LMFDB - Embedded newform 98.7.d.b.19.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,7,Mod(19,98)] 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("98.19"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	98.d (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-128,0,0,0,0,-1092] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$22.5453001947$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.44930433024.14
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 77x^{4} + 230x^{2} + 529 $ x^8 + 10x^6 + 77x^4 + 230*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.3
Root			$0.946809 - 1.63992i$ of defining polynomial
Character	$\chi$	$=$	98.19
Dual form			98.7.d.b.31.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.82843 - 4.89898i) q^{2} +(-3.32777 + 1.92129i) q^{3} +(-16.0000 - 27.7128i) q^{4} +(-177.318 - 102.374i) q^{5} +21.7369i q^{6} -181.019 q^{8} +(-357.117 + 618.545i) q^{9} +(-1003.06 + 579.117i) q^{10} +(588.941 + 1020.08i) q^{11} +(106.489 + 61.4812i) q^{12} -1399.64i q^{13} +786.762 q^{15} +(-512.000 + 886.810i) q^{16} +(5251.28 - 3031.83i) q^{17} +(2020.16 + 3499.02i) q^{18} +(2714.93 + 1567.47i) q^{19} +6551.96i q^{20} +6663.11 q^{22} +(-4326.30 + 7493.36i) q^{23} +(602.390 - 347.790i) q^{24} +(13148.5 + 22773.9i) q^{25} +(-6856.79 - 3958.77i) q^{26} -5545.73i q^{27} +32565.6 q^{29} +(2225.30 - 3854.33i) q^{30} +(-36631.4 + 21149.2i) q^{31} +(2896.31 + 5016.55i) q^{32} +(-3919.72 - 2263.05i) q^{33} -34301.2i q^{34} +22855.5 q^{36} +(-18789.4 + 32544.2i) q^{37} +(15358.0 - 8866.94i) q^{38} +(2689.10 + 4657.66i) q^{39} +(32097.9 + 18531.7i) q^{40} +93520.9i q^{41} +92007.0 q^{43} +(18846.1 - 32642.4i) q^{44} +(126646. - 73119.3i) q^{45} +(24473.2 + 42388.9i) q^{46} +(-21609.4 - 12476.2i) q^{47} -3934.79i q^{48} +148758. q^{50} +(-11650.0 + 20178.4i) q^{51} +(-38787.9 + 22394.2i) q^{52} +(-54.8113 - 94.9359i) q^{53} +(-27168.4 - 15685.7i) q^{54} -241170. i q^{55} -12046.2 q^{57} +(92109.4 - 159538. i) q^{58} +(-282835. + 163295. i) q^{59} +(-12588.2 - 21803.4i) q^{60} +(73265.5 + 42299.9i) q^{61} +239276. i q^{62} +32768.0 q^{64} +(-143287. + 248180. i) q^{65} +(-22173.3 + 12801.7i) q^{66} +(55501.0 + 96130.5i) q^{67} +(-168041. - 97018.4i) q^{68} -33248.2i q^{69} -441825. q^{71} +(64645.1 - 111969. i) q^{72} +(402010. - 232100. i) q^{73} +(106289. + 184098. i) q^{74} +(-87510.4 - 50524.1i) q^{75} -100318. i q^{76} +30423.7 q^{78} +(-297506. + 515295. i) q^{79} +(181573. - 104831. i) q^{80} +(-249684. - 432465. i) q^{81} +(458157. + 264517. i) q^{82} +654116. i q^{83} -1.24152e6 q^{85} +(260235. - 450741. i) q^{86} +(-108371. + 62567.8i) q^{87} +(-106610. - 184653. i) q^{88} +(258350. + 149159. i) q^{89} -827251. i q^{90} +276883. q^{92} +(81267.2 - 140759. i) q^{93} +(-122241. + 70575.9i) q^{94} +(-320937. - 555879. i) q^{95} +(-19276.5 - 11129.3i) q^{96} -169894. i q^{97} -841284. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 128 q^{4} - 1092 q^{9} + 4440 q^{11} - 8640 q^{15} - 4096 q^{16} + 9984 q^{18} + 3072 q^{22} - 40584 q^{23} + 40700 q^{25} - 36528 q^{29} + 42240 q^{30} + 69888 q^{36} + 23192 q^{37} - 208608 q^{39}+ \cdots - 2663856 q^{99}+O(q^{100}) $ 8 * q - 128 * q^4 - 1092 * q^9 + 4440 * q^11 - 8640 * q^15 - 4096 * q^16 + 9984 * q^18 + 3072 * q^22 - 40584 * q^23 + 40700 * q^25 - 36528 * q^29 + 42240 * q^30 + 69888 * q^36 + 23192 * q^37 - 208608 * q^39 - 89392 * q^43 + 142080 * q^44 - 33792 * q^46 + 729600 * q^50 - 157824 * q^51 - 248616 * q^53 - 945984 * q^57 + 840192 * q^58 + 138240 * q^60 + 262144 * q^64 - 1293600 * q^65 + 434776 * q^67 - 903216 * q^71 + 319488 * q^72 + 981504 * q^74 + 2603520 * q^78 - 2092904 * q^79 + 252828 * q^81 - 4235520 * q^85 + 2334720 * q^86 - 49152 * q^88 + 2597376 * q^92 - 995328 * q^93 + 190560 * q^95 - 2663856 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.82843	−	4.89898i	0.353553	−	0.612372i
$2$	2.82843	−	4.89898i	0.353553	−	0.612372i
$3$	−3.32777	+	1.92129i	−0.123251	+	0.0711588i	−0.560358	−	0.828251i	$-0.689336\pi$
$3$	−3.32777	+	1.92129i	−0.123251	+	0.0711588i	0.437107	+	0.899409i	$0.356003\pi$
$4$	−16.0000	−	27.7128i	−0.250000	−	0.433013i
$5$	−177.318	−	102.374i	−1.41854	−	0.818995i	−0.422370	−	0.906424i	$-0.638802\pi$
$5$	−177.318	−	102.374i	−1.41854	−	0.818995i	−0.996171	+	0.0874287i	$0.972135\pi$
$6$			21.7369i			0.100634i
$7$		0			0
$7$		0			0
$8$	−181.019			−0.353553
$9$	−357.117	+	618.545i	−0.489873	+	0.848485i
$10$	−1003.06	+	579.117i	−1.00306	+	0.579117i
$11$	588.941	+	1020.08i	0.442480	+	0.766398i	0.997873	−	0.0651901i	$-0.0207654\pi$
$11$	588.941	+	1020.08i	0.442480	+	0.766398i	−0.555393	+	0.831588i	$0.687432\pi$
$12$	106.489	+	61.4812i	0.0616253	+	0.0355794i
$13$		−	1399.64i		−	0.637067i	−0.947912	−	0.318534i	$-0.896810\pi$
$13$		−	1399.64i		−	0.637067i	0.947912	−	0.318534i	$-0.103190\pi$
$14$		0			0
$15$	786.762			0.233115
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$	5251.28	−	3031.83i	1.06885	−	0.617103i	0.140985	−	0.990012i	$-0.454973\pi$
$17$	5251.28	−	3031.83i	1.06885	−	0.617103i	0.927868	+	0.372909i	$0.121640\pi$
$18$	2020.16	+	3499.02i	0.346392	+	0.599969i
$19$	2714.93	+	1567.47i	0.395821	+	0.228527i	0.684679	−	0.728845i	$-0.259942\pi$
$19$	2714.93	+	1567.47i	0.395821	+	0.228527i	−0.288858	+	0.957372i	$0.593276\pi$
$20$			6551.96i			0.818995i
$21$		0			0
$22$	6663.11			0.625761
$23$	−4326.30	+	7493.36i	−0.355576	+	0.615876i	−0.987216	−	0.159386i	$-0.949049\pi$
$23$	−4326.30	+	7493.36i	−0.355576	+	0.615876i	0.631640	+	0.775262i	$0.282382\pi$
$24$	602.390	−	347.790i	0.0435757	−	0.0251584i
$25$	13148.5	+	22773.9i	0.841505	+	1.45753i
$26$	−6856.79	−	3958.77i	−0.390123	−	0.225237i
$27$		−	5545.73i		−	0.281753i
$28$		0			0
$29$	32565.6			1.33526			0.667629	−	0.744494i	$-0.267309\pi$
$29$	32565.6			1.33526			0.667629	+	0.744494i	$0.267309\pi$
$30$	2225.30	−	3854.33i	0.0824185	−	0.142753i
$31$	−36631.4	+	21149.2i	−1.22961	+	0.709918i	−0.966949	−	0.254969i	$-0.917935\pi$
$31$	−36631.4	+	21149.2i	−1.22961	+	0.709918i	−0.262665	+	0.964887i	$0.584601\pi$
$32$	2896.31	+	5016.55i	0.0883883	+	0.153093i
$33$	−3919.72	−	2263.05i	−0.109072	−	0.0629727i
$34$		−	34301.2i		−	0.872715i
$35$		0			0
$36$	22855.5			0.489873
$37$	−18789.4	+	32544.2i	−0.370943	+	0.642492i	−0.989711	−	0.143082i	$-0.954299\pi$
$37$	−18789.4	+	32544.2i	−0.370943	+	0.642492i	0.618768	+	0.785574i	$0.287632\pi$
$38$	15358.0	−	8866.94i	0.279887	−	0.161593i
$39$	2689.10	+	4657.66i	0.0453329	+	0.0785189i
$40$	32097.9	+	18531.7i	0.501530	+	0.289558i
$41$			93520.9i			1.35693i	0.734634	+	0.678464i	$0.237354\pi$
$41$			93520.9i			1.35693i	−0.734634	+	0.678464i	$0.762646\pi$
$42$		0			0
$43$	92007.0			1.15722			0.578610	−	0.815605i	$-0.303596\pi$
$43$	92007.0			1.15722			0.578610	+	0.815605i	$0.303596\pi$
$44$	18846.1	−	32642.4i	0.221240	−	0.383199i
$45$	126646.	−	73119.3i	1.38981	−	0.802407i
$46$	24473.2	+	42388.9i	0.251430	+	0.435490i
$47$	−21609.4	−	12476.2i	−0.208137	−	0.120168i	0.392308	−	0.919834i	$-0.371677\pi$
$47$	−21609.4	−	12476.2i	−0.208137	−	0.120168i	−0.600445	+	0.799666i	$0.705010\pi$
$48$		−	3934.79i		−	0.0355794i
$49$		0			0
$50$	148758.			1.19007
$51$	−11650.0	+	20178.4i	−0.0878245	+	0.152117i
$52$	−38787.9	+	22394.2i	−0.275858	+	0.159267i
$53$	−54.8113	−	94.9359i	−0.000368165	−	0.000637680i	0.865841	−	0.500319i	$-0.166784\pi$
$53$	−54.8113	−	94.9359i	−0.000368165	−	0.000637680i	−0.866209	+	0.499681i	$0.833451\pi$
$54$	−27168.4	−	15685.7i	−0.172537	−	0.0996146i
$55$		−	241170.i		−	1.44956i
$56$		0			0
$57$	−12046.2			−0.0650468
$58$	92109.4	−	159538.i	0.472085	−	0.817675i
$59$	−282835.	+	163295.i	−1.37714	+	0.795091i	−0.991814	−	0.127691i	$-0.959243\pi$
$59$	−282835.	+	163295.i	−1.37714	+	0.795091i	−0.385323	+	0.922782i	$0.625910\pi$
$60$	−12588.2	−	21803.4i	−0.0582787	−	0.100942i
$61$	73265.5	+	42299.9i	0.322783	+	0.186359i	0.652632	−	0.757675i	$-0.273665\pi$
$61$	73265.5	+	42299.9i	0.322783	+	0.186359i	−0.329850	+	0.944034i	$0.606998\pi$
$62$			239276.i			1.00398i
$63$		0			0
$64$	32768.0			0.125000
$65$	−143287.	+	248180.i	−0.521755	+	0.903706i
$66$	−22173.3	+	12801.7i	−0.0771255	+	0.0445284i
$67$	55501.0	+	96130.5i	0.184534	+	0.319622i	0.943419	−	0.331602i	$-0.107589\pi$
$67$	55501.0	+	96130.5i	0.184534	+	0.319622i	−0.758885	+	0.651224i	$0.774256\pi$
$68$	−168041.	−	97018.4i	−0.534427	−	0.308551i
$69$		−	33248.2i		−	0.101209i
$70$		0			0
$71$	−441825.			−1.23446			−0.617228	−	0.786784i	$-0.711744\pi$
