	0.0998323i
$471$			3.98721e14i			0.792600i
$472$	2.89725e14	+	1.96324e14i	0.569252	+	0.385739i
$473$	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
$478$	2.13523e14	+	1.88075e14i	0.391374	+	0.344729i
$479$	−4.52427e14			−0.819791			−0.409895	−	0.912133i	$-0.634435\pi$
$479$	−4.52427e14			−0.819791			−0.409895	+	0.912133i	$0.634435\pi$
$480$	8.40399e14	+	2.12039e14i	1.50542	+	0.379829i
$481$	1.04332e15			1.84765
$482$	−2.74279e14	−	2.41590e14i	−0.480212	−	0.422980i
$483$	−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	−0.407786	−	0.913078i	$-0.633699\pi$
$487$	3.05458e14	−	3.05458e14i	0.505292	−	0.505292i	0.913078	+	0.407786i	$0.133699\pi$
$488$	−5.82278e14	−	3.94566e14i	−0.952405	−	0.645373i
$489$		−	6.40480e14i		−	1.03587i
$490$	−5.01242e13	+	1.46916e13i	−0.0801621	+	0.0234959i
$491$	5.09391e14			0.805570			0.402785	−	0.915295i	$-0.368042\pi$
$491$	5.09391e14			0.805570			0.402785	+	0.915295i	$0.368042\pi$
$492$	1.22894e15	+	9.51490e14i	1.92186	+	1.48798i
$493$	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
$498$	9.02913e13	−	1.02508e14i	0.132094	−	0.149968i
$499$		−	2.62021e14i		−	0.379126i	−0.981869	−	0.189563i	$-0.939293\pi$
$499$		−	2.62021e14i		−	0.379126i	0.981869	−	0.189563i	$-0.0607071\pi$
$500$	−6.98756e14	+	4.66455e12i	−0.999978	+	0.00667536i
$501$			1.99820e15i			2.82833i
$502$	−2.24650e14	−	1.97876e14i	−0.314511	−	0.277027i
$503$	−9.59059e14	−	9.59059e14i	−1.32807	−	1.32807i	−0.907052	−	0.421020i	$-0.861672\pi$
$503$	−9.59059e14	−	9.59059e14i	−1.32807	−	1.32807i	−0.421020	−	0.907052i	$-0.638328\pi$
$504$	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
$508$	−6.56742e12	−	5.08474e12i	−0.00861280	−	0.00666835i
$509$	−2.42915e14			−0.315142			−0.157571	−	0.987508i	$-0.550366\pi$
$509$	−2.42915e14			−0.315142			−0.157571	+	0.987508i	$0.550366\pi$
$510$	−2.24455e14	−	7.65785e14i	−0.288067	−	0.982813i
$511$		−	7.62910e14i		−	0.968631i
$512$	−7.77656e14	−	1.70517e14i	−0.976794	−	0.214182i
$513$	−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
$518$	1.16121e15	−	1.31833e15i	1.36803	−	1.55314i
$519$	−8.64686e14			−1.00795
$520$	7.50046e14	+	2.94125e14i	0.865106	+	0.339245i
$521$	1.22559e15			1.39874			0.699371	−	0.714758i	$-0.253463\pi$
$521$	1.22559e15			1.39874			0.699371	+	0.714758i	$0.253463\pi$
$522$	−4.30876e14	+	4.89178e14i	−0.486592	+	0.552432i
$523$	−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
$528$	1.75650e14	−	2.98234e14i	0.186278	−	0.316279i
$529$			7.76286e14i			0.814734i
$530$	−7.16974e14	+	1.31154e15i	−0.744708	+	1.36227i
$531$	9.43568e14			0.969959
$532$	−4.74968e14	+	6.13467e14i	−0.483226	+	0.624133i
$533$	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
$538$	8.20592e14	+	7.22792e14i	0.784919	+	0.691370i
$539$			2.08583e13i			0.0197488i
$540$	6.39301e14	−	2.32206e14i	0.599156	−	0.217624i
$541$		−	7.62437e14i		−	0.707325i	−0.935373	−	0.353663i	$-0.884936\pi$
$541$		−	7.62437e14i		−	0.707325i	0.935373	−	0.353663i	$-0.115064\pi$
$542$	9.86540e14	−	1.12003e15i	0.905980	−	1.02857i
