LMFDB - Embedded newform 136.4.k.a.81.4

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} + 142x^{12} + 7785x^{10} + 208489x^{8} + 2822686x^{6} + 17977041x^{4} + 45020416x^{2} + 31719424 $ x^14 + 142x^12 + 7785x^10 + 208489x^8 + 2822686x^6 + 17977041x^4 + 45020416x^2 + 31719424
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.4
Root			$1.06483i$ of defining polynomial
Character	$\chi$	$=$	136.81
Dual form			136.4.k.a.89.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.06483 - 1.06483i) q^{3} +(-0.550686 - 0.550686i) q^{5} +(-11.3140 + 11.3140i) q^{7} -24.7323i q^{9} +O(q^{10})$	\(q+(-1.06483 - 1.06483i) q^{3} +(-0.550686 - 0.550686i) q^{5} +(-11.3140 + 11.3140i) q^{7} -24.7323i q^{9} +(-5.56218 + 5.56218i) q^{11} -64.3974 q^{13} +1.17278i q^{15} +(-58.0103 + 39.3421i) q^{17} -9.88432i q^{19} +24.0950 q^{21} +(-134.915 + 134.915i) q^{23} -124.393i q^{25} +(-55.0862 + 55.0862i) q^{27} +(-148.529 - 148.529i) q^{29} +(4.85251 + 4.85251i) q^{31} +11.8456 q^{33} +12.4609 q^{35} +(65.3789 + 65.3789i) q^{37} +(68.5724 + 68.5724i) q^{39} +(225.441 - 225.441i) q^{41} +227.690i q^{43} +(-13.6197 + 13.6197i) q^{45} +240.883 q^{47} +86.9871i q^{49} +(103.664 + 19.8785i) q^{51} -247.863i q^{53} +6.12603 q^{55} +(-10.5251 + 10.5251i) q^{57} -321.574i q^{59} +(313.816 - 313.816i) q^{61} +(279.821 + 279.821i) q^{63} +(35.4627 + 35.4627i) q^{65} -17.8872 q^{67} +287.323 q^{69} +(551.226 + 551.226i) q^{71} +(406.882 + 406.882i) q^{73} +(-132.458 + 132.458i) q^{75} -125.861i q^{77} +(-346.988 + 346.988i) q^{79} -550.456 q^{81} -1282.66i q^{83} +(53.6106 + 10.2803i) q^{85} +316.318i q^{87} -187.071 q^{89} +(728.591 - 728.591i) q^{91} -10.3342i q^{93} +(-5.44315 + 5.44315i) q^{95} +(41.7026 + 41.7026i) q^{97} +(137.565 + 137.565i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7}+O(q^{10}) $ 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7	$ 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7} + 16 q^{11} + 72 q^{13} - 40 q^{17} - 60 q^{21} + 246 q^{23} + 572 q^{27} + 260 q^{29} + 566 q^{31} - 904 q^{33} - 804 q^{35} - 28 q^{37} + 476 q^{39} - 786 q^{41} - 604 q^{45} + 448 q^{47} - 380 q^{51} + 1612 q^{55} + 1004 q^{57} + 660 q^{61} - 2250 q^{63} - 796 q^{65} - 284 q^{67} - 2532 q^{69} + 326 q^{71} + 730 q^{73} - 864 q^{75} + 342 q^{79} - 950 q^{81} + 4148 q^{85} - 4516 q^{89} - 3112 q^{91} + 3356 q^{95} - 1194 q^{97} + 2876 q^{99}+O(q^{100}) $ 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7 + 16 * q^11 + 72 * q^13 - 40 * q^17 - 60 * q^21 + 246 * q^23 + 572 * q^27 + 260 * q^29 + 566 * q^31 - 904 * q^33 - 804 * q^35 - 28 * q^37 + 476 * q^39 - 786 * q^41 - 604 * q^45 + 448 * q^47 - 380 * q^51 + 1612 * q^55 + 1004 * q^57 + 660 * q^61 - 2250 * q^63 - 796 * q^65 - 284 * q^67 - 2532 * q^69 + 326 * q^71 + 730 * q^73 - 864 * q^75 + 342 * q^79 - 950 * q^81 + 4148 * q^85 - 4516 * q^89 - 3112 * q^91 + 3356 * q^95 - 1194 * q^97 + 2876 * 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
$3$	−1.06483	−	1.06483i	−0.204927	−	0.204927i	0.597180	−	0.802107i	$-0.296288\pi$
$3$	−1.06483	−	1.06483i	−0.204927	−	0.204927i	−0.802107	+	0.597180i	$0.796288\pi$
$4$		0			0
$5$	−0.550686	−	0.550686i	−0.0492548	−	0.0492548i	0.682050	−	0.731305i	$-0.261088\pi$
$5$	−0.550686	−	0.550686i	−0.0492548	−	0.0492548i	−0.731305	+	0.682050i	$0.761088\pi$
$6$		0			0
$7$	−11.3140	+	11.3140i	−0.610898	+	0.610898i	−0.943180	−	0.332282i	$-0.892181\pi$
$7$	−11.3140	+	11.3140i	−0.610898	+	0.610898i	0.332282	+	0.943180i	$0.392181\pi$
$8$		0			0
$9$		−	24.7323i		−	0.916010i
$10$		0			0
$11$	−5.56218	+	5.56218i	−0.152460	+	0.152460i	−0.779216	−	0.626756i	$-0.784382\pi$
$11$	−5.56218	+	5.56218i	−0.152460	+	0.152460i	0.626756	+	0.779216i	$0.284382\pi$
$12$		0			0
$13$	−64.3974			−1.37389			−0.686947	−	0.726708i	$-0.741049\pi$
$13$	−64.3974			−1.37389			−0.686947	+	0.726708i	$0.741049\pi$
$14$		0			0
$15$			1.17278i			0.0201873i
$16$		0			0
$17$	−58.0103	+	39.3421i	−0.827622	+	0.561286i
$17$	−58.0103	+	39.3421i	−0.827622	+	0.561286i
$18$		0			0
$19$		−	9.88432i		−	0.119348i	−0.998218	−	0.0596741i	$-0.980994\pi$
$19$		−	9.88432i		−	0.119348i	0.998218	−	0.0596741i	$-0.0190062\pi$
$20$		0			0
$21$	24.0950			0.250379
$22$		0			0
$23$	−134.915	+	134.915i	−1.22311	+	1.22311i	−0.256596	+	0.966519i	$0.582601\pi$
$23$	−134.915	+	134.915i	−1.22311	+	1.22311i	−0.966519	+	0.256596i	$0.917399\pi$
$24$		0			0
$25$		−	124.393i		−	0.995148i
$26$		0			0
$27$	−55.0862	+	55.0862i	−0.392643	+	0.392643i
$28$		0			0
$29$	−148.529	−	148.529i	−0.951075	−	0.951075i	0.0477823	−	0.998858i	$-0.484785\pi$
$29$	−148.529	−	148.529i	−0.951075	−	0.951075i	−0.998858	+	0.0477823i	$0.984785\pi$
$30$		0			0
$31$	4.85251	+	4.85251i	0.0281141	+	0.0281141i	0.721024	−	0.692910i	$-0.243672\pi$
$31$	4.85251	+	4.85251i	0.0281141	+	0.0281141i	−0.692910	+	0.721024i	$0.743672\pi$
$32$		0			0
$33$	11.8456			0.0624865
$34$		0			0
$35$	12.4609			0.0601794
$36$		0			0
$37$	65.3789	+	65.3789i	0.290493	+	0.290493i	0.837275	−	0.546782i	$-0.184147\pi$
$37$	65.3789	+	65.3789i	0.290493	+	0.290493i	−0.546782	+	0.837275i	$0.684147\pi$
$38$		0			0
$39$	68.5724	+	68.5724i	0.281548	+	0.281548i
$40$		0			0
$41$	225.441	−	225.441i	0.858731	−	0.858731i	−0.132458	−	0.991189i	$-0.542287\pi$
$41$	225.441	−	225.441i	0.858731	−	0.858731i	0.991189	+	0.132458i	$0.0422869\pi$
$42$		0			0
$43$			227.690i			0.807497i	0.914870	+	0.403748i	$0.132293\pi$
$43$			227.690i			0.807497i	−0.914870	+	0.403748i	$0.867707\pi$
$44$		0			0
$45$	−13.6197	+	13.6197i	−0.0451179	+	0.0451179i
$46$		0			0
$47$	240.883			0.747582			0.373791	−	0.927513i	$-0.378058\pi$
$47$	240.883			0.747582			0.373791	+	0.927513i	$0.378058\pi$
$48$		0			0
$49$			86.9871i			0.253607i
$50$		0			0
$51$	103.664	+	19.8785i	0.284625	+	0.0545794i
$52$		0			0
$53$		−	247.863i		−	0.642389i	−0.947013	−	0.321195i	$-0.895916\pi$
$53$		−	247.863i		−	0.642389i	0.947013	−	0.321195i	$-0.104084\pi$
$54$		0			0
$55$	6.12603			0.0150188
$56$		0			0
$57$	−10.5251	+	10.5251i	−0.0244577	+	0.0244577i
$58$		0			0
$59$		−	321.574i		−	0.709582i	−0.934946	−	0.354791i	$-0.884552\pi$
$59$		−	321.574i		−	0.709582i	0.934946	−	0.354791i	$-0.115448\pi$
$60$		0			0
$61$	313.816	−	313.816i	0.658688	−	0.658688i	−0.296382	−	0.955070i	$-0.595780\pi$
$61$	313.816	−	313.816i	0.658688	−	0.658688i	0.955070	+	0.296382i	$0.0957800\pi$
