LMFDB - Embedded newform 49.10.c.h.30.1

Error: no document with id 214650719 found in table mf_hecke_traces.

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,10,Mod(18,49)] 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("49.18"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	49.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,66,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$25.2367559720$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 5242 x^{14} + 24024 x^{13} + 10505991 x^{12} - 53910056 x^{11} + \cdots + 89\!\cdots\!16 $ x^16 - 4x^15 - 5242x^14 + 24024x^13 + 10505991x^12 - 53910056x^11 - 9779568598x^10 + 54819837928x^9 + 3963633390800x^8 - 23235313319744x^7 - 467753893701144x^6 + 2306370917243232x^5 + 26209670720799040x^4 - 90637606103367168x^3 - 744297532540383840x^2 + 1282950647298147456*x + 8963293398458481216
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 7^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			30.1
Root			$-35.2710 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	49.30
Dual form			49.10.c.h.18.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-13.9891 + 24.2298i) q^{2} +(-13.0785 - 22.6526i) q^{3} +(-135.388 - 234.499i) q^{4} +(184.056 - 318.794i) q^{5} +731.823 q^{6} -6748.99 q^{8} +(9499.41 - 16453.5i) q^{9} +(5149.53 + 8919.25i) q^{10} +(12010.0 + 20801.9i) q^{11} +(-3541.34 + 6133.79i) q^{12} +31305.0 q^{13} -9628.67 q^{15} +(163731. - 283590. i) q^{16} +(277543. + 480718. i) q^{17} +(265776. + 460337. i) q^{18} +(-418550. + 724950. i) q^{19} -99675.8 q^{20} -672033. q^{22} +(535152. - 926911. i) q^{23} +(88266.5 + 152882. i) q^{24} +(908810. + 1.57410e6i) q^{25} +(-437927. + 758512. i) q^{26} -1.01180e6 q^{27} -2.75169e6 q^{29} +(134696. - 233301. i) q^{30} +(-2.90989e6 - 5.04008e6i) q^{31} +(2.85314e6 + 4.94179e6i) q^{32} +(314144. - 544114. i) q^{33} -1.55303e7 q^{34} -5.14443e6 q^{36} +(-6.03518e6 + 1.04532e7i) q^{37} +(-1.17103e7 - 2.02828e7i) q^{38} +(-409422. - 709139. i) q^{39} +(-1.24219e6 + 2.15154e6i) q^{40} -2.79029e7 q^{41} +2.48859e6 q^{43} +(3.25201e6 - 5.63265e6i) q^{44} +(-3.49684e6 - 6.05670e6i) q^{45} +(1.49726e7 + 2.59332e7i) q^{46} +(-1.31905e7 + 2.28467e7i) q^{47} -8.56540e6 q^{48} -5.08536e7 q^{50} +(7.25968e6 - 1.25741e7i) q^{51} +(-4.23832e6 - 7.34099e6i) q^{52} +(2.06333e7 + 3.57380e7i) q^{53} +(1.41541e7 - 2.45157e7i) q^{54} +8.84201e6 q^{55} +2.18960e7 q^{57} +(3.84935e7 - 6.66728e7i) q^{58} +(8.28849e7 + 1.43561e8i) q^{59} +(1.30361e6 + 2.25792e6i) q^{60} +(-6.01056e7 + 1.04106e8i) q^{61} +1.62827e8 q^{62} +8.00911e6 q^{64} +(5.76186e6 - 9.97983e6i) q^{65} +(8.78917e6 + 1.52233e7i) q^{66} +(-5.59120e7 - 9.68424e7i) q^{67} +(7.51520e7 - 1.30167e8i) q^{68} -2.79959e7 q^{69} +2.60320e8 q^{71} +(-6.41114e7 + 1.11044e8i) q^{72} +(-8.49711e6 - 1.47174e7i) q^{73} +(-1.68853e8 - 2.92462e8i) q^{74} +(2.37717e7 - 4.11738e7i) q^{75} +2.26667e8 q^{76} +2.29097e7 q^{78} +(-1.72344e8 + 2.98508e8i) q^{79} +(-6.02712e7 - 1.04393e8i) q^{80} +(-1.73744e8 - 3.00933e8i) q^{81} +(3.90336e8 - 6.76082e8i) q^{82} +2.05123e8 q^{83} +2.04333e8 q^{85} +(-3.48131e7 + 6.02980e7i) q^{86} +(3.59879e7 + 6.23328e7i) q^{87} +(-8.10551e7 - 1.40392e8i) q^{88} +(-2.19170e8 + 3.79613e8i) q^{89} +1.95670e8 q^{90} -2.89813e8 q^{92} +(-7.61139e7 + 1.31833e8i) q^{93} +(-3.69046e8 - 6.39207e8i) q^{94} +(1.54073e8 + 2.66862e8i) q^{95} +(7.46296e7 - 1.29262e8i) q^{96} -5.25507e8 q^{97} +4.56350e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 66 q^{2} - 1706 q^{4} - 117084 q^{8} - 27940 q^{9} + 82092 q^{11} - 164672 q^{15} - 1569570 q^{16} + 307774 q^{18} - 2600152 q^{22} + 2388480 q^{23} + 6191476 q^{25} - 36887784 q^{29} + 16703832 q^{30}+ \cdots - 6259461064 q^{99}+O(q^{100}) $ 16 * q + 66 * q^2 - 1706 * q^4 - 117084 * q^8 - 27940 * q^9 + 82092 * q^11 - 164672 * q^15 - 1569570 * q^16 + 307774 * q^18 - 2600152 * q^22 + 2388480 * q^23 + 6191476 * q^25 - 36887784 * q^29 + 16703832 * q^30 + 66365310 * q^32 - 163874260 * q^36 + 8944484 * q^37 + 128986088 * q^39 - 72060264 * q^43 + 20548980 * q^44 + 151133592 * q^46 - 358848780 * q^50 + 192522580 * q^51 + 140198712 * q^53 + 112011672 * q^57 - 407992572 * q^58 - 748541080 * q^60 + 1606537220 * q^64 + 69983508 * q^65 - 459952056 * q^67 + 431701008 * q^71 - 1088280558 * q^72 - 1222590060 * q^74 + 2845895808 * q^78 + 792601400 * q^79 - 1704517060 * q^81 - 736682888 * q^85 + 812465940 * q^86 - 1818979932 * q^88 + 5226574128 * q^92 + 2571584104 * q^93 + 3568335216 * q^95 - 6259461064 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (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 $

$2$	−13.9891	+	24.2298i	−0.618235	+	1.07082i	0.371572	+	0.928404i	$0.378819\pi$
$2$	−13.9891	+	24.2298i	−0.618235	+	1.07082i	−0.989808	+	0.142411i	$0.954515\pi$
$3$	−13.0785	−	22.6526i	−0.0932206	−	0.161463i	0.815644	−	0.578554i	$-0.196383\pi$
$3$	−13.0785	−	22.6526i	−0.0932206	−	0.161463i	−0.908865	+	0.417091i	$0.863050\pi$
$4$	−135.388	−	234.499i	−0.264430	−	0.458006i
$5$	184.056	−	318.794i	0.131699	−	0.228110i	−0.792632	−	0.609700i	$-0.791290\pi$
$5$	184.056	−	318.794i	0.131699	−	0.228110i	0.924332	+	0.381590i	$0.124623\pi$
$6$	731.823			0.230529
$7$		0			0
$7$		0			0
$8$	−6748.99			−0.582551
$9$	9499.41	−	16453.5i	0.482620	−	0.835922i
$10$	5149.53	+	8919.25i	0.162843	+	0.282052i
$11$	12010.0	+	20801.9i	0.247329	+	0.428386i	0.962784	−	0.270273i	$-0.0871139\pi$
$11$	12010.0	+	20801.9i	0.247329	+	0.428386i	−0.715455	+	0.698659i	$0.753781\pi$
$12$	−3541.34	+	6133.79i	−0.0493006	+	0.0853912i
$13$	31305.0			0.303996			0.151998	−	0.988381i	$-0.451429\pi$
$13$	31305.0			0.303996			0.151998	+	0.988381i	$0.451429\pi$
$14$		0			0
$15$	−9628.67			−0.0491084
$16$	163731.	−	283590.i	0.624584	−	1.08181i
$17$	277543.	+	480718.i	0.805953	+	1.39595i	0.915646	+	0.401987i	$0.131680\pi$
$17$	277543.	+	480718.i	0.805953	+	1.39595i	−0.109692	+	0.993966i	$0.534987\pi$
$18$	265776.	+	460337.i	0.596745	+	1.03359i
$19$	−418550.	+	724950.i	−0.736812	+	1.27620i	0.217112	+	0.976147i	$0.430336\pi$
$19$	−418550.	+	724950.i	−0.736812	+	1.27620i	−0.953924	+	0.300049i	$0.902997\pi$
$20$	−99675.8			−0.139301
$21$		0			0
$22$	−672033.			−0.611630
$23$	535152.	−	926911.i	0.398751	−	0.690657i	−0.594821	−	0.803858i	$-0.702777\pi$
$23$	535152.	−	926911.i	0.398751	−	0.690657i	0.993572	+	0.113201i	$0.0361104\pi$
$24$	88266.5	+	152882.i	0.0543057	+	0.0940603i
$25$	908810.	+	1.57410e6i	0.465310	+	0.805941i
$26$	−437927.	+	758512.i	−0.187941	+	0.325524i
$27$	−1.01180e6			−0.366402
$28$		0			0
$29$	−2.75169e6			−0.722450			−0.361225	−	0.932479i	$-0.617641\pi$
$29$	−2.75169e6			−0.722450			−0.361225	+	0.932479i	$0.617641\pi$
$30$	134696.	−	233301.i	0.0303606	−	0.0525860i
$31$	−2.90989e6	−	5.04008e6i	−0.565912	−	0.980189i	−0.996964	−	0.0778618i	$-0.975191\pi$
$31$	−2.90989e6	−	5.04008e6i	−0.565912	−	0.980189i	0.431052	−	0.902327i	$-0.358143\pi$
$32$	2.85314e6	+	4.94179e6i	0.481004	+	0.833123i
$33$	314144.	−	544114.i	0.0461123	−	0.0798688i
$34$	−1.55303e7			−1.99308
$35$		0			0
$36$	−5.14443e6			−0.510477
$37$	−6.03518e6	+	1.04532e7i	−0.529398	+	0.916945i	0.470014	+	0.882659i	$0.344249\pi$
$37$	−6.03518e6	+	1.04532e7i	−0.529398	+	0.916945i	−0.999412	+	0.0342857i	$0.989084\pi$
$38$	−1.17103e7	−	2.02828e7i	−0.911046	−	1.57798i
$39$	−409422.	−	709139.i	−0.0283387	−	0.0490841i
$40$	−1.24219e6	+	2.15154e6i	−0.0767216	+	0.132886i
$41$	−2.79029e7			−1.54214			−0.771068	−	0.636753i	$-0.780277\pi$
$41$	−2.79029e7			−1.54214			−0.771068	+	0.636753i	$0.780277\pi$
$42$		0			0
$43$	2.48859e6			0.111006			0.0555029	−	0.998459i	$-0.482324\pi$
$43$	2.48859e6			0.111006			0.0555029	+	0.998459i	$0.482324\pi$
$44$	3.25201e6	−	5.63265e6i	0.130802	−	0.226556i
$45$	−3.49684e6	−	6.05670e6i	−0.127122	−	0.220181i
$46$	1.49726e7	+	2.59332e7i	0.493044	+	0.853978i
$47$	−1.31905e7	+	2.28467e7i	−0.394296	+	0.682940i	−0.993011	−	0.118022i	$-0.962345\pi$
$47$	−1.31905e7	+	2.28467e7i	−0.394296	+	0.682940i	0.598715	+	0.800962i	$0.295678\pi$
$48$	−8.56540e6			−0.232896
$49$		0			0
$50$	−5.08536e7			−1.15069
$51$	7.25968e6	−	1.25741e7i	0.150263	−	0.260263i
$52$	−4.23832e6	−	7.34099e6i	−0.0803857	−	0.139232i
$53$	2.06333e7	+	3.57380e7i	0.359193	+	0.622140i	0.987826	−	0.155561i	$-0.0497187\pi$
$53$	2.06333e7	+	3.57380e7i	0.359193	+	0.622140i	−0.628633	+	0.777702i	$0.716385\pi$
$54$	1.41541e7	−	2.45157e7i	0.226522	−	0.392348i
$55$	8.84201e6			0.130292
$56$		0			0
$57$	2.18960e7			0.274744
$58$	3.84935e7	−	6.66728e7i	0.446644	−	0.773611i
$59$	8.28849e7	+	1.43561e8i	0.890515	+	1.54242i	0.839259	+	0.543733i	$0.182989\pi$
$59$	8.28849e7	+	1.43561e8i	0.890515	+	1.54242i	0.0512569	+	0.998686i	$0.483677\pi$
