LMFDB - Embedded newform 136.4.k.b.81.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(81,136)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("136.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	136.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 119x^{12} + 5319x^{10} + 112122x^{8} + 1120191x^{6} + 4382607x^{4} + 1699337x^{2} + 2704 $ x^14 + 119x^12 + 5319x^10 + 112122x^8 + 1120191x^6 + 4382607x^4 + 1699337x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.7
Root			$-6.66182i$ of defining polynomial
Character	$\chi$	$=$	136.81
Dual form			136.4.k.b.89.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.66182 + 6.66182i) q^{3} +(3.32200 + 3.32200i) q^{5} +(-12.8505 + 12.8505i) q^{7} +61.7597i q^{9} +O(q^{10})$	\(q+(6.66182 + 6.66182i) q^{3} +(3.32200 + 3.32200i) q^{5} +(-12.8505 + 12.8505i) q^{7} +61.7597i q^{9} +(30.6918 - 30.6918i) q^{11} -42.1996 q^{13} +44.2612i q^{15} +(52.4291 + 46.5208i) q^{17} -112.030i q^{19} -171.216 q^{21} +(-49.9045 + 49.9045i) q^{23} -102.929i q^{25} +(-231.563 + 231.563i) q^{27} +(134.772 + 134.772i) q^{29} +(75.2466 + 75.2466i) q^{31} +408.927 q^{33} -85.3788 q^{35} +(246.574 + 246.574i) q^{37} +(-281.126 - 281.126i) q^{39} +(170.879 - 170.879i) q^{41} -112.595i q^{43} +(-205.166 + 205.166i) q^{45} -188.446 q^{47} +12.7288i q^{49} +(39.3601 + 659.187i) q^{51} -642.572i q^{53} +203.916 q^{55} +(746.326 - 746.326i) q^{57} -431.347i q^{59} +(-41.0366 + 41.0366i) q^{61} +(-793.644 - 793.644i) q^{63} +(-140.187 - 140.187i) q^{65} +173.324 q^{67} -664.910 q^{69} +(-232.895 - 232.895i) q^{71} +(-197.129 - 197.129i) q^{73} +(685.692 - 685.692i) q^{75} +788.811i q^{77} +(936.244 - 936.244i) q^{79} -1417.75 q^{81} -168.817i q^{83} +(19.6274 + 328.712i) q^{85} +1795.65i q^{87} +1105.14 q^{89} +(542.286 - 542.286i) q^{91} +1002.56i q^{93} +(372.165 - 372.165i) q^{95} +(1200.37 + 1200.37i) q^{97} +(1895.52 + 1895.52i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7}+O(q^{10}) $ 14 * q + 6 * q^3 + 6 * q^5 + 10 * q^7	$ 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7} - 66 q^{11} - 124 q^{13} + 130 q^{17} - 148 q^{21} - 162 q^{23} - 204 q^{27} + 158 q^{29} - 350 q^{31} + 116 q^{33} + 236 q^{35} + 582 q^{37} - 320 q^{39} + 878 q^{41} - 26 q^{45} - 448 q^{47} - 590 q^{51} + 1460 q^{55} + 292 q^{57} - 1130 q^{61} + 114 q^{63} + 20 q^{65} - 64 q^{67} + 2076 q^{69} - 3274 q^{71} - 1426 q^{73} + 946 q^{75} + 1718 q^{79} + 166 q^{81} - 2018 q^{85} + 476 q^{89} + 2128 q^{91} - 2444 q^{95} + 1926 q^{97} + 3870 q^{99}+O(q^{100}) $ 14 * q + 6 * q^3 + 6 * q^5 + 10 * q^7 - 66 * q^11 - 124 * q^13 + 130 * q^17 - 148 * q^21 - 162 * q^23 - 204 * q^27 + 158 * q^29 - 350 * q^31 + 116 * q^33 + 236 * q^35 + 582 * q^37 - 320 * q^39 + 878 * q^41 - 26 * q^45 - 448 * q^47 - 590 * q^51 + 1460 * q^55 + 292 * q^57 - 1130 * q^61 + 114 * q^63 + 20 * q^65 - 64 * q^67 + 2076 * q^69 - 3274 * q^71 - 1426 * q^73 + 946 * q^75 + 1718 * q^79 + 166 * q^81 - 2018 * q^85 + 476 * q^89 + 2128 * q^91 - 2444 * q^95 + 1926 * q^97 + 3870 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	6.66182	+	6.66182i	1.28207	+	1.28207i	0.939489	+	0.342579i	$0.111301\pi$
$3$	6.66182	+	6.66182i	1.28207	+	1.28207i	0.342579	+	0.939489i	$0.388699\pi$
$4$		0			0
$5$	3.32200	+	3.32200i	0.297129	+	0.297129i	0.839888	−	0.542759i	$-0.182620\pi$
$5$	3.32200	+	3.32200i	0.297129	+	0.297129i	−0.542759	+	0.839888i	$0.682620\pi$
$6$		0			0
$7$	−12.8505	+	12.8505i	−0.693862	+	0.693862i	−0.963079	−	0.269217i	$-0.913235\pi$
$7$	−12.8505	+	12.8505i	−0.693862	+	0.693862i	0.269217	+	0.963079i	$0.413235\pi$
$8$		0			0
$9$			61.7597i			2.28740i
$10$		0			0
$11$	30.6918	−	30.6918i	0.841266	−	0.841266i	−0.147757	−	0.989024i	$-0.547205\pi$
$11$	30.6918	−	30.6918i	0.841266	−	0.841266i	0.989024	+	0.147757i	$0.0472055\pi$
$12$		0			0
$13$	−42.1996			−0.900312			−0.450156	−	0.892950i	$-0.648632\pi$
$13$	−42.1996			−0.900312			−0.450156	+	0.892950i	$0.648632\pi$
$14$		0			0
$15$			44.2612i			0.761879i
$16$		0			0
$17$	52.4291	+	46.5208i	0.747996	+	0.663703i
$17$	52.4291	+	46.5208i	0.747996	+	0.663703i
$18$		0			0
$19$		−	112.030i		−	1.35271i	−0.736575	−	0.676355i	$-0.763558\pi$
$19$		−	112.030i		−	1.35271i	0.736575	−	0.676355i	$-0.236442\pi$
$20$		0			0
$21$	−171.216			−1.77916
$22$		0			0
$23$	−49.9045	+	49.9045i	−0.452427	+	0.452427i	−0.896159	−	0.443733i	$-0.853654\pi$
$23$	−49.9045	+	49.9045i	−0.452427	+	0.452427i	0.443733	+	0.896159i	$0.353654\pi$
$24$		0			0
$25$		−	102.929i		−	0.823429i
$26$		0			0
$27$	−231.563	+	231.563i	−1.65053	+	1.65053i
$28$		0			0
$29$	134.772	+	134.772i	0.862982	+	0.862982i	0.991683	−	0.128701i	$-0.0410807\pi$
$29$	134.772	+	134.772i	0.862982	+	0.862982i	−0.128701	+	0.991683i	$0.541081\pi$
$30$		0			0
$31$	75.2466	+	75.2466i	0.435958	+	0.435958i	0.890649	−	0.454691i	$-0.150250\pi$
$31$	75.2466	+	75.2466i	0.435958	+	0.435958i	−0.454691	+	0.890649i	$0.650250\pi$
$32$		0			0
$33$	408.927			2.15712
$34$		0			0
$35$	−85.3788			−0.412333
$36$		0			0
$37$	246.574	+	246.574i	1.09558	+	1.09558i	0.994921	+	0.100658i	$0.0320949\pi$
$37$	246.574	+	246.574i	1.09558	+	1.09558i	0.100658	+	0.994921i	$0.467905\pi$
$38$		0			0
$39$	−281.126	−	281.126i	−1.15426	−	1.15426i
$40$		0			0
$41$	170.879	−	170.879i	0.650899	−	0.650899i	−0.302311	−	0.953209i	$-0.597758\pi$
$41$	170.879	−	170.879i	0.650899	−	0.650899i	0.953209	+	0.302311i	$0.0977580\pi$
$42$		0			0
$43$		−	112.595i		−	0.399317i	−0.979866	−	0.199658i	$-0.936017\pi$
$43$		−	112.595i		−	0.399317i	0.979866	−	0.199658i	$-0.0639833\pi$
$44$		0			0
$45$	−205.166	+	205.166i	−0.679652	+	0.679652i
$46$		0			0
$47$	−188.446			−0.584845			−0.292423	−	0.956289i	$-0.594461\pi$
$47$	−188.446			−0.584845			−0.292423	+	0.956289i	$0.594461\pi$
$48$		0			0
$49$			12.7288i			0.0371102i
$50$		0			0
$51$	39.3601	+	659.187i	0.108069	+	1.80989i
$52$		0			0
$53$		−	642.572i		−	1.66536i	−0.553754	−	0.832680i	$-0.686805\pi$
$53$		−	642.572i		−	1.66536i	0.553754	−	0.832680i	$-0.313195\pi$
$54$		0			0
$55$	203.916			0.499929
$56$		0			0
$57$	746.326	−	746.326i	1.73427	−	1.73427i
$58$		0			0
$59$		−	431.347i		−	0.951806i	−0.879498	−	0.475903i	$-0.842121\pi$
$59$		−	431.347i		−	0.951806i	0.879498	−	0.475903i	$-0.157879\pi$
$60$		0			0
$61$	−41.0366	+	41.0366i	−0.0861343	+	0.0861343i	−0.748861	−	0.662727i	$-0.769399\pi$
