LMFDB - Embedded newform 136.4.k.b.89.3

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			89.3
Root			$-0.657265i$ of defining polynomial
Character	$\chi$	$=$	136.89
Dual form			136.4.k.b.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.657265 + 0.657265i) q^{3} +(13.8302 - 13.8302i) q^{5} +(-14.0096 - 14.0096i) q^{7} +26.1360i q^{9} +O(q^{10})$	\(q+(-0.657265 + 0.657265i) q^{3} +(13.8302 - 13.8302i) q^{5} +(-14.0096 - 14.0096i) q^{7} +26.1360i q^{9} +(-29.5053 - 29.5053i) q^{11} -19.0633 q^{13} +18.1802i q^{15} +(44.8758 - 53.8438i) q^{17} -149.109i q^{19} +18.4160 q^{21} +(80.3748 + 80.3748i) q^{23} -257.548i q^{25} +(-34.9244 - 34.9244i) q^{27} +(104.053 - 104.053i) q^{29} +(-73.6635 + 73.6635i) q^{31} +38.7856 q^{33} -387.510 q^{35} +(-196.739 + 196.739i) q^{37} +(12.5296 - 12.5296i) q^{39} +(283.302 + 283.302i) q^{41} +20.5128i q^{43} +(361.466 + 361.466i) q^{45} +81.5700 q^{47} +49.5355i q^{49} +(5.89436 + 64.8850i) q^{51} -626.850i q^{53} -816.127 q^{55} +(98.0038 + 98.0038i) q^{57} +301.882i q^{59} +(352.453 + 352.453i) q^{61} +(366.154 - 366.154i) q^{63} +(-263.649 + 263.649i) q^{65} +924.294 q^{67} -105.655 q^{69} +(-748.251 + 748.251i) q^{71} +(4.67121 - 4.67121i) q^{73} +(169.277 + 169.277i) q^{75} +826.712i q^{77} +(364.373 + 364.373i) q^{79} -659.763 q^{81} +772.652i q^{83} +(-124.029 - 1365.31i) q^{85} +136.781i q^{87} -221.223 q^{89} +(267.068 + 267.068i) q^{91} -96.8328i q^{93} +(-2062.20 - 2062.20i) q^{95} +(-7.27967 + 7.27967i) q^{97} +(771.150 - 771.150i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.657265	+	0.657265i	−0.126491	+	0.126491i	−0.767518	−	0.641027i	$-0.778509\pi$
$3$	−0.657265	+	0.657265i	−0.126491	+	0.126491i	0.641027	+	0.767518i	$0.278509\pi$
$4$		0			0
$5$	13.8302	−	13.8302i	1.23701	−	1.23701i	0.275792	−	0.961217i	$-0.411060\pi$
$5$	13.8302	−	13.8302i	1.23701	−	1.23701i	0.961217	−	0.275792i	$-0.0889401\pi$
$6$		0			0
$7$	−14.0096	−	14.0096i	−0.756445	−	0.756445i	0.219228	−	0.975674i	$-0.429646\pi$
$7$	−14.0096	−	14.0096i	−0.756445	−	0.756445i	−0.975674	+	0.219228i	$0.929646\pi$
$8$		0			0
$9$			26.1360i			0.968000i
$10$		0			0
$11$	−29.5053	−	29.5053i	−0.808743	−	0.808743i	0.175701	−	0.984444i	$-0.443781\pi$
$11$	−29.5053	−	29.5053i	−0.808743	−	0.808743i	−0.984444	+	0.175701i	$0.943781\pi$
$12$		0			0
$13$	−19.0633			−0.406708			−0.203354	−	0.979105i	$-0.565184\pi$
$13$	−19.0633			−0.406708			−0.203354	+	0.979105i	$0.565184\pi$
$14$		0			0
$15$			18.1802i			0.312940i
$16$		0			0
$17$	44.8758	−	53.8438i	0.640235	−	0.768179i
$17$	44.8758	−	53.8438i	0.640235	−	0.768179i
$18$		0			0
$19$		−	149.109i		−	1.80041i	−0.435463	−	0.900207i	$-0.643415\pi$
$19$		−	149.109i		−	1.80041i	0.435463	−	0.900207i	$-0.356585\pi$
$20$		0			0
$21$	18.4160			0.191367
$22$		0			0
$23$	80.3748	+	80.3748i	0.728665	+	0.728665i	0.970354	−	0.241689i	$-0.0777013\pi$
$23$	80.3748	+	80.3748i	0.728665	+	0.728665i	−0.241689	+	0.970354i	$0.577701\pi$
$24$		0			0
$25$		−	257.548i		−	2.06038i
$26$		0			0
$27$	−34.9244	−	34.9244i	−0.248934	−	0.248934i
$28$		0			0
$29$	104.053	−	104.053i	0.666282	−	0.666282i	−0.290571	−	0.956853i	$-0.593845\pi$
$29$	104.053	−	104.053i	0.666282	−	0.666282i	0.956853	+	0.290571i	$0.0938453\pi$
$30$		0			0
$31$	−73.6635	+	73.6635i	−0.426785	+	0.426785i	−0.887532	−	0.460746i	$-0.847582\pi$
$31$	−73.6635	+	73.6635i	−0.426785	+	0.426785i	0.460746	+	0.887532i	$0.347582\pi$
$32$		0			0
$33$	38.7856			0.204597
$34$		0			0
$35$	−387.510			−1.87146
$36$		0			0
$37$	−196.739	+	196.739i	−0.874154	+	0.874154i	−0.992922	−	0.118768i	$-0.962105\pi$
$37$	−196.739	+	196.739i	−0.874154	+	0.874154i	0.118768	+	0.992922i	$0.462105\pi$
$38$		0			0
$39$	12.5296	−	12.5296i	0.0514448	−	0.0514448i
$40$		0			0
$41$	283.302	+	283.302i	1.07913	+	1.07913i	0.996588	+	0.0825411i	$0.0263036\pi$
$41$	283.302	+	283.302i	1.07913	+	1.07913i	0.0825411	+	0.996588i	$0.473696\pi$
$42$		0			0
$43$			20.5128i			0.0727482i	0.999338	+	0.0363741i	$0.0115808\pi$
$43$			20.5128i			0.0727482i	−0.999338	+	0.0363741i	$0.988419\pi$
$44$		0			0
$45$	361.466	+	361.466i	1.19743	+	1.19743i
$46$		0			0
$47$	81.5700			0.253153			0.126577	−	0.991957i	$-0.459601\pi$
$47$	81.5700			0.253153			0.126577	+	0.991957i	$0.459601\pi$
$48$		0			0
$49$			49.5355i			0.144418i
$50$		0			0
$51$	5.89436	+	64.8850i	0.0161838	+	0.178151i
$52$		0			0
$53$		−	626.850i		−	1.62461i	−0.583231	−	0.812306i	$-0.698212\pi$
$53$		−	626.850i		−	1.62461i	0.583231	−	0.812306i	$-0.301788\pi$
$54$		0			0
$55$	−816.127			−2.00085
$56$		0			0
$57$	98.0038	+	98.0038i	0.227736	+	0.227736i
$58$		0			0
$59$			301.882i			0.666130i	0.942904	+	0.333065i	$0.108083\pi$
$59$			301.882i			0.666130i	−0.942904	+	0.333065i	$0.891917\pi$
$60$		0			0
$61$	352.453	+	352.453i	0.739787	+	0.739787i	0.972537	−	0.232749i	$-0.0747722\pi$
$61$	352.453	+	352.453i	0.739787	+	0.739787i	−0.232749	+	0.972537i	$0.574772\pi$
$62$		0			0
$63$	366.154	−	366.154i	0.732239	−	0.732239i
$64$		0			0
$65$	−263.649	+	263.649i	−0.503102	+	0.503102i
$66$		0			0
$67$	924.294			1.68538			0.842690	−	0.538399i	$-0.180971\pi$
$67$	924.294			1.68538			0.842690	+	0.538399i	$0.180971\pi$
$68$		0			0
$69$	−105.655			−0.184339
$70$		0			0
$71$	−748.251	+	748.251i	−1.25072	+	1.25072i	−0.295321	+	0.955398i	$0.595426\pi$
$71$	−748.251	+	748.251i	−1.25072	+	1.25072i	−0.955398	+	0.295321i	$0.904574\pi$
$72$		0			0
$73$	4.67121	−	4.67121i	0.00748936	−	0.00748936i	−0.703352	−	0.710842i	$-0.748314\pi$
$73$	4.67121	−	4.67121i	0.00748936	−	0.00748936i	0.710842	+	0.703352i	$0.248314\pi$
$74$		0			0
$75$	169.277	+	169.277i	0.260619	+	0.260619i
$76$		0			0
$77$			826.712i			1.22354i
$78$		0			0
$79$	364.373	+	364.373i	0.518925	+	0.518925i	0.917246	−	0.398321i	$-0.130407\pi$
$79$	364.373	+	364.373i	0.518925	+	0.518925i	−0.398321	+	0.917246i	$0.630407\pi$
$80$		0			0
$81$	−659.763			−0.905025
$82$		0			0
$83$			772.652i			1.02180i	0.859640	+	0.510901i	$0.170688\pi$
$83$			772.652i			1.02180i	−0.859640	+	0.510901i	$0.829312\pi$