$60$	1.30361e6	+	2.25792e6i	0.0129857	+	0.0224920i
$61$	−6.01056e7	+	1.04106e8i	−0.555816	+	0.962701i	0.442024	+	0.897003i	$0.354261\pi$
$61$	−6.01056e7	+	1.04106e8i	−0.555816	+	0.962701i	−0.997840	+	0.0656975i	$0.979073\pi$
$62$	1.62827e8			1.39947
$63$		0			0
$64$	8.00911e6			0.0596725
$65$	5.76186e6	−	9.97983e6i	0.0400361	−	0.0693446i
$66$	8.78917e6	+	1.52233e7i	0.0570165	+	0.0987554i
$67$	−5.59120e7	−	9.68424e7i	−0.338976	−	0.587123i	0.645265	−	0.763959i	$-0.276747\pi$
$67$	−5.59120e7	−	9.68424e7i	−0.338976	−	0.587123i	−0.984240	+	0.176836i	$0.943414\pi$
$68$	7.51520e7	−	1.30167e8i	0.426237	−	0.738263i
$69$	−2.79959e7			−0.148687
$70$		0			0
$71$	2.60320e8			1.21575			0.607876	−	0.794032i	$-0.292022\pi$
$71$	2.60320e8			1.21575			0.607876	+	0.794032i	$0.292022\pi$
$72$	−6.41114e7	+	1.11044e8i	−0.281151	+	0.486967i
$73$	−8.49711e6	−	1.47174e7i	−0.0350202	−	0.0606567i	0.847984	−	0.530022i	$-0.177816\pi$
$73$	−8.49711e6	−	1.47174e7i	−0.0350202	−	0.0606567i	−0.883004	+	0.469365i	$0.844483\pi$
$74$	−1.68853e8	−	2.92462e8i	−0.654586	−	1.13378i
$75$	2.37717e7	−	4.11738e7i	0.0867530	−	0.150261i
$76$	2.26667e8			0.779340
$77$		0			0
$78$	2.29097e7			0.0700799
$79$	−1.72344e8	+	2.98508e8i	−0.497822	+	0.862253i	−0.999997	−	0.00251341i	$-0.999200\pi$
$79$	−1.72344e8	+	2.98508e8i	−0.497822	+	0.862253i	0.502175	+	0.864766i	$0.332533\pi$
$80$	−6.02712e7	−	1.04393e8i	−0.164515	−	0.284948i
$81$	−1.73744e8	−	3.00933e8i	−0.448464	−	0.776762i
$82$	3.90336e8	−	6.76082e8i	0.953403	−	1.65134i
$83$	2.05123e8			0.474420			0.237210	−	0.971458i	$-0.423767\pi$
$83$	2.05123e8			0.474420			0.237210	+	0.971458i	$0.423767\pi$
$84$		0			0
$85$	2.04333e8			0.424575
$86$	−3.48131e7	+	6.02980e7i	−0.0686277	+	0.118867i
$87$	3.59879e7	+	6.23328e7i	0.0673472	+	0.116649i
$88$	−8.10551e7	−	1.40392e8i	−0.144082	−	0.249557i
$89$	−2.19170e8	+	3.79613e8i	−0.370276	+	0.641337i	−0.989608	−	0.143792i	$-0.954070\pi$
$89$	−2.19170e8	+	3.79613e8i	−0.370276	+	0.641337i	0.619332	+	0.785129i	$0.287404\pi$
$90$	1.95670e8			0.314364
$91$		0			0
$92$	−2.89813e8			−0.421767
$93$	−7.61139e7	+	1.31833e8i	−0.105509	+	0.182748i
$94$	−3.69046e8	−	6.39207e8i	−0.487535	−	0.844435i
$95$	1.54073e8	+	2.66862e8i	0.194075	+	0.336149i
$96$	7.46296e7	−	1.29262e8i	0.0896789	−	0.155328i
$97$	−5.25507e8			−0.602706			−0.301353	−	0.953513i	$-0.597438\pi$
$97$	−5.25507e8			−0.602706			−0.301353	+	0.953513i	$0.597438\pi$
$98$		0			0
$99$	4.56350e8			0.477463
$100$	2.46084e8	−	4.26230e8i	0.246084	−	0.426230i
$101$	8.23048e8	+	1.42556e9i	0.787008	+	1.36314i	0.927792	+	0.373097i	$0.121704\pi$
$101$	8.23048e8	+	1.42556e9i	0.787008	+	1.36314i	−0.140785	+	0.990040i	$0.544963\pi$
$102$	2.03112e8	+	3.51801e8i	0.185796	+	0.321807i
$103$	−8.93793e8	+	1.54809e9i	−0.782473	+	1.35528i	0.148024	+	0.988984i	$0.452709\pi$
$103$	−8.93793e8	+	1.54809e9i	−0.782473	+	1.35528i	−0.930497	+	0.366300i	$0.880625\pi$
$104$	−2.11277e8			−0.177093
$105$		0			0
$106$	−1.15456e9			−0.888263
$107$	9.51875e8	−	1.64870e9i	0.702026	−	1.21594i	−0.265729	−	0.964048i	$-0.585613\pi$
$107$	9.51875e8	−	1.64870e9i	0.702026	−	1.21594i	0.967754	−	0.251896i	$-0.0810541\pi$
$108$	1.36986e8	+	2.37266e8i	0.0968876	+	0.167814i
$109$	1.20867e9	+	2.09347e9i	0.820139	+	1.42052i	0.905578	+	0.424179i	$0.139437\pi$
$109$	1.20867e9	+	2.09347e9i	0.820139	+	1.42052i	−0.0854393	+	0.996343i	$0.527229\pi$
$110$	−1.23691e8	+	2.14240e8i	−0.0805513	+	0.139519i
$111$	3.15724e8			0.197403
$112$		0			0
$113$	−9.42971e8			−0.544058			−0.272029	−	0.962289i	$-0.587695\pi$
$113$	−9.42971e8			−0.544058			−0.272029	+	0.962289i	$0.587695\pi$
$114$	−3.06305e8	+	5.30536e8i	−0.169856	+	0.294200i
$115$	−1.96996e8	−	3.41206e8i	−0.105031	−	0.181918i
$116$	3.72546e8	+	6.45268e8i	0.191038	+	0.330887i
$117$	2.97379e8	−	5.15075e8i	0.146715	−	0.254117i
$118$	−4.63793e9			−2.20219
$119$		0			0
$120$	6.49838e7			0.0286081
$121$	8.90495e8	−	1.54238e9i	0.377657	−	0.654121i
$122$	−1.68164e9	−	2.91269e9i	−0.687250	−	1.19035i
$123$	3.64928e8	+	6.32074e8i	0.143759	+	0.248997i
$124$	−7.87930e8	+	1.36473e9i	−0.299288	+	0.518383i
$125$	1.38805e9			0.508524
$126$		0			0
$127$	−2.93087e9			−0.999724			−0.499862	−	0.866105i	$-0.666616\pi$
$127$	−2.93087e9			−0.999724			−0.499862	+	0.866105i	$0.666616\pi$
$128$	−1.57285e9	+	2.72425e9i	−0.517896	+	0.897021i
$129$	−3.25470e7	−	5.63731e7i	−0.0103480	−	0.0179233i
$130$	1.61206e8	+	2.79217e8i	0.0495035	+	0.0857426i
$131$	9.26425e8	−	1.60462e9i	0.274846	−	0.476047i	−0.695250	−	0.718768i	$-0.744706\pi$
$131$	9.26425e8	−	1.60462e9i	0.274846	−	0.476047i	0.970096	+	0.242720i	$0.0780398\pi$
$132$	−1.70126e8			−0.0487739
$133$		0			0
$134$	3.12863e9			0.838267
$135$	−1.86227e8	+	3.22555e8i	−0.0482549	+	0.0835799i
$136$	−1.87313e9	−	3.24436e9i	−0.469509	−	0.813213i
$137$	−1.47751e9	−	2.55913e9i	−0.358334	−	0.620653i	0.629348	−	0.777123i	$-0.283322\pi$
$137$	−1.47751e9	−	2.55913e9i	−0.358334	−	0.620653i	−0.987683	+	0.156470i	$0.949989\pi$
$138$	3.91637e8	−	6.78335e8i	0.0919237	−	0.159217i
$139$	−3.45455e9			−0.784919			−0.392459	−	0.919769i	$-0.628376\pi$
$139$	−3.45455e9			−0.784919			−0.392459	+	0.919769i	$0.628376\pi$
$140$		0			0
$141$	6.90048e8			0.147026
$142$	−3.64164e9	+	6.30750e9i	−0.751621	+	1.30185i
$143$	3.75972e8	+	6.51202e8i	0.0751870	+	0.130228i
$144$	−3.11069e9	−	5.38788e9i	−0.602873	−	1.04421i
$145$	−5.06463e8	+	8.77220e8i	−0.0951463	+	0.164798i
$146$	4.75467e8			0.0866028
$147$		0			0
$148$	3.26837e9			0.559955
$149$	1.63628e9	−	2.83412e9i	0.271969	−	0.471064i	−0.697397	−	0.716685i	$-0.745658\pi$
$149$	1.63628e9	−	2.83412e9i	0.271969	−	0.471064i	0.969366	+	0.245621i	$0.0789918\pi$
$150$	6.65088e8	+	1.15197e9i	0.107268	+	0.185793i
$151$	3.25370e9	+	5.63557e9i	0.509309	+	0.882148i	0.999942	+	0.0107822i	$0.00343214\pi$
$151$	3.25370e9	+	5.63557e9i	0.509309	+	0.882148i	−0.490633	+	0.871366i	$0.663235\pi$
$152$	2.82479e9	−	4.89268e9i	0.429230	−	0.743449i
$153$	1.05460e10			1.55588
$154$		0			0
$155$	−2.14233e9			−0.298121
$156$	−1.10862e8	+	1.92018e8i	−0.0149872	+	0.0259586i
$157$	3.88733e9	+	6.73305e9i	0.510626	+	0.884430i	0.999924	+	0.0123138i	$0.00391971\pi$
$157$	3.88733e9	+	6.73305e9i	0.510626	+	0.884430i	−0.489298	+	0.872117i	$0.662747\pi$
$158$	−4.82186e9	−	8.35171e9i	−0.615542	−	1.06615i
$159$	5.39705e8	−	9.34797e8i	0.0669683	−	0.115993i
$160$	2.10055e9			0.253392
$161$		0			0
$162$	9.72207e9			1.10902
$163$	8.06708e9	−	1.39726e10i	0.895101	−	1.55036i	0.0614218	−	0.998112i	$-0.480437\pi$
$163$	8.06708e9	−	1.39726e10i	0.895101	−	1.55036i	0.833679	−	0.552249i	$-0.186230\pi$
$164$	3.77773e9	+	6.54322e9i	0.407787	+	0.706308i
$165$	−1.15640e8	−	2.00294e8i	−0.0121459	−	0.0210374i
$166$	−2.86948e9	+	4.97008e9i	−0.293303	+	0.508016i
$167$	1.98293e10			1.97280			0.986399	−	0.164370i	$-0.0525592\pi$
$167$	1.98293e10			1.97280			0.986399	+	0.164370i	$0.0525592\pi$
$168$		0			0
$169$	−9.62450e9			−0.907586
$170$	−2.85843e9	+	4.95095e9i	−0.262487	+	0.454641i
$171$	7.95196e9	+	1.37732e10i	0.711200	+	1.23183i
$172$	−3.36926e8	−	5.83573e8i	−0.0293533	−	0.0508413i
$173$	2.78786e9	−	4.82872e9i	0.236627	−	0.409849i	−0.723117	−	0.690725i	$-0.757292\pi$
$173$	2.78786e9	−	4.82872e9i	0.236627	−	0.409849i	0.959744	+	0.280876i	$0.0906248\pi$
$174$	−2.01375e9			−0.166546
$175$		0			0
$176$	7.86561e9			0.617910
$177$	2.16802e9	−	3.75512e9i	0.166029	−	0.287570i
$178$	−6.13197e9	−	1.06209e10i	−0.457836	−	0.792995i
$179$	−8.78341e8	−	1.52133e9i	−0.0639476	−	0.110761i	0.832279	−	0.554357i	$-0.187036\pi$
$179$	−8.78341e8	−	1.52133e9i	−0.0639476	−	0.110761i	−0.896227	+	0.443596i	$0.853702\pi$
$180$	−9.46861e8	+	1.64001e9i	−0.0672295	+	0.116445i
$181$	−1.11902e10			−0.774968			−0.387484	−	0.921876i	$-0.626656\pi$
$181$	−1.11902e10			−0.774968			−0.387484	+	0.921876i	$0.626656\pi$
$182$		0			0
$183$	3.14436e9			0.207254
$184$	−3.61174e9	+	6.25571e9i	−0.232293	+	0.402343i
$185$	2.22162e9	+	3.84796e9i	0.139443	+	0.241522i
$186$	−2.12953e9	−	3.68845e9i	−0.130459	−	0.225962i
$187$	−6.66656e9	+	1.15468e10i	−0.398671	+	0.690518i
$188$	7.14337e9			0.417054
$189$		0			0
$190$	−8.62136e9			−0.479937
$191$	−2.49142e9	+	4.31527e9i	−0.135456	+	0.234616i	−0.925771	−	0.378084i	$-0.876583\pi$
$191$	−2.49142e9	+	4.31527e9i	−0.135456	+	0.234616i	0.790316	+	0.612700i	$0.209917\pi$
$192$	−1.04747e8	−	1.81427e8i	−0.00556271	−	0.00963489i
$193$	1.14199e10	+	1.97798e10i	0.592453	+	1.02616i	0.993901	+	0.110276i	$0.0351736\pi$
$193$	1.14199e10	+	1.97798e10i	0.592453	+	1.02616i	−0.401448	+	0.915882i	$0.631493\pi$
$194$	7.35136e9	−	1.27329e10i	0.372614	−	0.645387i
$195$	−3.01425e8			−0.0149288
$196$		0			0