$71$	−441825.			−1.23446			−0.617228	+	0.786784i	$0.711744\pi$
$72$	64645.1	−	111969.i	0.173196	−	0.299985i
$73$	402010.	−	232100.i	1.03340	−	0.596633i	0.115442	−	0.993314i	$-0.463172\pi$
$73$	402010.	−	232100.i	1.03340	−	0.596633i	0.917956	+	0.396681i	$0.129838\pi$
$74$	106289.	+	184098.i	0.262296	+	0.454311i
$75$	−87510.4	−	50524.1i	−0.207432	−	0.119761i
$76$		−	100318.i		−	0.228527i
$77$		0			0
$78$	30423.7			0.0641104
$79$	−297506.	+	515295.i	−0.603412	+	1.04514i	0.388888	+	0.921285i	$0.372859\pi$
$79$	−297506.	+	515295.i	−0.603412	+	1.04514i	−0.992300	+	0.123856i	$0.960474\pi$
$80$	181573.	−	104831.i	0.354635	−	0.204749i
$81$	−249684.	−	432465.i	−0.469824	−	0.813759i
$82$	458157.	+	264517.i	0.830945	+	0.479747i
$83$			654116.i			1.14398i	0.820259	+	0.571992i	$0.193829\pi$
$83$			654116.i			1.14398i	−0.820259	+	0.571992i	$0.806171\pi$
$84$		0			0
$85$	−1.24152e6			−2.02162
$86$	260235.	−	450741.i	0.409139	−	0.708649i
$87$	−108371.	+	62567.8i	−0.164571	+	0.0950153i
$88$	−106610.	−	184653.i	−0.156440	−	0.270963i
$89$	258350.	+	149159.i	0.366470	+	0.211582i	0.671915	−	0.740628i	$-0.265472\pi$
$89$	258350.	+	149159.i	0.366470	+	0.211582i	−0.305445	+	0.952210i	$0.598805\pi$
$90$		−	827251.i		−	1.13477i
$91$		0			0
$92$	276883.			0.355576
$93$	81267.2	−	140759.i	0.101034	−	0.174996i
$94$	−122241.	+	70575.9i	−0.147175	+	0.0849714i
$95$	−320937.	−	555879.i	−0.374325	−	0.648350i
$96$	−19276.5	−	11129.3i	−0.0217878	−	0.0125792i
$97$		−	169894.i		−	0.186150i	−0.995659	−	0.0930752i	$-0.970330\pi$
$97$		−	169894.i		−	0.186150i	0.995659	−	0.0930752i	$-0.0296697\pi$
$98$		0			0
$99$	−841284.			−0.867036
$100$	420753.	−	728765.i	0.420753	−	0.728765i
$101$	−968373.	+	559091.i	−0.939894	+	0.542648i	−0.889927	−	0.456103i	$-0.849245\pi$
$101$	−968373.	+	559091.i	−0.939894	+	0.542648i	−0.0499667	+	0.998751i	$0.515912\pi$
$102$	65902.4	+	114146.i	0.0621013	+	0.107563i
$103$	−1.04290e6	−	602120.i	−0.954403	−	0.551025i	−0.0599571	−	0.998201i	$-0.519096\pi$
$103$	−1.04290e6	−	602120.i	−0.954403	−	0.551025i	−0.894446	+	0.447176i	$0.852430\pi$
$104$			253361.i			0.225237i
$105$		0			0
$106$	−620.119			−0.000520664
$107$	61019.6	−	105689.i	0.0498102	−	0.0862738i	−0.840045	−	0.542516i	$-0.817472\pi$
$107$	61019.6	−	105689.i	0.0498102	−	0.0862738i	0.889855	+	0.456242i	$0.150805\pi$
$108$	−153688.	+	88731.8i	−0.122002	+	0.0704381i
$109$	−553060.	−	957927.i	−0.427063	−	0.739696i	0.569547	−	0.821959i	$-0.307119\pi$
$109$	−553060.	−	957927.i	−0.427063	−	0.739696i	−0.996611	+	0.0822630i	$0.973785\pi$
$110$	−1.18149e6	−	682131.i	−0.887668	−	0.512495i
$111$		−	144399.i		−	0.105583i
$112$		0			0
$113$	266739.			0.184864			0.0924318	−	0.995719i	$-0.470536\pi$
$113$	266739.			0.184864			0.0924318	+	0.995719i	$0.470536\pi$
$114$	−34071.9	+	59014.2i	−0.0229975	+	0.0398329i
$115$	1.53426e6	−	885803.i	1.00880	−	0.582430i
$116$	−521049.	−	902484.i	−0.333814	−	0.578183i
$117$	865739.	+	499835.i	0.540542	+	0.312082i
$118$			1.84747e6i			1.12443i
$119$		0			0
$120$	−142419.			−0.0824185
$121$	192077.	−	332687.i	0.108423	−	0.187793i
$122$	414453.	−	239284.i	0.228242	−	0.131775i
$123$	−179680.	−	311216.i	−0.0965573	−	0.167242i
$124$	1.17221e6	+	676773.i	0.614807	+	0.354959i
$125$		−	2.18509e6i		−	1.11876i
$126$		0			0
$127$	1.34435e6			0.656297			0.328149	−	0.944626i	$-0.393575\pi$
$127$	1.34435e6			0.656297			0.328149	+	0.944626i	$0.393575\pi$
$128$	92681.9	−	160530.i	0.0441942	−	0.0765466i
$129$	−306178.	+	176772.i	−0.142628	+	0.0823463i
$130$	810553.	+	1.40392e6i	0.368936	+	0.639017i
$131$	3.17383e6	+	1.83241e6i	1.41179	+	0.815097i	0.995557	−	0.0941610i	$-0.0300168\pi$
$131$	3.17383e6	+	1.83241e6i	1.41179	+	0.815097i	0.416233	+	0.909258i	$0.363350\pi$
$132$			144835.i			0.0629727i
$133$		0			0
$134$	627922.			0.260970
$135$	−567741.	+	983356.i	−0.230754	+	0.399677i
$136$	−950583.	+	548819.i	−0.377897	+	0.218179i
$137$	1.66505e6	+	2.88395e6i	0.647537	+	1.12157i	0.983709	+	0.179767i	$0.0575344\pi$
$137$	1.66505e6	+	2.88395e6i	0.647537	+	1.12157i	−0.336172	+	0.941801i	$0.609132\pi$
$138$	−162882.	−	94040.1i	−0.0619779	−	0.0357829i
$139$			1.18963e6i			0.442962i	0.975165	+	0.221481i	$0.0710890\pi$
$139$			1.18963e6i			0.442962i	−0.975165	+	0.221481i	$0.928911\pi$
$140$		0			0
$141$	95881.3			0.0342040
$142$	−1.24967e6	+	2.16449e6i	−0.436446	+	0.755947i
$143$	1.42774e6	−	824304.i	0.488247	−	0.281890i
$144$	−365688.	−	633390.i	−0.122468	−	0.212121i
$145$	−5.77445e6	−	3.33388e6i	−1.89412	−	1.09357i
$146$		−	2.62592e6i		−	0.843766i
$147$		0			0
$148$	1.20252e6			0.370943
$149$	−810722.	+	1.40421e6i	−0.245083	+	0.424496i	−0.962155	−	0.272503i	$-0.912148\pi$
$149$	−810722.	+	1.40421e6i	−0.245083	+	0.424496i	0.717072	+	0.696999i	$0.245482\pi$
$150$	−495033.	+	285808.i	−0.146677	+	0.0846838i
$151$	2.17515e6	+	3.76747e6i	0.631770	+	1.09426i	0.987190	+	0.159550i	$0.0510045\pi$
$151$	2.17515e6	+	3.76747e6i	0.631770	+	1.09426i	−0.355420	+	0.934707i	$0.615662\pi$
$152$	−491455.	−	283742.i	−0.139944	−	0.0807965i
$153$			4.33087e6i			1.20921i
$154$		0			0
$155$	8.66053e6			2.32568
$156$	86051.3	−	149045.i	0.0226665	−	0.0392595i
$157$	−4.01914e6	+	2.32045e6i	−1.03857	+	0.599616i	−0.919427	−	0.393261i	$-0.871347\pi$
$157$	−4.01914e6	+	2.32045e6i	−1.03857	+	0.599616i	−0.119139	+	0.992878i	$0.538013\pi$
$158$	1.68295e6	+	2.91495e6i	0.426677	+	0.739026i
$159$	364.798	+	210.616i	9.07531e−5	+	5.23963e-5i
$160$		−	1.18603e6i		−	0.289558i
$161$		0			0
$162$	−2.82485e6			−0.664431
$163$	2.63299e6	−	4.56047e6i	0.607975	−	1.05304i	−0.383599	−	0.923500i	$-0.625315\pi$
$163$	2.63299e6	−	4.56047e6i	0.607975	−	1.05304i	0.991574	−	0.129544i	$-0.0413513\pi$
$164$	2.59173e6	−	1.49633e6i	0.587567	−	0.339232i
$165$	463356.	+	802557.i	0.103149	+	0.178659i
$166$	3.20450e6	+	1.85012e6i	0.700545	+	0.404460i
$167$		−	1.99529e6i		−	0.428406i	−0.976789	−	0.214203i	$-0.931285\pi$
$167$		−	1.99529e6i		−	0.428406i	0.976789	−	0.214203i	$-0.0687154\pi$
$168$		0			0
$169$	2.86783e6			0.594145
$170$	−3.51156e6	+	6.08220e6i	−0.714749	+	1.23798i
$171$	−1.93910e6	+	1.11954e6i	−0.387804	+	0.223898i
$172$	−1.47211e6	−	2.54977e6i	−0.289305	−	0.501091i
$173$	1.70906e6	+	986723.i	0.330079	+	0.190571i	0.655876	−	0.754869i	$-0.272299\pi$
$173$	1.70906e6	+	986723.i	0.330079	+	0.190571i	−0.325797	+	0.945440i	$0.605633\pi$
$174$			707874.i			0.134372i
$175$		0			0
$176$	−1.20615e6			−0.221240
$177$	627473.	−	1.08681e6i	0.113155	−	0.195991i
$178$	1.46145e6	−	843769.i	0.259134	−	0.149611i
$179$	3.29662e6	+	5.70992e6i	0.574791	+	0.995568i	0.996064	+	0.0886338i	$0.0282501\pi$
$179$	3.29662e6	+	5.70992e6i	0.574791	+	0.995568i	−0.421273	+	0.906934i	$0.638417\pi$
$180$	−4.05268e6	−	2.33982e6i	−0.694905	−	0.401203i
$181$		−	2.60968e6i		−	0.440100i	−0.975489	−	0.220050i	$-0.929378\pi$
$181$		−	2.60968e6i		−	0.440100i	0.975489	−	0.220050i	$-0.0706220\pi$
$182$		0			0
$183$	−325081.			−0.0530442
$184$	783143.	−	1.35644e6i	0.125715	−	0.217745i
$185$	6.66337e6	−	3.84710e6i	1.05240	−	0.607601i
$186$	−459717.	−	796253.i	−0.0714417	−	0.123741i
$187$	6.18539e6	+	3.57113e6i	0.945893	+	0.546111i
$188$			798475.i			0.120168i
$189$		0			0
$190$	−3.63099e6			−0.529376
$191$	−996449.	+	1.72590e6i	−0.143006	+	0.247694i	−0.928627	−	0.371014i	$-0.879010\pi$
$191$	−996449.	+	1.72590e6i	−0.143006	+	0.247694i	0.785621	+	0.618708i	$0.212344\pi$
$192$	−109044.	+	62956.7i	−0.0154063	+	0.00889485i
$193$	−6.20065e6	−	1.07398e7i	−0.862513	−	1.49392i	−0.869496	−	0.493940i	$-0.835556\pi$
$193$	−6.20065e6	−	1.07398e7i	−0.862513	−	1.49392i	0.00698351	−	0.999976i	$-0.497777\pi$
$194$	−832309.	−	480534.i	−0.113993	−	0.0658141i
$195$		−	1.10118e6i		−	0.148510i
$196$		0			0
$197$	−5.13349e6			−0.671450			−0.335725	−	0.941960i	$-0.608981\pi$
$197$	−5.13349e6			−0.671450			−0.335725	+	0.941960i	$0.608981\pi$
$198$	−2.37951e6	+	4.12143e6i	−0.306544	+	0.530949i
$199$	−532732.	+	307573.i	−0.0676004	+	0.0390291i	−0.533419	−	0.845851i	$-0.679093\pi$
$199$	−532732.	+	307573.i	−0.0676004	+	0.0390291i	0.465819	+	0.884880i	$0.345760\pi$
$200$	−2.38014e6	−	4.12252e6i	−0.297517	−	0.515315i
$201$	−369389.	−	213267.i	−0.0454878	−	0.0262624i
$202$			6.32539e6i			0.767420i
$203$		0			0
$204$	745601.			0.0878245
$205$	9.57414e6	−	1.65829e7i	1.11132	−	1.92486i
$206$	−5.89954e6	+	3.40610e6i	−0.674865	+	0.389633i
$207$	−3.08999e6	−	5.35202e6i	−0.348374	−	0.603402i
$208$	1.24121e6	+	716614.i	0.137929	+	0.0796334i
$209$			3.69258e6i			0.404475i
$210$		0			0
$211$	2.56281e6			0.272815			0.136408	−	0.990653i	$-0.456444\pi$