$61$	−41.0366	+	41.0366i	−0.0861343	+	0.0861343i	0.662727	+	0.748861i	$0.269399\pi$
$62$		0			0
$63$	−793.644	−	793.644i	−1.58714	−	1.58714i
$64$		0			0
$65$	−140.187	−	140.187i	−0.267509	−	0.267509i
$66$		0			0
$67$	173.324			0.316042			0.158021	−	0.987436i	$-0.449489\pi$
$67$	173.324			0.316042			0.158021	+	0.987436i	$0.449489\pi$
$68$		0			0
$69$	−664.910			−1.16008
$70$		0			0
$71$	−232.895	−	232.895i	−0.389290	−	0.389290i	0.485144	−	0.874434i	$-0.338767\pi$
$71$	−232.895	−	232.895i	−0.389290	−	0.389290i	−0.874434	+	0.485144i	$0.838767\pi$
$72$		0			0
$73$	−197.129	−	197.129i	−0.316058	−	0.316058i	0.531193	−	0.847251i	$-0.321744\pi$
$73$	−197.129	−	197.129i	−0.316058	−	0.316058i	−0.847251	+	0.531193i	$0.821744\pi$
$74$		0			0
$75$	685.692	−	685.692i	1.05569	−	1.05569i
$76$		0			0
$77$			788.811i			1.16745i
$78$		0			0
$79$	936.244	−	936.244i	1.33336	−	1.33336i	0.431022	−	0.902342i	$-0.358153\pi$
$79$	936.244	−	936.244i	1.33336	−	1.33336i	0.902342	−	0.431022i	$-0.141847\pi$
$80$		0			0
$81$	−1417.75			−1.94479
$82$		0			0
$83$		−	168.817i		−	0.223253i	−0.993750	−	0.111627i	$-0.964394\pi$
$83$		−	168.817i		−	0.223253i	0.993750	−	0.111627i	$-0.0356061\pi$
$84$		0			0
$85$	19.6274	+	328.712i	0.0250458	+	0.419457i
$86$		0			0
$87$			1795.65i			2.21280i
$88$		0			0
$89$	1105.14			1.31623			0.658113	−	0.752919i	$-0.271355\pi$
$89$	1105.14			1.31623			0.658113	+	0.752919i	$0.271355\pi$
$90$		0			0
$91$	542.286	−	542.286i	0.624693	−	0.624693i
$92$		0			0
$93$			1002.56i			1.11786i
$94$		0			0
$95$	372.165	−	372.165i	0.401929	−	0.401929i
$96$		0			0
$97$	1200.37	+	1200.37i	1.25648	+	1.25648i	0.952760	+	0.303724i	$0.0982300\pi$
$97$	1200.37	+	1200.37i	1.25648	+	1.25648i	0.303724	+	0.952760i	$0.401770\pi$
$98$		0			0
$99$	1895.52	+	1895.52i	1.92431	+	1.92431i
$100$		0			0
$101$	−1580.90			−1.55748			−0.778741	−	0.627346i	$-0.784141\pi$
$101$	−1580.90			−1.55748			−0.778741	+	0.627346i	$0.784141\pi$
$102$		0			0
$103$	−1573.60			−1.50536			−0.752678	−	0.658389i	$-0.771238\pi$
$103$	−1573.60			−1.50536			−0.752678	+	0.658389i	$0.771238\pi$
$104$		0			0
$105$	−568.778	−	568.778i	−0.528639	−	0.528639i
$106$		0			0
$107$	−377.986	−	377.986i	−0.341508	−	0.341508i	0.515426	−	0.856934i	$-0.327634\pi$
$107$	−377.986	−	377.986i	−0.341508	−	0.341508i	−0.856934	+	0.515426i	$0.827634\pi$
$108$		0			0
$109$	525.797	−	525.797i	0.462038	−	0.462038i	−0.437285	−	0.899323i	$-0.644060\pi$
$109$	525.797	−	525.797i	0.462038	−	0.462038i	0.899323	+	0.437285i	$0.144060\pi$
$110$		0			0
$111$			3285.26i			2.80921i
$112$		0			0
$113$	−1632.42	+	1632.42i	−1.35899	+	1.35899i	−0.483820	+	0.875167i	$0.660751\pi$
$113$	−1632.42	+	1632.42i	−1.35899	+	1.35899i	−0.875167	+	0.483820i	$0.839249\pi$
$114$		0			0
$115$	−331.566			−0.268858
$116$		0			0
$117$		−	2606.24i		−	2.05937i
$118$		0			0
$119$	−1271.56	+	75.9247i	−0.979525	+	0.0584875i
$120$		0			0
$121$		−	552.974i		−	0.415458i
$122$		0			0
$123$	2276.73			1.66899
$124$		0			0
$125$	757.179	−	757.179i	0.541793	−	0.541793i
$126$		0			0
$127$		−	435.370i		−	0.304195i	−0.988365	−	0.152098i	$-0.951397\pi$
$127$		−	435.370i		−	0.304195i	0.988365	−	0.152098i	$-0.0486028\pi$
$128$		0			0
$129$	750.090	−	750.090i	0.511952	−	0.511952i
$130$		0			0
$131$	−671.915	−	671.915i	−0.448133	−	0.448133i	0.446600	−	0.894734i	$-0.352635\pi$
$131$	−671.915	−	671.915i	−0.448133	−	0.448133i	−0.894734	+	0.446600i	$0.852635\pi$
$132$		0			0
$133$	1439.65	+	1439.65i	0.938595	+	0.938595i
$134$		0			0
$135$	−1538.51			−0.980841
$136$		0			0
$137$	−2377.80			−1.48284			−0.741419	−	0.671042i	$-0.765847\pi$
$137$	−2377.80			−1.48284			−0.741419	+	0.671042i	$0.765847\pi$
$138$		0			0
$139$	495.076	+	495.076i	0.302099	+	0.302099i	0.841835	−	0.539735i	$-0.181476\pi$
$139$	495.076	+	495.076i	0.302099	+	0.302099i	−0.539735	+	0.841835i	$0.681476\pi$
$140$		0			0
$141$	−1255.40	−	1255.40i	−0.749811	−	0.749811i
$142$		0			0
$143$	−1295.18	+	1295.18i	−0.757402	+	0.757402i
$144$		0			0
$145$			895.424i			0.512834i
$146$		0			0
$147$	−84.7970	+	84.7970i	−0.0475778	+	0.0475778i
$148$		0			0
$149$	1188.43			0.653424			0.326712	−	0.945124i	$-0.394059\pi$
$149$	1188.43			0.653424			0.326712	+	0.945124i	$0.394059\pi$
$150$		0			0
$151$		−	1584.28i		−	0.853818i	−0.904295	−	0.426909i	$-0.859603\pi$
$151$		−	1584.28i		−	0.853818i	0.904295	−	0.426909i	$-0.140397\pi$
$152$		0			0
$153$	−2873.11	+	3238.01i	−1.51815	+	1.71096i
$154$		0			0
$155$			499.939i			0.259071i
$156$		0			0
$157$	96.8200			0.0492171			0.0246085	−	0.999697i	$-0.492166\pi$
$157$	96.8200			0.0492171			0.0246085	+	0.999697i	$0.492166\pi$
$158$		0			0
$159$	4280.70	−	4280.70i	2.13511	−	2.13511i
$160$		0			0
$161$		−	1282.60i		−	0.627844i
$162$		0			0
$163$	−2761.84	+	2761.84i	−1.32714	+	1.32714i	−0.419288	+	0.907853i	$0.637720\pi$
$163$	−2761.84	+	2761.84i	−1.32714	+	1.32714i	−0.907853	+	0.419288i	$0.862280\pi$
$164$		0			0
$165$	1358.45	+	1358.45i	0.640943	+	0.640943i
$166$		0			0
$167$	−1767.91	−	1767.91i	−0.819189	−	0.819189i	0.166801	−	0.985991i	$-0.446656\pi$
$167$	−1767.91	−	1767.91i	−0.819189	−	0.819189i	−0.985991	+	0.166801i	$0.946656\pi$
$168$		0			0
$169$	−416.194			−0.189438
$170$		0			0
$171$	6918.96			3.09419
$172$		0			0
$173$	751.536	+	751.536i	0.330279	+	0.330279i	0.852692	−	0.522414i	$-0.174968\pi$
$173$	751.536	+	751.536i	0.330279	+	0.330279i	−0.522414	+	0.852692i	$0.674968\pi$
$174$		0			0
$175$	1322.69	+	1322.69i	0.571346	+	0.571346i
$176$		0			0
$177$	2873.55	−	2873.55i	1.22028	−	1.22028i
$178$		0			0
$179$			2532.00i			1.05727i	0.848851	+	0.528633i	$0.177295\pi$
$179$			2532.00i			1.05727i	−0.848851	+	0.528633i	$0.822705\pi$
$180$		0			0
$181$	800.555	−	800.555i	0.328756	−	0.328756i	−0.523358	−	0.852113i	$-0.675321\pi$
$181$	800.555	−	800.555i	0.328756	−	0.328756i	0.852113	+	0.523358i	$0.175321\pi$
$182$		0			0
$183$	−546.757			−0.220860
$184$		0			0
$185$			1638.24i			0.651056i
$186$		0			0
$187$	3036.95	−	181.337i	1.18761	−	0.0709125i
$188$		0			0
$189$		−	5951.41i		−	2.29048i
$190$		0			0
$191$	−1570.32			−0.594891			−0.297446	−	0.954739i	$-0.596135\pi$
$191$	−1570.32			−0.594891			−0.297446	+	0.954739i	$0.596135\pi$
$192$		0			0
$193$	−3122.69	+	3122.69i	−1.16464	+	1.16464i	−0.181195	+	0.983447i	$0.557996\pi$