$197$	5.67202e9			0.268312			0.134156	−	0.990960i	$-0.457168\pi$
$197$	5.67202e9			0.268312			0.134156	+	0.990960i	$0.457168\pi$
$198$	−6.38392e9	+	1.10573e10i	−0.295185	+	0.511275i
$199$	−1.16733e10	−	2.02188e10i	−0.527662	−	0.913938i	−0.999480	−	0.0322416i	$-0.989735\pi$
$199$	−1.16733e10	−	2.02188e10i	−0.527662	−	0.913938i	0.471818	−	0.881696i	$-0.343598\pi$
$200$	−6.13355e9	−	1.06236e10i	−0.271067	−	0.469502i
$201$	−1.46249e9	+	2.53310e9i	−0.0631990	+	0.109464i
$202$	−4.60547e10			−1.94622
$203$		0			0
$204$	−3.93150e9			−0.158936
$205$	−5.13569e9	+	8.89528e9i	−0.203098	+	0.351777i
$206$	−2.50067e10	−	4.33128e10i	−0.967505	−	1.67577i
$207$	−1.01673e10	−	1.76102e10i	−0.384891	−	0.666650i
$208$	5.12559e9	−	8.87778e9i	0.189871	−	0.328866i
$209$	−2.01071e10			−0.728939
$210$		0			0
$211$	−5.44845e9			−0.189235			−0.0946175	−	0.995514i	$-0.530163\pi$
$211$	−5.44845e9			−0.189235			−0.0946175	+	0.995514i	$0.530163\pi$
$212$	5.58702e9	−	9.67699e9i	0.189963	−	0.329025i
$213$	−3.40459e9	−	5.89693e9i	−0.113333	−	0.196299i
$214$	2.66317e10	+	4.61274e10i	0.868034	+	1.50348i
$215$	4.58039e8	−	7.93347e8i	0.0146194	−	0.0253216i
$216$	6.82862e9			0.213448
$217$		0			0
$218$	−6.76325e10			−2.02816
$219$	−2.22259e8	+	3.84963e8i	−0.00652920	+	0.0113089i
$220$	−1.19710e9	−	2.07344e9i	−0.0344532	−	0.0596747i
$221$	8.68847e9	+	1.50489e10i	0.245007	+	0.424364i
$222$	−4.41669e9	+	7.64993e9i	−0.122042	+	0.211382i
$223$	−3.89215e10			−1.05394			−0.526972	−	0.849882i	$-0.676673\pi$
$223$	−3.89215e10			−1.05394			−0.526972	+	0.849882i	$0.676673\pi$
$224$		0			0
$225$	3.45326e10			0.898272
$226$	1.31913e10	−	2.28480e10i	0.336356	−	0.582585i
$227$	1.80782e10	+	3.13123e10i	0.451895	+	0.782706i	0.998504	−	0.0546826i	$-0.0174147\pi$
$227$	1.80782e10	+	3.13123e10i	0.451895	+	0.782706i	−0.546608	+	0.837388i	$0.684081\pi$
$228$	−2.96446e9	−	5.13460e9i	−0.0726506	−	0.125834i
$229$	−3.46246e10	+	5.99716e10i	−0.832004	+	1.44107i	0.0644419	+	0.997921i	$0.479473\pi$
$229$	−3.46246e10	+	5.99716e10i	−0.832004	+	1.44107i	−0.896446	+	0.443152i	$0.853860\pi$
$230$	1.10231e10			0.259735
$231$		0			0
$232$	1.85711e10			0.420864
$233$	1.35062e10	−	2.33934e10i	0.300214	−	0.519985i	−0.675970	−	0.736929i	$-0.736275\pi$
$233$	1.35062e10	−	2.33934e10i	0.300214	−	0.519985i	0.976184	+	0.216943i	$0.0696087\pi$
$234$	8.32010e9	+	1.44108e10i	0.181408	+	0.314208i
$235$	4.85558e9	+	8.41011e9i	0.103857	+	0.179886i
$236$	2.24433e10	−	3.88729e10i	0.470958	−	0.815723i
$237$	9.01598e9			0.185629
$238$		0			0
$239$	−1.48226e9			−0.0293856			−0.0146928	−	0.999892i	$-0.504677\pi$
$239$	−1.48226e9			−0.0293856			−0.0146928	+	0.999892i	$0.504677\pi$
$240$	−1.57651e9	+	2.73060e9i	−0.0306723	+	0.0531260i
$241$	1.15154e10	+	1.99452e10i	0.219888	+	0.380857i	0.954774	−	0.297334i	$-0.0960974\pi$
$241$	1.15154e10	+	1.99452e10i	0.219888	+	0.380857i	−0.734885	+	0.678191i	$0.762764\pi$
$242$	2.49144e10	+	4.31530e10i	0.466962	+	0.808801i
$243$	−1.45022e10	+	2.51186e10i	−0.266813	+	0.462133i
$244$	3.25503e10			0.587897
$245$		0			0
$246$	−2.04200e10			−0.355507
$247$	−1.31027e10	+	2.26946e10i	−0.223988	+	0.387959i
$248$	1.96388e10	+	3.40154e10i	0.329673	+	0.571010i
$249$	−2.68270e9	−	4.64657e9i	−0.0442257	−	0.0766011i
$250$	−1.94176e10	+	3.36322e10i	−0.314387	+	0.544535i
$251$	5.02026e10			0.798352			0.399176	−	0.916874i	$-0.369296\pi$
$251$	5.02026e10			0.798352			0.399176	+	0.916874i	$0.369296\pi$
$252$		0			0
$253$	2.57086e10			0.394491
$254$	4.10002e10	−	7.10144e10i	0.618065	−	1.07052i
$255$	−2.67237e9	−	4.62868e9i	−0.0395791	−	0.0685530i
$256$	−4.19551e10	−	7.26683e10i	−0.610526	−	1.05746i
$257$	2.87778e10	−	4.98446e10i	0.411489	−	0.712721i	−0.583563	−	0.812068i	$-0.698342\pi$
$257$	2.87778e10	−	4.98446e10i	0.411489	−	0.712721i	0.995053	+	0.0993469i	$0.0316754\pi$
$258$	1.82121e9			0.0255901
$259$		0			0
$260$	−3.12035e9			−0.0423470
$261$	−2.61394e10	+	4.52747e10i	−0.348669	+	0.603912i
$262$	2.59197e10	+	4.48942e10i	0.339839	+	0.588619i
$263$	−1.41321e10	−	2.44776e10i	−0.182141	−	0.315477i	0.760469	−	0.649375i	$-0.224969\pi$
$263$	−1.41321e10	−	2.44776e10i	−0.182141	−	0.315477i	−0.942609	+	0.333898i	$0.891636\pi$
$264$	−2.12016e9	+	3.67222e9i	−0.0268627	+	0.0465276i
$265$	1.51907e10			0.189222
$266$		0			0
$267$	1.14656e10			0.138069
$268$	−1.51396e10	+	2.62226e10i	−0.179271	+	0.310506i
$269$	−2.44048e10	−	4.22704e10i	−0.284178	−	0.492211i	0.688231	−	0.725491i	$-0.258387\pi$
$269$	−2.44048e10	−	4.22704e10i	−0.284178	−	0.492211i	−0.972410	+	0.233280i	$0.925054\pi$
$270$	−5.21029e9	−	9.02449e9i	−0.0596658	−	0.103344i
$271$	5.13728e10	−	8.89803e10i	0.578591	−	1.00215i	−0.417051	−	0.908883i	$-0.636936\pi$
$271$	5.13728e10	−	8.89803e10i	0.578591	−	1.00215i	0.995641	−	0.0932653i	$-0.0297305\pi$
$272$	1.81769e11			2.01354
$273$		0			0
$274$	8.26761e10			0.886140
$275$	−2.18295e10	+	3.78099e10i	−0.230169	+	0.398665i
$276$	3.79032e9	+	6.56502e9i	0.0393174	+	0.0680997i
$277$	−8.73648e10	−	1.51320e11i	−0.891616	−	1.54432i	−0.837938	−	0.545765i	$-0.816239\pi$
$277$	−8.73648e10	−	1.51320e11i	−0.891616	−	1.54432i	−0.0536774	−	0.998558i	$-0.517094\pi$
$278$	4.83259e10	−	8.37030e10i	0.485265	−	0.840503i
$279$	−1.10569e11			−1.09248
$280$		0			0
$281$	−1.30452e10			−0.124816			−0.0624082	−	0.998051i	$-0.519878\pi$
$281$	−1.30452e10			−0.124816			−0.0624082	+	0.998051i	$0.519878\pi$
$282$	−9.65314e9	+	1.67197e10i	−0.0908966	+	0.157437i
$283$	−4.97443e10	−	8.61597e10i	−0.461004	−	0.798482i	0.538007	−	0.842940i	$-0.319177\pi$
$283$	−4.97443e10	−	8.61597e10i	−0.461004	−	0.798482i	−0.999011	+	0.0444579i	$0.985844\pi$
$284$	−3.52443e10	−	6.10448e10i	−0.321481	−	0.556822i
$285$	4.03008e9	−	6.98031e9i	0.0361836	−	0.0626719i
$286$	−2.10380e10			−0.185933
$287$		0			0
$288$	1.08413e11			0.928568
$289$	−9.47661e10	+	1.64140e11i	−0.799122	+	1.38412i
$290$	−1.41699e10	−	2.45430e10i	−0.117646	−	0.203768i
$291$	6.87284e9	+	1.19041e10i	0.0561846	+	0.0973146i
$292$	−2.30082e9	+	3.98513e9i	−0.0185208	+	0.0320789i
$293$	−9.14442e9			−0.0724856			−0.0362428	−	0.999343i	$-0.511539\pi$
$293$	−9.14442e9			−0.0724856			−0.0362428	+	0.999343i	$0.511539\pi$
$294$		0			0
$295$	6.10217e10			0.469122
$296$	4.07314e10	−	7.05488e10i	0.308401	−	0.534167i
$297$	−1.21517e10	−	2.10473e10i	−0.0906217	−	0.156961i
$298$	4.57801e10	+	7.92934e10i	0.336282	+	0.582457i
$299$	1.67529e10	−	2.90169e10i	0.121219	−	0.209957i
$300$	−1.28736e10			−0.0917604
$301$		0			0
$302$	−1.82065e11			−1.25949
$303$	2.15284e10	−	3.72883e10i	0.146731	−	0.254145i
$304$	1.37059e11	+	2.37393e11i	0.920401	+	1.59418i
$305$	2.21255e10	+	3.83226e10i	0.146401	+	0.253574i
$306$	−1.47528e11	+	2.55527e11i	−0.961898	+	1.66606i
$307$	1.24895e11			0.802456			0.401228	−	0.915978i	$-0.368583\pi$
$307$	1.24895e11			0.802456			0.401228	+	0.915978i	$0.368583\pi$
$308$		0			0
$309$	4.67578e10			0.291770
$310$	2.99692e10	−	5.19081e10i	0.184309	−	0.319233i
$311$	−9.17920e10	−	1.58988e11i	−0.556395	−	0.963704i	−0.997794	−	0.0663929i	$-0.978851\pi$
$311$	−9.17920e10	−	1.58988e11i	−0.556395	−	0.963704i	0.441399	−	0.897311i	$-0.354482\pi$
$312$	2.76318e9	+	4.78597e9i	0.0165087	+	0.0285940i
$313$	5.16816e10	−	8.95152e10i	0.304359	−	0.527166i	−0.672759	−	0.739861i	$-0.734891\pi$
$313$	5.16816e10	−	8.95152e10i	0.304359	−	0.527166i	0.977118	+	0.212696i	$0.0682244\pi$
$314$	−2.17521e11			−1.26275
$315$		0			0
$316$	9.33333e10			0.526556
$317$	7.58797e10	−	1.31427e11i	0.422045	−	0.731003i	−0.574094	−	0.818789i	$-0.694646\pi$
$317$	7.58797e10	−	1.31427e11i	0.422045	−	0.731003i	0.996139	+	0.0877858i	$0.0279791\pi$
$318$	1.50999e10	+	2.61539e10i	0.0828044	+	0.143421i
$319$	−3.30477e10	−	5.72402e10i	−0.178683	−	0.309488i
$320$	1.47412e9	−	2.55325e9i	0.00785884	−	0.0136119i
$321$	−4.97963e10			−0.261773
$322$		0			0
$323$	−4.64663e11			−2.37534
$324$	−4.70458e10	+	8.14857e10i	−0.237175	+	0.410798i
$325$	2.84503e10	+	4.92773e10i	0.141453	+	0.245003i
$326$	2.25702e11	+	3.90927e11i	1.10677	+	1.91698i
$327$	3.16151e10	−	5.47589e10i	0.152908	−	0.264844i
$328$	1.88317e11			0.898372
$329$		0			0
$330$	6.47079e9			0.0300362
$331$	8.95900e10	−	1.55174e11i	0.410236	−	0.710550i	−0.584679	−	0.811264i	$-0.698780\pi$
$331$	8.95900e10	−	1.55174e11i	0.410236	−	0.710550i	0.994915	+	0.100715i	$0.0321130\pi$
$332$	−2.77712e10	−	4.81012e10i	−0.125451	−	0.217287i
$333$	1.14661e11	+	1.98599e11i	0.510996	+	0.885072i
$334$	−2.77393e11	+	4.80459e11i	−1.21965	+	2.11250i
$335$	−4.11637e10			−0.178572
$336$		0			0
$337$	2.75888e10			0.116520			0.0582598	−	0.998301i	$-0.481445\pi$
$337$	2.75888e10			0.116520			0.0582598	+	0.998301i	$0.481445\pi$
$338$	1.34638e11	−	2.33199e11i	0.561102	−	0.971857i