$84$		0			0
$85$	−124.029	−	1365.31i	−0.158269	−	1.74222i
$86$		0			0
$87$			136.781i			0.168557i
$88$		0			0
$89$	−221.223			−0.263479			−0.131739	−	0.991284i	$-0.542056\pi$
$89$	−221.223			−0.263479			−0.131739	+	0.991284i	$0.542056\pi$
$90$		0			0
$91$	267.068	+	267.068i	0.307653	+	0.307653i
$92$		0			0
$93$		−	96.8328i		−	0.107969i
$94$		0			0
$95$	−2062.20	−	2062.20i	−2.22713	−	2.22713i
$96$		0			0
$97$	−7.27967	+	7.27967i	−0.00761998	+	0.00761998i	−0.710907	−	0.703287i	$-0.751715\pi$
$97$	−7.27967	+	7.27967i	−0.00761998	+	0.00761998i	0.703287	+	0.710907i	$0.251715\pi$
$98$		0			0
$99$	771.150	−	771.150i	0.782863	−	0.782863i
$100$		0			0
$101$	−136.310			−0.134290			−0.0671452	−	0.997743i	$-0.521389\pi$
$101$	−136.310			−0.134290			−0.0671452	+	0.997743i	$0.521389\pi$
$102$		0			0
$103$	1034.95			0.990061			0.495030	−	0.868876i	$-0.335157\pi$
$103$	1034.95			0.990061			0.495030	+	0.868876i	$0.335157\pi$
$104$		0			0
$105$	254.696	−	254.696i	0.236722	−	0.236722i
$106$		0			0
$107$	1102.37	−	1102.37i	0.995986	−	0.995986i	−0.00400590	−	0.999992i	$-0.501275\pi$
$107$	1102.37	−	1102.37i	0.995986	−	0.995986i	0.999992	+	0.00400590i	$0.00127512\pi$
$108$		0			0
$109$	700.081	+	700.081i	0.615189	+	0.615189i	0.944293	−	0.329105i	$-0.106747\pi$
$109$	700.081	+	700.081i	0.615189	+	0.615189i	−0.329105	+	0.944293i	$0.606747\pi$
$110$		0			0
$111$		−	258.619i		−	0.221145i
$112$		0			0
$113$	−554.781	−	554.781i	−0.461853	−	0.461853i	0.437409	−	0.899262i	$-0.355896\pi$
$113$	−554.781	−	554.781i	−0.461853	−	0.461853i	−0.899262	+	0.437409i	$0.855896\pi$
$114$		0			0
$115$	2223.20			1.80273
$116$		0			0
$117$		−	498.239i		−	0.393694i
$118$		0			0
$119$	−1383.02	+	125.638i	−1.06539	+	0.0967832i
$120$		0			0
$121$			410.122i			0.308131i
$122$		0			0
$123$	−372.408			−0.272999
$124$		0			0
$125$	−1833.16	−	1833.16i	−1.31171	−	1.31171i
$126$		0			0
$127$		−	299.992i		−	0.209606i	−0.994493	−	0.104803i	$-0.966579\pi$
$127$		−	299.992i		−	0.209606i	0.994493	−	0.104803i	$-0.0334212\pi$
$128$		0			0
$129$	−13.4823	−	13.4823i	−0.00920197	−	0.00920197i
$130$		0			0
$131$	280.857	−	280.857i	0.187317	−	0.187317i	−0.607218	−	0.794535i	$-0.707715\pi$
$131$	280.857	−	280.857i	0.187317	−	0.187317i	0.794535	+	0.607218i	$0.207715\pi$
$132$		0			0
$133$	−2088.95	+	2088.95i	−1.36191	+	1.36191i
$134$		0			0
$135$	−966.023			−0.615867
$136$		0			0
$137$	579.082			0.361127			0.180563	−	0.983563i	$-0.442208\pi$
$137$	579.082			0.361127			0.180563	+	0.983563i	$0.442208\pi$
$138$		0			0
$139$	767.549	−	767.549i	0.468364	−	0.468364i	−0.433020	−	0.901384i	$-0.642552\pi$
$139$	767.549	−	767.549i	0.468364	−	0.468364i	0.901384	+	0.433020i	$0.142552\pi$
$140$		0			0
$141$	−53.6131	+	53.6131i	−0.0320216	+	0.0320216i
$142$		0			0
$143$	562.468	+	562.468i	0.328923	+	0.328923i
$144$		0			0
$145$		−	2878.15i		−	1.64839i
$146$		0			0
$147$	−32.5579	−	32.5579i	−0.0182676	−	0.0182676i
$148$		0			0
$149$	−2225.28			−1.22350			−0.611752	−	0.791049i	$-0.709535\pi$
$149$	−2225.28			−1.22350			−0.611752	+	0.791049i	$0.709535\pi$
$150$		0			0
$151$		−	372.666i		−	0.200842i	−0.994945	−	0.100421i	$-0.967981\pi$
$151$		−	372.666i		−	0.200842i	0.994945	−	0.100421i	$-0.0320189\pi$
$152$		0			0
$153$	1407.26	+	1172.88i	0.743598	+	0.619747i
$154$		0			0
$155$			2037.56i			1.05588i
$156$		0			0
$157$	2991.93			1.52090			0.760451	−	0.649395i	$-0.224978\pi$
$157$	2991.93			1.52090			0.760451	+	0.649395i	$0.224978\pi$
$158$		0			0
$159$	412.007	+	412.007i	0.205498	+	0.205498i
$160$		0			0
$161$		−	2252.03i		−	1.10239i
$162$		0			0
$163$	1108.03	+	1108.03i	0.532441	+	0.532441i	0.921298	−	0.388857i	$-0.127130\pi$
$163$	1108.03	+	1108.03i	0.532441	+	0.532441i	−0.388857	+	0.921298i	$0.627130\pi$
$164$		0			0
$165$	536.411	−	536.411i	0.253088	−	0.253088i
$166$		0			0
$167$	1574.09	−	1574.09i	0.729380	−	0.729380i	−0.241116	−	0.970496i	$-0.577513\pi$
$167$	1574.09	−	1574.09i	0.729380	−	0.729380i	0.970496	+	0.241116i	$0.0775135\pi$
$168$		0			0
$169$	−1833.59			−0.834588
$170$		0			0
$171$	3897.10			1.74280
$172$		0			0
$173$	−1669.29	+	1669.29i	−0.733605	+	0.733605i	−0.971332	−	0.237727i	$-0.923598\pi$
$173$	−1669.29	+	1669.29i	−0.733605	+	0.733605i	0.237727	+	0.971332i	$0.423598\pi$
$174$		0			0
$175$	−3608.13	+	3608.13i	−1.55857	+	1.55857i
$176$		0			0
$177$	−198.416	−	198.416i	−0.0842593	−	0.0842593i
$178$		0			0
$179$		−	1069.31i		−	0.446501i	−0.974761	−	0.223251i	$-0.928333\pi$
$179$		−	1069.31i		−	0.446501i	0.974761	−	0.223251i	$-0.0716669\pi$
$180$		0			0
$181$	−273.285	−	273.285i	−0.112227	−	0.112227i	0.648763	−	0.760990i	$-0.275287\pi$
$181$	−273.285	−	273.285i	−0.112227	−	0.112227i	−0.760990	+	0.648763i	$0.775287\pi$
$182$		0			0
$183$	−463.310			−0.187152
$184$		0			0
$185$			5441.87i			2.16267i
$186$		0			0
$187$	−2912.75	+	264.604i	−1.13905	+	0.103474i
$188$		0			0
$189$			978.552i			0.376609i
$190$		0			0
$191$	1523.56			0.577178			0.288589	−	0.957453i	$-0.406814\pi$
$191$	1523.56			0.577178			0.288589	+	0.957453i	$0.406814\pi$
$192$		0			0
$193$	924.653	+	924.653i	0.344860	+	0.344860i	0.858191	−	0.513331i	$-0.171589\pi$
$193$	924.653	+	924.653i	0.344860	+	0.344860i	−0.513331	+	0.858191i	$0.671589\pi$
$194$		0			0
$195$		−	346.574i		−	0.127275i
$196$		0			0
$197$	433.229	+	433.229i	0.156682	+	0.156682i	0.781094	−	0.624413i	$-0.214662\pi$
$197$	433.229	+	433.229i	0.156682	+	0.156682i	−0.624413	+	0.781094i	$0.714662\pi$
$198$		0			0
$199$	−1227.91	+	1227.91i	−0.437408	+	0.437408i	−0.891139	−	0.453731i	$-0.850093\pi$
$199$	−1227.91	+	1227.91i	−0.437408	+	0.437408i	0.453731	+	0.891139i	$0.350093\pi$
$200$		0			0
$201$	−607.506	+	607.506i	−0.213185	+	0.213185i
$202$		0			0
$203$	−2915.48			−1.00801
$204$		0			0
$205$	7836.23			2.66978
$206$		0			0
$207$	−2100.68	+	2100.68i	−0.705348	+	0.705348i
$208$		0			0
$209$	−4399.49	+	4399.49i	−1.45607	+	1.45607i
$210$		0			0
$211$	−2709.54	−	2709.54i	−0.884038	−	0.884038i	0.109904	−	0.993942i	$-0.464946\pi$