$193$	−3122.69	+	3122.69i	−1.16464	+	1.16464i	−0.983447	+	0.181195i	$0.942004\pi$
$194$		0			0
$195$		−	1867.80i		−	0.685929i
$196$		0			0
$197$	−1658.05	+	1658.05i	−0.599651	+	0.599651i	−0.940220	−	0.340569i	$-0.889380\pi$
$197$	−1658.05	+	1658.05i	−0.599651	+	0.599651i	0.340569	+	0.940220i	$0.389380\pi$
$198$		0			0
$199$	−2378.76	−	2378.76i	−0.847368	−	0.847368i	0.142436	−	0.989804i	$-0.454506\pi$
$199$	−2378.76	−	2378.76i	−0.847368	−	0.847368i	−0.989804	+	0.142436i	$0.954506\pi$
$200$		0			0
$201$	1154.65	+	1154.65i	0.405188	+	0.405188i
$202$		0			0
$203$	−3463.77			−1.19758
$204$		0			0
$205$	1135.32			0.386802
$206$		0			0
$207$	−3082.09	−	3082.09i	−1.03488	−	1.03488i
$208$		0			0
$209$	−3438.41	−	3438.41i	−1.13799	−	1.13799i
$210$		0			0
$211$	2856.71	−	2856.71i	0.932058	−	0.932058i	−0.0657765	−	0.997834i	$-0.520952\pi$
$211$	2856.71	−	2856.71i	0.932058	−	0.932058i	0.997834	+	0.0657765i	$0.0209524\pi$
$212$		0			0
$213$		−	3103.01i		−	0.998192i
$214$		0			0
$215$	374.042	−	374.042i	0.118649	−	0.118649i
$216$		0			0
$217$	−1933.92			−0.604990
$218$		0			0
$219$		−	2626.48i		−	0.810416i
$220$		0			0
$221$	−2212.49	−	1963.16i	−0.673430	−	0.597540i
$222$		0			0
$223$		−	4863.37i		−	1.46043i	−0.683219	−	0.730213i	$-0.739421\pi$
$223$		−	4863.37i		−	1.46043i	0.683219	−	0.730213i	$-0.260579\pi$
$224$		0			0
$225$	6356.84			1.88351
$226$		0			0
$227$	−209.052	+	209.052i	−0.0611246	+	0.0611246i	−0.737008	−	0.675884i	$-0.763762\pi$
$227$	−209.052	+	209.052i	−0.0611246	+	0.0611246i	0.675884	+	0.737008i	$0.263762\pi$
$228$		0			0
$229$			4823.88i			1.39201i	0.718035	+	0.696007i	$0.245042\pi$
$229$			4823.88i			1.39201i	−0.718035	+	0.696007i	$0.754958\pi$
$230$		0			0
$231$	−5254.92	+	5254.92i	−1.49675	+	1.49675i
$232$		0			0
$233$	−563.164	−	563.164i	−0.158344	−	0.158344i	0.623489	−	0.781832i	$-0.285715\pi$
$233$	−563.164	−	563.164i	−0.158344	−	0.158344i	−0.781832	+	0.623489i	$0.785715\pi$
$234$		0			0
$235$	−626.019	−	626.019i	−0.173774	−	0.173774i
$236$		0			0
$237$	12474.2			3.41893
$238$		0			0
$239$	3541.85			0.958590			0.479295	−	0.877654i	$-0.340892\pi$
$239$	3541.85			0.958590			0.479295	+	0.877654i	$0.340892\pi$
$240$		0			0
$241$	1567.21	+	1567.21i	0.418890	+	0.418890i	0.884821	−	0.465931i	$-0.154280\pi$
$241$	1567.21	+	1567.21i	0.418890	+	0.418890i	−0.465931	+	0.884821i	$0.654280\pi$
$242$		0			0
$243$	−3192.60	−	3192.60i	−0.842822	−	0.842822i
$244$		0			0
$245$	−42.2851	+	42.2851i	−0.0110265	+	0.0110265i
$246$		0			0
$247$			4727.63i			1.21786i
$248$		0			0
$249$	1124.63	−	1124.63i	0.286226	−	0.286226i
$250$		0			0
$251$	−3994.43			−1.00449			−0.502243	−	0.864726i	$-0.667492\pi$
$251$	−3994.43			−1.00449			−0.502243	+	0.864726i	$0.667492\pi$
$252$		0			0
$253$			3063.32i			0.761223i
$254$		0			0
$255$	−2059.07	+	2320.57i	−0.505662	+	0.569882i
$256$		0			0
$257$		−	5119.61i		−	1.24262i	−0.783566	−	0.621309i	$-0.786601\pi$
$257$		−	5119.61i		−	1.24262i	0.783566	−	0.621309i	$-0.213399\pi$
$258$		0			0
$259$	−6337.19			−1.52036
$260$		0			0
$261$	−8323.47	+	8323.47i	−1.97398	+	1.97398i
$262$		0			0
$263$			7499.22i			1.75826i	0.476585	+	0.879128i	$0.341874\pi$
$263$			7499.22i			1.75826i	−0.476585	+	0.879128i	$0.658126\pi$
$264$		0			0
$265$	2134.63	−	2134.63i	0.494827	−	0.494827i
$266$		0			0
$267$	7362.22	+	7362.22i	1.68749	+	1.68749i
$268$		0			0
$269$	−297.809	−	297.809i	−0.0675008	−	0.0675008i	0.672550	−	0.740051i	$-0.265199\pi$
$269$	−297.809	−	297.809i	−0.0675008	−	0.0675008i	−0.740051	+	0.672550i	$0.765199\pi$
$270$		0			0
$271$	−115.716			−0.0259381			−0.0129691	−	0.999916i	$-0.504128\pi$
$271$	−115.716			−0.0259381			−0.0129691	+	0.999916i	$0.504128\pi$
$272$		0			0
$273$	7225.23			1.60180
$274$		0			0
$275$	−3159.07	−	3159.07i	−0.692723	−	0.692723i
$276$		0			0
$277$	−515.483	−	515.483i	−0.111814	−	0.111814i	0.648986	−	0.760800i	$-0.275193\pi$
$277$	−515.483	−	515.483i	−0.111814	−	0.111814i	−0.760800	+	0.648986i	$0.775193\pi$
$278$		0			0
$279$	−4647.21	+	4647.21i	−0.997209	+	0.997209i
$280$		0			0
$281$		−	3919.76i		−	0.832146i	−0.909331	−	0.416073i	$-0.863406\pi$
$281$		−	3919.76i		−	0.832146i	0.909331	−	0.416073i	$-0.136594\pi$
$282$		0			0
$283$	3901.47	−	3901.47i	0.819500	−	0.819500i	−0.166536	−	0.986035i	$-0.553258\pi$
$283$	3901.47	−	3901.47i	0.819500	−	0.819500i	0.986035	+	0.166536i	$0.0532581\pi$
$284$		0			0
$285$	4958.59			1.03060
$286$		0			0
$287$			4391.77i			0.903268i
$288$		0			0
$289$	584.626	+	4878.09i	0.118996	+	0.992895i
$290$		0			0
$291$			15993.3i			3.22180i
$292$		0			0
$293$	498.738			0.0994423			0.0497212	−	0.998763i	$-0.484167\pi$
$293$	498.738			0.0994423			0.0497212	+	0.998763i	$0.484167\pi$
$294$		0			0
$295$	1432.93	−	1432.93i	0.282809	−	0.282809i
$296$		0			0
$297$			14214.2i			2.77707i
$298$		0			0
$299$	2105.95	−	2105.95i	0.407325	−	0.407325i
$300$		0			0
$301$	1446.91	+	1446.91i	0.277071	+	0.277071i
$302$		0			0
$303$	−10531.7	−	10531.7i	−1.99680	−	1.99680i
$304$		0			0
$305$	−272.647			−0.0511860
$306$		0			0
$307$	8441.03			1.56924			0.784618	−	0.619980i	$-0.212859\pi$
$307$	8441.03			1.56924			0.784618	+	0.619980i	$0.212859\pi$
$308$		0			0
$309$	−10483.1	−	10483.1i	−1.92997	−	1.92997i
$310$		0			0
$311$	−1397.48	−	1397.48i	−0.254804	−	0.254804i	0.568133	−	0.822937i	$-0.307666\pi$
$311$	−1397.48	−	1397.48i	−0.254804	−	0.254804i	−0.822937	+	0.568133i	$0.807666\pi$
$312$		0			0
$313$	2992.99	−	2992.99i	0.540492	−	0.540492i	−0.383181	−	0.923673i	$-0.625172\pi$
$313$	2992.99	−	2992.99i	0.540492	−	0.540492i	0.923673	+	0.383181i	$0.125172\pi$
$314$		0			0
$315$		−	5272.97i		−	0.943169i
$316$		0			0
$317$	−4475.45	+	4475.45i	−0.792953	+	0.792953i	−0.981973	−	0.189020i	$-0.939469\pi$
$317$	−4475.45	+	4475.45i	−0.792953	+	0.792953i	0.189020	+	0.981973i	$0.439469\pi$
$318$		0			0
$319$	8272.78			1.45200
$320$		0			0
$321$		−	5036.16i		−	0.875672i
$322$		0			0
$323$	5211.74	−	5873.65i	0.897799	−	1.01182i
$324$		0			0
$325$			4343.55i			0.741343i
$326$		0			0
$327$	7005.53			1.18473
$328$		0			0
$329$	2421.63	−	2421.63i	0.405802	−	0.405802i
$330$		0			0
$331$			2319.73i			0.385208i	0.981277	+	0.192604i	$0.0616932\pi$
$331$			2319.73i			0.385208i	−0.981277	+	0.192604i	$0.938307\pi$
$332$		0			0
$333$	−15228.3	+	15228.3i	−2.50603	+	2.50603i
$334$		0			0