$339$	1.23326e10	+	2.13607e10i	0.0507174	+	0.0878451i
$340$	−2.76643e10	−	4.79160e10i	−0.112270	−	0.194458i
$341$	6.98954e10	−	1.21062e11i	0.279933	−	0.484858i
$342$	−4.44962e11			−1.75876
$343$		0			0
$344$	−1.67955e10			−0.0646665
$345$	−5.15281e9	+	8.92492e9i	−0.0195820	+	0.0339171i
$346$	7.79992e10	+	1.35099e11i	0.292582	+	0.506767i
$347$	8.59095e10	+	1.48800e11i	0.318096	+	0.550959i	0.980091	−	0.198550i	$-0.0636232\pi$
$347$	8.59095e10	+	1.48800e11i	0.318096	+	0.550959i	−0.661995	+	0.749509i	$0.730290\pi$
$348$	9.74467e9	−	1.68783e10i	0.0356173	−	0.0616909i
$349$	−1.67811e11			−0.605487			−0.302743	−	0.953072i	$-0.597903\pi$
$349$	−1.67811e11			−0.605487			−0.302743	+	0.953072i	$0.597903\pi$
$350$		0			0
$351$	−3.16743e10			−0.111385
$352$	−6.85323e10	+	1.18701e11i	−0.237932	+	0.412111i
$353$	−2.08964e11	−	3.61936e11i	−0.716283	−	1.24064i	−0.962462	−	0.271415i	$-0.912508\pi$
$353$	−2.08964e11	−	3.61936e11i	−0.716283	−	1.24064i	0.246179	−	0.969224i	$-0.420825\pi$
$354$	6.06571e10	+	1.05061e11i	0.205290	+	0.355572i
$355$	4.79134e10	−	8.29884e10i	0.160114	−	0.277325i
$356$	1.18692e11			0.391649
$357$		0			0
$358$	4.91487e10			0.158139
$359$	−1.28092e11	+	2.21862e11i	−0.407003	+	0.704950i	−0.994552	−	0.104238i	$-0.966760\pi$
$359$	−1.28092e11	+	2.21862e11i	−0.407003	+	0.704950i	0.587549	+	0.809188i	$0.300093\pi$
$360$	2.36001e10	+	4.08766e10i	0.0740548	+	0.128267i
$361$	−1.89025e11	−	3.27401e11i	−0.585783	−	1.01461i
$362$	1.56540e11	−	2.71136e11i	0.479113	−	0.829847i
$363$	−4.65853e10			−0.140822
$364$		0			0
$365$	−6.25576e9			−0.0184486
$366$	−4.39867e10	+	7.61872e10i	−0.128132	+	0.221930i
$367$	−7.42135e10	−	1.28542e11i	−0.213543	−	0.369868i	0.739278	−	0.673401i	$-0.235167\pi$
$367$	−7.42135e10	−	1.28542e11i	−0.213543	−	0.369868i	−0.952821	+	0.303533i	$0.901834\pi$
$368$	−1.75242e11	−	3.03528e11i	−0.498107	−	0.862746i
$369$	−2.65061e11	+	4.59100e11i	−0.744265	+	1.28911i
$370$	−1.24313e11			−0.344834
$371$		0			0
$372$	4.12197e10			0.111599
$373$	−2.02449e11	+	3.50652e11i	−0.541535	+	0.937966i	0.457281	+	0.889322i	$0.348823\pi$
$373$	−2.02449e11	+	3.50652e11i	−0.541535	+	0.937966i	−0.998816	+	0.0486440i	$0.984510\pi$
$374$	−1.86518e11	−	3.23059e11i	−0.492945	−	0.853806i
$375$	−1.81536e10	−	3.14430e10i	−0.0474049	−	0.0821076i
$376$	8.90227e10	−	1.54192e11i	0.229697	−	0.397847i
$377$	−8.61415e10			−0.219622
$378$		0			0
$379$	6.69861e11			1.66766			0.833832	−	0.552019i	$-0.186142\pi$
$379$	6.69861e11			1.66766			0.833832	+	0.552019i	$0.186142\pi$
$380$	4.17193e10	−	7.22600e10i	0.102639	−	0.177776i
$381$	3.83314e10	+	6.63919e10i	0.0931949	+	0.161418i
$382$	−6.97054e10	−	1.20733e11i	−0.167487	−	0.290096i
$383$	3.73083e11	−	6.46199e11i	0.885954	−	1.53452i	0.0413384	−	0.999145i	$-0.486838\pi$
$383$	3.73083e11	−	6.46199e11i	0.885954	−	1.53452i	0.844616	−	0.535373i	$-0.179829\pi$
$384$	8.22819e10			0.193114
$385$		0			0
$386$	−6.39014e11			−1.46510
$387$	2.36401e10	−	4.09459e10i	0.0535736	−	0.0927922i
$388$	7.11475e10	+	1.23231e11i	0.159374	+	0.276043i
$389$	−2.07879e10	−	3.60057e10i	−0.0460296	−	0.0797257i	0.842093	−	0.539333i	$-0.181324\pi$
$389$	−2.07879e10	−	3.60057e10i	−0.0460296	−	0.0797257i	−0.888122	+	0.459607i	$0.847990\pi$
$390$	4.21666e9	−	7.30347e9i	0.00922949	−	0.0159860i
$391$	5.94111e11			1.28550
$392$		0			0
$393$	−4.84649e10			−0.102485
$394$	−7.93463e10	+	1.37432e11i	−0.165880	+	0.287312i
$395$	6.34417e10	+	1.09884e11i	0.131126	+	0.227116i
$396$	−6.17844e10	−	1.07014e11i	−0.126256	−	0.218681i
$397$	−1.92110e11	+	3.32743e11i	−0.388143	+	0.672283i	−0.992200	−	0.124658i	$-0.960217\pi$
$397$	−1.92110e11	+	3.32743e11i	−0.388143	+	0.672283i	0.604057	+	0.796941i	$0.293550\pi$
$398$	6.53196e11			1.30488
$399$		0			0
$400$	5.95201e11			1.16250
$401$	1.63410e11	−	2.83034e11i	0.315593	−	0.546624i	−0.663970	−	0.747759i	$-0.731130\pi$
$401$	1.63410e11	−	2.83034e11i	0.315593	−	0.546624i	0.979563	+	0.201135i	$0.0644631\pi$
$402$	−4.09177e10	−	7.08715e10i	−0.0781437	−	0.135349i
$403$	−9.10941e10	−	1.57780e11i	−0.172035	−	0.297974i
$404$	2.22862e11	−	3.86008e11i	0.416217	−	0.720909i
$405$	−1.27914e11			−0.236250
$406$		0			0
$407$	−2.89929e11			−0.523742
$408$	−4.89955e10	+	8.48627e10i	−0.0875358	+	0.151616i
$409$	4.89087e11	+	8.47124e11i	0.864234	+	1.49690i	0.867805	+	0.496904i	$0.165530\pi$
$409$	4.89087e11	+	8.47124e11i	0.864234	+	1.49690i	−0.00357099	+	0.999994i	$0.501137\pi$
$410$	−1.43687e11	−	2.48873e11i	−0.251125	−	0.434962i
$411$	−3.86472e10	+	6.69390e10i	−0.0668083	+	0.115715i
$412$	4.84036e11			0.827638
$413$		0			0
$414$	5.68922e11			0.951812
$415$	3.77540e10	−	6.53919e10i	0.0624808	−	0.108220i
$416$	8.93175e10	+	1.54703e11i	0.146223	+	0.253266i
$417$	4.51803e10	+	7.82545e10i	0.0731706	+	0.126735i
$418$	2.81280e11	−	4.87191e11i	0.450656	−	0.780559i
$419$	3.51461e11			0.557075			0.278537	−	0.960425i	$-0.410150\pi$
$419$	3.51461e11			0.557075			0.278537	+	0.960425i	$0.410150\pi$
$420$		0			0
$421$	2.97438e11			0.461453			0.230726	−	0.973019i	$-0.425890\pi$
$421$	2.97438e11			0.461453			0.230726	+	0.973019i	$0.425890\pi$
$422$	7.62187e10	−	1.32015e11i	0.116992	−	0.202636i
$423$	2.50604e11	+	4.34060e11i	0.380590	+	0.659201i
$424$	−1.39254e11	−	2.41195e11i	−0.209248	−	0.362428i
$425$	−5.04467e11	+	8.73763e11i	−0.750037	+	1.29910i
$426$	1.90508e11			0.280266
$427$		0			0
$428$	−5.15490e11			−0.742547
$429$	9.83428e9	−	1.70335e10i	0.0140180	−	0.0242798i
$430$	1.28151e10	+	2.21964e10i	0.0180765	+	0.0313094i
$431$	2.70847e11	+	4.69121e11i	0.378074	+	0.654843i	0.990782	−	0.135466i	$-0.0432531\pi$
$431$	2.70847e11	+	4.69121e11i	0.378074	+	0.654843i	−0.612708	+	0.790309i	$0.709920\pi$
$432$	−1.65663e11	+	2.86936e11i	−0.228848	+	0.396377i
$433$	−1.98641e11			−0.271565			−0.135782	−	0.990739i	$-0.543355\pi$
$433$	−1.98641e11			−0.271565			−0.135782	+	0.990739i	$0.543355\pi$
$434$		0			0
$435$	2.64951e10			0.0354784
$436$	3.27278e11	−	5.66863e11i	0.433739	−	0.751258i
$437$	4.47976e11	+	7.75918e11i	0.587609	+	1.01777i
$438$	−6.21838e9	−	1.07706e10i	−0.00807317	−	0.0139831i
$439$	−4.05086e11	+	7.01630e11i	−0.520544	+	0.901608i	0.479171	+	0.877722i	$0.340937\pi$
$439$	−4.05086e11	+	7.01630e11i	−0.520544	+	0.901608i	−0.999715	+	0.0238867i	$0.992396\pi$
$440$	−5.96746e10			−0.0759019
$441$		0			0
$442$	−4.86174e11			−0.605887
$443$	5.92033e11	−	1.02543e12i	0.730346	−	1.26500i	−0.226389	−	0.974037i	$-0.572692\pi$
$443$	5.92033e11	−	1.02543e12i	0.730346	−	1.26500i	0.956735	−	0.290960i	$-0.0939746\pi$
$444$	−4.27453e10	−	7.40370e10i	−0.0521993	−	0.0904119i
$445$	8.06789e10	+	1.39740e11i	0.0975304	+	0.168928i
$446$	5.44476e11	−	9.43060e11i	0.651586	−	1.12858i
$447$	−8.56003e10			−0.101412
$448$		0			0
$449$	1.11962e12			1.30006			0.650031	−	0.759908i	$-0.274756\pi$
$449$	1.11962e12			1.30006			0.650031	+	0.759908i	$0.274756\pi$
$450$	−4.83079e11	+	8.36717e11i	−0.555344	+	0.961884i
$451$	−3.35113e11	−	5.80433e11i	−0.381415	−	0.660629i
$452$	1.27667e11	+	2.21126e11i	0.143865	+	0.249182i
$453$	8.51069e10	−	1.47409e11i	0.0949561	−	0.164469i
$454$	−1.01159e12			−1.11751
$455$		0			0
$456$	−1.47776e11			−0.160052
$457$	−3.80731e11	+	6.59446e11i	−0.408315	+	0.707223i	−0.994701	−	0.102809i	$-0.967217\pi$
$457$	−3.80731e11	+	6.59446e11i	−0.408315	+	0.707223i	0.586386	+	0.810032i	$0.300550\pi$
$458$	−9.68733e11	−	1.67789e12i	−1.02875	−	1.78185i
$459$	−2.80818e11	−	4.86390e11i	−0.295303	−	0.511479i
$460$	−5.33417e10	+	9.23906e10i	−0.0555465	+	0.0962094i
$461$	2.12296e11			0.218921			0.109460	−	0.993991i	$-0.465088\pi$
$461$	2.12296e11			0.218921			0.109460	+	0.993991i	$0.465088\pi$
$462$		0			0
$463$	−1.52072e12			−1.53793			−0.768964	−	0.639292i	$-0.779228\pi$
$463$	−1.52072e12			−1.53793			−0.768964	+	0.639292i	$0.779228\pi$
$464$	−4.50536e11	+	7.80351e11i	−0.451231	+	0.781554i
$465$	2.80184e10	+	4.85293e10i	0.0277911	+	0.0481355i
$466$	3.77877e11	+	6.54503e11i	0.371206	+	0.642947i
$467$	2.39955e11	−	4.15614e11i	0.233455	−	0.404356i	−0.725368	−	0.688362i	$-0.758330\pi$
$467$	2.39955e11	−	4.15614e11i	0.233455	−	0.404356i	0.958823	+	0.284006i	$0.0916635\pi$
$468$	−1.61046e11			−0.155183
$469$		0			0
$470$	−2.71700e11			−0.256832
$471$	1.01681e11	−	1.76116e11i	0.0952017	−	0.164894i
$472$	−5.59389e11	−	9.68891e11i	−0.518771	−	0.898537i
$473$	2.98879e10	+	5.17674e10i	0.0274549	+	0.0475533i
$474$	−1.26125e11	+	2.18455e11i	−0.114762	+	0.198774i
$475$	−1.52153e12			−1.37138
$476$		0			0
$477$	7.84017e11			0.693415
$478$	2.07355e10	−	3.59149e10i	0.0181672	−	0.0314666i
$479$	3.22408e11	+	5.58427e11i	0.279831	+	0.484682i	0.971343	−	0.237684i	$-0.0763882\pi$
$479$	3.22408e11	+	5.58427e11i	0.279831	+	0.484682i	−0.691511	+	0.722365i	$0.743055\pi$
