LMFDB - Embedded newform 28.9.c.a.15.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [28,9,Mod(15,28)] 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("28.15"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	28.c (of order $2$, degree $1$, 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:	$11.4066010817$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			15.14
Character	$\chi$	$=$	28.15
Dual form			28.9.c.a.15.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.44338 + 15.8123i) q^{2} -4.01293i q^{3} +(-244.060 + 77.2712i) q^{4} +1160.46 q^{5} +(63.4538 - 9.80514i) q^{6} +907.493i q^{7} +(-1818.17 - 3670.35i) q^{8} +6544.90 q^{9} +(2835.44 + 18349.5i) q^{10} +19382.1i q^{11} +(310.084 + 979.395i) q^{12} -16160.5 q^{13} +(-14349.6 + 2217.35i) q^{14} -4656.84i q^{15} +(53594.3 - 37717.6i) q^{16} -65274.8 q^{17} +(15991.7 + 103490. i) q^{18} +62986.6i q^{19} +(-283221. + 89670.0i) q^{20} +3641.71 q^{21} +(-306476. + 47357.8i) q^{22} +362618. i q^{23} +(-14728.9 + 7296.19i) q^{24} +956037. q^{25} +(-39486.4 - 255535. i) q^{26} -52593.1i q^{27} +(-70123.1 - 221482. i) q^{28} +150564. q^{29} +(73635.5 - 11378.4i) q^{30} -1.14181e6i q^{31} +(727355. + 755293. i) q^{32} +77778.9 q^{33} +(-159491. - 1.03215e6i) q^{34} +1.05311e6i q^{35} +(-1.59735e6 + 505732. i) q^{36} +1.80017e6 q^{37} +(-995965. + 153900. i) q^{38} +64851.1i q^{39} +(-2.10991e6 - 4.25929e6i) q^{40} +1.03838e6 q^{41} +(8898.09 + 57583.9i) q^{42} -5.88269e6i q^{43} +(-1.49768e6 - 4.73038e6i) q^{44} +7.59508e6 q^{45} +(-5.73384e6 + 886016. i) q^{46} +4.22877e6i q^{47} +(-151358. - 215070. i) q^{48} -823543. q^{49} +(2.33597e6 + 1.51172e7i) q^{50} +261943. i q^{51} +(3.94413e6 - 1.24874e6i) q^{52} -8.69385e6 q^{53} +(831619. - 128505. i) q^{54} +2.24921e7i q^{55} +(3.33082e6 - 1.64998e6i) q^{56} +252761. q^{57} +(367885. + 2.38077e6i) q^{58} -2.14783e7i q^{59} +(359840. + 1.13655e6i) q^{60} -1.49778e6 q^{61} +(1.80546e7 - 2.78988e6i) q^{62} +5.93945e6i q^{63} +(-1.01657e7 + 1.33466e7i) q^{64} -1.87536e7 q^{65} +(190044. + 1.22987e6i) q^{66} +5.84369e6i q^{67} +(1.59309e7 - 5.04386e6i) q^{68} +1.45516e6 q^{69} +(-1.66521e7 + 2.57315e6i) q^{70} -2.91579e6i q^{71} +(-1.18997e7 - 2.40221e7i) q^{72} -2.52599e7 q^{73} +(4.39850e6 + 2.84649e7i) q^{74} -3.83651e6i q^{75} +(-4.86705e6 - 1.53725e7i) q^{76} -1.75891e7 q^{77} +(-1.02545e6 + 158456. i) q^{78} -2.89042e7i q^{79} +(6.21939e7 - 4.37697e7i) q^{80} +4.27300e7 q^{81} +(2.53716e6 + 1.64192e7i) q^{82} -4.80898e7i q^{83} +(-888794. + 281399. i) q^{84} -7.57486e7 q^{85} +(9.30191e7 - 1.43737e7i) q^{86} -604203. i q^{87} +(7.11389e7 - 3.52399e7i) q^{88} -1.75331e7 q^{89} +(1.85577e7 + 1.20096e8i) q^{90} -1.46656e7i q^{91} +(-2.80200e7 - 8.85005e7i) q^{92} -4.58200e6 q^{93} +(-6.68667e7 + 1.03325e7i) q^{94} +7.30933e7i q^{95} +(3.03094e6 - 2.91883e6i) q^{96} +8.33031e7 q^{97} +(-2.01223e6 - 1.30221e7i) q^{98} +1.26854e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 383 q^{4} - 336 q^{5} + 5502 q^{6} - 12069 q^{8} - 56296 q^{9} + 41972 q^{10} - 31290 q^{12} - 28560 q^{13} + 7203 q^{14} + 166193 q^{16} - 165648 q^{17} - 11609 q^{18} - 71568 q^{20} - 955748 q^{22}+ \cdots - 2470629 q^{98}+O(q^{100}) $ 24 * q + 3 * q^2 - 383 * q^4 - 336 * q^5 + 5502 * q^6 - 12069 * q^8 - 56296 * q^9 + 41972 * q^10 - 31290 * q^12 - 28560 * q^13 + 7203 * q^14 + 166193 * q^16 - 165648 * q^17 - 11609 * q^18 - 71568 * q^20 - 955748 * q^22 + 133322 * q^24 + 989640 * q^25 - 1066632 * q^26 - 372155 * q^28 + 997296 * q^29 + 3246560 * q^30 - 2265357 * q^32 - 5521600 * q^33 + 1423618 * q^34 - 649451 * q^36 + 5387056 * q^37 + 3945690 * q^38 + 11452504 * q^40 - 12346320 * q^41 + 5642350 * q^42 - 2412372 * q^44 + 17486448 * q^45 + 537288 * q^46 + 20895070 * q^48 - 19765032 * q^49 - 28121691 * q^50 - 12804764 * q^52 + 10812720 * q^53 - 42610652 * q^54 - 7109361 * q^56 + 6748288 * q^57 + 36144266 * q^58 - 98388944 * q^60 + 33644464 * q^61 + 12180756 * q^62 - 1102631 * q^64 - 9084960 * q^65 + 83635608 * q^66 + 106943886 * q^68 - 90944448 * q^69 + 11611236 * q^70 - 48881753 * q^72 - 7651728 * q^73 - 66897318 * q^74 + 64861986 * q^76 - 47482176 * q^77 - 41838760 * q^78 + 154560168 * q^80 + 299710744 * q^81 - 13781390 * q^82 + 571438 * q^84 - 280618528 * q^85 - 139907676 * q^86 - 65086060 * q^88 + 215250672 * q^89 + 40480132 * q^90 + 111569640 * q^92 + 181272192 * q^93 + 171294732 * q^94 - 684707590 * q^96 + 114327024 * q^97 - 2470629 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

$2$	2.44338	+	15.8123i	0.152712	+	0.988271i
$2$	2.44338	+	15.8123i	0.152712	+	0.988271i
$3$		−	4.01293i		−	0.0495424i	−0.999693	−	0.0247712i	$-0.992114\pi$
$3$		−	4.01293i		−	0.0495424i	0.999693	−	0.0247712i	$-0.00788572\pi$
$4$	−244.060	+	77.2712i	−0.953358	+	0.301841i
$5$	1160.46			1.85673			0.928366	−	0.371667i	$-0.121214\pi$
$5$	1160.46			1.85673			0.928366	+	0.371667i	$0.121214\pi$
$6$	63.4538	−	9.80514i	0.0489613	−	0.00756569i
$7$			907.493i			0.377964i
$7$			907.493i			0.377964i
$8$	−1818.17	−	3670.35i	−0.443889	−	0.896082i
$9$	6544.90			0.997546
$10$	2835.44	+	18349.5i	0.283544	+	1.83495i
$11$			19382.1i			1.32382i	0.749583	+	0.661910i	$0.230254\pi$
$11$			19382.1i			1.32382i	−0.749583	+	0.661910i	$0.769746\pi$
$12$	310.084	+	979.395i	0.0149539	+	0.0472316i
$13$	−16160.5			−0.565825			−0.282912	−	0.959146i	$-0.591301\pi$
$13$	−16160.5			−0.565825			−0.282912	+	0.959146i	$0.591301\pi$
$14$	−14349.6	+	2217.35i	−0.373531	+	0.0577195i
$15$		−	4656.84i		−	0.0919869i
$16$	53594.3	−	37717.6i	0.817784	−	0.575525i
$17$	−65274.8			−0.781537			−0.390769	−	0.920489i	$-0.627791\pi$
$17$	−65274.8			−0.781537			−0.390769	+	0.920489i	$0.627791\pi$
$18$	15991.7	+	103490.i	0.152337	+	0.985845i
$19$			62986.6i			0.483319i	0.970361	+	0.241659i	$0.0776917\pi$
$19$			62986.6i			0.483319i	−0.970361	+	0.241659i	$0.922308\pi$
$20$	−283221.	+	89670.0i	−1.77013	+	0.560437i
$21$	3641.71			0.0187253
$22$	−306476.	+	47357.8i	−1.30829	+	0.202163i
$23$			362618.i			1.29580i	0.761725	+	0.647900i	$0.224353\pi$
$23$			362618.i			1.29580i	−0.761725	+	0.647900i	$0.775647\pi$
$24$	−14728.9	+	7296.19i	−0.0443940	+	0.0219913i
$25$	956037.			2.44746
$26$	−39486.4	−	255535.i	−0.0864080	−	0.559188i
$27$		−	52593.1i		−	0.0989632i
$28$	−70123.1	−	221482.i	−0.114085	−	0.360336i
$29$	150564.			0.212877			0.106439	−	0.994319i	$-0.466055\pi$
$29$	150564.			0.212877			0.106439	+	0.994319i	$0.466055\pi$
$30$	73635.5	−	11378.4i	0.0909080	−	0.0140475i
$31$		−	1.14181e6i		−	1.23636i	−0.786035	−	0.618182i	$-0.787870\pi$
$31$		−	1.14181e6i		−	1.23636i	0.786035	−	0.618182i	$-0.212130\pi$
$32$	727355.	+	755293.i	0.693659	+	0.720303i
$33$	77778.9			0.0655852
$34$	−159491.	−	1.03215e6i	−0.119350	−	0.772370i
$35$			1.05311e6i			0.701779i
$36$	−1.59735e6	+	505732.i	−0.951018	+	0.301100i
$37$	1.80017e6			0.960520			0.480260	−	0.877126i	$-0.340542\pi$
$37$	1.80017e6			0.960520			0.480260	+	0.877126i	$0.340542\pi$
$38$	−995965.	+	153900.i	−0.477650	+	0.0738084i
$39$			64851.1i			0.0280323i
$40$	−2.10991e6	−	4.25929e6i	−0.824183	−	1.66378i
$41$	1.03838e6			0.367468			0.183734	−	0.982976i	$-0.441181\pi$
$41$	1.03838e6			0.367468			0.183734	+	0.982976i	$0.441181\pi$
$42$	8898.09	+	57583.9i	0.00285956	+	0.0185056i
$43$		−	5.88269e6i		−	1.72069i	−0.509713	−	0.860345i	$-0.670248\pi$
$43$		−	5.88269e6i		−	1.72069i	0.509713	−	0.860345i	$-0.329752\pi$
$44$	−1.49768e6	−	4.73038e6i	−0.399583	−	1.26208i
$45$	7.59508e6			1.85218
$46$	−5.73384e6	+	886016.i	−1.28060	+	0.197884i
$47$			4.22877e6i			0.866607i	0.901248	+	0.433304i	$0.142652\pi$
$47$			4.22877e6i			0.866607i	−0.901248	+	0.433304i	$0.857348\pi$
$48$	−151358.	−	215070.i	−0.0285129	−	0.0405150i
$49$	−823543.			−0.142857
$50$	2.33597e6	+	1.51172e7i	0.373755	+	2.41875i
$51$			261943.i			0.0387192i
$52$	3.94413e6	−	1.24874e6i	0.539434	−	0.170789i
$53$	−8.69385e6			−1.10181			−0.550907	−	0.834566i	$-0.685718\pi$
$53$	−8.69385e6			−1.10181			−0.550907	+	0.834566i	$0.685718\pi$
$54$	831619.	−	128505.i	0.0978024	−	0.0151128i
$55$			2.24921e7i			2.45798i
$56$	3.33082e6	−	1.64998e6i	0.338687	−	0.167774i
$57$	252761.			0.0239448
$58$	367885.	+	2.38077e6i	0.0325088	+	0.210380i
$59$		−	2.14783e7i		−	1.77252i	−0.463186	−	0.886261i	$-0.653294\pi$
$59$		−	2.14783e7i		−	1.77252i	0.463186	−	0.886261i	$-0.346706\pi$
$60$	359840.	+	1.13655e6i	0.0277654	+	0.0876965i
$61$	−1.49778e6			−0.108175			−0.0540877	−	0.998536i	$-0.517225\pi$
$61$	−1.49778e6			−0.108175			−0.0540877	+	0.998536i	$0.517225\pi$
$62$	1.80546e7	−	2.78988e6i	1.22186	−	0.188807i