$335$	575.781	+	575.781i	0.0939053	+	0.0939053i
$336$		0			0
$337$	−6731.46	−	6731.46i	−1.08809	−	1.08809i	−0.995725	−	0.0923638i	$-0.970558\pi$
$337$	−6731.46	−	6731.46i	−1.08809	−	1.08809i	−0.0923638	−	0.995725i	$-0.529442\pi$
$338$		0			0
$339$	−21749.8			−3.48463
$340$		0			0
$341$	4618.91			0.733513
$342$		0			0
$343$	−4571.30	−	4571.30i	−0.719612	−	0.719612i
$344$		0			0
$345$	−2208.83	−	2208.83i	−0.344694	−	0.344694i
$346$		0			0
$347$	−3449.11	+	3449.11i	−0.533596	+	0.533596i	−0.921641	−	0.388045i	$-0.873151\pi$
$347$	−3449.11	+	3449.11i	−0.533596	+	0.533596i	0.388045	+	0.921641i	$0.373151\pi$
$348$		0			0
$349$		−	5593.15i		−	0.857863i	−0.903337	−	0.428932i	$-0.858890\pi$
$349$		−	5593.15i		−	0.857863i	0.903337	−	0.428932i	$-0.141110\pi$
$350$		0			0
$351$	9771.87	−	9771.87i	1.48599	−	1.48599i
$352$		0			0
$353$	6209.78			0.936298			0.468149	−	0.883649i	$-0.344921\pi$
$353$	6209.78			0.936298			0.468149	+	0.883649i	$0.344921\pi$
$354$		0			0
$355$		−	1547.36i		−	0.231338i
$356$		0			0
$357$	−8976.68	−	7965.09i	−1.33080	−	1.18083i
$358$		0			0
$359$			2744.78i			0.403521i	0.979435	+	0.201761i	$0.0646663\pi$
$359$			2744.78i			0.403521i	−0.979435	+	0.201761i	$0.935334\pi$
$360$		0			0
$361$	−5691.78			−0.829827
$362$		0			0
$363$	3683.81	−	3683.81i	0.532645	−	0.532645i
$364$		0			0
$365$		−	1309.73i		−	0.187820i
$366$		0			0
$367$	8194.03	−	8194.03i	1.16546	−	1.16546i	0.182202	−	0.983261i	$-0.441678\pi$
$367$	8194.03	−	8194.03i	1.16546	−	1.16546i	0.983261	−	0.182202i	$-0.0583225\pi$
$368$		0			0
$369$	10553.5	+	10553.5i	1.48886	+	1.48886i
$370$		0			0
$371$	8257.38	+	8257.38i	1.15553	+	1.15553i
$372$		0			0
$373$	−92.8158			−0.0128842			−0.00644211	−	0.999979i	$-0.502051\pi$
$373$	−92.8158			−0.0128842			−0.00644211	+	0.999979i	$0.502051\pi$
$374$		0			0
$375$	10088.4			1.38923
$376$		0			0
$377$	−5687.31	−	5687.31i	−0.776954	−	0.776954i
$378$		0			0
$379$	4237.26	+	4237.26i	0.574283	+	0.574283i	0.933322	−	0.359039i	$-0.116896\pi$
$379$	4237.26	+	4237.26i	0.574283	+	0.574283i	−0.359039	+	0.933322i	$0.616896\pi$
$380$		0			0
$381$	2900.36	−	2900.36i	0.389999	−	0.389999i
$382$		0			0
$383$		−	337.482i		−	0.0450249i	−0.999747	−	0.0225124i	$-0.992833\pi$
$383$		−	337.482i		−	0.0450249i	0.999747	−	0.0225124i	$-0.00716654\pi$
$384$		0			0
$385$	−2620.43	+	2620.43i	−0.346882	+	0.346882i
$386$		0			0
$387$	6953.86			0.913397
$388$		0			0
$389$		−	4718.94i		−	0.615064i	−0.951538	−	0.307532i	$-0.900497\pi$
$389$		−	4718.94i		−	0.615064i	0.951538	−	0.307532i	$-0.0995031\pi$
$390$		0			0
$391$	−4938.05	+	294.851i	−0.638691	+	0.0381362i
$392$		0			0
$393$		−	8952.35i		−	1.14908i
$394$		0			0
$395$	6220.41			0.792361
$396$		0			0
$397$	−301.684	+	301.684i	−0.0381388	+	0.0381388i	−0.725919	−	0.687780i	$-0.758585\pi$
$397$	−301.684	+	301.684i	−0.0381388	+	0.0381388i	0.687780	+	0.725919i	$0.258585\pi$
$398$		0			0
$399$			19181.3i			2.40669i
$400$		0			0
$401$	−303.535	+	303.535i	−0.0378000	+	0.0378000i	−0.725754	−	0.687954i	$-0.758509\pi$
$401$	−303.535	+	303.535i	−0.0378000	+	0.0378000i	0.687954	+	0.725754i	$0.258509\pi$
$402$		0			0
$403$	−3175.38	−	3175.38i	−0.392498	−	0.392498i
$404$		0			0
$405$	−4709.77	−	4709.77i	−0.577853	−	0.577853i
$406$		0			0
$407$	15135.6			1.84335
$408$		0			0
$409$	−3587.59			−0.433729			−0.216864	−	0.976202i	$-0.569583\pi$
$409$	−3587.59			−0.433729			−0.216864	+	0.976202i	$0.569583\pi$
$410$		0			0
$411$	−15840.5	−	15840.5i	−1.90110	−	1.90110i
$412$		0			0
$413$	5543.02	+	5543.02i	0.660422	+	0.660422i
$414$		0			0
$415$	560.809	−	560.809i	0.0663350	−	0.0663350i
$416$		0			0
$417$			6596.22i			0.774624i
$418$		0			0
$419$	−583.914	+	583.914i	−0.0680813	+	0.0680813i	−0.740328	−	0.672246i	$-0.765330\pi$
$419$	−583.914	+	583.914i	−0.0680813	+	0.0680813i	0.672246	+	0.740328i	$0.265330\pi$
$420$		0			0
$421$	6708.56			0.776616			0.388308	−	0.921530i	$-0.373060\pi$
$421$	6708.56			0.776616			0.388308	+	0.921530i	$0.373060\pi$
$422$		0			0
$423$		−	11638.4i		−	1.33777i
$424$		0			0
$425$	4788.32	−	5396.46i	0.546513	−	0.615921i
$426$		0			0
$427$		−	1054.68i		−	0.119531i
$428$		0			0
$429$	−17256.5			−1.94208
$430$		0			0
$431$	−5841.72	+	5841.72i	−0.652867	+	0.652867i	−0.953682	−	0.300815i	$-0.902741\pi$
$431$	−5841.72	+	5841.72i	−0.652867	+	0.652867i	0.300815	+	0.953682i	$0.402741\pi$
$432$		0			0
$433$			3424.92i			0.380118i	0.981773	+	0.190059i	$0.0608679\pi$
$433$			3424.92i			0.380118i	−0.981773	+	0.190059i	$0.939132\pi$
$434$		0			0
$435$	−5965.16	+	5965.16i	−0.657488	+	0.657488i
$436$		0			0
$437$	5590.82	+	5590.82i	0.612003	+	0.612003i
$438$		0			0
$439$	4163.78	+	4163.78i	0.452680	+	0.452680i	0.896243	−	0.443563i	$-0.146286\pi$
$439$	4163.78	+	4163.78i	0.452680	+	0.452680i	−0.443563	+	0.896243i	$0.646286\pi$
$440$		0			0
$441$	−786.127			−0.0848858
$442$		0			0
$443$	−1000.49			−0.107302			−0.0536512	−	0.998560i	$-0.517086\pi$
$443$	−1000.49			−0.107302			−0.0536512	+	0.998560i	$0.517086\pi$
$444$		0			0
$445$	3671.26	+	3671.26i	0.391089	+	0.391089i
$446$		0			0
$447$	7917.12	+	7917.12i	0.837734	+	0.837734i
$448$		0			0
$449$	2445.14	−	2445.14i	0.257001	−	0.257001i	−0.566832	−	0.823833i	$-0.691831\pi$
$449$	2445.14	−	2445.14i	0.257001	−	0.257001i	0.823833	+	0.566832i	$0.191831\pi$
$450$		0			0
$451$		−	10489.2i		−	1.09516i
$452$		0			0
$453$	10554.2	−	10554.2i	1.09465	−	1.09465i
$454$		0			0
$455$	3602.95			0.371229
$456$		0			0
$457$		−	8280.13i		−	0.847545i	−0.905769	−	0.423772i	$-0.860706\pi$
$457$		−	8280.13i		−	0.847545i	0.905769	−	0.423772i	$-0.139294\pi$
$458$		0			0
$459$	−22913.2	+	1368.15i	−2.33005	+	0.139128i
$460$		0			0
$461$		−	14706.0i		−	1.48574i	−0.669437	−	0.742869i	$-0.733465\pi$
$461$		−	14706.0i		−	1.48574i	0.669437	−	0.742869i	$-0.266535\pi$
$462$		0			0
$463$	−5655.22			−0.567646			−0.283823	−	0.958877i	$-0.591603\pi$
$463$	−5655.22			−0.567646			−0.283823	+	0.958877i	$0.591603\pi$
$464$		0			0
$465$	−3330.50	+	3330.50i	−0.332147	+	0.332147i
$466$		0			0
$467$		−	9.81407i		−	0.000972464i	−1.00000		0.000486232i	$-0.999845\pi$
$467$		−	9.81407i		−	0.000972464i	1.00000		0.000486232i	$-0.000154773\pi$
$468$		0			0
$469$	−2227.30	+	2227.30i	−0.219290	+	0.219290i
$470$		0			0
$471$	644.998	+	644.998i	0.0630996	+	0.0630996i
$472$		0			0
$473$	−3455.75	−	3455.75i	−0.335932	−	0.335932i