$480$	−2.74720e10	−	4.75829e10i	−0.0236213	−	0.0409134i
$481$	−1.88931e11	+	3.27238e11i	−0.160935	+	0.278748i
$482$	−6.44358e11			−0.543770
$483$		0			0
$484$	−4.82250e11			−0.399455
$485$	−9.67226e10	+	1.67528e11i	−0.0793761	+	0.137483i
$486$	−4.05746e11	−	7.02772e11i	−0.329906	−	0.571414i
$487$	9.75399e11	+	1.68944e12i	0.785782	+	1.36101i	0.928531	+	0.371256i	$0.121073\pi$
$487$	9.75399e11	+	1.68944e12i	0.785782	+	1.36101i	−0.142748	+	0.989759i	$0.545594\pi$
$488$	4.05652e11	−	7.02610e11i	0.323791	−	0.560822i
$489$	−4.22021e11			−0.333767
$490$		0			0
$491$	−1.45708e12			−1.13140			−0.565700	−	0.824611i	$-0.691394\pi$
$491$	−1.45708e12			−1.13140			−0.565700	+	0.824611i	$0.691394\pi$
$492$	9.88139e10	−	1.71151e11i	0.0760283	−	0.131685i
$493$	−7.63711e11	−	1.32279e12i	−0.582261	−	1.00851i
$494$	−3.66589e11	−	6.34951e11i	−0.276955	−	0.479699i
$495$	8.39938e10	−	1.45482e11i	0.0628817	−	0.108914i
$496$	−1.90576e12			−1.41384
$497$		0			0
$498$	1.50114e11			0.109368
$499$	−1.78952e11	+	3.09953e11i	−0.129206	+	0.223792i	−0.923369	−	0.383913i	$-0.874576\pi$
$499$	−1.78952e11	+	3.09953e11i	−0.129206	+	0.223792i	0.794163	+	0.607705i	$0.207910\pi$
$500$	−1.87926e11	−	3.25497e11i	−0.134469	−	0.232907i
$501$	−2.59337e11	−	4.49184e11i	−0.183905	−	0.318533i
$502$	−7.02288e11	+	1.21640e12i	−0.493569	+	0.854887i
$503$	1.62028e12			1.12858			0.564292	−	0.825575i	$-0.309149\pi$
$503$	1.62028e12			1.12858			0.564292	+	0.825575i	$0.309149\pi$
$504$		0			0
$505$	6.05946e11			0.414594
$506$	−3.59640e11	+	6.22915e11i	−0.243888	+	0.422427i
$507$	1.25874e11	+	2.18020e11i	0.0846057	+	0.146541i
$508$	3.96805e11	+	6.87287e11i	0.264357	+	0.457880i
$509$	−1.16034e12	+	2.00977e12i	−0.766223	+	1.32714i	0.173375	+	0.984856i	$0.444533\pi$
$509$	−1.16034e12	+	2.00977e12i	−0.766223	+	1.32714i	−0.939598	+	0.342281i	$0.888801\pi$
$510$	1.49536e11			0.0978768
$511$		0			0
$512$	7.37052e11			0.474005
$513$	4.23489e11	−	7.33504e11i	0.269969	−	0.467600i
$514$	8.05150e11	+	1.39456e12i	0.508795	+	0.881258i
$515$	3.29015e11	+	5.69871e11i	0.206103	+	0.356980i
$516$	−8.81296e9	+	1.52645e10i	−0.00547266	+	0.00947892i
$517$	−6.33671e11			−0.390083
$518$		0			0
$519$	−1.45844e11			−0.0882339
$520$	−3.88867e10	+	6.73537e10i	−0.0233231	+	0.0403968i
$521$	1.08605e12	+	1.88110e12i	0.645775	+	1.11851i	0.984122	+	0.177493i	$0.0567989\pi$
$521$	1.08605e12	+	1.88110e12i	0.645775	+	1.11851i	−0.338347	+	0.941021i	$0.609868\pi$
$522$	−7.31331e11	−	1.26670e12i	−0.431119	−	0.746720i
$523$	1.45855e12	−	2.52628e12i	0.852439	−	1.47647i	−0.0265609	−	0.999647i	$-0.508456\pi$
$523$	1.45855e12	−	2.52628e12i	0.852439	−	1.47647i	0.879000	−	0.476821i	$-0.158211\pi$
$524$	−5.01708e11			−0.290710
$525$		0			0
$526$	7.90782e11			0.450424
$527$	1.61524e12	−	2.79768e12i	0.912198	−	1.57997i
$528$	−1.02870e11	−	1.78176e11i	−0.0576019	−	0.0997695i
$529$	3.27801e11	+	5.67767e11i	0.181995	+	0.315224i
$530$	−2.12504e11	+	3.68068e11i	−0.116984	+	0.202622i
$531$	3.14943e12			1.71912
$532$		0			0
$533$	−8.73501e11			−0.468803
$534$	−1.60394e11	+	2.77810e11i	−0.0853594	+	0.147847i
$535$	−3.50396e11	−	6.06904e11i	−0.184913	−	0.320278i
$536$	3.77349e11	+	6.53588e11i	0.197470	+	0.342029i
$537$	−2.29747e10	+	3.97934e10i	−0.0119225	+	0.0206503i
$538$	1.36560e12			0.702756
$539$		0			0
$540$	1.00852e11			0.0510402
$541$	6.76763e11	−	1.17219e12i	0.339663	−	0.588314i	−0.644706	−	0.764431i	$-0.723020\pi$
$541$	6.76763e11	−	1.17219e12i	0.339663	−	0.588314i	0.984369	+	0.176117i	$0.0563535\pi$
$542$	1.43732e12	+	2.48950e12i	0.715411	+	1.23913i
$543$	1.46351e11	+	2.53487e11i	0.0722430	+	0.125128i
$544$	−1.58374e12	+	2.74312e12i	−0.775333	+	1.34292i
$545$	8.89848e11			0.432048
$546$		0			0
$547$	−2.85747e12			−1.36470			−0.682352	−	0.731023i	$-0.739043\pi$
$547$	−2.85747e12			−1.36470			−0.682352	+	0.731023i	$0.739043\pi$
$548$	−4.00075e11	+	6.92951e11i	−0.189509	+	0.328239i
$549$	1.14193e12	+	1.97789e12i	0.536495	+	0.929237i
$550$	−6.10750e11	−	1.05785e12i	−0.284598	−	0.492938i
$551$	1.15172e12	−	1.99484e12i	0.532310	−	0.921988i
$552$	1.88944e11			0.0866179
$553$		0			0
$554$	4.88861e12			2.20491
$555$	5.81108e10	−	1.00651e11i	0.0259979	−	0.0450297i
$556$	4.67705e11	+	8.10089e11i	0.207556	+	0.359498i
$557$	−5.64143e11	−	9.77123e11i	−0.248336	−	0.430131i	0.714728	−	0.699403i	$-0.246551\pi$
$557$	−5.64143e11	−	9.77123e11i	−0.248336	−	0.430131i	−0.963064	+	0.269271i	$0.913217\pi$
$558$	1.54676e12	−	2.67906e12i	0.675411	−	1.16985i
$559$	7.79053e10			0.0337453
$560$		0			0
$561$	3.48754e11			0.148657
$562$	1.82490e11	−	3.16082e11i	0.0771659	−	0.133655i
$563$	−1.33529e12	−	2.31279e12i	−0.560127	−	0.970169i	−0.997485	−	0.0708814i	$-0.977419\pi$
$563$	−1.33529e12	−	2.31279e12i	−0.560127	−	0.970169i	0.437357	−	0.899288i	$-0.355915\pi$
$564$	−9.34244e10	−	1.61816e11i	−0.0388780	−	0.0673387i
$565$	−1.73559e11	+	3.00613e11i	−0.0716521	+	0.124105i
$566$	2.78351e12			1.14004
$567$		0			0
$568$	−1.75690e12			−0.708237
$569$	−2.19771e12	+	3.80654e12i	−0.878952	+	1.52239i	−0.0264587	+	0.999650i	$0.508423\pi$
$569$	−2.19771e12	+	3.80654e12i	−0.878952	+	1.52239i	−0.852493	+	0.522739i	$0.824910\pi$
$570$	1.12754e11	+	1.95296e11i	0.0447400	+	0.0774920i
$571$	−1.11664e12	−	1.93408e12i	−0.439594	−	0.761399i	0.558064	−	0.829798i	$-0.311544\pi$
$571$	−1.11664e12	−	1.93408e12i	−0.439594	−	0.761399i	−0.997658	+	0.0683988i	$0.978211\pi$
$572$	1.01804e11	−	1.76330e11i	0.0397634	−	0.0688722i
$573$	1.30336e11			0.0505091
$574$		0			0
$575$	1.94541e12			0.742173
$576$	7.60818e10	−	1.31778e11i	0.0287991	−	0.0498816i
$577$	−1.20531e12	−	2.08766e12i	−0.452697	−	0.784094i	0.545855	−	0.837879i	$-0.316205\pi$
$577$	−1.20531e12	−	2.08766e12i	−0.452697	−	0.784094i	−0.998553	+	0.0537849i	$0.982871\pi$
$578$	−2.65138e12	−	4.59233e12i	−0.988091	−	1.71142i
$579$	2.98709e11	−	5.17380e11i	0.110458	−	0.191318i
$580$	2.74277e11			0.100638
$581$		0			0
$582$	−3.84578e11			−0.138941
$583$	−4.95611e11	+	8.58424e11i	−0.177678	+	0.307746i
$584$	5.73469e10	+	9.93277e10i	0.0204010	+	0.0353356i
$585$	−1.09468e11	−	1.89605e11i	−0.0386445	−	0.0669342i
$586$	1.27922e11	−	2.21567e11i	0.0448132	−	0.0776187i
$587$	6.14106e11			0.213487			0.106744	−	0.994287i	$-0.465958\pi$
$587$	6.14106e11			0.213487			0.106744	+	0.994287i	$0.465958\pi$
$588$		0			0
$589$	4.87174e12			1.66788
$590$	−8.53637e11	+	1.47854e12i	−0.290028	+	0.502343i
$591$	−7.41814e10	−	1.28486e11i	−0.0250122	−	0.0433224i
$592$	1.97629e12	+	3.42304e12i	0.661307	+	1.14542i
$593$	−3.76059e11	+	6.51353e11i	−0.124885	+	0.216307i	−0.921688	−	0.387932i	$-0.873189\pi$
$593$	−3.76059e11	+	6.51353e11i	−0.124885	+	0.216307i	0.796803	+	0.604239i	$0.206523\pi$
$594$	6.79962e11			0.224102
$595$		0			0
$596$	−8.86132e11			−0.287667
$597$	−3.05339e11	+	5.28863e11i	−0.0983779	+	0.170396i
$598$	4.68716e11	+	8.11839e11i	0.149884	+	0.259606i
$599$	−1.45096e12	−	2.51314e12i	−0.460507	−	0.797621i	0.538479	−	0.842639i	$-0.318999\pi$
$599$	−1.45096e12	−	2.51314e12i	−0.460507	−	0.797621i	−0.998986	+	0.0450173i	$0.985666\pi$
$600$	−1.60435e11	+	2.77882e11i	−0.0505380	+	0.0875345i
$601$	−3.12492e12			−0.977021			−0.488510	−	0.872558i	$-0.662460\pi$
$601$	−3.12492e12			−0.977021			−0.488510	+	0.872558i	$0.662460\pi$
$602$		0			0
$603$	−2.12452e12			−0.654385
$604$	8.81024e11	−	1.52598e12i	0.269353	−	0.466533i
$605$	−3.27801e11	−	5.67769e11i	−0.0994744	−	0.172295i
$606$	6.02326e11	+	1.04326e12i	0.181428	+	0.314243i
$607$	2.43067e12	−	4.21004e12i	0.726735	−	1.25874i	−0.231520	−	0.972830i	$-0.574370\pi$
$607$	2.43067e12	−	4.21004e12i	0.726735	−	1.25874i	0.958256	−	0.285913i	$-0.0922967\pi$
$608$	−4.77674e12			−1.41764
$609$		0			0
$610$	−1.23806e12			−0.362042
$611$	−4.12929e11	+	7.15214e11i	−0.119864	+	0.207611i
$612$	−1.42780e12	−	2.47302e12i	−0.411420	−	0.712601i
$613$	−1.93588e11	−	3.35305e11i	−0.0553742	−	0.0959109i	0.837010	−	0.547188i	$-0.184302\pi$
$613$	−1.93588e11	−	3.35305e11i	−0.0553742	−	0.0959109i	−0.892384	+	0.451277i	$0.850969\pi$
$614$	−1.74716e12	+	3.02617e12i	−0.496107	+	0.859282i
$615$	2.68668e11			0.0757318
$616$		0			0
$617$	1.25661e12			0.349073			0.174537	−	0.984651i	$-0.444157\pi$
$617$	1.25661e12			0.349073			0.174537	+	0.984651i	$0.444157\pi$
$618$	−6.54099e11	+	1.13293e12i	−0.180383	+	0.312432i
$619$	−1.94092e12	−	3.36177e12i	−0.531374	−	0.920366i	−0.999329	−	0.0366142i	$-0.988343\pi$
$619$	−1.94092e12	−	3.36177e12i	−0.531374	−	0.920366i	0.467956	−	0.883752i	$-0.344991\pi$
$620$	2.90046e11	+	5.02374e11i	0.0788323	+	0.136541i
$621$	−5.41466e11	+	9.37847e11i	−0.146103	+	0.253058i
$622$	5.13634e12			1.37593
$623$		0			0
$624$	−2.68140e11			−0.0707995
$625$	−1.51954e12	+	2.63192e12i	−0.398338	+	0.689942i