$63$			5.93945e6i			0.377037i
$64$	−1.01657e7	+	1.33466e7i	−0.605925	+	0.795522i
$65$	−1.87536e7			−1.05058
$66$	190044.	+	1.22987e6i	0.0100156	+	0.0648160i
$67$			5.84369e6i			0.289994i	0.989432	+	0.144997i	$0.0463172\pi$
$67$			5.84369e6i			0.289994i	−0.989432	+	0.144997i	$0.953683\pi$
$68$	1.59309e7	−	5.04386e6i	0.745085	−	0.235900i
$69$	1.45516e6			0.0641971
$70$	−1.66521e7	+	2.57315e6i	−0.693548	+	0.107170i
$71$		−	2.91579e6i		−	0.114742i	−0.998353	−	0.0573711i	$-0.981728\pi$
$71$		−	2.91579e6i		−	0.114742i	0.998353	−	0.0573711i	$-0.0182718\pi$
$72$	−1.18997e7	−	2.40221e7i	−0.442800	−	0.893882i
$73$	−2.52599e7			−0.889489			−0.444744	−	0.895658i	$-0.646705\pi$
$73$	−2.52599e7			−0.889489			−0.444744	+	0.895658i	$0.646705\pi$
$74$	4.39850e6	+	2.84649e7i	0.146682	+	0.949254i
$75$		−	3.83651e6i		−	0.121253i
$76$	−4.86705e6	−	1.53725e7i	−0.145885	−	0.460776i
$77$	−1.75891e7			−0.500357
$78$	−1.02545e6	+	158456.i	−0.0277035	+	0.00428086i
$79$		−	2.89042e7i		−	0.742083i	−0.928616	−	0.371042i	$-0.879001\pi$
$79$		−	2.89042e7i		−	0.742083i	0.928616	−	0.371042i	$-0.120999\pi$
$80$	6.21939e7	−	4.37697e7i	1.51841	−	1.06860i
$81$	4.27300e7			0.992643
$82$	2.53716e6	+	1.64192e7i	0.0561166	+	0.363158i
$83$		−	4.80898e7i		−	1.01331i	−0.862150	−	0.506653i	$-0.830883\pi$
$83$		−	4.80898e7i		−	1.01331i	0.862150	−	0.506653i	$-0.169117\pi$
$84$	−888794.	+	281399.i	−0.0178519	+	0.00565205i
$85$	−7.57486e7			−1.45111
$86$	9.30191e7	−	1.43737e7i	1.70051	−	0.262769i
$87$		−	604203.i		−	0.0105464i
$88$	7.11389e7	−	3.52399e7i	1.18625	−	0.587630i
$89$	−1.75331e7			−0.279447			−0.139723	−	0.990191i	$-0.544621\pi$
$89$	−1.75331e7			−0.279447			−0.139723	+	0.990191i	$0.544621\pi$
$90$	1.85577e7	+	1.20096e8i	0.282849	+	1.83045i
$91$		−	1.46656e7i		−	0.213862i
$92$	−2.80200e7	−	8.85005e7i	−0.391125	−	1.23536i
$93$	−4.58200e6			−0.0612524
$94$	−6.68667e7	+	1.03325e7i	−0.856443	+	0.132341i
$95$			7.30933e7i			0.897394i
$96$	3.03094e6	−	2.91883e6i	0.0356855	−	0.0343655i
$97$	8.33031e7			0.940966			0.470483	−	0.882409i	$-0.344080\pi$
$97$	8.33031e7			0.940966			0.470483	+	0.882409i	$0.344080\pi$
$98$	−2.01223e6	−	1.30221e7i	−0.0218159	−	0.141182i
$99$			1.26854e8i			1.32057i
$100$	−2.33330e8	+	7.38742e7i	−2.33330	+	0.738742i
$101$	1.20539e8			1.15836			0.579180	−	0.815200i	$-0.303373\pi$
$101$	1.20539e8			1.15836			0.579180	+	0.815200i	$0.303373\pi$
$102$	−4.14193e6	+	640028.i	−0.0382651	+	0.00591287i
$103$		−	1.94768e8i		−	1.73049i	−0.501350	−	0.865244i	$-0.667163\pi$
$103$		−	1.94768e8i		−	1.73049i	0.501350	−	0.865244i	$-0.332837\pi$
$104$	2.93826e7	+	5.93148e7i	0.251163	+	0.507025i
$105$	4.22605e6			0.0347678
$106$	−2.12424e7	−	1.37470e8i	−0.168260	−	1.08889i
$107$			3.81176e7i			0.290797i	0.989373	+	0.145399i	$0.0464464\pi$
$107$			3.81176e7i			0.290797i	−0.989373	+	0.145399i	$0.953554\pi$
$108$	4.06393e6	+	1.28359e7i	0.0298711	+	0.0943474i
$109$	2.35498e7			0.166833			0.0834164	−	0.996515i	$-0.473417\pi$
$109$	2.35498e7			0.166833			0.0834164	+	0.996515i	$0.473417\pi$
$110$	−3.55652e8	+	5.49568e7i	−2.42915	+	0.375362i
$111$		−	7.22396e6i		−	0.0475864i
$112$	3.42284e7	+	4.86365e7i	0.217528	+	0.309093i
$113$	−7.45348e6			−0.0457136			−0.0228568	−	0.999739i	$-0.507276\pi$
$113$	−7.45348e6			−0.0457136			−0.0228568	+	0.999739i	$0.507276\pi$
$114$	617592.	+	3.99674e6i	0.00365664	+	0.0236639i
$115$			4.20803e8i			2.40596i
$116$	−3.67466e7	+	1.16343e7i	−0.202948	+	0.0642550i
$117$	−1.05769e8			−0.564436
$118$	3.39622e8	−	5.24797e7i	1.75173	−	0.270685i
$119$		−	5.92364e7i		−	0.295393i
$120$	−1.70922e7	+	8.46693e6i	−0.0824278	+	0.0408320i
$121$	−1.61305e8			−0.752501
$122$	−3.65965e6	−	2.36834e7i	−0.0165196	−	0.106907i
$123$		−	4.16694e6i		−	0.0182053i
$124$	8.82289e7	+	2.78669e8i	0.373185	+	1.17870i
$125$	6.56137e8			2.68754
$126$	−9.39165e7	+	1.45124e7i	−0.372614	+	0.0575779i
$127$		−	2.36616e8i		−	0.909557i	−0.890605	−	0.454778i	$-0.849718\pi$
$127$		−	2.36616e8i		−	0.909557i	0.890605	−	0.454778i	$-0.150282\pi$
$128$	−2.35880e8	−	1.28133e8i	−0.878723	−	0.477332i
$129$	−2.36069e7			−0.0852471
$130$	−4.58223e7	−	2.96538e8i	−0.160436	−	1.03826i
$131$		−	6.81100e7i		−	0.231273i	−0.993292	−	0.115637i	$-0.963109\pi$
$131$		−	6.81100e7i		−	0.231273i	0.993292	−	0.115637i	$-0.0368908\pi$
$132$	−1.89827e7	+	6.01007e6i	−0.0625262	+	0.0197963i
$133$	−5.71599e7			−0.182677
$134$	−9.24024e7	+	1.42784e7i	−0.286592	+	0.0442854i
$135$		−	6.10321e7i		−	0.183748i
$136$	1.18681e8	+	2.39581e8i	0.346916	+	0.700321i
$137$	3.57972e8			1.01617			0.508085	−	0.861307i	$-0.330354\pi$
$137$	3.57972e8			1.01617			0.508085	+	0.861307i	$0.330354\pi$
$138$	3.55552e6	+	2.30095e7i	0.00980363	+	0.0634441i
$139$			2.03272e8i			0.544526i	0.962223	+	0.272263i	$0.0877721\pi$
$139$			2.03272e8i			0.544526i	−0.962223	+	0.272263i	$0.912228\pi$
$140$	−8.13749e7	−	2.57021e8i	−0.211825	−	0.669047i
$141$	1.69698e7			0.0429338
$142$	4.61055e7	−	7.12440e6i	0.113396	−	0.0175225i
$143$		−	3.13224e8i		−	0.749050i
$144$	3.50769e8	−	2.46858e8i	0.815777	−	0.574112i
$145$	1.74723e8			0.395256
$146$	−6.17197e7	−	3.99418e8i	−0.135835	−	0.879056i
$147$			3.30482e6i			0.00707748i
$148$	−4.39349e8	+	1.39101e8i	−0.915720	+	0.289924i
$149$	−6.25903e8			−1.26988			−0.634939	−	0.772563i	$-0.718975\pi$
$149$	−6.25903e8			−1.26988			−0.634939	+	0.772563i	$0.718975\pi$
$150$	6.06642e7	−	9.37408e6i	0.119831	−	0.0185167i
$151$			1.60911e8i			0.309513i	0.987953	+	0.154756i	$0.0494592\pi$
$151$			1.60911e8i			0.309513i	−0.987953	+	0.154756i	$0.950541\pi$
$152$	2.31183e8	−	1.14520e8i	0.433093	−	0.214540i
$153$	−4.27217e8			−0.779619
$154$	−4.29769e7	−	2.78124e8i	−0.0764103	−	0.494488i
$155$		−	1.32502e9i		−	2.29560i
$156$	−5.01112e6	−	1.58275e7i	−0.00846129	−	0.0267248i
$157$	−7.58784e8			−1.24888			−0.624439	−	0.781074i	$-0.714672\pi$
$157$	−7.58784e8			−1.24888			−0.624439	+	0.781074i	$0.714672\pi$
$158$	4.57043e8	−	7.06241e7i	0.733379	−	0.113325i
$159$			3.48878e7i			0.0545865i
$160$	8.44064e8	+	8.76485e8i	1.28794	+	1.33741i
$161$	−3.29073e8			−0.489767
$162$	1.04406e8	+	6.75661e8i	0.151588	+	0.981000i
$163$			9.92814e8i			1.40643i	0.710978	+	0.703214i	$0.248252\pi$
$163$			9.92814e8i			1.40643i	−0.710978	+	0.703214i	$0.751748\pi$
$164$	−2.53426e8	+	8.02367e7i	−0.350329	+	0.110917i
$165$	9.02591e7			0.121774
$166$	7.60412e8	−	1.17502e8i	1.00142	−	0.154744i
$167$			285117.i			0.000366570i	1.00000		0.000183285i	$5.83415e-5\pi$
$167$			285117.i			0.000366570i	−1.00000		0.000183285i	$0.999942\pi$
$168$	−6.62124e6	−	1.33663e7i	−0.00831194	−	0.0167794i
$169$	−5.54568e8			−0.679842
$170$	−1.85083e8	−	1.19776e9i	−0.221601	−	1.43409i
$171$			4.12241e8i			0.482133i
$172$	4.54563e8	+	1.43573e9i	0.519374	+	1.64043i
$173$	−7.05462e8			−0.787570			−0.393785	−	0.919203i	$-0.628834\pi$
$173$	−7.05462e8			−0.787570			−0.393785	+	0.919203i	$0.628834\pi$
$174$	9.55386e6	−	1.47630e6i	0.0104227	−	0.00161056i
$175$			8.67597e8i			0.925051i
$176$	7.31044e8	+	1.03877e9i	0.761892	+	1.08260i
$177$	−8.61909e7			−0.0878150
$178$	−4.28402e7	−	2.77240e8i	−0.0426748	−	0.276169i
$179$			4.86516e8i			0.473898i	0.971522	+	0.236949i	$0.0761474\pi$
$179$			4.86516e8i			0.473898i	−0.971522	+	0.236949i	$0.923853\pi$
$180$	−1.85365e9	+	5.86881e8i	−1.76579	+	0.559062i
$181$	8.72888e8			0.813288			0.406644	−	0.913587i	$-0.366699\pi$
$181$	8.72888e8			0.813288			0.406644	+	0.913587i	$0.366699\pi$
$182$	2.31897e8	−	3.58336e7i	0.211353	−	0.0326591i
$183$			6.01049e6i			0.00535927i
$184$	1.33094e9	−	6.59302e8i	1.16114	−	0.575192i
$185$	2.08902e9			1.78343
$186$	−1.11956e7	−	7.24521e7i	−0.00935395	−	0.0605340i
$187$		−	1.26516e9i		−	1.03462i
$188$	−3.26762e8	−	1.03207e9i	−0.261577	−	0.826187i
$189$	4.77278e7			0.0374046
$190$	−1.15578e9	+	1.78595e8i	−0.886868	+	0.137042i
$191$			4.23807e8i			0.318445i	0.987243	+	0.159223i	$0.0508987\pi$
$191$			4.23807e8i			0.318445i	−0.987243	+	0.159223i	$0.949101\pi$
$192$	5.35592e7	+	4.07944e7i	0.0394121	+	0.0300190i
$193$	−1.80170e9			−1.29854			−0.649268	−	0.760559i	$-0.724925\pi$
$193$	−1.80170e9			−1.29854			−0.649268	+	0.760559i	$0.724925\pi$
$194$	2.03541e8	+	1.31722e9i	0.143696	+	0.929930i
$195$			7.52569e7i			0.0520485i
$196$	2.00994e8	−	6.36362e7i	0.136194	−	0.0431201i
$197$	−7.79622e8			−0.517630			−0.258815	−	0.965927i	$-0.583332\pi$
$197$	−7.79622e8			−0.517630			−0.258815	+	0.965927i	$0.583332\pi$
$198$	−2.00585e9	+	3.09952e8i	−1.30508	+	0.201666i
$199$		−	1.27435e9i		−	0.812599i	−0.913740	−	0.406300i	$-0.866819\pi$
$199$		−	1.27435e9i		−	0.812599i	0.913740	−	0.406300i	$-0.133181\pi$