$543$	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	$0.844188\pi$
$548$	4.04643e14	−	5.22635e14i	0.349767	−	0.451758i
$549$	−1.89635e15			−1.62282
$550$	−7.66973e13	+	2.68295e14i	−0.0649808	+	0.227309i
$551$		−	4.71801e14i		−	0.395754i
$552$	1.41275e15	−	2.08486e15i	1.17328	−	1.73146i
$553$	−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	−0.277273	−	0.960791i	$-0.589431\pi$
$557$	8.64876e14	−	8.64876e14i	0.683519	−	0.683519i	0.960791	+	0.277273i	$0.0894305\pi$
$558$	−9.03688e14	−	7.95985e14i	−0.707181	−	0.622897i
$559$	−4.19051e14			−0.324714
$560$	1.20645e15	−	6.20390e14i	0.925707	−	0.476026i
$561$	−3.18668e14			−0.242127
$562$	−3.70563e14	−	3.26398e14i	−0.278812	−	0.245583i
$563$	−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
$568$	2.16227e15	+	1.46521e15i	1.53460	+	1.03988i
$569$			1.13013e15i			0.794350i	0.917743	+	0.397175i	$0.130009\pi$
$569$			1.13013e15i			0.794350i	−0.917743	+	0.397175i	$0.869991\pi$
$570$	−8.11250e14	+	1.48400e15i	−0.564733	+	1.03305i
$571$	7.85962e14			0.541880			0.270940	−	0.962596i	$-0.412666\pi$
$571$	7.85962e14			0.541880			0.270940	+	0.962596i	$0.412666\pi$
$572$	1.96958e14	−	2.54389e14i	0.134491	−	0.173708i
$573$	−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	$0.864124\pi$
$578$	−5.79079e14	+	6.57434e14i	−0.373366	+	0.423886i
$579$			1.48716e15i			0.949789i
$580$	−3.49145e14	+	7.47447e14i	−0.220878	+	0.472854i
$581$		−	2.13811e14i		−	0.133987i
$582$	−2.11686e15	−	1.86457e15i	−1.31406	−	1.15745i
$583$	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	$0.665462\pi$
$588$	1.35329e14	−	1.74790e14i	0.0793990	−	0.102551i
$589$	8.71588e14			0.506614
$590$	1.14590e15	−	3.35869e14i	0.659874	−	0.193412i
$591$			1.34873e15i			0.769475i
$592$	−1.78520e15	+	3.03107e15i	−1.00906	+	1.71327i
$593$	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
$598$	1.54731e15	−	1.75667e15i	0.827410	−	0.939366i
$599$	−8.14020e13			−0.0431308			−0.0215654	−	0.999767i	$-0.506865\pi$
$599$	−8.14020e13			−0.0431308			−0.0215654	+	0.999767i	$0.506865\pi$
$600$	2.38341e15	−	1.75066e15i	1.25132	−	0.919118i
$601$	−1.05056e15			−0.546527			−0.273264	−	0.961939i	$-0.588103\pi$
$601$	−1.05056e15			−0.546527			−0.273264	+	0.961939i	$0.588103\pi$
$602$	−4.66399e14	+	5.29507e14i	−0.240424	+	0.272955i
$603$	−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	−0.562291	−	0.826940i	$-0.690080\pi$
$607$	5.37289e14	−	5.37289e14i	0.264649	−	0.264649i	0.826940	+	0.562291i	$0.190080\pi$
$608$	7.02150e14	−	1.38576e15i	0.342736	−	0.676423i
$609$			1.74366e15i			0.843465i
$610$	−2.30299e15	+	6.75017e14i	−1.10402	+	0.323594i
$611$	−4.07085e14			−0.193401
$612$	1.56261e15	+	1.20983e15i	0.735731	+	0.569630i
$613$	−7.77970e14	−	7.77970e14i	−0.363020	−	0.363020i	0.501904	−	0.864923i	$-0.332633\pi$
$613$	−7.77970e14	−	7.77970e14i	−0.363020	−	0.363020i	−0.864923	+	0.501904i	$0.832633\pi$
$614$	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	$0.731696\pi$
$618$	−6.61605e14	−	5.82754e14i	−0.295231	−	0.260045i
$619$		−	1.67025e15i		−	0.738724i	−0.929286	−	0.369362i	$-0.879576\pi$