$626$	1.44595e12	+	2.50447e12i	0.376331	+	0.651825i
$627$	2.62970e11	+	4.55478e11i	0.0679521	+	0.117697i
$628$	1.05260e12	−	1.82315e12i	0.270050	−	0.467740i
$629$	−6.70009e12			−1.70668
$630$		0			0
$631$	−5.76195e12			−1.44690			−0.723448	−	0.690379i	$-0.757444\pi$
$631$	−5.76195e12			−1.44690			−0.723448	+	0.690379i	$0.757444\pi$
$632$	1.16315e12	−	2.01463e12i	0.290006	−	0.502306i
$633$	7.12574e10	+	1.23421e11i	0.0176406	+	0.0305544i
$634$	2.12297e12	+	3.67710e12i	0.521846	+	0.903864i
$635$	−5.39444e11	+	9.34344e11i	−0.131663	+	0.228047i
$636$	−2.92279e11			−0.0708338
$637$		0			0
$638$	1.84922e12			0.441872
$639$	2.47289e12	−	4.28316e12i	0.586746	−	1.01627i
$640$	5.78983e11	+	1.00283e12i	0.136413	+	0.236275i
$641$	2.30350e12	+	3.98978e12i	0.538923	+	0.933442i	0.998962	+	0.0455436i	$0.0145020\pi$
$641$	2.30350e12	+	3.98978e12i	0.538923	+	0.933442i	−0.460039	+	0.887899i	$0.652165\pi$
$642$	6.96604e11	−	1.20655e12i	0.161837	−	0.280310i
$643$	1.65916e12			0.382770			0.191385	−	0.981515i	$-0.438702\pi$
$643$	1.65916e12			0.382770			0.191385	+	0.981515i	$0.438702\pi$
$644$		0			0
$645$	−2.39618e10			−0.00545132
$646$	6.50020e12	−	1.12587e13i	1.46852	−	2.54355i
$647$	6.64116e11	+	1.15028e12i	0.148996	+	0.258069i	0.930857	−	0.365385i	$-0.119062\pi$
$647$	6.64116e11	+	1.15028e12i	0.148996	+	0.258069i	−0.781861	+	0.623453i	$0.785729\pi$
$648$	1.17260e12	+	2.03100e12i	0.261253	+	0.452503i
$649$	−1.99089e12	+	3.44832e12i	−0.440500	+	0.762969i
$650$	−1.59197e12			−0.349804
$651$		0			0
$652$	−4.36875e12			−0.946766
$653$	−2.10400e12	+	3.64423e12i	−0.452830	+	0.784325i	−0.998561	−	0.0536359i	$-0.982919\pi$
$653$	−2.10400e12	+	3.64423e12i	−0.452830	+	0.784325i	0.545730	+	0.837961i	$0.316252\pi$
$654$	8.84531e11	+	1.53205e12i	0.189066	+	0.327472i
$655$	−3.41028e11	−	5.90677e11i	−0.0723942	−	0.125390i
$656$	−4.56857e12	+	7.91300e12i	−0.963193	+	1.66830i
$657$	−3.22870e11			−0.0676057
$658$		0			0
$659$	1.53134e11			0.0316291			0.0158146	−	0.999875i	$-0.494966\pi$
$659$	1.53134e11			0.0316291			0.0158146	+	0.999875i	$0.494966\pi$
$660$	−3.13126e10	+	5.42350e10i	−0.00642349	+	0.0111258i
$661$	1.52944e12	+	2.64906e12i	0.311620	+	0.539742i	0.978713	−	0.205233i	$-0.0657951\pi$
$661$	1.52944e12	+	2.64906e12i	0.311620	+	0.539742i	−0.667093	+	0.744974i	$0.732462\pi$
$662$	2.50656e12	+	4.34149e12i	0.507245	+	0.878574i
$663$	2.27264e11	−	3.93633e11i	0.0456793	−	0.0791189i
$664$	−1.38437e12			−0.276374
$665$		0			0
$666$	−6.41602e12			−1.26366
$667$	−1.47257e12	+	2.55057e12i	−0.288078	+	0.498966i
$668$	−2.68465e12	−	4.64995e12i	−0.521667	−	0.903554i
$669$	5.09034e11	+	8.81673e11i	0.0982493	+	0.170173i
$670$	5.75841e11	−	9.97387e11i	0.110399	−	0.191217i
$671$	−2.88746e12			−0.549877
$672$		0			0
$673$	6.90574e12			1.29761			0.648803	−	0.760957i	$-0.275270\pi$
$673$	6.90574e12			1.29761			0.648803	+	0.760957i	$0.275270\pi$
$674$	−3.85942e11	+	6.68472e11i	−0.0720365	+	0.124771i
$675$	−9.19533e11	−	1.59268e12i	−0.170490	−	0.295298i
$676$	1.30304e12	+	2.25694e12i	0.239993	+	0.415680i
$677$	−4.61556e12	+	7.99438e12i	−0.844452	+	1.46263i	0.0416442	+	0.999133i	$0.486740\pi$
$677$	−4.61556e12	+	7.99438e12i	−0.844452	+	1.46263i	−0.886096	+	0.463501i	$0.846593\pi$
$678$	−6.90088e11			−0.125421
$679$		0			0
$680$	−1.37904e12			−0.247336
$681$	4.72870e11	−	8.19035e11i	0.0842519	−	0.145929i
$682$	1.95554e12	+	3.38710e12i	0.346129	+	0.599513i
$683$	1.53456e12	+	2.65793e12i	0.269830	+	0.467359i	0.968818	−	0.247775i	$-0.0796992\pi$
$683$	1.53456e12	+	2.65793e12i	0.269830	+	0.467359i	−0.698988	+	0.715133i	$0.746366\pi$
$684$	2.15320e12	−	3.72946e12i	0.376125	−	0.651468i
$685$	−1.08778e12			−0.188770
$686$		0			0
$687$	1.81135e12			0.310240
$688$	4.07459e11	−	7.05740e11i	0.0693324	−	0.120087i
$689$	6.45925e11	+	1.11878e12i	0.109193	+	0.189128i
$690$	−1.44166e11	−	2.49703e11i	−0.0242126	−	0.0419375i
$691$	2.40201e12	−	4.16041e12i	0.400796	−	0.694200i	−0.593026	−	0.805183i	$-0.702067\pi$
$691$	2.40201e12	−	4.16041e12i	0.400796	−	0.694200i	0.993822	+	0.110984i	$0.0354001\pi$
$692$	−1.50977e12			−0.250285
$693$		0			0
$694$	−4.80718e12			−0.786633
$695$	−6.35829e11	+	1.10129e12i	−0.103373	+	0.179048i
$696$	−2.42882e11	−	4.20684e11i	−0.0392332	−	0.0679539i
$697$	−7.74426e12	−	1.34135e13i	−1.24289	−	2.15275i
$698$	2.34751e12	−	4.06601e12i	0.374333	−	0.648365i
$699$	−7.06561e11			−0.111944
$700$		0			0
$701$	5.62845e12			0.880354			0.440177	−	0.897911i	$-0.354916\pi$
$701$	5.62845e12			0.880354			0.440177	+	0.897911i	$0.354916\pi$
$702$	4.43094e11	−	7.67462e11i	0.0688619	−	0.119272i
$703$	−5.05205e12	−	8.75042e12i	−0.780134	−	1.35123i
$704$	9.61891e10	+	1.66604e11i	0.0147587	+	0.0255629i
$705$	1.27007e11	−	2.19983e11i	0.0193632	−	0.0335381i
$706$	1.16928e13			1.77133
$707$		0			0
$708$	−1.17410e12			−0.175612
$709$	−6.19129e12	+	1.07236e13i	−0.920180	+	1.59380i	−0.121046	+	0.992647i	$0.538625\pi$
$709$	−6.19129e12	+	1.07236e13i	−0.920180	+	1.59380i	−0.799135	+	0.601152i	$0.794709\pi$
$710$	1.34053e12	+	2.32186e12i	0.197976	+	0.342905i
$711$	3.27433e12	+	5.67130e12i	0.480517	+	0.832280i
$712$	1.47918e12	−	2.56201e12i	0.215705	−	0.373612i
$713$	−6.22894e12			−0.902633
$714$		0			0
$715$	2.76799e11			0.0396084
$716$	−2.37834e11	+	4.11940e11i	−0.0338193	+	0.0585768i
$717$	1.93858e10	+	3.35771e10i	0.00273935	+	0.00474469i
$718$	−3.58378e12	−	6.20729e12i	−0.503247	−	0.871650i
$719$	2.54128e11	−	4.40162e11i	0.0354627	−	0.0614232i	−0.847749	−	0.530397i	$-0.822043\pi$
$719$	2.54128e11	−	4.40162e11i	0.0354627	−	0.0614232i	0.883212	+	0.468974i	$0.155376\pi$
$720$	−2.29016e12			−0.317592
$721$		0			0
$722$	1.05771e13			1.44861
$723$	3.01208e11	−	5.21707e11i	0.0409962	−	0.0710075i
$724$	1.51502e12	+	2.62409e12i	0.204925	+	0.354940i
$725$	−2.50076e12	−	4.33144e12i	−0.336164	−	0.582253i
$726$	6.51685e11	−	1.12875e12i	0.0870609	−	0.150794i
$727$	6.46095e12			0.857811			0.428905	−	0.903349i	$-0.358899\pi$
$727$	6.46095e12			0.857811			0.428905	+	0.903349i	$0.358899\pi$
$728$		0			0
$729$	−6.08094e12			−0.797438
$730$	8.75123e10	−	1.51576e11i	0.0114055	−	0.0197550i
$731$	6.90691e11	+	1.19631e12i	0.0894655	+	0.154959i
$732$	−4.25709e11	−	7.37350e11i	−0.0548041	−	0.0949235i
$733$	4.43052e12	−	7.67388e12i	0.566874	−	0.981854i	−0.429999	−	0.902829i	$-0.641486\pi$
$733$	4.43052e12	−	7.67388e12i	0.566874	−	0.981854i	0.996873	−	0.0790248i	$-0.0251806\pi$
$734$	4.15271e12			0.528080
$735$		0			0
$736$	6.10746e12			0.767204
$737$	1.34300e12	−	2.32615e12i	0.167677	−	0.290425i
$738$	−7.41592e12	−	1.28448e13i	−0.920262	−	1.59394i
$739$	−2.37645e12	−	4.11613e12i	−0.293108	−	0.507679i	0.681435	−	0.731879i	$-0.261356\pi$
$739$	−2.37645e12	−	4.11613e12i	−0.293108	−	0.507679i	−0.974543	+	0.224200i	$0.928023\pi$
$740$	6.01562e11	−	1.04194e12i	0.0737458	−	0.127732i
$741$	6.85454e11			0.0835211
$742$		0			0
$743$	−5.50742e12			−0.662977			−0.331488	−	0.943459i	$-0.607551\pi$
$743$	−5.50742e12			−0.662977			−0.331488	+	0.943459i	$0.607551\pi$
$744$	5.13692e11	−	8.89741e11i	0.0614646	−	0.106460i
$745$	−6.02333e11	−	1.04327e12i	−0.0716364	−	0.124078i
$746$	−5.66415e12	−	9.81060e12i	−0.669592	−	1.15977i
$747$	1.94855e12	−	3.37498e12i	0.228964	−	0.396578i
$748$	3.61029e12			0.421682
$749$		0			0
$750$	1.01581e12			0.117229
$751$	−2.76192e11	+	4.78379e11i	−0.0316834	+	0.0548773i	−0.881432	−	0.472310i	$-0.843420\pi$
$751$	−2.76192e11	+	4.78379e11i	−0.0316834	+	0.0548773i	0.849749	+	0.527188i	$0.176753\pi$
$752$	4.31939e12	+	7.48141e12i	0.492541	+	0.853106i
$753$	−6.56574e11	−	1.13722e12i	−0.0744228	−	0.128904i
$754$	1.20504e12	−	2.08719e12i	0.135778	−	0.235175i
$755$	2.39545e12			0.268303
$756$		0			0
$757$	1.08256e13			1.19818			0.599090	−	0.800682i	$-0.295529\pi$
$757$	1.08256e13			1.19818			0.599090	+	0.800682i	$0.295529\pi$
$758$	−9.37073e12	+	1.62306e13i	−1.03101	+	1.78576i
$759$	−3.36230e11	−	5.82367e11i	−0.0367746	−	0.0636956i
$760$	−1.03984e12	−	1.80105e12i	−0.113059	−	0.195824i
$761$	−5.74707e12	+	9.95421e12i	−0.621177	+	1.07591i	0.368090	+	0.929790i	$0.380012\pi$
$761$	−5.74707e12	+	9.95421e12i	−0.621177	+	1.07591i	−0.989267	+	0.146120i	$0.953321\pi$
$762$	−2.14488e12			−0.230465
$763$		0			0
$764$	1.34924e12			0.143274
$765$	1.94105e12	−	3.36199e12i	0.204908	−	0.354911i
$766$	1.04382e13	+	1.80795e13i	1.09546	+	1.89739i
$767$	2.59471e12	+	4.49417e12i	0.270713	+	0.468889i
$768$	−1.09742e12	+	1.90078e12i	−0.113827	+	0.197155i
$769$	1.23333e13			1.27178			0.635889	−	0.771781i	$-0.280634\pi$
$769$	1.23333e13			1.27178			0.635889	+	0.771781i	$0.280634\pi$
$770$		0			0
$771$	−1.50548e12			−0.153437
$772$	3.09223e12	−	5.35591e12i	0.313325	−	0.542694i