$200$	−1.73824e9	−	3.50899e9i	−1.08640	−	2.19312i
$201$	2.34504e7			0.0143670
$202$	2.94524e8	+	1.90601e9i	0.176895	+	1.14477i
$203$			1.36636e8i			0.0804600i
$204$	−2.02407e7	−	6.39298e7i	−0.0116870	−	0.0369133i
$205$	1.20499e9			0.682290
$206$	3.07974e9	−	4.75893e8i	1.71019	−	0.264266i
$207$			2.37330e9i			1.29262i
$208$	−8.66112e8	+	6.09536e8i	−0.462723	+	0.325646i
$209$	−1.22081e9			−0.639827
$210$	1.03259e7	+	6.68237e7i	0.00530944	+	0.0343600i
$211$			5.31720e8i			0.268258i	0.990964	+	0.134129i	$0.0428237\pi$
$211$			5.31720e8i			0.268258i	−0.990964	+	0.134129i	$0.957176\pi$
$212$	2.12182e9	−	6.71784e8i	1.05042	−	0.332572i
$213$	−1.17009e7			−0.00568460
$214$	−6.02728e8	+	9.31359e7i	−0.287386	+	0.0444081i
$215$		−	6.82662e9i		−	3.19486i
$216$	−1.93035e8	+	9.56232e7i	−0.0886791	+	0.0439287i
$217$	1.03618e9			0.467302
$218$	5.75412e7	+	3.72377e8i	0.0254773	+	0.164876i
$219$			1.01366e8i			0.0440674i
$220$	−1.73799e9	−	5.48941e9i	−0.741919	−	2.34334i
$221$	1.05487e9			0.442213
$222$	1.14228e8	−	1.76509e7i	0.0470283	−	0.00726700i
$223$		−	2.09487e9i		−	0.847107i	−0.905871	−	0.423554i	$-0.860783\pi$
$223$		−	2.09487e9i		−	0.847107i	0.905871	−	0.423554i	$-0.139217\pi$
$224$	−6.85423e8	+	6.60069e8i	−0.272249	+	0.262179i
$225$	6.25716e9			2.44145
$226$	−1.82117e7	−	1.17857e8i	−0.00698099	−	0.0451774i
$227$			4.25811e9i			1.60366i	0.597549	+	0.801832i	$0.296141\pi$
$227$			4.25811e9i			1.60366i	−0.597549	+	0.801832i	$0.703859\pi$
$228$	−6.16888e7	+	1.95311e7i	−0.0228279	+	0.00722751i
$229$	4.88997e9			1.77813			0.889067	−	0.457776i	$-0.151354\pi$
$229$	4.88997e9			1.77813			0.889067	+	0.457776i	$0.151354\pi$
$230$	−6.65388e9	+	1.02818e9i	−2.37774	+	0.367417i
$231$			7.05838e7i			0.0247889i
$232$	−2.73751e8	−	5.52622e8i	−0.0944938	−	0.190755i
$233$	1.50158e9			0.509477			0.254738	−	0.967010i	$-0.418011\pi$
$233$	1.50158e9			0.509477			0.254738	+	0.967010i	$0.418011\pi$
$234$	−2.58434e8	−	1.67245e9i	−0.0861959	−	0.557815i
$235$			4.90731e9i			1.60906i
$236$	1.65965e9	+	5.24199e9i	0.535019	+	1.68985i
$237$	−1.15991e8			−0.0367646
$238$	9.36665e8	−	1.44737e8i	0.291929	−	0.0451100i
$239$			2.12215e9i			0.650405i	0.945644	+	0.325202i	$0.105432\pi$
$239$			2.12215e9i			0.650405i	−0.945644	+	0.325202i	$0.894568\pi$
$240$	−1.75645e8	−	2.49580e8i	−0.0529408	−	0.0752255i
$241$	−5.41957e9			−1.60656			−0.803279	−	0.595602i	$-0.796913\pi$
$241$	−5.41957e9			−1.60656			−0.803279	+	0.595602i	$0.796913\pi$
$242$	−3.94131e8	−	2.55061e9i	−0.114916	−	0.743675i
$243$		−	5.16536e8i		−	0.148141i
$244$	3.65548e8	−	1.15735e8i	0.103130	−	0.0326518i
$245$	−9.55687e8			−0.265247
$246$	6.58890e7	−	1.01814e7i	0.0179917	−	0.00278015i
$247$		−	1.01790e9i		−	0.273474i
$248$	−4.19084e9	+	2.07600e9i	−1.10788	+	0.548808i
$249$	−1.92981e8			−0.0502016
$250$	1.60320e9	+	1.03751e10i	0.410418	+	2.65601i
$251$		−	3.54176e9i		−	0.892328i	−0.894951	−	0.446164i	$-0.852790\pi$
$251$		−	3.54176e9i		−	0.892328i	0.894951	−	0.446164i	$-0.147210\pi$
$252$	−4.58948e8	−	1.44958e9i	−0.113805	−	0.359451i
$253$	−7.02829e9			−1.71541
$254$	3.74146e9	−	5.78145e8i	0.898888	−	0.138900i
$255$			3.03974e8i			0.0718912i
$256$	1.44973e9	−	4.04290e9i	0.337543	−	0.941310i
$257$	1.72362e9			0.395101			0.197551	−	0.980293i	$-0.436701\pi$
$257$	1.72362e9			0.395101			0.197551	+	0.980293i	$0.436701\pi$
$258$	−5.76806e7	−	3.73280e8i	−0.0130182	−	0.0842472i
$259$			1.63364e9i			0.363042i
$260$	4.57700e9	−	1.44911e9i	1.00158	−	0.317109i
$261$	9.85425e8			0.212355
$262$	1.07698e9	−	1.66419e8i	0.228561	−	0.0353181i
$263$		−	2.25807e9i		−	0.471970i	−0.971757	−	0.235985i	$-0.924168\pi$
$263$		−	2.25807e9i		−	0.471970i	0.971757	−	0.235985i	$-0.0758317\pi$
$264$	−1.41415e8	−	2.85476e8i	−0.0291126	−	0.0587697i
$265$	−1.00888e10			−2.04577
$266$	−1.39664e8	−	9.03831e8i	−0.0278969	−	0.180535i
$267$			7.03592e7i			0.0138445i
$268$	−4.51549e8	−	1.42621e9i	−0.0875319	−	0.276468i
$269$	1.27419e9			0.243346			0.121673	−	0.992570i	$-0.461174\pi$
$269$	1.27419e9			0.243346			0.121673	+	0.992570i	$0.461174\pi$
$270$	9.65059e8	−	1.49125e8i	0.181593	−	0.0280605i
$271$		−	5.55250e9i		−	1.02946i	−0.857351	−	0.514732i	$-0.827891\pi$
$271$		−	5.55250e9i		−	1.02946i	0.857351	−	0.514732i	$-0.172109\pi$
$272$	−3.49836e9	+	2.46201e9i	−0.639129	+	0.449794i
$273$	−5.88519e7			−0.0105952
$274$	8.74663e8	+	5.66037e9i	0.155181	+	1.00425i
$275$			1.85300e10i			3.23999i
$276$	−3.55147e8	+	1.12442e8i	−0.0612028	+	0.0193773i
$277$	−8.47781e9			−1.44001			−0.720004	−	0.693970i	$-0.755860\pi$
$277$	−8.47781e9			−1.44001			−0.720004	+	0.693970i	$0.755860\pi$
$278$	−3.21421e9	+	4.96672e8i	−0.538139	+	0.0831554i
$279$		−	7.47301e9i		−	1.23333i
$280$	3.86527e9	−	1.91473e9i	0.628851	−	0.311512i
$281$	1.01166e10			1.62258			0.811292	−	0.584641i	$-0.198765\pi$
$281$	1.01166e10			1.62258			0.811292	+	0.584641i	$0.198765\pi$
$282$	4.14637e7	+	2.68332e8i	0.00655649	+	0.0424302i
$283$			5.61750e9i			0.875784i	0.899028	+	0.437892i	$0.144275\pi$
$283$			5.61750e9i			0.875784i	−0.899028	+	0.437892i	$0.855725\pi$
$284$	2.25307e8	+	7.11628e8i	0.0346339	+	0.109390i
$285$	2.93318e8			0.0444590
$286$	4.95280e9	−	7.65327e8i	0.740265	−	0.114389i
$287$			9.42320e8i			0.138890i
$288$	4.76046e9	+	4.94331e9i	0.691957	+	0.718535i
$289$	−2.71496e9			−0.389200
$290$	4.26916e8	+	2.76278e9i	0.0603601	+	0.390620i
$291$		−	3.34290e8i		−	0.0466177i
$292$	6.16493e9	−	1.95186e9i	0.848002	−	0.268484i
$293$	2.03149e9			0.275641			0.137820	−	0.990457i	$-0.455990\pi$
$293$	2.03149e9			0.275641			0.137820	+	0.990457i	$0.455990\pi$
$294$	−5.22570e7	+	8.07495e6i	−0.00699447	+	0.00108081i
$295$		−	2.49246e10i		−	3.29110i
$296$	−3.27301e9	−	6.60725e9i	−0.426364	−	0.860704i
$297$	1.01936e9			0.131009
$298$	−1.52932e9	−	9.89698e9i	−0.193925	−	1.25498i
$299$		−	5.86010e9i		−	0.733196i
$300$	2.96452e8	+	9.36338e8i	0.0365990	+	0.115597i
$301$	5.33850e9			0.650359
$302$	−2.54438e9	+	3.93168e8i	−0.305882	+	0.0472661i
$303$		−	4.83717e8i		−	0.0573879i
$304$	2.37570e9	+	3.37572e9i	0.278162	+	0.395251i
$305$	−1.73811e9			−0.200853
$306$	−1.04385e9	−	6.75529e9i	−0.119057	−	0.770475i
$307$			7.01172e9i			0.789352i	0.918820	+	0.394676i	$0.129143\pi$
$307$			7.01172e9i			0.789352i	−0.918820	+	0.394676i	$0.870857\pi$
$308$	4.29279e9	−	1.35913e9i	0.477020	−	0.151028i
$309$	−7.81591e8			−0.0857325
$310$	2.09517e10	−	3.23753e9i	2.26867	−	0.350564i
$311$			6.89457e8i			0.0736997i	0.999321	+	0.0368499i	$0.0117323\pi$
$311$			6.89457e8i			0.0736997i	−0.999321	+	0.0368499i	$0.988268\pi$
$312$	2.38026e8	−	1.17910e8i	0.0251192	−	0.0124432i
$313$	−1.55060e10			−1.61556			−0.807780	−	0.589484i	$-0.799331\pi$
$313$	−1.55060e10			−1.61556			−0.807780	+	0.589484i	$0.799331\pi$
$314$	−1.85400e9	−	1.19982e10i	−0.190718	−	1.23423i
$315$			6.89248e9i			0.700056i
$316$	2.23346e9	+	7.05435e9i	0.223991	+	0.707471i
$317$	1.11332e9			0.110251			0.0551255	−	0.998479i	$-0.482444\pi$
$317$	1.11332e9			0.110251			0.0551255	+	0.998479i	$0.482444\pi$
$318$	−5.51658e8	+	8.52444e7i	−0.0539463	+	0.00833599i
$319$			2.91824e9i			0.281811i
$320$	−1.17969e10	+	1.54882e10i	−1.12504	+	1.47707i
$321$	1.52963e8			0.0144068
$322$	−8.04053e8	−	5.20342e9i	−0.0747930	−	0.484022i
$323$		−	4.11144e9i		−	0.377732i
$324$	−1.04287e10	+	3.30180e9i	−0.946344	+	0.299620i
$325$	−1.54501e10			−1.38483
$326$	−1.56987e10	+	2.42583e9i	−1.38993	+	0.214778i
$327$		−	9.45038e7i		−	0.00826529i
$328$	−1.88795e9	−	3.81121e9i	−0.163115	−	0.329282i
$329$	−3.83758e9			−0.327547
$330$	2.20538e8	+	1.42721e9i	0.0185963	+	0.120346i
$331$		−	7.04374e9i		−	0.586802i	−0.955989	−	0.293401i	$-0.905213\pi$
$331$		−	7.04374e9i		−	0.586802i	0.955989	−	0.293401i	$-0.0947871\pi$
$332$	3.71596e9	+	1.17368e10i	0.305857	+	0.966044i
$333$	1.17819e10			0.958162
$334$	−4.50836e6	+	696650.i	−0.000362271	+	5.59795e-5i
$335$			6.78136e9i			0.538440i
$336$	1.95175e8	−	1.37356e8i	0.0153132	−	0.0107769i
$337$	1.22526e10			0.949964			0.474982	−	0.879995i	$-0.342455\pi$
$337$	1.22526e10			0.949964			0.474982	+	0.879995i	$0.342455\pi$
$338$	−1.35502e9	−	8.76902e9i	−0.103820	−	0.671868i
$339$			2.99103e7i			0.00226476i
$340$	1.84872e10	−	5.85319e9i	1.38342	−	0.438003i
$341$	2.21306e10			1.63672
$342$	−6.51849e9	+	1.00726e9i	−0.476478	+	0.0736272i
$343$		−	7.47359e8i		−	0.0539949i
$344$	−2.15916e10	+	1.06957e10i	−1.54188	+	0.763795i
$345$	1.68865e9			0.119197
$346$	−1.72371e9	−	1.11550e10i	−0.120271	−	0.778332i
$347$			1.64635e10i			1.13554i	0.823186	+	0.567771i	$0.192194\pi$
$347$			1.64635e10i			1.13554i	−0.823186	+	0.567771i	$0.807806\pi$
$348$	4.66875e7	+	1.47462e8i	0.00318334	+	0.0100545i