$62$		0			0
$63$	279.821	+	279.821i	0.559589	+	0.559589i
$64$		0			0
$65$	35.4627	+	35.4627i	0.0676708	+	0.0676708i
$66$		0			0
$67$	−17.8872			−0.0326159			−0.0163080	−	0.999867i	$-0.505191\pi$
$67$	−17.8872			−0.0326159			−0.0163080	+	0.999867i	$0.505191\pi$
$68$		0			0
$69$	287.323			0.501299
$70$		0			0
$71$	551.226	+	551.226i	0.921388	+	0.921388i	0.997128	−	0.0757399i	$-0.0241319\pi$
$71$	551.226	+	551.226i	0.921388	+	0.921388i	−0.0757399	+	0.997128i	$0.524132\pi$
$72$		0			0
$73$	406.882	+	406.882i	0.652355	+	0.652355i	0.953559	−	0.301205i	$-0.0973888\pi$
$73$	406.882	+	406.882i	0.652355	+	0.652355i	−0.301205	+	0.953559i	$0.597389\pi$
$74$		0			0
$75$	−132.458	+	132.458i	−0.203933	+	0.203933i
$76$		0			0
$77$		−	125.861i		−	0.186275i
$78$		0			0
$79$	−346.988	+	346.988i	−0.494167	+	0.494167i	−0.909616	−	0.415449i	$-0.863624\pi$
$79$	−346.988	+	346.988i	−0.494167	+	0.494167i	0.415449	+	0.909616i	$0.363624\pi$
$80$		0			0
$81$	−550.456			−0.755083
$82$		0			0
$83$		−	1282.66i		−	1.69626i	−0.529787	−	0.848131i	$-0.677728\pi$
$83$		−	1282.66i		−	1.69626i	0.529787	−	0.848131i	$-0.322272\pi$
$84$		0			0
$85$	53.6106	+	10.2803i	0.0684104	+	0.0131183i
$86$		0			0
$87$			316.318i			0.389803i
$88$		0			0
$89$	−187.071			−0.222803			−0.111402	−	0.993775i	$-0.535534\pi$
$89$	−187.071			−0.222803			−0.111402	+	0.993775i	$0.535534\pi$
$90$		0			0
$91$	728.591	−	728.591i	0.839309	−	0.839309i
$92$		0			0
$93$		−	10.3342i		−	0.0115227i
$94$		0			0
$95$	−5.44315	+	5.44315i	−0.00587848	+	0.00587848i
$96$		0			0
$97$	41.7026	+	41.7026i	0.0436521	+	0.0436521i	0.728596	−	0.684944i	$-0.240173\pi$
$97$	41.7026	+	41.7026i	0.0436521	+	0.0436521i	−0.684944	+	0.728596i	$0.740173\pi$
$98$		0			0
$99$	137.565	+	137.565i	0.139655	+	0.139655i
$100$		0			0
$101$	−462.190			−0.455343			−0.227671	−	0.973738i	$-0.573111\pi$
$101$	−462.190			−0.455343			−0.227671	+	0.973738i	$0.573111\pi$
$102$		0			0
$103$	−1983.00			−1.89700			−0.948499	−	0.316781i	$-0.897398\pi$
$103$	−1983.00			−1.89700			−0.948499	+	0.316781i	$0.897398\pi$
$104$		0			0
$105$	−13.2688	−	13.2688i	−0.0123324	−	0.0123324i
$106$		0			0
$107$	−401.041	−	401.041i	−0.362337	−	0.362337i	0.502335	−	0.864673i	$-0.332474\pi$
$107$	−401.041	−	401.041i	−0.362337	−	0.362337i	−0.864673	+	0.502335i	$0.832474\pi$
$108$		0			0
$109$	−921.300	+	921.300i	−0.809583	+	0.809583i	−0.984571	−	0.174987i	$-0.944012\pi$
$109$	−921.300	+	921.300i	−0.809583	+	0.809583i	0.174987	+	0.984571i	$0.444012\pi$
$110$		0			0
$111$		−	139.235i		−	0.119060i
$112$		0			0
$113$	159.353	−	159.353i	0.132661	−	0.132661i	−0.637659	−	0.770319i	$-0.720097\pi$
$113$	159.353	−	159.353i	0.132661	−	0.132661i	0.770319	+	0.637659i	$0.220097\pi$
$114$		0			0
$115$	148.591			0.120489
$116$		0			0
$117$			1592.69i			1.25850i
$118$		0			0
$119$	211.212	−	1101.44i	0.162704	−	0.848481i
$120$		0			0
$121$			1269.12i			0.953512i
$122$		0			0
$123$	−480.114			−0.351955
$124$		0			0
$125$	−137.337	+	137.337i	−0.0982706	+	0.0982706i
$126$		0			0
$127$			343.077i			0.239710i	0.992791	+	0.119855i	$0.0382429\pi$
$127$			343.077i			0.239710i	−0.992791	+	0.119855i	$0.961757\pi$
$128$		0			0
$129$	242.452	−	242.452i	0.165478	−	0.165478i
$130$		0			0
$131$	−1596.55	−	1596.55i	−1.06482	−	1.06482i	−0.997748	−	0.0670726i	$-0.978634\pi$
$131$	−1596.55	−	1596.55i	−1.06482	−	1.06482i	−0.0670726	−	0.997748i	$-0.521366\pi$
$132$		0			0
$133$	111.831	+	111.831i	0.0729097	+	0.0729097i
$134$		0			0
$135$	60.6704			0.0386791
$136$		0			0
$137$	−2058.38			−1.28364			−0.641822	−	0.766853i	$-0.721821\pi$
$137$	−2058.38			−1.28364			−0.641822	+	0.766853i	$0.721821\pi$
$138$		0			0
$139$	−1028.61	−	1028.61i	−0.627663	−	0.627663i	0.319816	−	0.947480i	$-0.396379\pi$
$139$	−1028.61	−	1028.61i	−0.627663	−	0.627663i	−0.947480	+	0.319816i	$0.896379\pi$
$140$		0			0
$141$	−256.500	−	256.500i	−0.153200	−	0.153200i
$142$		0			0
$143$	358.190	−	358.190i	0.209464	−	0.209464i
$144$		0			0
$145$			163.586i			0.0936901i
$146$		0			0
$147$	92.6268	−	92.6268i	0.0519709	−	0.0519709i
$148$		0			0
$149$	−4.50965			−0.00247949			−0.00123975	−	0.999999i	$-0.500395\pi$
$149$	−4.50965			−0.00247949			−0.00123975	+	0.999999i	$0.500395\pi$
$150$		0			0
$151$			3134.62i			1.68935i	0.535280	+	0.844674i	$0.320206\pi$
$151$			3134.62i			1.68935i	−0.535280	+	0.844674i	$0.679794\pi$
$152$		0			0
$153$	973.020	+	1434.73i	0.514144	+	0.758109i
$154$		0			0
$155$		−	5.34441i		−	0.00276951i
$156$		0			0
$157$	376.411			0.191343			0.0956716	−	0.995413i	$-0.469500\pi$
$157$	376.411			0.191343			0.0956716	+	0.995413i	$0.469500\pi$
$158$		0			0
$159$	−263.933	+	263.933i	−0.131643	+	0.131643i
$160$		0			0
$161$		−	3052.85i		−	1.49440i
$162$		0			0
$163$	2317.65	−	2317.65i	1.11369	−	1.11369i	0.121047	−	0.992647i	$-0.461375\pi$
$163$	2317.65	−	2317.65i	1.11369	−	1.11369i	0.992647	−	0.121047i	$-0.0386253\pi$
$164$		0			0
$165$	−6.52320	−	6.52320i	−0.00307776	−	0.00307776i
$166$		0			0
$167$	1251.37	+	1251.37i	0.579843	+	0.579843i	0.934860	−	0.355017i	$-0.115525\pi$
$167$	1251.37	+	1251.37i	0.579843	+	0.579843i	−0.355017	+	0.934860i	$0.615525\pi$
$168$		0			0
$169$	1950.02			0.887583
$170$		0			0
$171$	−244.461			−0.109324
$172$		0			0
$173$	1702.69	+	1702.69i	0.748284	+	0.748284i	0.974157	−	0.225873i	$-0.0725233\pi$
$173$	1702.69	+	1702.69i	0.748284	+	0.748284i	−0.225873	+	0.974157i	$0.572523\pi$
$174$		0			0
$175$	1407.39	+	1407.39i	0.607934	+	0.607934i
$176$		0			0
$177$	−342.423	+	342.423i	−0.145413	+	0.145413i
$178$		0			0
$179$		−	3072.78i		−	1.28308i	−0.767091	−	0.641538i	$-0.778297\pi$
$179$		−	3072.78i		−	1.28308i	0.767091	−	0.641538i	$-0.221703\pi$
$180$		0			0
$181$	−103.960	+	103.960i	−0.0426921	+	0.0426921i	−0.728131	−	0.685438i	$-0.759611\pi$
$181$	−103.960	+	103.960i	−0.0426921	+	0.0426921i	0.685438	+	0.728131i	$0.259611\pi$
$182$		0			0
$183$	−668.323			−0.269966
$184$		0			0
$185$		−	72.0064i		−	0.0286163i
$186$		0			0
$187$	103.836	−	541.492i	0.0406055	−	0.211753i
$188$		0			0
$189$		−	1246.49i		−	0.479729i
$190$		0			0
$191$	383.373			0.145235			0.0726175	−	0.997360i	$-0.476865\pi$
$191$	383.373			0.145235			0.0726175	+	0.997360i	$0.476865\pi$
$192$		0			0
$193$	814.189	−	814.189i	0.303661	−	0.303661i	−0.538783	−	0.842444i	$-0.681116\pi$
$193$	814.189	−	814.189i	0.303661	−	0.303661i	0.842444	+	0.538783i	$0.181116\pi$