$474$		0			0
$475$	−11531.1			−1.11386
$476$		0			0
$477$	39685.1			3.80934
$478$		0			0
$479$	−6139.22	−	6139.22i	−0.585612	−	0.585612i	0.350828	−	0.936440i	$-0.385900\pi$
$479$	−6139.22	−	6139.22i	−0.585612	−	0.585612i	−0.936440	+	0.350828i	$0.885900\pi$
$480$		0			0
$481$	−10405.3	−	10405.3i	−0.986364	−	0.986364i
$482$		0			0
$483$	8544.44	−	8544.44i	0.804938	−	0.804938i
$484$		0			0
$485$			7975.25i			0.746675i
$486$		0			0
$487$	−1175.05	+	1175.05i	−0.109336	+	0.109336i	−0.759658	−	0.650322i	$-0.774634\pi$
$487$	−1175.05	+	1175.05i	−0.109336	+	0.109336i	0.650322	+	0.759658i	$0.274634\pi$
$488$		0			0
$489$	−36797.8			−3.40297
$490$		0			0
$491$			10356.5i			0.951897i	0.879473	+	0.475949i	$0.157895\pi$
$491$			10356.5i			0.951897i	−0.879473	+	0.475949i	$0.842105\pi$
$492$		0			0
$493$	796.273	+	13335.7i	0.0727430	+	1.21827i
$494$		0			0
$495$			12593.8i			1.14354i
$496$		0			0
$497$	5985.64			0.540227
$498$		0			0
$499$	−8966.23	+	8966.23i	−0.804376	+	0.804376i	−0.983776	−	0.179400i	$-0.942584\pi$
$499$	−8966.23	+	8966.23i	−0.804376	+	0.804376i	0.179400	+	0.983776i	$0.442584\pi$
$500$		0			0
$501$		−	23554.9i		−	2.10051i
$502$		0			0
$503$	−2044.07	+	2044.07i	−0.181194	+	0.181194i	−0.791876	−	0.610682i	$-0.790895\pi$
$503$	−2044.07	+	2044.07i	−0.181194	+	0.181194i	0.610682	+	0.791876i	$0.290895\pi$
$504$		0			0
$505$	−5251.76	−	5251.76i	−0.462773	−	0.462773i
$506$		0			0
$507$	−2772.61	−	2772.61i	−0.242872	−	0.242872i
$508$		0			0
$509$	−1600.79			−0.139398			−0.0696992	−	0.997568i	$-0.522204\pi$
$509$	−1600.79			−0.139398			−0.0696992	+	0.997568i	$0.522204\pi$
$510$		0			0
$511$	5066.42			0.438601
$512$		0			0
$513$	25942.1	+	25942.1i	2.23269	+	2.23269i
$514$		0			0
$515$	−5227.51	−	5227.51i	−0.447284	−	0.447284i
$516$		0			0
$517$	−5783.76	+	5783.76i	−0.492011	+	0.492011i
$518$		0			0
$519$			10013.2i			0.846880i
$520$		0			0
$521$	−7529.39	+	7529.39i	−0.633145	+	0.633145i	−0.948856	−	0.315710i	$-0.897757\pi$
$521$	−7529.39	+	7529.39i	−0.633145	+	0.633145i	0.315710	+	0.948856i	$0.397757\pi$
$522$		0			0
$523$	3831.19			0.320318			0.160159	−	0.987091i	$-0.448799\pi$
$523$	3831.19			0.320318			0.160159	+	0.987091i	$0.448799\pi$
$524$		0			0
$525$			17623.0i			1.46501i
$526$		0			0
$527$	444.580	+	7445.65i	0.0367480	+	0.615441i
$528$		0			0
$529$			7186.07i			0.590620i
$530$		0			0
$531$	26639.8			2.17716
$532$		0			0
$533$	−7211.03	+	7211.03i	−0.586012	+	0.586012i
$534$		0			0
$535$		−	2511.34i		−	0.202944i
$536$		0			0
$537$	−16867.7	+	16867.7i	−1.35549	+	1.35549i
$538$		0			0
$539$	390.670	+	390.670i	0.0312196	+	0.0312196i
$540$		0			0
$541$	7837.15	+	7837.15i	0.622819	+	0.622819i	0.946251	−	0.323432i	$-0.104837\pi$
$541$	7837.15	+	7837.15i	0.622819	+	0.622819i	−0.323432	+	0.946251i	$0.604837\pi$
$542$		0			0
$543$	10666.3			0.842974
$544$		0			0
$545$	3493.39			0.274570
$546$		0			0
$547$	1644.94	+	1644.94i	0.128579	+	0.128579i	0.768467	−	0.639889i	$-0.221020\pi$
$547$	1644.94	+	1644.94i	0.128579	+	0.128579i	−0.639889	+	0.768467i	$0.721020\pi$
$548$		0			0
$549$	−2534.41	−	2534.41i	−0.197023	−	0.197023i
$550$		0			0
$551$	15098.5	−	15098.5i	1.16737	−	1.16737i
$552$		0			0
$553$			24062.4i			1.85034i
$554$		0			0
$555$	−10913.6	+	10913.6i	−0.834699	+	0.834699i
$556$		0			0
$557$	21686.9			1.64973			0.824867	−	0.565327i	$-0.191250\pi$
$557$	21686.9			1.64973			0.824867	+	0.565327i	$0.191250\pi$
$558$		0			0
$559$			4751.48i			0.359510i
$560$		0			0
$561$	21439.7	+	19023.6i	1.61352	+	1.43169i
$562$		0			0
$563$		−	6899.00i		−	0.516445i	−0.966086	−	0.258222i	$-0.916863\pi$
$563$		−	6899.00i		−	0.516445i	0.966086	−	0.258222i	$-0.0831367\pi$
$564$		0			0
$565$	−10845.8			−0.807589
$566$		0			0
$567$	18218.8	−	18218.8i	1.34942	−	1.34942i
$568$		0			0
$569$		−	1260.55i		−	0.0928733i	−0.998921	−	0.0464366i	$-0.985213\pi$
$569$		−	1260.55i		−	0.0928733i	0.998921	−	0.0464366i	$-0.0147866\pi$
$570$		0			0
$571$	−5090.01	+	5090.01i	−0.373048	+	0.373048i	−0.868586	−	0.495538i	$-0.834971\pi$
$571$	−5090.01	+	5090.01i	−0.373048	+	0.373048i	0.495538	+	0.868586i	$0.334971\pi$
$572$		0			0
$573$	−10461.2	−	10461.2i	−0.762691	−	0.762691i
$574$		0			0
$575$	5136.61	+	5136.61i	0.372541	+	0.372541i
$576$		0			0
$577$	4379.28			0.315965			0.157983	−	0.987442i	$-0.449501\pi$
$577$	4379.28			0.315965			0.157983	+	0.987442i	$0.449501\pi$
$578$		0			0
$579$	−41605.6			−2.98630
$580$		0			0
$581$	2169.38	+	2169.38i	0.154907	+	0.154907i
$582$		0			0
$583$	−19721.7	−	19721.7i	−1.40101	−	1.40101i
$584$		0			0
$585$	8657.92	−	8657.92i	0.611899	−	0.611899i
$586$		0			0
$587$			10694.5i			0.751974i	0.926625	+	0.375987i	$0.122696\pi$
$587$			10694.5i			0.751974i	−0.926625	+	0.375987i	$0.877304\pi$
$588$		0			0
$589$	8429.90	−	8429.90i	0.589725	−	0.589725i
$590$		0			0
$591$	−22091.3			−1.53759
$592$		0			0
$593$		−	15444.3i		−	1.06952i	−0.845005	−	0.534758i	$-0.820403\pi$
$593$		−	15444.3i		−	1.06952i	0.845005	−	0.534758i	$-0.179597\pi$
$594$		0			0
$595$	−4476.34	−	3971.89i	−0.308423	−	0.273667i
$596$		0			0
$597$		−	31693.8i		−	2.17277i
$598$		0			0
$599$	13084.4			0.892511			0.446255	−	0.894906i	$-0.352757\pi$
$599$	13084.4			0.892511			0.446255	+	0.894906i	$0.352757\pi$
$600$		0			0
$601$	−3566.27	+	3566.27i	−0.242049	+	0.242049i	−0.817697	−	0.575648i	$-0.804750\pi$
$601$	−3566.27	+	3566.27i	−0.242049	+	0.242049i	0.575648	+	0.817697i	$0.304750\pi$
$602$		0			0
$603$			10704.4i			0.722915i
$604$		0			0
$605$	1836.98	−	1836.98i	0.123444	−	0.123444i
$606$		0			0
$607$	1894.89	+	1894.89i	0.126707	+	0.126707i	0.767617	−	0.640909i	$-0.221443\pi$
$607$	1894.89	+	1894.89i	0.126707	+	0.126707i	−0.640909	+	0.767617i	$0.721443\pi$
$608$		0			0
$609$	−23075.0	−	23075.0i	−1.53538	−	1.53538i
$610$		0			0
$611$	7952.36			0.526543
$612$		0			0
$613$	−12527.1			−0.825389			−0.412695	−	0.910869i	$-0.635412\pi$
$613$	−12527.1			−0.825389			−0.412695	+	0.910869i	$0.635412\pi$
$614$		0			0
$615$	7563.31	+	7563.31i	0.495906	+	0.495906i
$616$		0			0
$617$	10166.5	+	10166.5i	0.663351	+	0.663351i	0.956168	−	0.292817i	$-0.0945928\pi$
$617$	10166.5	+	10166.5i	0.663351	+	0.663351i	−0.292817	+	0.956168i	$0.594593\pi$
$618$		0			0
$619$	−7654.66	+	7654.66i	−0.497038	+	0.497038i	−0.910515	−	0.413477i	$-0.864314\pi$