$349$	1.08550e10			0.731695			0.365847	−	0.930675i	$-0.380779\pi$
$349$	1.08550e10			0.731695			0.365847	+	0.930675i	$0.380779\pi$
$350$	−1.37187e10	+	2.11987e9i	−0.914201	+	0.141266i
$351$			8.49931e8i			0.0559958i
$352$	−1.46391e10	+	1.40976e10i	−0.953552	+	0.918281i
$353$	2.47906e10			1.59657			0.798286	−	0.602279i	$-0.205740\pi$
$353$	2.47906e10			1.59657			0.798286	+	0.602279i	$0.205740\pi$
$354$	−2.10598e8	−	1.36288e9i	−0.0134104	−	0.0867850i
$355$		−	3.38365e9i		−	0.213046i
$356$	4.27913e9	−	1.35481e9i	0.266413	−	0.0843484i
$357$	−2.37712e8			−0.0146345
$358$	−7.69295e9	+	1.18874e9i	−0.468339	+	0.0723696i
$359$			2.53049e10i			1.52345i	0.647902	+	0.761724i	$0.275647\pi$
$359$			2.53049e10i			1.52345i	−0.647902	+	0.761724i	$0.724353\pi$
$360$	−1.38091e10	−	2.78766e10i	−0.822161	−	1.65970i
$361$	1.30163e10			0.766403
$362$	2.13280e9	+	1.38024e10i	0.124198	+	0.803748i
$363$			6.47307e8i			0.0372807i
$364$	1.13323e9	+	3.57927e9i	0.0645521	+	0.203887i
$365$	−2.93131e10			−1.65154
$366$	−9.50399e7	+	1.46859e7i	−0.00529641	+	0.000818423i
$367$			4.68115e9i			0.258041i	0.991642	+	0.129020i	$0.0411833\pi$
$367$			4.68115e9i			0.258041i	−0.991642	+	0.129020i	$0.958817\pi$
$368$	1.36771e10	+	1.94343e10i	0.745765	+	1.05969i
$369$	6.79607e9			0.366566
$370$	5.10428e9	+	3.30323e10i	0.272350	+	1.76251i
$371$		−	7.88960e9i		−	0.416447i
$372$	1.11828e9	−	3.54057e8i	0.0583955	−	0.0184885i
$373$	−1.29821e9			−0.0670669			−0.0335335	−	0.999438i	$-0.510676\pi$
$373$	−1.29821e9			−0.0670669			−0.0335335	+	0.999438i	$0.510676\pi$
$374$	2.00051e10	−	3.09127e9i	1.02248	−	0.157998i
$375$		−	2.63303e9i		−	0.133147i
$376$	1.55211e10	−	7.68862e9i	0.776551	−	0.384678i
$377$	−2.43319e9			−0.120451
$378$	1.16617e8	+	7.54689e8i	0.00571211	+	0.0369658i
$379$			3.41839e10i			1.65678i	0.560151	+	0.828391i	$0.310743\pi$
$379$			3.41839e10i			1.65678i	−0.560151	+	0.828391i	$0.689257\pi$
$380$	−5.64801e9	−	1.78391e10i	−0.270870	−	0.855538i
$381$	−9.49525e8			−0.0450616
$382$	−6.70137e9	+	1.03552e9i	−0.314710	+	0.0486302i
$383$		−	1.79591e10i		−	0.834623i	−0.908764	−	0.417311i	$-0.862972\pi$
$383$		−	1.79591e10i		−	0.834623i	0.908764	−	0.417311i	$-0.137028\pi$
$384$	−5.14189e8	+	9.46572e8i	−0.0236482	+	0.0435340i
$385$	−2.04114e10			−0.929029
$386$	−4.40226e9	−	2.84891e10i	−0.198302	−	1.28331i
$387$		−	3.85016e10i		−	1.71647i
$388$	−2.03309e10	+	6.43693e9i	−0.897078	+	0.284022i
$389$	−1.96160e10			−0.856666			−0.428333	−	0.903621i	$-0.640899\pi$
$389$	−1.96160e10			−0.856666			−0.428333	+	0.903621i	$0.640899\pi$
$390$	−1.18999e9	+	1.83882e8i	−0.0514380	+	0.00794840i
$391$		−	2.36698e10i		−	1.01272i
$392$	1.49734e9	+	3.02269e9i	0.0634127	+	0.128012i
$393$	−2.73321e8			−0.0114578
$394$	−1.90492e9	−	1.23276e10i	−0.0790480	−	0.511558i
$395$		−	3.35421e10i		−	1.37785i
$396$	−9.80213e9	−	3.09598e10i	−0.398602	−	1.25898i
$397$	−3.28502e9			−0.132244			−0.0661221	−	0.997812i	$-0.521063\pi$
$397$	−3.28502e9			−0.132244			−0.0661221	+	0.997812i	$0.521063\pi$
$398$	2.01504e10	−	3.11373e9i	0.803068	−	0.124093i
$399$			2.29379e8i			0.00905027i
$400$	5.12382e10	−	3.60594e10i	2.00149	−	1.40857i
$401$	−2.00250e10			−0.774455			−0.387227	−	0.921984i	$-0.626567\pi$
$401$	−2.00250e10			−0.774455			−0.387227	+	0.921984i	$0.626567\pi$
$402$	5.72982e7	+	3.70805e8i	0.00219400	+	0.0141985i
$403$			1.84522e10i			0.699565i
$404$	−2.94188e10	+	9.31423e9i	−1.10433	+	0.349640i
$405$	4.95864e10			1.84307
$406$	−2.16053e9	+	3.33853e8i	−0.0795162	+	0.0122872i
$407$			3.48910e10i			1.27156i
$408$	9.61424e8	−	4.76257e8i	0.0346956	−	0.0171870i
$409$	2.17825e10			0.778423			0.389211	−	0.921149i	$-0.372748\pi$
$409$	2.17825e10			0.778423			0.389211	+	0.921149i	$0.372748\pi$
$410$	2.94426e9	+	1.90538e10i	0.104194	+	0.674288i
$411$		−	1.43652e9i		−	0.0503435i
$412$	1.50500e10	+	4.75350e10i	0.522332	+	1.64978i
$413$	1.94914e10			0.669950
$414$	−3.75274e10	+	5.79888e9i	−1.27746	+	0.197398i
$415$		−	5.58062e10i		−	1.88144i
$416$	−1.17544e10	−	1.22059e10i	−0.392490	−	0.407565i
$417$	8.15717e8			0.0269771
$418$	−2.98291e9	−	1.93039e10i	−0.0977090	−	0.632323i
$419$			2.31483e10i			0.751039i	0.926815	+	0.375519i	$0.122536\pi$
$419$			2.31483e10i			0.751039i	−0.926815	+	0.375519i	$0.877464\pi$
$420$	−1.03141e9	+	3.26552e8i	−0.0331462	+	0.0104943i
$421$	−3.00500e10			−0.956567			−0.478284	−	0.878205i	$-0.658741\pi$
$421$	−3.00500e10			−0.956567			−0.478284	+	0.878205i	$0.658741\pi$
$422$	−8.40773e9	+	1.29920e9i	−0.265112	+	0.0409661i
$423$			2.76768e10i			0.864480i
$424$	1.58069e10	+	3.19095e10i	0.489084	+	0.987316i
$425$	−6.24051e10			−1.91278
$426$	−2.85898e7	−	1.85018e8i	−0.000868104	−	0.00561793i
$427$		−	1.35923e9i		−	0.0408865i
$428$	−2.94539e9	−	9.30296e9i	−0.0877744	−	0.277234i
$429$	−1.25695e9			−0.0371097
$430$	1.07945e11	−	1.66801e10i	3.15739	−	0.487892i
$431$		−	5.00154e10i		−	1.44942i	−0.689054	−	0.724710i	$-0.741974\pi$
$431$		−	5.00154e10i		−	1.44942i	0.689054	−	0.724710i	$-0.258026\pi$
$432$	−1.98368e9	−	2.81869e9i	−0.0569558	−	0.0809305i
$433$	−2.69783e9			−0.0767473			−0.0383737	−	0.999263i	$-0.512218\pi$
$433$	−2.69783e9			−0.0767473			−0.0383737	+	0.999263i	$0.512218\pi$
$434$	2.53179e9	+	1.63845e10i	0.0713623	+	0.461820i
$435$		−	7.01152e8i		−	0.0195819i
$436$	−5.74756e9	+	1.81972e9i	−0.159051	+	0.0503569i
$437$	−2.28401e10			−0.626285
$438$	−1.60284e9	+	2.47677e8i	−0.0435505	+	0.00672960i
$439$			1.81410e10i			0.488432i	0.969721	+	0.244216i	$0.0785306\pi$
$439$			1.81410e10i			0.488432i	−0.969721	+	0.244216i	$0.921469\pi$
$440$	8.25537e10	−	4.08944e10i	2.20255	−	1.09107i
$441$	−5.39000e9			−0.142507
$442$	2.57746e9	+	1.66800e10i	0.0675310	+	0.437026i
$443$			5.30088e10i			1.37636i	0.725538	+	0.688182i	$0.241591\pi$
$443$			5.30088e10i			1.37636i	−0.725538	+	0.688182i	$0.758409\pi$
$444$	5.58204e8	+	1.76308e9i	0.0143635	+	0.0453669i
$445$	−2.03464e10			−0.518858
$446$	3.31248e10	−	5.11858e9i	0.837171	−	0.129363i
$447$			2.51171e9i			0.0629127i
$448$	−1.21120e10	−	9.22533e9i	−0.300679	−	0.229018i
$449$	1.34755e10			0.331557			0.165779	−	0.986163i	$-0.446986\pi$
$449$	1.34755e10			0.331557			0.165779	+	0.986163i	$0.446986\pi$
$450$	1.52887e10	+	9.89404e10i	0.372837	+	2.41281i
$451$			2.01259e10i			0.486462i
$452$	1.81909e9	−	5.75940e8i	0.0435814	−	0.0137982i
$453$	6.45726e8			0.0153340
$454$	−6.73307e10	+	1.04042e10i	−1.58486	+	0.244898i
$455$		−	1.70188e10i		−	0.397084i
$456$	−4.59562e8	−	9.27721e8i	−0.0106288	−	0.0214565i
$457$	−6.62186e10			−1.51815			−0.759076	−	0.651002i	$-0.774349\pi$
$457$	−6.62186e10			−1.51815			−0.759076	+	0.651002i	$0.774349\pi$
$458$	1.19481e10	+	7.73219e10i	0.271542	+	1.75728i
$459$			3.43300e9i			0.0773434i
$460$	−3.25160e10	−	1.02701e11i	−0.726215	−	2.29374i
$461$	−3.98261e9			−0.0881787			−0.0440894	−	0.999028i	$-0.514039\pi$
$461$	−3.98261e9			−0.0881787			−0.0440894	+	0.999028i	$0.514039\pi$
$462$	−1.11609e9	+	1.72463e8i	−0.0244981	+	0.00378555i
$463$		−	4.92342e10i		−	1.07138i	−0.844415	−	0.535689i	$-0.820052\pi$
$463$		−	4.92342e10i		−	1.07138i	0.844415	−	0.535689i	$-0.179948\pi$
$464$	8.06937e9	−	5.67891e9i	0.174088	−	0.122516i
$465$	−5.31722e9			−0.113729
$466$	3.66893e9	+	2.37435e10i	0.0778030	+	0.503501i
$467$			4.98718e10i			1.04855i	0.851551	+	0.524273i	$0.175663\pi$
$467$			4.98718e10i			1.04855i	−0.851551	+	0.524273i	$0.824337\pi$
$468$	2.58139e10	−	8.17289e9i	0.538110	−	0.170370i
$469$	−5.30311e9			−0.109607
$470$	−7.75960e10	+	1.19904e10i	−1.59019	+	0.245722i
$471$			3.04495e9i			0.0618724i
$472$	−7.88329e10	+	3.90512e10i	−1.58832	+	0.786803i
$473$	1.14019e11			2.27788
$474$	−2.83410e8	−	1.83408e9i	−0.00561438	−	0.0363334i
$475$			6.02175e10i			1.18290i
$476$	4.57727e9	+	1.44572e10i	0.0891617	+	0.281616i
$477$	−5.69003e10			−1.09911
$478$	−3.35561e10	+	5.18522e9i	−0.642776	+	0.0993243i
$479$		−	7.96914e10i		−	1.51380i	−0.653529	−	0.756901i	$-0.726712\pi$
$479$		−	7.96914e10i		−	1.51380i	0.653529	−	0.756901i	$-0.273288\pi$
$480$	3.51728e9	−	3.38717e9i	0.0662585	−	0.0638076i
$481$	−2.90917e10			−0.543486
$482$	−1.32421e10	−	8.56960e10i	−0.245340	−	1.58772i
$483$			1.32055e9i			0.0242642i
$484$	3.93681e10	−	1.24643e10i	0.717403	−	0.227135i
$485$	9.66697e10			1.74712
$486$	8.16764e9	−	1.26210e9i	0.146403	−	0.0226228i
$487$			2.12476e10i			0.377740i	0.982002	+	0.188870i	$0.0604825\pi$
$487$			2.12476e10i			0.377740i	−0.982002	+	0.188870i	$0.939517\pi$
$488$	2.72322e9	+	5.49738e9i	0.0480179	+	0.0969341i
$489$	3.98410e9			0.0696778
$490$	−2.33511e9	−	1.51116e10i	−0.0405064	−	0.262136i