$211$	−2709.54	−	2709.54i	−0.884038	−	0.884038i	−0.993942	+	0.109904i	$0.964946\pi$
$212$		0			0
$213$		−	983.598i		−	0.316409i
$214$		0			0
$215$	283.696	+	283.696i	0.0899902	+	0.0899902i
$216$		0			0
$217$	2063.99			0.645680
$218$		0			0
$219$			6.14044i			0.00189467i
$220$		0			0
$221$	−855.482	+	1026.44i	−0.260389	+	0.312425i
$222$		0			0
$223$			961.202i			0.288641i	0.989531	+	0.144320i	$0.0460996\pi$
$223$			961.202i			0.288641i	−0.989531	+	0.144320i	$0.953900\pi$
$224$		0			0
$225$	6731.28			1.99445
$226$		0			0
$227$	283.703	+	283.703i	0.0829518	+	0.0829518i	0.747365	−	0.664413i	$-0.231319\pi$
$227$	283.703	+	283.703i	0.0829518	+	0.0829518i	−0.664413	+	0.747365i	$0.731319\pi$
$228$		0			0
$229$		−	4714.07i		−	1.36033i	−0.733061	−	0.680163i	$-0.761909\pi$
$229$		−	4714.07i		−	1.36033i	0.733061	−	0.680163i	$-0.238091\pi$
$230$		0			0
$231$	−543.369	−	543.369i	−0.154766	−	0.154766i
$232$		0			0
$233$	1247.11	−	1247.11i	0.350647	−	0.350647i	−0.509703	−	0.860350i	$-0.670245\pi$
$233$	1247.11	−	1247.11i	0.350647	−	0.350647i	0.860350	+	0.509703i	$0.170245\pi$
$234$		0			0
$235$	1128.13	−	1128.13i	0.313153	−	0.313153i
$236$		0			0
$237$	−478.979			−0.131278
$238$		0			0
$239$	−4592.48			−1.24294			−0.621471	−	0.783437i	$-0.713465\pi$
$239$	−4592.48			−1.24294			−0.621471	+	0.783437i	$0.713465\pi$
$240$		0			0
$241$	1566.85	−	1566.85i	0.418796	−	0.418796i	−0.465993	−	0.884789i	$-0.654303\pi$
$241$	1566.85	−	1566.85i	0.418796	−	0.418796i	0.884789	+	0.465993i	$0.154303\pi$
$242$		0			0
$243$	1376.60	−	1376.60i	0.363411	−	0.363411i
$244$		0			0
$245$	685.085	+	685.085i	0.178647	+	0.178647i
$246$		0			0
$247$			2842.50i			0.732243i
$248$		0			0
$249$	−507.837	−	507.837i	−0.129248	−	0.129248i
$250$		0			0
$251$	1441.62			0.362527			0.181263	−	0.983435i	$-0.441981\pi$
$251$	1441.62			0.362527			0.181263	+	0.983435i	$0.441981\pi$
$252$		0			0
$253$		−	4742.96i		−	1.17861i
$254$		0			0
$255$	978.891	+	815.851i	0.240394	+	0.200355i
$256$		0			0
$257$			3232.05i			0.784474i	0.919864	+	0.392237i	$0.128299\pi$
$257$			3232.05i			0.784474i	−0.919864	+	0.392237i	$0.871701\pi$
$258$		0			0
$259$	5512.45			1.32250
$260$		0			0
$261$	2719.53	+	2719.53i	0.644961	+	0.644961i
$262$		0			0
$263$		−	7437.71i		−	1.74384i	−0.489651	−	0.871918i	$-0.662876\pi$
$263$		−	7437.71i		−	1.74384i	0.489651	−	0.871918i	$-0.337124\pi$
$264$		0			0
$265$	−8669.45	−	8669.45i	−2.00966	−	2.00966i
$266$		0			0
$267$	145.402	−	145.402i	0.0333276	−	0.0333276i
$268$		0			0
$269$	141.374	−	141.374i	0.0320436	−	0.0320436i	−0.690903	−	0.722947i	$-0.742787\pi$
$269$	141.374	−	141.374i	0.0320436	−	0.0320436i	0.722947	+	0.690903i	$0.242787\pi$
$270$		0			0
$271$	−4326.06			−0.969702			−0.484851	−	0.874597i	$-0.661126\pi$
$271$	−4326.06			−0.969702			−0.484851	+	0.874597i	$0.661126\pi$
$272$		0			0
$273$	−351.069			−0.0778304
$274$		0			0
$275$	−7599.03	+	7599.03i	−1.66632	+	1.66632i
$276$		0			0
$277$	−2535.63	+	2535.63i	−0.550005	+	0.550005i	−0.926442	−	0.376437i	$-0.877149\pi$
$277$	−2535.63	+	2535.63i	−0.550005	+	0.550005i	0.376437	+	0.926442i	$0.377149\pi$
$278$		0			0
$279$	−1925.27	−	1925.27i	−0.413128	−	0.413128i
$280$		0			0
$281$		−	3975.41i		−	0.843962i	−0.906605	−	0.421981i	$-0.861335\pi$
$281$		−	3975.41i		−	0.843962i	0.906605	−	0.421981i	$-0.138665\pi$
$282$		0			0
$283$	2650.52	+	2650.52i	0.556738	+	0.556738i	0.928377	−	0.371639i	$-0.121204\pi$
$283$	2650.52	+	2650.52i	0.556738	+	0.556738i	−0.371639	+	0.928377i	$0.621204\pi$
$284$		0			0
$285$	2710.82			0.563422
$286$		0			0
$287$		−	7937.86i		−	1.63260i
$288$		0			0
$289$	−885.319	−	4832.57i	−0.180199	−	0.983630i
$290$		0			0
$291$		−	9.56934i		−	0.00192771i
$292$		0			0
$293$	−6632.00			−1.32234			−0.661170	−	0.750236i	$-0.729940\pi$
$293$	−6632.00			−1.32234			−0.661170	+	0.750236i	$0.729940\pi$
$294$		0			0
$295$	4175.08	+	4175.08i	0.824009	+	0.824009i
$296$		0			0
$297$			2060.91i			0.402647i
$298$		0			0
$299$	−1532.21	−	1532.21i	−0.296354	−	0.296354i
$300$		0			0
$301$	287.375	−	287.375i	0.0550300	−	0.0550300i
$302$		0			0
$303$	89.5916	−	89.5916i	0.0169865	−	0.0169865i
$304$		0			0
$305$	9748.99			1.83025
$306$		0			0
$307$	10072.6			1.87255			0.936277	−	0.351264i	$-0.114248\pi$
$307$	10072.6			1.87255			0.936277	+	0.351264i	$0.114248\pi$
$308$		0			0
$309$	−680.234	+	680.234i	−0.125233	+	0.125233i
$310$		0			0
$311$	−3563.62	+	3563.62i	−0.649756	+	0.649756i	−0.952934	−	0.303178i	$-0.901952\pi$
$311$	−3563.62	+	3563.62i	−0.649756	+	0.649756i	0.303178	+	0.952934i	$0.401952\pi$
$312$		0			0
$313$	4449.93	+	4449.93i	0.803594	+	0.803594i	0.983655	−	0.180061i	$-0.0576297\pi$
$313$	4449.93	+	4449.93i	0.803594	+	0.803594i	−0.180061	+	0.983655i	$0.557630\pi$
$314$		0			0
$315$		−	10128.0i		−	1.81157i
$316$		0			0
$317$	959.905	+	959.905i	0.170075	+	0.170075i	0.787012	−	0.616938i	$-0.211627\pi$
$317$	959.905	+	959.905i	0.170075	+	0.170075i	−0.616938	+	0.787012i	$0.711627\pi$
$318$		0			0
$319$	−6140.23			−1.07770
$320$		0			0
$321$			1449.10i			0.251966i
$322$		0			0
$323$	−8028.58	−	6691.37i	−1.38304	−	1.15269i
$324$		0			0
$325$			4909.72i			0.837976i
$326$		0			0
$327$	−920.277			−0.155631
$328$		0			0
$329$	−1142.76	−	1142.76i	−0.191497	−	0.191497i
$330$		0			0
$331$		−	4843.08i		−	0.804229i	−0.915589	−	0.402115i	$-0.868275\pi$
$331$		−	4843.08i		−	0.804229i	0.915589	−	0.402115i	$-0.131725\pi$
$332$		0			0
$333$	−5141.97	−	5141.97i	−0.846181	−	0.846181i
$334$		0			0
$335$	12783.2	−	12783.2i	2.08483	−	2.08483i
$336$		0			0
$337$	7489.09	−	7489.09i	1.21055	−	1.21055i	0.239709	−	0.970845i	$-0.422948\pi$
$337$	7489.09	−	7489.09i	1.21055	−	1.21055i	0.970845	−	0.239709i	$-0.0770522\pi$
$338$		0			0
$339$	729.276			0.116840
$340$		0			0
$341$	4346.92			0.690320
$342$		0			0
$343$	−4111.31	+	4111.31i	−0.647201	+	0.647201i
$344$		0			0
$345$	−1461.23	+	1461.23i	−0.228029	+	0.228029i
$346$		0			0
$347$	8294.92	+	8294.92i	1.28327	+	1.28327i	0.938795	+	0.344475i	$0.111943\pi$
$347$	8294.92	+	8294.92i	1.28327	+	1.28327i	0.344475	+	0.938795i	$0.388057\pi$