$211$	2.56281e6			0.272815			0.136408	+	0.990653i	$0.456444\pi$
$212$	−1753.96	+	3037.95i	−0.000184082	+	0.000318840i
$213$	1.47029e6	−	848873.i	0.152147	−	0.0878424i
$214$	−345179.	−	597868.i	−0.0352211	−	0.0610048i
$215$	−1.63145e7	−	9.41916e6i	−1.64156	−	0.947757i
$216$			1.00389e6i			0.0996146i
$217$		0			0
$218$	−6.25716e6			−0.603959
$219$	−891863.	+	1.54475e6i	−0.0849113	+	0.147071i
$220$	−6.68350e6	+	3.85872e6i	−0.627676	+	0.362389i
$221$	−4.24346e6	−	7.34988e6i	−0.393136	−	0.680932i
$222$	−707408.	−	408422.i	−0.0646564	−	0.0373294i
$223$		−	7.82377e6i		−	0.705507i	−0.935716	−	0.352753i	$-0.885245\pi$
$223$		−	7.82377e6i		−	0.705507i	0.935716	−	0.352753i	$-0.114755\pi$
$224$		0			0
$225$	−1.87823e7			−1.64892
$226$	754452.	−	1.30675e6i	0.0653591	−	0.113205i
$227$	−7.09348e6	+	4.09542e6i	−0.606432	+	0.350124i	−0.771568	−	0.636147i	$-0.780527\pi$
$227$	−7.09348e6	+	4.09542e6i	−0.606432	+	0.350124i	0.165136	+	0.986271i	$0.447194\pi$
$228$	192739.	+	333835.i	0.0162617	+	0.0281661i
$229$	1.13038e7	+	6.52628e6i	0.941282	+	0.543449i	0.890362	−	0.455254i	$-0.150451\pi$
$229$	1.13038e7	+	6.52628e6i	0.941282	+	0.543449i	0.0509198	+	0.998703i	$0.483785\pi$
$230$		−	1.00217e7i		−	0.823681i
$231$		0			0
$232$	−5.89500e6			−0.472085
$233$	−692495.	+	1.19944e6i	−0.0547456	+	0.0948221i	−0.892099	−	0.451839i	$-0.850768\pi$
$233$	−692495.	+	1.19944e6i	−0.0547456	+	0.0948221i	0.837354	+	0.546661i	$0.184101\pi$
$234$	4.89736e6	−	2.82749e6i	0.382221	−	0.220675i
$235$	2.55448e6	+	4.42449e6i	0.196834	+	0.340926i
$236$	9.05072e6	+	5.22544e6i	0.688569	+	0.397545i
$237$		−	2.28638e6i		−	0.171752i
$238$		0			0
$239$	4.37563e6			0.320514			0.160257	−	0.987075i	$-0.448768\pi$
$239$	4.37563e6			0.320514			0.160257	+	0.987075i	$0.448768\pi$
$240$	−402822.	+	697708.i	−0.0291393	+	0.0504708i
$241$	7.53336e6	−	4.34939e6i	0.538193	−	0.310726i	−0.206154	−	0.978520i	$-0.566095\pi$
$241$	7.53336e6	−	4.34939e6i	0.538193	−	0.310726i	0.744346	+	0.667794i	$0.232761\pi$
$242$	−1.08655e6	−	1.88196e6i	−0.0766663	−	0.132790i
$243$	5.16298e6	+	2.98085e6i	0.359817	+	0.207740i
$244$		−	2.70719e6i		−	0.186359i
$245$		0			0
$246$	−2.03285e6			−0.136553
$247$	2.19389e6	−	3.79992e6i	0.145587	−	0.252164i
$248$	6.63100e6	−	3.82841e6i	0.434734	−	0.250994i
$249$	−1.25674e6	−	2.17674e6i	−0.0814046	−	0.140997i
$250$	−1.07047e7	−	6.18035e6i	−0.685100	−	0.395543i
$251$			2.65980e7i			1.68201i	0.541031	+	0.841003i	$0.318034\pi$
$251$			2.65980e7i			1.68201i	−0.541031	+	0.841003i	$0.681966\pi$
$252$		0			0
$253$	−1.01917e7			−0.629342
$254$	3.80239e6	−	6.58593e6i	0.232036	−	0.401898i
$255$	4.13150e6	−	2.38532e6i	0.249165	−	0.143856i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	6.53561e6	+	3.77334e6i	0.385023	+	0.222293i	0.680002	−	0.733211i	$-0.261979\pi$
$257$	6.53561e6	+	3.77334e6i	0.385023	+	0.222293i	−0.294978	+	0.955504i	$0.595312\pi$
$258$			1.99995e6i			0.116455i
$259$		0			0
$260$	9.17036e6			0.521755
$261$	−1.16297e7	+	2.01433e7i	−0.654106	+	1.13295i
$262$	1.79539e7	−	1.03657e7i	0.998286	−	0.576361i
$263$	6.58421e6	+	1.14042e7i	0.361940	+	0.626898i	0.988280	−	0.152652i	$-0.0487812\pi$
$263$	6.58421e6	+	1.14042e7i	0.361940	+	0.626898i	−0.626340	+	0.779550i	$0.715448\pi$
$264$	709544.	+	409656.i	0.0385627	+	0.0222642i
$265$			22445.1i			0.00120610i
$266$		0			0
$267$	−1.14631e6			−0.0602236
$268$	1.77603e6	−	3.07618e6i	0.0922670	−	0.159811i
$269$	−1.58364e7	+	9.14314e6i	−0.813578	+	0.469719i	−0.848197	−	0.529681i	$-0.822312\pi$
$269$	−1.58364e7	+	9.14314e6i	−0.813578	+	0.469719i	0.0346189	+	0.999401i	$0.488978\pi$
$270$	3.21163e6	+	5.56270e6i	0.163168	+	0.282615i
$271$	−2.40850e7	−	1.39055e7i	−1.21015	−	0.698679i	−0.247357	−	0.968925i	$-0.579562\pi$
$271$	−2.40850e7	−	1.39055e7i	−1.21015	−	0.698679i	−0.962792	+	0.270245i	$0.912895\pi$
$272$			6.20918e6i			0.308551i
$273$		0			0
$274$	1.88379e7			0.915756
$275$	−1.54874e7	+	2.68250e7i	−0.744699	+	1.28986i
$276$	−921401.	+	531971.i	−0.0438250	+	0.0253024i
$277$	2.62709e6	+	4.55026e6i	0.123605	+	0.214090i	0.921187	−	0.389121i	$-0.127221\pi$
$277$	2.62709e6	+	4.55026e6i	0.123605	+	0.214090i	−0.797582	+	0.603211i	$0.793888\pi$
$278$	5.82796e6	+	3.36477e6i	0.271258	+	0.156611i
$279$		−	3.02109e7i		−	1.39108i
$280$		0			0
$281$	−3.12195e7			−1.40704			−0.703522	−	0.710674i	$-0.748390\pi$
$281$	−3.12195e7			−1.40704			−0.703522	+	0.710674i	$0.748390\pi$
$282$	271193.	−	469720.i	0.0120929	−	0.0209456i
$283$	−1.57141e7	+	9.07252e6i	−0.693313	+	0.400284i	−0.804852	−	0.593476i	$-0.797755\pi$
$283$	−1.57141e7	+	9.07252e6i	−0.693313	+	0.400284i	0.111539	+	0.993760i	$0.464422\pi$
$284$	7.06921e6	+	1.22442e7i	0.308614	+	0.534535i
$285$	2.13601e6	+	1.23322e6i	0.0922716	+	0.0532730i
$286$		−	9.32593e6i		−	0.398652i
$287$		0			0
$288$	−4.13729e6			−0.173196
$289$	6.31515e6	−	1.09382e7i	0.261632	−	0.453159i
$290$	−3.26652e7	+	1.88593e7i	−1.33934	+	0.773270i
$291$	326416.	+	565369.i	0.0132462	+	0.0229431i
$292$	−1.28643e7	−	7.42721e6i	−0.516699	−	0.298316i
$293$		−	5.83393e6i		−	0.231931i	−0.993253	−	0.115965i	$-0.963004\pi$
$293$		−	5.83393e6i		−	0.231931i	0.993253	−	0.115965i	$-0.0369962\pi$
$294$		0			0
$295$	6.68689e7			2.60470
$296$	3.40124e6	−	5.89112e6i	0.131148	−	0.227155i
$297$	5.65707e6	−	3.26611e6i	0.215935	−	0.124670i
$298$	4.58613e6	+	7.94342e6i	0.173300	+	0.300164i
$299$	1.04880e7	+	6.05524e6i	0.392355	+	0.226526i
$300$			3.23354e6i			0.119761i
$301$		0			0
$302$	2.46090e7			0.893457
$303$	2.14835e6	−	3.72105e6i	0.0772283	−	0.133763i
$304$	−2.78009e6	+	1.60509e6i	−0.0989552	+	0.0571318i
$305$	−8.66085e6	−	1.50010e7i	−0.305254	−	0.528715i
$306$	2.12168e7	+	1.22495e7i	0.740485	+	0.427519i
$307$			2.26871e7i			0.784087i	0.919947	+	0.392043i	$0.128232\pi$
$307$			2.26871e7i			0.784087i	−0.919947	+	0.392043i	$0.871768\pi$
$308$		0			0
$309$	4.62738e6			0.156841
$310$	2.44957e7	−	4.24278e7i	0.822251	−	1.42418i
$311$	3.43241e7	−	1.98170e7i	1.14108	−	0.658805i	0.194385	−	0.980925i	$-0.437729\pi$
$311$	3.43241e7	−	1.98170e7i	1.14108	−	0.658805i	0.946699	+	0.322121i	$0.104396\pi$
$312$	−486780.	−	843127.i	−0.0160276	−	0.0277606i
$313$	8.73442e6	+	5.04282e6i	0.284840	+	0.164452i	0.635613	−	0.772008i	$-0.280748\pi$
$313$	8.73442e6	+	5.04282e6i	0.284840	+	0.164452i	−0.350772	+	0.936461i	$0.614081\pi$
$314$			2.62529e7i			0.847986i
$315$		0			0
$316$	1.90404e7			0.603412
$317$	−1.49186e7	+	2.58398e7i	−0.468329	+	0.811169i	−0.999345	−	0.0361928i	$-0.988477\pi$
$317$	−1.49186e7	+	2.58398e7i	−0.468329	+	0.811169i	0.531016	+	0.847362i	$0.321810\pi$
$318$	2063.61	−	1191.43i	6.41721e−5	−	3.70498e-5i
$319$	1.91792e7	+	3.32194e7i	0.590825	+	1.02334i
$320$	−5.81034e6	−	3.35460e6i	−0.177318	−	0.102374i
$321$			468945.i			0.0141777i
$322$		0			0
$323$	1.90092e7			0.564099
$324$	−7.98987e6	+	1.38389e7i	−0.234912	+	0.406879i
$325$	3.18752e7	−	1.84032e7i	0.928545	−	0.536095i
$326$	−1.48944e7	−	2.57979e7i	−0.429903	−	0.744614i
$327$	3.68091e6	+	2.12517e6i	0.105272	+	0.0607786i
$328$		−	1.69291e7i		−	0.479747i
$329$		0			0
$330$	5.24228e6			0.145874
$331$	−895080.	+	1.55032e6i	−0.0246819	+	0.0427502i	−0.878103	−	0.478473i	$-0.841191\pi$
$331$	−895080.	+	1.55032e6i	−0.0246819	+	0.0427502i	0.853421	+	0.521223i	$0.174524\pi$
$332$	1.81274e7	−	1.04659e7i	0.495360	−	0.285996i
$333$	−1.34200e7	−	2.32442e7i	−0.363430	−	0.629479i
$334$	−9.77486e6	−	5.64352e6i	−0.262344	−	0.151464i
$335$		−	2.27275e7i		−	0.604530i
$336$		0			0
$337$	−1.30113e6			−0.0339964			−0.0169982	−	0.999856i	$-0.505411\pi$
$337$	−1.30113e6			−0.0339964			−0.0169982	+	0.999856i	$0.505411\pi$
$338$	8.11143e6	−	1.40494e7i	0.210062	−	0.363838i
$339$	−887645.	+	512482.i	−0.0227845	+	0.0131547i
$340$	1.98644e7	+	3.44061e7i	0.505404	+	0.875385i
$341$	−4.31475e7	−	2.49112e7i	−1.08816	−	0.628249i
$342$			1.26661e7i			0.316640i
$343$		0			0
$344$	−1.66550e7			−0.409139
$345$	−3.40376e6	+	5.89549e6i	−0.0828900	+	0.143570i
$346$	9.66788e6	−	5.58175e6i	0.233401	−	0.134754i
$347$	1.33571e7	+	2.31351e7i	0.319685	+	0.553711i	0.980422	−	0.196907i	$-0.0630896\pi$
$347$	1.33571e7	+	2.31351e7i	0.319685	+	0.553711i	−0.660737	+	0.750617i	$0.729756\pi$
$348$	3.46786e6	+	2.00217e6i	0.0822856	+	0.0475076i
$349$			2.39729e7i			0.563956i	0.959421	+	0.281978i	$0.0909904\pi$
$349$			2.39729e7i			0.563956i	−0.959421	+	0.281978i	$0.909010\pi$
$350$		0			0
$351$	−7.76202e6			−0.179495
$352$	−3.41151e6	+	5.90891e6i	−0.0782202	+	0.135481i
$353$	−6.92640e7	+	3.99896e7i	−1.57465	+	0.909123i	−0.579060	+	0.815285i	$0.696580\pi$