$194$		0			0
$195$		−	75.5237i		−	0.0277352i
$196$		0			0
$197$	485.107	−	485.107i	0.175444	−	0.175444i	−0.613922	−	0.789366i	$-0.710409\pi$
$197$	485.107	−	485.107i	0.175444	−	0.175444i	0.789366	+	0.613922i	$0.210409\pi$
$198$		0			0
$199$	584.657	+	584.657i	0.208268	+	0.208268i	0.803531	−	0.595263i	$-0.202952\pi$
$199$	584.657	+	584.657i	0.208268	+	0.208268i	−0.595263	+	0.803531i	$0.702952\pi$
$200$		0			0
$201$	19.0469	+	19.0469i	0.00668389	+	0.00668389i
$202$		0			0
$203$	3360.92			1.16202
$204$		0			0
$205$	−248.294			−0.0845933
$206$		0			0
$207$	3336.74	+	3336.74i	1.12038	+	1.12038i
$208$		0			0
$209$	54.9784	+	54.9784i	0.0181959	+	0.0181959i
$210$		0			0
$211$	−2529.29	+	2529.29i	−0.825230	+	0.825230i	−0.986853	−	0.161623i	$-0.948327\pi$
$211$	−2529.29	+	2529.29i	−0.825230	+	0.825230i	0.161623	+	0.986853i	$0.448327\pi$
$212$		0			0
$213$		−	1173.93i		−	0.377635i
$214$		0			0
$215$	125.385	−	125.385i	0.0397731	−	0.0397731i
$216$		0			0
$217$	−109.803			−0.0343497
$218$		0			0
$219$		−	866.522i		−	0.267371i
$220$		0			0
$221$	3735.71	−	2533.53i	1.13706	−	0.771147i
$222$		0			0
$223$			3158.03i			0.948328i	0.880437	+	0.474164i	$0.157250\pi$
$223$			3158.03i			0.948328i	−0.880437	+	0.474164i	$0.842750\pi$
$224$		0			0
$225$	−3076.53			−0.911565
$226$		0			0
$227$	−977.635	+	977.635i	−0.285850	+	0.285850i	−0.835437	−	0.549587i	$-0.814785\pi$
$227$	−977.635	+	977.635i	−0.285850	+	0.285850i	0.549587	+	0.835437i	$0.314785\pi$
$228$		0			0
$229$		−	3423.08i		−	0.987789i	−0.869522	−	0.493894i	$-0.835573\pi$
$229$		−	3423.08i		−	0.987789i	0.869522	−	0.493894i	$-0.164427\pi$
$230$		0			0
$231$	−134.021	+	134.021i	−0.0381729	+	0.0381729i
$232$		0			0
$233$	−2621.33	−	2621.33i	−0.737035	−	0.737035i	0.234968	−	0.972003i	$-0.424501\pi$
$233$	−2621.33	−	2621.33i	−0.737035	−	0.737035i	−0.972003	+	0.234968i	$0.924501\pi$
$234$		0			0
$235$	−132.651	−	132.651i	−0.0368220	−	0.0368220i
$236$		0			0
$237$	738.969			0.202537
$238$		0			0
$239$	−3375.35			−0.913528			−0.456764	−	0.889588i	$-0.650992\pi$
$239$	−3375.35			−0.913528			−0.456764	+	0.889588i	$0.650992\pi$
$240$		0			0
$241$	4303.60	+	4303.60i	1.15029	+	1.15029i	0.986495	+	0.163793i	$0.0523728\pi$
$241$	4303.60	+	4303.60i	1.15029	+	1.15029i	0.163793	+	0.986495i	$0.447627\pi$
$242$		0			0
$243$	2073.47	+	2073.47i	0.547380	+	0.547380i
$244$		0			0
$245$	47.9025	−	47.9025i	0.0124913	−	0.0124913i
$246$		0			0
$247$			636.524i			0.163972i
$248$		0			0
$249$	−1365.81	+	1365.81i	−0.347610	+	0.347610i
$250$		0			0
$251$	647.628			0.162860			0.0814301	−	0.996679i	$-0.474051\pi$
$251$	647.628			0.162860			0.0814301	+	0.996679i	$0.474051\pi$
$252$		0			0
$253$		−	1500.84i		−	0.372952i
$254$		0			0
$255$	−46.1395	−	68.0331i	−0.0113309	−	0.0167075i
$256$		0			0
$257$		−	4665.47i		−	1.13239i	−0.824272	−	0.566194i	$-0.808415\pi$
$257$		−	4665.47i		−	1.13239i	0.824272	−	0.566194i	$-0.191585\pi$
$258$		0			0
$259$	−1479.39			−0.354923
$260$		0			0
$261$	−3673.46	+	3673.46i	−0.871194	+	0.871194i
$262$		0			0
$263$		−	4412.25i		−	1.03449i	−0.855837	−	0.517245i	$-0.826957\pi$
$263$		−	4412.25i		−	1.03449i	0.855837	−	0.517245i	$-0.173043\pi$
$264$		0			0
$265$	−136.495	+	136.495i	−0.0316408	+	0.0316408i
$266$		0			0
$267$	199.200	+	199.200i	0.0456585	+	0.0456585i
$268$		0			0
$269$	−4749.32	−	4749.32i	−1.07647	−	1.07647i	−0.996823	−	0.0796493i	$-0.974620\pi$
$269$	−4749.32	−	4749.32i	−1.07647	−	1.07647i	−0.0796493	−	0.996823i	$-0.525380\pi$
$270$		0			0
$271$	−8108.32			−1.81751			−0.908755	−	0.417330i	$-0.862966\pi$
$271$	−8108.32			−1.81751			−0.908755	+	0.417330i	$0.862966\pi$
$272$		0			0
$273$	−1551.66			−0.343995
$274$		0			0
$275$	691.899	+	691.899i	0.151720	+	0.151720i
$276$		0			0
$277$	4621.10	+	4621.10i	1.00236	+	1.00236i	0.999997	+	0.00236716i	$0.000753491\pi$
$277$	4621.10	+	4621.10i	1.00236	+	1.00236i	0.00236716	+	0.999997i	$0.499247\pi$
$278$		0			0
$279$	120.014	−	120.014i	0.0257528	−	0.0257528i
$280$		0			0
$281$			703.922i			0.149439i	0.997205	+	0.0747196i	$0.0238062\pi$
$281$			703.922i			0.149439i	−0.997205	+	0.0747196i	$0.976194\pi$
$282$		0			0
$283$	−4788.71	+	4788.71i	−1.00586	+	1.00586i	−0.00587938	+	0.999983i	$0.501871\pi$
$283$	−4788.71	+	4788.71i	−1.00586	+	1.00586i	−0.999983	+	0.00587938i	$0.998129\pi$
$284$		0			0
$285$	11.5921			0.00240932
$286$		0			0
$287$			5101.28i			1.04919i
$288$		0			0
$289$	1817.39	−	4564.50i	0.369915	−	0.929065i
$290$		0			0
$291$		−	88.8126i		−	0.0178910i
$292$		0			0
$293$	−8418.78			−1.67860			−0.839301	−	0.543668i	$-0.817035\pi$
$293$	−8418.78			−1.67860			−0.839301	+	0.543668i	$0.817035\pi$
$294$		0			0
$295$	−177.086	+	177.086i	−0.0349503	+	0.0349503i
$296$		0			0
$297$		−	612.799i		−	0.119725i
$298$		0			0
$299$	8688.14	−	8688.14i	1.68043	−	1.68043i
$300$		0			0
$301$	−2576.08	−	2576.08i	−0.493298	−	0.493298i
$302$		0			0
$303$	492.155	+	492.155i	0.0933121	+	0.0933121i
$304$		0			0
$305$	−345.627			−0.0648871
$306$		0			0
$307$	−8695.79			−1.61660			−0.808298	−	0.588773i	$-0.799611\pi$
$307$	−8695.79			−1.61660			−0.808298	+	0.588773i	$0.799611\pi$
$308$		0			0
$309$	2111.56	+	2111.56i	0.388746	+	0.388746i
$310$		0			0
$311$	2093.94	+	2093.94i	0.381788	+	0.381788i	0.871746	−	0.489958i	$-0.162988\pi$
$311$	2093.94	+	2093.94i	0.381788	+	0.381788i	−0.489958	+	0.871746i	$0.662988\pi$
$312$		0			0
$313$	−437.951	+	437.951i	−0.0790876	+	0.0790876i	−0.745544	−	0.666456i	$-0.767810\pi$
$313$	−437.951	+	437.951i	−0.0790876	+	0.0790876i	0.666456	+	0.745544i	$0.267810\pi$
$314$		0			0
$315$		−	308.186i		−	0.0551249i
$316$		0			0
$317$	−1595.87	+	1595.87i	−0.282753	+	0.282753i	−0.834206	−	0.551453i	$-0.814074\pi$
$317$	−1595.87	+	1595.87i	−0.282753	+	0.282753i	0.551453	+	0.834206i	$0.314074\pi$
$318$		0			0
$319$	1652.29			0.290002
$320$		0			0
$321$			854.084i			0.148506i
$322$		0			0
$323$	388.870	+	573.392i	0.0669886	+	0.0987752i
$324$		0			0
$325$			8010.61i			1.36723i
$326$		0			0
$327$	1962.06			0.331811
$328$		0			0
$329$	−2725.35	+	2725.35i	−0.456697	+	0.456697i
$330$		0			0
$331$		−	6697.10i		−	1.11210i	−0.831148	−	0.556051i	$-0.812316\pi$
$331$		−	6697.10i		−	1.11210i	0.831148	−	0.556051i	$-0.187684\pi$
$332$		0			0
$333$	1616.97	−	1616.97i	0.266094	−	0.266094i
$334$		0			0
$335$	9.85021	+	9.85021i	0.00160649	+	0.00160649i
$336$		0			0