$619$		−	1.67025e15i		−	0.738724i	0.929286	−	0.369362i	$-0.120424\pi$
$620$	−1.38081e15	−	6.44998e14i	−0.605311	−	0.282751i
$621$		−	1.97633e15i		−	0.858728i
$622$	8.97581e14	−	1.01903e15i	0.386569	−	0.438875i
$623$	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
$628$	−9.88071e14	−	7.65000e14i	−0.403655	−	0.312524i
$629$	3.23875e15			1.31159
$630$	1.75442e15	−	3.20931e15i	0.704303	−	1.28836i
$631$			1.35945e15i			0.541004i	0.962719	+	0.270502i	$0.0871897\pi$
$631$			1.35945e15i			0.541004i	−0.962719	+	0.270502i	$0.912810\pi$
$632$	4.91968e14	−	7.26019e14i	0.194085	−	0.286420i
$633$	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
$638$	2.47214e14	+	2.17750e14i	0.0925888	+	0.0815539i
$639$	7.04203e15			2.61483
$640$	−2.13787e15	+	1.67577e15i	−0.787031	+	0.616913i
$641$	−2.53848e15			−0.926520			−0.463260	−	0.886223i	$-0.653320\pi$
$641$	−2.53848e15			−0.926520			−0.463260	+	0.886223i	$0.653320\pi$
$642$	2.42961e15	+	2.14004e15i	0.879213	+	0.774426i
$643$	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	−0.936954	−	0.349451i	$-0.886368\pi$
$647$	−1.69427e15	+	1.69427e15i	−0.587503	+	0.587503i	0.349451	+	0.936954i	$0.386368\pi$
$648$	6.86649e14	−	1.01332e15i	0.236087	−	0.348404i
$649$		−	4.76847e14i		−	0.162567i
$650$	2.40313e15	−	1.33462e15i	0.812371	−	0.451164i
$651$	−3.22117e15			−1.07974
$652$	1.58717e15	+	1.22885e15i	0.527549	+	0.408447i
$653$	2.27945e15	+	2.27945e15i	0.751291	+	0.751291i	0.974720	−	0.223429i	$-0.0717251\pi$
$653$	2.27945e15	+	2.27945e15i	0.751291	+	0.751291i	−0.223429	+	0.974720i	$0.571725\pi$
$654$	−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
$658$	−4.53081e14	+	5.14387e14i	−0.143197	+	0.162573i
$659$			2.48138e15i			0.777721i	0.921297	+	0.388860i	$0.127131\pi$
$659$			2.48138e15i			0.777721i	−0.921297	+	0.388860i	$0.872869\pi$
$660$	−4.03167e14	−	1.10999e15i	−0.125312	−	0.345005i
$661$		−	3.17662e15i		−	0.979169i	−0.871956	−	0.489585i	$-0.837148\pi$
$661$		−	3.17662e15i		−	0.979169i	0.871956	−	0.489585i	$-0.162852\pi$
$662$	−1.89863e15	−	1.67235e15i	−0.580393	−	0.511220i
$663$	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
$668$	−4.95173e15	−	3.83381e15i	−1.44041	−	1.11522i
$669$	−1.85126e15			−0.534101
$670$	−2.55139e15	+	4.66719e15i	−0.730072	+	1.33550i
$671$			9.58350e14i			0.271988i
$672$	−2.59497e15	+	5.12142e15i	−0.730469	+	1.44165i
$673$	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	−0.981992	−	0.188923i	$-0.939500\pi$
$677$	−2.93460e15	+	2.93460e15i	−0.793069	+	0.793069i	0.188923	+	0.981992i	$0.439500\pi$
$678$	−4.92018e15	+	5.58592e15i	−1.31892	+	1.49738i
$679$	−4.41533e15			−1.17403
$680$	2.32834e15	+	9.13040e14i	0.614112	+	0.240819i
$681$	−9.69212e15			−2.53577
$682$	−4.02263e14	+	4.56693e14i	−0.104399	+	0.118525i
$683$	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
$688$	7.17025e14	−	1.21743e15i	0.177336	−	0.301097i
$689$		−	5.88002e15i		−	1.44269i
$690$	−2.41692e15	−	8.24593e15i	−0.588291	−	2.00710i
$691$	2.33044e15			0.562742			0.281371	−	0.959599i	$-0.409211\pi$
