LMFDB - Embedded newform 13.8.e.a.10.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,8,Mod(4,13)] 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("13.4"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	13.e (of order $6$, 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:	$4.06100533129$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 1279 x^{12} + 629380 x^{10} + 148562016 x^{8} + 16872573312 x^{6} + 790180980480 x^{4} + \cdots + 4669637050368 $ x^14 + 1279x^12 + 629380x^10 + 148562016x^8 + 16872573312x^6 + 790180980480x^4 + 10484997239808x^2 + 4669637050368
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{3}\cdot 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.4
Root			$-0.679146i$ of defining polynomial
Character	$\chi$	$=$	13.10
Dual form			13.8.e.a.4.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.588158 - 0.339573i) q^{2} +(-31.2267 - 54.0862i) q^{3} +(-63.7694 + 110.452i) q^{4} +439.155i q^{5} +(-36.7324 - 21.2075i) q^{6} +(-1128.14 - 651.329i) q^{7} +173.548i q^{8} +(-856.712 + 1483.87i) q^{9} +(149.125 + 258.293i) q^{10} +(497.807 - 287.409i) q^{11} +7965.23 q^{12} +(-7892.42 - 676.938i) q^{13} -884.695 q^{14} +(23752.2 - 13713.4i) q^{15} +(-8103.55 - 14035.8i) q^{16} +(-5634.27 + 9758.85i) q^{17} +1163.66i q^{18} +(35549.9 + 20524.7i) q^{19} +(-48505.5 - 28004.7i) q^{20} +81355.4i q^{21} +(195.193 - 338.083i) q^{22} +(-22132.8 - 38335.2i) q^{23} +(9386.56 - 5419.33i) q^{24} -114732. q^{25} +(-4871.86 + 2281.91i) q^{26} -29576.4 q^{27} +(143881. - 83069.7i) q^{28} +(72756.1 + 126017. i) q^{29} +(9313.38 - 16131.2i) q^{30} +122045. i q^{31} +(-28770.4 - 16610.6i) q^{32} +(-31089.7 - 17949.6i) q^{33} +7652.99i q^{34} +(286035. - 495427. i) q^{35} +(-109264. - 189251. i) q^{36} +(36374.8 - 21001.0i) q^{37} +27878.6 q^{38} +(209841. + 448010. i) q^{39} -76214.6 q^{40} +(-75942.3 + 43845.3i) q^{41} +(27626.1 + 47849.8i) q^{42} +(-374876. + 649305. i) q^{43} +73311.5i q^{44} +(-651649. - 376230. i) q^{45} +(-26035.2 - 15031.4i) q^{46} -940126. i q^{47} +(-506094. + 876580. i) q^{48} +(436688. + 756366. i) q^{49} +(-67480.7 + 38960.0i) q^{50} +703759. q^{51} +(578064. - 828564. i) q^{52} -924214. q^{53} +(-17395.6 + 10043.4i) q^{54} +(126217. + 218614. i) q^{55} +(113037. - 195786. i) q^{56} -2.56368e6i q^{57} +(85584.1 + 49412.0i) q^{58} +(547626. + 316172. i) q^{59} +3.49797e6i q^{60} +(32203.2 - 55777.7i) q^{61} +(41443.3 + 71781.9i) q^{62} +(1.93297e6 - 1.11600e6i) q^{63} +2.05195e6 q^{64} +(297281. - 3.46600e6i) q^{65} -24380.9 q^{66} +(-1.68358e6 + 972013. i) q^{67} +(-718588. - 1.24463e6i) q^{68} +(-1.38227e6 + 2.39416e6i) q^{69} -388519. i q^{70} +(-4.09113e6 - 2.36202e6i) q^{71} +(-257523. - 148681. i) q^{72} +1.92731e6i q^{73} +(14262.8 - 24703.8i) q^{74} +(3.58271e6 + 6.20544e6i) q^{75} +(-4.53399e6 + 2.61770e6i) q^{76} -748791. q^{77} +(275552. + 192244. i) q^{78} -1.50287e6 q^{79} +(6.16388e6 - 3.55872e6i) q^{80} +(2.79720e6 + 4.84490e6i) q^{81} +(-29777.4 + 51575.9i) q^{82} -1.87974e6i q^{83} +(-8.98585e6 - 5.18798e6i) q^{84} +(-4.28565e6 - 2.47432e6i) q^{85} +509191. i q^{86} +(4.54386e6 - 7.87020e6i) q^{87} +(49879.3 + 86393.4i) q^{88} +(3.78860e6 - 2.18735e6i) q^{89} -511030. q^{90} +(8.46281e6 + 5.90424e6i) q^{91} +5.64559e6 q^{92} +(6.60097e6 - 3.81107e6i) q^{93} +(-319241. - 552942. i) q^{94} +(-9.01354e6 + 1.56119e7i) q^{95} +2.07477e6i q^{96} +(-1.53602e6 - 886819. i) q^{97} +(513683. + 296575. i) q^{98} +984906. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} + 26 q^{3} + 383 q^{4} - 264 q^{6} - 2772 q^{7} - 3491 q^{9} - 509 q^{10} + 6516 q^{11} + 38380 q^{12} + 5109 q^{13} - 47916 q^{14} - 19266 q^{15} - 633 q^{16} - 38403 q^{17} + 43254 q^{19}+ \cdots + 16173003 q^{98}+O(q^{100}) $ 14 * q - 3 * q^2 + 26 * q^3 + 383 * q^4 - 264 * q^6 - 2772 * q^7 - 3491 * q^9 - 509 * q^10 + 6516 * q^11 + 38380 * q^12 + 5109 * q^13 - 47916 * q^14 - 19266 * q^15 - 633 * q^16 - 38403 * q^17 + 43254 * q^19 + 89409 * q^20 - 125882 * q^22 - 68550 * q^23 + 224454 * q^24 + 39380 * q^25 + 361959 * q^26 - 432400 * q^27 - 234780 * q^28 + 221583 * q^29 - 157890 * q^30 - 878067 * q^32 + 219756 * q^33 + 659616 * q^35 + 635675 * q^36 - 565347 * q^37 + 953640 * q^38 + 30082 * q^39 - 77182 * q^40 + 1716057 * q^41 + 206406 * q^42 - 882692 * q^43 - 4616853 * q^45 - 3267480 * q^46 + 1133630 * q^48 + 2653979 * q^49 + 145128 * q^50 - 38964 * q^51 + 4962178 * q^52 - 1791210 * q^53 + 9597234 * q^54 + 2453536 * q^55 - 7457952 * q^56 - 14978127 * q^58 - 1189032 * q^59 + 3858525 * q^61 + 1904142 * q^62 + 7718520 * q^63 + 14570922 * q^64 + 10424661 * q^65 - 31956396 * q^66 + 4674330 * q^67 + 9569619 * q^68 - 13743840 * q^69 - 25203126 * q^71 - 6851607 * q^72 + 8640105 * q^74 + 10316152 * q^75 + 12934506 * q^76 + 19599336 * q^77 + 50085750 * q^78 - 30688440 * q^79 + 29127963 * q^80 + 13886221 * q^81 - 37359719 * q^82 - 96398508 * q^84 - 22436313 * q^85 + 12769686 * q^87 + 27045536 * q^88 + 2123160 * q^89 + 41193546 * q^90 + 37205532 * q^91 - 47685588 * q^92 + 36638964 * q^93 + 19138810 * q^94 - 43420386 * q^95 - 68556288 * q^97 + 16173003 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.588158	−	0.339573i	0.0519863	−	0.0300143i	−0.473782	−	0.880642i	$-0.657111\pi$
$2$	0.588158	−	0.339573i	0.0519863	−	0.0300143i	0.525768	+	0.850628i	$0.323778\pi$
$3$	−31.2267	−	54.0862i	−0.667731	−	1.15654i	−0.978537	−	0.206071i	$-0.933932\pi$
$3$	−31.2267	−	54.0862i	−0.667731	−	1.15654i	0.310806	−	0.950473i	$-0.399401\pi$
$4$	−63.7694	+	110.452i	−0.498198	+	0.862905i
$5$			439.155i			1.57117i	0.618754	+	0.785585i	$0.287638\pi$
$5$			439.155i			1.57117i	−0.618754	+	0.785585i	$0.712362\pi$
$6$	−36.7324	−	21.2075i	−0.0694257	−	0.0400829i
$7$	−1128.14	−	651.329i	−1.24313	−	0.717724i	−0.273403	−	0.961899i	$-0.588149\pi$
$7$	−1128.14	−	651.329i	−1.24313	−	0.717724i	−0.969731	+	0.244175i	$0.921483\pi$
$8$			173.548i			0.119841i
$9$	−856.712	+	1483.87i	−0.391729	+	0.678495i
$10$	149.125	+	258.293i	0.0471576	+	0.0816793i
$11$	497.807	−	287.409i	0.112768	−	0.0651067i	−0.442555	−	0.896741i	$-0.645928\pi$
$11$	497.807	−	287.409i	0.112768	−	0.0651067i	0.555323	+	0.831635i	$0.312595\pi$
$12$	7965.23			1.33065
$13$	−7892.42	−	676.938i	−0.996342	−	0.0854568i
$13$	−7892.42	−	676.938i	−0.996342	−	0.0854568i
$14$	−884.695			−0.0861679
$15$	23752.2	−	13713.4i	1.81713	−	1.04912i
$16$	−8103.55	−	14035.8i	−0.494601	−	0.856675i
$17$	−5634.27	+	9758.85i	−0.278142	+	0.481756i	−0.970923	−	0.239392i	$-0.923052\pi$
$17$	−5634.27	+	9758.85i	−0.278142	+	0.481756i	0.692781	+	0.721148i	$0.256385\pi$
$18$			1163.66i			0.0470299i
$19$	35549.9	+	20524.7i	1.18905	+	0.686499i	0.958091	−	0.286464i	$-0.0924800\pi$
$19$	35549.9	+	20524.7i	1.18905	+	0.686499i	0.230960	+	0.972963i	$0.425813\pi$
$20$	−48505.5	−	28004.7i	−1.35577	−	0.782754i
$21$			81355.4i			1.91699i
$22$	195.193	−	338.083i	0.00390826	−	0.00676931i
$23$	−22132.8	−	38335.2i	−0.379306	−	0.656977i	0.611655	−	0.791124i	$-0.290504\pi$
$23$	−22132.8	−	38335.2i	−0.379306	−	0.656977i	−0.990961	+	0.134147i	$0.957171\pi$
$24$	9386.56	−	5419.33i	0.138601	−	0.0800215i
$25$	−114732.			−1.46857
$26$	−4871.86	+	2281.91i	−0.0543610	+	0.0254619i
$27$	−29576.4			−0.289183
$28$	143881.	−	83069.7i	1.23865	−	0.715138i
$29$	72756.1	+	126017.i	0.553957	+	0.959482i	0.997984	+	0.0634685i	$0.0202162\pi$
$29$	72756.1	+	126017.i	0.553957	+	0.959482i	−0.444027	+	0.896014i	$0.646450\pi$
$30$	9313.38	−	16131.2i	0.0629771	−	0.109080i
$31$			122045.i			0.735793i	0.929867	+	0.367896i	$0.119922\pi$
$31$			122045.i			0.735793i	−0.929867	+	0.367896i	$0.880078\pi$
$32$	−28770.4	−	16610.6i	−0.155210	−	0.0896107i
$33$	−31089.7	−	17949.6i	−0.150597	−	0.0869475i
$34$			7652.99i			0.0333930i
$35$	286035.	−	495427.i	1.12767	−	1.95318i
$36$	−109264.	−	189251.i	−0.390318	−	0.676050i
$37$	36374.8	−	21001.0i	0.118058	−	0.0681608i	−0.439808	−	0.898092i	$-0.644954\pi$
$37$	36374.8	−	21001.0i	0.118058	−	0.0681608i	0.557866	+	0.829931i	$0.311620\pi$
$38$	27878.6			0.0824191
$39$	209841.	+	448010.i	0.566454	+	1.20938i
$40$	−76214.6			−0.188290
$41$	−75942.3	+	43845.3i	−0.172084	+	0.0993526i	−0.583568	−	0.812064i	$-0.698344\pi$
$41$	−75942.3	+	43845.3i	−0.172084	+	0.0993526i	0.411484	+	0.911417i	$0.365011\pi$
$42$	27626.1	+	47849.8i	0.0575370	+	0.0996570i
$43$	−374876.	+	649305.i	−0.719032	+	1.24540i	0.242352	+	0.970188i	$0.422081\pi$
$43$	−374876.	+	649305.i	−0.719032	+	1.24540i	−0.961384	+	0.275212i	$0.911252\pi$
$44$			73311.5i			0.129744i
$45$	−651649.	−	376230.i	−1.06603	−	0.615473i
$46$	−26035.2	−	15031.4i	−0.0394374	−	0.0227692i
$47$		−	940126.i		−	1.32082i	−0.750905	−	0.660410i	$-0.770383\pi$
$47$		−	940126.i		−	1.32082i	0.750905	−	0.660410i	$-0.229617\pi$
$48$	−506094.	+	876580.i	−0.660521	+	1.14406i
$49$	436688.	+	756366.i	0.530255	+	0.918429i
$50$	−67480.7	+	38960.0i	−0.0763457	+	0.0440782i
$51$	703759.			0.742896
$52$	578064.	−	828564.i	0.570117	−	0.817174i
$53$	−924214.			−0.852721			−0.426360	−	0.904553i	$-0.640204\pi$
$53$	−924214.			−0.852721			−0.426360	+	0.904553i	$0.640204\pi$
$54$	−17395.6	+	10043.4i	−0.0150335	+	0.00867962i
$55$	126217.	+	218614.i	0.102294	+	0.177178i
$56$	113037.	−	195786.i	0.0860127	−	0.148978i
$57$		−	2.56368e6i		−	1.83359i
$58$	85584.1	+	49412.0i	0.0575964	+	0.0332533i
$59$	547626.	+	316172.i	0.347138	+	0.200420i	0.663424	−	0.748244i	$-0.269103\pi$
$59$	547626.	+	316172.i	0.347138	+	0.200420i	−0.316286	+	0.948664i	$0.602436\pi$