$773$	4.58322e12	+	7.93837e12i	0.461703	+	0.799694i	0.999046	−	0.0436703i	$-0.0139051\pi$
$773$	4.58322e12	+	7.93837e12i	0.461703	+	0.799694i	−0.537343	+	0.843364i	$0.680572\pi$
$774$	6.61407e11	+	1.14559e12i	0.0662422	+	0.114735i
$775$	5.28907e12	−	9.16095e12i	0.526650	−	0.912184i
$776$	3.54664e12			0.351107
$777$		0			0
$778$	1.16321e12			0.113829
$779$	1.16788e13	−	2.02282e13i	1.13626	−	1.96807i
$780$	4.08094e10	+	7.06840e10i	0.00394761	+	0.00683747i
$781$	3.12644e12	+	5.41514e12i	0.300691	+	0.520811i
$782$	−8.31106e12	+	1.43952e13i	−0.794741	+	1.37653i
$783$	2.78415e12			0.264707
$784$		0			0
$785$	2.86194e12			0.268997
$786$	6.77980e11	−	1.17429e12i	0.0633600	−	0.109743i
$787$	5.22251e12	+	9.04565e12i	0.485281	+	0.840531i	0.999857	−	0.0169139i	$-0.00538413\pi$
$787$	5.22251e12	+	9.04565e12i	0.485281	+	0.840531i	−0.514576	+	0.857445i	$0.672051\pi$
$788$	−7.67925e11	−	1.33008e12i	−0.0709497	−	0.122888i
$789$	−3.69654e11	+	6.40260e11i	−0.0339585	+	0.0588179i
$790$	−3.54996e12			−0.324266
$791$		0			0
$792$	−3.07990e12			−0.278147
$793$	−1.88160e12	+	3.25903e12i	−0.168966	+	0.292657i
$794$	−5.37487e12	−	9.30954e12i	−0.479927	−	0.831259i
$795$	−1.98672e11	−	3.44109e11i	−0.0176394	−	0.0305523i
$796$	−3.16086e12	+	5.47477e12i	−0.279059	+	0.483345i
$797$	3.08633e11			0.0270944			0.0135472	−	0.999908i	$-0.495688\pi$
$797$	3.08633e11			0.0270944			0.0135472	+	0.999908i	$0.495688\pi$
$798$		0			0
$799$	−1.46437e13			−1.27114
$800$	−5.18593e12	+	8.98229e12i	−0.447632	+	0.775322i
$801$	4.16397e12	+	7.21220e12i	0.357405	+	0.619044i
$802$	4.57190e12	+	7.91876e12i	0.390222	+	0.675884i
$803$	2.04100e11	−	3.53512e11i	0.0173230	−	0.0300043i
$804$	7.92014e11			0.0668468
$805$		0			0
$806$	5.09728e12			0.425433
$807$	−6.38357e11	+	1.10567e12i	−0.0529825	+	0.0917684i
$808$	−5.55474e12	−	9.62109e12i	−0.458472	−	0.794097i
$809$	1.13783e13	+	1.97078e13i	0.933920	+	1.61760i	0.776548	+	0.630058i	$0.216969\pi$
$809$	1.13783e13	+	1.97078e13i	0.933920	+	1.61760i	0.157372	+	0.987539i	$0.449698\pi$
$810$	1.78940e12	−	3.09933e12i	0.146058	−	0.252980i
$811$	4.95274e12			0.402024			0.201012	−	0.979589i	$-0.435577\pi$
$811$	4.95274e12			0.402024			0.201012	+	0.979589i	$0.435577\pi$
$812$		0			0
$813$	−2.68751e12			−0.215746
$814$	4.05584e12	−	7.02492e12i	0.323796	−	0.560831i
$815$	−2.96958e12	−	5.14347e12i	−0.235769	−	0.408363i
$816$	−2.37727e12	−	4.11755e12i	−0.187703	−	0.325112i
$817$	−1.04160e12	+	1.80411e12i	−0.0817904	+	0.141665i
$818$	−2.73675e13			−2.13720
$819$		0			0
$820$	2.78125e12			0.214821
$821$	7.73549e12	−	1.33983e13i	0.594215	−	1.02921i	−0.399442	−	0.916758i	$-0.630796\pi$
$821$	7.73549e12	−	1.33983e13i	0.594215	−	1.02921i	0.993657	−	0.112452i	$-0.0358704\pi$
$822$	−1.08128e12	−	1.87283e12i	−0.0826065	−	0.143079i
$823$	−7.05371e12	−	1.22174e13i	−0.535942	−	0.928280i	−0.999117	−	0.0420125i	$-0.986623\pi$
$823$	−7.05371e12	−	1.22174e13i	−0.535942	−	0.928280i	0.463175	−	0.886267i	$-0.346710\pi$
$824$	6.03220e12	−	1.04481e13i	0.455830	−	0.789521i
$825$	1.14199e12			0.0858261
$826$		0			0
$827$	−1.45951e13			−1.08500			−0.542502	−	0.840054i	$-0.682523\pi$
$827$	−1.45951e13			−1.08500			−0.542502	+	0.840054i	$0.682523\pi$
$828$	−2.75305e12	+	4.76843e12i	−0.203553	+	0.352564i
$829$	−4.87961e12	−	8.45174e12i	−0.358831	−	0.621514i	0.628935	−	0.777458i	$-0.283491\pi$
$829$	−4.87961e12	−	8.45174e12i	−0.358831	−	0.621514i	−0.987766	+	0.155944i	$0.950158\pi$
$830$	1.05629e12	+	1.82954e12i	0.0772557	+	0.133811i
$831$	−2.28520e12	+	3.95808e12i	−0.166234	+	0.287925i
$832$	2.50725e11			0.0181402
$833$		0			0
$834$	−2.52812e12			−0.180947
$835$	3.64969e12	−	6.32144e12i	0.259816	−	0.450015i
$836$	2.72226e12	+	4.71510e12i	0.192753	+	0.333859i
$837$	2.94423e12	+	5.09955e12i	0.207351	+	0.359143i
$838$	−4.91661e12	+	8.51581e12i	−0.344403	+	0.596524i
$839$	−4.87991e10			−0.00340004			−0.00170002	−	0.999999i	$-0.500541\pi$
$839$	−4.87991e10			−0.00340004			−0.00170002	+	0.999999i	$0.500541\pi$
$840$		0			0
$841$	−6.93537e12			−0.478066
$842$	−4.16088e12	+	7.20686e12i	−0.285286	+	0.494130i
$843$	1.70611e11	+	2.95507e11i	0.0116354	+	0.0201532i
$844$	7.37655e11	+	1.27766e12i	0.0500394	+	0.0866709i
$845$	−1.77144e12	+	3.06823e12i	−0.119529	+	0.207030i
$846$	−1.40229e13			−0.941176
$847$		0			0
$848$	1.35132e13			0.897384
$849$	−1.30116e12	+	2.25368e12i	−0.0859501	+	0.148870i
$850$	−1.41141e13	−	2.44463e13i	−0.927399	−	1.60630i
$851$	6.45948e12	+	1.11881e13i	0.422196	+	0.731266i
$852$	−9.21883e11	+	1.59675e12i	−0.0599374	+	0.103815i
$853$	−2.28806e13			−1.47978			−0.739888	−	0.672730i	$-0.765121\pi$
$853$	−2.28806e13			−1.47978			−0.739888	+	0.672730i	$0.765121\pi$
$854$		0			0
$855$	5.85441e12			0.374659
$856$	−6.42419e12	+	1.11270e13i	−0.408966	+	0.708349i
$857$	−5.60945e11	−	9.71584e11i	−0.0355227	−	0.0615272i	0.847717	−	0.530448i	$-0.177976\pi$
$857$	−5.60945e11	−	9.71584e11i	−0.0355227	−	0.0615272i	−0.883240	+	0.468921i	$0.844643\pi$
$858$	2.75145e11	+	4.76565e11i	0.0173328	+	0.0300213i
$859$	6.42437e12	−	1.11273e13i	0.402588	−	0.697304i	−0.591449	−	0.806342i	$-0.701444\pi$
$859$	6.42437e12	−	1.11273e13i	0.402588	−	0.697304i	0.994037	+	0.109039i	$0.0347773\pi$
$860$	−2.48052e11			−0.0154632
$861$		0			0
$862$	−1.51556e13			−0.934955
$863$	−1.33409e13	+	2.31071e13i	−0.818720	+	1.41807i	0.0879049	+	0.996129i	$0.471983\pi$
$863$	−1.33409e13	+	2.31071e13i	−0.818720	+	1.41807i	−0.906625	+	0.421937i	$0.861350\pi$
$864$	−2.88681e12	−	5.00010e12i	−0.176241	−	0.305258i
$865$	−1.02624e12	−	1.77751e12i	−0.0623272	−	0.107954i
$866$	2.77880e12	−	4.81303e12i	0.167891	−	0.290795i
$867$	4.95759e12			0.297978
$868$		0			0
$869$	−8.27938e12			−0.492503
$870$	−3.70642e11	+	6.41970e11i	−0.0219340	+	0.0379908i
$871$	−1.75032e12	−	3.03165e12i	−0.103047	−	0.178483i
$872$	−8.15728e12	−	1.41288e13i	−0.477773	−	0.827527i
$873$	−4.99201e12	+	8.64641e12i	−0.290878	+	0.503816i
$874$	−2.50671e13			−1.45312
$875$		0			0
$876$	1.20365e11			0.00690607
$877$	8.25422e12	−	1.42967e13i	0.471170	−	0.816091i	−0.528286	−	0.849067i	$-0.677165\pi$
$877$	8.25422e12	−	1.42967e13i	0.471170	−	0.816091i	0.999456	+	0.0329757i	$0.0104984\pi$
$878$	−1.13336e13	−	1.96303e13i	−0.643637	−	1.11481i
$879$	1.19595e11	+	2.07145e11i	0.00675715	+	0.0117037i
$880$	1.44771e12	−	2.50751e12i	0.0813784	−	0.140952i
$881$	−5.82217e12			−0.325606			−0.162803	−	0.986659i	$-0.552054\pi$
$881$	−5.82217e12			−0.325606			−0.162803	+	0.986659i	$0.552054\pi$
$882$		0			0
$883$	2.17502e13			1.20404			0.602020	−	0.798481i	$-0.294363\pi$
$883$	2.17502e13			1.20404			0.602020	+	0.798481i	$0.294363\pi$
$884$	2.35263e12	−	4.07488e12i	0.129574	−	0.224429i
$885$	−7.98072e11	−	1.38230e12i	−0.0437318	−	0.0757457i
$886$	1.65640e13	+	2.86896e13i	0.903052	+	1.56413i
$887$	1.53406e12	−	2.65707e12i	0.0832119	−	0.144127i	−0.821416	−	0.570330i	$-0.806816\pi$
$887$	1.53406e12	−	2.65707e12i	0.0832119	−	0.144127i	0.904628	+	0.426202i	$0.140149\pi$
$888$	−2.13082e12			−0.114997
$889$		0			0
$890$	−4.51449e12			−0.241187
$891$	4.17332e12	−	7.22840e12i	0.221836	−	0.384231i
$892$	5.26951e12	+	9.12706e12i	0.278695	+	0.482713i
$893$	−1.10418e13	−	1.91250e13i	−0.581043	−	1.00640i
$894$	1.19747e12	−	2.07408e12i	0.0626968	−	0.108594i
$895$	−6.46654e11			−0.0336875
$896$		0			0
$897$	−8.76411e11			−0.0452004
$898$	−1.56625e13	+	2.71283e13i	−0.803744	+	1.39213i
$899$	8.00711e12	+	1.38687e13i	0.408844	+	0.708138i
$900$	−4.67531e12	−	8.09787e12i	−0.237530	−	0.411414i
$901$	−1.14533e13	+	1.98376e13i	−0.578985	+	1.00283i
$902$	1.87517e13			0.943216
$903$		0			0
$904$	6.36410e12			0.316941
$905$	−2.05962e12	+	3.56736e12i	−0.102063	+	0.176778i
$906$	2.38113e12	+	4.12424e12i	0.117410	+	0.203361i
$907$	1.44304e13	+	2.49942e13i	0.708021	+	1.22633i	0.965590	+	0.260068i	$0.0837451\pi$
$907$	1.44304e13	+	2.49942e13i	0.708021	+	1.22633i	−0.257569	+	0.966260i	$0.582922\pi$
$908$	4.89514e12	−	8.47863e12i	0.238989	−	0.413942i
$909$	3.12739e13			1.51930
$910$		0			0
$911$	−8.43639e12			−0.405811			−0.202905	−	0.979198i	$-0.565038\pi$
$911$	−8.43639e12			−0.405811			−0.202905	+	0.979198i	$0.565038\pi$
$912$	3.58505e12	−	6.20949e12i	0.171601	−	0.297221i
$913$	2.46352e12	+	4.26694e12i	0.117338	+	0.203235i
$914$	−1.06521e13	−	1.84501e13i	−0.504870	−	0.874460i
$915$	5.78737e11	−	1.00240e12i	0.0272952	−	0.0472767i
$916$	1.87511e13			0.880028
$917$		0			0
$918$	1.57135e13			0.730266
$919$	1.18539e13	−	2.05315e13i	0.548202	−	0.949514i	−0.450196	−	0.892930i	$-0.648646\pi$
$919$	1.18539e13	−	2.05315e13i	0.548202	−	0.949514i	0.998398	−	0.0565842i	$-0.0180209\pi$
$920$	1.32952e12	+	2.30280e12i	0.0611857	+	0.105977i
$921$	−1.63343e12	−	2.82919e12i	−0.0748054	−	0.129567i