$691$	2.33044e15			0.562742			0.281371	+	0.959599i	$0.409211\pi$
$692$	1.65902e15	−	2.14278e15i	0.397436	−	0.513326i
$693$	−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
$698$	4.74498e15	+	4.17946e15i	1.08400	+	0.954807i
$699$			6.49993e15i			1.47328i
$700$	9.88251e14	−	4.52199e15i	0.222243	−	1.01693i
$701$			6.75327e15i			1.50683i	0.657544	+	0.753416i	$0.271595\pi$
$701$			6.75327e15i			1.50683i	−0.657544	+	0.753416i	$0.728405\pi$
$702$	−1.76855e15	+	2.00785e15i	−0.391529	+	0.444506i
$703$	−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
$708$	−3.09379e15	+	3.99592e15i	−0.653593	+	0.844178i
$709$	−7.86850e15			−1.64945			−0.824723	−	0.565538i	$-0.808669\pi$
$709$	−7.86850e15			−1.64945			−0.824723	+	0.565538i	$0.808669\pi$
$710$	8.55209e15	−	2.50666e15i	1.77890	−	0.521403i
$711$		−	2.36448e15i		−	0.488037i
$712$	−6.97927e15	−	4.72932e15i	−1.42945	−	0.968632i
$713$	−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
$718$	2.49425e15	+	2.19698e15i	0.487816	+	0.429677i
$719$	8.23402e14			0.159810			0.0799048	−	0.996802i	$-0.474538\pi$
$719$	8.23402e14			0.159810			0.0799048	+	0.996802i	$0.474538\pi$
$720$	−2.23713e15	+	6.97353e15i	−0.430887	+	1.34315i
$721$	−1.37997e15			−0.263770
$722$	−1.68122e15	−	1.48085e15i	−0.318912	−	0.280903i
$723$	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	−0.0734587	−	0.997298i	$-0.523404\pi$
$727$	5.05866e15	−	5.05866e15i	0.923840	−	0.923840i	0.997298	+	0.0734587i	$0.0234037\pi$
$728$	−2.99371e15	+	4.41795e15i	−0.542609	+	0.800752i
$729$		−	8.80202e15i		−	1.58336i
$730$	4.57335e15	+	2.50009e15i	0.816504	+	0.446355i
$731$	−1.30084e15			−0.230505
$732$	6.21778e15	−	8.03086e15i	1.09351	−	1.41238i
$733$	−2.69997e15	−	2.69997e15i	−0.471288	−	0.471288i	0.431043	−	0.902331i	$-0.358146\pi$
$733$	−2.69997e15	−	2.69997e15i	−0.471288	−	0.471288i	−0.902331	+	0.431043i	$0.858146\pi$
$734$	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
$738$	−8.68033e15	+	9.85485e15i	−1.45957	+	1.65707i
$739$			6.30115e15i			1.05166i	0.850589	+	0.525830i	$0.176245\pi$
$739$			6.30115e15i			1.05166i	−0.850589	+	0.525830i	$0.823755\pi$
$740$	4.09754e15	+	1.12812e16i	0.678811	+	1.86888i
$741$		−	6.65319e15i		−	1.09403i
$742$	−7.42992e15	−	6.54440e15i	−1.21273	−	1.06819i
$743$	1.39645e15	+	1.39645e15i	0.226248	+	0.226248i	0.811123	−	0.584875i	$-0.198856\pi$
$743$	1.39645e15	+	1.39645e15i	0.226248	+	0.226248i	−0.584875	+	0.811123i	$0.698856\pi$
$744$	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
$748$	6.11408e14	−	7.89692e14i	0.0954712	−	0.123310i
$749$	5.06766e15			0.785520
$750$	5.70870e14	−	1.00740e16i	0.0878416	−	1.55011i
$751$		−	2.91690e15i		−	0.445556i	−0.974869	−	0.222778i	$-0.928488\pi$
$751$		−	2.91690e15i		−	0.445556i	0.974869	−	0.222778i	$-0.0715125\pi$
$752$	6.96550e14	−	1.18266e15i	0.105622	−	0.179334i
$753$	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	−0.529328	−	0.848418i	$-0.677556\pi$
$757$	2.18243e15	−	2.18243e15i	0.319090	−	0.319090i	0.848418	+	0.529328i	$0.177556\pi$