$337$	4150.56	+	4150.56i	0.670906	+	0.670906i	0.957925	−	0.287019i	$-0.0926641\pi$
$337$	4150.56	+	4150.56i	0.670906	+	0.670906i	−0.287019	+	0.957925i	$0.592664\pi$
$338$		0			0
$339$	−339.368			−0.0543715
$340$		0			0
$341$	−53.9811			−0.00857255
$342$		0			0
$343$	−4864.87	−	4864.87i	−0.765826	−	0.765826i
$344$		0			0
$345$	−158.225	−	158.225i	−0.0246914	−	0.0246914i
$346$		0			0
$347$	−8101.21	+	8101.21i	−1.25330	+	1.25330i	−0.299070	+	0.954231i	$0.596677\pi$
$347$	−8101.21	+	8101.21i	−1.25330	+	1.25330i	−0.954231	+	0.299070i	$0.903323\pi$
$348$		0			0
$349$		−	8598.99i		−	1.31889i	−0.751752	−	0.659446i	$-0.770791\pi$
$349$		−	8598.99i		−	1.31889i	0.751752	−	0.659446i	$-0.229209\pi$
$350$		0			0
$351$	3547.41	−	3547.41i	0.539449	−	0.539449i
$352$		0			0
$353$	−1740.63			−0.262449			−0.131224	−	0.991353i	$-0.541891\pi$
$353$	−1740.63			−0.262449			−0.131224	+	0.991353i	$0.541891\pi$
$354$		0			0
$355$		−	607.105i		−	0.0907655i
$356$		0			0
$357$	−1397.76	+	947.950i	−0.207219	+	0.140535i
$358$		0			0
$359$			5571.88i			0.819143i	0.912278	+	0.409572i	$0.134322\pi$
$359$			5571.88i			0.819143i	−0.912278	+	0.409572i	$0.865678\pi$
$360$		0			0
$361$	6761.30			0.985756
$362$		0			0
$363$	1351.41	−	1351.41i	0.195401	−	0.195401i
$364$		0			0
$365$		−	448.128i		−	0.0642632i
$366$		0			0
$367$	5941.88	−	5941.88i	0.845132	−	0.845132i	−0.144389	−	0.989521i	$-0.546122\pi$
$367$	5941.88	−	5941.88i	0.845132	−	0.845132i	0.989521	+	0.144389i	$0.0461217\pi$
$368$		0			0
$369$	−5575.67	−	5575.67i	−0.786606	−	0.786606i
$370$		0			0
$371$	2804.32	+	2804.32i	0.392435	+	0.392435i
$372$		0			0
$373$	12564.3			1.74411			0.872055	−	0.489408i	$-0.162787\pi$
$373$	12564.3			1.74411			0.872055	+	0.489408i	$0.162787\pi$
$374$		0			0
$375$	292.483			0.0402767
$376$		0			0
$377$	9564.89	+	9564.89i	1.30668	+	1.30668i
$378$		0			0
$379$	6313.30	+	6313.30i	0.855652	+	0.855652i	0.990822	−	0.135170i	$-0.0431581\pi$
$379$	6313.30	+	6313.30i	0.855652	+	0.855652i	−0.135170	+	0.990822i	$0.543158\pi$
$380$		0			0
$381$	365.320	−	365.320i	0.0491231	−	0.0491231i
$382$		0			0
$383$		−	12369.5i		−	1.65026i	−0.564940	−	0.825132i	$-0.691101\pi$
$383$		−	12369.5i		−	1.65026i	0.564940	−	0.825132i	$-0.308899\pi$
$384$		0			0
$385$	−69.3098	+	69.3098i	−0.00917495	+	0.00917495i
$386$		0			0
$387$	5631.28			0.739675
$388$		0			0
$389$			8052.58i			1.04957i	0.851235	+	0.524784i	$0.175854\pi$
$389$			8052.58i			1.04957i	−0.851235	+	0.524784i	$0.824146\pi$
$390$		0			0
$391$	2518.61	−	13134.3i	0.325759	−	1.69879i
$392$		0			0
$393$			3400.13i			0.436422i
$394$		0			0
$395$	382.162			0.0486802
$396$		0			0
$397$	−4330.03	+	4330.03i	−0.547400	+	0.547400i	−0.925688	−	0.378288i	$-0.876513\pi$
$397$	−4330.03	+	4330.03i	−0.547400	+	0.547400i	0.378288	+	0.925688i	$0.376513\pi$
$398$		0			0
$399$		−	238.163i		−	0.0298824i
$400$		0			0
$401$	1850.97	−	1850.97i	0.230506	−	0.230506i	−0.582398	−	0.812904i	$-0.697885\pi$
$401$	1850.97	−	1850.97i	0.230506	−	0.230506i	0.812904	+	0.582398i	$0.197885\pi$
$402$		0			0
$403$	−312.489	−	312.489i	−0.0386257	−	0.0386257i
$404$		0			0
$405$	303.128	+	303.128i	0.0371915	+	0.0371915i
$406$		0			0
$407$	−727.299			−0.0885771
$408$		0			0
$409$	−5790.18			−0.700015			−0.350008	−	0.936747i	$-0.613821\pi$
$409$	−5790.18			−0.700015			−0.350008	+	0.936747i	$0.613821\pi$
$410$		0			0
$411$	2191.83	+	2191.83i	0.263054	+	0.263054i
$412$		0			0
$413$	3638.29	+	3638.29i	0.433483	+	0.433483i
$414$		0			0
$415$	−706.340	+	706.340i	−0.0835490	+	0.0835490i
$416$		0			0
$417$			2190.59i			0.257251i
$418$		0			0
$419$	4728.50	−	4728.50i	0.551318	−	0.551318i	−0.375503	−	0.926821i	$-0.622530\pi$
$419$	4728.50	−	4728.50i	0.551318	−	0.551318i	0.926821	+	0.375503i	$0.122530\pi$
$420$		0			0
$421$	327.455			0.0379078			0.0189539	−	0.999820i	$-0.493966\pi$
$421$	327.455			0.0379078			0.0189539	+	0.999820i	$0.493966\pi$
$422$		0			0
$423$		−	5957.57i		−	0.684792i
$424$		0			0
$425$	4893.90	+	7216.11i	0.558563	+	0.823606i
$426$		0			0
$427$			7101.01i			0.804783i
$428$		0			0
$429$	−762.825			−0.0858497
$430$		0			0
$431$	6657.93	−	6657.93i	0.744087	−	0.744087i	−0.229275	−	0.973362i	$-0.573635\pi$
$431$	6657.93	−	6657.93i	0.744087	−	0.744087i	0.973362	+	0.229275i	$0.0736355\pi$
$432$		0			0
$433$		−	14393.2i		−	1.59744i	−0.601700	−	0.798722i	$-0.705510\pi$
$433$		−	14393.2i		−	1.59744i	0.601700	−	0.798722i	$-0.294490\pi$
$434$		0			0
$435$	174.192	−	174.192i	0.0191997	−	0.0191997i
$436$		0			0
$437$	1333.54	+	1333.54i	0.145977	+	0.145977i
$438$		0			0
$439$	−1292.15	−	1292.15i	−0.140481	−	0.140481i	0.633369	−	0.773850i	$-0.281671\pi$
$439$	−1292.15	−	1292.15i	−0.140481	−	0.140481i	−0.773850	+	0.633369i	$0.781671\pi$
$440$		0			0
$441$	2151.39			0.232306
$442$		0			0
$443$	−8825.03			−0.946478			−0.473239	−	0.880934i	$-0.656915\pi$
$443$	−8825.03			−0.946478			−0.473239	+	0.880934i	$0.656915\pi$
$444$		0			0
$445$	103.017	+	103.017i	0.0109741	+	0.0109741i
$446$		0			0
$447$	4.80202	+	4.80202i	0.000508116	+	0.000508116i
$448$		0			0
$449$	−1972.32	+	1972.32i	−0.207304	+	0.207304i	−0.803121	−	0.595816i	$-0.796829\pi$
$449$	−1972.32	+	1972.32i	−0.207304	+	0.207304i	0.595816	+	0.803121i	$0.296829\pi$
$450$		0			0
$451$			2507.89i			0.261844i
$452$		0			0
$453$	3337.85	−	3337.85i	0.346194	−	0.346194i
$454$		0			0
$455$	−802.449			−0.0826800
$456$		0			0
$457$			14264.3i			1.46008i	0.683404	+	0.730040i	$0.260499\pi$
$457$			14264.3i			1.46008i	−0.683404	+	0.730040i	$0.739501\pi$
$458$		0			0
$459$	1028.36	−	5362.78i	0.104575	−	0.545344i
$460$		0			0
$461$		−	10219.4i		−	1.03247i	−0.856448	−	0.516233i	$-0.827334\pi$
$461$		−	10219.4i		−	1.03247i	0.856448	−	0.516233i	$-0.172666\pi$
$462$		0			0
$463$	−12707.3			−1.27550			−0.637750	−	0.770244i	$-0.720135\pi$
$463$	−12707.3			−1.27550			−0.637750	+	0.770244i	$0.720135\pi$
$464$		0			0
$465$	−5.69091	+	5.69091i	−0.000567548	+	0.000567548i
$466$		0			0
$467$			10029.1i			0.993773i	0.867816	+	0.496886i	$0.165523\pi$
$467$			10029.1i			0.993773i	−0.867816	+	0.496886i	$0.834477\pi$
$468$		0			0
$469$	202.376	−	202.376i	0.0199250	−	0.0199250i
$470$		0			0
$471$	−400.815	−	400.815i	−0.0392114	−	0.0392114i
$472$		0			0
$473$	−1266.45	−	1266.45i	−0.123111	−	0.123111i
$474$		0			0
$475$	−1229.54			−0.118769
$476$		0			0
$477$	−6130.22			−0.588435
$478$		0			0