$491$		−	5.22814e10i		−	0.899541i	−0.893144	−	0.449770i	$-0.851506\pi$
$491$		−	5.22814e10i		−	0.899541i	0.893144	−	0.449770i	$-0.148494\pi$
$492$	3.21985e8	+	1.01698e9i	0.00549509	+	0.0173561i
$493$	−9.82802e9			−0.166371
$494$	1.60953e10	−	2.48711e9i	0.270266	−	0.0417626i
$495$			1.47208e11i			2.45195i
$496$	−4.30662e10	−	6.11944e10i	−0.711558	−	1.01108i
$497$	2.64606e9			0.0433685
$498$	−4.71527e8	−	3.05148e9i	−0.00766636	−	0.0496128i
$499$		−	9.06684e10i		−	1.46236i	−0.682186	−	0.731179i	$-0.738970\pi$
$499$		−	9.06684e10i		−	1.46236i	0.682186	−	0.731179i	$-0.261030\pi$
$500$	−1.60137e11	+	5.07005e10i	−2.56219	+	0.811208i
$501$	1.14416e6			1.81608e−5
$502$	5.60036e10	−	8.65389e9i	0.881862	−	0.136269i
$503$			5.58346e10i			0.872231i	0.899891	+	0.436116i	$0.143646\pi$
$503$			5.58346e10i			0.872231i	−0.899891	+	0.436116i	$0.856354\pi$
$504$	2.17998e10	−	1.07989e10i	0.337856	−	0.167363i
$505$	1.39881e11			2.15076
$506$	−1.71728e10	−	1.11134e11i	−0.261963	−	1.69529i
$507$			2.22545e9i			0.0336810i
$508$	1.82836e10	+	5.77485e10i	0.274541	+	0.867134i
$509$	1.09782e11			1.63554			0.817771	−	0.575544i	$-0.195210\pi$
$509$	1.09782e11			1.63554			0.817771	+	0.575544i	$0.195210\pi$
$510$	−4.80654e9	+	7.42726e8i	−0.0710480	+	0.0109786i
$511$		−	2.29232e10i		−	0.336195i
$512$	6.74699e10	+	1.30453e10i	0.981816	+	0.189835i
$513$	3.31266e9			0.0478308
$514$	4.21146e9	+	2.72544e10i	0.0603365	+	0.390467i
$515$		−	2.26020e11i		−	3.21305i
$516$	5.76148e9	−	1.82413e9i	0.0812710	−	0.0257310i
$517$	−8.19622e10			−1.14723
$518$	−2.58317e10	+	3.99161e9i	−0.358784	+	0.0554408i
$519$			2.83097e9i			0.0390181i
$520$	3.40972e10	+	6.88323e10i	0.466343	+	0.941410i
$521$	2.91079e10			0.395057			0.197529	−	0.980297i	$-0.436708\pi$
$521$	2.91079e10			0.395057			0.197529	+	0.980297i	$0.436708\pi$
$522$	2.40777e9	+	1.55819e10i	0.0324290	+	0.209864i
$523$			1.06525e11i			1.42379i	0.702286	+	0.711895i	$0.252163\pi$
$523$			1.06525e11i			1.42379i	−0.702286	+	0.711895i	$0.747837\pi$
$524$	5.26294e9	+	1.66229e10i	0.0698078	+	0.220487i
$525$	3.48161e9			0.0458292
$526$	3.57054e10	−	5.51734e9i	0.466434	−	0.0720753i
$527$			7.45312e10i			0.966264i
$528$	4.16851e9	−	2.93363e9i	0.0536346	−	0.0377459i
$529$	−5.31810e10			−0.679100
$530$	−2.46509e10	−	1.59528e11i	−0.312413	−	2.02178i
$531$		−	1.40573e11i		−	1.76817i
$532$	1.39504e10	−	4.41681e9i	0.174157	−	0.0551395i
$533$	−1.67807e10			−0.207923
$534$	−1.11254e9	+	1.71915e8i	−0.0136821	+	0.00211421i
$535$			4.42338e10i			0.539932i
$536$	2.14484e10	−	1.06248e10i	0.259858	−	0.128725i
$537$	1.95235e9			0.0234780
$538$	3.11333e9	+	2.01479e10i	0.0371618	+	0.240492i
$539$		−	1.59620e10i		−	0.189117i
$540$	4.71602e9	+	1.48955e10i	0.0554627	+	0.175178i
$541$	7.17214e10			0.837259			0.418629	−	0.908157i	$-0.362511\pi$
$541$	7.17214e10			0.837259			0.418629	+	0.908157i	$0.362511\pi$
$542$	8.77980e10	−	1.35669e10i	1.01739	−	0.157211i
$543$		−	3.50284e9i		−	0.0402922i
$544$	−4.74779e10	−	4.93016e10i	−0.542121	−	0.562944i
$545$	2.73286e10			0.309764
$546$	−1.43798e8	−	9.30585e8i	−0.00161801	−	0.0104709i
$547$			4.49852e10i			0.502482i	0.967925	+	0.251241i	$0.0808387\pi$
$547$			4.49852e10i			0.502482i	−0.967925	+	0.251241i	$0.919161\pi$
$548$	−8.73665e10	+	2.76609e10i	−0.968774	+	0.306722i
$549$	−9.80282e9			−0.107910
$550$	−2.93002e11	+	4.52758e10i	−3.20199	+	0.494784i
$551$			9.48351e9i			0.102887i
$552$	−2.64573e9	−	5.34096e9i	−0.0284964	−	0.0575258i
$553$	2.62304e10			0.280481
$554$	−2.07146e10	−	1.34054e11i	−0.219906	−	1.42312i
$555$		−	8.38310e9i		−	0.0883553i
$556$	−1.57071e10	−	4.96105e10i	−0.164360	−	0.519128i
$557$	−6.23193e10			−0.647443			−0.323722	−	0.946152i	$-0.604934\pi$
$557$	−6.23193e10			−0.647443			−0.323722	+	0.946152i	$0.604934\pi$
$558$	1.18166e11	−	1.82594e10i	1.21886	−	0.188344i
$559$			9.50674e10i			0.973608i
$560$	3.97207e10	+	5.64405e10i	0.403891	+	0.573904i
$561$	−5.07700e9			−0.0512573
$562$	2.47186e10	+	1.59966e11i	0.247787	+	1.60355i
$563$		−	1.28228e11i		−	1.27629i	−0.769916	−	0.638145i	$-0.779702\pi$
$563$		−	1.28228e11i		−	1.27629i	0.769916	−	0.638145i	$-0.220298\pi$
$564$	−4.14164e9	+	1.31127e9i	−0.0409313	+	0.0129592i
$565$	−8.64945e9			−0.0848779
$566$	−8.88257e10	+	1.37257e10i	−0.865512	+	0.133742i
$567$			3.87772e10i			0.375184i
$568$	−1.07020e10	+	5.30141e9i	−0.102818	+	0.0509328i
$569$	−8.65619e10			−0.825806			−0.412903	−	0.910775i	$-0.635485\pi$
$569$	−8.65619e10			−0.825806			−0.412903	+	0.910775i	$0.635485\pi$
$570$	7.16690e8	+	4.63805e9i	0.00678941	+	0.0439376i
$571$		−	3.02123e10i		−	0.284210i	−0.989852	−	0.142105i	$-0.954613\pi$
$571$		−	3.02123e10i		−	0.284210i	0.989852	−	0.142105i	$-0.0453871\pi$
$572$	2.42032e10	+	7.64454e10i	0.226094	+	0.714113i
$573$	1.70071e9			0.0157765
$574$	−1.49003e10	+	2.30245e9i	−0.137261	+	0.0212101i
$575$			3.46676e11i			3.17141i
$576$	−6.65337e10	+	8.73524e10i	−0.604438	+	0.793569i
$577$	3.53121e10			0.318581			0.159290	−	0.987232i	$-0.449079\pi$
$577$	3.53121e10			0.318581			0.159290	+	0.987232i	$0.449079\pi$
$578$	−6.63370e9	−	4.29299e10i	−0.0594353	−	0.384635i
$579$			7.23012e9i			0.0643326i
$580$	−4.26429e10	+	1.35011e10i	−0.376820	+	0.119304i
$581$	4.36411e10			0.382994
$582$	5.28590e9	−	8.16798e8i	0.0460709	−	0.00711906i
$583$		−	1.68505e11i		−	1.45860i
$584$	4.59268e10	+	9.27128e10i	0.394834	+	0.797055i
$585$	−1.22740e11			−1.04801
$586$	4.96371e9	+	3.21226e10i	0.0420936	+	0.272408i
$587$		−	1.19018e11i		−	1.00244i	−0.865318	−	0.501222i	$-0.832884\pi$
$587$		−	1.19018e11i		−	1.00244i	0.865318	−	0.501222i	$-0.167116\pi$
$588$	−2.55368e8	−	8.06574e8i	−0.00213627	−	0.00674738i
$589$	7.19186e10			0.597558
$590$	3.94117e11	−	6.09005e10i	3.25250	−	0.502589i
$591$			3.12857e9i			0.0256446i
$592$	9.64788e10	−	6.78980e10i	0.785498	−	0.552803i
$593$	−1.75125e11			−1.41622			−0.708109	−	0.706103i	$-0.750452\pi$
$593$	−1.75125e11			−1.41622			−0.708109	+	0.706103i	$0.750452\pi$
$594$	2.49069e9	+	1.61185e10i	0.0200067	+	0.129473i
$595$		−	6.87413e10i		−	0.548466i
$596$	1.52758e11	−	4.83643e10i	1.21065	−	0.383301i
$597$	−5.11388e9			−0.0402581
$598$	9.26618e10	−	1.43185e10i	0.724596	−	0.111967i
$599$			1.59940e11i			1.24237i	0.783664	+	0.621185i	$0.213348\pi$
$599$			1.59940e11i			1.24237i	−0.783664	+	0.621185i	$0.786652\pi$
$600$	−1.40813e10	+	6.97543e9i	−0.108652	+	0.0538228i
$601$	−2.26232e11			−1.73403			−0.867013	−	0.498286i	$-0.833963\pi$
$601$	−2.26232e11			−1.73403			−0.867013	+	0.498286i	$0.833963\pi$
$602$	1.30440e10	+	8.44142e10i	0.0993174	+	0.642731i
$603$			3.82464e10i			0.289282i
$604$	−1.24338e10	−	3.92719e10i	−0.0934235	−	0.295076i
$605$	−1.87188e11			−1.39719
$606$	7.64869e9	−	1.18191e9i	0.0567148	−	0.00876380i
$607$			2.81020e10i			0.207006i	0.994629	+	0.103503i	$0.0330051\pi$
$607$			2.81020e10i			0.207006i	−0.994629	+	0.103503i	$0.966995\pi$
$608$	−4.75733e10	+	4.58136e10i	−0.348136	+	0.335259i
$609$	5.48310e8			0.00398618
$610$	−4.24687e9	−	2.74836e10i	−0.0306726	−	0.198497i
$611$		−	6.83391e10i		−	0.490348i
$612$	1.04266e11	−	3.30116e10i	0.743256	−	0.235321i
$613$	8.24402e10			0.583845			0.291922	−	0.956442i	$-0.405705\pi$
$613$	8.24402e10			0.583845			0.291922	+	0.956442i	$0.405705\pi$
$614$	−1.10872e11	+	1.71323e10i	−0.780094	+	0.120543i
$615$		−	4.83556e9i		−	0.0338023i
$616$	3.19799e10	+	6.45581e10i	0.222103	+	0.448361i
$617$	−1.37897e11			−0.951510			−0.475755	−	0.879578i	$-0.657825\pi$
$617$	−1.37897e11			−0.951510			−0.475755	+	0.879578i	$0.657825\pi$
$618$	−1.90973e9	−	1.23588e10i	−0.0130923	−	0.0847270i
$619$			9.55261e10i			0.650668i	0.945599	+	0.325334i	$0.105477\pi$
$619$			9.55261e10i			0.650668i	−0.945599	+	0.325334i	$0.894523\pi$
$620$	1.02386e11	+	3.23384e11i	0.692904	+	2.18853i
$621$	1.90712e10			0.128237
$622$	−1.09019e10	+	1.68461e9i	−0.0728353	+	0.0112548i
$623$		−	1.59112e10i		−	0.105621i
$624$	2.44603e9	+	3.47565e9i	0.0161333	+	0.0229244i
$625$	3.87967e11			2.54258
$626$	−3.78872e10	−	2.45186e11i	−0.246715	−	1.59661i
$627$			4.89903e9i			0.0316986i
$628$	1.85189e11	−	5.86322e10i	1.19063	−	0.376962i
$629$	−1.17506e11			−0.750682
$630$	−1.08986e11	+	1.68410e10i	−0.691845	+	0.106907i
$631$		−	2.80979e10i		−	0.177238i	−0.996066	−	0.0886190i	$-0.971755\pi$
$631$		−	2.80979e10i		−	0.177238i	0.996066	−	0.0886190i	$-0.0282453\pi$
$632$	−1.06089e11	+	5.25528e10i	−0.664967	+	0.329403i
$633$	2.13376e9			0.0132902
$634$	2.72027e9	+	1.76042e10i	0.0168366	+	0.108958i
$635$		−	2.74583e11i		−	1.68880i
$636$	−2.69582e9	−	8.51471e9i	−0.0164764	−	0.0520405i
$637$	1.33089e10			0.0808321
$638$	−4.61441e10	+	7.13038e9i	−0.278506	+	0.0430358i