$758$	−5.60849e15	+	6.36737e15i	−0.814077	+	0.924229i
$759$	−3.43140e15			−0.494472
$760$	−2.12100e15	−	4.85761e15i	−0.303435	−	0.694941i
$761$	3.33090e14			0.0473093			0.0236546	−	0.999720i	$-0.492470\pi$
$761$	3.33090e14			0.0473093			0.0236546	+	0.999720i	$0.492470\pi$
$762$	7.92730e13	−	8.99993e13i	0.0111782	−	0.0126907i
$763$	−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
$768$	3.16745e15	−	1.10510e16i	0.427782	−	1.49251i
$769$		−	5.52657e15i		−	0.741073i	−0.928818	−	0.370536i	$-0.879174\pi$
$769$		−	5.52657e15i		−	0.741073i	0.928818	−	0.370536i	$-0.120826\pi$
$770$	−1.62187e15	−	8.86622e14i	−0.215933	−	0.118043i
$771$	1.67674e16			2.21650
$772$	−3.68534e15	−	2.85333e15i	−0.483707	−	0.374504i
$773$	1.66942e15	+	1.66942e15i	0.217560	+	0.217560i	0.807469	−	0.589910i	$-0.200837\pi$
$773$	1.66942e15	+	1.66942e15i	0.217560	+	0.217560i	−0.589910	+	0.807469i	$0.700837\pi$
$774$	−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
$778$	−9.04953e15	−	7.97099e15i	−1.13825	−	1.00259i
$779$		−	9.50479e15i		−	1.18710i
$780$	−4.92354e15	+	1.05403e16i	−0.610600	+	1.30717i
$781$		−	3.55880e15i		−	0.438251i
$782$	4.80326e15	−	5.45318e15i	0.587352	−	0.666826i
$783$	−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	$-0.548868\pi$
$788$	−3.34229e15	−	2.58772e15i	−0.391877	−	0.303406i
$789$	−6.04310e15			−0.703617
$790$	−8.41651e14	−	2.87150e15i	−0.0973157	−	0.332017i
$791$			1.16511e16i			1.33781i
$792$	2.42106e15	+	1.64057e15i	0.276068	+	0.187071i
$793$	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	−0.680882	−	0.732394i	$-0.738403\pi$
$797$	4.67660e14	−	4.67660e14i	0.0515121	−	0.0515121i	0.732394	+	0.680882i	$0.238403\pi$
$798$	−8.40689e15	−	7.40494e15i	−0.919643	−	0.810038i
$799$	−1.26370e15			−0.137289
$800$	−2.34578e14	+	9.26522e15i	−0.0253101	+	0.999680i
$801$	−2.27299e16			−2.43567
$802$	8.50734e15	+	7.49342e15i	0.905388	+	0.797482i
$803$	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
$808$	1.28520e16	+	8.70884e15i	1.31283	+	0.889606i
$809$			3.69378e15i			0.374761i	0.982287	+	0.187381i	$0.0599997\pi$
$809$			3.69378e15i			0.374761i	−0.982287	+	0.187381i	$0.940000\pi$
$810$	−1.17471e15	−	4.00781e15i	−0.118376	−	0.403868i
$811$	1.58975e16			1.59116			0.795578	−	0.605851i	$-0.207167\pi$
$811$	1.58975e16			1.59116			0.795578	+	0.605851i	$0.207167\pi$
$812$	−4.32097e15	−	3.34545e15i	−0.429559	−	0.332580i
$813$	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
$818$	−8.44846e15	+	9.59161e15i	−0.806556	+	0.915690i
$819$			1.43883e16i			1.36442i
$820$	−7.03379e15	+	1.50579e16i	−0.662542	+	1.41836i
$821$		−	1.46304e15i		−	0.136889i	−0.997655	−	0.0684446i	$-0.978196\pi$
$821$		−	1.46304e15i		−	0.136889i	0.997655	−	0.0684446i	$-0.0218036\pi$
$822$	7.16214e15	+	6.30854e15i	0.665653	+	0.586319i
$823$	−1.27813e16	−	1.27813e16i	−1.17998	−	1.17998i	−0.979749	−	0.200232i	$-0.935831\pi$
$823$	−1.27813e16	−	1.27813e16i	−1.17998	−	1.17998i	−0.200232	−	0.979749i	$-0.564169\pi$
$824$	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	$0.657639\pi$
$828$	1.68261e16	+	1.30274e16i	1.50251	+	1.16330i