$348$		0			0
$349$			2041.99i			0.313196i	0.987662	+	0.156598i	$0.0500527\pi$
$349$			2041.99i			0.313196i	−0.987662	+	0.156598i	$0.949947\pi$
$350$		0			0
$351$	665.775	+	665.775i	0.101243	+	0.101243i
$352$		0			0
$353$	−4432.80			−0.668368			−0.334184	−	0.942508i	$-0.608461\pi$
$353$	−4432.80			−0.668368			−0.334184	+	0.942508i	$0.608461\pi$
$354$		0			0
$355$			20696.9i			3.09430i
$356$		0			0
$357$	826.433	−	991.587i	0.122519	−	0.147004i
$358$		0			0
$359$		−	6501.59i		−	0.955823i	−0.878408	−	0.477912i	$-0.841394\pi$
$359$		−	6501.59i		−	0.955823i	0.878408	−	0.477912i	$-0.158606\pi$
$360$		0			0
$361$	−15374.4			−2.24149
$362$		0			0
$363$	−269.559	−	269.559i	−0.0389757	−	0.0389757i
$364$		0			0
$365$		−	129.207i		−	0.0185288i
$366$		0			0
$367$	1010.18	+	1010.18i	0.143681	+	0.143681i	0.775288	−	0.631607i	$-0.217605\pi$
$367$	1010.18	+	1010.18i	0.143681	+	0.143681i	−0.631607	+	0.775288i	$0.717605\pi$
$368$		0			0
$369$	−7404.37	+	7404.37i	−1.04460	+	1.04460i
$370$		0			0
$371$	−8781.89	+	8781.89i	−1.22893	+	1.22893i
$372$		0			0
$373$	−197.385			−0.0274000			−0.0137000	−	0.999906i	$-0.504361\pi$
$373$	−197.385			−0.0274000			−0.0137000	+	0.999906i	$0.504361\pi$
$374$		0			0
$375$	2409.75			0.331837
$376$		0			0
$377$	−1983.60	+	1983.60i	−0.270983	+	0.270983i
$378$		0			0
$379$	−2494.51	+	2494.51i	−0.338085	+	0.338085i	−0.855646	−	0.517561i	$-0.826840\pi$
$379$	−2494.51	+	2494.51i	−0.338085	+	0.338085i	0.517561	+	0.855646i	$0.326840\pi$
$380$		0			0
$381$	197.174	+	197.174i	0.0265132	+	0.0265132i
$382$		0			0
$383$			8128.59i			1.08447i	0.840227	+	0.542235i	$0.182422\pi$
$383$			8128.59i			1.08447i	−0.840227	+	0.542235i	$0.817578\pi$
$384$		0			0
$385$	11433.6	+	11433.6i	1.51353	+	1.51353i
$386$		0			0
$387$	−536.123			−0.0704203
$388$		0			0
$389$			9656.29i			1.25860i	0.777164	+	0.629298i	$0.216657\pi$
$389$			9656.29i			1.25860i	−0.777164	+	0.629298i	$0.783343\pi$
$390$		0			0
$391$	7934.57	−	720.801i	1.02626	−	0.0932289i
$392$		0			0
$393$			369.194i			0.0473878i
$394$		0			0
$395$	10078.7			1.28383
$396$		0			0
$397$	−7763.36	−	7763.36i	−0.981440	−	0.981440i	0.0183907	−	0.999831i	$-0.494146\pi$
$397$	−7763.36	−	7763.36i	−0.981440	−	0.981440i	−0.999831	+	0.0183907i	$0.994146\pi$
$398$		0			0
$399$		−	2745.98i		−	0.344539i
$400$		0			0
$401$	−4785.33	−	4785.33i	−0.595930	−	0.595930i	0.343297	−	0.939227i	$-0.388456\pi$
$401$	−4785.33	−	4785.33i	−0.595930	−	0.595930i	−0.939227	+	0.343297i	$0.888456\pi$
$402$		0			0
$403$	1404.27	−	1404.27i	0.173577	−	0.173577i
$404$		0			0
$405$	−9124.64	+	9124.64i	−1.11952	+	1.11952i
$406$		0			0
$407$	11609.7			1.41393
$408$		0			0
$409$	−1865.88			−0.225579			−0.112789	−	0.993619i	$-0.535979\pi$
$409$	−1865.88			−0.225579			−0.112789	+	0.993619i	$0.535979\pi$
$410$		0			0
$411$	−380.611	+	380.611i	−0.0456792	+	0.0456792i
$412$		0			0
$413$	4229.23	−	4229.23i	0.503891	−	0.503891i
$414$		0			0
$415$	10685.9	+	10685.9i	1.26398	+	1.26398i
$416$		0			0
$417$			1008.97i			0.118487i
$418$		0			0
$419$	−8620.58	−	8620.58i	−1.00511	−	1.00511i	−0.999987	−	0.00512717i	$-0.998368\pi$
$419$	−8620.58	−	8620.58i	−1.00511	−	1.00511i	−0.00512717	−	0.999987i	$-0.501632\pi$
$420$		0			0
$421$	−527.717			−0.0610911			−0.0305455	−	0.999533i	$-0.509724\pi$
$421$	−527.717			−0.0610911			−0.0305455	+	0.999533i	$0.509724\pi$
$422$		0			0
$423$			2131.92i			0.245053i
$424$		0			0
$425$	−13867.4	−	11557.7i	−1.58274	−	1.31913i
$426$		0			0
$427$		−	9875.43i		−	1.11922i
$428$		0			0
$429$	−739.381			−0.0832113
$430$		0			0
$431$	11309.0	+	11309.0i	1.26389	+	1.26389i	0.949192	+	0.314697i	$0.101903\pi$
$431$	11309.0	+	11309.0i	1.26389	+	1.26389i	0.314697	+	0.949192i	$0.398097\pi$
$432$		0			0
$433$			4972.33i			0.551859i	0.961178	+	0.275930i	$0.0889857\pi$
$433$			4972.33i			0.551859i	−0.961178	+	0.275930i	$0.911014\pi$
$434$		0			0
$435$	1891.71	+	1891.71i	0.208507	+	0.208507i
$436$		0			0
$437$	11984.6	−	11984.6i	1.31190	−	1.31190i
$438$		0			0
$439$	−1777.24	+	1777.24i	−0.193219	+	0.193219i	−0.797085	−	0.603867i	$-0.793626\pi$
$439$	−1777.24	+	1777.24i	−0.193219	+	0.193219i	0.603867	+	0.797085i	$0.293626\pi$
$440$		0			0
$441$	−1294.66			−0.139797
$442$		0			0
$443$	−13068.0			−1.40153			−0.700766	−	0.713391i	$-0.747158\pi$
$443$	−13068.0			−1.40153			−0.700766	+	0.713391i	$0.747158\pi$
$444$		0			0
$445$	−3059.56	+	3059.56i	−0.325926	+	0.325926i
$446$		0			0
$447$	1462.60	−	1462.60i	0.154762	−	0.154762i
$448$		0			0
$449$	13217.4	+	13217.4i	1.38924	+	1.38924i	0.826914	+	0.562329i	$0.190094\pi$
$449$	13217.4	+	13217.4i	1.38924	+	1.38924i	0.562329	+	0.826914i	$0.309906\pi$
$450$		0			0
$451$		−	16717.8i		−	1.74548i
$452$		0			0
$453$	244.940	+	244.940i	0.0254046	+	0.0254046i
$454$		0			0
$455$	7387.21			0.761138
$456$		0			0
$457$		−	4435.14i		−	0.453976i	−0.973898	−	0.226988i	$-0.927112\pi$
$457$		−	4435.14i		−	0.453976i	0.973898	−	0.226988i	$-0.0728878\pi$
$458$		0			0
$459$	−3447.73	+	313.203i	−0.350602	+	0.0318498i
$460$		0			0
$461$			17021.9i			1.71972i	0.510534	+	0.859858i	$0.329448\pi$
$461$			17021.9i			1.71972i	−0.510534	+	0.859858i	$0.670552\pi$
$462$		0			0
$463$	6416.08			0.644018			0.322009	−	0.946737i	$-0.395642\pi$
$463$	6416.08			0.644018			0.322009	+	0.946737i	$0.395642\pi$
$464$		0			0
$465$	−1339.22	−	1339.22i	−0.133558	−	0.133558i
$466$		0			0
$467$		−	8877.84i		−	0.879695i	−0.898072	−	0.439847i	$-0.855033\pi$
$467$		−	8877.84i		−	0.879695i	0.898072	−	0.439847i	$-0.144967\pi$
$468$		0			0
$469$	−12948.9	−	12948.9i	−1.27490	−	1.27490i
$470$		0			0
$471$	−1966.49	+	1966.49i	−0.192380	+	0.192380i
$472$		0			0
$473$	605.236	−	605.236i	0.0588346	−	0.0588346i
$474$		0			0
$475$	−38402.6			−3.70954
$476$		0			0
$477$	16383.4			1.57263
$478$		0			0
$479$	−9242.01	+	9242.01i	−0.881583	+	0.881583i	−0.993696	−	0.112112i	$-0.964238\pi$
$479$	−9242.01	+	9242.01i	−0.881583	+	0.881583i	0.112112	+	0.993696i	$0.464238\pi$
$480$		0			0
$481$	3750.49	−	3750.49i	0.355526	−	0.355526i