$639$		−	1.90836e10i		−	0.114461i
$640$	−2.73729e11	−	1.48693e11i	−1.63155	−	0.886279i
$641$	3.74662e10			0.221926			0.110963	−	0.993825i	$-0.464607\pi$
$641$	3.74662e10			0.221926			0.110963	+	0.993825i	$0.464607\pi$
$642$	3.73748e8	+	2.41871e9i	0.00220008	+	0.0142378i
$643$			1.06082e11i			0.620578i	0.950642	+	0.310289i	$0.100426\pi$
$643$			1.06082e11i			0.620578i	−0.950642	+	0.310289i	$0.899574\pi$
$644$	8.03136e10	−	2.54279e10i	0.466923	−	0.147832i
$645$	−2.73948e10			−0.158281
$646$	6.50114e10	−	1.00458e10i	0.373301	−	0.0576840i
$647$		−	2.17529e11i		−	1.24137i	−0.784061	−	0.620684i	$-0.786855\pi$
$647$		−	2.17529e11i		−	1.24137i	0.784061	−	0.620684i	$-0.213145\pi$
$648$	−7.76904e10	−	1.56834e11i	−0.440623	−	0.889489i
$649$	4.16293e11			2.34650
$650$	−3.77504e10	−	2.44301e11i	−0.211480	−	1.36859i
$651$		−	4.15813e9i		−	0.0231512i
$652$	−7.67160e10	−	2.42306e11i	−0.424517	−	1.34083i
$653$	−2.11253e11			−1.16185			−0.580925	−	0.813957i	$-0.697309\pi$
$653$	−2.11253e11			−1.16185			−0.580925	+	0.813957i	$0.697309\pi$
$654$	1.49433e9	−	2.30909e8i	0.00816835	−	0.00126221i
$655$		−	7.90388e10i		−	0.429413i
$656$	5.56511e10	−	3.91651e10i	0.300510	−	0.211487i
$657$	−1.65324e11			−0.887306
$658$	−9.37667e9	−	6.06810e10i	−0.0500202	−	0.323705i
$659$		−	6.25992e10i		−	0.331915i	−0.986133	−	0.165958i	$-0.946928\pi$
$659$		−	6.25992e10i		−	0.331915i	0.986133	−	0.165958i	$-0.0530715\pi$
$660$	−2.20286e10	+	6.97443e9i	−0.116094	+	0.0367564i
$661$	2.36129e11			1.23693			0.618464	−	0.785813i	$-0.287755\pi$
$661$	2.36129e11			1.23693			0.618464	+	0.785813i	$0.287755\pi$
$662$	1.11378e11	−	1.72106e10i	0.579919	−	0.0896114i
$663$		−	4.23314e9i		−	0.0219083i
$664$	−1.76506e11	+	8.74354e10i	−0.908005	+	0.449796i
$665$	−6.63316e10			−0.339183
$666$	2.87878e10	+	1.86300e11i	0.146322	+	0.946924i
$667$			5.45972e10i			0.275846i
$668$	−2.20313e7	−	6.95856e7i	−0.000110646	−	0.000349473i
$669$	−8.40659e9			−0.0419677
$670$	−1.07229e11	+	1.65695e10i	−0.532125	+	0.0822261i
$671$		−	2.90301e10i		−	0.143205i
$672$	2.64881e9	+	2.75055e9i	0.0129890	+	0.0134879i
$673$	−1.12131e11			−0.546595			−0.273298	−	0.961930i	$-0.588114\pi$
$673$	−1.12131e11			−0.546595			−0.273298	+	0.961930i	$0.588114\pi$
$674$	2.99377e10	+	1.93742e11i	0.145071	+	0.938822i
$675$		−	5.02809e10i		−	0.242208i
$676$	1.35348e11	−	4.28522e10i	0.648134	−	0.205204i
$677$	−2.65170e11			−1.26232			−0.631160	−	0.775652i	$-0.717421\pi$
$677$	−2.65170e11			−1.26232			−0.631160	+	0.775652i	$0.717421\pi$
$678$	−4.72952e8	+	7.30824e7i	−0.00223820	+	0.000345855i
$679$			7.55969e10i			0.355652i
$680$	1.37724e11	+	2.78024e11i	0.644130	+	1.30031i
$681$	1.70875e10			0.0794494
$682$	5.40735e10	+	3.49936e11i	0.249947	+	1.61753i
$683$			1.33391e11i			0.612974i	0.951875	+	0.306487i	$0.0991536\pi$
$683$			1.33391e11i			0.612974i	−0.951875	+	0.306487i	$0.900846\pi$
$684$	−3.18543e10	−	1.00611e11i	−0.145527	−	0.459645i
$685$	4.15411e11			1.88676
$686$	1.18175e10	−	1.82609e9i	0.0533616	−	0.00824565i
$687$		−	1.96231e10i		−	0.0880930i
$688$	−2.21881e11	−	3.15279e11i	−0.990299	−	1.40715i
$689$	1.40497e11			0.623434
$690$	4.12603e9	+	2.67016e10i	0.0182027	+	0.117799i
$691$			2.70586e11i			1.18684i	0.804892	+	0.593421i	$0.202223\pi$
$691$			2.70586e11i			1.18684i	−0.804892	+	0.593421i	$0.797777\pi$
$692$	1.72175e11	−	5.45119e10i	0.750836	−	0.237721i
$693$	−1.15119e11			−0.499129
$694$	−2.60326e11	+	4.02266e10i	−1.12222	+	0.173410i
$695$			2.35889e11i			1.01104i
$696$	−2.21764e9	+	1.09854e9i	−0.00945047	+	0.00468145i
$697$	−6.77799e10			−0.287190
$698$	2.65231e10	+	1.71644e11i	0.111738	+	0.723113i
$699$		−	6.02574e9i		−	0.0252407i
$700$	−6.70403e10	−	2.11745e11i	−0.279218	−	0.881905i
$701$	3.15702e11			1.30739			0.653695	−	0.756758i	$-0.273218\pi$
$701$	3.15702e11			1.30739			0.653695	+	0.756758i	$0.273218\pi$
$702$	−1.34394e10	+	2.07671e9i	−0.0553390	+	0.00855120i
$703$			1.13386e11i			0.464237i
$704$	−2.58685e11	−	1.97033e11i	−1.05313	−	0.802136i
$705$	1.96927e10			0.0797166
$706$	6.05730e10	+	3.91997e11i	0.243815	+	1.57785i
$707$			1.09389e11i			0.437819i
$708$	2.10357e10	−	6.66008e9i	0.0837191	−	0.0265061i
$709$	−1.59751e11			−0.632206			−0.316103	−	0.948725i	$-0.602374\pi$
$709$	−1.59751e11			−0.632206			−0.316103	+	0.948725i	$0.602374\pi$
$710$	5.35035e10	−	8.26757e9i	0.210547	−	0.0325345i
$711$		−	1.89175e11i		−	0.740262i
$712$	3.18782e10	+	6.43527e10i	0.124043	+	0.250407i
$713$	4.14040e11			1.60208
$714$	−5.80821e8	−	3.75878e9i	−0.00223486	−	0.0144628i
$715$		−	3.63483e11i		−	1.39079i
$716$	−3.75936e10	−	1.18739e11i	−0.143042	−	0.451794i
$717$	8.51603e9			0.0322226
$718$	−4.00130e11	+	6.18297e10i	−1.50558	+	0.232648i
$719$			3.47088e11i			1.29875i	0.760470	+	0.649373i	$0.224969\pi$
$719$			3.47088e11i			1.29875i	−0.760470	+	0.649373i	$0.775031\pi$
$720$	4.07053e11	−	2.86468e11i	1.51468	−	1.06597i
$721$	1.76751e11			0.654063
$722$	3.18037e10	+	2.05817e11i	0.117039	+	0.757414i
$723$			2.17484e10i			0.0795928i
$724$	−2.13037e11	+	6.74491e10i	−0.775355	+	0.245483i
$725$	1.43945e11			0.521007
$726$	−1.02354e10	+	1.58162e9i	−0.0368434	+	0.00569319i
$727$			2.41140e10i			0.0863241i	0.999068	+	0.0431620i	$0.0137432\pi$
$727$			2.41140e10i			0.0863241i	−0.999068	+	0.0431620i	$0.986257\pi$
$728$	−5.38277e10	+	2.66645e10i	−0.191637	+	0.0949309i
$729$	2.78279e11			0.985303
$730$	−7.16231e10	−	4.63508e11i	−0.252210	−	1.63217i
$731$			3.83992e11i			1.34478i
$732$	−4.64438e8	−	1.46692e9i	−0.00161765	−	0.00510931i
$733$	4.76781e10			0.165159			0.0825797	−	0.996584i	$-0.473684\pi$
$733$	4.76781e10			0.165159			0.0825797	+	0.996584i	$0.473684\pi$
$734$	−7.40199e10	+	1.14378e10i	−0.255014	+	0.0394058i
$735$			3.83511e9i			0.0131410i
$736$	−2.73883e11	+	2.63752e11i	−0.933369	+	0.898844i
$737$	−1.13263e11			−0.383899
$738$	1.66054e10	+	1.07462e11i	0.0559789	+	0.362267i
$739$		−	7.26864e9i		−	0.0243711i	−0.999926	−	0.0121856i	$-0.996121\pi$
$739$		−	7.26864e9i		−	0.0243711i	0.999926	−	0.0121856i	$-0.00387888\pi$
$740$	−5.09846e11	+	1.61421e11i	−1.70025	+	0.538311i
$741$	−4.08475e9			−0.0135485
$742$	1.24753e11	−	1.92773e10i	0.411562	−	0.0635962i
$743$		−	5.55063e11i		−	1.82132i	−0.413152	−	0.910662i	$-0.635572\pi$
$743$		−	5.55063e11i		−	1.82132i	0.413152	−	0.910662i	$-0.364428\pi$
$744$	8.33085e9	+	1.68175e10i	0.0271893	+	0.0548872i
$745$	−7.26334e11			−2.35782
$746$	−3.17202e9	−	2.05277e10i	−0.0102419	−	0.0662803i
$747$		−	3.14743e11i		−	1.01082i
$748$	9.77604e10	+	3.08774e11i	0.312289	+	0.986359i
$749$	−3.45914e10			−0.109911
$750$	4.16344e10	−	6.43351e9i	0.131585	−	0.0203331i
$751$			3.75022e11i			1.17895i	0.807785	+	0.589477i	$0.200666\pi$
$751$			3.75022e11i			1.17895i	−0.807785	+	0.589477i	$0.799334\pi$
$752$	1.59499e11	+	2.26638e11i	0.498754	+	0.708698i
$753$	−1.42129e10			−0.0442081
$754$	−5.94522e9	−	3.84744e10i	−0.0183943	−	0.119038i
$755$			1.86731e11i			0.574682i
$756$	−1.16484e10	+	3.68799e9i	−0.0356600	+	0.0112902i
$757$	−1.52495e10			−0.0464378			−0.0232189	−	0.999730i	$-0.507391\pi$
$757$	−1.52495e10			−0.0464378			−0.0232189	+	0.999730i	$0.507391\pi$
$758$	−5.40528e11	+	8.35245e10i	−1.63735	+	0.253010i
$759$			2.82040e10i			0.0849854i
$760$	2.68278e11	−	1.32896e11i	0.804138	−	0.398343i
$761$	−3.61831e11			−1.07887			−0.539433	−	0.842029i	$-0.681361\pi$
$761$	−3.61831e11			−1.07887			−0.539433	+	0.842029i	$0.681361\pi$
$762$	−2.32006e9	−	1.50142e10i	−0.00688143	−	0.0445331i
$763$			2.13713e10i			0.0630569i
$764$	−3.27481e10	−	1.03434e11i	−0.0961197	−	0.303592i
$765$	−4.95767e11			−1.44754
$766$	2.83976e11	−	4.38811e10i	0.824833	−	0.127457i
$767$			3.47100e11i			1.00294i
$768$	−1.62239e10	−	5.81769e9i	−0.0466348	−	0.0167227i
$769$	3.75734e11			1.07442			0.537211	−	0.843448i	$-0.319478\pi$
$769$	3.75734e11			1.07442			0.537211	+	0.843448i	$0.319478\pi$
$770$	−4.98729e10	−	3.22752e11i	−0.141874	−	0.918133i
$771$		−	6.91676e9i		−	0.0195743i
$772$	4.39723e11	−	1.39220e11i	1.23797	−	0.391951i
$773$	5.78485e11			1.62022			0.810111	−	0.586277i	$-0.199407\pi$
$773$	5.78485e11			1.62022			0.810111	+	0.586277i	$0.199407\pi$
$774$	6.08801e11	−	9.40743e10i	1.69633	−	0.262124i
$775$		−	1.09161e12i		−	3.02594i
$776$	−1.51459e11	−	3.05751e11i	−0.417685	−	0.843183i
$777$	6.55569e9			0.0179860
$778$	−4.79294e10	−	3.10174e11i	−0.130823	−	0.846618i
$779$			6.54039e10i			0.177604i
$780$	−5.81520e9	−	1.83672e10i	−0.0157104	−	0.0496209i
$781$	5.65141e10			0.151898
$782$	3.74275e11	−	5.78345e10i	1.00084	−	0.154654i
$783$		−	7.91862e9i		−	0.0210670i
$784$	−4.41372e10	+	3.10621e10i	−0.116826	+	0.0822178i