$829$	1.32392e16			1.17439			0.587193	−	0.809447i	$-0.300233\pi$
$829$	1.32392e16			1.17439			0.587193	+	0.809447i	$0.300233\pi$
$830$	1.28171e15	+	7.00669e14i	0.112944	+	0.0617424i
$831$		−	1.04993e15i		−	0.0919080i
$832$	4.21732e15	−	9.81842e15i	0.366740	−	0.853814i
$833$	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
$838$	−4.06586e15	+	4.61601e15i	−0.339868	+	0.385855i
$839$	−4.47473e14			−0.0371600			−0.0185800	−	0.999827i	$-0.505915\pi$
$839$	−4.47473e14			−0.0371600			−0.0185800	+	0.999827i	$0.505915\pi$
$840$	7.83870e15	+	1.79525e16i	0.646707	+	1.48112i
$841$	−8.87737e15			−0.727623
$842$	3.63863e15	−	4.13097e15i	0.296293	−	0.336384i
$843$	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
$848$	1.70827e16	+	1.00611e16i	1.33776	+	0.787897i
$849$			5.32480e15i			0.414296i
$850$	7.45996e15	−	4.14302e15i	0.576676	−	0.320267i
$851$	3.48746e16			2.67853
$852$	−2.30895e16	+	2.98223e16i	−1.76197	+	2.27575i
$853$	−6.25567e15	−	6.25567e15i	−0.474301	−	0.474301i	0.429003	−	0.903303i	$-0.358865\pi$
$853$	−6.25567e15	−	6.25567e15i	−0.474301	−	0.474301i	−0.903303	+	0.429003i	$0.858865\pi$
$854$	−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	$0.887183\pi$
$858$	3.48613e15	+	3.07064e15i	0.255955	+	0.225450i
$859$			2.41892e16i			1.76466i	0.470636	+	0.882328i	$0.344025\pi$
$859$			2.41892e16i			1.76466i	−0.470636	+	0.882328i	$0.655975\pi$
$860$	−1.64578e15	−	4.53110e15i	−0.119297	−	0.328445i
$861$			3.51274e16i			2.53004i
$862$	−9.47191e15	+	1.07535e16i	−0.677872	+	0.769594i
$863$	7.54062e15	+	7.54062e15i	0.536226	+	0.536226i	0.922418	−	0.386193i	$-0.126210\pi$
$863$	7.54062e15	+	7.54062e15i	0.536226	+	0.536226i	−0.386193	+	0.922418i	$0.626210\pi$
$864$	−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
$868$	6.18026e15	−	7.98239e15i	0.425743	−	0.549888i
$869$	−1.19493e15			−0.0817961
$870$	−1.04526e16	−	5.71406e15i	−0.710996	−	0.388677i
$871$		−	2.09244e16i		−	1.41434i
$872$	8.40245e15	−	1.23999e16i	0.564372	−	0.832869i
$873$	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	−0.977538	−	0.210758i	$-0.932407\pi$
$877$	−1.17806e16	+	1.17806e16i	−0.766780	+	0.766780i	0.210758	+	0.977538i	$0.432407\pi$
$878$	−7.33565e15	−	6.46137e15i	−0.474481	−	0.417931i
$879$	−2.16836e16			−1.39378
$880$	3.52419e15	+	1.13057e15i	0.225115	+	0.0722176i
$881$	4.60229e14			0.0292150			0.0146075	−	0.999893i	$-0.495350\pi$
$881$	4.60229e14			0.0292150			0.0146075	+	0.999893i	$0.495350\pi$
$882$	1.40164e15	+	1.23459e15i	0.0884218	+	0.0778834i
$883$	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	−0.750467	−	0.660908i	$-0.770171\pi$
$887$	−1.46450e15	+	1.46450e15i	−0.0895593	+	0.0895593i	0.660908	+	0.750467i	$0.270171\pi$
$888$	−4.20502e16	−	2.84943e16i	−2.55562	−	1.73175i
$889$		−	1.87720e14i		−	0.0113384i
$890$	−2.76040e16	+	8.09085e15i	−1.65702	+	0.485679i
$891$	−1.66778e15			−0.0994974
$892$	3.55189e15	−	4.58761e15i	0.210597	−	0.272007i
$893$	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
$898$	−4.35933e15	+	4.94918e15i	−0.249115	+	0.282822i