$619$	−7654.66	+	7654.66i	−0.497038	+	0.497038i	0.413477	+	0.910515i	$0.364314\pi$
$620$		0			0
$621$		−	23112.1i		−	1.49349i
$622$		0			0
$623$	−14201.6	+	14201.6i	−0.913280	+	0.913280i
$624$		0			0
$625$	−7835.38			−0.501464
$626$		0			0
$627$		−	45812.2i		−	2.91796i
$628$		0			0
$629$	1456.83	+	24398.4i	0.0923492	+	1.54663i
$630$		0			0
$631$		−	11450.8i		−	0.722425i	−0.932484	−	0.361212i	$-0.882363\pi$
$631$		−	11450.8i		−	0.722425i	0.932484	−	0.361212i	$-0.117637\pi$
$632$		0			0
$633$	38061.8			2.38992
$634$		0			0
$635$	1446.30	−	1446.30i	0.0903852	−	0.0903852i
$636$		0			0
$637$		−	537.150i		−	0.0334108i
$638$		0			0
$639$	14383.5	−	14383.5i	0.890461	−	0.890461i
$640$		0			0
$641$	−9289.85	−	9289.85i	−0.572429	−	0.572429i	0.360377	−	0.932807i	$-0.382648\pi$
$641$	−9289.85	−	9289.85i	−0.572429	−	0.572429i	−0.932807	+	0.360377i	$0.882648\pi$
$642$		0			0
$643$	7724.20	+	7724.20i	0.473737	+	0.473737i	0.903122	−	0.429385i	$-0.141270\pi$
$643$	7724.20	+	7724.20i	0.473737	+	0.473737i	−0.429385	+	0.903122i	$0.641270\pi$
$644$		0			0
$645$	4983.60			0.304231
$646$		0			0
$647$	−25904.7			−1.57406			−0.787031	−	0.616913i	$-0.788383\pi$
$647$	−25904.7			−1.57406			−0.787031	+	0.616913i	$0.788383\pi$
$648$		0			0
$649$	−13238.8	−	13238.8i	−0.800722	−	0.800722i
$650$		0			0
$651$	−12883.4	−	12883.4i	−0.775638	−	0.775638i
$652$		0			0
$653$	8354.65	−	8354.65i	0.500678	−	0.500678i	−0.410971	−	0.911649i	$-0.634810\pi$
$653$	8354.65	−	8354.65i	0.500678	−	0.500678i	0.911649	+	0.410971i	$0.134810\pi$
$654$		0			0
$655$		−	4464.20i		−	0.266307i
$656$		0			0
$657$	12174.7	−	12174.7i	0.722950	−	0.722950i
$658$		0			0
$659$	3572.25			0.211161			0.105581	−	0.994411i	$-0.466330\pi$
$659$	3572.25			0.211161			0.105581	+	0.994411i	$0.466330\pi$
$660$		0			0
$661$			24975.8i			1.46966i	0.678250	+	0.734832i	$0.262739\pi$
$661$			24975.8i			1.46966i	−0.678250	+	0.734832i	$0.737261\pi$
$662$		0			0
$663$	−1660.98	−	27817.4i	−0.0972957	−	1.62947i
$664$		0			0
$665$			9565.01i			0.557767i
$666$		0			0
$667$	−13451.4			−0.780873
$668$		0			0
$669$	32398.9	−	32398.9i	1.87237	−	1.87237i
$670$		0			0
$671$			2518.97i			0.144924i
$672$		0			0
$673$	19807.9	−	19807.9i	1.13453	−	1.13453i	0.145118	−	0.989414i	$-0.453644\pi$
$673$	19807.9	−	19807.9i	1.13453	−	1.13453i	0.989414	−	0.145118i	$-0.0463561\pi$
$674$		0			0
$675$	23834.5	+	23834.5i	1.35910	+	1.35910i
$676$		0			0
$677$	15269.7	+	15269.7i	0.866855	+	0.866855i	0.992123	−	0.125268i	$-0.0399789\pi$
$677$	15269.7	+	15269.7i	0.866855	+	0.866855i	−0.125268	+	0.992123i	$0.539979\pi$
$678$		0			0
$679$	−30850.7			−1.74365
$680$		0			0
$681$	−2785.34			−0.156732
$682$		0			0
$683$	−3094.93	−	3094.93i	−0.173388	−	0.173388i	0.615078	−	0.788466i	$-0.289125\pi$
$683$	−3094.93	−	3094.93i	−0.173388	−	0.173388i	−0.788466	+	0.615078i	$0.789125\pi$
$684$		0			0
$685$	−7899.04	−	7899.04i	−0.440594	−	0.440594i
$686$		0			0
$687$	−32135.8	+	32135.8i	−1.78466	+	1.78466i
$688$		0			0
$689$			27116.3i			1.49934i
$690$		0			0
$691$	−2449.33	+	2449.33i	−0.134843	+	0.134843i	−0.771307	−	0.636464i	$-0.780397\pi$
$691$	−2449.33	+	2449.33i	−0.134843	+	0.134843i	0.636464	+	0.771307i	$0.280397\pi$
$692$		0			0
$693$	−48716.7			−2.67041
$694$		0			0
$695$			3289.29i			0.179525i
$696$		0			0
$697$	16908.5	−	1009.61i	0.918873	−	0.0548659i
$698$		0			0
$699$		−	7503.39i		−	0.406015i
$700$		0			0
$701$	−17586.8			−0.947568			−0.473784	−	0.880641i	$-0.657112\pi$
$701$	−17586.8			−0.947568			−0.473784	+	0.880641i	$0.657112\pi$
$702$		0			0
$703$	27623.7	−	27623.7i	1.48200	−	1.48200i
$704$		0			0
$705$		−	8340.85i		−	0.445581i
$706$		0			0
$707$	20315.4	−	20315.4i	1.08068	−	1.08068i
$708$		0			0
$709$	−18441.4	−	18441.4i	−0.976844	−	0.976844i	0.0228940	−	0.999738i	$-0.492712\pi$
$709$	−18441.4	−	18441.4i	−0.976844	−	0.976844i	−0.999738	+	0.0228940i	$0.992712\pi$
$710$		0			0
$711$	57822.2	+	57822.2i	3.04993	+	3.04993i
$712$		0			0
$713$	−7510.30			−0.394478
$714$		0			0
$715$	−8605.19			−0.450092
$716$		0			0
$717$	23595.1	+	23595.1i	1.22898	+	1.22898i
$718$		0			0
$719$	6983.79	+	6983.79i	0.362241	+	0.362241i	0.864638	−	0.502396i	$-0.167548\pi$
$719$	6983.79	+	6983.79i	0.362241	+	0.362241i	−0.502396	+	0.864638i	$0.667548\pi$
$720$		0			0
$721$	20221.6	−	20221.6i	1.04451	−	1.04451i
$722$		0			0
$723$			20880.9i			1.07409i
$724$		0			0
$725$	13871.9	−	13871.9i	0.710605	−	0.710605i
$726$		0			0
$727$	21214.7			1.08227			0.541133	−	0.840937i	$-0.317995\pi$
$727$	21214.7			1.08227			0.541133	+	0.840937i	$0.317995\pi$
$728$		0			0
$729$		−	4257.83i		−	0.216320i
$730$		0			0
$731$	5238.03	−	5903.28i	0.265028	−	0.298687i
$732$		0			0
$733$			22474.8i			1.13250i	0.824232	+	0.566252i	$0.191607\pi$
$733$			22474.8i			1.13250i	−0.824232	+	0.566252i	$0.808393\pi$
$734$		0			0
$735$	−563.392			−0.0282735
$736$		0			0
$737$	5319.61	−	5319.61i	0.265876	−	0.265876i
$738$		0			0
$739$		−	10201.5i		−	0.507805i	−0.967230	−	0.253903i	$-0.918286\pi$
$739$		−	10201.5i		−	0.507805i	0.967230	−	0.253903i	$-0.0817143\pi$
$740$		0			0
$741$	−31494.6	+	31494.6i	−1.56138	+	1.56138i
$742$		0			0
$743$	15284.1	+	15284.1i	0.754669	+	0.754669i	0.975347	−	0.220678i	$-0.0708270\pi$
$743$	15284.1	+	15284.1i	0.754669	+	0.754669i	−0.220678	+	0.975347i	$0.570827\pi$
$744$		0			0
$745$	3947.97	+	3947.97i	0.194151	+	0.194151i
$746$		0			0
$747$	10426.1			0.510669
$748$		0			0
$749$	9714.64			0.473919
$750$		0			0
$751$	−11824.8	−	11824.8i	−0.574559	−	0.574559i	0.358840	−	0.933399i	$-0.383172\pi$
$751$	−11824.8	−	11824.8i	−0.574559	−	0.574559i	−0.933399	+	0.358840i	$0.883172\pi$
$752$		0			0
$753$	−26610.2	−	26610.2i	−1.28782	−	1.28782i
$754$		0			0
$755$	5262.96	−	5262.96i	0.253694	−	0.253694i
$756$		0			0
$757$			38306.1i			1.83918i	0.392877	+	0.919591i	$0.371480\pi$
$757$			38306.1i			1.83918i	−0.392877	+	0.919591i	$0.628520\pi$
$758$		0			0
$759$	−20407.3	+	20407.3i	−0.975939	+	0.975939i
$760$		0			0
$761$	−27925.7			−1.33023			−0.665114	−	0.746741i	$-0.731617\pi$
$761$	−27925.7			−1.33023			−0.665114	+	0.746741i	$0.731617\pi$
$762$		0			0
$763$			13513.5i			0.641182i
$764$		0			0
$765$	−20301.2	+	1212.18i	−0.959464	+	0.0572896i
$766$		0			0
$767$			18202.6i			0.856923i
$768$		0			0
$769$	24285.6			1.13883			0.569415	−	0.822050i	$-0.307170\pi$
$769$	24285.6			1.13883			0.569415	+	0.822050i	$0.307170\pi$