$482$		0			0
$483$	1480.18	+	1480.18i	0.139442	+	0.139442i
$484$		0			0
$485$			201.358i			0.0188520i
$486$		0			0
$487$	9727.42	+	9727.42i	0.905116	+	0.905116i	0.995873	−	0.0907567i	$-0.0289286\pi$
$487$	9727.42	+	9727.42i	0.905116	+	0.905116i	−0.0907567	+	0.995873i	$0.528929\pi$
$488$		0			0
$489$	−1456.54			−0.134698
$490$		0			0
$491$			17308.0i			1.59083i	0.606063	+	0.795416i	$0.292748\pi$
$491$			17308.0i			1.59083i	−0.606063	+	0.795416i	$0.707252\pi$
$492$		0			0
$493$	−933.150	−	10272.1i	−0.0852474	−	0.938401i
$494$		0			0
$495$		−	21330.3i		−	1.93682i
$496$		0			0
$497$	20965.3			1.89220
$498$		0			0
$499$	−9639.66	−	9639.66i	−0.864790	−	0.864790i	0.127100	−	0.991890i	$-0.459433\pi$
$499$	−9639.66	−	9639.66i	−0.864790	−	0.864790i	−0.991890	+	0.127100i	$0.959433\pi$
$500$		0			0
$501$			2069.18i			0.184520i
$502$		0			0
$503$	3224.29	+	3224.29i	0.285813	+	0.285813i	0.835422	−	0.549609i	$-0.185223\pi$
$503$	3224.29	+	3224.29i	0.285813	+	0.285813i	−0.549609	+	0.835422i	$0.685223\pi$
$504$		0			0
$505$	−1885.19	+	1885.19i	−0.166118	+	0.166118i
$506$		0			0
$507$	1205.15	−	1205.15i	0.105568	−	0.105568i
$508$		0			0
$509$	7813.35			0.680394			0.340197	−	0.940354i	$-0.389506\pi$
$509$	7813.35			0.680394			0.340197	+	0.940354i	$0.389506\pi$
$510$		0			0
$511$	−130.883			−0.0113306
$512$		0			0
$513$	−5207.53	+	5207.53i	−0.448184	+	0.448184i
$514$		0			0
$515$	14313.5	−	14313.5i	1.22471	−	1.22471i
$516$		0			0
$517$	−2406.75	−	2406.75i	−0.204736	−	0.204736i
$518$		0			0
$519$		−	2194.33i		−	0.185588i
$520$		0			0
$521$	−15007.3	−	15007.3i	−1.26196	−	1.26196i	−0.950139	−	0.311825i	$-0.899060\pi$
$521$	−15007.3	−	15007.3i	−1.26196	−	1.26196i	−0.311825	−	0.950139i	$-0.600940\pi$
$522$		0			0
$523$	−626.147			−0.0523508			−0.0261754	−	0.999657i	$-0.508333\pi$
$523$	−626.147			−0.0523508			−0.0261754	+	0.999657i	$0.508333\pi$
$524$		0			0
$525$		−	4743.00i		−	0.394289i
$526$		0			0
$527$	660.615	+	7272.03i	0.0546050	+	0.601091i
$528$		0			0
$529$			753.202i			0.0619053i
$530$		0			0
$531$	−7889.99			−0.644814
$532$		0			0
$533$	−5400.66	−	5400.66i	−0.438891	−	0.438891i
$534$		0			0
$535$		−	30492.1i		−	2.46409i
$536$		0			0
$537$	702.818	+	702.818i	0.0564783	+	0.0564783i
$538$		0			0
$539$	1461.56	−	1461.56i	0.116797	−	0.116797i
$540$		0			0
$541$	3206.78	−	3206.78i	0.254843	−	0.254843i	−0.568110	−	0.822953i	$-0.692325\pi$
$541$	3206.78	−	3206.78i	0.254843	−	0.254843i	0.822953	+	0.568110i	$0.192325\pi$
$542$		0			0
$543$	359.242			0.0283914
$544$		0			0
$545$	19364.5			1.52199
$546$		0			0
$547$	−1147.84	+	1147.84i	−0.0897221	+	0.0897221i	−0.750543	−	0.660821i	$-0.770208\pi$
$547$	−1147.84	+	1147.84i	−0.0897221	+	0.0897221i	0.660821	+	0.750543i	$0.270208\pi$
$548$		0			0
$549$	−9211.72	+	9211.72i	−0.716114	+	0.716114i
$550$		0			0
$551$	−15515.2	−	15515.2i	−1.19958	−	1.19958i
$552$		0			0
$553$		−	10209.4i		−	0.785077i
$554$		0			0
$555$	−3576.75	−	3576.75i	−0.273558	−	0.273558i
$556$		0			0
$557$	8652.56			0.658206			0.329103	−	0.944294i	$-0.393254\pi$
$557$	8652.56			0.658206			0.329103	+	0.944294i	$0.393254\pi$
$558$		0			0
$559$		−	391.042i		−	0.0295873i
$560$		0			0
$561$	1740.53	−	2088.36i	0.130990	−	0.157167i
$562$		0			0
$563$			2090.36i			0.156480i	0.996935	+	0.0782401i	$0.0249301\pi$
$563$			2090.36i			0.156480i	−0.996935	+	0.0782401i	$0.975070\pi$
$564$		0			0
$565$	−15345.4			−1.14263
$566$		0			0
$567$	9242.99	+	9242.99i	0.684601	+	0.684601i
$568$		0			0
$569$			9561.09i			0.704432i	0.935919	+	0.352216i	$0.114572\pi$
$569$			9561.09i			0.704432i	−0.935919	+	0.352216i	$0.885428\pi$
$570$		0			0
$571$	10413.8	+	10413.8i	0.763230	+	0.763230i	0.976905	−	0.213675i	$-0.0685434\pi$
$571$	10413.8	+	10413.8i	0.763230	+	0.763230i	−0.213675	+	0.976905i	$0.568543\pi$
$572$		0			0
$573$	−1001.38	+	1001.38i	−0.0730076	+	0.0730076i
$574$		0			0
$575$	20700.4	−	20700.4i	1.50133	−	1.50133i
$576$		0			0
$577$	11605.8			0.837358			0.418679	−	0.908134i	$-0.362493\pi$
$577$	11605.8			0.837358			0.418679	+	0.908134i	$0.362493\pi$
$578$		0			0
$579$	−1215.48			−0.0872432
$580$		0			0
$581$	10824.5	−	10824.5i	0.772937	−	0.772937i
$582$		0			0
$583$	−18495.4	+	18495.4i	−1.31389	+	1.31389i
$584$		0			0
$585$	−6890.73	−	6890.73i	−0.487003	−	0.487003i
$586$		0			0
$587$			16866.9i			1.18598i	0.805209	+	0.592991i	$0.202053\pi$
$587$			16866.9i			1.18598i	−0.805209	+	0.592991i	$0.797947\pi$
$588$		0			0
$589$	10983.9	+	10983.9i	0.768390	+	0.768390i
$590$		0			0
$591$	−569.492			−0.0396375
$592$		0			0
$593$		−	16644.1i		−	1.15260i	−0.817238	−	0.576300i	$-0.804496\pi$
$593$		−	16644.1i		−	1.15260i	0.817238	−	0.576300i	$-0.195504\pi$
$594$		0			0
$595$	−17389.8	+	20865.0i	−1.19817	+	1.43762i
$596$		0			0
$597$		−	1614.12i		−	0.110656i
$598$		0			0
$599$	136.992			0.00934445			0.00467222	−	0.999989i	$-0.498513\pi$
$599$	136.992			0.00934445			0.00467222	+	0.999989i	$0.498513\pi$
$600$		0			0
$601$	10440.7	+	10440.7i	0.708626	+	0.708626i	0.966246	−	0.257620i	$-0.0829384\pi$
$601$	10440.7	+	10440.7i	0.708626	+	0.708626i	−0.257620	+	0.966246i	$0.582938\pi$
$602$		0			0
$603$			24157.3i			1.63145i
$604$		0			0
$605$	5672.07	+	5672.07i	0.381161	+	0.381161i
$606$		0			0
$607$	−10671.1	+	10671.1i	−0.713552	+	0.713552i	−0.967277	−	0.253724i	$-0.918344\pi$
$607$	−10671.1	+	10671.1i	−0.713552	+	0.713552i	0.253724	+	0.967277i	$0.418344\pi$
$608$		0			0
$609$	1916.24	−	1916.24i	0.127504	−	0.127504i
$610$		0			0
$611$	−1554.99			−0.102960
$612$		0			0
$613$	5239.98			0.345254			0.172627	−	0.984987i	$-0.444774\pi$
$613$	5239.98			0.345254			0.172627	+	0.984987i	$0.444774\pi$
$614$		0			0
$615$	−5150.48	+	5150.48i	−0.337703	+	0.337703i
$616$		0			0
$617$	−13028.9	+	13028.9i	−0.850122	+	0.850122i	−0.990148	−	0.140026i	$-0.955282\pi$
$617$	−13028.9	+	13028.9i	−0.850122	+	0.850122i	0.140026	+	0.990148i	$0.455282\pi$
$618$		0			0
$619$	−18854.4	−	18854.4i	−1.22427	−	1.22427i	−0.966101	−	0.258165i	$-0.916882\pi$
$619$	−18854.4	−	18854.4i	−1.22427	−	1.22427i	−0.258165	−	0.966101i	$-0.583118\pi$