$922$	−2.96982e12	+	5.14388e12i	−0.135345	+	0.234424i
$923$	8.14931e12			0.369584
$924$		0			0
$925$	−2.19393e13			−0.985338
$926$	2.12735e13	−	3.68468e13i	0.950802	−	1.64684i
$927$	1.69810e13	+	2.94120e13i	0.755274	+	1.30817i
$928$	−7.85095e12	−	1.35983e13i	−0.347501	−	0.601890i
$929$	1.03773e13	−	1.79739e13i	0.457101	−	0.791722i	−0.541706	−	0.840568i	$-0.682221\pi$
$929$	1.03773e13	−	1.79739e13i	0.457101	−	0.791722i	0.998806	+	0.0488467i	$0.0155546\pi$
$930$	−1.56781e12			−0.0687256
$931$		0			0
$932$	−7.31430e12			−0.317542
$933$	−2.40100e12	+	4.15865e12i	−0.103735	+	0.179674i
$934$	6.71349e12	+	1.16281e13i	0.288660	+	0.499974i
$935$	2.45404e12	+	4.25052e12i	0.105010	+	0.181882i
$936$	−2.00701e12	+	3.47623e12i	−0.0854687	+	0.148036i
$937$	−5.69987e12			−0.241567			−0.120783	−	0.992679i	$-0.538541\pi$
$937$	−5.69987e12			−0.241567			−0.120783	+	0.992679i	$0.538541\pi$
$938$		0			0
$939$	−2.70367e12			−0.113490
$940$	1.31478e12	−	2.27726e12i	0.0549258	−	0.0951343i
$941$	8.58820e12	+	1.48752e13i	0.357066	+	0.618457i	0.987469	−	0.157811i	$-0.0504437\pi$
$941$	8.58820e12	+	1.48752e13i	0.357066	+	0.618457i	−0.630403	+	0.776268i	$0.717110\pi$
$942$	2.84484e12	+	4.92741e12i	0.117714	+	0.203887i
$943$	−1.49323e13	+	2.58635e13i	−0.614929	+	1.06509i
$944$	5.42833e13			2.22481
$945$		0			0
$946$	−1.67242e12			−0.0678944
$947$	6.22922e11	−	1.07893e12i	0.0251686	−	0.0435933i	−0.853167	−	0.521638i	$-0.825321\pi$
$947$	6.22922e11	−	1.07893e12i	0.0251686	−	0.0435933i	0.878335	+	0.478045i	$0.158654\pi$
$948$	−1.22066e12	−	2.11424e12i	−0.0490859	−	0.0850192i
$949$	−2.66002e11	−	4.60728e11i	−0.0106460	−	0.0184394i
$950$	2.12848e13	−	3.68663e13i	0.847839	−	1.46850i
$951$	−3.96956e12			−0.157373
$952$		0			0
$953$	4.96035e13			1.94802			0.974012	−	0.226496i	$-0.0727272\pi$
$953$	4.96035e13			1.94802			0.974012	+	0.226496i	$0.0727272\pi$
$954$	−1.09677e13	+	1.89966e13i	−0.428693	+	0.742519i
$955$	9.17121e11	+	1.58850e12i	0.0356789	+	0.0617977i
$956$	2.00681e11	+	3.47590e11i	0.00777044	+	0.0134588i
$957$	−8.64427e11	+	1.49723e12i	−0.0333138	+	0.0577012i
$958$	−1.80408e13			−0.692006
$959$		0			0
$960$	−7.71171e10			−0.00293042
$961$	−3.71513e12	+	6.43479e12i	−0.140514	+	0.243377i
$962$	−5.28594e12	−	9.15552e12i	−0.198992	−	0.344663i
$963$	−1.80845e13	−	3.13233e13i	−0.677623	−	1.17368i
$964$	3.11809e12	−	5.40070e12i	0.116290	−	0.201420i
$965$	8.40757e12			0.312103
$966$		0			0
$967$	3.34993e13			1.23202			0.616008	−	0.787740i	$-0.288749\pi$
$967$	3.34993e13			1.23202			0.616008	+	0.787740i	$0.288749\pi$
$968$	−6.00994e12	+	1.04095e13i	−0.220004	+	0.381059i
$969$	6.07708e12	+	1.05258e13i	0.221431	+	0.383530i
$970$	−2.70612e12	−	4.68713e12i	−0.0981463	−	0.169994i
$971$	−1.63791e13	+	2.83695e13i	−0.591295	+	1.02415i	0.402763	+	0.915304i	$0.368050\pi$
$971$	−1.63791e13	+	2.83695e13i	−0.591295	+	1.02415i	−0.994058	+	0.108849i	$0.965284\pi$
$972$	7.85372e12			0.282213
$973$		0			0
$974$	−5.45797e13			−1.94319
$975$	7.44172e11	−	1.28894e12i	0.0263726	−	0.0456787i
$976$	1.96823e13	+	3.40907e13i	0.694306	+	1.20257i
$977$	2.18842e12	+	3.79045e12i	0.0768430	+	0.133096i	0.901886	−	0.431974i	$-0.142183\pi$
$977$	2.18842e12	+	3.79045e12i	0.0768430	+	0.133096i	−0.825043	+	0.565070i	$0.808849\pi$
$978$	5.90368e12	−	1.02255e13i	0.206347	−	0.357403i
$979$	−1.05289e13			−0.366320
$980$		0			0
$981$	4.59265e13			1.58326
$982$	2.03832e13	−	3.53047e13i	0.699471	−	1.21152i
$983$	−1.23057e13	−	2.13140e13i	−0.420353	−	0.728073i	0.575621	−	0.817717i	$-0.304761\pi$
$983$	−1.23057e13	−	2.13140e13i	−0.420353	−	0.728073i	−0.995974	+	0.0896436i	$0.971427\pi$
$984$	−2.46290e12	−	4.26586e12i	−0.0837468	−	0.145054i
$985$	1.04397e12	−	1.80820e12i	0.0353365	−	0.0612047i
$986$	4.27344e13			1.43990
$987$		0			0
$988$	7.09580e12			0.236917
$989$	1.33178e12	−	2.30670e12i	0.0442637	−	0.0766670i
$990$	2.34999e12	+	4.07030e12i	0.0777513	+	0.134669i
$991$	−4.78192e12	−	8.28253e12i	−0.157496	−	0.272792i	0.776469	−	0.630156i	$-0.217009\pi$
$991$	−4.78192e12	−	8.28253e12i	−0.157496	−	0.272792i	−0.933965	+	0.357364i	$0.883676\pi$
$992$	1.66047e13	−	2.87601e13i	0.544412	−	0.942949i
$993$	−4.68681e12			−0.152970
$994$		0			0
$995$	−8.59417e12			−0.277971
$996$	−7.26411e11	+	1.25818e12i	−0.0233892	+	0.0405113i
$997$	−7.55274e12	−	1.30817e13i	−0.242090	−	0.419312i	0.719220	−	0.694783i	$-0.244499\pi$
$997$	−7.55274e12	−	1.30817e13i	−0.242090	−	0.419312i	−0.961309	+	0.275471i	$0.911166\pi$
$998$	−5.00673e12	−	8.67191e12i	−0.159760	−	0.276712i
$999$	6.10639e12	−	1.05766e13i	0.193972	−	0.335970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.10.c.h.30.1		16
7.2	even	3		49.10.a.g.1.8	yes	8
7.3	odd	6	inner	49.10.c.h.18.2		16
7.4	even	3	inner	49.10.c.h.18.1		16
7.5	odd	6		49.10.a.g.1.7	✓	8
7.6	odd	2	inner	49.10.c.h.30.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.10.a.g.1.7	✓	8	7.5	odd	6
49.10.a.g.1.8	yes	8	7.2	even	3
49.10.c.h.18.1		16	7.4	even	3	inner
49.10.c.h.18.2		16	7.3	odd	6	inner
49.10.c.h.30.1		16	1.1	even	1	trivial
49.10.c.h.30.2		16	7.6	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	49.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-13.9891 + 24.2298i) q^{2} +(-13.0785 - 22.6526i) q^{3} +(-135.388 - 234.499i) q^{4} +(184.056 - 318.794i) q^{5} +731.823 q^{6} -6748.99 q^{8} +(9499.41 - 16453.5i) q^{9} +(5149.53 + 8919.25i) q^{10} +(12010.0 + 20801.9i) q^{11} +(-3541.34 + 6133.79i) q^{12} +31305.0 q^{13} -9628.67 q^{15} +(163731. - 283590. i) q^{16} +(277543. + 480718. i) q^{17} +(265776. + 460337. i) q^{18} +(-418550. + 724950. i) q^{19} -99675.8 q^{20} -672033. q^{22} +(535152. - 926911. i) q^{23} +(88266.5 + 152882. i) q^{24} +(908810. + 1.57410e6i) q^{25} +(-437927. + 758512. i) q^{26} -1.01180e6 q^{27} -2.75169e6 q^{29} +(134696. - 233301. i) q^{30} +(-2.90989e6 - 5.04008e6i) q^{31} +(2.85314e6 + 4.94179e6i) q^{32} +(314144. - 544114. i) q^{33} -1.55303e7 q^{34} -5.14443e6 q^{36} +(-6.03518e6 + 1.04532e7i) q^{37} +(-1.17103e7 - 2.02828e7i) q^{38} +(-409422. - 709139. i) q^{39} +(-1.24219e6 + 2.15154e6i) q^{40} -2.79029e7 q^{41} +2.48859e6 q^{43} +(3.25201e6 - 5.63265e6i) q^{44} +(-3.49684e6 - 6.05670e6i) q^{45} +(1.49726e7 + 2.59332e7i) q^{46} +(-1.31905e7 + 2.28467e7i) q^{47} -8.56540e6 q^{48} -5.08536e7 q^{50} +(7.25968e6 - 1.25741e7i) q^{51} +(-4.23832e6 - 7.34099e6i) q^{52} +(2.06333e7 + 3.57380e7i) q^{53} +(1.41541e7 - 2.45157e7i) q^{54} +8.84201e6 q^{55} +2.18960e7 q^{57} +(3.84935e7 - 6.66728e7i) q^{58} +(8.28849e7 + 1.43561e8i) q^{59} +(1.30361e6 + 2.25792e6i) q^{60} +(-6.01056e7 + 1.04106e8i) q^{61} +1.62827e8 q^{62} +8.00911e6 q^{64} +(5.76186e6 - 9.97983e6i) q^{65} +(8.78917e6 + 1.52233e7i) q^{66} +(-5.59120e7 - 9.68424e7i) q^{67} +(7.51520e7 - 1.30167e8i) q^{68} -2.79959e7 q^{69} +2.60320e8 q^{71} +(-6.41114e7 + 1.11044e8i) q^{72} +(-8.49711e6 - 1.47174e7i) q^{73} +(-1.68853e8 - 2.92462e8i) q^{74} +(2.37717e7 - 4.11738e7i) q^{75} +2.26667e8 q^{76} +2.29097e7 q^{78} +(-1.72344e8 + 2.98508e8i) q^{79} +(-6.02712e7 - 1.04393e8i) q^{80} +(-1.73744e8 - 3.00933e8i) q^{81} +(3.90336e8 - 6.76082e8i) q^{82} +2.05123e8 q^{83} +2.04333e8 q^{85} +(-3.48131e7 + 6.02980e7i) q^{86} +(3.59879e7 + 6.23328e7i) q^{87} +(-8.10551e7 - 1.40392e8i) q^{88} +(-2.19170e8 + 3.79613e8i) q^{89} +1.95670e8 q^{90} -2.89813e8 q^{92} +(-7.61139e7 + 1.31833e8i) q^{93} +(-3.69046e8 - 6.39207e8i) q^{94} +(1.54073e8 + 2.66862e8i) q^{95} +(7.46296e7 - 1.29262e8i) q^{96} -5.25507e8 q^{97} +4.56350e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 66 q^{2} - 1706 q^{4} - 117084 q^{8} - 27940 q^{9} + 82092 q^{11} - 164672 q^{15} - 1569570 q^{16} + 307774 q^{18} - 2600152 q^{22} + 2388480 q^{23} + 6191476 q^{25} - 36887784 q^{29} + 16703832 q^{30}+ \cdots - 6259461064 q^{99}+O(q^{100}) \) 16 * q + 66 * q^2 - 1706 * q^4 - 117084 * q^8 - 27940 * q^9 + 82092 * q^11 - 164672 * q^15 - 1569570 * q^16 + 307774 * q^18 - 2600152 * q^22 + 2388480 * q^23 + 6191476 * q^25 - 36887784 * q^29 + 16703832 * q^30 + 66365310 * q^32 - 163874260 * q^36 + 8944484 * q^37 + 128986088 * q^39 - 72060264 * q^43 + 20548980 * q^44 + 151133592 * q^46 - 358848780 * q^50 + 192522580 * q^51 + 140198712 * q^53 + 112011672 * q^57 - 407992572 * q^58 - 748541080 * q^60 + 1606537220 * q^64 + 69983508 * q^65 - 459952056 * q^67 + 431701008 * q^71 - 1088280558 * q^72 - 1222590060 * q^74 + 2845895808 * q^78 + 792601400 * q^79 - 1704517060 * q^81 - 736682888 * q^85 + 812465940 * q^86 - 1818979932 * q^88 + 5226574128 * q^92 + 2571584104 * q^93 + 3568335216 * q^95 - 6259461064 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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