$353$	−6.92640e7	+	3.99896e7i	−1.57465	+	0.909123i	−0.995587	+	0.0938381i	$0.970086\pi$
$354$	−3.54952e6	−	6.14795e6i	−0.0800129	−	0.138586i
$355$	7.83434e7	+	4.52316e7i	1.75113	+	1.01101i
$356$		−	9.54615e6i		−	0.211582i
$357$		0			0
$358$	3.72970e7			0.812878
$359$	−2.25657e7	+	3.90849e7i	−0.487714	+	0.844746i	−0.999900	−	0.0141286i	$-0.995503\pi$
$359$	−2.25657e7	+	3.90849e7i	−0.487714	+	0.844746i	0.512186	+	0.858875i	$0.328836\pi$
$360$	−2.29254e7	+	1.32360e7i	−0.491372	+	0.283694i
$361$	−1.86090e7	−	3.22318e7i	−0.395551	−	0.685114i
$362$	−1.27848e7	−	7.38128e6i	−0.269505	−	0.155599i
$363$			1.47614e6i			0.0308609i
$364$		0			0
$365$	−9.50445e7			−1.95456
$366$	−919467.	+	1.59256e6i	−0.0187540	+	0.0324828i
$367$	−5.25836e7	+	3.03592e7i	−1.06378	+	0.614174i	−0.926476	−	0.376355i	$-0.877177\pi$
$367$	−5.25836e7	+	3.03592e7i	−1.06378	+	0.614174i	−0.137305	+	0.990529i	$0.543844\pi$
$368$	−4.43013e6	−	7.67320e6i	−0.0888940	−	0.153969i
$369$	−5.78469e7	−	3.33979e7i	−1.15133	−	0.664722i
$370$		−	4.35250e7i		−	0.859277i
$371$		0			0
$372$	−5.20110e6			−0.101034
$373$	4.65855e7	−	8.06884e7i	0.897685	−	1.55484i	0.0672398	−	0.997737i	$-0.478581\pi$
$373$	4.65855e7	−	8.06884e7i	0.897685	−	1.55484i	0.830446	−	0.557100i	$-0.188086\pi$
$374$	3.49898e7	−	2.02014e7i	0.668847	−	0.386159i
$375$	4.19818e6	+	7.27145e6i	0.0796098	+	0.137888i
$376$	3.91171e6	+	2.25843e6i	0.0735874	+	0.0424857i
$377$		−	4.55800e7i		−	0.850649i
$378$		0			0
$379$	2.78773e7			0.512075			0.256037	−	0.966667i	$-0.417583\pi$
$379$	2.78773e7			0.512075			0.256037	+	0.966667i	$0.417583\pi$
$380$	−1.02700e7	+	1.77881e7i	−0.187163	+	0.324175i
$381$	−4.47367e6	+	2.58288e6i	−0.0808890	+	0.0467013i
$382$	5.63677e6	+	9.76317e6i	0.101121	+	0.175146i
$383$	2.28477e6	+	1.31911e6i	0.0406673	+	0.0234793i	0.520196	−	0.854047i	$-0.325859\pi$
$383$	2.28477e6	+	1.31911e6i	0.0406673	+	0.0234793i	−0.479528	+	0.877526i	$0.659192\pi$
$384$			712274.i			0.0125792i
$385$		0			0
$386$	−7.01524e7			−1.21978
$387$	−3.28573e7	+	5.69105e7i	−0.566890	+	0.981883i
$388$	−4.70825e6	+	2.71831e6i	−0.0806055	+	0.0465376i
$389$	−1.56295e7	−	2.70710e7i	−0.265519	−	0.459892i	0.702181	−	0.711999i	$-0.252210\pi$
$389$	−1.56295e7	−	2.70710e7i	−0.265519	−	0.459892i	−0.967699	+	0.252107i	$0.918877\pi$
$390$	−5.39466e6	−	3.11461e6i	−0.0909433	−	0.0525061i
$391$			5.24663e7i			0.877708i
$392$		0			0
$393$	−1.40824e7			−0.232005
$394$	−1.45197e7	+	2.51488e7i	−0.237393	+	0.411178i
$395$	1.05506e8	−	6.09139e7i	1.71193	−	0.988383i
$396$	1.34605e7	+	2.33144e7i	0.216759	+	0.375438i
$397$	−2.89030e7	−	1.66872e7i	−0.461925	−	0.266693i	0.250928	−	0.968006i	$-0.419264\pi$
$397$	−2.89030e7	−	1.66872e7i	−0.461925	−	0.266693i	−0.712853	+	0.701313i	$0.752598\pi$
$398$			3.47979e6i			0.0551955i
$399$		0			0
$400$	−2.69282e7			−0.420753
$401$	2.03399e6	−	3.52297e6i	0.0315439	−	0.0546356i	−0.849822	−	0.527069i	$-0.823291\pi$
$401$	2.03399e6	−	3.52297e6i	0.0315439	−	0.0546356i	0.881366	+	0.472433i	$0.156624\pi$
$402$	−2.08958e6	+	1.20642e6i	−0.0321648	+	0.0185703i
$403$	2.96012e7	+	5.12707e7i	0.452266	+	0.783347i
$404$	3.09880e7	+	1.78909e7i	0.469947	+	0.271324i
$405$			1.02245e8i			1.53913i
$406$		0			0
$407$	−4.42634e7			−0.656540
$408$	2.10888e6	−	3.65268e6i	0.0310507	−	0.0537813i
$409$	3.28226e7	−	1.89501e7i	0.479736	−	0.276976i	−0.240570	−	0.970632i	$-0.577334\pi$
$409$	3.28226e7	−	1.89501e7i	0.479736	−	0.276976i	0.720307	+	0.693656i	$0.244001\pi$
$410$	−5.41595e7	−	9.38070e7i	−0.785820	−	1.36108i
$411$	−1.10818e7	−	6.39807e6i	−0.159619	−	0.0921559i
$412$			3.85357e7i			0.551025i
$413$		0			0
$414$	−3.49592e7			−0.492676
$415$	6.69647e7	−	1.15986e8i	0.936918	−	1.62279i
$416$	7.02136e6	−	4.05378e6i	0.0975306	−	0.0563093i
$417$	−2.28561e6	−	3.95880e6i	−0.0315206	−	0.0545953i
$418$	1.80899e7	+	1.04442e7i	0.247689	+	0.143003i
$419$		−	7.34255e7i		−	0.998171i	−0.866553	−	0.499085i	$-0.833669\pi$
$419$		−	7.34255e7i		−	0.998171i	0.866553	−	0.499085i	$-0.166331\pi$
$420$		0			0
$421$	5.94103e6			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$421$	5.94103e6			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$422$	7.24871e6	−	1.25551e7i	0.0964548	−	0.167065i
$423$	1.54342e7	−	8.91092e6i	0.203921	−	0.117734i
$424$	9921.90	+	17185.2i	0.000130166	+	0.000225454i
$425$	1.38093e8	+	7.97280e7i	1.79889	+	1.03859i
$426$		−	9.60391e6i		−	0.124228i
$427$		0			0
$428$	−3.90526e6			−0.0498102
$429$	−3.16745e6	+	5.48618e6i	−0.0401178	+	0.0694861i
$430$	−9.22885e7	+	5.32828e7i	−1.16076	+	0.670165i
$431$	−4.79406e7	−	8.30355e7i	−0.598785	−	1.03713i	−0.993001	−	0.118109i	$-0.962317\pi$
$431$	−4.79406e7	−	8.30355e7i	−0.598785	−	1.03713i	0.394215	−	0.919018i	$-0.371016\pi$
$432$	4.91801e6	+	2.83942e6i	0.0610012	+	0.0352191i
$433$		−	1.23332e8i		−	1.51919i	−0.650396	−	0.759595i	$-0.725397\pi$
$433$		−	1.23332e8i		−	1.51919i	0.650396	−	0.759595i	$-0.274603\pi$
$434$		0			0
$435$	2.56214e7			0.311268
$436$	−1.76979e7	+	3.06537e7i	−0.213532	+	0.369848i
$437$	−2.34912e7	+	1.35627e7i	−0.281489	+	0.162518i
$438$	5.04514e6	+	8.73843e6i	0.0600414	+	0.103995i
$439$	−5.55705e7	−	3.20836e7i	−0.656827	−	0.379219i	0.134240	−	0.990949i	$-0.457141\pi$
$439$	−5.55705e7	−	3.20836e7i	−0.656827	−	0.379219i	−0.791067	+	0.611730i	$0.790474\pi$
$440$			4.36564e7i			0.512495i
$441$		0			0
$442$	−4.80092e7			−0.555978
$443$	3.29363e7	−	5.70473e7i	0.378847	−	0.656182i	−0.612048	−	0.790821i	$-0.709654\pi$
$443$	3.29363e7	−	5.70473e7i	0.378847	−	0.656182i	0.990895	+	0.134639i	$0.0429874\pi$
$444$	−4.00171e6	+	2.31039e6i	−0.0457190	+	0.0263958i
$445$	−3.05400e7	−	5.28969e7i	−0.346569	−	0.600275i
$446$	−3.83285e7	−	2.21290e7i	−0.432033	−	0.249434i
$447$		−	6.23051e6i		−	0.0697592i
$448$		0			0
$449$	−1.02206e8			−1.12911			−0.564555	−	0.825395i	$-0.690952\pi$
$449$	−1.02206e8			−1.12911			−0.564555	+	0.825395i	$0.690952\pi$
$450$	−5.31242e7	+	9.20139e7i	−0.582982	+	1.00975i
$451$	−9.53984e7	+	5.50783e7i	−1.03995	+	0.600414i
$452$	−4.26783e6	−	7.39209e6i	−0.0462159	−	0.0800483i
$453$	−1.44768e7	−	8.35818e6i	−0.155732	−	0.0899119i
$454$			4.63344e7i			0.495150i
$455$		0			0
$456$	2.18060e6			0.0229975
$457$	2.81191e7	−	4.87037e7i	0.294613	−	0.510285i	−0.680282	−	0.732951i	$-0.738142\pi$
$457$	2.81191e7	−	4.87037e7i	0.294613	−	0.510285i	0.974895	+	0.222666i	$0.0714758\pi$
$458$	6.39442e7	−	3.69182e7i	0.665587	−	0.384277i
$459$	−1.68137e7	−	2.91222e7i	−0.173870	−	0.301152i
$460$	−4.90962e7	−	2.83457e7i	−0.504399	−	0.291215i
$461$		−	2.46600e7i		−	0.251705i	−0.992049	−	0.125852i	$-0.959833\pi$
$461$		−	2.46600e7i		−	0.251705i	0.992049	−	0.125852i	$-0.0401665\pi$
$462$		0			0
$463$	1.91959e8			1.93404			0.967018	−	0.254707i	$-0.0819791\pi$
$463$	1.91959e8			1.93404			0.967018	+	0.254707i	$0.0819791\pi$
$464$	−1.66736e7	+	2.88795e7i	−0.166907	+	0.289092i
$465$	−2.88202e7	+	1.66394e7i	−0.286641	+	0.165492i
$466$	3.91734e6	+	6.78504e6i	0.0387110	+	0.0670494i
$467$	−1.30705e8	−	7.54623e7i	−1.28334	−	0.740934i	−0.305879	−	0.952070i	$-0.598950\pi$
$467$	−1.30705e8	−	7.54623e7i	−1.28334	−	0.740934i	−0.977457	+	0.211137i	$0.932284\pi$
$468$		−	3.19894e7i		−	0.312082i
$469$		0			0
$470$	2.89007e7			0.278365
$471$	8.91650e6	−	1.54438e7i	0.0853359	−	0.147806i
$472$	5.11986e7	−	2.95595e7i	0.486892	−	0.281107i
$473$	5.41867e7	+	9.38542e7i	0.512047	+	0.886891i
$474$	−1.12009e7	−	6.46685e6i	−0.105176	−	0.0607236i
$475$			8.24395e7i			0.769227i
$476$		0			0
$477$	78296.3			0.000721416
$478$	1.23762e7	−	2.14361e7i	0.113319	−	0.196274i
$479$	−4.07391e7	+	2.35208e7i	−0.370685	+	0.214015i	−0.673758	−	0.738952i	$-0.735321\pi$
$479$	−4.07391e7	+	2.35208e7i	−0.370685	+	0.214015i	0.303073	+	0.952967i	$0.401988\pi$
$480$	2.27871e6	+	3.94683e6i	0.0206046	+	0.0356882i
$481$	4.55500e7	+	2.62983e7i	0.409311	+	0.236316i
$482$		−	4.92077e7i		−	0.439432i
$483$		0			0
$484$	−1.22929e7			−0.108423
$485$	−1.73928e7	+	3.01253e7i	−0.152456	+	0.264062i
$486$	2.92062e7	−	1.68622e7i	0.254429	−	0.146895i
$487$	2.18007e7	+	3.77599e7i	0.188748	+	0.326922i	0.944833	−	0.327552i	$-0.106224\pi$
$487$	2.18007e7	+	3.77599e7i	0.188748	+	0.326922i	−0.756085	+	0.654474i	$0.772890\pi$
$488$	−1.32625e7	−	7.65710e6i	−0.114121	−	0.0658877i
$489$			2.02349e7i			0.173051i
$490$		0			0
$491$	7.78280e7			0.657494			0.328747	−	0.944418i	$-0.393374\pi$
$491$	7.78280e7			0.657494			0.328747	+	0.944418i	$0.393374\pi$
$492$	−5.74977e6	+	9.95890e6i	−0.0482787	+	0.0836211i
$493$	1.71011e8	−	9.87332e7i	1.42719	−	0.823991i