$620$		0			0
$621$		−	5614.09i		−	0.362779i
$622$		0			0
$623$	3099.24	+	3099.24i	0.199307	+	0.199307i
$624$		0			0
$625$	−18512.5			−1.18480
$626$		0			0
$627$		−	5783.26i		−	0.368359i
$628$		0			0
$629$	1764.36	+	19422.0i	0.111843	+	1.23117i
$630$		0			0
$631$			11079.4i			0.698994i	0.936937	+	0.349497i	$0.113648\pi$
$631$			11079.4i			0.698994i	−0.936937	+	0.349497i	$0.886352\pi$
$632$		0			0
$633$	3561.77			0.223645
$634$		0			0
$635$	−4148.95	−	4148.95i	−0.259285	−	0.259285i
$636$		0			0
$637$		−	944.310i		−	0.0587362i
$638$		0			0
$639$	−19556.3	−	19556.3i	−1.21070	−	1.21070i
$640$		0			0
$641$	14869.0	−	14869.0i	0.916206	−	0.916206i	−0.0805445	−	0.996751i	$-0.525666\pi$
$641$	14869.0	−	14869.0i	0.916206	−	0.916206i	0.996751	+	0.0805445i	$0.0256659\pi$
$642$		0			0
$643$	−943.852	+	943.852i	−0.0578879	+	0.0578879i	−0.735458	−	0.677570i	$-0.763033\pi$
$643$	−943.852	+	943.852i	−0.0578879	+	0.0578879i	0.677570	+	0.735458i	$0.263033\pi$
$644$		0			0
$645$	−372.927			−0.0227658
$646$		0			0
$647$	1436.96			0.0873149			0.0436575	−	0.999047i	$-0.486099\pi$
$647$	1436.96			0.0873149			0.0436575	+	0.999047i	$0.486099\pi$
$648$		0			0
$649$	8907.11	−	8907.11i	0.538728	−	0.538728i
$650$		0			0
$651$	−1356.59	+	1356.59i	−0.0816724	+	0.0816724i
$652$		0			0
$653$	7507.79	+	7507.79i	0.449927	+	0.449927i	0.895330	−	0.445403i	$-0.146940\pi$
$653$	7507.79	+	7507.79i	0.449927	+	0.449927i	−0.445403	+	0.895330i	$0.646940\pi$
$654$		0			0
$655$		−	7768.60i		−	0.463426i
$656$		0			0
$657$	122.087	+	122.087i	0.00724971	+	0.00724971i
$658$		0			0
$659$	31072.9			1.83677			0.918384	−	0.395691i	$-0.129495\pi$
$659$	31072.9			1.83677			0.918384	+	0.395691i	$0.129495\pi$
$660$		0			0
$661$		−	45.5354i		−	0.00267946i	−0.999999	−	0.00133973i	$-0.999574\pi$
$661$		−	45.5354i		−	0.00267946i	0.999999	−	0.00133973i	$-0.000426449\pi$
$662$		0			0
$663$	−112.366	−	1236.92i	−0.00658210	−	0.0724556i
$664$		0			0
$665$			57781.0i			3.36940i
$666$		0			0
$667$	16726.5			0.970993
$668$		0			0
$669$	−631.765	−	631.765i	−0.0365104	−	0.0365104i
$670$		0			0
$671$		−	20798.5i		−	1.19660i
$672$		0			0
$673$	3841.90	+	3841.90i	0.220051	+	0.220051i	0.808520	−	0.588469i	$-0.200269\pi$
$673$	3841.90	+	3841.90i	0.220051	+	0.220051i	−0.588469	+	0.808520i	$0.700269\pi$
$674$		0			0
$675$	−8994.72	+	8994.72i	−0.512899	+	0.512899i
$676$		0			0
$677$	−13901.7	+	13901.7i	−0.789195	+	0.789195i	−0.981362	−	0.192167i	$-0.938449\pi$
$677$	−13901.7	+	13901.7i	−0.789195	+	0.789195i	0.192167	+	0.981362i	$0.438449\pi$
$678$		0			0
$679$	203.970			0.0115282
$680$		0			0
$681$	−372.937			−0.0209853
$682$		0			0
$683$	2843.20	−	2843.20i	0.159286	−	0.159286i	−0.622964	−	0.782250i	$-0.714072\pi$
$683$	2843.20	−	2843.20i	0.159286	−	0.159286i	0.782250	+	0.622964i	$0.214072\pi$
$684$		0			0
$685$	8008.82	−	8008.82i	0.446717	−	0.446717i
$686$		0			0
$687$	3098.39	+	3098.39i	0.172069	+	0.172069i
$688$		0			0
$689$			11949.8i			0.660744i
$690$		0			0
$691$	7663.83	+	7663.83i	0.421919	+	0.421919i	0.885864	−	0.463945i	$-0.153567\pi$
$691$	7663.83	+	7663.83i	0.421919	+	0.421919i	−0.463945	+	0.885864i	$0.653567\pi$
$692$		0			0
$693$	−21606.9			−1.18439
$694$		0			0
$695$		−	21230.7i		−	1.15874i
$696$		0			0
$697$	27967.4	−	2540.65i	1.51986	−	0.138069i
$698$		0			0
$699$			1639.36i			0.0887073i
$700$		0			0
$701$	24703.2			1.33099			0.665497	−	0.746400i	$-0.268220\pi$
$701$	24703.2			1.33099			0.665497	+	0.746400i	$0.268220\pi$
$702$		0			0
$703$	29335.5	+	29335.5i	1.57384	+	1.57384i
$704$		0			0
$705$			1482.96i			0.0792219i
$706$		0			0
$707$	1909.64	+	1909.64i	0.101583	+	0.101583i
$708$		0			0
$709$	−16359.8	+	16359.8i	−0.866578	+	0.866578i	−0.992092	−	0.125514i	$-0.959942\pi$
$709$	−16359.8	+	16359.8i	−0.866578	+	0.866578i	0.125514	+	0.992092i	$0.459942\pi$
$710$		0			0
$711$	−9523.24	+	9523.24i	−0.502320	+	0.502320i
$712$		0			0
$713$	−11841.4			−0.621967
$714$		0			0
$715$	15558.1			0.813761
$716$		0			0
$717$	3018.48	−	3018.48i	0.157221	−	0.157221i
$718$		0			0
$719$	−22148.4	+	22148.4i	−1.14881	+	1.14881i	−0.162029	+	0.986786i	$0.551804\pi$
$719$	−22148.4	+	22148.4i	−1.14881	+	1.14881i	−0.986786	+	0.162029i	$0.948196\pi$
$720$		0			0
$721$	−14499.1	−	14499.1i	−0.748927	−	0.748927i
$722$		0			0
$723$			2059.67i			0.105948i
$724$		0			0
$725$	−26798.7	−	26798.7i	−1.37280	−	1.37280i
$726$		0			0
$727$	14112.1			0.719927			0.359964	−	0.932966i	$-0.382789\pi$
$727$	14112.1			0.719927			0.359964	+	0.932966i	$0.382789\pi$
$728$		0			0
$729$		−	16004.0i		−	0.813088i
$730$		0			0
$731$	1104.49	+	920.529i	0.0558837	+	0.0465759i
$732$		0			0
$733$		−	6656.84i		−	0.335438i	−0.985835	−	0.167719i	$-0.946360\pi$
$733$		−	6656.84i		−	0.335438i	0.985835	−	0.167719i	$-0.0536401\pi$
$734$		0			0
$735$	−900.565			−0.0451943
$736$		0			0
$737$	−27271.5	−	27271.5i	−1.36304	−	1.36304i
$738$		0			0
$739$			22315.3i			1.11080i	0.831583	+	0.555401i	$0.187435\pi$
$739$			22315.3i			1.11080i	−0.831583	+	0.555401i	$0.812565\pi$
$740$		0			0
$741$	−1868.28	−	1868.28i	−0.0926219	−	0.0926219i
$742$		0			0
$743$	1762.71	−	1762.71i	0.0870359	−	0.0870359i	−0.662248	−	0.749284i	$-0.730398\pi$
$743$	1762.71	−	1762.71i	0.0870359	−	0.0870359i	0.749284	+	0.662248i	$0.230398\pi$
$744$		0			0
$745$	−30776.1	+	30776.1i	−1.51349	+	1.51349i
$746$		0			0
$747$	−20194.0			−0.989104
$748$		0			0
$749$	−30887.5			−1.50682
$750$		0			0
$751$	−10009.2	+	10009.2i	−0.486339	+	0.486339i	−0.907149	−	0.420810i	$-0.861746\pi$
$751$	−10009.2	+	10009.2i	−0.486339	+	0.486339i	0.420810	+	0.907149i	$0.361746\pi$
$752$		0			0
$753$	−947.526	+	947.526i	−0.0458563	+	0.0458563i
$754$		0			0
$755$	−5154.04	−	5154.04i	−0.248443	−	0.248443i
$756$		0			0
$757$			25115.6i			1.20587i	0.797792	+	0.602933i	$0.206001\pi$
$757$			25115.6i			1.20587i	−0.797792	+	0.602933i	$0.793999\pi$
$758$		0			0
$759$	3117.38	+	3117.38i	0.149083	+	0.149083i
$760$		0			0
$761$	−4006.26			−0.190837			−0.0954184	−	0.995437i	$-0.530419\pi$