$479$	−124.139	−	124.139i	−0.0118415	−	0.0118415i	0.701161	−	0.713003i	$-0.252665\pi$
$479$	−124.139	−	124.139i	−0.0118415	−	0.0118415i	−0.713003	+	0.701161i	$0.752665\pi$
$480$		0			0
$481$	−4210.23	−	4210.23i	−0.399106	−	0.399106i
$482$		0			0
$483$	−3250.77	+	3250.77i	−0.306243	+	0.306243i
$484$		0			0
$485$		−	45.9300i		−	0.00430015i
$486$		0			0
$487$	−11949.3	+	11949.3i	−1.11186	+	1.11186i	−0.118961	+	0.992899i	$0.537956\pi$
$487$	−11949.3	+	11949.3i	−1.11186	+	1.11186i	−0.992899	+	0.118961i	$0.962044\pi$
$488$		0			0
$489$	−4935.82			−0.456453
$490$		0			0
$491$			14377.8i			1.32151i	0.750602	+	0.660754i	$0.229763\pi$
$491$			14377.8i			1.32151i	−0.750602	+	0.660754i	$0.770237\pi$
$492$		0			0
$493$	14459.7	+	2772.77i	1.32096	+	0.253305i
$494$		0			0
$495$		−	151.510i		−	0.0137574i
$496$		0			0
$497$	−12473.1			−1.12575
$498$		0			0
$499$	6238.43	−	6238.43i	0.559661	−	0.559661i	−0.369550	−	0.929211i	$-0.620488\pi$
$499$	6238.43	−	6238.43i	0.559661	−	0.559661i	0.929211	+	0.369550i	$0.120488\pi$
$500$		0			0
$501$		−	2665.00i		−	0.237651i
$502$		0			0
$503$	5613.80	−	5613.80i	0.497628	−	0.497628i	−0.413071	−	0.910699i	$-0.635544\pi$
$503$	5613.80	−	5613.80i	0.497628	−	0.497628i	0.910699	+	0.413071i	$0.135544\pi$
$504$		0			0
$505$	254.521	+	254.521i	0.0224278	+	0.0224278i
$506$		0			0
$507$	−2076.44	−	2076.44i	−0.181890	−	0.181890i
$508$		0			0
$509$	−1096.19			−0.0954575			−0.0477287	−	0.998860i	$-0.515198\pi$
$509$	−1096.19			−0.0954575			−0.0477287	+	0.998860i	$0.515198\pi$
$510$		0			0
$511$	−9206.91			−0.797045
$512$		0			0
$513$	544.490	+	544.490i	0.0468612	+	0.0468612i
$514$		0			0
$515$	1092.01	+	1092.01i	0.0934362	+	0.0934362i
$516$		0			0
$517$	−1339.83	+	1339.83i	−0.113976	+	0.113976i
$518$		0			0
$519$		−	3626.16i		−	0.306688i
$520$		0			0
$521$	−6107.64	+	6107.64i	−0.513590	+	0.513590i	−0.915625	−	0.402034i	$-0.868303\pi$
$521$	−6107.64	+	6107.64i	−0.513590	+	0.513590i	0.402034	+	0.915625i	$0.368303\pi$
$522$		0			0
$523$	1232.00			0.103005			0.0515027	−	0.998673i	$-0.483599\pi$
$523$	1232.00			0.103005			0.0515027	+	0.998673i	$0.483599\pi$
$524$		0			0
$525$		−	2997.27i		−	0.249165i
$526$		0			0
$527$	−472.404	−	90.5876i	−0.0390479	−	0.00748778i
$528$		0			0
$529$		−	24236.9i		−	1.99202i
$530$		0			0
$531$	−7953.25			−0.649984
$532$		0			0
$533$	−14517.8	+	14517.8i	−1.17980	+	1.17980i
$534$		0			0
$535$			441.695i			0.0356937i
$536$		0			0
$537$	−3272.00	+	3272.00i	−0.262937	+	0.262937i
$538$		0			0
$539$	−483.838	−	483.838i	−0.0386649	−	0.0386649i
$540$		0			0
$541$	−13877.1	−	13877.1i	−1.10281	−	1.10281i	−0.994070	−	0.108745i	$-0.965317\pi$
$541$	−13877.1	−	13877.1i	−1.10281	−	1.10281i	−0.108745	−	0.994070i	$-0.534683\pi$
$542$		0			0
$543$	221.400			0.0174975
$544$		0			0
$545$	1014.69			0.0797517
$546$		0			0
$547$	5790.54	+	5790.54i	0.452624	+	0.452624i	0.896225	−	0.443600i	$-0.146299\pi$
$547$	5790.54	+	5790.54i	0.452624	+	0.452624i	−0.443600	+	0.896225i	$0.646299\pi$
$548$		0			0
$549$	−7761.37	−	7761.37i	−0.603364	−	0.603364i
$550$		0			0
$551$	−1468.11	+	1468.11i	−0.113509	+	0.113509i
$552$		0			0
$553$		−	7851.64i		−	0.603772i
$554$		0			0
$555$	−76.6749	+	76.6749i	−0.00586426	+	0.00586426i
$556$		0			0
$557$	−5282.15			−0.401817			−0.200908	−	0.979610i	$-0.564389\pi$
$557$	−5282.15			−0.401817			−0.200908	+	0.979610i	$0.564389\pi$
$558$		0			0
$559$		−	14662.6i		−	1.10941i
$560$		0			0
$561$	−687.167	+	466.031i	−0.0517152	+	0.0350728i
$562$		0			0
$563$			21573.9i			1.61498i	0.589882	+	0.807489i	$0.299174\pi$
$563$			21573.9i			1.61498i	−0.589882	+	0.807489i	$0.700826\pi$
$564$		0			0
$565$	−175.506			−0.0130683
$566$		0			0
$567$	6227.85	−	6227.85i	0.461279	−	0.461279i
$568$		0			0
$569$		−	10265.2i		−	0.756306i	−0.925743	−	0.378153i	$-0.876559\pi$
$569$		−	10265.2i		−	0.756306i	0.925743	−	0.378153i	$-0.123441\pi$
$570$		0			0
$571$	−10442.5	+	10442.5i	−0.765332	+	0.765332i	−0.977281	−	0.211949i	$-0.932019\pi$
$571$	−10442.5	+	10442.5i	−0.765332	+	0.765332i	0.211949	+	0.977281i	$0.432019\pi$
$572$		0			0
$573$	−408.228	−	408.228i	−0.0297626	−	0.0297626i
$574$		0			0
$575$	16782.5	+	16782.5i	1.21718	+	1.21718i
$576$		0			0
$577$	20433.6			1.47429			0.737143	−	0.675737i	$-0.236174\pi$
$577$	20433.6			1.47429			0.737143	+	0.675737i	$0.236174\pi$
$578$		0			0
$579$	−1733.95			−0.124457
$580$		0			0
$581$	14512.0	+	14512.0i	1.03624	+	1.03624i
$582$		0			0
$583$	1378.66	+	1378.66i	0.0979387	+	0.0979387i
$584$		0			0
$585$	877.072	−	877.072i	0.0619871	−	0.0619871i
$586$		0			0
$587$			20352.5i			1.43107i	0.698578	+	0.715534i	$0.253817\pi$
$587$			20352.5i			1.43107i	−0.698578	+	0.715534i	$0.746183\pi$
$588$		0			0
$589$	47.9637	−	47.9637i	0.00335537	−	0.00335537i
$590$		0			0
$591$	−1033.12			−0.0719065
$592$		0			0
$593$		−	16460.0i		−	1.13985i	−0.821696	−	0.569926i	$-0.806972\pi$
$593$		−	16460.0i		−	1.13985i	0.821696	−	0.569926i	$-0.193028\pi$
$594$		0			0
$595$	−722.861	+	490.238i	−0.0498057	+	0.0337778i
$596$		0			0
$597$		−	1245.12i		−	0.0853594i
$598$		0			0
$599$	9181.98			0.626320			0.313160	−	0.949700i	$-0.398612\pi$
$599$	9181.98			0.626320			0.313160	+	0.949700i	$0.398612\pi$
$600$		0			0
$601$	−3084.54	+	3084.54i	−0.209353	+	0.209353i	−0.803992	−	0.594640i	$-0.797295\pi$
$601$	−3084.54	+	3084.54i	−0.209353	+	0.209353i	0.594640	+	0.803992i	$0.297295\pi$
$602$		0			0
$603$			442.391i			0.0298765i
$604$		0			0
$605$	698.888	−	698.888i	0.0469650	−	0.0469650i
$606$		0			0
$607$	−12188.6	−	12188.6i	−0.815023	−	0.815023i	0.170359	−	0.985382i	$-0.445507\pi$
$607$	−12188.6	−	12188.6i	−0.815023	−	0.815023i	−0.985382	+	0.170359i	$0.945507\pi$
$608$		0			0
$609$	−3578.82	−	3578.82i	−0.238130	−	0.238130i
$610$		0			0
$611$	−15512.2			−1.02710
$612$		0			0
$613$	18427.6			1.21416			0.607082	−	0.794639i	$-0.292340\pi$
$613$	18427.6			1.21416			0.607082	+	0.794639i	$0.292340\pi$
$614$		0			0
$615$	264.392	+	264.392i	0.0173355	+	0.0173355i
$616$		0			0
$617$	8642.09	+	8642.09i	0.563886	+	0.563886i	0.930409	−	0.366523i	$-0.119452\pi$
$617$	8642.09	+	8642.09i	0.563886	+	0.563886i	−0.366523	+	0.930409i	$0.619452\pi$
$618$		0			0
$619$	126.171	−	126.171i	0.00819263	−	0.00819263i	−0.702999	−	0.711191i	$-0.748156\pi$
$619$	126.171	−	126.171i	0.00819263	−	0.00819263i	0.711191	+	0.702999i	$0.248156\pi$
$620$		0			0
$621$		−	14863.9i		−	0.960494i