$899$			6.13905e15i			0.348677i
$900$	1.34892e16	+	2.10341e16i	0.761472	+	1.18738i
$901$		−	1.82531e16i		−	1.02412i
$902$	4.98030e15	+	4.38674e15i	0.277728	+	0.244628i
$903$	−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	$0.660276\pi$
$908$	1.85956e16	−	2.40180e16i	0.999859	−	1.29141i
$909$	4.18561e16			2.23696
$910$	5.12159e15	+	1.74736e16i	0.272068	+	0.928228i
$911$		−	1.22841e15i		−	0.0648621i	−0.999474	−	0.0324311i	$-0.989675\pi$
$911$		−	1.22841e15i		−	0.0648621i	0.999474	−	0.0324311i	$-0.0103249\pi$
$912$	1.93289e16	+	1.13841e16i	1.01446	+	0.597484i
$913$	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
$918$	−5.49005e15	+	6.23290e15i	−0.277934	+	0.315541i
$919$	1.82570e16			0.918742			0.459371	−	0.888245i	$-0.348075\pi$
$919$	1.82570e16			0.918742			0.459371	+	0.888245i	$0.348075\pi$
$920$	2.50714e16	+	9.83156e15i	1.25414	+	0.491801i
$921$	−3.65688e16			−1.81837
$922$	−1.78079e16	+	2.02174e16i	−0.880221	+	0.999322i
$923$	−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
$928$	9.76063e15	+	4.94561e15i	0.465547	+	0.235888i
$929$		−	5.24697e15i		−	0.248784i	−0.992233	−	0.124392i	$-0.960302\pi$
$929$		−	5.24697e15i		−	0.248784i	0.992233	−	0.124392i	$-0.0396980\pi$
$930$	1.05559e16	−	1.93097e16i	0.497554	−	0.910162i
$931$	−1.35185e15			−0.0633440
$932$	−1.61075e16	−	1.24710e16i	−0.750309	−	0.580916i
$933$	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	$0.611384\pi$
$938$	−2.64397e16	−	2.32886e16i	−1.18889	−	1.04720i
$939$			1.64900e16i			0.737158i
$940$	−1.59878e15	−	4.40171e15i	−0.0710536	−	0.195622i
$941$			2.52020e16i			1.11350i	0.830678	+	0.556752i	$0.187953\pi$
$941$			2.52020e16i			1.11350i	−0.830678	+	0.556752i	$0.812047\pi$
$942$	1.19266e16	−	1.35404e16i	0.523888	−	0.594775i
$943$	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	$0.788681\pi$
$948$	1.00133e16	+	7.75270e15i	0.424750	+	0.328857i
$949$	−2.05037e16			−0.864703
$950$	−1.73885e16	−	4.97084e15i	−0.729092	−	0.208425i
$951$		−	2.40503e15i		−	0.100260i
$952$	−9.29326e15	+	1.37145e16i	−0.385181	+	0.568428i
$953$	−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
$958$	1.53643e16	+	1.35331e16i	0.615178	+	0.541860i
$959$	1.49387e16			0.594718
$960$	−2.21971e16	−	3.23390e16i	−0.878627	−	1.28007i
$961$	1.40674e16			0.553651
$962$	−3.54309e16	−	3.12081e16i	−1.38650	−	1.22125i
$963$	−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	−0.0655502	−	0.997849i	$-0.520880\pi$
$967$	2.45132e16	−	2.45132e16i	0.932299	−	0.932299i	0.997849	+	0.0655502i	$0.0208803\pi$
$968$	−1.40046e16	+	2.06672e16i	−0.529611	+	0.781570i
$969$		−	2.06533e16i		−	0.776619i
$970$	1.44692e16	−	2.64682e16i	0.541004	−	0.989645i
$971$	1.14412e16			0.425370			0.212685	−	0.977121i	$-0.431779\pi$
$971$	1.14412e16			0.425370			0.212685	+	0.977121i	$0.431779\pi$
$972$	2.76100e16	+	2.13767e16i	1.02071	+	0.790270i
$973$	−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	$0.675348\pi$
$978$	−1.91582e16	+	2.17505e16i	−0.684685	+	0.777329i
$979$			1.14869e16i			0.408224i