$761$	−4006.26			−0.190837			−0.0954184	+	0.995437i	$0.530419\pi$
$762$		0			0
$763$		−	19615.6i		−	0.930713i
$764$		0			0
$765$	35683.8	−	3241.63i	1.68647	−	0.153204i
$766$		0			0
$767$		−	5754.87i		−	0.270921i
$768$		0			0
$769$	−32308.1			−1.51503			−0.757517	−	0.652816i	$-0.773588\pi$
$769$	−32308.1			−1.51503			−0.757517	+	0.652816i	$0.773588\pi$
$770$		0			0
$771$	−2124.31	−	2124.31i	−0.0992286	−	0.0992286i
$772$		0			0
$773$		−	24553.2i		−	1.14245i	−0.820792	−	0.571227i	$-0.806468\pi$
$773$		−	24553.2i		−	1.14245i	0.820792	−	0.571227i	$-0.193532\pi$
$774$		0			0
$775$	18971.9	+	18971.9i	0.879342	+	0.879342i
$776$		0			0
$777$	−3623.14	+	3623.14i	−0.167284	+	0.167284i
$778$		0			0
$779$	42242.7	−	42242.7i	1.94288	−	1.94288i
$780$		0			0
$781$	44154.7			2.02302
$782$		0			0
$783$	−7267.99			−0.331720
$784$		0			0
$785$	41378.9	−	41378.9i	1.88137	−	1.88137i
$786$		0			0
$787$	21062.3	−	21062.3i	0.953990	−	0.953990i	−0.0449975	−	0.998987i	$-0.514328\pi$
$787$	21062.3	−	21062.3i	0.953990	−	0.953990i	0.998987	+	0.0449975i	$0.0143280\pi$
$788$		0			0
$789$	4888.55	+	4888.55i	0.220579	+	0.220579i
$790$		0			0
$791$			15544.5i			0.698733i
$792$		0			0
$793$	−6718.93	−	6718.93i	−0.300878	−	0.300878i
$794$		0			0
$795$	11396.3			0.508407
$796$		0			0
$797$			8510.79i			0.378253i	0.981953	+	0.189127i	$0.0605656\pi$
$797$			8510.79i			0.378253i	−0.981953	+	0.189127i	$0.939434\pi$
$798$		0			0
$799$	3660.52	−	4392.04i	0.162078	−	0.194467i
$800$		0			0
$801$		−	5781.89i		−	0.255047i
$802$		0			0
$803$	−275.651			−0.0121139
$804$		0			0
$805$	−31146.0	−	31146.0i	−1.36367	−	1.36367i
$806$		0			0
$807$			185.840i			0.00810643i
$808$		0			0
$809$	2049.52	+	2049.52i	0.0890694	+	0.0890694i	0.750238	−	0.661168i	$-0.229939\pi$
$809$	2049.52	+	2049.52i	0.0890694	+	0.0890694i	−0.661168	+	0.750238i	$0.729939\pi$
$810$		0			0
$811$	5122.57	−	5122.57i	0.221797	−	0.221797i	−0.587458	−	0.809255i	$-0.699871\pi$
$811$	5122.57	−	5122.57i	0.221797	−	0.221797i	0.809255	+	0.587458i	$0.199871\pi$
$812$		0			0
$813$	2843.36	−	2843.36i	0.122658	−	0.122658i
$814$		0			0
$815$	30648.6			1.31727
$816$		0			0
$817$	3058.63			0.130977
$818$		0			0
$819$	−6980.10	+	6980.10i	−0.297808	+	0.297808i
$820$		0			0
$821$	−14609.4	+	14609.4i	−0.621038	+	0.621038i	−0.945797	−	0.324759i	$-0.894717\pi$
$821$	−14609.4	+	14609.4i	−0.621038	+	0.621038i	0.324759	+	0.945797i	$0.394717\pi$
$822$		0			0
$823$	−30127.7	−	30127.7i	−1.27605	−	1.27605i	−0.942861	−	0.333185i	$-0.891877\pi$
$823$	−30127.7	−	30127.7i	−1.27605	−	1.27605i	−0.333185	−	0.942861i	$-0.608123\pi$
$824$		0			0
$825$		−	9989.15i		−	0.421548i
$826$		0			0
$827$	−3523.20	−	3523.20i	−0.148142	−	0.148142i	0.629145	−	0.777288i	$-0.283405\pi$
$827$	−3523.20	−	3523.20i	−0.148142	−	0.148142i	−0.777288	+	0.629145i	$0.783405\pi$
$828$		0			0
$829$	−10944.0			−0.458505			−0.229253	−	0.973367i	$-0.573628\pi$
$829$	−10944.0			−0.458505			−0.229253	+	0.973367i	$0.573628\pi$
$830$		0			0
$831$		−	3333.17i		−	0.139141i
$832$		0			0
$833$	2667.18	+	2222.95i	0.110939	+	0.0924616i
$834$		0			0
$835$		−	43539.8i		−	1.80450i
$836$		0			0
$837$	5145.31			0.212483
$838$		0			0
$839$	2914.60	+	2914.60i	0.119932	+	0.119932i	0.764526	−	0.644593i	$-0.222973\pi$
$839$	2914.60	+	2914.60i	0.119932	+	0.119932i	−0.644593	+	0.764526i	$0.722973\pi$
$840$		0			0
$841$			2734.88i			0.112136i
$842$		0			0
$843$	2612.90	+	2612.90i	0.106753	+	0.106753i
$844$		0			0
$845$	−25358.9	+	25358.9i	−1.03239	+	1.03239i
$846$		0			0
$847$	5745.63	−	5745.63i	0.233084	−	0.233084i
$848$		0			0
$849$	−3484.19			−0.140844
$850$		0			0
$851$	−31625.7			−1.27393
$852$		0			0
$853$	20986.4	−	20986.4i	0.842393	−	0.842393i	−0.146777	−	0.989170i	$-0.546890\pi$
$853$	20986.4	−	20986.4i	0.842393	−	0.842393i	0.989170	+	0.146777i	$0.0468899\pi$
$854$		0			0
$855$	53897.7	−	53897.7i	2.15586	−	2.15586i
$856$		0			0
$857$	2895.76	+	2895.76i	0.115423	+	0.115423i	0.762459	−	0.647036i	$-0.223992\pi$
$857$	2895.76	+	2895.76i	0.115423	+	0.115423i	−0.647036	+	0.762459i	$0.723992\pi$
$858$		0			0
$859$		−	25522.7i		−	1.01376i	−0.862016	−	0.506882i	$-0.830798\pi$
$859$		−	25522.7i		−	1.01376i	0.862016	−	0.506882i	$-0.169202\pi$
$860$		0			0
$861$	5217.28	+	5217.28i	0.206509	+	0.206509i
$862$		0			0
$863$	−45429.5			−1.79193			−0.895966	−	0.444122i	$-0.853516\pi$
$863$	−45429.5			−1.79193			−0.895966	+	0.444122i	$0.853516\pi$
$864$		0			0
$865$			46173.1i			1.81495i
$866$		0			0
$867$	3758.17	+	2594.39i	0.147214	+	0.101627i
$868$		0			0
$869$		−	21501.8i		−	0.839355i
$870$		0			0
$871$	−17620.1			−0.685458
$872$		0			0
$873$	−190.261	−	190.261i	−0.00737614	−	0.00737614i
$874$		0			0
$875$			51363.6i			1.98447i
$876$		0			0
$877$	9694.15	+	9694.15i	0.373259	+	0.373259i	0.868663	−	0.495404i	$-0.164980\pi$
$877$	9694.15	+	9694.15i	0.373259	+	0.373259i	−0.495404	+	0.868663i	$0.664980\pi$
$878$		0			0
$879$	4358.98	−	4358.98i	0.167264	−	0.167264i
$880$		0			0
$881$	−13839.3	+	13839.3i	−0.529236	+	0.529236i	−0.920344	−	0.391109i	$-0.872092\pi$
$881$	−13839.3	+	13839.3i	−0.529236	+	0.529236i	0.391109	+	0.920344i	$0.372092\pi$
$882$		0			0
$883$	−17155.0			−0.653809			−0.326904	−	0.945057i	$-0.606006\pi$
$883$	−17155.0			−0.653809			−0.326904	+	0.945057i	$0.606006\pi$
$884$		0			0
$885$	−5488.27			−0.208459
$886$		0			0
$887$	−8173.71	+	8173.71i	−0.309410	+	0.309410i	−0.844680	−	0.535271i	$-0.820210\pi$
$887$	−8173.71	+	8173.71i	−0.309410	+	0.309410i	0.535271	+	0.844680i	$0.320210\pi$
$888$		0			0
$889$	−4202.76	+	4202.76i	−0.158556	+	0.158556i
$890$		0			0
$891$	19466.5	+	19466.5i	0.731932	+	0.731932i
$892$		0			0
$893$		−	12162.8i		−	0.455781i
$894$		0			0
$895$	−14788.7	−	14788.7i	−0.552326	−	0.552326i
$896$		0			0
$897$	2014.13			0.0749721
$898$		0			0
$899$			15329.8i			0.568719i
$900$		0			0
$901$	−33752.0	−	28130.4i	−1.24799	−	1.04013i
$902$		0			0
$903$			377.763i			0.0139216i
$904$		0			0
$905$	−7559.17			−0.277652
$906$		0			0