$622$		0			0
$623$	2116.52	−	2116.52i	0.136110	−	0.136110i
$624$		0			0
$625$	−15397.9			−0.985467
$626$		0			0
$627$		−	117.086i		−	0.00745765i
$628$		0			0
$629$	−6364.80	−	1220.51i	−0.403468	−	0.0773685i
$630$		0			0
$631$			7037.77i			0.444008i	0.975046	+	0.222004i	$0.0712598\pi$
$631$			7037.77i			0.444008i	−0.975046	+	0.222004i	$0.928740\pi$
$632$		0			0
$633$	5386.55			0.338224
$634$		0			0
$635$	188.927	−	188.927i	0.0118069	−	0.0118069i
$636$		0			0
$637$		−	5601.74i		−	0.348429i
$638$		0			0
$639$	13633.1	−	13633.1i	0.844000	−	0.844000i
$640$		0			0
$641$	7680.83	+	7680.83i	0.473284	+	0.473284i	0.902976	−	0.429692i	$-0.141378\pi$
$641$	7680.83	+	7680.83i	0.473284	+	0.473284i	−0.429692	+	0.902976i	$0.641378\pi$
$642$		0			0
$643$	2990.50	+	2990.50i	0.183412	+	0.183412i	0.792841	−	0.609429i	$-0.208601\pi$
$643$	2990.50	+	2990.50i	0.183412	+	0.183412i	−0.609429	+	0.792841i	$0.708601\pi$
$644$		0			0
$645$	−267.029			−0.0163012
$646$		0			0
$647$	−5755.35			−0.349716			−0.174858	−	0.984594i	$-0.555947\pi$
$647$	−5755.35			−0.349716			−0.174858	+	0.984594i	$0.555947\pi$
$648$		0			0
$649$	1788.65	+	1788.65i	0.108183	+	0.108183i
$650$		0			0
$651$	116.921	+	116.921i	0.00703919	+	0.00703919i
$652$		0			0
$653$	8850.23	−	8850.23i	0.530377	−	0.530377i	−0.390308	−	0.920685i	$-0.627631\pi$
$653$	8850.23	−	8850.23i	0.530377	−	0.530377i	0.920685	+	0.390308i	$0.127631\pi$
$654$		0			0
$655$			1758.40i			0.104895i
$656$		0			0
$657$	10063.1	−	10063.1i	0.597563	−	0.597563i
$658$		0			0
$659$	19935.0			1.17839			0.589194	−	0.807992i	$-0.299445\pi$
$659$	19935.0			1.17839			0.589194	+	0.807992i	$0.299445\pi$
$660$		0			0
$661$			18848.1i			1.10909i	0.832155	+	0.554543i	$0.187107\pi$
$661$			18848.1i			1.10909i	−0.832155	+	0.554543i	$0.812893\pi$
$662$		0			0
$663$	−6675.70	−	1280.12i	−0.391045	−	0.0749863i
$664$		0			0
$665$		−	123.168i		−	0.00718230i
$666$		0			0
$667$	40077.5			2.32655
$668$		0			0
$669$	3362.77	−	3362.77i	0.194338	−	0.194338i
$670$		0			0
$671$			3491.00i			0.200847i
$672$		0			0
$673$	−621.525	+	621.525i	−0.0355989	+	0.0355989i	−0.724682	−	0.689083i	$-0.758013\pi$
$673$	−621.525	+	621.525i	−0.0355989	+	0.0355989i	0.689083	+	0.724682i	$0.258013\pi$
$674$		0			0
$675$	6852.37	+	6852.37i	0.390737	+	0.390737i
$676$		0			0
$677$	4437.82	+	4437.82i	0.251934	+	0.251934i	0.821763	−	0.569829i	$-0.192991\pi$
$677$	4437.82	+	4437.82i	0.251934	+	0.251934i	−0.569829	+	0.821763i	$0.692991\pi$
$678$		0			0
$679$	−943.645			−0.0533340
$680$		0			0
$681$	2082.04			0.117157
$682$		0			0
$683$	−21200.0	−	21200.0i	−1.18769	−	1.18769i	−0.977704	−	0.209990i	$-0.932657\pi$
$683$	−21200.0	−	21200.0i	−1.18769	−	1.18769i	−0.209990	−	0.977704i	$-0.567343\pi$
$684$		0			0
$685$	1133.52	+	1133.52i	0.0632257	+	0.0632257i
$686$		0			0
$687$	−3645.01	+	3645.01i	−0.202425	+	0.202425i
$688$		0			0
$689$			15961.7i			0.882574i
$690$		0			0
$691$	16123.0	−	16123.0i	0.887625	−	0.887625i	−0.106669	−	0.994295i	$-0.534019\pi$
$691$	16123.0	−	16123.0i	0.887625	−	0.887625i	0.994295	+	0.106669i	$0.0340186\pi$
$692$		0			0
$693$	−3112.83			−0.170630
$694$		0			0
$695$			1132.88i			0.0618309i
$696$		0			0
$697$	−4208.58	+	21947.2i	−0.228711	+	1.19270i
$698$		0			0
$699$			5582.56i			0.302077i
$700$		0			0
$701$	8900.26			0.479541			0.239770	−	0.970830i	$-0.422928\pi$
$701$	8900.26			0.479541			0.239770	+	0.970830i	$0.422928\pi$
$702$		0			0
$703$	646.226	−	646.226i	0.0346698	−	0.0346698i
$704$		0			0
$705$			282.502i			0.0150917i
$706$		0			0
$707$	5229.21	−	5229.21i	0.278168	−	0.278168i
$708$		0			0
$709$	−5531.75	−	5531.75i	−0.293017	−	0.293017i	0.545254	−	0.838271i	$-0.316433\pi$
$709$	−5531.75	−	5531.75i	−0.293017	−	0.293017i	−0.838271	+	0.545254i	$0.816433\pi$
$710$		0			0
$711$	8581.80	+	8581.80i	0.452662	+	0.452662i
$712$		0			0
$713$	−1309.35			−0.0687735
$714$		0			0
$715$	−394.500			−0.0206342
$716$		0			0
$717$	3594.19	+	3594.19i	0.187207	+	0.187207i
$718$		0			0
$719$	5839.10	+	5839.10i	0.302867	+	0.302867i	0.842135	−	0.539267i	$-0.181299\pi$
$719$	5839.10	+	5839.10i	0.302867	+	0.302867i	−0.539267	+	0.842135i	$0.681299\pi$
$720$		0			0
$721$	22435.6	−	22435.6i	1.15887	−	1.15887i
$722$		0			0
$723$		−	9165.23i		−	0.471451i
$724$		0			0
$725$	−18476.1	+	18476.1i	−0.946461	+	0.946461i
$726$		0			0
$727$	4729.65			0.241283			0.120642	−	0.992696i	$-0.461505\pi$
$727$	4729.65			0.241283			0.120642	+	0.992696i	$0.461505\pi$
$728$		0			0
$729$			10446.5i			0.530737i
$730$		0			0
$731$	−8957.80	−	13208.4i	−0.453237	−	0.668302i
$732$		0			0
$733$		−	33384.2i		−	1.68223i	−0.540857	−	0.841114i	$-0.681900\pi$
$733$		−	33384.2i		−	1.68223i	0.540857	−	0.841114i	$-0.318100\pi$
$734$		0			0
$735$	−102.016			−0.00511964
$736$		0			0
$737$	99.4918	−	99.4918i	0.00497263	−	0.00497263i
$738$		0			0
$739$		−	6988.23i		−	0.347857i	−0.984758	−	0.173928i	$-0.944354\pi$
$739$		−	6988.23i		−	0.347857i	0.984758	−	0.173928i	$-0.0556461\pi$
$740$		0			0
$741$	677.792	−	677.792i	0.0336023	−	0.0336023i
$742$		0			0
$743$	−8193.70	−	8193.70i	−0.404573	−	0.404573i	0.475268	−	0.879841i	$-0.342351\pi$
$743$	−8193.70	−	8193.70i	−0.404573	−	0.404573i	−0.879841	+	0.475268i	$0.842351\pi$
$744$		0			0
$745$	2.48340	+	2.48340i	0.000122127	+	0.000122127i
$746$		0			0
$747$	−31723.0			−1.55379
$748$		0			0
$749$	9074.75			0.442702
$750$		0			0
$751$	−19992.0	−	19992.0i	−0.971394	−	0.971394i	0.0282084	−	0.999602i	$-0.491020\pi$
$751$	−19992.0	−	19992.0i	−0.971394	−	0.971394i	−0.999602	+	0.0282084i	$0.991020\pi$
$752$		0			0
$753$	−689.616	−	689.616i	−0.0333745	−	0.0333745i
$754$		0			0
$755$	1726.19	−	1726.19i	0.0832086	−	0.0832086i
$756$		0			0
$757$			35534.2i			1.70609i	0.521834	+	0.853047i	$0.325248\pi$
$757$			35534.2i			1.70609i	−0.521834	+	0.853047i	$0.674752\pi$
$758$		0			0
$759$	−1598.14	+	1598.14i	−0.0764281	+	0.0764281i
$760$		0			0
$761$	12245.5			0.583312			0.291656	−	0.956523i	$-0.405794\pi$
$761$	12245.5			0.583312			0.291656	+	0.956523i	$0.405794\pi$
$762$		0			0
$763$		−	20847.2i		−	0.989146i
$764$		0			0
$765$	254.255	−	1325.91i	0.0120165	−	0.0626646i
$766$		0			0
$767$			20708.5i			0.974890i
$768$		0			0
$769$	−25923.6			−1.21564			−0.607822	−	0.794073i	$-0.707957\pi$
$769$	−25923.6			−1.21564			−0.607822	+	0.794073i	$0.707957\pi$
$770$		0			0
$771$	−4967.94	+	4967.94i	−0.232057	+	0.232057i