$494$	−1.24105e7	−	2.14956e7i	−0.102946	−	0.178307i
$495$	1.49174e8	+	8.61259e7i	1.22993	+	0.710098i
$496$		−	4.33135e7i		−	0.354959i
$497$		0			0
$498$	−1.42184e7			−0.115123
$499$	3.16871e7	−	5.48836e7i	0.255024	−	0.441714i	−0.709878	−	0.704324i	$-0.751250\pi$
$499$	3.16871e7	−	5.48836e7i	0.255024	−	0.441714i	0.964902	+	0.262610i	$0.0845834\pi$
$500$	−6.05549e7	+	3.49614e7i	−0.484439	+	0.279691i
$501$	3.83351e6	+	6.63984e6i	0.0304848	+	0.0528013i
$502$	1.30303e8	+	7.52304e7i	1.03001	+	0.594679i
$503$			1.88800e8i			1.48354i	0.670657	+	0.741768i	$0.266012\pi$
$503$			1.88800e8i			1.48354i	−0.670657	+	0.741768i	$0.733988\pi$
$504$		0			0
$505$	2.28946e8			1.77770
$506$	−2.88266e7	+	4.99291e7i	−0.222506	+	0.385391i
$507$	−9.54345e6	+	5.50991e6i	−0.0732287	+	0.0422786i
$508$	−2.15096e7	−	3.72557e7i	−0.164074	−	0.284185i
$509$	5.06490e7	+	2.92422e7i	0.384077	+	0.221747i	0.679590	−	0.733592i	$-0.262158\pi$
$509$	5.06490e7	+	2.92422e7i	0.384077	+	0.221747i	−0.295514	+	0.955338i	$0.595491\pi$
$510$		−	2.69869e7i		−	0.203443i
$511$		0			0
$512$	−5.93164e6			−0.0441942
$513$	8.69276e6	−	1.50563e7i	0.0643881	−	0.111523i
$514$	3.69710e7	−	2.13452e7i	0.272253	−	0.157185i
$515$	1.23283e8	+	2.13533e8i	0.902573	+	1.56330i
$516$	9.79769e6	+	5.65670e6i	0.0713140	+	0.0411731i
$517$		−	2.93909e7i		−	0.212687i
$518$		0			0
$519$	−7.58311e6			−0.0542432
$520$	2.59377e7	−	4.49254e7i	0.184468	−	0.319508i
$521$	−1.30779e7	+	7.55056e6i	−0.0924754	+	0.0533907i	−0.545525	−	0.838095i	$-0.683670\pi$
$521$	−1.30779e7	+	7.55056e6i	−0.0924754	+	0.0533907i	0.453049	+	0.891486i	$0.350336\pi$
$522$	6.57877e7	+	1.13948e8i	0.462523	+	0.801113i
$523$	−2.00789e8	−	1.15926e8i	−1.40358	−	0.810355i	−0.408818	−	0.912616i	$-0.634059\pi$
$523$	−2.00789e8	−	1.15926e8i	−1.40358	−	0.810355i	−0.994758	+	0.102261i	$0.967392\pi$
$524$		−	1.17274e8i		−	0.815097i
$525$		0			0
$526$	7.44918e7			0.511860
$527$	−1.28241e8	+	2.22120e8i	−0.876185	+	1.51760i
$528$	4.01379e6	−	2.31736e6i	0.0272680	−	0.0157432i
$529$	3.65843e7	+	6.33658e7i	0.247131	+	0.428044i
$530$	109958.	+	63484.3i	0.000738583	+	0.000426421i
$531$		−	2.33262e8i		−	1.55797i
$532$		0			0
$533$	1.30895e8			0.864455
$534$	−3.24224e6	+	5.61573e6i	−0.0212923	+	0.0368793i
$535$	−2.16397e7	+	1.24937e7i	−0.141316	+	0.0815886i
$536$	−1.00468e7	−	1.74015e7i	−0.0652426	−	0.113004i
$537$	−2.19408e7	−	1.26675e7i	−0.141687	−	0.0818029i
$538$			1.03443e8i			0.664284i
$539$		0			0
$540$	3.63354e7			0.230754
$541$	5.84563e6	−	1.01249e7i	0.0369181	−	0.0639441i	−0.846976	−	0.531631i	$-0.821579\pi$
$541$	5.84563e6	−	1.01249e7i	0.0369181	−	0.0639441i	0.883894	+	0.467687i	$0.154913\pi$
$542$	−1.36245e8	+	7.86612e7i	−0.855704	+	0.494041i
$543$	5.01394e6	+	8.68440e6i	0.0313170	+	0.0542426i
$544$	3.04186e7	+	1.75622e7i	0.188948	+	0.109089i
$545$			2.26476e8i			1.39905i
$546$		0			0
$547$	−1.11900e8			−0.683704			−0.341852	−	0.939754i	$-0.611054\pi$
$547$	−1.11900e8			−0.683704			−0.341852	+	0.939754i	$0.611054\pi$
$548$	5.32815e7	−	9.22863e7i	0.323769	−	0.560784i
$549$	−5.23288e7	+	3.02120e7i	−0.316245	+	0.182584i
$550$	8.76100e7	+	1.51745e8i	0.526581	+	0.912066i
$551$	8.84134e7	+	5.10455e7i	0.528522	+	0.305143i
$552$			6.01857e6i			0.0357829i
$553$		0			0
$554$	2.97222e7			0.174804
$555$	−1.47828e7	+	2.56045e7i	−0.0864723	+	0.149774i
$556$	3.29679e7	−	1.90340e7i	0.191808	−	0.110740i
$557$	6.89187e7	+	1.19371e8i	0.398815	+	0.690767i	0.993580	−	0.113132i	$-0.0360883\pi$
$557$	6.89187e7	+	1.19371e8i	0.398815	+	0.690767i	−0.594765	+	0.803899i	$0.702755\pi$
$558$	−1.48003e8	−	8.54494e7i	−0.851858	−	0.491820i
$559$		−	1.28776e8i		−	0.737227i
$560$		0			0
$561$	−2.74447e7			−0.155442
$562$	−8.83022e7	+	1.52944e8i	−0.497465	+	0.861635i
$563$	−3.23225e7	+	1.86614e7i	−0.181126	+	0.104573i	−0.587821	−	0.808991i	$-0.700014\pi$
$563$	−3.23225e7	+	1.86614e7i	−0.181126	+	0.104573i	0.406696	+	0.913564i	$0.366681\pi$
$564$	−1.53410e6	−	2.65714e6i	−0.00855099	−	0.0148107i
$565$	−4.72975e7	−	2.73072e7i	−0.262237	−	0.151402i
$566$			1.02644e8i			0.566088i
$567$		0			0
$568$	7.99789e7			0.436446
$569$	−7.09286e7	+	1.22852e8i	−0.385021	+	0.666876i	−0.991772	−	0.128016i	$-0.959139\pi$
$569$	−7.09286e7	+	1.22852e8i	−0.385021	+	0.666876i	0.606751	+	0.794892i	$0.292473\pi$
$570$	1.20831e7	−	6.97617e6i	0.0652459	−	0.0376697i
$571$	−1.23914e8	−	2.14626e8i	−0.665600	−	1.15285i	−0.979122	−	0.203273i	$-0.934842\pi$
$571$	−1.23914e8	−	2.14626e8i	−0.665600	−	1.15285i	0.313522	−	0.949581i	$-0.398491\pi$
$572$	−4.56876e7	−	2.63777e7i	−0.244124	−	0.140945i
$573$		−	7.65786e6i		−	0.0407046i
$574$		0			0
$575$	−2.27537e8			−1.19688
$576$	−1.17020e7	+	2.02685e7i	−0.0612341	+	0.106061i
$577$	1.24362e8	−	7.18004e7i	0.647381	−	0.373766i	−0.140071	−	0.990141i	$-0.544733\pi$
$577$	1.24362e8	−	7.18004e7i	0.647381	−	0.373766i	0.787452	+	0.616376i	$0.211400\pi$
$578$	−3.57239e7	−	6.18756e7i	−0.185001	−	0.320432i
$579$	4.12686e7	+	2.38265e7i	0.212610	+	0.122751i
$580$			2.13368e8i			1.09357i
$581$		0			0
$582$	3.69297e6			0.0187330
$583$	64561.3	−	111823.i	0.000325811	−	0.000564322i
$584$	−7.27715e7	+	4.20147e7i	−0.365362	+	0.210942i
$585$	−1.02340e8	−	1.77259e8i	−0.511187	−	0.885402i
$586$	−2.85803e7	−	1.65009e7i	−0.142028	−	0.0820000i
$587$		−	1.55774e8i		−	0.770160i	−0.922883	−	0.385080i	$-0.874174\pi$
$587$		−	1.55774e8i		−	0.770160i	0.922883	−	0.385080i	$-0.125826\pi$
$588$		0			0
$589$	−1.32603e8			−0.648942
$590$	1.89134e8	−	3.27589e8i	0.920901	−	1.59505i
$591$	1.70830e7	−	9.86290e6i	0.0827566	−	0.0477796i
$592$	−1.92403e7	−	3.33252e7i	−0.0927358	−	0.160623i
$593$	−5.93741e7	−	3.42796e7i	−0.284730	−	0.164389i	0.350833	−	0.936438i	$-0.385898\pi$
$593$	−5.93741e7	−	3.42796e7i	−0.284730	−	0.164389i	−0.635563	+	0.772049i	$0.719232\pi$
$594$		−	3.69518e7i		−	0.176310i
$595$		0			0
$596$	5.18862e7			0.245083
$597$	1.18187e6	−	2.04706e6i	0.00555453	−	0.00962072i
$598$	5.93290e7	−	3.42536e7i	0.277437	−	0.160178i
$599$	−3.22408e7	−	5.58427e7i	−0.150012	−	0.259828i	0.781220	−	0.624256i	$-0.214598\pi$
$599$	−3.22408e7	−	5.58427e7i	−0.150012	−	0.259828i	−0.931232	+	0.364428i	$0.881264\pi$
$600$	1.58411e7	+	9.14585e6i	0.0733383	+	0.0423419i
$601$		−	2.18773e8i		−	1.00779i	−0.863765	−	0.503895i	$-0.831900\pi$
$601$		−	2.18773e8i		−	1.00779i	0.863765	−	0.503895i	$-0.168100\pi$
$602$		0			0
$603$	−7.92815e7			−0.361593
$604$	6.96049e7	−	1.20559e8i	0.315885	−	0.547129i
$605$	−6.81173e7	+	3.93276e7i	−0.307604	+	0.177595i
$606$	−1.21529e7	−	2.10494e7i	−0.0546087	−	0.0945850i
$607$	3.08130e8	+	1.77899e8i	1.37774	+	0.795441i	0.991888	−	0.127118i	$-0.0405728\pi$
$607$	3.08130e8	+	1.77899e8i	1.37774	+	0.795441i	0.385856	+	0.922559i	$0.373906\pi$
$608$			1.81595e7i			0.0807965i
$609$		0			0
$610$	−9.79863e7			−0.431694
$611$	−1.74621e7	+	3.02453e7i	−0.0765550	+	0.132597i
$612$	1.20021e8	−	6.92939e7i	0.523602	−	0.302302i
$613$	−7.51758e6	−	1.30208e7i	−0.0326360	−	0.0565272i	0.849246	−	0.527997i	$-0.177057\pi$
$613$	−7.51758e6	−	1.30208e7i	−0.0326360	−	0.0565272i	−0.881882	+	0.471470i	$0.843724\pi$
$614$	1.11144e8	+	6.41688e7i	0.480153	+	0.277217i
$615$			7.35786e7i			0.316320i
$616$		0			0
$617$	4.45354e7			0.189605			0.0948025	−	0.995496i	$-0.469778\pi$
$617$	4.45354e7			0.189605			0.0948025	+	0.995496i	$0.469778\pi$
$618$	1.30882e7	−	2.26694e7i	0.0554517	−	0.0960451i
$619$	3.10076e7	−	1.79023e7i	0.130737	−	0.0754808i	−0.433205	−	0.901295i	$-0.642618\pi$
$619$	3.10076e7	−	1.79023e7i	0.130737	−	0.0754808i	0.563942	+	0.825814i	$0.309284\pi$
$620$	−1.38568e8	−	2.40008e8i	−0.581419	−	1.00705i
$621$	4.15562e7	+	2.39925e7i	0.173525	+	0.100184i
$622$		−	2.24204e8i		−	0.931691i
$623$		0			0
$624$	−5.50728e6			−0.0226665
$625$	−1.82511e7	+	3.16119e7i	−0.0747566	+	0.129482i
$626$	4.94093e7	−	2.85265e7i	0.201412	−	0.116285i
$627$	−7.09451e6	−	1.22881e7i	−0.0287819	−	0.0498518i
$628$	1.28612e8	+	7.42544e7i	0.519283	+	0.299808i
$629$			2.27864e8i			0.915640i
$630$		0			0
$631$	−4.30383e8			−1.71304			−0.856520	−	0.516115i	$-0.827378\pi$
$631$	−4.30383e8			−1.71304			−0.856520	+	0.516115i	$0.827378\pi$
$632$	5.38543e7	−	9.32784e7i	0.213338	−	0.369513i
$633$	−8.52842e6	+	4.92389e6i	−0.0336246	+	0.0194132i
$634$	8.43924e7	+	1.46172e8i	0.331158	+	0.573583i
$635$	−2.38376e8	−	1.37627e8i	−0.930984	−	0.537504i
$636$		−	13479.5i		−	5.23963e-5i
$637$		0			0
$638$	2.16988e8			0.835553
$639$	1.57784e8	−	2.73289e8i	0.604727	−	1.04742i
$640$	−3.28683e7	+	1.89765e7i	−0.125382	+	0.0723896i