$785$	−8.80537e11			−2.31883
$786$	−6.67828e8	−	4.32184e9i	−0.00174974	−	0.0113234i
$787$		−	3.21045e11i		−	0.836887i	−0.908243	−	0.418443i	$-0.862576\pi$
$787$		−	3.21045e11i		−	0.836887i	0.908243	−	0.418443i	$-0.137424\pi$
$788$	1.90274e11	−	6.02423e10i	0.493487	−	0.156242i
$789$	−9.06149e9			−0.0233825
$790$	5.30379e11	−	8.19563e10i	1.36169	−	0.210414i
$791$		−	6.76398e9i		−	0.0172781i
$792$	4.65597e11	−	2.30641e11i	1.18334	−	0.586187i
$793$	2.42049e10			0.0612084
$794$	−8.02658e9	−	5.19439e10i	−0.0201952	−	0.130693i
$795$			4.04858e10i			0.101353i
$796$	9.84706e10	+	3.11018e11i	0.245276	+	0.774698i
$797$	−4.01007e11			−0.993844			−0.496922	−	0.867795i	$-0.665537\pi$
$797$	−4.01007e11			−0.993844			−0.496922	+	0.867795i	$0.665537\pi$
$798$	−3.62701e9	+	5.60460e8i	−0.00894412	+	0.00138208i
$799$		−	2.76032e11i		−	0.677286i
$800$	6.95378e11	+	7.22088e11i	1.69770	+	1.76291i
$801$	−1.14752e11			−0.278761
$802$	−4.89289e10	−	3.16643e11i	−0.118268	−	0.765371i
$803$		−	4.89589e11i		−	1.17752i
$804$	−5.72329e9	+	1.81204e9i	−0.0136969	+	0.00433654i
$805$	−3.81876e11			−0.909366
$806$	−2.91772e11	+	4.50858e10i	−0.691360	+	0.106832i
$807$		−	5.11324e9i		−	0.0120560i
$808$	−2.19161e11	−	4.42422e11i	−0.514183	−	1.03799i
$809$	6.07680e11			1.41867			0.709334	−	0.704872i	$-0.248996\pi$
$809$	6.07680e11			1.41867			0.709334	+	0.704872i	$0.248996\pi$
$810$	1.21159e11	+	7.84076e11i	0.281458	+	1.82145i
$811$		−	1.44721e11i		−	0.334541i	−0.985911	−	0.167271i	$-0.946505\pi$
$811$		−	1.44721e11i		−	0.334541i	0.985911	−	0.167271i	$-0.0534953\pi$
$812$	−1.05580e10	−	3.33473e10i	−0.0242861	−	0.0767072i
$813$	−2.22818e10			−0.0510021
$814$	−5.51708e11	+	8.52521e10i	−1.25664	+	0.194181i
$815$			1.15212e12i			2.61136i
$816$	9.87987e9	+	1.40387e10i	0.0222839	+	0.0316640i
$817$	3.70531e11			0.831642
$818$	5.32231e10	+	3.44433e11i	0.118874	+	0.769292i
$819$		−	9.59845e10i		−	0.213337i
$820$	−2.94090e11	+	9.31113e10i	−0.650467	+	0.205943i
$821$	3.22018e11			0.708774			0.354387	−	0.935099i	$-0.384689\pi$
$821$	3.22018e11			0.708774			0.354387	+	0.935099i	$0.384689\pi$
$822$	2.27147e10	−	3.50996e9i	0.0497530	−	0.00768803i
$823$			6.28799e11i			1.37061i	0.728258	+	0.685303i	$0.240330\pi$
$823$			6.28799e11i			1.37061i	−0.728258	+	0.685303i	$0.759670\pi$
$824$	−7.14867e11	+	3.54121e11i	−1.55066	+	0.768145i
$825$	7.43595e10			0.160517
$826$	4.76250e10	+	3.08204e11i	0.102309	+	0.662092i
$827$			1.85110e11i			0.395739i	0.980228	+	0.197869i	$0.0634022\pi$
$827$			1.85110e11i			0.395739i	−0.980228	+	0.197869i	$0.936598\pi$
$828$	−1.83388e11	−	5.79227e11i	−0.390165	−	1.23233i
$829$	1.03814e11			0.219806			0.109903	−	0.993942i	$-0.464946\pi$
$829$	1.03814e11			0.219806			0.109903	+	0.993942i	$0.464946\pi$
$830$	8.82426e11	−	1.36356e11i	1.85937	−	0.287317i
$831$			3.40209e10i			0.0713414i
$832$	1.64283e11	−	2.15689e11i	0.342847	−	0.450126i
$833$	5.37566e10			0.111648
$834$	1.99311e9	+	1.28984e10i	0.00411972	+	0.0266607i
$835$			3.30866e8i			0.000680623i
$836$	2.97951e11	−	9.43335e10i	0.609985	−	0.193126i
$837$	−6.00512e10			−0.122354
$838$	−3.66028e11	+	5.65601e10i	−0.742230	+	0.114692i
$839$		−	8.82866e11i		−	1.78175i	−0.454247	−	0.890876i	$-0.650092\pi$
$839$		−	8.82866e11i		−	1.78175i	0.454247	−	0.890876i	$-0.349908\pi$
$840$	−7.68367e9	−	1.55111e10i	−0.0154330	−	0.0311548i
$841$	−4.77577e11			−0.954683
$842$	−7.34236e10	−	4.75160e11i	−0.146079	−	0.945347i
$843$		−	4.05970e10i		−	0.0803867i
$844$	−4.10867e10	−	1.29771e11i	−0.0809713	−	0.255746i
$845$	−6.43553e11			−1.26229
$846$	−4.37636e11	+	6.76252e10i	−0.854341	+	0.132016i
$847$		−	1.46383e11i		−	0.284419i
$848$	−4.65941e11	+	3.27911e11i	−0.901047	+	0.634122i
$849$	2.25426e10			0.0433884
$850$	−1.52480e11	−	9.86770e11i	−0.292103	−	1.89034i
$851$			6.52774e11i			1.24464i
$852$	2.85571e9	−	9.04141e8i	0.00541946	−	0.00171584i
$853$	−2.17908e10			−0.0411601			−0.0205801	−	0.999788i	$-0.506551\pi$
$853$	−2.17908e10			−0.0411601			−0.0205801	+	0.999788i	$0.506551\pi$
$854$	2.14925e10	−	3.32111e9i	0.0404069	−	0.00624384i
$855$			4.78388e11i			0.895191i
$856$	1.39905e11	−	6.93042e10i	0.260578	−	0.129082i
$857$	−2.93493e11			−0.544095			−0.272048	−	0.962284i	$-0.587701\pi$
$857$	−2.93493e11			−0.544095			−0.272048	+	0.962284i	$0.587701\pi$
$858$	−3.07121e9	−	1.98753e10i	−0.00566709	−	0.0366745i
$859$		−	4.37152e11i		−	0.802897i	−0.915882	−	0.401448i	$-0.868507\pi$
$859$		−	4.37152e11i		−	0.802897i	0.915882	−	0.401448i	$-0.131493\pi$
$860$	5.27501e11	+	1.66610e12i	0.964339	+	3.04585i
$861$	3.78147e9			0.00688094
$862$	7.90859e11	−	1.22207e11i	1.43242	−	0.221343i
$863$		−	6.59561e11i		−	1.18908i	−0.804065	−	0.594541i	$-0.797334\pi$
$863$		−	6.59561e11i		−	1.18908i	0.804065	−	0.594541i	$-0.202666\pi$
$864$	3.97232e10	−	3.82538e10i	0.0712835	−	0.0686467i
$865$	−8.18658e11			−1.46231
$866$	−6.59184e9	−	4.26590e10i	−0.0117202	−	0.0758471i
$867$			1.08950e10i			0.0192819i
$868$	−2.52890e11	+	8.00671e10i	−0.445506	+	0.141051i
$869$	5.60223e11			0.982385
$870$	1.10868e10	−	1.71318e9i	0.0193522	−	0.00299038i
$871$		−	9.44371e10i		−	0.164085i
$872$	−4.28176e10	−	8.64361e10i	−0.0740553	−	0.149496i
$873$	5.45210e11			0.938657
$874$	−5.58071e10	−	3.61155e11i	−0.0956409	−	0.618939i
$875$			5.95440e11i			1.01579i
$876$	−7.83270e9	−	2.47394e10i	−0.0133013	−	0.0420120i
$877$	−8.21396e11			−1.38853			−0.694263	−	0.719721i	$-0.744270\pi$
$877$	−8.21396e11			−1.38853			−0.694263	+	0.719721i	$0.744270\pi$
$878$	−2.86852e11	+	4.43255e10i	−0.482703	+	0.0745892i
$879$		−	8.15222e9i		−	0.0136559i
$880$	8.48346e11	+	1.20545e12i	1.41463	+	2.01010i
$881$	1.76522e11			0.293019			0.146509	−	0.989209i	$-0.453196\pi$
$881$	1.76522e11			0.293019			0.146509	+	0.989209i	$0.453196\pi$
$882$	−1.31699e10	−	8.52285e10i	−0.0217624	−	0.140835i
$883$			8.11916e11i			1.33558i	0.744352	+	0.667788i	$0.232759\pi$
$883$			8.11916e11i			1.33558i	−0.744352	+	0.667788i	$0.767241\pi$
$884$	−2.57452e11	+	8.15114e10i	−0.421588	+	0.133478i
$885$	−1.00021e11			−0.163049
$886$	−8.38193e11	+	1.29521e11i	−1.36022	+	0.210187i
$887$		−	8.65709e11i		−	1.39855i	−0.714854	−	0.699274i	$-0.753507\pi$
$887$		−	8.65709e11i		−	1.39855i	0.714854	−	0.699274i	$-0.246493\pi$
$888$	−2.65145e10	+	1.31344e10i	−0.0426413	+	0.0211231i
$889$	2.14728e11			0.343780
$890$	−4.97142e10	−	3.21725e11i	−0.0792356	−	0.512772i
$891$			8.28196e11i			1.31408i
$892$	1.61873e11	+	5.11274e11i	0.255691	+	0.807597i
$893$	−2.66356e11			−0.418848
$894$	−3.97159e10	+	6.13706e9i	−0.0621748	+	0.00960750i
$895$			5.64581e11i			0.879901i
$896$	1.16280e11	−	2.14060e11i	0.180415	−	0.332126i
$897$	−2.35162e10			−0.0363243
$898$	3.29257e10	+	2.13079e11i	0.0506326	+	0.327668i
$899$		−	1.71915e11i		−	0.263193i
$900$	−1.52712e12	+	4.83499e11i	−2.32757	+	0.736928i
$901$	5.67489e11			0.861109
$902$	−3.18237e11	+	4.91753e10i	−0.480756	+	0.0742884i
$903$		−	2.14231e10i		−	0.0322204i
$904$	1.35517e10	+	2.73569e10i	0.0202918	+	0.0409631i
$905$	1.01295e12			1.51006
$906$	1.57776e9	+	1.02104e10i	0.00234168	+	0.0151541i
$907$			4.55521e11i			0.673099i	0.941666	+	0.336550i	$0.109260\pi$
$907$			4.55521e11i			0.673099i	−0.941666	+	0.336550i	$0.890740\pi$
$908$	−3.29029e11	−	1.03923e12i	−0.484051	−	1.52887i
$909$	7.88918e11			1.15552
$910$	2.69106e11	−	4.15834e10i	0.392426	−	0.0606393i
$911$		−	2.85425e11i		−	0.414399i	−0.978299	−	0.207199i	$-0.933565\pi$
$911$		−	2.85425e11i		−	0.414399i	0.978299	−	0.207199i	$-0.0664349\pi$
$912$	1.35466e10	−	9.53353e9i	0.0195817	−	0.0137808i
$913$	9.32079e11			1.34144
$914$	−1.61798e11	−	1.04707e12i	−0.231839	−	1.50035i
$915$			6.97492e9i			0.00995073i
$916$	−1.19345e12	+	3.77854e11i	−1.69520	+	0.536713i
$917$	6.18093e10			0.0874132
$918$	−5.42838e10	+	8.38814e9i	−0.0764362	+	0.0118112i
$919$			5.24140e11i			0.734828i	0.930058	+	0.367414i	$0.119757\pi$
$919$			5.24140e11i			0.734828i	−0.930058	+	0.367414i	$0.880243\pi$
$920$	1.54449e12	−	7.65092e11i	2.15593	−	1.06798i
$921$	2.81375e10			0.0391064
$922$	−9.73104e9	−	6.29743e10i	−0.0134659	−	0.0871444i
$923$			4.71207e10i			0.0649240i
$924$	−5.45410e9	−	1.72267e10i	−0.00748230	−	0.0236327i
$925$	1.72103e12			2.35083
$926$	7.78508e11	−	1.20298e11i	1.05881	−	0.163612i
$927$		−	1.27474e12i		−	1.72624i
$928$	1.09513e11	+	1.13720e11i	0.147664	+	0.153336i
$929$	3.87417e11			0.520135			0.260068	−	0.965590i	$-0.416255\pi$
$929$	3.87417e11			0.520135			0.260068	+	0.965590i	$0.416255\pi$
$930$	−1.29920e10	−	8.40776e10i	−0.0173678	−	0.112395i
$931$		−	5.18722e10i		−	0.0690455i
$932$	−3.66475e11	+	1.16029e11i	−0.485714	+	0.153781i