$907$	2300.96	+	2300.96i	0.0842360	+	0.0842360i	0.747969	−	0.663733i	$-0.231029\pi$
$907$	2300.96	+	2300.96i	0.0842360	+	0.0842360i	−0.663733	+	0.747969i	$0.731029\pi$
$908$		0			0
$909$		−	3562.59i		−	0.129993i
$910$		0			0
$911$	30666.0	+	30666.0i	1.11527	+	1.11527i	0.992426	+	0.122844i	$0.0392016\pi$
$911$	30666.0	+	30666.0i	1.11527	+	1.11527i	0.122844	+	0.992426i	$0.460798\pi$
$912$		0			0
$913$	22797.3	−	22797.3i	0.826375	−	0.826375i
$914$		0			0
$915$	−6407.67	+	6407.67i	−0.231509	+	0.231509i
$916$		0			0
$917$	−7869.35			−0.283390
$918$		0			0
$919$	−33476.2			−1.20161			−0.600804	−	0.799397i	$-0.705153\pi$
$919$	−33476.2			−1.20161			−0.600804	+	0.799397i	$0.705153\pi$
$920$		0			0
$921$	−6620.37	+	6620.37i	−0.236861	+	0.236861i
$922$		0			0
$923$	14264.1	−	14264.1i	0.508678	−	0.508678i
$924$		0			0
$925$	50669.7	+	50669.7i	1.80109	+	1.80109i
$926$		0			0
$927$			27049.4i			0.958379i
$928$		0			0
$929$	8073.56	+	8073.56i	0.285129	+	0.285129i	0.835151	−	0.550021i	$-0.185380\pi$
$929$	8073.56	+	8073.56i	0.285129	+	0.285129i	−0.550021	+	0.835151i	$0.685380\pi$
$930$		0			0
$931$	7386.17			0.260013
$932$		0			0
$933$		−	4684.48i		−	0.164376i
$934$		0			0
$935$	−36624.4	+	43943.4i	−1.28101	+	1.53701i
$936$		0			0
$937$		−	55983.9i		−	1.95188i	−0.218030	−	0.975942i	$-0.569963\pi$
$937$		−	55983.9i		−	1.95188i	0.218030	−	0.975942i	$-0.430037\pi$
$938$		0			0
$939$	−5849.56			−0.203294
$940$		0			0
$941$	−10059.4	−	10059.4i	−0.348488	−	0.348488i	0.511058	−	0.859546i	$-0.329254\pi$
$941$	−10059.4	−	10059.4i	−0.348488	−	0.348488i	−0.859546	+	0.511058i	$0.829254\pi$
$942$		0			0
$943$			45540.6i			1.57265i
$944$		0			0
$945$	13533.6	+	13533.6i	0.465869	+	0.465869i
$946$		0			0
$947$	31125.6	−	31125.6i	1.06805	−	1.06805i	0.0705438	−	0.997509i	$-0.477527\pi$
$947$	31125.6	−	31125.6i	1.06805	−	1.06805i	0.997509	−	0.0705438i	$-0.0224734\pi$
$948$		0			0
$949$	−89.0487	+	89.0487i	−0.00304599	+	0.00304599i
$950$		0			0
$951$	−1261.82			−0.0430257
$952$		0			0
$953$	−23485.2			−0.798279			−0.399140	−	0.916890i	$-0.630691\pi$
$953$	−23485.2			−0.798279			−0.399140	+	0.916890i	$0.630691\pi$
$954$		0			0
$955$	21071.1	−	21071.1i	0.713974	−	0.713974i
$956$		0			0
$957$	4035.76	−	4035.76i	0.136319	−	0.136319i
$958$		0			0
$959$	−8112.69	−	8112.69i	−0.273172	−	0.273172i
$960$		0			0
$961$			18938.4i			0.635708i
$962$		0			0
$963$	28811.7	+	28811.7i	0.964115	+	0.964115i
$964$		0			0
$965$	25576.3			0.853190
$966$		0			0
$967$		−	44831.1i		−	1.49087i	−0.666578	−	0.745435i	$-0.732242\pi$
$967$		−	44831.1i		−	1.49087i	0.666578	−	0.745435i	$-0.267758\pi$
$968$		0			0
$969$	9674.91	−	878.899i	0.320746	−	0.0291376i
$970$		0			0
$971$		−	956.984i		−	0.0316283i	−0.999875	−	0.0158141i	$-0.994966\pi$
$971$		−	956.984i		−	0.0316283i	0.999875	−	0.0158141i	$-0.00503401\pi$
$972$		0			0
$973$	−21506.0			−0.708584
$974$		0			0
$975$	−3226.98	−	3226.98i	−0.105996	−	0.105996i
$976$		0			0
$977$			7036.77i			0.230426i	0.993341	+	0.115213i	$0.0367551\pi$
$977$			7036.77i			0.230426i	−0.993341	+	0.115213i	$0.963245\pi$
$978$		0			0
$979$	6527.25	+	6527.25i	0.213087	+	0.213087i
$980$		0			0
$981$	−18297.3	+	18297.3i	−0.595503	+	0.595503i
$982$		0			0
$983$	−15404.5	+	15404.5i	−0.499824	+	0.499824i	−0.911383	−	0.411559i	$-0.864984\pi$
$983$	−15404.5	+	15404.5i	−0.499824	+	0.499824i	0.411559	+	0.911383i	$0.364984\pi$
$984$		0			0
$985$	11983.3			0.387633
$986$		0			0
$987$	1502.19			0.0484451
$988$		0			0
$989$	−1648.71	+	1648.71i	−0.0530091	+	0.0530091i
$990$		0			0
$991$	36592.3	−	36592.3i	1.17295	−	1.17295i	0.191447	−	0.981503i	$-0.438682\pi$
$991$	36592.3	−	36592.3i	1.17295	−	1.17295i	0.981503	−	0.191447i	$-0.0613179\pi$
$992$		0			0
$993$	3183.19	+	3183.19i	0.101728	+	0.101728i
$994$		0			0
$995$			33964.4i			1.08216i
$996$		0			0
$997$	22009.5	+	22009.5i	0.699146	+	0.699146i	0.964226	−	0.265080i	$-0.0853984\pi$
$997$	22009.5	+	22009.5i	0.699146	+	0.699146i	−0.265080	+	0.964226i	$0.585398\pi$
$998$		0			0
$999$	13742.0			0.435213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.k.b.89.3	yes	14
4.3	odd	2		272.4.o.f.225.5		14
17.8	even	8		2312.4.a.l.1.9		14
17.9	even	8		2312.4.a.l.1.6		14
17.13	even	4	inner	136.4.k.b.81.3	✓	14
68.47	odd	4		272.4.o.f.81.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.k.b.81.3	✓	14	17.13	even	4	inner
136.4.k.b.89.3	yes	14	1.1	even	1	trivial
272.4.o.f.81.5		14	68.47	odd	4
272.4.o.f.225.5		14	4.3	odd	2
2312.4.a.l.1.6		14	17.9	even	8
2312.4.a.l.1.9		14	17.8	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)

\(f(q)\)	\(=\)	\(q+(-0.657265 + 0.657265i) q^{3} +(13.8302 - 13.8302i) q^{5} +(-14.0096 - 14.0096i) q^{7} +26.1360i q^{9} +O(q^{10})\)	\(q+(-0.657265 + 0.657265i) q^{3} +(13.8302 - 13.8302i) q^{5} +(-14.0096 - 14.0096i) q^{7} +26.1360i q^{9} +(-29.5053 - 29.5053i) q^{11} -19.0633 q^{13} +18.1802i q^{15} +(44.8758 - 53.8438i) q^{17} -149.109i q^{19} +18.4160 q^{21} +(80.3748 + 80.3748i) q^{23} -257.548i q^{25} +(-34.9244 - 34.9244i) q^{27} +(104.053 - 104.053i) q^{29} +(-73.6635 + 73.6635i) q^{31} +38.7856 q^{33} -387.510 q^{35} +(-196.739 + 196.739i) q^{37} +(12.5296 - 12.5296i) q^{39} +(283.302 + 283.302i) q^{41} +20.5128i q^{43} +(361.466 + 361.466i) q^{45} +81.5700 q^{47} +49.5355i q^{49} +(5.89436 + 64.8850i) q^{51} -626.850i q^{53} -816.127 q^{55} +(98.0038 + 98.0038i) q^{57} +301.882i q^{59} +(352.453 + 352.453i) q^{61} +(366.154 - 366.154i) q^{63} +(-263.649 + 263.649i) q^{65} +924.294 q^{67} -105.655 q^{69} +(-748.251 + 748.251i) q^{71} +(4.67121 - 4.67121i) q^{73} +(169.277 + 169.277i) q^{75} +826.712i q^{77} +(364.373 + 364.373i) q^{79} -659.763 q^{81} +772.652i q^{83} +(-124.029 - 1365.31i) q^{85} +136.781i q^{87} -221.223 q^{89} +(267.068 + 267.068i) q^{91} -96.8328i q^{93} +(-2062.20 - 2062.20i) q^{95} +(-7.27967 + 7.27967i) q^{97} +(771.150 - 771.150i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7}+O(q^{10}) \) 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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