$641$	−9.35546e7	−	1.62041e8i	−0.355215	−	0.615250i	0.631940	−	0.775017i	$-0.282259\pi$
$641$	−9.35546e7	−	1.62041e8i	−0.355215	−	0.615250i	−0.987155	+	0.159767i	$0.948926\pi$
$642$	2.29735e6	+	1.32638e6i	0.00868205	+	0.00501258i
$643$			2.52905e8i			0.951314i	0.879631	+	0.475657i	$0.157790\pi$
$643$			2.52905e8i			0.951314i	−0.879631	+	0.475657i	$0.842210\pi$
$644$		0			0
$645$	7.23876e7			0.269765
$646$	5.37660e7	−	9.31255e7i	0.199439	−	0.345439i
$647$	1.69714e8	−	9.79845e7i	0.626622	−	0.361780i	−0.152821	−	0.988254i	$-0.548836\pi$
$647$	1.69714e8	−	9.79845e7i	0.626622	−	0.361780i	0.779442	+	0.626474i	$0.215502\pi$
$648$	4.51976e7	+	7.82845e7i	0.166108	+	0.287707i
$649$	−3.33146e8	−	1.92342e8i	−1.21871	−	0.703624i
$650$		−	2.08208e8i		−	0.758153i
$651$		0			0
$652$	−1.68511e8			−0.607975
$653$	−5.55543e7	+	9.62230e7i	−0.199516	+	0.345572i	−0.948372	−	0.317161i	$-0.897270\pi$
$653$	−5.55543e7	+	9.62230e7i	−0.199516	+	0.345572i	0.748855	+	0.662733i	$0.230604\pi$
$654$	2.08223e7	−	1.20218e7i	0.0744383	−	0.0429770i
$655$	−3.75184e8	−	6.49838e8i	−1.33512	−	2.31250i
$656$	−8.29352e7	−	4.78827e7i	−0.293784	−	0.169616i
$657$			3.31548e8i			1.16910i
$658$		0			0
$659$	−2.24885e8			−0.785786			−0.392893	−	0.919584i	$-0.628526\pi$
$659$	−2.24885e8			−0.785786			−0.392893	+	0.919584i	$0.628526\pi$
$660$	1.48274e7	−	2.56818e7i	0.0515743	−	0.0893293i
$661$	−4.50307e8	+	2.59985e8i	−1.55921	+	0.900209i	−0.561875	+	0.827222i	$0.689920\pi$
$661$	−4.50307e8	+	2.59985e8i	−1.55921	+	0.900209i	−0.997333	+	0.0729865i	$0.976747\pi$
$662$	5.06334e6	+	8.76996e6i	0.0174527	+	0.0302290i
$663$	2.82425e7	+	1.63058e7i	0.0969085	+	0.0559501i
$664$		−	1.18408e8i		−	0.404460i
$665$		0			0
$666$	−1.51830e8			−0.513967
$667$	−1.40888e8	+	2.44026e8i	−0.474786	+	0.822353i
$668$	−5.52950e7	+	3.19246e7i	−0.185505	+	0.107102i
$669$	1.50317e7	+	2.60357e7i	0.0502030	+	0.0869541i
$670$	−1.11342e8	−	6.42831e7i	−0.370197	−	0.213733i
$671$			9.96486e7i			0.329840i
$672$		0			0
$673$	−3.68354e8			−1.20842			−0.604212	−	0.796823i	$-0.706512\pi$
$673$	−3.68354e8			−1.20842			−0.604212	+	0.796823i	$0.706512\pi$
$674$	−3.68016e6	+	6.37423e6i	−0.0120195	+	0.0208184i
$675$	1.26298e8	−	7.29182e7i	0.410663	−	0.237096i
$676$	−4.58852e7	−	7.94755e7i	−0.148536	−	0.257272i
$677$	−1.66006e7	−	9.58435e6i	−0.0535004	−	0.0308885i	0.473011	−	0.881056i	$-0.343167\pi$
$677$	−1.66006e7	−	9.58435e6i	−0.0535004	−	0.0308885i	−0.526512	+	0.850168i	$0.676500\pi$
$678$			5.79808e6i			0.0186035i
$679$		0			0
$680$	2.24740e8			0.714749
$681$	1.57370e7	−	2.72572e7i	0.0498287	−	0.0863059i
$682$	−2.44079e8	+	1.40919e8i	−0.769445	+	0.444239i
$683$	1.64133e8	+	2.84288e8i	0.515152	+	0.892269i	0.999845	+	0.0175849i	$0.00559772\pi$
$683$	1.64133e8	+	2.84288e8i	0.515152	+	0.892269i	−0.484694	+	0.874684i	$0.661069\pi$
$684$	6.20512e7	+	3.58253e7i	0.193902	+	0.111949i
$685$		−	6.81833e8i		−	2.12132i
$686$		0			0
$687$	−5.01554e7			−0.154685
$688$	−4.71076e7	+	8.15927e7i	−0.144652	+	0.250545i
$689$	−132876.	+	76715.9i	−0.000406245	+	0.000234546i
$690$	1.92546e7	+	3.33499e7i	0.0586121	+	0.101519i
$691$	1.70043e8	+	9.81746e7i	0.515378	+	0.297554i	0.735042	−	0.678022i	$-0.237163\pi$
$691$	1.70043e8	+	9.81746e7i	0.515378	+	0.297554i	−0.219664	+	0.975576i	$0.570496\pi$
$692$		−	6.31503e7i		−	0.190571i
$693$		0			0
$694$	1.51118e8			0.452103
$695$	1.21787e8	−	2.10942e8i	0.362783	−	0.628359i
$696$	1.96172e7	−	1.13260e7i	0.0581847	−	0.0335930i
$697$	2.83539e8	+	4.91104e8i	0.837364	+	1.45036i
$698$	1.17443e8	+	6.78057e7i	0.345351	+	0.199388i
$699$		−	5.32193e6i		−	0.0155825i
$700$		0			0
$701$	4.19696e8			1.21837			0.609187	−	0.793026i	$-0.291496\pi$
$701$	4.19696e8			1.21837			0.609187	+	0.793026i	$0.291496\pi$
$702$	−2.19543e7	+	3.80260e7i	−0.0634612	+	0.109918i
$703$	−1.02024e8	+	5.89035e7i	−0.293654	+	0.169541i
$704$	1.92984e7	+	3.34258e7i	0.0553100	+	0.0957998i
$705$	−1.70014e7	−	9.81578e6i	−0.0485197	−	0.0280129i
$706$			4.52430e8i			1.28569i
$707$		0			0
$708$	−4.01583e7			−0.113155
$709$	−3.23164e8	+	5.59736e8i	−0.906742	+	1.57052i	−0.0881797	+	0.996105i	$0.528105\pi$
$709$	−3.23164e8	+	5.59736e8i	−0.906742	+	1.57052i	−0.818562	+	0.574418i	$0.805228\pi$
$710$	4.43177e8	−	2.55869e8i	1.23823	−	0.714894i
$711$	−2.12489e8	−	3.68042e8i	−0.591191	−	1.02397i
$712$	−4.67664e7	−	2.70006e7i	−0.129567	−	0.0748055i
$713$		−	3.65990e8i		−	1.00972i
$714$		0			0
$715$	−3.37550e8			−0.923465
$716$	1.05492e8	−	1.82717e8i	0.287396	−	0.497784i
$717$	−1.45611e7	+	8.40684e6i	−0.0395035	+	0.0228074i
$718$	1.27651e8	+	2.21098e8i	0.344866	+	0.597326i
$719$	2.81417e8	+	1.62476e8i	0.757119	+	0.437123i	0.828260	−	0.560343i	$-0.189331\pi$
$719$	2.81417e8	+	1.62476e8i	0.757119	+	0.437123i	−0.0711415	+	0.997466i	$0.522664\pi$
$720$			1.49748e8i			0.401203i
$721$		0			0
$722$	−2.10537e8			−0.559393
$723$	−1.67128e7	+	2.89475e7i	−0.0442217	+	0.0765942i
$724$	−7.23215e7	+	4.17548e7i	−0.190569	+	0.110025i
$725$	4.28189e8	+	7.41646e8i	1.12363	+	1.94618i
$726$	7.23159e6	+	4.17516e6i	0.0188983	+	0.0109110i
$727$			5.08659e8i			1.32380i	0.749591	+	0.661902i	$0.230250\pi$
$727$			5.08659e8i			1.32380i	−0.749591	+	0.661902i	$0.769750\pi$
$728$		0			0
$729$	3.41130e8			0.880517
$730$	−2.68826e8	+	4.65621e8i	−0.691040	+	1.19692i
$731$	4.83154e8	−	2.78949e8i	1.23690	−	0.714123i
$732$	5.20129e6	+	9.00890e6i	0.0132611	+	0.0229688i
$733$	6.51976e8	+	3.76419e8i	1.65546	+	0.955782i	0.974769	+	0.223215i	$0.0716552\pi$
$733$	6.51976e8	+	3.76419e8i	1.65546	+	0.955782i	0.680695	+	0.732567i	$0.261678\pi$
$734$			3.43475e8i			0.868573i
$735$		0			0
$736$	−5.01212e7			−0.125715
$737$	−6.53736e7	+	1.13230e8i	−0.163305	+	0.282853i
$738$	−3.27231e8	+	1.88927e8i	−0.814115	+	0.470030i
$739$	7.92738e7	+	1.37306e8i	0.196425	+	0.340218i	0.947367	−	0.320150i	$-0.103733\pi$
$739$	7.92738e7	+	1.37306e8i	0.196425	+	0.340218i	−0.750942	+	0.660368i	$0.770400\pi$
$740$	−2.13228e8	−	1.23107e8i	−0.526198	−	0.303800i
$741$			1.68603e7i			0.0414392i
$742$		0			0
$743$	5.89089e8			1.43620			0.718099	−	0.695941i	$-0.245013\pi$
$743$	5.89089e8			1.43620			0.718099	+	0.695941i	$0.245013\pi$
$744$	−1.47109e7	+	2.54801e7i	−0.0357208	+	0.0618703i
$745$	2.87510e8	−	1.65994e8i	0.695320	−	0.401443i
$746$	−2.63527e8	−	4.56443e8i	−0.634759	−	1.09944i
$747$	−4.04600e8	−	2.33596e8i	−0.970654	−	0.560407i
$748$		−	2.28553e8i		−	0.546111i
$749$		0			0
$750$	4.74969e7			0.112585
$751$	1.83801e8	−	3.18353e8i	0.433939	−	0.751605i	−0.563269	−	0.826274i	$-0.690457\pi$
$751$	1.83801e8	−	3.18353e8i	0.433939	−	0.751605i	0.997208	+	0.0746684i	$0.0237898\pi$
$752$	2.21280e7	−	1.27756e7i	0.0520342	−	0.0300419i
$753$	−5.11023e7	−	8.85118e7i	−0.119689	−	0.207308i
$754$	−2.23296e8	−	1.28920e8i	−0.520914	−	0.300750i
$755$		−	8.90719e8i		−	2.06966i
$756$		0			0
$757$	6.54505e8			1.50878			0.754389	−	0.656427i	$-0.227933\pi$
$757$	6.54505e8			1.50878			0.754389	+	0.656427i	$0.227933\pi$
$758$	7.88490e7	−	1.36570e8i	0.181046	−	0.313581i
$759$	3.39157e7	−	1.95812e7i	0.0775667	−	0.0447832i
$760$	5.80958e7	+	1.00625e8i	0.132344	+	0.229226i
$761$	−5.61555e7	−	3.24214e7i	−0.127420	−	0.0735661i	0.434935	−	0.900462i	$-0.356771\pi$
$761$	−5.61555e7	−	3.24214e7i	−0.127420	−	0.0735661i	−0.562355	+	0.826896i	$0.690105\pi$
$762$			2.92219e7i			0.0660456i
$763$		0			0
$764$	6.37727e7			0.143006
$765$	4.43370e8	−	7.67939e8i	0.990335	−	1.71531i
$766$	1.29246e7	−	7.46202e6i	0.0287561	−	0.0166024i
$767$	2.28554e8	+	3.95867e8i	0.506526	+	0.877329i
$768$	3.48942e6	+	2.01462e6i	0.00770316	+	0.00444742i
$769$			7.56321e8i			1.66313i	0.555425	+	0.831566i	$0.312556\pi$
$769$			7.56321e8i			1.66313i	−0.555425	+	0.831566i	$0.687444\pi$
$770$		0			0
$771$	−2.89987e7			−0.0632725
$772$	−1.98421e8	+	3.43675e8i	−0.431256	+	0.746958i
$773$	−2.10354e8	+	1.21448e8i	−0.455421	+	0.262937i	−0.710117	−	0.704084i	$-0.751358\pi$
$773$	−2.10354e8	+	1.21448e8i	−0.455421	+	0.262937i	0.254696	+	0.967021i	$0.418025\pi$
$774$	1.85869e8	+	3.21934e8i	0.400852	+	0.694296i
$775$	−9.63298e8	−	5.56160e8i	−2.06945	−	1.19480i
$776$			3.07542e7i			0.0658141i
$777$		0			0
$778$	−1.76827e8			−0.375500
$779$	−1.46591e8	+	2.53903e8i	−0.310095	+	0.537100i
$780$	−3.05168e7	+	1.76189e7i	−0.0643066	+	0.0371274i
$781$	−2.60209e8	−	4.50696e8i	−0.546222	−	0.946085i
$782$	2.57031e8	+	1.48397e8i	0.537484	+	0.310317i
$783$		−	1.80600e8i		−	0.376212i
$784$		0			0
$785$	9.50219e8			1.96433
$786$	−3.98309e7	+	6.89892e7i	−0.0820262	+	0.142074i