$933$	2.76675e9			0.00365126
$934$	−7.88589e11	+	1.21856e11i	−1.03625	+	0.160125i
$935$		−	1.46816e12i		−	1.92100i
$936$	1.92306e11	+	3.88209e11i	0.250547	+	0.505781i
$937$	−2.60593e11			−0.338069			−0.169034	−	0.985610i	$-0.554065\pi$
$937$	−2.60593e11			−0.338069			−0.169034	+	0.985610i	$0.554065\pi$
$938$	−1.29575e10	−	8.38545e10i	−0.0167383	−	0.108322i
$939$			6.22246e10i			0.0800387i
$940$	−3.79194e11	−	1.19768e12i	−0.485679	−	1.53401i
$941$	−6.57147e10			−0.0838116			−0.0419058	−	0.999122i	$-0.513343\pi$
$941$	−6.57147e10			−0.0838116			−0.0419058	+	0.999122i	$0.513343\pi$
$942$	−4.81478e10	+	7.43999e9i	−0.0611467	+	0.00944862i
$943$			3.76535e11i			0.476166i
$944$	−8.10109e11	−	1.15111e12i	−1.02013	−	1.44954i
$945$	5.53861e10			0.0694503
$946$	2.78592e11	+	1.80290e12i	0.347859	+	2.25117i
$947$		−	6.26134e11i		−	0.778516i	−0.921129	−	0.389258i	$-0.872731\pi$
$947$		−	6.26134e11i		−	0.778516i	0.921129	−	0.389258i	$-0.127269\pi$
$948$	2.83087e10	−	8.96274e9i	0.0350498	−	0.0110970i
$949$	4.08213e11			0.503295
$950$	−9.52180e11	+	1.47135e11i	−1.16903	+	0.180643i
$951$		−	4.46768e9i		−	0.00546210i
$952$	−2.17418e11	+	1.07702e11i	−0.264697	+	0.131122i
$953$	−6.92442e11			−0.839483			−0.419741	−	0.907644i	$-0.637879\pi$
$953$	−6.92442e11			−0.839483			−0.419741	+	0.907644i	$0.637879\pi$
$954$	−1.39029e11	−	8.99727e11i	−0.167847	−	1.08622i
$955$			4.91810e11i			0.591267i
$956$	−1.63981e11	−	5.17931e11i	−0.196319	−	0.620069i
$957$	1.17107e10			0.0139616
$958$	1.26011e12	−	1.94717e11i	1.49605	−	0.231175i
$959$			3.24857e11i			0.384076i
$960$	6.21532e10	+	4.73402e10i	0.0731776	+	0.0557372i
$961$	−4.50834e11			−0.528595
$962$	−7.10821e10	−	4.60007e11i	−0.0829966	−	0.537111i
$963$			2.49475e11i			0.290083i
$964$	1.32270e12	−	4.18777e11i	1.53163	−	0.484925i
$965$	−2.09080e12			−2.41104
$966$	−2.08810e10	+	3.22661e9i	−0.0239796	+	0.00370542i
$967$		−	1.41310e12i		−	1.61610i	−0.589115	−	0.808049i	$-0.700523\pi$
$967$		−	1.41310e12i		−	1.61610i	0.589115	−	0.808049i	$-0.299477\pi$
$968$	2.93280e11	+	5.92047e11i	0.334027	+	0.674302i
$969$	−1.64989e10			−0.0187137
$970$	2.36201e11	+	1.52857e12i	0.266806	+	1.72663i
$971$			1.57159e12i			1.76792i	0.467565	+	0.883959i	$0.345131\pi$
$971$			1.57159e12i			1.76792i	−0.467565	+	0.883959i	$0.654869\pi$
$972$	3.99134e10	+	1.26066e11i	0.0447150	+	0.141232i
$973$	−1.84468e11			−0.205811
$974$	−3.35973e11	+	5.19160e10i	−0.373310	+	0.0576853i
$975$			6.20000e10i			0.0686078i
$976$	−8.02725e10	+	5.64927e10i	−0.0884642	+	0.0622577i
$977$	−8.02436e11			−0.880708			−0.440354	−	0.897824i	$-0.645147\pi$
$977$	−8.02436e11			−0.880708			−0.440354	+	0.897824i	$0.645147\pi$
$978$	9.73468e9	+	6.29979e10i	0.0106406	+	0.0688605i
$979$		−	3.39828e11i		−	0.369937i
$980$	2.33245e11	−	7.38471e10i	0.252876	−	0.0800625i
$981$	1.54131e11			0.166423
$982$	8.26690e11	−	1.27743e11i	0.888990	−	0.137370i
$983$		−	1.24806e11i		−	0.133666i	−0.997764	−	0.0668329i	$-0.978711\pi$
$983$		−	1.24806e11i		−	0.133666i	0.997764	−	0.0668329i	$-0.0212894\pi$
$984$	−1.52941e10	+	7.57620e9i	−0.0163134	+	0.00808112i
$985$	−9.04718e11			−0.961100
$986$	−2.40136e10	−	1.55404e11i	−0.0254068	−	0.164420i
$987$			1.53999e10i			0.0162274i
$988$	7.86541e10	+	2.48427e11i	0.0825455	+	0.260718i
$989$	2.13317e12			2.22967
$990$	−2.32771e12	+	3.59686e11i	−2.42319	+	0.374441i
$991$		−	4.38421e11i		−	0.454566i	−0.973829	−	0.227283i	$-0.927016\pi$
$991$		−	4.38421e11i		−	0.454566i	0.973829	−	0.227283i	$-0.0729842\pi$
$992$	8.62399e11	−	8.30499e11i	0.890557	−	0.857615i
$993$	−2.82661e10			−0.0290716
$994$	6.46534e9	+	4.18404e10i	0.00662287	+	0.0428598i
$995$		−	1.47883e12i		−	1.50878i
$996$	4.70989e10	−	1.49119e10i	0.0478601	−	0.0151529i
$997$	−1.55903e12			−1.57788			−0.788942	−	0.614468i	$-0.789371\pi$
$997$	−1.55903e12			−1.57788			−0.788942	+	0.614468i	$0.789371\pi$
$998$	1.43368e12	−	2.21538e11i	1.44521	−	0.223319i
$999$		−	9.46764e10i		−	0.0950561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.9.c.a.15.14	yes	24
4.3	odd	2	inner	28.9.c.a.15.13	✓	24
8.3	odd	2		448.9.d.d.127.12		24
8.5	even	2		448.9.d.d.127.13		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.9.c.a.15.13	✓	24	4.3	odd	2	inner
28.9.c.a.15.14	yes	24	1.1	even	1	trivial
448.9.d.d.127.12		24	8.3	odd	2
448.9.d.d.127.13		24	8.5	even	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:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	28.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.44338 + 15.8123i) q^{2} -4.01293i q^{3} +(-244.060 + 77.2712i) q^{4} +1160.46 q^{5} +(63.4538 - 9.80514i) q^{6} +907.493i q^{7} +(-1818.17 - 3670.35i) q^{8} +6544.90 q^{9} +(2835.44 + 18349.5i) q^{10} +19382.1i q^{11} +(310.084 + 979.395i) q^{12} -16160.5 q^{13} +(-14349.6 + 2217.35i) q^{14} -4656.84i q^{15} +(53594.3 - 37717.6i) q^{16} -65274.8 q^{17} +(15991.7 + 103490. i) q^{18} +62986.6i q^{19} +(-283221. + 89670.0i) q^{20} +3641.71 q^{21} +(-306476. + 47357.8i) q^{22} +362618. i q^{23} +(-14728.9 + 7296.19i) q^{24} +956037. q^{25} +(-39486.4 - 255535. i) q^{26} -52593.1i q^{27} +(-70123.1 - 221482. i) q^{28} +150564. q^{29} +(73635.5 - 11378.4i) q^{30} -1.14181e6i q^{31} +(727355. + 755293. i) q^{32} +77778.9 q^{33} +(-159491. - 1.03215e6i) q^{34} +1.05311e6i q^{35} +(-1.59735e6 + 505732. i) q^{36} +1.80017e6 q^{37} +(-995965. + 153900. i) q^{38} +64851.1i q^{39} +(-2.10991e6 - 4.25929e6i) q^{40} +1.03838e6 q^{41} +(8898.09 + 57583.9i) q^{42} -5.88269e6i q^{43} +(-1.49768e6 - 4.73038e6i) q^{44} +7.59508e6 q^{45} +(-5.73384e6 + 886016. i) q^{46} +4.22877e6i q^{47} +(-151358. - 215070. i) q^{48} -823543. q^{49} +(2.33597e6 + 1.51172e7i) q^{50} +261943. i q^{51} +(3.94413e6 - 1.24874e6i) q^{52} -8.69385e6 q^{53} +(831619. - 128505. i) q^{54} +2.24921e7i q^{55} +(3.33082e6 - 1.64998e6i) q^{56} +252761. q^{57} +(367885. + 2.38077e6i) q^{58} -2.14783e7i q^{59} +(359840. + 1.13655e6i) q^{60} -1.49778e6 q^{61} +(1.80546e7 - 2.78988e6i) q^{62} +5.93945e6i q^{63} +(-1.01657e7 + 1.33466e7i) q^{64} -1.87536e7 q^{65} +(190044. + 1.22987e6i) q^{66} +5.84369e6i q^{67} +(1.59309e7 - 5.04386e6i) q^{68} +1.45516e6 q^{69} +(-1.66521e7 + 2.57315e6i) q^{70} -2.91579e6i q^{71} +(-1.18997e7 - 2.40221e7i) q^{72} -2.52599e7 q^{73} +(4.39850e6 + 2.84649e7i) q^{74} -3.83651e6i q^{75} +(-4.86705e6 - 1.53725e7i) q^{76} -1.75891e7 q^{77} +(-1.02545e6 + 158456. i) q^{78} -2.89042e7i q^{79} +(6.21939e7 - 4.37697e7i) q^{80} +4.27300e7 q^{81} +(2.53716e6 + 1.64192e7i) q^{82} -4.80898e7i q^{83} +(-888794. + 281399. i) q^{84} -7.57486e7 q^{85} +(9.30191e7 - 1.43737e7i) q^{86} -604203. i q^{87} +(7.11389e7 - 3.52399e7i) q^{88} -1.75331e7 q^{89} +(1.85577e7 + 1.20096e8i) q^{90} -1.46656e7i q^{91} +(-2.80200e7 - 8.85005e7i) q^{92} -4.58200e6 q^{93} +(-6.68667e7 + 1.03325e7i) q^{94} +7.30933e7i q^{95} +(3.03094e6 - 2.91883e6i) q^{96} +8.33031e7 q^{97} +(-2.01223e6 - 1.30221e7i) q^{98} +1.26854e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 383 q^{4} - 336 q^{5} + 5502 q^{6} - 12069 q^{8} - 56296 q^{9} + 41972 q^{10} - 31290 q^{12} - 28560 q^{13} + 7203 q^{14} + 166193 q^{16} - 165648 q^{17} - 11609 q^{18} - 71568 q^{20} - 955748 q^{22}+ \cdots - 2470629 q^{98}+O(q^{100}) \) 24 * q + 3 * q^2 - 383 * q^4 - 336 * q^5 + 5502 * q^6 - 12069 * q^8 - 56296 * q^9 + 41972 * q^10 - 31290 * q^12 - 28560 * q^13 + 7203 * q^14 + 166193 * q^16 - 165648 * q^17 - 11609 * q^18 - 71568 * q^20 - 955748 * q^22 + 133322 * q^24 + 989640 * q^25 - 1066632 * q^26 - 372155 * q^28 + 997296 * q^29 + 3246560 * q^30 - 2265357 * q^32 - 5521600 * q^33 + 1423618 * q^34 - 649451 * q^36 + 5387056 * q^37 + 3945690 * q^38 + 11452504 * q^40 - 12346320 * q^41 + 5642350 * q^42 - 2412372 * q^44 + 17486448 * q^45 + 537288 * q^46 + 20895070 * q^48 - 19765032 * q^49 - 28121691 * q^50 - 12804764 * q^52 + 10812720 * q^53 - 42610652 * q^54 - 7109361 * q^56 + 6748288 * q^57 + 36144266 * q^58 - 98388944 * q^60 + 33644464 * q^61 + 12180756 * q^62 - 1102631 * q^64 - 9084960 * q^65 + 83635608 * q^66 + 106943886 * q^68 - 90944448 * q^69 + 11611236 * q^70 - 48881753 * q^72 - 7651728 * q^73 - 66897318 * q^74 + 64861986 * q^76 - 47482176 * q^77 - 41838760 * q^78 + 154560168 * q^80 + 299710744 * q^81 - 13781390 * q^82 + 571438 * q^84 - 280618528 * q^85 - 139907676 * q^86 - 65086060 * q^88 + 215250672 * q^89 + 40480132 * q^90 + 111569640 * q^92 + 181272192 * q^93 + 171294732 * q^94 - 684707590 * q^96 + 114327024 * q^97 - 2470629 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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