$772$		0			0
$773$			20813.4i			0.968444i	0.874945	+	0.484222i	$0.160897\pi$
$773$			20813.4i			0.968444i	−0.874945	+	0.484222i	$0.839103\pi$
$774$		0			0
$775$	603.621	−	603.621i	0.0279777	−	0.0279777i
$776$		0			0
$777$	1575.31	+	1575.31i	0.0727334	+	0.0727334i
$778$		0			0
$779$	−2228.33	−	2228.33i	−0.102488	−	0.102488i
$780$		0			0
$781$	−6132.04			−0.280950
$782$		0			0
$783$	16363.8			0.746866
$784$		0			0
$785$	−207.284	−	207.284i	−0.00942457	−	0.00942457i
$786$		0			0
$787$	−7676.37	−	7676.37i	−0.347691	−	0.347691i	0.511558	−	0.859249i	$-0.329069\pi$
$787$	−7676.37	−	7676.37i	−0.347691	−	0.347691i	−0.859249	+	0.511558i	$0.829069\pi$
$788$		0			0
$789$	−4698.31	+	4698.31i	−0.211995	+	0.211995i
$790$		0			0
$791$			3605.83i			0.162084i
$792$		0			0
$793$	−20208.9	+	20208.9i	−0.904967	+	0.904967i
$794$		0			0
$795$	290.688			0.0129681
$796$		0			0
$797$		−	35021.7i		−	1.55650i	−0.627953	−	0.778251i	$-0.716107\pi$
$797$		−	35021.7i		−	1.55650i	0.627953	−	0.778251i	$-0.283893\pi$
$798$		0			0
$799$	−13973.7	+	9476.84i	−0.618715	+	0.419608i
$800$		0			0
$801$			4626.69i			0.204090i
$802$		0			0
$803$	−4526.30			−0.198916
$804$		0			0
$805$	−1681.16	+	1681.16i	−0.0736063	+	0.0736063i
$806$		0			0
$807$			10114.5i			0.441197i
$808$		0			0
$809$	−29169.7	+	29169.7i	−1.26768	+	1.26768i	−0.320396	+	0.947284i	$0.603816\pi$
$809$	−29169.7	+	29169.7i	−1.26768	+	1.26768i	−0.947284	+	0.320396i	$0.896184\pi$
$810$		0			0
$811$	19287.7	+	19287.7i	0.835122	+	0.835122i	0.988212	−	0.153090i	$-0.0489225\pi$
$811$	19287.7	+	19287.7i	0.835122	+	0.835122i	−0.153090	+	0.988212i	$0.548923\pi$
$812$		0			0
$813$	8634.01	+	8634.01i	0.372457	+	0.372457i
$814$		0			0
$815$	−2552.59			−0.109710
$816$		0			0
$817$	2250.56			0.0963734
$818$		0			0
$819$	−18019.7	−	18019.7i	−0.768815	−	0.768815i
$820$		0			0
$821$	−23343.3	−	23343.3i	−0.992312	−	0.992312i	0.00765850	−	0.999971i	$-0.497562\pi$
$821$	−23343.3	−	23343.3i	−0.992312	−	0.992312i	−0.999971	+	0.00765850i	$0.997562\pi$
$822$		0			0
$823$	−18121.5	+	18121.5i	−0.767530	+	0.767530i	−0.977671	−	0.210141i	$-0.932608\pi$
$823$	−18121.5	+	18121.5i	−0.767530	+	0.767530i	0.210141	+	0.977671i	$0.432608\pi$
$824$		0			0
$825$		−	1473.51i		−	0.0621833i
$826$		0			0
$827$	11254.1	−	11254.1i	0.473208	−	0.473208i	−0.429743	−	0.902951i	$-0.641396\pi$
$827$	11254.1	−	11254.1i	0.473208	−	0.473208i	0.902951	+	0.429743i	$0.141396\pi$
$828$		0			0
$829$	−8519.63			−0.356935			−0.178467	−	0.983946i	$-0.557114\pi$
$829$	−8519.63			−0.356935			−0.178467	+	0.983946i	$0.557114\pi$
$830$		0			0
$831$		−	9841.40i		−	0.410824i
$832$		0			0
$833$	−3422.26	−	5046.15i	−0.142346	−	0.209890i
$834$		0			0
$835$		−	1378.22i		−	0.0571201i
$836$		0			0
$837$	−534.613			−0.0220776
$838$		0			0
$839$	22270.9	−	22270.9i	0.916422	−	0.916422i	−0.0803451	−	0.996767i	$-0.525602\pi$
$839$	22270.9	−	22270.9i	0.916422	−	0.916422i	0.996767	+	0.0803451i	$0.0256022\pi$
$840$		0			0
$841$			19732.9i			0.809089i
$842$		0			0
$843$	749.559	−	749.559i	0.0306242	−	0.0306242i
$844$		0			0
$845$	−1073.85	−	1073.85i	−0.0437177	−	0.0437177i
$846$		0			0
$847$	−14358.9	−	14358.9i	−0.582499	−	0.582499i
$848$		0			0
$849$	10198.3			0.412257
$850$		0			0
$851$	−17641.1			−0.710612
$852$		0			0
$853$	9366.17	+	9366.17i	0.375957	+	0.375957i	0.869641	−	0.493684i	$-0.164350\pi$
$853$	9366.17	+	9366.17i	0.375957	+	0.375957i	−0.493684	+	0.869641i	$0.664350\pi$
$854$		0			0
$855$	134.621	+	134.621i	0.00538474	+	0.00538474i
$856$		0			0
$857$	2498.85	−	2498.85i	0.0996021	−	0.0996021i	−0.655550	−	0.755152i	$-0.727563\pi$
$857$	2498.85	−	2498.85i	0.0996021	−	0.0996021i	0.755152	+	0.655550i	$0.227563\pi$
$858$		0			0
$859$		−	16355.9i		−	0.649659i	−0.945773	−	0.324829i	$-0.894693\pi$
$859$		−	16355.9i		−	0.649659i	0.945773	−	0.324829i	$-0.105307\pi$
$860$		0			0
$861$	5432.01	−	5432.01i	0.215009	−	0.215009i
$862$		0			0
$863$	−8944.44			−0.352807			−0.176403	−	0.984318i	$-0.556446\pi$
$863$	−8944.44			−0.352807			−0.176403	+	0.984318i	$0.556446\pi$
$864$		0			0
$865$		−	1875.29i		−	0.0737132i
$866$		0			0
$867$	−6795.65	+	2925.21i	−0.266197	+	0.114585i
$868$		0			0
$869$		−	3860.02i		−	0.150682i
$870$		0			0
$871$	1151.89			0.0448108
$872$		0			0
$873$	1031.40	−	1031.40i	0.0399857	−	0.0399857i
$874$		0			0
$875$		−	3107.67i		−	0.120067i
$876$		0			0
$877$	−36431.7	+	36431.7i	−1.40275	+	1.40275i	−0.611527	+	0.791224i	$0.709444\pi$
$877$	−36431.7	+	36431.7i	−1.40275	+	1.40275i	−0.791224	+	0.611527i	$0.790556\pi$
$878$		0			0
$879$	8964.59	+	8964.59i	0.343991	+	0.343991i
$880$		0			0
$881$	−5610.10	−	5610.10i	−0.214539	−	0.214539i	0.591653	−	0.806192i	$-0.298475\pi$
$881$	−5610.10	−	5610.10i	−0.214539	−	0.214539i	−0.806192	+	0.591653i	$0.798475\pi$
$882$		0			0
$883$	−18241.0			−0.695197			−0.347599	−	0.937643i	$-0.613003\pi$
$883$	−18241.0			−0.695197			−0.347599	+	0.937643i	$0.613003\pi$
$884$		0			0
$885$	377.134			0.0143246
$886$		0			0
$887$	−10469.9	−	10469.9i	−0.396329	−	0.396329i	0.480607	−	0.876936i	$-0.340416\pi$
$887$	−10469.9	−	10469.9i	−0.396329	−	0.396329i	−0.876936	+	0.480607i	$0.840416\pi$
$888$		0			0
$889$	−3881.57	−	3881.57i	−0.146438	−	0.146438i
$890$		0			0
$891$	3061.73	−	3061.73i	0.115120	−	0.115120i
$892$		0			0
$893$		−	2380.96i		−	0.0892226i
$894$		0			0
$895$	−1692.14	+	1692.14i	−0.0631976	+	0.0631976i
$896$		0			0
$897$	−18502.8			−0.688731
$898$		0			0
$899$		−	1441.48i		−	0.0534772i
$900$		0			0
$901$	9751.47	+	14378.6i	0.360564	+	0.531655i
$902$		0			0
$903$			5486.19i			0.202181i
$904$		0			0
$905$	114.498			0.00420558
$906$		0			0
$907$	29249.9	−	29249.9i	1.07081	−	1.07081i	0.0735198	−	0.997294i	$-0.476577\pi$
$907$	29249.9	−	29249.9i	1.07081	−	1.07081i	0.997294	−	0.0735198i	$-0.0234232\pi$
$908$		0			0
$909$			11431.0i			0.417098i
$910$		0			0
$911$	−15659.6	+	15659.6i	−0.569513	+	0.569513i	−0.931992	−	0.362479i	$-0.881931\pi$
$911$	−15659.6	+	15659.6i	−0.569513	+	0.569513i	0.362479	+	0.931992i	$0.381931\pi$
$912$		0			0
$913$	7134.36	+	7134.36i	0.258612	+	0.258612i
$914$		0			0
$915$	368.036	+	368.036i	0.0132971	+	0.0132971i
$916$		0			0
$917$	36126.8			1.30099
$918$		0			0
$919$	47353.8			1.69974			0.849868	−	0.526995i	$-0.176681\pi$
$919$	47353.8			1.69974			0.849868	+	0.526995i	$0.176681\pi$
$920$		0			0