$787$	−4.05449e8	+	2.34086e8i	−0.831787	+	0.480232i	−0.854464	−	0.519510i	$-0.826114\pi$
$787$	−4.05449e8	+	2.34086e8i	−0.831787	+	0.480232i	0.0226772	+	0.999743i	$0.492781\pi$
$788$	8.21358e7	+	1.42263e8i	0.167863	+	0.290746i
$789$	−4.38214e7	−	2.53003e7i	−0.0892186	−	0.0515104i
$790$		−	6.89162e8i		−	1.39778i
$791$		0			0
$792$	1.52289e8			0.306544
$793$	5.92045e7	−	1.02545e8i	0.118723	−	0.205634i
$794$	−1.63500e8	+	9.43969e7i	−0.326631	+	0.188580i
$795$	−43123.4	−	74692.0i	−8.58246e−5	−	0.000148653i
$796$	1.70474e7	+	9.84233e6i	0.0338002	+	0.0195146i
$797$		−	1.00075e8i		−	0.197674i	−0.995104	−	0.0988370i	$-0.968488\pi$
$797$		−	1.00075e8i		−	0.197674i	0.995104	−	0.0988370i	$-0.0315122\pi$
$798$		0			0
$799$	−1.51302e8			−0.296623
$800$	−7.61643e7	+	1.31921e8i	−0.148758	+	0.257657i
$801$	−1.84523e8	+	1.06534e8i	−0.359048	+	0.207296i
$802$	−1.15060e7	−	1.99289e7i	−0.0223049	−	0.0386332i
$803$	4.73520e8	+	2.73387e8i	0.914517	+	0.527997i
$804$			1.36491e7i			0.0262624i
$805$		0			0
$806$	3.34899e8			0.639600
$807$	3.51332e7	−	6.08525e7i	0.0668493	−	0.115786i
$808$	1.75294e8	−	1.01206e8i	0.332303	−	0.191855i
$809$	2.93609e8	+	5.08545e8i	0.554528	+	0.960470i	0.997940	+	0.0641523i	$0.0204343\pi$
$809$	2.93609e8	+	5.08545e8i	0.554528	+	0.960470i	−0.443413	+	0.896318i	$0.646232\pi$
$810$	5.00895e8	+	2.89192e8i	0.942522	+	0.544166i
$811$			8.86023e8i			1.66105i	0.556983	+	0.830524i	$0.311959\pi$
$811$			8.86023e8i			1.66105i	−0.556983	+	0.830524i	$0.688041\pi$
$812$		0			0
$813$	1.06866e8			0.198869
$814$	−1.25196e8	+	2.16845e8i	−0.232122	+	0.402047i
$815$	−9.33750e8	+	5.39101e8i	−1.72487	+	0.995857i
$816$	−1.19296e7	−	2.06627e7i	−0.0219561	−	0.0380291i
$817$	2.49793e8	+	1.44218e8i	0.458051	+	0.264456i
$818$		−	2.14396e8i		−	0.391703i
$819$		0			0
$820$	−6.12745e8			−1.11132
$821$	2.75533e8	−	4.77237e8i	0.497902	−	0.862391i	−0.502095	−	0.864812i	$-0.667437\pi$
$821$	2.75533e8	−	4.77237e8i	0.497902	−	0.862391i	0.999997	+	0.00242121i	$0.000770695\pi$
$822$	−6.26880e7	+	3.61929e7i	−0.112867	+	0.0651641i
$823$	−2.66987e8	−	4.62435e8i	−0.478951	−	0.829567i	0.520758	−	0.853704i	$-0.325649\pi$
$823$	−2.66987e8	−	4.62435e8i	−0.478951	−	0.829567i	−0.999709	+	0.0241376i	$0.992316\pi$
$824$	1.88785e8	+	1.08995e8i	0.337432	+	0.194817i
$825$		−	1.19023e8i		−	0.211967i
$826$		0			0
$827$	−5.33590e8			−0.943390			−0.471695	−	0.881762i	$-0.656358\pi$
$827$	−5.33590e8			−0.943390			−0.471695	+	0.881762i	$0.656358\pi$
$828$	−9.88797e7	+	1.71265e8i	−0.174187	+	0.301701i
$829$	9.66350e8	−	5.57922e8i	1.69618	−	0.979287i	0.746849	−	0.664993i	$-0.231566\pi$
$829$	9.66350e8	−	5.57922e8i	1.69618	−	0.979287i	0.949326	−	0.314294i	$-0.101768\pi$
$830$	−3.78809e8	−	6.56117e8i	−0.662501	−	1.14749i
$831$	−1.74847e7	−	1.00948e7i	−0.0304688	−	0.0175912i
$832$		−	4.58633e7i		−	0.0796334i
$833$		0			0
$834$	−2.58588e7			−0.0445769
$835$	−2.04266e8	+	3.53799e8i	−0.350862	+	0.607711i
$836$	1.02332e8	−	5.90814e7i	0.175143	−	0.101119i
$837$	1.17288e8	+	2.03148e8i	0.200021	+	0.346447i
$838$	−3.59710e8	−	2.07679e8i	−0.611252	−	0.352907i
$839$		−	2.23881e8i		−	0.379081i	−0.981873	−	0.189540i	$-0.939300\pi$
$839$		−	2.23881e8i		−	0.379081i	0.981873	−	0.189540i	$-0.0606998\pi$
$840$		0			0
$841$	4.65694e8			0.782912
$842$	1.68038e7	−	2.91050e7i	0.0281495	−	0.0487563i
$843$	1.03891e8	−	5.99817e7i	0.173419	−	0.100123i
$844$	−4.10049e7	−	7.10226e7i	−0.0682038	−	0.118132i
$845$	−5.08516e8	−	2.93592e8i	−0.842819	−	0.486602i
$846$		−	1.00816e8i		−	0.166501i
$847$		0			0
$848$	112254.			0.000184082
$849$	3.48618e7	−	6.03825e7i	0.0569675	−	0.0986706i
$850$	7.81172e8	−	4.51010e8i	1.27201	−	0.734394i
$851$	−1.62577e8	−	2.81591e8i	−0.263797	−	0.456910i
$852$	−4.70493e7	−	2.71639e7i	−0.0760737	−	0.0439212i
$853$			2.97785e8i			0.479795i	0.970798	+	0.239898i	$0.0771139\pi$
$853$			2.97785e8i			0.479795i	−0.970798	+	0.239898i	$0.922886\pi$
$854$		0			0
$855$	4.58449e8			0.733487
$856$	−1.10457e7	+	1.91318e7i	−0.0176106	+	0.0305024i
$857$	6.81495e8	−	3.93461e8i	1.08273	−	0.625115i	0.151099	−	0.988519i	$-0.451719\pi$
$857$	6.81495e8	−	3.93461e8i	1.08273	−	0.625115i	0.931632	+	0.363404i	$0.118386\pi$
$858$	1.79178e7	+	3.10345e7i	0.0283676	+	0.0491341i
$859$	6.63597e8	+	3.83128e8i	1.04695	+	0.604456i	0.921793	−	0.387681i	$-0.126724\pi$
$859$	6.63597e8	+	3.83128e8i	1.04695	+	0.604456i	0.125155	+	0.992137i	$0.460057\pi$
$860$			6.02826e8i			0.947757i
$861$		0			0
$862$	−5.42385e8			−0.846811
$863$	5.83252e8	−	1.01022e9i	0.907452	−	1.57175i	0.0898596	−	0.995954i	$-0.471358\pi$
$863$	5.83252e8	−	1.01022e9i	0.907452	−	1.57175i	0.817592	−	0.575798i	$-0.195308\pi$
$864$	2.78205e7	−	1.60622e7i	0.0431344	−	0.0249036i
$865$	−2.02030e8	−	3.49927e8i	−0.312154	−	0.540666i
$866$	−6.04201e8	−	3.48836e8i	−0.930310	−	0.537115i
$867$			4.85329e7i			0.0744695i
$868$		0			0
$869$	−7.00853e8			−1.06799
$870$	7.24682e7	−	1.25519e8i	0.110050	−	0.190612i
$871$	1.34548e8	−	7.76813e7i	0.203621	−	0.117561i
$872$	1.00114e8	+	1.73403e8i	0.150990	+	0.261522i
$873$	1.05087e8	+	6.06722e7i	0.157946	+	0.0911900i
$874$			1.53444e8i			0.229835i
$875$		0			0
$876$	5.70792e7			0.0849113
$877$	−3.78221e8	+	6.55098e8i	−0.560721	+	0.971198i	0.436712	+	0.899601i	$0.356143\pi$
$877$	−3.78221e8	+	6.55098e8i	−0.560721	+	0.971198i	−0.997434	+	0.0715966i	$0.977191\pi$
$878$	−3.14354e8	+	1.81492e8i	−0.464446	+	0.268148i
$879$	1.12087e7	+	1.94140e7i	0.0165039	+	0.0285856i
$880$	2.13872e8	+	1.23479e8i	0.313838	+	0.181194i
$881$			3.69412e8i			0.540235i	0.962827	+	0.270118i	$0.0870626\pi$
$881$			3.69412e8i			0.540235i	−0.962827	+	0.270118i	$0.912937\pi$
$882$		0			0
$883$	−5.87419e8			−0.853230			−0.426615	−	0.904433i	$-0.640294\pi$
$883$	−5.87419e8			−0.853230			−0.426615	+	0.904433i	$0.640294\pi$
$884$	−1.35791e8	+	2.35196e8i	−0.196568	+	0.340466i
$885$	−2.22524e8	+	1.28474e8i	−0.321031	+	0.185347i
$886$	−1.86316e8	−	3.22708e8i	−0.267885	−	0.463991i
$887$	1.86648e7	+	1.07761e7i	0.0267456	+	0.0154416i	0.513313	−	0.858201i	$-0.328418\pi$
$887$	1.86648e7	+	1.07761e7i	0.0267456	+	0.0154416i	−0.486568	+	0.873643i	$0.661751\pi$
$888$			2.61390e7i			0.0373294i
$889$		0			0
$890$	−3.45521e8			−0.490122
$891$	2.94098e8	−	5.09392e8i	0.415775	−	0.720144i
$892$	−2.16819e8	+	1.25180e8i	−0.305493	+	0.176377i
$893$	−3.91120e7	−	6.77440e7i	−0.0549232	−	0.0951298i
$894$	−3.05232e7	−	1.76226e7i	−0.0427186	−	0.0246636i
$895$		−	1.34996e9i		−	1.88300i
$896$		0			0
$897$	−4.65354e7			−0.0644772
$898$	−2.89082e8	+	5.00704e8i	−0.399201	+	0.691436i
$899$	−1.19292e9	+	6.88735e8i	−1.64185	+	0.947923i
$900$	3.00516e8	+	5.20509e8i	0.412231	+	0.714004i
$901$	−575659.	−	332357.i	−0.000787029	−	0.000454391i
$902$			6.23140e8i			0.849113i
$903$		0			0
$904$	−4.82849e7			−0.0653591
$905$	−2.67164e8	+	4.62742e8i	−0.360439	+	0.624299i
$906$	−8.18931e7	+	4.72810e7i	−0.110119	+	0.0635773i
$907$	5.70573e8	+	9.88262e8i	0.764697	+	1.32449i	0.940406	+	0.340052i	$0.110445\pi$
$907$	5.70573e8	+	9.88262e8i	0.764697	+	1.32449i	−0.175709	+	0.984442i	$0.556222\pi$
$908$	2.26991e8	+	1.31054e8i	0.303216	+	0.175062i
$909$		−	7.98644e8i		−	1.06331i
$910$		0			0
$911$	−3.29876e8			−0.436310			−0.218155	−	0.975914i	$-0.570004\pi$
$911$	−3.29876e8			−0.436310			−0.218155	+	0.975914i	$0.570004\pi$
$912$	6.16766e6	−	1.06827e7i	0.00813085	−	0.0140831i
$913$	−6.67248e8	+	3.85236e8i	−0.876748	+	0.506191i
$914$	−1.59066e8	−	2.75510e8i	−0.208323	−	0.360826i
$915$	5.76425e7	+	3.32799e7i	0.0752454	+	0.0434429i
$916$		−	4.17682e8i		−	0.543449i
$917$		0			0
$918$	−1.90225e8			−0.245890
$919$	5.51180e7	−	9.54671e7i	0.0710144	−	0.123001i	−0.828332	−	0.560238i	$-0.810710\pi$
$919$	5.51180e7	−	9.54671e7i	0.0710144	−	0.123001i	0.899346	+	0.437237i	$0.144043\pi$
$920$	−2.77730e8	+	1.60348e8i	−0.356664	+	0.205920i
$921$	−4.35884e7	−	7.54974e7i	−0.0557946	−	0.0966392i
$922$	−1.20809e8	−	6.97491e7i	−0.154137	−	0.0889910i
$923$			6.18395e8i			0.786432i
$924$		0			0
$925$	−9.88210e8			−1.24860
$926$	5.42941e8	−	9.40401e8i	0.683785	−	1.18435i
$927$	7.44877e8	−	4.30055e8i	0.935072	−	0.539864i
$928$	9.43200e7	+	1.63367e8i	0.118021	+	0.204419i
$929$	−3.97224e8	−	2.29337e8i	−0.495436	−	0.286040i	0.231391	−	0.972861i	$-0.425672\pi$
$929$	−3.97224e8	−	2.29337e8i	−0.495436	−	0.286040i	−0.726827	+	0.686821i	$0.759006\pi$
$930$			1.88253e8i			0.234041i
$931$		0			0
$932$	4.43197e7			0.0547456
$933$	−7.61483e7	+	1.31893e8i	−0.0937595	+	0.162396i
$934$	−7.39377e8	+	4.26879e8i	−0.907455	+	0.523919i
$935$	−7.31185e8	−	1.26645e9i	−0.894525	−	1.54936i