$60$			3.49797e6i			2.09068i
$61$	32203.2	−	55777.7i	0.0181654	−	0.0314634i	−0.856800	−	0.515649i	$-0.827551\pi$
$61$	32203.2	−	55777.7i	0.0181654	−	0.0314634i	0.874965	+	0.484186i	$0.160884\pi$
$62$	41443.3	+	71781.9i	0.0220843	+	0.0382511i
$63$	1.93297e6	−	1.11600e6i	0.973944	−	0.562307i
$64$	2.05195e6			0.978444
$65$	297281.	−	3.46600e6i	0.134267	−	1.56542i
$66$	−24380.9			−0.0104387
$67$	−1.68358e6	+	972013.i	−0.683866	+	0.394830i	−0.801310	−	0.598249i	$-0.795863\pi$
$67$	−1.68358e6	+	972013.i	−0.683866	+	0.394830i	0.117444	+	0.993079i	$0.462530\pi$
$68$	−718588.	−	1.24463e6i	−0.277140	−	0.480020i
$69$	−1.38227e6	+	2.39416e6i	−0.506549	+	0.877368i
$70$		−	388519.i		−	0.135384i
$71$	−4.09113e6	−	2.36202e6i	−1.35656	−	0.783211i	−0.367402	−	0.930062i	$-0.619753\pi$
$71$	−4.09113e6	−	2.36202e6i	−1.35656	−	0.783211i	−0.989159	+	0.146851i	$0.953086\pi$
$72$	−257523.	−	148681.i	−0.0813114	−	0.0469452i
$73$			1.92731e6i			0.579857i	0.957048	+	0.289928i	$0.0936315\pi$
$73$			1.92731e6i			0.579857i	−0.957048	+	0.289928i	$0.906368\pi$
$74$	14262.8	−	24703.8i	0.00409159	−	0.00708685i
$75$	3.58271e6	+	6.20544e6i	0.980612	+	1.69847i
$76$	−4.53399e6	+	2.61770e6i	−1.18477	+	0.684025i
$77$	−748791.			−0.186915
$78$	275552.	+	192244.i	0.0657464	+	0.0458692i
$79$	−1.50287e6			−0.342947			−0.171474	−	0.985189i	$-0.554853\pi$
$79$	−1.50287e6			−0.342947			−0.171474	+	0.985189i	$0.554853\pi$
$80$	6.16388e6	−	3.55872e6i	1.34598	−	0.777103i
$81$	2.79720e6	+	4.84490e6i	0.584826	+	1.01295i
$82$	−29777.4	+	51575.9i	−0.00596400	+	0.0103300i
$83$		−	1.87974e6i		−	0.360848i	−0.983589	−	0.180424i	$-0.942253\pi$
$83$		−	1.87974e6i		−	0.360848i	0.983589	−	0.180424i	$-0.0577470\pi$
$84$	−8.98585e6	−	5.18798e6i	−1.65418	−	0.955039i
$85$	−4.28565e6	−	2.47432e6i	−0.756921	−	0.437008i
$86$			509191.i			0.0863250i
$87$	4.54386e6	−	7.87020e6i	0.739789	−	1.28135i
$88$	49879.3	+	86393.4i	0.00780244	+	0.0135142i
$89$	3.78860e6	−	2.18735e6i	0.569657	−	0.328892i	−0.187355	−	0.982292i	$-0.559992\pi$
$89$	3.78860e6	−	2.18735e6i	0.569657	−	0.328892i	0.757012	+	0.653400i	$0.226658\pi$
$90$	−511030.			−0.0738920
$91$	8.46281e6	+	5.90424e6i	1.17725	+	0.821333i
$92$	5.64559e6			0.755879
$93$	6.60097e6	−	3.81107e6i	0.850977	−	0.491312i
$94$	−319241.	−	552942.i	−0.0396435	−	0.0686645i
$95$	−9.01354e6	+	1.56119e7i	−1.07861	+	1.86820i
$96$			2.07477e6i			0.239343i
$97$	−1.53602e6	−	886819.i	−0.170881	−	0.0986583i	0.412120	−	0.911130i	$-0.364788\pi$
$97$	−1.53602e6	−	886819.i	−0.170881	−	0.0986583i	−0.583001	+	0.812471i	$0.698122\pi$
$98$	513683.	+	296575.i	0.0551320	+	0.0318305i
$99$			984906.i			0.102017i
$100$	7.31641e6	−	1.26724e7i	0.731641	−	1.26724i
$101$	−4.81973e6	−	8.34802e6i	−0.465477	−	0.806229i	0.533746	−	0.845645i	$-0.320784\pi$
$101$	−4.81973e6	−	8.34802e6i	−0.465477	−	0.806229i	−0.999223	+	0.0394154i	$0.987450\pi$
$102$	413921.	−	238977.i	0.0386204	−	0.0222975i
$103$	7.14668e6			0.644427			0.322214	−	0.946667i	$-0.395573\pi$
$103$	7.14668e6			0.644427			0.322214	+	0.946667i	$0.395573\pi$
$104$	117481.	−	1.36971e6i	0.0102412	−	0.119402i
$105$	−3.57277e7			−3.01191
$106$	−543583.	+	313838.i	−0.0443298	+	0.0255938i
$107$	1.03003e7	+	1.78406e7i	0.812839	+	1.40788i	0.910869	+	0.412695i	$0.135413\pi$
$107$	1.03003e7	+	1.78406e7i	0.812839	+	1.40788i	−0.0980299	+	0.995183i	$0.531254\pi$
$108$	1.88607e6	−	3.26677e6i	0.144070	−	0.249537i
$109$		−	1.05713e7i		−	0.781872i	−0.920418	−	0.390936i	$-0.872151\pi$
$109$		−	1.05713e7i		−	0.781872i	0.920418	−	0.390936i	$-0.127849\pi$
$110$	148471.	+	85719.8i	0.0106357	+	0.00614054i
$111$	−2.27173e6	−	1.31158e6i	−0.157662	−	0.0910261i
$112$			2.11123e7i			1.41995i
$113$	−1.34036e7	+	2.32157e7i	−0.873868	+	1.51358i	−0.0159047	+	0.999874i	$0.505063\pi$
$113$	−1.34036e7	+	2.32157e7i	−0.873868	+	1.51358i	−0.857964	+	0.513711i	$0.828270\pi$
$114$	−870556.	−	1.50785e6i	−0.0550338	−	0.0953214i
$115$	1.68351e7	−	9.71976e6i	1.03222	−	0.595954i
$116$	−1.85584e7			−1.10392
$117$	7.76602e6	−	1.11314e7i	0.448278	−	0.642537i
$118$	429454.			0.0240619
$119$	1.27124e7	−	7.33953e6i	0.691536	−	0.399258i
$120$	2.37993e6	+	4.12216e6i	0.125727	+	0.217766i
$121$	−9.57838e6	+	1.65902e7i	−0.491522	+	0.851341i
$122$		−	43741.4i		−	0.00218089i
$123$	4.74285e6	+	2.73829e6i	0.229811	+	0.132682i
$124$	−1.34801e7	−	7.78276e6i	−0.634919	−	0.366571i
$125$		−	1.60763e7i		−	0.736209i
$126$	757929.	−	1.31277e6i	0.0337545	−	0.0584645i
$127$	−4.03532e6	−	6.98938e6i	−0.174810	−	0.302779i	0.765286	−	0.643691i	$-0.222598\pi$
$127$	−4.03532e6	−	6.98938e6i	−0.174810	−	0.302779i	−0.940095	+	0.340912i	$0.889264\pi$
$128$	4.88947e6	−	2.82294e6i	0.206076	−	0.118978i
$129$	4.68246e7			1.92048
$130$	−1.00211e6	−	2.13950e6i	−0.0400050	−	0.0854104i
$131$	1.26390e7			0.491206			0.245603	−	0.969370i	$-0.421014\pi$
$131$	1.26390e7			0.491206			0.245603	+	0.969370i	$0.421014\pi$
$132$	3.96514e6	−	2.28928e6i	0.150055	−	0.0866342i
$133$	−2.67367e7	−	4.63094e7i	−0.985434	−	1.70682i
$134$	−660139.	+	1.14339e6i	−0.0237011	+	0.0410515i
$135$		−	1.29886e7i		−	0.454355i
$136$	−1.69363e6	−	977818.i	−0.0577341	−	0.0333328i
$137$	2.45282e7	+	1.41614e7i	0.814975	+	0.470526i	0.848680	−	0.528906i	$-0.177398\pi$
$137$	2.45282e7	+	1.41614e7i	0.814975	+	0.470526i	−0.0337058	+	0.999432i	$0.510731\pi$
$138$			1.87753e6i			0.0608148i
$139$	4.44074e6	−	7.69159e6i	0.140250	−	0.242920i	−0.787341	−	0.616518i	$-0.788543\pi$
$139$	4.44074e6	−	7.69159e6i	0.140250	−	0.242920i	0.927591	+	0.373598i	$0.121876\pi$
$140$	3.64805e7	+	6.31861e7i	1.12360	+	1.94614i
$141$	−5.08478e7	+	2.93570e7i	−1.52759	+	0.881952i
$142$	−3.20831e6			−0.0940301
$143$	−4.12346e6	+	1.93137e6i	−0.117919	+	0.0552317i
$144$	2.77696e7			0.774999
$145$	−5.53411e7	+	3.19512e7i	−1.50751	+	0.870361i
$146$	654461.	+	1.13356e6i	0.0174040	+	0.0301446i
$147$	2.72726e7	−	4.72376e7i	0.708136	−	1.22653i
$148$			5.35689e6i			0.135830i
$149$	−4.40391e7	−	2.54260e7i	−1.09065	−	0.629689i	−0.156902	−	0.987614i	$-0.550151\pi$
$149$	−4.40391e7	−	2.54260e7i	−1.09065	−	0.629689i	−0.933750	+	0.357926i	$0.883484\pi$
$150$	4.21440e6	+	2.43318e6i	0.101957	+	0.0588648i
$151$		−	9.76974e6i		−	0.230921i	−0.993312	−	0.115461i	$-0.963166\pi$
$151$		−	9.76974e6i		−	0.230921i	0.993312	−	0.115461i	$-0.0368344\pi$
$152$	−3.56203e6	+	6.16961e6i	−0.0822706	+	0.142497i
$153$	−9.65390e6	−	1.67210e7i	−0.217913	−	0.377436i
$154$	−440407.	+	254269.i	−0.00971699	+	0.00561011i
$155$	−5.35969e7			−1.15606
$156$	−6.28649e7	−	5.39196e6i	−1.32578	−	0.113713i
$157$	6.53474e7			1.34766			0.673828	−	0.738888i	$-0.264649\pi$
$157$	6.53474e7			1.34766			0.673828	+	0.738888i	$0.264649\pi$
$158$	−883927.	+	510335.i	−0.0178286	+	0.0102933i
$159$	2.88601e7	+	4.99872e7i	0.569388	+	0.986209i
$160$	7.29462e6	−	1.26347e7i	0.140794	−	0.243862i
$161$			5.76631e7i			1.08895i
$162$	3.29039e6	+	1.89971e6i	0.0608058	+	0.0351063i
$163$	1.74920e7	+	1.00990e7i	0.316361	+	0.182651i	0.649769	−	0.760132i	$-0.274866\pi$
$163$	1.74920e7	+	1.00990e7i	0.316361	+	0.182651i	−0.333409	+	0.942782i	$0.608199\pi$
$164$		−	1.11839e7i		−	0.197989i
$165$	7.88268e6	−	1.36532e7i	0.136609	−	0.236614i
$166$	−638309.	−	1.10558e6i	−0.0108306	−	0.0187591i
$167$	−5.86371e6	+	3.38542e6i	−0.0974238	+	0.0562477i	−0.547920	−	0.836531i	$-0.684580\pi$
$167$	−5.86371e6	+	3.38542e6i	−0.0974238	+	0.0562477i	0.450497	+	0.892778i	$0.351247\pi$
$168$	−1.41191e7			−0.229733
$169$	6.18320e7	+	1.06853e7i	0.985394	+	0.170288i
$170$	−3.36085e6			−0.0524660
$171$	−6.09120e7	+	3.51676e7i	−0.931572	+	0.537843i
$172$	−4.78112e7	−	8.28115e7i	−0.716441	−	1.24091i
$173$	4.33522e7	−	7.50883e7i	0.636576	−	1.10258i	−0.349603	−	0.936898i	$-0.613684\pi$
$173$	4.33522e7	−	7.50883e7i	0.636576	−	1.10258i	0.986179	−	0.165684i	$-0.0529831\pi$
$174$		−	6.17189e6i		−	0.0888170i
$175$	1.29434e8	+	7.47285e7i	1.82563	+	1.05403i
$176$	−8.06800e6	−	4.65806e6i	−0.111550	−	0.0644037i
$177$		−	3.94920e7i		−	0.535307i
$178$	1.48553e6	−	2.57301e6i	0.0197429	−	0.0341957i
$179$	−4.47221e7	−	7.74609e7i	−0.582823	−	1.00948i	−0.995143	−	0.0984398i	$-0.968615\pi$
$179$	−4.47221e7	−	7.74609e7i	−0.582823	−	1.00948i	0.412320	−	0.911039i	$-0.364719\pi$
$180$	8.31105e7	−	4.79839e7i	1.06219	−	0.613255i
$181$	−2.55748e7			−0.320581			−0.160290	−	0.987070i	$-0.551243\pi$
$181$	−2.55748e7			−0.320581			−0.160290	+	0.987070i	$0.551243\pi$
$182$	6.98239e6	+	598883.i	0.0858527	+	0.00736364i
$183$	−4.02240e6			−0.0485184
$184$	6.65300e6	−	3.84111e6i	0.0787328	−	0.0454564i
$185$	9.22271e6	+	1.59742e7i	0.107092	+	0.185489i
$186$	2.58827e6	−	4.48302e6i	0.0294927	−	0.0510829i
$187$			6.47736e6i			0.0724356i
$188$	1.03839e8	+	5.99512e7i	1.13974	+	0.658030i
$189$	3.33662e7	+	1.92640e7i	0.359493	+	0.207553i
$190$			1.22430e7i			0.129494i
$191$	−7.26412e7	+	1.25818e8i	−0.754339	+	1.30655i	0.191364	+	0.981519i	$0.438709\pi$
$191$	−7.26412e7	+	1.25818e8i	−0.754339	+	1.30655i	−0.945702	+	0.325034i	$0.894624\pi$
$192$	−6.40755e7	−	1.10982e8i	−0.653338	−	1.13161i
$193$	−7.90017e7	+	4.56117e7i	−0.791017	+	0.456694i	−0.840321	−	0.542090i	$-0.817633\pi$
$193$	−7.90017e7	+	4.56117e7i	−0.791017	+	0.456694i	0.0493033	+	0.998784i	$0.484300\pi$
$194$	−1.20456e6			−0.0118446
$195$	−1.96746e8	+	9.21528e7i	−1.90013	+	0.889995i
$196$	−1.11389e8			−1.05669
$197$	1.47447e8	−	8.51285e7i	1.37405	−	0.793311i	0.382619	−	0.923906i	$-0.375022\pi$
$197$	1.47447e8	−	8.51285e7i	1.37405	−	0.793311i	0.991436	+	0.130595i	$0.0416889\pi$