$921$	9259.57	+	9259.57i	0.331285	+	0.331285i
$922$		0			0
$923$	−35497.5	−	35497.5i	−1.26589	−	1.26589i
$924$		0			0
$925$	8132.71	−	8132.71i	0.289083	−	0.289083i
$926$		0			0
$927$			49044.1i			1.73767i
$928$		0			0
$929$	37835.4	−	37835.4i	1.33621	−	1.33621i	0.436511	−	0.899699i	$-0.356214\pi$
$929$	37835.4	−	37835.4i	1.33621	−	1.33621i	0.899699	−	0.436511i	$-0.143786\pi$
$930$		0			0
$931$	859.808			0.0302675
$932$		0			0
$933$		−	4459.39i		−	0.156478i
$934$		0			0
$935$	−355.373	+	241.011i	−0.0124299	+	0.00842984i
$936$		0			0
$937$		−	38169.1i		−	1.33077i	−0.746501	−	0.665384i	$-0.768268\pi$
$937$		−	38169.1i		−	1.33077i	0.746501	−	0.665384i	$-0.231732\pi$
$938$		0			0
$939$	932.689			0.0324144
$940$		0			0
$941$	−11995.1	+	11995.1i	−0.415545	+	0.415545i	−0.883665	−	0.468120i	$-0.844932\pi$
$941$	−11995.1	+	11995.1i	−0.415545	+	0.415545i	0.468120	+	0.883665i	$0.344932\pi$
$942$		0			0
$943$			60830.6i			2.10065i
$944$		0			0
$945$	−686.424	+	686.424i	−0.0236290	+	0.0236290i
$946$		0			0
$947$	19751.7	+	19751.7i	0.677766	+	0.677766i	0.959494	−	0.281728i	$-0.0909077\pi$
$947$	19751.7	+	19751.7i	0.677766	+	0.677766i	−0.281728	+	0.959494i	$0.590908\pi$
$948$		0			0
$949$	−26202.1	−	26202.1i	−0.896266	−	0.896266i
$950$		0			0
$951$	3398.67			0.115888
$952$		0			0
$953$	55587.9			1.88947			0.944737	−	0.327829i	$-0.106317\pi$
$953$	55587.9			1.88947			0.944737	+	0.327829i	$0.106317\pi$
$954$		0			0
$955$	−211.118	−	211.118i	−0.00715352	−	0.00715352i
$956$		0			0
$957$	−1759.42	−	1759.42i	−0.0594293	−	0.0594293i
$958$		0			0
$959$	23288.5	−	23288.5i	0.784176	−	0.784176i
$960$		0			0
$961$		−	29743.9i		−	0.998419i
$962$		0			0
$963$	−9918.65	+	9918.65i	−0.331904	+	0.331904i
$964$		0			0
$965$	−896.724			−0.0299136
$966$		0			0
$967$			31365.7i			1.04307i	0.853229	+	0.521537i	$0.174641\pi$
$967$			31365.7i			1.04307i	−0.853229	+	0.521537i	$0.825359\pi$
$968$		0			0
$969$	196.486	−	1024.65i	0.00651396	−	0.0339695i
$970$		0			0
$971$		−	28214.6i		−	0.932492i	−0.884655	−	0.466246i	$-0.845606\pi$
$971$		−	28214.6i		−	0.932492i	0.884655	−	0.466246i	$-0.154394\pi$
$972$		0			0
$973$	23275.3			0.766877
$974$		0			0
$975$	8529.97	−	8529.97i	0.280182	−	0.280182i
$976$		0			0
$977$		−	5458.76i		−	0.178752i	−0.995998	−	0.0893762i	$-0.971513\pi$
$977$		−	5458.76i		−	0.178752i	0.995998	−	0.0893762i	$-0.0284873\pi$
$978$		0			0
$979$	1040.52	−	1040.52i	0.0339686	−	0.0339686i
$980$		0			0
$981$	22785.8	+	22785.8i	0.741586	+	0.741586i
$982$		0			0
$983$	−3968.99	−	3968.99i	−0.128780	−	0.128780i	0.639779	−	0.768559i	$-0.279026\pi$
$983$	−3968.99	−	3968.99i	−0.128780	−	0.128780i	−0.768559	+	0.639779i	$0.779026\pi$
$984$		0			0
$985$	−534.283			−0.0172829
$986$		0			0
$987$	5804.08			0.187179
$988$		0			0
$989$	−30718.7	−	30718.7i	−0.987661	−	0.987661i
$990$		0			0
$991$	26605.4	+	26605.4i	0.852824	+	0.852824i	0.990480	−	0.137656i	$-0.0439567\pi$
$991$	26605.4	+	26605.4i	0.852824	+	0.852824i	−0.137656	+	0.990480i	$0.543957\pi$
$992$		0			0
$993$	−7131.29	+	7131.29i	−0.227900	+	0.227900i
$994$		0			0
$995$		−	643.924i		−	0.0205164i
$996$		0			0
$997$	13463.0	−	13463.0i	0.427661	−	0.427661i	−0.460170	−	0.887831i	$-0.652211\pi$
$997$	13463.0	−	13463.0i	0.427661	−	0.427661i	0.887831	+	0.460170i	$0.152211\pi$
$998$		0			0
$999$	−7202.96			−0.228120

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.k.a.81.4	✓	14
4.3	odd	2		272.4.o.g.81.4		14
17.2	even	8		2312.4.a.m.1.7		14
17.4	even	4	inner	136.4.k.a.89.4	yes	14
17.15	even	8		2312.4.a.m.1.8		14
68.55	odd	4		272.4.o.g.225.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.k.a.81.4	✓	14	1.1	even	1	trivial
136.4.k.a.89.4	yes	14	17.4	even	4	inner
272.4.o.g.81.4		14	4.3	odd	2
272.4.o.g.225.4		14	68.55	odd	4
2312.4.a.m.1.7		14	17.2	even	8
2312.4.a.m.1.8		14	17.15	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)

\(f(q)\)	\(=\)	\(q+(-1.06483 - 1.06483i) q^{3} +(-0.550686 - 0.550686i) q^{5} +(-11.3140 + 11.3140i) q^{7} -24.7323i q^{9} +O(q^{10})\)	\(q+(-1.06483 - 1.06483i) q^{3} +(-0.550686 - 0.550686i) q^{5} +(-11.3140 + 11.3140i) q^{7} -24.7323i q^{9} +(-5.56218 + 5.56218i) q^{11} -64.3974 q^{13} +1.17278i q^{15} +(-58.0103 + 39.3421i) q^{17} -9.88432i q^{19} +24.0950 q^{21} +(-134.915 + 134.915i) q^{23} -124.393i q^{25} +(-55.0862 + 55.0862i) q^{27} +(-148.529 - 148.529i) q^{29} +(4.85251 + 4.85251i) q^{31} +11.8456 q^{33} +12.4609 q^{35} +(65.3789 + 65.3789i) q^{37} +(68.5724 + 68.5724i) q^{39} +(225.441 - 225.441i) q^{41} +227.690i q^{43} +(-13.6197 + 13.6197i) q^{45} +240.883 q^{47} +86.9871i q^{49} +(103.664 + 19.8785i) q^{51} -247.863i q^{53} +6.12603 q^{55} +(-10.5251 + 10.5251i) q^{57} -321.574i q^{59} +(313.816 - 313.816i) q^{61} +(279.821 + 279.821i) q^{63} +(35.4627 + 35.4627i) q^{65} -17.8872 q^{67} +287.323 q^{69} +(551.226 + 551.226i) q^{71} +(406.882 + 406.882i) q^{73} +(-132.458 + 132.458i) q^{75} -125.861i q^{77} +(-346.988 + 346.988i) q^{79} -550.456 q^{81} -1282.66i q^{83} +(53.6106 + 10.2803i) q^{85} +316.318i q^{87} -187.071 q^{89} +(728.591 - 728.591i) q^{91} -10.3342i q^{93} +(-5.44315 + 5.44315i) q^{95} +(41.7026 + 41.7026i) q^{97} +(137.565 + 137.565i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7}+O(q^{10}) \) 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7	\( 14 q - 4 q^{3} + 8 q^{5} - 10 q^{7} + 16 q^{11} + 72 q^{13} - 40 q^{17} - 60 q^{21} + 246 q^{23} + 572 q^{27} + 260 q^{29} + 566 q^{31} - 904 q^{33} - 804 q^{35} - 28 q^{37} + 476 q^{39} - 786 q^{41} - 604 q^{45} + 448 q^{47} - 380 q^{51} + 1612 q^{55} + 1004 q^{57} + 660 q^{61} - 2250 q^{63} - 796 q^{65} - 284 q^{67} - 2532 q^{69} + 326 q^{71} + 730 q^{73} - 864 q^{75} + 342 q^{79} - 950 q^{81} + 4148 q^{85} - 4516 q^{89} - 3112 q^{91} + 3356 q^{95} - 1194 q^{97} + 2876 q^{99}+O(q^{100}) \) 14 * q - 4 * q^3 + 8 * q^5 - 10 * q^7 + 16 * q^11 + 72 * q^13 - 40 * q^17 - 60 * q^21 + 246 * q^23 + 572 * q^27 + 260 * q^29 + 566 * q^31 - 904 * q^33 - 804 * q^35 - 28 * q^37 + 476 * q^39 - 786 * q^41 - 604 * q^45 + 448 * q^47 - 380 * q^51 + 1612 * q^55 + 1004 * q^57 + 660 * q^61 - 2250 * q^63 - 796 * q^65 - 284 * q^67 - 2532 * q^69 + 326 * q^71 + 730 * q^73 - 864 * q^75 + 342 * q^79 - 950 * q^81 + 4148 * q^85 - 4516 * q^89 - 3112 * q^91 + 3356 * q^95 - 1194 * q^97 + 2876 * q^99

Introduction

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