$936$	−1.56715e8	−	9.04797e7i	−0.191110	−	0.110338i
$937$		−	9.98325e8i		−	1.21354i	−0.794878	−	0.606769i	$-0.792465\pi$
$937$		−	9.98325e8i		−	1.21354i	0.794878	−	0.606769i	$-0.207535\pi$
$938$		0			0
$939$	−3.87548e7			−0.0468089
$940$	8.17434e7	−	1.41584e8i	0.0984168	−	0.170463i
$941$	9.37585e8	−	5.41315e8i	1.12523	−	0.649652i	0.182500	−	0.983206i	$-0.441581\pi$
$941$	9.37585e8	−	5.41315e8i	1.12523	−	0.649652i	0.942731	+	0.333554i	$0.108248\pi$
$942$	−5.04394e7	−	8.73635e7i	−0.0603416	−	0.104515i
$943$	−7.00786e8	−	4.04599e8i	−0.835700	−	0.482491i
$944$		−	3.34428e8i		−	0.397545i
$945$		0			0
$946$	6.13053e8			0.724143
$947$	−3.98771e8	+	6.90692e8i	−0.469541	+	0.813269i	−0.999394	−	0.0348207i	$-0.988914\pi$
$947$	−3.98771e8	+	6.90692e8i	−0.469541	+	0.813269i	0.529852	+	0.848090i	$0.322247\pi$
$948$	−6.33619e7	+	3.65820e7i	−0.0743709	+	0.0429381i
$949$	−3.24856e8	−	5.62668e8i	−0.380095	−	0.658345i
$950$	4.03869e8	+	2.33174e8i	0.471053	+	0.271963i
$951$		−	1.14652e8i		−	0.133303i
$952$		0			0
$953$	−1.15116e9			−1.33002			−0.665009	−	0.746836i	$-0.731572\pi$
$953$	−1.15116e9			−1.33002			−0.665009	+	0.746836i	$0.731572\pi$
$954$	221455.	−	383572.i	0.000255059	−	0.000441775i
$955$	3.53376e8	−	2.04022e8i	0.405720	−	0.234243i
$956$	−7.00101e7	−	1.21261e8i	−0.0801285	−	0.138787i
$957$	−1.27648e8	−	7.36975e7i	−0.145639	−	0.0840847i
$958$			2.66107e8i			0.302663i
$959$		0			0
$960$	2.57806e7			0.0291393
$961$	4.50823e8	−	7.80848e8i	0.507967	−	0.879825i
$962$	2.57670e8	−	1.48766e8i	0.289426	−	0.167100i
$963$	4.35823e7	+	7.54868e7i	0.0488013	+	0.0845264i
$964$	−2.41068e8	−	1.39180e8i	−0.269096	−	0.155363i
$965$			2.53915e9i			2.82557i
$966$		0			0
$967$	−6.50101e8			−0.718954			−0.359477	−	0.933154i	$-0.617045\pi$
$967$	−6.50101e8			−0.718954			−0.359477	+	0.933154i	$0.617045\pi$
$968$	−3.47697e7	+	6.02229e7i	−0.0383332	+	0.0663950i
$969$	−6.32580e7	+	3.65220e7i	−0.0695255	+	0.0401406i
$970$	9.83887e7	+	1.70414e8i	0.107803	+	0.186720i
$971$	3.58613e8	+	2.07045e8i	0.391714	+	0.226156i	0.682902	−	0.730510i	$-0.260717\pi$
$971$	3.58613e8	+	2.07045e8i	0.391714	+	0.226156i	−0.291189	+	0.956666i	$0.594051\pi$
$972$		−	1.90774e8i		−	0.207740i
$973$		0			0
$974$	2.46647e8			0.266931
$975$	−7.07155e7	+	1.22483e8i	−0.0762958	+	0.132148i
$976$	−7.50239e7	+	4.33151e7i	−0.0806957	+	0.0465897i
$977$	6.21992e8	+	1.07732e9i	0.666962	+	1.15521i	0.978749	+	0.205061i	$0.0657391\pi$
$977$	6.21992e8	+	1.07732e9i	0.666962	+	1.15521i	−0.311787	+	0.950152i	$0.600928\pi$
$978$	9.91303e7	+	5.72329e7i	0.105972	+	0.0611828i
$979$			3.51383e8i			0.374483i
$980$		0			0
$981$	7.90029e8			0.836827
$982$	2.20131e8	−	3.81278e8i	0.232459	−	0.402631i
$983$	1.42952e9	−	8.25336e8i	1.50498	−	0.868901i	0.504997	−	0.863121i	$-0.331493\pi$
$983$	1.42952e9	−	8.25336e8i	1.50498	−	0.868901i	0.999983	−	0.00578009i	$-0.00183987\pi$
$984$	3.25256e7	+	5.63360e7i	0.0341382	+	0.0591291i
$985$	9.10258e8	+	5.25537e8i	0.952479	+	0.549914i
$986$		−	1.11704e9i		−	1.16530i
$987$		0			0
$988$	−1.40409e8			−0.145587
$989$	−3.98050e8	+	6.89442e8i	−0.411480	+	0.712703i
$990$	8.43858e8	−	4.87202e8i	0.869689	−	0.502115i
$991$	−9.28671e8	−	1.60851e9i	−0.954203	−	1.65273i	−0.736181	−	0.676785i	$-0.763373\pi$
$991$	−9.28671e8	−	1.60851e9i	−0.954203	−	1.65273i	−0.218023	−	0.975944i	$-0.569961\pi$
$992$	−2.12192e8	−	1.22509e8i	−0.217367	−	0.125497i
$993$		−	6.87882e6i		−	0.00702532i
$994$		0			0
$995$	1.25950e8			0.127859
$996$	−4.02158e7	+	6.96558e7i	−0.0407023	+	0.0704984i
$997$	−1.21780e9	+	7.03100e8i	−1.22883	+	0.709466i	−0.966785	−	0.255589i	$-0.917730\pi$
$997$	−1.21780e9	+	7.03100e8i	−1.22883	+	0.709466i	−0.262046	+	0.965055i	$0.584397\pi$
$998$	−1.79249e8	−	3.10469e8i	−0.180329	−	0.312339i
$999$	1.80481e8	+	1.04201e8i	0.181024	+	0.104514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.7.d.b.19.3		8
7.2	even	3		14.7.b.a.13.1	✓	4
7.3	odd	6	inner	98.7.d.b.31.3		8
7.4	even	3	inner	98.7.d.b.31.4		8
7.5	odd	6		14.7.b.a.13.2	yes	4
7.6	odd	2	inner	98.7.d.b.19.4		8
21.2	odd	6		126.7.c.a.55.3		4
21.5	even	6		126.7.c.a.55.4		4
28.19	even	6		112.7.c.c.97.2		4
28.23	odd	6		112.7.c.c.97.3		4
35.2	odd	12		350.7.d.a.349.2		8
35.9	even	6		350.7.b.a.251.4		4
35.12	even	12		350.7.d.a.349.3		8
35.19	odd	6		350.7.b.a.251.3		4
35.23	odd	12		350.7.d.a.349.7		8
35.33	even	12		350.7.d.a.349.6		8
56.5	odd	6		448.7.c.h.321.2		4
56.19	even	6		448.7.c.e.321.3		4
56.37	even	6		448.7.c.h.321.3		4
56.51	odd	6		448.7.c.e.321.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.7.b.a.13.1	✓	4	7.2	even	3
14.7.b.a.13.2	yes	4	7.5	odd	6
98.7.d.b.19.3		8	1.1	even	1	trivial
98.7.d.b.19.4		8	7.6	odd	2	inner
98.7.d.b.31.3		8	7.3	odd	6	inner
98.7.d.b.31.4		8	7.4	even	3	inner
112.7.c.c.97.2		4	28.19	even	6
112.7.c.c.97.3		4	28.23	odd	6
126.7.c.a.55.3		4	21.2	odd	6
126.7.c.a.55.4		4	21.5	even	6
350.7.b.a.251.3		4	35.19	odd	6
350.7.b.a.251.4		4	35.9	even	6
350.7.d.a.349.2		8	35.2	odd	12
350.7.d.a.349.3		8	35.12	even	12
350.7.d.a.349.6		8	35.33	even	12
350.7.d.a.349.7		8	35.23	odd	12
448.7.c.e.321.2		4	56.51	odd	6
448.7.c.e.321.3		4	56.19	even	6
448.7.c.h.321.2		4	56.5	odd	6
448.7.c.h.321.3		4	56.37	even	6

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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	98.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.82843 - 4.89898i) q^{2} +(-3.32777 + 1.92129i) q^{3} +(-16.0000 - 27.7128i) q^{4} +(-177.318 - 102.374i) q^{5} +21.7369i q^{6} -181.019 q^{8} +(-357.117 + 618.545i) q^{9} +(-1003.06 + 579.117i) q^{10} +(588.941 + 1020.08i) q^{11} +(106.489 + 61.4812i) q^{12} -1399.64i q^{13} +786.762 q^{15} +(-512.000 + 886.810i) q^{16} +(5251.28 - 3031.83i) q^{17} +(2020.16 + 3499.02i) q^{18} +(2714.93 + 1567.47i) q^{19} +6551.96i q^{20} +6663.11 q^{22} +(-4326.30 + 7493.36i) q^{23} +(602.390 - 347.790i) q^{24} +(13148.5 + 22773.9i) q^{25} +(-6856.79 - 3958.77i) q^{26} -5545.73i q^{27} +32565.6 q^{29} +(2225.30 - 3854.33i) q^{30} +(-36631.4 + 21149.2i) q^{31} +(2896.31 + 5016.55i) q^{32} +(-3919.72 - 2263.05i) q^{33} -34301.2i q^{34} +22855.5 q^{36} +(-18789.4 + 32544.2i) q^{37} +(15358.0 - 8866.94i) q^{38} +(2689.10 + 4657.66i) q^{39} +(32097.9 + 18531.7i) q^{40} +93520.9i q^{41} +92007.0 q^{43} +(18846.1 - 32642.4i) q^{44} +(126646. - 73119.3i) q^{45} +(24473.2 + 42388.9i) q^{46} +(-21609.4 - 12476.2i) q^{47} -3934.79i q^{48} +148758. q^{50} +(-11650.0 + 20178.4i) q^{51} +(-38787.9 + 22394.2i) q^{52} +(-54.8113 - 94.9359i) q^{53} +(-27168.4 - 15685.7i) q^{54} -241170. i q^{55} -12046.2 q^{57} +(92109.4 - 159538. i) q^{58} +(-282835. + 163295. i) q^{59} +(-12588.2 - 21803.4i) q^{60} +(73265.5 + 42299.9i) q^{61} +239276. i q^{62} +32768.0 q^{64} +(-143287. + 248180. i) q^{65} +(-22173.3 + 12801.7i) q^{66} +(55501.0 + 96130.5i) q^{67} +(-168041. - 97018.4i) q^{68} -33248.2i q^{69} -441825. q^{71} +(64645.1 - 111969. i) q^{72} +(402010. - 232100. i) q^{73} +(106289. + 184098. i) q^{74} +(-87510.4 - 50524.1i) q^{75} -100318. i q^{76} +30423.7 q^{78} +(-297506. + 515295. i) q^{79} +(181573. - 104831. i) q^{80} +(-249684. - 432465. i) q^{81} +(458157. + 264517. i) q^{82} +654116. i q^{83} -1.24152e6 q^{85} +(260235. - 450741. i) q^{86} +(-108371. + 62567.8i) q^{87} +(-106610. - 184653. i) q^{88} +(258350. + 149159. i) q^{89} -827251. i q^{90} +276883. q^{92} +(81267.2 - 140759. i) q^{93} +(-122241. + 70575.9i) q^{94} +(-320937. - 555879. i) q^{95} +(-19276.5 - 11129.3i) q^{96} -169894. i q^{97} -841284. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 128 q^{4} - 1092 q^{9} + 4440 q^{11} - 8640 q^{15} - 4096 q^{16} + 9984 q^{18} + 3072 q^{22} - 40584 q^{23} + 40700 q^{25} - 36528 q^{29} + 42240 q^{30} + 69888 q^{36} + 23192 q^{37} - 208608 q^{39}+ \cdots - 2663856 q^{99}+O(q^{100}) \) 8 * q - 128 * q^4 - 1092 * q^9 + 4440 * q^11 - 8640 * q^15 - 4096 * q^16 + 9984 * q^18 + 3072 * q^22 - 40584 * q^23 + 40700 * q^25 - 36528 * q^29 + 42240 * q^30 + 69888 * q^36 + 23192 * q^37 - 208608 * q^39 - 89392 * q^43 + 142080 * q^44 - 33792 * q^46 + 729600 * q^50 - 157824 * q^51 - 248616 * q^53 - 945984 * q^57 + 840192 * q^58 + 138240 * q^60 + 262144 * q^64 - 1293600 * q^65 + 434776 * q^67 - 903216 * q^71 + 319488 * q^72 + 981504 * q^74 + 2603520 * q^78 - 2092904 * q^79 + 252828 * q^81 - 4235520 * q^85 + 2334720 * q^86 - 49152 * q^88 + 2597376 * q^92 - 995328 * q^93 + 190560 * q^95 - 2663856 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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