$198$	334447.	+	579280.i	0.00306196	+	0.00530347i
$199$	−6.97613e7	+	1.20830e8i	−0.627521	+	1.08690i	0.360526	+	0.932749i	$0.382597\pi$
$199$	−6.97613e7	+	1.20830e8i	−0.627521	+	1.08690i	−0.988047	+	0.154150i	$0.950736\pi$
$200$		−	1.99116e7i		−	0.175995i
$201$	1.05145e8	+	6.07055e7i	0.913277	+	0.527281i
$202$	−5.66952e6	−	3.27330e6i	−0.0483968	−	0.0279419i
$203$		−	1.89553e8i		−	1.59035i
$204$	−4.48783e7	+	7.77314e7i	−0.370110	+	0.641049i
$205$	−1.92549e7	−	3.33504e7i	−0.156100	−	0.270373i
$206$	4.20337e6	−	2.42682e6i	0.0335014	−	0.0193420i
$207$	7.58459e7			0.594341
$208$	5.44553e7	+	1.16262e8i	0.419583	+	0.895808i
$209$	2.35960e7			0.178783
$210$	−2.10135e7	+	1.21321e7i	−0.156578	+	0.0904004i
$211$	−4.18539e7	−	7.24931e7i	−0.306724	−	0.531261i	0.670920	−	0.741530i	$-0.265899\pi$
$211$	−4.18539e7	−	7.24931e7i	−0.306724	−	0.531261i	−0.977644	+	0.210269i	$0.932566\pi$
$212$	5.89365e7	−	1.02081e8i	0.424824	−	0.735817i
$213$			2.95032e8i			2.09190i
$214$	1.21163e7	+	6.99538e6i	0.0845130	+	0.0487936i
$215$	−2.85146e8	−	1.64629e8i	−1.95673	−	1.12972i
$216$		−	5.13293e6i		−	0.0346559i
$217$	7.94917e7	−	1.37684e8i	0.528096	−	0.914689i
$218$	−3.58973e6	−	6.21759e6i	−0.0234673	−	0.0406466i
$219$	1.04241e8	−	6.01834e7i	0.670630	−	0.387188i
$220$	−3.21951e7			−0.203850
$221$	5.10742e7	−	7.32069e7i	0.318294	−	0.456225i
$222$	−1.78152e6			−0.0109283
$223$	−8.23600e7	+	4.75506e7i	−0.497335	+	0.287137i	−0.727612	−	0.685988i	$-0.759370\pi$
$223$	−8.23600e7	+	4.75506e7i	−0.497335	+	0.287137i	0.230277	+	0.973125i	$0.426037\pi$
$224$	2.16379e7	+	3.74779e7i	0.128631	+	0.222796i
$225$	9.82926e7	−	1.70248e8i	0.575283	−	0.996420i
$226$			1.82060e7i			0.104914i
$227$	8.55988e7	+	4.94205e7i	0.485710	+	0.280425i	0.722793	−	0.691064i	$-0.242858\pi$
$227$	8.55988e7	+	4.94205e7i	0.485710	+	0.280425i	−0.237083	+	0.971489i	$0.576191\pi$
$228$	2.83163e8	+	1.63484e8i	1.58221	+	0.913490i
$229$			8.72426e7i			0.480070i	0.970764	+	0.240035i	$0.0771589\pi$
$229$			8.72426e7i			0.480070i	−0.970764	+	0.240035i	$0.922841\pi$
$230$	6.60113e6	−	1.14335e7i	0.0357743	−	0.0619629i
$231$	2.33823e7	+	4.04993e7i	0.124809	+	0.216175i
$232$	−2.18701e7	+	1.26267e7i	−0.114985	+	0.0663867i
$233$	−2.42490e8			−1.25588			−0.627940	−	0.778262i	$-0.716102\pi$
$233$	−2.42490e8			−1.25588			−0.627940	+	0.778262i	$0.716102\pi$
$234$	787728.	−	9.18413e6i	0.00401903	−	0.0468579i
$235$	4.12861e8			2.07523
$236$	−6.98436e7	+	4.03242e7i	−0.345887	+	0.199698i
$237$	4.69298e7	+	8.12847e7i	0.228997	+	0.396634i
$238$	4.98462e6	−	8.63361e6i	0.0239669	−	0.0415119i
$239$		−	4.08512e8i		−	1.93558i	−0.251750	−	0.967792i	$-0.581006\pi$
$239$		−	4.08512e8i		−	1.93558i	0.251750	−	0.967792i	$-0.418994\pi$
$240$	−3.84955e8	−	2.22254e8i	−1.79751	−	1.03779i
$241$	1.89875e8	+	1.09624e8i	0.873792	+	0.504484i	0.868606	−	0.495503i	$-0.165016\pi$
$241$	1.89875e8	+	1.09624e8i	0.873792	+	0.504484i	0.00518518	+	0.999987i	$0.498349\pi$
$242$			1.30102e7i			0.0590108i
$243$	1.42353e8	−	2.46563e8i	0.636421	−	1.10231i
$244$	4.10716e6	+	7.11381e6i	0.0181000	+	0.0313500i
$245$	−3.32162e8	+	1.91774e8i	−1.44301	+	0.833121i
$246$	3.71939e6			0.0159294
$247$	−2.66681e8	−	1.86055e8i	−1.12604	−	0.785600i
$248$	−2.11807e7			−0.0881780
$249$	−1.01668e8	+	5.86980e7i	−0.417337	+	0.240949i
$250$	−5.45908e6	−	9.45541e6i	−0.0220968	−	0.0382728i
$251$	7.42822e6	−	1.28661e7i	0.0296501	−	0.0513556i	−0.850820	−	0.525458i	$-0.823894\pi$
$251$	7.42822e6	−	1.28661e7i	0.0296501	−	0.0513556i	0.880470	+	0.474102i	$0.157227\pi$
$252$			2.84667e8i			1.12056i
$253$	−2.20358e7	−	1.27223e7i	−0.0855473	−	0.0493907i
$254$	−4.74681e6	−	2.74057e6i	−0.0181754	−	0.0104936i
$255$			3.09059e8i			1.16722i
$256$	−1.29407e8	+	2.24140e8i	−0.482080	+	0.834987i
$257$	2.49812e8	+	4.32688e8i	0.918011	+	1.59004i	0.802432	+	0.596744i	$0.203539\pi$
$257$	2.49812e8	+	4.32688e8i	0.918011	+	1.59004i	0.115579	+	0.993298i	$0.463128\pi$
$258$	2.75402e7	−	1.59004e7i	0.0998386	−	0.0576418i
$259$	−5.47143e7			−0.195682
$260$	3.63868e8	+	2.53860e8i	1.28392	+	0.895750i
$261$	−2.49324e8			−0.868005
$262$	7.43374e6	−	4.29187e6i	0.0255360	−	0.0147432i
$263$	−1.51725e7	−	2.62796e7i	−0.0514295	−	0.0890785i	0.839165	−	0.543878i	$-0.183044\pi$
$263$	−1.51725e7	−	2.62796e7i	−0.0514295	−	0.0890785i	−0.890594	+	0.454799i	$0.849711\pi$
$264$	3.11513e6	−	5.39556e6i	0.0104199	−	0.0180477i
$265$		−	4.05873e8i		−	1.33977i
$266$	−3.14508e7	−	1.81581e7i	−0.102458	−	0.0591542i
$267$	−2.36611e8	−	1.36607e8i	−0.760756	−	0.439222i
$268$		−	2.47939e8i		−	0.786815i
$269$	−5.52630e7	+	9.57183e7i	−0.173102	+	0.299821i	−0.939503	−	0.342541i	$-0.888712\pi$
$269$	−5.52630e7	+	9.57183e7i	−0.173102	+	0.299821i	0.766401	+	0.642363i	$0.222046\pi$
$270$	−4.41059e6	−	7.63937e6i	−0.0136372	−	0.0236202i
$271$	4.36530e7	−	2.52031e7i	0.133236	−	0.0769238i	−0.431901	−	0.901921i	$-0.642157\pi$
$271$	4.36530e7	−	2.52031e7i	0.133236	−	0.0769238i	0.565136	+	0.824997i	$0.308824\pi$
$272$	1.82630e8			0.550278
$273$	5.50725e7	−	6.42091e8i	0.163820	−	1.90997i
$274$	1.92353e7			0.0564900
$275$	−5.71145e7	+	3.29751e7i	−0.165608	+	0.0956140i
$276$	−1.76293e8	−	3.05349e8i	−0.504724	−	0.874207i
$277$	−2.69297e8	+	4.66436e8i	−0.761294	+	1.31860i	0.180889	+	0.983503i	$0.442102\pi$
$277$	−2.69297e8	+	4.66436e8i	−0.761294	+	1.31860i	−0.942184	+	0.335097i	$0.891231\pi$
$278$		−	6.03182e6i		−	0.0168380i
$279$	−1.81099e8	−	1.04558e8i	−0.499232	−	0.288232i
$280$	8.59804e7	+	4.96408e7i	0.234070	+	0.135140i
$281$			1.43482e8i			0.385766i	0.981222	+	0.192883i	$0.0617839\pi$
$281$			1.43482e8i			0.385766i	−0.981222	+	0.192883i	$0.938216\pi$
$282$	−1.99377e7	+	3.45331e7i	−0.0529423	+	0.0916988i
$283$	5.06236e7	+	8.76826e7i	0.132770	+	0.229964i	0.924743	−	0.380591i	$-0.124279\pi$
$283$	5.06236e7	+	8.76826e7i	0.132770	+	0.229964i	−0.791973	+	0.610556i	$0.790946\pi$
$284$	5.21778e8	−	3.01249e8i	1.35167	−	0.780389i
$285$	1.12585e9			2.88088
$286$	−1.76940e6	+	2.53616e6i	−0.00447245	+	0.00641056i
$287$	1.14231e8			0.285231
$288$	4.92958e7	−	2.84610e7i	0.121601	−	0.0702062i
$289$	1.41679e8	+	2.45396e8i	0.345274	+	0.598032i
$290$	−2.16995e7	+	3.75847e7i	−0.0522465	+	0.0904937i
$291$			1.10770e8i			0.263509i
$292$	−2.12875e8	−	1.22903e8i	−0.500361	−	0.288884i
$293$	−2.65267e8	−	1.53152e8i	−0.616094	−	0.355702i	0.159252	−	0.987238i	$-0.449092\pi$
$293$	−2.65267e8	−	1.53152e8i	−0.616094	−	0.355702i	−0.775347	+	0.631536i	$0.782425\pi$
$294$		−	3.70442e7i		−	0.0850168i
$295$	−1.38849e8	+	2.40493e8i	−0.314894	+	0.545413i
$296$	3.64469e6	+	6.31279e6i	0.00816845	+	0.0141482i
$297$	−1.47233e7	+	8.50052e6i	−0.0326106	+	0.0188277i
$298$	−3.45359e7			−0.0755986
$299$	1.48731e8	+	3.17540e8i	0.321775	+	0.686988i
$300$	−9.13869e8			−1.95416
$301$	8.45822e8	−	4.88336e8i	1.78771	−	1.03213i
$302$	−3.31754e6	−	5.74615e6i	−0.00693094	−	0.0120047i
$303$	−3.01008e8	+	5.21362e8i	−0.621626	+	1.07669i
$304$		−	6.65293e8i		−	1.35817i
$305$	2.44951e7	+	1.41422e7i	0.0494344	+	0.0285409i
$306$	−1.13560e7	−	6.55641e6i	−0.0226570	−	0.0130810i
$307$			8.86416e6i			0.0174845i	0.999962	+	0.00874225i	$0.00278278\pi$
$307$			8.86416e6i			0.0174845i	−0.999962	+	0.00874225i	$0.997217\pi$
$308$	4.77499e7	−	8.27053e7i	0.0931205	−	0.161289i
$309$	−2.23167e8	−	3.86537e8i	−0.430304	−	0.745308i
$310$	−3.15234e7	+	1.82001e7i	−0.0600990	+	0.0346982i
$311$	−3.95364e8			−0.745309			−0.372654	−	0.927970i	$-0.621552\pi$
$311$	−3.95364e8			−0.745309			−0.372654	+	0.927970i	$0.621552\pi$
$312$	−7.77512e7	+	3.64175e7i	−0.144933	+	0.0678843i
$313$	−8.88408e8			−1.63760			−0.818799	−	0.574080i	$-0.805360\pi$
$313$	−8.88408e8			−1.63760			−0.818799	+	0.574080i	$0.805360\pi$
$314$	3.84346e7	−	2.21902e7i	0.0700597	−	0.0404490i
$315$	4.90099e8	+	8.48876e8i	0.883480	+	1.53023i
$316$	9.58373e7	−	1.65995e8i	0.170856	−	0.295931i
$317$			3.40256e8i			0.599928i	0.953951	+	0.299964i	$0.0969746\pi$
$317$			3.40256e8i			0.599928i	−0.953951	+	0.299964i	$0.903025\pi$
$318$	3.39486e7	+	1.96002e7i	0.0592007	+	0.0341796i
$319$	7.24369e7	+	4.18215e7i	0.124937	+	0.0721326i
$320$			9.01123e8i			1.53730i
$321$	6.43286e8	−	1.11420e9i	1.08552	−	1.88017i
$322$	1.95808e7	+	3.39150e7i	0.0326840	+	0.0566104i
$323$	−4.00595e8	+	2.31284e8i	−0.661450	+	0.381888i
$324$	−7.13504e8			−1.16544
$325$	9.05516e8	+	7.76666e7i	1.46320	+	0.125500i
$326$	1.37174e7			0.0219286
$327$	−5.71762e8	+	3.30107e8i	−0.904270	+	0.522080i
$328$	−7.60927e6	−	1.31796e7i	−0.0119065	−	0.0206227i
$329$	−6.12331e8	+	1.06059e9i	−0.947984	+	1.64196i
$330$		−	1.07070e7i		−	0.0164009i
$331$	−4.75802e8	−	2.74704e8i	−0.721154	−	0.416359i	0.0940230	−	0.995570i	$-0.470027\pi$
$331$	−4.75802e8	−	2.74704e8i	−0.721154	−	0.416359i	−0.815177	+	0.579211i	$0.803361\pi$
$332$	2.07621e8	+	1.19870e8i	0.311377	+	0.179774i
$333$			7.19673e7i			0.106802i
$334$	−2.29919e6	+	3.98232e6i	−0.00337647	+	0.00584821i
$335$	−4.26865e8	−	7.39351e8i	−0.620345	−	1.07447i
$336$	1.14188e9	−	6.59268e8i	1.64223	−	0.948144i
$337$	−6.88538e8			−0.979993			−0.489997	−	0.871724i	$-0.663002\pi$
$337$	−6.88538e8			−0.979993			−0.489997	+	0.871724i	$0.663002\pi$
$338$	3.99954e7	−	1.47118e7i	0.0563381	−	0.0207233i
$339$	1.67420e9			2.33404
$340$	5.46586e8	−	3.15572e8i	0.754193	−	0.435434i
$341$	3.50769e7	+	6.07550e7i	0.0479050	+	0.0829739i
$342$	−2.38839e7	+	4.13681e7i	−0.0322860	+	0.0559210i
$343$		−	6.49158e7i		−	0.0868602i
$344$	−1.12686e8	−	6.50591e7i	−0.149250	−	0.0861694i
$345$	−1.05141e9	−	6.07032e8i	−1.37849	−	0.795874i