$980$	2.14166e15	+	1.00040e15i	0.0756845	+	0.0353535i
$981$		−	4.03836e16i		−	1.41914i
$982$	−1.72987e16	−	1.52370e16i	−0.604507	−	0.532460i
$983$	−2.02024e16	−	2.02024e16i	−0.702034	−	0.702034i	0.262813	−	0.964847i	$-0.415350\pi$
$983$	−2.02024e16	−	2.02024e16i	−0.702034	−	0.702034i	−0.964847	+	0.262813i	$0.915350\pi$
$984$	−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
$988$	1.64873e16	+	1.27651e16i	0.557167	+	0.431379i
$989$	−1.40074e16			−0.470737
$990$	9.57562e15	−	2.80666e15i	0.320017	−	0.0937985i
$991$			7.59051e15i			0.252270i	0.992013	+	0.126135i	$0.0402573\pi$
$991$			7.59051e15i			0.252270i	−0.992013	+	0.126135i	$0.959743\pi$
$992$	−9.13633e15	+	1.80314e16i	−0.301966	+	0.595958i
$993$	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	−0.518430	−	0.855120i	$-0.673483\pi$
$997$	1.04726e16	−	1.04726e16i	0.336691	−	0.336691i	0.855120	+	0.518430i	$0.173483\pi$
$998$	−7.83765e15	+	8.89815e15i	−0.250592	+	0.284500i
$999$	−3.98612e16			−1.26748

Twists

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

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

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+(-33.9596 - 29.9123i) 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} +(51991.2 - 76725.8i) q^{8} -249879. i q^{9} +(-88945.8 - 303461. i) q^{10} -126280. q^{11} +(1.05821e6 + 819306. i) 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} +(-7.47443e6 + 8.48579e6i) q^{18} -8.18436e6i q^{19} +(-6.05664e6 + 1.29660e7i) q^{20} +3.02474e7i q^{21} +(4.28843e6 + 3.77732e6i) 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} +(-7.49560e7 - 5.80337e7i) q^{28} +5.76467e7 q^{29} +(-1.81321e8 - 9.91220e7i) q^{30} +1.06494e8i q^{31} +(1.69318e8 + 8.57917e7i) 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} +(-2.44813e8 + 2.77938e8i) q^{38} +8.12916e8 q^{39} +(5.93523e8 - 2.59153e8i) q^{40} +1.16134e9 q^{41} +(9.04767e8 - 1.02719e9i) 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} +(-1.39095e9 + 2.36169e9i) q^{48} -1.65175e8i q^{49} +(6.07359e8 - 2.12460e9i) q^{50} +2.52350e9 q^{51} +(-1.55969e9 + 2.01449e9i) 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} +(-1.95766e9 - 1.72434e9i) q^{58} +3.77611e9i q^{59} +(3.19264e9 + 8.78987e9i) q^{60} -7.58909e9i q^{61} +(3.18549e9 - 3.61651e9i) 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} +(-4.84168e9 + 6.25349e9i) q^{68} +2.71729e10 q^{69} +(1.28435e10 + 7.02108e9i) q^{70} +2.81818e10i q^{71} +(-1.91721e10 - 1.29915e10i) 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} +(-2.76063e10 - 2.43161e10i) q^{78} +9.46251e9 q^{79} +(-2.79077e10 - 8.95288e9i) q^{80} +1.32070e10 q^{81} +(-3.94386e10 - 3.47382e10i) 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} +(-6.56546e9 + 9.68894e9i) q^{88} -9.09638e10i q^{89} +(-7.58284e10 + 2.22257e10i) q^{90} -5.75810e10 q^{91} +(-5.21349e10 + 6.73372e10i) 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} +(-4.94076e9 + 5.60928e9i) 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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