$770$		0			0
$771$	34105.9	−	34105.9i	1.59312	−	1.59312i
$772$		0			0
$773$		−	34622.2i		−	1.61096i	−0.592620	−	0.805482i	$-0.701906\pi$
$773$		−	34622.2i		−	1.61096i	0.592620	−	0.805482i	$-0.298094\pi$
$774$		0			0
$775$	7745.03	−	7745.03i	0.358980	−	0.358980i
$776$		0			0
$777$	−42217.2	−	42217.2i	−1.94921	−	1.94921i
$778$		0			0
$779$	−19143.6	−	19143.6i	−0.880478	−	0.880478i
$780$		0			0
$781$	−14295.9			−0.654993
$782$		0			0
$783$	−62416.4			−2.84876
$784$		0			0
$785$	321.636	+	321.636i	0.0146238	+	0.0146238i
$786$		0			0
$787$	24356.1	+	24356.1i	1.10318	+	1.10318i	0.994025	+	0.109155i	$0.0348146\pi$
$787$	24356.1	+	24356.1i	1.10318	+	1.10318i	0.109155	+	0.994025i	$0.465185\pi$
$788$		0			0
$789$	−49958.4	+	49958.4i	−2.25420	+	2.25420i
$790$		0			0
$791$		−	41955.0i		−	1.88590i
$792$		0			0
$793$	1731.73	−	1731.73i	0.0775478	−	0.0775478i
$794$		0			0
$795$	28441.0			1.26880
$796$		0			0
$797$			34928.5i			1.55236i	0.630511	+	0.776180i	$0.282845\pi$
$797$			34928.5i			1.55236i	−0.630511	+	0.776180i	$0.717155\pi$
$798$		0			0
$799$	−9880.08	−	8766.68i	−0.437462	−	0.388164i
$800$		0			0
$801$			68252.9i			3.01073i
$802$		0			0
$803$	−12100.5			−0.531778
$804$		0			0
$805$	4260.79	−	4260.79i	0.186550	−	0.186550i
$806$		0			0
$807$		−	3967.90i		−	0.173081i
$808$		0			0
$809$	8078.36	−	8078.36i	0.351075	−	0.351075i	−0.509434	−	0.860510i	$-0.670145\pi$
$809$	8078.36	−	8078.36i	0.351075	−	0.351075i	0.860510	+	0.509434i	$0.170145\pi$
$810$		0			0
$811$	8872.74	+	8872.74i	0.384173	+	0.384173i	0.872603	−	0.488430i	$-0.162430\pi$
$811$	8872.74	+	8872.74i	0.384173	+	0.384173i	−0.488430	+	0.872603i	$0.662430\pi$
$812$		0			0
$813$	−770.878	−	770.878i	−0.0332545	−	0.0332545i
$814$		0			0
$815$	−18349.7			−0.788664
$816$		0			0
$817$	−12614.1			−0.540160
$818$		0			0
$819$	33491.5	+	33491.5i	1.42892	+	1.42892i
$820$		0			0
$821$	11448.3	+	11448.3i	0.486660	+	0.486660i	0.907251	−	0.420590i	$-0.138177\pi$
$821$	11448.3	+	11448.3i	0.486660	+	0.486660i	−0.420590	+	0.907251i	$0.638177\pi$
$822$		0			0
$823$	20327.2	−	20327.2i	0.860949	−	0.860949i	−0.130499	−	0.991448i	$-0.541658\pi$
$823$	20327.2	−	20327.2i	0.860949	−	0.860949i	0.991448	+	0.130499i	$0.0416579\pi$
$824$		0			0
$825$		−	42090.3i		−	1.77624i
$826$		0			0
$827$	12964.3	−	12964.3i	0.545117	−	0.545117i	−0.379907	−	0.925025i	$-0.624044\pi$
$827$	12964.3	−	12964.3i	0.545117	−	0.545117i	0.925025	+	0.379907i	$0.124044\pi$
$828$		0			0
$829$	7910.47			0.331414			0.165707	−	0.986175i	$-0.447009\pi$
$829$	7910.47			0.331414			0.165707	+	0.986175i	$0.447009\pi$
$830$		0			0
$831$		−	6868.10i		−	0.286705i
$832$		0			0
$833$	−592.154	+	667.360i	−0.0246302	+	0.0277583i
$834$		0			0
$835$		−	11746.0i		−	0.486810i
$836$		0			0
$837$	−34848.7			−1.43912
$838$		0			0
$839$	5748.24	−	5748.24i	0.236533	−	0.236533i	−0.578880	−	0.815413i	$-0.696510\pi$
$839$	5748.24	−	5748.24i	0.236533	−	0.236533i	0.815413	+	0.578880i	$0.196510\pi$
$840$		0			0
$841$			11937.9i			0.489477i
$842$		0			0
$843$	26112.7	−	26112.7i	1.06687	−	1.06687i
$844$		0			0
$845$	−1382.60	−	1382.60i	−0.0562874	−	0.0562874i
$846$		0			0
$847$	7106.00	+	7106.00i	0.288270	+	0.288270i
$848$		0			0
$849$	51981.8			2.10131
$850$		0			0
$851$	−24610.3			−0.991339
$852$		0			0
$853$	−11333.0	−	11333.0i	−0.454904	−	0.454904i	0.442074	−	0.896978i	$-0.354243\pi$
$853$	−11333.0	−	11333.0i	−0.454904	−	0.454904i	−0.896978	+	0.442074i	$0.854243\pi$
$854$		0			0
$855$	22984.8	+	22984.8i	0.919372	+	0.919372i
$856$		0			0
$857$	12897.1	−	12897.1i	0.514067	−	0.514067i	−0.401703	−	0.915770i	$-0.631582\pi$
$857$	12897.1	−	12897.1i	0.514067	−	0.514067i	0.915770	+	0.401703i	$0.131582\pi$
$858$		0			0
$859$			40310.0i			1.60112i	0.599255	+	0.800558i	$0.295463\pi$
$859$			40310.0i			1.60112i	−0.599255	+	0.800558i	$0.704537\pi$
$860$		0			0
$861$	−29257.2	+	29257.2i	−1.15805	+	1.15805i
$862$		0			0
$863$	27644.0			1.09040			0.545198	−	0.838308i	$-0.316455\pi$
$863$	27644.0			1.09040			0.545198	+	0.838308i	$0.316455\pi$
$864$		0			0
$865$			4993.21i			0.196271i
$866$		0			0
$867$	−28602.3	+	36391.7i	−1.12040	+	1.42552i
$868$		0			0
$869$		−	57470.0i		−	2.24343i
$870$		0			0
$871$	−7314.18			−0.284537
$872$		0			0
$873$	−74134.4	+	74134.4i	−2.87408	+	2.87408i
$874$		0			0
$875$			19460.3i			0.751860i
$876$		0			0
$877$	−2901.20	+	2901.20i	−0.111706	+	0.111706i	−0.760751	−	0.649044i	$-0.775169\pi$
$877$	−2901.20	+	2901.20i	−0.111706	+	0.111706i	0.649044	+	0.760751i	$0.275169\pi$
$878$		0			0
$879$	3322.51	+	3322.51i	0.127492	+	0.127492i
$880$		0			0
$881$	2998.29	+	2998.29i	0.114659	+	0.114659i	0.762109	−	0.647449i	$-0.224164\pi$
$881$	2998.29	+	2998.29i	0.114659	+	0.114659i	−0.647449	+	0.762109i	$0.724164\pi$
$882$		0			0
$883$	15185.5			0.578746			0.289373	−	0.957216i	$-0.406553\pi$
$883$	15185.5			0.578746			0.289373	+	0.957216i	$0.406553\pi$
$884$		0			0
$885$	19091.9			0.725161
$886$		0			0
$887$	−20845.7	−	20845.7i	−0.789096	−	0.789096i	0.192250	−	0.981346i	$-0.438422\pi$
$887$	−20845.7	−	20845.7i	−0.789096	−	0.789096i	−0.981346	+	0.192250i	$0.938422\pi$
$888$		0			0
$889$	5594.72	+	5594.72i	0.211070	+	0.211070i
$890$		0			0
$891$	−43513.4	+	43513.4i	−1.63609	+	1.63609i
$892$		0			0
$893$			21111.7i			0.791127i
$894$		0			0
$895$	−8411.30	+	8411.30i	−0.314144	+	0.314144i
$896$		0			0
$897$	28058.9			1.04444
$898$		0			0
$899$			20282.2i			0.752448i
$900$		0			0
$901$	29893.0	−	33689.5i	1.10531	−	1.24568i
$902$		0			0
$903$			19278.1i			0.710448i
$904$		0			0
$905$	5318.89			0.195366
$906$		0			0
$907$	−36035.0	+	36035.0i	−1.31921	+	1.31921i	−0.404806	+	0.914403i	$0.632661\pi$
$907$	−36035.0	+	36035.0i	−1.31921	+	1.31921i	−0.914403	+	0.404806i	$0.867339\pi$
$908$		0			0
$909$		−	97636.1i		−	3.56258i
$910$		0			0
$911$	−24511.1	+	24511.1i	−0.891426	+	0.891426i	−0.994657	−	0.103231i	$-0.967082\pi$
$911$	−24511.1	+	24511.1i	−0.891426	+	0.891426i	0.103231	+	0.994657i	$0.467082\pi$
$912$		0			0
$913$	−5181.29	−	5181.29i	−0.187815	−	0.187815i
$914$		0			0
$915$	−1816.33	−	1816.33i	−0.0656239	−	0.0656239i
$916$		0			0
$917$	17268.9			0.621886
$918$		0			0
$919$	28858.8			1.03587			0.517935	−	0.855420i	$-0.326701\pi$
$919$	28858.8			1.03587			0.517935	+	0.855420i	$0.326701\pi$
$920$		0			0
$921$	56232.7	+	56232.7i	2.01187	+	2.01187i