$346$		−	5.88850e7i		−	0.0764255i
$347$	3.43577e8	−	5.95094e8i	0.441440	−	0.764596i	−0.556357	−	0.830943i	$-0.687801\pi$
$347$	3.43577e8	−	5.95094e8i	0.441440	−	0.764596i	0.997797	+	0.0663474i	$0.0211346\pi$
$348$	5.79519e8	+	1.00376e9i	0.737123	+	1.27673i
$349$	−8.95711e8	+	5.17139e8i	−1.12792	+	0.651206i	−0.943411	−	0.331625i	$-0.892403\pi$
$349$	−8.95711e8	+	5.17139e8i	−1.12792	+	0.651206i	−0.184510	+	0.982831i	$0.559070\pi$
$350$	1.01503e8			0.126544
$351$	2.33430e8	+	2.00214e7i	0.288125	+	0.0247127i
$352$	−1.90961e7			−0.0233370
$353$	9.29168e8	−	5.36455e8i	1.12430	−	0.649116i	0.181806	−	0.983334i	$-0.441806\pi$
$353$	9.29168e8	−	5.36455e8i	1.12430	−	0.649116i	0.942496	+	0.334219i	$0.108472\pi$
$354$	−1.34104e7	−	2.32275e7i	−0.0160669	−	0.0278286i
$355$	1.03729e9	−	1.79664e9i	1.23056	−	2.13139i
$356$			5.57943e8i			0.655413i
$357$	−7.93935e8	−	4.58379e8i	−0.923520	−	0.533194i
$358$	−5.26073e7	−	3.03728e7i	−0.0605976	−	0.0349860i
$359$		−	6.57582e8i		−	0.750100i	−0.927005	−	0.375050i	$-0.877626\pi$
$359$		−	6.57582e8i		−	0.750100i	0.927005	−	0.375050i	$-0.122374\pi$
$360$	6.52939e7	−	1.13092e8i	0.0737588	−	0.127754i
$361$	3.95593e8	+	6.85188e8i	0.442562	+	0.766539i
$362$	−1.50420e7	+	8.68452e6i	−0.0166658	+	0.00962201i
$363$	1.19640e9			1.31282
$364$	−1.19180e9	+	5.58223e8i	−1.29524	+	0.606670i
$365$	−8.46387e8			−0.911054
$366$	−2.36581e6	+	1.36590e6i	−0.00252229	+	0.00145625i
$367$	4.47343e8	+	7.74821e8i	0.472400	+	0.818220i	0.999501	−	0.0315822i	$-0.0100546\pi$
$367$	4.47343e8	+	7.74821e8i	0.472400	+	0.818220i	−0.527102	+	0.849802i	$0.676721\pi$
$368$	−3.58709e8	+	6.21303e8i	−0.375211	+	0.649884i
$369$		−	1.50251e8i		−	0.155677i
$370$	1.08488e7	+	6.26357e6i	0.0111346	+	0.00642859i
$371$	1.04264e9	+	6.01967e8i	1.06005	+	0.612018i
$372$			9.72119e8i			0.979082i
$373$	−3.42088e8	+	5.92515e8i	−0.341317	+	0.591178i	−0.984677	−	0.174385i	$-0.944206\pi$
$373$	−3.42088e8	+	5.92515e8i	−0.341317	+	0.591178i	0.643361	+	0.765563i	$0.277540\pi$
$374$	2.19954e6	+	3.80971e6i	0.00217410	+	0.00376566i
$375$	−8.69507e8	+	5.02010e8i	−0.851458	+	0.491590i
$376$	1.63157e8			0.158288
$377$	−4.88916e8	−	1.04383e9i	−0.469937	−	1.00331i
$378$	2.61661e7			0.0249183
$379$	−9.87024e8	+	5.69859e8i	−0.931302	+	0.537687i	−0.887223	−	0.461341i	$-0.847369\pi$
$379$	−9.87024e8	+	5.69859e8i	−0.931302	+	0.537687i	−0.0440788	+	0.999028i	$0.514035\pi$
$380$	−1.14958e9	−	1.99112e9i	−1.07472	−	1.86147i
$381$	−2.52019e8	+	4.36510e8i	−0.233451	+	0.404350i
$382$			9.86680e7i			0.0905638i
$383$	1.16426e9	+	6.72186e8i	1.05890	+	0.611355i	0.925127	−	0.379657i	$-0.123958\pi$
$383$	1.16426e9	+	6.72186e8i	1.05890	+	0.611355i	0.133771	+	0.991012i	$0.457291\pi$
$384$	−3.05364e8	−	1.76302e8i	−0.275207	−	0.158891i
$385$		−	3.28835e8i		−	0.293674i
$386$	−3.09770e7	+	5.36537e7i	−0.0274147	+	0.0474837i
$387$	−6.42322e8	−	1.11253e9i	−0.563332	−	0.975719i
$388$	1.95901e8	−	1.13104e8i	0.170265	−	0.0983028i
$389$	4.06758e8			0.350359			0.175179	−	0.984537i	$-0.443949\pi$
$389$	4.06758e8			0.350359			0.175179	+	0.984537i	$0.443949\pi$
$390$	−8.44249e7	+	1.21010e8i	−0.0720683	+	0.103299i
$391$	4.98810e8			0.422004
$392$	−1.31266e8	+	7.57864e7i	−0.110065	+	0.0635463i
$393$	−3.94675e8	−	6.83597e8i	−0.327994	−	0.568102i
$394$	5.78147e7	−	1.00138e8i	0.0476213	−	0.0824826i
$395$		−	6.59995e8i		−	0.538829i
$396$	−1.08785e8	−	6.28068e7i	−0.0880308	−	0.0508246i
$397$	1.70506e8	+	9.84416e7i	0.136764	+	0.0789609i	0.566821	−	0.823841i	$-0.308173\pi$
$397$	1.70506e8	+	9.84416e7i	0.136764	+	0.0789609i	−0.430057	+	0.902802i	$0.641506\pi$
$398$			9.47562e7i			0.0753385i
$399$	−1.66980e9	+	2.89218e9i	−1.31601	+	2.27939i
$400$	9.29739e8	+	1.61036e9i	0.726359	+	1.25809i
$401$	8.66177e8	−	5.00088e8i	0.670813	−	0.387294i	−0.125572	−	0.992085i	$-0.540077\pi$
$401$	8.66177e8	−	5.00088e8i	0.670813	−	0.387294i	0.796385	+	0.604791i	$0.206743\pi$
$402$	8.24558e7			0.0633038
$403$	8.26171e7	−	9.63233e8i	0.0628785	−	0.733101i
$404$	1.22940e9			0.927599
$405$	−2.12766e9	+	1.22841e9i	−1.59151	+	0.918860i
$406$	−6.43670e7	−	1.11487e8i	−0.0477333	−	0.0826766i
$407$	1.20718e7	−	2.09089e7i	0.00887544	−	0.0153727i
$408$			1.22136e8i			0.0890293i
$409$	1.40643e9	+	8.12004e8i	1.01645	+	0.586850i	0.913075	−	0.407793i	$-0.133701\pi$
$409$	1.40643e9	+	8.12004e8i	1.01645	+	0.586850i	0.103379	+	0.994642i	$0.467035\pi$
$410$	−2.26498e7	−	1.30769e7i	−0.0162301	−	0.00937045i
$411$		−	1.76885e9i		−	1.25674i
$412$	−4.55739e8	+	7.89363e8i	−0.321053	+	0.556079i
$413$	−4.11864e8	−	7.13370e8i	−0.287693	−	0.498299i
$414$	4.46093e7	−	2.57552e7i	0.0308976	−	0.0178387i
$415$	8.25497e8			0.566953
$416$	2.15823e8	+	1.50573e8i	0.146985	+	0.102547i
$417$	−5.54678e8			−0.374598
$418$	1.38781e7	−	8.01255e6i	0.00929425	−	0.00536604i
$419$	9.59601e7	+	1.66208e8i	0.0637297	+	0.110383i	0.896130	−	0.443792i	$-0.146367\pi$
$419$	9.59601e7	+	1.66208e8i	0.0637297	+	0.110383i	−0.832400	+	0.554175i	$0.813034\pi$
$420$	2.27833e9	−	3.94618e9i	1.50053	−	2.59899i
$421$		−	1.17016e9i		−	0.764292i	−0.924102	−	0.382146i	$-0.875185\pi$
$421$		−	1.17016e9i		−	0.764292i	0.924102	−	0.382146i	$-0.124815\pi$
$422$	−4.92334e7	−	2.84249e7i	−0.0318909	−	0.0184122i
$423$	1.39502e9	+	8.05417e8i	0.896169	+	0.517404i
$424$		−	1.60396e8i		−	0.102191i
$425$	6.46433e8	−	1.11966e9i	0.408472	−	0.707495i
$426$	1.00185e8	+	1.73525e8i	0.0627868	+	0.108750i
$427$	−7.26592e7	+	4.19498e7i	−0.0451641	+	0.0260755i
$428$	−2.62736e9			−1.61982
$429$	2.33222e8	+	1.62712e8i	0.142616	+	0.0994990i
$430$	−2.23614e8			−0.135631
$431$	−1.83241e8	+	1.05794e8i	−0.110243	+	0.0636491i	−0.554108	−	0.832445i	$-0.686941\pi$
$431$	−1.83241e8	+	1.05794e8i	−0.110243	+	0.0636491i	0.443864	+	0.896094i	$0.353607\pi$
$432$	2.39674e8	+	4.15128e8i	0.143030	+	0.247736i
$433$	−5.87978e8	+	1.01841e9i	−0.348060	+	0.602857i	−0.985905	−	0.167308i	$-0.946493\pi$
$433$	−5.87978e8	+	1.01841e9i	−0.348060	+	0.602857i	0.637845	+	0.770165i	$0.279826\pi$
$434$		−	1.07973e8i		−	0.0634017i
$435$	3.45624e9	+	1.99546e9i	2.01322	+	1.16233i
$436$	1.16762e9	+	6.74125e8i	0.674681	+	0.389527i
$437$		−	1.81708e9i		−	1.04157i
$438$	4.08733e7	−	7.07947e7i	0.0232424	−	0.0402570i
$439$	−1.21215e9	−	2.09950e9i	−0.683802	−	1.18438i	−0.973812	−	0.227356i	$-0.926992\pi$
$439$	−1.21215e9	−	2.09950e9i	−0.683802	−	1.18438i	0.290010	−	0.957024i	$-0.406341\pi$
$440$	−3.79401e7	+	2.19047e7i	−0.0212331	+	0.0122590i
$441$	−1.49646e9			−0.830866
$442$	5.18059e6	−	6.04006e7i	0.00285366	−	0.0332708i
$443$	8.11271e7			0.0443356			0.0221678	−	0.999754i	$-0.492943\pi$
$443$	8.11271e7			0.0443356			0.0221678	+	0.999754i	$0.492943\pi$
$444$	2.89734e8	−	1.67278e8i	0.157094	−	0.0906981i
$445$	9.60586e8	+	1.66378e9i	0.516745	+	0.895028i
$446$	−3.22938e7	+	5.59345e7i	−0.0172364	+	0.0298543i
$447$			3.17588e9i			1.68185i
$448$	−2.31487e9	−	1.33649e9i	−1.21634	−	0.702253i
$449$	−2.29405e7	−	1.32447e7i	−0.0119603	−	0.00690525i	0.494008	−	0.869457i	$-0.335531\pi$
$449$	−2.29405e7	−	1.32447e7i	−0.0119603	−	0.00690525i	−0.505968	+	0.862552i	$0.668865\pi$
$450$		−	1.33510e8i		−	0.0690669i
$451$	−2.52030e7	+	4.36529e7i	−0.0129370	+	0.0224076i
$452$	−1.70947e9	−	2.96090e9i	−0.870719	−	1.50813i
$453$	−5.28408e8	+	3.05077e8i	−0.267070	+	0.154193i
$454$	6.71275e7			0.0336670
$455$	−2.59288e9	+	3.71649e9i	−1.29045	+	1.84966i
$456$	4.44921e8			0.219739
$457$	−2.28711e9	+	1.32046e9i	−1.12094	+	0.647172i	−0.941640	−	0.336623i	$-0.890715\pi$
$457$	−2.28711e9	+	1.32046e9i	−1.12094	+	0.647172i	−0.179296	+	0.983795i	$0.557382\pi$
$458$	2.96252e7	+	5.13124e7i	0.0144090	+	0.0249570i
$459$	1.66642e8	−	2.88632e8i	0.0804339	−	0.139316i
$460$			2.47929e9i			1.18761i
$461$	−1.91120e8	−	1.10343e8i	−0.0908558	−	0.0524556i	0.453884	−	0.891061i	$-0.350038\pi$
$461$	−1.91120e8	−	1.10343e8i	−0.0908558	−	0.0524556i	−0.544740	+	0.838605i	$0.683371\pi$
$462$	2.75049e7	+	1.58800e7i	0.0129767	+	0.00749209i
$463$		−	1.40461e9i		−	0.657691i	−0.944384	−	0.328845i	$-0.893341\pi$
$463$		−	1.40461e9i		−	0.657691i	0.944384	−	0.328845i	$-0.106659\pi$
$464$	1.17916e9	−	2.04237e9i	0.547976	−	0.949122i
$465$	1.67365e9	+	2.89885e9i	0.771934	+	1.33703i
$466$	−1.42622e8	+	8.23431e7i	−0.0652885	+	0.0376944i
$467$	1.70943e9			0.776681			0.388341	−	0.921516i	$-0.373048\pi$
$467$	1.70943e9			0.776681			0.388341	+	0.921516i	$0.373048\pi$
$468$	7.34246e8	+	1.56761e9i	0.331117	+	0.706932i
$469$	2.53240e9			1.13352
$470$	2.42827e8	−	1.40197e8i	0.107884	−	0.0622866i
$471$	−2.04058e9	−	3.53439e9i	−0.899872	−	1.55862i
$472$	−5.48711e7	+	9.50395e7i	−0.0240185	+	0.0416013i
$473$			4.30971e8i			0.187255i
$474$	5.52042e7	+	3.18722e7i	0.0238094	+	0.0137463i
$475$	−4.07872e9	−	2.35485e9i	−1.74621	−	1.00817i
$476$			1.87215e9i			0.795640i
$477$	7.91785e8	−	1.37141e9i	0.334036	−	0.578567i
$478$	−1.38720e8	−	2.40269e8i	−0.0580952	−	0.100624i
$479$	−1.87473e9	+	1.08237e9i	−0.779405	+	0.449990i	−0.836220	−	0.548395i	$-0.815239\pi$
$479$	−1.87473e9	+	1.08237e9i	−0.779405	+	0.449990i	0.0568141	+	0.998385i	$0.481906\pi$
$480$	−9.11147e8			−0.376049
$481$	−3.01302e8	+	1.41125e8i	−0.123451	+	0.0578226i
$482$	1.48902e8			0.0605669
$483$	3.11878e9	−	1.80063e9i	1.25942	−	0.727125i
$484$	−1.22161e9	−	2.11590e9i	−0.489751	−	0.848274i
$485$	3.89451e8	−	6.74549e8i	0.155009	−	0.268483i
$486$		−	1.93357e8i		−	0.0764069i
$487$	3.13354e9	+	1.80915e9i	1.22937	+	0.709779i	0.966899	−	0.255160i	$-0.0821282\pi$
$487$	3.13354e9	+	1.80915e9i	1.22937	+	0.709779i	0.262474	+	0.964939i	$0.415462\pi$
$488$	9.68011e6	+	5.58881e6i	0.00377060	+	0.00217696i
$489$		−	1.26143e9i		−	0.487847i
$490$	−1.30242e8	+	2.25587e8i	−0.0500111	+	0.0866218i
$491$	−8.96441e8	−	1.55268e9i	−0.341772	−	0.591966i	0.642990	−	0.765875i	$-0.277694\pi$
$491$	−8.96441e8	−	1.55268e9i	−0.341772	−	0.591966i	−0.984762	+	0.173908i	$0.944360\pi$
$492$	−6.04897e8	+	3.49238e8i	−0.228983	+	0.132204i
$493$	−1.63971e9			−0.616315
$494$	−2.20029e8	−	1.88721e7i	−0.0821176	−	0.00704328i
$495$	−4.32527e8			−0.160286
$496$	1.71300e9	−	9.89001e8i	0.630335	−	0.363924i
$497$	3.07690e9	+	5.32935e9i	1.12426	+	1.94727i
$498$	−3.98645e7	+	6.90474e7i	−0.0144639	+	0.0250521i
$499$			1.87794e9i			0.676596i	0.941039	+	0.338298i	$0.109851\pi$
$499$			1.87794e9i			0.676596i	−0.941039	+	0.338298i	$0.890149\pi$
$500$	1.77566e9	+	1.02518e9i	0.635279	+	0.366778i
$501$	3.66209e8	+	2.11431e8i	0.130106	+	0.0751166i
$502$		−	1.00897e7i		−	0.00355971i
$503$	5.65977e7	−	9.80300e7i	0.0198294	−	0.0343456i	−0.855940	−	0.517074i	$-0.827021\pi$
$503$	5.65977e7	−	9.80300e7i	0.0198294	−	0.0343456i	0.875770	+	0.482729i	$0.160354\pi$
$504$	1.93680e8	+	3.35464e8i	0.0673874	+	0.116718i
$505$	3.66608e9	−	2.11661e9i	1.26672	−	0.731343i
$506$	−1.72807e7			−0.00592971
$507$	−1.35288e9	−	3.67793e9i	−0.461032	−	1.25336i
$508$	1.02932e9			0.348359
$509$	4.69915e9	−	2.71305e9i	1.57945	−	0.911898i	0.584517	−	0.811381i	$-0.301284\pi$
$509$	4.69915e9	−	2.71305e9i	1.57945	−	0.911898i	0.994935	−	0.100516i	$-0.0320495\pi$
$510$	1.04948e8	+	1.81776e8i	0.0350332	+	0.0606792i
$511$	1.25531e9	−	2.17426e9i	0.416177	−	0.720840i
$512$			8.98445e8i			0.295833i
$513$	−1.05144e9	−	6.07048e8i	−0.343853	−	0.198524i
$514$	2.93858e8	+	1.69659e8i	0.0954480	+	0.0551069i
$515$			3.13850e9i			1.01250i
$516$	−2.98597e9	+	5.17186e9i	−0.956780	+	1.65719i
$517$	−2.70200e8	−	4.68001e8i	−0.0859942	−	0.148946i
$518$	−3.21807e7	+	1.85795e7i	−0.0101728	+	0.00587327i
$519$	−5.41499e9			−1.70025
$520$	6.01517e8	+	5.15925e7i	0.187602	+	0.0160907i
$521$	−2.65903e9			−0.823741			−0.411871	−	0.911242i	$-0.635124\pi$
$521$	−2.65903e9			−0.823741			−0.411871	+	0.911242i	$0.635124\pi$
$522$	−1.46642e8	+	8.46637e7i	−0.0451244	+	0.0260526i
$523$	−2.02223e9	−	3.50260e9i	−0.618122	−	1.07062i	−0.989828	−	0.142268i	$-0.954560\pi$
$523$	−2.02223e9	−	3.50260e9i	−0.618122	−	1.07062i	0.371706	−	0.928350i	$-0.378773\pi$
$524$	−8.05983e8	+	1.39600e9i	−0.244718	+	0.423864i
$525$		−	9.33410e9i		−	2.81524i
$526$	−1.78477e7	−	1.03044e7i	−0.00534726	−	0.00308724i
$527$	−1.19102e9	−	6.87637e8i	−0.354473	−	0.204655i
$528$			5.81823e8i			0.172017i
$529$	7.22687e8	−	1.25173e9i	0.212254	−	0.367634i
$530$	−1.37824e8	−	2.38717e8i	−0.0402122	−	0.0696496i
$531$	−9.38316e8	+	5.41737e8i	−0.271968	+	0.157021i
$532$	6.81994e9			1.96377
$533$	6.29049e8	−	2.94637e8i	0.179945	−	0.0842835i
$534$	−1.85553e8			−0.0527318
$535$	−7.83478e9	+	4.52341e9i	−2.21202	+	1.27711i
$536$	−1.68691e8	−	2.92181e8i	−0.0473168	−	0.0819551i
$537$	−2.79305e9	+	4.83770e9i	−0.778338	+	1.34812i
$538$			7.50633e7i			0.0207821i
$539$	4.34772e8	+	2.51016e8i	0.119592	+	0.0690463i
$540$	1.43462e9	+	8.28278e8i	0.392065	+	0.226359i
$541$			6.97904e9i			1.89498i	0.319782	+	0.947491i	$0.396390\pi$
$541$			6.97904e9i			1.89498i	−0.319782	+	0.947491i	$0.603610\pi$
$542$	1.71166e7	−	2.96467e7i	0.00461763	−	0.00799796i
$543$	7.98617e8	+	1.38325e9i	0.214062	+	0.370766i
$544$	3.24200e8	−	1.87177e8i	0.0863410	−	0.0498490i
$545$	4.64244e9			1.22845
$546$	−1.85645e8	−	3.96352e8i	−0.0488101	−	0.104209i
$547$	5.47434e7			0.0143013			0.00715065	−	0.999974i	$-0.497724\pi$
$547$	5.47434e7			0.0143013			0.00715065	+	0.999974i	$0.497724\pi$
$548$	−3.12830e9	+	1.80612e9i	−0.812038	+	0.468830i
$549$	5.51778e7	+	9.55708e7i	0.0142318	+	0.0246503i
$550$	−2.23949e7	+	3.87891e7i	−0.00573957	+	0.00994123i
$551$			5.97320e9i			1.52116i
$552$	−4.15503e8	−	2.39891e8i	−0.105145	−	0.0607053i
$553$	1.69544e9	+	9.78866e8i	0.426330	+	0.246142i
$554$			3.65784e8i			0.0913989i
$555$	5.75989e8	−	9.97643e8i	0.143017	−	0.247713i
$556$	5.66366e8	+	9.80975e8i	0.139745	+	0.242045i
$557$	1.87977e8	−	1.08528e8i	0.0460905	−	0.0266103i	−0.476778	−	0.879024i	$-0.658195\pi$
$557$	1.87977e8	−	1.08528e8i	0.0460905	−	0.0266103i	0.522868	+	0.852414i	$0.324862\pi$
$558$	−1.42020e8			−0.0346043
$559$	3.39822e9	−	4.87082e9i	0.822830	−	1.17940i
$560$	−9.27158e9			−2.23098
$561$	3.50336e8	−	2.02266e8i	0.0837750	−	0.0483675i
$562$	4.87225e7	+	8.43899e7i	0.0115785	+	0.0200546i
$563$	2.39971e9	−	4.15643e9i	0.566735	−	0.981614i	−0.430151	−	0.902757i	$-0.641540\pi$
$563$	2.39971e9	−	4.15643e9i	0.566735	−	0.981614i	0.996886	−	0.0788572i	$-0.0251271\pi$
$564$		−	7.48831e9i		−	1.75755i
$565$	−1.01953e10	−	5.88625e9i	−2.37810	−	1.37300i
$566$	5.95493e7	+	3.43808e7i	0.0138044	+	0.00797000i
$567$		−	7.28760e9i		−	1.67897i
$568$	4.09923e8	−	7.10008e8i	0.0938607	−	0.162571i
$569$	2.61206e9	+	4.52422e9i	0.594415	+	1.02956i	0.993629	+	0.112699i	$0.0359497\pi$
$569$	2.61206e9	+	4.52422e9i	0.594415	+	1.02956i	−0.399214	+	0.916858i	$0.630717\pi$
$570$	6.62179e8	−	3.82309e8i	0.149766	−	0.0864674i
$571$	−9.53468e8			−0.214328			−0.107164	−	0.994241i	$-0.534177\pi$
$571$	−9.53468e8			−0.214328			−0.107164	+	0.994241i	$0.534177\pi$
$572$	4.96273e7	−	5.78605e8i	0.0110875	−	0.129270i
$573$	9.07338e9			2.01478
$574$	6.71858e7	−	3.87897e7i	0.0148281	−	0.00856101i
$575$	2.53935e9	+	4.39829e9i	0.557039	+	0.964820i
$576$	−1.75793e9	+	3.04482e9i	−0.383285	+	0.663870i
$577$			7.41729e6i			0.00160742i	1.00000		0.000803711i	$0.000255829\pi$
$577$			7.41729e6i			0.00160742i	−1.00000		0.000803711i	$0.999744\pi$
$578$	1.66659e8	+	9.62209e7i	0.0358990	+	0.0207263i
$579$	4.93392e9	+	2.84860e9i	1.05637	+	0.609898i
$580$		−	8.15004e9i		−	1.73445i
$581$	−1.22433e9	+	2.12060e9i	−0.258989	+	0.448583i
$582$	3.76144e7	+	6.51500e7i	0.00790903	+	0.0136988i
$583$	−4.60080e8	+	2.65627e8i	−0.0961597	+	0.0555178i
$584$	−3.34481e8			−0.0694906
$585$	4.88840e9	+	3.41049e9i	1.00953	+	0.704321i
$586$	−2.08025e8			−0.0427046
$587$	5.20465e9	−	3.00490e9i	1.06208	−	0.613193i	0.136074	−	0.990699i	$-0.456551\pi$
$587$	5.20465e9	−	3.00490e9i	1.06208	−	0.613193i	0.926007	+	0.377505i	$0.123218\pi$
$588$	3.47832e9	+	6.02463e9i	0.705584	+	1.22211i
$589$	−2.50495e9	+	4.33870e9i	−0.505121	+	0.874895i
$590$			1.88597e8i			0.0378053i
$591$	−9.20856e9	−	5.31656e9i	−1.83500	−	1.05944i
$592$	−5.89531e8	−	3.40366e8i	−0.116783	−	0.0674248i
$593$			1.00461e9i			0.197836i	0.995096	+	0.0989178i	$0.0315381\pi$
$593$			1.00461e9i			0.197836i	−0.995096	+	0.0989178i	$0.968462\pi$
$594$	−5.77310e6	+	9.99930e6i	−0.00113020	+	0.00195757i
$595$	3.22320e9	+	5.58274e9i	0.627303	+	1.08652i
$596$	5.61669e9	−	3.24280e9i	1.08672	−	0.627420i
$597$	8.71365e9			1.67606
$598$	1.95305e8	+	1.36259e8i	0.0373474	+	0.0260561i
$599$	−4.70768e9			−0.894979			−0.447489	−	0.894289i	$-0.647682\pi$
$599$	−4.70768e9			−0.894979			−0.447489	+	0.894289i	$0.647682\pi$
$600$	−1.07694e9	+	6.21773e8i	−0.203546	+	0.117517i
$601$	−3.02639e9	−	5.24187e9i	−0.568676	−	0.984975i	−0.996697	−	0.0812066i	$-0.974123\pi$
$601$	−3.02639e9	−	5.24187e9i	−0.568676	−	0.984975i	0.428022	−	0.903768i	$-0.359211\pi$
$602$	3.31651e8	−	5.74437e8i	0.0619575	−	0.107314i
$603$		−	3.33094e9i		−	0.618666i
$604$	1.07909e9	+	6.23010e8i	0.199263	+	0.115045i
$605$	−7.28569e9	−	4.20640e9i	−1.33760	−	0.772265i
$606$			4.08857e8i			0.0746307i
$607$	3.56363e9	−	6.17239e9i	0.646744	−	1.12019i	−0.337152	−	0.941450i	$-0.609464\pi$
$607$	3.56363e9	−	6.17239e9i	0.646744	−	1.12019i	0.983896	−	0.178743i	$-0.0572031\pi$
$608$	−6.81855e8	−	1.18101e9i	−0.123035	−	0.213103i
$609$	−1.02522e10	+	5.91910e9i	−1.83931	+	1.06193i
$610$	1.92093e7			0.00342655
$611$	−6.36406e8	+	7.41987e9i	−0.112873	+	1.31599i
$612$	2.46249e9			0.434255
$613$	−8.66562e8	+	5.00310e8i	−0.151946	+	0.0877258i	−0.574045	−	0.818824i	$-0.694627\pi$
$613$	−8.66562e8	+	5.00310e8i	−0.151946	+	0.0877258i	0.422100	+	0.906549i	$0.361293\pi$
$614$	3.01003e6	+	5.21352e6i	0.000524785	+	0.000908954i
$615$	−1.20253e9	+	2.08285e9i	−0.208465	+	0.361073i
$616$		−	1.29951e8i		−	0.0224000i
$617$	−3.21958e9	−	1.85882e9i	−0.551825	−	0.318596i	0.198033	−	0.980195i	$-0.436545\pi$
$617$	−3.21958e9	−	1.85882e9i	−0.551825	−	0.318596i	−0.749858	+	0.661599i	$0.769878\pi$
$618$	−2.62515e8	−	1.51563e8i	−0.0447398	−	0.0258305i
$619$			8.30664e9i			1.40769i	0.710352	+	0.703847i	$0.248536\pi$
$619$			8.30664e9i			1.40769i	−0.710352	+	0.703847i	$0.751464\pi$
$620$	3.41784e9	−	5.91987e9i	0.575945	−	0.997565i
$621$	6.54611e8	+	1.13382e9i	0.109689	+	0.189987i
$622$	−2.32537e8	+	1.34255e8i	−0.0387458	+	0.0223699i
$623$	−5.69874e9			−0.944214
$624$	4.58770e9	−	6.57575e9i	0.755872	−	1.08343i
$625$	−1.90347e9			−0.311864
$626$	−5.22524e8	+	3.01680e8i	−0.0851327	+	0.0491514i
$627$	−7.36823e8	−	1.27622e9i	−0.119379	−	0.206770i
$628$	−4.16716e9	+	7.21773e9i	−0.671400	+	1.16290i
$629$			4.73302e8i			0.0758335i
$630$	5.76511e8	+	3.32849e8i	0.0918577	+	0.0530340i
$631$	6.78879e9	+	3.91951e9i	1.07570	+	0.621053i	0.929732	−	0.368237i	$-0.120038\pi$
$631$	6.78879e9	+	3.91951e9i	1.07570	+	0.621053i	0.145963	+	0.989290i	$0.453372\pi$
$632$		−	2.60821e8i		−	0.0410991i
$633$	−2.61392e9	+	4.52744e9i	−0.409618	+	0.709479i
$634$	1.15542e8	+	2.00124e8i	0.0180064	+	0.0311880i
$635$	3.06942e9	−	1.77213e9i	0.475717	−	0.274655i
$636$	−7.36157e9			−1.13467
$637$	−2.93451e9	−	6.26517e9i	−0.449830	−	0.960384i