$922$		0			0
$923$	9828.08	+	9828.08i	0.350482	+	0.350482i
$924$		0			0
$925$	25379.5	−	25379.5i	0.902132	−	0.902132i
$926$		0			0
$927$		−	97185.2i		−	3.44335i
$928$		0			0
$929$	−16267.7	+	16267.7i	−0.574516	+	0.574516i	−0.933387	−	0.358871i	$-0.883162\pi$
$929$	−16267.7	+	16267.7i	−0.574516	+	0.574516i	0.358871	+	0.933387i	$0.383162\pi$
$930$		0			0
$931$	1426.01			0.0501994
$932$		0			0
$933$		−	18619.6i		−	0.653351i
$934$		0			0
$935$	10691.2	+	9486.36i	0.373945	+	0.331804i
$936$		0			0
$937$		−	36332.8i		−	1.26675i	−0.773846	−	0.633374i	$-0.781670\pi$
$937$		−	36332.8i		−	1.26675i	0.773846	−	0.633374i	$-0.218330\pi$
$938$		0			0
$939$	39877.6			1.38590
$940$		0			0
$941$	−6122.90	+	6122.90i	−0.212116	+	0.212116i	−0.805166	−	0.593050i	$-0.797924\pi$
$941$	−6122.90	+	6122.90i	−0.212116	+	0.212116i	0.593050	+	0.805166i	$0.297924\pi$
$942$		0			0
$943$			17055.3i			0.588968i
$944$		0			0
$945$	19770.6	−	19770.6i	0.680569	−	0.680569i
$946$		0			0
$947$	−28975.5	−	28975.5i	−0.994275	−	0.994275i	0.00570881	−	0.999984i	$-0.498183\pi$
$947$	−28975.5	−	28975.5i	−0.994275	−	0.994275i	−0.999984	+	0.00570881i	$0.998183\pi$
$948$		0			0
$949$	8318.77	+	8318.77i	0.284551	+	0.284551i
$950$		0			0
$951$	−59629.2			−2.03324
$952$		0			0
$953$	−30977.5			−1.05295			−0.526474	−	0.850191i	$-0.676486\pi$
$953$	−30977.5			−1.05295			−0.526474	+	0.850191i	$0.676486\pi$
$954$		0			0
$955$	−5216.60	−	5216.60i	−0.176759	−	0.176759i
$956$		0			0
$957$	55111.8	+	55111.8i	1.86156	+	1.86156i
$958$		0			0
$959$	30555.9	−	30555.9i	1.02889	−	1.02889i
$960$		0			0
$961$		−	18466.9i		−	0.619881i
$962$		0			0
$963$	23344.3	−	23344.3i	0.781164	−	0.781164i
$964$		0			0
$965$	−20747.1			−0.692097
$966$		0			0
$967$			15226.3i			0.506355i	0.967420	+	0.253177i	$0.0814756\pi$
$967$			15226.3i			0.506355i	−0.967420	+	0.253177i	$0.918524\pi$
$968$		0			0
$969$	73848.9	−	4409.52i	2.44826	−	0.146186i
$970$		0			0
$971$		−	26521.7i		−	0.876541i	−0.898843	−	0.438271i	$-0.855591\pi$
$971$		−	26521.7i		−	0.876541i	0.898843	−	0.438271i	$-0.144409\pi$
$972$		0			0
$973$	−12724.0			−0.419231
$974$		0			0
$975$	−28935.9	+	28935.9i	−0.950453	+	0.950453i
$976$		0			0
$977$			25941.9i			0.849493i	0.905312	+	0.424746i	$0.139637\pi$
$977$			25941.9i			0.849493i	−0.905312	+	0.424746i	$0.860363\pi$
$978$		0			0
$979$	33918.6	−	33918.6i	1.10730	−	1.10730i
$980$		0			0
$981$	32473.1	+	32473.1i	1.05687	+	1.05687i
$982$		0			0
$983$	−32799.7	−	32799.7i	−1.06424	−	1.06424i	−0.997790	−	0.0664490i	$-0.978833\pi$
$983$	−32799.7	−	32799.7i	−1.06424	−	1.06424i	−0.0664490	−	0.997790i	$-0.521167\pi$
$984$		0			0
$985$	−11016.1			−0.356347
$986$		0			0
$987$	32265.0			1.04053
$988$		0			0
$989$	5619.02	+	5619.02i	0.180662	+	0.180662i
$990$		0			0
$991$	−18399.3	−	18399.3i	−0.589782	−	0.589782i	0.347791	−	0.937572i	$-0.386932\pi$
$991$	−18399.3	−	18399.3i	−0.589782	−	0.589782i	−0.937572	+	0.347791i	$0.886932\pi$
$992$		0			0
$993$	−15453.6	+	15453.6i	−0.493863	+	0.493863i
$994$		0			0
$995$		−	15804.5i		−	0.503555i
$996$		0			0
$997$	27935.7	−	27935.7i	0.887395	−	0.887395i	−0.106878	−	0.994272i	$-0.534085\pi$
$997$	27935.7	−	27935.7i	0.887395	−	0.887395i	0.994272	+	0.106878i	$0.0340853\pi$
$998$		0			0
$999$	−114195.			−3.61658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.k.b.81.7	✓	14
4.3	odd	2		272.4.o.f.81.1		14
17.2	even	8		2312.4.a.l.1.14		14
17.4	even	4	inner	136.4.k.b.89.7	yes	14
17.15	even	8		2312.4.a.l.1.1		14
68.55	odd	4		272.4.o.f.225.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.k.b.81.7	✓	14	1.1	even	1	trivial
136.4.k.b.89.7	yes	14	17.4	even	4	inner
272.4.o.f.81.1		14	4.3	odd	2
272.4.o.f.225.1		14	68.55	odd	4
2312.4.a.l.1.1		14	17.15	even	8
2312.4.a.l.1.14		14	17.2	even	8

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(6.66182 + 6.66182i) q^{3} +(3.32200 + 3.32200i) q^{5} +(-12.8505 + 12.8505i) q^{7} +61.7597i q^{9} +O(q^{10})\)	\(q+(6.66182 + 6.66182i) q^{3} +(3.32200 + 3.32200i) q^{5} +(-12.8505 + 12.8505i) q^{7} +61.7597i q^{9} +(30.6918 - 30.6918i) q^{11} -42.1996 q^{13} +44.2612i q^{15} +(52.4291 + 46.5208i) q^{17} -112.030i q^{19} -171.216 q^{21} +(-49.9045 + 49.9045i) q^{23} -102.929i q^{25} +(-231.563 + 231.563i) q^{27} +(134.772 + 134.772i) q^{29} +(75.2466 + 75.2466i) q^{31} +408.927 q^{33} -85.3788 q^{35} +(246.574 + 246.574i) q^{37} +(-281.126 - 281.126i) q^{39} +(170.879 - 170.879i) q^{41} -112.595i q^{43} +(-205.166 + 205.166i) q^{45} -188.446 q^{47} +12.7288i q^{49} +(39.3601 + 659.187i) q^{51} -642.572i q^{53} +203.916 q^{55} +(746.326 - 746.326i) q^{57} -431.347i q^{59} +(-41.0366 + 41.0366i) q^{61} +(-793.644 - 793.644i) q^{63} +(-140.187 - 140.187i) q^{65} +173.324 q^{67} -664.910 q^{69} +(-232.895 - 232.895i) q^{71} +(-197.129 - 197.129i) q^{73} +(685.692 - 685.692i) q^{75} +788.811i q^{77} +(936.244 - 936.244i) q^{79} -1417.75 q^{81} -168.817i q^{83} +(19.6274 + 328.712i) q^{85} +1795.65i q^{87} +1105.14 q^{89} +(542.286 - 542.286i) q^{91} +1002.56i q^{93} +(372.165 - 372.165i) q^{95} +(1200.37 + 1200.37i) q^{97} +(1895.52 + 1895.52i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7}+O(q^{10}) \) 14 * q + 6 * q^3 + 6 * q^5 + 10 * q^7	\( 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7} - 66 q^{11} - 124 q^{13} + 130 q^{17} - 148 q^{21} - 162 q^{23} - 204 q^{27} + 158 q^{29} - 350 q^{31} + 116 q^{33} + 236 q^{35} + 582 q^{37} - 320 q^{39} + 878 q^{41} - 26 q^{45} - 448 q^{47} - 590 q^{51} + 1460 q^{55} + 292 q^{57} - 1130 q^{61} + 114 q^{63} + 20 q^{65} - 64 q^{67} + 2076 q^{69} - 3274 q^{71} - 1426 q^{73} + 946 q^{75} + 1718 q^{79} + 166 q^{81} - 2018 q^{85} + 476 q^{89} + 2128 q^{91} - 2444 q^{95} + 1926 q^{97} + 3870 q^{99}+O(q^{100}) \) 14 * q + 6 * q^3 + 6 * q^5 + 10 * q^7 - 66 * q^11 - 124 * q^13 + 130 * q^17 - 148 * q^21 - 162 * q^23 - 204 * q^27 + 158 * q^29 - 350 * q^31 + 116 * q^33 + 236 * q^35 + 582 * q^37 - 320 * q^39 + 878 * q^41 - 26 * q^45 - 448 * q^47 - 590 * q^51 + 1460 * q^55 + 292 * q^57 - 1130 * q^61 + 114 * q^63 + 20 * q^65 - 64 * q^67 + 2076 * q^69 - 3274 * q^71 - 1426 * q^73 + 946 * q^75 + 1718 * q^79 + 166 * q^81 - 2018 * q^85 + 476 * q^89 + 2128 * q^91 - 2444 * q^95 + 1926 * q^97 + 3870 * q^99

Introduction

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