$638$	5.68058e7			0.00866004
$639$	7.00984e9	−	4.04713e9i	1.06281	−	0.613613i
$640$	1.23971e9	+	2.14724e9i	0.186935	+	0.323780i
$641$	6.36068e8	−	1.10170e9i	0.0953895	−	0.165220i	−0.814382	−	0.580330i	$-0.802924\pi$
$641$	6.36068e8	−	1.10170e9i	0.0953895	−	0.165220i	0.909771	+	0.415110i	$0.136257\pi$
$642$		−	8.73770e8i		−	0.130324i
$643$	4.91826e9	+	2.83956e9i	0.729581	+	0.421224i	0.818269	−	0.574836i	$-0.194934\pi$
$643$	4.91826e9	+	2.83956e9i	0.729581	+	0.421224i	−0.0886881	+	0.996059i	$0.528267\pi$
$644$	−6.36899e9	−	3.67714e9i	−0.939659	−	0.542512i
$645$			2.05633e10i			3.01740i
$646$	−1.57076e8	+	2.72063e8i	−0.0229242	+	0.0397059i
$647$	−4.91513e9	−	8.51325e9i	−0.713460	−	1.23575i	−0.963551	−	0.267526i	$-0.913794\pi$
$647$	−4.91513e9	−	8.51325e9i	−0.713460	−	1.23575i	0.250091	−	0.968222i	$-0.419540\pi$
$648$	−8.40823e8	+	4.85449e8i	−0.121393	+	0.0700860i
$649$	3.63483e8			0.0521948
$650$	5.58960e8	−	2.61808e8i	0.0798332	−	0.0373927i
$651$	−9.92905e9			−1.41050
$652$	−2.23091e9	+	1.28801e9i	−0.315221	+	0.181993i
$653$	1.92707e9	+	3.33778e9i	0.270832	+	0.469096i	0.969075	−	0.246765i	$-0.0793677\pi$
$653$	1.92707e9	+	3.33778e9i	0.270832	+	0.469096i	−0.698243	+	0.715861i	$0.746034\pi$
$654$	−2.24191e8	+	3.88310e8i	−0.0313397	+	0.0542820i
$655$			5.55049e9i			0.771769i
$656$	1.23080e9	+	7.10605e8i	0.170226	+	0.0982799i
$657$	−2.85987e9	−	1.65115e9i	−0.393430	−	0.227147i
$658$			8.31725e8i			0.113812i
$659$	2.45749e9	−	4.25650e9i	0.334498	−	0.579367i	−0.648891	−	0.760882i	$-0.724767\pi$
$659$	2.45749e9	−	4.25650e9i	0.334498	−	0.579367i	0.983388	+	0.181515i	$0.0581001\pi$
$660$	1.00535e9	+	1.74131e9i	0.136117	+	0.235762i
$661$	1.10777e10	−	6.39573e9i	1.49192	−	0.861360i	0.491962	−	0.870616i	$-0.336280\pi$
$661$	1.10777e10	−	6.39573e9i	1.49192	−	0.861360i	0.999957	+	0.00925625i	$0.00294640\pi$
$662$	−3.73129e8			−0.0499869
$663$	−5.55436e9	−	4.76401e8i	−0.740179	−	0.0634856i
$664$	3.26225e8			0.0432443
$665$	2.03370e10	−	1.17416e10i	2.68171	−	1.54828i
$666$	2.44382e7	+	4.23281e7i	0.00320559	+	0.00555225i
$667$	3.22060e9	−	5.57824e9i	0.420239	−	0.727875i
$668$		−	8.63544e8i		−	0.112090i
$669$	5.14366e9	+	2.96969e9i	0.664172	+	0.383460i
$670$	−5.02127e8	−	2.89903e8i	−0.0644989	−	0.0372384i
$671$		−	3.70220e7i		−	0.00473076i
$672$	1.35136e9	−	2.34062e9i	0.171782	−	0.297536i
$673$	−5.49257e9	−	9.51341e9i	−0.694581	−	1.20305i	−0.970322	−	0.241818i	$-0.922256\pi$
$673$	−5.49257e9	−	9.51341e9i	−0.694581	−	1.20305i	0.275741	−	0.961232i	$-0.411077\pi$
$674$	−4.04969e8	+	2.33809e8i	−0.0509462	+	0.0294138i
$675$	3.39337e9			0.424686
$676$	−5.12321e9	+	6.14806e9i	−0.637864	+	0.765464i
$677$	3.14306e9			0.389307			0.194653	−	0.980872i	$-0.437642\pi$
$677$	3.14306e9			0.389307			0.194653	+	0.980872i	$0.437642\pi$
$678$	9.84691e8	−	5.68512e8i	0.121338	−	0.0700544i
$679$	1.15522e9	+	2.00090e9i	0.141619	+	0.245291i
$680$	4.29414e8	−	7.43766e8i	0.0523715	−	0.0907100i
$681$		−	6.17296e9i		−	0.748994i
$682$	4.12615e7	+	2.38223e7i	0.00498081	+	0.00287567i
$683$	−1.33989e10	−	7.73584e9i	−1.60915	−	0.929042i	−0.989561	−	0.144113i	$-0.953967\pi$
$683$	−1.33989e10	−	7.73584e9i	−1.60915	−	0.929042i	−0.619586	−	0.784929i	$-0.712699\pi$
$684$		−	8.97046e9i		−	1.07181i
$685$	−6.21904e9	+	1.07717e10i	−0.739276	+	1.28046i
$686$	−2.20436e7	−	3.81807e7i	−0.00260705	−	0.00451554i
$687$	4.71862e9	−	2.72430e9i	0.555222	−	0.320557i
$688$	1.21513e10			1.42254
$689$	7.29428e9	+	6.25635e8i	0.849601	+	0.0728708i
$690$	−8.24526e8			−0.0955504
$691$	−4.00359e9	+	2.31148e9i	−0.461612	+	0.266512i	−0.712722	−	0.701447i	$-0.752538\pi$
$691$	−4.00359e9	+	2.31148e9i	−0.461612	+	0.266512i	0.251110	+	0.967959i	$0.419204\pi$
$692$	5.52909e9	+	9.57666e9i	0.634282	+	1.09861i
$693$	6.41498e8	−	1.11111e9i	0.0732199	−	0.126821i
$694$		−	4.66678e8i		−	0.0529980i
$695$	3.37780e9	+	1.95017e9i	0.381669	+	0.220357i
$696$	1.36586e9	+	7.88579e8i	0.153558	+	0.0886569i
$697$		−	9.88145e8i		−	0.110537i
$698$	−3.51213e8	+	6.08319e8i	−0.0390910	+	0.0677076i
$699$	7.57216e9	+	1.31154e10i	0.838590	+	1.45248i
$700$	−1.65078e10	+	9.53079e9i	−1.81906	+	1.05023i
$701$	−1.41767e10			−1.55440			−0.777200	−	0.629253i	$-0.783361\pi$
$701$	−1.41767e10			−1.55440			−0.777200	+	0.629253i	$0.783361\pi$
$702$	1.44092e8	−	6.74906e7i	0.0157203	−	0.00736315i
$703$	1.72416e9			0.187169
$704$	1.02147e9	−	5.89747e8i	0.110337	−	0.0637033i
$705$	−1.28923e10	−	2.23301e10i	−1.38570	−	2.40010i
$706$	3.64332e8	−	6.31041e8i	0.0389655	−	0.0674902i
$707$			1.25569e10i			1.33634i
$708$	4.36197e9	+	2.51838e9i	0.461919	+	0.266689i
$709$	7.07624e9	+	4.08547e9i	0.745660	+	0.430507i	0.824124	−	0.566410i	$-0.191668\pi$
$709$	7.07624e9	+	4.08547e9i	0.745660	+	0.430507i	−0.0784635	+	0.996917i	$0.525001\pi$
$710$		−	1.40895e9i		−	0.147737i
$711$	1.28753e9	−	2.23007e9i	0.134343	−	0.232688i
$712$	3.79610e8	+	6.57504e8i	0.0394147	+	0.0682682i
$713$	4.67864e9	−	2.70121e9i	0.483399	−	0.279091i
$714$	−6.22612e8			−0.0640138
$715$	−8.48170e8	−	1.81084e9i	−0.0867784	−	0.185271i
$716$	1.14076e10			1.16145
$717$	−2.20949e10	+	1.27565e10i	−2.23859	+	1.29245i
$718$	−2.23297e8	−	3.86762e8i	−0.0225137	−	0.0389949i
$719$	−7.71168e9	+	1.33570e10i	−0.773745	+	1.34017i	0.161752	+	0.986831i	$0.448286\pi$
$719$	−7.71168e9	+	1.33570e10i	−0.773745	+	1.34017i	−0.935497	+	0.353334i	$0.885048\pi$
$720$			1.21952e10i			1.21766i
$721$	−8.06242e9	−	4.65484e9i	−0.801110	−	0.462521i
$722$	4.65343e8	+	2.68666e8i	0.0460143	+	0.0265664i
$723$		−	1.36928e10i		−	1.34744i
$724$	1.63089e9	−	2.82479e9i	0.159713	−	0.276631i
$725$	−8.34748e9	−	1.44583e10i	−0.813527	−	1.40907i
$726$	7.03674e8	−	4.06266e8i	0.0682486	−	0.0394033i
$727$	5.70391e9			0.550557			0.275279	−	0.961365i	$-0.411230\pi$
$727$	5.70391e9			0.550557			0.275279	+	0.961365i	$0.411230\pi$
$728$	−1.02467e9	+	1.46870e9i	−0.0984292	+	0.141083i
$729$	−5.54588e9			−0.530181
$730$	−4.97809e8	+	2.87410e8i	−0.0473623	+	0.0273446i
$731$	−4.22431e9	−	7.31672e9i	−0.399986	−	0.692796i
$732$	2.56506e8	−	4.44282e8i	0.0241718	−	0.0418668i
$733$		−	1.66495e10i		−	1.56148i	−0.624854	−	0.780742i	$-0.714841\pi$
$733$		−	1.66495e10i		−	1.56148i	0.624854	−	0.780742i	$-0.285159\pi$
$734$	5.26217e8	+	3.03811e8i	0.0491166	+	0.0283575i
$735$	2.07446e10	+	1.19769e10i	1.92708	+	1.11260i
$736$			1.47056e9i			0.135959i
$737$	−5.58730e8	+	9.67749e8i	−0.0514122	+	0.0890485i
$738$	−5.10212e7	−	8.83714e7i	−0.00467255	−	0.00809309i
$739$	−4.26718e9	+	2.46366e9i	−0.388943	+	0.224556i	−0.681702	−	0.731630i	$-0.738760\pi$
$739$	−4.26718e9	+	2.46366e9i	−0.388943	+	0.224556i	0.292759	+	0.956186i	$0.405427\pi$
$740$	−2.35251e9			−0.213412
$741$	−1.73545e9	+	2.02336e10i	−0.156693	+	1.82688i
$742$	8.17647e8			0.0734772
$743$	−8.58753e9	+	4.95801e9i	−0.768082	+	0.443452i	−0.832190	−	0.554491i	$-0.812913\pi$
$743$	−8.58753e9	+	4.95801e9i	−0.768082	+	0.443452i	0.0641082	+	0.997943i	$0.479580\pi$
$744$	6.61405e8	+	1.14559e9i	0.0588792	+	0.101982i
$745$	1.11660e10	−	1.93400e10i	0.989348	−	1.71360i
$746$			4.64656e8i			0.0409775i
$747$	2.78929e9	+	1.61040e9i	0.244834	+	0.141355i
$748$	−7.15436e8	−	4.13057e8i	−0.0625051	−	0.0360873i
$749$		−	2.68354e10i		−	2.33358i
$750$	−3.40938e8	+	5.90522e8i	−0.0295094	+	0.0511119i
$751$	1.12646e10	+	1.95109e10i	0.970456	+	1.68088i	0.694180	+	0.719801i	$0.255767\pi$
$751$	1.12646e10	+	1.95109e10i	0.970456	+	1.68088i	0.276276	+	0.961078i	$0.410900\pi$
$752$	−1.31954e10	+	7.61835e9i	−1.13151	+	0.653279i
$753$	−9.27835e8			−0.0791933
$754$	−6.42017e8	−	4.47915e8i	−0.0545439	−	0.0380536i
$755$	4.29043e9			0.362816
$756$	−4.25549e9	+	2.45691e9i	−0.358198	+	0.206806i
$757$	1.10819e10	+	1.91944e10i	0.928493	+	1.60820i	0.785846	+	0.618423i	$0.212228\pi$
$757$	1.10819e10	+	1.91944e10i	0.928493	+	1.60820i	0.142647	+	0.989774i	$0.454439\pi$
$758$	−3.87017e8	+	6.70333e8i	−0.0322766	+	0.0559047i
$759$			1.58911e9i			0.131919i
$760$	−2.70942e9	−	1.56428e9i	−0.223887	−	0.129261i
$761$	6.64485e9	+	3.83641e9i	0.546561	+	0.315557i	0.747734	−	0.663999i	$-0.231142\pi$
$761$	6.64485e9	+	3.83641e9i	0.546561	+	0.315557i	−0.201173	+	0.979556i	$0.564475\pi$
$762$			3.42316e8i			0.0280275i
$763$	−6.88540e9	+	1.19259e10i	−0.561168	+	0.971972i
$764$	−9.26457e9	−	1.60467e10i	−0.751620	−	1.30184i
$765$	7.34313e9	−	4.23956e9i	0.593016	−	0.342378i
$766$	9.13025e8			0.0733976
$767$	−4.10807e9	−	2.86607e9i	−0.328741	−	0.229352i
$768$	1.61639e10			1.28760
$769$	−7.77528e9	+	4.48906e9i	−0.616558	+	0.355970i	−0.775528	−	0.631314i	$-0.782516\pi$
$769$	−7.77528e9	+	4.48906e9i	−0.616558	+	0.355970i	0.158970	+	0.987283i	$0.449183\pi$
$770$	−1.11664e8	−	1.93407e8i	−0.00881443	−	0.0152670i
$771$	1.56016e10	−	2.70228e10i	1.22597	−	2.12344i
$772$		−	1.16345e10i		−	0.910097i
$773$	9.70027e9	+	5.60045e9i	0.755363	+	0.436109i	0.827628	−	0.561276i	$-0.189690\pi$
$773$	9.70027e9	+	5.60045e9i	0.755363	+	0.436109i	−0.0722655	+	0.997385i	$0.523023\pi$
$774$	−7.55573e8	−	4.36230e8i	−0.0585711	−	0.0338160i
$775$		−	1.40026e10i		−	1.08057i
$776$	1.53906e8	−	2.66573e8i	0.0118233	−	0.0204786i
$777$	1.70855e9	+	2.95929e9i	0.130663	+	0.226315i
$778$	2.39238e8	−	1.38124e8i	0.0182138	−	0.0105158i
$779$	−3.59965e9			−0.272822
$780$	2.36791e9	−	2.76075e10i	0.178663	−	2.08303i
$781$	−2.71546e9			−0.203969
$782$	2.93379e8	−	1.69382e8i	0.0219384	−	0.0126662i
$783$	−2.15186e9	−	3.72714e9i	−0.160195	−	0.277466i
$784$	7.07745e9	−	1.22585e10i	0.524530	−	0.908513i
$785$			2.86976e10i			2.11740i
$786$	−4.64262e8	−	2.68042e8i	−0.0341024	−	0.0196890i
$787$	−9.57297e8	−	5.52696e8i	−0.0700060	−	0.0404180i	0.464588	−	0.885527i	$-0.346202\pi$
$787$	−9.57297e8	−	5.52696e8i	−0.0700060	−	0.0404180i	−0.534594	+	0.845109i	$0.679536\pi$
$788$			2.17144e10i			1.58090i
$789$	−9.47575e8	+	1.64125e9i	−0.0686822	+	0.118961i
$790$	−2.24116e8	−	3.88181e8i	−0.0161726	−	0.0280117i
$791$	3.02421e10	−	1.74603e10i	2.17267	−	1.25439i
$792$	−1.70929e8			−0.0122258
$793$	−2.91920e8	+	4.18421e8i	−0.0207877	+	0.0297960i
$794$	1.33712e8			0.00947982
$795$	−2.19521e10	+	1.26741e10i	−1.54950	+	0.894605i
$796$	−8.89727e9	−	1.54105e10i	−0.625260	−	1.08298i
$797$	−7.49691e9	+	1.29850e10i	−0.524540	+	0.908529i	0.475052	+	0.879958i	$0.342429\pi$
$797$	−7.49691e9	+	1.29850e10i	−0.524540	+	0.908529i	−0.999592	+	0.0285717i	$0.990904\pi$
$798$			2.26807e9i			0.157996i
$799$	9.17454e9	+	5.29693e9i	0.636313	+	0.367375i
$800$	3.30089e9	+	1.90577e9i	0.227938	+	0.131600i
$801$			7.49571e9i			0.515346i
$802$	3.39632e8	−	5.88261e8i	0.0232487	−	0.0402679i
$803$	5.53925e8	+	9.59426e8i	0.0377526	+	0.0653894i
$804$	−1.34101e10	+	7.74230e9i	−0.909986	+	0.525381i
$805$	−2.53230e10			−1.71092
$806$	−2.78496e8	−	5.94588e8i	−0.0187347	−	0.0399985i
$807$	6.90272e9			0.462342
$808$	1.44878e9	−	8.36455e8i	0.0966192	−	0.0557831i
$809$	−7.66062e9	−	1.32686e10i	−0.508679	−	0.881059i	−0.999949	−	0.0100514i	$-0.996800\pi$
$809$	−7.66062e9	−	1.32686e10i	−0.508679	−	0.881059i	0.491270	−	0.871007i	$-0.336533\pi$
$810$	−8.34267e8	+	1.44499e9i	−0.0551579	+	0.0955363i
$811$		−	1.14391e10i		−	0.753041i	−0.926408	−	0.376521i	$-0.877120\pi$
$811$		−	1.14391e10i		−	0.753041i	0.926408	−	0.376521i	$-0.122880\pi$
$812$	2.09364e10	+	1.20877e10i	1.37232	+	0.792311i
$813$	−2.72628e9	−	1.57402e9i	−0.177931	−	0.102729i
$814$		−	1.63970e7i		−	0.00106556i
$815$	−4.43503e9	+	7.68170e9i	−0.286976	+	0.497056i
$816$	−5.70294e9	−	9.87779e9i	−0.367438	−	0.636420i
$817$	−2.66536e10	+	1.53885e10i	−1.70993	+	0.987229i
$818$	1.10294e9			0.0704555
$819$	−1.60113e10	+	7.49946e9i	−1.01843	+	0.477020i
$820$	4.91149e9			0.311075
$821$	1.88617e10	−	1.08898e10i	1.18954	−	0.686782i	0.231339	−	0.972873i	$-0.425689\pi$
$821$	1.88617e10	−	1.08898e10i	1.18954	−	0.686782i	0.958202	+	0.286091i	$0.0923561\pi$
$822$	−6.00654e8	−	1.04036e9i	−0.0377201	−	0.0653332i
$823$	−1.08157e9	+	1.87333e9i	−0.0676324	+	0.117143i	−0.897859	−	0.440284i	$-0.854878\pi$
$823$	−1.08157e9	+	1.87333e9i	−0.0676324	+	0.117143i	0.830226	+	0.557426i	$0.188211\pi$
$824$			1.24029e9i			0.0772287i
$825$	3.56699e9	+	2.05941e9i	0.221164	+	0.127689i
$826$	−4.84482e8	−	2.79716e8i	−0.0299122	−	0.0172698i
$827$			2.27847e10i			1.40079i	0.713755	+	0.700395i	$0.246993\pi$
$827$			2.27847e10i			1.40079i	−0.713755	+	0.700395i	$0.753007\pi$
$828$	−4.83665e9	+	8.37732e9i	−0.296100	+	0.512860i
$829$	4.91919e9	+	8.52030e9i	0.299884	+	0.519414i	0.976109	−	0.217281i	$-0.0697187\pi$
$829$	4.91919e9	+	8.52030e9i	0.299884	+	0.519414i	−0.676225	+	0.736695i	$0.736385\pi$
$830$	4.85523e8	−	2.80317e8i	0.0294738	−	0.0170167i
$831$	3.36370e10			2.03336
$832$	−1.61948e10	−	1.38904e9i	−0.974865	−	0.0836148i
$833$	−9.84168e9			−0.589945
$834$	−3.26238e8	+	1.88354e8i	−0.0194739	+	0.0112433i
$835$	−1.48672e9	−	2.57508e9i	−0.0883746	−	0.153069i
$836$	−1.50470e9	+	2.60622e9i	−0.0890692	+	0.154272i
$837$		−	3.60967e9i		−	0.212779i
$838$	1.12879e8	+	6.51709e7i	0.00662614	+	0.00382560i
$839$	−1.81235e10	−	1.04636e10i	−1.05944	−	0.611666i	−0.134160	−	0.990960i	$-0.542834\pi$
$839$	−1.81235e10	−	1.04636e10i	−1.05944	−	0.611666i	−0.925276	+	0.379294i	$0.876167\pi$
$840$		−	6.20047e9i		−	0.360950i
$841$	−1.96195e9	+	3.39821e9i	−0.113737	+	0.196999i
$842$	−3.97356e8	−	6.88240e8i	−0.0229397	−	0.0397327i
$843$	7.76038e9	−	4.48046e9i	0.446156	−	0.257588i
$844$	1.06760e10			0.611237
$845$	−4.69253e9	+	2.71539e10i	−0.267552	+	1.54822i
$846$	1.09399e9			0.0621180
$847$	2.16114e10	−	1.24774e10i	1.22206	−	0.705555i
$848$	7.48941e9	+	1.29720e10i	0.421757	+	0.730504i
$849$	3.16161e9	−	5.47607e9i	0.177309	−	0.307109i
$850$		−	8.78045e8i		−	0.0490400i
$851$	−1.61016e9	−	9.29625e8i	−0.0895602	−	0.0517076i
$852$	−3.25868e10	−	1.88140e10i	−1.80511	−	1.04218i
$853$		−	2.52741e10i		−	1.39429i	−0.716928	−	0.697147i	$-0.754452\pi$
$853$		−	2.52741e10i		−	1.39429i	0.716928	−	0.697147i	$-0.245548\pi$
$854$	−2.84901e7	+	4.93462e7i	−0.00156528	+	0.00271114i
$855$	−1.54440e10	−	2.67498e10i	−0.845043	−	1.46366i
$856$	−3.09620e9	+	1.78759e9i	−0.168721	+	0.0974114i
$857$	−2.67167e10			−1.44994			−0.724969	−	0.688782i	$-0.758146\pi$
$857$	−2.67167e10			−1.44994			−0.724969	+	0.688782i	$0.758146\pi$
$858$	1.92424e8	+	1.65043e7i	0.0104005	+	0.000892056i
$859$	−8.51182e9			−0.458191			−0.229095	−	0.973404i	$-0.573577\pi$
$859$	−8.51182e9			−0.458191			−0.229095	+	0.973404i	$0.573577\pi$
$860$	3.63671e10	−	2.09966e10i	1.94968	−	1.12565i
$861$	−3.56705e9	−	6.17832e9i	−0.190458	−	0.329882i
$862$	−7.18499e7	+	1.24448e8i	−0.00382077	+	0.00661776i
$863$			5.94525e9i			0.314871i	0.987529	+	0.157435i	$0.0503226\pi$
$863$			5.94525e9i			0.314871i	−0.987529	+	0.157435i	$0.949677\pi$
$864$	8.50924e8	+	4.91281e8i	0.0448841	+	0.0259139i
$865$	3.29754e10	+	1.90384e10i	1.73234	+	1.00017i
$866$			7.98646e8i			0.0417871i
$867$	8.84835e9	−	1.53258e10i	0.461100	−	0.798649i
$868$	1.01383e10	+	1.75600e10i	0.526193	+	0.911393i
$869$	−7.48140e8	+	4.31939e8i	−0.0386735	+	0.0223282i
$870$	2.71042e9			0.139547
$871$	1.39455e10	−	6.53186e9i	0.715105	−	0.334945i
$872$	1.83463e9			0.0937002
$873$	2.63184e9	−	1.51950e9i	0.133878	−	0.0772947i
$874$	−6.17032e8	−	1.06873e9i	−0.0312621	−	0.0541475i
$875$	−1.04710e10	+	1.81363e10i	−0.528395	+	0.915207i
$876$			1.53514e10i			0.771587i
$877$	9.21976e9	+	5.32303e9i	0.461552	+	0.266477i	0.712697	−	0.701472i	$-0.247474\pi$
$877$	9.21976e9	+	5.32303e9i	0.461552	+	0.266477i	−0.251144	+	0.967950i	$0.580807\pi$
$878$	−1.42587e9	−	8.23226e8i	−0.0710966	−	0.0410477i
$879$			1.91297e10i			0.950054i
$880$	2.04561e9	−	3.54310e9i	0.101189	−	0.175265i
$881$	−1.91599e9	−	3.31860e9i	−0.0944014	−	0.163508i	0.814957	−	0.579521i	$-0.196760\pi$
$881$	−1.91599e9	−	3.31860e9i	−0.0944014	−	0.163508i	−0.909359	+	0.416013i	$0.863427\pi$
$882$	−8.80157e8	+	5.08159e8i	−0.0431937	+	0.0249379i
$883$	−1.75487e10			−0.857792			−0.428896	−	0.903354i	$-0.641097\pi$
$883$	−1.75487e10			−0.857792			−0.428896	+	0.903354i	$0.641097\pi$
$884$	4.82886e9	+	1.03096e10i	0.235105	+	0.501948i
$885$	1.73431e10			0.841058
$886$	4.77155e7	−	2.75486e7i	0.00230485	−	0.00133070i
$887$	5.37291e9	+	9.30616e9i	0.258510	+	0.447752i	0.965843	−	0.259128i	$-0.0834352\pi$
$887$	5.37291e9	+	9.30616e9i	0.258510	+	0.447752i	−0.707333	+	0.706880i	$0.750102\pi$
$888$	2.27623e8	−	3.94255e8i	0.0109086	−	0.0188943i
$889$			1.05133e10i			0.501860i
$890$	1.12995e9	+	6.52378e8i	0.0537273	+	0.0310195i
$891$	2.78493e9	+	1.60788e9i	0.131899	+	0.0761521i
$892$		−	1.21291e10i		−	0.572204i
$893$	1.92958e10	−	3.34214e10i	0.906741	−	1.57052i
$894$	1.07844e9	+	1.86792e9i	0.0504795	+	0.0874331i
$895$	3.40174e10	−	1.96399e10i	1.58606	−	0.915714i
$896$	−7.35465e9			−0.341573
$897$	1.25302e10	−	1.79600e10i	0.579673	−	0.830871i
$898$	−1.79902e7			−0.000829025
$899$	−1.53798e10	+	8.87954e9i	−0.705980	+	0.407598i
$900$	1.25361e10	+	2.17132e10i	0.573210	+	0.992830i
$901$	5.20727e9	−	9.01926e9i	0.237178	−	0.410803i
$902$			3.42331e7i			0.00155319i
$903$	−5.28244e10	−	3.04982e10i	−2.38741	−	1.37837i
$904$	−4.02904e9	−	2.32616e9i	−0.181389	−	0.104725i
$905$		−	1.12313e10i		−	0.503687i
$906$	−2.07192e8	+	3.58866e8i	−0.00925600	+	0.0160319i
$907$	−1.03600e10	−	1.79440e10i	−0.461034	−	0.798534i	0.537979	−	0.842958i	$-0.319188\pi$
$907$	−1.03600e10	−	1.79440e10i	−0.461034	−	0.798534i	−0.999013	+	0.0444245i	$0.985855\pi$
$908$	−1.09172e10	+	6.30303e9i	−0.483960	+	0.279415i
$909$	1.65165e10			0.729363
$910$	−2.63003e8	+	3.06635e9i	−0.0115695	+	0.134889i
$911$	−3.76677e10			−1.65065			−0.825325	−	0.564658i	$-0.809008\pi$
$911$	−3.76677e10			−1.65065			−0.825325	+	0.564658i	$0.809008\pi$
$912$	−3.59832e10	+	2.07749e10i	−1.57079	+	0.906894i
$913$	−5.40254e8	−	9.35747e8i	−0.0234936	−	0.0406921i
$914$	−8.96788e8	+	1.55328e9i	−0.0388489	+	0.0672882i
$915$		−	1.76646e9i		−	0.0762307i
$916$	−9.63610e9	−	5.56341e9i	−0.414255	−	0.239170i
$917$	−1.42585e10	−	8.23217e9i	−0.610636	−	0.352551i
$918$		−	2.26348e8i		−	0.00965667i
$919$	−7.80748e9	+	1.35229e10i	−0.331823	+	0.574734i	−0.982869	−	0.184304i	$-0.940997\pi$
$919$	−7.80748e9	+	1.35229e10i	−0.331823	+	0.574734i	0.651046	+	0.759038i	$0.274330\pi$
$920$	1.68685e9	+	2.92170e9i	0.0714197	+	0.123703i
$921$	4.79429e8	−	2.76798e8i	0.0202216	−	0.0116749i
$922$	−1.49878e8			−0.00629768
$923$	3.06900e10	+	2.14115e10i	1.28467	+	0.896273i
$924$	−5.96429e9			−0.248718
$925$	−4.17337e9	+	2.40950e9i	−0.173377	+	0.100099i
$926$	−4.76967e8	−	8.26131e8i	−0.0197401	−	0.0341909i
$927$	−6.12264e9	+	1.06047e10i	−0.252441	+	0.437241i
$928$		−	4.83408e9i		−	0.198562i
$929$	2.38983e10	+	1.37977e10i	0.977941	+	0.564615i	0.901648	−	0.432471i	$-0.142358\pi$
$929$	2.38983e10	+	1.37977e10i	0.977941	+	0.564615i	0.0762934	+	0.997085i	$0.475691\pi$
$930$	1.96874e9	+	1.13665e9i	0.0802599	+	0.0463381i
$931$			3.58516e10i			1.45608i
$932$	1.54634e10	−	2.67835e10i	0.625677	−	1.08370i
$933$	1.23459e10	+	2.13838e10i	0.497666	+	0.861982i
$934$	1.00542e9	−	5.80477e8i	0.0403768	−	0.0233115i
$935$	−2.84457e9			−0.113809
$936$	1.93183e9	+	1.34778e9i	0.0770022	+	0.0537221i
$937$	−3.75571e9			−0.149143			−0.0745715	−	0.997216i	$-0.523759\pi$
$937$	−3.75571e9			−0.149143			−0.0745715	+	0.997216i	$0.523759\pi$
$938$	1.48945e9	−	8.59935e8i	0.0589273	−	0.0340217i
$939$	2.77421e10	+	4.80506e10i	1.09348	+	1.89395i
$940$	−2.63279e10	+	4.56013e10i	−1.03388	+	1.79073i
$941$		−	3.77084e10i		−	1.47528i	−0.675193	−	0.737641i	$-0.735940\pi$
$941$		−	3.77084e10i		−	1.47528i	0.675193	−	0.737641i	$-0.264060\pi$
$942$	−2.40037e9	−	1.38585e9i	−0.0935620	−	0.0540181i
$943$	3.36164e9	+	1.94084e9i	0.130545	+	0.0753701i
$944$		−	1.02485e10i		−	0.396512i
$945$	−8.45988e9	+	1.46529e10i	−0.326102	+	0.564825i
$946$	1.46346e8	+	2.53479e8i	0.00562033	+	0.00973470i
$947$	−3.96761e10	+	2.29070e10i	−1.51811	+	0.876483i	−0.518340	+	0.855174i	$0.673450\pi$
$947$	−3.96761e10	+	2.29070e10i	−1.51811	+	0.876483i	−0.999773	+	0.0213086i	$0.993217\pi$
$948$	−1.19707e10			−0.456343
$949$	1.30467e9	−	1.52111e10i	0.0495527	−	0.577736i
$950$	−3.19857e9			−0.121039
$951$	1.84032e10	−	1.06251e10i	0.693843	−	0.400590i
$952$	1.27376e9	+	2.20622e9i	0.0478475	+	0.0828743i
$953$	9.15154e9	−	1.58509e10i	0.342507	−	0.593239i	−0.642391	−	0.766377i	$-0.722057\pi$
$953$	9.15154e9	−	1.58509e10i	0.342507	−	0.593239i	0.984898	+	0.173138i	$0.0553907\pi$
$954$		−	1.07547e9i		−	0.0401034i
$955$	−5.52538e10	−	3.19008e10i	−2.05282	−	1.18519i
$956$	4.51209e10	+	2.60506e10i	1.67023	+	0.964305i
$957$		−	5.22378e9i		−	0.192661i
$958$	−7.35089e8	+	1.27321e9i	−0.0270123	+	0.0467866i
$959$	−1.84474e10	−	3.19519e10i	−0.675415	−	1.16985i
$960$	4.87383e10	−	2.81391e10i	1.77796	−	1.02650i
$961$	1.26175e10			0.458609
$962$	−1.29291e8	+	1.85318e8i	−0.00468225	+	0.00671127i
$963$	−3.52974e10			−1.27365
$964$	−2.42164e10	+	1.39813e10i	−0.870643	+	0.502666i
$965$	−2.00306e10	−	3.46940e10i	−0.717544	−	1.24282i
$966$	1.22289e9	−	2.11811e9i	0.0436483	−	0.0756010i
$967$		−	2.62013e10i		−	0.931816i	−0.884833	−	0.465908i	$-0.845728\pi$
$967$		−	2.62013e10i		−	0.931816i	0.884833	−	0.465908i	$-0.154272\pi$
$968$	−2.87920e9	−	1.66231e9i	−0.102026	−	0.0589045i
$969$	2.50185e10	+	1.44445e10i	0.883342	+	0.509998i
$970$		−	5.28988e8i		−	0.0186099i
$971$	−1.52480e9	+	2.64103e9i	−0.0534497	+	0.0925777i	−0.891512	−	0.452996i	$-0.850355\pi$
$971$	−1.52480e9	+	2.64103e9i	−0.0534497	+	0.0925777i	0.838063	+	0.545574i	$0.183688\pi$
$972$	1.81555e10	+	3.14463e10i	0.634128	+	1.09834i
$973$	−1.00195e10	+	5.78477e9i	−0.348700	+	0.201322i
$974$	2.45735e9			0.0852141
$975$	−2.40756e10	−	5.14012e10i	−0.831879	−	1.77606i
$976$	−1.04384e9			−0.0359385
$977$	3.81568e10	−	2.20298e10i	1.30900	−	0.755754i	0.327074	−	0.944999i	$-0.393937\pi$
$977$	3.81568e10	−	2.20298e10i	1.30900	−	0.755754i	0.981930	+	0.189245i	$0.0606040\pi$
$978$	−4.28349e8	−	7.41922e8i	−0.0146424	−	0.0253613i
$979$	1.25733e9	−	2.17775e9i	0.0428261	−	0.0741770i
$980$		−	4.89172e10i		−	1.66024i
$981$	1.56864e10	+	9.05656e9i	0.530496	+	0.306282i
$982$	−1.05450e9	−	6.08814e8i	−0.0355349	−	0.0205161i
$983$			3.19323e10i			1.07224i	0.844141	+	0.536122i	$0.180111\pi$
$983$			3.19323e10i			1.07224i	−0.844141	+	0.536122i	$0.819889\pi$
$984$	−4.75224e8	+	8.23113e8i	−0.0159007	+	0.0275408i
$985$	3.73846e10	+	6.47521e10i	1.24643	+	2.15887i
$986$	−9.64408e8	+	5.56801e8i	−0.0320399	+	0.0184983i
$987$	7.64843e10			2.53199
$988$	3.75561e10	−	1.75907e10i	1.23889	−	0.580277i
$989$	3.31883e10			1.09093
$990$	−2.54394e8	+	1.46874e8i	−0.00833266	+	0.00481086i
$991$	−1.83299e10	−	3.17483e10i	−0.598277	−	1.03625i	−0.993075	−	0.117478i	$-0.962519\pi$
$991$	−1.83299e10	−	3.17483e10i	−0.598277	−	1.03625i	0.394798	−	0.918768i	$-0.370814\pi$
$992$	2.02724e9	−	3.51129e9i	0.0659349	−	0.114203i
$993$			3.43124e10i			1.11206i
$994$	3.61941e9	+	2.08966e9i	0.116892	+	0.0674876i
$995$	−5.30632e10	−	3.06360e10i	−1.70770	−	0.985943i
$996$		−	1.49725e10i		−	0.480162i
$997$	−2.93042e10	+	5.07563e10i	−0.936476	+	1.62202i	−0.164495	+	0.986378i	$0.552600\pi$
$997$	−2.93042e10	+	5.07563e10i	−0.936476	+	1.62202i	−0.771981	+	0.635646i	$0.780734\pi$
$998$	6.37697e8	+	1.10452e9i	0.0203076	+	0.0351737i
$999$	−1.07584e9	+	6.21135e8i	−0.0341403	+	0.0197109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.8.e.a.10.4	yes	14
3.2	odd	2		117.8.q.b.10.4		14
4.3	odd	2		208.8.w.a.49.7		14
13.2	odd	12		169.8.a.g.1.8		14
13.3	even	3		169.8.b.d.168.8		14
13.4	even	6	inner	13.8.e.a.4.4	✓	14
13.10	even	6		169.8.b.d.168.7		14
13.11	odd	12		169.8.a.g.1.7		14
39.17	odd	6		117.8.q.b.82.4		14
52.43	odd	6		208.8.w.a.17.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.8.e.a.4.4	✓	14	13.4	even	6	inner
13.8.e.a.10.4	yes	14	1.1	even	1	trivial
117.8.q.b.10.4		14	3.2	odd	2
117.8.q.b.82.4		14	39.17	odd	6
169.8.a.g.1.7		14	13.11	odd	12
169.8.a.g.1.8		14	13.2	odd	12
169.8.b.d.168.7		14	13.10	even	6
169.8.b.d.168.8		14	13.3	even	3
208.8.w.a.17.7		14	52.43	odd	6
208.8.w.a.49.7		14	4.3	odd	2

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:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	13.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.588158 - 0.339573i) q^{2} +(-31.2267 - 54.0862i) q^{3} +(-63.7694 + 110.452i) q^{4} +439.155i q^{5} +(-36.7324 - 21.2075i) q^{6} +(-1128.14 - 651.329i) q^{7} +173.548i q^{8} +(-856.712 + 1483.87i) q^{9} +(149.125 + 258.293i) q^{10} +(497.807 - 287.409i) q^{11} +7965.23 q^{12} +(-7892.42 - 676.938i) q^{13} -884.695 q^{14} +(23752.2 - 13713.4i) q^{15} +(-8103.55 - 14035.8i) q^{16} +(-5634.27 + 9758.85i) q^{17} +1163.66i q^{18} +(35549.9 + 20524.7i) q^{19} +(-48505.5 - 28004.7i) q^{20} +81355.4i q^{21} +(195.193 - 338.083i) q^{22} +(-22132.8 - 38335.2i) q^{23} +(9386.56 - 5419.33i) q^{24} -114732. q^{25} +(-4871.86 + 2281.91i) q^{26} -29576.4 q^{27} +(143881. - 83069.7i) q^{28} +(72756.1 + 126017. i) q^{29} +(9313.38 - 16131.2i) q^{30} +122045. i q^{31} +(-28770.4 - 16610.6i) q^{32} +(-31089.7 - 17949.6i) q^{33} +7652.99i q^{34} +(286035. - 495427. i) q^{35} +(-109264. - 189251. i) q^{36} +(36374.8 - 21001.0i) q^{37} +27878.6 q^{38} +(209841. + 448010. i) q^{39} -76214.6 q^{40} +(-75942.3 + 43845.3i) q^{41} +(27626.1 + 47849.8i) q^{42} +(-374876. + 649305. i) q^{43} +73311.5i q^{44} +(-651649. - 376230. i) q^{45} +(-26035.2 - 15031.4i) q^{46} -940126. i q^{47} +(-506094. + 876580. i) q^{48} +(436688. + 756366. i) q^{49} +(-67480.7 + 38960.0i) q^{50} +703759. q^{51} +(578064. - 828564. i) q^{52} -924214. q^{53} +(-17395.6 + 10043.4i) q^{54} +(126217. + 218614. i) q^{55} +(113037. - 195786. i) q^{56} -2.56368e6i q^{57} +(85584.1 + 49412.0i) q^{58} +(547626. + 316172. i) q^{59} +3.49797e6i q^{60} +(32203.2 - 55777.7i) q^{61} +(41443.3 + 71781.9i) q^{62} +(1.93297e6 - 1.11600e6i) q^{63} +2.05195e6 q^{64} +(297281. - 3.46600e6i) q^{65} -24380.9 q^{66} +(-1.68358e6 + 972013. i) q^{67} +(-718588. - 1.24463e6i) q^{68} +(-1.38227e6 + 2.39416e6i) q^{69} -388519. i q^{70} +(-4.09113e6 - 2.36202e6i) q^{71} +(-257523. - 148681. i) q^{72} +1.92731e6i q^{73} +(14262.8 - 24703.8i) q^{74} +(3.58271e6 + 6.20544e6i) q^{75} +(-4.53399e6 + 2.61770e6i) q^{76} -748791. q^{77} +(275552. + 192244. i) q^{78} -1.50287e6 q^{79} +(6.16388e6 - 3.55872e6i) q^{80} +(2.79720e6 + 4.84490e6i) q^{81} +(-29777.4 + 51575.9i) q^{82} -1.87974e6i q^{83} +(-8.98585e6 - 5.18798e6i) q^{84} +(-4.28565e6 - 2.47432e6i) q^{85} +509191. i q^{86} +(4.54386e6 - 7.87020e6i) q^{87} +(49879.3 + 86393.4i) q^{88} +(3.78860e6 - 2.18735e6i) q^{89} -511030. q^{90} +(8.46281e6 + 5.90424e6i) q^{91} +5.64559e6 q^{92} +(6.60097e6 - 3.81107e6i) q^{93} +(-319241. - 552942. i) q^{94} +(-9.01354e6 + 1.56119e7i) q^{95} +2.07477e6i q^{96} +(-1.53602e6 - 886819. i) q^{97} +(513683. + 296575. i) q^{98} +984906. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} + 26 q^{3} + 383 q^{4} - 264 q^{6} - 2772 q^{7} - 3491 q^{9} - 509 q^{10} + 6516 q^{11} + 38380 q^{12} + 5109 q^{13} - 47916 q^{14} - 19266 q^{15} - 633 q^{16} - 38403 q^{17} + 43254 q^{19}+ \cdots + 16173003 q^{98}+O(q^{100}) \) 14 * q - 3 * q^2 + 26 * q^3 + 383 * q^4 - 264 * q^6 - 2772 * q^7 - 3491 * q^9 - 509 * q^10 + 6516 * q^11 + 38380 * q^12 + 5109 * q^13 - 47916 * q^14 - 19266 * q^15 - 633 * q^16 - 38403 * q^17 + 43254 * q^19 + 89409 * q^20 - 125882 * q^22 - 68550 * q^23 + 224454 * q^24 + 39380 * q^25 + 361959 * q^26 - 432400 * q^27 - 234780 * q^28 + 221583 * q^29 - 157890 * q^30 - 878067 * q^32 + 219756 * q^33 + 659616 * q^35 + 635675 * q^36 - 565347 * q^37 + 953640 * q^38 + 30082 * q^39 - 77182 * q^40 + 1716057 * q^41 + 206406 * q^42 - 882692 * q^43 - 4616853 * q^45 - 3267480 * q^46 + 1133630 * q^48 + 2653979 * q^49 + 145128 * q^50 - 38964 * q^51 + 4962178 * q^52 - 1791210 * q^53 + 9597234 * q^54 + 2453536 * q^55 - 7457952 * q^56 - 14978127 * q^58 - 1189032 * q^59 + 3858525 * q^61 + 1904142 * q^62 + 7718520 * q^63 + 14570922 * q^64 + 10424661 * q^65 - 31956396 * q^66 + 4674330 * q^67 + 9569619 * q^68 - 13743840 * q^69 - 25203126 * q^71 - 6851607 * q^72 + 8640105 * q^74 + 10316152 * q^75 + 12934506 * q^76 + 19599336 * q^77 + 50085750 * q^78 - 30688440 * q^79 + 29127963 * q^80 + 13886221 * q^81 - 37359719 * q^82 - 96398508 * q^84 - 22436313 * q^85 + 12769686 * q^87 + 27045536 * q^88 + 2123160 * q^89 + 41193546 * q^90 + 37205532 * q^91 - 47685588 * q^92 + 36638964 * q^93 + 19138810 * q^94 - 43420386 * q^95 - 68556288 * q^97 + 16173003 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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